Finite Group Databasebeta

← C41×#18974 #23795175

Subgroups — C41×#18974 #23795175

Order 10496.

930 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3546C211yesmaximal, characteristic
2C41×#3254C211yesmaximal, characteristic, complemented
3C41×#3248C211yesmaximal, characteristic, complemented
4C41×#3228C211yesmaximal, characteristic, complemented
5C41×#1654C211yesmaximal, characteristic, complemented
6C41×#1652C211yesmaximal, characteristic, complemented
7C41×#1650C211yesmaximal, characteristic, complemented
8C41×#1647C211yesmaximal, characteristic, complemented
9C41×#1642C211yesmaximal, characteristic, complemented
10C41×#1641C211yesmaximal, characteristic, complemented
11C41×#1639C211yesmaximal, characteristic, complemented
12C41×#1639C211yesmaximal, characteristic, complemented
13C41×#1547C211yesmaximal, characteristic, complemented
14C41×#1495C211yesmaximal, characteristic, complemented
15C41×#1480C211yesmaximal, characteristic, complemented
16C41×#560—22no—
17C41×#556C2211yescharacteristic
18C41×#553—21no—
19C41×#550—21no—
20C41×#550C2211yescharacteristic
21C41×#547C2211yescharacteristic
22C41×#546—21no—
23C41×#546—21no—
24D42×C41C2211yescharacteristic
25C41×#542—21no—
26C41×#538—22no—
27C41×#537—21no—
28C41×#535—21no—
29C41×#535—21no—
30C41×#533C2211yescharacteristic, complemented
31C41×#532C2211yescharacteristic
32C41×#532C2211yescharacteristic
33C41×#529C2211yescharacteristic
34C41×#500C2211yescharacteristic, complemented
35C41×#498C2211yescharacteristic, complemented
36C41×#486C2211yescharacteristic
37C41×#486C2211yescharacteristic
38C41×#482—22no—
39C41×#479—21no—
40C41×#478—22no—
41C41×#477—21no—
42C41×#475C2211yescharacteristic, complemented
43C41×#474C2211yescharacteristic
44C41×#474C2211yescharacteristic
45C41×#474C2211yescharacteristic, complemented
46C41×#468—21no—
47C41×#468—21no—
48C41×#467—21no—
49C41×#465—21no—
50C41×#464—21no—
51C41×#462C2211yescharacteristic, complemented
52C41×#461C2211yescharacteristic
53C41×#461C2211yescharacteristic
54C41×#461C2211yescharacteristic, complemented
55C41×#460—21no—
56C41×#431C2211yescharacteristic, complemented
57C41×#423C2211yescharacteristic, complemented
58C2×C4⋊C8×C41C2211yescharacteristic, complemented
59C41×#332C2211yescharacteristic, complemented
60C41×#332C2211yescharacteristic, complemented
61C41×#331C2211yescharacteristic
62C41×#331C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic, complemented
64C41×Q8⋊C8C2211yescharacteristic, complemented
65C41×D4⋊C8C2211yescharacteristic
66C41×D4⋊C8C2211yescharacteristic
67C41×D4⋊C8C2211yescharacteristic
68C41×D4⋊C8C2211yescharacteristic
69C41×D4⋊C8C2211yescharacteristic, complemented
70C41×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C41—21no—
72C2×#41×C41—21no—
73C2×#41×C41—21no—
74C2×#41×C41—21no—
75C22×D4×C41—21no—
76C22×D4×C41—21no—
77C2×Q16×C41—21no—
78C2×SD16×C41—21no—
79C2×SD16×C41—21no—
80C2×SD16×C41—21no—
81C2×M16×C41—21no—
82C22×C8×C41—21no—
83C4⋊Q8×C41D411yescharacteristic
