Finite Group Databasebeta

← #30571144

Subgroups — #30571144

Order 15616.

1770 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459624C211yesmaximal, characteristic, complemented
2C2×#16840497C211yesmaximal, characteristic
3#21458876C214yesmaximal, complemented
4#21458870C214yesmaximal, complemented
5#21458632C214yesmaximal, complemented
6#21458631C214yesmaximal, complemented
7#21456821C214yesmaximal, complemented
8#21456762C211yesmaximal, characteristic
9#21456757C211yesmaximal, characteristic
10#21455915C214yesmaximal, complemented
11#21455858C211yesmaximal, characteristic, complemented
12#21454902C211yesmaximal, characteristic, complemented
13C61×#3104C211yesmaximal, characteristic, complemented
14#16840497—22no—
15#16840497—22no—
16#16840497C2214yes—
17#16840497C2214yes—
18Q8×Dic122C2212yescomplemented
19#16840492C2212yescomplemented
20#16840490—22no—
21#16840490C2212yescomplemented
22#16840489—22no—
23#16840487C2212yescomplemented
24#16840391—22no—
25#16840390—21no—
26#16840319C2211yescharacteristic
27#16840314C2214yes—
28C2×#14519774C2211yescharacteristic
29C2×#14519766C2212yes—
30C2×#14519765—21no—
31C2×#14519762—22no—
32#16840239—21no—
33C2×C4×Dic122C2211yescharacteristic
34C2×C4×D244—21no—
35C2×#14519739C2212yes—
36#16840155C2218yescomplemented
37#16840136C2212yes—
38#16840135C2212yes—
39#16840123C2218yescomplemented
40#16840110C2212yes—
41#16840109C2212yes—
42#16840097C2212yes—
43#16840057C2212yescomplemented
44#16840041C2218yescomplemented
45#16839987C2218yescomplemented
46#16839986C2218yescomplemented
47#16839972C2212yescomplemented
48#16839966C2218yescomplemented
49#16839963C2214yes—
50#16839962C2214yes—
51#16839918C2212yes—
52#16839915C2214yes—
53#16839912C2214yes—
54#16839892C2214yescomplemented
55#16839889C2214yescomplemented
56#16839865C2218yescomplemented
57#16839861C2218yescomplemented
58C4×#11758202C2214yescomplemented
59#16839816C2214yes—
60#16839815C2211yescharacteristic
61C61×#533C2211yescharacteristic
62C2×C4×Q8×C61C2211yescharacteristic
63C61×#484C2212yes—
64C61×#477C2212yescomplemented
65C61×#462C2212yescomplemented
66C61×#451C2212yes—
67C4×Q16×C61C2214yescomplemented
68C61×#431C2211yescharacteristic
69C22×Dic122D411yescharacteristic
70C22×D244—21no—
71C22×D244—21no—
72C22×D244C2312yes—
73C22×C4×D61—22no—
74C2×#11758202C2314yes—
75C2×#11758190C2318yes—
76C2×#11758201C2318yes—
77#14519777—22no—
78#14519777C2311yescharacteristic
79#14519777C2311yescharacteristic
80#14519776—22no—
81#14519776—24no—
82#14519776C2314yes—
83#14519775—24no—
84#14519775C2314yes—
85#14519774—21no—
86#14519774—21no—
87#14519774C2312yes—
88#14519774C2312yes—
89#14519769—21no—
90#14519769—22no—
91#14519768—22no—
92#14519767—24no—
93#14519767—24no—
94#14519767—24no—
95#14519766—24no—
96#14519766C2318yes—
97#14519765—24no—
98#14519765—24no—
99#14519762—28no—
100#14519762—28no—
