Subgroups — #17996839

Order 4736.

152 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	#14557333	C₂	1	4	yes	maximal, complemented
3	#14557309	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#499	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₂₉₆	—	2	1	no	—
6	C₂×D₂₉₆	C₂²	1	2	yes	—
7	#11924533	—	2	1	no	—
8	C₂×#10596925	C₂²	1	2	yes	—
9	#125×C₃₇	—	2	1	no	—
10	#107×C₃₇	C₂²	1	2	yes	—
11	#106×C₃₇	—	2	1	no	—
12	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×D₁₄₈	—	2	2	no	—
14	C₂×D₁₄₈	—	4	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	2	no	—
19	C₄²×C₃₇	D₄	1	1	yes	characteristic
20	D₂₉₆	—	2	4	no	—
21	D₂₉₆	—	4	2	no	—
22	#10596925	—	2	2	no	—
23	C₂²×D₃₇	—	4	2	no	—
24	C₂×C₄×C₃₇	—	4	2	no	—
25	C₂×C₄×C₃₇	D₈	1	2	yes	—
26	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
27	D₁₄₈	—	4	2	no	—
28	D₁₄₈	—	4	2	no	—
29	D₁₄₈	—	8	4	no	—
30	C₈×C₃₇	SD₁₆	1	2	yes	—
31	C₈×C₃₇	#41	1	2	yes	—
32	C₂²×C₃₇	C₂×D₈	1	1	yes	characteristic
33	C₂×D₃₇	—	8	2	no	—
34	C₂×D₃₇	—	8	4	no	—
35	C₄×C₃₇	—	2	2	no	—
36	C₄×C₃₇	—	8	2	no	—
37	C₄×C₃₇	#124	1	1	yes	characteristic
38	C₄×C₃₇	C₂×SD₁₆	1	1	yes	characteristic
39	#2244	—	37	1	no	maximal, Sylow
40	C₂×C₃₇	#486	1	1	yes	characteristic
41	C₂×C₃₇	#509	1	2	yes	—
42	D₃₇	—	16	2	no	—
43	#499	D₃₇	1	1	yes	characteristic, complemented
44	#493	—	37	1	no	—
45	#357	—	37	4	no	—
46	#346	—	37	1	no	—
47	C₃₇	#2244	1	1	yes	characteristic, complemented, Sylow
48	C₂×D₈	—	37	2	no	—
49	C₂×D₈	—	74	1	no	—
50	#127	—	74	1	no	—
51	#125	—	2	1	no	—
52	C₂×C₁₆	—	37	2	no	—
53	#107	C₂×D₃₇	1	2	yes	—
54	#106	—	2	1	no	—
55	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
56	C₂×D₄	—	74	2	no	—
57	C₂×D₄	—	148	2	no	—
58	D₈	—	74	4	no	—
59	D₈	—	148	2	no	—
60	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
61	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
62	C₄⋊C₄	—	2	2	no	—
63	C₄⋊C₄	—	4	2	no	—
64	C₄²	C₂²⋊D₃₇	1	1	yes	characteristic
65	C₁₆	—	74	2	no	—
66	C₂³	—	148	2	no	—
67	D₄	—	296	4	no	—
68	D₄	—	148	2	no	—
69	D₄	—	148	2	no	—
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	#10596939	1	2	yes	—
72	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
73	C₈	#10596941	1	2	yes	—
74	C₈	#10596966	1	2	yes	—
75	C₂²	—	296	4	no	—
76	C₂²	—	296	2	no	—
77	C₂²	C₂×#10596939	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	8	2	no	—
80	C₄	#11924525	1	1	yes	characteristic
81	C₄	C₂×#10596941	1	1	yes	characteristic
82	C₂	—	592	2	no	—
83	C₂	#14557881	1	1	yes	characteristic
84	C₂	#14557968	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#10596939
commutator, cosocle	C₂×C₈×C₃₇	C₂³
Frattini	C₂×C₈	C₂²×D₃₇
Fitting	C₃₇×#499	C₂
socle	C₂²×C₃₇	C₂×D₈
prime radical	#14557910	C₂
hypercenter	#499	D₃₇
hypocenter	C₃₇	#2244
LCS	G ▷ C₂×C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

Complements

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

N	H ≅ G/N	type
2. #14557333	C₂	semidirect
3. #14557309	C₂	semidirect
4. C₃₇×#499	C₂	semidirect
43. #499	D₃₇	semidirect
47. C₃₇	#2244	semidirect

Maximal subgroups

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

subgroup	index
#14557910	2
#14557333	2
#14557309	2
C₃₇×#499	2
#2244	37