Finite Group Databasebeta

← C41×#25665 #23801866

Subgroups — C41×#25665 #23801866

Order 10496.

1136 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3505C211yesmaximal, characteristic
2C41×#2591C211yesmaximal, characteristic, complemented
3C41×#2583C211yesmaximal, characteristic, complemented
4C41×#2579C211yesmaximal, characteristic, complemented
5C41×#2044C212yesmaximal, complemented
6C41×#2044C212yesmaximal, complemented
7C41×#1996C211yesmaximal, characteristic, complemented
8C41×#1964C211yesmaximal, characteristic, complemented
9C41×#1867C212yesmaximal, complemented
10C41×#1867C212yesmaximal, complemented
11C4×#99×C41C211yesmaximal, characteristic, complemented
12C41×#553—22no—
13C41×#553—21no—
14C41×#552—21no—
15C41×#551—22no—
16C41×#548—21no—
17C41×#546—21no—
18C41×#539—21no—
19C41×#538—21no—
20C41×#534C2212yes—
21C41×#529—21no—
22C41×#525—21no—
23C2×C22⋊Q8×C41C2211yescharacteristic
24C2×#121×C41C2211yescharacteristic
25C41×#518C2212yes—
26C2×C4×D4×C41C2211yescharacteristic
27C22×C4⋊C4×C41C2211yescharacteristic
28C2×#99×C41C2212yes—
29C2×#99×C41C2212yes—
30C2×#99×C41C2212yes—
31C41×#400—21no—
32C41×#398—21no—
33C41×#398—21no—
34C41×#396—21no—
35C41×#395—21no—
36C41×#394—21no—
37C41×#389—22no—
38C41×#388—22no—
39C41×#387—21no—
40C41×#386C2211yescharacteristic
41C41×#386C2211yescharacteristic
42C41×#386C2212yes—
43C41×#386C2212yes—
44C41×#385—21no—
45C41×#385C2212yes—
46C41×#385C2212yes—
47C41×#385C2211yescharacteristic
48C41×#385C2211yescharacteristic
49C41×#380C2211yescharacteristic
50C4×C22⋊C4×C41C2211yescharacteristic
51C4×C22⋊C4×C41C2211yescharacteristic
52C41×#342C2212yes—
53C41×#342C2212yes—
54C41×#342C2212yes—
55C2×#41×C41—21no—
56C22×Q8×C41D411yescharacteristic
57C22×D4×C41D411yescharacteristic
58C22×D4×C41C2311yescharacteristic
59C22×D4×C41C2312yes—
60C23×C4×C41D411yescharacteristic
61C23×C4×C41C2311yescharacteristic
62C23×C4×C41C2311yescharacteristic
63C23×C4×C41C2311yescharacteristic
64#126×C41—22no—
65#126×C41—22no—
66#126×C41—22no—
67#125×C41—21no—
68#125×C41—22no—
69#124×C41—21no—
70#124×C41—22no—
71#123×C41—22no—
72#123×C41—22no—
73#123×C41—22no—
74#123×C41—22no—
75#123×C41—22no—
76C22⋊Q8×C41—21no—
77C22⋊Q8×C41—22no—
78C22⋊Q8×C41—21no—
79C22⋊Q8×C41—21no—
80C22⋊Q8×C41—21no—
81C22⋊Q8×C41—21no—
82#121×C41—21no—
83#121×C41—22no—
84#121×C41—21no—
85#121×C41—21no—
86#121×C41—21no—
87#121×C41—21no—
88#121×C41—22no—
89#121×C41—22no—
90#120×C41—22no—
91#120×C41—22no—
92C4×Q8×C41—21no—
93C4×D4×C41—22no—
94C4×D4×C41—21no—
95C4×D4×C41—21no—
96C4×D4×C41—21no—
97C4×D4×C41—21no—
98C4×D4×C41—21no—
99C4×D4×C41—22no—
100C4×D4×C41—22no—
101C4×D4×C41—22no—
102C4×D4×C41—22no—
103#117×C41—21no—
104#117×C41—22no—
105#117×C41—22no—
106C2×C4⋊C4×C41—21no—
107C2×C4⋊C4×C41—21no—
108C2×C4⋊C4×C41—21no—
109C2×C4⋊C4×C41—21no—
110C2×C4⋊C4×C41—21no—
111C2×C4⋊C4×C41—21no—
112C2×C4⋊C4×C41—21no—
113C2×C4⋊C4×C41—22no—
114C2×C4⋊C4×C41—21no—
115C2×C4⋊C4×C41—21no—
116C2×C4⋊C4×C41—22no—
117C2×C4⋊C4×C41D411yescharacteristic
118C2×C4⋊C4×C41D411yescharacteristic
119C2×C4⋊C4×C41D412yes—
