Finite Group Databasebeta

← #30622475

Subgroups — #30622475

Order 15616.

854 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462350C211yesmaximal, characteristic
2#21462338C211yesmaximal, characteristic, complemented
3#21461967C211yesmaximal, characteristic, complemented
4#21461964C211yesmaximal, characteristic
5#21461949C211yesmaximal, characteristic
6#21461931C211yesmaximal, characteristic, complemented
7#21461898C211yesmaximal, characteristic, complemented
8#21461897C211yesmaximal, characteristic
9#21461813C211yesmaximal, characteristic, complemented
10#21461812C211yesmaximal, characteristic
11#21461620C211yesmaximal, characteristic, complemented
12#21461591C211yesmaximal, characteristic, complemented
13#21461590C211yesmaximal, characteristic
14#103×#6923C211yesmaximal, characteristic, complemented
15#464×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×#14519845C2211yescharacteristic
19C2×#14519845C2211yescharacteristic
20C2×#14519840C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519840C2211yescharacteristic
23C2×#14519840C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25C2×#14519839C2211yescharacteristic
26#16840721C2211yescharacteristic
27C2×#14519831C2211yescharacteristic
28C2×C8×#6923C2211yescharacteristic
29(C2×#6923)⋊Q8C2211yescharacteristic
30(C2×#6923)⋊Q8C2211yescharacteristic
31(C2×#6923)⋊Q8C2211yescharacteristic
32#16840714C2211yescharacteristic
33#16840712—21no—
34#16840712—21no—
35#16840711—21no—
36#16840711—21no—
37#16840709—21no—
38#16840708C2211yescharacteristic
39#16840706—21no—
40C4⋊C4×#6923C2211yescharacteristic
41C4⋊C4×#6923C2211yescharacteristic
42C4×C4⋊#6923—21no—
43C4×C4⋊#6923C2211yescharacteristic
44C4×C4⋊#6923C2211yescharacteristic
45C22⋊C4×#6923—21no—
46#16840636C2211yescharacteristic
47#16840636C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×Q16×D61C2211yescharacteristic
53C2×SD16×D61C2211yescharacteristic
54#124×D61C2211yescharacteristic
55C4×Q8×D61C2211yescharacteristic
56#16839987C411yescharacteristic, complemented
57#16839986C411yescharacteristic, complemented
58#16839985C411yescharacteristic, complemented
59#16839984C411yescharacteristic, complemented
60#16839983C411yescharacteristic, complemented
61#16839982C411yescharacteristic, complemented
62#16839981C411yescharacteristic, complemented
63C4⋊C8×D61C2211yescharacteristic
64#103×D61C2211yescharacteristic
65#102×D61C2211yescharacteristic
66C61×#464C411yescharacteristic, complemented
67C23×#6923—21no—
68C2×D61⋊C8C2311yescharacteristic
69C2×D61⋊C8C2311yescharacteristic
70Q8×#6923—22no—
71Q8×#6923—41no—
72D4×#6923—22no—
73D4×#6923—41no—
74C2×C4⋊#6923—21no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923D411yescharacteristic
78C2×C4⋊#6923D411yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C4⋊#6923C2311yescharacteristic
82C2×C4⋊#6923C2311yescharacteristic
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C22⋊#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923C2311yescharacteristic
91C2×C4×#6923C2311yescharacteristic
92#14519845—41no—
93#14519845—41no—
94#14519840—22no—
95#14519840—22no—
96#14519840—22no—
97#14519840—41no—
98#14519839—22no—
99#14519839—41no—
100#14519832—21no—
101#14519832—21no—
102#14519831—41no—
103C8×#6923—41no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4—21no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4D411yescharacteristic
114(C2×#6923)⋊C4D411yescharacteristic
115C2×Q8×D61C2311yescharacteristic
116C2×Q8×D61C2311yescharacteristic
117C2×D4×D61C2311yescharacteristic
