Group #22586279 — subgroups

Subgroups — #22586279

Order 9088.

108 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 43 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×Dic₇₁⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊(C₇₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊C₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₇₁⋊C₈	C₄	1	1	yes	characteristic
5	C₂×C₄×Dic₇₁	C₄	1	1	yes	characteristic
6	C₂×C₇₁⋊C₁₆	—	2	1	no	—
7	Dic₇₁⋊C₈	—	2	1	no	—
8	Dic₇₁⋊C₈	—	2	1	no	—
9	C₂²×C₈×C₇₁	C₂²	1	1	yes	characteristic
10	C₂×C₁₆×C₇₁	—	2	1	no	—
11	C₂²×Dic₇₁	C₈	1	1	yes	characteristic
12	C₂²×Dic₇₁	C₈	1	1	yes	characteristic
13	C₂×C₇₁⋊C₈	—	2	1	no	—
14	C₂×C₇₁⋊C₈	—	4	1	no	—
15	C₄×Dic₇₁	—	2	1	no	—
16	C₄×Dic₇₁	—	2	1	no	—
17	C₇₁⋊C₁₆	—	4	1	no	—
18	C₂²×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₇₁	—	4	1	no	—
20	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
21	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
22	C₁₆×C₇₁	—	4	1	no	—
23	C₂³×C₇₁	C₂×C₈	1	1	yes	characteristic
24	C₂×C₄×C₇₁	—	2	1	no	—
25	C₂×C₄×C₇₁	—	2	1	no	—
26	C₂×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₇₁	M₁₆	1	1	yes	characteristic
28	C₂×Dic₇₁	—	2	1	no	—
29	C₂×Dic₇₁	—	2	1	no	—
30	C₂×Dic₇₁	—	2	1	no	—
31	C₂×Dic₇₁	—	4	1	no	—
32	C₂×Dic₇₁	C₁₆	1	2	yes	complemented
33	C₈×C₇₁	—	2	1	no	—
34	C₈×C₇₁	—	2	1	no	—
35	C₇₁⋊C₈	—	4	1	no	—
36	C₂²×C₇₁	—	2	1	no	—
37	C₂²×C₇₁	—	2	1	no	—
38	C₂²×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
39	C₂²×C₇₁	C₂×C₁₆	1	1	yes	characteristic
40	C₂²×C₇₁	M₃₂	1	1	yes	characteristic
41	C₄×C₇₁	—	2	1	no	—
42	C₄×C₇₁	#99	1	1	yes	characteristic
43	C₄×C₇₁	#101	1	1	yes	characteristic
44	Dic₇₁	—	2	2	no	—
45	Dic₇₁	—	4	1	no	—
46	C₂×C₇₁	—	2	1	no	—
47	C₂×C₇₁	—	2	1	no	—
48	C₂×C₇₁	#324	1	1	yes	characteristic
49	C₂×C₇₁	C₂²⋊C₁₆	1	1	yes	characteristic
50	C₂×C₇₁	#349	1	1	yes	characteristic
51	#1322	—	71	1	no	maximal, Sylow
52	C₇₁	#1322	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₄⋊C₈	—	71	1	no	—
54	C₂²⋊C₁₆	—	71	1	no	—
55	C₂²⋊C₁₆	D₇₁	1	1	yes	characteristic
56	C₂²×C₈	—	71	1	no	—
57	C₂²×C₈	C₂×D₇₁	1	1	yes	characteristic
58	C₂×C₄²	—	71	1	no	—
59	C₂×C₁₆	—	2	1	no	—
60	C₂×C₁₆	—	142	1	no	—
61	C₄⋊C₈	—	142	1	no	—
62	C₄⋊C₈	—	142	1	no	—
63	C₂²×C₄	—	71	1	no	—
64	C₂²×C₄	—	71	1	no	—
65	C₂²×C₄	C₄×D₇₁	1	1	yes	characteristic
66	C₂×C₈	—	4	1	no	—
67	C₂×C₈	—	284	1	no	—
68	C₂×C₈	—	142	1	no	—
69	C₂×C₈	D₂₈₄	1	1	yes	characteristic
70	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
71	C₄²	—	142	1	no	—
72	C₄²	—	142	1	no	—
73	C₁₆	—	4	1	no	—
74	C₁₆	—	284	1	no	—
75	C₂³	C₈×D₇₁	1	1	yes	characteristic
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	284	1	no	—
79	C₂×C₄	—	71	2	no	—
80	C₂×C₄	—	142	1	no	—
81	C₂×C₄	—	142	1	no	—
82	C₂×C₄	—	142	1	no	—
83	C₂×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
84	C₂×C₄	#11765848	1	1	yes	characteristic
85	C₈	—	2	1	no	—
86	C₈	—	2	1	no	—
87	C₈	—	284	1	no	—
88	C₂²	—	2	1	no	—
89	C₂²	—	2	1	no	—
90	C₂²	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
91	C₂²	C₁₆×D₇₁	1	1	yes	characteristic
92	C₂²	#14556067	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	284	1	no	—
95	C₄	—	142	2	no	—
96	C₄	#14556042	1	1	yes	characteristic
97	C₄	#14556046	1	1	yes	characteristic
98	C₂	—	2	1	no	—
99	C₂	—	2	1	no	—
100	C₂	#17985724	1	1	yes	characteristic
101	C₂	(C₂×D₇₁)⋊C₁₆	1	1	yes	characteristic
102	C₂	#17985780	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₇₁⋊C₈

