Finite Group Databasebeta

← #30571062

Subgroups — #30571062

Order 15616.

1814 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459681C211yesmaximal, characteristic, complemented
2C2×#16840497C211yesmaximal, characteristic, complemented
3#21458830C214yesmaximal, complemented
4#21458813C214yesmaximal, complemented
5#21458514C214yesmaximal, complemented
6#21458477C214yesmaximal, complemented
7#21456783C214yesmaximal, complemented
8#21456762C211yesmaximal, characteristic, complemented
9#21456734C211yesmaximal, characteristic
10#21455863C214yesmaximal, complemented
11#21455858C211yesmaximal, characteristic, complemented
12#21454899C211yesmaximal, characteristic, complemented
13C61×#3103C211yesmaximal, characteristic, complemented
14#16840498C2212yescomplemented
15#16840497—22no—
16#16840497—22no—
17#16840497C2214yes—
18#16840497C2214yes—
19#16840487C2212yescomplemented
20#16840482C2212yescomplemented
21#16840481—22no—
22#16840469C2212yescomplemented
23#16840452—22no—
24#16840357—22no—
25#16840333—21no—
26#16840319C2211yescharacteristic
27C2×#14519774C2211yescharacteristic
28#16840293C2214yes—
29C2×#14519766C2212yes—
30C2×#14519765—21no—
31C2×#14519762—22no—
32#16840245—21no—
33C2×C4×Dic122C2211yescharacteristic
34C2×C4×D244—21no—
35C2×#14519739C2212yes—
36#16840143C2218yescomplemented
37#16840138C2212yes—
38#16840135C2212yes—
39#16840118C2218yescomplemented
40#16840110C2212yes—
41#16840109C2212yes—
42#16840097C2212yes—
43#16840061C2218yescomplemented
44#16840057C2212yescomplemented
45#16839987C2218yescomplemented
46#16839979C2218yescomplemented
47#16839976C2218yescomplemented
48#16839972C2212yescomplemented
49#16839963C2214yes—
50#16839957C2214yes—
51#16839918C2212yes—
52#16839915C2214yes—
53#16839895C2214yes—
54C8×Dic122C2214yescomplemented
55#16839886C2214yescomplemented
56C4×#11758202C2214yescomplemented
57#16839849C2218yescomplemented
58#16839842C2218yescomplemented
59#16839815C2211yescharacteristic
60#16839812C2214yes—
61C61×#532C2211yescharacteristic
62C2×C4×Q8×C61C2211yescharacteristic
63C61×#481C2212yes—
64C61×#475C2212yescomplemented
65C61×#460C2212yescomplemented
66C61×#448C2212yes—
67C4×SD16×C61C2214yescomplemented
68C61×#431C2211yescharacteristic
69C22×Dic122D411yescharacteristic
70C22×D244—21no—
71C22×D244—21no—
72C22×D244C2312yes—
73C22×C4×D61—22no—
74C2×#11758202C2314yes—
75C2×#11758190C2318yes—
76C2×#11758199C2318yes—
77#14519777C2311yescharacteristic
78#14519777C2311yescharacteristic
79#14519775—22no—
80#14519774—21no—
81#14519774—21no—
82#14519774C2312yes—
83#14519774C2312yes—
84#14519770—24no—
85#14519770—24no—
86#14519769—21no—
87#14519768C2314yes—
88#14519767—24no—
89#14519766—24no—
90#14519766C2318yes—
91#14519765—24no—
92#14519765—24no—
93#14519764—22no—
94#14519764C2314yes—
95#14519762—28no—
96#14519762—28no—
97#14519758—24no—
98#14519758—24no—
99#14519756—21no—
100#14519756—22no—
101#14519756—22no—
102#14519756C2312yes—
103#14519754—24no—
104Q8×Dic61—22no—
105C4×Dic122—21no—
106C4×Dic122D412yes—
107C4×Dic122D412yes—
108C4×Dic122C2312yes—
109C4×Dic122C2312yes—
110C4×Dic122C2312yes—
111#14519742C2314yes—
112C4×D244—24no—
113C4×D244—24no—
114D4×Dic61—24no—
115D4×Dic61—22no—
116D4×Dic61C2314yes—
117#14519739—24no—
118#14519739C2318yes—
119#14519736—21no—
120#14519736—22no—
121#14519733—24no—
