Finite Group Databasebeta

← C41×#18628 #23794829

Subgroups — C41×#18628 #23794829

Order 10496.

998 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3519C211yesmaximal, characteristic
2C41×#3248C211yesmaximal, characteristic, complemented
3C41×#3131C211yesmaximal, characteristic, complemented
4C41×#3110C211yesmaximal, characteristic, complemented
5C41×#1646C211yesmaximal, characteristic, complemented
6C41×#1646C211yesmaximal, characteristic, complemented
7C41×#1644C211yesmaximal, characteristic, complemented
8C41×#1643C211yesmaximal, characteristic, complemented
9C41×#1642C211yesmaximal, characteristic, complemented
10C41×#1641C211yesmaximal, characteristic, complemented
11C41×#1639C211yesmaximal, characteristic, complemented
12C41×#1639C211yesmaximal, characteristic, complemented
13C41×#1551C211yesmaximal, characteristic, complemented
14C41×#1494C211yesmaximal, characteristic, complemented
15C2×C41×D4⋊C8C211yesmaximal, characteristic, complemented
16C41×#555C2211yescharacteristic
17C41×#554C2211yescharacteristic
18C41×#553—21no—
19C41×#553—21no—
20C41×#550C2211yescharacteristic
21C41×#546—22no—
22C41×#546—21no—
23D42×C41—21no—
24D42×C41C2211yescharacteristic
25C41×#540—21no—
26C41×#538—22no—
27C41×#533C2211yescharacteristic, complemented
28C41×#532C2211yescharacteristic
29C41×#529C2211yescharacteristic
30C41×#525—21no—
31C2×#121×C41—21no—
32C41×#518—21no—
33C2×C4×D4×C41C2211yescharacteristic
34C41×#488—22no—
35C41×#487C2211yescharacteristic, complemented
36C41×#487C2211yescharacteristic, complemented
37C41×#486C2211yescharacteristic, complemented
38C41×#486C2211yescharacteristic, complemented
39C41×#484—21no—
40C41×#479—21no—
41C41×#475C2211yescharacteristic, complemented
42C41×#474C2211yescharacteristic
43C41×#474C2211yescharacteristic, complemented
44C41×#474C2211yescharacteristic, complemented
45C41×#467—21no—
46C41×#465—21no—
47C41×#464—21no—
48C41×#462C2211yescharacteristic, complemented
49C41×#461C2211yescharacteristic
50C41×#461C2211yescharacteristic, complemented
51C41×#461C2211yescharacteristic, complemented
52C41×#450—21no—
53C41×#440—21no—
54C41×#440—21no—
55C41×#432C2211yescharacteristic, complemented
56C2×C4⋊C8×C41C2211yescharacteristic, complemented
57C41×#416—22no—
58C2×C4×C8×C41C2211yescharacteristic, complemented
59C41×#333C2211yescharacteristic, complemented
60C41×#333C2211yescharacteristic, complemented
61C41×#331C2211yescharacteristic, complemented
62C41×#331C2211yescharacteristic, complemented
63C41×Q8⋊C8C2211yescharacteristic, complemented
64C41×Q8⋊C8C2211yescharacteristic, complemented
65C41×D4⋊C8C2211yescharacteristic
66C41×D4⋊C8C2211yescharacteristic
67C41×D4⋊C8C2211yescharacteristic, complemented
68C41×D4⋊C8C2211yescharacteristic, complemented
69C41×D4⋊C8C2211yescharacteristic, complemented
70C41×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C41—21no—
72C2×#41×C41D412yes—
73C22×D4×C41—22no—
74C22×D4×C41—21no—
75C22×D4×C41—21no—
76C22×D4×C41D411yescharacteristic
77C23×C4×C41—21no—
78C2×Q16×C41—21no—
79C2×SD16×C41—21no—
80C2×SD16×C41—21no—
81C2×SD16×C41—21no—
82C22×C8×C41—21no—
83C22×C8×C41—21no—
84C4⋊Q8×C41C2311yescharacteristic
