Group #22590134 — subgroups

Subgroups — #22590134

Order 9088.

140 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 81 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×#14556068	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556064	C₂	1	1	yes	maximal, characteristic
3	#17985828	C₂	1	4	yes	maximal, complemented
4	C₂×#108×C₇₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#11765849	—	2	1	no	—
6	#14556068	C₄	1	2	yes	—
7	#14556068	C₄	1	2	yes	—
8	C₂×C₇₁⋊C₁₆	C₂²	1	2	yes	—
9	#14556064	—	2	1	no	—
10	#14556064	C₂²	1	2	yes	—
11	C₂×M₁₆×C₇₁	—	2	1	no	—
12	C₂²×C₈×C₇₁	C₂²	1	1	yes	characteristic
13	#108×C₇₁	—	2	1	no	—
14	#108×C₇₁	C₂²	1	2	yes	—
15	#11765849	—	2	2	no	—
16	#11765849	—	4	1	no	—
17	C₂×C₇₁⋊C₈	—	4	1	no	—
18	C₇₁⋊C₁₆	C₂×C₄	1	4	yes	—
19	C₂²×C₄×C₇₁	D₄	1	1	yes	characteristic
20	M₁₆×C₇₁	—	2	2	no	—
21	M₁₆×C₇₁	—	4	1	no	—
22	C₂×C₈×C₇₁	—	4	1	no	—
23	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
26	C₂×C₈×C₇₁	Q₈	1	1	yes	characteristic
27	C₂×C₈×C₇₁	Q₈	1	1	yes	characteristic
28	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
29	C₂³×C₇₁	Q₁₆	1	1	yes	characteristic
30	C₂×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
33	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
34	C₂×C₄×C₇₁	Q₁₆	1	1	yes	characteristic
35	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
36	C₈×C₇₁	—	4	2	no	—
37	C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
38	C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
39	C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
40	C₈×C₇₁	C₂×Q₈	1	1	yes	characteristic
41	C₇₁⋊C₈	—	4	2	no	—
42	C₂²×C₇₁	—	4	1	no	—
43	C₂²×C₇₁	#107	1	1	yes	characteristic
44	C₂²×C₇₁	#107	1	1	yes	characteristic
45	C₂²×C₇₁	C₂×Q₁₆	1	1	yes	characteristic
46	C₄×C₇₁	#107	1	1	yes	characteristic
47	C₄×C₇₁	#107	1	1	yes	characteristic
48	C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
50	C₂×C₇₁	—	2	1	no	—
51	C₂×C₇₁	—	2	1	no	—
52	C₂×C₇₁	—	2	1	no	—
53	C₂×C₇₁	C₂×#107	1	1	yes	characteristic
54	#2161	—	71	1	no	maximal, Sylow
55	C₇₁	#2161	1	1	yes	characteristic, complemented, Sylow
56	C₂×M₃₂	—	71	1	no	—
57	C₂×#108	—	71	1	no	—
58	C₂×#108	D₇₁	1	1	yes	characteristic
59	#368	—	71	4	no	—
60	C₂×M₁₆	—	2	1	no	—
61	C₂×M₁₆	—	142	1	no	—
62	C₂²×C₈	C₂×D₇₁	1	1	yes	characteristic
63	M₃₂	—	71	2	no	—
64	M₃₂	—	71	2	no	—
65	C₂×C₁₆	—	71	2	no	—
66	#108	—	2	1	no	—
67	#108	—	71	2	no	—
68	#108	—	142	1	no	—
69	#108	C₂×D₇₁	1	2	yes	—
70	C₂²×C₄	C₂²⋊D₇₁	1	1	yes	characteristic
71	M₁₆	—	2	2	no	—
72	M₁₆	—	4	1	no	—
73	M₁₆	—	284	1	no	—
74	M₁₆	—	142	2	no	—
75	C₂×C₈	—	4	1	no	—
76	C₂×C₈	—	284	1	no	—
77	C₂×C₈	Dic₁₄₂	1	1	yes	characteristic
78	C₂×C₈	Dic₁₄₂	1	1	yes	characteristic
79	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
80	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
81	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
82	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
83	C₁₆	—	71	4	no	—
84	C₂³	#11765855	1	1	yes	characteristic
85	C₂×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
86	C₂×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
87	C₂×C₄	#11765850	1	1	yes	characteristic
88	C₂×C₄	#11765850	1	1	yes	characteristic
89	C₂×C₄	#11765855	1	1	yes	characteristic
90	C₂×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
91	C₈	—	4	2	no	—
92	C₈	—	284	2	no	—
93	C₈	Dic₇₁⋊C₄	1	1	yes	characteristic
94	C₈	Dic₇₁⋊C₄	1	1	yes	characteristic
95	C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
96	C₈	C₂×Dic₁₄₂	1	1	yes	characteristic
97	C₂²	—	4	1	no	—
98	C₂²	#14556061	1	1	yes	characteristic
99	C₂²	#14556061	1	1	yes	characteristic
100	C₂²	C₂×#11765855	1	1	yes	characteristic
101	C₄	#14556061	1	1	yes	characteristic
102	C₄	#14556061	1	1	yes	characteristic
103	C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
104	C₄	C₂×#11765850	1	1	yes	characteristic
105	C₂	—	2	1	no	—
106	C₂	—	2	1	no	—
107	C₂	—	2	1	no	—
108	C₂	C₂×#14556061	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556068

