Finite Group Databasebeta

← C83×#61066 #35288890

Subgroups — C83×#61066 #35288890

Order 21248.

2912 conjugacy classes of subgroups.

The subgroup lattice has 1616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C83C211yesmaximal, characteristic, complemented
2C22×AGL(1,ℤ/8)×C83C211yesmaximal, characteristic, complemented
3D4×#41×C83C211yesmaximal, characteristic, complemented
4C2×#546×C83C211yesmaximal, characteristic, complemented
5C83×#3282C212yesmaximal, complemented
6C83×#3280C212yesmaximal, complemented
7C83×#3275C212yesmaximal, complemented
8C83×#3273C212yesmaximal, complemented
9C83×#3268C212yesmaximal, complemented
10C83×#3267C212yesmaximal, complemented
11C83×#3266C212yesmaximal, complemented
12C83×#3264C212yesmaximal, complemented
13C83×#3153C211yesmaximal, characteristic, complemented
14C83×#3056C211yesmaximal, characteristic, complemented
15C83×#3055C211yesmaximal, characteristic, complemented
16C83×#3040C211yesmaximal, characteristic, complemented
17C83×#3036C211yesmaximal, characteristic, complemented
18C83×#3007C211yesmaximal, characteristic, complemented
19C83×#3006C211yesmaximal, characteristic, complemented
20C83×#3005C211yesmaximal, characteristic, complemented
21C83×#3003C211yesmaximal, characteristic, complemented
22C4×AGL(1,ℤ/8)×C83C211yesmaximal, characteristic, complemented
23D4×M16×C83C211yesmaximal, characteristic, complemented
24C22×#41×C83C2211yescharacteristic
25C22×#41×C83C2211yescharacteristic, complemented
26C22×#41×C83C2211yescharacteristic, complemented
27C23×D4×C83C2211yescharacteristic, complemented
28#575×C83—28no—
29C2×#137×C83C2211yescharacteristic, complemented
30C2×#137×C83C2211yescharacteristic, complemented
31C2×#137×C83C2211yescharacteristic, complemented
32C2×#137×C83C2212yescomplemented
33C2×AGL(1,ℤ/8)×C83—28no—
34C2×AGL(1,ℤ/8)×C83C2211yescharacteristic
35C2×AGL(1,ℤ/8)×C83C2211yescharacteristic
36C2×AGL(1,ℤ/8)×C83C2212yescomplemented
37C2×AGL(1,ℤ/8)×C83C2211yescharacteristic, complemented
38C2×AGL(1,ℤ/8)×C83C2211yescharacteristic, complemented
39C2×AGL(1,ℤ/8)×C83C2211yescharacteristic, complemented
40C2×AGL(1,ℤ/8)×C83C2212yescomplemented
41C2×AGL(1,ℤ/8)×C83C2211yescharacteristic, complemented
42C2×AGL(1,ℤ/8)×C83C2212yescomplemented
43C2×#135×C83C2212yescomplemented
44C2×#135×C83C2212yescomplemented
45C22×SD16×C83C2212yescomplemented
46C22×D8×C83C2212yescomplemented
47C22×M16×C83C2211yescharacteristic, complemented
48C22×M16×C83C2211yescharacteristic, complemented
49#550×C83C2211yescharacteristic, complemented
50D4×Q8×C83C2211yescharacteristic, complemented
51#548×C83C2211yescharacteristic, complemented
52#548×C83C2211yescharacteristic, complemented
53#547×C83—21no—
54#547×C83C2211yescharacteristic, complemented
55#546×C83—21no—
56#546×C83—21no—
57#546×C83—21no—
58#546×C83—21no—
59#546×C83—21no—
60#546×C83—21no—
61#546×C83C2212yes—
62#546×C83C2212yescomplemented
63#546×C83C2212yescomplemented
64#546×C83C2212yescomplemented
65#546×C83C2211yescharacteristic, complemented
66#546×C83C2211yescharacteristic, complemented
67D42×C83—21no—
68D42×C83C2211yescharacteristic, complemented
69#532×C83—21no—
70#532×C83C2211yescharacteristic, complemented
71C2×#124×C83C2211yescharacteristic, complemented
72#525×C83—21no—
73#525×C83—21no—
74#525×C83C2211yescharacteristic
75#525×C83C2211yescharacteristic, complemented
76C2×#123×C83—21no—
77C2×C22⋊Q8×C83C2211yescharacteristic, complemented
78C2×#121×C83—21no—
79C2×#121×C83C2211yescharacteristic, complemented
80C2×#120×C83—21no—
81C4×#41×C83C2211yescharacteristic, complemented
82C2×C4×D4×C83—21no—
83C2×C4×D4×C83C2211yescharacteristic
84C2×C4×D4×C83C2211yescharacteristic, complemented
85C22×C22⋊C4×C83—21no—
86#497×C83C2212yescomplemented
87#496×C83C2212yescomplemented
88#495×C83C2212yescomplemented
89#495×C83C2212yescomplemented
90#470×C83C2212yescomplemented
91#469×C83C2212yescomplemented
92#468×C83C2212yescomplemented
93#468×C83C2212yescomplemented
94#467×C83C2212yescomplemented
95#466×C83C2212yescomplemented
96#465×C83C2212yescomplemented
97#465×C83C2212yescomplemented
98#464×C83C2212yescomplemented
99#464×C83C2212yescomplemented
100#463×C83C2212yescomplemented
101#463×C83C2212yescomplemented
102#463×C83C2212yescomplemented
103#463×C83C2212yescomplemented
104#461×C83C2212yescomplemented
105#459×C83C2212yescomplemented
106#452×C83C2212yescomplemented
107#452×C83C2212yescomplemented
108#452×C83C2212yescomplemented
109#452×C83C2212yescomplemented
110#451×C83C2212yescomplemented
111#450×C83C2212yescomplemented
112#450×C83C2212yescomplemented
113#450×C83C2212yescomplemented
114#449×C83C2212yescomplemented
115#449×C83C2212yescomplemented
116#449×C83C2212yescomplemented
117#449×C83C2212yescomplemented
118#448×C83C2212yescomplemented
119#447×C83C2212yescomplemented
120#447×C83C2212yescomplemented
121#447×C83C2212yescomplemented
122#442×C83C2212yescomplemented
123#440×C83C2212yescomplemented
124C4×SD16×C83C2212yescomplemented
125C4×D8×C83C2212yescomplemented
126#436×C83C2212yescomplemented
127#435×C83C2212yescomplemented
128#435×C83C2212yescomplemented
129C8×D4×C83C2212yescomplemented
130#428×C83C2211yescharacteristic, complemented
131#423×C83C2211yescharacteristic, complemented
132#419×C83C2211yescharacteristic, complemented
133#418×C83C2211yescharacteristic, complemented
134#418×C83C2211yescharacteristic, complemented
135#417×C83C2211yescharacteristic, complemented
136#417×C83C2211yescharacteristic, complemented
137#417×C83C2211yescharacteristic, complemented
138#407×C83C2211yescharacteristic, complemented
139#407×C83C2211yescharacteristic, complemented
140C4×M16×C83C2211yescharacteristic, complemented
141C25×C83—21no—
142C2×#41×C83—21no—
143C2×#41×C83—21no—
144C2×#41×C83—21no—
145C2×#41×C83—21no—
146C2×#41×C83—21no—
147C2×#41×C83—21no—
148C2×#41×C83—24no—
149C2×#41×C83—24no—
150C2×#41×C83—24no—
151C2×#41×C83—42no—
152C2×#41×C83—42no—
153C2×#41×C83—42no—
154C2×#41×C83C2311yescharacteristic
155C2×#41×C83C2311yescharacteristic
156C2×#41×C83C2312yes—
157C2×#41×C83C2312yes—
158C2×#41×C83C2311yescharacteristic
159C2×#41×C83C2311yescharacteristic
160C2×#41×C83C2311yescharacteristic
161C2×#41×C83C2311yescharacteristic, complemented
162C2×#41×C83C2311yescharacteristic, complemented
