Group #22589847 — subgroups

Subgroups — #22589847

Order 9088.

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	#17986041	C₂	1	2	yes	maximal
2	C₂×#14556062	C₂	1	1	yes	maximal, characteristic
3	#17986025	C₂	1	1	yes	maximal, characteristic
4	#17985767	C₂	1	2	yes	maximal
5	#341×C₇₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11765849	C₂²	1	1	yes	characteristic
7	#14556087	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₇₁	C₂²	1	2	yes	—
9	#14556062	—	2	2	no	—
10	#14556062	—	2	2	no	—
11	#14556060	—	2	2	no	—
12	Dic₇₁⋊C₈	—	2	2	no	—
13	C₂×M₁₆×C₇₁	C₂²	1	2	yes	—
14	C₂²×C₈×C₇₁	C₂²	1	1	yes	characteristic
15	C₂²×Dic₇₁	—	2	2	no	—
16	#11765849	—	2	2	no	—
17	C₂×C₇₁⋊C₈	—	2	1	no	—
18	C₄⋊Dic₇₁	—	2	2	no	—
19	C₄⋊Dic₇₁	—	2	2	no	—
20	C₄⋊Dic₇₁	D₄	1	1	yes	characteristic
21	C₄⋊Dic₇₁	D₄	1	1	yes	characteristic
22	C₂²⋊Dic₇₁	—	2	1	no	—
23	C₄×Dic₇₁	—	2	1	no	—
24	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
25	M₁₆×C₇₁	—	2	2	no	—
26	M₁₆×C₇₁	Q₈	1	4	yes	—
27	C₂×C₈×C₇₁	—	2	2	no	—
28	C₂×C₈×C₇₁	—	2	2	no	—
29	C₂×C₈×C₇₁	D₄	1	2	yes	—
30	C₂³×C₇₁	#41	1	1	yes	characteristic
31	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₇₁	C₂×Q₈	1	2	yes	—
34	C₂×C₄×C₇₁	#41	1	2	yes	—
35	C₂×Dic₇₁	—	2	1	no	—
36	C₂×Dic₇₁	—	2	1	no	—
37	C₂×Dic₇₁	—	4	2	no	—
38	C₂×Dic₇₁	—	8	2	no	—
39	C₈×C₇₁	—	2	4	no	—
40	C₈×C₇₁	—	2	2	no	—
41	C₇₁⋊C₈	—	4	1	no	—
42	C₂²×C₇₁	—	2	1	no	—
43	C₂²×C₇₁	—	2	1	no	—
44	C₂²×C₇₁	#121	1	1	yes	characteristic
45	C₂²×C₇₁	#125	1	2	yes	—
46	C₄×C₇₁	C₂²⋊Q₈	1	2	yes	—
47	C₄×C₇₁	#123	1	1	yes	characteristic
48	C₄×C₇₁	C₄⋊Q₈	1	1	yes	characteristic
49	Dic₇₁	—	4	1	no	—
50	Dic₇₁	—	4	1	no	—
51	Dic₇₁	—	8	2	no	—
52	C₂×C₇₁	—	2	2	no	—
53	C₂×C₇₁	#398	1	1	yes	characteristic
54	C₂×C₇₁	#472	1	1	yes	characteristic
55	C₂×C₇₁	#473	1	1	yes	characteristic
56	#2089	—	71	1	no	maximal, Sylow
57	C₇₁	#2089	1	1	yes	characteristic, complemented, Sylow
58	#428	—	71	2	no	—
59	C₂×#107	—	71	1	no	—
60	#424	—	71	1	no	—
61	#343	—	71	2	no	—
62	#341	D₇₁	1	1	yes	characteristic
63	C₂×M₁₆	—	71	1	no	—
64	C₂×M₁₆	C₂×D₇₁	1	2	yes	—
65	C₂²×C₈	C₂×D₇₁	1	1	yes	characteristic
66	#117	—	71	1	no	—
67	C₂×C₄⋊C₄	—	71	2	no	—
68	#107	—	142	2	no	—
69	#107	—	142	2	no	—
70	#106	—	142	2	no	—
71	C₄⋊C₈	—	142	2	no	—
72	C₂²×C₄	—	142	2	no	—
73	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
74	M₁₆	—	2	2	no	—
75	M₁₆	—	142	2	no	—
76	M₁₆	Dic₁₄₂	1	4	yes	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	142	1	no	—
80	C₂×C₈	D₂₈₄	1	2	yes	—
81	C₄⋊C₄	—	71	1	no	—
82	C₄⋊C₄	—	71	1	no	—
83	C₄⋊C₄	—	142	2	no	—
84	C₄⋊C₄	—	142	2	no	—
85	C₂²⋊C₄	—	142	1	no	—
86	C₄²	—	142	1	no	—
87	C₂³	#11765866	1	1	yes	characteristic
88	C₂×C₄	—	284	2	no	—
89	C₂×C₄	—	568	2	no	—
90	C₂×C₄	—	142	1	no	—
91	C₂×C₄	—	142	1	no	—
92	C₂×C₄	D₄×D₇₁	1	1	yes	characteristic
93	C₂×C₄	C₂×D₂₈₄	1	1	yes	characteristic
94	C₂×C₄	C₂×Dic₁₄₂	1	2	yes	—
95	C₂×C₄	#11765864	1	2	yes	—
96	C₈	—	2	4	no	—
97	C₈	—	2	2	no	—
98	C₈	—	284	1	no	—
99	C₂²	—	2	1	no	—
100	C₂²	—	2	1	no	—
101	C₂²	#14556103	1	1	yes	characteristic
102	C₂²	#14556119	1	2	yes	—
103	C₄	—	284	1	no	—
104	C₄	—	284	1	no	—
105	C₄	—	568	2	no	—
106	C₄	#14556105	1	2	yes	—
107	C₄	#14556112	1	1	yes	characteristic
108	C₄	#14556128	1	1	yes	characteristic
109	C₂	—	2	2	no	—
110	C₂	#17985931	1	1	yes	characteristic
111	C₂	#17986270	1	1	yes	characteristic
112	C₂	#17986275	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17986041