C₂

yes

maximal, characteristic

C₂×#14556064

C₂

yes

maximal, characteristic

#17985828

C₂

yes

maximal, complemented

C₂×#108×C₇₁

C₂

yes

maximal, characteristic

C₂×#11765849

—

#14556068

C₄

yes

—

#14556068

C₄

yes

—

C₂×C₇₁⋊C₁₆

C₂²

yes

—

#14556064

—

#14556064

C₂²

yes

—

C₂×M₁₆×C₇₁

—

C₂²×C₈×C₇₁

C₂²

yes

characteristic

#108×C₇₁

—

#108×C₇₁

C₂²

yes

—

#11765849

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₇₁⋊C₁₆

C₂×C₄

yes

—

C₂²×C₄×C₇₁

D₄

yes

characteristic

M₁₆×C₇₁

—

M₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂×C₈×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

Q₈

yes

characteristic

C₂×C₈×C₇₁

Q₈

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₂³×C₇₁

Q₁₆

yes

characteristic

C₂×C₄×C₇₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₁

D₈

yes

characteristic

C₂×C₄×C₇₁

D₈

yes

characteristic

C₂×C₄×C₇₁

Q₁₆

yes

characteristic

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₈×C₇₁

—

C₈×C₇₁

C₄⋊C₄

yes

characteristic

C₈×C₇₁

C₄⋊C₄

yes

characteristic

C₈×C₇₁

C₂²×C₄

yes

characteristic

C₈×C₇₁

C₂×Q₈

yes

characteristic

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

yes

C₂²×C₇₁

yes

C₂²×C₇₁

C₂×Q₁₆

yes

C₄×C₇₁

yes

C₄×C₇₁

yes

C₄×C₇₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₁

C₂×D₈

yes

characteristic

C₂×C₇₁

—

C₂×C₇₁

—

C₂×C₇₁

—

C₂×C₇₁

yes

—

C₇₁

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×#108

—

C₂×#108

D₇₁

yes

characteristic

#368

—

C₂×M₁₆

—

C₂×M₁₆

—

142

—

C₂²×C₈

C₂×D₇₁

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

#108

—

#108

—

#108

—

142

—

#108

C₂×D₇₁

yes

—

C₂²×C₄

C₂²⋊D₇₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

284

—

M₁₆

—

142

—

C₂×C₈

—

C₂×C₈

—

284

—

C₂×C₈

Dic₁₄₂

yes

characteristic

C₂×C₈

Dic₁₄₂

yes

characteristic

C₂×C₈

C₄×D₇₁

yes

characteristic

C₂×C₈

C₄×D₇₁

yes

characteristic

C₂×C₈

C₂²⋊D₇₁

yes

characteristic

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₁₆

—

C₂³

#11765855

yes

characteristic

C₂×C₄

Dic₇₁⋊C₄

yes

characteristic

C₂×C₄

Dic₇₁⋊C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

C₈

—

C₈

—

284

—

C₈

Dic₇₁⋊C₄

yes

characteristic

C₈

Dic₇₁⋊C₄

yes

characteristic

C₈

C₂×C₄×D₇₁

yes

characteristic

C₈

C₂×Dic₁₄₂

yes

characteristic

C₂²

—

C₂²

yes

C₂²

yes

100

C₂²

C₂×#11765855

yes

characteristic

101

C₄

#14556061

yes

characteristic

102

C₄

#14556061

yes

characteristic

103

C₄

C₂×Dic₇₁⋊C₄

yes

characteristic

104

C₄

C₂×#11765850

yes

characteristic

105

C₂

—

106

C₂

—

107

C₂

—

108

C₂

C₂×#14556061

yes

characteristic

	subgroup	G/H
center	C₄	C₂×#11765850
commutator	C₈×C₇₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	C₂×#108×C₇₁	C₂
socle	C₂×C₇₁	C₂×#107
hypercenter	C₂×#108	D₇₁
hypocenter	C₇₁	#2161
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

subgroup

G/H

center

C₄

C₂×#11765850

commutator

C₈×C₇₁

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

C₂×#108×C₇₁

C₂

C₂×C₇₁

D₇₁

C₇₁

G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

N	H ≅ G/N	type
3. #17985828	C₂	semidirect
55. C₇₁	#2161	semidirect

H ≅ G/N

type

3. #17985828

C₂

semidirect

55. C₇₁

#2161

semidirect

Subgroups — #22590134

Conjugacy classes of subgroups

Complements