85C4⋊Q8×C41C2311yescharacteristic
86C4⋊Q8×C41C2311yescharacteristic
87#127×C41—21no—
88#127×C41C2311yescharacteristic
89#126×C41—22no—
90#126×C41—21no—
91#125×C41—21no—
92#125×C41—21no—
93#125×C41D411yescharacteristic
94#124×C41—22no—
95#124×C41D411yescharacteristic
96#124×C41D412yes—
97#123×C41—22no—
98#123×C41—22no—
99#123×C41—22no—
100#123×C41—21no—
101C22⋊Q8×C41—21no—
102C22⋊Q8×C41—22no—
103C22⋊Q8×C41—21no—
104C22⋊Q8×C41—21no—
105C22⋊Q8×C41D411yescharacteristic
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—21no—
113#121×C41—21no—
114#121×C41—21no—
115#121×C41—21no—
116#121×C41—21no—
117#121×C41—21no—
118#121×C41D411yescharacteristic
119#120×C41—22no—
120#120×C41—22no—
121#120×C41—22no—
122C4×Q8×C41—21no—
123C4×Q8×C41—21no—
124C4×Q8×C41C2311yescharacteristic
125C4×D4×C41—22no—
126C4×D4×C41—22no—
127C4×D4×C41—22no—
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×C41D411yescharacteristic
136C4×D4×C41D411yescharacteristic
137C4×D4×C41C2311yescharacteristic
138C4×D4×C41C2311yescharacteristic
139C4×D4×C41C2311yescharacteristic
140#117×C41—21no—
141#117×C41—21no—
142#117×C41—21no—
143#117×C41—21no—
144C2×C4⋊C4×C41—21no—
145C2×C4⋊C4×C41D411yescharacteristic
146C2×C22⋊C4×C41—22no—
147C2×C22⋊C4×C41—22no—
148C2×C22⋊C4×C41—21no—
149C2×C42×C41C2311yescharacteristic
150#107×C41—21no—
151#107×C41—21no—
152#107×C41—21no—
153#106×C41—21no—
154C4⋊C8×C41—21no—
155C4⋊C8×C41C2311yescharacteristic
156C4⋊C8×C41C2311yescharacteristic
157C4⋊C8×C41C2311yescharacteristic
158C4⋊C8×C41C2311yescharacteristic
159#103×C41—22no—
160#103×C41—22no—
161#103×C41—21no—
162#103×C41—21no—
163#103×C41—21no—
164#103×C41—21no—
165#103×C41—21no—
166#102×C41—22no—
167#102×C41—22no—
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—
177C24×C41—21no—
178#41×C41—44no—
179#41×C41—81no—
180#41×C41—81no—
181C2×Q8×C41—21no—
182C2×Q8×C41—21no—
183C2×Q8×C41C2×D411yescharacteristic
184C2×Q8×C41C2×D412yes—
185C2×D4×C41—22no—
186C2×D4×C41—22no—
187C2×D4×C41—22no—
188C2×D4×C41—21no—
189C2×D4×C41—22no—
190C2×D4×C41—22no—
191C2×D4×C41—22no—
192C2×D4×C41—22no—
193C2×D4×C41—21no—
194C2×D4×C41—21no—
195C2×D4×C41—21no—
196C2×D4×C41—41no—
197C2×D4×C41—42no—
198C2×D4×C41—42no—
199C2×D4×C41—81no—
200C2×D4×C41—81no—
201C2×D4×C41—84no—
202C2×D4×C41C2×D411yescharacteristic
203C2×D4×C41C2×D411yescharacteristic
204C2×D4×C41C2×D411yescharacteristic
205C2×D4×C41C2×D412yes—
206C22×C4×C41—22no—
207C22×C4×C41—22no—
208C22×C4×C41—21no—
209C22×C4×C41—21no—
210C22×C4×C41—21no—
211C22×C4×C41—21no—
212C22×C4×C41—21no—
213C22×C4×C41—22no—
214C22×C4×C41—21no—
215C22×C4×C41—81no—
216C22×C4×C41—81no—
217C22×C4×C41C2×D411yescharacteristic
218C22×C4×C41C2×D411yescharacteristic
219C22×C4×C41C2×D411yescharacteristic
220Q16×C41—81no—
221SD16×C41—42no—
222SD16×C41—42no—
223SD16×C41—81no—
224C2×C8×C41—21no—
225C2×C8×C41—21no—
226C2×C8×C41—21no—
227C2×C8×C41—21no—
228C2×C8×C41—21no—
229C2×C8×C41—21no—
230C2×C8×C41—42no—
231C2×C8×C41—81no—
232C4⋊C4×C41—22no—
233C4⋊C4×C41—22no—
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—21no—
241C4⋊C4×C41—21no—
242C4⋊C4×C41—21no—
243C4⋊C4×C41—21no—
244C4⋊C4×C41—21no—
245C4⋊C4×C41—41no—
246C4⋊C4×C41—41no—
