Finite Group Databasebeta

← C83×#62788 #35290612

Subgroups — C83×#62788 #35290612

Order 21248.

7094 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3523C214yesmaximal, complemented
2C83×#3522C214yesmaximal, complemented
3C83×#3516C218yesmaximal, complemented
4C83×#3507C216yesmaximal, complemented
5C83×#3502C211yesmaximal, characteristic, complemented
6C83×#3497C211yesmaximal, characteristic, complemented
7C83×#3492C216yesmaximal, complemented
8C83×#3486C212yesmaximal, complemented
9C83×#3482C218yesmaximal, complemented
10C83×#3480C214yesmaximal, complemented
11Q8×#41×C83C214yesmaximal, complemented
12C83×#3461C216yesmaximal, complemented
13C83×#3444C216yesmaximal, complemented
14C4×2−1+4×C83C212yesmaximal, complemented
15C22×C4×Q8×C83C211yesmaximal, characteristic, complemented
16C2×2−1+4×C83C2212yes—
17C23×Q8×C83C2211yescharacteristic
18#559×C83C22112yescomplemented
19Q82×C83C2214yescomplemented
20#557×C83C22112yescomplemented
21#557×C83C2214yescomplemented
22#557×C83C2218yescomplemented
23#556×C83C22112yescomplemented
24#556×C83C22124yescomplemented
25#554×C83C22124yes—
26#554×C83C22112yescomplemented
27#553×C83C22124yes—
28#552×C83C22124yes—
29#552×C83C22124yescomplemented
30#550×C83C2214yescomplemented
31D4×Q8×C83C2218yes—
32D4×Q8×C83C2218yes—
33D4×Q8×C83C2214yescomplemented
34#548×C83C2218yes—
35#548×C83C2218yes—
36#548×C83C2218yescomplemented
37#547×C83C22124yes—
38#544×C83C2216yes—
39#542×C83C22124yescomplemented
40#541×C83C22124yescomplemented
41#539×C83C22124yes—
42#537×C83C2216yes—
43#536×C83C22112yes—
44#533×C83C2216yes—
45#533×C83C2216yes—
46#533×C83C2216yes—
47#533×C83C22124yescomplemented
48#532×C83C2216yes—
49#532×C83C2216yes—
50#532×C83C2216yes—
51#529×C83C22112yes—
52#529×C83C22112yes—
53#529×C83C22112yes—
54#529×C83C22112yes—
55#529×C83C22112yes—
56#529×C83C22112yes—
57#529×C83C22124yescomplemented
58#525×C83C2214yes—
59#525×C83C22112yes—
60#525×C83C22112yes—
61#520×C83C22112yes—
62#520×C83C2218yescomplemented
63#519×C83C2212yes—
64#519×C83C2218yescomplemented
65C4×#41×C83C22112yes—
66C4×#41×C83C22112yes—
67C4×#41×C83C22112yes—
68C4×#41×C83C2218yescomplemented
69C2×C4×Q8×C83C2211yescharacteristic
70C2×C4×Q8×C83C2213yes—
71C2×C4×Q8×C83C2214yes—
72C2×C4×Q8×C83C2214yes—
73C2×C4×Q8×C83C2211yescharacteristic
74C2×C4×Q8×C83C2213yes—
75C2×C4×Q8×C83C2214yes—
76C2×C4×Q8×C83C2214yes—
77C2×C4×Q8×C83C2218yescomplemented
78C22×C4⋊C4×C83C2213yes—
79C22×C42×C83C2213yes—
802−1+4×C83—216no—
81C2×#41×C83C2314yes—
82C2×#41×C83C23112yes—
83C2×#41×C83C2318yes—
84C2×#41×C83C23112yes—
85C22×Q8×C83—28no—
86C22×Q8×C83C2313yes—
87C22×Q8×C83C2314yes—
88C22×Q8×C83C2314yes—
89C22×Q8×C83C2318yes—
