Group #22590466 — subgroups

Subgroups — #22590466

Order 9088.

140 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 45 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×Dic₅₆₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#17986415	C₂	1	1	yes	maximal, characteristic
3	#17986275	C₂	1	2	yes	maximal
4	#17985814	C₂	1	2	yes	maximal, complemented
5	#368×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#14556161	—	2	2	no	—
7	C₂×Dic₂₈₄	C₂²	1	2	yes	—
8	#14556134	C₂²	1	1	yes	characteristic
9	Dic₅₆₈	—	2	1	no	—
10	Dic₅₆₈	—	2	1	no	—
11	#14556068	C₂²	1	1	yes	characteristic
12	#14556067	—	2	1	no	—
13	C₁₆×D₇₁	—	2	1	no	—
14	#14556046	—	2	2	no	—
15	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
16	#108×C₇₁	C₂²	1	2	yes	—
17	#11765865	D₄	1	1	yes	characteristic
18	C₂×Dic₁₄₂	—	2	2	no	—
19	Dic₂₈₄	—	2	2	no	—
20	Dic₂₈₄	—	2	2	no	—
21	Dic₂₈₄	—	4	2	no	—
22	#11765854	—	4	2	no	—
23	#11765849	D₄	1	1	yes	characteristic
24	#11765848	—	2	1	no	—
25	C₈×D₇₁	—	2	1	no	—
26	C₇₁⋊C₁₆	—	2	1	no	—
27	M₁₆×C₇₁	—	2	2	no	—
28	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
29	C₁₆×C₇₁	D₄	1	1	yes	characteristic
30	C₁₆×C₇₁	D₄	1	1	yes	characteristic
31	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
32	C₂²⋊D₇₁	—	2	1	no	—
33	C₂×Dic₇₁	—	4	2	no	—
34	D₂₈₄	D₈	1	1	yes	characteristic
35	C₄×D₇₁	—	2	1	no	—
36	Dic₁₄₂	—	4	2	no	—
37	Dic₁₄₂	—	4	2	no	—
38	Dic₁₄₂	D₈	1	1	yes	characteristic
39	C₈×C₇₁	—	4	2	no	—
40	C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
41	C₈×C₇₁	#41	1	1	yes	characteristic
42	C₇₁⋊C₈	—	2	1	no	—
43	C₂²×C₇₁	#135	1	1	yes	characteristic
44	C₂×D₇₁	—	2	1	no	—
45	C₄×C₇₁	#121	1	1	yes	characteristic
46	C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
47	Dic₇₁	—	2	1	no	—
48	Dic₇₁	—	8	2	no	—
49	C₂×C₇₁	—	2	1	no	—
50	C₂×C₇₁	#466	1	1	yes	characteristic
51	D₇₁	—	4	1	no	—
52	#2222	—	71	1	no	maximal, Sylow
53	C₇₁	#2222	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₃₂	—	71	1	no	—
55	#504	—	71	1	no	—
56	#473	—	71	2	no	—
57	#368	D₇₁	1	1	yes	characteristic, complemented
58	#362	—	71	2	no	—
59	#137	—	142	2	no	—
60	C₂×Q₁₆	—	71	2	no	—
61	#131	—	71	1	no	—
62	Q₃₂	—	142	1	no	—
63	Q₃₂	—	142	1	no	—
64	M₃₂	—	71	1	no	—
65	M₃₂	—	142	1	no	—
66	C₂×C₁₆	—	142	1	no	—
67	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
68	#108	C₂×D₇₁	1	2	yes	—
69	#101	—	142	2	no	—
70	#41	—	71	1	no	—
71	C₂×Q₈	—	142	2	no	—
72	Q₁₆	—	284	2	no	—
73	Q₁₆	—	142	2	no	—
74	Q₁₆	—	142	2	no	—
75	SD₁₆	—	284	2	no	—
76	M₁₆	—	2	2	no	—
77	M₁₆	—	71	1	no	—
78	M₁₆	—	142	1	no	—
79	C₂×C₈	—	142	1	no	—
80	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
81	C₁₆	—	142	1	no	—
82	C₁₆	D₂₈₄	1	1	yes	characteristic
83	C₁₆	D₂₈₄	1	1	yes	characteristic
84	Q₈	—	284	2	no	—
85	Q₈	—	284	2	no	—
86	Q₈	—	71	1	no	—
87	D₄	—	71	1	no	—
88	D₄	—	142	1	no	—
89	C₂×C₄	—	284	2	no	—
90	C₂×C₄	—	142	1	no	—
91	C₂×C₄	D₄×D₇₁	1	1	yes	characteristic
92	C₈	—	4	2	no	—
93	C₈	—	142	1	no	—
94	C₈	C₂×D₂₈₄	1	1	yes	characteristic
95	C₈	#11765866	1	1	yes	characteristic
96	C₂²	—	142	1	no	—
97	C₂²	#14556151	1	1	yes	characteristic
98	C₄	—	568	2	no	—
99	C₄	—	142	1	no	—
100	C₄	#14556103	1	1	yes	characteristic
101	C₄	D₈×D₇₁	1	1	yes	characteristic
102	C₂	—	2	1	no	—
103	C₂	—	284	1	no	—
104	C₂	#17986236	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₅₆₈