163C22×Q8×C83C2311yescharacteristic
164C22×Q8×C83C2311yescharacteristic
165C22×Q8×C83C2311yescharacteristic, complemented
166C22×D4×C83—24no—
167C22×D4×C83—21no—
168C22×D4×C83—21no—
169C22×D4×C83—21no—
170C22×D4×C83—21no—
171C22×D4×C83—21no—
172C22×D4×C83—21no—
173C22×D4×C83—21no—
174C22×D4×C83—21no—
175C22×D4×C83—42no—
176C22×D4×C83D411yescharacteristic
177C22×D4×C83C2311yescharacteristic
178C22×D4×C83C2311yescharacteristic
179C22×D4×C83C2312yes—
180C22×D4×C83C2312yes—
181C22×D4×C83C2311yescharacteristic
182C22×D4×C83C2311yescharacteristic, complemented
183C23×C4×C83—21no—
184C23×C4×C83—21no—
185C23×C4×C83—21no—
186C23×C4×C83—21no—
187C23×C4×C83C2311yescharacteristic
188C23×C4×C83C2311yescharacteristic
189#137×C83—24no—
190#137×C83—28no—
191#137×C83—24no—
192#137×C83—42no—
193AGL(1,ℤ/8)×C83—24no—
194AGL(1,ℤ/8)×C83—24no—
195AGL(1,ℤ/8)×C83—24no—
196AGL(1,ℤ/8)×C83—28no—
197AGL(1,ℤ/8)×C83—28no—
198AGL(1,ℤ/8)×C83—28no—
199AGL(1,ℤ/8)×C83—24no—
200AGL(1,ℤ/8)×C83—42no—
201AGL(1,ℤ/8)×C83D418yescomplemented
202#135×C83—28no—
203#135×C83—28no—
204C2×Q16×C83C2312yescomplemented
205C2×Q16×C83C2312yescomplemented
206C2×Q16×C83C2312yescomplemented
207C2×SD16×C83—28no—
208C2×SD16×C83C2312yes—
209C2×SD16×C83C2312yes—
210C2×SD16×C83C2312yes—
211C2×SD16×C83C2312yes—
212C2×SD16×C83C2312yes—
213C2×SD16×C83C2312yes—
214C2×SD16×C83C2312yescomplemented
215C2×SD16×C83C2312yescomplemented
216C2×SD16×C83C2312yescomplemented
217C2×D8×C83—28no—
218C2×D8×C83C2312yes—
219C2×D8×C83C2312yes—
220C2×D8×C83C2312yes—
221C2×D8×C83C2312yes—
222C2×D8×C83C2312yes—
223C2×D8×C83C2312yes—
224C2×M16×C83—24no—
225C2×M16×C83—24no—
226C2×M16×C83C2312yes—
227C2×M16×C83C2311yescharacteristic
228C2×M16×C83C2311yescharacteristic
229C2×M16×C83C2311yescharacteristic
230C2×M16×C83C2311yescharacteristic
231C2×M16×C83C2312yescomplemented
232C22×C8×C83C2312yes—
233C22×C8×C83C2312yescomplemented
234C4⋊Q8×C83—21no—
235C4⋊Q8×C83C2311yescharacteristic, complemented
236#127×C83—21no—
237#127×C83C2311yescharacteristic, complemented
238#124×C83—21no—
239#124×C83—21no—
240#124×C83—21no—
241#124×C83—21no—
242#124×C83C2312yes—
243#124×C83C2312yes—
244#124×C83C2311yescharacteristic, complemented
245#124×C83C2311yescharacteristic, complemented
246#123×C83—21no—
247#123×C83—21no—
248#123×C83—22no—
249#123×C83—22no—
250#123×C83—22no—
251#123×C83—22no—
252#123×C83—21no—
253#123×C83—21no—
254#123×C83—21no—
255#123×C83—21no—
256C22⋊Q8×C83—21no—
257C22⋊Q8×C83—21no—
258C22⋊Q8×C83—21no—
259C22⋊Q8×C83—21no—
260C22⋊Q8×C83—21no—
261C22⋊Q8×C83—21no—
262C22⋊Q8×C83C2312yes—
263C22⋊Q8×C83C2311yescharacteristic
264C22⋊Q8×C83C2312yes—
265C22⋊Q8×C83C2311yescharacteristic
266C22⋊Q8×C83C2311yescharacteristic, complemented
267C22⋊Q8×C83C2311yescharacteristic, complemented
268#121×C83—21no—
269#121×C83—21no—
270#121×C83—21no—
271#121×C83—21no—
272#121×C83—21no—
273#121×C83—21no—
274#121×C83—21no—
275#121×C83—21no—
276#121×C83—22no—
277#121×C83—22no—
278#121×C83—22no—
279#121×C83—22no—
280#121×C83—21no—
281#121×C83—21no—
282#121×C83—21no—
283#121×C83—21no—
284#121×C83C2311yescharacteristic
285#121×C83C2312yes—
286#121×C83C2311yescharacteristic
287#121×C83C2312yes—
288#121×C83C2311yescharacteristic, complemented
289#121×C83C2311yescharacteristic, complemented
290#120×C83—21no—
291#120×C83—21no—
292#120×C83—22no—
293#120×C83—22no—
294#120×C83—22no—
295#120×C83—22no—
296#120×C83—21no—
297#120×C83—21no—
298#120×C83—21no—
299#120×C83—21no—
300C4×Q8×C83C2311yescharacteristic, complemented
301C4×Q8×C83C2311yescharacteristic, complemented
302C4×D4×C83—21no—
303C4×D4×C83—21no—
304C4×D4×C83—21no—
305C4×D4×C83—21no—
306C4×D4×C83—21no—
307C4×D4×C83—21no—
308C4×D4×C83—21no—
309C4×D4×C83—21no—
310C4×D4×C83—21no—
311C4×D4×C83—21no—
312C4×D4×C83—21no—
313C4×D4×C83—21no—
314C4×D4×C83—21no—
315C4×D4×C83—21no—
316C4×D4×C83D411yescharacteristic
317C4×D4×C83D411yescharacteristic
318C4×D4×C83D411yescharacteristic
319C4×D4×C83D411yescharacteristic
320C4×D4×C83C2312yes—
321C4×D4×C83C2312yes—
322C4×D4×C83C2311yescharacteristic
323C4×D4×C83C2311yescharacteristic
324C4×D4×C83C2311yescharacteristic
325C4×D4×C83C2311yescharacteristic
326C4×D4×C83C2311yescharacteristic, complemented
327C4×D4×C83C2311yescharacteristic, complemented
328#117×C83—21no—
329#117×C83C2311yescharacteristic
330C2×C4⋊C4×C83—21no—
331C2×C4⋊C4×C83—21no—
332C2×C4⋊C4×C83D411yescharacteristic
333C2×C4⋊C4×C83C2311yescharacteristic
334C2×C22⋊C4×C83—21no—
335C2×C22⋊C4×C83—21no—
336C2×C22⋊C4×C83—21no—
337C2×C22⋊C4×C83—21no—
338C2×C22⋊C4×C83—21no—
339C2×C22⋊C4×C83—22no—
340C2×C22⋊C4×C83—22no—
341C2×C22⋊C4×C83—22no—
342C2×C22⋊C4×C83—22no—
343C2×C22⋊C4×C83—21no—
344C2×C22⋊C4×C83—21no—
345C2×C22⋊C4×C83D411yescharacteristic
346C2×C22⋊C4×C83D411yescharacteristic
347C2×C42×C83—21no—
348C2×C42×C83C2311yescharacteristic
349#107×C83C2312yescomplemented
350#106×C83C2312yescomplemented
351C4⋊C8×C83C2312yescomplemented
352C4⋊C8×C83C2312yescomplemented
353#103×C83C2312yescomplemented
354#103×C83C2312yescomplemented
355#103×C83C2312yescomplemented
356#103×C83C2312yescomplemented
357#103×C83C2312yescomplemented
358#102×C83C2312yes—
359#102×C83C2312yes—
360#102×C83C2312yes—
361#102×C83C2312yes—
362#102×C83C2312yescomplemented
363#102×C83C2312yescomplemented
364#102×C83C2312yescomplemented
365C22⋊C8×C83C2312yes—
366C22⋊C8×C83C2312yes—
367C22⋊C8×C83C2312yescomplemented
368C22⋊C8×C83C2312yescomplemented
369#97×C83C2312yescomplemented
370C4×C8×C83C2312yescomplemented
371C24×C83—21no—
372C24×C83—21no—
373C24×C83—22no—
374C24×C83—22no—
375C24×C83—21no—
376C24×C83—21no—
377C24×C83—44no—
378C24×C83—44no—
379C24×C83—82no—
380C24×C83C2×D411yescharacteristic
381C24×C83C2×D411yescharacteristic
382#41×C83—22no—
383#41×C83—22no—
384#41×C83—22no—
385#41×C83—24no—
386#41×C83—22no—
387#41×C83—22no—
388#41×C83—24no—
389#41×C83—22no—
390#41×C83—22no—
391#41×C83—22no—
392#41×C83—22no—
393#41×C83—44no—
394#41×C83—44no—
395#41×C83—41no—
396#41×C83—41no—
397#41×C83—42no—
398#41×C83—42no—
399#41×C83—41no—
400#41×C83—41no—
401#41×C83—44no—
402#41×C83—44no—
403#41×C83—44no—
404#41×C83—44no—
405#41×C83C2×D414yes—
406C2×Q8×C83—21no—
407C2×Q8×C83—21no—
408C2×Q8×C83—21no—
409C2×Q8×C83—22no—
410C2×Q8×C83—22no—
411C2×Q8×C83—22no—
412C2×Q8×C83—22no—
413C2×Q8×C83—41no—
414C2×Q8×C83—41no—
