Group #22590601 — subgroups

Subgroups — #22590601

Order 9088.

184 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 61 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	C₂×#14556073	C₂	1	2	yes	maximal, complemented
3	C₂×D₁₁₃₆	C₂	1	1	yes	maximal, characteristic
4	#17986383	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₈₄	C₂²	1	2	yes	—
7	C₂×#11765854	—	2	2	no	—
8	C₂×D₅₆₈	C₂²	1	2	yes	—
9	#14556116	—	2	2	no	—
10	Dic₅₆₈	—	2	2	no	—
11	#14556073	—	2	4	no	—
12	D₁₁₃₆	—	2	2	no	—
13	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₄₂	—	2	2	no	—
17	C₂×D₂₈₄	—	2	2	no	—
18	Dic₂₈₄	—	2	2	no	—
19	Dic₂₈₄	—	2	2	no	—
20	#11765854	—	4	4	no	—
21	D₅₆₈	—	2	2	no	—
22	D₅₆₈	—	2	2	no	—
23	(C₂×D₇₁)⋊C₄	—	4	4	no	—
24	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
25	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
26	C₄²×C₇₁	D₄	1	1	yes	characteristic
27	C₁₆×C₇₁	D₄	1	2	yes	—
28	C₁₆×C₇₁	D₄	1	2	yes	—
29	C₂²×D₇₁	—	4	2	no	—
30	C₂×C₄×C₇₁	D₈	1	2	yes	—
31	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
32	C₂×Dic₇₁	—	4	2	no	—
33	D₂₈₄	—	4	2	no	—
34	D₂₈₄	—	4	2	no	—
35	Dic₁₄₂	—	4	2	no	—
36	Dic₁₄₂	—	4	2	no	—
37	C₈×C₇₁	D₈	1	2	yes	—
38	C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
39	C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₇₁	C₂×D₈	1	1	yes	characteristic
41	C₂×D₇₁	—	8	2	no	—
42	C₂×D₇₁	—	8	4	no	—
43	C₄×C₇₁	—	2	2	no	—
44	C₄×C₇₁	#127	1	1	yes	characteristic
45	C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
46	Dic₇₁	—	8	2	no	—
47	C₂×C₇₁	#493	1	1	yes	characteristic
48	C₂×C₇₁	#508	1	2	yes	—
49	D₇₁	—	16	2	no	—
50	#2249	—	71	1	no	maximal, Sylow
51	C₇₁	#2249	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₃₂	—	71	1	no	—
53	C₂×SD₃₂	—	71	2	no	—
54	C₂×D₁₆	—	71	1	no	—
55	#495	—	71	2	no	—
56	C₄×C₁₆	D₇₁	1	1	yes	characteristic, complemented
57	C₂×Q₁₆	—	71	2	no	—
58	C₂×SD₁₆	—	142	2	no	—
59	C₂×D₈	—	71	2	no	—
60	#124	—	142	2	no	—
61	Q₃₂	—	142	2	no	—
62	SD₃₂	—	142	4	no	—
63	D₁₆	—	142	2	no	—
64	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
65	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
66	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
67	C₂×Q₈	—	142	2	no	—
68	C₂×D₄	—	142	2	no	—
69	Q₁₆	—	142	2	no	—
70	Q₁₆	—	142	2	no	—
71	SD₁₆	—	284	4	no	—
72	D₈	—	142	2	no	—
73	D₈	—	142	2	no	—
74	C₂×C₈	D₂₈₄	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
76	C₂²⋊C₄	—	284	4	no	—
77	C₄²	D₂₈₄	1	1	yes	characteristic
78	C₁₆	D₂₈₄	1	2	yes	—
79	C₁₆	D₂₈₄	1	2	yes	—
80	C₂³	—	284	2	no	—
81	Q₈	—	284	2	no	—
82	Q₈	—	284	2	no	—
83	D₄	—	284	2	no	—
84	D₄	—	284	2	no	—
85	C₂×C₄	—	284	2	no	—
86	C₂×C₄	D₅₆₈	1	2	yes	—
87	C₂×C₄	C₂×D₂₈₄	1	1	yes	characteristic
88	C₈	D₅₆₈	1	2	yes	—
89	C₈	C₂×D₂₈₄	1	1	yes	characteristic
90	C₈	C₂×D₂₈₄	1	1	yes	characteristic
91	C₂²	—	568	2	no	—
92	C₂²	—	568	4	no	—
93	C₂²	C₂×D₅₆₈	1	1	yes	characteristic
94	C₄	—	2	2	no	—
95	C₄	—	568	2	no	—
96	C₄	#14556125	1	1	yes	characteristic
97	C₄	C₂×D₅₆₈	1	1	yes	characteristic
98	C₂	—	1136	2	no	—
99	C₂	#17986376	1	1	yes	characteristic
100	C₂	#17986431	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₅₆₈

