Finite Group Databasebeta

← C41×#18671 #23794872

Subgroups — C41×#18671 #23794872

Order 10496.

928 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3517C211yesmaximal, characteristic
2C41×#3233C211yesmaximal, characteristic, complemented
3C41×#3167C211yesmaximal, characteristic, complemented
4C41×#3116C211yesmaximal, characteristic, complemented
5C41×#1654C211yesmaximal, characteristic, complemented
6C41×#1653C211yesmaximal, characteristic, complemented
7C41×#1642C211yesmaximal, characteristic, complemented
8C41×#1641C211yesmaximal, characteristic, complemented
9C41×#1636C211yesmaximal, characteristic, complemented
10C41×#1635C211yesmaximal, characteristic, complemented
11C41×#1631C211yesmaximal, characteristic, complemented
12C41×#1631C211yesmaximal, characteristic, complemented
13C41×#1553C211yesmaximal, characteristic, complemented
14C41×#1494C211yesmaximal, characteristic, complemented
15C41×#1476C211yesmaximal, characteristic, complemented
16C41×#557C2211yescharacteristic
17C41×#553—22no—
18C41×#553—21no—
19C41×#550—21no—
20C41×#550—21no—
21C41×#550C2211yescharacteristic
22C41×#550C2211yescharacteristic
23C41×#547—21no—
24C41×#547C2211yescharacteristic
25C41×#540—22no—
26C41×#540—21no—
27C41×#533C2211yescharacteristic
28C41×#532—21no—
29C41×#532C2211yescharacteristic
30C41×#529—21no—
31C41×#529C2211yescharacteristic
32C41×#520—21no—
33C4×#41×C41C2211yescharacteristic
34C41×#499—21no—
35C41×#498C2211yescharacteristic
36C41×#492C2211yescharacteristic
37C41×#488—21no—
38C41×#487C2211yescharacteristic
39C41×#486C2211yescharacteristic
40C41×#485—21no—
41C41×#485—21no—
42C41×#482—21no—
43C41×#477C2211yescharacteristic
44C41×#477C2211yescharacteristic
45C41×#476C2211yescharacteristic
46C41×#476C2211yescharacteristic
47C41×#475C2211yescharacteristic
48C41×#474C2211yescharacteristic
49C41×#465—22no—
50C41×#462C2211yescharacteristic
51C41×#461C2211yescharacteristic
52C41×#452—21no—
53C41×#441—21no—
54C41×#440—21no—
55C4×SD16×C41—22no—
56C41×#432C2211yescharacteristic
57C41×#431C2211yescharacteristic
58C2×C4×C8×C41C2211yescharacteristic
59C41×#332C2211yescharacteristic
60C41×#332C2211yescharacteristic
61C41×#331C2211yescharacteristic
62C41×#331C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic
64C41×Q8⋊C8C2211yescharacteristic
65C41×Q8⋊C8C2211yescharacteristic
66C41×Q8⋊C8C2211yescharacteristic
67C41×D4⋊C8C2211yescharacteristic
68C41×D4⋊C8C2211yescharacteristic
69C41×D4⋊C8C2211yescharacteristic
70C41×D4⋊C8C2211yescharacteristic
71C2×#41×C41—21no—
72C2×#41×C41—21no—
73C2×#41×C41—21no—
74C2×#41×C41—21no—
75C2×#41×C41D411yescharacteristic
76C2×Q16×C41—21no—
77C2×SD16×C41—22no—
78C2×SD16×C41—21no—
79C22×C8×C41—21no—
80C4⋊Q8×C41—21no—
81C4⋊Q8×C41C2311yescharacteristic
82C4⋊Q8×C41C2311yescharacteristic
83C4⋊Q8×C41C2311yescharacteristic
84#127×C41—22no—
85#127×C41—21no—