120C2×C4⋊C4×C41D411yescharacteristic
121C2×C22⋊C4×C41—22no—
122C2×C22⋊C4×C41—21no—
123C2×C22⋊C4×C41—22no—
124C2×C22⋊C4×C41—21no—
125C2×C22⋊C4×C41—22no—
126C2×C22⋊C4×C41D411yescharacteristic
127C2×C22⋊C4×C41D412yes—
128C2×C22⋊C4×C41C2312yes—
129C2×C22⋊C4×C41C2311yescharacteristic
130C2×C22⋊C4×C41C2311yescharacteristic
131C2×C22⋊C4×C41C2311yescharacteristic
132C2×C22⋊C4×C41C2312yes—
133C2×C22⋊C4×C41C2312yes—
134C2×C42×C41—21no—
135C2×C42×C41—21no—
136C2×C42×C41D411yescharacteristic
137#99×C41—24no—
138#99×C41—24no—
139#99×C41—24no—
140#95×C41—21no—
141#95×C41—21no—
142#95×C41—21no—
143#95×C41—21no—
144#95×C41—21no—
145#95×C41—22no—
146#95×C41—22no—
147#95×C41—21no—
148#95×C41—21no—
149#95×C41—22no—
150#95×C41—22no—
151C24×C41C2×D412yes—
152C24×C41C2×D411yescharacteristic
153C24×C41C2411yescharacteristic
154#41×C41—82no—
155C2×Q8×C41—21no—
156C2×Q8×C41—21no—
157C2×Q8×C41—81no—
158C2×D4×C41—21no—
159C2×D4×C41—22no—
160C2×D4×C41—21no—
161C2×D4×C41—22no—
162C2×D4×C41—22no—
163C2×D4×C41—22no—
164C2×D4×C41—22no—
165C2×D4×C41—22no—
166C2×D4×C41—22no—
167C2×D4×C41—22no—
168C2×D4×C41—22no—
169C2×D4×C41—22no—
170C2×D4×C41—21no—
171C2×D4×C41—21no—
172C2×D4×C41—81no—
173C22×C4×C41—22no—
174C22×C4×C41—21no—
175C22×C4×C41—21no—
176C22×C4×C41—21no—
177C22×C4×C41—22no—
178C22×C4×C41—22no—
179C22×C4×C41—21no—
180C22×C4×C41—21no—
181C22×C4×C41—22no—
182C22×C4×C41—21no—
183C22×C4×C41—21no—
184C22×C4×C41—21no—
185C22×C4×C41—21no—
186C22×C4×C41—21no—
187C22×C4×C41—42no—
188C22×C4×C41—81no—
189C22×C4×C41—81no—
190C22×C4×C41—81no—
191C22×C4×C41C2×D411yescharacteristic
192C22×C4×C41C2×D412yes—
193C22×C4×C41C2×D411yescharacteristic
194C22×C4×C41C2×D412yes—
195C22×C4×C41C2×D411yescharacteristic
196C22×C4×C41C2×D412yes—
197C22×C4×C41C2×D411yescharacteristic
198C22×C4×C41C2×D411yescharacteristic
199C22×C4×C41C2×D411yescharacteristic
200C22×C4×C41C2×D411yescharacteristic
201C22×C4×C41C2×D411yescharacteristic
202C22×C4×C41C2×D411yescharacteristic
203C4⋊C4×C41—22no—
204C4⋊C4×C41—22no—
205C4⋊C4×C41—22no—
206C4⋊C4×C41—22no—
207C4⋊C4×C41—21no—
208C4⋊C4×C41—22no—
209C4⋊C4×C41—21no—
210C4⋊C4×C41—21no—
211C4⋊C4×C41—21no—
212C4⋊C4×C41—21no—
213C4⋊C4×C41—22no—
214C4⋊C4×C41—21no—
215C4⋊C4×C41—42no—
216C4⋊C4×C41—44no—
217C4⋊C4×C41—41no—
218C4⋊C4×C41—41no—
219C4⋊C4×C41—41no—
220C4⋊C4×C41—41no—
221C4⋊C4×C41—81no—
222C4⋊C4×C41—82no—
223C4⋊C4×C41—81no—
224C22⋊C4×C41—22no—
225C22⋊C4×C41—22no—
226C22⋊C4×C41—22no—
227C22⋊C4×C41—22no—
228C22⋊C4×C41—22no—
229C22⋊C4×C41—22no—
230C22⋊C4×C41—21no—
231C22⋊C4×C41—22no—
232C22⋊C4×C41—21no—
233C22⋊C4×C41—22no—
234C22⋊C4×C41—22no—
235C22⋊C4×C41—22no—
236C22⋊C4×C41—21no—
237C22⋊C4×C41—21no—
238C22⋊C4×C41—22no—
239C22⋊C4×C41—22no—
240C22⋊C4×C41—22no—
241C22⋊C4×C41—22no—
242C22⋊C4×C41—22no—
243C22⋊C4×C41—44no—
244C22⋊C4×C41—42no—
245C22⋊C4×C41—82no—
246C22⋊C4×C41—81no—
247C22⋊C4×C41#4114yescomplemented
248C42×C41—22no—
249C42×C41—22no—
250C42×C41—21no—
251C42×C41—21no—
252C42×C41—81no—
253C42×C41—81no—
254C23×C41—22no—
255C23×C41—21no—
256C23×C41—21no—
257C23×C41—21no—
258C23×C41—22no—
259C23×C41—22no—
