Group #20244985 — subgroups

Subgroups — #20244985

Order 6016.

184 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13093964	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#15688899	C₂	1	2	yes	maximal, complemented
4	C₄×C₄₇⋊C₁₆	C₂	1	2	yes	maximal, complemented
5	C₄₇×#405	C₂	1	1	yes	maximal, characteristic
6	#13093964	C₄	1	4	yes	complemented
7	C₂×C₄₇⋊C₁₆	C₄	1	4	yes	complemented
8	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₄₇⋊C₁₆	C₂²	1	2	yes	—
11	C₂×M₁₆×C₄₇	C₄	1	1	yes	characteristic
12	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
13	#117×C₄₇	C₄	1	1	yes	characteristic
14	#97×C₄₇	C₄	1	2	yes	—
15	C₄×C₈×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
17	M₁₆×C₄₇	C₈	1	4	yes	—
18	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
20	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
23	C₄⋊C₄×C₄₇	C₈	1	2	yes	—
24	C₂²⋊C₄×C₄₇	C₈	1	2	yes	—
25	C₄²×C₄₇	C₂×C₄	1	2	yes	—
26	C₄₇⋊C₁₆	C₂×C₄	1	2	yes	—
27	C₄₇⋊C₁₆	C₂×C₄	1	2	yes	—
28	C₄₇⋊C₁₆	C₂×C₄	1	4	yes	—
29	C₂³×C₄₇	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₄₇	C₄²	1	2	yes	—
31	C₂×C₄×C₄₇	C₂×C₈	1	4	yes	—
32	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₄₇	C₂×C₈	1	2	yes	—
34	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₄₇	C₄²	1	2	yes	—
36	C₈×C₄₇	C₂×C₈	1	4	yes	—
37	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
38	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
39	C₂²×C₄₇	—	2	2	no	—
40	C₂²×C₄₇	C₄×C₈	1	2	yes	—
41	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₄₇	—	2	4	no	—
43	C₄×C₄₇	C₄×C₈	1	2	yes	—
44	C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
45	C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
46	#2108	—	47	1	no	maximal, Sylow
47	C₂×C₄₇	—	2	2	no	—
48	C₂×C₄₇	C₂×C₄×C₈	1	1	yes	characteristic
49	C₂×C₄₇	#504	1	2	yes	—
50	C₂×M₃₂	—	47	1	no	—
51	C₂²×C₁₆	—	47	1	no	—
52	#405	D₄₇	1	1	yes	characteristic
53	#346	—	47	2	no	—
54	C₄×C₁₆	—	47	2	no	—
55	C₄₇	#2108	1	1	yes	characteristic, complemented, Sylow
56	C₂×M₁₆	Dic₄₇	1	1	yes	characteristic
57	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
58	#117	Dic₄₇	1	1	yes	characteristic
59	M₃₂	—	47	4	no	—
60	C₂×C₁₆	—	47	4	no	—
61	C₂×C₁₆	—	47	1	no	—
62	C₂×C₁₆	—	47	2	no	—
63	C₂×C₁₆	—	47	1	no	—
64	#97	Dic₄₇	1	2	yes	—
65	C₄×C₈	C₂×D₄₇	1	2	yes	—
66	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
67	M₁₆	C₄₇⋊C₈	1	4	yes	—
68	C₂×C₈	C₄×D₄₇	1	2	yes	—
69	C₂×C₈	C₄×D₄₇	1	2	yes	—
70	C₂×C₈	C₂×Dic₄₇	1	2	yes	—
71	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
73	C₄⋊C₄	C₄₇⋊C₈	1	2	yes	—
74	C₂²⋊C₄	C₄₇⋊C₈	1	2	yes	—
75	C₄²	C₂×Dic₄₇	1	2	yes	—
76	C₁₆	—	47	2	no	—
77	C₁₆	—	47	2	no	—
78	C₁₆	—	47	4	no	—
79	C₂³	C₂×C₄₇⋊C₈	1	1	yes	characteristic
80	C₂×C₄	C₂×C₄₇⋊C₈	1	4	yes	—
81	C₂×C₄	C₂×C₄₇⋊C₈	1	1	yes	characteristic
82	C₂×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
83	C₂×C₄	C₄×Dic₄₇	1	2	yes	—
84	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
85	C₈	C₂×C₄₇⋊C₈	1	4	yes	—
86	C₈	C₄×Dic₄₇	1	2	yes	—
87	C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
88	C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
89	C₂²	—	2	2	no	—
90	C₂²	C₄×C₄₇⋊C₈	1	2	yes	—
91	C₂²	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
92	C₄	—	2	4	no	—
93	C₄	C₄×C₄₇⋊C₈	1	2	yes	—
94	C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
95	C₄	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
96	C₂	—	2	2	no	—
97	C₂	C₂×C₄×C₄₇⋊C₈	1	1	yes	characteristic
98	C₂	#15689540	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093964

