Subgroups — #14558540

Order 2368.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596953	C₂	1	1	yes	maximal, characteristic
2	C₂×D₃₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#11924603	C₂	1	2	yes	maximal, complemented
4	C₄⋊#64438	C₂	1	2	yes	maximal, complemented
5	#11924494	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
7	C₂×#64438	C₂²	1	1	yes	characteristic
8	C₂×#64438	C₂²	1	2	yes	—
9	C₂×#64438	C₂²	1	1	yes	characteristic
10	#10596953	—	2	2	no	—
11	D₃₇⋊C₈	—	2	2	no	—
12	C₄⋊C₄×C₃₇	C₄	1	1	yes	characteristic
13	#10596938	C₄	1	2	yes	—
14	C₄⋊Dic₃₇	C₄	1	1	yes	characteristic
15	C₄×Dic₃₇	C₂²	1	2	yes	—
16	C₂²×D₃₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₃₇	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₃₇	C₂×C₄	1	2	yes	—
20	C₂×Dic₃₇	C₂³	1	1	yes	characteristic
21	C₄×D₃₇	D₄	1	2	yes	—
22	C₄×D₃₇	Q₈	1	2	yes	—
23	#64438	—	2	1	no	—
24	#64438	—	2	1	no	—
25	#64438	—	2	2	no	—
26	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₃₇	—	2	1	no	—
28	C₂×D₃₇	—	2	1	no	—
29	C₂×D₃₇	C₄⋊C₄	1	2	yes	—
30	C₄×C₃₇	—	2	2	no	—
31	C₄×C₃₇	C₄⋊C₄	1	2	yes	—
32	Dic₃₇	—	2	2	no	—
33	Dic₃₇	C₂×D₄	1	1	yes	characteristic
34	Dic₃₇	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₃₇	#131	1	1	yes	characteristic
37	C₂×C₃₇	#131	1	1	yes	characteristic
38	D₃₇	—	2	2	no	—
39	#424	—	37	1	no	maximal, Sylow
40	C₃₇	#424	1	1	yes	characteristic, complemented, Sylow
41	C₂×M₁₆	—	37	1	no	—
42	C₂²×C₈	—	37	1	no	—
43	#117	—	37	1	no	—
44	C₄⋊C₈	—	37	2	no	—
45	C₄⋊C₈	—	37	2	no	—
46	C₂²×C₄	—	37	1	no	—
47	M₁₆	—	74	2	no	—
48	C₂×C₈	—	37	1	no	—
49	C₂×C₈	—	37	1	no	—
50	C₂×C₈	—	37	2	no	—
51	C₂×C₈	—	74	2	no	—
52	C₄⋊C₄	—	37	1	no	—
53	C₄⋊C₄	#3866	1	1	yes	characteristic
54	C₂²⋊C₄	—	37	2	no	—
55	C₄²	—	37	2	no	—
56	C₂³	—	37	1	no	—
57	C₂×C₄	—	37	1	no	—
58	C₂×C₄	—	37	2	no	—
59	C₂×C₄	—	37	2	no	—
60	C₂×C₄	—	37	2	no	—
61	C₂×C₄	C₂×#3866	1	2	yes	—
62	C₂×C₄	C₂×#3866	1	1	yes	characteristic
63	C₈	—	74	1	no	—
64	C₈	—	74	1	no	—
65	C₈	—	74	2	no	—
66	C₂²	—	37	2	no	—
67	C₂²	—	74	1	no	—
68	C₂²	—	74	1	no	—
69	C₂²	C₂²×#3866	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	37	1	no	—
72	C₄	—	37	1	no	—
73	C₄	—	74	2	no	—
74	C₄	C₄⋊#3866	1	2	yes	—
75	C₂	—	74	2	no	—
76	C₂	C₂×C₄⋊#3866	1	1	yes	characteristic
77	C₂	#11924623	1	1	yes	characteristic
78	C₂	#11924624	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#3866
commutator, socle	C₂²×C₃₇	C₂²×C₄
Fitting	C₄⋊C₄×C₃₇	C₄
prime radical	C₂²×D₃₇	C₂×C₄
cosocle	C₂×Dic₃₇	C₂³
hypercenter	C₄⋊C₄	#3866
hypocenter	C₃₇	#424
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #11924603	C₂	semidirect
4. C₄⋊#64438	C₂	semidirect
40. C₃₇	#424	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10596953	2
C₂×D₃₇⋊C₈	2
#11924603	2
C₄⋊#64438	2
#11924494	2
#424	37