Finite Group Databasebeta

← C83×#62793 #35290617

Subgroups — C83×#62793 #35290617

Order 21248.

7190 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3524C218yesmaximal, complemented
2C83×#3518C214yesmaximal, complemented
3C83×#3517C214yesmaximal, complemented
4C83×#3506C216yesmaximal, complemented
5C83×#3502C211yesmaximal, characteristic, complemented
6C83×#3497C211yesmaximal, characteristic, complemented
7C83×#3493C216yesmaximal, complemented
8C83×#3487C212yesmaximal, complemented
9C83×#3483C214yesmaximal, complemented
10C83×#3482C214yesmaximal, complemented
11C83×#3480C218yesmaximal, complemented
12C83×#3460C216yesmaximal, complemented
13C83×#3444C216yesmaximal, complemented
14C4×2−1+4×C83C212yesmaximal, complemented
15C2×C4×#41×C83C211yesmaximal, characteristic, complemented
16C2×2−1+4×C83C2212yes—
17C22×#41×C83C2211yescharacteristic
18#559×C83C22124yescomplemented
19Q82×C83C2214yescomplemented
20#557×C83C2218yescomplemented
21#557×C83C2214yescomplemented
22#556×C83C22124yescomplemented
23#556×C83C22112yescomplemented
24#555×C83C22124yescomplemented
25#555×C83C22112yescomplemented
26#553×C83C22124yescomplemented
27#553×C83C22124yescomplemented
28#552×C83C22124yescomplemented
29#550×C83C2218yes—
30#550×C83C2218yes—
31#550×C83C2214yescomplemented
32#550×C83C22112yescomplemented
33D4×Q8×C83C2214yescomplemented
34#548×C83C2218yes—
35#548×C83C2218yes—
36#548×C83C2218yescomplemented
37#547×C83C22112yescomplemented
38#544×C83C2216yes—
39#542×C83C22124yescomplemented
40#540×C83C22124yescomplemented
41#538×C83C22124yes—
42#537×C83C2216yes—
43#535×C83C22112yes—
44#533×C83C2216yes—
45#533×C83C2216yescomplemented
46#533×C83C2216yescomplemented
47#532×C83C2216yes—
48#532×C83C2216yescomplemented
49#532×C83C2216yescomplemented
50#532×C83C22124yescomplemented
51#529×C83C2214yes—
52#529×C83C22112yes—
53#529×C83C22112yescomplemented
54#529×C83C22112yescomplemented
55#529×C83C22112yescomplemented
56#529×C83C22112yescomplemented
57#529×C83C22124yescomplemented
58#525×C83C22112yes—
59#525×C83C22112yes—
60#525×C83C22112yes—
61#520×C83C22112yes—
62#520×C83C2218yescomplemented
63#519×C83C2212yes—
64#519×C83C2218yescomplemented
65C4×#41×C83C2214yes—
66C4×#41×C83C2214yes—
67C4×#41×C83C2214yes—
68C4×#41×C83C2214yes—
69C4×#41×C83C22112yes—
70C4×#41×C83C2218yescomplemented
71C4×#41×C83C22112yescomplemented
72C4×#41×C83C22112yescomplemented
73C2×C4×Q8×C83C2211yescharacteristic
74C2×C4×Q8×C83C2211yescharacteristic
75C2×C4×Q8×C83C2218yescomplemented
76C2×C4×D4×C83C2213yes—
77C2×C4×D4×C83C2213yes—
78C2×#117×C83C2213yes—
79C22×C42×C83C2213yes—
802−1+4×C83—216no—
81C2×#41×C83—28no—
82C2×#41×C83C2314yes—
83C2×#41×C83C2314yes—
84C2×#41×C83C23112yes—
85C2×#41×C83C2318yes—
86C2×#41×C83C23112yes—
87C2×#41×C83C23112yes—
