Group #22589935 — subgroups

Subgroups — #22589935

Order 9088.

184 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 109 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	C₂×#14556067	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×D₇₁	C₂	1	1	yes	maximal, characteristic
3	#17985953	C₂	1	1	yes	maximal, characteristic
4	#17985775	C₂	1	1	yes	maximal, characteristic, complemented
5	#17985774	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×Dic₇₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11765848	C₄	1	1	yes	characteristic
9	C₂×C₈×D₇₁	C₂²	1	1	yes	characteristic
10	#14556085	C₄	1	1	yes	characteristic
11	#14556067	C₄	1	4	yes	complemented
12	C₂×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
14	C₁₆×D₇₁	C₄	1	4	yes	complemented
15	#14556039	C₄	1	1	yes	characteristic
16	#14556038	C₄	1	1	yes	characteristic
17	C₈×Dic₇₁	C₂²	1	1	yes	characteristic
18	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
20	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₇₁	C₂×C₄	1	1	yes	characteristic
22	#11765848	C₈	1	4	yes	—
23	C₂×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₂×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₈×D₇₁	C₂×C₄	1	2	yes	—
26	C₈×D₇₁	C₂×C₄	1	2	yes	—
27	Dic₇₁⋊C₄	C₈	1	2	yes	—
28	(C₂×D₇₁)⋊C₄	C₈	1	2	yes	—
29	C₄×Dic₇₁	C₂×C₄	1	1	yes	characteristic
30	C₇₁⋊C₁₆	C₂×C₄	1	2	yes	—
31	C₇₁⋊C₁₆	C₂×C₄	1	2	yes	—
32	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
33	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
34	C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
35	C₁₆×C₇₁	C₂×C₄	1	2	yes	—
36	C₁₆×C₇₁	C₂×C₄	1	2	yes	—
37	C₂²×D₇₁	C₂×C₈	1	1	yes	characteristic
38	C₂×C₄×C₇₁	C₂×C₈	1	2	yes	—
39	C₂×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
40	C₂×Dic₇₁	C₂×C₈	1	2	yes	—
41	C₂×Dic₇₁	C₂×C₈	1	1	yes	characteristic
42	C₄×D₇₁	C₄²	1	2	yes	—
43	C₄×D₇₁	C₂×C₈	1	2	yes	—
44	C₈×C₇₁	C₂×C₈	1	2	yes	—
45	C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
46	C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
47	C₇₁⋊C₈	C₄²	1	2	yes	—
48	C₇₁⋊C₈	C₂×C₈	1	2	yes	—
49	C₂²×C₇₁	C₂²×C₈	1	1	yes	characteristic
50	C₂×D₇₁	—	2	2	no	—
51	C₂×D₇₁	C₄×C₈	1	2	yes	—
52	C₄×C₇₁	—	2	2	no	—
53	C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
54	C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
55	Dic₇₁	—	2	2	no	—
56	Dic₇₁	C₄×C₈	1	2	yes	—
57	C₂×C₇₁	C₂×C₄×C₈	1	1	yes	characteristic
58	C₂×C₇₁	#504	1	2	yes	—
59	D₇₁	—	2	2	no	—
60	#2108	—	71	1	no	maximal, Sylow
61	C₇₁	#2108	1	1	yes	characteristic, complemented, Sylow
62	C₂×M₃₂	—	71	1	no	—
63	C₂²×C₁₆	—	71	1	no	—
64	#405	—	71	1	no	—
65	#346	—	71	1	no	—
66	#346	—	71	1	no	—
67	C₄×C₁₆	—	71	1	no	—
68	C₄×C₁₆	D₇₁	1	1	yes	characteristic, complemented
69	C₂×M₁₆	—	71	1	no	—
70	C₂²×C₈	—	71	1	no	—
71	#117	—	71	1	no	—
72	M₃₂	—	71	4	no	—
73	C₂×C₁₆	—	71	1	no	—
74	C₂×C₁₆	—	71	1	no	—
75	C₂×C₁₆	—	71	4	no	—
76	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
77	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
78	#97	—	71	1	no	—
79	#97	—	71	1	no	—
80	C₄×C₈	—	71	1	no	—
81	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
82	C₂²×C₄	—	71	1	no	—
83	M₁₆	—	71	4	no	—
84	C₂×C₈	—	71	1	no	—
85	C₂×C₈	—	71	1	no	—
86	C₂×C₈	—	71	2	no	—
87	C₂×C₈	—	71	2	no	—
88	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
89	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
90	C₄⋊C₄	—	71	2	no	—
91	C₂²⋊C₄	—	71	2	no	—
92	C₄²	—	71	1	no	—
93	C₄²	C₄×D₇₁	1	1	yes	characteristic
94	C₁₆	—	71	2	no	—
95	C₁₆	—	71	2	no	—
96	C₁₆	C₄×D₇₁	1	2	yes	—
97	C₁₆	C₄×D₇₁	1	2	yes	—
98	C₂³	—	71	1	no	—
99	C₂×C₄	—	71	1	no	—
100	C₂×C₄	—	71	2	no	—
101	C₂×C₄	—	71	2	no	—
102	C₂×C₄	—	71	2	no	—
103	C₂×C₄	C₈×D₇₁	1	2	yes	—
104	C₂×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
105	C₈	—	71	2	no	—
106	C₈	—	71	2	no	—
107	C₈	C₈×D₇₁	1	2	yes	—
108	C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
109	C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
110	C₂²	—	71	2	no	—
111	C₂²	—	142	2	no	—
112	C₂²	C₂×C₈×D₇₁	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	71	2	no	—
115	C₄	—	142	2	no	—
116	C₄	C₄²×D₇₁	1	1	yes	characteristic
117	C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
118	C₂	—	142	2	no	—
119	C₂	C₄×C₈×D₇₁	1	1	yes	characteristic
120	C₂	#17986415	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556067