101#14519756—21no—
102#14519756C2312yes—
103#14519754—24no—
104Q8×Dic61C2314yes—
105C4×Dic122—22no—
106C4×Dic122—22no—
107C4×Dic122—21no—
108C4×Dic122D412yes—
109C4×Dic122D412yes—
110C4×Dic122C2312yes—
111C4×Dic122C2312yes—
112C4×Dic122C2312yes—
113#14519742—22no—
114#14519742—22no—
115#14519742—24no—
116#14519742C2314yes—
117C4×D244—24no—
118C4×D244—24no—
119#14519739—24no—
120#14519739C2318yes—
121#14519736—21no—
122#14519733—24no—
123C2×C4⋊Dic61D411yescharacteristic
124C2×#11758196D412yes—
125C2×#11758198—22no—
126C2×#11758198—22no—
127C2×#11758198—22no—
128C2×C4×Dic61C2312yes—
129#14519710C2314yes—
130C4⋊#92418C2312yes—
131#14519706C2318yes—
132#14519701C2314yes—
133#14519700C2314yes—
134#14519699C2318yes—
135#14519697C2318yes—
136C22⋊#92418C2312yes—
137#14519687C2318yes—
138C4×#92418C2312yes—
139C22×Q8×C61C2311yescharacteristic
140C2×Q16×C61C2314yes—
141C4⋊Q8×C61C2311yescharacteristic
142C4⋊Q8×C61C2311yescharacteristic
143#125×C61—21no—
144C22⋊Q8×C61—21no—
145C22⋊Q8×C61C2312yes—
146C4×Q8×C61—21no—
147C4×Q8×C61—21no—
148C4×Q8×C61—21no—
149C4×Q8×C61C2312yes—
150C4×Q8×C61C2312yes—
151C4×Q8×C61C2312yes—
152#117×C61—21no—
153C2×C4⋊C4×C61—21no—
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C42×C61—21no—
156C2×C42×C61C2311yescharacteristic
157#107×C61C2314yes—
158C4⋊C8×C61C2312yes—
159#103×C61C2314yes—
160#103×C61C2314yes—
161C22⋊C8×C61C2312yes—
162C4×C8×C61C2312yes—
163C23×D61—22no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—42no—
167C2×Q8×C61C2412yes—
168C2×Q8×C61C2412yes—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2411yescharacteristic
174C22×Dic61C2×D412yes—
175C22×Dic61C2×D412yes—
176C2×D244—22no—
177C2×D244—22no—
178C2×D244—22no—
179C2×D244—22no—
180C2×D244—22no—
181C2×D244—44no—
182C2×D244—44no—
183C2×D244—82no—
184C2×D244C2414yes—
185C2×C4×D61—28no—
186C2×C4×D61—84no—
187C2×Dic122—24no—
188C2×Dic122—21no—
189C2×Dic122—24no—
190C2×Dic122C2×D412yes—
191C2×Dic122C2×D412yes—
192C2×Dic122C2412yes—
193Q16×C61—44no—
194C2×C8×C61C2414yes—
195C4⋊C4×C61—22no—
196C4⋊C4×C61—22no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—22no—
202C4⋊C4×C61—22no—
203C4⋊C4×C61C2412yes—
204C4⋊C4×C61C2412yes—
205C22⋊C4×C61—22no—
206C42×C61—22no—
207C42×C61—22no—
208C42×C61—22no—
209C42×C61C2×D411yescharacteristic
210C42×C61C2×D411yescharacteristic
211C42×C61C2411yescharacteristic
212C42×C61C2411yescharacteristic
213C22⋊Dic61—22no—
214#11758202—44no—
215#11758201—48no—
216#11758198—28no—
217#11758198—28no—
218#11758198—28no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—24no—
223C4⋊Dic61C2×D412yes—
224C4⋊Dic61C2×D412yes—
225C4⋊Dic61C2412yes—
226#11758196—22no—
227#11758196—22no—
228#11758196—24no—
229#11758196—24no—
230#11758196—24no—
231#11758196—24no—
232#11758196C2×D414yes—
233#11758196C2×D414yes—
234C4×Dic61—22no—
235C4×Dic61—24no—
236C4×Dic61—24no—
237C4×Dic61C2×D414yes—