84C4⋊Q8×C41C2311yescharacteristic
85C4⋊Q8×C41C2311yescharacteristic
86C4⋊Q8×C41C2311yescharacteristic
87#127×C41—22no—
88#127×C41—21no—
89#127×C41D411yescharacteristic
90#127×C41C2311yescharacteristic
91#126×C41—22no—
92#126×C41—22no—
93#126×C41—21no—
94#125×C41—21no—
95#125×C41D411yescharacteristic
96#124×C41—22no—
97#124×C41—21no—
98#124×C41—21no—
99#124×C41—21no—
100#124×C41D411yescharacteristic
101#123×C41—22no—
102#123×C41—22no—
103#123×C41—21no—
104#123×C41—22no—
105C22⋊Q8×C41—22no—
106C22⋊Q8×C41—21no—
107C22⋊Q8×C41—21no—
108C22⋊Q8×C41—21no—
109C22⋊Q8×C41—21no—
110C22⋊Q8×C41D411yescharacteristic
111#121×C41—22no—
112#121×C41—22no—
113#121×C41—22no—
114#121×C41—22no—
115#121×C41—22no—
116#121×C41—21no—
117#121×C41—22no—
118#121×C41—21no—
119#121×C41—21no—
120#121×C41—21no—
121#121×C41—21no—
122#121×C41—21no—
123#121×C41D411yescharacteristic
124#121×C41D411yescharacteristic
125#121×C41D411yescharacteristic
126#121×C41D412yes—
127#120×C41—22no—
128#120×C41—22no—
129#120×C41—22no—
130#120×C41—22no—
131C4×Q8×C41—21no—
132C4×Q8×C41—21no—
133C4×Q8×C41—21no—
134C4×Q8×C41C2311yescharacteristic
135C4×D4×C41—22no—
136C4×D4×C41—21no—
137C4×D4×C41—21no—
138C4×D4×C41—21no—
139C4×D4×C41—21no—
140C4×D4×C41D412yes—
141C4×D4×C41C2311yescharacteristic
142C4×D4×C41C2311yescharacteristic
143C4×D4×C41C2311yescharacteristic
144#117×C41—21no—
145#117×C41—21no—
146#117×C41—21no—
147C2×C4⋊C4×C41—21no—
148C2×C22⋊C4×C41—22no—
149C2×C42×C41C2311yescharacteristic
150#107×C41—22no—
151#107×C41—21no—
152#107×C41—21no—
153#107×C41—21no—
154#106×C41—21no—
155#106×C41—22no—
156C4⋊C8×C41—21no—
157C4⋊C8×C41—21no—
158C4⋊C8×C41—21no—
159C4⋊C8×C41C2311yescharacteristic
160C4⋊C8×C41C2311yescharacteristic
161C4⋊C8×C41C2311yescharacteristic
162C4⋊C8×C41C2311yescharacteristic
163#103×C41—21no—
164#103×C41—21no—
165#103×C41—21no—
166#103×C41—21no—
167#103×C41—21no—
168#102×C41—21no—
169#102×C41—21no—
170#102×C41—21no—
171#102×C41—22no—
172#102×C41—22no—
173C22⋊C8×C41—21no—
174C4×C8×C41C2311yescharacteristic
175C4×C8×C41C2311yescharacteristic
176C24×C41—22no—
177#41×C41—81no—
178#41×C41—81no—
179#41×C41—81no—
180#41×C41—81no—
181#41×C41—81no—
182#41×C41—81no—
183#41×C41—81no—
184#41×C41—81no—
185C2×Q8×C41—21no—
186C2×Q8×C41—21no—
187C2×Q8×C41—21no—
188C2×Q8×C41—21no—
189C2×Q8×C41C2×D411yescharacteristic
190C2×D4×C41—22no—
191C2×D4×C41—22no—
192C2×D4×C41—22no—
193C2×D4×C41—22no—
194C2×D4×C41—22no—
195C2×D4×C41—21no—
196C2×D4×C41—21no—
197C2×D4×C41—22no—
198C2×D4×C41—21no—
199C2×D4×C41—21no—
200C2×D4×C41—21no—
201C2×D4×C41—21no—
202C2×D4×C41—21no—
203C2×D4×C41—81no—
204C2×D4×C41—81no—
205C2×D4×C41—81no—
206C2×D4×C41—81no—
207C2×D4×C41C2×D411yescharacteristic
208C2×D4×C41C2×D411yescharacteristic
209C2×D4×C41C2×D411yescharacteristic
210C2×D4×C41C2×D412yes—
211C22×C4×C41—22no—
212C22×C4×C41—22no—
213C22×C4×C41—21no—
214C22×C4×C41—21no—
215C22×C4×C41—21no—
216C22×C4×C41—22no—
217C22×C4×C41C2×D411yescharacteristic
218C22×C4×C41C2×D411yescharacteristic
219C22×C4×C41C2×D411yescharacteristic
