Finite Group Databasebeta

← C41×#18704 #23794905

Subgroups — C41×#18704 #23794905

Order 10496.

972 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3546C211yesmaximal, characteristic, complemented
2C41×#3251C211yesmaximal, characteristic, complemented
3C41×#3214C211yesmaximal, characteristic, complemented
4C41×#3169C211yesmaximal, characteristic, complemented
5C41×#1650C211yesmaximal, characteristic, complemented
6C41×#1647C211yesmaximal, characteristic, complemented
7C41×#1642C211yesmaximal, characteristic, complemented
8C41×#1639C211yesmaximal, characteristic, complemented
9C41×#1628C211yesmaximal, characteristic, complemented
10C41×#1625C211yesmaximal, characteristic, complemented
11C41×#1621C211yesmaximal, characteristic, complemented
12C41×#1619C211yesmaximal, characteristic, complemented
13C41×#1557C211yesmaximal, characteristic, complemented
14C41×#1494C211yesmaximal, characteristic, complemented
15C41×#1492C211yesmaximal, 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×#500C2211yescharacteristic, complemented
35C41×#496—21no—
36C41×#493C2211yescharacteristic
37C41×#489—21no—
38C41×#486C2211yescharacteristic
39C41×#486C2211yescharacteristic, complemented
40C41×#478—21no—
41C41×#475C2211yescharacteristic, complemented
42C41×#474C2211yescharacteristic
43C41×#469—21no—
44C41×#468—21no—
45C41×#466—22no—
46C41×#463—21no—
47C41×#461C2211yescharacteristic
48C41×#461C2211yescharacteristic, complemented
49C41×#460C2211yescharacteristic, complemented
50C41×#459C2211yescharacteristic
51C41×#459C2211yescharacteristic
52C41×#459C2211yescharacteristic, complemented
53C41×#449—21no—
54C41×#449—21no—
55C4×D8×C41—22no—
56C41×#432C2211yescharacteristic, 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—21no—
80C2×SD16×C41—21no—
81C2×D8×C41—22no—
82C2×D8×C41—21no—
83C2×D8×C41—21no—
84C2×D8×C41—21no—
85C2×M16×C41—21no—
86C22×C8×C41—21no—
87C4⋊Q8×C41D411yescharacteristic
88C4⋊Q8×C41C2311yescharacteristic
89C4⋊Q8×C41C2311yescharacteristic
90#127×C41—22no—
91#127×C41—21no—
92#127×C41D411yescharacteristic
93#127×C41C2311yescharacteristic
94#127×C41C2311yescharacteristic
95#126×C41—22no—
96#126×C41—22no—
97#126×C41—21no—
98#125×C41D411yescharacteristic
99#124×C41—22no—
100#124×C41—21no—
101#124×C41—21no—
102#124×C41—21no—
103#124×C41—21no—
104#124×C41D411yescharacteristic
105#123×C41—22no—
106#123×C41—22no—
107#123×C41—21no—
108#123×C41—22no—
109C22⋊Q8×C41—22no—
110C22⋊Q8×C41—21no—
111C22⋊Q8×C41—21no—
112C22⋊Q8×C41D411yescharacteristic
113#121×C41—22no—
114#121×C41—22no—
115#121×C41—22no—
116#121×C41—22no—
117#121×C41—22no—
118#121×C41—21no—
119#121×C41—22no—
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×C41—21no—
127#121×C41D411yescharacteristic
128#121×C41D411yescharacteristic
129#121×C41D411yescharacteristic
130#121×C41D412yes—
131#120×C41—22no—
132#120×C41—22no—
133#120×C41—22no—
134#120×C41—22no—
135C4×Q8×C41—21no—
136C4×Q8×C41C2311yescharacteristic
137C4×D4×C41—22no—
138C4×D4×C41—21no—
139C4×D4×C41—21no—
140C4×D4×C41—21no—
141C4×D4×C41—21no—
142C4×D4×C41—21no—
143C4×D4×C41—21no—
144C4×D4×C41D412yes—
145C4×D4×C41C2311yescharacteristic
146C4×D4×C41C2311yescharacteristic
147C4×D4×C41C2311yescharacteristic
148#117×C41—21no—
149#117×C41—21no—
150C2×C4⋊C4×C41—21no—
151C2×C22⋊C4×C41—22no—
152C2×C42×C41C2311yescharacteristic
153#107×C41—22no—
154#107×C41—21no—
155#106×C41—21no—
156C4⋊C8×C41—21no—
