Group #46830751 — subgroups

Subgroups — #46830751

Order 34624.

270 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 111 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×#22575836	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₁₀₈₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#31772628	C₂	1	2	yes	maximal, complemented
4	#31772616	C₂	1	2	yes	maximal, complemented
5	#31772612	C₂	1	4	yes	maximal, complemented
6	#31772608	C₂	1	4	yes	maximal, complemented
7	#117×C₅₄₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#22575836	—	2	4	no	—
9	C₂×Dic₁₀₈₂	—	2	4	no	—
10	C₂×Dic₁₀₈₂	C₂²	1	2	yes	—
11	C₂×Dic₁₀₈₂	C₂²	1	2	yes	—
12	C₂×Dic₁₀₈₂	C₂²	1	1	yes	characteristic
13	C₂×D₂₁₆₄	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊D₅₄₁	C₂²	1	2	yes	—
15	C₂²×Dic₅₄₁	C₂²	1	2	yes	—
16	C₂×C₄×D₅₄₁	C₂²	1	2	yes	—
17	C₄⋊Dic₅₄₁	C₂²	1	8	yes	—
18	#22575813	C₂²	1	8	yes	—
19	C₂²×C₄×C₅₄₁	C₂²	1	1	yes	characteristic
20	C₄⋊C₄×C₅₄₁	C₂²	1	2	yes	—
21	C₂²⋊C₄×C₅₄₁	C₂²	1	2	yes	—
22	C₄²×C₅₄₁	C₂²	1	2	yes	—
23	C₂²×D₅₄₁	C₂³	1	2	yes	—
24	Dic₁₀₈₂	—	2	4	no	—
25	Dic₁₀₈₂	—	2	4	no	—
26	Dic₁₀₈₂	—	2	2	no	—
27	D₂₁₆₄	—	2	2	no	—
28	C₂²⋊D₅₄₁	—	2	4	no	—
29	C₂×Dic₅₄₁	—	2	4	no	—
30	C₂×Dic₅₄₁	C₂³	1	4	yes	—
31	C₂×Dic₅₄₁	C₂³	1	2	yes	—
32	C₄×D₅₄₁	—	2	4	no	—
33	C₂³×C₅₄₁	C₂³	1	1	yes	characteristic
34	C₂×C₄×C₅₄₁	D₄	1	4	yes	—
35	C₂×C₄×C₅₄₁	C₂³	1	4	yes	—
36	C₂×C₄×C₅₄₁	C₂³	1	1	yes	characteristic
37	C₂×C₄×C₅₄₁	C₂³	1	1	yes	characteristic
38	C₂²×C₅₄₁	—	2	2	no	—
39	C₂²×C₅₄₁	C₂×D₄	1	2	yes	—
40	C₂²×C₅₄₁	C₂⁴	1	1	yes	characteristic
41	C₂×D₅₄₁	—	2	2	no	—
42	C₂×D₅₄₁	—	2	4	no	—
43	C₄×C₅₄₁	—	2	4	no	—
44	C₄×C₅₄₁	C₂×D₄	1	2	yes	—
45	C₄×C₅₄₁	C₂×D₄	1	2	yes	—
46	Dic₅₄₁	—	2	2	no	—
47	Dic₅₄₁	—	2	4	no	—
48	C₂×C₅₄₁	—	2	2	no	—
49	C₂×C₅₄₁	C₂²×D₄	1	1	yes	characteristic
50	C₂×C₅₄₁	2₋¹⁺⁴	1	2	yes	—
51	D₅₄₁	—	4	2	no	—
52	C₅₄₁	#536	1	1	yes	characteristic, complemented, Sylow
53	#536	—	541	1	no	maximal, Sylow
54	C₂×#41	—	541	1	no	—
55	C₂²×Q₈	—	541	1	no	—
56	C₄⋊Q₈	—	541	2	no	—
57	#124	—	541	2	no	—
58	#123	—	541	4	no	—
59	C₂²⋊Q₈	—	541	4	no	—
60	#117	D₅₄₁	1	1	yes	characteristic, complemented
61	#41	—	1082	4	no	—
62	C₂×Q₈	—	541	2	no	—
63	C₂×Q₈	—	541	2	no	—
64	C₂×Q₈	—	541	1	no	—
65	C₂×Q₈	—	1082	4	no	—
66	C₂×D₄	—	541	2	no	—
67	C₂×D₄	—	541	1	no	—
68	C₂²×C₄	—	541	2	no	—
69	C₂²×C₄	—	541	2	no	—
70	C₂²×C₄	C₂×D₅₄₁	1	1	yes	characteristic
71	C₄⋊C₄	—	541	8	no	—
72	C₄⋊C₄	C₂×D₅₄₁	1	2	yes	—
73	C₂²⋊C₄	—	541	8	no	—
74	C₂²⋊C₄	C₂×D₅₄₁	1	2	yes	—
75	C₄²	C₂×D₅₄₁	1	2	yes	—
76	C₂³	—	541	2	no	—
77	C₂³	C₂²×D₅₄₁	1	1	yes	characteristic
78	Q₈	—	1082	4	no	—
79	Q₈	—	1082	4	no	—
80	Q₈	—	1082	2	no	—
81	D₄	—	1082	4	no	—
82	D₄	—	1082	2	no	—
83	C₂×C₄	—	541	4	no	—
84	C₂×C₄	—	541	2	no	—
85	C₂×C₄	—	1082	4	no	—
86	C₂×C₄	—	1082	4	no	—
87	C₂×C₄	D₂₁₆₄	1	4	yes	—
88	C₂×C₄	C₂²×D₅₄₁	1	4	yes	—
89	C₂×C₄	C₂²×D₅₄₁	1	1	yes	characteristic
90	C₂×C₄	C₂²×D₅₄₁	1	1	yes	characteristic
91	C₂²	—	2	2	no	—
92	C₂²	—	1082	4	no	—
93	C₂²	—	1082	2	no	—
94	C₂²	C₂×D₂₁₆₄	1	2	yes	—
95	C₂²	C₂³×D₅₄₁	1	1	yes	characteristic
96	C₄	—	2	4	no	—
97	C₄	—	1082	2	no	—
98	C₄	—	1082	4	no	—
99	C₄	C₂×D₂₁₆₄	1	2	yes	—
100	C₄	C₂×D₂₁₆₄	1	2	yes	—
101	C₂	—	2	2	no	—
102	C₂	—	2164	2	no	—
103	C₂	C₂²×D₂₁₆₄	1	1	yes	characteristic
104	C₂	#31772675	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#22575836