260C23×C41—41no—
261C23×C41—41no—
262C23×C41—41no—
263C23×C41—41no—
264C23×C41—42no—
265C23×C41—42no—
266C23×C41C22×D411yescharacteristic
267C23×C41C22×D411yescharacteristic
268C23×C41C22×D411yescharacteristic
269C23×C41C2×#4112yes—
270C23×C412−1+412yes—
271Q8×C41—42no—
272Q8×C41—81no—
273D4×C41—42no—
274D4×C41—42no—
275D4×C41—42no—
276D4×C41—42no—
277D4×C41—42no—
278D4×C41—42no—
279D4×C41—42no—
280D4×C41—81no—
281D4×C41—82no—
282D4×C41—82no—
283C2×C4×C41—22no—
284C2×C4×C41—22no—
285C2×C4×C41—22no—
286C2×C4×C41—21no—
287C2×C4×C41—22no—
288C2×C4×C41—21no—
289C2×C4×C41—21no—
290C2×C4×C41—22no—
291C2×C4×C41—22no—
292C2×C4×C41—21no—
293C2×C4×C41—21no—
294C2×C4×C41—22no—
295C2×C4×C41—22no—
296C2×C4×C41—24no—
297C2×C4×C41—41no—
298C2×C4×C41—41no—
299C2×C4×C41—41no—
300C2×C4×C41—41no—
301C2×C4×C41—41no—
302C2×C4×C41—41no—
303C2×C4×C41—42no—
304C2×C4×C41—42no—
305C2×C4×C41—42no—
306C2×C4×C41—41no—
307C2×C4×C41—41no—
308C2×C4×C41—41no—
309C2×C4×C41—41no—
310C2×C4×C41—41no—
311C2×C4×C41—42no—
312C2×C4×C41—41no—
313C2×C4×C41—42no—
314C2×C4×C41—42no—
315C2×C4×C41—41no—
316C2×C4×C41—42no—
317C2×C4×C41—41no—
318C2×C4×C41—41no—
319C2×C4×C41—42no—
320C2×C4×C41—41no—
321C2×C4×C41—41no—
322C2×C4×C41—42no—
323C2×C4×C41—41no—
324C2×C4×C41—41no—
325C2×C4×C41—41no—
326C2×C4×C41—41no—
327C2×C4×C41—42no—
328C2×C4×C41—81no—
329C2×C4×C41—82no—
330C2×C4×C41—82no—
331C2×C4×C41#12011yescharacteristic
332C2×C4×C41#12011yescharacteristic
333C2×C4×C41#12011yescharacteristic
334C2×C4×C41#12011yescharacteristic
335#25665C4111yesmaximal, characteristic, direct product factor, Sylow
336C22×C41—21no—
337C22×C41—21no—
338C22×C41—21no—
339C22×C41—21no—
340C22×C41—21no—
341C22×C41—21no—
342C22×C41—42no—
343C22×C41—42no—
344C22×C41—42no—
345C22×C41—41no—
346C22×C41—42no—
347C22×C41—42no—
348C22×C41—41no—
349C22×C41—41no—
350C22×C41—42no—
351C22×C41—81no—
352C22×C41—82no—
353C22×C41—82no—
354C22×C41C2×#12011yescharacteristic
355C22×C41#53211yescharacteristic
356C22×C41#53611yescharacteristic
357C22×C41#54712yes—
358C22×C41#54812yes—
359C4×C41—21no—
360C4×C41—21no—
361C4×C41—21no—
362C4×C41—21no—
363C4×C41—44no—
364C4×C41—41no—
365C4×C41—42no—
366C4×C41—42no—
367C4×C41—41no—
368C4×C41—42no—
369C4×C41—41no—
370C4×C41—42no—
371C4×C41—81no—
372C4×C41—81no—
373C4×C41—82no—
374C4×C41—81no—
375#3505C2×C4111yescharacteristic
376#2591C2×C4111yescharacteristic, complemented
377#2583C2×C4111yescharacteristic, complemented
378#2579C2×C4111yescharacteristic, complemented
379#2044C2×C4112yescomplemented
380#2044C2×C4112yescomplemented
381#1996C2×C4111yescharacteristic, complemented
382#1964C2×C4111yescharacteristic, complemented
383#1867C2×C4112yescomplemented
384#1867C2×C4112yescomplemented
385C4×#99C2×C4111yescharacteristic, complemented
386C2×C41—22no—
387C2×C41—21no—
388C2×C41—22no—
389C2×C41—21no—
390C2×C41—81no—
391C2×C41—82no—
392C2×C41#243211yescharacteristic
393C2×C41#302511yescharacteristic
394C2×C41#302611yescharacteristic
395#553—22no—
396#553—21no—
397#552—21no—
398#551—22no—
399#548—21no—
400#546—21no—
401#539—21no—
