Finite Group Databasebeta

← C41×#62788 #23838989

Subgroups — C41×#62788 #23838989

Order 10496.

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
1C41×#3523C214yesmaximal, complemented
2C41×#3522C214yesmaximal, complemented
3C41×#3516C218yesmaximal, complemented
4C41×#3507C216yesmaximal, complemented
5C41×#3502C211yesmaximal, characteristic, complemented
6C41×#3497C211yesmaximal, characteristic, complemented
7C41×#3492C216yesmaximal, complemented
8C41×#3486C212yesmaximal, complemented
9C41×#3482C218yesmaximal, complemented
10C41×#3480C214yesmaximal, complemented
11Q8×#41×C41C214yesmaximal, complemented
12C41×#3461C216yesmaximal, complemented
13C41×#3444C216yesmaximal, complemented
14C4×2−1+4×C41C212yesmaximal, complemented
15C22×C4×Q8×C41C211yesmaximal, characteristic, complemented
16C2×2−1+4×C41C2212yes—
17C23×Q8×C41C2211yescharacteristic
18C41×#559C22112yescomplemented
19Q82×C41C2214yescomplemented
20C41×#557C22112yescomplemented
21C41×#557C2214yescomplemented
22C41×#557C2218yescomplemented
23C41×#556C22112yescomplemented
24C41×#556C22124yescomplemented
25C41×#554C22124yes—
26C41×#554C22112yescomplemented
27C41×#553C22124yes—
28C41×#552C22124yes—
29C41×#552C22124yescomplemented
30C41×#550C2214yescomplemented
31D4×Q8×C41C2218yes—
32D4×Q8×C41C2218yes—
33D4×Q8×C41C2214yescomplemented
34C41×#548C2218yes—
35C41×#548C2218yes—
36C41×#548C2218yescomplemented
37C41×#547C22124yes—
38C41×#544C2216yes—
39C41×#542C22124yescomplemented
40C41×#541C22124yescomplemented
41C41×#539C22124yes—
42C41×#537C2216yes—
43C41×#536C22112yes—
44C41×#533C2216yes—
45C41×#533C2216yes—
46C41×#533C2216yes—
47C41×#533C22124yescomplemented
48C41×#532C2216yes—
49C41×#532C2216yes—
50C41×#532C2216yes—
51C41×#529C22112yes—
52C41×#529C22112yes—
53C41×#529C22112yes—
54C41×#529C22112yes—
55C41×#529C22112yes—
56C41×#529C22112yes—
57C41×#529C22124yescomplemented
58C41×#525C2214yes—
59C41×#525C22112yes—
60C41×#525C22112yes—
61C41×#520C22112yes—
62C41×#520C2218yescomplemented
63C41×#519C2212yes—
64C41×#519C2218yescomplemented
65C4×#41×C41C22112yes—
66C4×#41×C41C22112yes—
67C4×#41×C41C22112yes—
68C4×#41×C41C2218yescomplemented
69C2×C4×Q8×C41C2211yescharacteristic
70C2×C4×Q8×C41C2213yes—
71C2×C4×Q8×C41C2214yes—
72C2×C4×Q8×C41C2214yes—
73C2×C4×Q8×C41C2211yescharacteristic
74C2×C4×Q8×C41C2213yes—
75C2×C4×Q8×C41C2214yes—
76C2×C4×Q8×C41C2214yes—
77C2×C4×Q8×C41C2218yescomplemented
78C22×C4⋊C4×C41C2213yes—
79C22×C42×C41C2213yes—
802−1+4×C41—216no—
81C2×#41×C41C2314yes—
82C2×#41×C41C23112yes—
83C2×#41×C41C2318yes—
84C2×#41×C41C23112yes—
85C22×Q8×C41—28no—
86C22×Q8×C41C2313yes—
87C22×Q8×C41C2314yes—
