Subgroups — #37535593

Order 23168.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₄₄₈	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₇₂₄	C₂	1	2	yes	maximal
3	#26041107	C₂	1	1	yes	maximal, characteristic
4	#26041084	C₂	1	2	yes	maximal
5	#346×C₁₈₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₇₂₄	C₂²	1	2	yes	—
7	C₄×Dic₃₆₂	—	2	2	no	—
8	Dic₁₄₄₈	C₄	1	4	yes	complemented
9	#19153750	C₂²	1	2	yes	—
10	#19153741	—	2	2	no	—
11	C₂×C₁₆×C₁₈₁	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₁₈₁	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₁₈₁	C₂²	1	1	yes	characteristic
14	C₂×Dic₃₆₂	—	2	2	no	—
15	Dic₇₂₄	—	2	2	no	—
16	Dic₇₂₄	C₂×C₄	1	4	yes	—
17	C₄⋊Dic₁₈₁	—	2	2	no	—
18	#15668428	—	4	2	no	—
19	C₄×Dic₁₈₁	—	4	2	no	—
20	C₂×C₈×C₁₈₁	D₄	1	1	yes	characteristic
21	C₂×C₈×C₁₈₁	C₂³	1	1	yes	characteristic
22	C₄²×C₁₈₁	D₄	1	1	yes	characteristic
23	C₁₆×C₁₈₁	—	2	1	no	—
24	C₁₆×C₁₈₁	C₂×C₄	1	2	yes	—
25	Dic₃₆₂	—	2	4	no	—
26	Dic₃₆₂	—	4	2	no	—
27	C₂×Dic₁₈₁	—	4	2	no	—
28	C₂×Dic₁₈₁	—	4	2	no	—
29	C₂×C₄×C₁₈₁	D₈	1	2	yes	—
30	C₂×C₄×C₁₈₁	C₂×D₄	1	1	yes	characteristic
31	C₈×C₁₈₁	—	2	1	no	—
32	C₈×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₁₈₁	#41	1	1	yes	characteristic
34	C₂²×C₁₈₁	C₂×D₈	1	1	yes	characteristic
35	C₄×C₁₈₁	—	2	2	no	—
36	C₄×C₁₈₁	C₄×D₄	1	1	yes	characteristic
37	C₄×C₁₈₁	#135	1	1	yes	characteristic
38	Dic₁₈₁	—	4	4	no	—
39	Dic₁₈₁	—	8	2	no	—
40	C₂×C₁₈₁	C₄×D₈	1	1	yes	characteristic
41	C₂×C₁₈₁	#510	1	2	yes	—
42	C₁₈₁	#2176	1	1	yes	characteristic, complemented, Sylow
43	#2176	—	181	1	no	maximal, Sylow
44	C₂×Q₃₂	—	181	1	no	—
45	C₄×Q₁₆	—	181	2	no	—
46	#367	—	181	1	no	—
47	#358	—	181	2	no	—
48	#346	D₁₈₁	1	1	yes	characteristic
49	C₂×Q₁₆	—	181	2	no	—
50	C₄×Q₈	—	362	2	no	—
51	Q₃₂	—	181	4	no	—
52	C₂×C₁₆	C₂×D₁₈₁	1	1	yes	characteristic
53	C₂×C₁₆	C₂×D₁₈₁	1	1	yes	characteristic
54	#107	—	181	2	no	—
55	#103	—	362	2	no	—
56	C₄×C₈	C₂×D₁₈₁	1	1	yes	characteristic
57	C₂×Q₈	—	362	2	no	—
58	Q₁₆	—	362	2	no	—
59	Q₁₆	—	181	4	no	—
60	C₂×C₈	D₇₂₄	1	1	yes	characteristic
61	C₂×C₈	C₂²×D₁₈₁	1	1	yes	characteristic
62	C₄⋊C₄	—	362	2	no	—
63	C₄⋊C₄	—	724	2	no	—
64	C₄²	—	724	2	no	—
65	C₄²	D₇₂₄	1	1	yes	characteristic
66	C₁₆	—	2	1	no	—
67	C₁₆	C₄×D₁₈₁	1	2	yes	—
68	Q₈	—	362	4	no	—
69	Q₈	—	724	2	no	—
70	C₂×C₄	—	724	2	no	—
71	C₂×C₄	—	724	2	no	—
72	C₂×C₄	D₁₄₄₈	1	2	yes	—
73	C₂×C₄	C₂×D₇₂₄	1	1	yes	characteristic
74	C₈	—	2	1	no	—
75	C₈	C₂×C₄×D₁₈₁	1	1	yes	characteristic
76	C₈	#15668449	1	1	yes	characteristic
77	C₂²	C₂×D₁₄₄₈	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	1448	2	no	—
80	C₄	—	724	4	no	—
81	C₄	C₄×D₇₂₄	1	1	yes	characteristic
82	C₄	#19153838	1	1	yes	characteristic
83	C₂	C₄×D₁₄₄₈	1	1	yes	characteristic
84	C₂	#26041722	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₄₄₈
commutator	C₈×C₁₈₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₈₁
Fitting	#346×C₁₈₁	C₂
socle, prime radical	C₂²×C₁₈₁	C₂×D₈
cosocle	C₂×C₈×C₁₈₁	C₂³
hypercenter	#346	D₁₈₁
hypocenter	C₁₈₁	#2176
LCS	G ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
8. Dic₁₄₄₈	C₄	semidirect
42. C₁₈₁	#2176	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₄₄₈	2
C₄×Dic₇₂₄	2
#26041107	2
#26041084	2
#346×C₁₈₁	2
#2176	181