86#127×C41—21no—
87#127×C41C2311yescharacteristic
88#126×C41—22no—
89#126×C41—21no—
90#125×C41—22no—
91#125×C41—21no—
92#125×C41—21no—
93#125×C41D411yescharacteristic
94#124×C41—21no—
95#124×C41D411yescharacteristic
96#123×C41—22no—
97#123×C41—22no—
98#123×C41—22no—
99#123×C41—21no—
100#123×C41—22no—
101C22⋊Q8×C41—21no—
102C22⋊Q8×C41—21no—
103C22⋊Q8×C41—21no—
104C22⋊Q8×C41D411yescharacteristic
105#121×C41—22no—
106#121×C41—22no—
107#121×C41—22no—
108#121×C41—22no—
109#121×C41—22no—
110#121×C41—21no—
111#121×C41—22no—
112#121×C41—22no—
113#121×C41—21no—
114#121×C41—21no—
115#121×C41—21no—
116#121×C41D411yescharacteristic
117#121×C41D412yes—
118C4×Q8×C41—21no—
119C4×Q8×C41—21no—
120C4×Q8×C41—21no—
121C4×Q8×C41—21no—
122C4×Q8×C41D411yescharacteristic
123C4×Q8×C41C2311yescharacteristic
124C4×Q8×C41C2311yescharacteristic
125C4×D4×C41—22no—
126C4×D4×C41—22no—
127C4×D4×C41—22no—
128C4×D4×C41—22no—
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×C41D411yescharacteristic
136C4×D4×C41D412yes—
137C4×D4×C41C2311yescharacteristic
138C4×D4×C41C2311yescharacteristic
139#117×C41—22no—
140#117×C41—21no—
141#117×C41—21no—
142#117×C41—21no—
143#117×C41D411yescharacteristic
144C2×C4⋊C4×C41—22no—
145C2×C4⋊C4×C41—21no—
146C2×C42×C41—21no—
147C2×C42×C41C2311yescharacteristic
148#107×C41—21no—
149#107×C41—21no—
150#107×C41—21no—
151#106×C41—22no—
152#106×C41—21no—
153#106×C41—21no—
154#106×C41—21no—
155C4⋊C8×C41C2311yescharacteristic
156C4⋊C8×C41C2311yescharacteristic
157C4⋊C8×C41C2311yescharacteristic
158C4⋊C8×C41C2311yescharacteristic
159#103×C41—21no—
160#103×C41—21no—
161#103×C41—21no—
162#103×C41—22no—
163#103×C41—21no—
164#103×C41—21no—
165#102×C41—22no—
166#102×C41—21no—
167#102×C41—21no—
168#102×C41—21no—
169C22⋊C8×C41—21no—
170C22⋊C8×C41—21no—
171#97×C41—21no—
172C4×C8×C41—21no—
173C4×C8×C41—21no—
174C4×C8×C41C2311yescharacteristic
175C4×C8×C41C2311yescharacteristic
176#41×C41—22no—
177#41×C41—41no—
178#41×C41—42no—
179#41×C41—42no—
180#41×C41—81no—
181#41×C41—81no—
182#41×C41—81no—
183#41×C41—81no—
184#41×C41—81no—
185#41×C41—81no—
186C2×Q8×C41—21no—
187C2×Q8×C41—21no—
188C2×Q8×C41—21no—
189C2×Q8×C41C2×D411yescharacteristic
190C2×Q8×C41C2×D411yescharacteristic
191C2×D4×C41—22no—
192C2×D4×C41—21no—
193C2×D4×C41—22no—
194C2×D4×C41—22no—
195C2×D4×C41—22no—
196C2×D4×C41—22no—
197C2×D4×C41—21no—
198C2×D4×C41—22no—
199C2×D4×C41—21no—
200C2×D4×C41—21no—
201C2×D4×C41C2×D411yescharacteristic
202C2×D4×C41C2×D411yescharacteristic
203C2×D4×C41C2×D412yes—
204C22×C4×C41—22no—
205C22×C4×C41—22no—
206C22×C4×C41—22no—
207C22×C4×C41—21no—
208C22×C4×C41—21no—
209C22×C4×C41—21no—
210C22×C4×C41—21no—
211C22×C4×C41—22no—
212C22×C4×C41C2×D411yescharacteristic
213C22×C4×C41C2×D411yescharacteristic
214C22×C4×C41C2×D411yescharacteristic
215Q16×C41—42no—
216SD16×C41—44no—
217SD16×C41—42no—
218C2×C8×C41—21no—
