Finite Group Databasebeta

← #29649976

Subgroups — #29649976

Order 15616.

626 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455831C211yesmaximal, characteristic
2#21454795C211yesmaximal, characteristic, complemented
3#21454775C211yesmaximal, characteristic, complemented
4#21444700C211yesmaximal, characteristic, complemented
5#21444693C211yesmaximal, characteristic, complemented
6#21444686C211yesmaximal, characteristic, complemented
7#21444679C211yesmaximal, characteristic, complemented
8#21444640C211yesmaximal, characteristic, complemented
9#21444635C211yesmaximal, characteristic, complemented
10#21444634C211yesmaximal, characteristic, complemented
11#21444628C211yesmaximal, characteristic, complemented
12#21444597C211yesmaximal, characteristic, complemented
13#21444254C211yesmaximal, characteristic, complemented
14#21444112C211yesmaximal, characteristic, complemented
15C61×#1482C211yesmaximal, characteristic, complemented
16C4×#11758222C2211yescharacteristic
17#16840100C411yescharacteristic
18#16840083C411yescharacteristic
19#16840066C411yescharacteristic
20#16840059C411yescharacteristic
21#16839981C411yescharacteristic
22#16839974C411yescharacteristic
23#16839922C411yescharacteristic
24#16839905C411yescharacteristic
25#16839893C2211yescharacteristic
26Q8×#92418C2211yescharacteristic
27#16839886C2211yescharacteristic
28#16839886C2211yescharacteristic
29C4×#11758202C2211yescharacteristic
30C4×#11758201C2211yescharacteristic
31C4×#11758200C2211yescharacteristic
32C4×#11758199C2211yescharacteristic
33#16839840C2211yescharacteristic
34#16839834—21no—
35D4×#92418—21no—
36D4×#92418C2211yescharacteristic
37#16839827C2211yescharacteristic
38#16839827C2211yescharacteristic
39#16839825—21no—
40#16839825—21no—
41#16839823—21no—
42#16839819C2211yescharacteristic
43#16839815C2211yescharacteristic
44#16839813—21no—
45#16839718—21no—
46C2×C4×#92418C2211yescharacteristic
47C4×C8×D61—21no—
48#16839514C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839512C2211yescharacteristic
52#16839494C2211yescharacteristic
53#16839494C2211yescharacteristic
54#16839491C2211yescharacteristic
55#16839491C2211yescharacteristic
56#16839484C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839483C2211yescharacteristic
59#16839483C2211yescharacteristic
60C61×#529C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C61×#431C2211yescharacteristic
63C61×Q8⋊C8C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×D4⋊C8C2211yescharacteristic
67C2×#11758222C2×C411yescharacteristic
68C2×#11758202C2×C411yescharacteristic
69C2×#11758200C2×C411yescharacteristic
70C2×#11758201C2×C411yescharacteristic
71C2×#11758199C2×C411yescharacteristic
72C2×#11758194—21no—
73C22×#92418—21no—
74C22×#92418D411yescharacteristic
75C22×#92418D411yescharacteristic
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78C4×Dic122C2×C411yescharacteristic
79C4×Dic122C2311yescharacteristic
80C4×D244C2×C411yescharacteristic
81C4×D244C2311yescharacteristic
82C4×C22⋊D61—21no—
83C4×C22⋊D61—21no—
84#14519736C2×C411yescharacteristic
85#14519734—21no—
86C42×D61—21no—
87#14519710C2×C411yescharacteristic
88#14519710C2×C411yescharacteristic
89#14519708C2×C411yescharacteristic
90#14519708C2×C411yescharacteristic
91C4⋊#92418—21no—
92C4⋊#92418—21no—
93C4⋊#92418C2×C411yescharacteristic
94C4⋊#92418C2×C411yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519706—21no—
98#14519706—21no—
99#14519701C2×C411yescharacteristic
100#14519701C2×C411yescharacteristic
101#14519700C2×C411yescharacteristic
102#14519700C2×C411yescharacteristic
103#14519698C2×C411yescharacteristic
104#14519698C2×C411yescharacteristic
105#14519697C2×C411yescharacteristic
106#14519697C2×C411yescharacteristic
107C22⋊#92418—21no—
108C22⋊#92418—21no—
109C22⋊#92418—21no—
110C22⋊#92418C2×C411yescharacteristic
111C22⋊#92418C2×C411yescharacteristic
112#14519689—21no—
113#14519689—21no—
114#14519688—21no—
115#14519688—21no—
116C4×#92418—21no—
117C4×#92418D411yescharacteristic
118C4×#92418D411yescharacteristic
119C4×#92418C2311yescharacteristic
120C4×#92418C2311yescharacteristic
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C8×Dic61—21no—
124C8×Dic61—21no—
125#126×C61—21no—
126#125×C61C2×C411yescharacteristic
127#124×C61C2×C411yescharacteristic
128#123×C61—21no—
129C22⋊Q8×C61C2×C411yescharacteristic