415C2×Q8×C83C2412yes—
416C2×Q8×C83C2411yescharacteristic
417C2×Q8×C83C2411yescharacteristic
418C2×Q8×C83C2411yescharacteristic
419C2×D4×C83—21no—
420C2×D4×C83—22no—
421C2×D4×C83—24no—
422C2×D4×C83—24no—
423C2×D4×C83—22no—
424C2×D4×C83—21no—
425C2×D4×C83—21no—
426C2×D4×C83—22no—
427C2×D4×C83—22no—
428C2×D4×C83—21no—
429C2×D4×C83—21no—
430C2×D4×C83—21no—
431C2×D4×C83—21no—
432C2×D4×C83—21no—
433C2×D4×C83—21no—
434C2×D4×C83—21no—
435C2×D4×C83—21no—
436C2×D4×C83—22no—
437C2×D4×C83—22no—
438C2×D4×C83—21no—
439C2×D4×C83—22no—
440C2×D4×C83—21no—
441C2×D4×C83—21no—
442C2×D4×C83—21no—
443C2×D4×C83—22no—
444C2×D4×C83—22no—
445C2×D4×C83—21no—
446C2×D4×C83—21no—
447C2×D4×C83—22no—
448C2×D4×C83—22no—
449C2×D4×C83—42no—
450C2×D4×C83—42no—
451C2×D4×C83—41no—
452C2×D4×C83—41no—
453C2×D4×C83—44no—
454C2×D4×C83—44no—
455C2×D4×C83—44no—
456C2×D4×C83—42no—
457C2×D4×C83—44no—
458C2×D4×C83—44no—
459C2×D4×C83—44no—
460C2×D4×C83—44no—
461C2×D4×C83—82no—
462C2×D4×C83C2×D411yescharacteristic
463C2×D4×C83C2×D411yescharacteristic
464C2×D4×C83C2×D411yescharacteristic
465C2×D4×C83C2×D411yescharacteristic
466C2×D4×C83C2×D414yescomplemented
467C2×D4×C83C2412yes—
468C2×D4×C83C2411yescharacteristic
469C2×D4×C83C2411yescharacteristic
470C2×D4×C83C2412yes—
471C2×D4×C83C2411yescharacteristic
472C22×C4×C83—21no—
473C22×C4×C83—22no—
474C22×C4×C83—22no—
475C22×C4×C83—22no—
476C22×C4×C83—22no—
477C22×C4×C83—21no—
478C22×C4×C83—21no—
479C22×C4×C83—21no—
480C22×C4×C83—21no—
481C22×C4×C83—21no—
482C22×C4×C83—22no—
483C22×C4×C83—22no—
484C22×C4×C83—21no—
485C22×C4×C83—21no—
486C22×C4×C83—21no—
487C22×C4×C83—21no—
488C22×C4×C83—21no—
489C22×C4×C83—21no—
490C22×C4×C83—21no—
491C22×C4×C83—22no—
492C22×C4×C83—22no—
493C22×C4×C83—44no—
494C22×C4×C83—44no—
495C22×C4×C83—44no—
496C22×C4×C83—82no—
497C22×C4×C83C2×D411yescharacteristic
498C22×C4×C83C2×D411yescharacteristic
499C22×C4×C83C2×D411yescharacteristic
500C22×C4×C83C2×D411yescharacteristic
501C22×C4×C83C2×D411yescharacteristic
502C22×C4×C83C2×D411yescharacteristic
503C22×C4×C83C2×D411yescharacteristic
504C22×C4×C83C2×D411yescharacteristic
505C22×C4×C83C2411yescharacteristic
506C22×C4×C83C2411yescharacteristic
507C22×C4×C83C2411yescharacteristic
508C22×C4×C83C2411yescharacteristic
509C22×C4×C83C2411yescharacteristic
510Q16×C83—24no—
511Q16×C83—24no—
512Q16×C83—42no—
513SD16×C83—24no—
514SD16×C83—24no—
515SD16×C83—24no—
516SD16×C83—24no—
517SD16×C83—24no—
518SD16×C83—24no—
519SD16×C83—42no—
520SD16×C83—42no—
521SD16×C83C2×D418yescomplemented
522D8×C83—24no—
523D8×C83—24no—
524D8×C83—24no—
525D8×C83—24no—
526D8×C83—42no—
527D8×C83C2×D418yescomplemented
528M16×C83—22no—
529M16×C83—22no—
530M16×C83—22no—
531M16×C83—24no—
532M16×C83—24no—
533M16×C83C2×D414yescomplemented
534C2×C8×C83—24no—
535C2×C8×C83—24no—
536C2×C8×C83C2412yes—
537C2×C8×C83C2412yes—
538C2×C8×C83C2412yes—
539C2×C8×C83C2412yes—
540C4⋊C4×C83—21no—
541C4⋊C4×C83—21no—
542C4⋊C4×C83—21no—
543C4⋊C4×C83—22no—
544C4⋊C4×C83—22no—
545C4⋊C4×C83—21no—
546C4⋊C4×C83—21no—
547C4⋊C4×C83—21no—
548C4⋊C4×C83—21no—
549C4⋊C4×C83—21no—
550C4⋊C4×C83—21no—
551C4⋊C4×C83C2×D411yescharacteristic
552C4⋊C4×C83C2×D411yescharacteristic
553C4⋊C4×C83C2×D411yescharacteristic
554C4⋊C4×C83C2×D411yescharacteristic
555C4⋊C4×C83C2411yescharacteristic
556C4⋊C4×C83C2411yescharacteristic
557C4⋊C4×C83C2412yes—
558C22⋊C4×C83—22no—
559C22⋊C4×C83—22no—
560C22⋊C4×C83—21no—
561C22⋊C4×C83—21no—
562C22⋊C4×C83—21no—
563C22⋊C4×C83—21no—
564C22⋊C4×C83—21no—
565C22⋊C4×C83—22no—
566C22⋊C4×C83—22no—
567C22⋊C4×C83—22no—
568C22⋊C4×C83—22no—
569C22⋊C4×C83—21no—
570C22⋊C4×C83—21no—
571C22⋊C4×C83—21no—
572C22⋊C4×C83—21no—
573C22⋊C4×C83—22no—
574C22⋊C4×C83—22no—
575C22⋊C4×C83—22no—
576C22⋊C4×C83—22no—
577C22⋊C4×C83—21no—
578C22⋊C4×C83—21no—
579C22⋊C4×C83—21no—
580C22⋊C4×C83—21no—
581C22⋊C4×C83—21no—
582C22⋊C4×C83—21no—
583C22⋊C4×C83C2×D411yescharacteristic
584C22⋊C4×C83C2×D411yescharacteristic
585C22⋊C4×C83C2×D411yescharacteristic
586C22⋊C4×C83C2×D411yescharacteristic
587C22⋊C4×C83C2×D411yescharacteristic
588C22⋊C4×C83C2×D411yescharacteristic
589C22⋊C4×C83C2×D411yescharacteristic
590C22⋊C4×C83C2×D411yescharacteristic
591C42×C83—21no—
592C42×C83—21no—
593C42×C83—21no—
594C42×C83C2×D411yescharacteristic
595C42×C83C2×D411yescharacteristic
596C42×C83C2411yescharacteristic
597C42×C83C2411yescharacteristic
598C23×C83—22no—
599C23×C83—24no—
600C23×C83—22no—
601C23×C83—21no—
602C23×C83—22no—
603C23×C83—22no—
604C23×C83—22no—
605C23×C83—21no—
606C23×C83—21no—
607C23×C83—41no—
608C23×C83—41no—
609C23×C83—41no—
610C23×C83—42no—
611C23×C83—42no—
612C23×C83—44no—
613C23×C83—44no—
614C23×C83—42no—
615C23×C83—42no—
616C23×C83—42no—
617C23×C83—42no—
618C23×C83—42no—
619C23×C83—44no—
620C23×C83—42no—
621C23×C83—42no—
622C23×C83—44no—
623C23×C83—81no—
624C23×C83—81no—
625C23×C83—82no—
626C23×C83—82no—
627C23×C83—816no—
628C23×C83C22×D411yescharacteristic
629C23×C83C22×D411yescharacteristic
630C23×C83C22×D411yescharacteristic
631C23×C83C22×D411yescharacteristic
632C23×C83C22×D411yescharacteristic
633Q8×C83—21no—
634Q8×C83—21no—
635Q8×C83—21no—
636Q8×C83—22no—
637Q8×C83—21no—
638Q8×C83—22no—
639Q8×C83—21no—
640Q8×C83—42no—
641Q8×C83—42no—
642Q8×C83—42no—
643Q8×C83C22×D412yes—
644D4×C83—24no—
645D4×C83—22no—
646D4×C83—22no—
647D4×C83—24no—
648D4×C83—21no—
649D4×C83—22no—
650D4×C83—21no—
651D4×C83—22no—
652D4×C83—21no—
653D4×C83—21no—
654D4×C83—22no—
655D4×C83—21no—
656D4×C83—41no—
657D4×C83—41no—
658D4×C83—44no—
659D4×C83—44no—
660D4×C83—42no—
661D4×C83—42no—
662D4×C83—42no—
663D4×C83—42no—
664D4×C83—42no—
665D4×C83—44no—
666D4×C83—42no—
667D4×C83—44no—
668D4×C83—42no—
669D4×C83—42no—
670D4×C83—42no—
671D4×C83—42no—
672D4×C83—42no—
673D4×C83—42no—
674D4×C83—81no—
675D4×C83—81no—
676D4×C83—81no—
677D4×C83—82no—
678D4×C83—82no—
679D4×C83C22×D412yes—
680D4×C83C22×D414yes—
681C2×C4×C83—22no—
682C2×C4×C83—22no—
683C2×C4×C83—21no—
684C2×C4×C83—22no—
685C2×C4×C83—22no—
686C2×C4×C83—22no—
687C2×C4×C83—22no—
688C2×C4×C83—24no—
689C2×C4×C83—21no—
690C2×C4×C83—21no—
691C2×C4×C83—21no—
692C2×C4×C83—21no—
693C2×C4×C83—21no—
694C2×C4×C83—21no—
695C2×C4×C83—21no—
696C2×C4×C83—21no—
697C2×C4×C83—21no—
698C2×C4×C83—21no—
699C2×C4×C83—22no—
700C2×C4×C83—22no—
701C2×C4×C83—21no—
702C2×C4×C83—21no—
