Group #22590176 — subgroups

Subgroups — #22590176

Order 9088.

146 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 63 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	#17986417	C₂	1	2	yes	maximal, complemented
2	#17986117	C₂	1	1	yes	maximal, characteristic
3	#17985784	C₂	1	2	yes	maximal, complemented
4	C₄×C₇₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#364×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#14556150	C₄	1	1	yes	characteristic
7	#14556134	C₂²	1	2	yes	—
8	#14556067	—	2	2	no	—
9	C₂×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
11	C₁₆×D₇₁	—	2	2	no	—
12	#14556064	C₄	1	1	yes	characteristic
13	#14556056	C₄	1	2	yes	—
14	M₃₂×C₇₁	C₂²	1	2	yes	—
15	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
16	#11765865	C₂×C₄	1	2	yes	—
17	Dic₂₈₄	C₈	1	1	yes	characteristic
18	#11765854	C₈	1	2	yes	—
19	D₅₆₈	C₈	1	1	yes	characteristic
20	#11765849	C₂×C₄	1	2	yes	—
21	#11765848	—	2	2	no	—
22	C₈×D₇₁	—	2	2	no	—
23	C₇₁⋊C₁₆	—	2	1	no	—
24	C₇₁⋊C₁₆	D₄	1	1	yes	characteristic
25	C₇₁⋊C₁₆	D₄	1	1	yes	characteristic
26	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
28	C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
29	C₁₆×C₇₁	—	2	2	no	—
30	C₂×C₄×C₇₁	—	2	1	no	—
31	C₂×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
32	C₂²⋊D₇₁	—	2	2	no	—
33	D₂₈₄	C₂×C₈	1	2	yes	—
34	C₄×D₇₁	—	2	2	no	—
35	Dic₁₄₂	C₂×C₈	1	2	yes	—
36	C₈×C₇₁	C₂×C₈	1	1	yes	characteristic
37	C₈×C₇₁	C₂×C₈	1	1	yes	characteristic
38	C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
39	C₈×C₇₁	#41	1	1	yes	characteristic
40	C₇₁⋊C₈	—	2	2	no	—
41	C₂²×C₇₁	#131	1	1	yes	characteristic
42	C₂×D₇₁	—	2	2	no	—
43	C₄×C₇₁	—	2	2	no	—
44	C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
45	C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
46	Dic₇₁	—	2	2	no	—
47	C₂×C₇₁	—	2	1	no	—
48	C₂×C₇₁	C₈×D₄	1	1	yes	characteristic
49	D₇₁	—	4	2	no	—
50	#2170	—	71	1	no	maximal, Sylow
51	C₇₁	#2170	1	1	yes	characteristic, complemented, Sylow
52	#504	—	71	2	no	—
53	#443	—	71	1	no	—
54	#364	D₇₁	1	1	yes	characteristic, complemented
55	#350	—	71	2	no	—
56	C₄×C₁₆	—	71	1	no	—
57	#135	—	71	1	no	—
58	#131	—	71	2	no	—
59	M₃₂	—	142	2	no	—
60	M₃₂	C₂×D₇₁	1	2	yes	—
61	C₂×C₁₆	—	71	1	no	—
62	C₂×C₁₆	—	71	1	no	—
63	C₂×C₁₆	—	142	2	no	—
64	#108	—	71	1	no	—
65	#104	—	71	2	no	—
66	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
67	#41	—	71	2	no	—
68	Q₁₆	—	71	1	no	—
69	SD₁₆	—	71	2	no	—
70	D₈	—	71	1	no	—
71	M₁₆	—	71	2	no	—
72	M₁₆	—	142	2	no	—
73	C₂×C₈	—	142	2	no	—
74	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
76	C₄²	C₄×D₇₁	1	1	yes	characteristic
77	C₁₆	—	2	2	no	—
78	C₁₆	—	71	1	no	—
79	C₁₆	—	71	1	no	—
80	C₁₆	—	142	1	no	—
81	Q₈	—	71	2	no	—
82	D₄	—	71	2	no	—
83	D₄	—	142	2	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	142	2	no	—
86	C₂×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
87	C₈	—	142	2	no	—
88	C₈	C₈×D₇₁	1	1	yes	characteristic
89	C₈	C₈×D₇₁	1	1	yes	characteristic
90	C₈	D₄×D₇₁	1	1	yes	characteristic
91	C₈	#11765866	1	1	yes	characteristic
92	C₂²	—	142	2	no	—
93	C₂²	#14556136	1	1	yes	characteristic
94	C₄	—	2	2	no	—
95	C₄	—	142	2	no	—
96	C₄	#14556090	1	1	yes	characteristic
97	C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
98	C₂	—	2	1	no	—
99	C₂	—	284	2	no	—
100	C₂	#17986064	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17986417