C₂

yes

maximal, characteristic

C₂×C₁₆×D₇₁

C₂

yes

maximal, characteristic

#17985953

C₂

yes

maximal, characteristic

#17985775

C₂

yes

maximal, characteristic, complemented

#17985774

C₂

yes

maximal, characteristic, complemented

C₁₆×Dic₇₁

C₂

yes

maximal, characteristic, complemented

C₄×C₁₆×C₇₁

C₂

yes

maximal, characteristic, complemented

C₂×#11765848

C₄

yes

characteristic

C₂×C₈×D₇₁

C₂²

yes

characteristic

#14556085

C₄

yes

characteristic

#14556067

C₄

yes

complemented

C₂×C₇₁⋊C₁₆

C₂²

yes

characteristic

C₂×C₇₁⋊C₁₆

C₂²

yes

characteristic

C₁₆×D₇₁

C₄

yes

complemented

#14556039

C₄

yes

characteristic

#14556038

C₄

yes

characteristic

C₈×Dic₇₁

C₂²

yes

characteristic

C₂×C₁₆×C₇₁

C₂²

yes

characteristic

C₂×C₁₆×C₇₁

C₂²

yes

characteristic

C₄×C₈×C₇₁

C₂²

yes

characteristic

C₂×C₄×D₇₁

C₂×C₄

yes

characteristic

#11765848

C₈

yes

—

C₂×C₇₁⋊C₈

C₂×C₄

yes

characteristic

C₂×C₇₁⋊C₈

C₂×C₄

yes

characteristic

C₈×D₇₁

C₂×C₄

yes

—

C₈×D₇₁

C₂×C₄

yes

—

Dic₇₁⋊C₄

C₈

yes

—

(C₂×D₇₁)⋊C₄

C₈

yes

—

C₄×Dic₇₁

C₂×C₄

yes

characteristic

C₇₁⋊C₁₆

C₂×C₄

yes

—

C₇₁⋊C₁₆

C₂×C₄

yes

—

C₂×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₄²×C₇₁

C₂×C₄

yes

characteristic

C₁₆×C₇₁

C₂×C₄

yes

—

C₁₆×C₇₁

C₂×C₄

yes

—

C₂²×D₇₁

C₂×C₈

yes

characteristic

C₂×C₄×C₇₁

C₂×C₈

yes

—

C₂×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂×Dic₇₁

C₂×C₈

yes

—

C₂×Dic₇₁

C₂×C₈

yes

characteristic

C₄×D₇₁

C₄²

yes

—

C₄×D₇₁

C₂×C₈

yes

—

C₈×C₇₁

C₂×C₈

yes

—

C₈×C₇₁

C₂²×C₄

yes

characteristic

C₈×C₇₁

C₂²×C₄

yes

characteristic

C₇₁⋊C₈

C₄²

yes

—

C₇₁⋊C₈

C₂×C₈

yes

—

C₂²×C₇₁

C₂²×C₈

yes

characteristic

C₂×D₇₁

—

C₂×D₇₁

C₄×C₈

yes

—

C₄×C₇₁

—

C₄×C₇₁

C₂×C₄²

yes

characteristic

C₄×C₇₁

C₂²×C₈

yes

characteristic

Dic₇₁

—

Dic₇₁

C₄×C₈

yes

—

C₂×C₇₁

C₂×C₄×C₈

yes

characteristic

C₂×C₇₁

#504

yes

—

D₇₁

—

#2108

—

maximal, Sylow

C₇₁

#2108

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

#346

—

#346

—

C₄×C₁₆

—

C₄×C₁₆

D₇₁

yes

