Subgroups — #17994201

Order 4736.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557913	C₂	1	1	yes	maximal, characteristic, complemented
2	#14557879	C₂	1	4	yes	maximal, complemented
3	C₈×#64436	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#493	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₄₈	—	2	2	no	—
6	#11924536	C₂²	1	2	yes	—
7	#11924457	—	2	8	no	—
8	C₄×#64436	C₂²	1	2	yes	—
9	C₂×D₈×C₃₇	—	2	2	no	—
10	#127×C₃₇	C₂²	1	2	yes	—
11	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
12	C₂×D₄×C₃₇	—	2	2	no	—
13	C₂×D₄×C₃₇	—	2	4	no	—
14	C₂×Dic₇₄	—	2	2	no	—
15	D₈×C₃₇	—	4	4	no	—
16	C₂×C₈×C₃₇	D₄	1	2	yes	—
17	C₄²×C₃₇	C₂³	1	1	yes	characteristic
18	C₄⋊Dic₃₇	—	2	4	no	—
19	C₂×#64436	D₄	1	4	yes	—
20	Dic₁₄₈	—	4	4	no	—
21	C₂³×C₃₇	—	4	2	no	—
22	D₄×C₃₇	—	4	4	no	—
23	D₄×C₃₇	—	4	8	no	—
24	C₂×C₄×C₃₇	C₂×D₄	1	2	yes	—
25	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
26	C₂×Dic₃₇	—	4	2	no	—
27	Dic₇₄	—	4	4	no	—
28	C₈×C₃₇	D₈	1	4	yes	—
29	#64436	—	2	4	no	—
30	C₂²×C₃₇	—	8	2	no	—
31	C₂²×C₃₇	—	8	4	no	—
32	C₂²×C₃₇	#127	1	1	yes	characteristic
33	C₄×C₃₇	C₂×D₈	1	2	yes	—
34	C₄×C₃₇	#135	1	4	yes	—
35	Dic₃₇	—	8	2	no	—
36	#1709	—	37	1	no	maximal, Sylow
37	C₂×C₃₇	—	16	2	no	—
38	C₂×C₃₇	#493	1	1	yes	characteristic
39	C₂×C₃₇	#495	1	2	yes	—
40	#494	—	37	1	no	—
41	#493	D₃₇	1	1	yes	characteristic
42	#486	—	37	4	no	—
43	C₈²	—	37	1	no	—
44	C₃₇	#1709	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₁₆	—	74	2	no	—
46	C₂×D₈	—	2	2	no	—
47	C₄⋊Q₈	—	37	2	no	—
48	#127	C₂×D₃₇	1	2	yes	—
49	#102	—	74	8	no	—
50	C₄×C₈	—	37	2	no	—
51	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
52	C₂×Q₈	—	74	2	no	—
53	C₂×D₄	—	2	4	no	—
54	C₂×D₄	—	2	2	no	—
55	Q₁₆	—	148	4	no	—
56	D₈	—	4	4	no	—
57	C₂×C₈	—	37	4	no	—
58	C₂×C₈	C₂²⋊D₃₇	1	2	yes	—
59	C₄⋊C₄	—	74	4	no	—
60	C₄²	C₂²×D₃₇	1	1	yes	characteristic
61	C₂³	—	4	2	no	—
62	Q₈	—	148	4	no	—
63	D₄	—	4	4	no	—
64	D₄	—	4	8	no	—
65	C₂×C₄	—	148	2	no	—
66	C₂×C₄	D₄×D₃₇	1	2	yes	—
67	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
68	C₈	—	74	4	no	—
69	C₈	#10596939	1	4	yes	—
70	C₂²	—	8	2	no	—
71	C₂²	—	8	4	no	—
72	C₂²	#11924532	1	1	yes	characteristic
73	C₄	—	296	2	no	—
74	C₄	C₂×#10596939	1	2	yes	—
75	C₄	#11924555	1	4	yes	—
76	C₂	—	16	2	no	—
77	C₂	#14557909	1	1	yes	characteristic
78	C₂	#14557916	1	2	yes	—

	subgroup	G/H
center	C₂²	#11924532
commutator, cosocle	C₄²×C₃₇	C₂³
Frattini	C₄²	C₂²×D₃₇
Fitting, prime radical	C₃₇×#493	C₂
socle	C₂²×C₃₇	#127
hypercenter	#493	D₃₇
hypocenter	C₃₇	#1709
LCS	G ▷ C₄²×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

Complements

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

N	H ≅ G/N	type
1. #14557913	C₂	semidirect
2. #14557879	C₂	semidirect
3. C₈×#64436	C₂	semidirect
44. C₃₇	#1709	semidirect

Maximal subgroups

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

subgroup	index
#14557913	2
#14557879	2
C₈×#64436	2
C₃₇×#493	2
#1709	37