703C2×C4×C83—41no—
704C2×C4×C83—41no—
705C2×C4×C83—42no—
706C2×C4×C83—42no—
707C2×C4×C83—42no—
708C2×C4×C83—42no—
709C2×C4×C83—42no—
710C2×C4×C83—44no—
711C2×C4×C83—42no—
712C2×C4×C83—44no—
713C2×C4×C83—42no—
714C2×C4×C83—42no—
715C2×C4×C83—42no—
716C2×C4×C83—42no—
717C2×C4×C83—42no—
718C2×C4×C83—81no—
719C2×C4×C83—82no—
720C2×C4×C83—82no—
721C2×C4×C83C22×D411yescharacteristic
722C2×C4×C83C22×D411yescharacteristic
723C2×C4×C83C22×D411yescharacteristic
724C2×C4×C83C22×D411yescharacteristic
725C2×C4×C83C22×D411yescharacteristic
726C2×C4×C83C22×D411yescharacteristic
727C2×C4×C83C22×D411yescharacteristic
728C2×C4×C83C22×D411yescharacteristic
729C2×C4×C83C22×D411yescharacteristic
730C2×C4×C83C22×D412yes—
731C2×C4×C83H(5,𝔽2)12yes—
732C2×C4×C83C2511yescharacteristic
733C8×C83—22no—
734C8×C83—22no—
735C8×C83—22no—
736C8×C83C22×D414yes—
737C22×C83—21no—
738C22×C83—21no—
739C22×C83—21no—
740C22×C83—21no—
741C22×C83—21no—
742C22×C83—21no—
743C22×C83—21no—
744C22×C83—21no—
745C22×C83—21no—
746C22×C83—21no—
747C22×C83—22no—
748C22×C83—24no—
749C22×C83—21no—
750C22×C83—21no—
751C22×C83—21no—
752C22×C83—44no—
753C22×C83—48no—
754C22×C83—42no—
755C22×C83—41no—
756C22×C83—41no—
757C22×C83—42no—
758C22×C83—42no—
759C22×C83—41no—
760C22×C83—41no—
761C22×C83—41no—
762C22×C83—41no—
763C22×C83—42no—
764C22×C83—41no—
765C22×C83—41no—
766C22×C83—42no—
767C22×C83—82no—
768C22×C83—84no—
769C22×C83—88no—
770C22×C83—84no—
771C22×C83—84no—
772C22×C83—88no—
773C22×C83D4212yes—
774C22×C83#57512yescomplemented
775C22×C83C23×D411yescharacteristic
776C4×C83—21no—
777C4×C83—21no—
778C4×C83—21no—
779C4×C83—21no—
780C4×C83—21no—
781C4×C83—21no—
782C4×C83—22no—
783C4×C83—21no—
784C4×C83—21no—
785C4×C83—42no—
786C4×C83—41no—
787C4×C83—42no—
788C4×C83—41no—
789C4×C83—41no—
790C4×C83—41no—
791C4×C83D4212yes—
792C4×C83C23×D411yescharacteristic
793C4×C83C2×H(5,𝔽2)11yescharacteristic
794#61066C8311yesmaximal, characteristic, direct product factor, Sylow
795C2×C83—22no—
796C2×C83—22no—
797C2×C83—41no—
798C2×C83—41no—
799C2×C83—41no—
800C2×C83—44no—
801C2×C83—42no—
802C2×C83—81no—
803C2×C83—81no—
804C2×C83—82no—
805C2×C83C2×D4211yescharacteristic
806C2×C83C2×#57511yescharacteristic
807C2×C83#358511yescharacteristic
808C2×#575C2×C8311yescharacteristic, complemented
809C22×AGL(1,ℤ/8)C2×C8311yescharacteristic, complemented
810D4×#41C2×C8311yescharacteristic, complemented
811C2×#546C2×C8311yescharacteristic, complemented
812#3282C2×C8312yescomplemented
813#3280C2×C8312yescomplemented
814#3275C2×C8312yescomplemented
815#3273C2×C8312yescomplemented
816#3268C2×C8312yescomplemented
817#3267C2×C8312yescomplemented
818#3266C2×C8312yescomplemented
819#3264C2×C8312yescomplemented
820#3153C2×C8311yescharacteristic, complemented
821#3056C2×C8311yescharacteristic, complemented
822#3055C2×C8311yescharacteristic, complemented
823#3040C2×C8311yescharacteristic, complemented
824#3036C2×C8311yescharacteristic, complemented
825#3007C2×C8311yescharacteristic, complemented
826#3006C2×C8311yescharacteristic, complemented
827#3005C2×C8311yescharacteristic, complemented
828#3003C2×C8311yescharacteristic, complemented
829C4×AGL(1,ℤ/8)C2×C8311yescharacteristic, complemented
830D4×M16C2×C8311yescharacteristic, complemented
831C83#6106611yescharacteristic, direct product factor, Sylow
832C22×#41C22×C8311yescharacteristic
833C22×#41C22×C8311yescharacteristic, complemented
834C22×#41C22×C8311yescharacteristic, complemented
835C23×D4C22×C8311yescharacteristic, complemented
836#575—28no—
837C2×#137C22×C8311yescharacteristic, complemented
838C2×#137C22×C8311yescharacteristic, complemented
839C2×#137C22×C8311yescharacteristic, complemented
840C2×#137C22×C8312yescomplemented
841C2×AGL(1,ℤ/8)—28no—
842C2×AGL(1,ℤ/8)C22×C8311yescharacteristic
843C2×AGL(1,ℤ/8)C22×C8311yescharacteristic
844C2×AGL(1,ℤ/8)C22×C8311yescharacteristic, complemented
845C2×AGL(1,ℤ/8)C22×C8311yescharacteristic, complemented
846C2×AGL(1,ℤ/8)C22×C8311yescharacteristic, complemented
847C2×AGL(1,ℤ/8)C22×C8312yescomplemented
848C2×AGL(1,ℤ/8)C22×C8312yescomplemented
849C2×AGL(1,ℤ/8)C22×C8311yescharacteristic, complemented
850C2×AGL(1,ℤ/8)C22×C8312yescomplemented
851C2×#135C22×C8312yescomplemented
852C2×#135C22×C8312yescomplemented
853C22×SD16C22×C8312yescomplemented
854C22×D8C22×C8312yescomplemented
855C22×M16C22×C8311yescharacteristic, complemented
856C22×M16C22×C8311yescharacteristic, complemented
857#550C22×C8311yescharacteristic, complemented
858D4×Q8C22×C8311yescharacteristic, complemented
859#548C22×C8311yescharacteristic, complemented
860#548C22×C8311yescharacteristic, complemented
861#547—21no—
862#547C22×C8311yescharacteristic, complemented
863#546—21no—
864#546—21no—
865#546—21no—
866#546—21no—
867#546—21no—
868#546—21no—
869#546C22×C8312yes—
870#546C22×C8312yescomplemented
871#546C22×C8312yescomplemented
872#546C22×C8312yescomplemented
873#546C22×C8311yescharacteristic, complemented
874#546C22×C8311yescharacteristic, complemented
875D42—21no—
876D42C22×C8311yescharacteristic, complemented
877#532—21no—
878#532C22×C8311yescharacteristic, complemented
879C2×#124C22×C8311yescharacteristic, complemented
880#525—21no—
881#525—21no—
882#525C22×C8311yescharacteristic
883#525C22×C8311yescharacteristic, complemented
884C2×#123—21no—
885C2×C22⋊Q8C22×C8311yescharacteristic, complemented
886C2×#121—21no—
887C2×#121C22×C8311yescharacteristic, complemented
888C2×#120—21no—
889C4×#41C22×C8311yescharacteristic, complemented
890C2×C4×D4—21no—
891C2×C4×D4C22×C8311yescharacteristic
892C2×C4×D4C22×C8311yescharacteristic, complemented
893C22×C22⋊C4—21no—
894#497C22×C8312yescomplemented
895#496C22×C8312yescomplemented
896#495C22×C8312yescomplemented
897#495C22×C8312yescomplemented
898#470C22×C8312yescomplemented
899#469C22×C8312yescomplemented
900#468C22×C8312yescomplemented
901#468C22×C8312yescomplemented
902#467C22×C8312yescomplemented
903#466C22×C8312yescomplemented
904#465C22×C8312yescomplemented
905#465C22×C8312yescomplemented
906#464C22×C8312yescomplemented
907#464C22×C8312yescomplemented
908#463C22×C8312yescomplemented
909#463C22×C8312yescomplemented
910#463C22×C8312yescomplemented
911#463C22×C8312yescomplemented
912#461C22×C8312yescomplemented
913#459C22×C8312yescomplemented
