Finite Group Databasebeta

← C83×#24438 #35252262

Subgroups — C83×#24438 #35252262

Order 21248.

1498 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C83C211yesmaximal, characteristic, complemented
2C2×#465×C83C211yesmaximal, characteristic, complemented
3C2×#449×C83C211yesmaximal, characteristic, complemented
4C2×#449×C83C211yesmaximal, characteristic, complemented
5C2×#416×C83C211yesmaximal, characteristic, complemented
6C83×#2414C211yesmaximal, characteristic, complemented
7C83×#2043C211yesmaximal, characteristic, complemented
8C83×#2035C211yesmaximal, characteristic, complemented
9C83×#2013C211yesmaximal, characteristic, complemented
10C83×#2000C211yesmaximal, characteristic, complemented
11C83×#1879C211yesmaximal, characteristic, complemented
12C83×#1873C211yesmaximal, characteristic, complemented
13C83×#1869C211yesmaximal, characteristic, complemented
14C83×#1864C211yesmaximal, characteristic, complemented
15C83×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C83C2211yescharacteristic
17C22×#41×C83C2211yescharacteristic
18C22×SD16×C83C2211yescharacteristic
19C22×SD16×C83C2211yescharacteristic
20C22×D8×C83C2211yescharacteristic
21C23×C8×C83C2211yescharacteristic
22#547×C83—24no—
23#547×C83—24no—
24C2×C4⋊Q8×C83C2211yescharacteristic
25C2×#123×C83—21no—
26C2×#123×C83—21no—
27C2×C22⋊Q8×C83C2211yescharacteristic
28C2×C22⋊Q8×C83C2211yescharacteristic
29C2×#121×C83—21no—
30C2×#121×C83C2211yescharacteristic
31C2×#121×C83C2211yescharacteristic
32C2×C4×D4×C83C2211yescharacteristic
33C2×C4×D4×C83C2211yescharacteristic
34C2×#117×C83C2211yescharacteristic
35C22×C4⋊C4×C83—21no—
36#465×C83—24no—
37#449×C83—24no—
38#449×C83—24no—
39C2×#106×C83C2211yescharacteristic
40#416×C83—24no—
41C2×#103×C83C2211yescharacteristic
42C2×#103×C83C2211yescharacteristic
43C2×#103×C83C2211yescharacteristic
44C2×#103×C83C2211yescharacteristic
45C2×#103×C83C2211yescharacteristic
46C2×#103×C83C2211yescharacteristic
47C2×#102×C83C2211yescharacteristic
48C2×#102×C83C2211yescharacteristic
49C2×#102×C83C2211yescharacteristic
50C2×#102×C83C2211yescharacteristic
51C2×C22⋊C8×C83C2211yescharacteristic
52C2×C22⋊C8×C83C2211yescharacteristic
53C2×C22⋊C8×C83C2211yescharacteristic
54#394×C83—21no—
55#392×C83—21no—
56#390×C83—21no—
57#390×C83C2211yescharacteristic
58#389×C83C2211yescharacteristic
59#388×C83—21no—
60#380×C83C2211yescharacteristic
61#340×C83C2211yescharacteristic
62#340×C83C2211yescharacteristic
63#336×C83C2211yescharacteristic
64#336×C83C2211yescharacteristic
65C2×#41×C83—22no—
66C2×#41×C83—22no—
67C2×#41×C83—22no—
68C2×#41×C83—22no—
69C2×#41×C83—22no—
70C2×#41×C83—22no—
71C2×#41×C83—22no—
72C2×#41×C83—41no—
73C2×#41×C83—41no—
74C2×#41×C83—41no—
75C2×#41×C83—41no—
76C2×#41×C83D414yescomplemented
