Finite Group Databasebeta

← #29667574

Subgroups — #29667574

Order 15616.

550 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457186C211yesmaximal, characteristic
2#21456998C211yesmaximal, characteristic
3#21454981C211yesmaximal, characteristic
4#21445391C211yesmaximal, characteristic, complemented
5#21445370C211yesmaximal, characteristic, complemented
6#21445344C211yesmaximal, characteristic, complemented
7#21445315C211yesmaximal, characteristic, complemented
8#21445274C211yesmaximal, characteristic, complemented
9#21445239C211yesmaximal, characteristic, complemented
10#21445215C211yesmaximal, characteristic, complemented
11#21445198C211yesmaximal, characteristic, complemented
12#21444608C211yesmaximal, characteristic, complemented
13#21444509C211yesmaximal, characteristic, complemented
14#21444476C211yesmaximal, characteristic, complemented
15C61×#3231C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840161—21no—
18#16840119—21no—
19#16840103—21no—
20#16840086—21no—
21#16840069—21no—
22#16840054C2211yescharacteristic
23#16840054C2211yescharacteristic
24#16840049C2211yescharacteristic
25#16840049C2211yescharacteristic
26#16840044C2211yescharacteristic
27#16840039C2211yescharacteristic
28#16840018—21no—
29#16840010—21no—
30#16839984—21no—
31#16839969C2211yescharacteristic
32#16839964C2211yescharacteristic
33#16839892C2211yescharacteristic
34C8×Dic122C2211yescharacteristic
35#16839841C2211yescharacteristic
36#16839830—21no—
37C8×D244C2211yescharacteristic
38#16839825—21no—
39#16839822—21no—
40#16839815C2211yescharacteristic
41#16839787—21no—
42#16839786C2211yescharacteristic
43C2×C4⋊#92418C2211yescharacteristic
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839511C2211yescharacteristic
49#16839511C2211yescharacteristic
50#16839511C2211yescharacteristic
51#16839511C2211yescharacteristic
52#16839508C2211yescharacteristic
53#16839508C2211yescharacteristic
54#16839508C2211yescharacteristic
55#16839508C2211yescharacteristic
56C61×#533C2211yescharacteristic
57C61×#533C2211yescharacteristic
58C61×#500C2211yescharacteristic
59C61×#498C2211yescharacteristic
60C61×#487C2211yescharacteristic
61C61×#487C2211yescharacteristic
62C61×#485—21no—
63C61×#485—21no—
64C61×#479—21no—
65C61×#479—21no—
66C61×#431C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758201—21no—
69C2×#11758194—21no—
70C2×#11758189—21no—
71C22×#92418—21no—
72C2×C8×D61—21no—
73#14519771—21no—
74#14519769D411yescharacteristic
75#14519765D411yescharacteristic
76#14519760—21no—
77#14519756D411yescharacteristic
78#14519751D411yescharacteristic
79C4×Dic122C2311yescharacteristic
80C4×D244C2311yescharacteristic
81C4×C22⋊D61—21no—
82#14519734—21no—
83#14519710—21no—
84#14519710—21no—
85#14519710—21no—
86#14519708—21no—
87#14519708—21no—
88#14519708—21no—
89C4⋊#92418—21no—
90C4⋊#92418—21no—
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519706—21no—
98#14519706—21no—
99#14519701—21no—
100#14519701—21no—
101#14519700—21no—
102#14519700—21no—
103#14519700—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107C22⋊#92418—21no—
108#14519689—21no—
109#14519689—21no—
110#14519687—21no—
111C4×#92418—21no—
112C8×Dic61—21no—
113C4⋊Q8×C61C2311yescharacteristic
114C4⋊Q8×C61C2311yescharacteristic
115C4⋊Q8×C61C2311yescharacteristic
116C4⋊Q8×C61C2311yescharacteristic
117#125×C61—21no—
118#125×C61—21no—
119C22⋊Q8×C61—21no—
120C22⋊Q8×C61—21no—
121C22⋊Q8×C61—21no—
122C22⋊Q8×C61—21no—
123C4×Q8×C61—21no—
124C4×Q8×C61—21no—
125C4×Q8×C61—21no—
126C4×Q8×C61—21no—
127#117×C61—21no—
128#117×C61—21no—
129C2×C42×C61C2311yescharacteristic
130#107×C61—21no—
131#107×C61—21no—
132#106×C61—21no—
133#106×C61—21no—
134C4⋊C8×C61D411yescharacteristic
135C4⋊C8×C61D411yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#103×C61—21no—
140C22⋊C8×C61D411yescharacteristic
141C22⋊C8×C61D411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61#4111yescharacteristic
151C2×C22⋊D61—21no—
