Finite Group Databasebeta

← C41×#18471 #23794672

Subgroups — C41×#18471 #23794672

Order 10496.

906 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3560C211yesmaximal, characteristic
2C41×#3239C211yesmaximal, characteristic, complemented
3C41×#3227C211yesmaximal, characteristic, complemented
4C41×#2821C211yesmaximal, characteristic, complemented
5C41×#1618C212yesmaximal, complemented
6C41×#1616C212yesmaximal, complemented
7C41×#1615C212yesmaximal, complemented
8C41×#1613C212yesmaximal, complemented
9C41×#1521C211yesmaximal, characteristic, complemented
10C41×#1514C211yesmaximal, characteristic, complemented
11C41×#1473C211yesmaximal, characteristic, complemented
12C41×#563—21no—
13C41×#560—21no—
14C41×#553—21no—
15C41×#553—21no—
16C41×#551—21no—
17C41×#547—21no—
18C41×#546—21no—
19C41×#546—21no—
20C41×#542—21no—
21C41×#539—21no—
22C41×#539C2211yescharacteristic
23C41×#538—21no—
24C41×#538—21no—
25C41×#538C2211yescharacteristic
26C41×#537C2211yescharacteristic
27C41×#534C2211yescharacteristic
28C41×#532C2211yescharacteristic
29C2×C4⋊Q8×C41C2211yescharacteristic, complemented
30C41×#529C2211yescharacteristic
31C2×#126×C41C2211yescharacteristic
32C41×#501—21no—
33C41×#498—21no—
34C41×#489—21no—
35C41×#486—21no—
36C41×#484C2212yescomplemented
37C41×#481C2212yes—
38C41×#481C2212yes—
39C41×#481C2212yescomplemented
40C41×#476—21no—
41C41×#476—21no—
42C41×#475—21no—
43C41×#474—21no—
44C41×#432C2211yescharacteristic, complemented
45C41×#431C2211yescharacteristic, complemented
46C41×#400C2212yescomplemented
47C41×#399C2212yes—
48C41×#398—21no—
49C41×#397—21no—
50C41×#395—21no—
51C41×#393—21no—
52C41×#383C2211yescharacteristic, complemented
53C41×#328C2212yescomplemented
54C41×#327C2212yes—
55C41×#327C2212yes—
56C41×#327C2212yescomplemented
57C41×#324C2212yescomplemented
58C41×#323C2212yes—
59C2×#41×C41—21no—
60C2×#41×C41—21no—
61C22×Q8×C41—21no—
62C22×D4×C41—21no—
63C4⋊Q8×C41—21no—
64C4⋊Q8×C41—21no—
65C4⋊Q8×C41—21no—
66C4⋊Q8×C41—21no—
67C4⋊Q8×C41—21no—
68C4⋊Q8×C41D411yescharacteristic
69#127×C41D411yescharacteristic
70#126×C41—21no—
71#126×C41—21no—
72#126×C41—21no—
73#126×C41—21no—
74#126×C41—21no—
75#126×C41—21no—
76#126×C41—21no—
77#126×C41—21no—
78#126×C41—21no—
79#125×C41—21no—
80#125×C41—21no—
81#125×C41D411yescharacteristic
82#124×C41—21no—
83#124×C41—21no—
84#124×C41—21no—
85#124×C41—21no—
86#124×C41D411yescharacteristic
87#123×C41—21no—
88#123×C41—21no—
89#123×C41—21no—
90#123×C41—21no—
91#123×C41—21no—
92#123×C41—21no—
93#123×C41—21no—
94#123×C41—21no—
95#123×C41—21no—
96#123×C41—21no—
97#123×C41—21no—
98#123×C41—21no—
99C22⋊Q8×C41—21no—
100C22⋊Q8×C41—21no—
101C22⋊Q8×C41—21no—
102C22⋊Q8×C41—21no—
103C22⋊Q8×C41—21no—
104C22⋊Q8×C41—21no—
105C22⋊Q8×C41—21no—
106C22⋊Q8×C41C2311yescharacteristic
107#121×C41—21no—
108#121×C41—21no—
109#121×C41—21no—
110#121×C41—21no—
111#121×C41—21no—
112#121×C41—21no—
113#121×C41—21no—
114#121×C41—21no—
115#121×C41—21no—
116#121×C41—21no—
117#121×C41—21no—
118#121×C41—21no—
119#121×C41C2311yescharacteristic
120#121×C41C2311yescharacteristic
121#121×C41C2311yescharacteristic
122#120×C41—21no—
123#120×C41—21no—
124#120×C41—21no—
125#120×C41—21no—
126#120×C41—21no—
