Finite Group Databasebeta

← C41×#18962 #23795163

Subgroups — C41×#18962 #23795163

Order 10496.

964 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3546C211yesmaximal, characteristic, complemented
2C41×#3253C211yesmaximal, characteristic, complemented
3C41×#3247C211yesmaximal, characteristic, complemented
4C41×#3207C211yesmaximal, characteristic, complemented
5C41×#1638C211yesmaximal, characteristic, complemented
6C41×#1635C211yesmaximal, characteristic, complemented
7C41×#1631C211yesmaximal, characteristic, complemented
8C41×#1629C211yesmaximal, characteristic, complemented
9C41×#1628C211yesmaximal, characteristic, complemented
10C41×#1625C211yesmaximal, characteristic, complemented
11C41×#1621C211yesmaximal, characteristic, complemented
12C41×#1619C211yesmaximal, 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×#532C2211yescharacteristic
31C41×#532C2211yescharacteristic
32C41×#532C2211yescharacteristic, complemented
33C41×#529C2211yescharacteristic
34C41×#493C2211yescharacteristic
35C41×#492C2211yescharacteristic
36C41×#487C2211yescharacteristic, complemented
37C41×#486C2211yescharacteristic, complemented
38C41×#478—21no—
39C41×#477C2211yescharacteristic, complemented
40C41×#476—21no—
41C41×#476C2211yescharacteristic
42C41×#476C2211yescharacteristic
43C41×#476C2211yescharacteristic, complemented
44C41×#469—21no—
45C41×#469—21no—
46C41×#466—21no—
47C41×#465—21no—
48C41×#463—21no—
49C41×#463—22no—
50C41×#460C2211yescharacteristic, complemented
51C41×#459—21no—
52C41×#459C2211yescharacteristic
53C41×#459C2211yescharacteristic
54C41×#459C2211yescharacteristic, complemented
55C41×#449—22no—
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—
75C2×#41×C41—21no—
76C22×D4×C41—21no—
77C22×D4×C41—21no—
78C2×SD16×C41—21no—
79C2×SD16×C41—22no—
80C2×D8×C41—22no—
81C2×D8×C41—21no—
82C2×D8×C41—21no—
83C2×D8×C41—21no—
84C2×M16×C41—21no—
85C22×C8×C41—21no—
86C4⋊Q8×C41D411yescharacteristic
87C4⋊Q8×C41C2311yescharacteristic
88C4⋊Q8×C41C2311yescharacteristic
89#127×C41—22no—
90#127×C41—21no—
91#127×C41D411yescharacteristic
92#127×C41C2311yescharacteristic
93#127×C41C2311yescharacteristic
94#126×C41—22no—
95#126×C41—22no—
96#126×C41—21no—
97#125×C41D411yescharacteristic
98#124×C41—22no—
99#124×C41—21no—
100#124×C41—21no—
101#124×C41—21no—
102#124×C41—21no—
103#124×C41D411yescharacteristic
104#123×C41—22no—
105#123×C41—22no—
106#123×C41—21no—
107#123×C41—22no—
108C22⋊Q8×C41—22no—
109C22⋊Q8×C41—21no—
110C22⋊Q8×C41—21no—
111C22⋊Q8×C41D411yescharacteristic
112#121×C41—22no—
113#121×C41—22no—
114#121×C41—22no—
115#121×C41—22no—
116#121×C41—22no—
117#121×C41—21no—
118#121×C41—22no—
119#121×C41—21no—
120#121×C41—21no—
121#121×C41—21no—
122#121×C41—21no—
123#121×C41—21no—
124#121×C41—21no—
125#121×C41—21no—
126#121×C41D411yescharacteristic
127#121×C41D411yescharacteristic
128#121×C41D411yescharacteristic
129#121×C41D412yes—
130#120×C41—22no—
131#120×C41—22no—
132#120×C41—22no—
133#120×C41—22no—
134C4×Q8×C41—21no—
135C4×Q8×C41C2311yescharacteristic
136C4×D4×C41—22no—
137C4×D4×C41—21no—
138C4×D4×C41—21no—
139C4×D4×C41—21no—
140C4×D4×C41—21no—
141C4×D4×C41—21no—
142C4×D4×C41—21no—
143C4×D4×C41D412yes—
144C4×D4×C41C2311yescharacteristic
145C4×D4×C41C2311yescharacteristic
146C4×D4×C41C2311yescharacteristic
147#117×C41—21no—
148#117×C41—21no—
149C2×C4⋊C4×C41—21no—