220Q16×C41—81no—
221SD16×C41—81no—
222SD16×C41—81no—
223SD16×C41—81no—
224M16×C41—81no—
225C2×C8×C41—21no—
226C2×C8×C41—21no—
227C2×C8×C41—21no—
228C2×C8×C41—21no—
229C2×C8×C41—21no—
230C2×C8×C41—21no—
231C2×C8×C41—81no—
232C4⋊C4×C41—22no—
233C4⋊C4×C41—22no—
234C4⋊C4×C41—21no—
235C4⋊C4×C41—21no—
236C4⋊C4×C41—21no—
237C4⋊C4×C41—21no—
238C4⋊C4×C41—21no—
239C4⋊C4×C41—21no—
240C4⋊C4×C41—21no—
241C4⋊C4×C41—21no—
242C4⋊C4×C41—21no—
243C4⋊C4×C41—21no—
244C4⋊C4×C41—41no—
245C4⋊C4×C41—41no—
246C4⋊C4×C41C2×D411yescharacteristic
247C4⋊C4×C41C2×D411yescharacteristic
248C4⋊C4×C41C2×D411yescharacteristic
249C4⋊C4×C41C2×D411yescharacteristic
250C4⋊C4×C41C2×D412yes—
251C22⋊C4×C41—22no—
252C22⋊C4×C41—22no—
253C22⋊C4×C41—22no—
254C22⋊C4×C41—22no—
255C22⋊C4×C41—22no—
256C22⋊C4×C41—21no—
257C22⋊C4×C41—21no—
258C22⋊C4×C41—21no—
259C22⋊C4×C41—21no—
260C22⋊C4×C41—21no—
261C22⋊C4×C41—21no—
262C22⋊C4×C41—22no—
263C22⋊C4×C41—22no—
264C22⋊C4×C41—21no—
265C22⋊C4×C41—21no—
266C22⋊C4×C41—21no—
267C22⋊C4×C41—41no—
268C42×C41—22no—
269C42×C41—21no—
270C42×C41—41no—
271C42×C41C2×D411yescharacteristic
272C42×C41C2×D411yescharacteristic
273C42×C41C2×D411yescharacteristic
274C42×C41C2411yescharacteristic
275C23×C41—21no—
276C23×C41—21no—
277C23×C41—22no—
278C23×C41—21no—
279C23×C41—82no—
280C23×C41—82no—
281C23×C41—82no—
282C23×C41#12011yescharacteristic
283Q8×C41—21no—
284Q8×C41—21no—
285Q8×C41—41no—
286Q8×C41—41no—
287Q8×C41—41no—
288Q8×C41—41no—
289Q8×C41—41no—
290Q8×C41—41no—
291Q8×C41—81no—
292D4×C41—21no—
293D4×C41—21no—
294D4×C41—21no—
295D4×C41—21no—
296D4×C41—21no—
297D4×C41—21no—
298D4×C41—42no—
299D4×C41—41no—
300D4×C41—41no—
301D4×C41—41no—
302D4×C41—41no—
303D4×C41—81no—
304D4×C41—81no—
305D4×C41—81no—
306D4×C41—81no—
307D4×C41—81no—
308D4×C41—82no—
309D4×C41—82no—
310D4×C41—82no—
311D4×C41—82no—
312D4×C41—82no—
313D4×C41—82no—
314C2×C4×C41—21no—
315C2×C4×C41—21no—
316C2×C4×C41—21no—
317C2×C4×C41—21no—
318C2×C4×C41—21no—
319C2×C4×C41—21no—
320C2×C4×C41—21no—
321C2×C4×C41—22no—
322C2×C4×C41—21no—
323C2×C4×C41—21no—
324C2×C4×C41—41no—
325C2×C4×C41—41no—
326C2×C4×C41—41no—
327C2×C4×C41—41no—
328C2×C4×C41—41no—
329C2×C4×C41—41no—
330C2×C4×C41—41no—
331C2×C4×C41—41no—
332C2×C4×C41—41no—
333C2×C4×C41—82no—
334C2×C4×C41—82no—
335C2×C4×C41—82no—
336C2×C4×C41#12011yescharacteristic
337C2×C4×C41#12011yescharacteristic
338C2×C4×C41#12011yescharacteristic
339C2×C4×C41C22×D411yescharacteristic
340C2×C4×C41C22×D411yescharacteristic
341C2×C4×C41C22×D411yescharacteristic
342C8×C41—41no—
343C8×C41—41no—
344C8×C41—41no—
345C8×C41—41no—
346C8×C41—41no—
347C8×C41—41no—
348#18974C4111yesmaximal, characteristic, direct product factor, Sylow
349C22×C41—21no—
350C22×C41—21no—
351C22×C41—21no—
352C22×C41—41no—
353C22×C41—41no—
354C22×C41—41no—
355C22×C41—41no—
356C22×C41—42no—
357C22×C41—42no—
358C22×C41—41no—
359C22×C41—41no—
360C22×C41—42no—
361C22×C41—41no—
362C22×C41—41no—
363C22×C41—41no—
364C22×C41—164no—
365C22×C41C2×#12011yescharacteristic