247C4⋊C4×C41C2×D411yescharacteristic
248C4⋊C4×C41C2×D411yescharacteristic
249C4⋊C4×C41C2×D411yescharacteristic
250C4⋊C4×C41C2×D411yescharacteristic
251C22⋊C4×C41—22no—
252C22⋊C4×C41—22no—
253C22⋊C4×C41—22no—
254C22⋊C4×C41—22no—
255C22⋊C4×C41—22no—
256C22⋊C4×C41—21no—
257C22⋊C4×C41—21no—
258C22⋊C4×C41—21no—
259C22⋊C4×C41—21no—
260C22⋊C4×C41—22no—
261C22⋊C4×C41—21no—
262C22⋊C4×C41—21no—
263C22⋊C4×C41—22no—
264C22⋊C4×C41—21no—
265C22⋊C4×C41—21no—
266C22⋊C4×C41—21no—
267C22⋊C4×C41—41no—
268C42×C41—22no—
269C42×C41—21no—
270C42×C41—41no—
271C42×C41C2×D411yescharacteristic
272C42×C41C2×D411yescharacteristic
273C42×C41C2×D411yescharacteristic
274C42×C41C2411yescharacteristic
275C23×C41—21no—
276C23×C41—21no—
277C23×C41—21no—
278C23×C41—22no—
279C23×C41—42no—
280C23×C41—44no—
281C23×C41—42no—
282C23×C41—81no—
283C23×C41—82no—
284C23×C41—82no—
285C23×C41#12011yescharacteristic
286Q8×C41—21no—
287Q8×C41—21no—
288Q8×C41—42no—
289Q8×C41—41no—
290Q8×C41—41no—
291Q8×C41—41no—
292Q8×C41—41no—
293D4×C41—21no—
294D4×C41—21no—
295D4×C41—21no—
296D4×C41—21no—
297D4×C41—21no—
298D4×C41—42no—
299D4×C41—42no—
300D4×C41—44no—
301D4×C41—42no—
302D4×C41—44no—
303D4×C41—41no—
304D4×C41—41no—
305D4×C41—41no—
306D4×C41—41no—
307D4×C41—82no—
308D4×C41—82no—
309D4×C41—82no—
310D4×C41—82no—
311D4×C41#13512yes—
312C2×C4×C41—22no—
313C2×C4×C41—21no—
314C2×C4×C41—21no—
315C2×C4×C41—21no—
316C2×C4×C41—21no—
317C2×C4×C41—21no—
318C2×C4×C41—21no—
319C2×C4×C41—21no—
320C2×C4×C41—22no—
321C2×C4×C41—21no—
322C2×C4×C41—21no—
323C2×C4×C41—41no—
324C2×C4×C41—41no—
325C2×C4×C41—41no—
326C2×C4×C41—41no—
327C2×C4×C41—41no—
328C2×C4×C41—41no—
329C2×C4×C41—41no—
330C2×C4×C41—41no—
331C2×C4×C41—81no—
332C2×C4×C41—81no—
333C2×C4×C41—82no—
334C2×C4×C41—81no—
335C2×C4×C41—82no—
336C2×C4×C41—82no—
337C2×C4×C41#12011yescharacteristic
338C2×C4×C41#12011yescharacteristic
339C2×C4×C41#12011yescharacteristic
340C2×C4×C41C22×D411yescharacteristic
341C2×C4×C41C22×D411yescharacteristic
342C2×C4×C41C22×D411yescharacteristic
343C8×C41—41no—
344C8×C41—41no—
345C8×C41—41no—
346C8×C41—41no—
347C8×C41—41no—
348C8×C41—41no—
349#18628C4111yesmaximal, characteristic, direct product factor, Sylow
350C22×C41—21no—
351C22×C41—21no—
352C22×C41—22no—
353C22×C41—41no—
354C22×C41—41no—
355C22×C41—41no—
356C22×C41—41no—
357C22×C41—42no—
358C22×C41—41no—
359C22×C41—42no—
360C22×C41—41no—
361C22×C41—42no—
362C22×C41—41no—
363C22×C41—41no—
364C22×C41—84no—
365C22×C41—164no—
366C22×C41#45512yes—
367C22×C41C2×#12011yescharacteristic
368C4×C41—21no—
369C4×C41—21no—
370C4×C41—21no—
371C4×C41—21no—
372C4×C41—41no—
373C4×C41—41no—
374C4×C41—41no—
375C4×C41—41no—
376C4×C41—41no—
377C4×C41—42no—
378C4×C41—81no—
379C4×C41—81no—
380C4×C41C2×#13511yescharacteristic
381C4×C41#57511yescharacteristic
382C4×C41#57611yescharacteristic
383C4×C41#57711yescharacteristic
384#3519C2×C4111yescharacteristic
385#3248C2×C4111yescharacteristic, complemented
386#3131C2×C4111yescharacteristic, complemented
387#3110C2×C4111yescharacteristic, complemented
388#1646C2×C4111yescharacteristic, complemented
389#1646C2×C4111yescharacteristic, complemented
