Group #22590108 — subgroups

Subgroups — C₂×#17985821 #22590108

Order 9088.

152 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₂×#14556068	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556064	C₂	1	1	yes	maximal, characteristic
3	#17985821	C₂	1	4	yes	maximal, direct product factor
4	C₂×#106×C₇₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#11765849	—	2	1	no	—
6	#14556068	C₄	1	2	yes	complemented
7	#14556068	C₂²	1	2	yes	—
8	C₂×C₇₁⋊C₁₆	C₄	1	2	yes	complemented
9	#14556064	—	2	1	no	—
10	#14556064	C₂²	1	2	yes	—
11	C₂²×C₈×C₇₁	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
13	#106×C₇₁	—	2	1	no	—
14	#106×C₇₁	C₂²	1	2	yes	—
15	#11765849	—	2	2	no	—
16	#11765849	—	4	1	no	—
17	C₂×C₇₁⋊C₈	—	4	1	no	—
18	C₇₁⋊C₁₆	C₂×C₄	1	4	yes	complemented
19	C₂²×C₄×C₇₁	—	4	1	no	—
20	C₂²×C₄×C₇₁	D₄	1	1	yes	characteristic
21	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
24	C₂×C₈×C₇₁	Q₈	1	1	yes	characteristic
25	C₂×C₈×C₇₁	Q₈	1	1	yes	characteristic
26	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
27	C₄⋊C₄×C₇₁	—	2	2	no	—
28	C₄⋊C₄×C₇₁	—	4	1	no	—
29	C₂³×C₇₁	SD₁₆	1	1	yes	characteristic
30	C₂×C₄×C₇₁	—	4	2	no	—
31	C₂×C₄×C₇₁	—	8	2	no	—
32	C₂×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₁	SD₁₆	1	1	yes	characteristic
35	C₂×C₄×C₇₁	SD₁₆	1	1	yes	characteristic
36	C₂×C₄×C₇₁	SD₁₆	1	1	yes	characteristic
37	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
38	C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
39	C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
40	C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
41	C₈×C₇₁	C₂×Q₈	1	1	yes	characteristic
42	C₇₁⋊C₈	—	4	2	no	—
43	C₂²×C₇₁	—	2	2	no	—
44	C₂²×C₇₁	#106	1	1	yes	characteristic
45	C₂²×C₇₁	#106	1	1	yes	characteristic
46	C₂²×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
47	C₄×C₇₁	—	8	2	no	—
48	C₄×C₇₁	#106	1	1	yes	characteristic
49	C₄×C₇₁	#106	1	1	yes	characteristic
50	C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
52	C₂×C₇₁	—	2	1	no	—
53	C₂×C₇₁	—	2	1	no	—
54	C₂×C₇₁	#365	1	2	yes	complemented
55	C₂×C₇₁	C₂×#106	1	1	yes	characteristic
56	C₂×#365	—	71	1	no	maximal, Sylow
57	C₇₁	C₂×#365	1	1	yes	characteristic, complemented, Sylow
58	C₂×M₃₂	—	71	1	no	—
59	C₂×#108	—	71	1	no	—
60	C₂×#106	D₇₁	1	1	yes	characteristic
61	#365	—	71	4	no	—
62	C₂×M₁₆	—	142	1	no	—
63	C₂²×C₈	C₂×D₇₁	1	1	yes	characteristic
64	C₂×C₄⋊C₄	—	2	1	no	—
65	M₃₂	—	71	2	no	—
66	M₃₂	—	71	2	no	—
67	C₂×C₁₆	—	71	2	no	—
68	#108	—	71	2	no	—
69	#108	—	142	1	no	—
70	#106	—	2	1	no	—
71	#106	C₂×D₇₁	1	2	yes	—
72	C₂²×C₄	—	4	1	no	—
73	C₂²×C₄	C₂²⋊D₇₁	1	1	yes	characteristic
74	M₁₆	—	284	1	no	—
75	M₁₆	—	142	2	no	—
76	C₂×C₈	—	284	1	no	—
77	C₂×C₈	Dic₁₄₂	1	1	yes	characteristic
78	C₂×C₈	Dic₁₄₂	1	1	yes	characteristic
79	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
80	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
81	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
82	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
83	C₄⋊C₄	—	2	2	no	—
84	C₄⋊C₄	—	4	1	no	—
85	C₁₆	—	71	4	no	—
86	C₂³	#11765853	1	1	yes	characteristic
87	C₂×C₄	—	4	2	no	—
88	C₂×C₄	—	8	2	no	—
89	C₂×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
90	C₂×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
91	C₂×C₄	#11765852	1	1	yes	characteristic
92	C₂×C₄	#11765852	1	1	yes	characteristic
93	C₂×C₄	#11765853	1	1	yes	characteristic
94	C₂×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
95	C₈	—	284	2	no	—
96	C₈	Dic₇₁⋊C₄	1	1	yes	characteristic
97	C₈	Dic₇₁⋊C₄	1	1	yes	characteristic
98	C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
99	C₈	C₂×Dic₁₄₂	1	1	yes	characteristic
100	C₂²	—	2	2	no	—
101	C₂²	#14556059	1	1	yes	characteristic
102	C₂²	#14556059	1	1	yes	characteristic
103	C₂²	C₂×#11765853	1	1	yes	characteristic
104	C₄	—	8	2	no	—
105	C₄	#14556059	1	1	yes	characteristic
106	C₄	#14556059	1	1	yes	characteristic
107	C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
108	C₄	C₂×#11765852	1	1	yes	characteristic
109	C₂	—	2	1	no	—
110	C₂	—	2	1	no	—
111	C₂	#17985821	1	2	yes	direct product factor
112	C₂	C₂×#14556059	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556068