77C22×Q8×C83C2311yescharacteristic
78C22×Q8×C83C2311yescharacteristic
79C22×D4×C83—21no—
80C22×D4×C83—21no—
81C22×D4×C83—21no—
82C22×D4×C83—21no—
83C22×D4×C83D411yescharacteristic
84C22×D4×C83C2311yescharacteristic
85C22×D4×C83C2311yescharacteristic
86C23×C4×C83—21no—
87C23×C4×C83—21no—
88C23×C4×C83—21no—
89C23×C4×C83C2311yescharacteristic
90C23×C4×C83C2311yescharacteristic
91C2×SD16×C83—22no—
92C2×SD16×C83—22no—
93C2×SD16×C83—22no—
94C2×SD16×C83—41no—
95C2×SD16×C83—41no—
96C2×SD16×C83—41no—
97C2×D8×C83—22no—
98C2×D8×C83—22no—
99C2×D8×C83—22no—
100C22×C8×C83—22no—
101C22×C8×C83—22no—
102C22×C8×C83—41no—
103C22×C8×C83C2311yescharacteristic
104C22×C8×C83C2311yescharacteristic
105C22×C8×C83C2311yescharacteristic
106C22×C8×C83C2311yescharacteristic
107C4⋊Q8×C83—22no—
108C4⋊Q8×C83—22no—
109#123×C83—28no—
110#123×C83—28no—
111C22⋊Q8×C83—22no—
112C22⋊Q8×C83—22no—
113C22⋊Q8×C83—22no—
114C22⋊Q8×C83D414yescomplemented
115#121×C83—28no—
116#121×C83—22no—
117#121×C83—22no—
118#121×C83—22no—
119#121×C83—41no—
120C4×D4×C83—22no—
121C4×D4×C83—22no—
122C4×D4×C83—22no—
123C4×D4×C83—22no—
124#117×C83—22no—
125#117×C83—41no—
126C2×C4⋊C4×C83—28no—
127C2×C4⋊C4×C83—21no—
128C2×C4⋊C4×C83—21no—
129C2×C4⋊C4×C83—21no—
130C2×C4⋊C4×C83—21no—
131C2×C4⋊C4×C83—21no—
132C2×C4⋊C4×C83D411yescharacteristic
133C2×C4⋊C4×C83C2311yescharacteristic
134C2×C4⋊C4×C83C2311yescharacteristic
135C2×C4⋊C4×C83C2311yescharacteristic
136C2×C4⋊C4×C83C2311yescharacteristic
137C2×C22⋊C4×C83—21no—
138C2×C22⋊C4×C83—21no—
139C2×C22⋊C4×C83—21no—
140C2×C22⋊C4×C83—21no—
141C2×C22⋊C4×C83—21no—
142C2×C22⋊C4×C83—21no—
143C2×C22⋊C4×C83—21no—
144C2×C22⋊C4×C83—21no—
145C2×C22⋊C4×C83—21no—
146C2×C22⋊C4×C83D411yescharacteristic
147C2×C22⋊C4×C83D411yescharacteristic
148C2×C42×C83—21no—
149C2×C42×C83C2311yescharacteristic
150#106×C83—22no—
151#103×C83—22no—
152#103×C83—22no—
153#103×C83—22no—
154#103×C83—22no—
155#103×C83—22no—
156#103×C83—41no—
157#102×C83—22no—
158#102×C83—22no—
159#102×C83—22no—
160#102×C83D414yescomplemented
161C22⋊C8×C83—22no—
162C22⋊C8×C83—22no—
163C22⋊C8×C83—41no—
164#95×C83—21no—
165#95×C83—21no—
166C24×C83—21no—
167C24×C83—21no—
168C24×C83C2×D411yescharacteristic
169C24×C83C2×D411yescharacteristic
170#41×C83—28no—
171#41×C83—44no—
172#41×C83—44no—
173#41×C83—44no—
174#41×C83—44no—
175#41×C83—44no—
176#41×C83—44no—
177#41×C83—44no—
178C2×Q8×C83—21no—
179C2×Q8×C83—21no—
180C2×Q8×C83—21no—
181C2×Q8×C83—21no—
182C2×Q8×C83—21no—
183C2×Q8×C83—21no—
184C2×Q8×C83—21no—
185C2×Q8×C83—21no—
186C2×Q8×C83—21no—
187C2×Q8×C83—21no—
188C2×Q8×C83C2×D412yes—
189C2×Q8×C83C2×D412yes—
190C2×D4×C83—24no—
191C2×D4×C83—22no—
192C2×D4×C83—24no—
193C2×D4×C83—22no—
194C2×D4×C83—21no—
195C2×D4×C83—21no—
196C2×D4×C83—21no—