219C2×C8×C41—21no—
220C2×C8×C41—21no—
221C2×C8×C41—21no—
222C2×C8×C41—21no—
223C2×C8×C41—21no—
224C2×C8×C41—42no—
225C4⋊C4×C41—22no—
226C4⋊C4×C41—22no—
227C4⋊C4×C41—22no—
228C4⋊C4×C41—22no—
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—21no—
236C4⋊C4×C41—21no—
237C4⋊C4×C41—21no—
238C4⋊C4×C41—21no—
239C4⋊C4×C41—21no—
240C4⋊C4×C41—41no—
241C4⋊C4×C41—41no—
242C4⋊C4×C41C2×D411yescharacteristic
243C4⋊C4×C41C2×D412yes—
244C4⋊C4×C41C2×D411yescharacteristic
245C4⋊C4×C41C2×D411yescharacteristic
246C4⋊C4×C41C2×D411yescharacteristic
247C22⋊C4×C41—22no—
248C22⋊C4×C41—22no—
249C22⋊C4×C41—22no—
250C22⋊C4×C41—21no—
251C22⋊C4×C41—21no—
252C22⋊C4×C41—21no—
253C22⋊C4×C41—21no—
254C22⋊C4×C41—22no—
255C22⋊C4×C41—21no—
256C22⋊C4×C41—21no—
257C22⋊C4×C41—22no—
258C22⋊C4×C41—21no—
259C22⋊C4×C41—21no—
260C22⋊C4×C41—41no—
261C42×C41—22no—
262C42×C41—21no—
263C42×C41—21no—
264C42×C41—21no—
265C42×C41—21no—
266C42×C41—41no—
267C42×C41C2×D411yescharacteristic
268C42×C41C2×D411yescharacteristic
269C42×C41C2×D411yescharacteristic
270C42×C41C2411yescharacteristic
271C23×C41—21no—
272C23×C41—21no—
273C23×C41—22no—
274C23×C41#12011yescharacteristic
275Q8×C41—21no—
276Q8×C41—21no—
277Q8×C41—21no—
278Q8×C41—42no—
279Q8×C41—41no—
280Q8×C41—41no—
281Q8×C41—41no—
282Q8×C41—41no—
283Q8×C41#13512yes—
284D4×C41—21no—
285D4×C41—21no—
286D4×C41—21no—
287D4×C41—21no—
288D4×C41—42no—
289D4×C41—42no—
290D4×C41—44no—
291D4×C41—41no—
292D4×C41—41no—
293D4×C41—41no—
294D4×C41—41no—
295D4×C41—81no—
296D4×C41—82no—
297D4×C41—82no—
298D4×C41—82no—
299D4×C41—82no—
300D4×C41—82no—
301C2×C4×C41—21no—
302C2×C4×C41—21no—
303C2×C4×C41—21no—
304C2×C4×C41—21no—
305C2×C4×C41—21no—
306C2×C4×C41—21no—
307C2×C4×C41—21no—
308C2×C4×C41—21no—
309C2×C4×C41—21no—
310C2×C4×C41—22no—
311C2×C4×C41—21no—
312C2×C4×C41—41no—
313C2×C4×C41—42no—
314C2×C4×C41—44no—
315C2×C4×C41—41no—
316C2×C4×C41—41no—
317C2×C4×C41—41no—
318C2×C4×C41—41no—
319C2×C4×C41—41no—
320C2×C4×C41—41no—
321C2×C4×C41—81no—
322C2×C4×C41—82no—
323C2×C4×C41—82no—
324C2×C4×C41—82no—
325C2×C4×C41#12011yescharacteristic
326C2×C4×C41#12011yescharacteristic
327C2×C4×C41#12011yescharacteristic
328C2×C4×C41C22×D411yescharacteristic
329C2×C4×C41C22×D411yescharacteristic
330C2×C4×C41C22×D411yescharacteristic
331C8×C41—22no—
332C8×C41—41no—
333C8×C41—41no—
334C8×C41—41no—
335C8×C41—41no—
336C8×C41—41no—
337#18671C4111yesmaximal, characteristic, direct product factor, Sylow
338C22×C41—21no—
339C22×C41—21no—
340C22×C41—21no—
341C22×C41—41no—
342C22×C41—42no—
343C22×C41—41no—
344C22×C41—41no—
345C22×C41—41no—
346C22×C41—42no—
347C22×C41—41no—
348C22×C41—42no—
349C22×C41—41no—
350C22×C41C2×#12011yescharacteristic
351C4×C41—21no—
352C4×C41—22no—
353C4×C41—21no—
354C4×C41—21no—
355C4×C41—21no—
356C4×C41—41no—
357C4×C41—41no—
358C4×C41—41no—
359C4×C41—42no—
360C4×C41—41no—
361C4×C41—41no—