366C4×C41—21no—
367C4×C41—21no—
368C4×C41—21no—
369C4×C41—21no—
370C4×C41—41no—
371C4×C41—41no—
372C4×C41—41no—
373C4×C41—41no—
374C4×C41—42no—
375C4×C41—41no—
376C4×C41—81no—
377C4×C41—81no—
378C4×C41#57611yescharacteristic
379C4×C41#57611yescharacteristic
380C4×C41#57711yescharacteristic
381C4×C41#57711yescharacteristic
382#3546C2×C4111yescharacteristic
383#3254C2×C4111yescharacteristic, complemented
384#3248C2×C4111yescharacteristic, complemented
385#3228C2×C4111yescharacteristic, complemented
386#1654C2×C4111yescharacteristic, complemented
387#1652C2×C4111yescharacteristic, complemented
388#1650C2×C4111yescharacteristic, complemented
389#1647C2×C4111yescharacteristic, complemented
390#1642C2×C4111yescharacteristic, complemented
391#1641C2×C4111yescharacteristic, complemented
392#1639C2×C4111yescharacteristic, complemented
393#1639C2×C4111yescharacteristic, complemented
394#1547C2×C4111yescharacteristic, complemented
395#1495C2×C4111yescharacteristic, complemented
396#1480C2×C4111yescharacteristic, complemented
397C2×C41—41no—
398C2×C41—81no—
399C2×C41—82no—
400C2×C41—81no—
401C2×C41—81no—
402C2×C41#301211yescharacteristic
403C2×C41#301211yescharacteristic
404C2×C41#302211yescharacteristic
405#560—22no—
406#556C22×C4111yescharacteristic
407#553—21no—
408#550—21no—
409#550C22×C4111yescharacteristic
410#547C22×C4111yescharacteristic
411#546—21no—
412#546—21no—
413D42C22×C4111yescharacteristic
414#542—21no—
415#538—22no—
416#537—21no—
417#535—21no—
418#535—21no—
419#533C22×C4111yescharacteristic, complemented
420#532C22×C4111yescharacteristic
421#532C22×C4111yescharacteristic
422#529C22×C4111yescharacteristic
423#500C22×C4111yescharacteristic, complemented
424#498C22×C4111yescharacteristic, complemented
425#486C22×C4111yescharacteristic
426#486C22×C4111yescharacteristic
427#482—22no—
428#479—21no—
429#478—22no—
430#477—21no—
431#475C22×C4111yescharacteristic, complemented
432#474C22×C4111yescharacteristic
433#474C22×C4111yescharacteristic
434#474C22×C4111yescharacteristic, complemented
435#468—21no—
436#468—21no—
437#467—21no—
438#465—21no—
439#464—21no—
440#462C22×C4111yescharacteristic, complemented
441#461C22×C4111yescharacteristic
442#461C22×C4111yescharacteristic
443#461C22×C4111yescharacteristic, complemented
444#460—21no—
445#431C22×C4111yescharacteristic, complemented
446#423C22×C4111yescharacteristic, complemented
447C2×C4⋊C8C22×C4111yescharacteristic, complemented
448#332C22×C4111yescharacteristic, complemented
449#332C22×C4111yescharacteristic, complemented
450#331C22×C4111yescharacteristic
451#331C22×C4111yescharacteristic
452Q8⋊C8C22×C4111yescharacteristic, complemented
453Q8⋊C8C22×C4111yescharacteristic, complemented
454D4⋊C8C22×C4111yescharacteristic
455D4⋊C8C22×C4111yescharacteristic
456D4⋊C8C22×C4111yescharacteristic
457D4⋊C8C22×C4111yescharacteristic
458D4⋊C8C22×C4111yescharacteristic, complemented
459D4⋊C8C22×C4111yescharacteristic, complemented
460C41#1897411yescharacteristic, direct product factor, Sylow