197C2×D4×C83—21no—
198C2×D4×C83—21no—
199C2×D4×C83—21no—
200C2×D4×C83—21no—
201C2×D4×C83—21no—
202C2×D4×C83—21no—
203C2×D4×C83—41no—
204C2×D4×C83—42no—
205C2×D4×C83—42no—
206C2×D4×C83—42no—
207C2×D4×C83—42no—
208C2×D4×C83—42no—
209C2×D4×C83—42no—
210C2×D4×C83—42no—
211C2×D4×C83—81no—
212C2×D4×C83—81no—
213C2×D4×C83—81no—
214C2×D4×C83C2×D412yes—
215C2×D4×C83C2×D412yes—
216C2×D4×C83#4112yes—
217C22×C4×C83—21no—
218C22×C4×C83—21no—
219C22×C4×C83—21no—
220C22×C4×C83—21no—
221C22×C4×C83—24no—
222C22×C4×C83—24no—
223C22×C4×C83—21no—
224C22×C4×C83—21no—
225C22×C4×C83—21no—
226C22×C4×C83—21no—
227C22×C4×C83—24no—
228C22×C4×C83—21no—
229C22×C4×C83—21no—
230C22×C4×C83—21no—
231C22×C4×C83—21no—
232C22×C4×C83—21no—
233C22×C4×C83—21no—
234C22×C4×C83—21no—
235C22×C4×C83—21no—
236C22×C4×C83—42no—
237C22×C4×C83—42no—
238C22×C4×C83—42no—
239C22×C4×C83—42no—
240C22×C4×C83—42no—
241C22×C4×C83—42no—
242C22×C4×C83C2×D411yescharacteristic
243C22×C4×C83C2×D411yescharacteristic
244C22×C4×C83C2×D411yescharacteristic
245C22×C4×C83C2×D412yes—
246C22×C4×C83C2×D412yes—
247C22×C4×C83C2×D411yescharacteristic
248C22×C4×C83C2411yescharacteristic
249SD16×C83—44no—
250SD16×C83—44no—
251D8×C83—44no—
252C2×C8×C83—21no—
253C2×C8×C83—21no—
254C2×C8×C83—21no—
255C2×C8×C83—21no—
256C2×C8×C83—21no—
257C2×C8×C83—21no—
258C2×C8×C83—21no—
259C2×C8×C83—21no—
260C2×C8×C83—21no—
261C2×C8×C83—21no—
262C2×C8×C83—21no—
263C2×C8×C83—44no—
264C2×C8×C83C2×D412yes—
265C4⋊C4×C83—24no—
266C4⋊C4×C83—24no—
267C4⋊C4×C83—24no—
268C4⋊C4×C83—22no—
269C4⋊C4×C83—24no—
270C4⋊C4×C83—21no—
271C4⋊C4×C83—21no—
272C4⋊C4×C83—21no—
273C4⋊C4×C83—21no—
274C4⋊C4×C83—21no—
275C4⋊C4×C83—21no—
276C4⋊C4×C83—81no—
277C4⋊C4×C83C2×D412yes—
278C4⋊C4×C83C2×D412yes—
279C22⋊C4×C83—24no—
280C22⋊C4×C83—24no—
281C22⋊C4×C83—24no—
282C22⋊C4×C83—22no—
283C22⋊C4×C83—22no—
284C22⋊C4×C83—42no—
285C22⋊C4×C83—42no—
286C22⋊C4×C83—42no—
287C22⋊C4×C83—42no—
288C22⋊C4×C83—81no—
289C22⋊C4×C83—81no—
290C42×C83—21no—
291C42×C83—21no—
292C42×C83—42no—
293C23×C83—22no—
294C23×C83—21no—
295C23×C83—22no—
296C23×C83—21no—
297C23×C83—22no—
298C23×C83—21no—
299C23×C83—21no—
300C23×C83—21no—
301C23×C83—21no—
302C23×C83—21no—
303C23×C83—21no—
304C23×C83—21no—
305C23×C83—21no—
306C23×C83—21no—
307C23×C83—21no—
308C23×C83—21no—
309C23×C83—41no—
310C23×C83—41no—
311C23×C83—41no—
312C23×C83—41no—
313C23×C83—41no—
314C23×C83—41no—
315C23×C83—41no—
316C23×C83—41no—
317C23×C83—41no—
318C23×C83—41no—
319C23×C83—41no—
320C23×C83#12012yes—
321C23×C83C22×D411yescharacteristic
322Q8×C83—22no—
323Q8×C83—22no—
324Q8×C83—22no—
325Q8×C83—22no—
326Q8×C83—41no—
327Q8×C83—41no—
328Q8×C83—41no—
329Q8×C83—41no—
330D4×C83—22no—
331D4×C83—22no—
332D4×C83—22no—
333D4×C83—44no—
334D4×C83—48no—
335D4×C83—48no—