88C22×Q8×C83C2318yes—
89C22×Q8×C83C2311yescharacteristic
90C22×D4×C83C2313yes—
91C23×C4×C83C2313yes—
92C23×C4×C83C2313yes—
93C23×C4×C83C2313yes—
94C4⋊Q8×C83C2316yes—
95C4⋊Q8×C83C2316yes—
96C4⋊Q8×C83C2316yes—
97C4⋊Q8×C83C23124yes—
98#127×C83C2316yes—
99#127×C83C23124yes—
100#126×C83C2318yes—
101#126×C83C23124yes—
102#126×C83C23148yes—
103#125×C83C2314yes—
104#125×C83C23112yes—
105#125×C83C23112yes—
106#125×C83C23124yes—
107#124×C83C2314yes—
108#124×C83C23112yes—
109#124×C83C23112yes—
110#124×C83C23124yes—
111#124×C83C23148yes—
112#123×C83C2318yes—
113#123×C83C23124yes—
114#123×C83C23124yes—
115#123×C83C23148yes—
116C22⋊Q8×C83C2314yes—
117C22⋊Q8×C83C23112yes—
118C22⋊Q8×C83C23112yes—
119C22⋊Q8×C83C23112yes—
120C22⋊Q8×C83C23112yes—
121C22⋊Q8×C83C23112yes—
122C22⋊Q8×C83C23124yes—
123#121×C83C2314yes—
124#121×C83C23112yes—
125#121×C83C23112yes—
126#121×C83C23112yes—
127#121×C83C23112yes—
128#121×C83C23112yes—
129#121×C83C23124yes—
130#121×C83C23124yes—
131#121×C83C23124yes—
132#121×C83C23148yes—
133#120×C83C23124yes—
134C4×Q8×C83C2314yes—
135C4×Q8×C83C2314yes—
136C4×Q8×C83C2314yes—
137C4×Q8×C83C2314yes—
138C4×Q8×C83C23112yes—
139C4×Q8×C83C2318yes—
140C4×Q8×C83C23124yes—
141C4×Q8×C83C23112yes—
142C4×Q8×C83C2314yes—
143C4×Q8×C83C2318yes—
144C4×Q8×C83C23112yes—
145C4×Q8×C83C23112yes—
146C4×Q8×C83C23112yes—
147C4×D4×C83C23112yes—
148C4×D4×C83C23112yes—
149C4×D4×C83C23112yes—
150C4×D4×C83C23112yes—
151C4×D4×C83C2318yes—
152C4×D4×C83C23112yes—
153C4×D4×C83C23124yes—
154C4×D4×C83C23112yes—
155C4×D4×C83C2314yes—
156C4×D4×C83C23124yes—
157C4×D4×C83C23124yes—
158C4×D4×C83C23124yes—
159C4×D4×C83C23124yes—
160C4×D4×C83C23124yes—
161C4×D4×C83C23112yes—
162C4×D4×C83C23112yes—
163C4×D4×C83C23112yes—
164#117×C83C23112yes—
165#117×C83C23112yes—
166#117×C83C23112yes—
167#117×C83C23124yes—
168#117×C83C2318yes—
169#117×C83C23124yes—
170#117×C83C23112yes—
171#117×C83C23112yes—
172#117×C83C23124yes—
173C2×C4⋊C4×C83C2313yes—
174C2×C4⋊C4×C83C2313yes—
175C2×C4⋊C4×C83C23124yes—
176C2×C22⋊C4×C83C2316yes—
177C2×C42×C83C2311yescharacteristic
178C2×C42×C83C2313yes—
179C2×C42×C83C2313yes—
180C2×C42×C83C2313yes—
181C2×C42×C83C2316yes—
182C2×C42×C83C2316yes—
183C2×C42×C83C2316yes—
184C2×C42×C83C2316yes—
185C2×C42×C83C23124yes—
186C24×C83C2413yes—
187#41×C83—216no—
188#41×C83—216no—
189#41×C83—232no—
190#41×C83—248no—
191#41×C83—424no—
192#41×C83—424no—
193C2×Q8×C83—232no—
194C2×Q8×C83#4118yescomplemented
195C2×Q8×C83C24112yes—
196C2×Q8×C83C2414yes—
197C2×Q8×C83C24112yes—
198C2×Q8×C83C2414yes—
199C2×D4×C83—212no—
200C2×D4×C83C2418yes—
201C2×D4×C83C24112yes—
202C2×D4×C83C24112yes—
203C2×D4×C83C2414yes—
204C2×D4×C83C24124yes—
205C2×D4×C83C24124yes—
206C2×D4×C83C24112yes—
207C22×C4×C83—212no—
208C22×C4×C83—46no—
209C22×C4×C83—46no—