88C22×Q8×C41C2314yes—
89C22×Q8×C41C2318yes—
90C22×Q8×C41C2311yescharacteristic
91C23×C4×C41C2311yescharacteristic
92C23×C4×C41C2313yes—
93C23×C4×C41C2313yes—
94C4⋊Q8×C41C2316yes—
95C4⋊Q8×C41C2316yes—
96C4⋊Q8×C41C2316yes—
97C4⋊Q8×C41C23124yes—
98C4⋊Q8×C41C23124yes—
99#127×C41C2316yes—
100#126×C41C23124yes—
101#126×C41C23124yes—
102#126×C41C23148yes—
103#125×C41C23112yes—
104#125×C41C23112yes—
105#125×C41C23112yes—
106#125×C41C23124yes—
107#125×C41C23148yes—
108#124×C41C23112yes—
109#124×C41C23112yes—
110#124×C41C23112yes—
111#124×C41C23124yes—
112#123×C41C2318yes—
113#123×C41C23124yes—
114#123×C41C23124yes—
115#123×C41C23148yes—
116C22⋊Q8×C41C2314yes—
117C22⋊Q8×C41C2314yes—
118C22⋊Q8×C41C23112yes—
119C22⋊Q8×C41C23112yes—
120C22⋊Q8×C41C23112yes—
121C22⋊Q8×C41C23112yes—
122C22⋊Q8×C41C23124yes—
123C22⋊Q8×C41C23124yes—
124C22⋊Q8×C41C23124yes—
125C22⋊Q8×C41C23148yes—
126#121×C41C2314yes—
127#121×C41C2314yes—
128#121×C41C23112yes—
129#121×C41C23112yes—
130#121×C41C23112yes—
131#121×C41C23112yes—
132#121×C41C23124yes—
133#120×C41C2318yes—
134C4×Q8×C41C2314yes—
135C4×Q8×C41C2314yes—
136C4×Q8×C41C23112yes—
137C4×Q8×C41C23112yes—
138C4×Q8×C41C2314yes—
139C4×Q8×C41C2314yes—
140C4×Q8×C41C23112yes—
141C4×Q8×C41C23112yes—
142C4×Q8×C41C23112yes—
143C4×Q8×C41C2318yes—
144C4×Q8×C41C23124yes—
145C4×Q8×C41C23112yes—
146C4×Q8×C41C23112yes—
147C4×Q8×C41C23112yes—
148C4×Q8×C41C23112yes—
149C4×Q8×C41C23112yes—
150C4×Q8×C41C2318yes—
151C4×D4×C41C2318yes—
152C4×D4×C41C2318yes—
153C4×D4×C41C23112yes—
154C4×D4×C41C23124yes—
155C4×D4×C41C23112yes—
156C4×D4×C41C23124yes—
157C4×D4×C41C23124yes—
158C4×D4×C41C23124yes—
159C4×D4×C41C23112yes—
160C4×D4×C41C23112yes—
161C4×D4×C41C23112yes—
162C4×D4×C41C23112yes—
163C4×D4×C41C23124yes—
164#117×C41C2314yes—
165#117×C41C23112yes—
166#117×C41C23124yes—
167#117×C41C23112yes—
168#117×C41C23124yes—
169#117×C41C23124yes—
170#117×C41C23124yes—
171C2×C4⋊C4×C41C2313yes—
172C2×C4⋊C4×C41C2313yes—
173C2×C4⋊C4×C41C2316yes—
174C2×C4⋊C4×C41C23112yes—
175C2×C4⋊C4×C41C23112yes—
176C2×C4⋊C4×C41C23124yes—
177C2×C42×C41C2313yes—
178C2×C42×C41C2316yes—
179C2×C42×C41C2316yes—
180C2×C42×C41C2316yes—
181C2×C42×C41C2313yes—
182C2×C42×C41C2313yes—
183C2×C42×C41C2316yes—
184C2×C42×C41C2313yes—
185C2×C42×C41C23124yes—
186C24×C41C2411yescharacteristic
187#41×C41—232no—
188#41×C41—248no—
189#41×C41—216no—
190#41×C41—424no—
191C2×Q8×C41—216no—
192C2×Q8×C41—216no—
193C2×Q8×C41—232no—
194C2×Q8×C41—212no—
195C2×Q8×C41#4118yescomplemented
196C2×Q8×C41C2414yes—
197C2×Q8×C41C24112yes—
198C2×Q8×C41C24112yes—
199C2×Q8×C41C24112yes—
200C2×Q8×C41C2414yes—
201C2×D4×C41C2418yes—
202C2×D4×C41C2414yes—
