Group #22590560 — subgroups

Subgroups — #22590560

Order 9088.

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

normal subgroups only

This group has 124 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	#17986257	C₂	1	1	yes	maximal, characteristic
2	#17986048	C₂	1	1	yes	maximal, characteristic
3	#17985822	C₂	1	2	yes	maximal, complemented
4	#17985816	C₂	1	2	yes	maximal, complemented
5	#349×C₇₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₈₄	C₂²	1	1	yes	characteristic
7	C₂×#11765849	—	2	1	no	—
8	#14556107	—	2	1	no	—
9	#14556064	—	2	1	no	—
10	#14556064	C₂²	1	2	yes	—
11	#14556060	C₂²	1	1	yes	characteristic
12	#14556053	—	2	1	no	—
13	C₂×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
14	M₃₂×C₇₁	C₂²	1	2	yes	—
15	C₂×Dic₁₄₂	—	2	1	no	—
16	Dic₂₈₄	—	2	2	no	—
17	#11765849	—	2	2	no	—
18	#11765849	—	4	1	no	—
19	C₂×C₇₁⋊C₈	—	4	1	no	—
20	C₄⋊Dic₇₁	—	2	1	no	—
21	Dic₇₁⋊C₄	—	4	1	no	—
22	C₂²⋊Dic₇₁	—	4	1	no	—
23	C₂²×C₄×C₇₁	D₄	1	1	yes	characteristic
24	M₁₆×C₇₁	—	2	2	no	—
25	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
26	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
27	C₁₆×C₇₁	—	2	2	no	—
28	C₂³×C₇₁	SD₁₆	1	1	yes	characteristic
29	C₂×C₄×C₇₁	—	2	1	no	—
30	C₂×C₄×C₇₁	—	2	1	no	—
31	C₂×C₄×C₇₁	SD₁₆	1	1	yes	characteristic
32	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₇₁	—	4	1	no	—
34	C₂×Dic₇₁	—	4	1	no	—
35	Dic₁₄₂	—	4	1	no	—
36	Dic₁₄₂	—	4	1	no	—
37	C₈×C₇₁	—	2	1	no	—
38	C₈×C₇₁	#41	1	2	yes	—
39	C₇₁⋊C₈	—	4	2	no	—
40	C₂²×C₇₁	—	2	1	no	—
41	C₂²×C₇₁	—	4	1	no	—
42	C₂²×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
43	C₄×C₇₁	—	2	1	no	—
44	C₄×C₇₁	#123	1	1	yes	characteristic
45	C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
46	Dic₇₁	—	8	1	no	—
47	Dic₇₁	—	8	1	no	—
48	C₂×C₇₁	—	2	1	no	—
49	C₂×C₇₁	—	4	1	no	—
50	C₂×C₇₁	#481	1	1	yes	characteristic
51	#2239	—	71	1	no	maximal, Sylow
52	C₇₁	#2239	1	1	yes	characteristic, complemented, Sylow
53	#470	—	71	1	no	—
54	#430	—	71	1	no	—
55	#365	—	71	2	no	—
56	#362	—	71	2	no	—
57	#349	D₇₁	1	1	yes	characteristic
58	C₂×Q₁₆	—	71	1	no	—
59	C₂×M₁₆	—	142	1	no	—
60	C₂×M₁₆	C₂×D₇₁	1	1	yes	characteristic
61	C₂²⋊Q₈	—	142	1	no	—
62	M₃₂	C₂×D₇₁	1	2	yes	—
63	#108	—	71	2	no	—
64	#108	—	142	1	no	—
65	#106	—	71	1	no	—
66	#103	—	142	1	no	—
67	C₂×Q₈	—	142	1	no	—
68	C₂²×C₄	D₂₈₄	1	1	yes	characteristic
69	Q₁₆	—	142	2	no	—
70	M₁₆	—	2	2	no	—
71	M₁₆	—	284	1	no	—
72	M₁₆	—	142	2	no	—
73	C₂×C₈	—	284	1	no	—
74	C₂×C₈	D₂₈₄	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
76	C₄⋊C₄	—	284	1	no	—
77	C₄⋊C₄	—	142	1	no	—
78	C₂²⋊C₄	—	284	1	no	—
79	C₁₆	—	2	2	no	—
80	C₂³	#11765854	1	1	yes	characteristic
81	Q₈	—	284	1	no	—
82	Q₈	—	284	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	284	1	no	—
86	C₂×C₄	—	284	1	no	—
87	C₂×C₄	#11765854	1	1	yes	characteristic
88	C₂×C₄	C₂×D₂₈₄	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	—	284	2	no	—
91	C₈	#11765864	1	2	yes	—
92	C₂²	—	2	1	no	—
93	C₂²	—	4	1	no	—
94	C₂²	C₂×#11765854	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	568	1	no	—
97	C₄	—	568	1	no	—
98	C₄	#14556112	1	1	yes	characteristic
99	C₄	#14556156	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	4	1	no	—
102	C₂	#17986318	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17986257