157C4⋊C8×C41C2311yescharacteristic
158C4⋊C8×C41C2311yescharacteristic
159C4⋊C8×C41C2311yescharacteristic
160C4⋊C8×C41C2311yescharacteristic
161#103×C41—21no—
162#103×C41—21no—
163#103×C41—21no—
164#102×C41—22no—
165#102×C41—21no—
166#102×C41—22no—
167#102×C41—21no—
168#102×C41—21no—
169#102×C41—21no—
170#102×C41—21no—
171C22⋊C8×C41—21no—
172#97×C41—21no—
173C4×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—81no—
186#41×C41—81no—
187C2×Q8×C41—21no—
188C2×Q8×C41—21no—
189C2×Q8×C41—21no—
190C2×Q8×C41C2×D411yescharacteristic
191C2×D4×C41—22no—
192C2×D4×C41—22no—
193C2×D4×C41—22no—
194C2×D4×C41—22no—
195C2×D4×C41—22no—
196C2×D4×C41—21no—
197C2×D4×C41—21no—
198C2×D4×C41—22no—
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—21no—
207C2×D4×C41—41no—
208C2×D4×C41—81no—
209C2×D4×C41—81no—
210C2×D4×C41—81no—
211C2×D4×C41—81no—
212C2×D4×C41C2×D411yescharacteristic
213C2×D4×C41C2×D411yescharacteristic
214C2×D4×C41C2×D411yescharacteristic
215C2×D4×C41C2×D412yes—
216C22×C4×C41—22no—
217C22×C4×C41—22no—
218C22×C4×C41—21no—
219C22×C4×C41—21no—
220C22×C4×C41—21no—
221C22×C4×C41—22no—
222C22×C4×C41—41no—
223C22×C4×C41C2×D411yescharacteristic
224C22×C4×C41C2×D411yescharacteristic
225C22×C4×C41C2×D411yescharacteristic
226SD16×C41—81no—
227SD16×C41—81no—
228SD16×C41—81no—
229D8×C41—44no—
230D8×C41—81no—
231D8×C41—81no—
232D8×C41—81no—
233M16×C41—81no—
234C2×C8×C41—21no—
235C2×C8×C41—21no—
236C2×C8×C41—21no—
237C2×C8×C41—21no—
238C2×C8×C41—21no—
239C2×C8×C41—21no—
240C2×C8×C41—42no—
241C4⋊C4×C41—22no—
242C4⋊C4×C41—22no—
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×C41—21no—
250C4⋊C4×C41—21no—
251C4⋊C4×C41C2×D411yescharacteristic
252C4⋊C4×C41C2×D411yescharacteristic
253C4⋊C4×C41C2×D411yescharacteristic
254C4⋊C4×C41C2×D411yescharacteristic
255C4⋊C4×C41C2×D412yes—
256C22⋊C4×C41—22no—
257C22⋊C4×C41—22no—
258C22⋊C4×C41—22no—
259C22⋊C4×C41—22no—
260C22⋊C4×C41—22no—
261C22⋊C4×C41—21no—
262C22⋊C4×C41—21no—
263C22⋊C4×C41—21no—
264C22⋊C4×C41—21no—
265C22⋊C4×C41—21no—
266C22⋊C4×C41—21no—
267C22⋊C4×C41—22no—
268C22⋊C4×C41—22no—
269C22⋊C4×C41—21no—
270C22⋊C4×C41—21no—
271C22⋊C4×C41—21no—
272C22⋊C4×C41—41no—
273C22⋊C4×C41—41no—
274C42×C41—22no—
275C42×C41—21no—
276C42×C41C2×D411yescharacteristic
277C42×C41C2×D411yescharacteristic
278C42×C41C2×D411yescharacteristic
279C42×C41C2411yescharacteristic
280C23×C41—21no—
281C23×C41—21no—
282C23×C41—22no—
283C23×C41—21no—
284C23×C41—41no—
285C23×C41—82no—
286C23×C41—82no—
287C23×C41—82no—
288C23×C41#12011yescharacteristic
289Q8×C41—21no—
290Q8×C41—21no—
291Q8×C41—41no—
292Q8×C41—41no—
293Q8×C41—41no—
294Q8×C41—41no—
295Q8×C41—81no—
296D4×C41—21no—
297D4×C41—21no—
298D4×C41—21no—
299D4×C41—21no—
300D4×C41—21no—
301D4×C41—21no—
302D4×C41—42no—
303D4×C41—42no—
304D4×C41—41no—
305D4×C41—41no—
306D4×C41—41no—
307D4×C41—41no—
308D4×C41—41no—
309D4×C41—41no—
310D4×C41—41no—
311D4×C41—41no—
312D4×C41—81no—
313D4×C41—81no—
314D4×C41—81no—
315D4×C41—82no—
316D4×C41—81no—
317D4×C41—81no—
318D4×C41—82no—
319D4×C41—82no—
320D4×C41—82no—
321D4×C41—82no—
322D4×C41—82no—
323D4×C41—82no—
324C2×C4×C41—21no—
325C2×C4×C41—21no—
326C2×C4×C41—21no—
327C2×C4×C41—21no—
328C2×C4×C41—21no—
329C2×C4×C41—21no—
330C2×C4×C41—21no—
331C2×C4×C41—22no—
332C2×C4×C41—21no—
333C2×C4×C41—21no—
334C2×C4×C41—41no—
335C2×C4×C41—41no—
336C2×C4×C41—41no—
337C2×C4×C41—41no—
338C2×C4×C41—41no—
339C2×C4×C41—41no—