C₂

yes

maximal

C₂×#14556062

C₂

yes

maximal, characteristic

#17986025

C₂

yes

maximal, characteristic

#17985767

C₂

yes

maximal

#341×C₇₁

C₂

yes

maximal, characteristic

C₂×#11765849

C₂²

yes

characteristic

#14556087

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₁

C₂²

yes

—

#14556062

—

#14556062

—

#14556060

—

Dic₇₁⋊C₈

—

C₂×M₁₆×C₇₁

C₂²

yes

—

C₂²×C₈×C₇₁

C₂²

yes

characteristic

C₂²×Dic₇₁

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

D₄

yes

characteristic

C₄⋊Dic₇₁

D₄

yes

characteristic

C₂²⋊Dic₇₁

—

C₄×Dic₇₁

—

C₂²×C₄×C₇₁

C₂³

yes

characteristic

M₁₆×C₇₁

—

M₁₆×C₇₁

Q₈

yes

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

D₄

yes

—

C₂³×C₇₁

#41

yes

characteristic

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×C₄×C₇₁

C₂×Q₈

yes

—

C₂×C₄×C₇₁

#41

yes

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

#121

yes

characteristic

C₂²×C₇₁

#125

yes

—

C₄×C₇₁

C₂²⋊Q₈

yes

—

C₄×C₇₁

#123

yes

characteristic

C₄×C₇₁

C₄⋊Q₈

yes

characteristic

Dic₇₁

—

Dic₇₁

—

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

yes

C₂×C₇₁

yes

C₂×C₇₁

yes

—

C₇₁

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₁

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₁

yes

—

C₂²×C₈

C₂×D₇₁

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

#107

—

142

—

#107

—

142

—

#106

—

142

—

C₄⋊C₈

—

142

—

C₂²×C₄

—

142

—

C₂²×C₄

C₂²×D₇₁

yes

characteristic

M₁₆

—

M₁₆

—

142

—

M₁₆

Dic₁₄₂

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

142

—

C₂×C₈

D₂₈₄

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

142

—

C₄⋊C₄

—

142

—

C₂²⋊C₄

—

142

—

C₄²

—

142

—

C₂³

#11765866

yes

characteristic

C₂×C₄

—

284

—

C₂×C₄

—

568

—

C₂×C₄

—

142

—

C₂×C₄

—

142

—

C₂×C₄

D₄×D₇₁

yes

characteristic

C₂×C₄

C₂×D₂₈₄

yes

characteristic

C₂×C₄

C₂×Dic₁₄₂

yes

—

C₂×C₄

#11765864

yes

—

C₈

—

C₈

—

C₈

—

284

—

C₂²

—

100

C₂²

—

101

C₂²

#14556103

yes

characteristic

102

C₂²

#14556119

yes

—

103

C₄

—

284

—

104

C₄

—

284

—

105

C₄

—

568

—

106

C₄

#14556105

yes

—

107

C₄

#14556112

yes

characteristic

108

C₄

#14556128

yes

characteristic

109

C₂

—

110

C₂

#17985931

yes

characteristic

111

C₂

#17986270

yes

characteristic

112

C₂

#17986275

yes

characteristic

	subgroup	G/H
center	C₂²	#14556103
commutator	C₂²×C₄×C₇₁	C₂³
Frattini	C₂²×C₄	C₂²×D₇₁
Fitting	#341×C₇₁	C₂
socle	C₂²×C₇₁	#121
hypercenter	#341	D₇₁
hypocenter	C₇₁	#2089
LCS	G ▷ C₂²×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂²

#14556103

commutator

C₂²×C₄×C₇₁

C₂³

Frattini

C₂²×C₄

C₂²×D₇₁

Fitting

#341×C₇₁

C₂

C₂²×C₇₁

D₇₁

C₇₁

G ▷ C₂²×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
57. C₇₁	#2089	semidirect

H ≅ G/N

type

57. C₇₁

#2089

semidirect

Subgroups — #22589847

Conjugacy classes of subgroups

Complements