390#1644C2×C4111yescharacteristic, complemented
391#1643C2×C4111yescharacteristic, complemented
392#1642C2×C4111yescharacteristic, complemented
393#1641C2×C4111yescharacteristic, complemented
394#1639C2×C4111yescharacteristic, complemented
395#1639C2×C4111yescharacteristic, complemented
396#1551C2×C4111yescharacteristic, complemented
397#1494C2×C4111yescharacteristic, complemented
398C2×D4⋊C8C2×C4111yescharacteristic, complemented
399C2×C41—22no—
400C2×C41—42no—
401C2×C41—81no—
402C2×C41—82no—
403C2×C41—81no—
404C2×C41#300211yescharacteristic
405C2×C41#301211yescharacteristic
406C2×C41C2×#45511yescharacteristic
407#555C22×C4111yescharacteristic
408#554C22×C4111yescharacteristic
409#553—21no—
410#553—21no—
411#550C22×C4111yescharacteristic
412#546—22no—
413#546—21no—
414D42—21no—
415D42C22×C4111yescharacteristic
416#540—21no—
417#538—22no—
418#533C22×C4111yescharacteristic, complemented
419#532C22×C4111yescharacteristic
420#529C22×C4111yescharacteristic
421#525—21no—
422C2×#121—21no—
423#518—21no—
424C2×C4×D4C22×C4111yescharacteristic
425#488—22no—
426#487C22×C4111yescharacteristic, complemented
427#487C22×C4111yescharacteristic, complemented
428#486C22×C4111yescharacteristic, complemented
429#486C22×C4111yescharacteristic, complemented
430#484—21no—
431#479—21no—
432#475C22×C4111yescharacteristic, complemented
433#474C22×C4111yescharacteristic
434#474C22×C4111yescharacteristic, complemented
435#474C22×C4111yescharacteristic, complemented
436#467—21no—
437#465—21no—
438#464—21no—
439#462C22×C4111yescharacteristic, complemented
440#461C22×C4111yescharacteristic
441#461C22×C4111yescharacteristic, complemented
442#461C22×C4111yescharacteristic, complemented
443#450—21no—
444#440—21no—
445#440—21no—
446#432C22×C4111yescharacteristic, complemented
447C2×C4⋊C8C22×C4111yescharacteristic, complemented
448#416—22no—
449C2×C4×C8C22×C4111yescharacteristic, complemented
450#333C22×C4111yescharacteristic, complemented
451#333C22×C4111yescharacteristic, complemented
452#331C22×C4111yescharacteristic, complemented
453#331C22×C4111yescharacteristic, complemented
454Q8⋊C8C22×C4111yescharacteristic, complemented
455Q8⋊C8C22×C4111yescharacteristic, complemented
456D4⋊C8C22×C4111yescharacteristic
457D4⋊C8C22×C4111yescharacteristic
458D4⋊C8C22×C4111yescharacteristic, complemented
459D4⋊C8C22×C4111yescharacteristic, complemented
460D4⋊C8C22×C4111yescharacteristic, complemented
461D4⋊C8C22×C4111yescharacteristic, complemented
462C41#1862811yescharacteristic, direct product factor, Sylow
463C2×#41—21no—
464C2×#41D4×C4112yes—
465C22×D4—22no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4D4×C4111yescharacteristic
469C23×C4—21no—
470C2×Q16—21no—
471C2×SD16—21no—
472C2×SD16—21no—
473C2×SD16—21no—
474C22×C8—21no—
475C22×C8—21no—
476C4⋊Q8C23×C4111yescharacteristic
477C4⋊Q8C23×C4111yescharacteristic
478C4⋊Q8C23×C4111yescharacteristic
479#127—21no—
480#127C23×C4111yescharacteristic
481#126—22no—
482#126—21no—
483#125—21no—
484#125—21no—
485#125D4×C4111yescharacteristic
486#124—22no—
487#124D4×C4111yescharacteristic
488#124D4×C4112yes—
489#123—22no—
490#123—22no—
491#123—22no—
492#123—21no—
493C22⋊Q8—21no—
