Subgroups — #14557557

Order 2368.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596934	C₂	1	2	yes	maximal
2	C₄⋊#64436	C₂	1	4	yes	maximal, complemented
3	C₂×C₄²×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₃₇	C₄	1	2	yes	—
5	C₂²×C₄×C₃₇	C₂²	1	1	yes	characteristic
6	C₄²×C₃₇	C₄	1	1	yes	characteristic
7	C₄²×C₃₇	C₄	1	1	yes	characteristic
8	C₄²×C₃₇	C₂²	1	2	yes	—
9	#10596934	—	2	4	no	—
10	C₂×#64436	C₂²	1	4	yes	—
11	C₂³×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₃₇	—	2	4	no	—
13	C₂×C₄×C₃₇	C₂×C₄	1	2	yes	—
14	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₃₇	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₃₇	D₄	1	2	yes	—
17	C₂×C₄×C₃₇	Q₈	1	2	yes	—
18	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
19	#64436	—	2	4	no	—
20	C₂²×C₃₇	—	2	2	no	—
21	C₂²×C₃₇	C₄⋊C₄	1	2	yes	—
22	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
23	C₄×C₃₇	—	2	2	no	—
24	C₄×C₃₇	C₄⋊C₄	1	2	yes	—
25	C₄×C₃₇	M₁₆	1	4	yes	complemented
26	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
27	C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₃₇	—	2	2	no	—
29	C₂×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₃₇	C₂×M₁₆	1	2	yes	—
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	D₃₇	1	1	yes	characteristic
35	C₄⋊C₈	—	37	4	no	—
36	C₂²×C₄	Dic₃₇	1	2	yes	—
37	C₂²×C₄	C₂×D₃₇	1	1	yes	characteristic
38	M₁₆	—	74	4	no	—
39	C₂×C₈	—	37	4	no	—
40	C₄²	Dic₃₇	1	1	yes	characteristic
41	C₄²	Dic₃₇	1	1	yes	characteristic
42	C₄²	C₂×D₃₇	1	2	yes	—
43	C₂³	C₂×Dic₃₇	1	1	yes	characteristic
44	C₂×C₄	—	2	4	no	—
45	C₂×C₄	Dic₇₄	1	2	yes	—
46	C₂×C₄	D₁₄₈	1	2	yes	—
47	C₂×C₄	C₂×Dic₃₇	1	2	yes	—
48	C₂×C₄	C₂×Dic₃₇	1	2	yes	—
49	C₂×C₄	C₂×Dic₃₇	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
51	C₈	—	74	4	no	—
52	C₂²	—	2	2	no	—
53	C₂²	C₄⋊Dic₃₇	1	2	yes	—
54	C₂²	C₂²×Dic₃₇	1	1	yes	characteristic
55	C₄	—	2	2	no	—
56	C₄	#10596934	1	4	yes	complemented
57	C₄	C₄⋊Dic₃₇	1	2	yes	—
58	C₄	C₂×Dic₇₄	1	1	yes	characteristic
59	C₄	C₂×D₁₄₈	1	1	yes	characteristic
60	C₂	—	2	2	no	—
61	C₂	C₂×C₄⋊Dic₃₇	1	1	yes	characteristic
62	C₂	C₂×#10596934	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃₇
commutator, socle	C₂²×C₃₇	C₂²×C₄
Fitting	C₂×C₄²×C₃₇	C₂
prime radical	C₂³×C₃₇	C₂×C₄
cosocle	C₂×C₄×C₃₇	C₂³
hypercenter	C₂×C₄²	D₃₇
hypocenter	C₃₇	#423
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₄⋊#64436	C₂	semidirect
25. C₄×C₃₇	M₁₆	semidirect
32. C₃₇	#423	semidirect
56. C₄	#10596934	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10596934	2
C₄⋊#64436	2
C₂×C₄²×C₃₇	2
#423	37