Subgroups — #37535977

Order 23168.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19153761	C₂	1	4	yes	maximal, complemented
2	#26041659	C₂	1	1	yes	maximal, characteristic, complemented
3	#26041656	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₆×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₇₂₄	—	2	1	no	—
6	C₂×Dic₇₂₄	C₂²	1	2	yes	—
7	C₂×D₁₄₄₈	—	2	1	no	—
8	C₂×D₁₄₄₈	C₂²	1	2	yes	—
9	#19153816	—	2	1	no	—
10	#19153813	—	2	1	no	—
11	#19153761	—	2	8	no	—
12	C₂×C₁₆×C₁₈₁	C₂²	1	2	yes	—
13	C₄×C₈×C₁₈₁	C₂²	1	1	yes	characteristic
14	C₂×Dic₃₆₂	—	2	2	no	—
15	C₂×D₇₂₄	—	2	2	no	—
16	C₂×D₇₂₄	—	4	2	no	—
17	Dic₇₂₄	—	2	4	no	—
18	Dic₇₂₄	—	4	2	no	—
19	D₁₄₄₈	—	2	4	no	—
20	D₁₄₄₈	—	4	2	no	—
21	C₄⋊Dic₁₈₁	—	4	2	no	—
22	C₂×C₈×C₁₈₁	D₄	1	1	yes	characteristic
23	C₂×C₈×C₁₈₁	C₂³	1	1	yes	characteristic
24	C₄²×C₁₈₁	D₄	1	1	yes	characteristic
25	C₁₆×C₁₈₁	D₄	1	4	yes	complemented
26	C₂²×D₁₈₁	—	4	2	no	—
27	Dic₃₆₂	—	4	2	no	—
28	Dic₃₆₂	—	4	2	no	—
29	D₇₂₄	—	4	2	no	—
30	D₇₂₄	—	4	2	no	—
31	D₇₂₄	—	8	4	no	—
32	C₂×Dic₁₈₁	—	4	2	no	—
33	C₂×C₄×C₁₈₁	D₈	1	2	yes	—
34	C₂×C₄×C₁₈₁	C₂×D₄	1	1	yes	characteristic
35	C₈×C₁₈₁	D₈	1	2	yes	—
36	C₈×C₁₈₁	C₂×D₄	1	2	yes	—
37	C₂²×C₁₈₁	C₂×D₈	1	1	yes	characteristic
38	C₂×D₁₈₁	—	8	2	no	—
39	C₂×D₁₈₁	—	8	4	no	—
40	C₄×C₁₈₁	SD₃₂	1	4	yes	complemented
41	C₄×C₁₈₁	#127	1	1	yes	characteristic
42	C₄×C₁₈₁	C₂×D₈	1	1	yes	characteristic
43	Dic₁₈₁	—	8	2	no	—
44	C₂×C₁₈₁	#493	1	1	yes	characteristic
45	C₂×C₁₈₁	C₂×SD₃₂	1	2	yes	—
46	D₁₈₁	—	16	2	no	—
47	C₁₈₁	#2248	1	1	yes	characteristic, complemented, Sylow
48	#2248	—	181	1	no	maximal, Sylow
49	C₂×SD₃₂	—	181	4	no	—
50	#494	—	181	1	no	—
51	#493	—	181	1	no	—
52	C₄×C₁₆	D₁₈₁	1	1	yes	characteristic, complemented
53	C₂×Q₁₆	—	362	1	no	—
54	C₂×Q₁₆	—	181	2	no	—
55	C₂×D₈	—	362	1	no	—
56	C₂×D₈	—	181	2	no	—
57	C₄⋊Q₈	—	362	1	no	—
58	#127	—	362	1	no	—
59	SD₃₂	—	362	8	no	—
60	C₂×C₁₆	C₂×D₁₈₁	1	2	yes	—
61	C₄×C₈	C₂×D₁₈₁	1	1	yes	characteristic
62	C₂×Q₈	—	362	2	no	—
63	C₂×D₄	—	362	2	no	—
64	C₂×D₄	—	724	2	no	—
65	Q₁₆	—	362	4	no	—
66	Q₁₆	—	724	2	no	—
67	D₈	—	362	4	no	—
68	D₈	—	724	2	no	—
69	C₂×C₈	D₇₂₄	1	1	yes	characteristic
70	C₂×C₈	C₂²×D₁₈₁	1	1	yes	characteristic
71	C₄⋊C₄	—	724	2	no	—
72	C₄²	D₇₂₄	1	1	yes	characteristic
73	C₁₆	D₇₂₄	1	4	yes	complemented
74	C₂³	—	724	2	no	—
75	Q₈	—	724	2	no	—
76	Q₈	—	724	2	no	—
77	D₄	—	1448	4	no	—
78	D₄	—	724	2	no	—
79	D₄	—	724	2	no	—
80	C₂×C₄	—	724	2	no	—
81	C₂×C₄	D₁₄₄₈	1	2	yes	—
82	C₂×C₄	C₂×D₇₂₄	1	1	yes	characteristic
83	C₈	D₁₄₄₈	1	2	yes	—
84	C₈	C₂×D₇₂₄	1	2	yes	—
85	C₂²	—	1448	2	no	—
86	C₂²	—	1448	4	no	—
87	C₂²	C₂×D₁₄₄₈	1	1	yes	characteristic
88	C₄	—	1448	2	no	—
89	C₄	#19153761	1	4	yes	complemented
90	C₄	#19153813	1	1	yes	characteristic
91	C₄	C₂×D₁₄₄₈	1	1	yes	characteristic
92	C₂	—	2896	2	no	—
93	C₂	#26041656	1	1	yes	characteristic
94	C₂	C₂×#19153761	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₄₄₈
commutator, cosocle	C₂×C₈×C₁₈₁	C₂³
Frattini	C₂×C₈	C₂²×D₁₈₁
Fitting	C₄×C₁₆×C₁₈₁	C₂
socle	C₂²×C₁₈₁	C₂×D₈
prime radical	#26041656	C₂
hypercenter	C₄×C₁₆	D₁₈₁
hypocenter	C₁₈₁	#2248
LCS	G ▷ C₂×C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#19153761	C₂	semidirect
2. #26041659	C₂	semidirect
4. C₄×C₁₆×C₁₈₁	C₂	semidirect
25. C₁₆×C₁₈₁	D₄	semidirect
40. C₄×C₁₈₁	SD₃₂	semidirect
47. C₁₈₁	#2248	semidirect
52. C₄×C₁₆	D₁₈₁	semidirect
73. C₁₆	D₇₂₄	semidirect
89. C₄	#19153761	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19153761	2
#26041659	2
#26041656	2
C₄×C₁₆×C₁₈₁	2
#2248	181