Subgroups — #17994710

Order 4736.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924455	C₂	1	2	yes	maximal
2	#14557303	C₂	1	4	yes	maximal
3	C₃₇×#519	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596934	C₂²	1	4	yes	—
5	#11924455	—	2	4	no	—
6	C₂²×Q₈×C₃₇	C₂²	1	1	yes	characteristic
7	C₄×Q₈×C₃₇	—	2	4	no	—
8	#117×C₃₇	C₄	1	4	yes	—
9	#117×C₃₇	C₂²	1	2	yes	—
10	C₂×Q₈×C₃₇	—	2	4	no	—
11	C₂×Q₈×C₃₇	D₄	1	4	yes	—
12	C₂²×C₄×C₃₇	C₂×C₄	1	2	yes	—
13	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
14	C₄⋊C₄×C₃₇	—	2	4	no	—
15	C₄⋊C₄×C₃₇	—	2	2	no	—
16	C₂²⋊C₄×C₃₇	C₂×C₄	1	4	yes	—
17	C₄²×C₃₇	—	2	4	no	—
18	C₄²×C₃₇	—	2	2	no	—
19	#10596934	—	2	4	no	—
20	#10596934	—	2	4	no	—
21	C₂×#64436	—	2	4	no	—
22	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
23	Q₈×C₃₇	—	2	8	no	—
24	C₂×C₄×C₃₇	—	2	4	no	—
25	C₂×C₄×C₃₇	—	2	4	no	—
26	C₂×C₄×C₃₇	C₂²⋊C₄	1	4	yes	—
27	C₂×C₄×C₃₇	C₂×D₄	1	2	yes	—
28	C₂×C₄×C₃₇	#41	1	4	yes	—
29	#64436	—	4	4	no	—
30	C₂²×C₃₇	—	4	1	no	—
31	C₂²×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
32	C₂²×C₃₇	#117	1	2	yes	—
33	C₄×C₃₇	—	2	4	no	—
34	C₄×C₃₇	—	4	4	no	—
35	C₄×C₃₇	#123	1	4	yes	—
36	#1830	—	37	1	no	maximal, Sylow
37	C₂×C₃₇	—	2	1	no	—
38	C₂×C₃₇	—	2	2	no	—
39	C₂×C₃₇	#381	1	1	yes	characteristic
40	#519	D₃₇	1	1	yes	characteristic
41	C₂×#101	—	37	2	no	—
42	#344	—	37	4	no	—
43	C₃₇	#1830	1	1	yes	characteristic, complemented, Sylow
44	C₂²×Q₈	C₂×D₃₇	1	1	yes	characteristic
45	C₂×M₁₆	—	37	4	no	—
46	C₄×Q₈	—	2	4	no	—
47	#117	Dic₃₇	1	4	yes	—
48	#117	C₂×D₃₇	1	2	yes	—
49	#101	—	74	4	no	—
50	C₂×Q₈	—	2	4	no	—
51	C₂×Q₈	C₂²⋊D₃₇	1	4	yes	—
52	C₂²×C₄	C₂×Dic₃₇	1	2	yes	—
53	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
54	M₁₆	—	74	4	no	—
55	M₁₆	—	74	4	no	—
56	C₂×C₈	—	74	4	no	—
57	C₄⋊C₄	—	2	4	no	—
58	C₄⋊C₄	—	2	2	no	—
59	C₂²⋊C₄	C₂×Dic₃₇	1	4	yes	—
60	C₄²	—	2	4	no	—
61	C₄²	—	2	2	no	—
62	C₂³	C₂²×Dic₃₇	1	1	yes	characteristic
63	Q₈	—	2	8	no	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	2	4	no	—
66	C₂×C₄	C₂²⋊Dic₃₇	1	4	yes	—
67	C₂×C₄	#10596962	1	4	yes	—
68	C₂×C₄	C₂×C₂²⋊D₃₇	1	2	yes	—
69	C₈	—	148	4	no	—
70	C₂²	—	4	1	no	—
71	C₂²	C₂×C₂²⋊Dic₃₇	1	1	yes	characteristic
72	C₂²	#11924495	1	2	yes	—
73	C₄	—	2	4	no	—
74	C₄	—	4	4	no	—
75	C₄	#11924519	1	4	yes	—
76	C₂	—	2	1	no	—
77	C₂	—	2	2	no	—
78	C₂	#14557396	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14557396
commutator, prime radical	C₂³×C₃₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₇
Fitting	C₃₇×#519	C₂
socle	C₂×C₃₇	#381
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	#519	D₃₇
hypocenter	C₃₇	#1830
LCS	G ▷ C₂³×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #519

Complements

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

N	H ≅ G/N	type
43. C₃₇	#1830	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11924455	2
#14557303	2
C₃₇×#519	2
#1830	37