90C22×Q8×C83C2311yescharacteristic
91C23×C4×C83C2311yescharacteristic
92C23×C4×C83C2313yes—
93C23×C4×C83C2313yes—
94C4⋊Q8×C83C2316yes—
95C4⋊Q8×C83C2316yes—
96C4⋊Q8×C83C2316yes—
97C4⋊Q8×C83C23124yes—
98C4⋊Q8×C83C23124yes—
99#127×C83C2316yes—
100#126×C83C23124yes—
101#126×C83C23124yes—
102#126×C83C23148yes—
103#125×C83C23112yes—
104#125×C83C23112yes—
105#125×C83C23112yes—
106#125×C83C23124yes—
107#125×C83C23148yes—
108#124×C83C23112yes—
109#124×C83C23112yes—
110#124×C83C23112yes—
111#124×C83C23124yes—
112#123×C83C2318yes—
113#123×C83C23124yes—
114#123×C83C23124yes—
115#123×C83C23148yes—
116C22⋊Q8×C83C2314yes—
117C22⋊Q8×C83C2314yes—
118C22⋊Q8×C83C23112yes—
119C22⋊Q8×C83C23112yes—
120C22⋊Q8×C83C23112yes—
121C22⋊Q8×C83C23112yes—
122C22⋊Q8×C83C23124yes—
123C22⋊Q8×C83C23124yes—
124C22⋊Q8×C83C23124yes—
125C22⋊Q8×C83C23148yes—
126#121×C83C2314yes—
127#121×C83C2314yes—
128#121×C83C23112yes—
129#121×C83C23112yes—
130#121×C83C23112yes—
131#121×C83C23112yes—
132#121×C83C23124yes—
133#120×C83C2318yes—
134C4×Q8×C83C2314yes—
135C4×Q8×C83C2314yes—
136C4×Q8×C83C23112yes—
137C4×Q8×C83C23112yes—
138C4×Q8×C83C2314yes—
139C4×Q8×C83C2314yes—
140C4×Q8×C83C23112yes—
141C4×Q8×C83C23112yes—
142C4×Q8×C83C23112yes—
143C4×Q8×C83C2318yes—
144C4×Q8×C83C23124yes—
145C4×Q8×C83C23112yes—
146C4×Q8×C83C23112yes—
147C4×Q8×C83C23112yes—
148C4×Q8×C83C23112yes—
149C4×Q8×C83C23112yes—
150C4×Q8×C83C2318yes—
151C4×D4×C83C2318yes—
152C4×D4×C83C2318yes—
153C4×D4×C83C23112yes—
154C4×D4×C83C23124yes—
155C4×D4×C83C23112yes—
156C4×D4×C83C23124yes—
157C4×D4×C83C23124yes—
158C4×D4×C83C23124yes—
159C4×D4×C83C23112yes—
160C4×D4×C83C23112yes—
161C4×D4×C83C23112yes—
162C4×D4×C83C23112yes—
163C4×D4×C83C23124yes—
164#117×C83C2314yes—
165#117×C83C23112yes—
166#117×C83C23124yes—
167#117×C83C23112yes—
168#117×C83C23124yes—
169#117×C83C23124yes—
170#117×C83C23124yes—
171C2×C4⋊C4×C83C2313yes—
172C2×C4⋊C4×C83C2313yes—
173C2×C4⋊C4×C83C2316yes—
174C2×C4⋊C4×C83C23112yes—
175C2×C4⋊C4×C83C23112yes—
176C2×C4⋊C4×C83C23124yes—
177C2×C42×C83C2313yes—
178C2×C42×C83C2316yes—
179C2×C42×C83C2316yes—
180C2×C42×C83C2316yes—
181C2×C42×C83C2313yes—
182C2×C42×C83C2313yes—
183C2×C42×C83C2316yes—
184C2×C42×C83C2313yes—
185C2×C42×C83C23124yes—
186C24×C83C2411yescharacteristic
187#41×C83—232no—
188#41×C83—248no—
189#41×C83—216no—
190#41×C83—424no—
191C2×Q8×C83—216no—
192C2×Q8×C83—216no—
193C2×Q8×C83—232no—
194C2×Q8×C83—212no—
195C2×Q8×C83#4118yescomplemented
196C2×Q8×C83C2414yes—
197C2×Q8×C83C24112yes—
198C2×Q8×C83C24112yes—
199C2×Q8×C83C24112yes—
200C2×Q8×C83C2414yes—
201C2×D4×C83C2418yes—
202C2×D4×C83C2414yes—
203C2×D4×C83C2418yes—
204C2×D4×C83C2418yes—
205C2×D4×C83C24112yes—
206C2×D4×C83C24112yes—
