Subgroups — #26042136

Order 11584.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19153871	C₂	1	1	yes	maximal, characteristic
2	#19153871	C₂	1	1	yes	maximal, characteristic
3	#19153807	C₂	1	1	yes	maximal, characteristic
4	C₂×#13089685	—	2	1	no	—
5	C₂×#13089685	—	2	1	no	—
6	C₄⋊Dic₁₈₁	—	2	1	no	—
7	C₄⋊Dic₁₈₁	C₄	1	1	yes	characteristic
8	#15668428	—	2	1	no	—
9	C₄×Dic₁₈₁	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₁₈₁	C₄	1	1	yes	characteristic
11	#13089685	—	2	2	no	—
12	#13089685	—	2	2	no	—
13	C₂×Dic₁₈₁	—	2	1	no	—
14	C₂×Dic₁₈₁	D₄	1	1	yes	characteristic
15	C₂×Dic₁₈₁	D₄	1	1	yes	characteristic
16	C₂×C₄×C₁₈₁	—	2	1	no	—
17	C₂×C₄×C₁₈₁	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₁₈₁	—	2	1	no	—
20	C₄×C₁₈₁	—	4	1	no	—
21	Dic₁₈₁	—	2	1	no	—
22	Dic₁₈₁	—	2	1	no	—
23	Dic₁₈₁	—	4	1	no	—
24	C₂×C₁₈₁	#101	1	1	yes	characteristic
25	C₂×C₁₈₁	#104	1	1	yes	characteristic
26	C₂×C₁₈₁	#104	1	1	yes	characteristic
27	C₁₈₁	#330	1	1	yes	characteristic, complemented, Sylow
28	#330	—	181	1	no	maximal, Sylow
29	#125	—	181	1	no	—
30	#97	—	181	1	no	—
31	#97	—	181	1	no	—
32	C₂×C₈	—	362	1	no	—
33	C₂×C₈	—	362	1	no	—
34	C₄⋊C₄	—	362	1	no	—
35	C₄⋊C₄	—	362	1	no	—
36	C₄⋊C₄	—	181	1	no	—
37	C₄⋊C₄	#10624382	1	1	yes	characteristic
38	C₄²	—	181	1	no	—
39	C₂×C₄	—	2	1	no	—
40	C₂×C₄	—	362	1	no	—
41	C₂×C₄	—	181	1	no	—
42	C₂×C₄	—	181	1	no	—
43	C₂×C₄	C₂×#10624382	1	1	yes	characteristic
44	C₈	—	362	2	no	—
45	C₈	—	362	2	no	—
46	C₂²	C₂²⋊#10624382	1	1	yes	characteristic
47	C₄	—	2	1	no	—
48	C₄	—	4	1	no	—
49	C₄	—	362	1	no	—
50	C₄	—	362	1	no	—
51	C₄	—	724	1	no	—
52	C₂	#19153877	1	1	yes	characteristic
53	C₂	#19153880	1	1	yes	characteristic
54	C₂	#19153881	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#10624382
commutator	C₂×C₄×C₁₈₁	C₂×C₄
Frattini	C₂×C₄	C₂×#10624382
Fitting	C₄⋊C₄×C₁₈₁	C₄
socle, prime radical	C₂²×C₁₈₁	C₂²⋊C₄
cosocle	C₄×Dic₁₈₁	C₂²
hypercenter	C₄⋊C₄	#10624382
hypocenter	C₁₈₁	#330
LCS	G ▷ C₂×C₄×C₁₈₁ ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
27. C₁₈₁	#330	semidirect

Maximal subgroups

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

subgroup	index
#19153871	2
#19153807	2
#330	181