C₂

yes

maximal, characteristic

C₂×#14556064

C₂

yes

maximal, characteristic

#17985821

C₂

yes

maximal, direct product factor

C₂×#106×C₇₁

C₂

yes

maximal, characteristic

C₂×#11765849

—

#14556068

C₄

yes

complemented

#14556068

C₂²

yes

—

C₂×C₇₁⋊C₁₆

C₄

yes

complemented

#14556064

—

#14556064

C₂²

yes

—

C₂²×C₈×C₇₁

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₁

—

#106×C₇₁

—

#106×C₇₁

C₂²

yes

—

#11765849

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₇₁⋊C₁₆

C₂×C₄

yes

complemented

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂×C₈×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

Q₈

yes

characteristic

C₂×C₈×C₇₁

Q₈

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₂³×C₇₁

SD₁₆

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₁

SD₁₆

yes

characteristic

C₂×C₄×C₇₁

SD₁₆

yes

characteristic

C₂×C₄×C₇₁

SD₁₆

yes

characteristic

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₈×C₇₁

C₄⋊C₄

yes

characteristic

C₈×C₇₁

C₄⋊C₄

yes

characteristic

C₈×C₇₁

C₂²×C₄

yes

characteristic

C₈×C₇₁

C₂×Q₈

yes

characteristic

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

yes

C₂²×C₇₁

yes

C₂²×C₇₁

C₂×SD₁₆

yes

characteristic

C₄×C₇₁

—

C₄×C₇₁

yes

C₄×C₇₁

yes

C₄×C₇₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₁

C₂×SD₁₆

yes

characteristic

C₂×C₇₁

—

C₂×C₇₁

—

C₂×C₇₁

yes

C₂×C₇₁

yes

—

C₇₁

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×#108

—

C₂×#106

D₇₁

yes

characteristic

#365

—

C₂×M₁₆

—

142

—

C₂²×C₈

C₂×D₇₁

yes

characteristic

C₂×C₄⋊C₄

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

#108

—

#108

—

142

—

#106

—

#106

C₂×D₇₁

yes

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₇₁

yes

characteristic

M₁₆

—

284

—

M₁₆

—

142

—

C₂×C₈

—

284

—

C₂×C₈

Dic₁₄₂

yes

characteristic

C₂×C₈

Dic₁₄₂

yes

characteristic

C₂×C₈

C₄×D₇₁

yes

characteristic

C₂×C₈

C₄×D₇₁

yes

characteristic

C₂×C₈

C₂²⋊D₇₁

yes

characteristic

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₁₆

—

C₂³

#11765853

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

Dic₇₁⋊C₄

yes

characteristic

C₂×C₄

Dic₇₁⋊C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

C₈

—

284

—

C₈

Dic₇₁⋊C₄

yes

characteristic

C₈

Dic₇₁⋊C₄

yes

characteristic

C₈

C₂×C₄×D₇₁

yes

characteristic

C₈

C₂×Dic₁₄₂

yes

characteristic

100

C₂²

—

101

C₂²

#14556059

yes

characteristic

102

C₂²

#14556059

yes

characteristic

103

C₂²

C₂×#11765853

yes

characteristic

104

C₄

—

105

C₄

#14556059

yes

characteristic

106

C₄

#14556059

yes

characteristic

107

C₄

C₂×Dic₇₁⋊C₄

yes

characteristic

108

C₄

C₂×#11765852

yes

characteristic

109

C₂

—

110

C₂

—

111

C₂

#17985821

yes

direct product factor

112

C₂

C₂×#14556059

yes

characteristic

	subgroup	G/H
center	C₂²	#14556059
commutator	C₈×C₇₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	C₂×#106×C₇₁	C₂
socle	C₂²×C₇₁	#106
hypercenter	C₂×#106	D₇₁
hypocenter	C₇₁	C₂×#365
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#106

subgroup

G/H

center

C₂²

#14556059

commutator

C₈×C₇₁

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

C₂×#106×C₇₁

C₂

C₂²×C₇₁

D₇₁

C₇₁

G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#106

N	H ≅ G/N	type
3. #17985821	C₂	direct (N × H)
6. #14556068	C₄	semidirect
8. C₂×C₇₁⋊C₁₆	C₄	semidirect
18. C₇₁⋊C₁₆	C₂×C₄	semidirect
54. C₂×C₇₁	#365	semidirect
57. C₇₁	C₂×#365	semidirect
111. C₂	#17985821	direct (N × H)

H ≅ G/N

type

3. #17985821

C₂

direct (N × H)

6. #14556068

C₄

semidirect

8. C₂×C₇₁⋊C₁₆

C₄

semidirect

18. C₇₁⋊C₁₆

C₂×C₄

semidirect

54. C₂×C₇₁

#365

semidirect

57. C₇₁

C₂×#365

semidirect

111. C₂

#17985821

direct (N × H)

Subgroups — C₂×#17985821 #22590108

Conjugacy classes of subgroups

Complements

Subgroups — C2×#17985821 #22590108

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17985821 #22590108