210C22×C4×C83C2411yescharacteristic
211C22×C4×C83C2411yescharacteristic
212C22×C4×C83C2416yes—
213C22×C4×C83C2416yes—
214C22×C4×C83C2416yes—
215C22×C4×C83C24124yes—
216C22×C4×C83C2411yescharacteristic
217C22×C4×C83C2418yes—
218C22×C4×C83C2416yes—
219C22×C4×C83C2413yes—
220C22×C4×C83C2413yes—
221C22×C4×C83C2416yes—
222C22×C4×C83C2416yes—
223C22×C4×C83C24124yes—
224C22×C4×C83C2413yes—
225C4⋊C4×C83C24112yes—
226C4⋊C4×C83C24112yes—
227C4⋊C4×C83C24124yes—
228C4⋊C4×C83C24112yes—
229C4⋊C4×C83C2414yes—
230C4⋊C4×C83C2418yes—
231C4⋊C4×C83C24112yes—
232C4⋊C4×C83C2414yes—
233C4⋊C4×C83C2418yes—
234C4⋊C4×C83C2418yes—
235C4⋊C4×C83C2418yes—
236C4⋊C4×C83C24124yes—
237C4⋊C4×C83C24112yes—
238C4⋊C4×C83C24112yes—
239C22⋊C4×C83C24124yes—
240C22⋊C4×C83C2418yes—
241C22⋊C4×C83C2418yes—
242C22⋊C4×C83C24124yes—
243C22⋊C4×C83C2418yes—
244C22⋊C4×C83C2418yes—
245C22⋊C4×C83C2418yes—
246C22⋊C4×C83C24124yes—
247C22⋊C4×C83C24124yes—
248C22⋊C4×C83C24124yes—
249C42×C83C2411yescharacteristic
250C42×C83C2411yescharacteristic
251C42×C83C2416yes—
252C42×C83C2416yes—
253C42×C83C2416yes—
254C42×C83C2416yes—
255C42×C83C2416yes—
256C42×C83C24124yes—
257C42×C83C24124yes—
258C42×C83C2411yescharacteristic
259C42×C83C2416yes—
260C42×C83C2411yescharacteristic
261C42×C83C2418yes—
262C23×C83—26no—
263C23×C83—43no—
264C23×C83—43no—
265C23×C83C2516yes—
266C23×C83C2518yes—
267C23×C83C2511yescharacteristic
268Q8×C83—224no—
269Q8×C83—28no—
270Q8×C83—412no—
271Q8×C83C2×#41116yes—
272D4×C83—216no—
273D4×C83—224no—
274D4×C83—224no—
275D4×C83—28no—
276D4×C83—412no—
277D4×C83—424no—
278D4×C83—424no—
279C2×C4×C83—22no—
280C2×C4×C83—212no—
281C2×C4×C83—212no—
282C2×C4×C83—248no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83—212no—
286C2×C4×C83—212no—
287C2×C4×C83—216no—
288C2×C4×C83—43no—
289C2×C4×C83—46no—
290C2×C4×C83—46no—
291C2×C4×C83—43no—
292C2×C4×C83—424no—
293C2×C4×C83C2×#41112yes—
294C2×C4×C83C2511yescharacteristic
295C2×C4×C83C2511yescharacteristic
296C2×C4×C83C2511yescharacteristic
297C2×C4×C83C2511yescharacteristic
298C2×C4×C83C2516yes—
299C2×C4×C83C2518yes—
300C2×C4×C83C2518yes—
301C2×C4×C83C2516yes—
302C2×C4×C83C2518yes—
303C2×C4×C83C2516yes—
304C2×C4×C83C2511yescharacteristic
305C2×C4×C83C2511yescharacteristic
306C22×C83—21no—
307C22×C83—21no—
308C22×C83—28no—
309C22×C83—26no—
310C22×C83—26no—
311C22×C83—26no—
312C22×C83—28no—
313C22×C83—28no—
314C22×C83—412no—
315C22×C83C22×#4112yes—
316C22×C83C2611yescharacteristic
317C4×C83—21no—
318C4×C83—21no—
319C4×C83—28no—
320C4×C83—21no—
321C4×C83—21no—
322C4×C83—26no—
323C4×C83—26no—
324C4×C83—28no—
325C4×C83—28no—
326C4×C83C22×#41112yes—
327C4×C83#58512yes—
328C4×C83#58512yes—
329#62793C8311yesmaximal, characteristic, direct product factor, Sylow
330C2×C83—22no—
331C2×C83—48no—
332C2×C83—46no—