characteristic, complemented

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₁

yes

characteristic

C₂×C₁₆

C₂×D₇₁

yes

characteristic

#97

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₇₁

yes

characteristic

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₇₁

yes

characteristic

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₄×D₇₁

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

C₄×D₇₁

yes

—

C₁₆

C₄×D₇₁

yes

—

C₂³

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

C₈×D₇₁

yes

—

104

C₂×C₄

C₂×C₄×D₇₁

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

C₈×D₇₁

yes

—

108

C₈

C₂×C₄×D₇₁

yes

characteristic

109

C₈

C₂×C₄×D₇₁

yes

characteristic

110

C₂²

—

111

C₂²

—

142

—

112

C₂²

C₂×C₈×D₇₁

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

142

—

116

C₄

C₄²×D₇₁

yes

characteristic

117

C₄

C₂×C₈×D₇₁

yes

characteristic

118

C₂

—

142

—

119

C₂

C₄×C₈×D₇₁

yes

characteristic

120

C₂

#17986415

yes

—

	subgroup	G/H
center	C₂×C₁₆	C₂×D₇₁
commutator	C₂×C₇₁	C₂×C₄×C₈
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	C₄×C₁₆×C₇₁	C₂
socle	C₂²×C₇₁	C₂²×C₈
hypercenter	C₄×C₁₆	D₇₁
hypocenter	C₇₁	#2108
LCS	G ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

subgroup

G/H

center

C₂×C₁₆

C₂×D₇₁

commutator

C₂×C₇₁

C₂×C₄×C₈

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

C₄×C₁₆×C₇₁

C₂

socle

C₂²×C₇₁

C₂²×C₈

hypercenter

C₄×C₁₆

D₇₁

C₇₁

G ▷ C₂×C₇₁ ▷ C₇₁

C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

N	H ≅ G/N	type
4. #17985775	C₂	semidirect
5. #17985774	C₂	semidirect
6. C₁₆×Dic₇₁	C₂	semidirect
7. C₄×C₁₆×C₇₁	C₂	semidirect
11. #14556067	C₄	semidirect
14. C₁₆×D₇₁	C₄	semidirect
61. C₇₁	#2108	semidirect
68. C₄×C₁₆	D₇₁	semidirect

H ≅ G/N

type

4. #17985775

C₂

semidirect

5. #17985774

C₂

semidirect

6. C₁₆×Dic₇₁

C₂

semidirect

7. C₄×C₁₆×C₇₁

C₂

semidirect

11. #14556067

C₄

semidirect

14. C₁₆×D₇₁

C₄

semidirect

61. C₇₁

#2108

semidirect

68. C₄×C₁₆

D₇₁

semidirect

Subgroups — #22589935

Conjugacy classes of subgroups

Complements