Group #22589333 — subgroups

Subgroups — #22589333

Order 9088.

228 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14556120	C₂	1	1	yes	maximal, characteristic
2	#17986023	C₂	1	1	yes	maximal, characteristic
3	#17985767	C₂	1	4	yes	maximal
4	C₄×M₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#11765849	C₂²	1	2	yes	—
6	#14556120	—	2	2	no	—
7	#14556120	—	2	1	no	—
8	#14556120	—	2	1	no	—
9	C₂×C₄⋊Dic₇₁	C₂²	1	2	yes	—
10	C₂×Dic₇₁⋊C₄	C₄	1	4	yes	—
11	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
12	C₂×M₁₆×C₇₁	C₂²	1	2	yes	—
13	C₂×C₄²×C₇₁	C₂²	1	1	yes	characteristic
14	#97×C₇₁	—	2	1	no	—
15	C₄×C₈×C₇₁	—	2	1	no	—
16	C₂²×Dic₇₁	C₂×C₄	1	4	yes	—
17	#11765849	—	2	4	no	—
18	C₂×C₇₁⋊C₈	—	2	2	no	—
19	C₄⋊Dic₇₁	—	2	2	no	—
20	C₄⋊Dic₇₁	—	2	2	no	—
21	Dic₇₁⋊C₄	—	2	4	no	—
22	Dic₇₁⋊C₄	—	2	4	no	—
23	C₂²×C₄×C₇₁	C₂×C₄	1	2	yes	—
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	C₄²×C₇₁	D₄	1	2	yes	—
29	C₄²×C₇₁	D₄	1	1	yes	characteristic
30	C₄²×C₇₁	D₄	1	1	yes	characteristic
31	C₂³×C₇₁	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₇₁	—	4	2	no	—
33	C₂×C₄×C₇₁	C₂²⋊C₄	1	2	yes	—
34	C₂×C₄×C₇₁	C₂²⋊C₄	1	2	yes	—
35	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₇₁	C₂×Q₈	1	2	yes	—
38	C₂×C₄×C₇₁	#41	1	2	yes	—
39	C₂×Dic₇₁	—	2	4	no	—
40	C₂×Dic₇₁	—	4	4	no	—
41	C₈×C₇₁	—	2	4	no	—
42	C₇₁⋊C₈	—	4	2	no	—
43	C₂²×C₇₁	—	2	2	no	—
44	C₂²×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₂²×C₇₁	C₄×Q₈	1	2	yes	—
46	C₄×C₇₁	—	2	2	no	—
47	C₄×C₇₁	—	2	2	no	—
48	C₄×C₇₁	C₂²⋊Q₈	1	2	yes	—
49	C₄×C₇₁	#124	1	1	yes	characteristic
50	C₄×C₇₁	C₄⋊Q₈	1	1	yes	characteristic
51	Dic₇₁	—	4	4	no	—
52	C₂×C₇₁	—	2	2	no	—
53	C₂×C₇₁	#391	1	1	yes	characteristic
54	C₂×C₇₁	#413	1	2	yes	—
55	#1998	—	71	1	no	maximal, Sylow
56	C₇₁	#1998	1	1	yes	characteristic, complemented, Sylow
57	C₂×#125	—	71	1	no	—
58	#423	—	71	1	no	—
59	C₄×M₁₆	D₇₁	1	1	yes	characteristic
60	#343	—	71	4	no	—
61	C₂×M₁₆	—	71	2	no	—
62	C₂×M₁₆	C₂×D₇₁	1	2	yes	—
63	#125	—	142	2	no	—
64	#125	—	142	1	no	—
65	#125	—	142	1	no	—
66	C₂×C₄⋊C₄	—	71	4	no	—
67	C₂×C₄⋊C₄	—	71	2	no	—
68	C₂×C₄²	C₂×D₇₁	1	1	yes	characteristic
69	C₄⋊C₈	—	142	2	no	—
70	#97	—	2	1	no	—
71	C₄×C₈	—	2	1	no	—
72	C₂²×C₄	—	71	4	no	—
73	C₂²×C₄	C₄×D₇₁	1	2	yes	—
74	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
75	M₁₆	—	2	2	no	—
76	M₁₆	—	142	4	no	—
77	M₁₆	Dic₁₄₂	1	4	yes	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	142	2	no	—
80	C₄⋊C₄	—	142	4	no	—
81	C₄⋊C₄	—	142	4	no	—
82	C₄⋊C₄	—	142	2	no	—
83	C₄⋊C₄	—	142	2	no	—
84	C₄²	D₂₈₄	1	2	yes	—
85	C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
86	C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
87	C₂³	C₂×C₄×D₇₁	1	1	yes	characteristic
88	C₂×C₄	—	4	2	no	—
89	C₂×C₄	—	284	4	no	—
90	C₂×C₄	—	142	4	no	—
91	C₂×C₄	(C₂×D₇₁)⋊C₄	1	2	yes	—
92	C₂×C₄	(C₂×D₇₁)⋊C₄	1	2	yes	—
93	C₂×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
94	C₂×C₄	C₂×D₂₈₄	1	1	yes	characteristic
95	C₂×C₄	C₂×Dic₁₄₂	1	2	yes	—
96	C₂×C₄	#11765865	1	2	yes	—
97	C₈	—	2	4	no	—
98	C₈	—	284	2	no	—
99	C₂²	—	2	2	no	—
100	C₂²	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
101	C₂²	C₄×Dic₁₄₂	1	2	yes	—
102	C₄	—	2	2	no	—
103	C₄	—	2	2	no	—
104	C₄	—	284	4	no	—
105	C₄	#14556107	1	2	yes	—
106	C₄	#14556116	1	1	yes	characteristic
107	C₄	#14556128	1	1	yes	characteristic
108	C₂	—	2	2	no	—
109	C₂	#17985905	1	1	yes	characteristic
110	C₂	#17985981	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556120

