Subgroups — #17996354

Order 4736.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924476	C₂	1	1	yes	maximal, characteristic
2	#14557488	C₂	1	1	yes	maximal, characteristic
3	#14557351	C₂	1	4	yes	maximal, complemented
4	C₂²×C₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#10596934	C₄	1	1	yes	characteristic
6	#11924495	C₄	1	1	yes	characteristic
7	#11924476	—	2	2	no	—
8	C₂×#10596925	C₂²	1	2	yes	—
9	#11924446	C₄	1	2	yes	—
10	C₈×Dic₃₇	C₂²	1	2	yes	—
11	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₃₇	—	2	2	no	—
13	C₂×C₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₃₇	D₄	1	2	yes	—
17	C₂×C₈×C₃₇	Q₈	1	2	yes	—
18	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
19	C₂²⋊Dic₃₇	C₈	1	2	yes	—
20	C₄⋊Dic₃₇	C₈	1	2	yes	—
21	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
22	#10596934	—	2	2	no	—
23	C₂×#64436	C₂×C₄	1	2	yes	—
24	C₁₆×C₃₇	—	2	2	no	—
25	#10596925	—	2	2	no	—
26	C₂³×C₃₇	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₃₇	M₁₆	1	2	yes	—
30	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₃₇	C₂×C₈	1	4	yes	—
32	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
33	C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
34	C₈×C₃₇	C₂×Q₈	1	1	yes	characteristic
35	#64436	—	2	2	no	—
36	C₂²×C₃₇	—	2	2	no	—
37	C₂²×C₃₇	C₄⋊C₈	1	2	yes	—
38	C₂²×C₃₇	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₃₇	C₄⋊C₈	1	2	yes	—
40	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₄×C₃₇	C₂×M₁₆	1	1	yes	characteristic
42	Dic₃₇	—	2	4	no	—
43	#2151	—	37	1	no	maximal, Sylow
44	C₂×C₃₇	—	2	2	no	—
45	C₂×C₃₇	C₂×C₄⋊C₈	1	1	yes	characteristic
46	C₂×C₃₇	#504	1	2	yes	—
47	C₂×M₃₂	—	37	1	no	—
48	C₂²×C₁₆	D₃₇	1	1	yes	characteristic
49	#405	—	37	1	no	—
50	C₄⋊C₁₆	—	37	4	no	—
51	C₃₇	#2151	1	1	yes	characteristic, complemented, Sylow
52	C₂×M₁₆	—	37	1	no	—
53	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
54	#117	—	37	1	no	—
55	M₃₂	—	74	2	no	—
56	C₂×C₁₆	—	2	2	no	—
57	C₂×C₁₆	—	37	2	no	—
58	C₂×C₁₆	C₂×D₃₇	1	2	yes	—
59	#97	—	37	2	no	—
60	C₄×C₈	—	37	2	no	—
61	C₂²×C₄	C₄×D₃₇	1	1	yes	characteristic
62	M₁₆	—	74	2	no	—
63	C₂×C₈	—	37	2	no	—
64	C₂×C₈	Dic₇₄	1	2	yes	—
65	C₂×C₈	C₄×D₃₇	1	1	yes	characteristic
66	C₂×C₈	C₂²⋊D₃₇	1	2	yes	—
67	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
68	C₄⋊C₄	—	37	2	no	—
69	C₂²⋊C₄	—	37	2	no	—
70	C₄²	—	37	2	no	—
71	C₁₆	—	2	2	no	—
72	C₁₆	—	74	2	no	—
73	C₂³	C₈×D₃₇	1	1	yes	characteristic
74	C₂×C₄	—	37	4	no	—
75	C₂×C₄	C₈×D₃₇	1	1	yes	characteristic
76	C₂×C₄	#10596929	1	2	yes	—
77	C₂×C₄	#10596936	1	2	yes	—
78	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
79	C₈	—	74	2	no	—
80	C₈	#10596936	1	2	yes	—
81	C₈	C₂×Dic₇₄	1	1	yes	characteristic
82	C₈	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
83	C₂²	—	2	2	no	—
84	C₂²	#11924465	1	2	yes	—
85	C₂²	C₂×C₈×D₃₇	1	1	yes	characteristic
86	C₄	—	74	4	no	—
87	C₄	#11924465	1	2	yes	—
88	C₄	C₂×#10596936	1	1	yes	characteristic
89	C₄	C₂×#10596929	1	1	yes	characteristic
90	C₂	—	2	2	no	—
91	C₂	C₂×#11924465	1	1	yes	characteristic
92	C₂	#14557949	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₃₇
commutator, socle	C₂²×C₃₇	C₂²×C₈
Fitting	C₂²×C₁₆×C₃₇	C₂
prime radical	C₂³×C₃₇	C₂×C₈
cosocle	C₂×C₈×C₃₇	C₂³
hypercenter	C₂²×C₁₆	D₃₇
hypocenter	C₃₇	#2151
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
3. #14557351	C₂	semidirect
51. C₃₇	#2151	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11924476	2
#14557488	2
#14557351	2
C₂²×C₁₆×C₃₇	2
#2151	37