Group #20265672 — subgroups

Subgroups — C₂×#15692231 #20265672

Order 6464.

322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 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	C₂²×C₄×D₁₀₁	C₂	1	1	yes	maximal, characteristic
2	#15692231	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊Dic₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#13108053	C₂	1	2	yes	maximal, complemented
5	C₂×#13108051	C₂	1	2	yes	maximal
6	C₂²×Q₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₁₀₁	C₂²	1	1	yes	characteristic
8	C₂²×Dic₁₀₁	C₂²	1	1	yes	characteristic
9	C₂²×Dic₁₀₁	C₂²	1	2	yes	—
10	C₂×C₄×D₁₀₁	—	2	4	no	—
11	C₂×C₄×D₁₀₁	C₂²	1	4	yes	—
12	C₄⋊Dic₁₀₁	C₂²	1	4	yes	complemented
13	#13108053	C₂²	1	8	yes	complemented
14	#13108051	C₂²	1	8	yes	—
15	C₂×Q₈×C₁₀₁	—	2	4	no	—
16	C₂×Q₈×C₁₀₁	C₂²	1	4	yes	complemented
17	C₂²×C₄×C₁₀₁	C₂²	1	2	yes	—
18	C₂²×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
19	C₂³×C₁₀₁	C₂³	1	1	yes	characteristic
20	C₂²×D₁₀₁	—	2	2	no	—
21	C₂²×D₁₀₁	—	2	2	no	—
22	C₂²×D₁₀₁	Q₈	1	4	yes	complemented
23	C₂²×D₁₀₁	C₂³	1	2	yes	—
24	Q₈×C₁₀₁	—	2	8	no	—
25	C₂×C₄×C₁₀₁	—	2	4	no	—
26	C₂×C₄×C₁₀₁	D₄	1	4	yes	—
27	C₂×C₄×C₁₀₁	C₂³	1	4	yes	—
28	C₂×C₄×C₁₀₁	C₂³	1	2	yes	—
29	C₂×Dic₁₀₁	—	2	2	no	—
30	C₂×Dic₁₀₁	—	2	4	no	—
31	C₂×Dic₁₀₁	C₂³	1	4	yes	—
32	C₂×Dic₁₀₁	C₂³	1	2	yes	—
33	C₄×D₁₀₁	—	2	8	no	—
34	C₂²×C₁₀₁	C₂×D₄	1	2	yes	—
35	C₂²×C₁₀₁	C₂×Q₈	1	2	yes	—
36	C₂²×C₁₀₁	#41	1	2	yes	—
37	C₂²×C₁₀₁	C₂⁴	1	1	yes	characteristic
38	C₂×D₁₀₁	—	2	8	no	—
39	C₂×D₁₀₁	—	2	2	no	—
40	C₂×D₁₀₁	—	2	2	no	—
41	C₂×D₁₀₁	C₂×Q₈	1	4	yes	complemented
42	C₄×C₁₀₁	—	2	4	no	—
43	C₄×C₁₀₁	C₂×D₄	1	4	yes	—
44	Dic₁₀₁	—	2	2	no	—
45	Dic₁₀₁	—	2	4	no	—
46	C₂×C₁₀₁	C₂²⋊Q₈	1	4	yes	complemented
47	C₂×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
48	C₂×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
49	C₂×C₁₀₁	C₂×#41	1	1	yes	characteristic
50	D₁₀₁	—	2	4	no	—
51	C₁₀₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₂²⋊Q₈	—	101	1	no	maximal, Sylow
53	C₂²×Q₈	D₁₀₁	1	1	yes	characteristic, complemented
54	C₂³×C₄	—	101	1	no	—
55	C₂²⋊Q₈	—	101	8	no	—
56	C₂×C₄⋊C₄	—	101	2	no	—
57	C₂×C₄⋊C₄	—	101	1	no	—
58	C₂×C₂²⋊C₄	—	101	2	no	—
59	C₂⁴	—	101	1	no	—
60	C₂×Q₈	—	2	4	no	—
61	C₂×Q₈	C₂×D₁₀₁	1	4	yes	complemented
62	C₂²×C₄	—	101	2	no	—
63	C₂²×C₄	—	101	1	no	—
64	C₂²×C₄	—	101	4	no	—
65	C₂²×C₄	—	202	4	no	—
66	C₂²×C₄	C₂×D₁₀₁	1	2	yes	—
67	C₂²×C₄	C₂×D₁₀₁	1	1	yes	characteristic
68	C₄⋊C₄	—	101	8	no	—
69	C₄⋊C₄	—	101	4	no	—
70	C₂²⋊C₄	—	101	8	no	—
71	C₂³	—	101	4	no	—
72	C₂³	—	101	2	no	—
73	C₂³	—	202	2	no	—
74	C₂³	—	202	2	no	—
75	C₂³	C₂²×D₁₀₁	1	1	yes	characteristic
76	Q₈	—	2	8	no	—
77	C₂×C₄	—	2	4	no	—
78	C₂×C₄	—	101	4	no	—
79	C₂×C₄	—	101	2	no	—
80	C₂×C₄	—	202	2	no	—
81	C₂×C₄	—	202	4	no	—
82	C₂×C₄	—	202	8	no	—
83	C₂×C₄	C₂²⋊D₁₀₁	1	4	yes	—
84	C₂×C₄	C₂²×D₁₀₁	1	4	yes	—
85	C₂×C₄	C₂²×D₁₀₁	1	2	yes	—
86	C₂²	—	101	4	no	—
87	C₂²	—	202	2	no	—
88	C₂²	—	202	2	no	—
89	C₂²	—	202	8	no	—
90	C₂²	C₂×C₂²⋊D₁₀₁	1	2	yes	—
91	C₂²	Q₈×D₁₀₁	1	2	yes	—
92	C₂²	#13108075	1	2	yes	—
93	C₂²	C₂³×D₁₀₁	1	1	yes	characteristic
94	C₄	—	2	4	no	—
95	C₄	—	202	2	no	—
96	C₄	—	202	4	no	—
97	C₄	C₂×C₂²⋊D₁₀₁	1	4	yes	—
98	C₂	—	202	4	no	—
99	C₂	#15692231	1	4	yes	direct product factor
100	C₂	C₂²×C₂²⋊D₁₀₁	1	1	yes	characteristic
101	C₂	C₂×Q₈×D₁₀₁	1	1	yes	characteristic
102	C₂	C₂×#13108075	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄×D₁₀₁