238C4×Dic61C2414yes—
239C2×#92418C2414yes—
240#11758190—48no—
241C23×C61C22×D411yescharacteristic
242C22×D61—24no—
243C22×D61—44no—
244C22×D61—44no—
245C22×D61—44no—
246Q8×C61—24no—
247Q8×C61—22no—
248Q8×C61—22no—
249Q8×C61—42no—
250Q8×C61—81no—
251C2×C4×C61—22no—
252C2×C4×C61—22no—
253C2×C4×C61—22no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—41no—
257C2×C4×C61—42no—
258C2×C4×C61—42no—
259C2×C4×C61#13714yes—
260C2×C4×C61C22×D411yescharacteristic
261C2×C4×C61C22×D411yescharacteristic
262C2×C4×C61C22×D411yescharacteristic
263C2×C4×C61C22×D411yescharacteristic
264C2×C4×C61C22×D411yescharacteristic
265C2×C4×C61C2511yescharacteristic
266C2×Dic61—24no—
267C2×Dic61—22no—
268C2×Dic61—22no—
269C2×Dic61—42no—
270C2×Dic61C22×D414yes—
271C2×Dic61C22×D414yes—
272D244—28no—
273D244—44no—
274D244—44no—
275D244—44no—
276D244—82no—
277D244—82no—
278C4×D61—88no—
279Dic122—24no—
280Dic122—24no—
281Dic122—24no—
282Dic122—84no—
283Dic122—81no—
284C8×C61—24no—
285#92418—24no—
286#61892—611nomaximal, Sylow
287C22×C61—21no—
288C22×C61—21no—
289C22×C61C2×#13712yes—
290C22×C61C23×D411yescharacteristic
291C2×D61—44no—
292C2×D61—44no—
293C2×D61—44no—
294C2×D61—88no—
295C4×C61—21no—
296C4×C61—21no—
297C4×C61—21no—
298C4×C61—42no—
299C4×C61—42no—
300C4×C61—42no—
301C4×C61—42no—
302C4×C61C2×#13712yes—
303C4×C61C2×#13712yes—
304C4×C61#58512yes—
305Dic61—24no—
306Dic61—24no—
307Dic61—42no—
308Dic61—42no—
309#3502—611no—
310C2×#559—611no—
311#3400—614no—
312#3400—614no—
313#3375—614no—
314#3375—614no—
315#3215—614no—
316#3208—611no—
317#3208—611no—
318#3110—614no—
319#3104—611no—
320#3104D6111yescharacteristic, complemented
321#2983—611no—
322C2×C61—22no—
323C2×C61#348711yescharacteristic
324C2×C61C22×#13711yescharacteristic
325C2×C61#358511yescharacteristic
326D61—84no—
327#559—614no—
328#559—614no—
329#559—1222no—
330#559—1222no—
331Q82—612no—
332Q82—612no—
333#557—612no—
334#557—612no—
335#557—1222no—
336#557—1222no—
337#544—1221no—
338#544—1222no—
339#533—614no—
340#533—611no—
341#533C2×D6111yescharacteristic
342C2×#127—611no—
343C2×#124—612no—
344C2×#124—1221no—
345C2×#123—1222no—
346#519—1221no—
347C2×C4×Q8—611no—
348C2×C4×Q8C2×D6111yescharacteristic
349C2×C4×D4—612no—
350C2×C4×D4—1221no—
351#497—618no—
352#492—612no—
353#492—612no—
354#489—618no—
355#486—612no—
356#486—612no—
357#484—612no—
358#484C2×D6112yes—
359#477—612no—
360#477C2×D6112yescomplemented
361#474—618no—
362#464—618no—
363#464—618no—
364#462—612no—
365#462C2×D6112yescomplemented
366#461—618no—
367#460—614no—
368#460—614no—
369#451—612no—
370#451C2×D6112yes—
371#450—614no—
372#450—614no—
373#446—614no—
374#446—614no—
375#440—618no—
376#440—618no—
377C4×Q16—614no—
378C4×Q16C2×D6114yescomplemented
379#432—614no—
380#431—611no—
381#431C2×D6111yescharacteristic
382C61#6189211yescharacteristic, complemented, Sylow
383C22×Q8—611no—