333C2×C83C23×#4111yescharacteristic
334C2×C83C2×#58511yescharacteristic
335C2×C83C2×#58511yescharacteristic
336#3524C2×C8318yescomplemented
337#3518C2×C8314yescomplemented
338#3517C2×C8314yescomplemented
339#3506C2×C8316yescomplemented
340#3502C2×C8311yescharacteristic, complemented
341#3497C2×C8311yescharacteristic, complemented
342#3493C2×C8316yescomplemented
343#3487C2×C8312yescomplemented
344#3483C2×C8314yescomplemented
345#3482C2×C8314yescomplemented
346#3480C2×C8318yescomplemented
347#3460C2×C8316yescomplemented
348#3444C2×C8316yescomplemented
349C4×2−1+4C2×C8312yescomplemented
350C2×C4×#41C2×C8311yescharacteristic, complemented
351C83#6279311yescharacteristic, direct product factor, Sylow
352C2×2−1+4C22×C8312yes—
353C22×#41C22×C8311yescharacteristic
354#559C22×C83124yescomplemented
355Q82C22×C8314yescomplemented
356#557C22×C8318yescomplemented
357#557C22×C8314yescomplemented
358#556C22×C83124yescomplemented
359#556C22×C83112yescomplemented
360#555C22×C83124yescomplemented
361#555C22×C83112yescomplemented
362#553C22×C83124yescomplemented
363#553C22×C83124yescomplemented
364#552C22×C83124yescomplemented
365#550C22×C8318yes—
366#550C22×C8318yes—
367#550C22×C8314yescomplemented
368#550C22×C83112yescomplemented
369D4×Q8C22×C8314yescomplemented
370#548C22×C8318yes—
371#548C22×C8318yes—
372#548C22×C8318yescomplemented
373#547C22×C83112yescomplemented
374#544C22×C8316yes—
375#542C22×C83124yescomplemented
376#540C22×C83124yescomplemented
377#538C22×C83124yes—
378#537C22×C8316yes—
379#535C22×C83112yes—
380#533C22×C8316yes—
381#533C22×C8316yescomplemented
382#533C22×C8316yescomplemented
383#532C22×C8316yes—
384#532C22×C8316yescomplemented
385#532C22×C8316yescomplemented
386#532C22×C83124yescomplemented
387#529C22×C8314yes—
388#529C22×C83112yes—
389#529C22×C83112yescomplemented
390#529C22×C83112yescomplemented
391#529C22×C83112yescomplemented
392#529C22×C83112yescomplemented
393#529C22×C83124yescomplemented
394#525C22×C83112yes—
395#525C22×C83112yes—
396#525C22×C83112yes—
397#520C22×C83112yes—
398#520C22×C8318yescomplemented
399#519C22×C8312yes—
400#519C22×C8318yescomplemented
401C4×#41C22×C8314yes—
402C4×#41C22×C8314yes—
403C4×#41C22×C8314yes—
404C4×#41C22×C8314yes—
405C4×#41C22×C83112yes—
406C4×#41C22×C8318yescomplemented
407C4×#41C22×C83112yescomplemented
408C4×#41C22×C83112yescomplemented
409C2×C4×Q8C22×C8311yescharacteristic
410C2×C4×Q8C22×C8311yescharacteristic
411C2×C4×Q8C22×C8318yescomplemented
412C2×C4×D4C22×C8313yes—
413C2×C4×D4C22×C8313yes—
414C2×#117C22×C8313yes—
415C22×C42C22×C8313yes—
4162−1+4—216no—
417C2×#41—28no—
418C2×#41C23×C8314yes—
419C2×#41C23×C8314yes—
420C2×#41C23×C83112yes—
421C2×#41C23×C8318yes—
422C2×#41C23×C83112yes—
423C2×#41C23×C83112yes—
424C22×Q8C23×C8318yes—
425C22×Q8C23×C8311yescharacteristic
