Finite Group Databasebeta

← C41×#18594 #23794795

Subgroups — C41×#18594 #23794795

Order 10496.

994 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3514C211yesmaximal, characteristic, complemented
2C41×#3251C211yesmaximal, characteristic, complemented
3C41×#3184C211yesmaximal, characteristic, complemented
4C41×#3035C211yesmaximal, characteristic, complemented
5C41×#1652C211yesmaximal, characteristic, complemented
6C41×#1651C211yesmaximal, characteristic, complemented
7C41×#1640C211yesmaximal, characteristic, complemented
8C41×#1639C211yesmaximal, characteristic, complemented
9C41×#1628C211yesmaximal, characteristic, complemented
10C41×#1627C211yesmaximal, characteristic, complemented
11C41×#1620C211yesmaximal, characteristic, complemented
12C41×#1619C211yesmaximal, characteristic, complemented
13C41×#1547C211yesmaximal, characteristic, complemented
14C41×#1489C211yesmaximal, characteristic, complemented
15C41×#1483C211yesmaximal, characteristic, complemented
16C2×#135×C41—21no—
17C41×#559C2211yescharacteristic
18C41×#556C2211yescharacteristic
19C41×#555—21no—
20C41×#551—22no—
21D4×Q8×C41C2211yescharacteristic
22C41×#548—21no—
23C41×#546—21no—
24C41×#546—21no—
25D42×C41C2211yescharacteristic
26C41×#542—21no—
27C41×#538—22no—
28C41×#532C2211yescharacteristic
29C41×#532C2211yescharacteristic, complemented
30C41×#529—21no—
31C41×#529C2211yescharacteristic
32C2×#124×C41—21no—
33C41×#518—21no—
34C4×#41×C41C2211yescharacteristic
35C41×#498C2211yescharacteristic, complemented
36C41×#493C2211yescharacteristic
37C41×#486C2211yescharacteristic
38C41×#486C2211yescharacteristic, complemented
39C41×#478—21no—
40C41×#475C2211yescharacteristic, complemented
41C41×#474C2211yescharacteristic
42C41×#469—22no—
43C41×#469—21no—
44C41×#468—21no—
45C41×#464—21no—
46C41×#463—21no—
47C41×#463—21no—
48C41×#462C2211yescharacteristic, complemented
49C41×#461C2211yescharacteristic
50C41×#460C2211yescharacteristic, complemented
51C41×#460C2211yescharacteristic, complemented
52C41×#459C2211yescharacteristic
53C41×#459C2211yescharacteristic
54C41×#442—22no—
55C41×#423C2211yescharacteristic, complemented
56C2×C4⋊C8×C41C2211yescharacteristic, complemented
57C41×#416—21no—
58C4×M16×C41C2211yescharacteristic, complemented
59C41×#332C2211yescharacteristic, complemented
60C41×#332C2211yescharacteristic, complemented
61C41×#331C2211yescharacteristic
62C41×#331C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic, complemented
64C41×Q8⋊C8C2211yescharacteristic, complemented
65C41×Q8⋊C8C2211yescharacteristic, complemented
66C41×Q8⋊C8C2211yescharacteristic, complemented
67C41×D4⋊C8C2211yescharacteristic
68C41×D4⋊C8C2211yescharacteristic
69C41×D4⋊C8C2211yescharacteristic
70C41×D4⋊C8C2211yescharacteristic
71C2×#41×C41—21no—
72C2×#41×C41—21no—
73C2×#41×C41D411yescharacteristic
74C22×Q8×C41—21no—
75C22×D4×C41—21no—
76C22×D4×C41—21no—
77#135×C41—44no—
78C2×Q16×C41—21no—
79C2×SD16×C41—21no—
80C2×SD16×C41—21no—
81C2×SD16×C41—21no—
82C2×D8×C41—21no—
83C2×D8×C41—22no—
84C2×D8×C41—21no—
