Group #20261236 — subgroups

Subgroups — C₂×#15690791 #20261236

Order 6208.

342 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 127 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	C₂³×Dic₉₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#15690791	C₂	1	8	yes	maximal, direct product factor
3	C₂×#13095490	C₂	1	2	yes	maximal, complemented
4	C₂×C₂²⋊Dic₉₇	C₂	1	2	yes	maximal, complemented
5	C₂×C₂²⋊Dic₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₄×C₉₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₉₇	—	2	4	no	—
8	C₂²×Dic₉₇	C₂²	1	2	yes	—
9	C₂²×Dic₉₇	C₂²	1	2	yes	—
10	C₂²×Dic₉₇	C₂²	1	4	yes	complemented
11	#13095490	C₂²	1	8	yes	complemented
12	C₂²⋊Dic₉₇	C₂²	1	4	yes	complemented
13	C₂²⋊Dic₉₇	C₂²	1	8	yes	complemented
14	C₂⁴×C₉₇	C₂²	1	1	yes	characteristic
15	C₂⁴×C₉₇	C₂²	1	1	yes	characteristic
16	C₂×D₄×C₉₇	—	2	4	no	—
17	C₂×D₄×C₉₇	C₂²	1	4	yes	—
18	C₂²×C₄×C₉₇	C₂²	1	1	yes	characteristic
19	C₂³×C₉₇	—	2	4	no	—
20	C₂³×C₉₇	—	2	2	no	—
21	C₂³×C₉₇	—	2	4	no	—
22	C₂³×C₉₇	D₄	1	4	yes	—
23	C₂³×C₉₇	C₂³	1	2	yes	—
24	C₂³×C₉₇	C₂³	1	2	yes	—
25	C₂³×C₉₇	C₂³	1	1	yes	characteristic
26	D₄×C₉₇	—	2	8	no	—
27	C₂×C₄×C₉₇	—	2	2	no	—
28	C₂×C₄×C₉₇	C₂³	1	2	yes	—
29	C₂×Dic₉₇	—	2	4	no	—
30	C₂×Dic₉₇	—	2	8	no	—
31	C₂×Dic₉₇	—	2	4	no	—
32	C₂×Dic₉₇	C₂³	1	4	yes	—
33	C₂×Dic₉₇	C₂³	1	4	yes	—
34	C₂²×C₉₇	—	2	8	no	—
35	C₂²×C₉₇	—	2	4	no	—
36	C₂²×C₉₇	—	2	2	no	—
37	C₂²×C₉₇	—	2	4	no	—
38	C₂²×C₉₇	—	4	4	no	—
39	C₂²×C₉₇	C₂×D₄	1	4	yes	—
40	C₂²×C₉₇	C₂×D₄	1	2	yes	—
41	C₂²×C₉₇	#41	1	4	yes	—
42	C₂²×C₉₇	C₂⁴	1	1	yes	characteristic
43	C₄×C₉₇	—	2	2	no	—
44	Dic₉₇	—	2	4	no	—
45	Dic₉₇	—	2	4	no	—
46	C₂×C₉₇	—	2	4	no	—
47	C₂×C₉₇	—	4	2	no	—
48	C₂×C₉₇	#123	1	4	yes	complemented
49	C₂×C₉₇	C₂²×D₄	1	1	yes	characteristic
50	C₂×C₉₇	C₂×#41	1	2	yes	—
51	C₉₇	C₂×#123	1	1	yes	characteristic, complemented, Sylow
52	C₂×#123	—	97	1	no	maximal, Sylow
53	C₂²×D₄	D₉₇	1	1	yes	characteristic
54	C₂³×C₄	—	97	1	no	—
55	#123	—	97	8	no	—
56	C₂×C₄⋊C₄	—	97	2	no	—
57	C₂×C₂²⋊C₄	—	97	1	no	—
58	C₂×C₂²⋊C₄	—	97	2	no	—
59	C₂⁴	C₂×D₉₇	1	1	yes	characteristic
60	C₂⁴	C₂×D₉₇	1	1	yes	characteristic
61	C₂×D₄	—	2	4	no	—
62	C₂×D₄	C₂×D₉₇	1	4	yes	—
63	C₂²×C₄	—	97	4	no	—
64	C₂²×C₄	—	97	2	no	—
65	C₂²×C₄	—	97	2	no	—
66	C₂²×C₄	—	194	4	no	—
67	C₂²×C₄	C₂×D₉₇	1	1	yes	characteristic
68	C₄⋊C₄	—	97	8	no	—
69	C₂²⋊C₄	—	97	4	no	—
70	C₂²⋊C₄	—	97	8	no	—
71	C₂³	—	2	4	no	—
72	C₂³	—	2	2	no	—
73	C₂³	—	2	4	no	—
74	C₂³	C₂²⋊D₉₇	1	4	yes	—
75	C₂³	C₂²×D₉₇	1	2	yes	—
76	C₂³	C₂²×D₉₇	1	2	yes	—
77	C₂³	C₂²×D₉₇	1	1	yes	characteristic
78	D₄	—	2	8	no	—
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	97	4	no	—
81	C₂×C₄	—	97	4	no	—
82	C₂×C₄	—	194	8	no	—
83	C₂×C₄	—	194	4	no	—
84	C₂×C₄	—	194	4	no	—
85	C₂×C₄	C₂²×D₉₇	1	2	yes	—
86	C₂²	—	2	8	no	—
87	C₂²	—	2	4	no	—
88	C₂²	—	2	2	no	—
89	C₂²	—	2	4	no	—
90	C₂²	—	4	4	no	—
91	C₂²	C₂×C₂²⋊D₉₇	1	4	yes	—
92	C₂²	C₂×C₂²⋊D₉₇	1	2	yes	—
93	C₂²	#13095510	1	4	yes	—
94	C₂²	C₂³×D₉₇	1	1	yes	characteristic
95	C₄	—	2	2	no	—
96	C₄	—	194	4	no	—
97	C₄	—	194	4	no	—
98	C₂	—	2	4	no	—
99	C₂	—	4	2	no	—
100	C₂	#15690791	1	4	yes	direct product factor
101	C₂	C₂²×C₂²⋊D₉₇	1	1	yes	characteristic
102	C₂	C₂×#13095510	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×Dic₉₇

