Subgroups — #14557822

Order 2368.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924535	C₂	1	1	yes	maximal, characteristic, complemented
2	#11924498	C₂	1	1	yes	maximal, characteristic
3	#11924467	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924465	C₂	1	1	yes	maximal, characteristic, complemented
5	#11924458	C₂	1	1	yes	maximal, characteristic
6	#11924456	C₂	1	1	yes	maximal, characteristic
7	#106×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₁₄₈	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₃₇	—	2	1	no	—
10	C₂×Dic₇₄	—	2	1	no	—
11	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
14	#10596938	—	2	1	no	—
15	C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
16	#10596936	—	2	1	no	—
17	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
18	C₂×#64436	C₂²	1	1	yes	characteristic
19	C₂²×D₃₇	—	2	1	no	—
20	C₂×C₄×C₃₇	—	2	1	no	—
21	C₂×C₄×C₃₇	—	2	1	no	—
22	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
23	C₂×Dic₃₇	—	2	1	no	—
24	C₂×Dic₃₇	D₄	1	1	yes	characteristic
25	C₂×Dic₃₇	D₄	1	1	yes	characteristic
26	D₁₄₈	—	2	1	no	—
27	D₁₄₈	Q₈	1	2	yes	complemented
28	C₄×D₃₇	—	4	2	no	—
29	Dic₇₄	—	4	2	no	—
30	C₈×C₃₇	—	2	1	no	—
31	#64436	—	2	1	no	—
32	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
33	C₂×D₃₇	—	2	2	no	—
34	C₂×D₃₇	—	4	1	no	—
35	C₂×D₃₇	—	4	1	no	—
36	C₄×C₃₇	—	4	1	no	—
37	C₄×C₃₇	—	4	1	no	—
38	C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
39	C₄×C₃₇	#41	1	1	yes	characteristic
40	Dic₃₇	—	2	1	no	—
41	Dic₃₇	—	4	1	no	—
42	Dic₃₇	SD₁₆	1	2	yes	—
43	C₂×C₃₇	C₂²⋊Q₈	1	1	yes	characteristic
44	C₂×C₃₇	C₂×SD₁₆	1	1	yes	characteristic
45	C₂×C₃₇	AGL(1,ℤ/8)	1	1	yes	characteristic
46	D₃₇	—	4	2	no	—
47	#476	—	37	1	no	maximal, Sylow
48	C₃₇	#476	1	1	yes	characteristic, complemented, Sylow
49	C₄⋊Q₈	—	37	1	no	—
50	C₄×D₄	—	37	1	no	—
51	#106	—	37	1	no	—
52	#106	D₃₇	1	1	yes	characteristic, complemented
53	C₄⋊C₈	—	37	1	no	—
54	#102	—	37	1	no	—
55	#102	—	37	1	no	—
56	C₂×Q₈	—	74	1	no	—
57	C₂×D₄	—	37	1	no	—
58	C₂²×C₄	—	74	1	no	—
59	C₂×C₈	—	37	1	no	—
60	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
61	C₄⋊C₄	—	37	1	no	—
62	C₄⋊C₄	—	74	1	no	—
63	C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
64	C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
65	C₂²⋊C₄	—	74	1	no	—
66	C₄²	—	37	1	no	—
67	C₂³	—	74	1	no	—
68	Q₈	—	148	2	no	—
69	D₄	—	37	2	no	—
70	D₄	—	74	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	37	1	no	—
74	C₂×C₄	—	37	1	no	—
75	C₂×C₄	—	74	1	no	—
76	C₂×C₄	—	148	2	no	—
77	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	74	1	no	—
80	C₂²	—	74	2	no	—
81	C₂²	—	148	1	no	—
82	C₂²	—	148	1	no	—
83	C₂²	D₄×D₃₇	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	37	2	no	—
87	C₄	—	74	1	no	—
88	C₄	—	148	1	no	—
89	C₄	#10596962	1	1	yes	characteristic
90	C₄	Q₈×D₃₇	1	1	yes	characteristic
91	C₂	—	148	2	no	—
92	C₂	#11924514	1	1	yes	characteristic
93	C₂	SD₁₆×D₃₇	1	1	yes	characteristic
94	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	#106×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₄
prime radical	C₂×D₁₄₈	C₂²
hypercenter	#106	D₃₇
hypocenter	C₃₇	#476
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
1. #11924535	C₂	semidirect
3. #11924467	C₂	semidirect
4. #11924465	C₂	semidirect
7. #106×C₃₇	C₂	semidirect
27. D₁₄₈	Q₈	semidirect
48. C₃₇	#476	semidirect
52. #106	D₃₇	semidirect

Maximal subgroups

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

subgroup	index
#11924535	2
#11924498	2
#11924467	2
#11924465	2
#11924458	2
#11924456	2
#106×C₃₇	2
#476	37