150C2×C22⋊C4×C41—22no—
151C2×C42×C41C2311yescharacteristic
152#107×C41—21no—
153#106×C41—21no—
154#106×C41—21no—
155#106×C41—21no—
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—22no—
165#102×C41—21no—
166#102×C41—21no—
167#102×C41—21no—
168#102×C41—22no—
169#102×C41—21no—
170#102×C41—21no—
171#102×C41—21no—
172#102×C41—21no—
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—
185#41×C41—82no—
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—21no—
204C2×D4×C41—21no—
205C2×D4×C41—21no—
206C2×D4×C41—41no—
207C2×D4×C41—81no—
208C2×D4×C41—81no—
209C2×D4×C41—81no—
210C2×D4×C41—81no—
211C2×D4×C41C2×D411yescharacteristic
212C2×D4×C41C2×D411yescharacteristic
213C2×D4×C41C2×D411yescharacteristic
214C2×D4×C41C2×D412yes—
215C22×C4×C41—22no—
216C22×C4×C41—22no—
217C22×C4×C41—21no—
218C22×C4×C41—21no—
219C22×C4×C41—21no—
220C22×C4×C41—22no—
221C22×C4×C41—41no—
222C22×C4×C41C2×D411yescharacteristic
223C22×C4×C41C2×D411yescharacteristic
224C22×C4×C41C2×D411yescharacteristic
225SD16×C41—81no—
226SD16×C41—82no—
227D8×C41—81no—
228D8×C41—81no—
229D8×C41—81no—
230D8×C41—82no—
231M16×C41—81no—
232C2×C8×C41—21no—
233C2×C8×C41—21no—
234C2×C8×C41—21no—
235C2×C8×C41—21no—
236C2×C8×C41—21no—
237C2×C8×C41—21no—
238C2×C8×C41—81no—
239C4⋊C4×C41—22no—
240C4⋊C4×C41—22no—
241C4⋊C4×C41—21no—
242C4⋊C4×C41—21no—
243C4⋊C4×C41—21no—
244C4⋊C4×C41—21no—
245C4⋊C4×C41—21no—
246C4⋊C4×C41—21no—
247C4⋊C4×C41—21no—
248C4⋊C4×C41—21no—
249C4⋊C4×C41C2×D412yes—
250C4⋊C4×C41C2×D411yescharacteristic
251C4⋊C4×C41C2×D411yescharacteristic
252C4⋊C4×C41C2×D411yescharacteristic
253C4⋊C4×C41C2×D411yescharacteristic
254C22⋊C4×C41—22no—
255C22⋊C4×C41—22no—
256C22⋊C4×C41—22no—
257C22⋊C4×C41—22no—
258C22⋊C4×C41—22no—
259C22⋊C4×C41—21no—
260C22⋊C4×C41—21no—
261C22⋊C4×C41—21no—
262C22⋊C4×C41—21no—
263C22⋊C4×C41—21no—
264C22⋊C4×C41—21no—
265C22⋊C4×C41—22no—
266C22⋊C4×C41—22no—
267C22⋊C4×C41—21no—
268C22⋊C4×C41—21no—
269C22⋊C4×C41—21no—
270C22⋊C4×C41—41no—
271C22⋊C4×C41—41no—
272C42×C41—22no—
273C42×C41—21no—
274C42×C41C2×D411yescharacteristic
275C42×C41C2×D411yescharacteristic
276C42×C41C2×D411yescharacteristic
277C42×C41C2411yescharacteristic
278C23×C41—21no—
279C23×C41—21no—
280C23×C41—22no—
281C23×C41—21no—
282C23×C41—41no—
283C23×C41—82no—
284C23×C41—82no—
285C23×C41—82no—
286C23×C41#12011yescharacteristic
287Q8×C41—21no—
288Q8×C41—21no—
289Q8×C41—42no—
290Q8×C41—41no—
291Q8×C41—41no—
292Q8×C41—81no—
293D4×C41—21no—
294D4×C41—21no—
295D4×C41—21no—
296D4×C41—21no—
297D4×C41—21no—
298D4×C41—21no—
299D4×C41—42no—
300D4×C41—42no—
301D4×C41—41no—
302D4×C41—41no—
303D4×C41—41no—
304D4×C41—41no—
305D4×C41—41no—
306D4×C41—41no—
307D4×C41—41no—
308D4×C41—41no—
309D4×C41—81no—
310D4×C41—81no—
311D4×C41—81no—
312D4×C41—81no—
313D4×C41—81no—
314D4×C41—82no—
315D4×C41—82no—
316D4×C41—82no—
317D4×C41—82no—
318D4×C41—82no—
319D4×C41—82no—
320D4×C41—82no—
321C2×C4×C41—21no—
322C2×C4×C41—21no—
323C2×C4×C41—21no—
324C2×C4×C41—21no—
325C2×C4×C41—21no—
326C2×C4×C41—21no—
327C2×C4×C41—21no—
328C2×C4×C41—22no—
329C2×C4×C41—21no—
330C2×C4×C41—21no—
331C2×C4×C41—41no—
332C2×C4×C41—41no—
333C2×C4×C41—41no—
334C2×C4×C41—41no—
335C2×C4×C41—41no—
336C2×C4×C41—41no—
337C2×C4×C41—41no—
338C2×C4×C41—41no—
339C2×C4×C41—82no—
340C2×C4×C41—82no—
341C2×C4×C41—82no—
342C2×C4×C41—82no—
343C2×C4×C41#12011yescharacteristic