203C2×D4×C41C2418yes—
204C2×D4×C41C2418yes—
205C2×D4×C41C24112yes—
206C2×D4×C41C24112yes—
207C22×C4×C41—212no—
208C22×C4×C41—24no—
209C22×C4×C41—46no—
210C22×C4×C41C2411yescharacteristic
211C22×C4×C41C2411yescharacteristic
212C22×C4×C41C2411yescharacteristic
213C22×C4×C41C2416yes—
214C22×C4×C41C2416yes—
215C22×C4×C41C2416yes—
216C22×C4×C41C2413yes—
217C22×C4×C41C24124yes—
218C22×C4×C41C2411yescharacteristic
219C22×C4×C41C2411yescharacteristic
220C22×C4×C41C2418yes—
221C22×C4×C41C2413yes—
222C22×C4×C41C2416yes—
223C22×C4×C41C2413yes—
224C22×C4×C41C24124yes—
225C22×C4×C41C2413yes—
226C22×C4×C41C2411yescharacteristic
227C4⋊C4×C41C24112yes—
228C4⋊C4×C41C24112yes—
229C4⋊C4×C41C24124yes—
230C4⋊C4×C41C24112yes—
231C4⋊C4×C41C24124yes—
232C4⋊C4×C41C24112yes—
233C4⋊C4×C41C2418yes—
234C4⋊C4×C41C2418yes—
235C4⋊C4×C41C2414yes—
236C4⋊C4×C41C2414yes—
237C4⋊C4×C41C24112yes—
238C4⋊C4×C41C24112yes—
239C4⋊C4×C41C24124yes—
240C4⋊C4×C41C24124yes—
241C4⋊C4×C41C24124yes—
242C22⋊C4×C41C2418yes—
243C22⋊C4×C41C2418yes—
244C22⋊C4×C41C24124yes—
245C22⋊C4×C41C2418yes—
246C22⋊C4×C41C2418yes—
247C22⋊C4×C41C2418yes—
248C22⋊C4×C41C24124yes—
249C22⋊C4×C41C24124yes—
250C22⋊C4×C41C24124yes—
251C42×C41C2416yes—
252C42×C41C2416yes—
253C42×C41C2416yes—
254C42×C41C2416yes—
255C42×C41C2416yes—
256C42×C41C2416yes—
257C42×C41C24124yes—
258C42×C41C24124yes—
259C42×C41C2416yes—
260C42×C41C2416yes—
261C42×C41C2418yes—
262C23×C41—22no—
263C23×C41—22no—
264C23×C41—22no—
265C23×C41C2518yes—
266C23×C41C2511yescharacteristic
267C23×C41C2511yescharacteristic
268C23×C41C2511yescharacteristic
269Q8×C41—224no—
270Q8×C41—224no—
271Q8×C41—28no—
272Q8×C41—412no—
273Q8×C41C2×#41116yes—
274D4×C41—216no—
275D4×C41—216no—
276D4×C41—216no—
277D4×C41—224no—
278D4×C41—28no—
279D4×C41—412no—
280C2×C4×C41—26no—
281C2×C4×C41—22no—
282C2×C4×C41—212no—
283C2×C4×C41—212no—
284C2×C4×C41—212no—
285C2×C4×C41—248no—
286C2×C4×C41—22no—
287C2×C4×C41—22no—
288C2×C4×C41—22no—
289C2×C4×C41—22no—
290C2×C4×C41—216no—
291C2×C4×C41—43no—
292C2×C4×C41—46no—
293C2×C4×C41—43no—
294C2×C4×C41—424no—
295C2×C4×C41C2×#41112yes—
296C2×C4×C412−1+414yescomplemented
297C2×C4×C41C2511yescharacteristic
298C2×C4×C41C2511yescharacteristic
299C2×C4×C41C2516yes—
300C2×C4×C41C2518yes—
301C2×C4×C41C2516yes—
302C2×C4×C41C2518yes—
303C2×C4×C41C2518yes—
304C2×C4×C41C2516yes—
305C2×C4×C41C2516yes—
306C2×C4×C41C2511yescharacteristic
307C2×C4×C41C2511yescharacteristic
308#62788C4111yesmaximal, characteristic, direct product factor, Sylow
309C22×C41—28no—
310C22×C41—21no—
311C22×C41—21no—
312C22×C41—21no—
313C22×C41—21no—
314C22×C41—21no—
315C22×C41—21no—
316C22×C41—28no—
