Finite Group Databasebeta

← C43×#61066 #24981083

Subgroups — C43×#61066 #24981083

Order 11008.

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×C43×#575C211yesmaximal, characteristic, complemented
2C22×AGL(1,ℤ/8)×C43C211yesmaximal, characteristic, complemented
3D4×#41×C43C211yesmaximal, characteristic, complemented
4C2×C43×#546C211yesmaximal, characteristic, complemented
5C43×#3282C212yesmaximal, complemented
6C43×#3280C212yesmaximal, complemented
7C43×#3275C212yesmaximal, complemented
8C43×#3273C212yesmaximal, complemented
9C43×#3268C212yesmaximal, complemented
10C43×#3267C212yesmaximal, complemented
11C43×#3266C212yesmaximal, complemented
12C43×#3264C212yesmaximal, complemented
13C43×#3153C211yesmaximal, characteristic, complemented
14C43×#3056C211yesmaximal, characteristic, complemented
15C43×#3055C211yesmaximal, characteristic, complemented
16C43×#3040C211yesmaximal, characteristic, complemented
17C43×#3036C211yesmaximal, characteristic, complemented
18C43×#3007C211yesmaximal, characteristic, complemented
19C43×#3006C211yesmaximal, characteristic, complemented
20C43×#3005C211yesmaximal, characteristic, complemented
21C43×#3003C211yesmaximal, characteristic, complemented
22C4×AGL(1,ℤ/8)×C43C211yesmaximal, characteristic, complemented
23D4×M16×C43C211yesmaximal, characteristic, complemented
24C22×#41×C43C2211yescharacteristic
25C22×#41×C43C2211yescharacteristic, complemented
26C22×#41×C43C2211yescharacteristic, complemented
27C23×D4×C43C2211yescharacteristic, complemented
28C43×#575—28no—
29C2×#137×C43C2211yescharacteristic, complemented
30C2×#137×C43C2211yescharacteristic, complemented
31C2×#137×C43C2211yescharacteristic, complemented
32C2×#137×C43C2212yescomplemented
33C2×AGL(1,ℤ/8)×C43—28no—
34C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
35C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
36C2×AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
38C2×AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
39C2×AGL(1,ℤ/8)×C43C2212yescomplemented
40C2×AGL(1,ℤ/8)×C43C2212yescomplemented
41C2×AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
42C2×AGL(1,ℤ/8)×C43C2212yescomplemented
43C2×#135×C43C2212yescomplemented
44C2×#135×C43C2212yescomplemented
45C22×SD16×C43C2212yescomplemented
46C22×D8×C43C2212yescomplemented
47C22×M16×C43C2211yescharacteristic, complemented
48C22×M16×C43C2211yescharacteristic, complemented
49C43×#550C2211yescharacteristic, complemented
50D4×Q8×C43C2211yescharacteristic, complemented
51C43×#548C2211yescharacteristic, complemented
52C43×#548C2211yescharacteristic, complemented
53C43×#547—21no—
54C43×#547C2211yescharacteristic, complemented
55C43×#546—21no—
56C43×#546—21no—
57C43×#546—21no—
58C43×#546—21no—
59C43×#546—21no—
60C43×#546—21no—
61C43×#546C2212yes—
62C43×#546C2212yescomplemented
63C43×#546C2212yescomplemented
64C43×#546C2212yescomplemented
65C43×#546C2211yescharacteristic, complemented
66C43×#546C2211yescharacteristic, complemented
67D42×C43—21no—
68D42×C43C2211yescharacteristic, complemented
69C43×#532—21no—
70C43×#532C2211yescharacteristic, complemented
71C2×#124×C43C2211yescharacteristic, complemented
72C43×#525—21no—
73C43×#525—21no—
74C43×#525C2211yescharacteristic
75C43×#525C2211yescharacteristic, complemented
76C2×#123×C43—21no—
77C2×C22⋊Q8×C43C2211yescharacteristic, complemented
78C2×#121×C43—21no—
79C2×#121×C43C2211yescharacteristic, complemented
80C2×#120×C43—21no—
81C4×#41×C43C2211yescharacteristic, complemented
82C2×C4×D4×C43—21no—
83C2×C4×D4×C43C2211yescharacteristic
84C2×C4×D4×C43C2211yescharacteristic, complemented
85C22×C22⋊C4×C43—21no—
86C43×#497C2212yescomplemented
87C43×#496C2212yescomplemented
88C43×#495C2212yescomplemented
89C43×#495C2212yescomplemented
90C43×#470C2212yescomplemented
91C43×#469C2212yescomplemented
92C43×#468C2212yescomplemented
93C43×#468C2212yescomplemented
94C43×#467C2212yescomplemented
95C43×#466C2212yescomplemented
96C43×#465C2212yescomplemented
97C43×#465C2212yescomplemented
98C43×#464C2212yescomplemented
99C43×#464C2212yescomplemented
100C43×#463C2212yescomplemented
101C43×#463C2212yescomplemented
102C43×#463C2212yescomplemented
103C43×#463C2212yescomplemented
104C43×#461C2212yescomplemented
105C43×#459C2212yescomplemented
106C43×#452C2212yescomplemented
107C43×#452C2212yescomplemented
108C43×#452C2212yescomplemented
109C43×#452C2212yescomplemented
110C43×#451C2212yescomplemented
111C43×#450C2212yescomplemented
112C43×#450C2212yescomplemented
113C43×#450C2212yescomplemented
114C43×#449C2212yescomplemented
115C43×#449C2212yescomplemented
116C43×#449C2212yescomplemented
117C43×#449C2212yescomplemented
118C43×#448C2212yescomplemented
119C43×#447C2212yescomplemented
120C43×#447C2212yescomplemented
121C43×#447C2212yescomplemented
122C43×#442C2212yescomplemented
123C43×#440C2212yescomplemented
124C4×SD16×C43C2212yescomplemented
125C4×D8×C43C2212yescomplemented
126C43×#436C2212yescomplemented
127C43×#435C2212yescomplemented
128C43×#435C2212yescomplemented
129C8×D4×C43C2212yescomplemented
130C43×#428C2211yescharacteristic, complemented
131C43×#423C2211yescharacteristic, complemented
132C43×#419C2211yescharacteristic, complemented
133C43×#418C2211yescharacteristic, complemented
134C43×#418C2211yescharacteristic, complemented
135C43×#417C2211yescharacteristic, complemented
136C43×#417C2211yescharacteristic, complemented
137C43×#417C2211yescharacteristic, complemented
138C43×#407C2211yescharacteristic, complemented
139C43×#407C2211yescharacteristic, complemented
140C4×M16×C43C2211yescharacteristic, complemented
141C25×C43—21no—
142C2×#41×C43—21no—
143C2×#41×C43—21no—
144C2×#41×C43—21no—
145C2×#41×C43—21no—
