Subgroups — #14558611

Order 2368.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924623	C₂	1	8	yes	maximal, complemented
2	D₃₇⋊M₁₆	C₂	1	2	yes	maximal, complemented
3	C₂×#10596957	C₂	1	4	yes	maximal, complemented
4	C₂×#10596964	C₂	1	1	yes	maximal, characteristic
5	C₂×D₄×C₃₇	C₄	1	1	yes	characteristic
6	C₂×C₂²⋊D₃₇	C₄	1	2	yes	—
7	C₂²×Dic₃₇	C₂²	1	2	yes	—
8	#10596964	C₄	1	4	yes	—
9	#10596964	C₂²	1	4	yes	—
10	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₇₄	C₄	1	1	yes	characteristic
12	#10596957	C₂²	1	4	yes	—
13	#10596957	C₂²	1	8	yes	complemented
14	C₂×#64438	C₂²	1	8	yes	complemented
15	#10596953	C₂²	1	4	yes	complemented
16	D₃₇⋊C₈	C₂²	1	4	yes	complemented
17	C₂³×C₃₇	C₂×C₄	1	2	yes	—
18	C₂²×D₃₇	C₂×C₄	1	1	yes	characteristic
19	D₄×C₃₇	C₂×C₄	1	4	yes	—
20	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
21	C₂²⋊D₃₇	C₂×C₄	1	8	yes	—
22	C₂×Dic₃₇	C₂×C₄	1	2	yes	—
23	C₂×Dic₃₇	C₂×C₄	1	4	yes	—
24	C₂×Dic₃₇	C₂³	1	4	yes	—
25	C₂×Dic₃₇	C₂³	1	1	yes	characteristic
26	C₄×D₃₇	C₂×C₄	1	2	yes	—
27	C₄×D₃₇	C₂³	1	2	yes	—
28	Dic₇₄	C₂×C₄	1	4	yes	—
29	#64438	C₂³	1	8	yes	—
30	C₂²×C₃₇	—	4	2	no	—
31	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
32	C₂²×C₃₇	C₂²×C₄	1	4	yes	—
33	C₂×D₃₇	—	4	1	no	—
34	C₂×D₃₇	C₂²×C₄	1	2	yes	—
35	C₄×C₃₇	C₂²×C₄	1	2	yes	—
36	Dic₃₇	C₂²×C₄	1	4	yes	—
37	Dic₃₇	C₂²×C₄	1	1	yes	characteristic
38	Dic₃₇	C₂⁴	1	1	yes	characteristic
39	C₂×C₃₇	—	2	1	no	—
40	C₂×C₃₇	—	2	4	no	—
41	C₂×C₃₇	C₂³×C₄	1	1	yes	characteristic
42	D₃₇	—	2	2	no	—
43	#568	—	37	1	no	maximal, Sylow
44	C₃₇	#568	1	1	yes	characteristic, complemented, Sylow
45	C₂×#41	—	37	1	no	—
46	#131	—	37	8	no	—
47	C₂×M₁₆	—	37	4	no	—
48	C₂×M₁₆	—	37	2	no	—
49	#41	—	37	4	no	—
50	#41	—	37	4	no	—
51	C₂×Q₈	—	37	1	no	—
52	C₂×D₄	—	37	2	no	—
53	C₂×D₄	#3866	1	1	yes	characteristic
54	C₂²×C₄	—	37	2	no	—
55	C₂²×C₄	—	37	1	no	—
56	M₁₆	—	37	4	no	—
57	M₁₆	—	37	4	no	—
58	M₁₆	—	37	8	no	—
59	C₂×C₈	—	37	4	no	—
60	C₂×C₈	—	37	8	no	—
61	C₂³	—	37	1	no	—
62	C₂³	C₂×#3866	1	2	yes	—
63	Q₈	—	37	4	no	—
64	D₄	—	37	8	no	—
65	D₄	C₂×#3866	1	4	yes	—
66	C₂×C₄	—	37	4	no	—
67	C₂×C₄	—	37	1	no	—
68	C₂×C₄	—	37	2	no	—
69	C₂×C₄	—	37	4	no	—
70	C₂×C₄	—	37	2	no	—
71	C₂×C₄	—	37	2	no	—
72	C₂×C₄	C₂×#3866	1	1	yes	characteristic
73	C₈	—	37	8	no	—
74	C₂²	—	4	2	no	—
75	C₂²	—	37	2	no	—
76	C₂²	—	148	1	no	—
77	C₂²	C₂²×#3866	1	1	yes	characteristic
78	C₂²	C₂²×#3866	1	4	yes	—
79	C₄	—	37	1	no	—
80	C₄	—	37	1	no	—
81	C₄	—	37	4	no	—
82	C₄	C₂²×#3866	1	2	yes	—
83	C₂	—	2	1	no	—
84	C₂	—	2	4	no	—
85	C₂	—	74	2	no	—
86	C₂	C₂³×#3866	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂³×#3866
commutator, socle	C₂×C₃₇	C₂³×C₄
Fitting	C₂×D₄×C₃₇	C₄
prime radical	C₂×#10596964	C₂
cosocle	Dic₃₇	C₂⁴
hypercenter	C₂×D₄	#3866
hypocenter	C₃₇	#568
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. #11924623	C₂	semidirect
2. D₃₇⋊M₁₆	C₂	semidirect
3. C₂×#10596957	C₂	semidirect
13. #10596957	C₂²	semidirect
14. C₂×#64438	C₂²	semidirect
15. #10596953	C₂²	semidirect
16. D₃₇⋊C₈	C₂²	semidirect
44. C₃₇	#568	semidirect

Maximal subgroups

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

subgroup	index
#11924623	2
D₃₇⋊M₁₆	2
C₂×#10596957	2
C₂×#10596964	2
#568	37