Finite Group Databasebeta

← #29650707

Subgroups — #29650707

Order 15616.

592 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456383C211yesmaximal, characteristic
2#21454968C211yesmaximal, characteristic, complemented
3#21454964C211yesmaximal, characteristic, complemented
4#21444730C211yesmaximal, characteristic, complemented
5#21444725C211yesmaximal, characteristic, complemented
6#21444712C211yesmaximal, characteristic, complemented
7#21444706C211yesmaximal, characteristic, complemented
8#21444640C211yesmaximal, characteristic, complemented
9#21444635C211yesmaximal, characteristic, complemented
10#21444622C211yesmaximal, characteristic, complemented
11#21444616C211yesmaximal, characteristic, complemented
12#21444574C211yesmaximal, characteristic, complemented
13#21444285C211yesmaximal, characteristic, complemented
14#21444103C211yesmaximal, characteristic, complemented
15C61×#1495C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840161C411yescharacteristic
18#16840144C411yescharacteristic
19#16840119C411yescharacteristic
20#16840116C411yescharacteristic
21#16840001C411yescharacteristic
22#16839996C411yescharacteristic
23#16839993C411yescharacteristic
24#16839989C411yescharacteristic
25#16839893C2211yescharacteristic
26#16839889C2211yescharacteristic
27Q8×#92418C2211yescharacteristic
28#16839886C2211yescharacteristic
29C4×#11758202C2211yescharacteristic
30C4×#11758201C2211yescharacteristic
31C4×#11758200C2211yescharacteristic
32C4×#11758199C2211yescharacteristic
33#16839840—21no—
34#16839840C2211yescharacteristic
35#16839839C2211yescharacteristic
36#16839838—21no—
37#16839834—21no—
38#16839831—21no—
39D4×#92418C2211yescharacteristic
40#16839827C2211yescharacteristic
41#16839823—21no—
42#16839822—21no—
43#16839815C2211yescharacteristic
44#16839789—21no—
45#16839787—21no—
46#16839786C2211yescharacteristic
47C2×C4×#92418C2211yescharacteristic
48#16839512C2211yescharacteristic
49#16839512C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839512C2211yescharacteristic
52#16839494C2211yescharacteristic
53#16839494C2211yescharacteristic
54#16839491C2211yescharacteristic
55#16839491C2211yescharacteristic
56#16839484C2211yescharacteristic
57#16839484C2211yescharacteristic
58C8×#92418C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#529C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C61×#423C2211yescharacteristic
63C61×Q8⋊C8C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×D4⋊C8C2211yescharacteristic
67C2×#11758202C2×C411yescharacteristic
68C2×#11758200C2×C411yescharacteristic
69C2×#11758201C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71C2×#11758194—21no—
72C2×#11758194—21no—
73C2×#11758189—21no—
74C22×#92418—21no—
75C22×#92418C2×C411yescharacteristic
76C22×#92418C2×C411yescharacteristic
77C2×C8×D61—21no—
78#14519771—21no—
79#14519769C2×C411yescharacteristic
80#14519765C2×C411yescharacteristic
81#14519760—21no—
82#14519756C2×C411yescharacteristic
83#14519751C2×C411yescharacteristic
84C4×Dic122C2311yescharacteristic
85C4×D244C2311yescharacteristic
86C4×C22⋊D61—21no—
87#14519734—21no—
88#14519710C2×C411yescharacteristic
89#14519710C2×C411yescharacteristic
90#14519708C2×C411yescharacteristic
91#14519708C2×C411yescharacteristic
92C4⋊#92418—21no—
93C4⋊#92418—21no—
94C4⋊#92418—21no—
95C4⋊#92418D411yescharacteristic
96C4⋊#92418D411yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519706—21no—
100#14519706—21no—
101#14519701C2×C411yescharacteristic
102#14519701C2×C411yescharacteristic
103#14519700C2×C411yescharacteristic
104#14519700C2×C411yescharacteristic
105#14519698C2×C411yescharacteristic
106#14519698C2×C411yescharacteristic
107#14519697C2×C411yescharacteristic
108#14519697C2×C411yescharacteristic
109C22⋊#92418—21no—
110C22⋊#92418—21no—
111C22⋊#92418D411yescharacteristic
112C22⋊#92418D411yescharacteristic
113#14519689—21no—
114#14519689—21no—
115#14519688—21no—
116#14519687—21no—
117C4×#92418—21no—
118C4×#92418C2×C411yescharacteristic
119C4×#92418C2×C411yescharacteristic
120C4×#92418C2311yescharacteristic
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C8×Dic61—21no—
125C2×M16×C61—21no—
126#126×C61—21no—
127#125×C61C2×C411yescharacteristic
128#124×C61C2×C411yescharacteristic
129#123×C61—21no—
130C22⋊Q8×C61C2×C411yescharacteristic
131#121×C61C2×C411yescharacteristic