85C2×M16×C41—21no—
86C2×M16×C41—21no—
87C22×C8×C41—21no—
88C4⋊Q8×C41—21no—
89C4⋊Q8×C41C2311yescharacteristic
90C4⋊Q8×C41C2311yescharacteristic
91#127×C41C2311yescharacteristic
92#127×C41C2311yescharacteristic
93#126×C41—22no—
94#126×C41—22no—
95#126×C41—21no—
96#125×C41D411yescharacteristic
97#124×C41—22no—
98#124×C41—22no—
99#124×C41—22no—
100#124×C41—21no—
101#124×C41—21no—
102#124×C41—21no—
103#124×C41—21no—
104#124×C41—21no—
105#124×C41D411yescharacteristic
106#123×C41—22no—
107#123×C41—22no—
108#123×C41—22no—
109#123×C41—21no—
110C22⋊Q8×C41—22no—
111C22⋊Q8×C41—21no—
112C22⋊Q8×C41—21no—
113C22⋊Q8×C41—22no—
114C22⋊Q8×C41D411yescharacteristic
115#121×C41—22no—
116#121×C41—22no—
117#121×C41—21no—
118#121×C41—21no—
119#121×C41—21no—
120#121×C41—21no—
121#121×C41—21no—
122#121×C41D411yescharacteristic
123#121×C41D412yes—
124#120×C41—22no—
125#120×C41—22no—
126C4×Q8×C41—21no—
127C4×Q8×C41D411yescharacteristic
128C4×Q8×C41C2311yescharacteristic
129C4×Q8×C41C2311yescharacteristic
130C4×D4×C41—22no—
131C4×D4×C41—22no—
132C4×D4×C41—21no—
133C4×D4×C41—21no—
134C4×D4×C41—21no—
135C4×D4×C41—21no—
136C4×D4×C41—21no—
137C4×D4×C41—21no—
138C4×D4×C41—21no—
139C4×D4×C41—21no—
140C4×D4×C41—21no—
141C4×D4×C41D411yescharacteristic
142C4×D4×C41D412yes—
143C4×D4×C41C2311yescharacteristic
144C4×D4×C41C2311yescharacteristic
145#117×C41—22no—
146#117×C41—21no—
147#117×C41—21no—
148#117×C41—21no—
149#117×C41D411yescharacteristic
150C2×C22⋊C4×C41—22no—
151C2×C22⋊C4×C41—22no—
152C2×C22⋊C4×C41—22no—
153C2×C42×C41—21no—
154C2×C42×C41C2311yescharacteristic
155#107×C41—21no—
156#106×C41—22no—
157#106×C41—21no—
158C4⋊C8×C41—21no—
159C4⋊C8×C41—21no—
160C4⋊C8×C41C2311yescharacteristic
161C4⋊C8×C41C2311yescharacteristic
162C4⋊C8×C41C2311yescharacteristic
163C4⋊C8×C41C2311yescharacteristic
164#103×C41—21no—
165#103×C41—21no—
166#103×C41—21no—
167#102×C41—22no—
168#102×C41—21no—
169#102×C41—21no—
170#102×C41—21no—
171#102×C41—22no—
172#102×C41—21no—
173#102×C41—21no—
174#97×C41—21no—
175C4×C8×C41C2311yescharacteristic
176C4×C8×C41C2311yescharacteristic
177C24×C41—22no—
178#41×C41—22no—
179#41×C41—41no—
180#41×C41—42no—
181#41×C41—42no—
182#41×C41—81no—
183#41×C41—81no—
184C2×Q8×C41—22no—
185C2×Q8×C41—21no—
186C2×Q8×C41—21no—
187C2×Q8×C41—81no—
188C2×Q8×C41—81no—
189C2×Q8×C41C2×D411yescharacteristic
190C2×Q8×C41C2×D411yescharacteristic
191C2×D4×C41—22no—
192C2×D4×C41—21no—
193C2×D4×C41—22no—
194C2×D4×C41—21no—
195C2×D4×C41—22no—
196C2×D4×C41—21no—
197C2×D4×C41—21no—
198C2×D4×C41—21no—
199C2×D4×C41—21no—
200C2×D4×C41—21no—
201C2×D4×C41—42no—
202C2×D4×C41—42no—
203C2×D4×C41—41no—
204C2×D4×C41—81no—
205C2×D4×C41—81no—
206C2×D4×C41C2×D411yescharacteristic
207C2×D4×C41C2×D411yescharacteristic
208C2×D4×C41C2×D412yes—
209C22×C4×C41—22no—
210C22×C4×C41—22no—
211C22×C4×C41—21no—
212C22×C4×C41—21no—
213C22×C4×C41—21no—
214C22×C4×C41—21no—
215C22×C4×C41—22no—
216C22×C4×C41—41no—
217C22×C4×C41C2×D411yescharacteristic
218C22×C4×C41C2×D411yescharacteristic
219C22×C4×C41C2×D411yescharacteristic
