Subgroups — #37548736

Order 23168.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042200	C₂	1	1	yes	maximal, characteristic
2	#26042143	C₂	1	1	yes	maximal, characteristic
3	#26041657	C₂	1	1	yes	maximal, characteristic
4	C₂×#15668452	—	2	1	no	—
5	C₄⋊#13089685	—	2	1	no	—
6	C₂×Dic₇₂₄	C₄	1	1	yes	characteristic
7	C₂×#15668439	—	2	1	no	—
8	#19153814	—	2	1	no	—
9	C₈×Dic₁₈₁	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆×C₁₈₁	C₄	1	1	yes	characteristic
11	C₂×#13089685	—	4	1	no	—
12	#15668452	—	4	1	no	—
13	C₂×Dic₃₆₂	—	2	1	no	—
14	Dic₇₂₄	—	4	1	no	—
15	#15668439	—	4	1	no	—
16	#15668439	—	4	1	no	—
17	C₂×#13089678	D₄	1	1	yes	characteristic
18	#15668428	—	4	1	no	—
19	#15668428	—	4	1	no	—
20	C₄×Dic₁₈₁	D₄	1	1	yes	characteristic
21	C₂×Q₈×C₁₈₁	—	2	1	no	—
22	Q₁₆×C₁₈₁	—	4	1	no	—
23	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
24	#13089685	—	8	1	no	—
25	Dic₃₆₂	—	4	1	no	—
26	Dic₃₆₂	—	4	1	no	—
27	C₂×Dic₁₈₁	—	4	1	no	—
28	C₂×Dic₁₈₁	D₈	1	1	yes	characteristic
29	C₂×Dic₁₈₁	SD₁₆	1	1	yes	characteristic
30	#13089678	D₈	1	1	yes	characteristic
31	#13089678	SD₁₆	1	1	yes	characteristic
32	Q₈×C₁₈₁	—	4	1	no	—
33	Q₈×C₁₈₁	—	4	1	no	—
34	C₂×C₄×C₁₈₁	—	4	1	no	—
35	C₂×C₄×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
36	C₈×C₁₈₁	—	2	1	no	—
37	C₂²×C₁₈₁	#102	1	1	yes	characteristic
38	C₄×C₁₈₁	—	8	1	no	—
39	C₄×C₁₈₁	#100	1	1	yes	characteristic
40	C₄×C₁₈₁	#102	1	1	yes	characteristic
41	Dic₁₈₁	—	2	1	no	—
42	Dic₁₈₁	—	8	1	no	—
43	Dic₁₈₁	SD₃₂	1	1	yes	characteristic
44	Dic₁₈₁	Q₃₂	1	1	yes	characteristic
45	C₂×C₁₈₁	#331	1	1	yes	characteristic
46	C₂×C₁₈₁	#358	1	1	yes	characteristic
47	C₂×C₁₈₁	#362	1	1	yes	characteristic
48	C₁₈₁	#1362	1	1	yes	characteristic, complemented, Sylow
49	#1362	—	181	1	no	maximal, Sylow
50	#494	—	181	1	no	—
51	C₄⋊C₁₆	—	181	1	no	—
52	#335	—	181	1	no	—
53	C₂×Q₁₆	—	362	1	no	—
54	C₂×Q₁₆	—	181	1	no	—
55	C₂×Q₁₆	#10624382	1	1	yes	characteristic
56	C₄⋊Q₈	—	362	1	no	—
57	C₂×C₁₆	—	362	1	no	—
58	C₄⋊C₈	—	362	1	no	—
59	C₄×C₈	—	181	1	no	—
60	C₂×Q₈	—	2	1	no	—
61	C₂×Q₈	—	362	1	no	—
62	Q₁₆	—	4	1	no	—
63	Q₁₆	—	724	1	no	—
64	Q₁₆	—	724	1	no	—
65	Q₁₆	—	724	1	no	—
66	C₂×C₈	—	181	1	no	—
67	C₂×C₈	—	724	1	no	—
68	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
69	C₄⋊C₄	—	724	1	no	—
70	C₄⋊C₄	—	724	1	no	—
71	C₄²	—	181	1	no	—
72	C₁₆	—	724	1	no	—
73	Q₈	—	4	1	no	—
74	Q₈	—	4	1	no	—
75	Q₈	—	724	1	no	—
76	Q₈	—	724	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	181	1	no	—
79	C₂×C₄	—	181	1	no	—
80	C₂×C₄	—	724	1	no	—
81	C₂×C₄	C₂²⋊#10624382	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	1448	1	no	—
84	C₈	—	181	1	no	—
85	C₈	—	181	1	no	—
86	C₂²	#19153878	1	1	yes	characteristic
87	C₄	—	8	1	no	—
88	C₄	—	362	1	no	—
89	C₄	—	1448	1	no	—
90	C₄	—	181	1	no	—
91	C₄	—	181	1	no	—
92	C₄	#19153876	1	1	yes	characteristic
93	C₄	#19153878	1	1	yes	characteristic
94	C₂	#26042137	1	1	yes	characteristic
95	C₂	#26042192	1	1	yes	characteristic
96	C₂	#26042198	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19153878
commutator	C₂×C₈×C₁₈₁	C₂×C₄
Frattini	C₂×C₈	C₂×#10624382
Fitting	C₂×Q₁₆×C₁₈₁	C₄
socle, prime radical	C₂²×C₁₈₁	#102
cosocle	C₈×Dic₁₈₁	C₂²
hypercenter	C₂×Q₁₆	#10624382
hypocenter	C₁₈₁	#1362
LCS	G ▷ C₂×C₈×C₁₈₁ ▷ C₂×C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
48. C₁₈₁	#1362	semidirect

Maximal subgroups

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

subgroup	index
#26042200	2
#26042143	2
#26041657	2
#1362	181