207C22×C4×C83—212no—
208C22×C4×C83—24no—
209C22×C4×C83—46no—
210C22×C4×C83C2411yescharacteristic
211C22×C4×C83C2411yescharacteristic
212C22×C4×C83C2411yescharacteristic
213C22×C4×C83C2416yes—
214C22×C4×C83C2416yes—
215C22×C4×C83C2416yes—
216C22×C4×C83C2413yes—
217C22×C4×C83C24124yes—
218C22×C4×C83C2411yescharacteristic
219C22×C4×C83C2411yescharacteristic
220C22×C4×C83C2418yes—
221C22×C4×C83C2413yes—
222C22×C4×C83C2416yes—
223C22×C4×C83C2413yes—
224C22×C4×C83C24124yes—
225C22×C4×C83C2413yes—
226C22×C4×C83C2411yescharacteristic
227C4⋊C4×C83C24112yes—
228C4⋊C4×C83C24112yes—
229C4⋊C4×C83C24124yes—
230C4⋊C4×C83C24112yes—
231C4⋊C4×C83C24124yes—
232C4⋊C4×C83C24112yes—
233C4⋊C4×C83C2418yes—
234C4⋊C4×C83C2418yes—
235C4⋊C4×C83C2414yes—
236C4⋊C4×C83C2414yes—
237C4⋊C4×C83C24112yes—
238C4⋊C4×C83C24112yes—
239C4⋊C4×C83C24124yes—
240C4⋊C4×C83C24124yes—
241C4⋊C4×C83C24124yes—
242C22⋊C4×C83C2418yes—
243C22⋊C4×C83C2418yes—
244C22⋊C4×C83C24124yes—
245C22⋊C4×C83C2418yes—
246C22⋊C4×C83C2418yes—
247C22⋊C4×C83C2418yes—
248C22⋊C4×C83C24124yes—
249C22⋊C4×C83C24124yes—
250C22⋊C4×C83C24124yes—
251C42×C83C2416yes—
252C42×C83C2416yes—
253C42×C83C2416yes—
254C42×C83C2416yes—
255C42×C83C2416yes—
256C42×C83C2416yes—
257C42×C83C24124yes—
258C42×C83C24124yes—
259C42×C83C2416yes—
260C42×C83C2416yes—
261C42×C83C2418yes—
262C23×C83—22no—
263C23×C83—22no—
264C23×C83—22no—
265C23×C83C2518yes—
266C23×C83C2511yescharacteristic
267C23×C83C2511yescharacteristic
268C23×C83C2511yescharacteristic
269Q8×C83—224no—
270Q8×C83—224no—
271Q8×C83—28no—
272Q8×C83—412no—
273Q8×C83C2×#41116yes—
274D4×C83—216no—
275D4×C83—216no—
276D4×C83—216no—
277D4×C83—224no—
278D4×C83—28no—
279D4×C83—412no—
280C2×C4×C83—26no—
281C2×C4×C83—22no—
282C2×C4×C83—212no—
283C2×C4×C83—212no—
284C2×C4×C83—212no—
285C2×C4×C83—248no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—216no—
291C2×C4×C83—43no—
292C2×C4×C83—46no—
293C2×C4×C83—43no—
294C2×C4×C83—424no—
295C2×C4×C83C2×#41112yes—
296C2×C4×C832−1+414yescomplemented
297C2×C4×C83C2511yescharacteristic
298C2×C4×C83C2511yescharacteristic
299C2×C4×C83C2516yes—
300C2×C4×C83C2518yes—
301C2×C4×C83C2516yes—
302C2×C4×C83C2518yes—
303C2×C4×C83C2518yes—
304C2×C4×C83C2516yes—
305C2×C4×C83C2516yes—
306C2×C4×C83C2511yescharacteristic
307C2×C4×C83C2511yescharacteristic
308C22×C83—28no—
309C22×C83—21no—
310C22×C83—21no—
311C22×C83—21no—
312C22×C83—21no—
313C22×C83—21no—
314C22×C83—21no—
315C22×C83—28no—
316C22×C83—28no—
317C22×C83—28no—
318C22×C83C22×#4112yes—
319C22×C83C2×2−1+412yes—
320C22×C83#58512yes—
321C22×C83C2611yescharacteristic
322C4×C83—28no—
323C4×C83—26no—
324C4×C83—21no—
325C4×C83—21no—
326C4×C83—28no—
327C4×C83—26no—