317C22×C41—28no—
318C22×C41—28no—
319C22×C41C22×#4112yes—
320C22×C41C2×2−1+412yes—
321C22×C41#58512yes—
322C22×C41C2611yescharacteristic
323C4×C41—28no—
324C4×C41—26no—
325C4×C41—21no—
326C4×C41—21no—
327C4×C41—28no—
328C4×C41—26no—
329C4×C41—26no—
330C4×C41—28no—
331C4×C41C22×#41112yes—
332C4×C41C2×2−1+412yes—
333C4×C41C2×2−1+412yes—
334#3523C2×C4114yescomplemented
335#3522C2×C4114yescomplemented
336#3516C2×C4118yescomplemented
337#3507C2×C4116yescomplemented
338#3502C2×C4111yescharacteristic, complemented
339#3497C2×C4111yescharacteristic, complemented
340#3492C2×C4116yescomplemented
341#3486C2×C4112yescomplemented
342#3482C2×C4118yescomplemented
343#3480C2×C4114yescomplemented
344Q8×#41C2×C4114yescomplemented
345#3461C2×C4116yescomplemented
346#3444C2×C4116yescomplemented
347C4×2−1+4C2×C4112yescomplemented
348C22×C4×Q8C2×C4111yescharacteristic, complemented
349C2×C41—22no—
350C2×C41—22no—
351C2×C41—22no—
352C2×C41—48no—
353C2×C41C23×#4111yescharacteristic
354C2×C41C22×2−1+411yescharacteristic
355C2×C41C2×#58511yescharacteristic
356C2×2−1+4C22×C4112yes—
357C23×Q8C22×C4111yescharacteristic
358#559C22×C41112yescomplemented
359Q82C22×C4114yescomplemented
360#557C22×C41112yescomplemented
361#557C22×C4114yescomplemented
362#557C22×C4118yescomplemented
363#556C22×C41112yescomplemented
364#556C22×C41124yescomplemented
365#554C22×C41124yes—
366#554C22×C41112yescomplemented
367#553C22×C41124yes—
368#552C22×C41124yes—
369#552C22×C41124yescomplemented
370#550C22×C4114yescomplemented
371D4×Q8C22×C4118yes—
372D4×Q8C22×C4118yes—
373D4×Q8C22×C4114yescomplemented
374#548C22×C4118yes—
375#548C22×C4118yes—
376#548C22×C4118yescomplemented
377#547C22×C41124yes—
378#544C22×C4116yes—
379#542C22×C41124yescomplemented
380#541C22×C41124yescomplemented
381#539C22×C41124yes—
382#537C22×C4116yes—
383#536C22×C41112yes—
384#533C22×C4116yes—
385#533C22×C4116yes—
386#533C22×C4116yes—
387#533C22×C41124yescomplemented
388#532C22×C4116yes—
389#532C22×C4116yes—
390#532C22×C4116yes—
391#529C22×C41112yes—
392#529C22×C41112yes—
393#529C22×C41112yes—
394#529C22×C41112yes—
395#529C22×C41112yes—
396#529C22×C41112yes—
397#529C22×C41124yescomplemented
398#525C22×C4114yes—
399#525C22×C41112yes—
400#525C22×C41112yes—
401#520C22×C41112yes—
402#520C22×C4118yescomplemented
403#519C22×C4112yes—
404#519C22×C4118yescomplemented
405C4×#41C22×C41112yes—
406C4×#41C22×C41112yes—
407C4×#41C22×C41112yes—
408C4×#41C22×C4118yescomplemented
409C2×C4×Q8C22×C4111yescharacteristic
410C2×C4×Q8C22×C4113yes—
411C2×C4×Q8C22×C4114yes—
412C2×C4×Q8C22×C4114yes—
413C2×C4×Q8C22×C4111yescharacteristic
414C2×C4×Q8C22×C4113yes—
