Group #22590153 — subgroups

Subgroups — #22590153

Order 9088.

122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 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	#17985957	C₂	1	1	yes	maximal, characteristic
2	#17985819	C₂	1	2	yes	maximal, complemented
3	#17985781	C₂	1	1	yes	maximal, characteristic
4	#17985776	C₂	1	2	yes	maximal, complemented
5	#349×C₇₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₇₁⋊C₈	C₄	1	1	yes	characteristic
7	#14556087	C₄	1	1	yes	characteristic
8	#14556068	C₂²	1	2	yes	—
9	#14556038	C₄	1	1	yes	characteristic
10	#14556038	C₂²	1	1	yes	characteristic
11	C₈×Dic₇₁	C₄	1	1	yes	characteristic
12	C₈×Dic₇₁	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
14	M₃₂×C₇₁	C₂²	1	2	yes	—
15	C₂×C₇₁⋊C₈	—	2	2	no	—
16	C₂×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
17	C₂×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
18	C₄⋊Dic₇₁	—	2	1	no	—
19	C₂²⋊Dic₇₁	—	2	1	no	—
20	C₄×Dic₇₁	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₇₁	C₂×C₄	1	1	yes	characteristic
22	C₇₁⋊C₁₆	—	2	2	no	—
23	C₂²×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
24	M₁₆×C₇₁	—	2	2	no	—
25	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
26	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
27	C₁₆×C₇₁	—	2	2	no	—
28	C₂³×C₇₁	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₇₁	—	2	1	no	—
30	C₂×C₄×C₇₁	—	2	1	no	—
31	C₂×C₄×C₇₁	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
33	C₂×Dic₇₁	—	2	1	no	—
34	C₂×Dic₇₁	—	2	1	no	—
35	C₈×C₇₁	—	2	1	no	—
36	C₈×C₇₁	#41	1	2	yes	—
37	C₇₁⋊C₈	—	2	1	no	—
38	C₇₁⋊C₈	M₁₆	1	2	yes	—
39	C₂²×C₇₁	—	2	1	no	—
40	C₂²×C₇₁	—	4	1	no	—
41	C₂²×C₇₁	C₂×M₁₆	1	1	yes	characteristic
42	C₄×C₇₁	—	2	1	no	—
43	C₄×C₇₁	#117	1	1	yes	characteristic
44	C₄×C₇₁	C₂×M₁₆	1	1	yes	characteristic
45	Dic₇₁	—	4	1	no	—
46	Dic₇₁	—	4	1	no	—
47	C₂×C₇₁	—	2	1	no	—
48	C₂×C₇₁	—	4	1	no	—
49	C₂×C₇₁	#432	1	1	yes	characteristic
50	#2166	—	71	1	no	maximal, Sylow
51	C₇₁	#2166	1	1	yes	characteristic, complemented, Sylow
52	#405	—	71	1	no	—
53	#364	—	71	2	no	—
54	#349	—	71	1	no	—
55	#349	D₇₁	1	1	yes	characteristic
56	#347	—	71	2	no	—
57	C₂×M₁₆	C₂×D₇₁	1	1	yes	characteristic
58	C₂²×C₈	—	71	1	no	—
59	#117	—	71	1	no	—
60	M₃₂	—	71	2	no	—
61	M₃₂	C₂×D₇₁	1	2	yes	—
62	#97	—	71	1	no	—
63	#97	—	71	1	no	—
64	C₄×C₈	—	71	1	no	—
65	C₄×C₈	—	71	1	no	—
66	C₂²×C₄	C₄×D₇₁	1	1	yes	characteristic
67	M₁₆	—	2	2	no	—
68	C₂×C₈	—	71	1	no	—
69	C₂×C₈	—	71	1	no	—
70	C₂×C₈	—	142	2	no	—
71	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
73	C₄⋊C₄	—	142	1	no	—
74	C₂²⋊C₄	—	142	1	no	—
75	C₄²	—	71	1	no	—
76	C₄²	—	71	1	no	—
77	C₁₆	—	2	2	no	—
78	C₁₆	—	142	2	no	—
79	C₂³	#11765848	1	1	yes	characteristic
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	142	1	no	—
83	C₂×C₄	—	142	1	no	—
84	C₂×C₄	#11765848	1	1	yes	characteristic
85	C₂×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	71	2	no	—
88	C₈	—	142	1	no	—
89	C₈	#11765864	1	2	yes	—
90	C₂²	—	2	1	no	—
91	C₂²	—	4	1	no	—
92	C₂²	C₂×#11765848	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	284	1	no	—
95	C₄	—	284	1	no	—
96	C₄	#14556084	1	1	yes	characteristic
97	C₄	M₁₆×D₇₁	1	1	yes	characteristic
98	C₂	—	2	1	no	—
99	C₂	—	4	1	no	—
100	C₂	#17986053	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17985957

