Subgroups — #37548688

Order 23168.

94 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
2	C₄×#15668452	C₂	1	1	yes	maximal, characteristic
3	#26041403	C₂	1	1	yes	maximal, characteristic
4	C₂×#15668452	—	2	1	no	—
5	C₂×#15668452	—	2	1	no	—
6	C₄×Dic₃₆₂	C₄	1	1	yes	characteristic
7	#19153745	—	2	1	no	—
8	C₄×#13089678	C₂²	1	1	yes	characteristic
9	C₈×Dic₁₈₁	—	2	1	no	—
10	C₄⋊C₈×C₁₈₁	C₄	1	1	yes	characteristic
11	#15668452	—	2	2	no	—
12	#15668452	—	4	1	no	—
13	C₂×Dic₃₆₂	C₈	1	1	yes	characteristic
14	C₂×#13089678	D₄	1	1	yes	characteristic
15	C₂×#13089678	D₄	1	1	yes	characteristic
16	C₄⋊Dic₁₈₁	C₈	1	1	yes	characteristic
17	#15668428	—	2	1	no	—
18	C₄×Dic₁₈₁	—	2	1	no	—
19	C₂×C₈×C₁₈₁	—	2	1	no	—
20	C₄²×C₁₈₁	C₂×C₄	1	1	yes	characteristic
21	Dic₃₆₂	—	2	1	no	—
22	Dic₃₆₂	C₁₆	1	2	yes	complemented
23	C₂×Dic₁₈₁	—	2	1	no	—
24	C₂×Dic₁₈₁	—	2	1	no	—
25	#13089678	—	2	1	no	—
26	#13089678	SD₁₆	1	1	yes	characteristic
27	#13089678	Q₁₆	1	1	yes	characteristic
28	C₂×C₄×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₈₁	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₁₈₁	M₁₆	1	1	yes	characteristic
31	C₈×C₁₈₁	—	4	1	no	—
32	C₂²×C₁₈₁	C₂²⋊C₈	1	1	yes	characteristic
33	C₄×C₁₈₁	—	2	1	no	—
34	C₄×C₁₈₁	#103	1	1	yes	characteristic
35	C₄×C₁₈₁	#104	1	1	yes	characteristic
36	C₄×C₁₈₁	C₂×C₁₆	1	1	yes	characteristic
37	C₄×C₁₈₁	M₃₂	1	1	yes	characteristic
38	Dic₁₈₁	—	2	2	no	—
39	Dic₁₈₁	—	4	1	no	—
40	C₂×C₁₈₁	Q₈⋊C₈	1	1	yes	characteristic
41	C₂×C₁₈₁	C₂²⋊C₁₆	1	1	yes	characteristic
42	C₂×C₁₈₁	#350	1	1	yes	characteristic
43	C₁₈₁	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
44	Q₈⋊C₁₆	—	181	1	no	maximal, Sylow
45	C₈×Q₈	—	181	1	no	—
46	C₄⋊C₁₆	—	181	1	no	—
47	C₄×C₁₆	—	181	1	no	—
48	C₄×Q₈	—	181	1	no	—
49	C₂×C₁₆	—	362	1	no	—
50	C₂×C₁₆	—	362	1	no	—
51	C₄⋊C₈	—	362	1	no	—
52	C₄⋊C₈	#10624382	1	1	yes	characteristic
53	C₄×C₈	—	362	1	no	—
54	C₄×C₈	—	181	1	no	—
55	C₂×Q₈	—	181	1	no	—
56	C₂×C₈	—	2	1	no	—
57	C₂×C₈	—	181	1	no	—
58	C₂×C₈	—	181	1	no	—
59	C₄⋊C₄	—	362	1	no	—
60	C₄⋊C₄	—	181	1	no	—
61	C₄²	—	362	1	no	—
62	C₄²	C₂×#10624382	1	1	yes	characteristic
63	C₁₆	—	362	2	no	—
64	C₁₆	—	724	1	no	—
65	Q₈	—	362	1	no	—
66	Q₈	—	181	2	no	—
67	C₂×C₄	—	362	1	no	—
68	C₂×C₄	—	362	1	no	—
69	C₂×C₄	C₂²⋊#10624382	1	1	yes	characteristic
70	C₂×C₄	D₁₈₁⋊C₈	1	1	yes	characteristic
71	C₂×C₄	#15668459	1	1	yes	characteristic
72	C₈	—	4	1	no	—
73	C₈	—	362	1	no	—
74	C₈	—	181	1	no	—
75	C₈	—	181	1	no	—
76	C₂²	#19153873	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	362	2	no	—
79	C₄	—	724	1	no	—
80	C₄	#19153879	1	1	yes	characteristic
81	C₄	#19153880	1	1	yes	characteristic
82	C₄	D₁₈₁⋊C₁₆	1	1	yes	characteristic
83	C₄	#19153891	1	1	yes	characteristic
84	C₂	#26042129	1	1	yes	characteristic
85	C₂	#26042174	1	1	yes	characteristic
86	C₂	#26042178	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#10624382
commutator	C₄×C₁₈₁	C₂×C₁₆
Frattini	C₄²	C₂×#10624382
Fitting	C₄⋊C₈×C₁₈₁	C₄
socle, prime radical	C₂²×C₁₈₁	C₂²⋊C₈
cosocle	C₄×#13089678	C₂²
hypercenter	C₄⋊C₈	#10624382
hypocenter	C₁₈₁	Q₈⋊C₁₆
LCS	G ▷ C₄×C₁₈₁ ▷ C₂×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
22. Dic₃₆₂	C₁₆	semidirect
43. C₁₈₁	Q₈⋊C₁₆	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
C₄×#15668452	2
#26041403	2
Q₈⋊C₁₆	181