127C4×Q8×C41D411yescharacteristic
128C4×D4×C41—21no—
129C4×D4×C41—21no—
130C4×D4×C41—21no—
131C4×D4×C41—21no—
132C4×D4×C41—21no—
133C4×D4×C41—21no—
134C4×D4×C41—21no—
135C4×D4×C41—21no—
136C4×D4×C41D411yescharacteristic
137C4×D4×C41D411yescharacteristic
138C4×D4×C41D411yescharacteristic
139#117×C41—21no—
140#117×C41—21no—
141C2×C4⋊C4×C41—21no—
142C2×C4⋊C4×C41—21no—
143C2×C4⋊C4×C41—22no—
144C2×C4⋊C4×C41D411yescharacteristic
145C2×C4⋊C4×C41D411yescharacteristic
146C2×C4⋊C4×C41C2312yes—
147C2×C4⋊C4×C41C2311yescharacteristic
148C2×C22⋊C4×C41—21no—
149C2×C22⋊C4×C41—21no—
150C2×C22⋊C4×C41—22no—
151C2×C22⋊C4×C41D411yescharacteristic
152C2×C22⋊C4×C41D411yescharacteristic
153C2×C22⋊C4×C41C2311yescharacteristic
154C2×C42×C41C2311yescharacteristic
155#107×C41—22no—
156#106×C41—22no—
157#106×C41—22no—
158#106×C41—22no—
159C4⋊C8×C41—21no—
160C4⋊C8×C41—21no—
161#103×C41—22no—
162#102×C41—22no—
163#102×C41—22no—
164#102×C41—22no—
165C22⋊C8×C41C2312yes—
166C22⋊C8×C41C2312yes—
167#97×C41—21no—
168C4×C8×C41—21no—
169#95×C41—21no—
170#95×C41—21no—
171#95×C41—22no—
172#95×C41—22no—
173#95×C41C2312yes—
174C24×C41—21no—
175C24×C41C2×D411yescharacteristic
176#41×C41—82no—
177#41×C41—82no—
178C2×Q8×C41—21no—
179C2×Q8×C41—21no—
180C2×Q8×C41—41no—
181C2×Q8×C41—41no—
182C2×Q8×C41—82no—
183C2×Q8×C41C2×D411yescharacteristic
184C2×D4×C41—21no—
185C2×D4×C41—21no—
186C2×D4×C41—21no—
187C2×D4×C41—21no—
188C2×D4×C41—21no—
189C2×D4×C41—21no—
190C2×D4×C41—21no—
191C2×D4×C41—21no—
192C2×D4×C41—21no—
193C2×D4×C41—21no—
194C2×D4×C41—21no—
195C2×D4×C41—21no—
196C2×D4×C41—82no—
197C2×D4×C41C2×D411yescharacteristic
198C2×D4×C41C2×D411yescharacteristic
199C2×D4×C41C2×D411yescharacteristic
200C22×C4×C41—21no—
201C22×C4×C41—21no—
202C22×C4×C41—21no—
203C22×C4×C41—21no—
204C22×C4×C41—21no—
205C22×C4×C41—21no—
206C22×C4×C41—21no—
207C22×C4×C41—21no—
208C22×C4×C41—22no—
209C22×C4×C41—22no—
210C22×C4×C41C2×D411yescharacteristic
211C22×C4×C41C2×D411yescharacteristic
212C22×C4×C41C2×D411yescharacteristic
213C22×C4×C41C2×D411yescharacteristic
214C22×C4×C41C2×D411yescharacteristic
215C22×C4×C41C2411yescharacteristic
216C2×C8×C41—22no—
217C2×C8×C41—22no—
218C4⋊C4×C41—21no—
219C4⋊C4×C41—21no—
220C4⋊C4×C41—21no—
221C4⋊C4×C41—21no—
222C4⋊C4×C41—21no—
223C4⋊C4×C41—21no—
224C4⋊C4×C41—21no—
225C4⋊C4×C41—21no—
226C4⋊C4×C41—21no—
227C4⋊C4×C41—21no—
228C4⋊C4×C41—21no—
229C4⋊C4×C41—21no—
230C4⋊C4×C41—21no—
231C4⋊C4×C41—21no—
232C4⋊C4×C41—21no—
233C4⋊C4×C41—21no—
234C4⋊C4×C41—21no—
235C4⋊C4×C41—22no—
236C4⋊C4×C41—22no—
237C4⋊C4×C41—41no—
238C4⋊C4×C41—41no—
239C4⋊C4×C41—82no—
240C4⋊C4×C41C2×D411yescharacteristic
241C4⋊C4×C41C2×D411yescharacteristic
242C4⋊C4×C41C2×D411yescharacteristic
243C4⋊C4×C41C2×D411yescharacteristic
244C22⋊C4×C41—21no—
245C22⋊C4×C41—21no—
246C22⋊C4×C41—21no—
247C22⋊C4×C41—21no—
248C22⋊C4×C41—21no—
249C22⋊C4×C41—21no—
250C22⋊C4×C41—21no—
251C22⋊C4×C41—21no—
252C22⋊C4×C41—21no—
253C22⋊C4×C41—21no—
254C22⋊C4×C41—21no—
255C22⋊C4×C41—21no—
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—21no—
263C22⋊C4×C41—21no—
264C22⋊C4×C41—21no—
265C22⋊C4×C41—21no—
266C22⋊C4×C41—21no—
267C22⋊C4×C41—21no—
268C22⋊C4×C41—21no—
269C22⋊C4×C41—82no—
270C42×C41—21no—
271C42×C41—21no—