336D4×C83—41no—
337D4×C83—41no—
338D4×C83—41no—
339D4×C83—41no—
340D4×C83—84no—
341D4×C83—84no—
342D4×C83#12114yes—
343C2×C4×C83—21no—
344C2×C4×C83—21no—
345C2×C4×C83—21no—
346C2×C4×C83—21no—
347C2×C4×C83—22no—
348C2×C4×C83—22no—
349C2×C4×C83—22no—
350C2×C4×C83—22no—
351C2×C4×C83—21no—
352C2×C4×C83—22no—
353C2×C4×C83—21no—
354C2×C4×C83—22no—
355C2×C4×C83—22no—
356C2×C4×C83—22no—
357C2×C4×C83—21no—
358C2×C4×C83—21no—
359C2×C4×C83—21no—
360C2×C4×C83—21no—
361C2×C4×C83—48no—
362C2×C4×C83—48no—
363C2×C4×C83—48no—
364C2×C4×C83—41no—
365C2×C4×C83—41no—
366C2×C4×C83—41no—
367C2×C4×C83—41no—
368C2×C4×C83—41no—
369C2×C4×C83—41no—
370C2×C4×C83—41no—
371C2×C4×C83—41no—
372C2×C4×C83—41no—
373C2×C4×C83—41no—
374C2×C4×C83—41no—
375C2×C4×C83—41no—
376C2×C4×C83—41no—
377C2×C4×C83—41no—
378C2×C4×C83—41no—
379C2×C4×C83—41no—
380C2×C4×C83—41no—
381C2×C4×C83—41no—
382C2×C4×C83#12012yes—
383C2×C4×C83#13512yes—
384C2×C4×C83C22×D411yescharacteristic
385C2×C4×C83C22×D411yescharacteristic
386C2×C4×C83C22×D411yescharacteristic
387C2×C4×C83C2×#4111yescharacteristic
388C2×C4×C83H(5,𝔽2)11yescharacteristic
389C2×C4×C83H(5,𝔽2)11yescharacteristic
390C8×C83—22no—
391C8×C83—41no—
392C8×C83—41no—
393C8×C83—41no—
394C22×C83—22no—
395C22×C83—24no—
396C22×C83—22no—
397C22×C83—22no—
398C22×C83—42no—
399C22×C83—42no—
400C22×C83—41no—
401C22×C83—42no—
402C22×C83—41no—
403C22×C83—42no—
404C22×C83—41no—
405C22×C83—42no—
406C22×C83—41no—
407C22×C83—42no—
408C22×C83—41no—
409C22×C83—41no—
410C22×C83—41no—
411C22×C83—41no—
412C22×C83—41no—
413C22×C83—41no—
414C22×C83—41no—
415C22×C83—81no—
416C22×C83—81no—
417C22×C83—81no—
418C22×C83—81no—
419C22×C83—81no—
420C22×C83—81no—
421C22×C83—81no—
422C22×C83C2×#12011yescharacteristic
423C22×C83D4211yescharacteristic
424C22×C83#54611yescharacteristic
425C22×C83C2×#13511yescharacteristic
426C22×C83#57511yescharacteristic
427C22×C83#57711yescharacteristic
428C22×C83#57711yescharacteristic
429C4×C83—22no—
430C4×C83—22no—
431C4×C83—41no—
432C4×C83—42no—
433C4×C83—42no—
434C4×C83—42no—
435C4×C83—41no—
436C4×C83—42no—
437C4×C83—81no—
438C4×C83—81no—
439C4×C83C2×#12111yescharacteristic
440C4×C83#53411yescharacteristic
441C4×C83D4211yescharacteristic
442C4×C83#54611yescharacteristic
443#24438C8311yesmaximal, characteristic, direct product factor, Sylow
444C2×C83—42no—
445C2×C83—44no—
446C2×C83—81no—
447C2×C83—161no—
448C2×C83#241011yescharacteristic
449C2×C83#300211yescharacteristic
450C2×C83#301011yescharacteristic
451C2×C83#326711yescharacteristic
452C2×C83#328411yescharacteristic
453C2×C83#330311yescharacteristic
454C2×C83#330711yescharacteristic
455C2×#547C2×C8311yescharacteristic, complemented
456C2×#465C2×C8311yescharacteristic, complemented
457C2×#449C2×C8311yescharacteristic, complemented
