Group #20265035 — subgroups

Subgroups — #20265035

Order 6464.

234 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 87 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×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#13108053	C₂	1	2	yes	maximal, complemented
3	C₂×C₂²⋊Dic₁₀₁	C₂	1	1	yes	maximal, characteristic
4	#15692162	C₂	1	2	yes	maximal, complemented
5	C₂×C₂²⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₀₁	—	2	4	no	—
7	C₂²×Dic₁₀₁	C₄	1	4	yes	complemented
8	C₂²×Dic₁₀₁	C₂²	1	2	yes	—
9	C₂²×Dic₁₀₁	C₂²	1	1	yes	characteristic
10	C₂²×Dic₁₀₁	C₂²	1	1	yes	characteristic
11	#13108053	—	2	4	no	—
12	C₂²⋊Dic₁₀₁	—	2	2	no	—
13	C₂⁴×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₁₀₁	C₂²	1	2	yes	—
15	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
16	C₂³×C₁₀₁	—	2	2	no	—
17	C₂³×C₁₀₁	—	2	2	no	—
18	C₂³×C₁₀₁	C₂×C₄	1	2	yes	—
19	C₂³×C₁₀₁	D₄	1	2	yes	—
20	C₂³×C₁₀₁	Q₈	1	2	yes	—
21	C₂³×C₁₀₁	C₂³	1	1	yes	characteristic
22	C₂×C₄×C₁₀₁	—	2	2	no	—
23	C₂×C₄×C₁₀₁	—	2	2	no	—
24	C₂×C₄×C₁₀₁	—	2	2	no	—
25	C₂×Dic₁₀₁	—	2	2	no	—
26	C₂×Dic₁₀₁	—	2	8	no	—
27	C₂×Dic₁₀₁	—	2	2	no	—
28	C₂×Dic₁₀₁	—	2	2	no	—
29	C₂×Dic₁₀₁	—	2	2	no	—
30	C₂×Dic₁₀₁	C₂×C₄	1	2	yes	—
31	C₂×Dic₁₀₁	C₂×C₄	1	2	yes	—
32	C₂×Dic₁₀₁	D₄	1	4	yes	—
33	C₂²×C₁₀₁	—	2	2	no	—
34	C₂²×C₁₀₁	—	2	2	no	—
35	C₂²×C₁₀₁	—	2	4	no	—
36	C₂²×C₁₀₁	—	2	4	no	—
37	C₂²×C₁₀₁	C₄⋊C₄	1	4	yes	complemented
38	C₂²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
39	C₂²×C₁₀₁	C₂×D₄	1	2	yes	—
40	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
42	C₂²×C₁₀₁	#41	1	2	yes	—
43	C₄×C₁₀₁	—	4	2	no	—
44	Dic₁₀₁	—	2	2	no	—
45	Dic₁₀₁	—	4	2	no	—
46	Dic₁₀₁	C₂²⋊C₄	1	4	yes	complemented
47	C₂×C₁₀₁	—	2	4	no	—
48	C₂×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
