Group #22590150 — subgroups

Subgroups — #22590150

Order 9088.

128 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 53 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	#17985951	C₂	1	1	yes	maximal, characteristic
2	#17985819	C₂	1	2	yes	maximal, complemented
3	#17985780	C₂	1	2	yes	maximal
4	#17985777	C₂	1	1	yes	maximal, characteristic, complemented
5	#347×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11765848	C₄	1	1	yes	characteristic
7	C₂×#11765848	C₂²	1	1	yes	characteristic
8	C₄²×D₇₁	C₄	1	1	yes	characteristic
9	#14556068	C₂²	1	2	yes	—
10	#14556039	C₄	1	1	yes	characteristic
11	C₈×Dic₇₁	C₄	1	1	yes	characteristic
12	C₈×Dic₇₁	C₂²	1	1	yes	characteristic
13	M₃₂×C₇₁	C₂²	1	2	yes	—
14	#97×C₇₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₇₁	—	2	1	no	—
16	C₂×C₄×D₇₁	C₂×C₄	1	1	yes	characteristic
17	#11765848	—	2	2	no	—
18	#11765848	—	2	2	no	—
19	C₂×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
20	C₂×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₇₁	—	2	1	no	—
22	C₄×Dic₇₁	C₂×C₄	1	1	yes	characteristic
23	C₇₁⋊C₁₆	—	2	2	no	—
24	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
26	C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
27	C₁₆×C₇₁	—	2	2	no	—
28	C₂²×D₇₁	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₇₁	—	2	1	no	—
30	C₂×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₇₁	—	2	1	no	—
32	C₂×Dic₇₁	M₁₆	1	1	yes	characteristic
33	C₄×D₇₁	—	2	1	no	—
34	C₄×D₇₁	—	2	1	no	—
35	C₄×D₇₁	—	4	2	no	—
36	C₈×C₇₁	—	2	1	no	—
37	C₈×C₇₁	#41	1	2	yes	—
38	C₇₁⋊C₈	—	2	1	no	—
39	C₇₁⋊C₈	M₁₆	1	2	yes	—
40	C₂²×C₇₁	C₂×M₁₆	1	1	yes	characteristic
41	C₂×D₇₁	—	2	1	no	—
42	C₂×D₇₁	—	4	1	no	—
43	C₄×C₇₁	—	4	1	no	—
44	C₄×C₇₁	#117	1	1	yes	characteristic
45	C₄×C₇₁	C₂×M₁₆	1	1	yes	characteristic
46	Dic₇₁	—	2	2	no	—
47	Dic₇₁	—	2	1	no	—
48	C₂×C₇₁	—	2	1	no	—
49	C₂×C₇₁	#432	1	1	yes	characteristic
50	D₇₁	—	4	1	no	—
51	#2165	—	71	1	no	maximal, Sylow
52	C₇₁	#2165	1	1	yes	characteristic, complemented, Sylow
53	C₄×M₁₆	—	71	1	no	—
54	#364	—	71	2	no	—
55	#349	—	71	2	no	—
56	#347	—	71	1	no	—
57	#347	D₇₁	1	1	yes	characteristic, complemented
58	C₂×M₁₆	—	71	1	no	—
59	C₂×M₁₆	—	71	1	no	—
60	C₂×C₄²	—	71	1	no	—
61	M₃₂	—	71	2	no	—
62	M₃₂	C₂×D₇₁	1	2	yes	—
63	#97	—	71	1	no	—
64	#97	C₂×D₇₁	1	1	yes	characteristic
65	C₄×C₈	—	71	1	no	—
66	C₄×C₈	—	71	1	no	—
67	C₂²×C₄	—	71	1	no	—
68	C₂²×C₄	—	142	1	no	—
69	M₁₆	—	142	2	no	—
70	M₁₆	—	142	2	no	—
71	C₂×C₈	—	71	1	no	—
72	C₂×C₈	—	71	1	no	—
73	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
75	C₄²	—	71	1	no	—
76	C₄²	—	142	1	no	—
77	C₄²	C₄×D₇₁	1	1	yes	characteristic
78	C₁₆	—	2	2	no	—
79	C₁₆	—	142	2	no	—
80	C₂³	—	71	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	284	2	no	—
83	C₂×C₄	—	71	1	no	—
84	C₂×C₄	—	142	1	no	—
85	C₂×C₄	—	142	1	no	—
86	C₂×C₄	—	142	1	no	—
87	C₂×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
88	C₈	—	2	1	no	—
89	C₈	—	71	2	no	—
90	C₈	—	142	1	no	—
91	C₈	#11765865	1	2	yes	—
92	C₂²	—	284	1	no	—
93	C₂²	—	142	1	no	—
94	C₂²	M₁₆×D₇₁	1	1	yes	characteristic
95	C₄	—	4	1	no	—
96	C₄	—	142	2	no	—
97	C₄	—	142	1	no	—
98	C₄	#14556085	1	1	yes	characteristic
99	C₄	M₁₆×D₇₁	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	284	1	no	—
102	C₂	#17986054	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17985951

