Subgroups — #14558258

Order 2368.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924534	C₂	1	2	yes	maximal
2	#11924527	C₂	1	2	yes	maximal
3	#11924526	C₂	1	4	yes	maximal
4	Q₈×Dic₃₇	C₂	1	2	yes	maximal
5	C₄×Dic₇₄	C₂	1	1	yes	maximal, characteristic
6	C₄×Dic₇₄	C₂	1	1	yes	maximal, characteristic
7	#11924501	C₂	1	2	yes	maximal
8	C₄⋊Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic
9	C₂×Q₈×C₃₇	C₂²	1	2	yes	—
10	C₂×Dic₇₄	C₂²	1	1	yes	characteristic
11	C₂×Dic₇₄	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
13	C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
14	C₄²×C₃₇	C₂²	1	1	yes	characteristic
15	C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
16	C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
17	C₄⋊Dic₃₇	C₂²	1	4	yes	—
18	#10596936	C₂²	1	4	yes	—
19	#10596936	C₂²	1	2	yes	—
20	#10596936	C₂²	1	2	yes	—
21	#10596936	C₂²	1	4	yes	—
22	C₄×Dic₃₇	C₂²	1	2	yes	—
23	C₄×Dic₃₇	C₂²	1	4	yes	—
24	C₄×Dic₃₇	C₂²	1	2	yes	—
25	Q₈×C₃₇	—	2	4	no	—
26	C₂×C₄×C₃₇	C₂³	1	4	yes	—
27	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
28	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
29	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
30	C₂×Dic₃₇	C₂³	1	2	yes	—
31	C₂×Dic₃₇	C₂³	1	2	yes	—
32	C₂×Dic₃₇	C₂³	1	2	yes	—
33	C₂×Dic₃₇	C₂³	1	2	yes	—
34	Dic₇₄	—	2	2	no	—
35	Dic₇₄	Q₈	1	4	yes	complemented
36	C₂²×C₃₇	C₂⁴	1	1	yes	characteristic
37	C₄×C₃₇	—	2	4	no	—
38	C₄×C₃₇	—	2	1	no	—
39	C₄×C₃₇	C₂×Q₈	1	2	yes	—
40	C₄×C₃₇	#41	1	2	yes	—
41	Dic₃₇	—	2	2	no	—
42	Dic₃₇	—	2	2	no	—
43	Dic₃₇	—	2	2	no	—
44	Dic₃₇	C₂×Q₈	1	4	yes	—
45	C₂×C₃₇	C₂²×Q₈	1	1	yes	characteristic
46	C₂×C₃₇	C₂×#41	1	1	yes	characteristic
47	C₂×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
48	#557	—	37	1	no	maximal, Sylow
49	C₃₇	#557	1	1	yes	characteristic, complemented, Sylow
50	C₄⋊Q₈	—	37	2	no	—
51	C₄⋊Q₈	D₃₇	1	1	yes	characteristic
52	#125	—	37	4	no	—
53	#125	—	37	2	no	—
54	C₄×Q₈	—	37	2	no	—
55	C₄×Q₈	—	37	2	no	—
56	C₄×Q₈	—	37	1	no	—
57	C₄×Q₈	—	37	1	no	—
58	C₂×Q₈	—	37	1	no	—
59	C₂×Q₈	—	37	1	no	—
60	C₂×Q₈	C₂×D₃₇	1	2	yes	—
61	C₄⋊C₄	—	37	2	no	—
62	C₄⋊C₄	—	37	2	no	—
63	C₄⋊C₄	—	37	4	no	—
64	C₄⋊C₄	—	37	4	no	—
65	C₄⋊C₄	—	37	1	no	—
66	C₄⋊C₄	—	37	4	no	—
67	C₄⋊C₄	—	37	1	no	—
68	C₄⋊C₄	C₂×D₃₇	1	2	yes	—
69	C₄⋊C₄	C₂×D₃₇	1	2	yes	—
70	C₄²	—	37	4	no	—
71	C₄²	—	37	2	no	—
72	C₄²	—	37	2	no	—
73	C₄²	C₂×D₃₇	1	1	yes	characteristic
74	Q₈	—	2	4	no	—
75	Q₈	—	37	4	no	—
76	Q₈	—	74	2	no	—
77	C₂×C₄	—	37	2	no	—
78	C₂×C₄	—	37	2	no	—
79	C₂×C₄	—	37	2	no	—
80	C₂×C₄	—	37	2	no	—
81	C₂×C₄	C₂²×D₃₇	1	4	yes	—
82	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
83	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
84	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
85	C₂²	C₂³×D₃₇	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	—	2	1	no	—
88	C₄	—	37	4	no	—
89	C₄	—	74	2	no	—
90	C₄	—	74	2	no	—
91	C₄	—	74	2	no	—
92	C₄	#10596964	1	2	yes	—
93	C₄	Q₈×D₃₇	1	2	yes	—
94	C₂	C₂×Q₈×D₃₇	1	1	yes	characteristic
95	C₂	C₂×#10596964	1	1	yes	characteristic
96	C₂	#11924584	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₃₇
commutator, socle, prime radical, cosocle	C₂²×C₃₇	C₂⁴
Fitting	C₄⋊Q₈×C₃₇	C₂
hypercenter	C₄⋊Q₈	D₃₇
hypocenter	C₃₇	#557
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
35. Dic₇₄	Q₈	semidirect
49. C₃₇	#557	semidirect

Maximal subgroups

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

subgroup	index
#11924534	2
#11924527	2
#11924526	2
Q₈×Dic₃₇	2
C₄×Dic₇₄	2
#11924501	2
C₄⋊Q₈×C₃₇	2
#557	37