49	C₂×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₁₀₁	#117	1	1	yes	characteristic
51	C₂×C₁₀₁	#121	1	2	yes	—
52	C₂×C₁₀₁	C₂²⋊Q₈	1	2	yes	—
53	C₁₀₁	#380	1	1	yes	characteristic, complemented, Sylow
54	#380	—	101	1	no	maximal, Sylow
55	C₂³×C₄	—	101	1	no	—
56	C₂×C₄⋊C₄	—	101	2	no	—
57	C₂×C₂²⋊C₄	—	101	1	no	—
58	C₂×C₂²⋊C₄	D₁₀₁	1	1	yes	characteristic
59	#95	—	101	2	no	—
60	C₂⁴	C₂×D₁₀₁	1	1	yes	characteristic
61	C₂²×C₄	—	101	1	no	—
62	C₂²×C₄	—	101	4	no	—
63	C₂²×C₄	—	101	1	no	—
64	C₂²×C₄	—	101	2	no	—
65	C₂²×C₄	—	202	4	no	—
66	C₂²×C₄	C₂×D₁₀₁	1	2	yes	—
67	C₄⋊C₄	—	202	4	no	—
68	C₂²⋊C₄	—	2	2	no	—
69	C₂²⋊C₄	—	202	2	no	—
70	C₂³	—	2	2	no	—
71	C₂³	—	2	2	no	—
72	C₂³	Dic₂₀₂	1	2	yes	—
73	C₂³	C₄×D₁₀₁	1	2	yes	—
74	C₂³	C₂²⋊D₁₀₁	1	2	yes	—
75	C₂³	C₂²×D₁₀₁	1	1	yes	characteristic
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	—	2	2	no	—
78	C₂×C₄	—	2	2	no	—
79	C₂×C₄	—	101	2	no	—
80	C₂×C₄	—	101	4	no	—
81	C₂×C₄	—	101	2	no	—
82	C₂×C₄	—	202	8	no	—
83	C₂×C₄	—	202	2	no	—
84	C₂×C₄	—	202	2	no	—
85	C₂×C₄	—	202	2	no	—
86	C₂×C₄	—	202	2	no	—
87	C₂²	—	2	2	no	—
88	C₂²	—	2	2	no	—
89	C₂²	—	2	4	no	—
90	C₂²	—	2	4	no	—
91	C₂²	#13108053	1	4	yes	complemented
92	C₂²	C₂×C₄×D₁₀₁	1	1	yes	characteristic
93	C₂²	D₄×D₁₀₁	1	2	yes	—
94	C₂²	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic
95	C₂²	C₂×Dic₂₀₂	1	1	yes	characteristic
96	C₂²	#13108073	1	2	yes	—
97	C₄	—	4	2	no	—
98	C₄	—	101	4	no	—
99	C₄	—	404	2	no	—
100	C₄	—	202	2	no	—
101	C₂	—	2	4	no	—
102	C₂	C₂²⋊C₄×D₁₀₁	1	1	yes	characteristic
103	C₂	C₂×#13108053	1	1	yes	characteristic
104	C₂	#15692211	1	1	yes	characteristic
105	C₂	#15692227	1	2	yes	—
106	C₂	#15692232	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×Dic₁₀₁

