Subgroups — #17992764

Order 4736.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557912	C₂	1	1	yes	maximal, characteristic
2	#14557332	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#356	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596942	—	2	1	no	—
5	C₂×#10596942	—	2	1	no	—
6	#11924536	C₄	1	1	yes	characteristic
7	#11924455	—	2	1	no	—
8	C₄×#64436	C₄	1	1	yes	characteristic
9	C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
10	#101×C₃₇	—	2	1	no	—
11	C₂×Q₈×C₃₇	D₄	1	1	yes	characteristic
12	C₂×Q₈×C₃₇	D₄	1	1	yes	characteristic
13	C₂×Dic₇₄	—	2	1	no	—
14	M₁₆×C₃₇	—	4	1	no	—
15	C₄⋊C₄×C₃₇	—	4	1	no	—
16	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
17	#10596942	—	4	2	no	—
18	#10596942	—	4	2	no	—
19	C₄⋊Dic₃₇	—	4	1	no	—
20	#10596934	—	4	1	no	—
21	C₂×#64436	—	2	1	no	—
22	Q₈×C₃₇	—	4	1	no	—
23	Q₈×C₃₇	—	4	1	no	—
24	C₂×C₄×C₃₇	—	2	1	no	—
25	C₂×C₄×C₃₇	—	2	1	no	—
26	C₂×C₄×C₃₇	—	2	1	no	—
27	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₃₇	—	4	1	no	—
29	Dic₇₄	—	4	1	no	—
30	Dic₇₄	—	4	1	no	—
31	C₈×C₃₇	—	8	1	no	—
32	#64436	—	2	2	no	—
33	#64436	—	8	1	no	—
34	C₂²×C₃₇	#99	1	1	yes	characteristic
35	C₄×C₃₇	—	2	2	no	—
36	C₄×C₃₇	—	2	1	no	—
37	C₄×C₃₇	—	4	1	no	—
38	C₄×C₃₇	—	4	1	no	—
39	Dic₃₇	—	8	1	no	—
40	#1411	—	37	1	no	maximal, Sylow
41	C₂×C₃₇	—	2	1	no	—
42	C₂×C₃₇	#353	1	1	yes	characteristic
43	#494	—	37	1	no	—
44	#356	—	37	1	no	—
45	#356	D₃₇	1	1	yes	characteristic
46	C₃₇	#1411	1	1	yes	characteristic, complemented, Sylow
47	C₂×Q₁₆	—	74	1	no	—
48	C₂×Q₁₆	—	74	1	no	—
49	C₄⋊Q₈	—	37	1	no	—
50	C₄⋊Q₈	C₂×D₃₇	1	1	yes	characteristic
51	#101	—	2	1	no	—
52	#101	—	74	1	no	—
53	C₄×C₈	—	37	1	no	—
54	C₂×Q₈	—	74	1	no	—
55	C₂×Q₈	D₁₄₈	1	1	yes	characteristic
56	C₂×Q₈	C₂²⋊D₃₇	1	1	yes	characteristic
57	Q₁₆	—	148	2	no	—
58	Q₁₆	—	148	2	no	—
59	M₁₆	—	4	1	no	—
60	M₁₆	—	148	1	no	—
61	C₂×C₈	—	74	1	no	—
62	C₄⋊C₄	—	4	1	no	—
63	C₄⋊C₄	—	148	1	no	—
64	C₄²	C₄×D₃₇	1	1	yes	characteristic
65	Q₈	—	4	1	no	—
66	Q₈	—	4	1	no	—
67	Q₈	—	148	1	no	—
68	Q₈	—	148	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	148	1	no	—
73	C₂×C₄	#10596938	1	1	yes	characteristic
74	C₈	—	8	1	no	—
75	C₈	—	296	1	no	—
76	C₈	—	74	2	no	—
77	C₂²	#11924450	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	2	1	no	—
80	C₄	—	4	1	no	—
81	C₄	—	4	1	no	—
82	C₄	—	296	1	no	—
83	C₂	—	2	1	no	—
84	C₂	#14557325	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14557325
commutator	C₄²×C₃₇	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₃₇
Fitting	C₃₇×#356	C₂
socle	C₂×C₃₇	#353
prime radical	C₂²×C₃₇	#99
cosocle	C₄⋊Q₈×C₃₇	C₂²
hypercenter	#356	D₃₇
hypocenter	C₃₇	#1411
LCS	G ▷ C₄²×C₃₇ ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #356

Complements

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

N	H ≅ G/N	type
46. C₃₇	#1411	semidirect

Maximal subgroups

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

subgroup	index
#14557912	2
#14557332	2
C₃₇×#356	2
#1411	37