458C2×#449C2×C8311yescharacteristic, complemented
459C2×#416C2×C8311yescharacteristic, complemented
460#2414C2×C8311yescharacteristic, complemented
461#2043C2×C8311yescharacteristic, complemented
462#2035C2×C8311yescharacteristic, complemented
463#2013C2×C8311yescharacteristic, complemented
464#2000C2×C8311yescharacteristic, complemented
465#1879C2×C8311yescharacteristic, complemented
466#1873C2×C8311yescharacteristic, complemented
467#1869C2×C8311yescharacteristic, complemented
468#1864C2×C8311yescharacteristic, complemented
469#1788C2×C8311yescharacteristic, complemented
470C83#2443811yescharacteristic, direct product factor, Sylow
471C22×#41C22×C8311yescharacteristic
472C22×#41C22×C8311yescharacteristic
473C22×SD16C22×C8311yescharacteristic
474C22×SD16C22×C8311yescharacteristic
475C22×D8C22×C8311yescharacteristic
476C23×C8C22×C8311yescharacteristic
477#547—24no—
478#547—24no—
479C2×C4⋊Q8C22×C8311yescharacteristic
480C2×#123—21no—
481C2×#123—21no—
482C2×C22⋊Q8C22×C8311yescharacteristic
483C2×C22⋊Q8C22×C8311yescharacteristic
484C2×#121—21no—
485C2×#121C22×C8311yescharacteristic
486C2×#121C22×C8311yescharacteristic
487C2×C4×D4C22×C8311yescharacteristic
488C2×C4×D4C22×C8311yescharacteristic
489C2×#117C22×C8311yescharacteristic
490C22×C4⋊C4—21no—
491#465—24no—
492#449—24no—
493#449—24no—
494C2×#106C22×C8311yescharacteristic
495#416—24no—
496C2×#103C22×C8311yescharacteristic
497C2×#103C22×C8311yescharacteristic
498C2×#103C22×C8311yescharacteristic
499C2×#103C22×C8311yescharacteristic
500C2×#103C22×C8311yescharacteristic
501C2×#103C22×C8311yescharacteristic
502C2×#102C22×C8311yescharacteristic
503C2×#102C22×C8311yescharacteristic
504C2×#102C22×C8311yescharacteristic
505C2×#102C22×C8311yescharacteristic
506C2×C22⋊C8C22×C8311yescharacteristic
507C2×C22⋊C8C22×C8311yescharacteristic
508C2×C22⋊C8C22×C8311yescharacteristic
509#394—21no—
510#392—21no—
511#390—21no—
512#390C22×C8311yescharacteristic
513#389C22×C8311yescharacteristic
514#388—21no—
515#380C22×C8311yescharacteristic
516#340C22×C8311yescharacteristic
517#340C22×C8311yescharacteristic
518#336C22×C8311yescharacteristic
519#336C22×C8311yescharacteristic
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—41no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41—41no—
531C2×#41D4×C8314yescomplemented
532C22×Q8C23×C8311yescharacteristic
533C22×Q8C23×C8311yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4D4×C8311yescharacteristic
539C22×D4C23×C8311yescharacteristic
540C22×D4C23×C8311yescharacteristic
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4C23×C8311yescharacteristic
545C23×C4C23×C8311yescharacteristic
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C22×C8—22no—
556C22×C8—22no—