426C22×D4C23×C8313yes—
427C23×C4C23×C8313yes—
428C23×C4C23×C8313yes—
429C23×C4C23×C8313yes—
430C4⋊Q8C23×C8316yes—
431C4⋊Q8C23×C8316yes—
432C4⋊Q8C23×C8316yes—
433C4⋊Q8C23×C83124yes—
434#127C23×C8316yes—
435#127C23×C83124yes—
436#126C23×C8318yes—
437#126C23×C83124yes—
438#126C23×C83148yes—
439#125C23×C8314yes—
440#125C23×C83112yes—
441#125C23×C83112yes—
442#125C23×C83124yes—
443#124C23×C8314yes—
444#124C23×C83112yes—
445#124C23×C83112yes—
446#124C23×C83124yes—
447#124C23×C83148yes—
448#123C23×C8318yes—
449#123C23×C83124yes—
450#123C23×C83124yes—
451#123C23×C83148yes—
452C22⋊Q8C23×C8314yes—
453C22⋊Q8C23×C83112yes—
454C22⋊Q8C23×C83112yes—
455C22⋊Q8C23×C83112yes—
456C22⋊Q8C23×C83112yes—
457C22⋊Q8C23×C83112yes—
458C22⋊Q8C23×C83124yes—
459#121C23×C8314yes—
460#121C23×C83112yes—
461#121C23×C83112yes—
462#121C23×C83112yes—
463#121C23×C83112yes—
464#121C23×C83112yes—
465#121C23×C83124yes—
466#121C23×C83124yes—
467#121C23×C83124yes—
468#121C23×C83148yes—
469#120C23×C83124yes—
470C4×Q8C23×C8314yes—
471C4×Q8C23×C8314yes—
472C4×Q8C23×C8314yes—
473C4×Q8C23×C8314yes—
474C4×Q8C23×C83112yes—
475C4×Q8C23×C8318yes—
476C4×Q8C23×C83124yes—
477C4×Q8C23×C83112yes—
478C4×Q8C23×C8314yes—
479C4×Q8C23×C8318yes—
480C4×Q8C23×C83112yes—
481C4×Q8C23×C83112yes—
482C4×Q8C23×C83112yes—
483C4×D4C23×C83112yes—
484C4×D4C23×C83112yes—
485C4×D4C23×C83112yes—
486C4×D4C23×C83112yes—
487C4×D4C23×C8318yes—
488C4×D4C23×C83112yes—
489C4×D4C23×C83124yes—
490C4×D4C23×C83112yes—
491C4×D4C23×C8314yes—
492C4×D4C23×C83124yes—
493C4×D4C23×C83124yes—
494C4×D4C23×C83124yes—
495C4×D4C23×C83124yes—
496C4×D4C23×C83124yes—
497C4×D4C23×C83112yes—
498C4×D4C23×C83112yes—
499C4×D4C23×C83112yes—
500#117C23×C83112yes—
501#117C23×C83112yes—
502#117C23×C83112yes—
503#117C23×C83124yes—
504#117C23×C8318yes—
505#117C23×C83124yes—
506#117C23×C83112yes—
507#117C23×C83112yes—
508#117C23×C83124yes—
509C2×C4⋊C4C23×C8313yes—
510C2×C4⋊C4C23×C8313yes—
511C2×C4⋊C4C23×C83124yes—
512C2×C22⋊C4C23×C8316yes—
513C2×C42C23×C8313yes—
514C2×C42C23×C8313yes—
515C2×C42C23×C8313yes—
516C2×C42C23×C83124yes—
517C2×C42C23×C8316yes—
518C2×C42C23×C8316yes—
519C2×C42C23×C8316yes—
520C2×C42C23×C8316yes—
521C2×C42C23×C8311yescharacteristic
522C24C24×C8313yes—
523#41—216no—
524#41—216no—
525#41—232no—
526#41—248no—
527#41—424no—
528#41—424no—
529C2×Q8—232no—
530C2×Q8#41×C8318yescomplemented
531C2×Q8C24×C83112yes—
532C2×Q8C24×C8314yes—
533C2×Q8C24×C83112yes—
534C2×Q8C24×C8314yes—
535C2×D4—212no—
536C2×D4C24×C8318yes—
537C2×D4C24×C83112yes—
538C2×D4C24×C83112yes—
539C2×D4C24×C8314yes—
540C2×D4C24×C83124yes—
541C2×D4C24×C83124yes—
542C2×D4C24×C83112yes—
543C22×C4—212no—
544C22×C4—46no—
545C22×C4—46no—
546C22×C4C24×C8311yescharacteristic
547C22×C4C24×C8311yescharacteristic
