Finite Group Databasebeta

← #29833350

Subgroups — #29833350

Order 15616.

696 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840199C211yesmaximal, characteristic
2#21454694C211yesmaximal, characteristic, complemented
3#21454666C211yesmaximal, characteristic, complemented
4#21447694C211yesmaximal, characteristic, complemented
5#21447693C211yesmaximal, characteristic, complemented
6#21447684C211yesmaximal, characteristic, complemented
7#21447681C211yesmaximal, characteristic, complemented
8#21447668C211yesmaximal, characteristic, complemented
9C4×D976C211yesmaximal, characteristic, complemented
10#21447663C211yesmaximal, characteristic, complemented
11#21447606C211yesmaximal, characteristic, complemented
12#21447525C211yesmaximal, characteristic, complemented
13#357×D61C211yesmaximal, characteristic, complemented
14#21447414C211yesmaximal, characteristic, complemented
15C4×SD32×C61C211yesmaximal, characteristic, complemented
16C2×#14519800C2211yescharacteristic
17C2×D8×D61C2211yescharacteristic
18#16840244—21no—
19#16840234—21no—
20#16840199C418yescomplemented
21C2×#14519720C2211yescharacteristic
22C2×D976C2211yescharacteristic
23C2×#14519718C2211yescharacteristic
24C2×#14519716C2211yescharacteristic
25C2×C16×D61C2211yescharacteristic
26#16839872—21no—
27#16839871—21no—
28#16839865—21no—
29#16839860—21no—
30Q16×Dic61C2211yescharacteristic, complemented
31C4×D488C2211yescharacteristic
32C4×D488C2211yescharacteristic, complemented
33D8×Dic61C2211yescharacteristic
34#16839844C2211yescharacteristic
35#16839844C2211yescharacteristic, complemented
36#16839799C2211yescharacteristic
37#107×D61C2211yescharacteristic
38#16839765—21no—
39#16839762—21no—
40#16839716C2211yescharacteristic
41#16839589C2211yescharacteristic, complemented
42#16839588C2211yescharacteristic, complemented
43#16839587C2211yescharacteristic, complemented
44#16839566C2211yescharacteristic, complemented
45#16839564C2211yescharacteristic
46#16839564C2211yescharacteristic, complemented
47#16839563C2211yescharacteristic
48#16839562C2211yescharacteristic
49#16839562C2211yescharacteristic, complemented
50#16839538C2211yescharacteristic, complemented
51#16839537C2211yescharacteristic, complemented
52C16×Dic61C2211yescharacteristic, complemented
53C2×SD32×C61C2211yescharacteristic
54C4×Q16×C61C2211yescharacteristic, complemented
55C4×D8×C61C2211yescharacteristic
56C61×#367C2211yescharacteristic, complemented
57C61×#358C2211yescharacteristic, complemented
58C61×#357C2211yescharacteristic
59C4×C16×C61C2211yescharacteristic, complemented
60C2×#11758226—21no—
61C2×D4×D61—21no—
62#14519800—22no—
63#14519800C2×C414yescomplemented
64C2×#11758201—21no—
65C2×D488C2311yescharacteristic
66C2×D488C2311yescharacteristic
67C2×#11758199—21no—
68D8×D61—22no—
69D8×D61C2×C414yescomplemented
70C2×#11758189D411yescharacteristic
71C2×C8×D61C2311yescharacteristic
72Q8×Dic61—21no—
73C4×D244—21no—
74C4×D244—21no—
75C4×D244—41no—
76D4×Dic61—21no—
77#14519739—21no—
78#14519739—21no—
79#14519739—41no—
80C4×C22⋊D61—41no—
81#14519737—41no—
82#14519735—21no—
83#14519734—41no—
84#14519734D411yescharacteristic
85C4⋊C4×D61—21no—
86C4⋊C4×D61—41no—
87C2×#11758198—41no—
88C22⋊C4×D61—41no—
89#14519720C2×C414yescomplemented
90D976C2×C414yescomplemented
91#14519718C2×C414yescomplemented
92#14519716C2×C414yescomplemented
93C2×#11758185C2311yescharacteristic
94C2×#11758185C2311yescharacteristic