415C2×C4×Q8C22×C4114yes—
416C2×C4×Q8C22×C4114yes—
417C2×C4×Q8C22×C4118yescomplemented
418C22×C4⋊C4C22×C4113yes—
419C22×C42C22×C4113yes—
420C41#6278811yescharacteristic, direct product factor, Sylow
4212−1+4—216no—
422C2×#41C23×C4114yes—
423C2×#41C23×C41112yes—
424C2×#41C23×C4118yes—
425C2×#41C23×C41112yes—
426C22×Q8—28no—
427C22×Q8C23×C4113yes—
428C22×Q8C23×C4114yes—
429C22×Q8C23×C4114yes—
430C22×Q8C23×C4118yes—
431C22×Q8C23×C4111yescharacteristic
432C23×C4C23×C4113yes—
433C23×C4C23×C4111yescharacteristic
434C23×C4C23×C4113yes—
435C4⋊Q8C23×C4116yes—
436C4⋊Q8C23×C4116yes—
437C4⋊Q8C23×C4116yes—
438C4⋊Q8C23×C41124yes—
439C4⋊Q8C23×C41124yes—
440#127C23×C4116yes—
441#126C23×C41124yes—
442#126C23×C41124yes—
443#126C23×C41148yes—
444#125C23×C41112yes—
445#125C23×C41112yes—
446#125C23×C41112yes—
447#125C23×C41124yes—
448#125C23×C41148yes—
449#124C23×C41112yes—
450#124C23×C41112yes—
451#124C23×C41112yes—
452#124C23×C41124yes—
453#123C23×C4118yes—
454#123C23×C41124yes—
455#123C23×C41124yes—
456#123C23×C41148yes—
457C22⋊Q8C23×C4114yes—
458C22⋊Q8C23×C4114yes—
459C22⋊Q8C23×C41112yes—
460C22⋊Q8C23×C41112yes—
461C22⋊Q8C23×C41112yes—
462C22⋊Q8C23×C41112yes—
463C22⋊Q8C23×C41124yes—
464C22⋊Q8C23×C41124yes—
465C22⋊Q8C23×C41124yes—
466C22⋊Q8C23×C41148yes—
467#121C23×C4114yes—
468#121C23×C4114yes—
469#121C23×C41112yes—
470#121C23×C41112yes—
471#121C23×C41112yes—
472#121C23×C41112yes—
473#121C23×C41124yes—
474#120C23×C4118yes—
475C4×Q8C23×C4114yes—
476C4×Q8C23×C4114yes—
477C4×Q8C23×C41112yes—
478C4×Q8C23×C41112yes—
479C4×Q8C23×C4114yes—
480C4×Q8C23×C4114yes—
481C4×Q8C23×C41112yes—
482C4×Q8C23×C41112yes—
483C4×Q8C23×C41112yes—
484C4×Q8C23×C4118yes—
485C4×Q8C23×C41124yes—
486C4×Q8C23×C41112yes—
487C4×Q8C23×C41112yes—
488C4×Q8C23×C41112yes—
489C4×Q8C23×C41112yes—
490C4×Q8C23×C41112yes—
491C4×Q8C23×C4118yes—
492C4×D4C23×C4118yes—
493C4×D4C23×C4118yes—
494C4×D4C23×C41112yes—
495C4×D4C23×C41124yes—
496C4×D4C23×C41112yes—
497C4×D4C23×C41124yes—
498C4×D4C23×C41124yes—
499C4×D4C23×C41124yes—
500C4×D4C23×C41112yes—
501C4×D4C23×C41112yes—
502C4×D4C23×C41112yes—
503C4×D4C23×C41112yes—
504C4×D4C23×C41124yes—
505#117C23×C4114yes—
506#117C23×C41112yes—
507#117C23×C41124yes—
508#117C23×C41112yes—
509#117C23×C41124yes—
510#117C23×C41124yes—
511#117C23×C41124yes—
512C2×C4⋊C4C23×C4113yes—
513C2×C4⋊C4C23×C4113yes—
514C2×C4⋊C4C23×C4116yes—
515C2×C4⋊C4C23×C41112yes—
516C2×C4⋊C4C23×C41112yes—
517C2×C4⋊C4C23×C41124yes—
518C2×C42C23×C4113yes—
519C2×C42C23×C4116yes—
520C2×C42C23×C4116yes—
521C2×C42C23×C4113yes—
522C2×C42C23×C4116yes—
523C2×C42C23×C4113yes—
524C2×C42C23×C4116yes—
525C2×C42C23×C4113yes—
526C2×C42C23×C41124yes—
