Group #20260948 — subgroups

Subgroups — #20260948

Order 6208.

124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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×#13095499	C₂	1	1	yes	maximal, characteristic, complemented
2	#15690797	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Dic₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#15690739	C₂	1	1	yes	maximal, characteristic, complemented
5	#15690735	C₂	1	1	yes	maximal, characteristic, complemented
6	#15690731	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₈×C₉₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₉₄	C₂²	1	1	yes	characteristic
9	C₂²×Dic₉₇	—	2	1	no	—
10	#13095499	—	2	2	no	—
11	C₂×#11715895	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₉₇	C₂²	1	1	yes	characteristic
13	C₂²⋊Dic₉₇	—	2	1	no	—
14	C₂²⋊Dic₉₇	—	2	1	no	—
15	C₂²⋊Dic₉₇	—	2	1	no	—
16	C₄×Dic₉₇	C₂²	1	1	yes	characteristic
17	C₂×D₄×C₉₇	C₂²	1	1	yes	characteristic
18	C₂×D₄×C₉₇	C₂²	1	1	yes	characteristic
19	D₈×C₉₇	—	2	2	no	—
20	C₂×C₈×C₉₇	C₂²	1	1	yes	characteristic
21	C₂³×C₉₇	—	2	1	no	—
22	C₂³×C₉₇	—	2	1	no	—
23	D₄×C₉₇	—	2	1	no	—
24	D₄×C₉₇	—	2	1	no	—
25	D₄×C₉₇	—	2	1	no	—
26	D₄×C₉₇	D₄	1	2	yes	—
27	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
28	C₂×Dic₉₇	—	2	1	no	—
29	C₂×Dic₉₇	—	2	1	no	—
30	C₂×Dic₉₇	—	4	2	no	—
31	C₂×Dic₉₇	D₄	1	1	yes	characteristic
32	C₂×Dic₉₇	D₄	1	1	yes	characteristic
33	Dic₁₉₄	—	2	1	no	—
34	Dic₁₉₄	—	2	1	no	—
35	C₈×C₉₇	—	2	1	no	—
36	#11715895	—	2	1	no	—
37	C₂²×C₉₇	—	2	2	no	—
38	C₂²×C₉₇	—	4	1	no	—
39	C₂²×C₉₇	—	4	1	no	—
40	C₂²×C₉₇	—	4	1	no	—
41	C₂²×C₉₇	—	4	1	no	—
42	C₂²×C₉₇	—	4	1	no	—
43	C₂²×C₉₇	C₂×D₄	1	1	yes	characteristic
44	C₄×C₉₇	C₂×D₄	1	1	yes	characteristic
45	C₄×C₉₇	#41	1	1	yes	characteristic
46	Dic₉₇	—	2	1	no	—
47	Dic₉₇	—	2	1	no	—
48	Dic₉₇	—	4	1	no	—
49	Dic₉₇	—	4	1	no	—
50	C₂×C₉₇	—	4	2	no	—
51	C₂×C₉₇	—	8	1	no	—
52	C₂×C₉₇	#121	1	1	yes	characteristic
53	C₂×C₉₇	#135	1	1	yes	characteristic
54	C₂×C₉₇	AGL(1,ℤ/8)	1	1	yes	characteristic
55	C₉₇	#463	1	1	yes	characteristic, complemented, Sylow
56	#463	—	97	1	no	maximal, Sylow
57	C₂×SD₁₆	—	97	1	no	—
58	C₂×D₈	D₉₇	1	1	yes	characteristic
59	#124	—	97	1	no	—
60	C₄×D₄	—	97	1	no	—
61	C₄⋊C₈	—	97	1	no	—
62	#103	—	97	1	no	—
63	#102	—	97	1	no	—
64	C₂×Q₈	—	97	1	no	—
65	C₂×D₄	C₂×D₉₇	1	1	yes	characteristic
66	C₂×D₄	C₂×D₉₇	1	1	yes	characteristic
67	C₂²×C₄	—	194	1	no	—
68	SD₁₆	—	194	2	no	—
69	D₈	—	2	2	no	—
70	C₂×C₈	—	97	1	no	—
71	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
72	C₄⋊C₄	—	97	1	no	—
73	C₂²⋊C₄	—	194	1	no	—
74	C₂²⋊C₄	—	194	1	no	—
75	C₂²⋊C₄	—	194	1	no	—
76	C₄²	—	97	1	no	—
77	C₂³	—	2	1	no	—
78	C₂³	—	2	1	no	—
79	Q₈	—	194	1	no	—
80	Q₈	—	194	1	no	—
81	D₄	—	2	1	no	—
82	D₄	—	2	1	no	—
83	D₄	—	2	1	no	—
84	D₄	C₂²⋊D₉₇	1	2	yes	—
85	C₂×C₄	—	97	1	no	—
86	C₂×C₄	—	97	1	no	—
87	C₂×C₄	—	388	2	no	—
88	C₂×C₄	—	194	1	no	—
89	C₂×C₄	—	194	1	no	—
90	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
91	C₈	—	2	1	no	—
92	C₈	—	194	1	no	—
93	C₂²	—	2	2	no	—
94	C₂²	—	4	1	no	—
95	C₂²	—	4	1	no	—
96	C₂²	—	4	1	no	—
97	C₂²	—	4	1	no	—
98	C₂²	—	4	1	no	—
99	C₂²	D₄×D₉₇	1	1	yes	characteristic
100	C₄	—	388	1	no	—
101	C₄	—	388	1	no	—
102	C₄	—	194	1	no	—
103	C₄	—	194	1	no	—
104	C₄	C₂×C₂²⋊D₉₇	1	1	yes	characteristic
105	C₄	#13095510	1	1	yes	characteristic
106	C₂	—	4	2	no	—
107	C₂	—	8	1	no	—
108	C₂	#15690782	1	1	yes	characteristic
109	C₂	#15690829	1	1	yes	characteristic
110	C₂	#15690834	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13095499