C₂

yes

maximal, complemented

#17986117

C₂

yes

maximal, characteristic

#17985784

C₂

yes

maximal, complemented

C₄×C₇₁⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#364×C₇₁

C₂

yes

maximal, characteristic, complemented

#14556150

C₄

yes

characteristic

#14556134

C₂²

yes

—

#14556067

—

C₂×C₇₁⋊C₁₆

C₂²

yes

characteristic

C₂×C₇₁⋊C₁₆

C₂²

yes

characteristic

C₁₆×D₇₁

—

#14556064

C₄

yes

characteristic

#14556056

C₄

yes

—

M₃₂×C₇₁

C₂²

yes

—

C₄×C₈×C₇₁

C₂²

yes

characteristic

#11765865

C₂×C₄

yes

—

Dic₂₈₄

C₈

yes

characteristic

#11765854

C₈

yes

—

D₅₆₈

C₈

yes

characteristic

#11765849

C₂×C₄

yes

—

#11765848

—

C₈×D₇₁

—

C₇₁⋊C₁₆

—

C₇₁⋊C₁₆

D₄

yes

characteristic

C₇₁⋊C₁₆

D₄

yes

characteristic

C₂×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₄²×C₇₁

C₂×C₄

yes

characteristic

C₁₆×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂²⋊D₇₁

—

D₂₈₄

C₂×C₈

yes

—

C₄×D₇₁

—

Dic₁₄₂

C₂×C₈

yes

—

C₈×C₇₁

C₂×C₈

yes

characteristic

C₈×C₇₁

C₂×C₈

yes

characteristic

C₈×C₇₁

C₂×D₄

yes

characteristic

C₈×C₇₁

#41

yes

characteristic

C₇₁⋊C₈

—

C₂²×C₇₁

#131

yes

characteristic

C₂×D₇₁

—

C₄×C₇₁

—

C₄×C₇₁

C₄×D₄

yes

characteristic

C₄×C₇₁

C₂²×C₈

yes

characteristic

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

C₈×D₄

yes

characteristic

D₇₁

—

#2170

—

maximal, Sylow

C₇₁

#2170

yes

characteristic, complemented, Sylow

#504

—

#443

—

#364

D₇₁

yes

characteristic, complemented

#350

—

C₄×C₁₆

—

#135

—

#131

—

M₃₂

—

142

—

M₃₂

C₂×D₇₁

yes

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

142

—

#108

—

#104

—

C₄×C₈

C₂×D₇₁

yes

characteristic

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

142

—

C₂×C₈

—

142

—

C₂×C₈

C₄×D₇₁

yes

characteristic

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₄²

C₄×D₇₁

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

—

142

—

Q₈

—

D₄

—

D₄

—

142

—

C₂×C₄

—

C₂×C₄

—

142

—

C₂×C₄

C₂×C₄×D₇₁

yes

characteristic

C₈

—

142

—

C₈

C₈×D₇₁

yes

characteristic

C₈

C₈×D₇₁

yes

characteristic

C₈

D₄×D₇₁

yes

characteristic

C₈

#11765866

yes

characteristic

C₂²

—

142

—

C₂²

#14556136

yes

characteristic

C₄

—

C₄

—

142

—

C₄

#14556090

yes

characteristic

C₄

C₂×C₈×D₇₁

yes

characteristic

C₂

—

C₂

—

284

—

100

C₂

#17986064

yes

characteristic

	subgroup	G/H
center	C₈	D₄×D₇₁
commutator	C₄×C₇₁	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	#364×C₇₁	C₂
socle	C₂×C₇₁	C₈×D₄
hypercenter	#364	D₇₁
hypocenter	C₇₁	#2170
LCS	G ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

subgroup

G/H

center

C₈

D₄×D₇₁

commutator

C₄×C₇₁

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

#364×C₇₁

C₂

socle

C₂×C₇₁

C₈×D₄

D₇₁

C₇₁

G ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

N	H ≅ G/N	type
1. #17986417	C₂	semidirect
3. #17985784	C₂	semidirect
4. C₄×C₇₁⋊C₁₆	C₂	semidirect
5. #364×C₇₁	C₂	semidirect
51. C₇₁	#2170	semidirect
54. #364	D₇₁	semidirect

H ≅ G/N

type

1. #17986417

C₂

semidirect

3. #17985784

C₂

semidirect

4. C₄×C₇₁⋊C₁₆

C₂

semidirect

5. #364×C₇₁

C₂

semidirect

51. C₇₁

#2170

semidirect

54. #364

D₇₁

semidirect

Subgroups — #22590176

Conjugacy classes of subgroups

Complements