527C24C24×C4111yescharacteristic
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×C4118yescomplemented
537C2×Q8C24×C4114yes—
538C2×Q8C24×C41112yes—
539C2×Q8C24×C41112yes—
540C2×Q8C24×C41112yes—
541C2×Q8C24×C4114yes—
542C2×D4C24×C4118yes—
543C2×D4C24×C4114yes—
544C2×D4C24×C4118yes—
545C2×D4C24×C4118yes—
546C2×D4C24×C41112yes—
547C2×D4C24×C41112yes—
548C22×C4—212no—
549C22×C4—24no—
550C22×C4—46no—
551C22×C4C24×C4111yescharacteristic
552C22×C4C24×C4111yescharacteristic
553C22×C4C24×C4111yescharacteristic
554C22×C4C24×C4111yescharacteristic
555C22×C4C24×C4111yescharacteristic
556C22×C4C24×C4118yes—
557C22×C4C24×C4116yes—
558C22×C4C24×C4116yes—
559C22×C4C24×C4116yes—
560C22×C4C24×C4113yes—
561C22×C4C24×C41124yes—
562C22×C4C24×C4113yes—
563C22×C4C24×C4116yes—
564C22×C4C24×C4113yes—
565C22×C4C24×C41124yes—
566C22×C4C24×C4113yes—
567C22×C4C24×C4111yescharacteristic
568C4⋊C4C24×C41112yes—
569C4⋊C4C24×C41112yes—
570C4⋊C4C24×C41124yes—
571C4⋊C4C24×C41112yes—
572C4⋊C4C24×C41124yes—
573C4⋊C4C24×C41112yes—
574C4⋊C4C24×C4118yes—
575C4⋊C4C24×C4118yes—
576C4⋊C4C24×C4114yes—
577C4⋊C4C24×C4114yes—
578C4⋊C4C24×C41112yes—
579C4⋊C4C24×C41112yes—
580C4⋊C4C24×C41124yes—
581C4⋊C4C24×C41124yes—
582C4⋊C4C24×C41124yes—
583C22⋊C4C24×C4118yes—
584C22⋊C4C24×C4118yes—
585C22⋊C4C24×C41124yes—
586C22⋊C4C24×C4118yes—
587C22⋊C4C24×C4118yes—
588C22⋊C4C24×C4118yes—
589C22⋊C4C24×C41124yes—
590C22⋊C4C24×C41124yes—
591C22⋊C4C24×C41124yes—
592C42C24×C4116yes—
593C42C24×C4116yes—
594C42C24×C4116yes—
595C42C24×C4118yes—
596C42C24×C4116yes—
597C42C24×C4116yes—
598C42C24×C4116yes—
599C42C24×C4116yes—
600C42C24×C4116yes—
601C42C24×C41124yes—
602C42C24×C41124yes—
603C23—22no—
604C23—22no—
605C23—22no—
606C23C25×C4118yes—
607C23C25×C4111yescharacteristic
608C23C25×C4111yescharacteristic
609C23C25×C4111yescharacteristic
610Q8—224no—
611Q8—224no—
612Q8—28no—
613Q8—412no—
614Q8C2×#41×C41116yes—
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×C41112yes—
637C2×C42−1+4×C4114yescomplemented
638C2×C4C25×C4111yescharacteristic
639C2×C4C25×C4111yescharacteristic
640C2×C4C25×C4116yes—
641C2×C4C25×C4118yes—
642C2×C4C25×C4116yes—
643C2×C4C25×C4118yes—
644C2×C4C25×C4118yes—
645C2×C4C25×C4116yes—
646C2×C4C25×C4116yes—
647C2×C4C25×C4111yescharacteristic
648C2×C4C25×C4111yescharacteristic
649C22—28no—
650C22—21no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—28no—
657C22—28no—
658C22—28no—
659C22C22×#41×C4112yes—
660C22C2×2−1+4×C4112yes—
661C22C41×#58512yes—
662C22C26×C4111yescharacteristic
663C4—28no—
664C4—26no—
665C4—21no—
666C4—21no—
667C4—28no—
668C4—26no—
669C4—26no—
670C4—28no—
671C4C22×#41×C41112yes—
