Subgroups — #26042174

Order 11584.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15668452	C₂	1	2	yes	maximal, complemented
2	C₂×C₈×D₁₈₁	C₂	1	1	yes	maximal, characteristic
3	#15668452	—	2	2	no	—
4	C₂×C₄×D₁₈₁	C₄	1	1	yes	characteristic
5	C₂×#13089678	C₂²	1	1	yes	characteristic
6	C₈×D₁₈₁	—	2	2	no	—
7	C₂×C₈×C₁₈₁	C₄	1	1	yes	characteristic
8	C₂²×D₁₈₁	C₈	1	1	yes	characteristic
9	C₂×Dic₁₈₁	C₈	1	1	yes	characteristic
10	C₄×D₁₈₁	—	2	1	no	—
11	C₄×D₁₈₁	—	2	1	no	—
12	#13089678	D₄	1	2	yes	—
13	C₂×C₄×C₁₈₁	C₂×C₄	1	1	yes	characteristic
14	C₈×C₁₈₁	—	2	1	no	—
15	C₂²×C₁₈₁	C₂×C₈	1	1	yes	characteristic
16	C₂×D₁₈₁	—	2	1	no	—
17	C₂×D₁₈₁	—	2	1	no	—
18	C₂×D₁₈₁	C₁₆	1	2	yes	complemented
19	C₄×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₁₈₁	M₁₆	1	1	yes	characteristic
21	Dic₁₈₁	—	2	1	no	—
22	C₂×C₁₈₁	C₂²⋊C₈	1	1	yes	characteristic
23	C₂×C₁₈₁	C₂×C₁₆	1	1	yes	characteristic
24	C₂×C₁₈₁	M₃₂	1	1	yes	characteristic
25	D₁₈₁	—	2	2	no	—
26	C₁₈₁	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₂²⋊C₁₆	—	181	1	no	maximal, Sylow
28	C₂²×C₈	—	181	1	no	—
29	C₂×C₁₆	—	181	2	no	—
30	C₂²×C₄	—	181	1	no	—
31	C₂×C₈	—	362	2	no	—
32	C₂×C₈	—	181	1	no	—
33	C₂×C₈	#10624382	1	1	yes	characteristic
34	C₁₆	—	362	2	no	—
35	C₂³	—	181	1	no	—
36	C₂×C₄	—	362	1	no	—
37	C₂×C₄	—	362	1	no	—
38	C₂×C₄	—	181	1	no	—
39	C₂×C₄	C₂×#10624382	1	1	yes	characteristic
40	C₈	—	2	1	no	—
41	C₈	—	181	2	no	—
42	C₂²	—	362	1	no	—
43	C₂²	—	362	1	no	—
44	C₂²	—	181	2	no	—
45	C₂²	D₁₈₁⋊C₈	1	1	yes	characteristic
46	C₄	—	362	1	no	—
47	C₄	C₂²⋊#10624382	1	1	yes	characteristic
48	C₄	#15668459	1	1	yes	characteristic
49	C₂	—	362	2	no	—
50	C₂	#19153873	1	1	yes	characteristic
51	C₂	D₁₈₁⋊C₁₆	1	1	yes	characteristic
52	C₂	#19153891	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#10624382
commutator	C₂×C₁₈₁	C₂×C₁₆
Fitting	C₂×C₈×C₁₈₁	C₄
socle	C₂²×C₁₈₁	C₂×C₈
prime radical	C₂²×D₁₈₁	C₈
cosocle	C₂×#13089678	C₂²
hypercenter	C₂×C₈	#10624382
hypocenter	C₁₈₁	C₂²⋊C₁₆
LCS	G ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#15668452	C₂	semidirect
18. C₂×D₁₈₁	C₁₆	semidirect
26. C₁₈₁	C₂²⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15668452	2
C₂×C₈×D₁₈₁	2
C₂²⋊C₁₆	181