220Q16×C41—42no—
221SD16×C41—42no—
222SD16×C41—42no—
223SD16×C41—81no—
224D8×C41—44no—
225D8×C41—42no—
226D8×C41—81no—
227M16×C41—42no—
228M16×C41—81no—
229C2×C8×C41—21no—
230C2×C8×C41—21no—
231C2×C8×C41—21no—
232C2×C8×C41—21no—
233C2×C8×C41—21no—
234C2×C8×C41—21no—
235C2×C8×C41—42no—
236C4⋊C4×C41—22no—
237C4⋊C4×C41—22no—
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—21no—
245C4⋊C4×C41—21no—
246C4⋊C4×C41—21no—
247C4⋊C4×C41C2×D411yescharacteristic
248C4⋊C4×C41C2×D411yescharacteristic
249C4⋊C4×C41C2×D411yescharacteristic
250C4⋊C4×C41C2×D412yes—
251C4⋊C4×C41C2×D411yescharacteristic
252C22⋊C4×C41—22no—
253C22⋊C4×C41—22no—
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—41no—
270C22⋊C4×C41—41no—
271C42×C41—22no—
272C42×C41—21no—
273C42×C41—21no—
274C42×C41—21no—
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—44no—
284C23×C41—41no—
285C23×C41—82no—
286C23×C41—82no—
287C23×C41#12011yescharacteristic
288Q8×C41—21no—
289Q8×C41—21no—
290Q8×C41—21no—
291Q8×C41—21no—
292Q8×C41—41no—
293Q8×C41—41no—
294Q8×C41—41no—
295Q8×C41—41no—
296Q8×C41—82no—
297D4×C41—21no—
298D4×C41—21no—
299D4×C41—21no—
300D4×C41—42no—
301D4×C41—42no—
302D4×C41—42no—
303D4×C41—44no—
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—82no—
314D4×C41—82no—
315D4×C41—82no—
316D4×C41AGL(1,ℤ/8)12yes—
317C2×C4×C41—21no—
318C2×C4×C41—21no—
319C2×C4×C41—21no—
320C2×C4×C41—21no—
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—22no—
328C2×C4×C41—41no—
329C2×C4×C41—42no—
330C2×C4×C41—41no—
331C2×C4×C41—41no—
332C2×C4×C41—41no—
333C2×C4×C41—41no—
334C2×C4×C41—41no—
335C2×C4×C41—81no—
336C2×C4×C41—82no—
337C2×C4×C41—82no—
338C2×C4×C41—82no—
339C2×C4×C41—82no—
340C2×C4×C41#12011yescharacteristic
341C2×C4×C41#12011yescharacteristic
342C2×C4×C41#12011yescharacteristic
343C2×C4×C41C22×D411yescharacteristic
344C2×C4×C41C22×D411yescharacteristic
345C2×C4×C41C22×D411yescharacteristic
346C8×C41—22no—
347C8×C41—41no—
348C8×C41—41no—
349C8×C41—41no—
350C8×C41—41no—
351C8×C41—41no—
352#18594C4111yesmaximal, characteristic, direct product factor, Sylow
353C22×C41—21no—
354C22×C41—22no—
355C22×C41—21no—
356C22×C41—21no—
357C22×C41—41no—
358C22×C41—41no—
359C22×C41—41no—
360C22×C41—42no—
361C22×C41—42no—
362C22×C41—41no—
363C22×C41—42no—
364C22×C41—41no—
365C22×C41—81no—
366C22×C41—81no—
367C22×C41—81no—
368C22×C41—164no—
369C22×C41C2×#12011yescharacteristic
370C4×C41—21no—
371C4×C41—21no—
372C4×C41—21no—
373C4×C41—21no—
374C4×C41—41no—
375C4×C41—41no—
376C4×C41—41no—
377C4×C41—42no—
378C4×C41—41no—
379C4×C41—41no—
380C4×C41—41no—
381C4×C41—81no—
382C4×C41C2×AGL(1,ℤ/8)11yescharacteristic
383C4×C41#57511yescharacteristic
384C4×C41#57611yescharacteristic
385C4×C41#57711yescharacteristic
386#3514C2×C4111yescharacteristic, complemented
387#3251C2×C4111yescharacteristic, complemented
388#3184C2×C4111yescharacteristic, complemented
389#3035C2×C4111yescharacteristic, complemented
390#1652C2×C4111yescharacteristic, complemented
391#1651C2×C4111yescharacteristic, complemented