C₂

yes

maximal, characteristic

C₂²⋊(C₇₁⋊C₁₆)

C₂

yes

maximal, characteristic

C₂²⋊C₁₆×C₇₁

C₂

yes

maximal, characteristic

C₂²×C₇₁⋊C₈

C₄

yes

characteristic

C₂×C₄×Dic₇₁

C₄

yes

characteristic

C₂×C₇₁⋊C₁₆

—

Dic₇₁⋊C₈

—

Dic₇₁⋊C₈

—

C₂²×C₈×C₇₁

C₂²

yes

characteristic

C₂×C₁₆×C₇₁

—

C₂²×Dic₇₁

C₈

yes

characteristic

C₂²×Dic₇₁

C₈

yes

characteristic

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₇₁⋊C₁₆

—

C₂²×C₄×C₇₁

C₂×C₄

yes

characteristic

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

D₄

yes

characteristic

C₁₆×C₇₁

—

C₂³×C₇₁

C₂×C₈

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₁

M₁₆

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

C₁₆

yes

complemented

C₈×C₇₁

—

C₈×C₇₁

—

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

C₂²⋊C₈

yes

characteristic

C₂²×C₇₁

C₂×C₁₆

yes

characteristic

C₂²×C₇₁

M₃₂

yes

characteristic

C₄×C₇₁

—

C₄×C₇₁

yes

C₄×C₇₁

yes

Dic₇₁

—

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

—

C₂×C₇₁

#324

yes

characteristic

C₂×C₇₁

C₂²⋊C₁₆

yes

C₂×C₇₁

yes

—

C₇₁

yes

characteristic, complemented, Sylow

C₂×C₄⋊C₈

—

C₂²⋊C₁₆

—

C₂²⋊C₁₆

D₇₁

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₂×D₇₁

yes

characteristic

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

142

—

C₄⋊C₈

—

142

—

C₄⋊C₈

—

142

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₇₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

284

—

C₂×C₈

—

142

—

C₂×C₈

D₂₈₄

yes

characteristic

C₂×C₈

C₂²⋊D₇₁

yes

characteristic

C₄²

—

142

—

C₄²

—

142

—

C₁₆

—

C₁₆

—

284

—

C₂³

C₈×D₇₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

284

—

C₂×C₄

—

C₂×C₄

—

142

—

C₂×C₄

—

142

—

C₂×C₄

—

142

—

C₂×C₄

(C₂×D₇₁)⋊C₄

yes

characteristic

C₂×C₄

#11765848

yes

characteristic

C₈

—

C₈

—

C₈

—

284

—

C₂²

—

C₂²

—

C₂²

(C₂×D₇₁)⋊C₈

yes

characteristic

C₂²

C₁₆×D₇₁

yes

characteristic

C₂²

#14556067

yes

characteristic

C₄

—

C₄

—

284

—

C₄

—

142

—

C₄

yes

C₄

yes

C₂

—

C₂

—

100

C₂

#17985724

yes

characteristic

101

C₂

(C₂×D₇₁)⋊C₁₆

yes

characteristic

102

C₂

#17985780

yes

characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₇₁)⋊C₄
commutator	C₂²×C₇₁	C₂×C₁₆
Frattini	C₂²×C₈	C₂×D₇₁
Fitting	C₂²⋊C₁₆×C₇₁	C₂
socle	C₂²×C₇₁	C₂²⋊C₈
hypercenter	C₂²⋊C₁₆	D₇₁
hypocenter	C₇₁	#1322
LCS	G ▷ C₂²×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

subgroup

G/H

center

C₂×C₄

(C₂×D₇₁)⋊C₄

commutator

C₂²×C₇₁

C₂×C₁₆

Frattini

C₂²×C₈

C₂×D₇₁

Fitting

C₂²⋊C₁₆×C₇₁

C₂

socle

C₂²×C₇₁

C₂²⋊C₈

hypercenter

C₂²⋊C₁₆

D₇₁

hypocenter

C₇₁

#1322

LCS

G ▷ C₂²×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

N	H ≅ G/N	type
32. C₂×Dic₇₁	C₁₆	semidirect
52. C₇₁	#1322	semidirect

H ≅ G/N

type

32. C₂×Dic₇₁

C₁₆

semidirect

52. C₇₁

#1322

semidirect

Subgroups — #22586279

Conjugacy classes of subgroups

Complements