Group #22589916 — subgroups

Subgroups — #22589916

Order 9088.

158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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	#17986048	C₂	1	1	yes	maximal, characteristic
2	#17986022	C₂	1	1	yes	maximal, characteristic
3	#17985769	C₂	1	2	yes	maximal
4	#17985758	C₂	1	2	yes	maximal
5	H(3,ℤ/4)×C₇₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11765849	C₂²	1	2	yes	—
7	C₂×#11765849	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₇₁	C₂²	1	1	yes	characteristic
9	#14556064	—	2	2	no	—
10	Dic₇₁⋊C₈	—	2	2	no	—
11	C₂×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
12	#117×C₇₁	C₂²	1	2	yes	—
13	C₂²×Dic₇₁	—	2	1	no	—
14	#11765849	—	2	2	no	—
15	#11765849	—	2	2	no	—
16	#11765849	—	2	2	no	—
17	C₂×C₇₁⋊C₈	—	2	1	no	—
18	C₂×C₇₁⋊C₈	—	2	2	no	—
19	C₄×Dic₇₁	—	2	1	no	—
20	C₄×Dic₇₁	Q₈	1	1	yes	characteristic
21	C₄×Dic₇₁	Q₈	1	1	yes	characteristic
22	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
23	M₁₆×C₇₁	—	2	2	no	—
24	C₂×C₈×C₇₁	D₄	1	2	yes	—
25	C₄⋊C₄×C₇₁	—	2	2	no	—
26	C₂²⋊C₄×C₇₁	—	2	2	no	—
27	C₄²×C₇₁	—	2	2	no	—
28	C₂³×C₇₁	#41	1	1	yes	characteristic
29	C₂×C₄×C₇₁	—	4	2	no	—
30	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₄×C₇₁	#41	1	2	yes	—
33	C₂×C₄×C₇₁	#41	1	2	yes	—
34	C₂×Dic₇₁	—	2	1	no	—
35	C₂×Dic₇₁	—	2	1	no	—
36	C₂×Dic₇₁	—	4	2	no	—
37	C₈×C₇₁	—	2	2	no	—
38	C₇₁⋊C₈	—	4	1	no	—
39	C₇₁⋊C₈	—	4	2	no	—
40	C₂²×C₇₁	—	4	1	no	—
41	C₂²×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
42	C₂²×C₇₁	#126	1	2	yes	—
43	C₄×C₇₁	—	8	2	no	—
44	C₄×C₇₁	#123	1	1	yes	characteristic
45	C₄×C₇₁	#124	1	1	yes	characteristic
46	C₄×C₇₁	#125	1	2	yes	—
47	Dic₇₁	—	2	2	no	—
48	Dic₇₁	—	4	1	no	—
49	C₂×C₇₁	—	2	1	no	—
50	C₂×C₇₁	—	2	2	no	—
51	C₂×C₇₁	#400	1	1	yes	characteristic
52	#2102	—	71	1	no	maximal, Sylow
53	C₇₁	#2102	1	1	yes	characteristic, complemented, Sylow
54	#430	—	71	1	no	—
55	#423	—	71	1	no	—
56	#344	—	71	2	no	—
57	#339	—	71	2	no	—
58	H(3,ℤ/4)	D₇₁	1	1	yes	characteristic
59	C₂×M₁₆	—	71	2	no	—
60	C₂×M₁₆	—	71	1	no	—
61	C₂×M₁₆	C₂×D₇₁	1	1	yes	characteristic
62	#117	C₂×D₇₁	1	2	yes	—
63	C₂×C₄²	—	71	1	no	—
64	#108	—	142	2	no	—
65	C₄⋊C₈	—	142	2	no	—
66	C₂²×C₄	—	142	1	no	—
67	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	142	2	no	—
70	M₁₆	—	142	2	no	—
71	M₁₆	—	142	2	no	—
72	C₂×C₈	—	142	1	no	—
73	C₂×C₈	—	142	2	no	—
74	C₂×C₈	D₂₈₄	1	2	yes	—
75	C₄⋊C₄	—	2	2	no	—
76	C₂²⋊C₄	—	2	2	no	—
77	C₄²	—	2	2	no	—
78	C₄²	—	71	1	no	—
79	C₄²	—	71	1	no	—
80	C₄²	—	142	1	no	—
81	C₂³	#11765864	1	1	yes	characteristic
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	284	2	no	—
84	C₂×C₄	—	142	1	no	—
85	C₂×C₄	—	142	1	no	—
86	C₂×C₄	C₂×D₂₈₄	1	1	yes	characteristic
87	C₂×C₄	Q₈×D₇₁	1	1	yes	characteristic
88	C₂×C₄	#11765864	1	2	yes	—
89	C₂×C₄	#11765865	1	2	yes	—
90	C₈	—	2	2	no	—
91	C₈	—	284	1	no	—
92	C₈	—	284	2	no	—
93	C₂²	—	4	1	no	—
94	C₂²	#14556108	1	1	yes	characteristic
95	C₂²	#14556121	1	2	yes	—
96	C₄	—	8	2	no	—
97	C₄	—	284	1	no	—
98	C₄	—	142	2	no	—
99	C₄	#14556112	1	1	yes	characteristic
100	C₄	#14556116	1	1	yes	characteristic
101	C₄	#14556118	1	2	yes	—
102	C₂	—	2	2	no	—
103	C₂	—	2	1	no	—
104	C₂	#17985939	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17986048