494C22⋊Q8—22no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C4111yescharacteristic
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—21no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121D4×C4111yescharacteristic
511#120—22no—
512#120—22no—
513#120—22no—
514C4×Q8—21no—
515C4×Q8—21no—
516C4×Q8C23×C4111yescharacteristic
517C4×D4—22no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4D4×C4111yescharacteristic
528C4×D4D4×C4111yescharacteristic
529C4×D4C23×C4111yescharacteristic
530C4×D4C23×C4111yescharacteristic
531C4×D4C23×C4111yescharacteristic
532#117—21no—
533#117—21no—
534#117—21no—
535#117—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4D4×C4111yescharacteristic
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—21no—
541C2×C42C23×C4111yescharacteristic
542#107—21no—
543#107—21no—
544#107—21no—
545#106—21no—
546C4⋊C8—21no—
547C4⋊C8C23×C4111yescharacteristic
548C4⋊C8C23×C4111yescharacteristic
549C4⋊C8C23×C4111yescharacteristic
550C4⋊C8C23×C4111yescharacteristic
551#103—22no—
552#103—22no—
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#103—21no—
558#102—22no—
559#102—22no—
560#102—21no—
561#102—21no—
562#102—21no—
563C22⋊C8—21no—
564#97—21no—
565C4×C8—21no—
566C4×C8C23×C4111yescharacteristic
567C4×C8C23×C4111yescharacteristic
568C24—22no—
569C24—21no—
570#41—44no—
571#41—81no—
572#41—81no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8C2×D4×C4111yescharacteristic
576C2×Q8C2×D4×C4112yes—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—41no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—84no—
594C2×D4C2×D4×C4111yescharacteristic
595C2×D4C2×D4×C4111yescharacteristic
596C2×D4C2×D4×C4111yescharacteristic
597C2×D4C2×D4×C4112yes—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4C2×D4×C4111yescharacteristic
610C22×C4C2×D4×C4111yescharacteristic
611C22×C4C2×D4×C4111yescharacteristic
612Q16—81no—
613SD16—42no—
614SD16—42no—
615SD16—81no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—42no—
623C2×C8—81no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4C2×D4×C4111yescharacteristic
640C4⋊C4C2×D4×C4111yescharacteristic
641C4⋊C4C2×D4×C4111yescharacteristic
642C4⋊C4C2×D4×C4111yescharacteristic
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—22no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—41no—
660C42—22no—
661C42—21no—
662C42—41no—
663C42C2×D4×C4111yescharacteristic
664C42C2×D4×C4111yescharacteristic
665C42C2×D4×C4111yescharacteristic
666C42C24×C4111yescharacteristic
667C23—21no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—42no—
672C23—44no—
673C23—42no—
674C23—81no—
675C23—82no—
676C23—82no—
677C23#120×C4111yescharacteristic
678Q8—21no—
679Q8—21no—
680Q8—42no—
681Q8—41no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—21no—
690D4—42no—
691D4—42no—
692D4—44no—
693D4—42no—
694D4—44no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4#135×C4112yes—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—82no—
726C2×C4—81no—
727C2×C4—82no—
728C2×C4—82no—
729C2×C4#120×C4111yescharacteristic
730C2×C4#120×C4111yescharacteristic
731C2×C4#120×C4111yescharacteristic
732C2×C4C22×D4×C4111yescharacteristic