118C2×Dic244C2×C411yescharacteristic, complemented
119C2×#11758202C2×C411yescharacteristic, complemented
120C2×#11758202C2×C411yescharacteristic, complemented
121Q16×D61—41no—
122Q16×D61—41no—
123C2×#11758190C2×C411yescharacteristic
124C2×#11758200C2×C411yescharacteristic
125C2×#11758201C2×C411yescharacteristic
126SD16×D61—41no—
127SD16×D61—41no—
128C2×C8×D61C2311yescharacteristic
129C2×C8×D61C2311yescharacteristic
130#14519766C2×C411yescharacteristic
131#14519765C2×C411yescharacteristic
132#14519764C2×C411yescharacteristic
133#14519763—21no—
134#14519763—21no—
135Q8×Dic61C2×C411yescharacteristic, complemented
136C4×Dic122—21no—
137C4×Dic122C2×C411yescharacteristic, complemented
138#14519742—21no—
139#14519742C2×C411yescharacteristic, complemented
140C4⋊C4×D61—21no—
141C4⋊C4×D61C2311yescharacteristic
142C22⋊C4×D61—21no—
143C22⋊C4×D61—21no—
144C42×D61—21no—
145C42×D61C2311yescharacteristic
146C4⋊#92418C2×C411yescharacteristic, complemented
147#14519706C2×C411yescharacteristic, complemented
148#14519706C2×C411yescharacteristic, complemented
149#14519702C2×C411yescharacteristic, complemented
150#14519701C2×C411yescharacteristic, complemented
151#14519700C2×C411yescharacteristic, complemented
152#14519699C2×C411yescharacteristic
153#14519698C2×C411yescharacteristic
154#14519697C2×C411yescharacteristic
155C2×Q16×C61C2×C411yescharacteristic, complemented
156C2×SD16×C61C2×C411yescharacteristic
157#124×C61C2×C411yescharacteristic
158C4×Q8×C61C2×C411yescharacteristic, complemented
159C4⋊C8×C61C2×C411yescharacteristic, complemented
160#103×C61C2×C411yescharacteristic, complemented
161#102×C61C2×C411yescharacteristic
162C23×D61—21no—
163C22×#6923—21no—
164C22×#6923—21no—
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923—42no—
168C22×#6923—42no—
169C22×#6923—81no—
170C22×#6923C2×D411yescharacteristic
171C22×#6923C2×D411yescharacteristic
172C22×#6923C2×D411yescharacteristic
173C22×#6923C2×D411yescharacteristic
174C2×Q8×C61C22×C411yescharacteristic
175C2×Q8×C61C22×C411yescharacteristic
176C2×D4×C61C22×C411yescharacteristic
177C2×C22⋊D61—21no—
178Q8×D61—21no—
179Q8×D61—21no—
180Q8×D61—21no—
181Q8×D61—21no—
182Q8×D61—21no—
183Q8×D61—21no—
184Q8×D61—21no—
185Q8×D61—21no—
186D4×D61—21no—
187D4×D61—21no—
188D4×D61—21no—
189D4×D61—21no—
190C2×D244C22×C411yescharacteristic
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61C2×D411yescharacteristic
195C2×C4×D61C2×D411yescharacteristic
196C2×C4×D61C2411yescharacteristic
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122C22×C411yescharacteristic
200C2×Dic122C22×C411yescharacteristic
201C22⋊#6923—42no—
202C22⋊#6923—42no—
203C22⋊#6923—81no—
204C2×#92420—21no—
205C2×#92420—21no—
206C4⋊#6923—22no—
207C4⋊#6923—21no—
208C4⋊#6923—21no—
209C4⋊#6923—21no—
210C4⋊#6923—21no—
211C4⋊#6923—21no—
212C4⋊#6923—21no—
213C4⋊#6923—21no—
214C4⋊#6923—41no—
215C4⋊#6923—42no—
216C4⋊#6923—42no—
217C4⋊#6923—81no—
218C4⋊#6923#4112yes—
219C4×#6923—21no—
220C4×#6923—21no—
221C4×#6923—21no—
222C4×#6923—21no—
223C4×#6923—42no—
224C4×#6923—81no—
225C4×#6923—81no—
226C4×#6923—81no—
227D61⋊C8—21no—
228D61⋊C8—21no—
229D61⋊C8—21no—
230D61⋊C8#4112yes—
231Q16×C61—41no—
232SD16×C61—41no—
233C2×C8×C61C22×C411yescharacteristic
234C2×C8×C61C22×C411yescharacteristic
235C4⋊C4×C61—21no—
236C4⋊C4×C61C22×C411yescharacteristic
237C22⋊C4×C61—21no—
238C22⋊C4×C61—21no—
239C42×C61—21no—
240C42×C61C22×C411yescharacteristic
241C22⋊Dic61—21no—
242C22⋊Dic61—21no—
243#11758202—41no—
244#11758202—41no—
245#11758201—41no—