328C4×C83—26no—
329C4×C83—28no—
330C4×C83C22×#41112yes—
331C4×C83C2×2−1+412yes—
332C4×C83C2×2−1+412yes—
333#62788C8311yesmaximal, characteristic, direct product factor, Sylow
334C2×C83—22no—
335C2×C83—22no—
336C2×C83—22no—
337C2×C83—48no—
338C2×C83C23×#4111yescharacteristic
339C2×C83C22×2−1+411yescharacteristic
340C2×C83C2×#58511yescharacteristic
341#3523C2×C8314yescomplemented
342#3522C2×C8314yescomplemented
343#3516C2×C8318yescomplemented
344#3507C2×C8316yescomplemented
345#3502C2×C8311yescharacteristic, complemented
346#3497C2×C8311yescharacteristic, complemented
347#3492C2×C8316yescomplemented
348#3486C2×C8312yescomplemented
349#3482C2×C8318yescomplemented
350#3480C2×C8314yescomplemented
351Q8×#41C2×C8314yescomplemented
352#3461C2×C8316yescomplemented
353#3444C2×C8316yescomplemented
354C4×2−1+4C2×C8312yescomplemented
355C22×C4×Q8C2×C8311yescharacteristic, complemented
356C83#6278811yescharacteristic, direct product factor, Sylow
357C2×2−1+4C22×C8312yes—
358C23×Q8C22×C8311yescharacteristic
359#559C22×C83112yescomplemented
360Q82C22×C8314yescomplemented
361#557C22×C83112yescomplemented
362#557C22×C8314yescomplemented
363#557C22×C8318yescomplemented
364#556C22×C83112yescomplemented
365#556C22×C83124yescomplemented
366#554C22×C83124yes—
367#554C22×C83112yescomplemented
368#553C22×C83124yes—
369#552C22×C83124yes—
370#552C22×C83124yescomplemented
371#550C22×C8314yescomplemented
372D4×Q8C22×C8318yes—
373D4×Q8C22×C8318yes—
374D4×Q8C22×C8314yescomplemented
375#548C22×C8318yes—
376#548C22×C8318yes—
377#548C22×C8318yescomplemented
378#547C22×C83124yes—
379#544C22×C8316yes—
380#542C22×C83124yescomplemented
381#541C22×C83124yescomplemented
382#539C22×C83124yes—
383#537C22×C8316yes—
384#536C22×C83112yes—
385#533C22×C8316yes—
386#533C22×C8316yes—
387#533C22×C8316yes—
388#533C22×C83124yescomplemented
389#532C22×C8316yes—
390#532C22×C8316yes—
391#532C22×C8316yes—
392#529C22×C83112yes—
393#529C22×C83112yes—
394#529C22×C83112yes—
395#529C22×C83112yes—
396#529C22×C83112yes—
397#529C22×C83112yes—
398#529C22×C83124yescomplemented
399#525C22×C8314yes—
400#525C22×C83112yes—
401#525C22×C83112yes—
402#520C22×C83112yes—
403#520C22×C8318yescomplemented
404#519C22×C8312yes—
405#519C22×C8318yescomplemented
406C4×#41C22×C83112yes—
407C4×#41C22×C83112yes—
408C4×#41C22×C83112yes—
409C4×#41C22×C8318yescomplemented
410C2×C4×Q8C22×C8311yescharacteristic
411C2×C4×Q8C22×C8313yes—
412C2×C4×Q8C22×C8314yes—
413C2×C4×Q8C22×C8314yes—
414C2×C4×Q8C22×C8311yescharacteristic
415C2×C4×Q8C22×C8313yes—
416C2×C4×Q8C22×C8314yes—
417C2×C4×Q8C22×C8314yes—
418C2×C4×Q8C22×C8318yescomplemented
419C22×C4⋊C4C22×C8313yes—
420C22×C42C22×C8313yes—
4212−1+4—216no—
