Subgroups — #14557867

Order 2368.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924512	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₃₇	C₂	1	1	yes	maximal, characteristic
3	#11924470	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924469	C₂	1	1	yes	maximal, characteristic, complemented
5	#11924460	C₂	1	1	yes	maximal, characteristic, complemented
6	#11924448	C₂	1	1	yes	maximal, characteristic
7	#103×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×C₃₇	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₃₇	—	2	1	no	—
10	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
13	#10596938	—	2	1	no	—
14	C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
15	C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
16	#10596936	—	2	1	no	—
17	#10596936	—	2	1	no	—
18	C₂×#64436	C₂²	1	1	yes	characteristic
19	C₂²×D₃₇	D₄	1	1	yes	characteristic
20	Q₈×C₃₇	—	2	1	no	—
21	Q₈×C₃₇	—	2	1	no	—
22	C₂×C₄×C₃₇	—	2	1	no	—
23	C₂×C₄×C₃₇	—	2	1	no	—
24	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
25	C₂×Dic₃₇	—	2	1	no	—
26	C₂×Dic₃₇	—	2	1	no	—
27	C₂×Dic₃₇	D₄	1	1	yes	characteristic
28	C₄×D₃₇	—	2	1	no	—
29	C₄×D₃₇	—	2	1	no	—
30	C₄×D₃₇	—	4	2	no	—
31	C₈×C₃₇	—	2	1	no	—
32	#64436	—	2	1	no	—
33	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
34	C₂×D₃₇	—	2	1	no	—
35	C₂×D₃₇	—	2	1	no	—
36	C₂×D₃₇	Q₁₆	1	2	yes	—
37	C₄×C₃₇	—	4	1	no	—
38	C₄×C₃₇	—	4	1	no	—
39	C₄×C₃₇	#41	1	1	yes	characteristic
40	C₄×C₃₇	#41	1	1	yes	characteristic
41	Dic₃₇	—	2	1	no	—
42	Dic₃₇	—	4	1	no	—
43	Dic₃₇	—	4	1	no	—
44	C₂×C₃₇	#123	1	1	yes	characteristic
45	C₂×C₃₇	C₂×Q₁₆	1	1	yes	characteristic
46	C₂×C₃₇	AGL(1,ℤ/8)	1	1	yes	characteristic
47	D₃₇	—	2	2	no	—
48	#484	—	37	1	no	maximal, Sylow
49	C₃₇	#484	1	1	yes	characteristic, complemented, Sylow
50	C₂²⋊Q₈	—	37	1	no	—
51	C₂×C₄⋊C₄	—	37	1	no	—
52	#107	—	37	1	no	—
53	#107	—	37	1	no	—
54	#103	—	37	1	no	—
55	#103	D₃₇	1	1	yes	characteristic, complemented
56	C₂²⋊C₈	—	37	1	no	—
57	C₂×Q₈	C₂×D₃₇	1	1	yes	characteristic
58	C₂²×C₄	—	37	1	no	—
59	C₂²×C₄	—	74	1	no	—
60	C₂×C₈	—	37	1	no	—
61	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
62	C₄⋊C₄	—	37	1	no	—
63	C₄⋊C₄	—	37	1	no	—
64	C₄⋊C₄	—	74	1	no	—
65	C₄⋊C₄	—	74	1	no	—
66	C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
67	C₂²⋊C₄	—	74	1	no	—
68	C₂³	—	37	1	no	—
69	Q₈	—	2	1	no	—
70	Q₈	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	37	1	no	—
74	C₂×C₄	—	74	1	no	—
75	C₂×C₄	—	74	1	no	—
76	C₂×C₄	—	74	1	no	—
77	C₂×C₄	—	74	1	no	—
78	C₂×C₄	—	148	2	no	—
79	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	74	1	no	—
82	C₂²	—	37	2	no	—
83	C₂²	—	74	1	no	—
84	C₂²	—	74	1	no	—
85	C₂²	D₄×D₃₇	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	74	1	no	—
89	C₄	—	148	1	no	—
90	C₄	—	148	1	no	—
91	C₄	#10596962	1	1	yes	characteristic
92	C₄	#10596964	1	1	yes	characteristic
93	C₂	—	74	2	no	—
94	C₂	#11924518	1	1	yes	characteristic
95	C₂	Q₁₆×D₃₇	1	1	yes	characteristic
96	C₂	#11924563	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₇
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	#103×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₄
prime radical	C₂²×D₃₇	D₄
hypercenter	#103	D₃₇
hypocenter	C₃₇	#484
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
3. #11924470	C₂	semidirect
4. #11924469	C₂	semidirect
5. #11924460	C₂	semidirect
7. #103×C₃₇	C₂	semidirect
49. C₃₇	#484	semidirect
55. #103	D₃₇	semidirect

Maximal subgroups

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

subgroup	index
#11924512	2
C₄⋊C₄×D₃₇	2
#11924470	2
#11924469	2
#11924460	2
#11924448	2
#103×C₃₇	2
#484	37