Subgroups — #14558548

Order 2368.

102 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	D₃₇⋊M₁₆	C₂	1	1	yes	maximal, characteristic
3	#11924607	C₂	1	2	yes	maximal, complemented
4	#11924606	C₂	1	2	yes	maximal, complemented
5	M₁₆×D₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
7	#10596957	—	2	1	no	—
8	C₂×#64438	—	2	1	no	—
9	#10596953	—	2	1	no	—
10	#10596953	C₂²	1	1	yes	characteristic
11	#10596953	C₂²	1	2	yes	—
12	#10596953	C₂²	1	1	yes	characteristic
13	D₃₇⋊C₈	—	2	1	no	—
14	M₁₆×C₃₇	C₄	1	1	yes	characteristic
15	#10596934	C₄	1	1	yes	characteristic
16	#10596929	C₄	1	2	yes	—
17	C₈×D₃₇	C₂²	1	2	yes	—
18	C₂²×D₃₇	Q₈	1	1	yes	characteristic
19	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₃₇	D₄	1	1	yes	characteristic
21	C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
22	C₄×D₃₇	D₄	1	1	yes	characteristic
23	C₄×D₃₇	Q₈	1	1	yes	characteristic
24	C₄×D₃₇	C₂³	1	1	yes	characteristic
25	#64438	—	2	1	no	—
26	#64438	—	2	1	no	—
27	#64438	—	2	2	no	—
28	C₈×C₃₇	C₂×C₄	1	2	yes	—
29	#64436	C₂×C₄	1	2	yes	—
30	C₂²×C₃₇	C₄⋊C₄	1	1	yes	characteristic
31	C₂×D₃₇	—	4	1	no	—
32	C₂×D₃₇	C₄⋊C₄	1	1	yes	characteristic
33	C₂×D₃₇	C₂×Q₈	1	1	yes	characteristic
34	C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
35	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
36	Dic₃₇	C₄⋊C₄	1	1	yes	characteristic
37	Dic₃₇	C₂×D₄	1	1	yes	characteristic
38	C₂×C₃₇	—	2	1	no	—
39	C₂×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
40	D₃₇	—	2	1	no	—
41	D₃₇	—	2	1	no	—
42	#430	—	37	1	no	maximal, Sylow
43	C₃₇	#430	1	1	yes	characteristic, complemented, Sylow
44	C₂×M₁₆	—	37	1	no	—
45	C₂×M₁₆	—	37	1	no	—
46	C₂×M₁₆	—	37	1	no	—
47	#108	—	37	2	no	—
48	#108	—	37	2	no	—
49	C₂²×C₄	—	37	1	no	—
50	M₁₆	—	37	1	no	—
51	M₁₆	—	37	2	no	—
52	M₁₆	—	37	1	no	—
53	M₁₆	—	37	2	no	—
54	M₁₆	—	37	1	no	—
55	M₁₆	—	74	1	no	—
56	M₁₆	—	74	1	no	—
57	M₁₆	#3866	1	1	yes	characteristic
58	C₂×C₈	—	37	2	no	—
59	C₂×C₈	—	74	1	no	—
60	C₂×C₈	—	74	1	no	—
61	C₂³	—	37	1	no	—
62	C₂×C₄	—	37	1	no	—
63	C₂×C₄	—	37	1	no	—
64	C₂×C₄	—	37	1	no	—
65	C₂×C₄	—	37	1	no	—
66	C₂×C₄	—	37	1	no	—
67	C₂×C₄	C₂×#3866	1	1	yes	characteristic
68	C₈	—	37	2	no	—
69	C₈	—	74	1	no	—
70	C₈	—	74	1	no	—
71	C₈	—	74	2	no	—
72	C₈	C₂×#3866	1	2	yes	—
73	C₂²	—	37	1	no	—
74	C₂²	—	37	1	no	—
75	C₂²	—	148	1	no	—
76	C₂²	C₄⋊#3866	1	1	yes	characteristic
77	C₄	—	37	1	no	—
78	C₄	—	37	1	no	—
79	C₄	C₄⋊#3866	1	1	yes	characteristic
80	C₄	C₂²×#3866	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	—	74	1	no	—
83	C₂	—	74	1	no	—
84	C₂	C₂×C₄⋊#3866	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₄⋊#3866
commutator	C₄×C₃₇	C₂²×C₄
Frattini	C₄	C₂²×#3866
Fitting	M₁₆×C₃₇	C₄
socle	C₂×C₃₇	C₂×C₄⋊C₄
prime radical	C₂²×D₃₇	Q₈
cosocle	C₄×D₃₇	C₂³
hypercenter	M₁₆	#3866
hypocenter	C₃₇	#430
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
3. #11924607	C₂	semidirect
4. #11924606	C₂	semidirect
43. C₃₇	#430	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
D₃₇⋊M₁₆	2
#11924607	2
#11924606	2
M₁₆×D₃₇	2
#430	37