Group #20244564 — subgroups

Subgroups — #20244564

Order 6016.

278 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 67 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×#13093938	C₂	1	3	yes	maximal
2	#15688889	C₂	1	3	yes	maximal, complemented
3	C₄₇×#543	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
5	C₂×C₂²⋊Dic₄₇	C₂²	1	3	yes	—
6	#13093938	—	2	6	no	—
7	C₂²⋊Q₈×C₄₇	—	2	6	no	—
8	C₂×C₂²⋊C₄×C₄₇	C₂²	1	3	yes	—
9	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
10	C₂³×D₄₇	Q₈	1	1	yes	characteristic, complemented
11	C₂×Q₈×C₄₇	—	2	2	no	—
12	C₂²×C₄×C₄₇	—	2	3	no	—
13	C₂×C₂²⋊D₄₇	—	2	3	no	—
14	C₂×C₂²⋊D₄₇	—	2	3	no	—
15	C₂²×Dic₄₇	—	2	3	no	—
16	C₂²×Dic₄₇	Q₈	1	1	yes	characteristic, complemented
17	C₄⋊C₄×C₄₇	—	2	6	no	—
18	C₂²⋊C₄×C₄₇	—	2	3	no	—
19	C₂²⋊C₄×C₄₇	D₄	1	6	yes	—
20	C₂²⋊Dic₄₇	—	2	3	no	—
21	C₂²⋊Dic₄₇	—	2	3	no	—
22	C₂³×C₄₇	—	8	1	no	—
23	C₂³×C₄₇	C₂×D₄	1	3	yes	—
24	C₂³×C₄₇	C₂×Q₈	1	1	yes	characteristic
25	C₂³×C₄₇	#41	1	3	yes	—
26	C₂²×D₄₇	—	2	3	no	—
27	C₂²×D₄₇	—	8	1	no	—
28	Q₈×C₄₇	—	8	2	no	—
29	C₂×C₄×C₄₇	—	2	6	no	—
30	C₂×C₄×C₄₇	—	8	3	no	—
31	C₂²⋊D₄₇	—	4	1	no	—
32	C₂²⋊D₄₇	—	4	3	no	—
33	C₂×Dic₄₇	—	2	3	no	—
34	C₂×Dic₄₇	—	4	3	no	—
35	C₂×Dic₄₇	—	8	3	no	—
36	C₂²×C₄₇	—	4	3	no	—
37	C₂²×C₄₇	—	4	3	no	—
38	C₂²×C₄₇	—	4	1	no	—
39	C₂²×C₄₇	#120	1	1	yes	characteristic
40	C₂²×C₄₇	C₂²⋊Q₈	1	3	yes	—
41	C₂²×C₄₇	#124	1	3	yes	—
42	C₂×D₄₇	—	4	1	no	—
43	C₂×D₄₇	—	8	3	no	—
44	C₄×C₄₇	—	4	6	no	—
45	Dic₄₇	—	4	1	no	—
46	Dic₄₇	—	8	3	no	—
47	#2032	—	47	1	no	maximal, Sylow
48	C₂×C₄₇	—	2	3	no	—
49	C₂×C₄₇	—	2	1	no	—
50	C₂×C₄₇	—	2	3	no	—
51	C₂×C₄₇	#393	1	1	yes	characteristic
52	D₄₇	—	8	1	no	—
53	#543	D₄₇	1	1	yes	characteristic, complemented
54	C₂×#99	—	47	3	no	—
55	#342	—	47	3	no	—
56	C₄₇	#2032	1	1	yes	characteristic, complemented, Sylow
57	C₂²×D₄	—	47	1	no	—
58	C₂²⋊Q₈	—	2	6	no	—
59	C₂×C₂²⋊C₄	—	47	3	no	—
60	C₂×C₂²⋊C₄	C₂×D₄₇	1	3	yes	—
61	#99	—	94	6	no	—
62	C₂⁴	—	47	1	no	—
63	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
64	C₂×Q₈	—	2	2	no	—
65	C₂×D₄	—	94	3	no	—
66	C₂×D₄	—	94	3	no	—
67	C₂²×C₄	—	2	3	no	—
68	C₂²×C₄	—	47	1	no	—
69	C₂²×C₄	—	94	3	no	—
70	C₄⋊C₄	—	2	6	no	—
71	C₂²⋊C₄	—	2	3	no	—
72	C₂²⋊C₄	—	94	3	no	—
73	C₂²⋊C₄	—	94	3	no	—
74	C₂²⋊C₄	C₂²⋊D₄₇	1	6	yes	—
75	C₂³	—	8	1	no	—
76	C₂³	—	94	3	no	—
77	C₂³	—	376	1	no	—
78	C₂³	Q₈×D₄₇	1	1	yes	characteristic
79	C₂³	#10625354	1	3	yes	—
80	C₂³	C₂×C₂²⋊D₄₇	1	3	yes	—
81	Q₈	—	8	2	no	—
82	D₄	—	188	1	no	—
83	D₄	—	188	3	no	—
84	C₂×C₄	—	2	6	no	—
85	C₂×C₄	—	8	3	no	—
86	C₂×C₄	—	94	3	no	—
87	C₂×C₄	—	376	3	no	—
88	C₂×C₄	—	188	3	no	—
89	C₂²	—	4	3	no	—
90	C₂²	—	4	3	no	—
91	C₂²	—	4	1	no	—
92	C₂²	—	376	3	no	—
93	C₂²	—	188	1	no	—
94	C₂²	#13093993	1	1	yes	characteristic
95	C₂²	#13094000	1	3	yes	—
96	C₂²	#13094013	1	3	yes	—
97	C₄	—	4	6	no	—
98	C₄	—	376	3	no	—
99	C₄	—	188	1	no	—
100	C₂	—	2	1	no	—
101	C₂	—	2	3	no	—
102	C₂	—	2	3	no	—
103	C₂	—	376	1	no	—
104	C₂	#15689034	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093938

