Subgroups — #26018440

Order 11392.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152030	C₂	1	1	yes	maximal, characteristic
2	#19151426	C₂	1	1	yes	maximal, characteristic, complemented
3	M₆₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#15668034	—	2	1	no	—
5	Dic₇₁₂	C₄	1	1	yes	characteristic, complemented
6	#15667957	—	2	1	no	—
7	D₁₄₂₄	C₄	1	1	yes	characteristic, complemented
8	#15667946	—	2	1	no	—
9	C₂×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
10	C₃₂×C₈₉	—	2	1	no	—
11	#13083574	—	4	1	no	—
12	Dic₃₅₆	—	2	1	no	—
13	#13083563	—	4	1	no	—
14	D₇₁₂	—	2	1	no	—
15	C₄⋊Dic₈₉	—	4	1	no	—
16	C₂×C₈×C₈₉	D₄	1	1	yes	characteristic
17	C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₈₉	D₄	1	1	yes	characteristic
19	C₂×C₄×C₈₉	D₈	1	1	yes	characteristic
20	C₂²⋊D₈₉	—	8	1	no	—
21	C₂×Dic₈₉	—	8	1	no	—
22	D₃₅₆	—	4	1	no	—
23	C₄×D₈₉	—	8	1	no	—
24	Dic₁₇₈	—	4	1	no	—
25	C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₈₉	SD₁₆	1	1	yes	characteristic
27	C₂²×C₈₉	D₁₆	1	1	yes	characteristic
28	C₂×D₈₉	—	8	1	no	—
29	C₄×C₈₉	#102	1	1	yes	characteristic
30	C₄×C₈₉	SD₃₂	1	1	yes	characteristic
31	Dic₈₉	—	8	1	no	—
32	Dic₈₉	—	16	1	no	—
33	C₂×C₈₉	—	2	1	no	—
34	C₂×C₈₉	#357	1	1	yes	characteristic
35	D₈₉	—	16	1	no	—
36	#1418	—	89	1	no	maximal, Sylow
37	C₈₉	#1418	1	1	yes	characteristic, complemented, Sylow
38	#508	—	89	1	no	—
39	M₆₄	D₈₉	1	1	yes	characteristic, complemented
40	#367	—	89	1	no	—
41	#135	—	178	1	no	—
42	Q₃₂	—	89	1	no	—
43	SD₃₂	—	178	1	no	—
44	D₁₆	—	89	1	no	—
45	C₂×C₁₆	C₂×D₈₉	1	1	yes	characteristic
46	#107	—	178	1	no	—
47	C₃₂	—	2	1	no	—
48	#41	—	356	1	no	—
49	Q₁₆	—	178	1	no	—
50	SD₁₆	—	356	1	no	—
51	D₈	—	178	1	no	—
52	C₂×C₈	D₃₅₆	1	1	yes	characteristic
53	C₄⋊C₄	—	356	1	no	—
54	C₁₆	C₄×D₈₉	1	1	yes	characteristic
55	C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
56	Q₈	—	356	1	no	—
57	D₄	—	356	1	no	—
58	D₄	—	712	1	no	—
59	C₂×C₄	—	712	1	no	—
60	C₂×C₄	—	712	1	no	—
61	C₂×C₄	D₇₁₂	1	1	yes	characteristic
62	C₈	#13083551	1	1	yes	characteristic
63	C₈	#13083563	1	1	yes	characteristic
64	C₂²	—	712	1	no	—
65	C₂²	D₁₄₂₄	1	1	yes	characteristic
66	C₄	—	1424	1	no	—
67	C₄	—	712	1	no	—
68	C₄	#15667934	1	1	yes	characteristic
69	C₄	#15667957	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	1424	1	no	—
72	C₂	#19151400	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19151400
commutator	C₁₆×C₈₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₈₉
Fitting	M₆₄×C₈₉	C₂
socle	C₂×C₈₉	#357
prime radical	#19152030	C₂
cosocle	C₂×C₁₆×C₈₉	C₂²
hypercenter	M₆₄	D₈₉
hypocenter	C₈₉	#1418
LCS	G ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
2. #19151426	C₂	semidirect
3. M₆₄×C₈₉	C₂	semidirect
5. Dic₇₁₂	C₄	semidirect
7. D₁₄₂₄	C₄	semidirect
37. C₈₉	#1418	semidirect
39. M₆₄	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152030	2
#19151426	2
M₆₄×C₈₉	2
#1418	89