Subgroups — #14557529

Order 2368.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#64436	C₂	1	1	yes	maximal, characteristic, complemented
2	#11924495	C₂	1	1	yes	maximal, characteristic, complemented
3	#11924460	C₂	1	2	yes	maximal, complemented
4	#11924457	C₂	1	2	yes	maximal, complemented
5	C₂×#41×C₃₇	C₂	1	1	yes	maximal, characteristic
6	#41×C₃₇	—	2	2	no	—
7	#41×C₃₇	C₄	1	4	yes	complemented
8	C₂×Q₈×C₃₇	C₂²	1	1	yes	characteristic
9	C₂×D₄×C₃₇	—	2	1	no	—
10	C₂×D₄×C₃₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₃₇	—	2	1	no	—
12	C₂²×C₄×C₃₇	C₂²	1	1	yes	characteristic
13	C₂²⋊Dic₃₇	—	2	1	no	—
14	C₄⋊Dic₃₇	C₂²	1	2	yes	—
15	C₄×Dic₃₇	—	2	1	no	—
16	C₂×#64436	—	2	2	no	—
17	C₂×#64436	C₂²	1	2	yes	—
18	C₂³×C₃₇	—	2	1	no	—
19	C₂³×C₃₇	D₄	1	1	yes	characteristic
20	Q₈×C₃₇	—	2	1	no	—
21	Q₈×C₃₇	C₂×C₄	1	2	yes	—
22	D₄×C₃₇	—	2	4	no	—
23	D₄×C₃₇	—	2	1	no	—
24	D₄×C₃₇	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₃₇	—	2	1	no	—
26	C₂×C₄×C₃₇	—	2	4	no	—
27	C₂×C₄×C₃₇	C₂×C₄	1	2	yes	—
28	C₂×C₄×C₃₇	D₄	1	2	yes	—
29	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
30	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
31	C₂×Dic₃₇	—	2	2	no	—
32	#64436	—	2	2	no	—
33	C₂²×C₃₇	—	2	2	no	—
34	C₂²×C₃₇	—	2	2	no	—
35	C₂²×C₃₇	—	4	2	no	—
36	C₂²×C₃₇	C₂²⋊C₄	1	2	yes	—
37	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
38	C₄×C₃₇	—	2	2	no	—
39	C₄×C₃₇	C₂²⋊C₄	1	2	yes	—
40	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
41	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
42	Dic₃₇	—	4	2	no	—
43	C₂×C₃₇	—	2	2	no	—
44	C₂×C₃₇	—	4	2	no	—
45	C₂×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₃₇	#135	1	2	yes	—
47	#416	—	37	1	no	maximal, Sylow
48	C₃₇	#416	1	1	yes	characteristic, complemented, Sylow
49	C₂×#41	D₃₇	1	1	yes	characteristic
50	C₂²×C₈	—	37	1	no	—
51	#117	—	37	1	no	—
52	#103	—	37	2	no	—
53	#102	—	37	2	no	—
54	#41	—	2	2	no	—
55	#41	Dic₃₇	1	4	yes	complemented
56	C₂×Q₈	C₂×D₃₇	1	1	yes	characteristic
57	C₂×D₄	—	2	1	no	—
58	C₂×D₄	C₂×D₃₇	1	1	yes	characteristic
59	C₂²×C₄	—	2	1	no	—
60	C₂²×C₄	C₂×D₃₇	1	1	yes	characteristic
61	C₂×C₈	—	37	2	no	—
62	C₂×C₈	—	74	2	no	—
63	C₄⋊C₄	—	37	2	no	—
64	C₂²⋊C₄	—	74	1	no	—
65	C₄²	—	74	1	no	—
66	C₂³	—	2	1	no	—
67	C₂³	C₂²⋊D₃₇	1	1	yes	characteristic
68	Q₈	—	2	1	no	—
69	Q₈	C₂×Dic₃₇	1	2	yes	—
70	D₄	—	2	4	no	—
71	D₄	—	2	1	no	—
72	D₄	C₂×Dic₃₇	1	2	yes	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	—	74	2	no	—
76	C₂×C₄	C₂×Dic₃₇	1	2	yes	—
77	C₂×C₄	C₂²⋊D₃₇	1	2	yes	—
78	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
79	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
80	C₈	—	74	2	no	—
81	C₂²	—	2	2	no	—
82	C₂²	—	2	2	no	—
83	C₂²	—	4	2	no	—
84	C₂²	C₂²⋊Dic₃₇	1	2	yes	—
85	C₂²	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	148	2	no	—
88	C₄	C₂²⋊Dic₃₇	1	2	yes	—
89	C₄	C₂²×Dic₃₇	1	1	yes	characteristic
90	C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
91	C₂	—	2	2	no	—
92	C₂	—	4	2	no	—
93	C₂	C₂×C₂²⋊Dic₃₇	1	1	yes	characteristic
94	C₂	#11924556	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₃₇
commutator	C₄×C₃₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₇
Fitting, prime radical	C₂×#41×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₄
cosocle	C₂×C₄×C₃₇	C₂³
hypercenter	C₂×#41	D₃₇
hypocenter	C₃₇	#416
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×#64436	C₂	semidirect
2. #11924495	C₂	semidirect
3. #11924460	C₂	semidirect
4. #11924457	C₂	semidirect
7. #41×C₃₇	C₄	semidirect
48. C₃₇	#416	semidirect
55. #41	Dic₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#64436	2
#11924495	2
#11924460	2
#11924457	2
C₂×#41×C₃₇	2
#416	37