362C4×C41—81no—
363C4×C41—81no—
364C4×C41C2×#13511yescharacteristic
365C4×C41#57511yescharacteristic
366C4×C41#57711yescharacteristic
367C4×C41#57711yescharacteristic
368#3517C2×C4111yescharacteristic
369#3233C2×C4111yescharacteristic, complemented
370#3167C2×C4111yescharacteristic, complemented
371#3116C2×C4111yescharacteristic, complemented
372#1654C2×C4111yescharacteristic, complemented
373#1653C2×C4111yescharacteristic, complemented
374#1642C2×C4111yescharacteristic, complemented
375#1641C2×C4111yescharacteristic, complemented
376#1636C2×C4111yescharacteristic, complemented
377#1635C2×C4111yescharacteristic, complemented
378#1631C2×C4111yescharacteristic, complemented
379#1631C2×C4111yescharacteristic, complemented
380#1553C2×C4111yescharacteristic, complemented
381#1494C2×C4111yescharacteristic, complemented
382#1476C2×C4111yescharacteristic, complemented
383C2×C41—41no—
384C2×C41—81no—
385C2×C41—81no—
386C2×C41—82no—
387C2×C41#300211yescharacteristic
388C2×C41#300911yescharacteristic
389C2×C41#301811yescharacteristic
390#557C22×C4111yescharacteristic
391#553—22no—
392#553—21no—
393#550—21no—
394#550—21no—
395#550C22×C4111yescharacteristic
396#550C22×C4111yescharacteristic
397#547—21no—
398#547C22×C4111yescharacteristic
399#540—22no—
400#540—21no—
401#533C22×C4111yescharacteristic
402#532—21no—
403#532C22×C4111yescharacteristic
404#529—21no—
405#529C22×C4111yescharacteristic
406#520—21no—
407C4×#41C22×C4111yescharacteristic
408#499—21no—
409#498C22×C4111yescharacteristic
410#492C22×C4111yescharacteristic
411#488—21no—
412#487C22×C4111yescharacteristic
413#486C22×C4111yescharacteristic
414#485—21no—
415#485—21no—
416#482—21no—
417#477C22×C4111yescharacteristic
418#477C22×C4111yescharacteristic
419#476C22×C4111yescharacteristic
420#476C22×C4111yescharacteristic
421#475C22×C4111yescharacteristic
422#474C22×C4111yescharacteristic
423#465—22no—
424#462C22×C4111yescharacteristic
425#461C22×C4111yescharacteristic
426#452—21no—
427#441—21no—
428#440—21no—
429C4×SD16—22no—
430#432C22×C4111yescharacteristic
431#431C22×C4111yescharacteristic
432C2×C4×C8C22×C4111yescharacteristic
433#332C22×C4111yescharacteristic
434#332C22×C4111yescharacteristic
435#331C22×C4111yescharacteristic
436#331C22×C4111yescharacteristic
437Q8⋊C8C22×C4111yescharacteristic
438Q8⋊C8C22×C4111yescharacteristic
439Q8⋊C8C22×C4111yescharacteristic
440Q8⋊C8C22×C4111yescharacteristic
441D4⋊C8C22×C4111yescharacteristic
442D4⋊C8C22×C4111yescharacteristic
443D4⋊C8C22×C4111yescharacteristic
444D4⋊C8C22×C4111yescharacteristic
445C41#1867111yescharacteristic, direct product factor, Sylow
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41D4×C4111yescharacteristic
451C2×Q16—21no—
452C2×SD16—22no—
453C2×SD16—21no—
454C22×C8—21no—
455C4⋊Q8—21no—
456C4⋊Q8C23×C4111yescharacteristic
457C4⋊Q8C23×C4111yescharacteristic
