Subgroups — #17996870

Order 4736.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557937	C₂	1	2	yes	maximal
2	#14557359	C₂	1	1	yes	maximal, characteristic
3	#14557358	C₂	1	2	yes	maximal
4	C₁₆×Dic₃₇	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#366	C₂	1	1	yes	maximal, characteristic
6	#11924535	—	2	2	no	—
7	C₂×#10596925	C₂²	1	1	yes	characteristic
8	#11924470	C₂²	1	2	yes	—
9	#11924469	—	2	2	no	—
10	C₈×Dic₃₇	C₂²	1	1	yes	characteristic
11	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
12	#107×C₃₇	C₂²	1	2	yes	—
13	C₂×Dic₇₄	—	4	2	no	—
14	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
15	C₄⋊C₄×C₃₇	—	2	2	no	—
16	C₄⋊Dic₃₇	—	2	2	no	—
17	#10596936	—	4	2	no	—
18	C₄×Dic₃₇	D₄	1	1	yes	characteristic
19	C₂×#64436	D₄	1	1	yes	characteristic
20	C₁₆×C₃₇	Q₈	1	2	yes	complemented
21	#10596925	Q₈	1	2	yes	complemented
22	C₂×C₄×C₃₇	—	4	2	no	—
23	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
24	C₂×Dic₃₇	—	4	2	no	—
25	C₂×Dic₃₇	D₈	1	1	yes	characteristic
26	C₂×Dic₃₇	D₈	1	1	yes	characteristic
27	Dic₇₄	—	8	4	no	—
28	C₈×C₃₇	C₂×Q₈	1	1	yes	characteristic
29	C₈×C₃₇	C₂×Q₈	1	1	yes	characteristic
30	#64436	Q₁₆	1	2	yes	—
31	C₂²×C₃₇	C₂×D₈	1	1	yes	characteristic
32	C₄×C₃₇	—	8	2	no	—
33	C₄×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
34	C₄×C₃₇	C₂×Q₁₆	1	1	yes	characteristic
35	Dic₃₇	—	8	2	no	—
36	Dic₃₇	D₁₆	1	2	yes	—
37	Dic₃₇	Q₃₂	1	2	yes	—
38	#2252	—	37	1	no	maximal, Sylow
39	C₂×C₃₇	#500	1	1	yes	characteristic
40	C₂×C₃₇	C₂×D₁₆	1	1	yes	characteristic
41	C₂×C₃₇	C₂×Q₃₂	1	1	yes	characteristic
42	#500	—	37	2	no	—
43	#366	—	37	1	no	—
44	#366	—	37	2	no	—
45	#366	D₃₇	1	1	yes	characteristic
46	C₄×C₁₆	—	37	1	no	—
47	C₃₇	#2252	1	1	yes	characteristic, complemented, Sylow
48	C₄⋊Q₈	—	74	2	no	—
49	C₂×C₁₆	—	37	1	no	—
50	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
51	#107	—	37	2	no	—
52	#107	—	74	2	no	—
53	#107	C₂×D₃₇	1	2	yes	—
54	C₄×C₈	—	37	1	no	—
55	C₂×Q₈	—	148	2	no	—
56	C₂×C₈	—	37	1	no	—
57	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
58	C₄⋊C₄	—	2	2	no	—
59	C₄⋊C₄	—	74	2	no	—
60	C₄⋊C₄	—	148	2	no	—
61	C₄²	—	37	1	no	—
62	C₁₆	—	37	2	no	—
63	C₁₆	Dic₇₄	1	2	yes	complemented
64	Q₈	—	296	4	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	—	37	1	no	—
67	C₂×C₄	—	37	1	no	—
68	C₂×C₄	—	148	2	no	—
69	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
70	C₈	—	37	2	no	—
71	C₈	C₂×Dic₇₄	1	1	yes	characteristic
72	C₈	Q₈×D₃₇	1	1	yes	characteristic
73	C₂²	D₈×D₃₇	1	1	yes	characteristic
74	C₄	—	8	2	no	—
75	C₄	—	37	2	no	—
76	C₄	—	37	2	no	—
77	C₄	—	296	2	no	—
78	C₄	#11924535	1	1	yes	characteristic
79	C₄	Q₁₆×D₃₇	1	1	yes	characteristic
80	C₂	#14557937	1	1	yes	characteristic
81	C₂	D₁₆×D₃₇	1	1	yes	characteristic
82	C₂	Q₃₂×D₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈×D₃₇
commutator, cosocle	C₂×C₈×C₃₇	C₂³
Frattini	C₂×C₈	C₂²×D₃₇
Fitting	C₃₇×#366	C₂
socle, prime radical	C₂²×C₃₇	C₂×D₈
hypercenter	#366	D₃₇
hypocenter	C₃₇	#2252
LCS	G ▷ C₂×C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

Complements

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

N	H ≅ G/N	type
20. C₁₆×C₃₇	Q₈	semidirect
21. #10596925	Q₈	semidirect
47. C₃₇	#2252	semidirect
63. C₁₆	Dic₇₄	semidirect

Maximal subgroups

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

subgroup	index
#14557937	2
#14557359	2
#14557358	2
C₁₆×Dic₃₇	2
C₃₇×#366	2
#2252	37