Subgroups — #17996483

Order 4736.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557965	C₂	1	1	yes	maximal, characteristic
2	#14557651	C₂	1	2	yes	maximal, complemented
3	#14557363	C₂	1	1	yes	maximal, characteristic, complemented
4	#14557341	C₂	1	2	yes	maximal, complemented
5	C₃₇×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	#11924558	C₂²	1	2	yes	—
7	#11924542	—	2	2	no	—
8	Dic₂₉₆	C₄	1	1	yes	characteristic, complemented
9	#11924481	C₄	1	2	yes	complemented
10	D₅₉₂	C₄	1	1	yes	characteristic, complemented
11	#11924472	C₂²	1	2	yes	—
12	#11924464	—	2	2	no	—
13	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
16	#10596962	—	2	2	no	—
17	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
18	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
19	C₄²×C₃₇	D₄	1	1	yes	characteristic
20	#10596934	—	2	2	no	—
21	Dic₁₄₈	C₂×C₄	1	2	yes	—
22	D₂₉₆	C₂×C₄	1	2	yes	—
23	#10596930	—	2	2	no	—
24	#10596929	—	4	2	no	—
25	C₈×D₃₇	—	4	2	no	—
26	C₁₆×C₃₇	—	2	1	no	—
27	C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×C₃₇	—	2	1	no	—
30	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
31	C₂²⋊D₃₇	—	4	2	no	—
32	D₁₄₈	—	2	2	no	—
33	C₄×D₃₇	—	4	2	no	—
34	Dic₇₄	—	2	2	no	—
35	C₈×C₃₇	D₈	1	2	yes	—
36	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
37	C₈×C₃₇	#41	1	1	yes	characteristic
38	#64436	—	4	2	no	—
39	C₂²×C₃₇	#135	1	1	yes	characteristic
40	C₂×D₃₇	—	4	2	no	—
41	C₄×C₃₇	—	4	1	no	—
42	C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
43	C₄×C₃₇	C₂×D₈	1	1	yes	characteristic
44	Dic₃₇	—	4	2	no	—
45	#2179	—	37	1	no	maximal, Sylow
46	C₂×C₃₇	—	2	1	no	—
47	C₂×C₃₇	C₄×D₈	1	1	yes	characteristic
48	D₃₇	—	8	2	no	—
49	#508	—	37	1	no	—
50	#443	—	37	2	no	—
51	#368	—	37	1	no	—
52	#359	—	37	2	no	—
53	#346	D₃₇	1	1	yes	characteristic, complemented
54	C₃₇	#2179	1	1	yes	characteristic, complemented, Sylow
55	#135	—	37	2	no	—
56	#131	—	74	2	no	—
57	Q₃₂	—	37	1	no	—
58	SD₃₂	—	37	2	no	—
59	D₁₆	—	37	1	no	—
60	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
61	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
62	#108	—	37	2	no	—
63	#104	—	74	2	no	—
64	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
65	#41	—	74	2	no	—
66	Q₁₆	—	37	2	no	—
67	SD₁₆	—	74	2	no	—
68	D₈	—	37	2	no	—
69	M₁₆	—	74	2	no	—
70	M₁₆	—	148	2	no	—
71	C₂×C₈	—	148	2	no	—
72	C₂×C₈	D₁₄₈	1	1	yes	characteristic
73	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
74	C₄²	D₁₄₈	1	1	yes	characteristic
75	C₁₆	—	2	1	no	—
76	C₁₆	C₄×D₃₇	1	1	yes	characteristic
77	C₁₆	C₄×D₃₇	1	1	yes	characteristic
78	Q₈	—	74	2	no	—
79	D₄	—	74	2	no	—
80	D₄	—	148	2	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	148	2	no	—
83	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
84	C₈	—	148	2	no	—
85	C₈	D₂₉₆	1	2	yes	—
86	C₈	C₂×C₄×D₃₇	1	1	yes	characteristic
87	C₈	#10596962	1	1	yes	characteristic
88	C₂²	—	148	2	no	—
89	C₂²	#11924558	1	1	yes	characteristic
90	C₄	—	4	1	no	—
91	C₄	—	148	2	no	—
92	C₄	C₄×D₁₄₈	1	1	yes	characteristic
93	C₄	C₂×D₂₉₆	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	296	2	no	—
96	C₂	C₄×D₂₉₆	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₂₉₆
commutator	C₈×C₃₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₃₇
Fitting	C₃₇×#346	C₂
socle	C₂×C₃₇	C₄×D₈
prime radical	#14557965	C₂
cosocle	C₂×C₈×C₃₇	C₂³
hypercenter	#346	D₃₇
hypocenter	C₃₇	#2179
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
2. #14557651	C₂	semidirect
3. #14557363	C₂	semidirect
4. #14557341	C₂	semidirect
5. C₃₇×#346	C₂	semidirect
8. Dic₂₉₆	C₄	semidirect
9. #11924481	C₄	semidirect
10. D₅₉₂	C₄	semidirect
53. #346	D₃₇	semidirect
54. C₃₇	#2179	semidirect

Maximal subgroups

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

subgroup	index
#14557965	2
#14557651	2
#14557363	2
#14557341	2
C₃₇×#346	2
#2179	37