146C2×#41×C43—21no—
147C2×#41×C43—21no—
148C2×#41×C43—24no—
149C2×#41×C43—24no—
150C2×#41×C43—24no—
151C2×#41×C43—42no—
152C2×#41×C43—42no—
153C2×#41×C43—42no—
154C2×#41×C43C2311yescharacteristic
155C2×#41×C43C2311yescharacteristic
156C2×#41×C43C2312yes—
157C2×#41×C43C2312yes—
158C2×#41×C43C2311yescharacteristic
159C2×#41×C43C2311yescharacteristic
160C2×#41×C43C2311yescharacteristic
161C2×#41×C43C2311yescharacteristic, complemented
162C2×#41×C43C2311yescharacteristic, complemented
163C22×Q8×C43C2311yescharacteristic
164C22×Q8×C43C2311yescharacteristic
165C22×Q8×C43C2311yescharacteristic, complemented
166C22×D4×C43—24no—
167C22×D4×C43—21no—
168C22×D4×C43—21no—
169C22×D4×C43—21no—
170C22×D4×C43—21no—
171C22×D4×C43—21no—
172C22×D4×C43—21no—
173C22×D4×C43—21no—
174C22×D4×C43—21no—
175C22×D4×C43—42no—
176C22×D4×C43D411yescharacteristic
177C22×D4×C43C2311yescharacteristic
178C22×D4×C43C2311yescharacteristic
179C22×D4×C43C2312yes—
180C22×D4×C43C2312yes—
181C22×D4×C43C2311yescharacteristic
182C22×D4×C43C2311yescharacteristic, complemented
183C23×C4×C43—21no—
184C23×C4×C43—21no—
185C23×C4×C43—21no—
186C23×C4×C43—21no—
187C23×C4×C43C2311yescharacteristic
188C23×C4×C43C2311yescharacteristic
189#137×C43—24no—
190#137×C43—28no—
191#137×C43—24no—
192#137×C43—42no—
193AGL(1,ℤ/8)×C43—24no—
194AGL(1,ℤ/8)×C43—24no—
195AGL(1,ℤ/8)×C43—24no—
196AGL(1,ℤ/8)×C43—28no—
197AGL(1,ℤ/8)×C43—28no—
198AGL(1,ℤ/8)×C43—28no—
199AGL(1,ℤ/8)×C43—24no—
200AGL(1,ℤ/8)×C43—42no—
201AGL(1,ℤ/8)×C43D418yescomplemented
202#135×C43—28no—
203#135×C43—28no—
204C2×Q16×C43C2312yescomplemented
205C2×Q16×C43C2312yescomplemented
206C2×Q16×C43C2312yescomplemented
207C2×SD16×C43—28no—
208C2×SD16×C43C2312yes—
209C2×SD16×C43C2312yes—
210C2×SD16×C43C2312yes—
211C2×SD16×C43C2312yes—
212C2×SD16×C43C2312yes—
213C2×SD16×C43C2312yes—
214C2×SD16×C43C2312yescomplemented
215C2×SD16×C43C2312yescomplemented
216C2×SD16×C43C2312yescomplemented
217C2×D8×C43—28no—
218C2×D8×C43C2312yes—
219C2×D8×C43C2312yes—
220C2×D8×C43C2312yes—
221C2×D8×C43C2312yes—
222C2×D8×C43C2312yes—
223C2×D8×C43C2312yes—
224C2×M16×C43—24no—
225C2×M16×C43—24no—
226C2×M16×C43C2311yescharacteristic
227C2×M16×C43C2312yes—
228C2×M16×C43C2311yescharacteristic
229C2×M16×C43C2311yescharacteristic
230C2×M16×C43C2311yescharacteristic
231C2×M16×C43C2312yescomplemented
232C22×C8×C43C2312yes—
233C22×C8×C43C2312yescomplemented
234C4⋊Q8×C43—21no—
235C4⋊Q8×C43C2311yescharacteristic, complemented
236#127×C43—21no—
237#127×C43C2311yescharacteristic, complemented
238#124×C43—21no—
239#124×C43—21no—
240#124×C43—21no—
241#124×C43—21no—
242#124×C43C2312yes—
243#124×C43C2312yes—
244#124×C43C2311yescharacteristic, complemented
245#124×C43C2311yescharacteristic, complemented
246#123×C43—21no—
247#123×C43—21no—
248#123×C43—22no—
249#123×C43—22no—
250#123×C43—22no—
251#123×C43—22no—
252#123×C43—21no—
253#123×C43—21no—
254#123×C43—21no—
255#123×C43—21no—
256C22⋊Q8×C43—21no—
257C22⋊Q8×C43—21no—
258C22⋊Q8×C43—21no—
259C22⋊Q8×C43—21no—
260C22⋊Q8×C43—21no—
261C22⋊Q8×C43—21no—
262C22⋊Q8×C43C2312yes—
263C22⋊Q8×C43C2312yes—
264C22⋊Q8×C43C2311yescharacteristic
265C22⋊Q8×C43C2311yescharacteristic
266C22⋊Q8×C43C2311yescharacteristic, complemented
267C22⋊Q8×C43C2311yescharacteristic, complemented
268#121×C43—21no—
269#121×C43—21no—
270#121×C43—21no—
271#121×C43—21no—
272#121×C43—21no—
273#121×C43—21no—
274#121×C43—21no—
275#121×C43—21no—
276#121×C43—22no—
277#121×C43—22no—
278#121×C43—22no—
279#121×C43—22no—
280#121×C43—21no—
281#121×C43—21no—
282#121×C43—21no—
283#121×C43—21no—
284#121×C43C2312yes—
285#121×C43C2312yes—
286#121×C43C2311yescharacteristic
287#121×C43C2311yescharacteristic
288#121×C43C2311yescharacteristic, complemented
289#121×C43C2311yescharacteristic, complemented
290#120×C43—21no—
291#120×C43—21no—
292#120×C43—22no—
293#120×C43—22no—
294#120×C43—22no—
295#120×C43—22no—
296#120×C43—21no—
297#120×C43—21no—
298#120×C43—21no—
299#120×C43—21no—
300C4×Q8×C43C2311yescharacteristic, complemented
301C4×Q8×C43C2311yescharacteristic, complemented
302C4×D4×C43—21no—
303C4×D4×C43—21no—
304C4×D4×C43—21no—
305C4×D4×C43—21no—
306C4×D4×C43—21no—
307C4×D4×C43—21no—
308C4×D4×C43—21no—
309C4×D4×C43—21no—
310C4×D4×C43—21no—
311C4×D4×C43—21no—
312C4×D4×C43—21no—
313C4×D4×C43—21no—
314C4×D4×C43—21no—
315C4×D4×C43—21no—
316C4×D4×C43D411yescharacteristic
317C4×D4×C43D411yescharacteristic
318C4×D4×C43D411yescharacteristic
319C4×D4×C43D411yescharacteristic
320C4×D4×C43C2312yes—
321C4×D4×C43C2312yes—
322C4×D4×C43C2311yescharacteristic
323C4×D4×C43C2311yescharacteristic
324C4×D4×C43C2311yescharacteristic
325C4×D4×C43C2311yescharacteristic
326C4×D4×C43C2311yescharacteristic, complemented
327C4×D4×C43C2311yescharacteristic, complemented
328#117×C43—21no—
329#117×C43C2311yescharacteristic
330C2×C4⋊C4×C43—21no—
331C2×C4⋊C4×C43—21no—
332C2×C4⋊C4×C43D411yescharacteristic
333C2×C4⋊C4×C43C2311yescharacteristic
334C2×C22⋊C4×C43—21no—
335C2×C22⋊C4×C43—21no—
336C2×C22⋊C4×C43—21no—
337C2×C22⋊C4×C43—21no—
338C2×C22⋊C4×C43—21no—
339C2×C22⋊C4×C43—22no—
340C2×C22⋊C4×C43—22no—
341C2×C22⋊C4×C43—22no—
342C2×C22⋊C4×C43—22no—
343C2×C22⋊C4×C43—21no—
344C2×C22⋊C4×C43—21no—
345C2×C22⋊C4×C43D411yescharacteristic
346C2×C22⋊C4×C43D411yescharacteristic
347C2×C42×C43—21no—
348C2×C42×C43C2311yescharacteristic
349#107×C43C2312yescomplemented
350#106×C43C2312yescomplemented
351C4⋊C8×C43C2312yescomplemented
352C4⋊C8×C43C2312yescomplemented
353#103×C43C2312yescomplemented
354#103×C43C2312yescomplemented
355#103×C43C2312yescomplemented
356#103×C43C2312yescomplemented
357#103×C43C2312yescomplemented
358#102×C43C2312yes—
359#102×C43C2312yes—
360#102×C43C2312yes—