C₂

yes

maximal, characteristic, complemented

#15690797

C₂

yes

maximal, characteristic, complemented

D₄×Dic₉₇

C₂

yes

maximal, characteristic, complemented

#15690739

C₂

yes

maximal, characteristic, complemented

#15690735

C₂

yes

maximal, characteristic, complemented

#15690731

C₂

yes

maximal, characteristic, complemented

C₂×D₈×C₉₇

C₂

yes

maximal, characteristic

C₂×Dic₁₉₄

C₂²

yes

characteristic

C₂²×Dic₉₇

—

#13095499

—

C₂×#11715895

C₂²

yes

characteristic

C₄⋊Dic₉₇

C₂²

yes

characteristic

C₂²⋊Dic₉₇

—

C₂²⋊Dic₉₇

—

C₂²⋊Dic₉₇

—

C₄×Dic₉₇

C₂²

yes

characteristic

C₂×D₄×C₉₇

C₂²

yes

characteristic

C₂×D₄×C₉₇

C₂²

yes

characteristic

D₈×C₉₇

—

C₂×C₈×C₉₇

C₂²

yes

characteristic

C₂³×C₉₇

—

C₂³×C₉₇

—

D₄×C₉₇

—

D₄×C₉₇

—

D₄×C₉₇

—

D₄×C₉₇

D₄

yes

—

C₂×C₄×C₉₇

C₂³

yes

characteristic

C₂×Dic₉₇

—

C₂×Dic₉₇

—

C₂×Dic₉₇

—

C₂×Dic₉₇

D₄

yes

characteristic

C₂×Dic₉₇

D₄

yes

characteristic

Dic₁₉₄

—

Dic₁₉₄

—

C₈×C₉₇

—

#11715895

—

C₂²×C₉₇

—

C₂²×C₉₇

—

C₂²×C₉₇

—

C₂²×C₉₇

—

C₂²×C₉₇

—

C₂²×C₉₇

—

C₂²×C₉₇

C₂×D₄

yes

characteristic

C₄×C₉₇

C₂×D₄

yes

characteristic

C₄×C₉₇

#41

yes

characteristic

Dic₉₇

—

Dic₉₇

—

Dic₉₇

—

Dic₉₇

—

C₂×C₉₇

—

C₂×C₉₇

—

C₂×C₉₇

yes

C₂×C₉₇

yes

C₂×C₉₇

yes

C₉₇

yes

characteristic, complemented, Sylow

#463

—

maximal, Sylow

C₂×SD₁₆

—

C₂×D₈

D₉₇

yes

characteristic

#124

—

C₄×D₄

—

C₄⋊C₈

—

#103

—

#102

—

C₂×Q₈

—

C₂×D₄

C₂×D₉₇

yes

characteristic

C₂×D₄

C₂×D₉₇

yes

characteristic

C₂²×C₄

—

194

—

SD₁₆

—

194

—

D₈

—

C₂×C₈

—

C₂×C₈

C₂×D₉₇

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

194

—

C₂²⋊C₄

—

194

—

C₂²⋊C₄

—

194

—

C₄²

—

C₂³

—

C₂³

—

Q₈

—

194

—

Q₈

—

194

—

D₄

—

D₄

—

D₄

—

D₄

C₂²⋊D₉₇

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

388

—

C₂×C₄

—

194

—

C₂×C₄

—

194

—

C₂×C₄

C₂²×D₉₇

yes

characteristic

C₈

—

C₈

—

194

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

D₄×D₉₇

yes

characteristic

100

C₄

—

388

—

101

C₄

—

388

—

102

C₄

—

194

—

103

C₄

—

194

—

104

C₄

C₂×C₂²⋊D₉₇

yes

characteristic

105

C₄

#13095510

yes

characteristic

106

C₂

—

107

C₂

—

108

C₂

#15690782

yes

characteristic

109

C₂

#15690829

yes

characteristic

110

C₂

#15690834

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×D₉₇
commutator	C₂×C₄×C₉₇	C₂³
Frattini	C₂×C₄	C₂²×D₉₇
Fitting	C₂×D₈×C₉₇	C₂
socle	C₂²×C₉₇	C₂×D₄
hypercenter	C₂×D₈	D₉₇
hypocenter	C₉₇	#463
LCS	G ▷ C₂×C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

subgroup

G/H

center

C₂²

D₄×D₉₇

commutator

C₂×C₄×C₉₇

C₂³

Frattini

C₂×C₄

C₂²×D₉₇

Fitting

C₂×D₈×C₉₇

C₂

socle

C₂²×C₉₇

C₂×D₄

hypercenter

C₂×D₈

D₉₇

hypocenter

C₉₇

#463

LCS

G ▷ C₂×C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

N	H ≅ G/N	type
1. C₂×#13095499	C₂	semidirect
2. #15690797	C₂	semidirect
3. D₄×Dic₉₇	C₂	semidirect
4. #15690739	C₂	semidirect
5. #15690735	C₂	semidirect
6. #15690731	C₂	semidirect
55. C₉₇	#463	semidirect

H ≅ G/N

type

1. C₂×#13095499

C₂

semidirect

2. #15690797

C₂

semidirect

3. D₄×Dic₉₇

C₂

semidirect

4. #15690739

C₂

semidirect

5. #15690735

C₂

semidirect

6. #15690731

C₂

semidirect

55. C₉₇

#463

semidirect

Subgroups — #20260948

Conjugacy classes of subgroups

Complements