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C22×D4—21no—
466C22×D4—21no—
467C2×Q16—21no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×M16—21no—
472C22×C8—21no—
473C4⋊Q8D4×C4111yescharacteristic
474C4⋊Q8C23×C4111yescharacteristic
475C4⋊Q8C23×C4111yescharacteristic
476C4⋊Q8C23×C4111yescharacteristic
477#127—22no—
478#127—21no—
479#127D4×C4111yescharacteristic
480#127C23×C4111yescharacteristic
481#126—22no—
482#126—22no—
483#126—21no—
484#125—21no—
485#125D4×C4111yescharacteristic
486#124—22no—
487#124—21no—
488#124—21no—
489#124—21no—
490#124D4×C4111yescharacteristic
491#123—22no—
492#123—22no—
493#123—21no—
494#123—22no—
495C22⋊Q8—22no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8D4×C4111yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—21no—
507#121—22no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121D4×C4111yescharacteristic
514#121D4×C4111yescharacteristic
515#121D4×C4111yescharacteristic
516#121D4×C4112yes—
517#120—22no—
518#120—22no—
519#120—22no—
520#120—22no—
521C4×Q8—21no—
522C4×Q8—21no—
523C4×Q8—21no—
524C4×Q8C23×C4111yescharacteristic
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4D4×C4112yes—
531C4×D4C23×C4111yescharacteristic
532C4×D4C23×C4111yescharacteristic
533C4×D4C23×C4111yescharacteristic
534#117—21no—
535#117—21no—
536#117—21no—
537C2×C4⋊C4—21no—
538C2×C22⋊C4—22no—
539C2×C42C23×C4111yescharacteristic
540#107—21no—
541#107—21no—
542#107—21no—
543#107—22no—
544#106—21no—
545#106—22no—
546C4⋊C8—21no—
547C4⋊C8—21no—
548C4⋊C8—21no—
549C4⋊C8C23×C4111yescharacteristic
550C4⋊C8C23×C4111yescharacteristic
551C4⋊C8C23×C4111yescharacteristic
552C4⋊C8C23×C4111yescharacteristic
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#103—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#102—22no—
562#102—22no—
563C22⋊C8—21no—
564C4×C8C23×C4111yescharacteristic
565C4×C8C23×C4111yescharacteristic
566C24—22no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573#41—81no—
574#41—81no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8C2×D4×C4111yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4C2×D4×C4111yescharacteristic
598C2×D4C2×D4×C4111yescharacteristic
599C2×D4C2×D4×C4111yescharacteristic
600C2×D4C2×D4×C4112yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4C2×D4×C4111yescharacteristic
608C22×C4C2×D4×C4111yescharacteristic
609C22×C4C2×D4×C4111yescharacteristic
610Q16—81no—
611SD16—81no—
612SD16—81no—
613SD16—81no—
614M16—81no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—81no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4C2×D4×C4111yescharacteristic
637C4⋊C4C2×D4×C4111yescharacteristic
638C4⋊C4C2×D4×C4111yescharacteristic
639C4⋊C4C2×D4×C4111yescharacteristic
640C4⋊C4C2×D4×C4112yes—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—41no—
658C42—22no—
659C42—21no—
660C42—41no—
661C42C2×D4×C4111yescharacteristic
662C42C2×D4×C4111yescharacteristic
663C42C2×D4×C4111yescharacteristic
664C42C24×C4111yescharacteristic
665C23—21no—
666C23—21no—