95C16×D61—22no—
96#14519711C2311yescharacteristic
97#14519711C2311yescharacteristic
98#14519710—21no—
99#14519708—21no—
100#14519701—21no—
101#14519699—21no—
102#14519699—21no—
103#14519698—21no—
104#14519697—21no—
105#14519697—21no—
106#14519688D411yescharacteristic
107#14519687D411yescharacteristic
108C8×Dic61C2311yescharacteristic
109C2×Q16×C61C2311yescharacteristic
110C2×D8×C61C2311yescharacteristic
111C4×Q8×C61—21no—
112C4×D4×C61—21no—
113SD32×C61C2×C414yescomplemented
114C2×C16×C61C2311yescharacteristic
115C2×C16×C61C2311yescharacteristic
116#107×C61C2311yescharacteristic
117#107×C61C2311yescharacteristic
118#103×C61—21no—
119#102×C61—21no—
120C4×C8×C61C2311yescharacteristic
121C23×D61—41no—
122C2×Q8×C61—21no—
123C2×D4×C61—21no—
124C22×C4×C61—41no—
125C2×C22⋊D61—41no—
126C22×Dic61—41no—
127#11758226—24no—
128#11758226—42no—
129D4×D61—24no—
130D4×D61—42no—
131C2×D244—21no—
132C2×D244—21no—
133C2×D244—41no—
134C2×C4×D61—41no—
135C2×C4×D61—41no—
136C2×C4×D61—41no—
137C2×C4×D61—41no—
138C2×C4×D61—41no—
139C2×C4×D61—41no—
140C2×C4×D61C2×D411yescharacteristic
141Q16×C61—21no—
142Q16×C61C22×C412yes—
143D8×C61—21no—
144D8×C61C22×C412yes—
145C2×C8×C61C2×D411yescharacteristic
146C2×C8×C61C2411yescharacteristic
147C4⋊C4×C61—21no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—41no—
150C22⋊C4×C61—41no—
151C42×C61—41no—
152C42×C61C2×D411yescharacteristic
153C22⋊Dic61—41no—
154#11758201—24no—
155#11758199—24no—
156#11758198—41no—
157#11758198—41no—
158#11758198—41no—
159#11758198—41no—
160#11758198—41no—
161#11758198D811yescharacteristic
162#11758198D811yescharacteristic
163C4⋊Dic61—21no—
164C4⋊Dic61—21no—
165C4⋊Dic61—41no—
166#11758196—41no—
167#11758196D811yescharacteristic
168#11758196D811yescharacteristic
169C4×Dic61—41no—
170C4×Dic61—41no—
171C4×Dic61C2×D411yescharacteristic
172C2×#92418C2×D411yescharacteristic
173C2×#92418C2×D411yescharacteristic
174D488—21no—
175D488—21no—
176D488C22×C412yes—
177D488C22×C412yes—
178#11758189—22no—
179C8×D61C22×C412yes—
180C8×D61#4112yes—
181C16×C61—21no—
182C16×C61C22×C412yes—
183#11758185—21no—
184#11758185C22×C412yes—
185C23×C61—41no—
186C22×D61—41no—
187C22×D61—41no—
188C22×D61—44no—
189C22×D61—161no—
190C22×D61—161no—
191C22×D61C2×D811yescharacteristic
192Q8×C61—22no—
193Q8×C61—41no—
194D4×C61—22no—
195D4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—161no—
200C2×C4×C61C2×D811yescharacteristic
201C2×C4×C61C2×D811yescharacteristic
202C2×C4×C61C22×D411yescharacteristic
203C22⋊D61—44no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—161no—
207C2×Dic61C2×D811yescharacteristic
208C2×Dic61C2×D811yescharacteristic
209C2×Dic61C2×D811yescharacteristic
210D244—22no—
211D244—22no—
212D244—44no—
213D244—41no—
214D244—41no—
215C4×D61—44no—
216C4×D61—161no—
217C4×D61—161no—
218C4×D61—161no—
219C4×D61—161no—
220C4×D61—161no—
221C4×D61C4×D412yes—
222C4×D61#13512yes—
223C8×C61—21no—
224C8×C61C23×C411yescharacteristic
225C8×C61C2×#4111yescharacteristic
226#92418—21no—
227#92418C4×D412yes—
228#33454—611nomaximal, Sylow
229C22×C61—42no—
230C22×C61—81no—
231C22×C61—81no—
232C22×C61C22×D811yescharacteristic
233C2×D61—21no—
234C2×D61—21no—
235C2×D61—42no—
236C2×D61—42no—
237C2×D61—81no—
238C2×D61—81no—
239C2×D61—81no—
240C2×D61—81no—
241C2×D61—164no—
242C2×D61C4×D812yes—
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—42no—
246C4×C61—81no—
247C4×C61—81no—