340C2×C4×C41—41no—
341C2×C4×C41—41no—
342C2×C4×C41—82no—
343C2×C4×C41—82no—
344C2×C4×C41—82no—
345C2×C4×C41—82no—
346C2×C4×C41#12011yescharacteristic
347C2×C4×C41#12011yescharacteristic
348C2×C4×C41#12011yescharacteristic
349C2×C4×C41C22×D411yescharacteristic
350C2×C4×C41C22×D411yescharacteristic
351C2×C4×C41C22×D411yescharacteristic
352C8×C41—22no—
353C8×C41—41no—
354C8×C41—41no—
355C8×C41—41no—
356C8×C41—41no—
357C8×C41—41no—
358#18704C4111yesmaximal, characteristic, direct product factor, Sylow
359C22×C41—21no—
360C22×C41—21no—
361C22×C41—21no—
362C22×C41—41no—
363C22×C41—41no—
364C22×C41—42no—
365C22×C41—41no—
366C22×C41—41no—
367C22×C41—41no—
368C22×C41—42no—
369C22×C41—41no—
370C22×C41—42no—
371C22×C41—41no—
372C22×C41—41no—
373C22×C41—41no—
374C22×C41—81no—
375C22×C41—81no—
376C22×C41—81no—
377C22×C41—164no—
378C22×C41C2×#12011yescharacteristic
379C4×C41—21no—
380C4×C41—21no—
381C4×C41—21no—
382C4×C41—21no—
383C4×C41—41no—
384C4×C41—42no—
385C4×C41—41no—
386C4×C41—41no—
387C4×C41—41no—
388C4×C41—41no—
389C4×C41—81no—
390C4×C41#57611yescharacteristic
391C4×C41#57611yescharacteristic
392C4×C41#57611yescharacteristic
393C4×C41#57711yescharacteristic
394#3546C2×C4111yescharacteristic, complemented
395#3251C2×C4111yescharacteristic, complemented
396#3214C2×C4111yescharacteristic, complemented
397#3169C2×C4111yescharacteristic, complemented
398#1650C2×C4111yescharacteristic, complemented
399#1647C2×C4111yescharacteristic, complemented
400#1642C2×C4111yescharacteristic, complemented
401#1639C2×C4111yescharacteristic, complemented
402#1628C2×C4111yescharacteristic, complemented
403#1625C2×C4111yescharacteristic, complemented
404#1621C2×C4111yescharacteristic, complemented
405#1619C2×C4111yescharacteristic, complemented
406#1557C2×C4111yescharacteristic, complemented
407#1494C2×C4111yescharacteristic, complemented
408#1492C2×C4111yescharacteristic, complemented
409C2×C41—41no—
410C2×C41—81no—
411C2×C41—82no—
412C2×C41—81no—
413C2×C41—81no—
414C2×C41—161no—
415C2×C41#300811yescharacteristic
416C2×C41#301211yescharacteristic
417C2×C41#301811yescharacteristic
418#560—22no—
419#556C22×C4111yescharacteristic
420#553—21no—
421#550—21no—
422#550C22×C4111yescharacteristic
423#547C22×C4111yescharacteristic
424#546—21no—
425#546—21no—
426D42C22×C4111yescharacteristic
427#542—21no—
428#538—22no—
429#537—21no—
430#535—21no—
431#535—21no—
432#532C22×C4111yescharacteristic
433#532C22×C4111yescharacteristic
434#532C22×C4111yescharacteristic, complemented
435#529C22×C4111yescharacteristic
436#500C22×C4111yescharacteristic, complemented
437#496—21no—
438#493C22×C4111yescharacteristic
439#489—21no—
440#486C22×C4111yescharacteristic
441#486C22×C4111yescharacteristic, complemented
442#478—21no—
443#475C22×C4111yescharacteristic, complemented
444#474C22×C4111yescharacteristic
445#469—21no—
446#468—21no—
447#466—22no—
448#463—21no—
449#461C22×C4111yescharacteristic
450#461C22×C4111yescharacteristic, complemented
451#460C22×C4111yescharacteristic, complemented
452#459C22×C4111yescharacteristic
453#459C22×C4111yescharacteristic
454#459C22×C4111yescharacteristic, complemented
455#449—21no—
456#449—21no—
457C4×D8—22no—
458#432C22×C4111yescharacteristic, complemented
459#423C22×C4111yescharacteristic, complemented
460C2×C4×C8C22×C4111yescharacteristic, complemented
461#332C22×C4111yescharacteristic, complemented