272C42×C41—21no—
273C42×C41C2×D411yescharacteristic
274C42×C41C2×D411yescharacteristic
275C42×C41C2×D411yescharacteristic
276C42×C41C2×D411yescharacteristic
277C23×C41—21no—
278C23×C41—21no—
279C23×C41—21no—
280C23×C41—21no—
281C23×C41—22no—
282C23×C41—41no—
283C23×C41—41no—
284C23×C41—81no—
285C23×C41—81no—
286C23×C41—81no—
287C23×C41C22×D411yescharacteristic
288Q8×C41—41no—
289Q8×C41—81no—
290Q8×C41—82no—
291Q8×C41—82no—
292Q8×C41—81no—
293D4×C41—41no—
294D4×C41—41no—
295D4×C41—41no—
296D4×C41—42no—
297D4×C41—42no—
298D4×C41—42no—
299D4×C41—81no—
300D4×C41—81no—
301D4×C41—81no—
302D4×C41—81no—
303D4×C41—81no—
304D4×C41—81no—
305D4×C41—81no—
306D4×C41—81no—
307D4×C41—81no—
308C2×C4×C41—22no—
309C2×C4×C41—21no—
310C2×C4×C41—21no—
311C2×C4×C41—21no—
312C2×C4×C41—21no—
313C2×C4×C41—21no—
314C2×C4×C41—21no—
315C2×C4×C41—21no—
316C2×C4×C41—21no—
317C2×C4×C41—22no—
318C2×C4×C41—41no—
319C2×C4×C41—41no—
320C2×C4×C41—41no—
321C2×C4×C41—41no—
322C2×C4×C41—42no—
323C2×C4×C41—42no—
324C2×C4×C41—42no—
325C2×C4×C41—42no—
326C2×C4×C41—42no—
327C2×C4×C41—42no—
328C2×C4×C41—81no—
329C2×C4×C41—81no—
330C2×C4×C41—81no—
331C2×C4×C41—81no—
332C2×C4×C41—81no—
333C2×C4×C41—81no—
334C2×C4×C41—81no—
335C2×C4×C41—81no—
336C2×C4×C41#12011yescharacteristic
337C2×C4×C41#12011yescharacteristic
338C2×C4×C41#12011yescharacteristic
339C2×C4×C41#12011yescharacteristic
340C2×C4×C41C22×D411yescharacteristic
341C2×C4×C41C22×D411yescharacteristic
342C8×C41—42no—
343C8×C41—42no—
344#18471C4111yesmaximal, characteristic, direct product factor, Sylow
345C22×C41—21no—
346C22×C41—21no—
347C22×C41—41no—
348C22×C41—41no—
349C22×C41—41no—
350C22×C41—41no—
351C22×C41—41no—
352C22×C41—41no—
353C22×C41—41no—
354C22×C41—41no—
355C22×C41—41no—
356C22×C41—41no—
357C22×C41—41no—
358C22×C41—41no—
359C22×C41—82no—
360C22×C41—162no—
361C22×C41C2×#12011yescharacteristic
362C22×C41#57712yes—
363C4×C41—21no—
364C4×C41—21no—
365C4×C41—21no—
366C4×C41—21no—
367C4×C41—21no—
368C4×C41—21no—
369C4×C41—41no—
370C4×C41—41no—
371C4×C41—41no—
372C4×C41—41no—
373C4×C41—41no—
374C4×C41—41no—
375C4×C41—41no—
376C4×C41—41no—
377C4×C41—82no—
378C4×C41—82no—
379#3560C2×C4111yescharacteristic
380#3239C2×C4111yescharacteristic, complemented
381#3227C2×C4111yescharacteristic, complemented
382#2821C2×C4111yescharacteristic, complemented
383#1618C2×C4112yescomplemented
384#1616C2×C4112yescomplemented
385#1615C2×C4112yescomplemented
386#1613C2×C4112yescomplemented
387#1521C2×C4111yescharacteristic, complemented
388#1514C2×C4111yescharacteristic, complemented
389#1473C2×C4111yescharacteristic, complemented
390C2×C41—22no—
391C2×C41—81no—
392C2×C41—81no—
393C2×C41—81no—
394C2×C41—81no—
395C2×C41#300911yescharacteristic
396C2×C41#302111yescharacteristic
397C2×C41#302811yescharacteristic
398#563—21no—
399#560—21no—
400#553—21no—
401#553—21no—
402#551—21no—
403#547—21no—
404#546—21no—
405#546—21no—
406#542—21no—
407#539—21no—
408#539C22×C4111yescharacteristic
409#538—21no—
410#538—21no—
411#538C22×C4111yescharacteristic
412#537C22×C4111yescharacteristic
413#534C22×C4111yescharacteristic
414#532C22×C4111yescharacteristic
415C2×C4⋊Q8C22×C4111yescharacteristic, complemented
416#529C22×C4111yescharacteristic