667C23—22no—
668C23—21no—
669C23—82no—
670C23—82no—
671C23—82no—
672C23#120×C4111yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—81no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697D4—82no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4#120×C4111yescharacteristic
727C2×C4#120×C4111yescharacteristic
728C2×C4#120×C4111yescharacteristic
729C2×C4C22×D4×C4111yescharacteristic
730C2×C4C22×D4×C4111yescharacteristic
731C2×C4C22×D4×C4111yescharacteristic
732C8—41no—
733C8—41no—
734C8—41no—
735C8—41no—
736C8—41no—
737C8—41no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—164no—
754C22C2×#120×C4111yescharacteristic
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—42no—
764C4—41no—
765C4—81no—
766C4—81no—
767C4C41×#57611yescharacteristic
768C4C41×#57611yescharacteristic
769C4C41×#57711yescharacteristic
770C4C41×#57711yescharacteristic
771C2—41no—
772C2—81no—
773C2—81no—
774C2—82no—
775C2—81no—
776C2C41×#301211yescharacteristic
777C2C41×#301211yescharacteristic
778C2C41×#302211yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#3546C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#3254C2semidirect
3. C41×#3248C2semidirect
4. C41×#3228C2semidirect
5. C41×#1654C2semidirect
6. C41×#1652C2semidirect
7. C41×#1650C2semidirect
8. C41×#1647C2semidirect
9. C41×#1642C2semidirect
10. C41×#1641C2semidirect
11. C41×#1639C2semidirect
12. C41×#1639C2semidirect
13. C41×#1547C2semidirect
14. C41×#1495C2semidirect
15. C41×#1480C2semidirect
30. C41×#533C22semidirect
34. C41×#500C22semidirect
35. C41×#498C22semidirect
42. C41×#475C22semidirect
45. C41×#474C22semidirect
51. C41×#462C22semidirect
54. C41×#461C22semidirect
56. C41×#431C22semidirect
57. C41×#423C22semidirect
58. C2×C4⋊C8×C41C22semidirect
59. C41×#332C22semidirect
60. C41×#332C22semidirect
63. C41×Q8⋊C8C22semidirect
64. C41×Q8⋊C8C22semidirect
69. C41×D4⋊C8C22semidirect
70. C41×D4⋊C8C22semidirect
348. #18974C41direct (N × H)
383. #3254C2×C41semidirect
384. #3248C2×C41semidirect
385. #3228C2×C41semidirect
386. #1654C2×C41semidirect
387. #1652C2×C41semidirect
388. #1650C2×C41semidirect
389. #1647C2×C41semidirect
390. #1642C2×C41semidirect
391. #1641C2×C41semidirect
392. #1639C2×C41semidirect
393. #1639C2×C41semidirect
394. #1547C2×C41semidirect
395. #1495C2×C41semidirect
396. #1480C2×C41semidirect
419. #533C22×C41semidirect
423. #500C22×C41semidirect
424. #498C22×C41semidirect
431. #475C22×C41semidirect
434. #474C22×C41semidirect
440. #462C22×C41semidirect
443. #461C22×C41semidirect
445. #431C22×C41semidirect
446. #423C22×C41semidirect
447. C2×C4⋊C8C22×C41semidirect
448. #332C22×C41semidirect
449. #332C22×C41semidirect
452. Q8⋊C8C22×C41semidirect
453. Q8⋊C8C22×C41semidirect
458. D4⋊C8C22×C41semidirect
459. D4⋊C8C22×C41semidirect
460. C41#18974direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35462
C41×#32542
C41×#32482
C41×#32282
C41×#16542
C41×#16522
C41×#16502
C41×#16472
C41×#16422
C41×#16412
C41×#16392
C41×#15472
C41×#14952
C41×#14802
#1897441