914#452C22×C8312yescomplemented
915#452C22×C8312yescomplemented
916#452C22×C8312yescomplemented
917#452C22×C8312yescomplemented
918#451C22×C8312yescomplemented
919#450C22×C8312yescomplemented
920#450C22×C8312yescomplemented
921#450C22×C8312yescomplemented
922#449C22×C8312yescomplemented
923#449C22×C8312yescomplemented
924#449C22×C8312yescomplemented
925#449C22×C8312yescomplemented
926#448C22×C8312yescomplemented
927#447C22×C8312yescomplemented
928#447C22×C8312yescomplemented
929#447C22×C8312yescomplemented
930#442C22×C8312yescomplemented
931#440C22×C8312yescomplemented
932C4×SD16C22×C8312yescomplemented
933C4×D8C22×C8312yescomplemented
934#436C22×C8312yescomplemented
935#435C22×C8312yescomplemented
936#435C22×C8312yescomplemented
937C8×D4C22×C8312yescomplemented
938#428C22×C8311yescharacteristic, complemented
939#423C22×C8311yescharacteristic, complemented
940#419C22×C8311yescharacteristic, complemented
941#418C22×C8311yescharacteristic, complemented
942#418C22×C8311yescharacteristic, complemented
943#417C22×C8311yescharacteristic, complemented
944#417C22×C8311yescharacteristic, complemented
945#417C22×C8311yescharacteristic, complemented
946#407C22×C8311yescharacteristic, complemented
947#407C22×C8311yescharacteristic, complemented
948C4×M16C22×C8311yescharacteristic, complemented
949C25—21no—
950C2×#41—21no—
951C2×#41—21no—
952C2×#41—21no—
953C2×#41—21no—
954C2×#41—21no—
955C2×#41—21no—
956C2×#41—24no—
957C2×#41—24no—
958C2×#41—24no—
959C2×#41—42no—
960C2×#41—42no—
961C2×#41—42no—
962C2×#41C23×C8311yescharacteristic
963C2×#41C23×C8311yescharacteristic
964C2×#41C23×C8312yes—
965C2×#41C23×C8312yes—
966C2×#41C23×C8311yescharacteristic
967C2×#41C23×C8311yescharacteristic
968C2×#41C23×C8311yescharacteristic
969C2×#41C23×C8311yescharacteristic, complemented
970C2×#41C23×C8311yescharacteristic, complemented
971C22×Q8C23×C8311yescharacteristic
972C22×Q8C23×C8311yescharacteristic
973C22×Q8C23×C8311yescharacteristic, complemented
974C22×D4—24no—
975C22×D4—21no—
976C22×D4—21no—
977C22×D4—21no—
978C22×D4—21no—
979C22×D4—21no—
980C22×D4—21no—
981C22×D4—21no—
982C22×D4—21no—
983C22×D4—42no—
984C22×D4D4×C8311yescharacteristic
985C22×D4C23×C8311yescharacteristic
986C22×D4C23×C8311yescharacteristic
987C22×D4C23×C8312yes—
988C22×D4C23×C8312yes—
989C22×D4C23×C8311yescharacteristic
990C22×D4C23×C8311yescharacteristic, complemented
991C23×C4—21no—
992C23×C4—21no—
993C23×C4—21no—
994C23×C4—21no—
995C23×C4C23×C8311yescharacteristic
996C23×C4C23×C8311yescharacteristic
997#137—24no—
998#137—28no—
999#137—24no—
1000#137—42no—
1001AGL(1,ℤ/8)—24no—
1002AGL(1,ℤ/8)—24no—
1003AGL(1,ℤ/8)—24no—
1004AGL(1,ℤ/8)—28no—
1005AGL(1,ℤ/8)—28no—
1006AGL(1,ℤ/8)—28no—
1007AGL(1,ℤ/8)—24no—
1008AGL(1,ℤ/8)—42no—
1009AGL(1,ℤ/8)D4×C8318yescomplemented
1010#135—28no—
1011#135—28no—
1012C2×Q16C23×C8312yescomplemented
1013C2×Q16C23×C8312yescomplemented
1014C2×Q16C23×C8312yescomplemented
1015C2×SD16—28no—
1016C2×SD16C23×C8312yes—
1017C2×SD16C23×C8312yes—
1018C2×SD16C23×C8312yes—
1019C2×SD16C23×C8312yes—
1020C2×SD16C23×C8312yes—
1021C2×SD16C23×C8312yes—
1022C2×SD16C23×C8312yescomplemented
1023C2×SD16C23×C8312yescomplemented
1024C2×SD16C23×C8312yescomplemented
1025C2×D8—28no—
1026C2×D8C23×C8312yes—
1027C2×D8C23×C8312yes—
1028C2×D8C23×C8312yes—
1029C2×D8C23×C8312yes—
1030C2×D8C23×C8312yes—
1031C2×D8C23×C8312yes—
1032C2×M16—24no—
1033C2×M16—24no—
1034C2×M16C23×C8311yescharacteristic
1035C2×M16C23×C8312yes—
1036C2×M16C23×C8311yescharacteristic
1037C2×M16C23×C8311yescharacteristic
1038C2×M16C23×C8311yescharacteristic
1039C2×M16C23×C8312yescomplemented
1040C22×C8C23×C8312yes—
1041C22×C8C23×C8312yescomplemented
1042C4⋊Q8—21no—
1043C4⋊Q8C23×C8311yescharacteristic, complemented
1044#127—21no—
1045#127C23×C8311yescharacteristic, complemented
1046#124—21no—
1047#124—21no—
1048#124—21no—
1049#124—21no—
1050#124C23×C8312yes—
1051#124C23×C8312yes—
1052#124C23×C8311yescharacteristic, complemented
1053#124C23×C8311yescharacteristic, complemented
1054#123—21no—
1055#123—21no—
1056#123—22no—
1057#123—22no—
1058#123—22no—
1059#123—22no—
1060#123—21no—
1061#123—21no—
1062#123—21no—
1063#123—21no—
1064C22⋊Q8—21no—
1065C22⋊Q8—21no—
1066C22⋊Q8—21no—
1067C22⋊Q8—21no—
1068C22⋊Q8—21no—
1069C22⋊Q8—21no—
1070C22⋊Q8C23×C8312yes—
1071C22⋊Q8C23×C8312yes—
1072C22⋊Q8C23×C8311yescharacteristic
1073C22⋊Q8C23×C8311yescharacteristic
1074C22⋊Q8C23×C8311yescharacteristic, complemented
1075C22⋊Q8C23×C8311yescharacteristic, complemented
1076#121—21no—
1077#121—21no—
1078#121—21no—
1079#121—21no—
1080#121—21no—
1081#121—21no—
1082#121—21no—
1083#121—21no—
1084#121—22no—
1085#121—22no—
1086#121—22no—
1087#121—22no—
1088#121—21no—
1089#121—21no—
1090#121—21no—
1091#121—21no—
1092#121C23×C8312yes—
1093#121C23×C8312yes—
1094#121C23×C8311yescharacteristic
1095#121C23×C8311yescharacteristic
1096#121C23×C8311yescharacteristic, complemented
1097#121C23×C8311yescharacteristic, complemented
1098#120—21no—
1099#120—21no—
1100#120—22no—
1101#120—22no—
1102#120—22no—
1103#120—22no—
1104#120—21no—
1105#120—21no—
1106#120—21no—
1107#120—21no—
1108C4×Q8C23×C8311yescharacteristic, complemented
1109C4×Q8C23×C8311yescharacteristic, complemented
1110C4×D4—21no—
1111C4×D4—21no—
1112C4×D4—21no—
1113C4×D4—21no—
1114C4×D4—21no—
1115C4×D4—21no—
1116C4×D4—21no—
1117C4×D4—21no—
1118C4×D4—21no—
1119C4×D4—21no—
1120C4×D4—21no—
1121C4×D4—21no—
1122C4×D4—21no—
1123C4×D4—21no—
1124C4×D4D4×C8311yescharacteristic
1125C4×D4D4×C8311yescharacteristic
1126C4×D4D4×C8311yescharacteristic
1127C4×D4D4×C8311yescharacteristic
1128C4×D4C23×C8312yes—
1129C4×D4C23×C8312yes—
1130C4×D4C23×C8311yescharacteristic
1131C4×D4C23×C8311yescharacteristic
1132C4×D4C23×C8311yescharacteristic
1133C4×D4C23×C8311yescharacteristic
1134C4×D4C23×C8311yescharacteristic, complemented
1135C4×D4C23×C8311yescharacteristic, complemented
1136#117—21no—
1137#117C23×C8311yescharacteristic
1138C2×C4⋊C4—21no—
1139C2×C4⋊C4—21no—
1140C2×C4⋊C4D4×C8311yescharacteristic
1141C2×C4⋊C4C23×C8311yescharacteristic
1142C2×C22⋊C4—21no—
1143C2×C22⋊C4—21no—
1144C2×C22⋊C4—21no—
1145C2×C22⋊C4—21no—
1146C2×C22⋊C4—21no—
1147C2×C22⋊C4—22no—
1148C2×C22⋊C4—22no—
1149C2×C22⋊C4—22no—
1150C2×C22⋊C4—22no—
1151C2×C22⋊C4—21no—
1152C2×C22⋊C4—21no—