417C2×#126C22×C4111yescharacteristic
418#501—21no—
419#498—21no—
420#489—21no—
421#486—21no—
422#484C22×C4112yescomplemented
423#481C22×C4112yes—
424#481C22×C4112yes—
425#481C22×C4112yescomplemented
426#476—21no—
427#476—21no—
428#475—21no—
429#474—21no—
430#432C22×C4111yescharacteristic, complemented
431#431C22×C4111yescharacteristic, complemented
432#400C22×C4112yescomplemented
433#399C22×C4112yes—
434#398—21no—
435#397—21no—
436#395—21no—
437#393—21no—
438#383C22×C4111yescharacteristic, complemented
439#328C22×C4112yescomplemented
440#327C22×C4112yes—
441#327C22×C4112yes—
442#327C22×C4112yescomplemented
443#324C22×C4112yescomplemented
444#323C22×C4112yes—
445C41#1847111yescharacteristic, direct product factor, Sylow
446C2×#41—21no—
447C2×#41—21no—
448C22×Q8—21no—
449C22×D4—21no—
450C4⋊Q8—21no—
451C4⋊Q8—21no—
452C4⋊Q8—21no—
453C4⋊Q8—21no—
454C4⋊Q8—21no—
455C4⋊Q8D4×C4111yescharacteristic
456#127D4×C4111yescharacteristic
457#126—21no—
458#126—21no—
459#126—21no—
460#126—21no—
461#126—21no—
462#126—21no—
463#126—21no—
464#126—21no—
465#126—21no—
466#125—21no—
467#125—21no—
468#125D4×C4111yescharacteristic
469#124—21no—
470#124—21no—
471#124—21no—
472#124—21no—
473#124D4×C4111yescharacteristic
474#123—21no—
475#123—21no—
476#123—21no—
477#123—21no—
478#123—21no—
479#123—21no—
480#123—21no—
481#123—21no—
482#123—21no—
483#123—21no—
484#123—21no—
485#123—21no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8C23×C4111yescharacteristic
494#121—21no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121—21no—
499#121—21no—
500#121—21no—
501#121—21no—
502#121—21no—
503#121—21no—
504#121—21no—
505#121—21no—
506#121C23×C4111yescharacteristic
507#121C23×C4111yescharacteristic
508#121C23×C4111yescharacteristic
509#120—21no—
510#120—21no—
511#120—21no—
512#120—21no—
513#120—21no—
514C4×Q8D4×C4111yescharacteristic
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4D4×C4111yescharacteristic
524C4×D4D4×C4111yescharacteristic
525C4×D4D4×C4111yescharacteristic
526#117—21no—
527#117—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4D4×C4111yescharacteristic
532C2×C4⋊C4D4×C4111yescharacteristic
533C2×C4⋊C4C23×C4112yes—
534C2×C4⋊C4C23×C4111yescharacteristic
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4D4×C4111yescharacteristic
539C2×C22⋊C4D4×C4111yescharacteristic
540C2×C22⋊C4C23×C4111yescharacteristic
541C2×C42C23×C4111yescharacteristic
542#107—22no—
543#106—22no—
544#106—22no—
545#106—22no—
546C4⋊C8—21no—
547C4⋊C8—21no—
548#103—22no—
549#102—22no—
550#102—22no—
551#102—22no—
552C22⋊C8C23×C4112yes—
553C22⋊C8C23×C4112yes—
554#97—21no—
555C4×C8—21no—
556#95—21no—
557#95—21no—
558#95—22no—
559#95—22no—
560#95C23×C4112yes—
561C24—21no—
562C24C2×D4×C4111yescharacteristic
563#41—82no—
564#41—82no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—41no—
568C2×Q8—41no—
569C2×Q8—82no—
570C2×Q8C2×D4×C4111yescharacteristic
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—82no—
584C2×D4C2×D4×C4111yescharacteristic
585C2×D4C2×D4×C4111yescharacteristic
586C2×D4C2×D4×C4111yescharacteristic
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4C2×D4×C4111yescharacteristic
598C22×C4C2×D4×C4111yescharacteristic
