Subgroups — #26022494

Order 11392.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152000	C₂	1	1	yes	maximal, characteristic, complemented
2	#19151975	C₂	1	1	yes	maximal, characteristic
3	#19151400	C₂	1	4	yes	maximal, complemented
4	#346×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₇₁₂	—	2	1	no	—
6	C₂×D₇₁₂	C₂²	1	2	yes	—
7	#15668009	—	2	1	no	—
8	#15668004	—	2	1	no	—
9	#15667946	C₂²	1	2	yes	—
10	#15667944	—	2	1	no	—
11	C₂×C₁₆×C₈₉	C₂²	1	2	yes	—
12	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×D₃₅₆	—	2	2	no	—
14	C₂×D₃₅₆	—	4	2	no	—
15	D₇₁₂	—	2	4	no	—
16	D₇₁₂	—	4	2	no	—
17	C₄⋊Dic₈₉	—	2	2	no	—
18	#13083553	—	4	2	no	—
19	C₂×C₈×C₈₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
21	C₄²×C₈₉	D₄	1	1	yes	characteristic
22	C₁₆×C₈₉	—	2	2	no	—
23	C₂²×D₈₉	—	4	2	no	—
24	C₂×C₄×C₈₉	D₈	1	2	yes	—
25	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
26	C₂×Dic₈₉	—	4	2	no	—
27	D₃₅₆	—	4	2	no	—
28	D₃₅₆	—	4	2	no	—
29	D₃₅₆	—	8	4	no	—
30	C₈×C₈₉	SD₁₆	1	2	yes	—
31	C₈×C₈₉	#41	1	2	yes	—
32	C₂²×C₈₉	C₂×D₈	1	1	yes	characteristic
33	C₂×D₈₉	—	8	2	no	—
34	C₂×D₈₉	—	8	4	no	—
35	C₄×C₈₉	—	2	2	no	—
36	C₄×C₈₉	#124	1	1	yes	characteristic
37	C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
38	Dic₈₉	—	8	2	no	—
39	C₂×C₈₉	#486	1	1	yes	characteristic
40	C₂×C₈₉	#509	1	2	yes	—
41	D₈₉	—	16	2	no	—
42	#2244	—	89	1	no	maximal, Sylow
43	C₈₉	#2244	1	1	yes	characteristic, complemented, Sylow
44	#499	—	89	1	no	—
45	#493	—	89	1	no	—
46	#357	—	89	4	no	—
47	#346	D₈₉	1	1	yes	characteristic, complemented
48	C₂×D₈	—	89	2	no	—
49	C₂×D₈	—	178	1	no	—
50	#127	—	178	1	no	—
51	#125	—	178	1	no	—
52	C₂×C₁₆	C₂×D₈₉	1	2	yes	—
53	#107	—	89	2	no	—
54	#106	—	178	1	no	—
55	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
56	C₂×D₄	—	356	2	no	—
57	C₂×D₄	—	178	2	no	—
58	D₈	—	356	2	no	—
59	D₈	—	178	4	no	—
60	C₂×C₈	D₃₅₆	1	1	yes	characteristic
61	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
62	C₄⋊C₄	—	356	2	no	—
63	C₄⋊C₄	—	178	2	no	—
64	C₄²	D₃₅₆	1	1	yes	characteristic
65	C₁₆	—	2	2	no	—
66	C₂³	—	356	2	no	—
67	D₄	—	356	2	no	—
68	D₄	—	356	2	no	—
69	D₄	—	712	4	no	—
70	C₂×C₄	—	356	2	no	—
71	C₂×C₄	D₇₁₂	1	2	yes	—
72	C₂×C₄	C₂×D₃₅₆	1	1	yes	characteristic
73	C₈	#13083563	1	2	yes	—
74	C₈	#13083574	1	2	yes	—
75	C₂²	—	712	2	no	—
76	C₂²	—	712	4	no	—
77	C₂²	C₂×D₇₁₂	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	712	2	no	—
80	C₄	#15668000	1	1	yes	characteristic
81	C₄	C₂×#13083563	1	1	yes	characteristic
82	C₂	—	1424	2	no	—
83	C₂	#19151945	1	1	yes	characteristic
84	C₂	#19152036	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₇₁₂
commutator, cosocle	C₂×C₈×C₈₉	C₂³
Frattini	C₂×C₈	C₂²×D₈₉
Fitting	#346×C₈₉	C₂
socle	C₂²×C₈₉	C₂×D₈
prime radical	#19151975	C₂
hypercenter	#346	D₈₉
hypocenter	C₈₉	#2244
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
1. #19152000	C₂	semidirect
3. #19151400	C₂	semidirect
4. #346×C₈₉	C₂	semidirect
43. C₈₉	#2244	semidirect
47. #346	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152000	2
#19151975	2
#19151400	2
#346×C₈₉	2
#2244	89