Subgroups — #17996825

Order 4736.

140 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	#14557336	C₂	1	4	yes	maximal
3	C₄×#10596925	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#500	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₄₈	—	2	1	no	—
6	C₂×Dic₁₄₈	C₂²	1	2	yes	—
7	#11924536	—	2	1	no	—
8	C₂×#10596925	C₂²	1	2	yes	—
9	C₄⋊Q₈×C₃₇	—	2	1	no	—
10	#107×C₃₇	—	2	1	no	—
11	#107×C₃₇	C₂²	1	2	yes	—
12	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×Q₈×C₃₇	—	4	1	no	—
14	C₂×Dic₇₄	—	2	2	no	—
15	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
16	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
17	C₄⋊C₄×C₃₇	—	2	2	no	—
18	C₄⋊C₄×C₃₇	—	4	1	no	—
19	C₄²×C₃₇	D₄	1	1	yes	characteristic
20	C₄⋊Dic₃₇	—	4	1	no	—
21	C₄⋊Dic₃₇	—	4	1	no	—
22	Dic₁₄₈	—	2	4	no	—
23	Dic₁₄₈	—	4	2	no	—
24	#10596925	—	2	2	no	—
25	Q₈×C₃₇	—	8	2	no	—
26	C₂×C₄×C₃₇	—	4	2	no	—
27	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
28	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
29	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₃₇	—	4	2	no	—
31	Dic₇₄	—	4	2	no	—
32	Dic₇₄	—	4	2	no	—
33	C₈×C₃₇	SD₁₆	1	2	yes	—
34	C₈×C₃₇	#41	1	2	yes	—
35	C₂²×C₃₇	C₂×D₈	1	1	yes	characteristic
36	C₄×C₃₇	—	8	2	no	—
37	C₄×C₃₇	SD₃₂	1	2	yes	—
38	C₄×C₃₇	Q₃₂	1	2	yes	—
39	C₄×C₃₇	#124	1	1	yes	characteristic
40	C₄×C₃₇	C₂×SD₁₆	1	1	yes	characteristic
41	Dic₃₇	—	8	2	no	—
42	#2241	—	37	1	no	maximal, Sylow
43	C₂×C₃₇	#486	1	1	yes	characteristic
44	C₂×C₃₇	C₂×SD₃₂	1	1	yes	characteristic
45	C₂×C₃₇	C₂×Q₃₂	1	1	yes	characteristic
46	#500	D₃₇	1	1	yes	characteristic
47	#494	—	37	1	no	—
48	#358	—	37	4	no	—
49	C₄×C₁₆	—	37	1	no	—
50	C₃₇	#2241	1	1	yes	characteristic, complemented, Sylow
51	C₂×Q₁₆	—	37	2	no	—
52	C₂×Q₁₆	—	74	1	no	—
53	C₄⋊Q₈	—	2	1	no	—
54	C₄⋊Q₈	—	74	1	no	—
55	C₂×C₁₆	—	37	2	no	—
56	#107	—	2	1	no	—
57	#107	C₂×D₃₇	1	2	yes	—
58	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
59	C₂×Q₈	—	4	1	no	—
60	C₂×Q₈	—	74	2	no	—
61	Q₁₆	—	74	4	no	—
62	Q₁₆	—	148	2	no	—
63	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	—	4	1	no	—
67	C₄⋊C₄	—	148	1	no	—
68	C₄⋊C₄	—	148	1	no	—
69	C₄²	C₂²⋊D₃₇	1	1	yes	characteristic
70	C₁₆	—	74	2	no	—
71	Q₈	—	8	2	no	—
72	Q₈	—	148	2	no	—
73	Q₈	—	148	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	148	2	no	—
76	C₂×C₄	#10596939	1	1	yes	characteristic
77	C₂×C₄	#10596939	1	1	yes	characteristic
78	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
79	C₈	#10596941	1	2	yes	—
80	C₈	#10596966	1	2	yes	—
81	C₂²	C₂×#10596939	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	296	2	no	—
84	C₄	#11924480	1	2	yes	—
85	C₄	#11924482	1	2	yes	—
86	C₄	#11924525	1	1	yes	characteristic
87	C₄	C₂×#10596941	1	1	yes	characteristic
88	C₂	#14557881	1	1	yes	characteristic
89	C₂	C₂×#11924480	1	1	yes	characteristic
90	C₂	C₂×#11924482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#10596939
commutator, cosocle	C₂×C₈×C₃₇	C₂³
Frattini	C₂×C₈	C₂²×D₃₇
Fitting	C₃₇×#500	C₂
socle, prime radical	C₂²×C₃₇	C₂×D₈
hypercenter	#500	D₃₇
hypocenter	C₃₇	#2241
LCS	G ▷ C₂×C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

Complements

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

N	H ≅ G/N	type
50. C₃₇	#2241	semidirect

Maximal subgroups

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

subgroup	index
#14557913	2
#14557336	2
C₄×#10596925	2
C₃₇×#500	2
#2241	37