Subgroups — #26042185

Order 11584.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19153875	C₂	1	2	yes	maximal
2	#19153805	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊#10624382	—	2	2	no	—
4	C₂×D₇₂₄	C₂²	1	1	yes	characteristic
5	#15668426	—	2	2	no	—
6	C₄×Dic₁₈₁	C₄	1	1	yes	characteristic, complemented
7	C₂×Q₈×C₁₈₁	C₄	1	1	yes	characteristic, complemented
8	C₂×#10624382	—	4	2	no	—
9	C₂²×D₁₈₁	D₄	1	2	yes	—
10	D₇₂₄	—	4	1	no	—
11	C₂×Dic₁₈₁	—	2	1	no	—
12	Q₈×C₁₈₁	—	4	1	no	—
13	C₂×C₄×C₁₈₁	—	2	1	no	—
14	C₂×C₄×C₁₈₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×D₁₈₁	—	2	2	no	—
17	C₂×D₁₈₁	—	4	2	no	—
18	#10624382	—	8	2	no	—
19	C₄×C₁₈₁	—	2	1	no	—
20	C₄×C₁₈₁	—	4	1	no	—
21	Dic₁₈₁	—	4	1	no	—
22	C₂×C₁₈₁	—	2	1	no	—
23	C₂×C₁₈₁	#99	1	1	yes	characteristic
24	D₁₈₁	—	4	2	no	—
25	C₁₈₁	#354	1	1	yes	characteristic, complemented, Sylow
26	#354	—	181	1	no	maximal, Sylow
27	#124	—	181	1	no	—
28	#99	—	181	2	no	—
29	C₂×Q₈	#10624382	1	1	yes	characteristic, complemented
30	C₂×D₄	—	181	1	no	—
31	C₂²⋊C₄	—	362	2	no	—
32	C₂²⋊C₄	—	362	2	no	—
33	C₄²	—	181	1	no	—
34	C₂³	—	181	2	no	—
35	Q₈	—	4	1	no	—
36	D₄	—	724	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	—	362	1	no	—
39	C₂×C₄	—	724	2	no	—
40	C₂×C₄	C₂×#10624382	1	1	yes	characteristic
41	C₂²	—	362	2	no	—
42	C₂²	—	724	2	no	—
43	C₂²	C₂²⋊#10624382	1	1	yes	characteristic
44	C₄	—	2	1	no	—
45	C₄	—	4	1	no	—
46	C₄	—	1448	2	no	—
47	C₄	—	724	1	no	—
48	C₂	—	2	1	no	—
49	C₂	—	724	2	no	—
50	C₂	#19153874	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19153874
commutator	C₂×C₄×C₁₈₁	C₂×C₄
Frattini	C₂×C₄	C₂×#10624382
Fitting	C₂×Q₈×C₁₈₁	C₄
socle	C₂×C₁₈₁	#99
prime radical, cosocle	C₂×D₇₂₄	C₂²
hypercenter	C₂×Q₈	#10624382
hypocenter	C₁₈₁	#354
LCS	G ▷ C₂×C₄×C₁₈₁ ▷ C₂²×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
6. C₄×Dic₁₈₁	C₄	semidirect
7. C₂×Q₈×C₁₈₁	C₄	semidirect
25. C₁₈₁	#354	semidirect
29. C₂×Q₈	#10624382	semidirect

Maximal subgroups

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

subgroup	index
#19153875	2
#19153805	2
#354	181