Subgroups — #37550062

Order 23168.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19153890	C₂	1	2	yes	maximal
2	#26042201	C₂	1	4	yes	maximal, complemented
3	#26041237	C₂	1	1	yes	maximal, characteristic
4	#19153890	—	2	2	no	—
5	#19153890	C₂²	1	4	yes	—
6	C₂×#15668452	—	2	2	no	—
7	C₂²×#13089678	C₂²	1	1	yes	characteristic
8	#19153775	C₄	1	1	yes	characteristic
9	#19153726	C₄	1	2	yes	—
10	C₈×Dic₁₈₁	C₂²	1	2	yes	—
11	C₂×M₁₆×C₁₈₁	C₄	1	1	yes	characteristic
12	#15668452	—	2	4	no	—
13	C₂×#13089678	C₂×C₄	1	1	yes	characteristic
14	C₂×#13089678	D₄	1	2	yes	—
15	C₂×#13089678	Q₈	1	2	yes	—
16	C₂×#13089678	C₂³	1	1	yes	characteristic
17	C₄⋊Dic₁₈₁	—	2	1	no	—
18	C₂²⋊Dic₁₈₁	—	2	1	no	—
19	C₄×Dic₁₈₁	C₂×C₄	1	2	yes	—
20	C₂²×C₄×C₁₈₁	C₂×C₄	1	1	yes	characteristic
21	M₁₆×C₁₈₁	C₈	1	4	yes	—
22	C₂×C₈×C₁₈₁	C₂×C₄	1	2	yes	—
23	C₂×Dic₁₈₁	—	2	2	no	—
24	#13089678	C₄⋊C₄	1	2	yes	—
25	#13089678	C₂×D₄	1	1	yes	characteristic
26	#13089678	C₂×Q₈	1	1	yes	characteristic
27	C₂³×C₁₈₁	M₁₆	1	1	yes	characteristic
28	C₂×C₄×C₁₈₁	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₁₈₁	C₂×C₈	1	2	yes	—
30	C₂×C₄×C₁₈₁	M₁₆	1	1	yes	characteristic
31	C₂×C₄×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₁₈₁	C₂×C₈	1	4	yes	—
33	C₂²×C₁₈₁	—	4	1	no	—
34	C₂²×C₁₈₁	C₄⋊C₈	1	2	yes	—
35	C₂²×C₁₈₁	C₂×M₁₆	1	1	yes	characteristic
36	C₄×C₁₈₁	C₄⋊C₈	1	2	yes	—
37	C₄×C₁₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₄×C₁₈₁	C₂²×C₈	1	1	yes	characteristic
39	Dic₁₈₁	—	4	2	no	—
40	C₂×C₁₈₁	—	2	1	no	—
41	C₂×C₁₈₁	—	2	2	no	—
42	C₂×C₁₈₁	C₂×C₄⋊C₈	1	1	yes	characteristic
43	C₁₈₁	#2153	1	1	yes	characteristic, complemented, Sylow
44	#2153	—	181	1	no	maximal, Sylow
45	C₂×M₃₂	—	181	2	no	—
46	#405	—	181	1	no	—
47	#364	—	181	4	no	—
48	C₂×M₁₆	#10624382	1	1	yes	characteristic
49	C₂²×C₈	—	181	1	no	—
50	#117	—	181	1	no	—
51	M₃₂	—	362	2	no	—
52	M₃₂	—	181	4	no	—
53	C₂×C₁₆	—	362	2	no	—
54	#97	—	181	2	no	—
55	C₄×C₈	—	181	2	no	—
56	C₂²×C₄	C₂×#10624382	1	1	yes	characteristic
57	M₁₆	#13089685	1	4	yes	—
58	C₂×C₈	—	181	2	no	—
59	C₂×C₈	—	181	2	no	—
60	C₂×C₈	—	181	1	no	—
61	C₂×C₈	—	181	1	no	—
62	C₂×C₈	C₂×#10624382	1	2	yes	—
63	C₄⋊C₄	—	362	1	no	—
64	C₂²⋊C₄	—	362	1	no	—
65	C₄²	—	181	2	no	—
66	C₁₆	—	362	4	no	—
67	C₂³	#15668459	1	1	yes	characteristic
68	C₂×C₄	—	362	2	no	—
69	C₂×C₄	C₄⋊#10624382	1	2	yes	—
70	C₂×C₄	C₂×#13089685	1	2	yes	—
71	C₂×C₄	#15668459	1	1	yes	characteristic
72	C₂×C₄	C₂²×#10624382	1	1	yes	characteristic
73	C₈	—	181	1	no	—
74	C₈	—	181	2	no	—
75	C₈	—	181	1	no	—
76	C₈	C₂×#13089685	1	4	yes	—
77	C₂²	—	4	1	no	—
78	C₂²	C₄⋊#13089685	1	2	yes	—
79	C₂²	C₂×#15668459	1	1	yes	characteristic
80	C₄	—	724	2	no	—
81	C₄	C₄⋊#13089685	1	2	yes	—
82	C₄	C₂×C₄⋊#10624382	1	1	yes	characteristic
83	C₄	C₂²×#13089685	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	2	2	no	—
86	C₂	C₂×C₄⋊#13089685	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×C₄⋊#10624382
commutator	C₄×C₁₈₁	C₂²×C₈
Frattini	C₂×C₄	C₂²×#10624382
Fitting	C₂×M₁₆×C₁₈₁	C₄
socle	C₂×C₁₈₁	C₂×C₄⋊C₈
prime radical	C₂³×C₁₈₁	M₁₆
cosocle	C₂×#13089678	C₂³
hypercenter	C₂×M₁₆	#10624382
hypocenter	C₁₈₁	#2153
LCS	G ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
2. #26042201	C₂	semidirect
43. C₁₈₁	#2153	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19153890	2
#26042201	2
#26041237	2
#2153	181