C₂

yes

maximal, characteristic

#17986022

C₂

yes

maximal, characteristic

#17985769

C₂

yes

maximal

#17985758

C₂

yes

maximal

H(3,ℤ/4)×C₇₁

C₂

yes

maximal, characteristic

C₂×#11765849

C₂²

yes

—

C₂×#11765849

C₂²

yes

characteristic

C₂×C₄×Dic₇₁

C₂²

yes

characteristic

#14556064

—

Dic₇₁⋊C₈

—

C₂×M₁₆×C₇₁

C₂²

yes

characteristic

#117×C₇₁

C₂²

yes

—

C₂²×Dic₇₁

—

#11765849

—

#11765849

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄×Dic₇₁

—

C₄×Dic₇₁

Q₈

yes

characteristic

C₄×Dic₇₁

Q₈

yes

characteristic

C₂²×C₄×C₇₁

C₂³

yes

characteristic

M₁₆×C₇₁

—

C₂×C₈×C₇₁

D₄

yes

—

C₄⋊C₄×C₇₁

—

C₂²⋊C₄×C₇₁

—

C₄²×C₇₁

—

C₂³×C₇₁

#41

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×C₄×C₇₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₁

#41

yes

—

C₂×C₄×C₇₁

#41

yes

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₈×C₇₁

—

C₇₁⋊C₈

—

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

C₂²⋊Q₈

yes

characteristic

C₂²×C₇₁

#126

yes

—

C₄×C₇₁

—

C₄×C₇₁

yes

C₄×C₇₁

yes

C₄×C₇₁

yes

—

Dic₇₁

—

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

—

C₂×C₇₁

yes

—

C₇₁

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₁

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₁

yes

characteristic

#117

C₂×D₇₁

yes

—

C₂×C₄²

—

#108

—

142

—

C₄⋊C₈

—

142

—

C₂²×C₄

—

142

—

C₂²×C₄

C₂²×D₇₁

yes

characteristic

M₁₆

—

M₁₆

—

142

—

M₁₆

—

142

—

M₁₆

—

142

—

C₂×C₈

—

142

—

C₂×C₈

—

142

—

C₂×C₈

D₂₈₄

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

142

—

C₂³

#11765864

yes

characteristic

C₂×C₄

—

C₂×C₄

—

284

—

C₂×C₄

—

142

—

C₂×C₄

—

142

—

C₂×C₄

C₂×D₂₈₄

yes

characteristic

C₂×C₄

Q₈×D₇₁

yes

characteristic

C₂×C₄

#11765864

yes

—

C₂×C₄

#11765865

yes

—

C₈

—

C₈

—

284

—

C₈

—

284

—

C₂²

—

C₂²

#14556108

yes

characteristic

C₂²

#14556121

yes

—

C₄

—

C₄

—

284

—

C₄

—

142

—

C₄

#14556112

yes

characteristic

100

C₄

#14556116

yes

characteristic

101

C₄

#14556118

yes

—

102

C₂

—

103

C₂

—

104

C₂

#17985939

yes

characteristic

	subgroup	G/H
center	C₄	#14556116
commutator	C₂²×C₄×C₇₁	C₂³
Frattini	C₂²×C₄	C₂²×D₇₁
Fitting	H(3,ℤ/4)×C₇₁	C₂
socle	C₂×C₇₁	#400
hypercenter	H(3,ℤ/4)	D₇₁
hypocenter	C₇₁	#2102
LCS	G ▷ C₂²×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

#14556116

commutator

C₂²×C₄×C₇₁

C₂³

Frattini

C₂²×C₄

C₂²×D₇₁

Fitting

H(3,ℤ/4)×C₇₁

C₂

C₂×C₇₁

D₇₁

C₇₁

G ▷ C₂²×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
53. C₇₁	#2102	semidirect

H ≅ G/N

type

53. C₇₁

#2102

semidirect

Subgroups — #22589916

Conjugacy classes of subgroups

Complements