Subgroups — #17992646

Order 4736.

98 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	#14557286	C₂	1	1	yes	maximal, characteristic
3	C₃₇×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₄₈	—	2	1	no	—
5	C₂×Dic₁₄₈	C₄	1	2	yes	—
6	#11924536	—	2	1	no	—
7	C₄⋊#64436	—	2	1	no	—
8	C₂×C₁₆×C₃₇	—	2	1	no	—
9	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
10	C₂×Dic₇₄	—	2	2	no	—
11	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
13	C₄²×C₃₇	D₄	1	1	yes	characteristic
14	C₄⋊Dic₃₇	—	4	1	no	—
15	C₄⋊Dic₃₇	—	4	1	no	—
16	C₂×#64436	—	4	1	no	—
17	Dic₁₄₈	—	4	2	no	—
18	Dic₁₄₈	—	4	1	no	—
19	Dic₁₄₈	—	4	1	no	—
20	C₁₆×C₃₇	—	4	1	no	—
21	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
23	C₂×C₄×C₃₇	SD₁₆	1	1	yes	characteristic
24	C₂×Dic₃₇	—	4	2	no	—
25	Dic₇₄	—	4	2	no	—
26	Dic₇₄	—	4	2	no	—
27	C₈×C₃₇	—	2	1	no	—
28	C₈×C₃₇	D₈	1	1	yes	characteristic
29	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
30	#64436	—	8	1	no	—
31	C₂²×C₃₇	#102	1	1	yes	characteristic
32	C₄×C₃₇	—	2	1	no	—
33	C₄×C₃₇	#100	1	1	yes	characteristic
34	C₄×C₃₇	#102	1	1	yes	characteristic
35	C₄×C₃₇	SD₃₂	1	1	yes	characteristic
36	C₄×C₃₇	Q₃₂	1	1	yes	characteristic
37	Dic₃₇	—	8	2	no	—
38	#1362	—	37	1	no	maximal, Sylow
39	C₂×C₃₇	#331	1	1	yes	characteristic
40	C₂×C₃₇	#358	1	1	yes	characteristic
41	C₂×C₃₇	#362	1	1	yes	characteristic
42	#494	—	37	1	no	—
43	C₄⋊C₁₆	D₃₇	1	1	yes	characteristic
44	#335	—	37	1	no	—
45	C₃₇	#1362	1	1	yes	characteristic, complemented, Sylow
46	C₂×Q₁₆	—	37	2	no	—
47	C₂×Q₁₆	—	74	1	no	—
48	C₄⋊Q₈	—	74	1	no	—
49	C₂×C₁₆	—	2	1	no	—
50	C₄⋊C₈	—	74	1	no	—
51	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
52	C₂×Q₈	—	74	2	no	—
53	Q₁₆	—	148	2	no	—
54	Q₁₆	—	148	1	no	—
55	Q₁₆	—	148	1	no	—
56	C₂×C₈	—	148	1	no	—
57	C₂×C₈	C₄×D₃₇	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
59	C₄⋊C₄	—	148	1	no	—
60	C₄⋊C₄	—	148	1	no	—
61	C₄²	D₁₄₈	1	1	yes	characteristic
62	C₁₆	—	4	1	no	—
63	Q₈	—	148	2	no	—
64	Q₈	—	148	2	no	—
65	C₂×C₄	—	148	2	no	—
66	C₂×C₄	#10596930	1	1	yes	characteristic
67	C₂×C₄	D₂₉₆	1	1	yes	characteristic
68	C₂×C₄	#10596938	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	296	1	no	—
71	C₈	#10596939	1	1	yes	characteristic
72	C₈	#10596941	1	1	yes	characteristic
73	C₂²	#11924458	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	296	2	no	—
76	C₄	#11924452	1	1	yes	characteristic
77	C₄	#11924456	1	1	yes	characteristic
78	C₄	#11924481	1	1	yes	characteristic
79	C₄	Dic₂₉₆	1	1	yes	characteristic
80	C₂	#14557276	1	1	yes	characteristic
81	C₂	#14557338	1	1	yes	characteristic
82	C₂	#14557350	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11924458
commutator	C₂×C₈×C₃₇	C₂×C₄
Frattini	C₄×C₈	C₂×D₃₇
Fitting	C₃₇×C₄⋊C₁₆	C₂
socle, prime radical	C₂²×C₃₇	#102
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	C₄⋊C₁₆	D₃₇
hypocenter	C₃₇	#1362
LCS	G ▷ C₂×C₈×C₃₇ ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
45. C₃₇	#1362	semidirect

Maximal subgroups

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

subgroup	index
#14557913	2
#14557286	2
C₃₇×C₄⋊C₁₆	2
#1362	37