C₂

yes

maximal, characteristic

#15692231

C₂

yes

maximal, direct product factor

C₂×C₄⋊Dic₁₀₁

C₂

yes

maximal, characteristic, complemented

C₂×#13108053

C₂

yes

maximal, complemented

C₂×#13108051

C₂

yes

maximal

C₂²×Q₈×C₁₀₁

C₂

yes

maximal, characteristic, complemented

C₂³×D₁₀₁

C₂²

yes

characteristic

C₂²×Dic₁₀₁

C₂²

yes

characteristic

C₂²×Dic₁₀₁

C₂²

yes

—

C₂×C₄×D₁₀₁

—

C₂×C₄×D₁₀₁

C₂²

yes

—

C₄⋊Dic₁₀₁

C₂²

yes

complemented

#13108053

C₂²

yes

complemented

#13108051

C₂²

yes

—

C₂×Q₈×C₁₀₁

—

C₂×Q₈×C₁₀₁

C₂²

yes

complemented

C₂²×C₄×C₁₀₁

C₂²

yes

—

C₂²×C₄×C₁₀₁

C₂²

yes

characteristic

C₂³×C₁₀₁

C₂³

yes

characteristic

C₂²×D₁₀₁

—

C₂²×D₁₀₁

—

C₂²×D₁₀₁

Q₈

yes

complemented

C₂²×D₁₀₁

C₂³

yes

—

Q₈×C₁₀₁

—

C₂×C₄×C₁₀₁

—

C₂×C₄×C₁₀₁

D₄

yes

—

C₂×C₄×C₁₀₁

C₂³

yes

—

C₂×C₄×C₁₀₁

C₂³

yes

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

C₂³

yes

—

C₂×Dic₁₀₁

C₂³

yes

—

C₄×D₁₀₁

—

C₂²×C₁₀₁

C₂×D₄

yes

—

C₂²×C₁₀₁

C₂×Q₈

yes

—

C₂²×C₁₀₁

#41

yes

—

C₂²×C₁₀₁

C₂⁴

yes

characteristic

C₂×D₁₀₁

—

C₂×D₁₀₁

—

C₂×D₁₀₁

—

C₂×D₁₀₁

C₂×Q₈

yes

complemented

C₄×C₁₀₁

—

C₄×C₁₀₁

C₂×D₄

yes

—

Dic₁₀₁

—

Dic₁₀₁

—

C₂×C₁₀₁

C₂²⋊Q₈

yes

complemented

C₂×C₁₀₁

C₂²×D₄

yes

characteristic

C₂×C₁₀₁

C₂²×Q₈

yes

characteristic

C₂×C₁₀₁

C₂×#41

yes

characteristic

D₁₀₁

—

C₁₀₁

C₂×C₂²⋊Q₈

yes

characteristic, complemented, Sylow

C₂×C₂²⋊Q₈

—

101

maximal, Sylow

C₂²×Q₈

D₁₀₁

yes

characteristic, complemented

C₂³×C₄

—

101

—

C₂²⋊Q₈

—

101

—

C₂×C₄⋊C₄

—

101

—

C₂×C₄⋊C₄

—

101

—

C₂×C₂²⋊C₄

—

101

—

C₂⁴

—

101

—

C₂×Q₈

—

C₂×Q₈

C₂×D₁₀₁

yes

complemented

C₂²×C₄

—

101

—

C₂²×C₄

—

101

—

C₂²×C₄

—

101

—

C₂²×C₄

—

202

—

C₂²×C₄

C₂×D₁₀₁

yes

—

C₂²×C₄

C₂×D₁₀₁

yes

characteristic

C₄⋊C₄

—

101

—

C₄⋊C₄

—

101

—

C₂²⋊C₄

—

101

—

C₂³

—

101

—

C₂³

—

101

—

C₂³

—

202

—

C₂³

—

202

—

C₂³

C₂²×D₁₀₁

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

101

—

C₂×C₄

—

101

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

