Group #20245613 — subgroups

Subgroups — #20245613

Order 6016.

160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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	#15689500	C₂	1	1	yes	maximal, characteristic
2	#15688923	C₂	1	4	yes	maximal, complemented
3	C₄×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#500	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₃₇₆	—	2	1	no	—
6	C₂×D₃₇₆	C₂²	1	2	yes	—
7	#13094021	—	2	1	no	—
8	C₂×C₄₇⋊C₁₆	C₂²	1	2	yes	—
9	C₄⋊Q₈×C₄₇	—	2	1	no	—
10	#107×C₄₇	—	2	1	no	—
11	#107×C₄₇	C₂²	1	2	yes	—
12	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×Q₈×C₄₇	—	4	1	no	—
14	C₂×D₁₈₈	—	2	2	no	—
15	C₂×D₁₈₈	—	4	1	no	—
16	C₂×D₁₈₈	—	4	1	no	—
17	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
18	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₄₇	—	2	2	no	—
20	C₄⋊C₄×C₄₇	—	4	1	no	—
21	C₄²×C₄₇	D₄	1	1	yes	characteristic
22	D₃₇₆	—	2	4	no	—
23	D₃₇₆	—	4	2	no	—
24	C₄₇⋊C₁₆	—	2	2	no	—
25	C₂²×D₄₇	—	4	2	no	—
26	Q₈×C₄₇	—	8	2	no	—
27	C₂×C₄×C₄₇	—	4	2	no	—
28	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
29	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
30	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
31	D₁₈₈	—	4	2	no	—
32	D₁₈₈	—	4	2	no	—
33	D₁₈₈	—	8	2	no	—
34	D₁₈₈	—	8	2	no	—
35	C₈×C₄₇	SD₁₆	1	2	yes	—
36	C₈×C₄₇	#41	1	2	yes	—
37	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
38	C₂×D₄₇	—	8	2	no	—
39	C₂×D₄₇	—	8	2	no	—
40	C₂×D₄₇	—	8	2	no	—
41	C₄×C₄₇	—	8	2	no	—
42	C₄×C₄₇	D₁₆	1	2	yes	—
43	C₄×C₄₇	SD₃₂	1	2	yes	—
44	C₄×C₄₇	#124	1	1	yes	characteristic
45	C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
46	#2240	—	47	1	no	maximal, Sylow
47	C₂×C₄₇	#486	1	1	yes	characteristic
48	C₂×C₄₇	C₂×D₁₆	1	1	yes	characteristic
49	C₂×C₄₇	C₂×SD₃₂	1	1	yes	characteristic
50	D₄₇	—	16	2	no	—
51	#500	D₄₇	1	1	yes	characteristic, complemented
52	#493	—	47	1	no	—
53	#357	—	47	4	no	—
54	C₄×C₁₆	—	47	1	no	—
55	C₄₇	#2240	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₈	—	47	2	no	—
57	C₂×D₈	—	94	1	no	—
58	C₄⋊Q₈	—	2	1	no	—
59	#127	—	94	1	no	—
60	C₂×C₁₆	—	47	2	no	—
61	#107	—	2	1	no	—
62	#107	C₂×D₄₇	1	2	yes	—
63	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
64	C₂×Q₈	—	4	1	no	—
65	C₂×D₄	—	94	2	no	—
66	C₂×D₄	—	188	1	no	—
67	C₂×D₄	—	188	1	no	—
68	D₈	—	94	4	no	—
69	D₈	—	188	2	no	—
70	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
71	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	4	1	no	—
74	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
75	C₁₆	—	94	2	no	—
76	C₂³	—	188	2	no	—
77	Q₈	—	8	2	no	—
78	D₄	—	376	2	no	—
79	D₄	—	376	2	no	—
80	D₄	—	188	2	no	—
81	D₄	—	188	2	no	—
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	#10625334	1	1	yes	characteristic
84	C₂×C₄	#10625334	1	1	yes	characteristic
85	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
86	C₈	#10625336	1	2	yes	—
87	C₈	#10625354	1	2	yes	—
88	C₂²	—	376	2	no	—
89	C₂²	—	376	2	no	—
90	C₂²	—	376	2	no	—
91	C₂²	C₂×#10625334	1	1	yes	characteristic
92	C₄	—	8	2	no	—
93	C₄	#13093965	1	2	yes	—
94	C₄	#13093967	1	2	yes	—
95	C₄	#13094013	1	1	yes	characteristic
96	C₄	C₂×#10625336	1	1	yes	characteristic
97	C₂	—	752	2	no	—
98	C₂	#15689471	1	1	yes	characteristic
99	C₂	C₂×#13093965	1	1	yes	characteristic
100	C₂	C₂×#13093967	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689500

C₂

yes

maximal, characteristic

#15688923

C₂

yes

maximal, complemented

C₄×C₄₇⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₄₇×#500

C₂

yes

maximal, characteristic, complemented

C₂×D₃₇₆

—

C₂×D₃₇₆

C₂²

yes

—

#13094021

—

C₂×C₄₇⋊C₁₆

C₂²

yes

—

C₄⋊Q₈×C₄₇

—

#107×C₄₇

—

#107×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

D₄

yes

characteristic

D₃₇₆

—

D₃₇₆

—

C₄₇⋊C₁₆

—

C₂²×D₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

C₈×C₄₇

SD₁₆

yes

—

C₈×C₄₇

#41

yes

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

D₁₆

yes

—

C₄×C₄₇

SD₃₂

yes

—

C₄×C₄₇

#124

yes

characteristic

C₄×C₄₇

C₂×SD₁₆

yes

—

C₂×C₄₇

yes

C₂×C₄₇

C₂×D₁₆

yes

characteristic

C₂×C₄₇

C₂×SD₃₂

yes

characteristic

D₄₇

—

#500

D₄₇

yes

characteristic, complemented

#493

—

#357

—

C₄×C₁₆

—

C₄₇

#2240

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

—

#127

—

C₂×C₁₆

—

#107

—

#107

C₂×D₄₇

yes

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

188

—

C₂×D₄

—

188

—

D₈

—

D₈

—

188

—

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²⋊D₄₇

yes

characteristic

C₁₆

—

C₂³

—

188

—

Q₈

—

D₄

—

376

—

D₄

—

376

—

D₄

—

188

—

D₄

—

188

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

C₈

#10625336

yes

—

C₈

#10625354

yes

—

C₂²

—

376

—

C₂²

—

376

—

C₂²

—

376

—

C₂²

C₂×#10625334

yes

characteristic

C₄

—

C₄

#13093965

yes

—

C₄

#13093967

yes

—

C₄

yes

C₄

yes

C₂

—

752

—

C₂

yes

C₂

yes

100

C₂

C₂×#13093967

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#10625334
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#500	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	#500	D₄₇
hypocenter	C₄₇	#2240
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

subgroup

G/H

center

C₂²

C₂×#10625334

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#500

C₂

socle

C₂²×C₄₇

C₂×D₈

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

N	H ≅ G/N	type
2. #15688923	C₂	semidirect
3. C₄×C₄₇⋊C₁₆	C₂	semidirect
4. C₄₇×#500	C₂	semidirect
51. #500	D₄₇	semidirect
55. C₄₇	#2240	semidirect

H ≅ G/N

type

2. #15688923

C₂

semidirect

3. C₄×C₄₇⋊C₁₆

C₂

semidirect

4. C₄₇×#500

C₂

semidirect

51. #500

D₄₇

semidirect

55. C₄₇

#2240

semidirect

Subgroups — #20245613

Conjugacy classes of subgroups

Complements