361#102×C43C2312yes—
362#102×C43C2312yescomplemented
363#102×C43C2312yescomplemented
364#102×C43C2312yescomplemented
365C22⋊C8×C43C2312yes—
366C22⋊C8×C43C2312yes—
367C22⋊C8×C43C2312yescomplemented
368C22⋊C8×C43C2312yescomplemented
369#97×C43C2312yescomplemented
370C4×C8×C43C2312yescomplemented
371C24×C43—21no—
372C24×C43—21no—
373C24×C43—22no—
374C24×C43—22no—
375C24×C43—21no—
376C24×C43—21no—
377C24×C43—44no—
378C24×C43—44no—
379C24×C43—82no—
380C24×C43C2×D411yescharacteristic
381C24×C43C2×D411yescharacteristic
382#41×C43—22no—
383#41×C43—22no—
384#41×C43—22no—
385#41×C43—24no—
386#41×C43—22no—
387#41×C43—22no—
388#41×C43—24no—
389#41×C43—22no—
390#41×C43—22no—
391#41×C43—22no—
392#41×C43—22no—
393#41×C43—44no—
394#41×C43—44no—
395#41×C43—41no—
396#41×C43—41no—
397#41×C43—42no—
398#41×C43—42no—
399#41×C43—41no—
400#41×C43—41no—
401#41×C43—44no—
402#41×C43—44no—
403#41×C43—44no—
404#41×C43—44no—
405#41×C43C2×D414yes—
406C2×Q8×C43—21no—
407C2×Q8×C43—21no—
408C2×Q8×C43—21no—
409C2×Q8×C43—22no—
410C2×Q8×C43—22no—
411C2×Q8×C43—22no—
412C2×Q8×C43—22no—
413C2×Q8×C43—41no—
414C2×Q8×C43—41no—
415C2×Q8×C43C2412yes—
416C2×Q8×C43C2411yescharacteristic
417C2×Q8×C43C2411yescharacteristic
418C2×Q8×C43C2411yescharacteristic
419C2×D4×C43—21no—
420C2×D4×C43—21no—
421C2×D4×C43—21no—
422C2×D4×C43—21no—
423C2×D4×C43—22no—
424C2×D4×C43—22no—
425C2×D4×C43—21no—
426C2×D4×C43—21no—
427C2×D4×C43—22no—
428C2×D4×C43—21no—
429C2×D4×C43—21no—
430C2×D4×C43—21no—
431C2×D4×C43—22no—
432C2×D4×C43—22no—
433C2×D4×C43—21no—
434C2×D4×C43—21no—
435C2×D4×C43—21no—
436C2×D4×C43—21no—
437C2×D4×C43—21no—
438C2×D4×C43—21no—
439C2×D4×C43—21no—
440C2×D4×C43—21no—
441C2×D4×C43—22no—
442C2×D4×C43—22no—
443C2×D4×C43—22no—
444C2×D4×C43—24no—
445C2×D4×C43—24no—
446C2×D4×C43—22no—
447C2×D4×C43—22no—
448C2×D4×C43—22no—
449C2×D4×C43—44no—
450C2×D4×C43—44no—
451C2×D4×C43—42no—
452C2×D4×C43—44no—
453C2×D4×C43—44no—
454C2×D4×C43—42no—
455C2×D4×C43—42no—
456C2×D4×C43—41no—
457C2×D4×C43—41no—
458C2×D4×C43—44no—
459C2×D4×C43—44no—
460C2×D4×C43—44no—
461C2×D4×C43—82no—
462C2×D4×C43C2×D411yescharacteristic
463C2×D4×C43C2×D411yescharacteristic
464C2×D4×C43C2×D411yescharacteristic
465C2×D4×C43C2×D411yescharacteristic
466C2×D4×C43C2×D414yescomplemented
467C2×D4×C43C2412yes—
468C2×D4×C43C2411yescharacteristic
469C2×D4×C43C2411yescharacteristic
470C2×D4×C43C2412yes—
471C2×D4×C43C2411yescharacteristic
472C22×C4×C43—21no—
473C22×C4×C43—22no—
474C22×C4×C43—22no—
475C22×C4×C43—22no—
476C22×C4×C43—22no—
477C22×C4×C43—21no—
478C22×C4×C43—22no—
479C22×C4×C43—22no—
480C22×C4×C43—21no—
481C22×C4×C43—21no—
482C22×C4×C43—21no—
483C22×C4×C43—21no—
484C22×C4×C43—21no—
485C22×C4×C43—21no—
486C22×C4×C43—21no—
487C22×C4×C43—22no—
488C22×C4×C43—22no—
489C22×C4×C43—21no—
490C22×C4×C43—21no—
491C22×C4×C43—21no—
492C22×C4×C43—21no—
493C22×C4×C43—44no—
494C22×C4×C43—44no—
495C22×C4×C43—44no—
496C22×C4×C43—82no—
497C22×C4×C43C2×D411yescharacteristic
498C22×C4×C43C2×D411yescharacteristic
499C22×C4×C43C2×D411yescharacteristic
500C22×C4×C43C2×D411yescharacteristic
501C22×C4×C43C2×D411yescharacteristic
502C22×C4×C43C2×D411yescharacteristic
503C22×C4×C43C2×D411yescharacteristic
504C22×C4×C43C2×D411yescharacteristic
505C22×C4×C43C2411yescharacteristic
506C22×C4×C43C2411yescharacteristic
507C22×C4×C43C2411yescharacteristic
508C22×C4×C43C2411yescharacteristic
509C22×C4×C43C2411yescharacteristic
510Q16×C43—24no—
511Q16×C43—24no—
512Q16×C43—42no—
513SD16×C43—24no—
514SD16×C43—24no—
515SD16×C43—24no—
516SD16×C43—24no—
517SD16×C43—24no—
518SD16×C43—24no—
519SD16×C43—42no—
520SD16×C43—42no—
521SD16×C43C2×D418yescomplemented
522D8×C43—24no—
523D8×C43—24no—
524D8×C43—24no—
525D8×C43—24no—
526D8×C43—42no—
527D8×C43C2×D418yescomplemented
528M16×C43—22no—
529M16×C43—22no—
530M16×C43—22no—
531M16×C43—24no—
532M16×C43—24no—
533M16×C43C2×D414yescomplemented
534C2×C8×C43—24no—
535C2×C8×C43—24no—
536C2×C8×C43C2412yes—
537C2×C8×C43C2412yes—
538C2×C8×C43C2412yes—
539C2×C8×C43C2412yes—
540C4⋊C4×C43—21no—
541C4⋊C4×C43—21no—
542C4⋊C4×C43—21no—
543C4⋊C4×C43—22no—
544C4⋊C4×C43—22no—
545C4⋊C4×C43—21no—
546C4⋊C4×C43—21no—
547C4⋊C4×C43—21no—
548C4⋊C4×C43—21no—
549C4⋊C4×C43—21no—
550C4⋊C4×C43—21no—
551C4⋊C4×C43C2×D411yescharacteristic
552C4⋊C4×C43C2×D411yescharacteristic
553C4⋊C4×C43C2×D411yescharacteristic
554C4⋊C4×C43C2×D411yescharacteristic
555C4⋊C4×C43C2411yescharacteristic
556C4⋊C4×C43C2411yescharacteristic
557C4⋊C4×C43C2412yes—
558C22⋊C4×C43—22no—
559C22⋊C4×C43—22no—
560C22⋊C4×C43—22no—
561C22⋊C4×C43—22no—
562C22⋊C4×C43—21no—
563C22⋊C4×C43—21no—
564C22⋊C4×C43—21no—
565C22⋊C4×C43—21no—
566C22⋊C4×C43—22no—
567C22⋊C4×C43—22no—
568C22⋊C4×C43—22no—
569C22⋊C4×C43—22no—
570C22⋊C4×C43—21no—
571C22⋊C4×C43—21no—
572C22⋊C4×C43—21no—
573C22⋊C4×C43—21no—
574C22⋊C4×C43—21no—
575C22⋊C4×C43—21no—
576C22⋊C4×C43—22no—
577C22⋊C4×C43—22no—
578C22⋊C4×C43—21no—
579C22⋊C4×C43—21no—
580C22⋊C4×C43—21no—
581C22⋊C4×C43—21no—
582C22⋊C4×C43—21no—
583C22⋊C4×C43C2×D411yescharacteristic
584C22⋊C4×C43C2×D411yescharacteristic
585C22⋊C4×C43C2×D411yescharacteristic
586C22⋊C4×C43C2×D411yescharacteristic
587C22⋊C4×C43C2×D411yescharacteristic
588C22⋊C4×C43C2×D411yescharacteristic
589C22⋊C4×C43C2×D411yescharacteristic
590C22⋊C4×C43C2×D411yescharacteristic
591C42×C43—21no—
592C42×C43—21no—
593C42×C43—21no—
594C42×C43C2×D411yescharacteristic
595C42×C43C2×D411yescharacteristic
596C42×C43C2411yescharacteristic
597C42×C43C2411yescharacteristic
598C23×C43—22no—
599C23×C43—24no—
600C23×C43—22no—
601C23×C43—21no—
602C23×C43—22no—
603C23×C43—22no—
604C23×C43—22no—
605C23×C43—21no—
606C23×C43—21no—
607C23×C43—41no—
608C23×C43—41no—
609C23×C43—41no—
610C23×C43—42no—
