Group #22590113 — subgroups

Subgroups — #22590113

Order 9088.

144 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14556064	C₂	1	1	yes	maximal, characteristic
2	#17986037	C₂	1	1	yes	maximal, characteristic
3	#17985822	C₂	1	4	yes	maximal, complemented
4	C₂×M₃₂×C₇₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#11765849	—	2	1	no	—
6	#14556087	—	2	1	no	—
7	#14556064	—	2	1	no	—
8	#14556064	C₂²	1	2	yes	—
9	#14556062	—	2	1	no	—
10	#14556060	C₂²	1	2	yes	—
11	C₂²×C₈×C₇₁	C₂²	1	1	yes	characteristic
12	M₃₂×C₇₁	C₄	1	2	yes	complemented
13	M₃₂×C₇₁	C₂²	1	2	yes	—
14	C₂×C₁₆×C₇₁	C₄	1	2	yes	complemented
15	#11765849	—	2	2	no	—
16	#11765849	—	4	1	no	—
17	C₂×C₇₁⋊C₈	—	4	1	no	—
18	C₄⋊Dic₇₁	—	2	2	no	—
19	C₂²⋊Dic₇₁	—	4	1	no	—
20	C₄×Dic₇₁	—	4	1	no	—
21	C₂²×C₄×C₇₁	D₄	1	1	yes	characteristic
22	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
25	C₂×C₈×C₇₁	Q₈	1	1	yes	characteristic
26	C₂×C₈×C₇₁	Q₈	1	1	yes	characteristic
27	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
28	C₁₆×C₇₁	C₂×C₄	1	4	yes	—
29	C₂³×C₇₁	SD₁₆	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	SD₁₆	1	1	yes	characteristic
33	C₂×C₄×C₇₁	SD₁₆	1	1	yes	characteristic
34	C₂×C₄×C₇₁	SD₁₆	1	1	yes	characteristic
35	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
36	C₂×Dic₇₁	—	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	#106	1	1	yes	characteristic
44	C₂²×C₇₁	#106	1	1	yes	characteristic
45	C₂²×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
46	C₄×C₇₁	#106	1	1	yes	characteristic
47	C₄×C₇₁	#106	1	1	yes	characteristic
48	C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
50	Dic₇₁	—	8	2	no	—
51	C₂×C₇₁	—	2	1	no	—
52	C₂×C₇₁	—	2	1	no	—
53	C₂×C₇₁	—	2	1	no	—
54	C₂×C₇₁	C₂×#106	1	1	yes	characteristic
55	#2155	—	71	1	no	maximal, Sylow
56	C₇₁	#2155	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₃₂	D₇₁	1	1	yes	characteristic
58	C₂×#108	—	71	1	no	—
59	#427	—	71	1	no	—
60	#365	—	71	4	no	—
61	C₂×M₁₆	—	142	1	no	—
62	C₂²×C₈	C₂×D₇₁	1	1	yes	characteristic
63	#117	—	142	1	no	—
64	M₃₂	Dic₇₁	1	2	yes	complemented
65	M₃₂	C₂×D₇₁	1	2	yes	—
66	C₂×C₁₆	Dic₇₁	1	2	yes	complemented
67	#108	—	71	2	no	—
68	#108	—	142	1	no	—
69	#107	—	142	1	no	—
70	#106	—	71	2	no	—
71	C₂²×C₄	D₂₈₄	1	1	yes	characteristic
72	M₁₆	—	284	1	no	—
73	M₁₆	—	142	2	no	—
74	C₂×C₈	—	284	1	no	—
75	C₂×C₈	Dic₁₄₂	1	1	yes	characteristic
76	C₂×C₈	Dic₁₄₂	1	1	yes	characteristic
77	C₂×C₈	D₂₈₄	1	1	yes	characteristic
78	C₂×C₈	C₂×Dic₇₁	1	1	yes	characteristic
79	C₂×C₈	C₂×Dic₇₁	1	1	yes	characteristic
80	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
81	C₄⋊C₄	—	142	2	no	—
82	C₂²⋊C₄	—	284	1	no	—
83	C₄²	—	284	1	no	—
84	C₁₆	C₂×Dic₇₁	1	4	yes	—
85	C₂³	#11765854	1	1	yes	characteristic
86	C₂×C₄	—	284	2	no	—
87	C₂×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
88	C₂×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
89	C₂×C₄	#11765854	1	1	yes	characteristic
90	C₂×C₄	#11765854	1	1	yes	characteristic
91	C₂×C₄	#11765854	1	1	yes	characteristic
92	C₂×C₄	C₂×D₂₈₄	1	1	yes	characteristic
93	C₈	—	284	2	no	—
94	C₈	C₄⋊Dic₇₁	1	1	yes	characteristic
95	C₈	C₄⋊Dic₇₁	1	1	yes	characteristic
96	C₈	C₂²×Dic₇₁	1	1	yes	characteristic
97	C₈	C₂×Dic₁₄₂	1	1	yes	characteristic
98	C₂²	—	4	1	no	—
99	C₂²	#14556060	1	1	yes	characteristic
100	C₂²	#14556060	1	1	yes	characteristic
101	C₂²	C₂×#11765854	1	1	yes	characteristic
102	C₄	—	568	2	no	—
103	C₄	#14556060	1	1	yes	characteristic
104	C₄	#14556060	1	1	yes	characteristic
105	C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
106	C₄	C₂×#11765854	1	1	yes	characteristic
107	C₂	—	2	1	no	—
108	C₂	—	2	1	no	—
109	C₂	—	2	1	no	—
110	C₂	C₂×#14556060	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556064

