Subgroups — #17994182

Order 4736.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557931	C₂	1	1	yes	maximal, characteristic, complemented
2	#14557929	C₂	1	2	yes	maximal, complemented
3	#14557905	C₂	1	2	yes	maximal
4	C₈×#64436	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#492	C₂	1	1	yes	maximal, characteristic
6	C₂×#10596940	—	2	4	no	—
7	#11924536	C₂²	1	2	yes	—
8	#11924468	—	2	2	no	—
9	#11924467	—	2	4	no	—
10	C₄×#64436	C₂²	1	2	yes	—
11	C₂×SD₁₆×C₃₇	—	2	2	no	—
12	C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
13	#127×C₃₇	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₃₇	—	2	1	no	—
16	C₂×D₄×C₃₇	—	2	2	no	—
17	C₂×D₄×C₃₇	—	2	1	no	—
18	C₂×Dic₇₄	—	2	2	no	—
19	SD₁₆×C₃₇	—	4	4	no	—
20	C₂×C₈×C₃₇	D₄	1	2	yes	—
21	C₄⋊C₄×C₃₇	—	2	2	no	—
22	C₄²×C₃₇	C₂³	1	1	yes	characteristic
23	#10596940	—	4	8	no	—
24	C₄⋊Dic₃₇	—	2	2	no	—
25	C₄⋊Dic₃₇	—	2	2	no	—
26	C₂×#64436	D₄	1	4	yes	—
27	C₂³×C₃₇	—	4	1	no	—
28	Q₈×C₃₇	—	4	2	no	—
29	D₄×C₃₇	—	4	4	no	—
30	D₄×C₃₇	—	4	2	no	—
31	C₂×C₄×C₃₇	—	4	1	no	—
32	C₂×C₄×C₃₇	C₂×D₄	1	2	yes	—
33	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
34	C₂×Dic₃₇	—	4	2	no	—
35	Dic₇₄	—	4	4	no	—
36	C₈×C₃₇	SD₁₆	1	4	yes	complemented
37	#64436	SD₁₆	1	8	yes	complemented
38	C₂²×C₃₇	—	8	2	no	—
39	C₂²×C₃₇	—	8	1	no	—
40	C₂²×C₃₇	#127	1	1	yes	characteristic
41	C₄×C₃₇	—	8	1	no	—
42	C₄×C₃₇	C₂×SD₁₆	1	4	yes	—
43	C₄×C₃₇	C₂×SD₁₆	1	2	yes	—
44	Dic₃₇	—	8	2	no	—
45	#1705	—	37	1	no	maximal, Sylow
46	C₂×C₃₇	—	16	1	no	—
47	C₂×C₃₇	#492	1	2	yes	—
48	C₂×C₃₇	#492	1	1	yes	characteristic
49	#498	—	37	2	no	—
50	#498	—	37	1	no	—
51	#492	—	37	2	no	—
52	#492	D₃₇	1	1	yes	characteristic
53	C₈²	—	37	1	no	—
54	C₃₇	#1705	1	1	yes	characteristic, complemented, Sylow
55	C₂×SD₁₆	—	2	2	no	—
56	C₂×SD₁₆	—	74	4	no	—
57	C₄⋊Q₈	—	37	2	no	—
58	C₄⋊Q₈	C₂×D₃₇	1	1	yes	characteristic
59	#127	C₂×D₃₇	1	1	yes	characteristic
60	#106	—	74	4	no	—
61	#106	—	74	2	no	—
62	C₄×C₈	—	37	2	no	—
63	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
64	C₂×Q₈	—	2	1	no	—
65	C₂×Q₈	—	74	2	no	—
66	C₂×D₄	—	2	2	no	—
67	C₂×D₄	—	2	1	no	—
68	SD₁₆	—	4	4	no	—
69	SD₁₆	—	148	8	no	—
70	C₂×C₈	—	37	4	no	—
71	C₂×C₈	C₂²⋊D₃₇	1	2	yes	—
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	74	2	no	—
74	C₄⋊C₄	—	74	2	no	—
75	C₄²	C₂²×D₃₇	1	1	yes	characteristic
76	C₂³	—	4	1	no	—
77	Q₈	—	4	2	no	—
78	Q₈	—	148	4	no	—
79	D₄	—	4	4	no	—
80	D₄	—	4	2	no	—
81	C₂×C₄	—	4	1	no	—
82	C₂×C₄	—	148	2	no	—
83	C₂×C₄	D₄×D₃₇	1	2	yes	—
84	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
85	C₈	—	37	8	no	—
86	C₈	#10596940	1	4	yes	complemented
87	C₂²	—	8	2	no	—
88	C₂²	—	8	1	no	—
89	C₂²	#11924532	1	1	yes	characteristic
90	C₄	—	8	1	no	—
91	C₄	—	296	2	no	—
92	C₄	SD₁₆×D₃₇	1	4	yes	—
93	C₄	C₂×#10596940	1	2	yes	—
94	C₂	—	16	1	no	—
95	C₂	#14557904	1	2	yes	—
96	C₂	#14557905	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11924532
commutator, cosocle	C₄²×C₃₇	C₂³
Frattini	C₄²	C₂²×D₃₇
Fitting	C₃₇×#492	C₂
socle	C₂²×C₃₇	#127
prime radical	#127×C₃₇	C₂²
hypercenter	#492	D₃₇
hypocenter	C₃₇	#1705
LCS	G ▷ C₄²×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #492

Complements

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

N	H ≅ G/N	type
1. #14557931	C₂	semidirect
2. #14557929	C₂	semidirect
4. C₈×#64436	C₂	semidirect
36. C₈×C₃₇	SD₁₆	semidirect
37. #64436	SD₁₆	semidirect
54. C₃₇	#1705	semidirect
86. C₈	#10596940	semidirect

Maximal subgroups

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

subgroup	index
#14557931	2
#14557929	2
#14557905	2
C₈×#64436	2
C₃₇×#492	2
#1705	37