Subgroups — #37535973

Order 23168.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19153762	C₂	1	4	yes	maximal
2	#26041659	C₂	1	1	yes	maximal, characteristic
3	C₄×#15668424	C₂	1	1	yes	maximal, characteristic
4	#494×C₁₈₁	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₇₂₄	—	2	1	no	—
6	C₂×Dic₇₂₄	C₂²	1	2	yes	—
7	#19153816	—	2	1	no	—
8	#19153762	—	2	8	no	—
9	C₂×#15668424	C₂²	1	2	yes	—
10	C₂×Q₁₆×C₁₈₁	—	2	1	no	—
11	C₂×Q₁₆×C₁₈₁	C₂²	1	2	yes	—
12	C₄⋊Q₈×C₁₈₁	—	2	1	no	—
13	C₄×C₈×C₁₈₁	C₂²	1	1	yes	characteristic
14	C₂×Dic₃₆₂	—	2	2	no	—
15	Dic₇₂₄	—	2	4	no	—
16	Dic₇₂₄	—	4	2	no	—
17	C₄⋊Dic₁₈₁	—	4	2	no	—
18	#15668424	D₄	1	4	yes	—
19	C₂×Q₈×C₁₈₁	—	2	2	no	—
20	Q₁₆×C₁₈₁	—	2	4	no	—
21	Q₁₆×C₁₈₁	—	4	2	no	—
22	C₂×C₈×C₁₈₁	D₄	1	1	yes	characteristic
23	C₂×C₈×C₁₈₁	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₁₈₁	—	4	2	no	—
25	C₄²×C₁₈₁	D₄	1	1	yes	characteristic
26	Dic₃₆₂	—	4	2	no	—
27	Dic₃₆₂	—	4	2	no	—
28	C₂×Dic₁₈₁	—	4	2	no	—
29	Q₈×C₁₈₁	—	4	2	no	—
30	Q₈×C₁₈₁	—	4	2	no	—
31	C₂×C₄×C₁₈₁	—	4	2	no	—
32	C₂×C₄×C₁₈₁	D₈	1	2	yes	—
33	C₂×C₄×C₁₈₁	C₂×D₄	1	1	yes	characteristic
34	C₈×C₁₈₁	D₈	1	2	yes	—
35	C₈×C₁₈₁	C₂×D₄	1	2	yes	—
36	C₂²×C₁₈₁	C₂×D₈	1	1	yes	characteristic
37	C₄×C₁₈₁	—	8	2	no	—
38	C₄×C₁₈₁	Q₃₂	1	4	yes	complemented
39	C₄×C₁₈₁	#127	1	1	yes	characteristic
40	C₄×C₁₈₁	C₂×D₈	1	1	yes	characteristic
41	Dic₁₈₁	—	8	2	no	—
42	C₂×C₁₈₁	#493	1	1	yes	characteristic
43	C₂×C₁₈₁	C₂×Q₃₂	1	2	yes	—
44	C₁₈₁	#2247	1	1	yes	characteristic, complemented, Sylow
45	#2247	—	181	1	no	maximal, Sylow
46	C₂×Q₃₂	—	181	4	no	—
47	#494	—	181	1	no	—
48	#494	D₁₈₁	1	1	yes	characteristic
49	C₄×C₁₆	—	181	1	no	—
50	C₂×Q₁₆	—	2	1	no	—
51	C₂×Q₁₆	—	362	1	no	—
52	C₂×Q₁₆	—	181	2	no	—
53	C₂×Q₁₆	C₂×D₁₈₁	1	2	yes	—
54	C₄⋊Q₈	—	2	1	no	—
55	C₄⋊Q₈	—	362	1	no	—
56	Q₃₂	—	362	8	no	—
57	C₂×C₁₆	—	181	2	no	—
58	C₄×C₈	C₂×D₁₈₁	1	1	yes	characteristic
59	C₂×Q₈	—	2	2	no	—
60	C₂×Q₈	—	362	2	no	—
61	Q₁₆	—	2	4	no	—
62	Q₁₆	—	4	2	no	—
63	Q₁₆	—	362	4	no	—
64	Q₁₆	—	724	2	no	—
65	C₂×C₈	C₂²⋊D₁₈₁	1	1	yes	characteristic
66	C₂×C₈	C₂²×D₁₈₁	1	1	yes	characteristic
67	C₄⋊C₄	—	4	2	no	—
68	C₄⋊C₄	—	724	2	no	—
69	C₄²	C₂²⋊D₁₈₁	1	1	yes	characteristic
70	C₁₆	—	181	4	no	—
71	Q₈	—	4	2	no	—
72	Q₈	—	4	2	no	—
73	Q₈	—	724	2	no	—
74	Q₈	—	724	2	no	—
75	C₂×C₄	—	4	2	no	—
76	C₂×C₄	—	724	2	no	—
77	C₂×C₄	#15668434	1	2	yes	—
78	C₂×C₄	C₂×C₂²⋊D₁₈₁	1	1	yes	characteristic
79	C₈	#15668434	1	2	yes	—
80	C₈	D₄×D₁₈₁	1	2	yes	—
81	C₂²	C₂×#15668434	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	1448	2	no	—
84	C₄	#19153762	1	4	yes	complemented
85	C₄	#19153812	1	1	yes	characteristic
86	C₄	C₂×#15668434	1	1	yes	characteristic
87	C₂	#26041655	1	1	yes	characteristic
88	C₂	C₂×#19153762	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#15668434
commutator, cosocle	C₂×C₈×C₁₈₁	C₂³
Frattini	C₂×C₈	C₂²×D₁₈₁
Fitting	#494×C₁₈₁	C₂
socle, prime radical	C₂²×C₁₈₁	C₂×D₈
hypercenter	#494	D₁₈₁
hypocenter	C₁₈₁	#2247
LCS	G ▷ C₂×C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
38. C₄×C₁₈₁	Q₃₂	semidirect
44. C₁₈₁	#2247	semidirect
84. C₄	#19153762	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19153762	2
#26041659	2
C₄×#15668424	2
#494×C₁₈₁	2
#2247	181