C₂²⋊D₁₀₁

yes

—

C₂×C₄

C₂²×D₁₀₁

yes

—

C₂×C₄

C₂²×D₁₀₁

yes

—

C₂²

—

101

—

C₂²

—

202

—

C₂²

—

202

—

C₂²

—

202

—

C₂²

C₂×C₂²⋊D₁₀₁

yes

—

C₂²

Q₈×D₁₀₁

yes

—

C₂²

#13108075

yes

—

C₂²

C₂³×D₁₀₁

yes

characteristic

C₄

—

C₄

—

202

—

C₄

—

202

—

C₄

C₂×C₂²⋊D₁₀₁

yes

—

C₂

—

202

—

C₂

#15692231

yes

direct product factor

100

C₂

C₂²×C₂²⋊D₁₀₁

yes

characteristic

101

C₂

C₂×Q₈×D₁₀₁

yes

characteristic

102

C₂

C₂×#13108075

yes

characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₀₁
commutator	C₂²×C₁₀₁	C₂⁴
Frattini	C₂²	C₂³×D₁₀₁
Fitting	C₂²×Q₈×C₁₀₁	C₂
socle	C₂³×C₁₀₁	C₂³
hypercenter	C₂²×Q₈	D₁₀₁
hypocenter	C₁₀₁	C₂×C₂²⋊Q₈
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

subgroup

G/H

center

C₂³

C₂²×D₁₀₁

commutator

C₂²×C₁₀₁

C₂⁴

Frattini

C₂²

C₂³×D₁₀₁

Fitting

C₂²×Q₈×C₁₀₁

C₂

socle

C₂³×C₁₀₁

C₂³

hypercenter

C₂²×Q₈

D₁₀₁

hypocenter

C₁₀₁

C₂×C₂²⋊Q₈

LCS

G ▷ C₂²×C₁₀₁ ▷ C₁₀₁

UCS

C₁ ◁ C₂³ ◁ C₂²×Q₈

N	H ≅ G/N	type
2. #15692231	C₂	direct (N × H)
3. C₂×C₄⋊Dic₁₀₁	C₂	semidirect
4. C₂×#13108053	C₂	semidirect
6. C₂²×Q₈×C₁₀₁	C₂	semidirect
12. C₄⋊Dic₁₀₁	C₂²	semidirect
13. #13108053	C₂²	semidirect
16. C₂×Q₈×C₁₀₁	C₂²	semidirect
22. C₂²×D₁₀₁	Q₈	semidirect
41. C₂×D₁₀₁	C₂×Q₈	semidirect
46. C₂×C₁₀₁	C₂²⋊Q₈	semidirect
51. C₁₀₁	C₂×C₂²⋊Q₈	semidirect
53. C₂²×Q₈	D₁₀₁	semidirect
61. C₂×Q₈	C₂×D₁₀₁	semidirect
99. C₂	#15692231	direct (N × H)

H ≅ G/N

type

2. #15692231

C₂

direct (N × H)

3. C₂×C₄⋊Dic₁₀₁

C₂

semidirect

4. C₂×#13108053

C₂

semidirect

6. C₂²×Q₈×C₁₀₁

C₂

semidirect

12. C₄⋊Dic₁₀₁

C₂²

semidirect

13. #13108053

C₂²

semidirect

16. C₂×Q₈×C₁₀₁

C₂²

semidirect

22. C₂²×D₁₀₁

Q₈

semidirect

41. C₂×D₁₀₁

C₂×Q₈

semidirect

46. C₂×C₁₀₁

C₂²⋊Q₈

semidirect

51. C₁₀₁

C₂×C₂²⋊Q₈

semidirect

53. C₂²×Q₈

D₁₀₁

semidirect

61. C₂×Q₈

C₂×D₁₀₁

semidirect

99. C₂

#15692231

direct (N × H)

Subgroups — C₂×#15692231 #20265672

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15692231 #20265672

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15692231 #20265672