C₂

yes

maximal, characteristic

C₂²×Dic₁₀₈₂

C₂

yes

maximal, characteristic, complemented

#31772628

C₂

yes

maximal, complemented

#31772616

C₂

yes

maximal, complemented

#31772612

C₂

yes

maximal, complemented

#31772608

C₂

yes

maximal, complemented

#117×C₅₄₁

C₂

yes

maximal, characteristic, complemented

#22575836

—

C₂×Dic₁₀₈₂

—

C₂×Dic₁₀₈₂

C₂²

yes

—

C₂×Dic₁₀₈₂

C₂²

yes

—

C₂×Dic₁₀₈₂

C₂²

yes

characteristic

C₂×D₂₁₆₄

C₂²

yes

characteristic

C₂×C₂²⋊D₅₄₁

C₂²

yes

—

C₂²×Dic₅₄₁

C₂²

yes

—

C₂×C₄×D₅₄₁

C₂²

yes

—

C₄⋊Dic₅₄₁

C₂²

yes

—

#22575813

C₂²

yes

—

C₂²×C₄×C₅₄₁

C₂²

yes

characteristic

C₄⋊C₄×C₅₄₁

C₂²

yes

—

C₂²⋊C₄×C₅₄₁

C₂²

yes

—

C₄²×C₅₄₁

C₂²

yes

—

C₂²×D₅₄₁

C₂³

yes

—

Dic₁₀₈₂

—

Dic₁₀₈₂

—

Dic₁₀₈₂

—

D₂₁₆₄

—

C₂²⋊D₅₄₁

—

C₂×Dic₅₄₁

—

C₂×Dic₅₄₁

C₂³

yes

—

C₂×Dic₅₄₁

C₂³

yes

—

C₄×D₅₄₁

—

C₂³×C₅₄₁

C₂³

yes

characteristic

C₂×C₄×C₅₄₁

D₄

yes

—

C₂×C₄×C₅₄₁

C₂³

yes

—

C₂×C₄×C₅₄₁

C₂³

yes

characteristic

C₂×C₄×C₅₄₁

C₂³

yes

characteristic

C₂²×C₅₄₁

—

C₂²×C₅₄₁

C₂×D₄

yes

—

C₂²×C₅₄₁

C₂⁴

yes

characteristic

C₂×D₅₄₁

—

C₂×D₅₄₁

—

C₄×C₅₄₁

—

C₄×C₅₄₁

C₂×D₄

yes

—

C₄×C₅₄₁

C₂×D₄

yes

—

Dic₅₄₁

—

Dic₅₄₁

—

C₂×C₅₄₁

—

C₂×C₅₄₁

C₂²×D₄

yes

characteristic

C₂×C₅₄₁

2₋¹⁺⁴

yes

—

D₅₄₁

—

C₅₄₁

#536

yes

characteristic, complemented, Sylow

#536

—

541

maximal, Sylow

C₂×#41

—

541

—

C₂²×Q₈

—

541

—

C₄⋊Q₈

—

541

—

#124

—

541

—

#123

—

541

—

C₂²⋊Q₈

—

541

—

#117

D₅₄₁

yes

characteristic, complemented

#41

—

1082

—

C₂×Q₈

—

541

—

C₂×Q₈

—

541

—

C₂×Q₈

—

541

—

C₂×Q₈

—

1082

—

C₂×D₄

—

541

—

C₂×D₄

—

541

—

C₂²×C₄

—

541

—

C₂²×C₄

—

541

—

C₂²×C₄

C₂×D₅₄₁

yes

characteristic

C₄⋊C₄

—

541

—

C₄⋊C₄

C₂×D₅₄₁

yes

—

C₂²⋊C₄

—

541

—

C₂²⋊C₄

C₂×D₅₄₁

yes