1153C2×C22⋊C4D4×C8311yescharacteristic
1154C2×C22⋊C4D4×C8311yescharacteristic
1155C2×C42—21no—
1156C2×C42C23×C8311yescharacteristic
1157#107C23×C8312yescomplemented
1158#106C23×C8312yescomplemented
1159C4⋊C8C23×C8312yescomplemented
1160C4⋊C8C23×C8312yescomplemented
1161#103C23×C8312yescomplemented
1162#103C23×C8312yescomplemented
1163#103C23×C8312yescomplemented
1164#103C23×C8312yescomplemented
1165#103C23×C8312yescomplemented
1166#102C23×C8312yes—
1167#102C23×C8312yes—
1168#102C23×C8312yes—
1169#102C23×C8312yes—
1170#102C23×C8312yescomplemented
1171#102C23×C8312yescomplemented
1172#102C23×C8312yescomplemented
1173C22⋊C8C23×C8312yes—
1174C22⋊C8C23×C8312yes—
1175C22⋊C8C23×C8312yescomplemented
1176C22⋊C8C23×C8312yescomplemented
1177#97C23×C8312yescomplemented
1178C4×C8C23×C8312yescomplemented
1179C24—21no—
1180C24—21no—
1181C24—22no—
1182C24—22no—
1183C24—21no—
1184C24—21no—
1185C24—44no—
1186C24—44no—
1187C24—82no—
1188C24C2×D4×C8311yescharacteristic
1189C24C2×D4×C8311yescharacteristic
1190#41—22no—
1191#41—22no—
1192#41—22no—
1193#41—24no—
1194#41—22no—
1195#41—22no—
1196#41—24no—
1197#41—22no—
1198#41—22no—
1199#41—22no—
1200#41—22no—
1201#41—44no—
1202#41—44no—
1203#41—41no—
1204#41—41no—
1205#41—42no—
1206#41—42no—
1207#41—41no—
1208#41—41no—
1209#41—44no—
1210#41—44no—
1211#41—44no—
1212#41—44no—
1213#41C2×D4×C8314yes—
1214C2×Q8—21no—
1215C2×Q8—21no—
1216C2×Q8—21no—
1217C2×Q8—22no—
1218C2×Q8—22no—
1219C2×Q8—22no—
1220C2×Q8—22no—
1221C2×Q8—41no—
1222C2×Q8—41no—
1223C2×Q8C24×C8312yes—
1224C2×Q8C24×C8311yescharacteristic
1225C2×Q8C24×C8311yescharacteristic
1226C2×Q8C24×C8311yescharacteristic
1227C2×D4—21no—
1228C2×D4—22no—
1229C2×D4—24no—
1230C2×D4—24no—
1231C2×D4—22no—
1232C2×D4—21no—
1233C2×D4—21no—
1234C2×D4—22no—
1235C2×D4—22no—
1236C2×D4—21no—
1237C2×D4—21no—
1238C2×D4—21no—
1239C2×D4—21no—
1240C2×D4—21no—
1241C2×D4—21no—
1242C2×D4—21no—
1243C2×D4—21no—
1244C2×D4—22no—
1245C2×D4—22no—
1246C2×D4—21no—
1247C2×D4—22no—
1248C2×D4—21no—
1249C2×D4—21no—
1250C2×D4—21no—
1251C2×D4—22no—
1252C2×D4—22no—
1253C2×D4—21no—
1254C2×D4—21no—
1255C2×D4—22no—
1256C2×D4—22no—
1257C2×D4—42no—
1258C2×D4—42no—
1259C2×D4—41no—
1260C2×D4—41no—
1261C2×D4—44no—
1262C2×D4—44no—
1263C2×D4—44no—
1264C2×D4—42no—
1265C2×D4—44no—
1266C2×D4—44no—
1267C2×D4—44no—
1268C2×D4—44no—
1269C2×D4—82no—
1270C2×D4C2×D4×C8311yescharacteristic
1271C2×D4C2×D4×C8311yescharacteristic
1272C2×D4C2×D4×C8311yescharacteristic
1273C2×D4C2×D4×C8311yescharacteristic
1274C2×D4C2×D4×C8314yescomplemented
1275C2×D4C24×C8312yes—
1276C2×D4C24×C8311yescharacteristic
1277C2×D4C24×C8311yescharacteristic
1278C2×D4C24×C8312yes—
1279C2×D4C24×C8311yescharacteristic
1280C22×C4—21no—
1281C22×C4—22no—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—22no—
1285C22×C4—21no—
1286C22×C4—21no—
1287C22×C4—21no—
1288C22×C4—21no—
1289C22×C4—21no—
1290C22×C4—22no—
1291C22×C4—22no—
1292C22×C4—21no—
1293C22×C4—21no—
1294C22×C4—21no—
1295C22×C4—21no—
1296C22×C4—21no—
1297C22×C4—21no—
1298C22×C4—21no—
1299C22×C4—22no—
1300C22×C4—22no—
1301C22×C4—44no—
1302C22×C4—44no—
1303C22×C4—44no—
1304C22×C4—82no—
1305C22×C4C2×D4×C8311yescharacteristic
1306C22×C4C2×D4×C8311yescharacteristic
1307C22×C4C2×D4×C8311yescharacteristic
1308C22×C4C2×D4×C8311yescharacteristic
1309C22×C4C2×D4×C8311yescharacteristic
1310C22×C4C2×D4×C8311yescharacteristic
1311C22×C4C2×D4×C8311yescharacteristic
1312C22×C4C2×D4×C8311yescharacteristic
1313C22×C4C24×C8311yescharacteristic
1314C22×C4C24×C8311yescharacteristic
1315C22×C4C24×C8311yescharacteristic
1316C22×C4C24×C8311yescharacteristic
1317C22×C4C24×C8311yescharacteristic
1318Q16—24no—
1319Q16—24no—
1320Q16—42no—
1321SD16—24no—
1322SD16—24no—
1323SD16—24no—
1324SD16—24no—
1325SD16—24no—
1326SD16—24no—
1327SD16—42no—
1328SD16—42no—
1329SD16C2×D4×C8318yescomplemented
1330D8—24no—
1331D8—24no—
1332D8—24no—
1333D8—24no—
1334D8—42no—
1335D8C2×D4×C8318yescomplemented
1336M16—22no—
1337M16—22no—
1338M16—22no—
1339M16—24no—
1340M16—24no—
1341M16C2×D4×C8314yescomplemented
1342C2×C8—24no—
1343C2×C8—24no—
1344C2×C8C24×C8312yes—
1345C2×C8C24×C8312yes—
1346C2×C8C24×C8312yes—
1347C2×C8C24×C8312yes—
1348C4⋊C4—21no—
1349C4⋊C4—21no—
1350C4⋊C4—21no—
1351C4⋊C4—22no—
1352C4⋊C4—22no—
1353C4⋊C4—21no—
1354C4⋊C4—21no—
1355C4⋊C4—21no—
1356C4⋊C4—21no—
1357C4⋊C4—21no—
1358C4⋊C4—21no—
1359C4⋊C4C2×D4×C8311yescharacteristic
1360C4⋊C4C2×D4×C8311yescharacteristic
1361C4⋊C4C2×D4×C8311yescharacteristic
1362C4⋊C4C2×D4×C8311yescharacteristic
1363C4⋊C4C24×C8311yescharacteristic
1364C4⋊C4C24×C8311yescharacteristic
1365C4⋊C4C24×C8312yes—
1366C22⋊C4—22no—
1367C22⋊C4—22no—
1368C22⋊C4—21no—
1369C22⋊C4—21no—
1370C22⋊C4—21no—
1371C22⋊C4—21no—
1372C22⋊C4—21no—
1373C22⋊C4—22no—
1374C22⋊C4—22no—
1375C22⋊C4—22no—
1376C22⋊C4—22no—
1377C22⋊C4—21no—
1378C22⋊C4—21no—
1379C22⋊C4—21no—
1380C22⋊C4—21no—
1381C22⋊C4—22no—
1382C22⋊C4—22no—
1383C22⋊C4—22no—
1384C22⋊C4—22no—
1385C22⋊C4—21no—
1386C22⋊C4—21no—
1387C22⋊C4—21no—
1388C22⋊C4—21no—
1389C22⋊C4—21no—
1390C22⋊C4—21no—
1391C22⋊C4C2×D4×C8311yescharacteristic
1392C22⋊C4C2×D4×C8311yescharacteristic
1393C22⋊C4C2×D4×C8311yescharacteristic
1394C22⋊C4C2×D4×C8311yescharacteristic
1395C22⋊C4C2×D4×C8311yescharacteristic
1396C22⋊C4C2×D4×C8311yescharacteristic
1397C22⋊C4C2×D4×C8311yescharacteristic
1398C22⋊C4C2×D4×C8311yescharacteristic
1399C42—21no—
1400C42—21no—
1401C42—21no—
1402C42C2×D4×C8311yescharacteristic
1403C42C2×D4×C8311yescharacteristic
1404C42C24×C8311yescharacteristic
1405C42C24×C8311yescharacteristic
1406C23—22no—
1407C23—24no—
1408C23—22no—
1409C23—21no—
1410C23—22no—
1411C23—22no—
1412C23—22no—
1413C23—21no—
1414C23—21no—
1415C23—41no—
1416C23—41no—
1417C23—41no—
1418C23—42no—
1419C23—42no—
1420C23—44no—
1421C23—44no—
1422C23—42no—
1423C23—42no—
1424C23—42no—
1425C23—42no—
1426C23—42no—
1427C23—44no—
1428C23—42no—
1429C23—42no—
1430C23—44no—
1431C23—82no—
1432C23—82no—
1433C23—81no—
1434C23—81no—
1435C23—816no—
1436C23C22×D4×C8311yescharacteristic
1437C23C22×D4×C8311yescharacteristic
1438C23C22×D4×C8311yescharacteristic
1439C23C22×D4×C8311yescharacteristic
1440C23C22×D4×C8311yescharacteristic
1441Q8—21no—
1442Q8—21no—
1443Q8—21no—
1444Q8—22no—
1445Q8—21no—
1446Q8—22no—
1447Q8—21no—
1448Q8—42no—
1449Q8—42no—
1450Q8—42no—
1451Q8C22×D4×C8312yes—
