Subgroups — #37548752

Order 23168.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042142	C₂	1	2	yes	maximal
2	C₁₆×Dic₁₈₁	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#13089685	—	2	2	no	—
4	C₂×#15668424	C₄	1	1	yes	characteristic
5	C₈×Dic₁₈₁	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₁₈₁	C₄	1	1	yes	characteristic
7	C₂×#13089685	—	4	2	no	—
8	C₂×#13089678	Q₈	1	1	yes	characteristic
9	C₄×Dic₁₈₁	D₄	1	1	yes	characteristic
10	#15668424	—	2	1	no	—
11	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₈₁	C₈	1	2	yes	complemented
13	#13089685	—	8	2	no	—
14	C₂×Dic₁₈₁	D₈	1	1	yes	characteristic
15	C₂×Dic₁₈₁	Q₁₆	1	1	yes	characteristic
16	#13089678	—	2	1	no	—
17	C₂×C₄×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₁₈₁	C₂×C₈	1	1	yes	characteristic
19	C₈×C₁₈₁	M₁₆	1	1	yes	characteristic
20	C₂²×C₁₈₁	#107	1	1	yes	characteristic
21	C₄×C₁₈₁	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₁₈₁	#108	1	1	yes	characteristic
23	Dic₁₈₁	—	2	1	no	—
24	Dic₁₈₁	D₁₆	1	1	yes	characteristic
25	Dic₁₈₁	Q₃₂	1	1	yes	characteristic
26	C₂×C₁₈₁	#335	1	1	yes	characteristic
27	C₂×C₁₈₁	#366	1	1	yes	characteristic
28	C₂×C₁₈₁	#368	1	1	yes	characteristic
29	C₁₈₁	#1371	1	1	yes	characteristic, complemented, Sylow
30	#1371	—	181	1	no	maximal, Sylow
31	C₄×C₁₆	—	181	1	no	—
32	#335	—	181	2	no	—
33	C₂×C₁₆	—	181	1	no	—
34	C₂×C₁₆	#10624382	1	1	yes	characteristic
35	C₄⋊C₈	—	362	2	no	—
36	C₄×C₈	—	181	1	no	—
37	C₂×C₈	—	181	1	no	—
38	C₂×C₈	—	724	2	no	—
39	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
40	C₄²	—	181	1	no	—
41	C₁₆	—	362	1	no	—
42	C₁₆	#13089685	1	2	yes	complemented
43	C₂×C₄	—	181	1	no	—
44	C₂×C₄	—	181	1	no	—
45	C₂×C₄	C₄⋊#10624382	1	1	yes	characteristic
46	C₈	—	362	1	no	—
47	C₈	—	1448	2	no	—
48	C₈	C₂×#13089685	1	1	yes	characteristic
49	C₈	#15668459	1	1	yes	characteristic
50	C₂²	#19153885	1	1	yes	characteristic
51	C₄	—	362	1	no	—
52	C₄	—	181	1	no	—
53	C₄	—	181	1	no	—
54	C₄	C₄⋊#13089685	1	1	yes	characteristic
55	C₄	#19153887	1	1	yes	characteristic
56	C₂	#26042142	1	1	yes	characteristic
57	C₂	#26042205	1	1	yes	characteristic
58	C₂	#26042207	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19153885
commutator	C₈×C₁₈₁	C₂×C₈
Frattini	C₂×C₈	C₂×#10624382
Fitting	C₂×C₁₆×C₁₈₁	C₄
socle, prime radical	C₂²×C₁₈₁	#107
cosocle	C₈×Dic₁₈₁	C₂²
hypercenter	C₂×C₁₆	#10624382
hypocenter	C₁₈₁	#1371
LCS	G ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
12. C₁₆×C₁₈₁	C₈	semidirect
29. C₁₈₁	#1371	semidirect
42. C₁₆	#13089685	semidirect

Maximal subgroups

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

subgroup	index
#26042142	2
C₁₆×Dic₁₈₁	2
#1371	181