C₂

yes

maximal, characteristic

C₂×#13108053

C₂

yes

maximal, complemented

C₂×C₂²⋊Dic₁₀₁

C₂

yes

maximal, characteristic

#15692162

C₂

yes

maximal, complemented

C₂×C₂²⋊C₄×C₁₀₁

C₂

yes

maximal, characteristic

C₂²×Dic₁₀₁

—

C₂²×Dic₁₀₁

C₄

yes

complemented

C₂²×Dic₁₀₁

C₂²

yes

—

C₂²×Dic₁₀₁

C₂²

yes

characteristic

C₂²×Dic₁₀₁

C₂²

yes

characteristic

#13108053

—

C₂²⋊Dic₁₀₁

—

C₂⁴×C₁₀₁

C₂²

yes

characteristic

C₂²×C₄×C₁₀₁

C₂²

yes

—

C₂²⋊C₄×C₁₀₁

—

C₂³×C₁₀₁

—

C₂³×C₁₀₁

—

C₂³×C₁₀₁

C₂×C₄

yes

—

C₂³×C₁₀₁

D₄

yes

—

C₂³×C₁₀₁

Q₈

yes

—

C₂³×C₁₀₁

C₂³

yes

characteristic

C₂×C₄×C₁₀₁

—

C₂×C₄×C₁₀₁

—

C₂×C₄×C₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

C₂×C₄

yes

—

C₂×Dic₁₀₁

C₂×C₄

yes

—

C₂×Dic₁₀₁

D₄

yes

—

C₂²×C₁₀₁

—

C₂²×C₁₀₁

—

C₂²×C₁₀₁

—

C₂²×C₁₀₁

—

C₂²×C₁₀₁

C₄⋊C₄

yes

complemented

C₂²×C₁₀₁

C₂²×C₄

yes

characteristic

C₂²×C₁₀₁

C₂×D₄

yes

—

C₂²×C₁₀₁

C₂×D₄

yes

characteristic

C₂²×C₁₀₁

C₂×Q₈

yes

characteristic

C₂²×C₁₀₁

#41

yes

—

C₄×C₁₀₁

—

Dic₁₀₁

—

Dic₁₀₁

—

Dic₁₀₁

C₂²⋊C₄

yes

complemented

C₂×C₁₀₁

—

C₂×C₁₀₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₁₀₁

C₂×C₄⋊C₄

yes

C₂×C₁₀₁

yes

C₂×C₁₀₁

yes

—

C₂×C₁₀₁

C₂²⋊Q₈

yes

—

C₁₀₁

#380

yes

characteristic, complemented, Sylow

#380

—

101

maximal, Sylow

C₂³×C₄

—

101

—

C₂×C₄⋊C₄

—

101

—

C₂×C₂²⋊C₄

—

101

—

C₂×C₂²⋊C₄

D₁₀₁

yes

characteristic

#95

—

101

—

C₂⁴

C₂×D₁₀₁

yes

characteristic

C₂²×C₄

—

101

—

C₂²×C₄

—

101

—

C₂²×C₄

—

101

—

C₂²×C₄

—

101

—

C₂²×C₄

—

202

—

C₂²×C₄

C₂×D₁₀₁

yes

—

C₄⋊C₄

—

202

—

C₂²⋊C₄

—

C₂²⋊C₄

—

202

—

C₂³

—

C₂³

—

C₂³

Dic₂₀₂

yes

—

C₂³

C₄×D₁₀₁

yes

—

C₂³

C₂²⋊D₁₀₁

yes

—

C₂³

C₂²×D₁₀₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

101

—

C₂×C₄

—

101

—

C₂×C₄

—

101

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#13108053

yes

complemented

C₂²

C₂×C₄×D₁₀₁

yes

characteristic

C₂²

D₄×D₁₀₁

yes

—

C₂²

C₂×C₂²⋊D₁₀₁

yes

characteristic

C₂²

C₂×Dic₂₀₂

yes

characteristic

C₂²

#13108073

yes

—

C₄

—

C₄

—

101

—

C₄

—

404

—

100

C₄

—

202

—

101

C₂

—

102

C₂

C₂²⋊C₄×D₁₀₁

yes

characteristic

103

C₂

C₂×#13108053

yes

characteristic

104

C₂

#15692211

yes

characteristic

105

C₂

#15692227

yes

—

106

C₂

#15692232

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₀₁
commutator	C₂²×C₁₀₁	C₂²×C₄
Fitting	C₂×C₂²⋊C₄×C₁₀₁	C₂
socle	C₂³×C₁₀₁	C₂³
hypercenter	C₂×C₂²⋊C₄	D₁₀₁
hypocenter	C₁₀₁	#380
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₂²⋊C₄

subgroup

G/H

center, Frattini

C₂³

C₂²×D₁₀₁

commutator

C₂²×C₁₀₁

C₂²×C₄

Fitting

C₂×C₂²⋊C₄×C₁₀₁

C₂

socle

C₂³×C₁₀₁

C₂³

hypercenter

C₂×C₂²⋊C₄

D₁₀₁

C₁₀₁

G ▷ C₂²×C₁₀₁ ▷ C₁₀₁

C₁ ◁ C₂³ ◁ C₂×C₂²⋊C₄

N	H ≅ G/N	type
2. C₂×#13108053	C₂	semidirect
4. #15692162	C₂	semidirect
7. C₂²×Dic₁₀₁	C₄	semidirect
37. C₂²×C₁₀₁	C₄⋊C₄	semidirect
46. Dic₁₀₁	C₂²⋊C₄	semidirect
53. C₁₀₁	#380	semidirect
91. C₂²	#13108053	semidirect

H ≅ G/N

type

2. C₂×#13108053

C₂

semidirect

4. #15692162

C₂

semidirect

7. C₂²×Dic₁₀₁

C₄

semidirect

37. C₂²×C₁₀₁

C₄⋊C₄

semidirect

46. Dic₁₀₁

C₂²⋊C₄

semidirect

53. C₁₀₁

#380

semidirect

91. C₂²

#13108053

semidirect

Subgroups — #20265035

Conjugacy classes of subgroups

Complements