Group #14583447 — subgroups

Subgroups — #14583447

Order 2752.

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

normal subgroups only

This group has 310 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×#10621900	C₂	1	2	yes	maximal, complemented
2	#13063325	C₂	1	1	yes	maximal, characteristic, complemented
3	#13063312	C₂	1	2	yes	maximal, complemented
4	#13063296	C₂	1	4	yes	maximal, complemented
5	D₄×Dic₄₃	C₂	1	4	yes	maximal, complemented
6	C₄²×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#127×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₄×C₄₃	C₂²	1	4	yes	—
9	C₂×D₄×C₄₃	C₂²	1	2	yes	—
10	C₂×C₂²⋊D₄₃	C₂²	1	4	yes	—
11	C₂²×Dic₄₃	C₂²	1	4	yes	—
12	#10621900	—	2	8	no	—
13	C₂×C₄×D₄₃	C₂²	1	2	yes	—
14	C₂×C₄×D₄₃	C₂²	1	1	yes	characteristic
15	C₂×Dic₈₆	C₂²	1	2	yes	—
16	C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₂²⋊Dic₄₃	C₂²	1	8	yes	—
18	C₄⋊Dic₄₃	C₂²	1	4	yes	—
19	C₄×Dic₄₃	C₂²	1	2	yes	—
20	C₄×Dic₄₃	C₂²	1	1	yes	characteristic
21	C₂³×C₄₃	C₂³	1	4	yes	—
22	C₂²×D₄₃	C₂³	1	1	yes	characteristic
23	D₄×C₄₃	—	2	4	no	—
24	D₄×C₄₃	—	2	8	no	—
25	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
26	C₂×C₄×C₄₃	C₂³	1	2	yes	—
27	C₂²⋊D₄₃	—	2	8	no	—
28	C₂×Dic₄₃	—	2	8	no	—
29	C₂×Dic₄₃	C₂³	1	2	yes	—
30	C₂×Dic₄₃	C₂³	1	4	yes	—
31	C₂×Dic₄₃	C₂³	1	1	yes	characteristic
32	C₄×D₄₃	—	2	4	no	—
33	C₄×D₄₃	D₄	1	4	yes	complemented
34	Dic₈₆	—	2	4	no	—
35	C₂²×C₄₃	—	2	4	no	—
36	C₂²×C₄₃	—	2	8	no	—
37	C₂²×C₄₃	C₂⁴	1	1	yes	characteristic
38	C₂×D₄₃	—	2	2	no	—
39	C₂×D₄₃	C₂×D₄	1	2	yes	—
40	C₄×C₄₃	C₂×D₄	1	2	yes	—
41	C₄×C₄₃	#41	1	4	yes	complemented
42	Dic₄₃	—	2	4	no	—
43	Dic₄₃	—	2	2	no	—
44	Dic₄₃	C₂×D₄	1	2	yes	—
45	C₂×C₄₃	—	4	4	no	—
46	C₂×C₄₃	C₂²×D₄	1	1	yes	characteristic
47	C₂×C₄₃	C₂×#41	1	2	yes	—
48	D₄₃	—	2	2	no	—
49	#532	—	43	1	no	maximal, Sylow
50	C₄₃	#532	1	1	yes	characteristic, complemented, Sylow
51	C₂×#41	—	43	2	no	—
52	C₄⋊Q₈	—	43	1	no	—
53	#127	D₄₃	1	1	yes	characteristic, complemented
54	#124	—	43	2	no	—
55	#121	—	43	4	no	—
56	C₄×D₄	—	43	4	no	—
57	C₂×C₄²	—	43	1	no	—
58	#41	—	86	8	no	—
59	C₂×Q₈	—	43	2	no	—
60	C₂×D₄	—	43	4	no	—
61	C₂×D₄	C₂×D₄₃	1	4	yes	—
62	C₂×D₄	C₂×D₄₃	1	2	yes	—
63	C₂²×C₄	—	43	1	no	—
64	C₂²×C₄	—	43	4	no	—
65	C₂²×C₄	—	43	2	no	—
66	C₄⋊C₄	—	43	4	no	—
67	C₂²⋊C₄	—	43	8	no	—
68	C₄²	—	43	2	no	—
69	C₄²	—	43	1	no	—
70	C₄²	C₂×D₄₃	1	1	yes	characteristic
71	C₂³	—	43	1	no	—
72	C₂³	C₂²×D₄₃	1	4	yes	—
73	Q₈	—	86	4	no	—
74	D₄	—	2	4	no	—
75	D₄	—	2	8	no	—
76	D₄	—	86	8	no	—
77	C₂×C₄	—	43	1	no	—
78	C₂×C₄	—	43	4	no	—
79	C₂×C₄	—	43	2	no	—
80	C₂×C₄	—	43	4	no	—
81	C₂×C₄	—	86	8	no	—
82	C₂×C₄	—	86	4	no	—
83	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
84	C₂×C₄	C₂²×D₄₃	1	2	yes	—
85	C₂²	—	2	4	no	—
86	C₂²	—	2	8	no	—
87	C₂²	—	43	2	no	—
88	C₂²	—	86	2	no	—
89	C₂²	C₂³×D₄₃	1	1	yes	characteristic
90	C₄	—	43	2	no	—
91	C₄	—	86	4	no	—
92	C₄	—	86	2	no	—
93	C₄	D₄×D₄₃	1	2	yes	—
94	C₄	#10621900	1	4	yes	complemented
95	C₂	—	4	4	no	—
96	C₂	—	86	2	no	—
97	C₂	C₂×D₄×D₄₃	1	1	yes	characteristic
98	C₂	C₂×#10621900	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10621900

