Subgroups — #17996848

Order 4736.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924482	C₂	1	4	yes	maximal
2	#14557913	C₂	1	1	yes	maximal, characteristic
3	C₄×#10596925	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#494	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₄₈	—	2	1	no	—
6	C₂×Dic₁₄₈	C₂²	1	2	yes	—
7	#11924536	—	2	1	no	—
8	#11924482	—	2	8	no	—
9	C₂×#10596925	C₂²	1	2	yes	—
10	C₂×Q₁₆×C₃₇	—	2	1	no	—
11	C₂×Q₁₆×C₃₇	C₂²	1	2	yes	—
12	C₄⋊Q₈×C₃₇	—	2	1	no	—
13	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×Q₈×C₃₇	—	2	2	no	—
15	C₂×Dic₇₄	—	2	2	no	—
16	Q₁₆×C₃₇	—	2	4	no	—
17	Q₁₆×C₃₇	—	4	2	no	—
18	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
19	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
20	C₄⋊C₄×C₃₇	—	4	2	no	—
21	C₄²×C₃₇	D₄	1	1	yes	characteristic
22	C₄⋊Dic₃₇	—	4	2	no	—
23	Dic₁₄₈	—	2	4	no	—
24	Dic₁₄₈	—	4	2	no	—
25	#10596925	D₄	1	4	yes	—
26	Q₈×C₃₇	—	4	2	no	—
27	Q₈×C₃₇	—	4	2	no	—
28	C₂×C₄×C₃₇	—	4	2	no	—
29	C₂×C₄×C₃₇	D₈	1	2	yes	—
30	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₃₇	—	4	2	no	—
32	Dic₇₄	—	4	2	no	—
33	Dic₇₄	—	4	2	no	—
34	C₈×C₃₇	D₈	1	2	yes	—
35	C₈×C₃₇	C₂×D₄	1	2	yes	—
36	C₂²×C₃₇	C₂×D₈	1	1	yes	characteristic
37	C₄×C₃₇	—	8	2	no	—
38	C₄×C₃₇	Q₃₂	1	4	yes	complemented
39	C₄×C₃₇	#127	1	1	yes	characteristic
40	C₄×C₃₇	C₂×D₈	1	1	yes	characteristic
41	Dic₃₇	—	8	2	no	—
42	#2247	—	37	1	no	maximal, Sylow
43	C₂×C₃₇	#493	1	1	yes	characteristic
44	C₂×C₃₇	C₂×Q₃₂	1	2	yes	—
45	C₂×Q₃₂	—	37	4	no	—
46	#494	—	37	1	no	—
47	#494	D₃₇	1	1	yes	characteristic
48	C₄×C₁₆	—	37	1	no	—
49	C₃₇	#2247	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₁₆	—	2	1	no	—
51	C₂×Q₁₆	—	37	2	no	—
52	C₂×Q₁₆	—	74	1	no	—
53	C₂×Q₁₆	C₂×D₃₇	1	2	yes	—
54	C₄⋊Q₈	—	2	1	no	—
55	C₄⋊Q₈	—	74	1	no	—
56	Q₃₂	—	74	8	no	—
57	C₂×C₁₆	—	37	2	no	—
58	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
59	C₂×Q₈	—	2	2	no	—
60	C₂×Q₈	—	74	2	no	—
61	Q₁₆	—	2	4	no	—
62	Q₁₆	—	4	2	no	—
63	Q₁₆	—	74	4	no	—
64	Q₁₆	—	148	2	no	—
65	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
66	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
67	C₄⋊C₄	—	4	2	no	—
68	C₄⋊C₄	—	148	2	no	—
69	C₄²	C₂²⋊D₃₇	1	1	yes	characteristic
70	C₁₆	—	37	4	no	—
71	Q₈	—	4	2	no	—
72	Q₈	—	4	2	no	—
73	Q₈	—	148	2	no	—
74	Q₈	—	148	2	no	—
75	C₂×C₄	—	4	2	no	—
76	C₂×C₄	—	148	2	no	—
77	C₂×C₄	#10596939	1	2	yes	—
78	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
79	C₈	#10596939	1	2	yes	—
80	C₈	D₄×D₃₇	1	2	yes	—
81	C₂²	C₂×#10596939	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	296	2	no	—
84	C₄	#11924482	1	4	yes	complemented
85	C₄	#11924532	1	1	yes	characteristic
86	C₄	C₂×#10596939	1	1	yes	characteristic
87	C₂	#14557909	1	1	yes	characteristic
88	C₂	C₂×#11924482	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#10596939
commutator, cosocle	C₂×C₈×C₃₇	C₂³
Frattini	C₂×C₈	C₂²×D₃₇
Fitting	C₃₇×#494	C₂
socle, prime radical	C₂²×C₃₇	C₂×D₈
hypercenter	#494	D₃₇
hypocenter	C₃₇	#2247
LCS	G ▷ C₂×C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
38. C₄×C₃₇	Q₃₂	semidirect
49. C₃₇	#2247	semidirect
84. C₄	#11924482	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11924482	2
#14557913	2
C₄×#10596925	2
C₃₇×#494	2
#2247	37