C₂

yes

maximal, characteristic, complemented

#15690791

C₂

yes

maximal, direct product factor

C₂×#13095490

C₂

yes

maximal, complemented

C₂×C₂²⋊Dic₉₇

C₂

yes

maximal, complemented

C₂×C₂²⋊Dic₉₇

C₂

yes

maximal, characteristic, complemented

C₂²×D₄×C₉₇

C₂

yes

maximal, characteristic

C₂²×Dic₉₇

—

C₂²×Dic₉₇

C₂²

yes

—

C₂²×Dic₉₇

C₂²

yes

—

C₂²×Dic₉₇

C₂²

yes

complemented

#13095490

C₂²

yes

complemented

C₂²⋊Dic₉₇

C₂²

yes

complemented

C₂²⋊Dic₉₇

C₂²

yes

complemented

C₂⁴×C₉₇

C₂²

yes

characteristic

C₂⁴×C₉₇

C₂²

yes

characteristic

C₂×D₄×C₉₇

—

C₂×D₄×C₉₇

C₂²

yes

—

C₂²×C₄×C₉₇

C₂²

yes

characteristic

C₂³×C₉₇

—

C₂³×C₉₇

—

C₂³×C₉₇

—

C₂³×C₉₇

D₄

yes

—

C₂³×C₉₇

C₂³

yes

—

C₂³×C₉₇

C₂³

yes

—

C₂³×C₉₇

C₂³

yes

characteristic

D₄×C₉₇

—

C₂×C₄×C₉₇

—

C₂×C₄×C₉₇

C₂³

yes

—

C₂×Dic₉₇

—

C₂×Dic₉₇

—

C₂×Dic₉₇

—

C₂×Dic₉₇

C₂³

yes

—

C₂×Dic₉₇

C₂³

yes

—

C₂²×C₉₇

—

C₂²×C₉₇

—

C₂²×C₉₇

—

C₂²×C₉₇

—

C₂²×C₉₇

—

C₂²×C₉₇

C₂×D₄

yes

—

C₂²×C₉₇

C₂×D₄

yes

—

C₂²×C₉₇

#41

yes

—

C₂²×C₉₇

C₂⁴

yes

characteristic

C₄×C₉₇

—

Dic₉₇

—

Dic₉₇

—

C₂×C₉₇

—

C₂×C₉₇

—

C₂×C₉₇

#123

yes

complemented

C₂×C₉₇

C₂²×D₄

yes

characteristic

C₂×C₉₇

C₂×#41

yes

—

C₉₇

C₂×#123

yes

characteristic, complemented, Sylow

C₂×#123

—

maximal, Sylow

C₂²×D₄

D₉₇

yes

characteristic

C₂³×C₄

—

#123

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂⁴

C₂×D₉₇

yes

characteristic

C₂⁴

C₂×D₉₇

yes

characteristic

C₂×D₄

—

C₂×D₄

C₂×D₉₇

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

194

—

C₂²×C₄

C₂×D₉₇

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂²⋊D₉₇

yes

—

C₂³

C₂²×D₉₇

yes

—

C₂³

C₂²×D₉₇

yes

—

C₂³

C₂²×D₉₇

yes

characteristic

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

