Subgroups — #17992634

Order 4736.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557913	C₂	1	1	yes	maximal, characteristic
2	#14557354	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#364	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₄₈	—	2	1	no	—
5	C₂×Dic₁₄₈	—	2	1	no	—
6	#11924536	C₄	1	2	yes	—
7	#11924476	—	2	1	no	—
8	M₃₂×C₃₇	—	2	1	no	—
9	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
10	C₂×Dic₇₄	—	2	2	no	—
11	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
12	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
13	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
14	C₄⋊Dic₃₇	—	4	2	no	—
15	Dic₁₄₈	—	4	1	no	—
16	Dic₁₄₈	—	4	1	no	—
17	Dic₁₄₈	—	4	1	no	—
18	Dic₁₄₈	—	4	1	no	—
19	C₁₆×C₃₇	—	4	1	no	—
20	#10596925	—	4	1	no	—
21	C₂×C₄×C₃₇	—	2	1	no	—
22	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×Dic₃₇	—	4	2	no	—
24	Dic₇₄	—	4	2	no	—
25	Dic₇₄	—	4	2	no	—
26	C₈×C₃₇	D₈	1	1	yes	characteristic
27	C₈×C₃₇	D₈	1	1	yes	characteristic
28	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
29	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
30	C₂²×C₃₇	#100	1	1	yes	characteristic
31	C₄×C₃₇	—	2	2	no	—
32	C₄×C₃₇	#102	1	1	yes	characteristic
33	C₄×C₃₇	#102	1	1	yes	characteristic
34	Dic₃₇	—	8	2	no	—
35	#1358	—	37	1	no	maximal, Sylow
36	C₂×C₃₇	—	2	1	no	—
37	C₂×C₃₇	#331	1	1	yes	characteristic
38	#494	—	37	1	no	—
39	#364	—	37	1	no	—
40	#364	D₃₇	1	1	yes	characteristic
41	C₃₇	#1358	1	1	yes	characteristic, complemented, Sylow
42	C₂×Q₁₆	—	74	1	no	—
43	C₂×Q₁₆	—	74	1	no	—
44	C₄⋊Q₈	—	37	2	no	—
45	M₃₂	—	2	1	no	—
46	M₃₂	—	74	1	no	—
47	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
48	C₂×Q₈	—	74	2	no	—
49	Q₁₆	—	148	1	no	—
50	Q₁₆	—	148	1	no	—
51	Q₁₆	—	148	1	no	—
52	Q₁₆	—	148	1	no	—
53	C₂×C₈	D₁₄₈	1	1	yes	characteristic
54	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
55	C₄⋊C₄	—	148	2	no	—
56	C₄²	C₄×D₃₇	1	1	yes	characteristic
57	C₁₆	—	4	1	no	—
58	C₁₆	—	148	1	no	—
59	Q₈	—	148	2	no	—
60	Q₈	—	148	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	148	2	no	—
63	C₂×C₄	#10596938	1	1	yes	characteristic
64	C₈	#10596930	1	1	yes	characteristic
65	C₈	D₂₉₆	1	1	yes	characteristic
66	C₈	#10596939	1	1	yes	characteristic
67	C₈	#10596941	1	1	yes	characteristic
68	C₂²	#11924452	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	—	296	2	no	—
71	C₄	#11924456	1	1	yes	characteristic
72	C₄	#11924458	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	#14557276	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14557276
commutator	C₄²×C₃₇	C₂×C₄
Frattini	C₄×C₈	C₂×D₃₇
Fitting	C₃₇×#364	C₂
socle	C₂×C₃₇	#331
prime radical	C₂²×C₃₇	#100
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	#364	D₃₇
hypocenter	C₃₇	#1358
LCS	G ▷ C₄²×C₃₇ ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
41. C₃₇	#1358	semidirect

Maximal subgroups

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

subgroup	index
#14557913	2
#14557354	2
C₃₇×#364	2
#1358	37