384C22×Q8C22×D6111yescharacteristic
385C22×D4—612no—
386C22×D4—1221no—
387C22×D4—1221no—
388C23×C4—1222no—
389C2×Q16—614no—
390C2×Q16C22×D6114yes—
391C2×SD16—618no—
392C2×SD16—618no—
393C4⋊Q8—614no—
394C4⋊Q8—614no—
395C4⋊Q8—611no—
396C4⋊Q8—611no—
397C4⋊Q8—1222no—
398C4⋊Q8—1224no—
399C4⋊Q8—1222no—
400C4⋊Q8—1224no—
401C4⋊Q8C22×D6111yescharacteristic
402C4⋊Q8C22×D6111yescharacteristic
403#127—612no—
404#127—612no—
405#127—1221no—
406#127—1221no—
407#125—21no—
408#125—1222no—
409#125—1224no—
410#125—1224no—
411#125—1224no—
412#125—1222no—
413#125—1221no—
414#124—618no—
415#124—1224no—
416#124—1224no—
417#124—1224no—
418#123—1228no—
419#123—1228no—
420C22⋊Q8—21no—
421C22⋊Q8—612no—
422C22⋊Q8—1224no—
423C22⋊Q8—1221no—
424C22⋊Q8C22×D6112yes—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×Q8—21no—
428C4×Q8—612no—
429C4×Q8—612no—
430C4×Q8—612no—
431C4×Q8—612no—
432C4×Q8—614no—
433C4×Q8—614no—
434C4×Q8—612no—
435C4×Q8—1222no—
436C4×Q8—1222no—
437C4×Q8—1224no—
438C4×Q8—1222no—
439C4×Q8—1222no—
440C4×Q8—1221no—
441C4×Q8C22×D6112yes—
442C4×Q8C22×D6112yes—
443C4×Q8C22×D6112yes—
444C4×D4—618no—
445C4×D4—1224no—
446C4×D4—1224no—
447C4×D4—1224no—
448#117—21no—
449#117—1224no—
450#117—1221no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—611no—
453C2×C4⋊C4—612no—
454C2×C4⋊C4C22×D6111yescharacteristic
455C2×C22⋊C4—1222no—
456C2×C22⋊C4—1222no—
457C2×C22⋊C4—1222no—
458C2×C42—21no—
459C2×C42—612no—
460C2×C42C22×D6111yescharacteristic
461#107—614no—
462#107C22×D6114yes—
463C4⋊C8—618no—
464C4⋊C8—612no—
465C4⋊C8C22×D6112yes—
466#103—614no—
467#103—614no—
468#103C22×D6114yes—
469#103C22×D6114yes—
470#102—618no—
471#102—618no—
472C22⋊C8—612no—
473C22⋊C8C22×D6112yes—
474#97—618no—
475C4×C8—612no—
476C4×C8C22×D6112yes—
477C24—1222no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—42no—
481C2×Q8—612no—
482C2×Q8—612no—
483C2×Q8—612no—
484C2×Q8—1224no—
485C2×Q8—1224no—
486C2×Q8—1221no—
487C2×Q8C23×D6112yes—
488C2×Q8C23×D6112yes—
489C2×D4—614no—
490C2×D4—1222no—
491C2×D4—1222no—
492C2×D4—1222no—
493C2×D4—1222no—
494C2×D4—1222no—
495C2×D4—4882no—
496C2×D4—2444no—
497C2×D4—2444no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—612no—
501C22×C4—612no—
502C22×C4—1228no—
503C22×C4—4884no—
504C22×C4D4×D6111yescharacteristic
505C22×C4D4×D6111yescharacteristic
506C22×C4C23×D6111yescharacteristic
507Q16—44no—
508Q16—2444no—
509SD16—2448no—
510SD16—2448no—
511C2×C8—614no—
512C2×C8C23×D6114yes—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—22no—
521C4⋊C4—614no—
522C4⋊C4—614no—
523C4⋊C4—612no—
524C4⋊C4—612no—
525C4⋊C4—612no—
526C4⋊C4—1224no—
527C4⋊C4—1224no—
528C4⋊C4—1224no—
529C4⋊C4—1224no—
530C4⋊C4—1224no—
531C4⋊C4—1222no—
532C4⋊C4—1222no—
533C4⋊C4—1221no—
534C4⋊C4—1221no—
535C4⋊C4—1221no—
536C4⋊C4C23×D6112yes—
537C4⋊C4C23×D6112yes—
538C22⋊C4—22no—
539C22⋊C4—1228no—
540C22⋊C4—1228no—
541C22⋊C4—1228no—
542C22⋊C4—1222no—