1452D4—24no—
1453D4—22no—
1454D4—22no—
1455D4—24no—
1456D4—21no—
1457D4—22no—
1458D4—21no—
1459D4—22no—
1460D4—21no—
1461D4—21no—
1462D4—22no—
1463D4—21no—
1464D4—41no—
1465D4—41no—
1466D4—44no—
1467D4—44no—
1468D4—42no—
1469D4—42no—
1470D4—42no—
1471D4—42no—
1472D4—42no—
1473D4—44no—
1474D4—42no—
1475D4—44no—
1476D4—42no—
1477D4—42no—
1478D4—42no—
1479D4—42no—
1480D4—42no—
1481D4—42no—
1482D4—81no—
1483D4—82no—
1484D4—82no—
1485D4—81no—
1486D4—81no—
1487D4C22×D4×C8312yes—
1488D4C22×D4×C8314yes—
1489C2×C4—22no—
1490C2×C4—22no—
1491C2×C4—21no—
1492C2×C4—22no—
1493C2×C4—22no—
1494C2×C4—22no—
1495C2×C4—22no—
1496C2×C4—24no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—22no—
1508C2×C4—22no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—41no—
1512C2×C4—41no—
1513C2×C4—42no—
1514C2×C4—42no—
1515C2×C4—42no—
1516C2×C4—42no—
1517C2×C4—42no—
1518C2×C4—44no—
1519C2×C4—42no—
1520C2×C4—44no—
1521C2×C4—42no—
1522C2×C4—42no—
1523C2×C4—42no—
1524C2×C4—42no—
1525C2×C4—42no—
1526C2×C4—82no—
1527C2×C4—82no—
1528C2×C4—81no—
1529C2×C4C22×D4×C8311yescharacteristic
1530C2×C4C22×D4×C8311yescharacteristic
1531C2×C4C22×D4×C8311yescharacteristic
1532C2×C4C22×D4×C8311yescharacteristic
1533C2×C4C22×D4×C8311yescharacteristic
1534C2×C4C22×D4×C8311yescharacteristic
1535C2×C4C22×D4×C8311yescharacteristic
1536C2×C4C22×D4×C8311yescharacteristic
1537C2×C4C22×D4×C8311yescharacteristic
1538C2×C4C22×D4×C8312yes—
1539C2×C4H(5,𝔽2)×C8312yes—
1540C2×C4C25×C8311yescharacteristic
1541C8—22no—
1542C8—22no—
1543C8—22no—
1544C8C22×D4×C8314yes—
1545C22—21no—
1546C22—21no—
1547C22—21no—
1548C22—21no—
1549C22—21no—
1550C22—21no—
1551C22—21no—
1552C22—21no—
1553C22—21no—
1554C22—21no—
1555C22—21no—
1556C22—21no—
1557C22—21no—
1558C22—22no—
1559C22—24no—
1560C22—44no—
1561C22—48no—
1562C22—41no—
1563C22—42no—
1564C22—42no—
1565C22—41no—
1566C22—41no—
1567C22—41no—
1568C22—42no—
1569C22—42no—
1570C22—41no—
1571C22—41no—
1572C22—41no—
1573C22—41no—
1574C22—42no—
1575C22—82no—
1576C22—88no—
1577C22—84no—
1578C22—84no—
1579C22—88no—
1580C22—84no—
1581C22D42×C8312yes—
1582C22#575×C8312yescomplemented
1583C22C23×D4×C8311yescharacteristic
1584C4—21no—
1585C4—21no—
1586C4—21no—
1587C4—21no—
1588C4—21no—
1589C4—21no—
1590C4—21no—
1591C4—21no—
1592C4—22no—
1593C4—41no—
1594C4—42no—
1595C4—41no—
1596C4—42no—
1597C4—41no—
1598C4—41no—
1599C4D42×C8312yes—
1600C4C23×D4×C8311yescharacteristic
1601C4C2×H(5,𝔽2)×C8311yescharacteristic
1602C2—22no—
1603C2—22no—
1604C2—41no—
1605C2—41no—
1606C2—41no—
1607C2—44no—
1608C2—42no—
1609C2—82no—
1610C2—81no—
1611C2—81no—
1612C2C2×D42×C8311yescharacteristic
1613C2C2×#575×C8311yescharacteristic
1614C2C83×#358511yescharacteristic
subgroupG/H
center, socleC22×C83C23×D4
commutator, Frattini, cosocleC2×C4C25×C83
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C83 ◁ C2×C4×D4×C83 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#575×C83C2semidirect
2. C22×AGL(1,ℤ/8)×C83C2semidirect
3. D4×#41×C83C2semidirect
4. C2×#546×C83C2semidirect
5. C83×#3282C2semidirect
6. C83×#3280C2semidirect
7. C83×#3275C2semidirect
8. C83×#3273C2semidirect
9. C83×#3268C2semidirect
10. C83×#3267C2semidirect
11. C83×#3266C2semidirect
12. C83×#3264C2semidirect
13. C83×#3153C2semidirect
14. C83×#3056C2semidirect
15. C83×#3055C2semidirect
16. C83×#3040C2semidirect
17. C83×#3036C2semidirect
18. C83×#3007C2semidirect
19. C83×#3006C2semidirect
20. C83×#3005C2semidirect
21. C83×#3003C2semidirect
22. C4×AGL(1,ℤ/8)×C83C2semidirect
23. D4×M16×C83C2semidirect
25. C22×#41×C83C22semidirect
26. C22×#41×C83C22semidirect
27. C23×D4×C83C22semidirect
29. C2×#137×C83C22semidirect
30. C2×#137×C83C22semidirect
31. C2×#137×C83C22semidirect
32. C2×#137×C83C22semidirect
36. C2×AGL(1,ℤ/8)×C83C22semidirect
37. C2×AGL(1,ℤ/8)×C83C22semidirect
38. C2×AGL(1,ℤ/8)×C83C22semidirect
39. C2×AGL(1,ℤ/8)×C83C22semidirect
40. C2×AGL(1,ℤ/8)×C83C22semidirect
41. C2×AGL(1,ℤ/8)×C83C22semidirect
42. C2×AGL(1,ℤ/8)×C83C22semidirect
43. C2×#135×C83C22semidirect
44. C2×#135×C83C22semidirect
45. C22×SD16×C83C22semidirect
46. C22×D8×C83C22semidirect
47. C22×M16×C83C22semidirect
48. C22×M16×C83C22semidirect
49. #550×C83C22semidirect
50. D4×Q8×C83C22semidirect
51. #548×C83C22semidirect
52. #548×C83C22semidirect
54. #547×C83C22semidirect
62. #546×C83C22semidirect
63. #546×C83C22semidirect
64. #546×C83C22semidirect
65. #546×C83C22semidirect
66. #546×C83C22semidirect
68. D42×C83C22semidirect
70. #532×C83C22semidirect
71. C2×#124×C83C22semidirect
75. #525×C83C22semidirect
77. C2×C22⋊Q8×C83C22semidirect
79. C2×#121×C83C22semidirect
81. C4×#41×C83C22semidirect
84. C2×C4×D4×C83C22semidirect
86. #497×C83C22semidirect
87. #496×C83C22semidirect
88. #495×C83C22semidirect
89. #495×C83C22semidirect
90. #470×C83C22semidirect
91. #469×C83C22semidirect
92. #468×C83C22semidirect
93. #468×C83C22semidirect
94. #467×C83C22semidirect
95. #466×C83C22semidirect
96. #465×C83C22semidirect
97. #465×C83C22semidirect
98. #464×C83C22semidirect
99. #464×C83C22semidirect
100. #463×C83C22semidirect
101. #463×C83C22semidirect
102. #463×C83C22semidirect
103. #463×C83C22semidirect
104. #461×C83C22semidirect
105. #459×C83C22semidirect
106. #452×C83C22semidirect
107. #452×C83C22semidirect
108. #452×C83C22semidirect
109. #452×C83C22semidirect
110. #451×C83C22semidirect
111. #450×C83C22semidirect
112. #450×C83C22semidirect
113. #450×C83C22semidirect
114. #449×C83C22semidirect
115. #449×C83C22semidirect
116. #449×C83C22semidirect
117. #449×C83C22semidirect
118. #448×C83C22semidirect
119. #447×C83C22semidirect
120. #447×C83C22semidirect
121. #447×C83C22semidirect
122. #442×C83C22semidirect
123. #440×C83C22semidirect
124. C4×SD16×C83C22semidirect
125. C4×D8×C83C22semidirect
126. #436×C83C22semidirect
127. #435×C83C22semidirect
128. #435×C83C22semidirect
129. C8×D4×C83C22semidirect
130. #428×C83C22semidirect
131. #423×C83C22semidirect
132. #419×C83C22semidirect
133. #418×C83C22semidirect
134. #418×C83C22semidirect
135. #417×C83C22semidirect
136. #417×C83C22semidirect
137. #417×C83C22semidirect
138. #407×C83C22semidirect
139. #407×C83C22semidirect
140. C4×M16×C83C22semidirect
161. C2×#41×C83C23semidirect
162. C2×#41×C83C23semidirect
165. C22×Q8×C83C23semidirect
182. C22×D4×C83C23semidirect