672C4C2×2−1+4×C4112yes—
673C4C2×2−1+4×C4112yes—
674C2—22no—
675C2—22no—
676C2—22no—
677C2—48no—
678C2C23×#41×C4111yescharacteristic
679C2C22×2−1+4×C4111yescharacteristic
680C2C2×C41×#58511yescharacteristic
subgroupG/H
centerC2×C4×C41C25
commutator, Frattini, cosocleC22C26×C41
socleC22×C41C26
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3523C2semidirect
2. C41×#3522C2semidirect
3. C41×#3516C2semidirect
4. C41×#3507C2semidirect
5. C41×#3502C2semidirect
6. C41×#3497C2semidirect
7. C41×#3492C2semidirect
8. C41×#3486C2semidirect
9. C41×#3482C2semidirect
10. C41×#3480C2semidirect
11. Q8×#41×C41C2semidirect
12. C41×#3461C2semidirect
13. C41×#3444C2semidirect
14. C4×2−1+4×C41C2semidirect
15. C22×C4×Q8×C41C2semidirect
18. C41×#559C22semidirect
19. Q82×C41C22semidirect
20. C41×#557C22semidirect
21. C41×#557C22semidirect
22. C41×#557C22semidirect
23. C41×#556C22semidirect
24. C41×#556C22semidirect
26. C41×#554C22semidirect
29. C41×#552C22semidirect
30. C41×#550C22semidirect
33. D4×Q8×C41C22semidirect
36. C41×#548C22semidirect
39. C41×#542C22semidirect
40. C41×#541C22semidirect
47. C41×#533C22semidirect
57. C41×#529C22semidirect
62. C41×#520C22semidirect
64. C41×#519C22semidirect
68. C4×#41×C41C22semidirect
77. C2×C4×Q8×C41C22semidirect
195. C2×Q8×C41#41semidirect
296. C2×C4×C412−1+4semidirect
308. #62788C41direct (N × H)
334. #3523C2×C41semidirect
335. #3522C2×C41semidirect
336. #3516C2×C41semidirect
337. #3507C2×C41semidirect
338. #3502C2×C41semidirect
339. #3497C2×C41semidirect
340. #3492C2×C41semidirect
341. #3486C2×C41semidirect
342. #3482C2×C41semidirect
343. #3480C2×C41semidirect
344. Q8×#41C2×C41semidirect
345. #3461C2×C41semidirect
346. #3444C2×C41semidirect
347. C4×2−1+4C2×C41semidirect
348. C22×C4×Q8C2×C41semidirect
358. #559C22×C41semidirect
359. Q82C22×C41semidirect
360. #557C22×C41semidirect
361. #557C22×C41semidirect
362. #557C22×C41semidirect
363. #556C22×C41semidirect
364. #556C22×C41semidirect
366. #554C22×C41semidirect
369. #552C22×C41semidirect
370. #550C22×C41semidirect
373. D4×Q8C22×C41semidirect
376. #548C22×C41semidirect
379. #542C22×C41semidirect
380. #541C22×C41semidirect
387. #533C22×C41semidirect
397. #529C22×C41semidirect
402. #520C22×C41semidirect
404. #519C22×C41semidirect
408. C4×#41C22×C41semidirect
417. C2×C4×Q8C22×C41semidirect
420. C41#62788direct (N × H)
536. C2×Q8#41×C41semidirect
637. C2×C42−1+4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#35232
C41×#35222
C41×#35162
C41×#35072
C41×#35022
C41×#34972
C41×#34922
C41×#34862
C41×#34822
C41×#34802
Q8×#41×C412
C41×#34612
C41×#34442
C4×2−1+4×C412
C22×C4×Q8×C412
#6278841