130#121×C61C2×C411yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132C4×D4×C61—21no—
133C4×D4×C61C2311yescharacteristic
134#117×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139C22⋊C8×C61—21no—
140C22⋊C8×C61—21no—
141C4×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—
152#11758222—22no—
153#11758222—22no—
154C2×D244C22×C411yescharacteristic
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×Dic122C22×C411yescharacteristic
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61C22×C411yescharacteristic
168C4⋊C4×C61C22×C411yescharacteristic
169C22⋊C4×C61—21no—
170C22⋊C4×C61—21no—
171C22⋊C4×C61—21no—
172C22⋊C4×C61—21no—
173C22⋊C4×C61—21no—
174C42×C61—21no—
175C42×C61C22×C411yescharacteristic
176C42×C61C2×D411yescharacteristic
177C42×C61#4111yescharacteristic
178C42×C61C2411yescharacteristic
179C22⋊Dic61—21no—
180#11758202—22no—
181#11758201—22no—
182#11758200—22no—
183#11758199—22no—
184#11758198—21no—
185#11758198—21no—
186C4⋊Dic61C22×C411yescharacteristic
187C4⋊Dic61C22×C411yescharacteristic
188#11758196—21no—
189#11758196—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193#11758194—42no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—41no—
197C2×#92418—41no—
198C2×#92418—42no—
199C2×#92418C22×C411yescharacteristic
200C2×#92418C22×C411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C8×D61—42no—
208C8×D61—42no—
209C23×C61—21no—
210C23×C61C4×D411yescharacteristic
211C22×D61—21no—
212Q8×C61—21no—
213Q8×C61—21no—
214D4×C61—21no—
215D4×C61—21no—
216D4×C61—42no—
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—24no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237D244—21no—
238D244#13112yes—
239C4×D61—24no—
240C4×D61—42no—
241C4×D61—41no—
242C4×D61—41no—
243Dic122—21no—
244Dic122#13112yes—
245C8×C61—41no—
246C8×C61—41no—
247C8×C61—41no—
248C8×C61—41no—
249#92418—21no—
250#92418—21no—
251#92418—21no—
252#92418—21no—
253#92418—21no—
254#92418—21no—
255#92418—21no—
256#92418—21no—
257#92418—41no—
258#92418—41no—
259#17909—611nomaximal, Sylow
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61C2×C4×D411yescharacteristic
267C2×D61—22no—
268C2×D61—41no—
269C2×D61—41no—
270C4×C61—21no—
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61C2×#13111yescharacteristic
278C4×C61C2×#13111yescharacteristic
279C4×C61#57511yescharacteristic
280C4×C61#57511yescharacteristic
281Dic61—22no—
282Dic61—41no—
283Dic61—41no—
284#3102—611no—
285#2966—611no—
286C8×#41—611no—
287#1588—611no—
288#1587—611no—
289#1586—611no—
290#1585—611no—
291#1580—611no—
292#1579—611no—
293SD16⋊C8—611no—
294SD16⋊C8—611no—
295#1572—611no—
296#1488—611no—
297#1482D6111yescharacteristic, complemented
298#1452—611no—
299C2×C61—41no—
300C2×C61—81no—
301C2×C61#292911yescharacteristic
302C2×C61#294311yescharacteristic
303C2×C61#295511yescharacteristic
304D61—42no—
305#529C2×D6111yescharacteristic
306C4×#41—611no—
307#485—611no—
308#482—611no—
309#479—611no—
310#478—611no—
311#464—611no—
312#463—611no—
313#452—611no—
314#449—611no—
315#446—611no—
316C8×Q8—611no—
317C8×Q8—611no—
318C8×Q8—611no—
319C4×Q16—611no—
320C4×SD16—611no—
321C4×SD16—611no—
322C4×D8—611no—
323#436—611no—
324#435—1221no—
325C8×D4—611no—
326C8×D4—611no—
327C8×D4—611no—
328C8×D4—1221no—
329C8×D4—1221no—
330C8×D4—1221no—
331#433—1221no—
332#432—611no—
333#431—611no—
334#431—1221no—
335#431C2×D6111yescharacteristic
336#431C2×D6111yescharacteristic
337#405—1221no—
338C2×C4×C8—611no—
339C2×C4×C8—1221no—
340#335—611no—
341#335—611no—
342#334—611no—
343#334—611no—
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346Q8⋊C8C2×D6111yescharacteristic
347Q8⋊C8C2×D6111yescharacteristic
348D4⋊C8—611no—
349D4⋊C8—611no—
350D4⋊C8C2×D6111yescharacteristic
351D4⋊C8C2×D6111yescharacteristic
352#322—611no—
353#322—611no—
354#322—611no—
355#322—611no—
356C61#1790911yescharacteristic, complemented, Sylow
357C2×#41—611no—
358C2×Q16—611no—
359C2×SD16—611no—
360C2×SD16—611no—
361C2×D8—611no—
362C2×M16—1221no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8—1221no—
366C22×C8—1221no—
367C22×C8—1221no—
368#126—21no—
369#125C4×D6111yescharacteristic
370#124C4×D6111yescharacteristic
371#123—21no—
372C22⋊Q8C4×D6111yescharacteristic
373#121C4×D6111yescharacteristic
374C4×Q8—611no—
375C4×Q8—611no—
376C4×Q8C22×D6111yescharacteristic
377C4×D4—21no—
378C4×D4—611no—
379C4×D4—611no—
380C4×D4—1221no—
