Subgroups — #17992636

Order 4736.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557906	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×#10596930	—	2	1	no	—
5	C₂×#10596930	—	2	1	no	—
6	#11924536	C₄	1	1	yes	characteristic
7	#11924533	C₄	1	1	yes	characteristic
8	#11924476	—	2	1	no	—
9	M₃₂×C₃₇	—	2	1	no	—
10	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
11	C₂×D₁₄₈	—	2	1	no	—
12	C₂×D₁₄₈	—	4	1	no	—
13	C₂×Dic₇₄	—	2	1	no	—
14	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
15	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
16	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₄⋊Dic₃₇	—	4	1	no	—
18	#10596930	—	4	1	no	—
19	#10596930	—	4	1	no	—
20	#10596930	—	4	1	no	—
21	#10596930	—	4	1	no	—
22	C₁₆×C₃₇	—	4	1	no	—
23	#10596925	—	4	1	no	—
24	C₂²×D₃₇	—	4	1	no	—
25	C₂×C₄×C₃₇	—	2	1	no	—
26	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₃₇	—	4	1	no	—
28	D₁₄₈	—	4	1	no	—
29	D₁₄₈	—	4	1	no	—
30	D₁₄₈	—	8	2	no	—
31	Dic₇₄	—	4	1	no	—
32	Dic₇₄	—	4	1	no	—
33	C₈×C₃₇	D₈	1	1	yes	characteristic
34	C₈×C₃₇	D₈	1	1	yes	characteristic
35	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
36	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
37	C₂²×C₃₇	#100	1	1	yes	characteristic
38	C₂×D₃₇	—	8	2	no	—
39	C₂×D₃₇	—	8	1	no	—
40	C₄×C₃₇	—	2	2	no	—
41	C₄×C₃₇	#102	1	1	yes	characteristic
42	C₄×C₃₇	#102	1	1	yes	characteristic
43	Dic₃₇	—	8	1	no	—
44	#1359	—	37	1	no	maximal, Sylow
45	C₂×C₃₇	—	2	1	no	—
46	C₂×C₃₇	#331	1	1	yes	characteristic
47	D₃₇	—	16	1	no	—
48	#492	—	37	1	no	—
49	#364	—	37	1	no	—
50	#364	D₃₇	1	1	yes	characteristic, complemented
51	C₃₇	#1359	1	1	yes	characteristic, complemented, Sylow
52	C₂×SD₁₆	—	74	1	no	—
53	C₂×SD₁₆	—	74	1	no	—
54	C₄⋊Q₈	—	37	1	no	—
55	#127	—	37	1	no	—
56	M₃₂	—	2	1	no	—
57	M₃₂	—	74	1	no	—
58	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
59	C₂×Q₈	—	74	1	no	—
60	C₂×D₄	—	74	1	no	—
61	C₂×D₄	—	148	1	no	—
62	SD₁₆	—	148	1	no	—
63	SD₁₆	—	148	1	no	—
64	SD₁₆	—	148	1	no	—
65	SD₁₆	—	148	1	no	—
66	C₂×C₈	D₁₄₈	1	1	yes	characteristic
67	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
68	C₄⋊C₄	—	148	1	no	—
69	C₄²	C₄×D₃₇	1	1	yes	characteristic
70	C₁₆	—	4	1	no	—
71	C₁₆	—	148	1	no	—
72	C₂³	—	148	1	no	—
73	Q₈	—	148	1	no	—
74	Q₈	—	148	1	no	—
75	D₄	—	296	2	no	—
76	D₄	—	148	1	no	—
77	D₄	—	148	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	148	1	no	—
80	C₂×C₄	#10596938	1	1	yes	characteristic
81	C₈	#10596930	1	1	yes	characteristic
82	C₈	D₂₉₆	1	1	yes	characteristic
83	C₈	#10596939	1	1	yes	characteristic
84	C₈	#10596941	1	1	yes	characteristic
85	C₂²	—	296	2	no	—
86	C₂²	—	296	1	no	—
87	C₂²	#11924452	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	296	1	no	—
90	C₄	#11924456	1	1	yes	characteristic
91	C₄	#11924458	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	592	1	no	—
94	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	#11924533	C₄
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	#364	D₃₇
hypocenter	C₃₇	#1359
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
50. #364	D₃₇	semidirect
51. C₃₇	#1359	semidirect

Maximal subgroups

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

subgroup	index
#14557906	2
#14557354	2
C₃₇×#364	2
#1359	37