122C2×C4⋊Dic61—22no—
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—
137C4×#92418C2312yes—
138C8×Dic61C2318yes—
139C2×#41×C61—21no—
140C22×Q8×C61C2311yescharacteristic
141C2×SD16×C61C2314yes—
142C4⋊Q8×C61C2311yescharacteristic
143#127×C61C2311yescharacteristic
144#124×C61—21no—
145#121×C61—21no—
146#121×C61C2312yes—
147C4×Q8×C61—21no—
148C4×Q8×C61—21no—
149C4×Q8×C61C2312yes—
150C4×Q8×C61C2312yes—
151C4×D4×C61—21no—
152C4×D4×C61C2312yes—
153C2×C4⋊C4×C61—21no—
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C42×C61—21no—
156C2×C42×C61C2311yescharacteristic
157#106×C61C2314yes—
158C4⋊C8×C61C2312yes—
159#103×C61C2314yes—
160#102×C61C2314yes—
161C22⋊C8×C61C2312yes—
162C4×C8×C61C2312yes—
163C23×D61—22no—
164#41×C61—44no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—42no—
168C2×Q8×C61C2412yes—
169C2×D4×C61—22no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61C2412yes—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—22no—
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2411yescharacteristic
179C22×Dic61—24no—
180C22×Dic61C2×D412yes—
181C22×Dic61C2×D412yes—
182C2×D244—22no—
183C2×D244—22no—
184C2×D244—22no—
185C2×D244—22no—
186C2×D244—22no—
187C2×D244—44no—
188C2×D244—44no—
189C2×D244—82no—
190C2×D244C2414yes—
191C2×C4×D61—28no—
192C2×C4×D61—84no—
193C2×Dic122—24no—
194C2×Dic122—21no—
195C2×Dic122C2×D412yes—
196C2×Dic122C2×D412yes—
197C2×Dic122C2412yes—
198SD16×C61—44no—
199C2×C8×C61C2414yes—
200C4⋊C4×C61—22no—
201C4⋊C4×C61—22no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61C2412yes—
205C4⋊C4×C61C2412yes—
206C22⋊C4×C61—22no—
207C22⋊C4×C61—22no—
208C42×C61—22no—
209C42×C61—22no—
210C42×C61C2×D411yescharacteristic
211C42×C61C2×D411yescharacteristic
212C42×C61C2411yescharacteristic
213C42×C61C2411yescharacteristic
214C22⋊Dic61—22no—
215C22⋊Dic61—24no—
216C22⋊Dic61—24no—
217C22⋊Dic61—24no—
218#11758202—44no—
219#11758199—48no—
220#11758198—28no—
221#11758198—28no—
222#11758198—28no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—24no—
227C4⋊Dic61C2×D412yes—
228C4⋊Dic61C2×D412yes—
229C4⋊Dic61C2412yes—
230#11758196—22no—
231#11758196—22no—
232#11758196—24no—
233#11758196—24no—
234#11758196C2×D414yes—
235#11758196C2×D414yes—
236C4×Dic61—22no—
237C4×Dic61—24no—
238C4×Dic61C2×D414yes—
239C4×Dic61C2414yes—
240C2×#92418C2414yes—
241#11758190—48no—
242C23×C61—22no—
243C23×C61C22×D411yescharacteristic
244C22×D61—24no—
245C22×D61—44no—
246C22×D61—44no—
247C22×D61—44no—
248Q8×C61—22no—
249Q8×C61—22no—
250Q8×C61—42no—
251Q8×C61—42no—
252D4×C61—24no—
253D4×C61—44no—
254D4×C61—42no—
255D4×C61—81no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—41no—
261C2×C4×C61—42no—
262C2×C4×C61—42no—
263C2×C4×C61—44no—
264C2×C4×C61#13514yes—
265C2×C4×C61C22×D411yescharacteristic
266C2×C4×C61C22×D411yescharacteristic
267C2×C4×C61C22×D411yescharacteristic
268C2×C4×C61C22×D411yescharacteristic
269C2×C4×C61C22×D411yescharacteristic
270C2×C4×C61C2511yescharacteristic
271C2×Dic61—24no—
272C2×Dic61—22no—
273C2×Dic61—22no—
274C2×Dic61—42no—
275C2×Dic61—84no—
276C2×Dic61C22×D414yes—
277C2×Dic61C22×D414yes—
278D244—28no—
279D244—44no—
280D244—44no—
281D244—44no—
282D244—82no—
283D244—82no—
284C4×D61—88no—
285Dic122—24no—
286Dic122—24no—
287Dic122—24no—
288Dic122—81no—
289C8×C61—24no—
290#92418—24no—