611C23×C43—42no—
612C23×C43—44no—
613C23×C43—44no—
614C23×C43—42no—
615C23×C43—42no—
616C23×C43—42no—
617C23×C43—42no—
618C23×C43—42no—
619C23×C43—44no—
620C23×C43—42no—
621C23×C43—42no—
622C23×C43—44no—
623C23×C43—81no—
624C23×C43—81no—
625C23×C43—82no—
626C23×C43—82no—
627C23×C43—816no—
628C23×C43C22×D411yescharacteristic
629C23×C43C22×D411yescharacteristic
630C23×C43C22×D411yescharacteristic
631C23×C43C22×D411yescharacteristic
632C23×C43C22×D411yescharacteristic
633Q8×C43—21no—
634Q8×C43—21no—
635Q8×C43—21no—
636Q8×C43—22no—
637Q8×C43—21no—
638Q8×C43—22no—
639Q8×C43—21no—
640Q8×C43—42no—
641Q8×C43—42no—
642Q8×C43—42no—
643Q8×C43C22×D412yes—
644D4×C43—24no—
645D4×C43—22no—
646D4×C43—22no—
647D4×C43—24no—
648D4×C43—21no—
649D4×C43—22no—
650D4×C43—21no—
651D4×C43—22no—
652D4×C43—21no—
653D4×C43—21no—
654D4×C43—22no—
655D4×C43—21no—
656D4×C43—41no—
657D4×C43—41no—
658D4×C43—44no—
659D4×C43—44no—
660D4×C43—42no—
661D4×C43—42no—
662D4×C43—42no—
663D4×C43—42no—
664D4×C43—42no—
665D4×C43—44no—
666D4×C43—44no—
667D4×C43—42no—
668D4×C43—42no—
669D4×C43—42no—
670D4×C43—42no—
671D4×C43—42no—
672D4×C43—42no—
673D4×C43—42no—
674D4×C43—81no—
675D4×C43—81no—
676D4×C43—81no—
677D4×C43—82no—
678D4×C43—82no—
679D4×C43C22×D412yes—
680D4×C43C22×D414yes—
681C2×C4×C43—22no—
682C2×C4×C43—22no—
683C2×C4×C43—21no—
684C2×C4×C43—22no—
685C2×C4×C43—22no—
686C2×C4×C43—22no—
687C2×C4×C43—22no—
688C2×C4×C43—24no—
689C2×C4×C43—21no—
690C2×C4×C43—21no—
691C2×C4×C43—21no—
692C2×C4×C43—21no—
693C2×C4×C43—21no—
694C2×C4×C43—21no—
695C2×C4×C43—21no—
696C2×C4×C43—21no—
697C2×C4×C43—21no—
698C2×C4×C43—21no—
699C2×C4×C43—22no—
700C2×C4×C43—22no—
701C2×C4×C43—21no—
702C2×C4×C43—21no—
703C2×C4×C43—41no—
704C2×C4×C43—41no—
705C2×C4×C43—42no—
706C2×C4×C43—42no—
707C2×C4×C43—42no—
708C2×C4×C43—42no—
709C2×C4×C43—44no—
710C2×C4×C43—42no—
711C2×C4×C43—42no—
712C2×C4×C43—44no—
713C2×C4×C43—42no—
714C2×C4×C43—42no—
715C2×C4×C43—42no—
716C2×C4×C43—42no—
717C2×C4×C43—42no—
718C2×C4×C43—81no—
719C2×C4×C43—82no—
720C2×C4×C43—82no—
721C2×C4×C43C22×D411yescharacteristic
722C2×C4×C43C22×D411yescharacteristic
723C2×C4×C43C22×D411yescharacteristic
724C2×C4×C43C22×D411yescharacteristic
725C2×C4×C43C22×D411yescharacteristic
726C2×C4×C43C22×D411yescharacteristic
727C2×C4×C43C22×D411yescharacteristic
728C2×C4×C43C22×D411yescharacteristic
729C2×C4×C43C22×D411yescharacteristic
730C2×C4×C43C22×D412yes—
731C2×C4×C43H(5,𝔽2)12yes—
732C2×C4×C43C2511yescharacteristic
733C8×C43—22no—
734C8×C43—22no—
735C8×C43—22no—
736C8×C43C22×D414yes—
737#61066C4311yesmaximal, characteristic, direct product factor, Sylow
738C22×C43—21no—
739C22×C43—21no—
740C22×C43—21no—
741C22×C43—21no—
742C22×C43—21no—
743C22×C43—21no—
744C22×C43—21no—
745C22×C43—24no—
746C22×C43—21no—
747C22×C43—21no—
748C22×C43—21no—
749C22×C43—22no—
750C22×C43—21no—
751C22×C43—21no—
752C22×C43—21no—
753C22×C43—44no—
754C22×C43—48no—
755C22×C43—42no—
756C22×C43—41no—
757C22×C43—42no—
758C22×C43—41no—
759C22×C43—42no—
760C22×C43—41no—
761C22×C43—41no—
762C22×C43—42no—
763C22×C43—41no—
764C22×C43—41no—
765C22×C43—42no—
766C22×C43—41no—
767C22×C43—41no—
768C22×C43—82no—
769C22×C43—84no—
770C22×C43—88no—
771C22×C43—84no—
772C22×C43—84no—
773C22×C43—88no—
774C22×C43D4212yes—
775C22×C43#57512yescomplemented
776C22×C43C23×D411yescharacteristic
777C4×C43—21no—
778C4×C43—21no—
779C4×C43—21no—
780C4×C43—21no—
781C4×C43—21no—
782C4×C43—21no—
783C4×C43—22no—
784C4×C43—21no—
785C4×C43—21no—
786C4×C43—42no—
787C4×C43—41no—
788C4×C43—42no—
789C4×C43—41no—
790C4×C43—41no—
791C4×C43—41no—
792C4×C43D4212yes—
793C4×C43C23×D411yescharacteristic
794C4×C43C2×H(5,𝔽2)11yescharacteristic
795C2×#575C2×C4311yescharacteristic, complemented
796C22×AGL(1,ℤ/8)C2×C4311yescharacteristic, complemented
797D4×#41C2×C4311yescharacteristic, complemented
798C2×#546C2×C4311yescharacteristic, complemented
799#3282C2×C4312yescomplemented
800#3280C2×C4312yescomplemented
801#3275C2×C4312yescomplemented
802#3273C2×C4312yescomplemented
803#3268C2×C4312yescomplemented
804#3267C2×C4312yescomplemented
805#3266C2×C4312yescomplemented
806#3264C2×C4312yescomplemented
807#3153C2×C4311yescharacteristic, complemented
808#3056C2×C4311yescharacteristic, complemented
809#3055C2×C4311yescharacteristic, complemented
810#3040C2×C4311yescharacteristic, complemented
811#3036C2×C4311yescharacteristic, complemented
812#3007C2×C4311yescharacteristic, complemented
813#3006C2×C4311yescharacteristic, complemented
814#3005C2×C4311yescharacteristic, complemented
815#3003C2×C4311yescharacteristic, complemented
816C4×AGL(1,ℤ/8)C2×C4311yescharacteristic, complemented
817D4×M16C2×C4311yescharacteristic, complemented
818C2×C43—22no—
819C2×C43—22no—
820C2×C43—41no—
821C2×C43—41no—
822C2×C43—41no—
823C2×C43—44no—
824C2×C43—42no—
825C2×C43—81no—
826C2×C43—81no—
827C2×C43—82no—
828C2×C43C2×D4211yescharacteristic
829C2×C43C2×#57511yescharacteristic
830C2×C43#358511yescharacteristic
831C22×#41C22×C4311yescharacteristic
832C22×#41C22×C4311yescharacteristic, complemented
833C22×#41C22×C4311yescharacteristic, complemented
834C23×D4C22×C4311yescharacteristic, complemented
835#575—28no—
836C2×#137C22×C4311yescharacteristic, complemented
837C2×#137C22×C4311yescharacteristic, complemented
838C2×#137C22×C4311yescharacteristic, complemented
839C2×#137C22×C4312yescomplemented
840C2×AGL(1,ℤ/8)—28no—
841C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
842C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
843C2×AGL(1,ℤ/8)C22×C4311yescharacteristic, complemented
844C2×AGL(1,ℤ/8)C22×C4311yescharacteristic, complemented
845C2×AGL(1,ℤ/8)C22×C4311yescharacteristic, complemented
