Subgroups — #14558556

Order 2368.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924603	C₂	1	2	yes	maximal, complemented
2	#11924593	C₂	1	2	yes	maximal
3	#11924591	C₂	1	2	yes	maximal, complemented
4	C₄²×D₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×D₃₇	C₄	1	1	yes	characteristic
6	C₂×C₄×D₃₇	C₄	1	1	yes	characteristic
7	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
8	C₂×#64438	C₂²	1	4	yes	—
9	C₄²×C₃₇	C₄	1	1	yes	characteristic
10	C₄×Dic₃₇	C₄	1	1	yes	characteristic
11	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
12	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
13	C₂²×D₃₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₃₇	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₃₇	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₃₇	C₂³	1	1	yes	characteristic
20	C₄×D₃₇	—	2	2	no	—
21	C₄×D₃₇	—	2	2	no	—
22	C₄×D₃₇	—	2	2	no	—
23	#64438	—	2	4	no	—
24	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
25	C₂×D₃₇	—	2	1	no	—
26	C₂×D₃₇	—	2	1	no	—
27	C₂×D₃₇	M₁₆	1	2	yes	—
28	C₄×C₃₇	—	2	1	no	—
29	C₄×C₃₇	—	2	1	no	—
30	C₄×C₃₇	—	2	1	no	—
31	Dic₃₇	—	2	1	no	—
32	Dic₃₇	M₁₆	1	2	yes	—
33	Dic₃₇	#41	1	2	yes	—
34	C₂×C₃₇	#117	1	1	yes	characteristic
35	C₂×C₃₇	C₂×M₁₆	1	1	yes	characteristic
36	C₂×C₃₇	C₂×M₁₆	1	1	yes	characteristic
37	D₃₇	—	2	2	no	—
38	#432	—	37	1	no	maximal, Sylow
39	C₃₇	#432	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₄²	—	37	1	no	—
41	C₄⋊C₈	—	37	2	no	—
42	C₂²⋊C₈	—	37	2	no	—
43	#97	—	37	2	no	—
44	C₂²×C₄	—	37	1	no	—
45	C₂²×C₄	—	37	1	no	—
46	C₂²×C₄	—	37	1	no	—
47	C₂×C₈	—	37	4	no	—
48	C₄²	—	37	1	no	—
49	C₄²	—	37	1	no	—
50	C₄²	—	37	1	no	—
51	C₄²	#3866	1	1	yes	characteristic
52	C₂³	—	37	1	no	—
53	C₂×C₄	—	37	1	no	—
54	C₂×C₄	—	37	1	no	—
55	C₂×C₄	—	37	1	no	—
56	C₂×C₄	—	74	2	no	—
57	C₂×C₄	—	74	2	no	—
58	C₂×C₄	—	74	2	no	—
59	C₂×C₄	C₂×#3866	1	1	yes	characteristic
60	C₂×C₄	C₂×#3866	1	1	yes	characteristic
61	C₂×C₄	C₂×#3866	1	1	yes	characteristic
62	C₈	—	74	4	no	—
63	C₂²	—	37	2	no	—
64	C₂²	—	74	1	no	—
65	C₂²	—	74	1	no	—
66	C₂²	C₂²×#3866	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	2	1	no	—
69	C₄	—	2	1	no	—
70	C₄	—	37	2	no	—
71	C₄	—	37	2	no	—
72	C₄	—	74	1	no	—
73	C₂	—	74	2	no	—
74	C₂	#11924615	1	1	yes	characteristic
75	C₂	D₃₇⋊M₁₆	1	1	yes	characteristic
76	C₂	D₃₇⋊M₁₆	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#3866
commutator, socle	C₂²×C₃₇	C₂²×C₄
Fitting	C₄²×C₃₇	C₄
prime radical	C₂²×D₃₇	C₂×C₄
cosocle	C₂×Dic₃₇	C₂³
hypercenter	C₄²	#3866
hypocenter	C₃₇	#432
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

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

N	H ≅ G/N	type
1. #11924603	C₂	semidirect
3. #11924591	C₂	semidirect
39. C₃₇	#432	semidirect

Maximal subgroups

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

subgroup	index
#11924603	2
#11924593	2
#11924591	2
C₄²×D₃₇	2
#432	37