422C2×#41C23×C8314yes—
423C2×#41C23×C83112yes—
424C2×#41C23×C8318yes—
425C2×#41C23×C83112yes—
426C22×Q8—28no—
427C22×Q8C23×C8313yes—
428C22×Q8C23×C8314yes—
429C22×Q8C23×C8314yes—
430C22×Q8C23×C8318yes—
431C22×Q8C23×C8311yescharacteristic
432C23×C4C23×C8313yes—
433C23×C4C23×C8311yescharacteristic
434C23×C4C23×C8313yes—
435C4⋊Q8C23×C8316yes—
436C4⋊Q8C23×C8316yes—
437C4⋊Q8C23×C8316yes—
438C4⋊Q8C23×C83124yes—
439C4⋊Q8C23×C83124yes—
440#127C23×C8316yes—
441#126C23×C83124yes—
442#126C23×C83124yes—
443#126C23×C83148yes—
444#125C23×C83112yes—
445#125C23×C83112yes—
446#125C23×C83112yes—
447#125C23×C83124yes—
448#125C23×C83148yes—
449#124C23×C83112yes—
450#124C23×C83112yes—
451#124C23×C83112yes—
452#124C23×C83124yes—
453#123C23×C8318yes—
454#123C23×C83124yes—
455#123C23×C83124yes—
456#123C23×C83148yes—
457C22⋊Q8C23×C8314yes—
458C22⋊Q8C23×C8314yes—
459C22⋊Q8C23×C83112yes—
460C22⋊Q8C23×C83112yes—
461C22⋊Q8C23×C83112yes—
462C22⋊Q8C23×C83112yes—
463C22⋊Q8C23×C83124yes—
464C22⋊Q8C23×C83124yes—
465C22⋊Q8C23×C83124yes—
466C22⋊Q8C23×C83148yes—
467#121C23×C8314yes—
468#121C23×C8314yes—
469#121C23×C83112yes—
470#121C23×C83112yes—
471#121C23×C83112yes—
472#121C23×C83112yes—
473#121C23×C83124yes—
474#120C23×C8318yes—
475C4×Q8C23×C8314yes—
476C4×Q8C23×C8314yes—
477C4×Q8C23×C83112yes—
478C4×Q8C23×C83112yes—
479C4×Q8C23×C8314yes—
480C4×Q8C23×C8314yes—
481C4×Q8C23×C83112yes—
482C4×Q8C23×C83112yes—
483C4×Q8C23×C83112yes—
484C4×Q8C23×C8318yes—
485C4×Q8C23×C83124yes—
486C4×Q8C23×C83112yes—
487C4×Q8C23×C83112yes—
488C4×Q8C23×C83112yes—
489C4×Q8C23×C83112yes—
490C4×Q8C23×C83112yes—
491C4×Q8C23×C8318yes—
492C4×D4C23×C8318yes—
493C4×D4C23×C8318yes—
494C4×D4C23×C83112yes—
495C4×D4C23×C83124yes—
496C4×D4C23×C83112yes—
497C4×D4C23×C83124yes—
498C4×D4C23×C83124yes—
499C4×D4C23×C83124yes—
500C4×D4C23×C83112yes—
501C4×D4C23×C83112yes—
502C4×D4C23×C83112yes—
503C4×D4C23×C83112yes—
504C4×D4C23×C83124yes—
505#117C23×C8314yes—
506#117C23×C83112yes—
507#117C23×C83124yes—
508#117C23×C83112yes—
509#117C23×C83124yes—
510#117C23×C83124yes—
511#117C23×C83124yes—
512C2×C4⋊C4C23×C8313yes—
513C2×C4⋊C4C23×C8313yes—
514C2×C4⋊C4C23×C8316yes—
515C2×C4⋊C4C23×C83112yes—
516C2×C4⋊C4C23×C83112yes—
517C2×C4⋊C4C23×C83124yes—
518C2×C42C23×C8313yes—
519C2×C42C23×C8316yes—
520C2×C42C23×C8316yes—
521C2×C42C23×C8313yes—
522C2×C42C23×C8316yes—
523C2×C42C23×C8313yes—
524C2×C42C23×C8316yes—
525C2×C42C23×C8313yes—
526C2×C42C23×C83124yes—
527C24C24×C8311yescharacteristic
528#41—232no—
529#41—248no—
530#41—216no—
531#41—424no—
532C2×Q8—216no—
533C2×Q8—216no—
534C2×Q8—232no—
535C2×Q8—212no—
536C2×Q8#41×C8318yescomplemented
537C2×Q8C24×C8314yes—
538C2×Q8C24×C83112yes—