846C2×AGL(1,ℤ/8)C22×C4312yescomplemented
847C2×AGL(1,ℤ/8)C22×C4312yescomplemented
848C2×AGL(1,ℤ/8)C22×C4311yescharacteristic, complemented
849C2×AGL(1,ℤ/8)C22×C4312yescomplemented
850C2×#135C22×C4312yescomplemented
851C2×#135C22×C4312yescomplemented
852C22×SD16C22×C4312yescomplemented
853C22×D8C22×C4312yescomplemented
854C22×M16C22×C4311yescharacteristic, complemented
855C22×M16C22×C4311yescharacteristic, complemented
856#550C22×C4311yescharacteristic, complemented
857D4×Q8C22×C4311yescharacteristic, complemented
858#548C22×C4311yescharacteristic, complemented
859#548C22×C4311yescharacteristic, complemented
860#547—21no—
861#547C22×C4311yescharacteristic, complemented
862#546—21no—
863#546—21no—
864#546—21no—
865#546—21no—
866#546—21no—
867#546—21no—
868#546C22×C4312yes—
869#546C22×C4312yescomplemented
870#546C22×C4312yescomplemented
871#546C22×C4312yescomplemented
872#546C22×C4311yescharacteristic, complemented
873#546C22×C4311yescharacteristic, complemented
874D42—21no—
875D42C22×C4311yescharacteristic, complemented
876#532—21no—
877#532C22×C4311yescharacteristic, complemented
878C2×#124C22×C4311yescharacteristic, complemented
879#525—21no—
880#525—21no—
881#525C22×C4311yescharacteristic
882#525C22×C4311yescharacteristic, complemented
883C2×#123—21no—
884C2×C22⋊Q8C22×C4311yescharacteristic, complemented
885C2×#121—21no—
886C2×#121C22×C4311yescharacteristic, complemented
887C2×#120—21no—
888C4×#41C22×C4311yescharacteristic, complemented
889C2×C4×D4—21no—
890C2×C4×D4C22×C4311yescharacteristic
891C2×C4×D4C22×C4311yescharacteristic, complemented
892C22×C22⋊C4—21no—
893#497C22×C4312yescomplemented
894#496C22×C4312yescomplemented
895#495C22×C4312yescomplemented
896#495C22×C4312yescomplemented
897#470C22×C4312yescomplemented
898#469C22×C4312yescomplemented
899#468C22×C4312yescomplemented
900#468C22×C4312yescomplemented
901#467C22×C4312yescomplemented
902#466C22×C4312yescomplemented
903#465C22×C4312yescomplemented
904#465C22×C4312yescomplemented
905#464C22×C4312yescomplemented
906#464C22×C4312yescomplemented
907#463C22×C4312yescomplemented
908#463C22×C4312yescomplemented
909#463C22×C4312yescomplemented
910#463C22×C4312yescomplemented
911#461C22×C4312yescomplemented
912#459C22×C4312yescomplemented
913#452C22×C4312yescomplemented
914#452C22×C4312yescomplemented
915#452C22×C4312yescomplemented
916#452C22×C4312yescomplemented
917#451C22×C4312yescomplemented
918#450C22×C4312yescomplemented
919#450C22×C4312yescomplemented
920#450C22×C4312yescomplemented
921#449C22×C4312yescomplemented
922#449C22×C4312yescomplemented
923#449C22×C4312yescomplemented
924#449C22×C4312yescomplemented
925#448C22×C4312yescomplemented
926#447C22×C4312yescomplemented
927#447C22×C4312yescomplemented
928#447C22×C4312yescomplemented
929#442C22×C4312yescomplemented
930#440C22×C4312yescomplemented
931C4×SD16C22×C4312yescomplemented
932C4×D8C22×C4312yescomplemented
933#436C22×C4312yescomplemented
934#435C22×C4312yescomplemented
935#435C22×C4312yescomplemented
936C8×D4C22×C4312yescomplemented
937#428C22×C4311yescharacteristic, complemented
938#423C22×C4311yescharacteristic, complemented
939#419C22×C4311yescharacteristic, complemented
940#418C22×C4311yescharacteristic, complemented
941#418C22×C4311yescharacteristic, complemented
942#417C22×C4311yescharacteristic, complemented
943#417C22×C4311yescharacteristic, complemented
944#417C22×C4311yescharacteristic, complemented
945#407C22×C4311yescharacteristic, complemented
946#407C22×C4311yescharacteristic, complemented
947C4×M16C22×C4311yescharacteristic, complemented
948C43#6106611yescharacteristic, direct product factor, Sylow
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×C4311yescharacteristic
963C2×#41C23×C4311yescharacteristic
964C2×#41C23×C4312yes—
965C2×#41C23×C4312yes—
966C2×#41C23×C4311yescharacteristic
967C2×#41C23×C4311yescharacteristic
968C2×#41C23×C4311yescharacteristic
969C2×#41C23×C4311yescharacteristic, complemented
970C2×#41C23×C4311yescharacteristic, complemented
971C22×Q8C23×C4311yescharacteristic
972C22×Q8C23×C4311yescharacteristic
973C22×Q8C23×C4311yescharacteristic, 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×C4311yescharacteristic
985C22×D4C23×C4311yescharacteristic
986C22×D4C23×C4311yescharacteristic
987C22×D4C23×C4312yes—
988C22×D4C23×C4312yes—
989C22×D4C23×C4311yescharacteristic
990C22×D4C23×C4311yescharacteristic, complemented
991C23×C4—21no—
992C23×C4—21no—
993C23×C4—21no—
994C23×C4—21no—
995C23×C4C23×C4311yescharacteristic
996C23×C4C23×C4311yescharacteristic
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×C4318yescomplemented
1010#135—28no—
1011#135—28no—
1012C2×Q16C23×C4312yescomplemented
1013C2×Q16C23×C4312yescomplemented
1014C2×Q16C23×C4312yescomplemented
1015C2×SD16—28no—
1016C2×SD16C23×C4312yes—
1017C2×SD16C23×C4312yes—
1018C2×SD16C23×C4312yes—
1019C2×SD16C23×C4312yes—
1020C2×SD16C23×C4312yes—
1021C2×SD16C23×C4312yes—
1022C2×SD16C23×C4312yescomplemented
1023C2×SD16C23×C4312yescomplemented
1024C2×SD16C23×C4312yescomplemented
1025C2×D8—28no—
1026C2×D8C23×C4312yes—
1027C2×D8C23×C4312yes—
1028C2×D8C23×C4312yes—
1029C2×D8C23×C4312yes—
1030C2×D8C23×C4312yes—
1031C2×D8C23×C4312yes—
1032C2×M16—24no—
1033C2×M16—24no—
1034C2×M16C23×C4311yescharacteristic
1035C2×M16C23×C4312yes—
1036C2×M16C23×C4311yescharacteristic
1037C2×M16C23×C4311yescharacteristic
1038C2×M16C23×C4311yescharacteristic
1039C2×M16C23×C4312yescomplemented
1040C22×C8C23×C4312yes—
1041C22×C8C23×C4312yescomplemented
1042C4⋊Q8—21no—
1043C4⋊Q8C23×C4311yescharacteristic, complemented
1044#127—21no—
1045#127C23×C4311yescharacteristic, complemented
1046#124—21no—
1047#124—21no—
1048#124—21no—
1049#124—21no—