548C22×C4C24×C8311yescharacteristic
549C22×C4C24×C8318yes—
550C22×C4C24×C8316yes—
551C22×C4C24×C8316yes—
552C22×C4C24×C8316yes—
553C22×C4C24×C8316yes—
554C22×C4C24×C83124yes—
555C22×C4C24×C8313yes—
556C22×C4C24×C8313yes—
557C22×C4C24×C8316yes—
558C22×C4C24×C8316yes—
559C22×C4C24×C83124yes—
560C22×C4C24×C8313yes—
561C4⋊C4C24×C83112yes—
562C4⋊C4C24×C83112yes—
563C4⋊C4C24×C83124yes—
564C4⋊C4C24×C83112yes—
565C4⋊C4C24×C8314yes—
566C4⋊C4C24×C8318yes—
567C4⋊C4C24×C83112yes—
568C4⋊C4C24×C8314yes—
569C4⋊C4C24×C8318yes—
570C4⋊C4C24×C8318yes—
571C4⋊C4C24×C8318yes—
572C4⋊C4C24×C83124yes—
573C4⋊C4C24×C83112yes—
574C4⋊C4C24×C83112yes—
575C22⋊C4C24×C83124yes—
576C22⋊C4C24×C8318yes—
577C22⋊C4C24×C8318yes—
578C22⋊C4C24×C83124yes—
579C22⋊C4C24×C8318yes—
580C22⋊C4C24×C8318yes—
581C22⋊C4C24×C8318yes—
582C22⋊C4C24×C83124yes—
583C22⋊C4C24×C83124yes—
584C22⋊C4C24×C83124yes—
585C42C24×C8311yescharacteristic
586C42C24×C8316yes—
587C42C24×C8311yescharacteristic
588C42C24×C8311yescharacteristic
589C42C24×C8311yescharacteristic
590C42C24×C8316yes—
591C42C24×C8316yes—
592C42C24×C8318yes—
593C42C24×C8316yes—
594C42C24×C8316yes—
595C42C24×C8316yes—
596C42C24×C83124yes—
597C42C24×C83124yes—
598C23—26no—
599C23—43no—
600C23—43no—
601C23C25×C8316yes—
602C23C25×C8318yes—
603C23C25×C8311yescharacteristic
604Q8—224no—
605Q8—28no—
606Q8—412no—
607Q8C2×#41×C83116yes—
608D4—216no—
609D4—224no—
610D4—224no—
611D4—28no—
612D4—412no—
613D4—424no—
614D4—424no—
615C2×C4—22no—
616C2×C4—212no—
617C2×C4—212no—
618C2×C4—248no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—212no—
622C2×C4—212no—
623C2×C4—216no—
624C2×C4—43no—
625C2×C4—46no—
626C2×C4—46no—
627C2×C4—43no—
628C2×C4—424no—
629C2×C4C2×#41×C83112yes—
630C2×C4C25×C8311yescharacteristic
631C2×C4C25×C8311yescharacteristic
632C2×C4C25×C8311yescharacteristic
633C2×C4C25×C8316yes—
634C2×C4C25×C8311yescharacteristic
635C2×C4C25×C8318yes—
636C2×C4C25×C8318yes—
637C2×C4C25×C8316yes—
638C2×C4C25×C8318yes—
639C2×C4C25×C8316yes—
640C2×C4C25×C8311yescharacteristic
641C2×C4C25×C8311yescharacteristic
642C22—21no—
643C22—21no—
644C22—28no—
645C22—26no—
646C22—26no—
647C22—26no—
648C22—28no—
649C22—28no—
650C22—412no—
651C22C22×#41×C8312yes—
652C22C26×C8311yescharacteristic
653C4—21no—
654C4—21no—
655C4—28no—
656C4—21no—
657C4—21no—
658C4—26no—
659C4—26no—
660C4—28no—
661C4—28no—
662C4C22×#41×C83112yes—
663C4#585×C8312yes—
664C4#585×C8312yes—
665C2—22no—
666C2—46no—
667C2—48no—
668C2C23×#41×C8311yescharacteristic
669C2C2×#585×C8311yescharacteristic
670C2C2×#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×#3524C2semidirect
2. C83×#3518C2semidirect
3. C83×#3517C2semidirect
4. C83×#3506C2semidirect
5. C83×#3502C2semidirect
6. C83×#3497C2semidirect
7. C83×#3493C2semidirect
8. C83×#3487C2semidirect