C₂

yes

maximal, characteristic

#17985819

C₂

yes

maximal, complemented

#17985780

C₂

yes

maximal

#17985777

C₂

yes

maximal, characteristic, complemented

#347×C₇₁

C₂

yes

maximal, characteristic, complemented

C₂×#11765848

C₄

yes

characteristic

C₂×#11765848

C₂²

yes

characteristic

C₄²×D₇₁

C₄

yes

characteristic

#14556068

C₂²

yes

—

#14556039

C₄

yes

characteristic

C₈×Dic₇₁

C₄

yes

characteristic

C₈×Dic₇₁

C₂²

yes

characteristic

M₃₂×C₇₁

C₂²

yes

—

#97×C₇₁

C₂²

yes

characteristic

C₂×C₄×D₇₁

—

C₂×C₄×D₇₁

C₂×C₄

yes

characteristic

#11765848

—

#11765848

—

C₂×C₇₁⋊C₈

C₂×C₄

yes

characteristic

C₂×C₇₁⋊C₈

C₂×C₄

yes

characteristic

C₄×Dic₇₁

—

C₄×Dic₇₁

C₂×C₄

yes

characteristic

C₇₁⋊C₁₆

—

C₂×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₄²×C₇₁

C₂×C₄

yes

characteristic

C₁₆×C₇₁

—

C₂²×D₇₁

M₁₆

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

M₁₆

yes

characteristic

C₄×D₇₁

—

C₄×D₇₁

—

C₄×D₇₁

—

C₈×C₇₁

—

C₈×C₇₁

#41

yes

—

C₇₁⋊C₈

—

C₇₁⋊C₈

M₁₆

yes

—

C₂²×C₇₁

C₂×M₁₆

yes

characteristic

C₂×D₇₁

—

C₂×D₇₁

—

C₄×C₇₁

—

C₄×C₇₁

#117

yes

characteristic

C₄×C₇₁

C₂×M₁₆

yes

characteristic

Dic₇₁

—

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

#432

yes

characteristic

D₇₁

—

#2165

—

maximal, Sylow

C₇₁

#2165

yes

characteristic, complemented, Sylow

C₄×M₁₆

—

—

—

—

D₇₁

yes

characteristic, complemented

C₂×M₁₆

—

C₂×M₁₆

—

C₂×C₄²

—

M₃₂

—

M₃₂

C₂×D₇₁

yes

—

#97

—

#97

C₂×D₇₁

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

142

—

M₁₆

—

142

—

M₁₆

—

142

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₇₁

yes

characteristic

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₄²

—

C₄²

—

142

—

C₄²

C₄×D₇₁

yes

characteristic

C₁₆

—

C₁₆

—

142

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

284

—

C₂×C₄

—

C₂×C₄

—

142

—

C₂×C₄

—

142

—

C₂×C₄

—

142

—

C₂×C₄

C₂×C₄×D₇₁

yes

characteristic

C₈

—

C₈

—

C₈

—

142

—

C₈

#11765865

yes

—

C₂²

—

284

—

C₂²

—

142

—

C₂²

M₁₆×D₇₁

yes

characteristic

C₄

—

C₄

—

142

—

C₄

—

142

—

C₄

#14556085

yes

characteristic

C₄

M₁₆×D₇₁

yes

characteristic

100

C₂

—

101

C₂

—

284

—

102

C₂

#17986054

yes

characteristic

	subgroup	G/H
center	C₄	#14556085
commutator	C₂×C₄×C₇₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	#347×C₇₁	C₂
socle	C₂×C₇₁	#432
hypercenter	#347	D₇₁
hypocenter	C₇₁	#2165
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ #97 ◁ #347

subgroup

G/H

center

C₄

#14556085

commutator

C₂×C₄×C₇₁

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

#347×C₇₁

C₂

C₂×C₇₁

D₇₁

C₇₁

G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₄ ◁ #97 ◁ #347

N	H ≅ G/N	type
2. #17985819	C₂	semidirect
4. #17985777	C₂	semidirect
5. #347×C₇₁	C₂	semidirect
52. C₇₁	#2165	semidirect
57. #347	D₇₁	semidirect

H ≅ G/N

type

2. #17985819

C₂

semidirect

4. #17985777

C₂

semidirect

5. #347×C₇₁

C₂

semidirect

52. C₇₁

#2165

semidirect

57. #347

D₇₁

semidirect

Subgroups — #22590150

Conjugacy classes of subgroups

Complements