599C22×C4C2×D4×C4111yescharacteristic
600C22×C4C2×D4×C4111yescharacteristic
601C22×C4C2×D4×C4111yescharacteristic
602C22×C4C24×C4111yescharacteristic
603C2×C8—22no—
604C2×C8—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—41no—
625C4⋊C4—41no—
626C4⋊C4—82no—
627C4⋊C4C2×D4×C4111yescharacteristic
628C4⋊C4C2×D4×C4111yescharacteristic
629C4⋊C4C2×D4×C4111yescharacteristic
630C4⋊C4C2×D4×C4111yescharacteristic
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—82no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42C2×D4×C4111yescharacteristic
661C42C2×D4×C4111yescharacteristic
662C42C2×D4×C4111yescharacteristic
663C42C2×D4×C4111yescharacteristic
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—41no—
670C23—41no—
671C23—81no—
672C23—81no—
673C23—81no—
674C23C22×D4×C4111yescharacteristic
675Q8—41no—
676Q8—81no—
677Q8—82no—
678Q8—82no—
679Q8—81no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—42no—
684D4—42no—
685D4—42no—
686D4—81no—
687D4—81no—
688D4—81no—
689D4—81no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—81no—
694D4—81no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4#120×C4111yescharacteristic
724C2×C4#120×C4111yescharacteristic
725C2×C4#120×C4111yescharacteristic
726C2×C4#120×C4111yescharacteristic
727C2×C4C22×D4×C4111yescharacteristic
728C2×C4C22×D4×C4111yescharacteristic
729C8—42no—
730C8—42no—
731C22—21no—
732C22—21no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—82no—
746C22—162no—
747C22C2×#120×C4111yescharacteristic
748C22C41×#57712yes—
749C4—21no—
750C4—21no—
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—82no—
764C4—82no—
765C2—22no—
766C2—81no—
767C2—81no—
768C2—81no—
769C2—81no—
770C2C41×#300911yescharacteristic
771C2C41×#302111yescharacteristic
772C2C41×#302811yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#3560C2
LCSG ▷ C22×C4 ▷ 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×#3239C2semidirect
3. C41×#3227C2semidirect
4. C41×#2821C2semidirect
5. C41×#1618C2semidirect
6. C41×#1616C2semidirect
7. C41×#1615C2semidirect
8. C41×#1613C2semidirect
9. C41×#1521C2semidirect
10. C41×#1514C2semidirect
11. C41×#1473C2semidirect
29. C2×C4⋊Q8×C41C22semidirect
36. C41×#484C22semidirect
39. C41×#481C22semidirect
44. C41×#432C22semidirect
45. C41×#431C22semidirect
46. C41×#400C22semidirect
52. C41×#383C22semidirect
53. C41×#328C22semidirect
56. C41×#327C22semidirect
57. C41×#324C22semidirect
344. #18471C41direct (N × H)
380. #3239C2×C41semidirect
381. #3227C2×C41semidirect
382. #2821C2×C41semidirect
383. #1618C2×C41semidirect
384. #1616C2×C41semidirect
385. #1615C2×C41semidirect
386. #1613C2×C41semidirect
387. #1521C2×C41semidirect
388. #1514C2×C41semidirect
389. #1473C2×C41semidirect
415. C2×C4⋊Q8C22×C41semidirect
422. #484C22×C41semidirect
425. #481C22×C41semidirect
430. #432C22×C41semidirect
431. #431C22×C41semidirect
432. #400C22×C41semidirect
438. #383C22×C41semidirect
439. #328C22×C41semidirect
442. #327C22×C41semidirect
443. #324C22×C41semidirect
445. C41#18471direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35602
C41×#32392
C41×#32272
C41×#28212
C41×#16182
C41×#16162
C41×#16152
C41×#16132
C41×#15212
C41×#15142
C41×#14732
#1847141