381C4×D4—1221no—
382C4×D4C22×D6111yescharacteristic
383#117—21no—
384#117—611no—
385#117—1221no—
386C2×C42—1221no—
387C2×C42C22×D6111yescharacteristic
388#107—611no—
389#107—611no—
390#106—611no—
391#106—611no—
392C4⋊C8—21no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—1221no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8C22×D6111yescharacteristic
402C4⋊C8C22×D6111yescharacteristic
403#103—611no—
404#103—611no—
405#103—611no—
406#103—611no—
407#102—611no—
408#102—611no—
409#102—611no—
410#102—611no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—611no—
414C22⋊C8—611no—
415C22⋊C8—1221no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418C22⋊C8—1221no—
419C22⋊C8—1221no—
420#97—1221no—
421#97—1221no—
422C4×C8—21no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—611no—
429C4×C8—1221no—
430C4×C8—1221no—
431C4×C8—1221no—
432C4×C8C22×D6111yescharacteristic
433C4×C8C22×D6111yescharacteristic
434#41—1222no—
435#41—1222no—
436C2×Q8—611no—
437C2×Q8C2×C4×D6111yescharacteristic
438C2×D4—21no—
439C2×D4—611no—
440C2×D4—1221no—
441C2×D4C2×C4×D6111yescharacteristic
442C22×C4—21no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4C2×C4×D6111yescharacteristic
447C22×C4D4×D6111yescharacteristic
448C22×C4#1175822411yescharacteristic
449Q16—1222no—
450SD16—1222no—
451SD16—1222no—
452D8—1222no—
453M16—2442no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—611no—
459C2×C8—611no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—611no—
463C2×C8—611no—
464C2×C8—611no—
465C2×C8—611no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—2442no—
469C2×C8—2442no—
470C2×C8—2441no—
471C2×C8—2441no—
472C2×C8—2442no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—611no—
478C4⋊C4—611no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4C2×C4×D6111yescharacteristic
482C4⋊C4C2×C4×D6111yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C42—21no—
492C42—1221no—
493C42—1221no—
494C42—1221no—
495C42C2×C4×D6111yescharacteristic
496C42D4×D6111yescharacteristic
497C42#1175822411yescharacteristic
498C42C23×D6111yescharacteristic
499C23—21no—
500C23—1221no—
501C23#1451973711yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—612no—
505Q8—1221no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—612no—
510D4—1224no—
511D4—1221no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—1224no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—2442no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4#1451973711yescharacteristic
530C2×C4#1451973711yescharacteristic
531C2×C4#1451973711yescharacteristic
532C2×C4C22×C4×D6111yescharacteristic
533C2×C4C2×D4×D6111yescharacteristic
534C2×C4C2×#1175822411yescharacteristic
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—1221no—
540C8—1221no—
541C8—1221no—
542C8—1221no—
543C8—1221no—
544C8—1221no—
545C8—1221no—
546C8—1221no—
547C8—2441no—
548C8—2441no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—1222no—
556C22—2441no—
557C22—2441no—
558C22C2×#1451973711yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—1222no—
567C4—2441no—
568C4—2441no—
569C4#131×D6111yescharacteristic
570C4#131×D6111yescharacteristic
571C4#1684055911yescharacteristic
572C4#1684055911yescharacteristic
573C2—41no—
574C2—81no—
575C2—2442no—
576C2#2145451611yescharacteristic
577C2#2145461511yescharacteristic
578C2#2145471811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1482C2
socleC22×C61C2×C4×D4
prime radical#16839905C4
cosocleC42×C61C24
hypercenter#1482D61
hypocenterC61#17909
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1482

Complements

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

NH ≅ G/Ntype
2. #21454795C2semidirect
3. #21454775C2semidirect
4. #21444700C2semidirect
5. #21444693C2semidirect
6. #21444686C2semidirect
7. #21444679C2semidirect
8. #21444640C2semidirect
9. #21444635C2semidirect
10. #21444634C2semidirect
11. #21444628C2semidirect
12. #21444597C2semidirect
13. #21444254C2semidirect
14. #21444112C2semidirect
15. C61×#1482C2semidirect
297. #1482D61semidirect
356. C61#17909semidirect

Maximal subgroups

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

subgroupindex
#214558312
#214547952
#214547752
#214447002
#214446932
#214446862
#214446792
#214446402
#214446352
#214446342
#214446282
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C61×#14822
#1790961