291#61885—611nomaximal, Sylow
292C22×C61—21no—
293C22×C61—21no—
294C22×C61—42no—
295C22×C61—42no—
296C22×C61—42no—
297C22×C61C2×#13512yes—
298C22×C61C23×D411yescharacteristic
299C2×D61—44no—
300C2×D61—44no—
301C2×D61—44no—
302C2×D61—88no—
303C4×C61—21no—
304C4×C61—21no—
305C4×C61—21no—
306C4×C61—42no—
307C4×C61—42no—
308C4×C61—42no—
309C4×C61C2×#13512yes—
310C4×C61C2×#13512yes—
311C4×C61#58512yes—
312Dic61—24no—
313Dic61—24no—
314Dic61—42no—
315Dic61—42no—
316#3507—611no—
317C2×#559—611no—
318#3396—614no—
319#3394—614no—
320#3365—614no—
321#3361—614no—
322#3211—614no—
323#3208—611no—
324#3205—611no—
325#3105—614no—
326#3104—611no—
327#3103D6111yescharacteristic, complemented
328#2982—611no—
329C2×C61—22no—
330C2×C61—82no—
331C2×C61#348711yescharacteristic
332C2×C61C22×#13511yescharacteristic
333C2×C61#358511yescharacteristic
334D61—84no—
335#559—612no—
336#559—614no—
337#559—614no—
338#559—1222no—
339#559—1222no—
340#557—612no—
341#556—612no—
342#556—1222no—
343#554—612no—
344#552—1222no—
345#539—1222no—
346#536—1221no—
347#533—611no—
348#532C2×D6111yescharacteristic
349C2×#127—611no—
350#529—614no—
351C2×#124—612no—
352C2×#124—1221no—
353C2×#123—1222no—
354#520—1221no—
355C2×C4×Q8—611no—
356C2×C4×Q8C2×D6111yescharacteristic
357C2×C4×D4—612no—
358C2×C4×D4—1221no—
359#495—618no—
360#493—612no—
361#492—612no—
362#488—618no—
363#486—612no—
364#486—612no—
365#484—612no—
366#481C2×D6112yes—
367#478—618no—
368#477—612no—
369#475C2×D6112yescomplemented
370#464—618no—
371#463—618no—
372#463—618no—
373#462—612no—
374#460—614no—
375#460C2×D6112yescomplemented
376#459—614no—
377#451—612no—
378#450—614no—
379#448C2×D6112yes—
380#447—614no—
381C8×Q8—614no—
382C8×Q8—614no—
383C4×Q16—614no—
384C4×SD16—618no—
385C4×SD16C2×D6114yescomplemented
386C4×D8—618no—
387#431—611no—
388#431—614no—
389#431C2×D6111yescharacteristic
390C61#6188511yescharacteristic, complemented, Sylow
391C2×#41—21no—
392C22×Q8—611no—
393C22×Q8C22×D6111yescharacteristic
394C22×D4—612no—
395C22×D4—1221no—
396C22×D4—1221no—
397C23×C4—1222no—
398C2×Q16—614no—
399C2×SD16—618no—
400C2×SD16C22×D6114yes—
401C2×D8—618no—
402C4⋊Q8—611no—
403C4⋊Q8—611no—
404C4⋊Q8—1222no—
405C4⋊Q8C22×D6111yescharacteristic
406#127—612no—
407#127—612no—
408#127—1221no—
409#127—1221no—
410#127C22×D6111yescharacteristic
411#126—1224no—
412#126—1224no—
413#125—614no—
414#125—1224no—
415#125—1221no—
416#124—21no—
417#124—618no—
418#124—614no—
419#124—1224no—
420#124—1224no—
421#124—1224no—
422#124—1222no—
423#123—1228no—
424#123—1228no—
425#123—1224no—
426#123—1224no—
427C22⋊Q8—612no—
428C22⋊Q8—1224no—
429C22⋊Q8—1222no—
430C22⋊Q8—1222no—
431C22⋊Q8—1221no—
432#121—21no—
433#121C22×D6112yes—
434C4×Q8—21no—
435C4×Q8—21no—
436C4×Q8—612no—
437C4×Q8—612no—
438C4×Q8—612no—
439C4×Q8—612no—
440C4×Q8—614no—
441C4×Q8—612no—
442C4×Q8—1222no—
443C4×Q8—1221no—
444C4×Q8C22×D6112yes—
445C4×Q8C22×D6112yes—
446C4×D4—21no—
447C4×D4—614no—
448C4×D4—618no—
449C4×D4—1224no—
450C4×D4—1224no—
451C4×D4—1224no—
452C4×D4—1222no—
453C4×D4—1224no—
454C4×D4C22×D6112yes—
455#117—1224no—
456#117—1222no—
457#117—1221no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—612no—
461C2×C4⋊C4—1222no—
462C2×C4⋊C4C22×D6111yescharacteristic
463C2×C22⋊C4—1222no—
464C2×C22⋊C4—1222no—
465C2×C22⋊C4—1222no—
466C2×C42—21no—
467C2×C42—612no—