344C2×C4×C41#12011yescharacteristic
345C2×C4×C41#12011yescharacteristic
346C2×C4×C41C22×D411yescharacteristic
347C2×C4×C41C22×D411yescharacteristic
348C2×C4×C41C22×D411yescharacteristic
349C8×C41—41no—
350C8×C41—41no—
351C8×C41—41no—
352C8×C41—41no—
353C8×C41—41no—
354C8×C41—41no—
355#18962C4111yesmaximal, characteristic, direct product factor, Sylow
356C22×C41—21no—
357C22×C41—21no—
358C22×C41—21no—
359C22×C41—41no—
360C22×C41—41no—
361C22×C41—41no—
362C22×C41—41no—
363C22×C41—42no—
364C22×C41—42no—
365C22×C41—41no—
366C22×C41—41no—
367C22×C41—42no—
368C22×C41—41no—
369C22×C41—41no—
370C22×C41—41no—
371C22×C41—81no—
372C22×C41—81no—
373C22×C41—81no—
374C22×C41—164no—
375C22×C41C2×#12011yescharacteristic
376C4×C41—21no—
377C4×C41—21no—
378C4×C41—21no—
379C4×C41—21no—
380C4×C41—41no—
381C4×C41—41no—
382C4×C41—41no—
383C4×C41—41no—
384C4×C41—42no—
385C4×C41—41no—
386C4×C41—81no—
387C4×C41#57611yescharacteristic
388C4×C41#57611yescharacteristic
389C4×C41#57711yescharacteristic
390C4×C41#57711yescharacteristic
391#3546C2×C4111yescharacteristic, complemented
392#3253C2×C4111yescharacteristic, complemented
393#3247C2×C4111yescharacteristic, complemented
394#3207C2×C4111yescharacteristic, complemented
395#1638C2×C4111yescharacteristic, complemented
396#1635C2×C4111yescharacteristic, complemented
397#1631C2×C4111yescharacteristic, complemented
398#1629C2×C4111yescharacteristic, complemented
399#1628C2×C4111yescharacteristic, complemented
400#1625C2×C4111yescharacteristic, complemented
401#1621C2×C4111yescharacteristic, complemented
402#1619C2×C4111yescharacteristic, complemented
403#1547C2×C4111yescharacteristic, complemented
404#1495C2×C4111yescharacteristic, complemented
405#1480C2×C4111yescharacteristic, complemented
406C2×C41—41no—
407C2×C41—81no—
408C2×C41—82no—
409C2×C41—81no—
410C2×C41—81no—
411C2×C41—161no—
412C2×C41#301211yescharacteristic
413C2×C41#301211yescharacteristic
414C2×C41#302111yescharacteristic
415#560—22no—
416#556C22×C4111yescharacteristic
417#553—21no—
418#550—21no—
419#550C22×C4111yescharacteristic
420#547C22×C4111yescharacteristic
421#546—21no—
422#546—21no—
423D42C22×C4111yescharacteristic
424#542—21no—
425#538—22no—
426#537—21no—
427#535—21no—
428#535—21no—
429#532C22×C4111yescharacteristic
430#532C22×C4111yescharacteristic
431#532C22×C4111yescharacteristic, complemented
432#529C22×C4111yescharacteristic
433#493C22×C4111yescharacteristic
434#492C22×C4111yescharacteristic
435#487C22×C4111yescharacteristic, complemented
436#486C22×C4111yescharacteristic, complemented
437#478—21no—
438#477C22×C4111yescharacteristic, complemented
439#476—21no—
440#476C22×C4111yescharacteristic
441#476C22×C4111yescharacteristic
442#476C22×C4111yescharacteristic, complemented
443#469—21no—
444#469—21no—
445#466—21no—
446#465—21no—
447#463—21no—
448#463—22no—
449#460C22×C4111yescharacteristic, complemented
450#459—21no—
451#459C22×C4111yescharacteristic
452#459C22×C4111yescharacteristic
453#459C22×C4111yescharacteristic, complemented
454#449—22no—
455#431C22×C4111yescharacteristic, complemented
456#423C22×C4111yescharacteristic, complemented
457C2×C4⋊C8C22×C4111yescharacteristic, complemented
458#332C22×C4111yescharacteristic, complemented
459#332C22×C4111yescharacteristic, complemented
460#331C22×C4111yescharacteristic
461#331C22×C4111yescharacteristic