392#1640C2×C4111yescharacteristic, complemented
393#1639C2×C4111yescharacteristic, complemented
394#1628C2×C4111yescharacteristic, complemented
395#1627C2×C4111yescharacteristic, complemented
396#1620C2×C4111yescharacteristic, complemented
397#1619C2×C4111yescharacteristic, complemented
398#1547C2×C4111yescharacteristic, complemented
399#1489C2×C4111yescharacteristic, complemented
400#1483C2×C4111yescharacteristic, complemented
401C2×C41—41no—
402C2×C41—42no—
403C2×C41—82no—
404C2×C41—81no—
405C2×C41—161no—
406C2×C41#300611yescharacteristic
407C2×C41#301211yescharacteristic
408C2×C41#301811yescharacteristic
409C2×#135—21no—
410#559C22×C4111yescharacteristic
411#556C22×C4111yescharacteristic
412#555—21no—
413#551—22no—
414D4×Q8C22×C4111yescharacteristic
415#548—21no—
416#546—21no—
417#546—21no—
418D42C22×C4111yescharacteristic
419#542—21no—
420#538—22no—
421#532C22×C4111yescharacteristic
422#532C22×C4111yescharacteristic, complemented
423#529—21no—
424#529C22×C4111yescharacteristic
425C2×#124—21no—
426#518—21no—
427C4×#41C22×C4111yescharacteristic
428#498C22×C4111yescharacteristic, complemented
429#493C22×C4111yescharacteristic
430#486C22×C4111yescharacteristic
431#486C22×C4111yescharacteristic, complemented
432#478—21no—
433#475C22×C4111yescharacteristic, complemented
434#474C22×C4111yescharacteristic
435#469—22no—
436#469—21no—
437#468—21no—
438#464—21no—
439#463—21no—
440#463—21no—
441#462C22×C4111yescharacteristic, complemented
442#461C22×C4111yescharacteristic
443#460C22×C4111yescharacteristic, complemented
444#460C22×C4111yescharacteristic, complemented
445#459C22×C4111yescharacteristic
446#459C22×C4111yescharacteristic
447#442—22no—
448#423C22×C4111yescharacteristic, complemented
449C2×C4⋊C8C22×C4111yescharacteristic, complemented
450#416—21no—
451C4×M16C22×C4111yescharacteristic, complemented
452#332C22×C4111yescharacteristic, complemented
453#332C22×C4111yescharacteristic, complemented
454#331C22×C4111yescharacteristic
455#331C22×C4111yescharacteristic
456Q8⋊C8C22×C4111yescharacteristic, complemented
457Q8⋊C8C22×C4111yescharacteristic, complemented
458Q8⋊C8C22×C4111yescharacteristic, complemented
459Q8⋊C8C22×C4111yescharacteristic, complemented
460D4⋊C8C22×C4111yescharacteristic
461D4⋊C8C22×C4111yescharacteristic
462D4⋊C8C22×C4111yescharacteristic
463D4⋊C8C22×C4111yescharacteristic
464C41#1859411yescharacteristic, direct product factor, Sylow
465C2×#41—21no—
466C2×#41—21no—
467C2×#41D4×C4111yescharacteristic
468C22×Q8—21no—
469C22×D4—21no—
470C22×D4—21no—
471#135—44no—
472C2×Q16—21no—
473C2×SD16—21no—
474C2×SD16—21no—
475C2×SD16—21no—
476C2×D8—21no—
477C2×D8—22no—
478C2×D8—21no—
479C2×M16—21no—
480C2×M16—21no—
481C22×C8—21no—
482C4⋊Q8—21no—
483C4⋊Q8C23×C4111yescharacteristic
484C4⋊Q8C23×C4111yescharacteristic
485#127C23×C4111yescharacteristic
486#127C23×C4111yescharacteristic
487#126—22no—
488#126—22no—
489#126—21no—
490#125D4×C4111yescharacteristic
491#124—22no—
492#124—22no—
493#124—22no—
494#124—21no—
495#124—21no—
496#124—21no—
497#124—21no—