539C2×Q8C24×C83112yes—
540C2×Q8C24×C83112yes—
541C2×Q8C24×C8314yes—
542C2×D4C24×C8318yes—
543C2×D4C24×C8314yes—
544C2×D4C24×C8318yes—
545C2×D4C24×C8318yes—
546C2×D4C24×C83112yes—
547C2×D4C24×C83112yes—
548C22×C4—212no—
549C22×C4—24no—
550C22×C4—46no—
551C22×C4C24×C8311yescharacteristic
552C22×C4C24×C8311yescharacteristic
553C22×C4C24×C8311yescharacteristic
554C22×C4C24×C8311yescharacteristic
555C22×C4C24×C8311yescharacteristic
556C22×C4C24×C8318yes—
557C22×C4C24×C8316yes—
558C22×C4C24×C8316yes—
559C22×C4C24×C8316yes—
560C22×C4C24×C8313yes—
561C22×C4C24×C83124yes—
562C22×C4C24×C8313yes—
563C22×C4C24×C8316yes—
564C22×C4C24×C8313yes—
565C22×C4C24×C83124yes—
566C22×C4C24×C8313yes—
567C22×C4C24×C8311yescharacteristic
568C4⋊C4C24×C83112yes—
569C4⋊C4C24×C83112yes—
570C4⋊C4C24×C83124yes—
571C4⋊C4C24×C83112yes—
572C4⋊C4C24×C83124yes—
573C4⋊C4C24×C83112yes—
574C4⋊C4C24×C8318yes—
575C4⋊C4C24×C8318yes—
576C4⋊C4C24×C8314yes—
577C4⋊C4C24×C8314yes—
578C4⋊C4C24×C83112yes—
579C4⋊C4C24×C83112yes—
580C4⋊C4C24×C83124yes—
581C4⋊C4C24×C83124yes—
582C4⋊C4C24×C83124yes—
583C22⋊C4C24×C8318yes—
584C22⋊C4C24×C8318yes—
585C22⋊C4C24×C83124yes—
586C22⋊C4C24×C8318yes—
587C22⋊C4C24×C8318yes—
588C22⋊C4C24×C8318yes—
589C22⋊C4C24×C83124yes—
590C22⋊C4C24×C83124yes—
591C22⋊C4C24×C83124yes—
592C42C24×C8316yes—
593C42C24×C8316yes—
594C42C24×C8316yes—
595C42C24×C8318yes—
596C42C24×C8316yes—
597C42C24×C8316yes—
598C42C24×C8316yes—
599C42C24×C8316yes—
600C42C24×C8316yes—
601C42C24×C83124yes—
602C42C24×C83124yes—
603C23—22no—
604C23—22no—
605C23—22no—
606C23C25×C8318yes—
607C23C25×C8311yescharacteristic
608C23C25×C8311yescharacteristic
609C23C25×C8311yescharacteristic
610Q8—224no—
611Q8—224no—
612Q8—28no—
613Q8—412no—
614Q8C2×#41×C83116yes—
615D4—216no—
616D4—216no—
617D4—216no—
618D4—224no—
619D4—28no—
620D4—412no—
621C2×C4—26no—
622C2×C4—22no—
623C2×C4—212no—
624C2×C4—212no—
625C2×C4—212no—
626C2×C4—248no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—216no—
632C2×C4—43no—
633C2×C4—46no—
634C2×C4—43no—
635C2×C4—424no—
636C2×C4C2×#41×C83112yes—
637C2×C42−1+4×C8314yescomplemented
638C2×C4C25×C8311yescharacteristic
639C2×C4C25×C8311yescharacteristic
640C2×C4C25×C8316yes—
641C2×C4C25×C8318yes—
642C2×C4C25×C8316yes—
643C2×C4C25×C8318yes—
644C2×C4C25×C8318yes—
645C2×C4C25×C8316yes—
646C2×C4C25×C8316yes—
647C2×C4C25×C8311yescharacteristic
648C2×C4C25×C8311yescharacteristic
649C22—28no—
650C22—21no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—28no—
657C22—28no—
658C22—28no—
659C22C22×#41×C8312yes—
660C22C2×2−1+4×C8312yes—
661C22#585×C8312yes—
662C22C26×C8311yescharacteristic
663C4—28no—
664C4—26no—
665C4—21no—
666C4—21no—
667C4—28no—
668C4—26no—