C₂

yes

maximal, characteristic

#17986048

C₂

yes

maximal, characteristic

#17985822

C₂

yes

maximal, complemented

#17985816

C₂

yes

maximal, complemented

#349×C₇₁

C₂

yes

maximal, characteristic

C₂×Dic₂₈₄

C₂²

yes

—

—

—

C₂²

yes

—

#14556060

C₂²

yes

characteristic

#14556053

—

C₂×M₁₆×C₇₁

C₂²

yes

characteristic

M₃₂×C₇₁

C₂²

yes

—

C₂×Dic₁₄₂

—

Dic₂₈₄

—

#11765849

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

Dic₇₁⋊C₄

—

C₂²⋊Dic₇₁

—

C₂²×C₄×C₇₁

D₄

yes

characteristic

M₁₆×C₇₁

—

C₂×C₈×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₁₆×C₇₁

—

C₂³×C₇₁

SD₁₆

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

SD₁₆

yes

characteristic

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

—

Dic₁₄₂

—

Dic₁₄₂

—

C₈×C₇₁

—

C₈×C₇₁

#41

yes

—

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

C₂×SD₁₆

yes

characteristic

C₄×C₇₁

—

C₄×C₇₁

yes

C₄×C₇₁

yes

Dic₇₁

—

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

—

C₂×C₇₁

yes

—

C₇₁

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₁

yes

characteristic

C₂×Q₁₆

—

C₂×M₁₆

—

142

—

C₂×M₁₆

C₂×D₇₁

yes

characteristic

C₂²⋊Q₈

—

142

—

M₃₂

C₂×D₇₁

yes

—

#108

—

#108

—

142

—

#106

—

#103

—

142

—

C₂×Q₈

—

142

—

C₂²×C₄

D₂₈₄

yes

characteristic

Q₁₆

—

142

—

M₁₆

—

M₁₆

—

284

—

M₁₆

—

142

—

C₂×C₈

—

284

—

C₂×C₈

D₂₈₄

yes

characteristic

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₄⋊C₄

—

284

—

C₄⋊C₄

—

142

—

C₂²⋊C₄

—

284

—

C₁₆

—

C₂³

#11765854

yes

characteristic

Q₈

—

284

—

Q₈

—

284

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

284

—

C₂×C₄

—

284

—

C₂×C₄

#11765854

yes

characteristic

C₂×C₄

C₂×D₂₈₄

yes

characteristic

C₈

—

C₈

—

284

—

C₈

#11765864

yes

—

C₂²

—

C₂²

—

C₂²

C₂×#11765854

yes

characteristic

C₄

—

C₄

—

568

—

C₄

—

568

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

—

102

C₂

#17986318

yes

characteristic

	subgroup	G/H
center	C₂	#17986318
commutator	C₂×C₈×C₇₁	C₂³
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	#349×C₇₁	C₂
socle	C₂×C₇₁	#481
hypercenter	#349	D₇₁
hypocenter	C₇₁	#2239
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

subgroup

G/H

center

C₂

#17986318

commutator

C₂×C₈×C₇₁

C₂³

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

#349×C₇₁

C₂

C₂×C₇₁

D₇₁

C₇₁

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

N	H ≅ G/N	type
3. #17985822	C₂	semidirect
4. #17985816	C₂	semidirect
52. C₇₁	#2239	semidirect

H ≅ G/N

type

3. #17985822

C₂

semidirect

4. #17985816

C₂

semidirect

52. C₇₁

#2239

semidirect

Subgroups — #22590560

Conjugacy classes of subgroups

Complements