—

C₄²

C₂×D₅₄₁

yes

—

C₂³

—

541

—

C₂³

C₂²×D₅₄₁

yes

characteristic

Q₈

—

1082

—

Q₈

—

1082

—

Q₈

—

1082

—

D₄

—

1082

—

D₄

—

1082

—

C₂×C₄

—

541

—

C₂×C₄

—

541

—

C₂×C₄

—

1082

—

C₂×C₄

—

1082

—

C₂×C₄

D₂₁₆₄

yes

—

C₂×C₄

C₂²×D₅₄₁

yes

—

C₂×C₄

C₂²×D₅₄₁

yes

characteristic

C₂×C₄

C₂²×D₅₄₁

yes

characteristic

C₂²

—

C₂²

—

1082

—

C₂²

—

1082

—

C₂²

C₂×D₂₁₆₄

yes

—

C₂²

C₂³×D₅₄₁

yes

characteristic

C₄

—

C₄

—

1082

—

C₄

—

1082

—

C₄

C₂×D₂₁₆₄

yes

—

100

C₄

C₂×D₂₁₆₄

yes

—

101

C₂

—

102

C₂

—

2164

—

103

C₂

C₂²×D₂₁₆₄

yes

characteristic

104

C₂

#31772675

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₅₄₁
commutator, socle, cosocle	C₂²×C₅₄₁	C₂⁴
Fitting	#117×C₅₄₁	C₂
prime radical	C₂×#22575836	C₂
hypercenter	#117	D₅₄₁
hypocenter	C₅₄₁	#536
LCS	G ▷ C₂²×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₂² ◁ #117

subgroup

G/H

center, Frattini

C₂²

C₂³×D₅₄₁

commutator, socle, cosocle

C₂²×C₅₄₁

C₂⁴

Fitting

#117×C₅₄₁

C₂

C₂

D₅₄₁

C₅₄₁

G ▷ C₂²×C₅₄₁ ▷ C₅₄₁

C₁ ◁ C₂² ◁ #117

N	H ≅ G/N	type
2. C₂²×Dic₁₀₈₂	C₂	semidirect
3. #31772628	C₂	semidirect
4. #31772616	C₂	semidirect
5. #31772612	C₂	semidirect
6. #31772608	C₂	semidirect
7. #117×C₅₄₁	C₂	semidirect
52. C₅₄₁	#536	semidirect
60. #117	D₅₄₁	semidirect

H ≅ G/N

type

2. C₂²×Dic₁₀₈₂

C₂

semidirect

3. #31772628

C₂

semidirect

4. #31772616

C₂

semidirect

5. #31772612

C₂

semidirect

6. #31772608

C₂

semidirect

7. #117×C₅₄₁

C₂

semidirect

52. C₅₄₁

#536

semidirect

60. #117

D₅₄₁

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#22575836	2
C₂²×Dic₁₀₈₂	2
#31772628	2
#31772616	2
#31772612	2
#31772608	2
#117×C₅₄₁	2
#536	541

subgroup

index

C₂²×Dic₁₀₈₂

#117×C₅₄₁

541

Subgroups — #46830751

Conjugacy classes of subgroups

Complements

Maximal subgroups