Group #17996103 — subgroups

Subgroups — #17996103

Order 4736.

176 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557575	C₂	1	2	yes	maximal
2	C₂×#11924470	C₂	1	1	yes	maximal, characteristic
3	#14557559	C₂	1	1	yes	maximal, characteristic
4	#14557301	C₂	1	2	yes	maximal
5	C₃₇×#341	C₂	1	1	yes	maximal, characteristic
6	C₂×#10596934	C₂²	1	1	yes	characteristic
7	#11924495	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₃₇	C₂²	1	2	yes	—
9	#11924470	—	2	2	no	—
10	#11924470	—	2	2	no	—
11	#11924468	—	2	2	no	—
12	#11924465	—	2	2	no	—
13	C₂×M₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
16	C₂²×Dic₃₇	—	2	2	no	—
17	M₁₆×C₃₇	—	2	2	no	—
18	M₁₆×C₃₇	Q₈	1	4	yes	—
19	C₂×C₈×C₃₇	—	2	2	no	—
20	C₂×C₈×C₃₇	—	2	2	no	—
21	C₂×C₈×C₃₇	D₄	1	2	yes	—
22	C₂²⋊Dic₃₇	—	2	1	no	—
23	C₄⋊Dic₃₇	—	2	2	no	—
24	C₄⋊Dic₃₇	—	2	2	no	—
25	C₄⋊Dic₃₇	D₄	1	1	yes	characteristic
26	C₄⋊Dic₃₇	D₄	1	1	yes	characteristic
27	C₄×Dic₃₇	—	2	1	no	—
28	#10596934	—	2	2	no	—
29	C₂×#64436	—	2	1	no	—
30	C₂³×C₃₇	#41	1	1	yes	characteristic
31	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₃₇	C₂×Q₈	1	2	yes	—
34	C₂×C₄×C₃₇	#41	1	2	yes	—
35	C₂×Dic₃₇	—	2	1	no	—
36	C₂×Dic₃₇	—	2	1	no	—
37	C₂×Dic₃₇	—	4	2	no	—
38	C₂×Dic₃₇	—	8	2	no	—
39	C₈×C₃₇	—	2	4	no	—
40	C₈×C₃₇	—	2	2	no	—
41	#64436	—	4	1	no	—
42	C₂²×C₃₇	—	2	1	no	—
43	C₂²×C₃₇	—	2	1	no	—
44	C₂²×C₃₇	#121	1	1	yes	characteristic
45	C₂²×C₃₇	#125	1	2	yes	—
46	C₄×C₃₇	C₂²⋊Q₈	1	2	yes	—
47	C₄×C₃₇	#123	1	1	yes	characteristic
48	C₄×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
49	Dic₃₇	—	4	1	no	—
50	Dic₃₇	—	4	1	no	—
51	Dic₃₇	—	8	2	no	—
52	#2089	—	37	1	no	maximal, Sylow
53	C₂×C₃₇	—	2	2	no	—
54	C₂×C₃₇	#398	1	1	yes	characteristic
55	C₂×C₃₇	#472	1	1	yes	characteristic
56	C₂×C₃₇	#473	1	1	yes	characteristic
57	#428	—	37	2	no	—
58	C₂×#107	—	37	1	no	—
59	#424	—	37	1	no	—
60	#343	—	37	2	no	—
61	#341	D₃₇	1	1	yes	characteristic
62	C₃₇	#2089	1	1	yes	characteristic, complemented, Sylow
63	C₂×M₁₆	—	37	1	no	—
64	C₂×M₁₆	C₂×D₃₇	1	2	yes	—
65	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
66	#117	—	37	1	no	—
67	C₂×C₄⋊C₄	—	37	2	no	—
68	#107	—	74	2	no	—
69	#107	—	74	2	no	—
70	#106	—	74	2	no	—
71	C₄⋊C₈	—	74	2	no	—
72	C₂²×C₄	—	74	2	no	—
73	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
74	M₁₆	—	2	2	no	—
75	M₁₆	—	74	2	no	—
76	M₁₆	Dic₇₄	1	4	yes	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	74	1	no	—
80	C₂×C₈	D₁₄₈	1	2	yes	—
81	C₄⋊C₄	—	37	1	no	—
82	C₄⋊C₄	—	37	1	no	—
83	C₄⋊C₄	—	74	2	no	—
84	C₄⋊C₄	—	74	2	no	—
85	C₂²⋊C₄	—	74	1	no	—
86	C₄²	—	74	1	no	—
87	C₂³	#10596966	1	1	yes	characteristic
88	C₂×C₄	—	296	2	no	—
89	C₂×C₄	—	74	1	no	—
90	C₂×C₄	—	74	1	no	—
91	C₂×C₄	—	148	2	no	—
92	C₂×C₄	C₂×Dic₇₄	1	2	yes	—
93	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
94	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
95	C₂×C₄	#10596964	1	2	yes	—
96	C₈	—	2	4	no	—
97	C₈	—	2	2	no	—
98	C₈	—	148	1	no	—
99	C₂²	—	2	1	no	—
100	C₂²	—	2	1	no	—
101	C₂²	#11924511	1	1	yes	characteristic
102	C₂²	#11924527	1	2	yes	—
103	C₄	—	296	2	no	—
104	C₄	—	148	1	no	—
105	C₄	—	148	1	no	—
106	C₄	#11924513	1	2	yes	—
107	C₄	#11924520	1	1	yes	characteristic
108	C₄	#11924536	1	1	yes	characteristic
109	C₂	—	2	2	no	—
110	C₂	#14557465	1	1	yes	characteristic
111	C₂	#14557804	1	1	yes	characteristic
112	C₂	#14557809	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14557575

