Subgroups — #37548694

Order 23168.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042176	C₂	1	1	yes	maximal, characteristic
2	#26042147	C₂	1	1	yes	maximal, characteristic
3	#26041538	C₂	1	1	yes	maximal, characteristic
4	#19153895	—	2	1	no	—
5	#19153890	—	2	1	no	—
6	C₂×Dic₇₂₄	C₄	1	1	yes	characteristic, complemented
7	C₂×#15668432	C₂²	1	1	yes	characteristic
8	#19153796	—	2	1	no	—
9	#19153739	—	2	1	no	—
10	#106×C₁₈₁	C₄	1	1	yes	characteristic, complemented
11	C₄⋊#10624382	—	4	1	no	—
12	C₂²⋊#10624382	—	4	1	no	—
13	C₄×#10624382	—	2	2	no	—
14	#15668452	—	4	1	no	—
15	C₂×Dic₃₆₂	—	2	1	no	—
16	C₂×C₄×D₁₈₁	D₄	1	1	yes	characteristic
17	Dic₇₂₄	—	4	1	no	—
18	#15668432	—	4	1	no	—
19	C₂×#13089678	D₄	1	1	yes	characteristic
20	C₄⋊Dic₁₈₁	—	4	1	no	—
21	#15668426	—	4	1	no	—
22	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
23	C₄⋊C₄×C₁₈₁	—	2	1	no	—
24	C₂×#10624382	—	4	2	no	—
25	C₂²×D₁₈₁	D₈	1	1	yes	characteristic
26	Dic₃₆₂	—	4	1	no	—
27	Dic₃₆₂	—	4	1	no	—
28	C₂×Dic₁₈₁	—	4	1	no	—
29	C₂×Dic₁₈₁	SD₁₆	1	1	yes	characteristic
30	C₄×D₁₈₁	—	2	1	no	—
31	C₄×D₁₈₁	—	2	1	no	—
32	#13089678	—	2	1	no	—
33	C₂×C₄×C₁₈₁	—	4	1	no	—
34	C₂×C₄×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
35	C₈×C₁₈₁	—	2	1	no	—
36	C₂²×C₁₈₁	#102	1	1	yes	characteristic
37	C₂×D₁₈₁	—	2	1	no	—
38	C₂×D₁₈₁	—	4	1	no	—
39	#10624382	—	8	2	no	—
40	C₄×C₁₈₁	—	8	1	no	—
41	C₄×C₁₈₁	#99	1	1	yes	characteristic
42	C₄×C₁₈₁	#104	1	1	yes	characteristic
43	Dic₁₈₁	—	2	1	no	—
44	Dic₁₈₁	—	8	1	no	—
45	C₂×C₁₈₁	—	2	1	no	—
46	C₂×C₁₈₁	#327	1	1	yes	characteristic
47	D₁₈₁	—	4	1	no	—
48	C₁₈₁	#1340	1	1	yes	characteristic, complemented, Sylow
49	#1340	—	181	1	no	maximal, Sylow
50	#470	—	181	1	no	—
51	#349	—	181	1	no	—
52	H(3,ℤ/4)	—	181	1	no	—
53	C₂×Q₁₆	—	181	1	no	—
54	C₂×M₁₆	—	181	1	no	—
55	C₂²⋊Q₈	—	362	1	no	—
56	#117	—	362	1	no	—
57	M₃₂	—	362	1	no	—
58	#106	#10624382	1	1	yes	characteristic, complemented
59	#103	—	362	1	no	—
60	C₂×Q₈	—	362	1	no	—
61	C₂²×C₄	—	181	1	no	—
62	Q₁₆	—	724	1	no	—
63	M₁₆	—	724	1	no	—
64	C₂×C₈	—	181	1	no	—
65	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
66	C₄⋊C₄	—	2	1	no	—
67	C₄⋊C₄	—	724	1	no	—
68	C₄⋊C₄	—	724	1	no	—
69	C₂²⋊C₄	—	724	1	no	—
70	C₂²⋊C₄	—	724	1	no	—
71	C₄²	—	362	2	no	—
72	C₁₆	—	724	1	no	—
73	C₂³	—	181	1	no	—
74	Q₈	—	724	1	no	—
75	Q₈	—	724	1	no	—
76	C₂×C₄	—	4	1	no	—
77	C₂×C₄	—	362	1	no	—
78	C₂×C₄	—	362	1	no	—
79	C₂×C₄	—	181	1	no	—
80	C₂×C₄	—	724	2	no	—
81	C₂×C₄	—	724	1	no	—
82	C₂×C₄	C₂²⋊#10624382	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	362	1	no	—
85	C₂²	—	362	1	no	—
86	C₂²	—	724	1	no	—
87	C₂²	#19153878	1	1	yes	characteristic
88	C₄	—	8	1	no	—
89	C₄	—	362	1	no	—
90	C₄	—	1448	2	no	—
91	C₄	—	1448	1	no	—
92	C₄	#19153875	1	1	yes	characteristic
93	C₄	#19153881	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	724	1	no	—
96	C₂	#26042131	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26042131
commutator	C₂×C₈×C₁₈₁	C₂×C₄
Frattini	C₂×C₈	C₂×#10624382
Fitting	#106×C₁₈₁	C₄
socle	C₂×C₁₈₁	#327
prime radical	C₂²×D₁₈₁	D₈
cosocle	C₂×#15668432	C₂²
hypercenter	#106	#10624382
hypocenter	C₁₈₁	#1340
LCS	G ▷ C₂×C₈×C₁₈₁ ▷ C₂×C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

Complements

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

N	H ≅ G/N	type
6. C₂×Dic₇₂₄	C₄	semidirect
10. #106×C₁₈₁	C₄	semidirect
48. C₁₈₁	#1340	semidirect
58. #106	#10624382	semidirect

Maximal subgroups

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

subgroup	index
#26042176	2
#26042147	2
#26041538	2
#1340	181