248C4×C61C2×C4×D411yescharacteristic
249C4×C61C2×#13511yescharacteristic
250Dic61—21no—
251Dic61—21no—
252Dic61—81no—
253Dic61—81no—
254Dic61C4×D812yes—
255C2×#509—611no—
256#2951—611no—
257#2948—611no—
258#2177—611no—
259#2177—611no—
260#2175—611no—
261#2175—611no—
262C4×SD32—611no—
263C4×SD32D6111yescharacteristic, complemented
264C4×D16—611no—
265C4×D16—611no—
266#2159—611no—
267#2138—611no—
268C2×#357—611no—
269#2108—611no—
270C2×C61—82no—
271C2×C61C2×C4×D811yescharacteristic
272C2×C61#341511yescharacteristic
273C2×C61#341611yescharacteristic
274D61—22no—
275D61—82no—
276D61—82no—
277C2×#135—611no—
278C22×D8—611no—
279#520—1221no—
280#518—1221no—
281#509—618no—
282C2×SD32—611no—
283C2×SD32C2×D6111yescharacteristic
284C2×D16—611no—
285C2×D16—611no—
286C2×M32—611no—
287C22×C16—611no—
288#442—1221no—
289#442—1221no—
290#440—1221no—
291#440—1221no—
292C4×Q16—611no—
293C4×Q16C2×D6111yescharacteristic, complemented
294C4×D8—611no—
295C4×D8—611no—
296C4×D8—611no—
297C4×D8—611no—
298C4×D8—611no—
299C4×D8C2×D6111yescharacteristic
300#427—611no—
301C2×#107—611no—
302#418—1221no—
303#417—1221no—
304#405—611no—
305#367—611no—
306#367C2×D6111yescharacteristic, complemented
307#366—611no—
308#366—611no—
309#358—611no—
310#358C2×D6111yescharacteristic, complemented
311#357—611no—
312#357—611no—
313#357—611no—
314#357—611no—
315#357—611no—
316#357C2×D6111yescharacteristic
317#346—611no—
318#346—611no—
319C4×C16—611no—
320C4×C16C2×D6111yescharacteristic, complemented
321C61#3345411yescharacteristic, complemented, Sylow
322C2×#41—1221no—
323C22×D4—1221no—
324#135—614no—
325#135—1222no—
326C2×Q16C22×D6111yescharacteristic
327C2×SD16—1221no—
328C2×D8—614no—
329C2×D8—611no—
330C2×D8—611no—
331C2×D8—1222no—
332C2×D8—1221no—
333C2×D8C22×D6111yescharacteristic
334C2×M16—611no—
335C22×C8—611no—
336C4×Q8—21no—
337C4×Q8—1221no—
338C4×D4—21no—
339C4×D4—1221no—
340C4×D4—1221no—
341C4×D4—1221no—
342C4×D4—1221no—
343C4×D4—1221no—
344C4×D4—2441no—
345C4×D4—2441no—
346C4×D4—2441no—
347C4×D4—2441no—
348#117—611no—
349#117—1221no—
350#117—2441no—
351C2×C4⋊C4—1221no—
352C2×C4⋊C4—2441no—
353C2×C22⋊C4—2441no—
354C2×C22⋊C4—2441no—
355SD32—614no—
356SD32C4×D6114yescomplemented
357D16—614no—
358D16—614no—
359M32—614no—
360C2×C16—611no—
361C2×C16—611no—
362C2×C16—1222no—
363C2×C16C22×D6111yescharacteristic
364C2×C16C22×D6111yescharacteristic
365#107—611no—
366#107—611no—
367#107—1221no—
368#107C22×D6111yescharacteristic
369#107C22×D6111yescharacteristic
370#106—1221no—
371#103—21no—
372#103—1221no—
373#102—21no—
374#102—1221no—
375#102—1221no—
376#102—1221no—
377#102—1221no—
378#102—1221no—
379#97—611no—
380#97—611no—
381C4×C8—611no—
382C4×C8C22×D6111yescharacteristic
383C24—2441no—
384#41—1224no—
385#41—2442no—
386C2×Q8—21no—
387C2×D4—21no—
388C2×D4—1224no—
389C2×D4—1221no—
390C2×D4—1221no—
391C2×D4—2441no—
392C2×D4—2442no—
393C2×D4—2441no—
394C22×C4—41no—
395C22×C4—611no—
396C22×C4—2441no—
397C22×C4—2441no—
398C22×C4—2441no—
399C22×C4—2441no—
400C22×C4—2441no—
401C22×C4—2441no—
402C22×C4—2441no—
403Q16—21no—
404Q16C2×C4×D6112yes—
405SD16—1224no—
406D8—21no—
407D8—612no—
408D8—612no—
409D8—1224no—
410D8—1221no—
411D8—1221no—
412D8C2×C4×D6112yes—
413M16—1222no—
414C2×C8—611no—
415C2×C8—612no—
416C2×C8—612no—
417C2×C8—611no—
418C2×C8D4×D6111yescharacteristic
419C2×C8C23×D6111yescharacteristic
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—41no—
423C4⋊C4—611no—