733C2×C4C22×D4×C4111yescharacteristic
734C2×C4C22×D4×C4111yescharacteristic
735C8—41no—
736C8—41no—
737C8—41no—
738C8—41no—
739C8—41no—
740C8—41no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—41no—
750C22—42no—
751C22—41no—
752C22—42no—
753C22—41no—
754C22—41no—
755C22—84no—
756C22—164no—
757C22C41×#45512yes—
758C22C2×#120×C4111yescharacteristic
759C4—21no—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—42no—
769C4—81no—
770C4—81no—
771C4C2×#135×C4111yescharacteristic
772C4C41×#57511yescharacteristic
773C4C41×#57611yescharacteristic
774C4C41×#57711yescharacteristic
775C2—22no—
776C2—42no—
777C2—81no—
778C2—81no—
779C2—82no—
780C2C41×#300211yescharacteristic
781C2C41×#301211yescharacteristic
782C2C2×C41×#45511yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#3519C2
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×#3248C2semidirect
3. C41×#3131C2semidirect
4. C41×#3110C2semidirect
5. C41×#1646C2semidirect
6. C41×#1646C2semidirect
7. C41×#1644C2semidirect
8. C41×#1643C2semidirect
9. C41×#1642C2semidirect
10. C41×#1641C2semidirect
11. C41×#1639C2semidirect
12. C41×#1639C2semidirect
13. C41×#1551C2semidirect
14. C41×#1494C2semidirect
15. C2×C41×D4⋊C8C2semidirect
27. C41×#533C22semidirect
35. C41×#487C22semidirect
36. C41×#487C22semidirect
37. C41×#486C22semidirect
38. C41×#486C22semidirect
41. C41×#475C22semidirect
43. C41×#474C22semidirect
44. C41×#474C22semidirect
48. C41×#462C22semidirect
50. C41×#461C22semidirect
51. C41×#461C22semidirect
55. C41×#432C22semidirect
56. C2×C4⋊C8×C41C22semidirect
58. C2×C4×C8×C41C22semidirect
59. C41×#333C22semidirect
60. C41×#333C22semidirect
61. C41×#331C22semidirect
62. C41×#331C22semidirect
63. C41×Q8⋊C8C22semidirect
64. C41×Q8⋊C8C22semidirect
67. C41×D4⋊C8C22semidirect
68. C41×D4⋊C8C22semidirect
69. C41×D4⋊C8C22semidirect
70. C41×D4⋊C8C22semidirect
349. #18628C41direct (N × H)
385. #3248C2×C41semidirect
386. #3131C2×C41semidirect
387. #3110C2×C41semidirect
388. #1646C2×C41semidirect
389. #1646C2×C41semidirect
390. #1644C2×C41semidirect
391. #1643C2×C41semidirect
392. #1642C2×C41semidirect
393. #1641C2×C41semidirect
394. #1639C2×C41semidirect
395. #1639C2×C41semidirect
396. #1551C2×C41semidirect
397. #1494C2×C41semidirect
398. C2×D4⋊C8C2×C41semidirect
418. #533C22×C41semidirect
426. #487C22×C41semidirect
427. #487C22×C41semidirect
428. #486C22×C41semidirect
429. #486C22×C41semidirect
432. #475C22×C41semidirect
434. #474C22×C41semidirect
435. #474C22×C41semidirect
439. #462C22×C41semidirect
441. #461C22×C41semidirect
442. #461C22×C41semidirect
446. #432C22×C41semidirect
447. C2×C4⋊C8C22×C41semidirect
449. C2×C4×C8C22×C41semidirect
450. #333C22×C41semidirect
451. #333C22×C41semidirect
452. #331C22×C41semidirect
453. #331C22×C41semidirect
454. Q8⋊C8C22×C41semidirect
455. Q8⋊C8C22×C41semidirect
458. D4⋊C8C22×C41semidirect
459. D4⋊C8C22×C41semidirect
460. D4⋊C8C22×C41semidirect
461. D4⋊C8C22×C41semidirect
462. C41#18628direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35192
C41×#32482
C41×#31312
C41×#31102
C41×#16462
C41×#16442
C41×#16432
C41×#16422
C41×#16412
C41×#16392
C41×#15512
C41×#14942
C2×C41×D4⋊C82
#1862841