246#11758200—41no—
247#11758198—21no—
248#11758198—21no—
249#11758198—21no—
250#11758198—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61C22×C411yescharacteristic
253#11758196—21no—
254#11758196—21no—
255#11758196—21no—
256C4×Dic61—21no—
257C4×Dic61—21no—
258C4×Dic61—21no—
259C4×Dic61C22×C411yescharacteristic
260C4×Dic61#4111yescharacteristic
261C4×Dic61#4111yescharacteristic
262C2×#92418C22×C411yescharacteristic
263C2×#92418C22×C411yescharacteristic
264Dic244—41no—
265#11758190—41no—
266C8×D61—21no—
267C8×D61—21no—
268C8×D61—21no—
269C8×D61—21no—
270C23×C61—21no—
271C22×D61—21no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61C22×D411yescharacteristic
279C2×#6923—21no—
280C2×#6923—21no—
281C2×#6923—21no—
282C2×#6923—21no—
283C2×#6923—21no—
284C2×#6923—22no—
285C2×#6923—21no—
286C2×#6923—21no—
287C2×#6923—21no—
288C2×#6923—21no—
289C2×#6923—21no—
290C2×#6923—21no—
291C2×#6923—41no—
292C2×#6923—41no—
293C2×#6923—41no—
294C2×#6923—41no—
295C2×#6923—41no—
296C2×#6923—41no—
297C2×#6923—41no—
298C2×#6923—41no—
299C2×#6923—41no—
300C2×#6923—41no—
301C2×#6923—41no—
302C2×#6923—84no—
303C2×#6923#13712yes—
304Q8×C61—21no—
305Q8×C61—21no—
306Q8×C61—21no—
307Q8×C61—21no—
308D4×C61—21no—
309D4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61C4×D411yescharacteristic
314C2×C4×C61C4×D411yescharacteristic
315C2×C4×C61C23×C411yescharacteristic
316C22⋊D61—41no—
317C22⋊D61—41no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61C4×D411yescharacteristic
322C2×Dic61C4×D411yescharacteristic
323C2×Dic61C2×#4111yescharacteristic
324D244—21no—
325D244—21no—
326C4×D61—21no—
327C4×D61—21no—
328C4×D61—21no—
329C4×D61—21no—
330C4×D61—41no—
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61C2×#4111yescharacteristic
337C4×D61C2×#4111yescharacteristic
338C4×D61H(5,𝔽2)11yescharacteristic
339C4×D61H(5,𝔽2)11yescharacteristic
340Dic122—21no—
341Dic122—21no—
342Dic122—21no—
343Dic122—21no—
344Dic122—41no—
345Dic122—41no—
346Dic122—41no—
347Dic122—41no—
348#92420—22no—
349#92420—41no—
350C8×C61—21no—
351C8×C61—21no—
352#92418—21no—
353#92418—21no—
354#23107—611nomaximal, Sylow
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61C2×C4×D411yescharacteristic
359C2×D61—41no—
360C2×D61—41no—
361C2×D61—41no—
362C2×D61—81no—
363C2×D61—81no—
364C2×D61—81no—
365C2×D61—81no—
366C2×D61#54611yescharacteristic
367C2×D61#55011yescharacteristic
368C2×D61C2×#13711yescharacteristic
369C2×D61#57511yescharacteristic
370C2×D61#57711yescharacteristic
371C2×D61#57711yescharacteristic
372#6923—22no—
373#6923—41no—
374#6923—41no—
375#6923—42no—
376#6923—41no—
377#6923—81no—
378#6923—81no—
379#6923—81no—
380C4×C61—21no—
381C4×C61—21no—
382C4×C61—41no—
383C4×C61—41no—
384C4×C61—41no—
385C4×C61C4×#4111yescharacteristic
386C4×C61#51811yescharacteristic
387Dic61—21no—
388Dic61—21no—
389Dic61—41no—
390Dic61—41no—
391Dic61—41no—
392Dic61#55311yescharacteristic
393Dic61#55511yescharacteristic
394C2×#464—611no—
395#2367—611no—
396#2355—611no—
397#1971—611no—
398#1968—611no—
399#1959—611no—
400#1948—611no—
401#1927—611no—
402#1926—611no—
403#1878—611no—
404#1877—611no—
405#1771—611no—
406#1763—611no—
407#1762—611no—
408C4×#103—611no—
409C2×C61—81no—
410C2×C61#236311yescharacteristic
411C2×C61C4×#13711yescharacteristic
412C2×C61#295211yescharacteristic
413D61—81no—
414D61#331111yescharacteristic
415D61#331611yescharacteristic
416D61#340011yescharacteristic
417D61#340111yescharacteristic
418C22×Q16—611no—
419C22×SD16—611no—
420C2×#124—611no—
421C2×C4×Q8—611no—