402#538—21no—
403#534C22×C4112yes—
404#529—21no—
405#525—21no—
406C2×C22⋊Q8C22×C4111yescharacteristic
407C2×#121C22×C4111yescharacteristic
408#518C22×C4112yes—
409C2×C4×D4C22×C4111yescharacteristic
410C22×C4⋊C4C22×C4111yescharacteristic
411C2×#99C22×C4112yes—
412C2×#99C22×C4112yes—
413C2×#99C22×C4112yes—
414#400—21no—
415#398—21no—
416#398—21no—
417#396—21no—
418#395—21no—
419#394—21no—
420#389—22no—
421#388—22no—
422#387—21no—
423#386C22×C4111yescharacteristic
424#386C22×C4111yescharacteristic
425#386C22×C4112yes—
426#386C22×C4112yes—
427#385—21no—
428#385C22×C4111yescharacteristic
429#385C22×C4111yescharacteristic
430#385C22×C4112yes—
431#385C22×C4112yes—
432#380C22×C4111yescharacteristic
433C4×C22⋊C4C22×C4111yescharacteristic
434C4×C22⋊C4C22×C4111yescharacteristic
435#342C22×C4112yes—
436#342C22×C4112yes—
437#342C22×C4112yes—
438C41#2566511yescharacteristic, direct product factor, Sylow
439C2×#41—21no—
440C22×Q8D4×C4111yescharacteristic
441C22×D4D4×C4111yescharacteristic
442C22×D4C23×C4111yescharacteristic
443C22×D4C23×C4112yes—
444C23×C4D4×C4111yescharacteristic
445C23×C4C23×C4111yescharacteristic
446C23×C4C23×C4111yescharacteristic
447C23×C4C23×C4111yescharacteristic
448#126—22no—
449#126—22no—
450#126—22no—
451#125—21no—
452#125—22no—
453#124—21no—
454#124—22no—
455#123—22no—
456#123—22no—
457#123—22no—
458#123—22no—
459#123—22no—
460C22⋊Q8—21no—
461C22⋊Q8—22no—
462C22⋊Q8—21no—
463C22⋊Q8—21no—
464C22⋊Q8—21no—
465C22⋊Q8—21no—
466#121—21no—
467#121—22no—
468#121—21no—
469#121—21no—
470#121—21no—
471#121—21no—
472#121—22no—
473#121—22no—
474#120—22no—
475#120—22no—
476C4×Q8—21no—
477C4×D4—22no—
478C4×D4—21no—
479C4×D4—21no—
480C4×D4—21no—
481C4×D4—21no—
482C4×D4—21no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—22no—
487#117—21no—
488#117—22no—
489#117—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4D4×C4111yescharacteristic
502C2×C4⋊C4D4×C4111yescharacteristic
503C2×C4⋊C4D4×C4112yes—
504C2×C4⋊C4D4×C4111yescharacteristic
505C2×C22⋊C4—22no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4D4×C4111yescharacteristic
511C2×C22⋊C4D4×C4112yes—
512C2×C22⋊C4C23×C4112yes—
513C2×C22⋊C4C23×C4111yescharacteristic
514C2×C22⋊C4C23×C4111yescharacteristic
515C2×C22⋊C4C23×C4111yescharacteristic
516C2×C22⋊C4C23×C4112yes—
517C2×C22⋊C4C23×C4112yes—
518C2×C42—21no—
519C2×C42—21no—
520C2×C42D4×C4111yescharacteristic
521#99—24no—
522#99—24no—
523#99—24no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—22no—
530#95—22no—
531#95—21no—
532#95—21no—
533#95—22no—
534#95—22no—
535C24C2×D4×C4112yes—
536C24C2×D4×C4111yescharacteristic
537C24C24×C4111yescharacteristic
538#41—82no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—81no—
542C2×D4—21no—
543C2×D4—22no—
544C2×D4—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—81no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—42no—
572C22×C4—81no—
573C22×C4—81no—
574C22×C4—81no—
575C22×C4C2×D4×C4111yescharacteristic
576C22×C4C2×D4×C4112yes—
577C22×C4C2×D4×C4111yescharacteristic
578C22×C4C2×D4×C4112yes—
579C22×C4C2×D4×C4111yescharacteristic