424C4⋊C4—611no—
425C4⋊C4—1221no—
426C4⋊C4—1221no—
427C4⋊C4—2441no—
428C4⋊C4—2441no—
429C22⋊C4—41no—
430C22⋊C4—611no—
431C22⋊C4—611no—
432C22⋊C4—2441no—
433C22⋊C4—2441no—
434C22⋊C4—2441no—
435C22⋊C4—2441no—
436C22⋊C4—2441no—
437C22⋊C4—2441no—
438C42—41no—
439C42—611no—
440C42—2441no—
441C42—2441no—
442C42D4×D6111yescharacteristic
443C16—21no—
444C16—612no—
445C16—1221no—
446C16C2×C4×D6112yes—
447C23—41no—
448C23—611no—
449C23—9761no—
450C23—9761no—
451C23—2444no—
452C23—2441no—
453C23—2441no—
454Q8—22no—
455Q8—41no—
456D4—22no—
457D4—41no—
458D4—1222no—
459D4—1222no—
460D4—2444no—
461D4—2444no—
462D4—2441no—
463D4—2441no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—161no—
468C2×C4—611no—
469C2×C4—612no—
470C2×C4—612no—
471C2×C4—611no—
472C2×C4—611no—
473C2×C4—9761no—
474C2×C4—9761no—
475C2×C4—9761no—
476C2×C4—9761no—
477C2×C4—9761no—
478C2×C4—9761no—
479C2×C4—2444no—
480C2×C4—2441no—
481C2×C4—2441no—
482C2×C4D8×D6111yescharacteristic
483C2×C4D8×D6111yescharacteristic
484C2×C4C2×D4×D6111yescharacteristic
485C8—21no—
486C8—612no—
487C8—1221no—
488C8C22×C4×D6111yescharacteristic
489C8#41×D6111yescharacteristic
490C22—42no—
491C22—81no—
492C22—81no—
493C22—612no—
494C22—1221no—
495C22—1221no—
496C22—9764no—
497C22—4881no—
498C22—4881no—
499C22—4881no—
500C22—4881no—
501C22—2442no—
502C22—2442no—
503C22C2×D8×D6111yescharacteristic
504C4—21no—
505C4—21no—
506C4—42no—
507C4—81no—
508C4—81no—
509C4—612no—
510C4—1221no—
511C4—1221no—
512C4—4881no—
513C4—4881no—
514C4C4×D4×D6111yescharacteristic
515C4#135×D6111yescharacteristic
516C2—82no—
517C2—1222no—
518C2—4882no—
519C2—4882no—
520C2C4×D8×D6111yescharacteristic
521C2#2145895711yescharacteristic
522C2#2145896111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutatorC8×C61C23×C4
FrattiniC2×C8C23×D61
FittingC4×SD32×C61C2
socleC22×C61C22×D8
prime radicalC2×#16840199C2
cosocleC2×C8×C61C24
hypercenterC4×SD32D61
hypocenterC61#33454
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
2. #21454694C2semidirect
3. #21454666C2semidirect
4. #21447694C2semidirect
5. #21447693C2semidirect
6. #21447684C2semidirect
7. #21447681C2semidirect
8. #21447668C2semidirect
9. C4×D976C2semidirect
10. #21447663C2semidirect
11. #21447606C2semidirect
12. #21447525C2semidirect
13. #357×D61C2semidirect
14. #21447414C2semidirect
15. C4×SD32×C61C2semidirect
20. #16840199C4semidirect
30. Q16×Dic61C22semidirect
32. C4×D488C22semidirect
35. #16839844C22semidirect
41. #16839589C22semidirect
42. #16839588C22semidirect
43. #16839587C22semidirect
44. #16839566C22semidirect
46. #16839564C22semidirect
49. #16839562C22semidirect
50. #16839538C22semidirect
51. #16839537C22semidirect
52. C16×Dic61C22semidirect
54. C4×Q16×C61C22semidirect
56. C61×#367C22semidirect
57. C61×#358C22semidirect
59. C4×C16×C61C22semidirect
63. #14519800C2×C4semidirect
69. D8×D61C2×C4semidirect
89. #14519720C2×C4semidirect
90. D976C2×C4semidirect
91. #14519718C2×C4semidirect
92. #14519716C2×C4semidirect
113. SD32×C61C2×C4semidirect
263. C4×SD32D61semidirect
293. C4×Q16C2×D61semidirect
306. #367C2×D61semidirect
310. #358C2×D61semidirect
320. C4×C16C2×D61semidirect
321. C61#33454semidirect
356. SD32C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168401992
#214546942
#214546662
#214476942
#214476932
#214476842
#214476812
#214476682
C4×D9762
#214476632
#214476062
#214475252
#357×D612
#214474142
C4×SD32×C612
#3345461