C₂

yes

maximal, complemented

#13063325

C₂

yes

maximal, characteristic, complemented

#13063312

C₂

yes

maximal, complemented

#13063296

C₂

yes

maximal, complemented

D₄×Dic₄₃

C₂

yes

maximal, complemented

C₄²×D₄₃

C₂

yes

maximal, characteristic, complemented

#127×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂×D₄×C₄₃

C₂²

yes

—

C₂×D₄×C₄₃

C₂²

yes

—

C₂×C₂²⋊D₄₃

C₂²

yes

—

C₂²×Dic₄₃

C₂²

yes

—

#10621900

—

C₂×C₄×D₄₃

C₂²

yes

—

C₂×C₄×D₄₃

C₂²

yes

characteristic

C₂×Dic₈₆

C₂²

yes

—

C₄²×C₄₃

C₂²

yes

characteristic

C₂²⋊Dic₄₃

C₂²

yes

—

C₄⋊Dic₄₃

C₂²

yes

—

C₄×Dic₄₃

C₂²

yes

—

C₄×Dic₄₃

C₂²

yes

characteristic

C₂³×C₄₃

C₂³

yes

—

C₂²×D₄₃

C₂³

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

C₂³

yes

characteristic

C₂×C₄×C₄₃

C₂³

yes

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂³

yes

—

C₂×Dic₄₃

C₂³

yes

—

C₂×Dic₄₃

C₂³

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

D₄

yes

complemented

Dic₈₆

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂⁴

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

C₂×D₄

yes

—

C₄×C₄₃

C₂×D₄

yes

—

C₄×C₄₃

#41

yes

complemented

Dic₄₃

—

Dic₄₃

—

Dic₄₃

C₂×D₄

yes

—

C₂×C₄₃

—

C₂×C₄₃

C₂²×D₄

yes

characteristic

C₂×C₄₃

C₂×#41

yes

—

D₄₃

—

#532

—

maximal, Sylow

C₄₃

#532

yes

characteristic, complemented, Sylow

C₂×#41

—

C₄⋊Q₈

—

#127

D₄₃

yes

characteristic, complemented

#124

—

#121

—

C₄×D₄

—

C₂×C₄²

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

C₂×D₄₃

yes

—

C₂×D₄

C₂×D₄₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂×D₄₃

yes

characteristic

C₂³

—

C₂³

C₂²×D₄₃

yes

—

Q₈

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₄

C₂²×D₄₃

yes

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₂³×D₄₃

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

D₄×D₄₃

yes

—

C₄

#10621900

yes

complemented

C₂

—

C₂

—

C₂

C₂×D₄×D₄₃

yes

characteristic

C₂

C₂×#10621900

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₃
commutator, socle, cosocle	C₂²×C₄₃	C₂⁴
Fitting	#127×C₄₃	C₂
hypercenter	#127	D₄₃
hypocenter	C₄₃	#532
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #127

subgroup

G/H

center, Frattini

C₂²

C₂³×D₄₃

commutator, socle, cosocle

C₂²×C₄₃

C₂⁴

Fitting

#127×C₄₃

C₂

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂² ◁ #127

N	H ≅ G/N	type
1. C₂×#10621900	C₂	semidirect
2. #13063325	C₂	semidirect
3. #13063312	C₂	semidirect
4. #13063296	C₂	semidirect
5. D₄×Dic₄₃	C₂	semidirect
6. C₄²×D₄₃	C₂	semidirect
7. #127×C₄₃	C₂	semidirect
33. C₄×D₄₃	D₄	semidirect
41. C₄×C₄₃	#41	semidirect
50. C₄₃	#532	semidirect
53. #127	D₄₃	semidirect
94. C₄	#10621900	semidirect

H ≅ G/N

type

1. C₂×#10621900

C₂

semidirect

2. #13063325

C₂

semidirect

3. #13063312

C₂

semidirect

4. #13063296

C₂

semidirect

5. D₄×Dic₄₃

C₂

semidirect

6. C₄²×D₄₃

C₂

semidirect

7. #127×C₄₃

C₂

semidirect

33. C₄×D₄₃

D₄

semidirect

41. C₄×C₄₃

#41

semidirect

50. C₄₃

#532

semidirect

53. #127

D₄₃

semidirect

94. C₄

#10621900

semidirect

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

subgroup	index
C₂×#10621900	2
#13063325	2
#13063312	2
#13063296	2
D₄×Dic₄₃	2
C₄²×D₄₃	2
#127×C₄₃	2
#532	43

subgroup

index

D₄×Dic₄₃

C₄²×D₄₃

#127×C₄₃

#532

Subgroups — #14583447

Conjugacy classes of subgroups

Complements

Maximal subgroups