152C2×D244C2×D411yescharacteristic
153C2×C4×D61—21no—
154C2×Dic122C2×D411yescharacteristic
155C2×C8×C61C2×D411yescharacteristic
156C2×C8×C61C2×D411yescharacteristic
157C2×C8×C61C2×D411yescharacteristic
158C2×C8×C61C2×D411yescharacteristic
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—41no—
168C4⋊C4×C61—41no—
169C4⋊C4×C61—41no—
170C4⋊C4×C61—41no—
171C22⋊C4×C61—41no—
172C22⋊C4×C61—41no—
173C42×C61—41no—
174C42×C61—41no—
175C42×C61C2×D411yescharacteristic
176C42×C61C2×D411yescharacteristic
177C42×C61#4111yescharacteristic
178C42×C61C2411yescharacteristic
179C22⋊Dic61—21no—
180#11758202—81no—
181#11758201—81no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186C4⋊Dic61C2×D411yescharacteristic
187C4⋊Dic61C2×D411yescharacteristic
188#11758196—21no—
189#11758196—21no—
190#11758196—21no—
191#11758196—21no—
192C4×Dic61—21no—
193#11758194—81no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—81no—
201#11758189—81no—
202C8×D61—81no—
203C23×C61#12111yescharacteristic
204C22×D61—21no—
205Q8×C61—41no—
206Q8×C61—41no—
207Q8×C61—41no—
208Q8×C61—41no—
209Q8×C61—81no—
210Q8×C61—81no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61#12111yescharacteristic
221C2×C4×C61#12111yescharacteristic
222C2×C4×C61#12111yescharacteristic
223C2×C4×C61C22×D411yescharacteristic
224C2×C4×C61C22×D411yescharacteristic
225C2×C4×C61C2×#4111yescharacteristic
226C22⋊D61—42no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230D244—21no—
231D244—21no—
232C4×D61—41no—
233C4×D61—41no—
234Dic122—21no—
235Dic122—21no—
236C8×C61—21no—
237C8×C61—21no—
238C8×C61—21no—
239C8×C61—21no—
240#92418—41no—
241#92418—41no—
242#92418—41no—
243#92418—41no—
244#92418—41no—
245#92418—41no—
246#19587—611nomaximal, Sylow
247C22×C61—21no—
248C22×C61—21no—
249C22×C61—21no—
250C22×C61C2×#12111yescharacteristic
251C2×D61—41no—
252C2×D61—41no—
253C2×D61—41no—
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—21no—
257C4×C61—21no—
258C4×C61—81no—
259C4×C61—81no—
260C4×C61—81no—
261C4×C61—81no—
262C4×C61#57711yescharacteristic
263C4×C61#57711yescharacteristic
264C4×C61#57811yescharacteristic
265C4×C61#57811yescharacteristic
266Dic61—41no—
267Dic61—41no—
268Dic61—41no—
269#3252—611no—
270#3233—611no—
271#3231D6111yescharacteristic, complemented
272#2994—611no—
273#1703—611no—
274#1700—611no—
275#1696—611no—
276#1691—611no—
277#1684—611no—
278#1679—611no—
279#1675—611no—
280#1672—611no—
281#1574—611no—
282#1550—611no—
283#1542—611no—
284C2×C61—41no—
285C2×C61#304611yescharacteristic
286C2×C61#306311yescharacteristic
287C2×C61#306711yescharacteristic
288D61—81no—
289#533C2×D6111yescharacteristic
290#533C2×D6111yescharacteristic
291#529—611no—
292#500C2×D6111yescharacteristic
293#499—1221no—
294#498C2×D6111yescharacteristic
295#488—1221no—
296#487C2×D6111yescharacteristic
297#487C2×D6111yescharacteristic
298#485—21no—
299#485—21no—
300#485—1221no—
301#482—1221no—
302#479—21no—
303#479—21no—
304#479—1221no—
305#477—611no—
306#477—611no—
307#476—611no—
308#476—611no—
309#475—611no—
310#474—611no—
311#470—1221no—
312#468—1221no—
313#464—1221no—
314#462—611no—
315#461—611no—
316#446—611no—
317C8×Q8—611no—
318#436—611no—
319#435—1221no—
320C8×D4—611no—
321C8×D4—1221no—
322#433—1221no—
323#431—611no—
324#431C2×D6111yescharacteristic
325#424—1221no—
326#423—611no—
327C2×C4⋊C8—611no—
328#335—611no—
329#335—611no—
330#334—611no—
331#334—611no—
332#333—611no—
333#333—611no—
334#333—611no—
335#333—611no—
336#332—611no—
337#332—611no—
338#332—611no—
339#332—611no—
340C61#1958711yescharacteristic, complemented, Sylow
341C2×Q16—1221no—
342C2×SD16—1221no—
343C2×M16—1221no—
344C2×M16—1221no—
345C22×C8—1221no—
346C22×C8—1221no—
347C4⋊Q8C22×D6111yescharacteristic
348C4⋊Q8C22×D6111yescharacteristic
349C4⋊Q8C22×D6111yescharacteristic
350C4⋊Q8C22×D6111yescharacteristic
351#126—1221no—
352#125—21no—
353#125—21no—
354#125—611no—
355#124—611no—
356#123—1221no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—611no—
