Subgroups — #37548858

Order 23168.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042190	C₂	1	2	yes	maximal
2	#26041658	C₂	1	1	yes	maximal, characteristic
3	#19153877	—	2	2	no	—
4	C₂×#15668439	—	2	2	no	—
5	#19153816	C₂²	1	1	yes	characteristic
6	C₄×#13089678	C₄	1	1	yes	characteristic
7	C₄⋊Q₈×C₁₈₁	C₄	1	1	yes	characteristic
8	#15668458	—	4	2	no	—
9	C₂×Dic₃₆₂	D₄	1	2	yes	—
10	#15668439	—	4	4	no	—
11	C₂×#13089678	—	2	1	no	—
12	C₄⋊Dic₁₈₁	—	4	1	no	—
13	C₂×Q₈×C₁₈₁	—	2	1	no	—
14	C₄⋊C₄×C₁₈₁	—	4	1	no	—
15	C₄²×C₁₈₁	C₂×C₄	1	1	yes	characteristic
16	#13089685	—	8	2	no	—
17	Dic₃₆₂	—	4	2	no	—
18	C₂×Dic₁₈₁	—	2	2	no	—
19	#13089678	—	2	2	no	—
20	Q₈×C₁₈₁	—	4	2	no	—
21	C₂×C₄×C₁₈₁	—	2	1	no	—
22	C₂×C₄×C₁₈₁	—	4	1	no	—
23	C₂×C₄×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
24	C₂²×C₁₈₁	#99	1	1	yes	characteristic
25	C₄×C₁₈₁	—	2	2	no	—
26	C₄×C₁₈₁	—	2	1	no	—
27	C₄×C₁₈₁	—	8	1	no	—
28	Dic₁₈₁	—	4	2	no	—
29	C₂×C₁₈₁	—	2	1	no	—
30	C₂×C₁₈₁	#353	1	1	yes	characteristic
31	C₁₈₁	#1411	1	1	yes	characteristic, complemented, Sylow
32	#1411	—	181	1	no	maximal, Sylow
33	#494	—	181	1	no	—
34	#356	—	181	2	no	—
35	C₂×Q₁₆	—	362	2	no	—
36	C₄⋊Q₈	—	181	1	no	—
37	C₄⋊Q₈	#10624382	1	1	yes	characteristic
38	#101	—	362	2	no	—
39	C₄×C₈	—	181	1	no	—
40	C₂×Q₈	—	2	1	no	—
41	C₂×Q₈	—	181	2	no	—
42	Q₁₆	—	724	4	no	—
43	M₁₆	—	724	2	no	—
44	C₂×C₈	—	362	1	no	—
45	C₄⋊C₄	—	4	1	no	—
46	C₄⋊C₄	—	724	1	no	—
47	C₄²	C₂×#10624382	1	1	yes	characteristic
48	Q₈	—	4	2	no	—
49	Q₈	—	724	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	4	1	no	—
52	C₂×C₄	—	362	2	no	—
53	C₂×C₄	C₂²⋊#10624382	1	1	yes	characteristic
54	C₈	—	362	2	no	—
55	C₈	—	1448	2	no	—
56	C₂²	#19153874	1	1	yes	characteristic
57	C₄	—	2	2	no	—
58	C₄	—	2	1	no	—
59	C₄	—	8	1	no	—
60	C₄	—	724	2	no	—
61	C₂	—	2	1	no	—
62	C₂	#26042183	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26042183
commutator	C₄²×C₁₈₁	C₂×C₄
Frattini	C₄²	C₂×#10624382
Fitting	C₄⋊Q₈×C₁₈₁	C₄
socle	C₂×C₁₈₁	#353
prime radical	C₂²×C₁₈₁	#99
cosocle	#19153816	C₂²
hypercenter	C₄⋊Q₈	#10624382
hypocenter	C₁₈₁	#1411
LCS	G ▷ C₄²×C₁₈₁ ▷ C₂×C₄×C₁₈₁ ▷ C₂²×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
31. C₁₈₁	#1411	semidirect

Maximal subgroups

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

subgroup	index
#26042190	2
#26041658	2
#1411	181