194

—

C₂×C₄

—

194

—

C₂×C₄

—

194

—

C₂×C₄

C₂²×D₉₇

yes

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₂×C₂²⋊D₉₇

yes

—

C₂²

C₂×C₂²⋊D₉₇

yes

—

C₂²

#13095510

yes

—

C₂²

C₂³×D₉₇

yes

characteristic

C₄

—

C₄

—

194

—

C₄

—

194

—

C₂

—

C₂

—

100

C₂

#15690791

yes

direct product factor

101

C₂

C₂²×C₂²⋊D₉₇

yes

characteristic

102

C₂

C₂×#13095510

yes

—

	subgroup	G/H
center	C₂³	C₂²×D₉₇
commutator	C₂²×C₉₇	C₂⁴
Frattini	C₂²	C₂³×D₉₇
Fitting	C₂²×D₄×C₉₇	C₂
socle	C₂³×C₉₇	C₂³
hypercenter	C₂²×D₄	D₉₇
hypocenter	C₉₇	C₂×#123
LCS	G ▷ C₂²×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂³ ◁ C₂²×D₄

subgroup

G/H

center

C₂³

C₂²×D₉₇

commutator

C₂²×C₉₇

C₂⁴

Frattini

C₂²

C₂³×D₉₇

Fitting

C₂²×D₄×C₉₇

C₂

socle

C₂³×C₉₇

C₂³

hypercenter

C₂²×D₄

D₉₇

C₉₇

G ▷ C₂²×C₉₇ ▷ C₉₇

C₁ ◁ C₂³ ◁ C₂²×D₄

N	H ≅ G/N	type
1. C₂³×Dic₉₇	C₂	semidirect
2. #15690791	C₂	direct (N × H)
3. C₂×#13095490	C₂	semidirect
4. C₂×C₂²⋊Dic₉₇	C₂	semidirect
5. C₂×C₂²⋊Dic₉₇	C₂	semidirect
10. C₂²×Dic₉₇	C₂²	semidirect
11. #13095490	C₂²	semidirect
12. C₂²⋊Dic₉₇	C₂²	semidirect
13. C₂²⋊Dic₉₇	C₂²	semidirect
48. C₂×C₉₇	#123	semidirect
51. C₉₇	C₂×#123	semidirect
100. C₂	#15690791	direct (N × H)

H ≅ G/N

type

1. C₂³×Dic₉₇

C₂

semidirect

2. #15690791

C₂

direct (N × H)

3. C₂×#13095490

C₂

semidirect

4. C₂×C₂²⋊Dic₉₇

C₂

semidirect

5. C₂×C₂²⋊Dic₉₇

C₂

semidirect

10. C₂²×Dic₉₇

C₂²

semidirect

11. #13095490

C₂²

semidirect

12. C₂²⋊Dic₉₇

C₂²

semidirect

13. C₂²⋊Dic₉₇

C₂²

semidirect

48. C₂×C₉₇

#123

semidirect

51. C₉₇

C₂×#123

semidirect

100. C₂

#15690791

direct (N × H)

Subgroups — C₂×#15690791 #20261236

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15690791 #20261236

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15690791 #20261236