Subgroups — #17992632

Order 4736.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557910	C₂	1	1	yes	maximal, characteristic
2	#14557354	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#364	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₉₆	—	2	1	no	—
5	C₂×D₂₉₆	—	2	1	no	—
6	#11924533	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×D₁₄₈	—	2	2	no	—
11	C₂×D₁₄₈	—	4	2	no	—
12	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
13	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
14	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
15	D₂₉₆	—	4	1	no	—
16	D₂₉₆	—	4	1	no	—
17	D₂₉₆	—	4	1	no	—
18	D₂₉₆	—	4	1	no	—
19	C₁₆×C₃₇	—	4	1	no	—
20	#10596925	—	4	1	no	—
21	C₂²×D₃₇	—	4	2	no	—
22	C₂×C₄×C₃₇	—	2	1	no	—
23	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
24	D₁₄₈	—	4	2	no	—
25	D₁₄₈	—	4	2	no	—
26	D₁₄₈	—	8	4	no	—
27	C₈×C₃₇	D₈	1	1	yes	characteristic
28	C₈×C₃₇	D₈	1	1	yes	characteristic
29	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
30	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
31	C₂²×C₃₇	#100	1	1	yes	characteristic
32	C₂×D₃₇	—	8	4	no	—
33	C₂×D₃₇	—	8	2	no	—
34	C₄×C₃₇	—	2	2	no	—
35	C₄×C₃₇	#102	1	1	yes	characteristic
36	C₄×C₃₇	#102	1	1	yes	characteristic
37	#1357	—	37	1	no	maximal, Sylow
38	C₂×C₃₇	—	2	1	no	—
39	C₂×C₃₇	#331	1	1	yes	characteristic
40	D₃₇	—	16	2	no	—
41	#493	—	37	1	no	—
42	#364	—	37	1	no	—
43	#364	D₃₇	1	1	yes	characteristic, complemented
44	C₃₇	#1357	1	1	yes	characteristic, complemented, Sylow
45	C₂×D₈	—	74	1	no	—
46	C₂×D₈	—	74	1	no	—
47	#127	—	37	2	no	—
48	M₃₂	—	2	1	no	—
49	M₃₂	—	74	1	no	—
50	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
51	C₂×D₄	—	74	2	no	—
52	C₂×D₄	—	148	2	no	—
53	D₈	—	148	1	no	—
54	D₈	—	148	1	no	—
55	D₈	—	148	1	no	—
56	D₈	—	148	1	no	—
57	C₂×C₈	D₁₄₈	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
59	C₄²	C₄×D₃₇	1	1	yes	characteristic
60	C₁₆	—	4	1	no	—
61	C₁₆	—	148	1	no	—
62	C₂³	—	148	2	no	—
63	D₄	—	296	4	no	—
64	D₄	—	148	2	no	—
65	D₄	—	148	2	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	#10596938	1	1	yes	characteristic
68	C₈	#10596930	1	1	yes	characteristic
69	C₈	D₂₉₆	1	1	yes	characteristic
70	C₈	#10596939	1	1	yes	characteristic
71	C₈	#10596941	1	1	yes	characteristic
72	C₂²	—	296	4	no	—
73	C₂²	—	296	2	no	—
74	C₂²	#11924452	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	#11924456	1	1	yes	characteristic
77	C₄	#11924458	1	1	yes	characteristic
78	C₂	—	2	1	no	—
79	C₂	—	592	2	no	—
80	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	#14557910	C₂
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	#364	D₃₇
hypocenter	C₃₇	#1357
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
2. #14557354	C₂	semidirect
3. C₃₇×#364	C₂	semidirect
43. #364	D₃₇	semidirect
44. C₃₇	#1357	semidirect

Maximal subgroups

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

subgroup	index
#14557910	2
#14557354	2
C₃₇×#364	2
#1357	37