669C4—26no—
670C4—28no—
671C4C22×#41×C83112yes—
672C4C2×2−1+4×C8312yes—
673C4C2×2−1+4×C8312yes—
674C2—22no—
675C2—22no—
676C2—22no—
677C2—48no—
678C2C23×#41×C8311yescharacteristic
679C2C22×2−1+4×C8311yescharacteristic
680C2C2×#585×C8311yescharacteristic
subgroupG/H
centerC2×C4×C83C25
commutator, Frattini, cosocleC22C26×C83
socleC22×C83C26
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#3523C2semidirect
2. C83×#3522C2semidirect
3. C83×#3516C2semidirect
4. C83×#3507C2semidirect
5. C83×#3502C2semidirect
6. C83×#3497C2semidirect
7. C83×#3492C2semidirect
8. C83×#3486C2semidirect
9. C83×#3482C2semidirect
10. C83×#3480C2semidirect
11. Q8×#41×C83C2semidirect
12. C83×#3461C2semidirect
13. C83×#3444C2semidirect
14. C4×2−1+4×C83C2semidirect
15. C22×C4×Q8×C83C2semidirect
18. #559×C83C22semidirect
19. Q82×C83C22semidirect
20. #557×C83C22semidirect
21. #557×C83C22semidirect
22. #557×C83C22semidirect
23. #556×C83C22semidirect
24. #556×C83C22semidirect
26. #554×C83C22semidirect
29. #552×C83C22semidirect
30. #550×C83C22semidirect
33. D4×Q8×C83C22semidirect
36. #548×C83C22semidirect
39. #542×C83C22semidirect
40. #541×C83C22semidirect
47. #533×C83C22semidirect
57. #529×C83C22semidirect
62. #520×C83C22semidirect
64. #519×C83C22semidirect
68. C4×#41×C83C22semidirect
77. C2×C4×Q8×C83C22semidirect
195. C2×Q8×C83#41semidirect
296. C2×C4×C832−1+4semidirect
333. #62788C83direct (N × H)
341. #3523C2×C83semidirect
342. #3522C2×C83semidirect
343. #3516C2×C83semidirect
344. #3507C2×C83semidirect
345. #3502C2×C83semidirect
346. #3497C2×C83semidirect
347. #3492C2×C83semidirect
348. #3486C2×C83semidirect
349. #3482C2×C83semidirect
350. #3480C2×C83semidirect
351. Q8×#41C2×C83semidirect
352. #3461C2×C83semidirect
353. #3444C2×C83semidirect
354. C4×2−1+4C2×C83semidirect
355. C22×C4×Q8C2×C83semidirect
356. C83#62788direct (N × H)
359. #559C22×C83semidirect
360. Q82C22×C83semidirect
361. #557C22×C83semidirect
362. #557C22×C83semidirect
363. #557C22×C83semidirect
364. #556C22×C83semidirect
365. #556C22×C83semidirect
367. #554C22×C83semidirect
370. #552C22×C83semidirect
371. #550C22×C83semidirect
374. D4×Q8C22×C83semidirect
377. #548C22×C83semidirect
380. #542C22×C83semidirect
381. #541C22×C83semidirect
388. #533C22×C83semidirect
398. #529C22×C83semidirect
403. #520C22×C83semidirect
405. #519C22×C83semidirect
409. C4×#41C22×C83semidirect
418. C2×C4×Q8C22×C83semidirect
536. C2×Q8#41×C83semidirect
637. C2×C42−1+4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#35232
C83×#35222
C83×#35162
C83×#35072
C83×#35022
C83×#34972
C83×#34922
C83×#34862
C83×#34822
C83×#34802
Q8×#41×C832
C83×#34612
C83×#34442
C4×2−1+4×C832
C22×C4×Q8×C832
#6278883