Subgroups — #37548865

Order 23168.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042190	C₂	1	2	yes	maximal
2	#26041648	C₂	1	1	yes	maximal, characteristic
3	#19153877	—	2	2	no	—
4	#19153816	C₂²	1	1	yes	characteristic
5	#19153808	C₄	1	1	yes	characteristic
6	#19153741	—	2	2	no	—
7	#97×C₁₈₁	C₄	1	1	yes	characteristic
8	#15668458	—	4	2	no	—
9	C₂×Dic₃₆₂	D₄	1	2	yes	—
10	C₄⋊Dic₁₈₁	—	2	1	no	—
11	C₄⋊Dic₁₈₁	—	4	1	no	—
12	#15668428	—	4	1	no	—
13	C₂×C₈×C₁₈₁	—	2	1	no	—
14	C₄²×C₁₈₁	C₂×C₄	1	1	yes	characteristic
15	#13089685	—	8	2	no	—
16	Dic₃₆₂	—	4	2	no	—
17	C₂×Dic₁₈₁	—	2	2	no	—
18	C₂×Dic₁₈₁	—	4	1	no	—
19	C₂×C₄×C₁₈₁	—	2	1	no	—
20	C₂×C₄×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₈×C₁₈₁	—	4	1	no	—
22	C₂²×C₁₈₁	#99	1	1	yes	characteristic
23	C₄×C₁₈₁	—	2	1	no	—
24	C₄×C₁₈₁	—	4	1	no	—
25	Dic₁₈₁	—	4	2	no	—
26	Dic₁₈₁	—	8	1	no	—
27	C₂×C₁₈₁	—	2	1	no	—
28	C₂×C₁₈₁	#354	1	1	yes	characteristic
29	C₁₈₁	#1413	1	1	yes	characteristic, complemented, Sylow
30	#1413	—	181	1	no	maximal, Sylow
31	#491	—	181	1	no	—
32	#356	—	181	2	no	—
33	C₄⋊Q₈	—	181	1	no	—
34	#125	—	181	1	no	—
35	#103	—	362	2	no	—
36	#101	—	362	2	no	—
37	#97	#10624382	1	1	yes	characteristic
38	C₂×Q₈	—	181	2	no	—
39	M₁₆	—	724	2	no	—
40	C₂×C₈	—	2	1	no	—
41	C₄⋊C₄	—	362	1	no	—
42	C₄⋊C₄	—	724	1	no	—
43	C₄⋊C₄	—	724	1	no	—
44	C₄²	C₂×#10624382	1	1	yes	characteristic
45	Q₈	—	724	2	no	—
46	C₂×C₄	—	2	1	no	—
47	C₂×C₄	—	362	2	no	—
48	C₂×C₄	—	724	1	no	—
49	C₂×C₄	C₂²⋊#10624382	1	1	yes	characteristic
50	C₈	—	4	1	no	—
51	C₈	—	1448	2	no	—
52	C₂²	#19153875	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	4	1	no	—
55	C₄	—	1448	1	no	—
56	C₄	—	724	2	no	—
57	C₂	—	2	1	no	—
58	C₂	#26042186	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26042186
commutator	C₄²×C₁₈₁	C₂×C₄
Frattini	C₄²	C₂×#10624382
Fitting	#97×C₁₈₁	C₄
socle	C₂×C₁₈₁	#354
prime radical	C₂²×C₁₈₁	#99
cosocle	#19153816	C₂²
hypercenter	#97	#10624382
hypocenter	C₁₈₁	#1413
LCS	G ▷ C₄²×C₁₈₁ ▷ C₂×C₄×C₁₈₁ ▷ C₂²×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
29. C₁₈₁	#1413	semidirect

Maximal subgroups

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

subgroup	index
#26042190	2
#26041648	2
#1413	181