1050#124C23×C4312yes—
1051#124C23×C4312yes—
1052#124C23×C4311yescharacteristic, complemented
1053#124C23×C4311yescharacteristic, 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×C4312yes—
1071C22⋊Q8C23×C4312yes—
1072C22⋊Q8C23×C4311yescharacteristic
1073C22⋊Q8C23×C4311yescharacteristic
1074C22⋊Q8C23×C4311yescharacteristic, complemented
1075C22⋊Q8C23×C4311yescharacteristic, 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×C4312yes—
1093#121C23×C4312yes—
1094#121C23×C4311yescharacteristic
1095#121C23×C4311yescharacteristic
1096#121C23×C4311yescharacteristic, complemented
1097#121C23×C4311yescharacteristic, 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×C4311yescharacteristic, complemented
1109C4×Q8C23×C4311yescharacteristic, 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×C4311yescharacteristic
1125C4×D4D4×C4311yescharacteristic
1126C4×D4D4×C4311yescharacteristic
1127C4×D4D4×C4311yescharacteristic
1128C4×D4C23×C4312yes—
1129C4×D4C23×C4312yes—
1130C4×D4C23×C4311yescharacteristic
1131C4×D4C23×C4311yescharacteristic
1132C4×D4C23×C4311yescharacteristic
1133C4×D4C23×C4311yescharacteristic
1134C4×D4C23×C4311yescharacteristic, complemented
1135C4×D4C23×C4311yescharacteristic, complemented
1136#117—21no—
1137#117C23×C4311yescharacteristic
1138C2×C4⋊C4—21no—
1139C2×C4⋊C4—21no—
1140C2×C4⋊C4D4×C4311yescharacteristic
1141C2×C4⋊C4C23×C4311yescharacteristic
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×C4311yescharacteristic
1154C2×C22⋊C4D4×C4311yescharacteristic
1155C2×C42—21no—
1156C2×C42C23×C4311yescharacteristic
1157#107C23×C4312yescomplemented
1158#106C23×C4312yescomplemented
1159C4⋊C8C23×C4312yescomplemented
1160C4⋊C8C23×C4312yescomplemented
1161#103C23×C4312yescomplemented
1162#103C23×C4312yescomplemented
1163#103C23×C4312yescomplemented
1164#103C23×C4312yescomplemented
1165#103C23×C4312yescomplemented
1166#102C23×C4312yes—
1167#102C23×C4312yes—
1168#102C23×C4312yes—
1169#102C23×C4312yes—
1170#102C23×C4312yescomplemented
1171#102C23×C4312yescomplemented
1172#102C23×C4312yescomplemented
1173C22⋊C8C23×C4312yes—
1174C22⋊C8C23×C4312yes—
1175C22⋊C8C23×C4312yescomplemented
1176C22⋊C8C23×C4312yescomplemented
1177#97C23×C4312yescomplemented
1178C4×C8C23×C4312yescomplemented
1179C24—21no—
1180C24—21no—
1181C24—22no—
1182C24—22no—
1183C24—21no—
1184C24—21no—
1185C24—44no—
1186C24—44no—
1187C24—82no—
1188C24C2×D4×C4311yescharacteristic
1189C24C2×D4×C4311yescharacteristic
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×C4314yes—
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×C4312yes—
1224C2×Q8C24×C4311yescharacteristic
1225C2×Q8C24×C4311yescharacteristic
1226C2×Q8C24×C4311yescharacteristic
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×C4311yescharacteristic
1271C2×D4C2×D4×C4311yescharacteristic
1272C2×D4C2×D4×C4311yescharacteristic
1273C2×D4C2×D4×C4311yescharacteristic
1274C2×D4C2×D4×C4314yescomplemented
1275C2×D4C24×C4312yes—
1276C2×D4C24×C4311yescharacteristic
1277C2×D4C24×C4311yescharacteristic
1278C2×D4C24×C4312yes—
1279C2×D4C24×C4311yescharacteristic
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×C4311yescharacteristic
1306C22×C4C2×D4×C4311yescharacteristic
1307C22×C4C2×D4×C4311yescharacteristic
1308C22×C4C2×D4×C4311yescharacteristic
1309C22×C4C2×D4×C4311yescharacteristic
1310C22×C4C2×D4×C4311yescharacteristic
1311C22×C4C2×D4×C4311yescharacteristic
1312C22×C4C2×D4×C4311yescharacteristic
1313C22×C4C24×C4311yescharacteristic
1314C22×C4C24×C4311yescharacteristic
1315C22×C4C24×C4311yescharacteristic
1316C22×C4C24×C4311yescharacteristic
1317C22×C4C24×C4311yescharacteristic
1318Q16—24no—
1319Q16—24no—
1320Q16—42no—
1321SD16—24no—
1322SD16—24no—
1323SD16—24no—
1324SD16—24no—
1325SD16—24no—
1326SD16—24no—
1327SD16—42no—
1328SD16—42no—
1329SD16C2×D4×C4318yescomplemented
1330D8—24no—
1331D8—24no—
1332D8—24no—
1333D8—24no—
1334D8—42no—
1335D8C2×D4×C4318yescomplemented
1336M16—22no—
1337M16—22no—
1338M16—22no—
1339M16—24no—
1340M16—24no—
1341M16C2×D4×C4314yescomplemented
1342C2×C8—24no—
1343C2×C8—24no—
1344C2×C8C24×C4312yes—
1345C2×C8C24×C4312yes—
1346C2×C8C24×C4312yes—
1347C2×C8C24×C4312yes—
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×C4311yescharacteristic
1360C4⋊C4C2×D4×C4311yescharacteristic
1361C4⋊C4C2×D4×C4311yescharacteristic
1362C4⋊C4C2×D4×C4311yescharacteristic
1363C4⋊C4C24×C4311yescharacteristic
1364C4⋊C4C24×C4311yescharacteristic
1365C4⋊C4C24×C4312yes—
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×C4311yescharacteristic
1392C22⋊C4C2×D4×C4311yescharacteristic
1393C22⋊C4C2×D4×C4311yescharacteristic
1394C22⋊C4C2×D4×C4311yescharacteristic
1395C22⋊C4C2×D4×C4311yescharacteristic
1396C22⋊C4C2×D4×C4311yescharacteristic
1397C22⋊C4C2×D4×C4311yescharacteristic
1398C22⋊C4C2×D4×C4311yescharacteristic
1399C42—21no—
1400C42—21no—
1401C42—21no—
1402C42C2×D4×C4311yescharacteristic
1403C42C2×D4×C4311yescharacteristic
1404C42C24×C4311yescharacteristic
1405C42C24×C4311yescharacteristic
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—81no—
1432C23—81no—
1433C23—82no—
1434C23—82no—
1435C23—816no—
1436C23C22×D4×C4311yescharacteristic
1437C23C22×D4×C4311yescharacteristic
1438C23C22×D4×C4311yescharacteristic
1439C23C22×D4×C4311yescharacteristic
1440C23C22×D4×C4311yescharacteristic
1441Q8—21no—
1442Q8—21no—
1443Q8—21no—
1444Q8—22no—
1445Q8—21no—
1446Q8—22no—
1447Q8—21no—
1448Q8—42no—
1449Q8—42no—
1450Q8—42no—
1451Q8C22×D4×C4312yes—
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×C4312yes—
1488D4C22×D4×C4314yes—
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×C4311yescharacteristic
1530C2×C4C22×D4×C4311yescharacteristic