422C2×C4×Q8—611no—
423C2×C4×D4—611no—
424#464—611no—
425#464—611no—
426#464—611no—
427#464—611no—
428#464—611no—
429#464—611no—
430#464—611no—
431#464#692311yescharacteristic, complemented
432C2×#106—611no—
433C2×#106—611no—
434C2×C4⋊C8—611no—
435C2×#103—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#102—611no—
441C2×#102—611no—
442C2×#102—611no—
443C2×#97—611no—
444C2×#97—611no—
445C2×C4×C8—611no—
446#391—611no—
447#391—611no—
448#391—611no—
449#390—611no—
450#388—1221no—
451#388—1221no—
452#387—1221no—
453#387—1221no—
454#385—1221no—
455#384—611no—
456#382—1221no—
457C4×C4⋊C4—611no—
458C4×C4⋊C4—611no—
459C4×C4⋊C4—611no—
460C4×C4⋊C4—611no—
461C4×C4⋊C4—1221no—
462C4×C22⋊C4—1221no—
463#340—611no—
464#340—611no—
465#340—611no—
466#340—611no—
467#336—611no—
468#336—611no—
469C61#2310711yescharacteristic, complemented, Sylow
470C22×Q8—611no—
471C22×Q8—611no—
472C22×D4—611no—
473C23×C4—1221no—
474C2×Q16—611no—
475C2×Q16—611no—
476C2×Q16—611no—
477C2×Q16—2441no—
478C2×Q16—2441no—
479C2×Q16C2×#692311yescharacteristic, complemented
480C2×SD16—611no—
481C2×SD16—611no—
482C2×SD16—611no—
483C2×SD16—2441no—
484C2×SD16—2441no—
485C2×SD16C2×#692311yescharacteristic
486C22×C8—611no—
487C22×C8—611no—
488C22×C8—611no—
489C22×C8—611no—
490#124—611no—
491#124—611no—
492#124—611no—
493#124—1221no—
494#124—1221no—
495#124C2×#692311yescharacteristic
496C4×Q8—611no—
497C4×Q8—611no—
498C4×Q8—611no—
499C4×Q8—1221no—
500C4×Q8—1221no—
501C4×Q8—1222no—
502C4×Q8—2441no—
503C4×Q8C2×#692311yescharacteristic, complemented
504C4×D4—1222no—
505C4×D4—2441no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C42—611no—
523C2×C42—611no—
524C2×C42—611no—
525C2×C42—1221no—
526C2×C42—1221no—
527C2×C42—1221no—
528C2×C42—1221no—
529C2×C42—1221no—
530#106—2441no—
531#106—2441no—
532C4⋊C8—611no—
533C4⋊C8—611no—
534C4⋊C8—611no—
535C4⋊C8C2×#692311yescharacteristic, complemented
536#103—611no—
537#103—611no—
538#103—611no—
539#103—1222no—
540#103—1222no—
541#103—1222no—
542#103—2441no—
543#103C2×#692311yescharacteristic, complemented
544#102—611no—
545#102—611no—
546#102—611no—
547#102—1222no—
548#102—2441no—
549#102C2×#692311yescharacteristic
550#97—1221no—
551#97—1221no—
552#97—2441no—
553C4×C8—2441no—
554#95—611no—
555#95—611no—
556#95—1221no—
557#95—1221no—
558#95—1221no—
559#95—1221no—
560#95—1221no—
561#95—1221no—
562#95—1221no—
563#95—1221no—
564#95—1221no—
565C24—1221no—
566C2×Q8—611no—
567C2×Q8—611no—
568C2×Q8—1221no—
569C2×Q8—1221no—
570C2×Q8—1221no—
571C2×Q8—1221no—
572C2×Q8—1221no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8—1221no—
576C2×Q8—1221no—
577C2×Q8—1221no—
578C2×Q8C22×#692311yescharacteristic
579C2×Q8C22×#692311yescharacteristic
580C2×D4—611no—
581C2×D4—1221no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4C22×#692311yescharacteristic
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—4881no—
602C22×C4—2442no—
603C22×C4—2442no—
604Q16—41no—
605Q16—2441no—
606Q16—2441no—
607Q16—2441no—
608SD16—41no—
609SD16—2441no—
610SD16—2441no—
611SD16—2441no—
612C2×C8—612no—
613C2×C8—611no—
614C2×C8—611no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8C22×#692311yescharacteristic
625C2×C8C22×#692311yescharacteristic
626C4⋊C4—21no—
627C4⋊C4—612no—
628C4⋊C4—611no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—1221no—
633C4⋊C4—1222no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—4881no—
642C4⋊C4—2441no—
643C4⋊C4—2442no—
644C4⋊C4—2442no—
645C4⋊C4C22×#692311yescharacteristic
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—1221no—