468C2×C42C22×D6111yescharacteristic
469#107—614no—
470#106C22×D6114yes—
471C4⋊C8—618no—
472C4⋊C8—612no—
473C4⋊C8C22×D6112yes—
474#103—614no—
475#103—614no—
476#103C22×D6114yes—
477#102—618no—
478#102—618no—
479#102C22×D6114yes—
480C22⋊C8—612no—
481C22⋊C8C22×D6112yes—
482C4×C8—618no—
483C4×C8—612no—
484C4×C8C22×D6112yes—
485C24—1222no—
486#41—44no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—42no—
490C2×Q8—612no—
491C2×Q8—612no—
492C2×Q8—612no—
493C2×Q8—1221no—
494C2×Q8—1224no—
495C2×Q8C23×D6112yes—
496C2×D4—22no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—614no—
500C2×D4—1222no—
501C2×D4—1222no—
502C2×D4—1222no—
503C2×D4—1222no—
504C2×D4—1222no—
505C2×D4—4882no—
506C2×D4—2444no—
507C2×D4—2444no—
508C2×D4C23×D6112yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—612no—
513C22×C4—612no—
514C22×C4—1228no—
515C22×C4—1224no—
516C22×C4—4884no—
517C22×C4D4×D6111yescharacteristic
518C22×C4D4×D6111yescharacteristic
519C22×C4C23×D6111yescharacteristic
520Q16—2444no—
521SD16—44no—
522SD16—2448no—
523D8—2448no—
524C2×C8—614no—
525C2×C8C23×D6114yes—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—612no—
531C4⋊C4—614no—
532C4⋊C4—614no—
533C4⋊C4—612no—
534C4⋊C4—612no—
535C4⋊C4—1224no—
536C4⋊C4—1224no—
537C4⋊C4—1224no—
538C4⋊C4—1221no—
539C4⋊C4—1222no—
540C4⋊C4—1222no—
541C4⋊C4—1221no—
542C4⋊C4—1221no—
543C4⋊C4C23×D6112yes—
544C4⋊C4C23×D6112yes—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—1228no—
548C22⋊C4—1228no—
549C22⋊C4—1228no—
550C22⋊C4—1224no—
551C22⋊C4—1224no—
552C22⋊C4—1224no—
553C22⋊C4—1222no—
554C42—22no—
555C42—22no—
556C42—614no—
557C42—614no—
558C42—1224no—
559C42—1222no—
560C42D4×D6111yescharacteristic
561C42D4×D6111yescharacteristic
562C42C23×D6111yescharacteristic
563C42C23×D6111yescharacteristic
564C23—22no—
565C23—1224no—
566C23—2444no—
567C23—2444no—
568C23—2444no—
569C23C2×D4×D6111yescharacteristic
570Q8—22no—
571Q8—22no—
572Q8—42no—
573Q8—42no—
574Q8—1224no—
575Q8—1224no—
576Q8—1224no—
577Q8—4881no—
578D4—24no—
579D4—44no—
580D4—42no—
581D4—81no—
582D4—1228no—
583D4—4882no—
584D4—4882no—
585D4—2444no—
586D4—2444no—
587D4—2444no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—44no—
596C2×C4—614no—
597C2×C4—614no—
598C2×C4—1224no—
599C2×C4—1222no—
600C2×C4—1222no—
601C2×C4—4888no—
602C2×C4—4884no—
603C2×C4—2442no—
604C2×C4#1451979814yes—
605C2×C4C2×D4×D6111yescharacteristic
606C2×C4C2×D4×D6111yescharacteristic
607C2×C4C2×D4×D6111yescharacteristic
608C2×C4C2×D4×D6111yescharacteristic
609C2×C4C2×D4×D6111yescharacteristic
610C2×C4C24×D6111yescharacteristic
611C8—24no—
612C8—1224no—
613C22—21no—
614C22—21no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—4888no—
619C22—2444no—
620C22—2444no—
621C22—2444no—
622C22C2×#1451979812yes—
623C22C22×D4×D6111yescharacteristic
624C4—21no—
625C4—21no—
626C4—21no—
627C4—42no—
628C4—42no—
629C4—42no—
630C4—1224no—
631C4—1224no—
632C4—2442no—
633C4—2442no—
634C4C2×#1451979812yes—
635C4C2×#1451979812yes—
636C4#1684059812yes—
637C2—22no—
638C2—82no—
639C2—4884no—
640C2#2145947311yescharacteristic
641C2C22×#1451979811yescharacteristic
642C2#2146059611yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3103C2
socleC22×C61C23×D4
prime radical#21456734C2
hypercenter#3103D61
hypocenterC61#61885
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3103