C₂

yes

maximal, characteristic

#17986037

C₂

yes

maximal, characteristic

#17985822

C₂

yes

maximal, complemented

C₂×M₃₂×C₇₁

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

—

#14556062

—

#14556060

C₂²

yes

—

C₂²×C₈×C₇₁

C₂²

yes

characteristic

M₃₂×C₇₁

C₄

yes

complemented

M₃₂×C₇₁

C₂²

yes

—

C₂×C₁₆×C₇₁

C₄

yes

complemented

#11765849

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

C₂²⋊Dic₇₁

—

C₄×Dic₇₁

—

C₂²×C₄×C₇₁

D₄

yes

characteristic

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

C₁₆×C₇₁

C₂×C₄

yes

—

C₂³×C₇₁

SD₁₆

yes

characteristic

C₂×C₄×C₇₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₁

SD₁₆

yes

characteristic

C₂×C₄×C₇₁

SD₁₆

yes

characteristic

C₂×C₄×C₇₁

SD₁₆

yes

characteristic

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×Dic₇₁

—

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×SD₁₆

yes

C₄×C₇₁

yes

C₄×C₇₁

yes

C₄×C₇₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₁

C₂×SD₁₆

yes

characteristic

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

—

C₂×C₇₁

—

C₂×C₇₁

yes

—

C₇₁

yes

characteristic, complemented, Sylow

C₂×M₃₂

D₇₁

yes

—

—

—

C₂×M₁₆

—

142

—

C₂²×C₈

C₂×D₇₁

yes

characteristic

#117

—

142

—

M₃₂

Dic₇₁

yes

complemented

M₃₂

C₂×D₇₁

yes

—

C₂×C₁₆

Dic₇₁

yes

complemented

#108

—

#108

—

142

—

#107

—

142

—

#106

—

C₂²×C₄

D₂₈₄

yes

characteristic

M₁₆

—

284

—

M₁₆

—

142

—

C₂×C₈

—

284

—

C₂×C₈

Dic₁₄₂

yes

characteristic

C₂×C₈

Dic₁₄₂

yes

characteristic

C₂×C₈

D₂₈₄

yes

characteristic

C₂×C₈

C₂×Dic₇₁

yes

characteristic

C₂×C₈

C₂×Dic₇₁

yes

characteristic

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₄⋊C₄

—

142

—

C₂²⋊C₄

—

284

—

C₄²

—

284

—

C₁₆

C₂×Dic₇₁

yes

—

C₂³

#11765854

yes

characteristic

C₂×C₄

—

284

—

C₂×C₄

C₄⋊Dic₇₁

yes

characteristic

C₂×C₄

C₄⋊Dic₇₁

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×D₂₈₄

yes

characteristic

C₈

—

284

—

C₈

C₄⋊Dic₇₁

yes

characteristic

C₈

C₄⋊Dic₇₁

yes

characteristic

C₈

C₂²×Dic₇₁

yes

characteristic

C₈

C₂×Dic₁₄₂

yes

characteristic

C₂²

—

C₂²

#14556060

yes

characteristic

100

C₂²

#14556060

yes

characteristic

101

C₂²

C₂×#11765854

yes

characteristic

102

C₄

—

568

—

103

C₄

#14556060

yes

characteristic

104

C₄

#14556060

yes

characteristic

105

C₄

C₂×C₄⋊Dic₇₁

yes

characteristic

106

C₄

C₂×#11765854

yes

characteristic

107

C₂

—

108

C₂

—

109

C₂

—

110

C₂

C₂×#14556060

yes

characteristic

	subgroup	G/H
center	C₄	#14556060
commutator	C₈×C₇₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	C₂×M₃₂×C₇₁	C₂
socle	C₂×C₇₁	C₂×#106
hypercenter	C₂×M₃₂	D₇₁
hypocenter	C₇₁	#2155
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₄

#14556060

commutator

C₈×C₇₁

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

C₂×M₃₂×C₇₁

C₂

socle

C₂×C₇₁

C₂×#106

hypercenter

C₂×M₃₂

D₇₁

hypocenter

C₇₁

#2155

LCS

G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
3. #17985822	C₂	semidirect
12. M₃₂×C₇₁	C₄	semidirect
14. C₂×C₁₆×C₇₁	C₄	semidirect
56. C₇₁	#2155	semidirect
64. M₃₂	Dic₇₁	semidirect
66. C₂×C₁₆	Dic₇₁	semidirect

H ≅ G/N

type

3. #17985822

C₂

semidirect

12. M₃₂×C₇₁

C₄

semidirect

14. C₂×C₁₆×C₇₁

C₄

semidirect

56. C₇₁

#2155

semidirect

64. M₃₂

Dic₇₁

semidirect

66. C₂×C₁₆

Dic₇₁

semidirect

Subgroups — #22590113

Conjugacy classes of subgroups

Complements