132C4×Q8×C61C2311yescharacteristic
133C4×D4×C61—21no—
134C4×D4×C61C2311yescharacteristic
135#117×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—21no—
138C4⋊C8×C61—21no—
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141C22⋊C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61#4111yescharacteristic
151C2×C22⋊D61—21no—
152C2×D244C22×C411yescharacteristic
153C2×C4×D61—21no—
154C2×Dic122C22×C411yescharacteristic
155M16×C61—81no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61C22×C411yescharacteristic
165C4⋊C4×C61C22×C411yescharacteristic
166C22⋊C4×C61—21no—
167C22⋊C4×C61—21no—
168C22⋊C4×C61—21no—
169C22⋊C4×C61—21no—
170C22⋊C4×C61—21no—
171C42×C61—21no—
172C42×C61C22×C411yescharacteristic
173C42×C61C2×D411yescharacteristic
174C42×C61#4111yescharacteristic
175C42×C61C2411yescharacteristic
176C22⋊Dic61—21no—
177#11758202—22no—
178#11758201—22no—
179#11758200—22no—
180#11758199—22no—
181#11758198—21no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185C4⋊Dic61C22×C411yescharacteristic
186C4⋊Dic61C22×C411yescharacteristic
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190#11758196—21no—
191C4×Dic61—21no—
192#11758194—81no—
193#11758194—81no—
194C2×#92418—22no—
195C2×#92418—22no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—81no—
199C2×#92418C22×C411yescharacteristic
200C2×#92418C22×C411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207#11758189—81no—
208C8×D61—81no—
209C23×C61—21no—
210C23×C61C4×D411yescharacteristic
211C22×D61—21no—
212Q8×C61—21no—
213Q8×C61—21no—
214D4×C61—21no—
215D4×C61—21no—
216D4×C61—81no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61C4×D411yescharacteristic
228C2×C4×C61C4×D411yescharacteristic
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61C23×C411yescharacteristic
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C22⋊D61—81no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237D244—21no—
238D244—21no—
239C4×D61—41no—
240C4×D61—41no—
241Dic122—21no—
242Dic122—21no—
243C8×C61—41no—
244C8×C61—41no—
245C8×C61—41no—
246C8×C61—41no—
247#92418—21no—
248#92418—21no—
249#92418—21no—
250#92418—21no—
251#92418—21no—
252#92418—21no—
253#92418—41no—
254#92418—41no—
255#92418#13112yes—
256#92418#13112yes—
257#17974—611nomaximal, Sylow
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61C2×C4×D411yescharacteristic
265C2×D61—41no—
266C2×D61—41no—
267C2×D61—41no—
268C4×C61—21no—
269C4×C61—21no—
270C4×C61—21no—
271C4×C61—21no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61C2×#13111yescharacteristic
276C4×C61C2×#13111yescharacteristic
277C4×C61#57711yescharacteristic
278C4×C61#57711yescharacteristic
279Dic61—41no—
280Dic61—41no—
281Dic61—41no—
282#3168—611no—
283#2993—611no—
284#2993—611no—
285#1594—611no—
286#1593—611no—
287#1590—611no—
288#1590—611no—
289#1580—611no—
290#1579—611no—
291C8×SD16—611no—
292C8×SD16—611no—
293#1566—611no—
294#1495—611no—
295#1495D6111yescharacteristic, complemented
296#1450—611no—
297C2×C61—41no—
298C2×C61—81no—
299C2×C61#293111yescharacteristic
300C2×C61#295211yescharacteristic
301C2×C61#295711yescharacteristic
302D61—81no—
303#529—611no—
304#529C2×D6111yescharacteristic
305#499—611no—
306#495—611no—
307#488—611no—
308#488—611no—
309#467—611no—
310#466—611no—
311#465—611no—
312#465—611no—
313#446—611no—
314#446—611no—
315C8×Q8—611no—
316C8×Q8—611no—
317C4×Q16—611no—
318C4×SD16—611no—
319C4×SD16—611no—
320C4×D8—611no—
321#436—611no—
322#436—611no—
323#436—1221no—
324#436—1221no—
325#435—1221no—
326#435—1221no—
327C8×D4—611no—
328C8×D4—611no—
329#433—1221no—
330#433—1221no—
331#431—611no—
332#431C2×D6111yescharacteristic
333#424—1221no—
334#424—1221no—
335#423—611no—
336#423C2×D6111yescharacteristic
337C2×C4×C8—611no—
338#334—611no—
339#334—611no—
340#334—611no—
341#334—611no—
342Q8⋊C8—611no—
343Q8⋊C8—611no—
344Q8⋊C8C2×D6111yescharacteristic
345Q8⋊C8C2×D6111yescharacteristic
346D4⋊C8—611no—
347D4⋊C8—611no—
348D4⋊C8C2×D6111yescharacteristic
349D4⋊C8C2×D6111yescharacteristic
350#322—611no—
351#322—611no—
352C82—611no—
353C82—611no—
354C61#1797411yescharacteristic, complemented, Sylow
355C2×Q16—611no—
356C2×SD16—611no—
357C2×SD16—611no—
358C2×D8—611no—
359C2×M16—21no—
360C2×M16—1221no—
361C2×M16—1221no—
362C2×M16—1221no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8—1221no—
366C22×C8—1221no—
367#126—21no—
368#126—1221no—