458C4⋊Q8C23×C4111yescharacteristic
459#127—22no—
460#127—21no—
461#127—21no—
462#127C23×C4111yescharacteristic
463#126—22no—
464#126—21no—
465#125—22no—
466#125—21no—
467#125—21no—
468#125D4×C4111yescharacteristic
469#124—21no—
470#124D4×C4111yescharacteristic
471#123—22no—
472#123—22no—
473#123—22no—
474#123—21no—
475#123—22no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8D4×C4111yescharacteristic
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#121—22no—
485#121—21no—
486#121—22no—
487#121—22no—
488#121—21no—
489#121—21no—
490#121—21no—
491#121D4×C4111yescharacteristic
492#121D4×C4112yes—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—21no—
497C4×Q8D4×C4111yescharacteristic
498C4×Q8C23×C4111yescharacteristic
499C4×Q8C23×C4111yescharacteristic
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—22no—
503C4×D4—22no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4D4×C4111yescharacteristic
511C4×D4D4×C4112yes—
512C4×D4C23×C4111yescharacteristic
513C4×D4C23×C4111yescharacteristic
514#117—22no—
515#117—21no—
516#117—21no—
517#117—21no—
518#117D4×C4111yescharacteristic
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C42—21no—
522C2×C42C23×C4111yescharacteristic
523#107—21no—
524#107—21no—
525#107—21no—
526#106—22no—
527#106—21no—
528#106—21no—
529#106—21no—
530C4⋊C8C23×C4111yescharacteristic
531C4⋊C8C23×C4111yescharacteristic
532C4⋊C8C23×C4111yescharacteristic
533C4⋊C8C23×C4111yescharacteristic
534#103—21no—
535#103—21no—
536#103—21no—
537#103—22no—
538#103—21no—
539#103—21no—
540#102—22no—
541#102—21no—
542#102—21no—
543#102—21no—
544C22⋊C8—21no—
545C22⋊C8—21no—
546#97—21no—
547C4×C8—21no—
548C4×C8—21no—
549C4×C8C23×C4111yescharacteristic
550C4×C8C23×C4111yescharacteristic
551#41—22no—
552#41—41no—
553#41—42no—
554#41—42no—
555#41—81no—
556#41—81no—
557#41—81no—
558#41—81no—
559#41—81no—
560#41—81no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8C2×D4×C4111yescharacteristic
565C2×Q8C2×D4×C4111yescharacteristic
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4C2×D4×C4111yescharacteristic
577C2×D4C2×D4×C4111yescharacteristic
578C2×D4C2×D4×C4112yes—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4C2×D4×C4111yescharacteristic
588C22×C4C2×D4×C4111yescharacteristic
589C22×C4C2×D4×C4111yescharacteristic
590Q16—42no—
591SD16—44no—
592SD16—42no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—42no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—21no—
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—41no—
616C4⋊C4—41no—
617C4⋊C4C2×D4×C4111yescharacteristic
618C4⋊C4C2×D4×C4112yes—
619C4⋊C4C2×D4×C4111yescharacteristic
620C4⋊C4C2×D4×C4111yescharacteristic
621C4⋊C4C2×D4×C4111yescharacteristic
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—22no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—41no—