C₂

yes

maximal, characteristic

#17985819

C₂

yes

maximal, complemented

#17985781

C₂

yes

maximal, characteristic

#17985776

C₂

yes

maximal, complemented

#349×C₇₁

C₂

yes

maximal, characteristic

C₂²×C₇₁⋊C₈

C₄

yes

characteristic

#14556087

C₄

yes

characteristic

#14556068

C₂²

yes

—

#14556038

C₄

yes

characteristic

#14556038

C₂²

yes

characteristic

C₈×Dic₇₁

C₄

yes

characteristic

C₈×Dic₇₁

C₂²

yes

characteristic

C₂×M₁₆×C₇₁

C₂²

yes

characteristic

M₃₂×C₇₁

C₂²

yes

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

C₂×C₄

yes

characteristic

C₂×C₇₁⋊C₈

C₂×C₄

yes

characteristic

C₄⋊Dic₇₁

—

C₂²⋊Dic₇₁

—

C₄×Dic₇₁

C₂×C₄

yes

characteristic

C₄×Dic₇₁

C₂×C₄

yes

characteristic

C₇₁⋊C₁₆

—

C₂²×C₄×C₇₁

C₂×C₄

yes

characteristic

M₁₆×C₇₁

—

C₂×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₁₆×C₇₁

—

C₂³×C₇₁

M₁₆

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

M₁₆

yes

characteristic

C₂×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₈×C₇₁

—

C₈×C₇₁

#41

yes

—

C₇₁⋊C₈

—

C₇₁⋊C₈

M₁₆

yes

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

C₂×M₁₆

yes

characteristic

C₄×C₇₁

—

C₄×C₇₁

#117

yes

characteristic

C₄×C₇₁

C₂×M₁₆

yes

characteristic

Dic₇₁

—

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

—

C₂×C₇₁

yes

—

C₇₁

yes

characteristic, complemented, Sylow

—

—

—

D₇₁

yes

characteristic

#347

—

C₂×M₁₆

C₂×D₇₁

yes

characteristic

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

C₂×D₇₁

yes

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

C₄×D₇₁

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

142

—

C₂×C₈

C₄×D₇₁

yes

characteristic

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₄⋊C₄

—

142

—

C₂²⋊C₄

—

142

—

C₄²

—

C₄²

—

C₁₆

—

C₁₆

—

142

—

C₂³

#11765848

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

142

—

C₂×C₄

—

142

—

C₂×C₄

#11765848

yes

characteristic

C₂×C₄

C₂×C₄×D₇₁

yes

characteristic

C₈

—

C₈

—

C₈

—

142

—

C₈

#11765864

yes

—

C₂²

—

C₂²

—

C₂²

C₂×#11765848

yes

characteristic

C₄

—

C₄

—

284

—

C₄

—

284

—

C₄

#14556084

yes

characteristic

C₄

M₁₆×D₇₁

yes

characteristic

C₂

—

C₂

—

100

C₂

#17986053

yes

characteristic

	subgroup	G/H
center	C₄	#14556084
commutator	C₂×C₄×C₇₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	#349×C₇₁	C₂
socle	C₂×C₇₁	#432
hypercenter	#349	D₇₁
hypocenter	C₇₁	#2166
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #349

subgroup

G/H

center

C₄

#14556084

commutator

C₂×C₄×C₇₁

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

#349×C₇₁

C₂

C₂×C₇₁

D₇₁

C₇₁

G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ #349

N	H ≅ G/N	type
2. #17985819	C₂	semidirect
4. #17985776	C₂	semidirect
51. C₇₁	#2166	semidirect

H ≅ G/N

type

2. #17985819

C₂

semidirect

4. #17985776

C₂

semidirect

51. C₇₁

#2166

semidirect

Subgroups — #22590153

Conjugacy classes of subgroups

Complements