369#125—611no—
370#125C4×D6111yescharacteristic
371#124—611no—
372#124C4×D6111yescharacteristic
373#123—21no—
374#123—1221no—
375C22⋊Q8—611no—
376C22⋊Q8C4×D6111yescharacteristic
377#121—611no—
378#121C4×D6111yescharacteristic
379C4×Q8—611no—
380C4×Q8C22×D6111yescharacteristic
381C4×D4—21no—
382C4×D4—611no—
383C4×D4—1221no—
384C4×D4C22×D6111yescharacteristic
385#117—21no—
386#117—1221no—
387C2×C42C22×D6111yescharacteristic
388#107—611no—
389#107—611no—
390#106—611no—
391#106—611no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8C22×D6111yescharacteristic
404C4⋊C8C22×D6111yescharacteristic
405#103—611no—
406#103—611no—
407#103—611no—
408#103—611no—
409#102—611no—
410#102—611no—
411#102—611no—
412#102—611no—
413C22⋊C8—21no—
414C22⋊C8—611no—
415C22⋊C8—611no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418C22⋊C8—1221no—
419C22⋊C8—1221no—
420#97—1221no—
421#97—1221no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—1221no—
429C4×C8—1221no—
430C4×C8C22×D6111yescharacteristic
431C4×C8C22×D6111yescharacteristic
432C2×Q8—611no—
433C2×Q8C2×C4×D6111yescharacteristic
434C2×D4—21no—
435C2×D4—611no—
436C2×D4—1221no—
437C2×D4C2×C4×D6111yescharacteristic
438C22×C4—21no—
439C22×C4—1221no—
440C22×C4C2×C4×D6111yescharacteristic
441C22×C4D4×D6111yescharacteristic
442C22×C4#1175822411yescharacteristic
443Q16—1222no—
444SD16—1222no—
445SD16—1222no—
446D8—1222no—
447M16—81no—
448M16—4881no—
449M16—4881no—
450M16—4881no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—611no—
456C2×C8—611no—
457C2×C8—611no—
458C2×C8—611no—
459C2×C8—611no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—611no—
463C2×C8—1222no—
464C2×C8—1222no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—4881no—
468C2×C8—4881no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—611no—
474C4⋊C4—611no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4C2×C4×D6111yescharacteristic
480C4⋊C4C2×C4×D6111yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—1221no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C42—21no—
492C42—1221no—
493C42C2×C4×D6111yescharacteristic
494C42D4×D6111yescharacteristic
495C42#1175822411yescharacteristic
496C42C23×D6111yescharacteristic
497C23—21no—
498C23—1221no—
499C23#1451973711yescharacteristic
500Q8—21no—
501Q8—21no—
502Q8—1221no—
503Q8—1221no—
504D4—21no—
505D4—21no—
506D4—81no—
507D4—1221no—
508D4—1221no—
509D4—4881no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—2441no—
524C2×C4—2441no—
525C2×C4#1451973711yescharacteristic
526C2×C4#1451973711yescharacteristic
527C2×C4#1451973711yescharacteristic
528C2×C4C22×C4×D6111yescharacteristic
529C2×C4C2×D4×D6111yescharacteristic
530C2×C4C2×#1175822411yescharacteristic
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—612no—
536C8—612no—
537C8—1221no—
538C8—1221no—
539C8—1221no—
540C8—1221no—
541C8—1221no—
542C8—1221no—
543C8—2441no—
544C8—2441no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—2441no—
552C22—2441no—
553C22—2441no—
554C22C2×#1451973711yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—2441no—
563C4—2441no—
564C4—2441no—
565C4#131×D6111yescharacteristic
566C4#131×D6111yescharacteristic
567C4#1684057111yescharacteristic
568C4#1684057211yescharacteristic
569C2—41no—
570C2—81no—
571C2—4881no—
572C2#2145452711yescharacteristic
573C2#2145469811yescharacteristic
574C2#2145473211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1495C2
socleC22×C61C2×C4×D4
prime radical#16839996C4
cosocleC42×C61C24
hypercenter#1495D61
hypocenterC61#17974
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1495

Complements

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

NH ≅ G/Ntype
2. #21454968C2semidirect
3. #21454964C2semidirect
4. #21444730C2semidirect
5. #21444725C2semidirect
6. #21444712C2semidirect
7. #21444706C2semidirect
8. #21444640C2semidirect
9. #21444635C2semidirect
10. #21444622C2semidirect
11. #21444616C2semidirect
12. #21444574C2semidirect
13. #21444285C2semidirect
14. #21444103C2semidirect
15. C61×#1495C2semidirect
295. #1495D61semidirect
354. C61#17974semidirect

Maximal subgroups

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

subgroupindex
#214563832
#214549682
#214549642
#214447302
#214447252
#214447122
#214447062
#214446402
#214446352
#214446222
#214446162
#214445742
#214442852
#214441032
C61×#14952
#1797461