557C22×C8—41no—
558C22×C8C23×C8311yescharacteristic
559C22×C8C23×C8311yescharacteristic
560C22×C8C23×C8311yescharacteristic
561C22×C8C23×C8311yescharacteristic
562C4⋊Q8—22no—
563C4⋊Q8—22no—
564#123—28no—
565#123—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8D4×C8314yescomplemented
570#121—28no—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—41no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579#117—22no—
580#117—41no—
581C2×C4⋊C4—28no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4D4×C8311yescharacteristic
588C2×C4⋊C4C23×C8311yescharacteristic
589C2×C4⋊C4C23×C8311yescharacteristic
590C2×C4⋊C4C23×C8311yescharacteristic
591C2×C4⋊C4C23×C8311yescharacteristic
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4D4×C8311yescharacteristic
602C2×C22⋊C4D4×C8311yescharacteristic
603C2×C42—21no—
604C2×C42C23×C8311yescharacteristic
605#106—22no—
606#103—22no—
607#103—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—41no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102D4×C8314yescomplemented
616C22⋊C8—22no—
617C22⋊C8—22no—
618C22⋊C8—41no—
619#95—21no—
620#95—21no—
621C24—21no—
622C24—21no—
623C24C2×D4×C8311yescharacteristic
624C24C2×D4×C8311yescharacteristic
625#41—28no—
626#41—44no—
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×D4×C8312yes—
644C2×Q8C2×D4×C8312yes—
645C2×D4—24no—
646C2×D4—22no—
647C2×D4—24no—
648C2×D4—22no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—41no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—81no—
667C2×D4—81no—
668C2×D4—81no—
669C2×D4C2×D4×C8312yes—
670C2×D4C2×D4×C8312yes—
671C2×D4#41×C8312yes—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—24no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4C2×D4×C8311yescharacteristic
698C22×C4C2×D4×C8311yescharacteristic
699C22×C4C2×D4×C8311yescharacteristic
700C22×C4C2×D4×C8312yes—
701C22×C4C2×D4×C8312yes—
702C22×C4C2×D4×C8311yescharacteristic
703C22×C4C24×C8311yescharacteristic
704SD16—44no—
705SD16—44no—
706D8—44no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—44no—
719C2×C8C2×D4×C8312yes—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—24no—
723C4⋊C4—22no—
724C4⋊C4—24no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—81no—
732C4⋊C4C2×D4×C8312yes—
733C4⋊C4C2×D4×C8312yes—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—81no—
744C22⋊C4—81no—
745C42—21no—
746C42—21no—
747C42—42no—
748C23—22no—
749C23—21no—
750C23—22no—
751C23—21no—
752C23—22no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23#120×C8312yes—
776C23C22×D4×C8311yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—44no—
789D4—48no—
790D4—48no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—84no—
796D4—84no—