462Q8⋊C8C22×C4111yescharacteristic, complemented
463Q8⋊C8C22×C4111yescharacteristic, complemented
464D4⋊C8C22×C4111yescharacteristic
465D4⋊C8C22×C4111yescharacteristic
466D4⋊C8C22×C4111yescharacteristic
467D4⋊C8C22×C4111yescharacteristic
468D4⋊C8C22×C4111yescharacteristic, complemented
469D4⋊C8C22×C4111yescharacteristic, complemented
470C41#1896211yescharacteristic, direct product factor, Sylow
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C22×D4—21no—
477C22×D4—21no—
478C2×SD16—21no—
479C2×SD16—22no—
480C2×D8—22no—
481C2×D8—21no—
482C2×D8—21no—
483C2×D8—21no—
484C2×M16—21no—
485C22×C8—21no—
486C4⋊Q8D4×C4111yescharacteristic
487C4⋊Q8C23×C4111yescharacteristic
488C4⋊Q8C23×C4111yescharacteristic
489#127—22no—
490#127—21no—
491#127D4×C4111yescharacteristic
492#127C23×C4111yescharacteristic
493#127C23×C4111yescharacteristic
494#126—22no—
495#126—22no—
496#126—21no—
497#125D4×C4111yescharacteristic
498#124—22no—
499#124—21no—
500#124—21no—
501#124—21no—
502#124—21no—
503#124D4×C4111yescharacteristic
504#123—22no—
505#123—22no—
506#123—21no—
507#123—22no—
508C22⋊Q8—22no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8D4×C4111yescharacteristic
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—21no—
518#121—22no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121D4×C4111yescharacteristic
527#121D4×C4111yescharacteristic
528#121D4×C4111yescharacteristic
529#121D4×C4112yes—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534C4×Q8—21no—
535C4×Q8C23×C4111yescharacteristic
536C4×D4—22no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4D4×C4112yes—
544C4×D4C23×C4111yescharacteristic
545C4×D4C23×C4111yescharacteristic
546C4×D4C23×C4111yescharacteristic
547#117—21no—
548#117—21no—
549C2×C4⋊C4—21no—
550C2×C22⋊C4—22no—
551C2×C42C23×C4111yescharacteristic
552#107—21no—
553#106—21no—
554#106—21no—
555#106—21no—
556C4⋊C8—21no—
557C4⋊C8—21no—
558C4⋊C8—21no—
559C4⋊C8C23×C4111yescharacteristic
560C4⋊C8C23×C4111yescharacteristic
561C4⋊C8C23×C4111yescharacteristic
562C4⋊C8C23×C4111yescharacteristic
563#103—21no—
564#103—22no—
565#102—21no—
566#102—21no—
567#102—21no—
568#102—22no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573C22⋊C8—21no—
574C4×C8C23×C4111yescharacteristic
575C4×C8C23×C4111yescharacteristic
576C24—22no—
577#41—81no—
578#41—81no—
579#41—81no—
580#41—81no—
581#41—81no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—82no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8C2×D4×C4111yescharacteristic
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—41no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4C2×D4×C4111yescharacteristic
612C2×D4C2×D4×C4111yescharacteristic
613C2×D4C2×D4×C4111yescharacteristic
614C2×D4C2×D4×C4112yes—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—41no—
622C22×C4C2×D4×C4111yescharacteristic
623C22×C4C2×D4×C4111yescharacteristic
624C22×C4C2×D4×C4111yescharacteristic
625SD16—81no—
626SD16—82no—
627D8—81no—
628D8—81no—
629D8—81no—
630D8—82no—
631M16—81no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—81no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4C2×D4×C4112yes—
650C4⋊C4C2×D4×C4111yescharacteristic
651C4⋊C4C2×D4×C4111yescharacteristic
652C4⋊C4C2×D4×C4111yescharacteristic
653C4⋊C4C2×D4×C4111yescharacteristic
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C42—22no—
