Subgroups — #14557638

Order 2368.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596942	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₇₄	C₂	1	1	yes	maximal, characteristic
3	#11924467	C₂	1	1	yes	maximal, characteristic
4	#11924460	C₂	1	1	yes	maximal, characteristic
5	#11924459	C₂	1	1	yes	maximal, characteristic
6	#11924447	C₂	1	1	yes	maximal, characteristic
7	C₄×Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₃₇	C₂²	1	1	yes	characteristic
9	C₂×Dic₇₄	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₃₇	—	2	1	no	—
11	C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
12	C₄²×C₃₇	—	2	1	no	—
13	C₄²×C₃₇	C₂²	1	1	yes	characteristic
14	#10596942	C₄	1	4	yes	complemented
15	C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
16	#10596936	—	2	1	no	—
17	C₄×Dic₃₇	—	2	1	no	—
18	C₂×#64436	C₂²	1	1	yes	characteristic
19	C₂×#64436	C₂²	1	1	yes	characteristic
20	Q₈×C₃₇	—	2	1	no	—
21	Q₈×C₃₇	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₃₇	—	2	1	no	—
23	C₂×C₄×C₃₇	—	2	1	no	—
24	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
25	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
26	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
27	C₂×Dic₃₇	—	2	1	no	—
28	C₂×Dic₃₇	—	2	1	no	—
29	Dic₇₄	—	2	1	no	—
30	Dic₇₄	C₂×C₄	1	2	yes	—
31	#64436	—	2	1	no	—
32	#64436	C₂×C₄	1	2	yes	—
33	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
34	C₄×C₃₇	—	2	2	no	—
35	C₄×C₃₇	—	2	1	no	—
36	C₄×C₃₇	—	2	1	no	—
37	C₄×C₃₇	—	4	1	no	—
38	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
39	C₄×C₃₇	#41	1	1	yes	characteristic
40	Dic₃₇	—	2	2	no	—
41	Dic₃₇	—	4	1	no	—
42	C₂×C₃₇	C₄×D₄	1	1	yes	characteristic
43	C₂×C₃₇	#137	1	1	yes	characteristic
44	C₂×C₃₇	#137	1	1	yes	characteristic
45	#441	—	37	1	no	maximal, Sylow
46	C₃₇	#441	1	1	yes	characteristic, complemented, Sylow
47	C₂×Q₁₆	—	37	1	no	—
48	C₄×Q₈	—	37	1	no	—
49	C₄×Q₈	D₃₇	1	1	yes	characteristic
50	#106	—	37	1	no	—
51	#103	—	37	1	no	—
52	#103	—	37	1	no	—
53	#97	—	37	1	no	—
54	C₂×Q₈	—	37	1	no	—
55	C₂×Q₈	C₂×D₃₇	1	1	yes	characteristic
56	Q₁₆	—	37	4	no	—
57	C₂×C₈	—	37	1	no	—
58	C₂×C₈	—	37	1	no	—
59	C₄⋊C₄	—	2	1	no	—
60	C₄⋊C₄	—	37	1	no	—
61	C₄⋊C₄	—	74	1	no	—
62	C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
63	C₄²	—	2	1	no	—
64	C₄²	—	74	1	no	—
65	C₄²	C₂×D₃₇	1	1	yes	characteristic
66	Q₈	—	2	1	no	—
67	Q₈	—	37	2	no	—
68	Q₈	—	74	1	no	—
69	Q₈	C₄×D₃₇	1	2	yes	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	74	1	no	—
73	C₂×C₄	—	74	1	no	—
74	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
75	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
76	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
77	C₈	—	37	2	no	—
78	C₈	—	74	1	no	—
79	C₂²	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
80	C₄	—	2	2	no	—
81	C₄	—	2	1	no	—
82	C₄	—	2	1	no	—
83	C₄	—	4	1	no	—
84	C₄	—	74	2	no	—
85	C₄	—	148	1	no	—
86	C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
87	C₄	#10596962	1	1	yes	characteristic
88	C₂	C₄×C₂²⋊D₃₇	1	1	yes	characteristic
89	C₂	#11924566	1	1	yes	characteristic
90	C₂	#11924567	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₇
commutator	C₄×C₃₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	C₄×Q₈×C₃₇	C₂
socle, prime radical	C₂²×C₃₇	C₂×D₄
cosocle	C₂×C₄×C₃₇	C₂³
hypercenter	C₄×Q₈	D₃₇
hypocenter	C₃₇	#441
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
14. #10596942	C₄	semidirect
46. C₃₇	#441	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10596942	2
C₄×Dic₇₄	2
#11924467	2
#11924460	2
#11924459	2
#11924447	2
C₄×Q₈×C₃₇	2
#441	37