1531C2×C4C22×D4×C4311yescharacteristic
1532C2×C4C22×D4×C4311yescharacteristic
1533C2×C4C22×D4×C4311yescharacteristic
1534C2×C4C22×D4×C4311yescharacteristic
1535C2×C4C22×D4×C4311yescharacteristic
1536C2×C4C22×D4×C4311yescharacteristic
1537C2×C4C22×D4×C4311yescharacteristic
1538C2×C4C22×D4×C4312yes—
1539C2×C4H(5,𝔽2)×C4312yes—
1540C2×C4C25×C4311yescharacteristic
1541C8—22no—
1542C8—22no—
1543C8—22no—
1544C8C22×D4×C4314yes—
1545C22—21no—
1546C22—21no—
1547C22—21no—
1548C22—21no—
1549C22—21no—
1550C22—21no—
1551C22—21no—
1552C22—22no—
1553C22—24no—
1554C22—21no—
1555C22—21no—
1556C22—21no—
1557C22—21no—
1558C22—21no—
1559C22—21no—
1560C22—44no—
1561C22—48no—
1562C22—41no—
1563C22—42no—
1564C22—42no—
1565C22—41no—
1566C22—41no—
1567C22—41no—
1568C22—42no—
1569C22—41no—
1570C22—41no—
1571C22—42no—
1572C22—42no—
1573C22—41no—
1574C22—41no—
1575C22—82no—
1576C22—88no—
1577C22—84no—
1578C22—84no—
1579C22—88no—
1580C22—84no—
1581C22D42×C4312yes—
1582C22C43×#57512yescomplemented
1583C22C23×D4×C4311yescharacteristic
1584C4—21no—
1585C4—21no—
1586C4—21no—
1587C4—21no—
1588C4—22no—
1589C4—21no—
1590C4—21no—
1591C4—21no—
1592C4—21no—
1593C4—42no—
1594C4—41no—
1595C4—41no—
1596C4—41no—
1597C4—42no—
1598C4—41no—
1599C4D42×C4312yes—
1600C4C23×D4×C4311yescharacteristic
1601C4C2×H(5,𝔽2)×C4311yescharacteristic
1602C2—22no—
1603C2—22no—
1604C2—41no—
1605C2—41no—
1606C2—41no—
1607C2—44no—
1608C2—42no—
1609C2—82no—
1610C2—81no—
1611C2—81no—
1612C2C2×D42×C4311yescharacteristic
1613C2C2×C43×#57511yescharacteristic
1614C2C43×#358511yescharacteristic
subgroupG/H
center, socleC22×C43C23×D4
commutator, Frattini, cosocleC2×C4C25×C43
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C4×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#575C2semidirect
2. C22×AGL(1,ℤ/8)×C43C2semidirect
3. D4×#41×C43C2semidirect
4. C2×C43×#546C2semidirect
5. C43×#3282C2semidirect
6. C43×#3280C2semidirect
7. C43×#3275C2semidirect
8. C43×#3273C2semidirect
9. C43×#3268C2semidirect
10. C43×#3267C2semidirect
11. C43×#3266C2semidirect
12. C43×#3264C2semidirect
13. C43×#3153C2semidirect
14. C43×#3056C2semidirect
15. C43×#3055C2semidirect
16. C43×#3040C2semidirect
17. C43×#3036C2semidirect
18. C43×#3007C2semidirect
19. C43×#3006C2semidirect
20. C43×#3005C2semidirect
21. C43×#3003C2semidirect
22. C4×AGL(1,ℤ/8)×C43C2semidirect
23. D4×M16×C43C2semidirect
25. C22×#41×C43C22semidirect
26. C22×#41×C43C22semidirect
27. C23×D4×C43C22semidirect
29. C2×#137×C43C22semidirect
30. C2×#137×C43C22semidirect
31. C2×#137×C43C22semidirect
32. C2×#137×C43C22semidirect
36. C2×AGL(1,ℤ/8)×C43C22semidirect
37. C2×AGL(1,ℤ/8)×C43C22semidirect
38. C2×AGL(1,ℤ/8)×C43C22semidirect
39. C2×AGL(1,ℤ/8)×C43C22semidirect
40. C2×AGL(1,ℤ/8)×C43C22semidirect
41. C2×AGL(1,ℤ/8)×C43C22semidirect
42. C2×AGL(1,ℤ/8)×C43C22semidirect
43. C2×#135×C43C22semidirect
44. C2×#135×C43C22semidirect
45. C22×SD16×C43C22semidirect
46. C22×D8×C43C22semidirect
47. C22×M16×C43C22semidirect
48. C22×M16×C43C22semidirect
49. C43×#550C22semidirect
50. D4×Q8×C43C22semidirect
51. C43×#548C22semidirect
52. C43×#548C22semidirect
54. C43×#547C22semidirect
62. C43×#546C22semidirect
63. C43×#546C22semidirect
64. C43×#546C22semidirect
65. C43×#546C22semidirect
66. C43×#546C22semidirect
68. D42×C43C22semidirect
70. C43×#532C22semidirect
71. C2×#124×C43C22semidirect
75. C43×#525C22semidirect
77. C2×C22⋊Q8×C43C22semidirect
79. C2×#121×C43C22semidirect
81. C4×#41×C43C22semidirect
84. C2×C4×D4×C43C22semidirect
86. C43×#497C22semidirect
87. C43×#496C22semidirect
88. C43×#495C22semidirect
89. C43×#495C22semidirect
90. C43×#470C22semidirect
91. C43×#469C22semidirect
92. C43×#468C22semidirect
93. C43×#468C22semidirect
94. C43×#467C22semidirect
95. C43×#466C22semidirect
96. C43×#465C22semidirect
97. C43×#465C22semidirect
98. C43×#464C22semidirect
99. C43×#464C22semidirect
100. C43×#463C22semidirect
101. C43×#463C22semidirect
102. C43×#463C22semidirect
103. C43×#463C22semidirect
104. C43×#461C22semidirect
105. C43×#459C22semidirect
106. C43×#452C22semidirect
107. C43×#452C22semidirect
108. C43×#452C22semidirect
109. C43×#452C22semidirect
110. C43×#451C22semidirect
111. C43×#450C22semidirect
112. C43×#450C22semidirect
113. C43×#450C22semidirect
114. C43×#449C22semidirect
115. C43×#449C22semidirect
116. C43×#449C22semidirect
117. C43×#449C22semidirect
118. C43×#448C22semidirect
119. C43×#447C22semidirect
120. C43×#447C22semidirect
121. C43×#447C22semidirect
122. C43×#442C22semidirect
123. C43×#440C22semidirect
124. C4×SD16×C43C22semidirect
125. C4×D8×C43C22semidirect
126. C43×#436C22semidirect
127. C43×#435C22semidirect
128. C43×#435C22semidirect
129. C8×D4×C43C22semidirect
130. C43×#428C22semidirect
131. C43×#423C22semidirect
132. C43×#419C22semidirect
133. C43×#418C22semidirect
134. C43×#418C22semidirect
135. C43×#417C22semidirect
136. C43×#417C22semidirect
137. C43×#417C22semidirect
138. C43×#407C22semidirect
139. C43×#407C22semidirect
140. C4×M16×C43C22semidirect
161. C2×#41×C43C23semidirect
162. C2×#41×C43C23semidirect
165. C22×Q8×C43C23semidirect
182. C22×D4×C43C23semidirect
201. AGL(1,ℤ/8)×C43D4semidirect
204. C2×Q16×C43C23semidirect
205. C2×Q16×C43C23semidirect
206. C2×Q16×C43C23semidirect
214. C2×SD16×C43C23semidirect
215. C2×SD16×C43C23semidirect
216. C2×SD16×C43C23semidirect
231. C2×M16×C43C23semidirect
233. C22×C8×C43C23semidirect
235. C4⋊Q8×C43C23semidirect
237. #127×C43C23semidirect
244. #124×C43C23semidirect
245. #124×C43C23semidirect
266. C22⋊Q8×C43C23semidirect
267. C22⋊Q8×C43C23semidirect
288. #121×C43C23semidirect
289. #121×C43C23semidirect
300. C4×Q8×C43C23semidirect
301. C4×Q8×C43C23semidirect
326. C4×D4×C43C23semidirect