498#124—21no—
499#124D4×C4111yescharacteristic
500#123—22no—
501#123—22no—
502#123—22no—
503#123—21no—
504C22⋊Q8—22no—
505C22⋊Q8—21no—
506C22⋊Q8—21no—
507C22⋊Q8—22no—
508C22⋊Q8D4×C4111yescharacteristic
509#121—22no—
510#121—22no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121D4×C4111yescharacteristic
517#121D4×C4112yes—
518#120—22no—
519#120—22no—
520C4×Q8—21no—
521C4×Q8D4×C4111yescharacteristic
522C4×Q8C23×C4111yescharacteristic
523C4×Q8C23×C4111yescharacteristic
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4—21no—
534C4×D4—21no—
535C4×D4D4×C4111yescharacteristic
536C4×D4D4×C4112yes—
537C4×D4C23×C4111yescharacteristic
538C4×D4C23×C4111yescharacteristic
539#117—22no—
540#117—21no—
541#117—21no—
542#117—21no—
543#117D4×C4111yescharacteristic
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
547C2×C42—21no—
548C2×C42C23×C4111yescharacteristic
549#107—21no—
550#106—22no—
551#106—21no—
552C4⋊C8—21no—
553C4⋊C8—21no—
554C4⋊C8C23×C4111yescharacteristic
555C4⋊C8C23×C4111yescharacteristic
556C4⋊C8C23×C4111yescharacteristic
557C4⋊C8C23×C4111yescharacteristic
558#103—21no—
559#103—21no—
560#103—21no—
561#102—22no—
562#102—21no—
563#102—21no—
564#102—21no—
565#102—22no—
566#102—21no—
567#102—21no—
568#97—21no—
569C4×C8C23×C4111yescharacteristic
570C4×C8C23×C4111yescharacteristic
571C24—22no—
572#41—22no—
573#41—41no—
574#41—42no—
575#41—42no—
576#41—81no—
577#41—81no—
578C2×Q8—22no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—81no—
582C2×Q8—81no—
583C2×Q8C2×D4×C4111yescharacteristic
584C2×Q8C2×D4×C4111yescharacteristic
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—41no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4C2×D4×C4111yescharacteristic
601C2×D4C2×D4×C4111yescharacteristic
602C2×D4C2×D4×C4112yes—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—41no—
611C22×C4C2×D4×C4111yescharacteristic
612C22×C4C2×D4×C4111yescharacteristic
613C22×C4C2×D4×C4111yescharacteristic
614Q16—42no—
615SD16—42no—
616SD16—42no—
617SD16—81no—
618D8—44no—
619D8—42no—
620D8—81no—
621M16—42no—
622M16—81no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—42no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4C2×D4×C4111yescharacteristic
642C4⋊C4C2×D4×C4111yescharacteristic
643C4⋊C4C2×D4×C4111yescharacteristic
644C4⋊C4C2×D4×C4112yes—
645C4⋊C4C2×D4×C4111yescharacteristic
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—41no—
664C22⋊C4—41no—
665C42—22no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42C2×D4×C4111yescharacteristic
671C42C2×D4×C4111yescharacteristic
672C42C2×D4×C4111yescharacteristic
673C42C24×C4111yescharacteristic
674C23—21no—
675C23—21no—
676C23—22no—
677C23—44no—
678C23—41no—
679C23—82no—
680C23—82no—
681C23#120×C4111yescharacteristic
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—21no—
686Q8—41no—
687Q8—41no—
688Q8—41no—
689Q8—41no—
690Q8—82no—
691D4—21no—
692D4—21no—
693D4—21no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—44no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—82no—