649C22⋊C4—1221no—
650C22⋊C4—1221no—
651C22⋊C4—1221no—
652C22⋊C4—1221no—
653C22⋊C4—1221no—
654C22⋊C4—4881no—
655C22⋊C4—2442no—
656C22⋊C4—2442no—
657C42—21no—
658C42—611no—
659C42—611no—
660C42—611no—
661C42—1221no—
662C42—1221no—
663C42—1221no—
664C42—1221no—
665C42—1221no—
666C42—1221no—
667C42—1221no—
668C42—4881no—
669C42—4881no—
670C42—4881no—
671C42—2442no—
672C42C22×#692311yescharacteristic
673C23—21no—
674C23—611no—
675C23—1221no—
676C23—2441no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—21no—
686Q8—1221no—
687Q8—1221no—
688Q8—1221no—
689Q8—1221no—
690Q8—2441no—
691Q8—2441no—
692Q8—2441no—
693Q8—2441no—
694D4—21no—
695D4—21no—
696D4—1221no—
697D4—1221no—
698D4—2441no—
699D4—2441no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—611no—
704C2×C4—611no—
705C2×C4—611no—
706C2×C4—611no—
707C2×C4—611no—
708C2×C4—612no—
709C2×C4—611no—
710C2×C4—611no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1222no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—4884no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4D4×#692311yescharacteristic
749C2×C4D4×#692311yescharacteristic
750C2×C4C23×#692311yescharacteristic
751C8—21no—
752C8—21no—
753C8—1222no—
754C8—1221no—
755C8—1221no—
756C8—2441no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—611no—
761C22—611no—
762C22—611no—
763C22—611no—
764C22—611no—
765C22—611no—
766C22—4881no—
767C22—4881no—
768C22—4881no—
769C22—4881no—
770C22—2441no—
771C22—2441no—
772C22—2441no—
773C22C2×D4×#692311yescharacteristic
774C4—21no—
775C4—21no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—611no—
780C4—611no—
781C4—1222no—
782C4—1221no—
783C4—1221no—
784C4—4881no—
785C4—4881no—
786C4—4881no—
787C4—2441no—
788C4—2441no—
789C4—2441no—
790C4—2442no—
791C4—2441no—
792C4—2441no—
793C4—2441no—
794C4#41×#692311yescharacteristic
795C4#1684082911yescharacteristic
796C2—81no—
797C2—611no—
798C2—611no—
799C2—611no—
800C2—611no—
801C2—4881no—
802C2#2146234611yescharacteristic
803C2#137×#692311yescharacteristic
804C2#2146258211yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#464C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#464#6923
hypocenterC61#23107
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. #21462338C2semidirect
3. #21461967C2semidirect
6. #21461931C2semidirect
7. #21461898C2semidirect
9. #21461813C2semidirect
11. #21461620C2semidirect
12. #21461591C2semidirect
14. #103×#6923C2semidirect
56. #16839987C4semidirect
57. #16839986C4semidirect
58. #16839985C4semidirect
59. #16839984C4semidirect
60. #16839983C4semidirect
61. #16839982C4semidirect
62. #16839981C4semidirect
66. C61×#464C4semidirect
118. C2×Dic244C2×C4semidirect
119. C2×#11758202C2×C4semidirect
120. C2×#11758202C2×C4semidirect
135. Q8×Dic61C2×C4semidirect
137. C4×Dic122C2×C4semidirect
139. #14519742C2×C4semidirect
146. C4⋊#92418C2×C4semidirect
147. #14519706C2×C4semidirect
148. #14519706C2×C4semidirect
149. #14519702C2×C4semidirect
150. #14519701C2×C4semidirect
151. #14519700C2×C4semidirect
155. C2×Q16×C61C2×C4semidirect
158. C4×Q8×C61C2×C4semidirect
159. C4⋊C8×C61C2×C4semidirect
160. #103×C61C2×C4semidirect
431. #464#6923semidirect
469. C61#23107semidirect
479. C2×Q16C2×#6923semidirect
503. C4×Q8C2×#6923semidirect
535. C4⋊C8C2×#6923semidirect
543. #103C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623502
#214623382
#214619672
#214619642
#214619492
#214619312
#214618982
#214618972
#214618132
#214618122
#214616202
#214615912
#214615902
#103×#69232
#464×D612
#2310761