797D4#121×C8314yes—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—48no—
817C2×C4—48no—
818C2×C4—48no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4#120×C8312yes—
838C2×C4#135×C8312yes—
839C2×C4C22×D4×C8311yescharacteristic
840C2×C4C22×D4×C8311yescharacteristic
841C2×C4C22×D4×C8311yescharacteristic
842C2×C4C2×#41×C8311yescharacteristic
843C2×C4H(5,𝔽2)×C8311yescharacteristic
844C2×C4H(5,𝔽2)×C8311yescharacteristic
845C8—22no—
846C8—41no—
847C8—41no—
848C8—41no—
849C22—22no—
850C22—24no—
851C22—22no—
852C22—22no—
853C22—41no—
854C22—42no—
855C22—41no—
856C22—42no—
857C22—41no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22C2×#120×C8311yescharacteristic
878C22D42×C8311yescharacteristic
879C22#546×C8311yescharacteristic
880C22C2×#135×C8311yescharacteristic
881C22#575×C8311yescharacteristic
882C22#577×C8311yescharacteristic
883C22#577×C8311yescharacteristic
884C4—22no—
885C4—22no—
886C4—41no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—41no—
891C4—42no—
892C4—81no—
893C4—81no—
894C4C2×#121×C8311yescharacteristic
895C4#534×C8311yescharacteristic
896C4D42×C8311yescharacteristic
897C4#546×C8311yescharacteristic
898C2—42no—
899C2—44no—
900C2—81no—
901C2—161no—
902C2C83×#241011yescharacteristic
903C2C83×#300211yescharacteristic
904C2C83×#301011yescharacteristic
905C2C83×#326711yescharacteristic
906C2C83×#328411yescharacteristic
907C2C83×#330311yescharacteristic
908C2C83×#330711yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C2×C4×D4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#547×C83C2semidirect
2. C2×#465×C83C2semidirect
3. C2×#449×C83C2semidirect
4. C2×#449×C83C2semidirect
5. C2×#416×C83C2semidirect
6. C83×#2414C2semidirect
7. C83×#2043C2semidirect
8. C83×#2035C2semidirect
9. C83×#2013C2semidirect
10. C83×#2000C2semidirect
11. C83×#1879C2semidirect
12. C83×#1873C2semidirect
13. C83×#1869C2semidirect
14. C83×#1864C2semidirect
15. C83×#1788C2semidirect
76. C2×#41×C83D4semidirect
114. C22⋊Q8×C83D4semidirect
160. #102×C83D4semidirect
443. #24438C83direct (N × H)
455. C2×#547C2×C83semidirect
456. C2×#465C2×C83semidirect
457. C2×#449C2×C83semidirect
458. C2×#449C2×C83semidirect
459. C2×#416C2×C83semidirect
460. #2414C2×C83semidirect
461. #2043C2×C83semidirect
462. #2035C2×C83semidirect
463. #2013C2×C83semidirect
464. #2000C2×C83semidirect
465. #1879C2×C83semidirect
466. #1873C2×C83semidirect
467. #1869C2×C83semidirect
468. #1864C2×C83semidirect
469. #1788C2×C83semidirect
470. C83#24438direct (N × H)
531. C2×#41D4×C83semidirect
569. C22⋊Q8D4×C83semidirect
615. #102D4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C832
C2×#465×C832
C2×#449×C832
C2×#416×C832
C83×#24142
C83×#20432
C83×#20352
C83×#20132
C83×#20002
C83×#18792
C83×#18732
C83×#18692
C83×#18642
C83×#17882
#2443883