543C42—22no—
544C42—22no—
545C42—22no—
546C42—614no—
547C42—614no—
548C42—1224no—
549C42—1224no—
550C42—1222no—
551C42D4×D6111yescharacteristic
552C42D4×D6111yescharacteristic
553C42C23×D6111yescharacteristic
554C42C23×D6111yescharacteristic
555C23—1224no—
556C23—2444no—
557C23—2444no—
558C23—2444no—
559C23C2×D4×D6111yescharacteristic
560Q8—24no—
561Q8—22no—
562Q8—22no—
563Q8—42no—
564Q8—81no—
565Q8—1224no—
566Q8—1224no—
567Q8—1224no—
568Q8—4881no—
569Q8—4884no—
570D4—1228no—
571D4—4882no—
572D4—4882no—
573D4—2444no—
574D4—2444no—
575D4—2444no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—614no—
585C2×C4—614no—
586C2×C4—1224no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—4888no—
590C2×C4—2442no—
591C2×C4#1451980914yes—
592C2×C4C2×D4×D6111yescharacteristic
593C2×C4C2×D4×D6111yescharacteristic
594C2×C4C2×D4×D6111yescharacteristic
595C2×C4C2×D4×D6111yescharacteristic
596C2×C4C2×D4×D6111yescharacteristic
597C2×C4C24×D6111yescharacteristic
598C8—24no—
599C8—1224no—
600C22—21no—
601C22—21no—
602C22—4888no—
603C22—2444no—
604C22—2444no—
605C22—2444no—
606C22C2×#1451980912yes—
607C22C22×D4×D6111yescharacteristic
608C4—21no—
609C4—21no—
610C4—21no—
611C4—42no—
612C4—42no—
613C4—42no—
614C4—42no—
615C4—1224no—
616C4—1224no—
617C4—2442no—
618C4—2442no—
619C4C2×#1451980912yes—
620C4C2×#1451980912yes—
621C4#1684059812yes—
622C2—22no—
623C2—4884no—
624C2#2145947311yescharacteristic
625C2C22×#1451980911yescharacteristic
626C2#2146059611yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3104C2
socleC22×C61C23×D4
prime radicalC2×#14519774C22
hypercenter#3104D61
hypocenterC61#61892
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
1. #21459624C2semidirect
3. #21458876C2semidirect
4. #21458870C2semidirect
5. #21458632C2semidirect
6. #21458631C2semidirect
7. #21456821C2semidirect
10. #21455915C2semidirect
11. #21455858C2semidirect
12. #21454902C2semidirect
13. C61×#3104C2semidirect
18. Q8×Dic122C22semidirect
19. #16840492C22semidirect
21. #16840490C22semidirect
23. #16840487C22semidirect
36. #16840155C22semidirect
39. #16840123C22semidirect
43. #16840057C22semidirect
44. #16840041C22semidirect
45. #16839987C22semidirect
46. #16839986C22semidirect
47. #16839972C22semidirect
48. #16839966C22semidirect
54. #16839892C22semidirect
55. #16839889C22semidirect
56. #16839865C22semidirect
57. #16839861C22semidirect
58. C4×#11758202C22semidirect
64. C61×#477C22semidirect
65. C61×#462C22semidirect
67. C4×Q16×C61C22semidirect
320. #3104D61semidirect
360. #477C2×D61semidirect
365. #462C2×D61semidirect
378. C4×Q16C2×D61semidirect
382. C61#61892semidirect

Maximal subgroups

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

subgroupindex
#214596242
C2×#168404972
#214588762
#214588702
#214586322
#214586312
#214568212
#214567622
#214567572
#214559152
#214558582
#214549022
C61×#31042
#6189261