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₁₆

C₂

yes

maximal, characteristic

#15688899

C₂

yes

maximal, complemented

C₄×C₄₇⋊C₁₆

C₂

yes

maximal, complemented

C₄₇×#405

C₂

yes

maximal, characteristic

#13093964

C₄

yes

complemented

C₂×C₄₇⋊C₁₆

C₄

yes

complemented

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

C₂×C₄₇⋊C₁₆

C₂²

yes

—

C₂×M₁₆×C₄₇

C₄

yes

characteristic

C₂²×C₈×C₄₇

C₂²

yes

characteristic

#117×C₄₇

C₄

yes

characteristic

#97×C₄₇

C₄

yes

—

C₄×C₈×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

M₁₆×C₄₇

C₈

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

C₈

yes

—

C₂²⋊C₄×C₄₇

C₈

yes

—

C₄²×C₄₇

C₂×C₄

yes

—

C₄₇⋊C₁₆

C₂×C₄

yes

—

C₄₇⋊C₁₆

C₂×C₄

yes

—

C₄₇⋊C₁₆

C₂×C₄

yes

—

C₂³×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

C₄²

yes

—

C₂×C₄×C₄₇

C₂×C₈

yes

—

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

C₂×C₈

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₈×C₄₇

C₄²

yes

—

C₈×C₄₇

C₂×C₈

yes

—

C₈×C₄₇

C₂²×C₄

yes

characteristic

C₈×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄₇

—

C₂²×C₄₇

C₄×C₈

yes

—

C₂²×C₄₇

C₂²×C₈

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

C₄×C₈

yes

—

C₄×C₄₇

C₂×C₄²

yes

characteristic

C₄×C₄₇

C₂²×C₈

yes

characteristic

#2108

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂×C₄×C₈

yes

characteristic

C₂×C₄₇

#504

yes

—

C₂×M₃₂

—

C₂²×C₁₆

—

#405

D₄₇

yes

characteristic

#346

—

C₄×C₁₆

—

C₄₇

#2108

yes

characteristic, complemented, Sylow

C₂×M₁₆

Dic₄₇

yes

characteristic

C₂²×C₈

C₂×D₄₇

yes

characteristic

#117

Dic₄₇

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

Dic₄₇

yes

—

C₄×C₈

C₂×D₄₇

yes

—

C₂²×C₄

C₂×Dic₄₇

yes

characteristic

M₁₆

C₄₇⋊C₈

yes

—

C₂×C₈

C₄×D₄₇

yes

—

C₂×C₈

C₄×D₄₇

yes

—

C₂×C₈

C₂×Dic₄₇

yes

—

C₂×C₈

C₂×Dic₄₇

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

C₄₇⋊C₈

yes

—

C₂²⋊C₄

C₄₇⋊C₈

yes

—

C₄²

C₂×Dic₄₇

yes

—

C₁₆

—

C₁₆

—

C₁₆

—

C₂³

C₂×C₄₇⋊C₈

yes

characteristic

C₂×C₄

C₂×C₄₇⋊C₈

yes

—

C₂×C₄

C₂×C₄₇⋊C₈

yes

characteristic

C₂×C₄

C₂×C₄₇⋊C₈

yes

—

C₂×C₄

C₄×Dic₄₇

yes

—

C₂×C₄

C₂²×Dic₄₇

yes

characteristic

C₈

C₂×C₄₇⋊C₈

yes

—

C₈

C₄×Dic₄₇

yes

—

C₈

C₂×C₄×D₄₇

yes

characteristic

C₈

C₂×C₄×D₄₇

yes

characteristic

C₂²

—

C₂²

C₄×C₄₇⋊C₈

yes

—

C₂²

C₂²×C₄₇⋊C₈

yes

characteristic

C₄

—

C₄

C₄×C₄₇⋊C₈

yes

—

C₄

C₂×C₄×Dic₄₇

yes

characteristic

C₄

C₂²×C₄₇⋊C₈

yes

characteristic

C₂

—

C₂

C₂×C₄×C₄₇⋊C₈

yes

characteristic

C₂

#15689540

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₄₇
commutator	C₂×C₄₇	C₂×C₄×C₈
Fitting	C₄₇×#405	C₂
socle	C₂²×C₄₇	C₂²×C₈
hypercenter	#405	D₄₇
hypocenter	C₄₇	#2108
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ #405

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₄₇

commutator

C₂×C₄₇

C₂×C₄×C₈

Fitting

C₄₇×#405

C₂

socle

C₂²×C₄₇

C₂²×C₈

D₄₇

C₄₇

G ▷ C₂×C₄₇ ▷ C₄₇

C₁ ◁ C₂×C₈ ◁ #405

N	H ≅ G/N	type
3. #15688899	C₂	semidirect
4. C₄×C₄₇⋊C₁₆	C₂	semidirect
6. #13093964	C₄	semidirect
7. C₂×C₄₇⋊C₁₆	C₄	semidirect
55. C₄₇	#2108	semidirect

H ≅ G/N

type

3. #15688899

C₂

semidirect

4. C₄×C₄₇⋊C₁₆

C₂

semidirect

6. #13093964

C₄

semidirect

7. C₂×C₄₇⋊C₁₆

C₄

semidirect

55. C₄₇

#2108

semidirect

Subgroups — #20244985

Conjugacy classes of subgroups

Complements