636C42—22no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—41no—
642C42C2×D4×C4111yescharacteristic
643C42C2×D4×C4111yescharacteristic
644C42C2×D4×C4111yescharacteristic
645C42C24×C4111yescharacteristic
646C23—21no—
647C23—21no—
648C23—22no—
649C23#120×C4111yescharacteristic
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—42no—
654Q8—41no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8#135×C4112yes—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—21no—
663D4—42no—
664D4—42no—
665D4—44no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—82no—
671D4—81no—
672D4—82no—
673D4—82no—
674D4—82no—
675D4—82no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—44no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—82no—
697C2×C4—81no—
698C2×C4—82no—
699C2×C4—82no—
700C2×C4#120×C4111yescharacteristic
701C2×C4#120×C4111yescharacteristic
702C2×C4#120×C4111yescharacteristic
703C2×C4C22×D4×C4111yescharacteristic
704C2×C4C22×D4×C4111yescharacteristic
705C2×C4C22×D4×C4111yescharacteristic
706C8—22no—
707C8—41no—
708C8—41no—
709C8—41no—
710C8—41no—
711C8—41no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—41no—
716C22—42no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—42no—
721C22—41no—
722C22—42no—
723C22—41no—
724C22C2×#120×C4111yescharacteristic
725C4—21no—
726C4—22no—
727C4—21no—
728C4—21no—
729C4—21no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—42no—
734C4—41no—
735C4—41no—
736C4—81no—
737C4—81no—
738C4C2×#135×C4111yescharacteristic
739C4C41×#57511yescharacteristic
740C4C41×#57711yescharacteristic
741C4C41×#57711yescharacteristic
742C2—41no—
743C2—81no—
744C2—81no—
745C2—82no—
746C2C41×#300211yescharacteristic
747C2C41×#300911yescharacteristic
748C2C41×#301811yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#3517C2
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
2. C41×#3233C2semidirect
3. C41×#3167C2semidirect
4. C41×#3116C2semidirect
5. C41×#1654C2semidirect
6. C41×#1653C2semidirect
7. C41×#1642C2semidirect
8. C41×#1641C2semidirect
9. C41×#1636C2semidirect
10. C41×#1635C2semidirect
11. C41×#1631C2semidirect
12. C41×#1631C2semidirect
13. C41×#1553C2semidirect
14. C41×#1494C2semidirect
15. C41×#1476C2semidirect
337. #18671C41direct (N × H)
369. #3233C2×C41semidirect
370. #3167C2×C41semidirect
371. #3116C2×C41semidirect
372. #1654C2×C41semidirect
373. #1653C2×C41semidirect
374. #1642C2×C41semidirect
375. #1641C2×C41semidirect
376. #1636C2×C41semidirect
377. #1635C2×C41semidirect
378. #1631C2×C41semidirect
379. #1631C2×C41semidirect
380. #1553C2×C41semidirect
381. #1494C2×C41semidirect
382. #1476C2×C41semidirect
445. C41#18671direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35172
C41×#32332
C41×#31672
C41×#31162
C41×#16542
C41×#16532
C41×#16422
C41×#16412
C41×#16362
C41×#16352
C41×#16312
C41×#15532
C41×#14942
C41×#14762
#1867141