C₂

yes

maximal

#15688889

C₂

yes

maximal, complemented

C₄₇×#543

C₂

yes

maximal, characteristic, complemented

C₂²×C₂²⋊D₄₇

C₂²

yes

characteristic

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

#13093938

—

C₂²⋊Q₈×C₄₇

—

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂³×D₄₇

Q₈

yes

characteristic, complemented

C₂×Q₈×C₄₇

—

C₂²×C₄×C₄₇

—

C₂×C₂²⋊D₄₇

—

C₂×C₂²⋊D₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

Q₈

yes

characteristic, complemented

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

D₄

yes

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂×Q₈

yes

characteristic

C₂³×C₄₇

#41

yes

—

C₂²×D₄₇

—

C₂²×D₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂²⋊D₄₇

—

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#120

yes

characteristic

C₂²×C₄₇

C₂²⋊Q₈

yes

—

C₂²×C₄₇

#124

yes

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

#2032

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#393

yes

characteristic

D₄₇

—

#543

D₄₇

yes

characteristic, complemented

C₂×#99

—

#342

—

C₄₇

#2032

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂²⋊Q₈

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₇

yes

—

#99

—

C₂⁴

—

C₂⁴

C₂²×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

C₂²⋊D₄₇

yes

—

C₂³

—

C₂³

—

C₂³

—

376

—

C₂³

Q₈×D₄₇

yes

characteristic

C₂³

#10625354

yes

—

C₂³

C₂×C₂²⋊D₄₇

yes

—

Q₈

—

D₄

—

188

—

D₄

—

188

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

376

—

C₂×C₄

—

188

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

376

—

C₂²

—

188

—

C₂²

#13093993

yes

characteristic

C₂²

#13094000

yes

—

C₂²

#13094013

yes

—

C₄

—

C₄

—

376

—

C₄

—

188

—

100

C₂

—

101

C₂

—

102

C₂

—

103

C₂

—

376

—

104

C₂

#15689034

yes

characteristic

	subgroup	G/H
center	C₂	#15689034
commutator	C₂⁴×C₄₇	C₂³
Frattini	C₂⁴	C₂²×D₄₇
Fitting	C₄₇×#543	C₂
socle	C₂×C₄₇	#393
hypercenter	#543	D₄₇
hypocenter	C₄₇	#2032
LCS	G ▷ C₂⁴×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ #543

subgroup

G/H

center

C₂

#15689034

commutator

C₂⁴×C₄₇

C₂³

Frattini

C₂⁴

C₂²×D₄₇

Fitting

C₄₇×#543

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂⁴×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂⁴ ◁ #543

N	H ≅ G/N	type
2. #15688889	C₂	semidirect
3. C₄₇×#543	C₂	semidirect
10. C₂³×D₄₇	Q₈	semidirect
16. C₂²×Dic₄₇	Q₈	semidirect
53. #543	D₄₇	semidirect
56. C₄₇	#2032	semidirect

H ≅ G/N

type

2. #15688889

C₂

semidirect

3. C₄₇×#543

C₂

semidirect

10. C₂³×D₄₇

Q₈

semidirect

16. C₂²×Dic₄₇

Q₈

semidirect

53. #543

D₄₇

semidirect

56. C₄₇

#2032

semidirect

Subgroups — #20244564

Conjugacy classes of subgroups

Complements