580C22×C4C2×D4×C4112yes—
581C22×C4C2×D4×C4111yescharacteristic
582C22×C4C2×D4×C4111yescharacteristic
583C22×C4C2×D4×C4111yescharacteristic
584C22×C4C2×D4×C4111yescharacteristic
585C22×C4C2×D4×C4111yescharacteristic
586C22×C4C2×D4×C4111yescharacteristic
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—22no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—44no—
601C4⋊C4—41no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—41no—
605C4⋊C4—81no—
606C4⋊C4—82no—
607C4⋊C4—81no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—21no—
615C22⋊C4—22no—
616C22⋊C4—21no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—44no—
628C22⋊C4—42no—
629C22⋊C4—82no—
630C22⋊C4—81no—
631C22⋊C4#41×C4114yescomplemented
632C42—22no—
633C42—22no—
634C42—21no—
635C42—21no—
636C42—81no—
637C42—81no—
638C23—22no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—22no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—42no—
649C23—42no—
650C23C22×D4×C4111yescharacteristic
651C23C22×D4×C4111yescharacteristic
652C23C22×D4×C4111yescharacteristic
653C23C2×#41×C4112yes—
654C232−1+4×C4112yes—
655Q8—42no—
656Q8—81no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—42no—
664D4—81no—
665D4—82no—
666D4—82no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—81no—
713C2×C4—82no—
714C2×C4—82no—
715C2×C4#120×C4111yescharacteristic
716C2×C4#120×C4111yescharacteristic
717C2×C4#120×C4111yescharacteristic
718C2×C4#120×C4111yescharacteristic
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—41no—
729C22—42no—
730C22—42no—
731C22—41no—
732C22—41no—
733C22—42no—
734C22—81no—
735C22—82no—
736C22—82no—
737C22C2×#120×C4111yescharacteristic
738C22C41×#53211yescharacteristic
739C22C41×#53611yescharacteristic
740C22C41×#54712yes—
741C22C41×#54812yes—
742C4—21no—
743C4—21no—
744C4—21no—
745C4—21no—
746C4—44no—
747C4—41no—
748C4—42no—
749C4—42no—
750C4—41no—
751C4—42no—
752C4—41no—
753C4—42no—
754C4—81no—
755C4—81no—
756C4—82no—
757C4—81no—
758C2—22no—
759C2—21no—
760C2—22no—
761C2—21no—
762C2—81no—
763C2—82no—
764C2C41×#243211yescharacteristic
765C2C41×#302511yescharacteristic
766C2C41×#302611yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC24C24×C41
prime radicalC41×#3505C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2591C2semidirect
3. C41×#2583C2semidirect
4. C41×#2579C2semidirect
5. C41×#2044C2semidirect
6. C41×#2044C2semidirect
7. C41×#1996C2semidirect
8. C41×#1964C2semidirect
9. C41×#1867C2semidirect
10. C41×#1867C2semidirect
11. C4×#99×C41C2semidirect
247. C22⋊C4×C41#41semidirect
335. #25665C41direct (N × H)
376. #2591C2×C41semidirect
377. #2583C2×C41semidirect
378. #2579C2×C41semidirect
379. #2044C2×C41semidirect
380. #2044C2×C41semidirect
381. #1996C2×C41semidirect
382. #1964C2×C41semidirect
383. #1867C2×C41semidirect
384. #1867C2×C41semidirect
385. C4×#99C2×C41semidirect
438. C41#25665direct (N × H)
631. C22⋊C4#41×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#35052
C41×#25912
C41×#25832
C41×#25792
C41×#20442
C41×#19962
C41×#19642
C41×#18672
C4×#99×C412
#2566541