Subgroups — #17996473

Order 4736.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₉₂	C₂	1	1	yes	maximal, characteristic
2	C₄×D₂₉₆	C₂	1	2	yes	maximal, complemented
3	#14557361	C₂	1	1	yes	maximal, characteristic, complemented
4	#14557335	C₂	1	2	yes	maximal, complemented
5	C₃₇×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₂₉₆	C₂²	1	2	yes	—
7	C₄×D₁₄₈	—	2	2	no	—
8	D₅₉₂	C₄	1	4	yes	complemented
9	#11924470	C₂²	1	2	yes	—
10	#11924458	—	2	2	no	—
11	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×D₁₄₈	—	2	2	no	—
15	C₂×C₄×D₃₇	—	4	2	no	—
16	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
17	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
18	C₄²×C₃₇	D₄	1	1	yes	characteristic
19	#10596938	—	4	2	no	—
20	C₄⋊Dic₃₇	—	2	2	no	—
21	D₂₉₆	—	2	2	no	—
22	D₂₉₆	C₂×C₄	1	4	yes	complemented
23	C₁₆×C₃₇	—	2	1	no	—
24	C₁₆×C₃₇	C₂×C₄	1	2	yes	complemented
25	C₂²×D₃₇	—	4	2	no	—
26	C₂×C₄×C₃₇	D₈	1	2	yes	—
27	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₃₇	—	4	2	no	—
29	D₁₄₈	—	2	4	no	—
30	D₁₄₈	—	4	2	no	—
31	C₄×D₃₇	—	8	4	no	—
32	C₈×C₃₇	—	2	1	no	—
33	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₃₇	#41	1	1	yes	characteristic
35	C₂²×C₃₇	C₂×D₈	1	1	yes	characteristic
36	C₂×D₃₇	—	4	4	no	—
37	C₂×D₃₇	—	8	2	no	—
38	C₂×D₃₇	—	8	2	no	—
39	C₄×C₃₇	—	2	2	no	—
40	C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
41	C₄×C₃₇	#135	1	1	yes	characteristic
42	Dic₃₇	—	8	2	no	—
43	#2177	—	37	1	no	maximal, Sylow
44	C₂×C₃₇	C₄×D₈	1	1	yes	characteristic
45	C₂×C₃₇	#509	1	2	yes	—
46	D₃₇	—	8	4	no	—
47	C₂×D₁₆	—	37	1	no	—
48	C₄×D₈	—	37	2	no	—
49	#367	—	37	1	no	—
50	#357	—	37	2	no	—
51	#346	D₃₇	1	1	yes	characteristic, complemented
52	C₃₇	#2177	1	1	yes	characteristic, complemented, Sylow
53	C₂×D₈	—	37	2	no	—
54	C₄×D₄	—	74	2	no	—
55	D₁₆	—	37	4	no	—
56	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
57	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
58	#107	—	37	2	no	—
59	#102	—	74	2	no	—
60	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
61	C₂×D₄	—	74	2	no	—
62	C₂²×C₄	—	148	2	no	—
63	D₈	—	37	4	no	—
64	D₈	—	74	2	no	—
65	C₂×C₈	D₁₄₈	1	1	yes	characteristic
66	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
67	C₄⋊C₄	—	74	2	no	—
68	C₂²⋊C₄	—	148	2	no	—
69	C₄²	D₁₄₈	1	1	yes	characteristic
70	C₁₆	—	2	1	no	—
71	C₁₆	C₄×D₃₇	1	2	yes	complemented
72	C₂³	—	148	2	no	—
73	D₄	—	74	4	no	—
74	D₄	—	148	2	no	—
75	C₂×C₄	—	296	4	no	—
76	C₂×C₄	—	148	2	no	—
77	C₂×C₄	D₂₉₆	1	2	yes	—
78	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
79	C₈	—	2	1	no	—
80	C₈	C₂×C₄×D₃₇	1	1	yes	characteristic
81	C₈	#10596962	1	1	yes	characteristic
82	C₂²	—	296	2	no	—
83	C₂²	—	296	2	no	—
84	C₂²	—	148	4	no	—
85	C₂²	C₂×D₂₉₆	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	296	2	no	—
88	C₄	C₄×D₁₄₈	1	1	yes	characteristic
89	C₄	#11924558	1	1	yes	characteristic
90	C₂	—	296	4	no	—
91	C₂	C₄×D₂₉₆	1	1	yes	characteristic
92	C₂	#14557971	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₂₉₆
commutator	C₈×C₃₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₃₇
Fitting	C₃₇×#346	C₂
socle	C₂²×C₃₇	C₂×D₈
prime radical	C₂×D₅₉₂	C₂
cosocle	C₂×C₈×C₃₇	C₂³
hypercenter	#346	D₃₇
hypocenter	C₃₇	#2177
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
2. C₄×D₂₉₆	C₂	semidirect
3. #14557361	C₂	semidirect
4. #14557335	C₂	semidirect
5. C₃₇×#346	C₂	semidirect
8. D₅₉₂	C₄	semidirect
22. D₂₉₆	C₂×C₄	semidirect
24. C₁₆×C₃₇	C₂×C₄	semidirect
51. #346	D₃₇	semidirect
52. C₃₇	#2177	semidirect
71. C₁₆	C₄×D₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅₉₂	2
C₄×D₂₉₆	2
#14557361	2
#14557335	2
C₃₇×#346	2
#2177	37