327. C4×D4×C43C23semidirect
349. #107×C43C23semidirect
350. #106×C43C23semidirect
351. C4⋊C8×C43C23semidirect
352. C4⋊C8×C43C23semidirect
353. #103×C43C23semidirect
354. #103×C43C23semidirect
355. #103×C43C23semidirect
356. #103×C43C23semidirect
357. #103×C43C23semidirect
362. #102×C43C23semidirect
363. #102×C43C23semidirect
364. #102×C43C23semidirect
367. C22⋊C8×C43C23semidirect
368. C22⋊C8×C43C23semidirect
369. #97×C43C23semidirect
370. C4×C8×C43C23semidirect
466. C2×D4×C43C2×D4semidirect
521. SD16×C43C2×D4semidirect
527. D8×C43C2×D4semidirect
533. M16×C43C2×D4semidirect
737. #61066C43direct (N × H)
775. C22×C43#575semidirect
795. C2×#575C2×C43semidirect
796. C22×AGL(1,ℤ/8)C2×C43semidirect
797. D4×#41C2×C43semidirect
798. C2×#546C2×C43semidirect
799. #3282C2×C43semidirect
800. #3280C2×C43semidirect
801. #3275C2×C43semidirect
802. #3273C2×C43semidirect
803. #3268C2×C43semidirect
804. #3267C2×C43semidirect
805. #3266C2×C43semidirect
806. #3264C2×C43semidirect
807. #3153C2×C43semidirect
808. #3056C2×C43semidirect
809. #3055C2×C43semidirect
810. #3040C2×C43semidirect
811. #3036C2×C43semidirect
812. #3007C2×C43semidirect
813. #3006C2×C43semidirect
814. #3005C2×C43semidirect
815. #3003C2×C43semidirect
816. C4×AGL(1,ℤ/8)C2×C43semidirect
817. D4×M16C2×C43semidirect
832. C22×#41C22×C43semidirect
833. C22×#41C22×C43semidirect
834. C23×D4C22×C43semidirect
836. C2×#137C22×C43semidirect
837. C2×#137C22×C43semidirect
838. C2×#137C22×C43semidirect
839. C2×#137C22×C43semidirect
843. C2×AGL(1,ℤ/8)C22×C43semidirect
844. C2×AGL(1,ℤ/8)C22×C43semidirect
845. C2×AGL(1,ℤ/8)C22×C43semidirect
846. C2×AGL(1,ℤ/8)C22×C43semidirect
847. C2×AGL(1,ℤ/8)C22×C43semidirect
848. C2×AGL(1,ℤ/8)C22×C43semidirect
849. C2×AGL(1,ℤ/8)C22×C43semidirect
850. C2×#135C22×C43semidirect
851. C2×#135C22×C43semidirect
852. C22×SD16C22×C43semidirect
853. C22×D8C22×C43semidirect
854. C22×M16C22×C43semidirect
855. C22×M16C22×C43semidirect
856. #550C22×C43semidirect
857. D4×Q8C22×C43semidirect
858. #548C22×C43semidirect
859. #548C22×C43semidirect
861. #547C22×C43semidirect
869. #546C22×C43semidirect
870. #546C22×C43semidirect
871. #546C22×C43semidirect
872. #546C22×C43semidirect
873. #546C22×C43semidirect
875. D42C22×C43semidirect
877. #532C22×C43semidirect
878. C2×#124C22×C43semidirect
882. #525C22×C43semidirect
884. C2×C22⋊Q8C22×C43semidirect
886. C2×#121C22×C43semidirect
888. C4×#41C22×C43semidirect
891. C2×C4×D4C22×C43semidirect
893. #497C22×C43semidirect
894. #496C22×C43semidirect
895. #495C22×C43semidirect
896. #495C22×C43semidirect
897. #470C22×C43semidirect
898. #469C22×C43semidirect
899. #468C22×C43semidirect
900. #468C22×C43semidirect
901. #467C22×C43semidirect
902. #466C22×C43semidirect
903. #465C22×C43semidirect
904. #465C22×C43semidirect
905. #464C22×C43semidirect
906. #464C22×C43semidirect
907. #463C22×C43semidirect
908. #463C22×C43semidirect
909. #463C22×C43semidirect
910. #463C22×C43semidirect
911. #461C22×C43semidirect
912. #459C22×C43semidirect
913. #452C22×C43semidirect
914. #452C22×C43semidirect
915. #452C22×C43semidirect
916. #452C22×C43semidirect
917. #451C22×C43semidirect
918. #450C22×C43semidirect
919. #450C22×C43semidirect
920. #450C22×C43semidirect
921. #449C22×C43semidirect
922. #449C22×C43semidirect
923. #449C22×C43semidirect
924. #449C22×C43semidirect
925. #448C22×C43semidirect
926. #447C22×C43semidirect
927. #447C22×C43semidirect
928. #447C22×C43semidirect
929. #442C22×C43semidirect
930. #440C22×C43semidirect
931. C4×SD16C22×C43semidirect
932. C4×D8C22×C43semidirect
933. #436C22×C43semidirect
934. #435C22×C43semidirect
935. #435C22×C43semidirect
936. C8×D4C22×C43semidirect
937. #428C22×C43semidirect
938. #423C22×C43semidirect
939. #419C22×C43semidirect
940. #418C22×C43semidirect
941. #418C22×C43semidirect
942. #417C22×C43semidirect
943. #417C22×C43semidirect
944. #417C22×C43semidirect
945. #407C22×C43semidirect
946. #407C22×C43semidirect
947. C4×M16C22×C43semidirect
948. C43#61066direct (N × H)
969. C2×#41C23×C43semidirect
970. C2×#41C23×C43semidirect
973. C22×Q8C23×C43semidirect
990. C22×D4C23×C43semidirect
1009. AGL(1,ℤ/8)D4×C43semidirect
1012. C2×Q16C23×C43semidirect
1013. C2×Q16C23×C43semidirect
1014. C2×Q16C23×C43semidirect
1022. C2×SD16C23×C43semidirect
1023. C2×SD16C23×C43semidirect
1024. C2×SD16C23×C43semidirect
1039. C2×M16C23×C43semidirect
1041. C22×C8C23×C43semidirect
1043. C4⋊Q8C23×C43semidirect
1045. #127C23×C43semidirect
1052. #124C23×C43semidirect
1053. #124C23×C43semidirect
1074. C22⋊Q8C23×C43semidirect
1075. C22⋊Q8C23×C43semidirect
1096. #121C23×C43semidirect
1097. #121C23×C43semidirect
1108. C4×Q8C23×C43semidirect
1109. C4×Q8C23×C43semidirect
1134. C4×D4C23×C43semidirect
1135. C4×D4C23×C43semidirect
1157. #107C23×C43semidirect
1158. #106C23×C43semidirect
1159. C4⋊C8C23×C43semidirect
1160. C4⋊C8C23×C43semidirect
1161. #103C23×C43semidirect
1162. #103C23×C43semidirect
1163. #103C23×C43semidirect
1164. #103C23×C43semidirect
1165. #103C23×C43semidirect
1170. #102C23×C43semidirect
1171. #102C23×C43semidirect
1172. #102C23×C43semidirect
1175. C22⋊C8C23×C43semidirect
1176. C22⋊C8C23×C43semidirect
1177. #97C23×C43semidirect
1178. C4×C8C23×C43semidirect
1274. C2×D4C2×D4×C43semidirect
1329. SD16C2×D4×C43semidirect
1335. D8C2×D4×C43semidirect
1341. M16C2×D4×C43semidirect
1582. C22C43×#575semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5752
C22×AGL(1,ℤ/8)×C432
D4×#41×C432
C2×C43×#5462
C43×#32822
C43×#32802
C43×#32752
C43×#32732
C43×#32682
C43×#32672
C43×#32662
C43×#32642
C43×#31532
C43×#30562
C43×#30552
C43×#30402
C43×#30362
C43×#30072
C43×#30062
C43×#30052
C43×#30032
C4×AGL(1,ℤ/8)×C432
D4×M16×C432
#6106643