Subgroups — #37548634

Order 23168.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#15668452	C₂	1	2	yes	maximal
2	C₈×#13089678	C₂	1	1	yes	maximal, characteristic
3	C₂×#15668452	C₄	1	4	yes	—
4	C₄×#13089678	C₄	1	1	yes	characteristic
5	C₄×#13089678	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₁₈₁	C₄	1	1	yes	characteristic
7	#15668452	—	2	4	no	—
8	C₂×#13089678	C₈	1	2	yes	—
9	C₂×#13089678	C₂×C₄	1	2	yes	—
10	C₂×C₈×C₁₈₁	C₈	1	2	yes	—
11	C₄²×C₁₈₁	C₂×C₄	1	1	yes	characteristic
12	#13089678	—	2	2	no	—
13	#13089678	M₁₆	1	4	yes	—
14	C₂×C₄×C₁₈₁	C₄²	1	1	yes	characteristic
15	C₂×C₄×C₁₈₁	C₂×C₈	1	1	yes	characteristic
16	C₂×C₄×C₁₈₁	C₂×C₈	1	1	yes	characteristic
17	C₈×C₁₈₁	C₁₆	1	4	yes	complemented
18	C₂²×C₁₈₁	C₄×C₈	1	1	yes	characteristic
19	C₄×C₁₈₁	#97	1	2	yes	—
20	C₄×C₁₈₁	C₂×C₁₆	1	2	yes	—
21	C₄×C₁₈₁	M₃₂	1	2	yes	—
22	C₂×C₁₈₁	#322	1	1	yes	characteristic
23	C₂×C₁₈₁	C₄×C₁₆	1	1	yes	characteristic
24	C₂×C₁₈₁	#346	1	1	yes	characteristic
25	C₁₈₁	#1312	1	1	yes	characteristic, complemented, Sylow
26	#1312	—	181	1	no	maximal, Sylow
27	C₄×C₁₆	—	181	2	no	—
28	C₈²	—	181	1	no	—
29	C₂×C₁₆	—	181	4	no	—
30	C₄×C₈	—	181	1	no	—
31	C₄×C₈	—	181	1	no	—
32	C₄×C₈	#10624382	1	1	yes	characteristic
33	C₂×C₈	—	181	2	no	—
34	C₂×C₈	—	181	2	no	—
35	C₂×C₈	#13089685	1	2	yes	—
36	C₄²	C₂×#10624382	1	1	yes	characteristic
37	C₁₆	—	362	4	no	—
38	C₂×C₄	C₄×#10624382	1	1	yes	characteristic
39	C₂×C₄	C₂×#13089685	1	1	yes	characteristic
40	C₂×C₄	D₁₈₁⋊C₈	1	1	yes	characteristic
41	C₈	—	362	2	no	—
42	C₈	—	181	4	no	—
43	C₈	#15668452	1	4	yes	complemented
44	C₂²	C₄×#13089685	1	1	yes	characteristic
45	C₄	#19153870	1	2	yes	—
46	C₄	C₂×#15668452	1	2	yes	—
47	C₄	#19153891	1	2	yes	—
48	C₂	#26042120	1	1	yes	characteristic
49	C₂	C₄×#15668452	1	1	yes	characteristic
50	C₂	#26042168	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂×#10624382
commutator	C₂×C₁₈₁	C₄×C₁₆
Fitting	C₄×C₈×C₁₈₁	C₄
socle, prime radical	C₂²×C₁₈₁	C₄×C₈
cosocle	C₄×#13089678	C₂²
hypercenter	C₄×C₈	#10624382
hypocenter	C₁₈₁	#1312
LCS	G ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
17. C₈×C₁₈₁	C₁₆	semidirect
25. C₁₈₁	#1312	semidirect
43. C₈	#15668452	semidirect

Maximal subgroups

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

subgroup	index
C₄×#15668452	2
C₈×#13089678	2
#1312	181