707D4—81no—
708D4—82no—
709D4—82no—
710D4AGL(1,ℤ/8)×C4112yes—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—82no—
730C2×C4—81no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4#120×C4111yescharacteristic
735C2×C4#120×C4111yescharacteristic
736C2×C4#120×C4111yescharacteristic
737C2×C4C22×D4×C4111yescharacteristic
738C2×C4C22×D4×C4111yescharacteristic
739C2×C4C22×D4×C4111yescharacteristic
740C8—22no—
741C8—41no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C22—21no—
747C22—22no—
748C22—21no—
749C22—21no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—42no—
757C22—41no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—164no—
762C22C2×#120×C4111yescharacteristic
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—81no—
775C4C2×AGL(1,ℤ/8)×C4111yescharacteristic
776C4C41×#57511yescharacteristic
777C4C41×#57611yescharacteristic
778C4C41×#57711yescharacteristic
779C2—41no—
780C2—42no—
781C2—81no—
782C2—82no—
783C2—161no—
784C2C41×#300611yescharacteristic
785C2C41×#301211yescharacteristic
786C2C41×#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×#3514C2semidirect
2. C41×#3251C2semidirect
3. C41×#3184C2semidirect
4. C41×#3035C2semidirect
5. C41×#1652C2semidirect
6. C41×#1651C2semidirect
7. C41×#1640C2semidirect
8. C41×#1639C2semidirect
9. C41×#1628C2semidirect
10. C41×#1627C2semidirect
11. C41×#1620C2semidirect
12. C41×#1619C2semidirect
13. C41×#1547C2semidirect
14. C41×#1489C2semidirect
15. C41×#1483C2semidirect
29. C41×#532C22semidirect
35. C41×#498C22semidirect
38. C41×#486C22semidirect
40. C41×#475C22semidirect
48. C41×#462C22semidirect
50. C41×#460C22semidirect
51. C41×#460C22semidirect
55. C41×#423C22semidirect
56. C2×C4⋊C8×C41C22semidirect
58. C4×M16×C41C22semidirect
59. C41×#332C22semidirect
60. C41×#332C22semidirect
63. C41×Q8⋊C8C22semidirect
64. C41×Q8⋊C8C22semidirect
65. C41×Q8⋊C8C22semidirect
66. C41×Q8⋊C8C22semidirect
352. #18594C41direct (N × H)
386. #3514C2×C41semidirect
387. #3251C2×C41semidirect
388. #3184C2×C41semidirect
389. #3035C2×C41semidirect
390. #1652C2×C41semidirect
391. #1651C2×C41semidirect
392. #1640C2×C41semidirect
393. #1639C2×C41semidirect
394. #1628C2×C41semidirect
395. #1627C2×C41semidirect
396. #1620C2×C41semidirect
397. #1619C2×C41semidirect
398. #1547C2×C41semidirect
399. #1489C2×C41semidirect
400. #1483C2×C41semidirect
422. #532C22×C41semidirect
428. #498C22×C41semidirect
431. #486C22×C41semidirect
433. #475C22×C41semidirect
441. #462C22×C41semidirect
443. #460C22×C41semidirect
444. #460C22×C41semidirect
448. #423C22×C41semidirect
449. C2×C4⋊C8C22×C41semidirect
451. C4×M16C22×C41semidirect
452. #332C22×C41semidirect
453. #332C22×C41semidirect
456. Q8⋊C8C22×C41semidirect
457. Q8⋊C8C22×C41semidirect
458. Q8⋊C8C22×C41semidirect
459. Q8⋊C8C22×C41semidirect
464. C41#18594direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35142
C41×#32512
C41×#31842
C41×#30352
C41×#16522
C41×#16512
C41×#16402
C41×#16392
C41×#16282
C41×#16272
C41×#16202
C41×#16192
C41×#15472
C41×#14892
C41×#14832
#1859441