673C42—21no—
674C42C2×D4×C4111yescharacteristic
675C42C2×D4×C4111yescharacteristic
676C42C2×D4×C4111yescharacteristic
677C42C24×C4111yescharacteristic
678C23—21no—
679C23—21no—
680C23—22no—
681C23—21no—
682C23—41no—
683C23—82no—
684C23—82no—
685C23—82no—
686C23#120×C4111yescharacteristic
687Q8—21no—
688Q8—21no—
689Q8—42no—
690Q8—41no—
691Q8—41no—
692Q8—81no—
693D4—21no—
694D4—21no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—42no—
700D4—42no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—81no—
710D4—81no—
711D4—81no—
712D4—81no—
713D4—82no—
714D4—81no—
715D4—82no—
716D4—82no—
717D4—82no—
718D4—82no—
719D4—82no—
720D4—82no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—82no—
740C2×C4—82no—
741C2×C4—82no—
742C2×C4—82no—
743C2×C4#120×C4111yescharacteristic
744C2×C4#120×C4111yescharacteristic
745C2×C4#120×C4111yescharacteristic
746C2×C4C22×D4×C4111yescharacteristic
747C2×C4C22×D4×C4111yescharacteristic
748C2×C4C22×D4×C4111yescharacteristic
749C8—41no—
750C8—41no—
751C8—41no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—164no—
774C22C2×#120×C4111yescharacteristic
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—41no—
785C4—81no—
786C4C41×#57611yescharacteristic
787C4C41×#57611yescharacteristic
788C4C41×#57711yescharacteristic
789C4C41×#57711yescharacteristic
790C2—41no—
791C2—81no—
792C2—81no—
793C2—82no—
794C2—81no—
795C2—161no—
796C2C41×#301211yescharacteristic
797C2C41×#301211yescharacteristic
798C2C41×#302111yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC42C24×C41
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
1. C41×#3546C2semidirect
2. C41×#3253C2semidirect
3. C41×#3247C2semidirect
4. C41×#3207C2semidirect
5. C41×#1638C2semidirect
6. C41×#1635C2semidirect
7. C41×#1631C2semidirect
8. C41×#1629C2semidirect
9. C41×#1628C2semidirect
10. C41×#1625C2semidirect
11. C41×#1621C2semidirect
12. C41×#1619C2semidirect
13. C41×#1547C2semidirect
14. C41×#1495C2semidirect
15. C41×#1480C2semidirect
32. C41×#532C22semidirect
36. C41×#487C22semidirect
37. C41×#486C22semidirect
39. C41×#477C22semidirect
43. C41×#476C22semidirect
50. C41×#460C22semidirect
54. C41×#459C22semidirect
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
355. #18962C41direct (N × H)
391. #3546C2×C41semidirect
392. #3253C2×C41semidirect
393. #3247C2×C41semidirect
394. #3207C2×C41semidirect
395. #1638C2×C41semidirect
396. #1635C2×C41semidirect
397. #1631C2×C41semidirect
398. #1629C2×C41semidirect
399. #1628C2×C41semidirect
400. #1625C2×C41semidirect
401. #1621C2×C41semidirect
402. #1619C2×C41semidirect
403. #1547C2×C41semidirect
404. #1495C2×C41semidirect
405. #1480C2×C41semidirect
431. #532C22×C41semidirect
435. #487C22×C41semidirect
436. #486C22×C41semidirect
438. #477C22×C41semidirect
442. #476C22×C41semidirect
449. #460C22×C41semidirect
453. #459C22×C41semidirect
455. #431C22×C41semidirect
456. #423C22×C41semidirect
457. C2×C4⋊C8C22×C41semidirect
458. #332C22×C41semidirect
459. #332C22×C41semidirect
462. Q8⋊C8C22×C41semidirect
463. Q8⋊C8C22×C41semidirect
468. D4⋊C8C22×C41semidirect
469. D4⋊C8C22×C41semidirect
470. C41#18962direct (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×#32532
C41×#32472
C41×#32072
C41×#16382
C41×#16352
C41×#16312
C41×#16292
C41×#16282
C41×#16252
C41×#16212
C41×#16192
C41×#15472
C41×#14952
C41×#14802
#1896241