Subgroups — #37548669

Order 23168.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042175	C₂	1	2	yes	maximal
2	#26041306	C₂	1	1	yes	maximal, characteristic
3	#19153890	—	2	2	no	—
4	C₂×#15668433	C₂²	1	1	yes	characteristic
5	C₂²×#13089678	C₄	1	1	yes	characteristic
6	C₄⋊#13089678	—	2	2	no	—
7	#117×C₁₈₁	C₄	1	1	yes	characteristic
8	#15668452	—	4	2	no	—
9	#15668433	—	4	1	no	—
10	C₂×#13089678	—	2	1	no	—
11	C₂×#13089678	—	4	1	no	—
12	C₂×#13089678	D₄	1	2	yes	—
13	C₂²×C₄×C₁₈₁	C₂×C₄	1	1	yes	characteristic
14	C₄⋊C₄×C₁₈₁	—	2	1	no	—
15	C₂²⋊C₄×C₁₈₁	C₈	1	2	yes	—
16	C₄²×C₁₈₁	—	2	1	no	—
17	#13089678	—	2	2	no	—
18	#13089678	—	4	1	no	—
19	C₂³×C₁₈₁	C₂×C₈	1	1	yes	characteristic
20	C₂×C₄×C₁₈₁	—	2	1	no	—
21	C₂×C₄×C₁₈₁	—	2	1	no	—
22	C₂×C₄×C₁₈₁	—	2	2	no	—
23	C₂×C₄×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₁₈₁	M₁₆	1	1	yes	characteristic
25	C₂²×C₁₈₁	—	2	1	no	—
26	C₂²×C₁₈₁	—	4	1	no	—
27	C₂²×C₁₈₁	C₂²⋊C₈	1	1	yes	characteristic
28	C₄×C₁₈₁	—	2	1	no	—
29	C₄×C₁₈₁	—	4	2	no	—
30	C₄×C₁₈₁	#99	1	1	yes	characteristic
31	C₄×C₁₈₁	#101	1	1	yes	characteristic
32	C₂×C₁₈₁	—	2	1	no	—
33	C₂×C₁₈₁	—	4	1	no	—
34	C₂×C₁₈₁	#324	1	1	yes	characteristic
35	C₁₈₁	#1328	1	1	yes	characteristic, complemented, Sylow
36	#1328	—	181	1	no	maximal, Sylow
37	#424	—	181	1	no	—
38	#349	—	181	2	no	—
39	C₂×M₁₆	—	181	1	no	—
40	C₂²×C₈	—	181	1	no	—
41	#117	#10624382	1	1	yes	characteristic
42	M₃₂	—	362	2	no	—
43	C₄⋊C₈	—	362	2	no	—
44	C₂²×C₄	C₂×#10624382	1	1	yes	characteristic
45	M₁₆	—	724	1	no	—
46	C₂×C₈	—	362	1	no	—
47	C₂×C₈	—	181	2	no	—
48	C₂×C₈	—	724	1	no	—
49	C₄⋊C₄	—	2	1	no	—
50	C₂²⋊C₄	#13089685	1	2	yes	—
51	C₄²	—	2	1	no	—
52	C₁₆	—	724	2	no	—
53	C₂³	C₂×#13089685	1	1	yes	characteristic
54	C₂×C₄	—	2	1	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	C₂²⋊#10624382	1	1	yes	characteristic
58	C₂×C₄	#15668458	1	1	yes	characteristic
59	C₈	—	362	2	no	—
60	C₈	—	724	1	no	—
61	C₂²	—	2	1	no	—
62	C₂²	—	4	1	no	—
63	C₂²	C₂²⋊#13089685	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	—	4	2	no	—
66	C₄	#19153875	1	1	yes	characteristic
67	C₄	#19153877	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4	1	no	—
70	C₂	#26042124	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19153875
commutator, prime radical	C₂³×C₁₈₁	C₂×C₈
Frattini	C₂²×C₄	C₂×#10624382
Fitting	#117×C₁₈₁	C₄
socle	C₂×C₁₈₁	#324
cosocle	C₂×#15668433	C₂²
hypercenter	#117	#10624382
hypocenter	C₁₈₁	#1328
LCS	G ▷ C₂³×C₁₈₁ ▷ C₂²×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
35. C₁₈₁	#1328	semidirect

Maximal subgroups

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

subgroup	index
#26042175	2
#26041306	2
#1328	181