C₂

yes

maximal, characteristic

#17986023

C₂

yes

maximal, characteristic

#17985767

C₂

yes

maximal

C₄×M₁₆×C₇₁

C₂

yes

maximal, characteristic

C₂×#11765849

C₂²

yes

—

#14556120

—

#14556120

—

#14556120

—

C₂×C₄⋊Dic₇₁

C₂²

yes

—

C₂×Dic₇₁⋊C₄

C₄

yes

—

C₄⋊(C₇₁⋊C₈)

—

C₂×M₁₆×C₇₁

C₂²

yes

—

C₂×C₄²×C₇₁

C₂²

yes

characteristic

#97×C₇₁

—

C₄×C₈×C₇₁

—

C₂²×Dic₇₁

C₂×C₄

yes

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

Dic₇₁⋊C₄

—

Dic₇₁⋊C₄

—

C₂²×C₄×C₇₁

C₂×C₄

yes

—

C₂²×C₄×C₇₁

C₂³

yes

characteristic

M₁₆×C₇₁

—

M₁₆×C₇₁

Q₈

yes

—

C₂×C₈×C₇₁

—

C₄²×C₇₁

D₄

yes

—

C₄²×C₇₁

D₄

yes

characteristic

C₄²×C₇₁

D₄

yes

characteristic

C₂³×C₇₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂²⋊C₄

yes

—

C₂×C₄×C₇₁

C₂²⋊C₄

yes

—

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

—

C₈×C₇₁

—

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₇₁

C₄×Q₈

yes

—

C₄×C₇₁

—

C₄×C₇₁

—

C₄×C₇₁

C₂²⋊Q₈

yes

—

C₄×C₇₁

#124

yes

characteristic

C₄×C₇₁

C₄⋊Q₈

yes

characteristic

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

#391

yes

characteristic

C₂×C₇₁

#413

yes

—

#1998

—

maximal, Sylow

C₇₁

#1998

yes

characteristic, complemented, Sylow

C₂×#125

—

#423

—

C₄×M₁₆

D₇₁

yes

characteristic

#343

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₁

yes

—

#125

—

142

—

#125

—

142

—

#125

—

142

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₇₁

yes

characteristic

C₄⋊C₈

—

142

—

#97

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

C₄×D₇₁

yes

—

C₂²×C₄

C₂²×D₇₁

yes

characteristic

M₁₆

—

M₁₆

—

142

—

M₁₆

Dic₁₄₂

yes

—

C₂×C₈

—

C₂×C₈

—

142

—

C₄⋊C₄

—

142

—

C₄⋊C₄

—

142

—

C₄⋊C₄

—

142

—

C₄⋊C₄

—

142

—

C₄²

D₂₈₄

yes

—

C₄²

C₂²⋊D₇₁

yes

characteristic

C₄²

C₂²⋊D₇₁

yes

characteristic

C₂³

C₂×C₄×D₇₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

284

—

C₂×C₄

—

142

—

C₂×C₄

(C₂×D₇₁)⋊C₄

yes

—

C₂×C₄

(C₂×D₇₁)⋊C₄

yes

—

C₂×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

C₂×C₄

C₂×D₂₈₄

yes

characteristic

C₂×C₄

C₂×Dic₁₄₂

yes

—

C₂×C₄

#11765865

yes

—

C₈

—

C₈

—

284

—

C₂²

—

100

C₂²

C₂×(C₂×D₇₁)⋊C₄

yes

characteristic

101

C₂²

C₄×Dic₁₄₂

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

284

—

105

C₄

#14556107

yes

—

106

C₄

#14556116

yes

characteristic

107

C₄

#14556128

yes

characteristic

108

C₂

—

109

C₂

#17985905

yes

characteristic

110

C₂

#17985981

yes

—

	subgroup	G/H
center	C₂²	C₂×(C₂×D₇₁)⋊C₄
commutator	C₂³×C₇₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₁
Fitting	C₄×M₁₆×C₇₁	C₂
socle	C₂²×C₇₁	C₂×C₂²⋊C₄
hypercenter	C₄×M₁₆	D₇₁
hypocenter	C₇₁	#1998
LCS	G ▷ C₂³×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

subgroup

G/H

center

C₂²

C₂×(C₂×D₇₁)⋊C₄

commutator

C₂³×C₇₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₁

Fitting

C₄×M₁₆×C₇₁

C₂

socle

C₂²×C₇₁

C₂×C₂²⋊C₄

hypercenter

C₄×M₁₆

D₇₁

hypocenter

C₇₁

#1998

LCS

G ▷ C₂³×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

N	H ≅ G/N	type
56. C₇₁	#1998	semidirect

H ≅ G/N

type

56. C₇₁

#1998

semidirect

Subgroups — #22589333

Conjugacy classes of subgroups

Complements