462#332C22×C4111yescharacteristic, complemented
463#331C22×C4111yescharacteristic
464#331C22×C4111yescharacteristic
465Q8⋊C8C22×C4111yescharacteristic, complemented
466Q8⋊C8C22×C4111yescharacteristic, complemented
467D4⋊C8C22×C4111yescharacteristic
468D4⋊C8C22×C4111yescharacteristic
469D4⋊C8C22×C4111yescharacteristic
470D4⋊C8C22×C4111yescharacteristic
471D4⋊C8C22×C4111yescharacteristic, complemented
472D4⋊C8C22×C4111yescharacteristic, complemented
473C41#1870411yescharacteristic, direct product factor, Sylow
474C2×#41—21no—
475C2×#41—21no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C22×D4—21no—
480C22×D4—21no—
481C2×SD16—21no—
482C2×SD16—21no—
483C2×SD16—21no—
484C2×D8—22no—
485C2×D8—21no—
486C2×D8—21no—
487C2×D8—21no—
488C2×M16—21no—
489C22×C8—21no—
490C4⋊Q8D4×C4111yescharacteristic
491C4⋊Q8C23×C4111yescharacteristic
492C4⋊Q8C23×C4111yescharacteristic
493#127—22no—
494#127—21no—
495#127D4×C4111yescharacteristic
496#127C23×C4111yescharacteristic
497#127C23×C4111yescharacteristic
498#126—22no—
499#126—22no—
500#126—21no—
501#125D4×C4111yescharacteristic
502#124—22no—
503#124—21no—
504#124—21no—
505#124—21no—
506#124—21no—
507#124D4×C4111yescharacteristic
508#123—22no—
509#123—22no—
510#123—21no—
511#123—22no—
512C22⋊Q8—22no—
513C22⋊Q8—21no—
514C22⋊Q8—21no—
515C22⋊Q8D4×C4111yescharacteristic
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—21no—
522#121—22no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121D4×C4111yescharacteristic
531#121D4×C4111yescharacteristic
532#121D4×C4111yescharacteristic
533#121D4×C4112yes—
534#120—22no—
535#120—22no—
536#120—22no—
537#120—22no—
538C4×Q8—21no—
539C4×Q8C23×C4111yescharacteristic
540C4×D4—22no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4D4×C4112yes—
548C4×D4C23×C4111yescharacteristic
549C4×D4C23×C4111yescharacteristic
550C4×D4C23×C4111yescharacteristic
551#117—21no—
552#117—21no—
553C2×C4⋊C4—21no—
554C2×C22⋊C4—22no—
555C2×C42C23×C4111yescharacteristic
556#107—22no—
557#107—21no—
558#106—21no—
559C4⋊C8—21no—
560C4⋊C8C23×C4111yescharacteristic
561C4⋊C8C23×C4111yescharacteristic
562C4⋊C8C23×C4111yescharacteristic
563C4⋊C8C23×C4111yescharacteristic
564#103—21no—
565#103—21no—
566#103—21no—
567#102—22no—
568#102—21no—
569#102—22no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574C22⋊C8—21no—
575#97—21no—
576C4×C8—21no—
577C4×C8C23×C4111yescharacteristic
578C4×C8C23×C4111yescharacteristic
579C24—22no—
580#41—81no—
581#41—81no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—81no—
586#41—81no—
587#41—81no—
588#41—81no—
589#41—81no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8C2×D4×C4111yescharacteristic
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4C2×D4×C4111yescharacteristic
616C2×D4C2×D4×C4111yescharacteristic
617C2×D4C2×D4×C4111yescharacteristic
618C2×D4C2×D4×C4112yes—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—41no—
626C22×C4C2×D4×C4111yescharacteristic
627C22×C4C2×D4×C4111yescharacteristic
628C22×C4C2×D4×C4111yescharacteristic
629SD16—81no—
630SD16—81no—
631SD16—81no—
632D8—44no—
633D8—81no—
634D8—81no—
635D8—81no—
636M16—81no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—42no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4C2×D4×C4111yescharacteristic
655C4⋊C4C2×D4×C4111yescharacteristic
656C4⋊C4C2×D4×C4111yescharacteristic
657C4⋊C4C2×D4×C4111yescharacteristic