Complements

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

NH ≅ G/Ntype
1. #21459681C2semidirect
2. C2×#16840497C2semidirect
3. #21458830C2semidirect
4. #21458813C2semidirect
5. #21458514C2semidirect
6. #21458477C2semidirect
7. #21456783C2semidirect
8. #21456762C2semidirect
10. #21455863C2semidirect
11. #21455858C2semidirect
12. #21454899C2semidirect
13. C61×#3103C2semidirect
14. #16840498C22semidirect
19. #16840487C22semidirect
20. #16840482C22semidirect
22. #16840469C22semidirect
36. #16840143C22semidirect
39. #16840118C22semidirect
43. #16840061C22semidirect
44. #16840057C22semidirect
45. #16839987C22semidirect
46. #16839979C22semidirect
47. #16839976C22semidirect
48. #16839972C22semidirect
54. C8×Dic122C22semidirect
55. #16839886C22semidirect
56. C4×#11758202C22semidirect
57. #16839849C22semidirect
58. #16839842C22semidirect
64. C61×#475C22semidirect
65. C61×#460C22semidirect
67. C4×SD16×C61C22semidirect
327. #3103D61semidirect
369. #475C2×D61semidirect
375. #460C2×D61semidirect
385. C4×SD16C2×D61semidirect
390. C61#61885semidirect

Maximal subgroups

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

subgroupindex
#214596812
C2×#168404972
#214588302
#214588132
#214585142
#214584772
#214567832
#214567622
#214567342
#214558632
#214558582
#214548992
C61×#31032
#6188561