362#121—611no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—611no—
368C4×D4—611no—
369C4×D4—1221no—
370#117—21no—
371#117—21no—
372#117—1221no—
373C2×C42C22×D6111yescharacteristic
374#107—21no—
375#107—21no—
376#107—1221no—
377#107—1221no—
378#107—1221no—
379#106—21no—
380#106—21no—
381#106—1221no—
382#106—1221no—
383#106—1221no—
384C4⋊C8—611no—
385C4⋊C8—611no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8C22⋊D6111yescharacteristic
395C4⋊C8C22⋊D6111yescharacteristic
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#102—1221no—
406#102—1221no—
407#102—1221no—
408C22⋊C8—1221no—
409C22⋊C8—1221no—
410C22⋊C8—1221no—
411C22⋊C8C22⋊D6111yescharacteristic
412C22⋊C8C22⋊D6111yescharacteristic
413#97—1221no—
414C4×C8—1221no—
415C4×C8—1221no—
416C4×C8C22×D6111yescharacteristic
417C4×C8C22×D6111yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—611no—
423C2×D4—611no—
424C2×D4—1221no—
425C22×C4—1221no—
426C22×C4D4×D6111yescharacteristic
427C22×C4#1175822411yescharacteristic
428C22×C4C2×C22⋊D6111yescharacteristic
429Q16—4881no—
430SD16—4881no—
431M16—4881no—
432M16—4881no—
433C2×C8—1221no—
434C2×C8—1221no—
435C2×C8—1221no—
436C2×C8—1221no—
437C2×C8—1221no—
438C2×C8—1221no—
439C2×C8—4881no—
440C2×C8—4881no—
441C2×C8C2×C22⋊D6111yescharacteristic
442C2×C8C2×C22⋊D6111yescharacteristic
443C2×C8C2×C22⋊D6111yescharacteristic
444C2×C8C2×C22⋊D6111yescharacteristic
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—611no—
458C4⋊C4—611no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C22⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—1221no—
466C22⋊C4—1221no—
467C22⋊C4—1221no—
468C22⋊C4—1221no—
469C22⋊C4—1221no—
470C42—41no—
471C42—41no—
472C42—1221no—
473C42D4×D6111yescharacteristic
474C42#1175822411yescharacteristic
475C42C2×C22⋊D6111yescharacteristic
476C42C23×D6111yescharacteristic
477C23—1221no—
478C23#1451974811yescharacteristic
479Q8—41no—
480Q8—41no—
481Q8—41no—
482Q8—41no—
483Q8—81no—
484Q8—81no—
485Q8—1221no—
486Q8—1221no—
487D4—1221no—
488D4—1221no—
489D4—2442no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—1221no—
500C2×C4—1221no—
501C2×C4—1221no—
502C2×C4—2441no—
503C2×C4—2441no—
504C2×C4#1451974811yescharacteristic
505C2×C4#1451974811yescharacteristic
506C2×C4#1451974811yescharacteristic
507C2×C4C2×D4×D6111yescharacteristic
508C2×C4C22×C22⋊D6111yescharacteristic
509C2×C4C2×#1175822411yescharacteristic
510C8—21no—
511C8—21no—
512C8—21no—
513C8—21no—
514C8—2441no—
515C8—2441no—
516C8—2441no—
517C8—2441no—
518C8—2441no—
519C8—2441no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—2441no—
524C22—2441no—
525C22—2441no—
526C22C2×#1451974811yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—81no—
532C4—81no—
533C4—81no—
534C4—81no—
535C4—2441no—
536C4—2441no—
537C4—2441no—
538C4#1684057011yescharacteristic
539C4#1684057111yescharacteristic
540C4#1684057711yescharacteristic
541C4#1684057811yescharacteristic
542C2—41no—
543C2—4881no—
544C2#2145536511yescharacteristic
545C2#2145550411yescharacteristic
546C2#2145553511yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3231C2
socleC22×C61C2×#121
prime radical#14519751D4
hypercenter#3231D61
hypocenterC61#19587
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3231

Complements

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

NH ≅ G/Ntype
4. #21445391C2semidirect
5. #21445370C2semidirect
6. #21445344C2semidirect
7. #21445315C2semidirect
8. #21445274C2semidirect
9. #21445239C2semidirect
10. #21445215C2semidirect
11. #21445198C2semidirect
12. #21444608C2semidirect
13. #21444509C2semidirect
14. #21444476C2semidirect
15. C61×#3231C2semidirect
271. #3231D61semidirect
340. C61#19587semidirect

Maximal subgroups

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

subgroupindex
#214571862
#214569982
#214549812
#214453912
#214453702
#214453442
#214453152
#214452742
#214452392
#214452152
#214451982
#214446082
#214445092
#214444762
C61×#32312
#1958761