C₂

yes

maximal, characteristic, complemented

#17986415

C₂

yes

maximal, characteristic

#17986275

C₂

yes

maximal

#17985814

C₂

yes

maximal, complemented

#368×C₇₁

C₂

yes

maximal, characteristic, complemented

#14556161

—

C₂×Dic₂₈₄

C₂²

yes

—

#14556134

C₂²

yes

characteristic

Dic₅₆₈

—

Dic₅₆₈

—

#14556068

C₂²

yes

characteristic

#14556067

—

C₁₆×D₇₁

—

#14556046

—

C₂×C₁₆×C₇₁

C₂²

yes

characteristic

#108×C₇₁

C₂²

yes

—

#11765865

D₄

yes

characteristic

C₂×Dic₁₄₂

—

Dic₂₈₄

—

Dic₂₈₄

—

Dic₂₈₄

—

#11765854

—

#11765849

D₄

yes

characteristic

#11765848

—

C₈×D₇₁

—

C₇₁⋊C₁₆

—

M₁₆×C₇₁

—

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₁₆×C₇₁

D₄

yes

characteristic

C₁₆×C₇₁

D₄

yes

characteristic

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂²⋊D₇₁

—

C₂×Dic₇₁

—

D₂₈₄

D₈

yes

characteristic

C₄×D₇₁

—

Dic₁₄₂

—

Dic₁₄₂

—

Dic₁₄₂

D₈

yes

characteristic

C₈×C₇₁

—

C₈×C₇₁

C₂×D₄

yes

characteristic

C₈×C₇₁

#41

yes

characteristic

C₇₁⋊C₈

—

C₂²×C₇₁

#135

yes

characteristic

C₂×D₇₁

—

C₄×C₇₁

#121

yes

characteristic

C₄×C₇₁

C₂×D₈

yes

characteristic

Dic₇₁

—

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

#466

yes

characteristic

D₇₁

—

#2222

—

maximal, Sylow

C₇₁

#2222

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

#504

—

#473

—

#368

D₇₁

yes

characteristic, complemented

#362

—

#137

—

142

—

C₂×Q₁₆

—

#131

—

Q₃₂

—

142

—

Q₃₂

—

142

—

M₃₂

—

M₃₂

—

142

—

C₂×C₁₆

—

142

—

C₂×C₁₆

C₂×D₇₁

yes

characteristic

#108

C₂×D₇₁

yes

—

#101

—

142

—

#41

—

C₂×Q₈

—

142

—

Q₁₆

—

284

—

Q₁₆

—

142

—

Q₁₆

—

142

—

SD₁₆

—

284

—

M₁₆

—

M₁₆

—

M₁₆

—

142

—

C₂×C₈

—

142

—

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₁₆

—

142

—

C₁₆

D₂₈₄

yes

characteristic

C₁₆

D₂₈₄

yes

characteristic

Q₈

—

284

—

Q₈

—

284

—

Q₈

—

D₄

—

D₄

—

142

—

C₂×C₄

—

284

—

C₂×C₄

—

142

—

C₂×C₄

D₄×D₇₁

yes

characteristic

C₈

—

C₈

—

142

—

C₈

C₂×D₂₈₄

yes

characteristic

C₈

#11765866

yes

characteristic

C₂²

—

142

—

C₂²

#14556151

yes

characteristic

C₄

—

568

—

C₄

—

142

—

100

C₄

#14556103

yes

characteristic

101

C₄

D₈×D₇₁

yes

characteristic

102

C₂

—

103

C₂

—

284

—

104

C₂

#17986236

yes

characteristic

	subgroup	G/H
center	C₂	#17986236
commutator	C₂×C₈×C₇₁	C₂³
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	#368×C₇₁	C₂
socle	C₂×C₇₁	#466
hypercenter	#368	D₇₁
hypocenter	C₇₁	#2222
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #368

subgroup

G/H

center

C₂

#17986236

commutator

C₂×C₈×C₇₁

C₂³

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

#368×C₇₁

C₂

C₂×C₇₁

D₇₁

C₇₁

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #368

N	H ≅ G/N	type
1. C₂×Dic₅₆₈	C₂	semidirect
4. #17985814	C₂	semidirect
5. #368×C₇₁	C₂	semidirect
53. C₇₁	#2222	semidirect
57. #368	D₇₁	semidirect

H ≅ G/N

type

1. C₂×Dic₅₆₈

C₂

semidirect

4. #17985814

C₂

semidirect

5. #368×C₇₁

C₂

semidirect

53. C₇₁

#2222

semidirect

57. #368

D₇₁

semidirect

Subgroups — #22590466

Conjugacy classes of subgroups

Complements