658C4⋊C4C2×D4×C4112yes—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C42—22no—
678C42—21no—
679C42C2×D4×C4111yescharacteristic
680C42C2×D4×C4111yescharacteristic
681C42C2×D4×C4111yescharacteristic
682C42C24×C4111yescharacteristic
683C23—21no—
684C23—21no—
685C23—22no—
686C23—21no—
687C23—41no—
688C23—82no—
689C23—82no—
690C23—82no—
691C23#120×C4111yescharacteristic
692Q8—21no—
693Q8—21no—
694Q8—41no—
695Q8—41no—
696Q8—41no—
697Q8—41no—
698Q8—81no—
699D4—21no—
700D4—21no—
701D4—21no—
702D4—21no—
703D4—21no—
704D4—21no—
705D4—42no—
706D4—42no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—81no—
716D4—81no—
717D4—82no—
718D4—81no—
719D4—81no—
720D4—81no—
721D4—82no—
722D4—82no—
723D4—82no—
724D4—82no—
725D4—82no—
726D4—82no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—82no—
746C2×C4—82no—
747C2×C4—82no—
748C2×C4—82no—
749C2×C4#120×C4111yescharacteristic
750C2×C4#120×C4111yescharacteristic
751C2×C4#120×C4111yescharacteristic
752C2×C4C22×D4×C4111yescharacteristic
753C2×C4C22×D4×C4111yescharacteristic
754C2×C4C22×D4×C4111yescharacteristic
755C8—22no—
756C8—41no—
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—164no—
780C22C2×#120×C4111yescharacteristic
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—41no—
786C4—42no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4C41×#57611yescharacteristic
793C4C41×#57611yescharacteristic
794C4C41×#57611yescharacteristic
795C4C41×#57711yescharacteristic
796C2—41no—
797C2—81no—
798C2—81no—
799C2—82no—
800C2—81no—
801C2—161no—
802C2C41×#300811yescharacteristic
803C2C41×#301211yescharacteristic
804C2C41×#301811yescharacteristic
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×#3251C2semidirect
3. C41×#3214C2semidirect
4. C41×#3169C2semidirect
5. C41×#1650C2semidirect
6. C41×#1647C2semidirect
7. C41×#1642C2semidirect
8. C41×#1639C2semidirect
9. C41×#1628C2semidirect
10. C41×#1625C2semidirect
11. C41×#1621C2semidirect
12. C41×#1619C2semidirect
13. C41×#1557C2semidirect
14. C41×#1494C2semidirect
15. C41×#1492C2semidirect
32. C41×#532C22semidirect
34. C41×#500C22semidirect
39. C41×#486C22semidirect
41. C41×#475C22semidirect
48. C41×#461C22semidirect
49. C41×#460C22semidirect
52. C41×#459C22semidirect
56. C41×#432C22semidirect
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
358. #18704C41direct (N × H)
394. #3546C2×C41semidirect
395. #3251C2×C41semidirect
396. #3214C2×C41semidirect
397. #3169C2×C41semidirect
398. #1650C2×C41semidirect
399. #1647C2×C41semidirect
400. #1642C2×C41semidirect
401. #1639C2×C41semidirect
402. #1628C2×C41semidirect
403. #1625C2×C41semidirect
404. #1621C2×C41semidirect
405. #1619C2×C41semidirect
406. #1557C2×C41semidirect
407. #1494C2×C41semidirect
408. #1492C2×C41semidirect
434. #532C22×C41semidirect
436. #500C22×C41semidirect
441. #486C22×C41semidirect
443. #475C22×C41semidirect
450. #461C22×C41semidirect
451. #460C22×C41semidirect
454. #459C22×C41semidirect
458. #432C22×C41semidirect
459. #423C22×C41semidirect
460. C2×C4×C8C22×C41semidirect
461. #332C22×C41semidirect
462. #332C22×C41semidirect
465. Q8⋊C8C22×C41semidirect
466. Q8⋊C8C22×C41semidirect
471. D4⋊C8C22×C41semidirect
472. D4⋊C8C22×C41semidirect
473. C41#18704direct (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×#32512
C41×#32142
C41×#31692
C41×#16502
C41×#16472
C41×#16422
C41×#16392
C41×#16282
C41×#16252
C41×#16212
C41×#16192
C41×#15572
C41×#14942
C41×#14922
#1870441