C₂

yes

maximal

C₂×#11924470

C₂

yes

maximal, characteristic

#14557559

C₂

yes

maximal, characteristic

#14557301

C₂

yes

maximal

C₃₇×#341

C₂

yes

maximal, characteristic

C₂×#10596934

C₂²

yes

characteristic

#11924495

C₂²

yes

characteristic

C₂×C₄⋊Dic₃₇

C₂²

yes

—

—

—

—

—

C₂×M₁₆×C₃₇

C₂²

yes

—

C₂²×C₈×C₃₇

C₂²

yes

characteristic

C₂²×C₄×C₃₇

C₂³

yes

characteristic

C₂²×Dic₃₇

—

M₁₆×C₃₇

—

M₁₆×C₃₇

Q₈

yes

—

C₂×C₈×C₃₇

—

C₂×C₈×C₃₇

—

C₂×C₈×C₃₇

D₄

yes

—

C₂²⋊Dic₃₇

—

C₄⋊Dic₃₇

—

C₄⋊Dic₃₇

—

C₄⋊Dic₃₇

D₄

yes

characteristic

C₄⋊Dic₃₇

D₄

yes

characteristic

C₄×Dic₃₇

—

#10596934

—

C₂×#64436

—

C₂³×C₃₇

#41

yes

characteristic

C₂×C₄×C₃₇

C₂×D₄

yes

characteristic

C₂×C₄×C₃₇

C₂×D₄

yes

characteristic

C₂×C₄×C₃₇

C₂×Q₈

yes

—

C₂×C₄×C₃₇

#41

yes

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₈×C₃₇

—

C₈×C₃₇

—

#64436

—

C₂²×C₃₇

—

C₂²×C₃₇

—

C₂²×C₃₇

#121

yes

characteristic

C₂²×C₃₇

#125

yes

—

C₄×C₃₇

C₂²⋊Q₈

yes

—

C₄×C₃₇

#123

yes

characteristic

C₄×C₃₇

C₄⋊Q₈

yes

characteristic

Dic₃₇

—

Dic₃₇

—

Dic₃₇

—

#2089

—

maximal, Sylow

C₂×C₃₇

—

C₂×C₃₇

yes

C₂×C₃₇

yes

C₂×C₃₇

yes

—

—

—

—

D₃₇

yes

characteristic

C₃₇

#2089

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₃₇

yes

—

C₂²×C₈

C₂×D₃₇

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

#107

—

#107

—

#106

—

C₄⋊C₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₃₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

Dic₇₄

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₄₈

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

#10596966

yes

characteristic

C₂×C₄

—

296

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

148

—

C₂×C₄

C₂×Dic₇₄

yes

—

C₂×C₄

C₂×D₁₄₈

yes

characteristic

C₂×C₄

D₄×D₃₇

yes

characteristic

C₂×C₄

#10596964

yes

—

C₈

—

C₈

—

C₈

—

148

—

C₂²

—

100

C₂²

—

101

C₂²

#11924511

yes

characteristic

102

C₂²

#11924527

yes

—

103

C₄

—

296

—

104

C₄

—

148

—

105

C₄

—

148

—

106

C₄

#11924513

yes

—

107

C₄

#11924520

yes

characteristic

108

C₄

#11924536

yes

characteristic

109

C₂

—

110

C₂

#14557465

yes

characteristic

111

C₂

#14557804

yes

characteristic

112

C₂

#14557809

yes

characteristic

	subgroup	G/H
center	C₂²	#11924511
commutator, cosocle	C₂²×C₄×C₃₇	C₂³
Frattini	C₂²×C₄	C₂²×D₃₇
Fitting	C₃₇×#341	C₂
socle	C₂²×C₃₇	#121
prime radical	C₂³×C₃₇	#41
hypercenter	#341	D₃₇
hypocenter	C₃₇	#2089
LCS	G ▷ C₂²×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂²

#11924511

commutator, cosocle

C₂²×C₄×C₃₇

C₂³

Frattini

C₂²×C₄

C₂²×D₃₇

Fitting

C₃₇×#341

C₂

C₂²×C₃₇

C₂³×C₃₇

D₃₇

C₃₇

G ▷ C₂²×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
62. C₃₇	#2089	semidirect

H ≅ G/N

type

62. C₃₇

#2089

semidirect

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

subgroup	index
#14557575	2
C₂×#11924470	2
#14557559	2
#14557301	2
C₃₇×#341	2
#2089	37

subgroup

index

C₃₇×#341

Subgroups — #17996103

Conjugacy classes of subgroups

Complements

Maximal subgroups