9. C83×#3483C2semidirect
10. C83×#3482C2semidirect
11. C83×#3480C2semidirect
12. C83×#3460C2semidirect
13. C83×#3444C2semidirect
14. C4×2−1+4×C83C2semidirect
15. C2×C4×#41×C83C2semidirect
18. #559×C83C22semidirect
19. Q82×C83C22semidirect
20. #557×C83C22semidirect
21. #557×C83C22semidirect
22. #556×C83C22semidirect
23. #556×C83C22semidirect
24. #555×C83C22semidirect
25. #555×C83C22semidirect
26. #553×C83C22semidirect
27. #553×C83C22semidirect
28. #552×C83C22semidirect
31. #550×C83C22semidirect
32. #550×C83C22semidirect
33. D4×Q8×C83C22semidirect
36. #548×C83C22semidirect
37. #547×C83C22semidirect
39. #542×C83C22semidirect
40. #540×C83C22semidirect
45. #533×C83C22semidirect
46. #533×C83C22semidirect
48. #532×C83C22semidirect
49. #532×C83C22semidirect
50. #532×C83C22semidirect
53. #529×C83C22semidirect
54. #529×C83C22semidirect
55. #529×C83C22semidirect
56. #529×C83C22semidirect
57. #529×C83C22semidirect
62. #520×C83C22semidirect
64. #519×C83C22semidirect
70. C4×#41×C83C22semidirect
71. C4×#41×C83C22semidirect
72. C4×#41×C83C22semidirect
75. C2×C4×Q8×C83C22semidirect
194. C2×Q8×C83#41semidirect
329. #62793C83direct (N × H)
336. #3524C2×C83semidirect
337. #3518C2×C83semidirect
338. #3517C2×C83semidirect
339. #3506C2×C83semidirect
340. #3502C2×C83semidirect
341. #3497C2×C83semidirect
342. #3493C2×C83semidirect
343. #3487C2×C83semidirect
344. #3483C2×C83semidirect
345. #3482C2×C83semidirect
346. #3480C2×C83semidirect
347. #3460C2×C83semidirect
348. #3444C2×C83semidirect
349. C4×2−1+4C2×C83semidirect
350. C2×C4×#41C2×C83semidirect
351. C83#62793direct (N × H)
354. #559C22×C83semidirect
355. Q82C22×C83semidirect
356. #557C22×C83semidirect
357. #557C22×C83semidirect
358. #556C22×C83semidirect
359. #556C22×C83semidirect
360. #555C22×C83semidirect
361. #555C22×C83semidirect
362. #553C22×C83semidirect
363. #553C22×C83semidirect
364. #552C22×C83semidirect
367. #550C22×C83semidirect
368. #550C22×C83semidirect
369. D4×Q8C22×C83semidirect
372. #548C22×C83semidirect
373. #547C22×C83semidirect
375. #542C22×C83semidirect
376. #540C22×C83semidirect
381. #533C22×C83semidirect
382. #533C22×C83semidirect
384. #532C22×C83semidirect
385. #532C22×C83semidirect
386. #532C22×C83semidirect
389. #529C22×C83semidirect
390. #529C22×C83semidirect
391. #529C22×C83semidirect
392. #529C22×C83semidirect
393. #529C22×C83semidirect
398. #520C22×C83semidirect
400. #519C22×C83semidirect
406. C4×#41C22×C83semidirect
407. C4×#41C22×C83semidirect
408. C4×#41C22×C83semidirect
411. C2×C4×Q8C22×C83semidirect
530. C2×Q8#41×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#35242
C83×#35182
C83×#35172
C83×#35062
C83×#35022
C83×#34972
C83×#34932
C83×#34872
C83×#34832
C83×#34822
C83×#34802
C83×#34602
C83×#34442
C4×2−1+4×C832
C2×C4×#41×C832
#6279383