Subgroups — #14558538

Order 2368.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596953	C₂	1	2	yes	maximal
2	#11924603	C₂	1	4	yes	maximal, complemented
3	C₄²×D₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×D₃₇	C₄	1	2	yes	—
5	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
6	C₂×#64438	C₂²	1	4	yes	—
7	#10596953	—	2	4	no	—
8	C₄²×C₃₇	C₄	1	1	yes	characteristic
9	C₄×Dic₃₇	C₄	1	1	yes	characteristic
10	C₄×Dic₃₇	C₂²	1	2	yes	—
11	C₂²×D₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₃₇	C₂×C₄	1	2	yes	—
13	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₃₇	C₂×C₄	1	2	yes	—
15	C₂×Dic₃₇	C₂³	1	1	yes	characteristic
16	C₄×D₃₇	—	2	4	no	—
17	C₄×D₃₇	D₄	1	2	yes	—
18	C₄×D₃₇	Q₈	1	2	yes	—
19	#64438	—	2	4	no	—
20	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
21	C₂×D₃₇	—	2	2	no	—
22	C₂×D₃₇	C₄⋊C₄	1	2	yes	—
23	C₄×C₃₇	—	2	2	no	—
24	C₄×C₃₇	C₄⋊C₄	1	2	yes	—
25	Dic₃₇	M₁₆	1	4	yes	complemented
26	Dic₃₇	C₂×D₄	1	1	yes	characteristic
27	Dic₃₇	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₃₇	C₂×M₁₆	1	2	yes	—
30	D₃₇	—	2	2	no	—
31	#423	—	37	1	no	maximal, Sylow
32	C₃₇	#423	1	1	yes	characteristic, complemented, Sylow
33	C₂×M₁₆	—	37	2	no	—
34	C₂×C₄²	—	37	1	no	—
35	C₄⋊C₈	—	37	4	no	—
36	C₂²×C₄	—	37	1	no	—
37	C₂²×C₄	—	37	2	no	—
38	M₁₆	—	74	4	no	—
39	C₂×C₈	—	37	4	no	—
40	C₄²	—	37	1	no	—
41	C₄²	—	37	2	no	—
42	C₄²	#3866	1	1	yes	characteristic
43	C₂³	—	37	1	no	—
44	C₂×C₄	—	37	1	no	—
45	C₂×C₄	—	37	2	no	—
46	C₂×C₄	—	37	2	no	—
47	C₂×C₄	—	37	2	no	—
48	C₂×C₄	—	74	4	no	—
49	C₂×C₄	C₂×#3866	1	2	yes	—
50	C₂×C₄	C₂×#3866	1	1	yes	characteristic
51	C₈	—	74	4	no	—
52	C₂²	—	37	2	no	—
53	C₂²	—	74	2	no	—
54	C₂²	C₂²×#3866	1	1	yes	characteristic
55	C₄	—	2	2	no	—
56	C₄	—	37	1	no	—
57	C₄	—	37	1	no	—
58	C₄	—	37	4	no	—
59	C₄	C₄⋊#3866	1	2	yes	—
60	C₂	—	74	2	no	—
61	C₂	C₂×C₄⋊#3866	1	1	yes	characteristic
62	C₂	D₃₇⋊M₁₆	1	2	yes	—

	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	#423
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
2. #11924603	C₂	semidirect
25. Dic₃₇	M₁₆	semidirect
32. C₃₇	#423	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
#11924603	2
C₄²×D₃₇	2
#423	37