201. AGL(1,ℤ/8)×C83D4semidirect
204. C2×Q16×C83C23semidirect
205. C2×Q16×C83C23semidirect
206. C2×Q16×C83C23semidirect
214. C2×SD16×C83C23semidirect
215. C2×SD16×C83C23semidirect
216. C2×SD16×C83C23semidirect
231. C2×M16×C83C23semidirect
233. C22×C8×C83C23semidirect
235. C4⋊Q8×C83C23semidirect
237. #127×C83C23semidirect
244. #124×C83C23semidirect
245. #124×C83C23semidirect
266. C22⋊Q8×C83C23semidirect
267. C22⋊Q8×C83C23semidirect
288. #121×C83C23semidirect
289. #121×C83C23semidirect
300. C4×Q8×C83C23semidirect
301. C4×Q8×C83C23semidirect
326. C4×D4×C83C23semidirect
327. C4×D4×C83C23semidirect
349. #107×C83C23semidirect
350. #106×C83C23semidirect
351. C4⋊C8×C83C23semidirect
352. C4⋊C8×C83C23semidirect
353. #103×C83C23semidirect
354. #103×C83C23semidirect
355. #103×C83C23semidirect
356. #103×C83C23semidirect
357. #103×C83C23semidirect
362. #102×C83C23semidirect
363. #102×C83C23semidirect
364. #102×C83C23semidirect
367. C22⋊C8×C83C23semidirect
368. C22⋊C8×C83C23semidirect
369. #97×C83C23semidirect
370. C4×C8×C83C23semidirect
466. C2×D4×C83C2×D4semidirect
521. SD16×C83C2×D4semidirect
527. D8×C83C2×D4semidirect
533. M16×C83C2×D4semidirect
774. C22×C83#575semidirect
794. #61066C83direct (N × H)
808. C2×#575C2×C83semidirect
809. C22×AGL(1,ℤ/8)C2×C83semidirect
810. D4×#41C2×C83semidirect
811. C2×#546C2×C83semidirect
812. #3282C2×C83semidirect
813. #3280C2×C83semidirect
814. #3275C2×C83semidirect
815. #3273C2×C83semidirect
816. #3268C2×C83semidirect
817. #3267C2×C83semidirect
818. #3266C2×C83semidirect
819. #3264C2×C83semidirect
820. #3153C2×C83semidirect
821. #3056C2×C83semidirect
822. #3055C2×C83semidirect
823. #3040C2×C83semidirect
824. #3036C2×C83semidirect
825. #3007C2×C83semidirect
826. #3006C2×C83semidirect
827. #3005C2×C83semidirect
828. #3003C2×C83semidirect
829. C4×AGL(1,ℤ/8)C2×C83semidirect
830. D4×M16C2×C83semidirect
831. C83#61066direct (N × H)
833. C22×#41C22×C83semidirect
834. C22×#41C22×C83semidirect
835. C23×D4C22×C83semidirect
837. C2×#137C22×C83semidirect
838. C2×#137C22×C83semidirect
839. C2×#137C22×C83semidirect
840. C2×#137C22×C83semidirect
844. C2×AGL(1,ℤ/8)C22×C83semidirect
845. C2×AGL(1,ℤ/8)C22×C83semidirect
846. C2×AGL(1,ℤ/8)C22×C83semidirect
847. C2×AGL(1,ℤ/8)C22×C83semidirect
848. C2×AGL(1,ℤ/8)C22×C83semidirect
849. C2×AGL(1,ℤ/8)C22×C83semidirect
850. C2×AGL(1,ℤ/8)C22×C83semidirect
851. C2×#135C22×C83semidirect
852. C2×#135C22×C83semidirect
853. C22×SD16C22×C83semidirect
854. C22×D8C22×C83semidirect
855. C22×M16C22×C83semidirect
856. C22×M16C22×C83semidirect
857. #550C22×C83semidirect
858. D4×Q8C22×C83semidirect
859. #548C22×C83semidirect
860. #548C22×C83semidirect
862. #547C22×C83semidirect
870. #546C22×C83semidirect
871. #546C22×C83semidirect
872. #546C22×C83semidirect
873. #546C22×C83semidirect
874. #546C22×C83semidirect
876. D42C22×C83semidirect
878. #532C22×C83semidirect
879. C2×#124C22×C83semidirect
883. #525C22×C83semidirect
885. C2×C22⋊Q8C22×C83semidirect
887. C2×#121C22×C83semidirect
889. C4×#41C22×C83semidirect
892. C2×C4×D4C22×C83semidirect
894. #497C22×C83semidirect
895. #496C22×C83semidirect
896. #495C22×C83semidirect
897. #495C22×C83semidirect
898. #470C22×C83semidirect
899. #469C22×C83semidirect
900. #468C22×C83semidirect
901. #468C22×C83semidirect
902. #467C22×C83semidirect
903. #466C22×C83semidirect
904. #465C22×C83semidirect
905. #465C22×C83semidirect
906. #464C22×C83semidirect
907. #464C22×C83semidirect
908. #463C22×C83semidirect
909. #463C22×C83semidirect
910. #463C22×C83semidirect
911. #463C22×C83semidirect
912. #461C22×C83semidirect
913. #459C22×C83semidirect
914. #452C22×C83semidirect
915. #452C22×C83semidirect
916. #452C22×C83semidirect
917. #452C22×C83semidirect
918. #451C22×C83semidirect
919. #450C22×C83semidirect
920. #450C22×C83semidirect
921. #450C22×C83semidirect
922. #449C22×C83semidirect
923. #449C22×C83semidirect
924. #449C22×C83semidirect
925. #449C22×C83semidirect
926. #448C22×C83semidirect
927. #447C22×C83semidirect
928. #447C22×C83semidirect
929. #447C22×C83semidirect
930. #442C22×C83semidirect
931. #440C22×C83semidirect
932. C4×SD16C22×C83semidirect
933. C4×D8C22×C83semidirect
934. #436C22×C83semidirect
935. #435C22×C83semidirect
936. #435C22×C83semidirect
937. C8×D4C22×C83semidirect
938. #428C22×C83semidirect
939. #423C22×C83semidirect
940. #419C22×C83semidirect
941. #418C22×C83semidirect
942. #418C22×C83semidirect
943. #417C22×C83semidirect
944. #417C22×C83semidirect
945. #417C22×C83semidirect
946. #407C22×C83semidirect
947. #407C22×C83semidirect
948. C4×M16C22×C83semidirect
969. C2×#41C23×C83semidirect
970. C2×#41C23×C83semidirect
973. C22×Q8C23×C83semidirect
990. C22×D4C23×C83semidirect
1009. AGL(1,ℤ/8)D4×C83semidirect
1012. C2×Q16C23×C83semidirect
1013. C2×Q16C23×C83semidirect
1014. C2×Q16C23×C83semidirect
1022. C2×SD16C23×C83semidirect
1023. C2×SD16C23×C83semidirect
1024. C2×SD16C23×C83semidirect
1039. C2×M16C23×C83semidirect
1041. C22×C8C23×C83semidirect
1043. C4⋊Q8C23×C83semidirect
1045. #127C23×C83semidirect
1052. #124C23×C83semidirect
1053. #124C23×C83semidirect
1074. C22⋊Q8C23×C83semidirect
1075. C22⋊Q8C23×C83semidirect
1096. #121C23×C83semidirect
1097. #121C23×C83semidirect
1108. C4×Q8C23×C83semidirect
1109. C4×Q8C23×C83semidirect
1134. C4×D4C23×C83semidirect
1135. C4×D4C23×C83semidirect
1157. #107C23×C83semidirect
1158. #106C23×C83semidirect
1159. C4⋊C8C23×C83semidirect
1160. C4⋊C8C23×C83semidirect
1161. #103C23×C83semidirect
1162. #103C23×C83semidirect
1163. #103C23×C83semidirect
1164. #103C23×C83semidirect
1165. #103C23×C83semidirect
1170. #102C23×C83semidirect
1171. #102C23×C83semidirect
1172. #102C23×C83semidirect
1175. C22⋊C8C23×C83semidirect
1176. C22⋊C8C23×C83semidirect
1177. #97C23×C83semidirect
1178. C4×C8C23×C83semidirect
1274. C2×D4C2×D4×C83semidirect
1329. SD16C2×D4×C83semidirect
1335. D8C2×D4×C83semidirect
1341. M16C2×D4×C83semidirect
1582. C22#575×C83semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#575×C832
C22×AGL(1,ℤ/8)×C832
D4×#41×C832
C2×#546×C832
C83×#32822
C83×#32802
C83×#32752
C83×#32732
C83×#32682
C83×#32672
C83×#32662
C83×#32642
C83×#31532
C83×#30562
C83×#30552
C83×#30402
C83×#30362
C83×#30072
C83×#30062
C83×#30052
C83×#30032
C4×AGL(1,ℤ/8)×C832
D4×M16×C832
#6106683