C₂

yes

maximal, characteristic, complemented

C₂×#14556073

C₂

yes

maximal, complemented

C₂×D₁₁₃₆

C₂

yes

maximal, characteristic

#17986383

C₂

yes

maximal, complemented

C₄×C₁₆×C₇₁

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₈₄

C₂²

yes

—

C₂×#11765854

—

C₂×D₅₆₈

C₂²

yes

—

#14556116

—

Dic₅₆₈

—

#14556073

—

D₁₁₃₆

—

C₂×C₁₆×C₇₁

C₂²

yes

characteristic

C₂×C₁₆×C₇₁

C₂²

yes

characteristic

C₄×C₈×C₇₁

C₂²

yes

characteristic

C₂×Dic₁₄₂

—

C₂×D₂₈₄

—

Dic₂₈₄

—

Dic₂₈₄

—

#11765854

—

D₅₆₈

—

D₅₆₈

—

(C₂×D₇₁)⋊C₄

—

C₂×C₈×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₄²×C₇₁

D₄

yes

characteristic

C₁₆×C₇₁

D₄

yes

—

C₁₆×C₇₁

D₄

yes

—

C₂²×D₇₁

—

C₂×C₄×C₇₁

D₈

yes

—

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×Dic₇₁

—

D₂₈₄

—

D₂₈₄

—

Dic₁₄₂

—

Dic₁₄₂

—

C₈×C₇₁

D₈

yes

—

C₈×C₇₁

C₂×D₄

yes

characteristic

C₈×C₇₁

C₂×D₄

yes

characteristic

C₂²×C₇₁

C₂×D₈

yes

characteristic

C₂×D₇₁

—

C₂×D₇₁

—

C₄×C₇₁

—

C₄×C₇₁

#127

yes

characteristic

C₄×C₇₁

C₂×D₈

yes

characteristic

Dic₇₁

—

C₂×C₇₁

#493

yes

characteristic

C₂×C₇₁

#508

yes

—

D₇₁

—

#2249

—

maximal, Sylow

C₇₁

#2249

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₂×SD₃₂

—

C₂×D₁₆

—

#495

—

C₄×C₁₆

D₇₁

yes

characteristic, complemented

C₂×Q₁₆

—

C₂×SD₁₆

—

142

—

C₂×D₈

—

#124

—

142

—

Q₃₂

—

142

—

SD₃₂

—

142

—

D₁₆

—

142

—

C₂×C₁₆

C₂×D₇₁

yes

characteristic

C₂×C₁₆

C₂×D₇₁

yes

characteristic

C₄×C₈

C₂×D₇₁

yes

characteristic

C₂×Q₈

—

142

—

C₂×D₄

—

142

—

Q₁₆

—

142

—

Q₁₆

—

142

—

SD₁₆

—

284

—

D₈

—

142

—

D₈

—

142

—

C₂×C₈

D₂₈₄

yes

characteristic

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₂²⋊C₄

—

284

—

C₄²

D₂₈₄

yes

characteristic

C₁₆

D₂₈₄

yes

—

C₁₆

D₂₈₄

yes

—

C₂³

—

284

—

Q₈

—

284

—

Q₈

—

284

—

D₄

—

284

—

D₄

—

284

—

C₂×C₄

—

284

—

C₂×C₄

D₅₆₈

yes

—

C₂×C₄

C₂×D₂₈₄

yes

characteristic

C₈

D₅₆₈

yes

—

C₈

C₂×D₂₈₄

yes

characteristic

C₈

C₂×D₂₈₄

yes

characteristic

C₂²

—

568

—

C₂²

—

568

—

C₂²

C₂×D₅₆₈

yes

characteristic

C₄

—

C₄

—

568

—

C₄

#14556125

yes

characteristic

C₄

C₂×D₅₆₈

yes

characteristic

C₂

—

1136

—

C₂

#17986376

yes

characteristic

100

C₂

#17986431

yes

—

	subgroup	G/H
center	C₂²	C₂×D₅₆₈
commutator	C₂×C₈×C₇₁	C₂³
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	C₄×C₁₆×C₇₁	C₂
socle	C₂²×C₇₁	C₂×D₈
hypercenter	C₄×C₁₆	D₇₁
hypocenter	C₇₁	#2249
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₂²

C₂×D₅₆₈

commutator

C₂×C₈×C₇₁

C₂³

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

C₄×C₁₆×C₇₁

C₂

socle

C₂²×C₇₁

C₂×D₈

hypercenter

C₄×C₁₆

D₇₁

hypocenter

C₇₁

#2249

LCS

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
1. C₂×Dic₅₆₈	C₂	semidirect
2. C₂×#14556073	C₂	semidirect
4. #17986383	C₂	semidirect
5. C₄×C₁₆×C₇₁	C₂	semidirect
51. C₇₁	#2249	semidirect
56. C₄×C₁₆	D₇₁	semidirect

H ≅ G/N

type

1. C₂×Dic₅₆₈

C₂

semidirect

2. C₂×#14556073

C₂

semidirect

4. #17986383

C₂

semidirect

5. C₄×C₁₆×C₇₁

C₂

semidirect

51. C₇₁

#2249

semidirect

56. C₄×C₁₆

D₇₁

semidirect

Subgroups — #22590601

Conjugacy classes of subgroups

Complements