Subgroups — #37548674

Order 23168.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#15668452	C₂	1	1	yes	maximal, characteristic, complemented
2	#26042167	C₂	1	1	yes	maximal, characteristic, complemented
3	#26041356	C₂	1	1	yes	maximal, characteristic
4	C₂×#15668452	—	2	1	no	—
5	C₂×#15668452	—	2	1	no	—
6	C₂×#15668432	—	2	1	no	—
7	C₄×D₇₂₄	C₄	1	1	yes	characteristic
8	#19153728	—	2	1	no	—
9	C₄×#13089678	C₂²	1	1	yes	characteristic
10	C₄⋊C₈×C₁₈₁	C₄	1	1	yes	characteristic
11	#15668452	—	2	2	no	—
12	#15668452	—	4	1	no	—
13	C₂×D₇₂₄	C₈	1	1	yes	characteristic
14	C₂×C₄×D₁₈₁	—	2	1	no	—
15	#15668432	—	4	1	no	—
16	#15668432	—	4	1	no	—
17	C₂×#13089678	D₄	1	1	yes	characteristic
18	C₂×#13089678	D₄	1	1	yes	characteristic
19	C₄⋊Dic₁₈₁	C₈	1	1	yes	characteristic
20	#15668426	—	2	1	no	—
21	C₂×C₈×C₁₈₁	—	2	1	no	—
22	C₄²×C₁₈₁	C₂×C₄	1	1	yes	characteristic
23	C₂²×D₁₈₁	—	2	1	no	—
24	D₇₂₄	—	4	1	no	—
25	C₂×Dic₁₈₁	—	2	1	no	—
26	C₄×D₁₈₁	—	4	1	no	—
27	C₄×D₁₈₁	—	4	1	no	—
28	#13089678	—	2	1	no	—
29	#13089678	D₈	1	1	yes	characteristic
30	#13089678	SD₁₆	1	1	yes	characteristic
31	C₂×C₄×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₈₁	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₁₈₁	M₁₆	1	1	yes	characteristic
34	C₈×C₁₈₁	—	4	1	no	—
35	C₂²×C₁₈₁	C₂²⋊C₈	1	1	yes	characteristic
36	C₂×D₁₈₁	—	4	1	no	—
37	C₂×D₁₈₁	—	4	1	no	—
38	C₂×D₁₈₁	—	4	1	no	—
39	C₄×C₁₈₁	—	2	1	no	—
40	C₄×C₁₈₁	—	2	1	no	—
41	C₄×C₁₈₁	#102	1	1	yes	characteristic
42	C₄×C₁₈₁	#104	1	1	yes	characteristic
43	Dic₁₈₁	—	4	1	no	—
44	C₂×C₁₈₁	D₄⋊C₈	1	1	yes	characteristic
45	C₂×C₁₈₁	#349	1	1	yes	characteristic
46	C₂×C₁₈₁	#350	1	1	yes	characteristic
47	D₁₈₁	—	8	1	no	—
48	C₁₈₁	#1330	1	1	yes	characteristic, complemented, Sylow
49	#1330	—	181	1	no	maximal, Sylow
50	#436	—	181	1	no	—
51	C₄⋊C₁₆	—	181	1	no	—
52	#346	—	181	1	no	—
53	C₂×M₁₆	—	362	1	no	—
54	C₄×D₄	—	181	1	no	—
55	C₂×C₁₆	—	362	1	no	—
56	C₂×C₁₆	—	362	1	no	—
57	C₄⋊C₈	#10624382	1	1	yes	characteristic
58	C₂²⋊C₈	—	362	1	no	—
59	C₄×C₈	—	181	1	no	—
60	C₂×D₄	—	181	1	no	—
61	C₂²×C₄	—	362	1	no	—
62	M₁₆	—	724	1	no	—
63	M₁₆	—	724	1	no	—
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	—	181	1	no	—
66	C₂×C₈	—	181	1	no	—
67	C₄⋊C₄	—	181	1	no	—
68	C₂²⋊C₄	—	362	1	no	—
69	C₄²	C₂×#10624382	1	1	yes	characteristic
70	C₁₆	—	362	2	no	—
71	C₁₆	—	724	1	no	—
72	C₂³	—	362	1	no	—
73	D₄	—	724	1	no	—
74	C₂×C₄	—	362	1	no	—
75	C₂×C₄	—	724	1	no	—
76	C₂×C₄	—	724	1	no	—
77	C₂×C₄	C₂²⋊#10624382	1	1	yes	characteristic
78	C₂×C₄	D₁₈₁⋊C₈	1	1	yes	characteristic
79	C₂×C₄	#15668459	1	1	yes	characteristic
80	C₈	—	4	1	no	—
81	C₈	—	362	1	no	—
82	C₈	—	181	1	no	—
83	C₈	—	181	1	no	—
84	C₂²	—	724	1	no	—
85	C₂²	—	724	1	no	—
86	C₂²	—	724	1	no	—
87	C₂²	#19153873	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	2	1	no	—
90	C₄	—	724	1	no	—
91	C₄	#19153878	1	1	yes	characteristic
92	C₄	#19153881	1	1	yes	characteristic
93	C₂	—	1448	1	no	—
94	C₂	#26042127	1	1	yes	characteristic
95	C₂	#26042176	1	1	yes	characteristic
96	C₂	#26042178	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#10624382
commutator	C₂×C₄×C₁₈₁	C₂×C₈
Frattini	C₄²	C₂×#10624382
Fitting	C₄⋊C₈×C₁₈₁	C₄
socle	C₂²×C₁₈₁	C₂²⋊C₈
prime radical	C₂×D₇₂₄	C₈
cosocle	C₄×#13089678	C₂²
hypercenter	C₄⋊C₈	#10624382
hypocenter	C₁₈₁	#1330
LCS	G ▷ C₂×C₄×C₁₈₁ ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₄⋊#15668452	C₂	semidirect
2. #26042167	C₂	semidirect
48. C₁₈₁	#1330	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
#26042167	2
#26041356	2
#1330	181