Group #20251770 — subgroups

Subgroups — #20251770

Order 6016.

408 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 165 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	#15689029	C₂	1	3	yes	maximal
2	#15689021	C₂	1	3	yes	maximal
3	#15689007	C₂	1	6	yes	maximal
4	#15688991	C₂	1	2	yes	maximal
5	C₄³×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₄₇	C₂²	1	3	yes	—
8	C₂×Dic₄₇⋊C₄	C₂²	1	6	yes	—
9	C₄₇⋊#95	C₂²	1	6	yes	—
10	C₄₇⋊#95	C₂²	1	6	yes	—
11	C₄₇⋊#95	C₂²	1	6	yes	—
12	C₂×C₄²×C₄₇	C₂²	1	3	yes	—
13	C₂×C₄²×C₄₇	C₂²	1	3	yes	—
14	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
16	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
17	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
18	C₂²×Dic₄₇	C₂³	1	2	yes	—
19	C₂²×Dic₄₇	C₂³	1	6	yes	—
20	C₂×Dic₉₄	—	2	6	no	—
21	C₄²×C₄₇	—	2	6	no	—
22	C₄²×C₄₇	—	2	6	no	—
23	C₄²×C₄₇	Q₈	1	4	yes	complemented
24	C₄⋊Dic₄₇	—	2	6	no	—
25	Dic₄₇⋊C₄	—	2	12	no	—
26	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
27	C₂×C₄×C₄₇	—	2	3	no	—
28	C₂×C₄×C₄₇	—	2	3	no	—
29	C₂×C₄×C₄₇	—	2	3	no	—
30	C₂×C₄×C₄₇	—	2	3	no	—
31	C₂×C₄×C₄₇	C₂×Q₈	1	6	yes	—
32	C₂×C₄×C₄₇	#41	1	6	yes	—
33	C₂×C₄×C₄₇	#41	1	6	yes	—
34	C₂×Dic₄₇	—	2	12	no	—
35	C₂×Dic₄₇	—	2	6	no	—
36	C₂×Dic₄₇	—	2	6	no	—
37	Dic₉₄	—	4	4	no	—
38	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
39	C₂²×C₄₇	C₂×#41	1	3	yes	—
40	C₂²×C₄₇	C₂×#41	1	3	yes	—
41	C₄×C₄₇	—	2	6	no	—
42	C₄×C₄₇	—	2	6	no	—
43	C₄×C₄₇	#126	1	4	yes	—
44	Dic₄₇	—	4	2	no	—
45	Dic₄₇	—	4	6	no	—
46	#2863	—	47	1	no	maximal, Sylow
47	C₂×C₄₇	C₂×#126	1	1	yes	characteristic
48	C₂×C₄₇	#529	1	3	yes	—
49	C₂×C₄₇	#533	1	3	yes	—
50	#391	—	47	3	no	—
51	#389	—	47	3	no	—
52	#387	—	47	6	no	—
53	#383	—	47	2	no	—
54	C₄³	D₄₇	1	1	yes	characteristic
55	C₄₇	#2863	1	1	yes	characteristic, complemented, Sylow
56	C₂²×Q₈	—	47	1	no	—
57	C₂×C₄⋊C₄	—	47	6	no	—
58	C₂×C₄⋊C₄	—	47	3	no	—
59	C₂×C₄²	C₂×D₄₇	1	3	yes	—
60	C₂×C₄²	C₂×D₄₇	1	3	yes	—
61	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
62	#95	—	47	6	no	—
63	#95	—	47	6	no	—
64	#95	—	47	6	no	—
65	C₂×Q₈	—	94	6	no	—
66	C₂²×C₄	—	47	2	no	—
67	C₂²×C₄	—	47	6	no	—
68	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
69	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
70	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
71	C₄⋊C₄	—	94	12	no	—
72	C₄⋊C₄	—	94	6	no	—
73	C₄²	—	2	6	no	—
74	C₄²	—	2	6	no	—
75	C₄²	Dic₉₄	1	4	yes	complemented
76	C₂³	C₂³×D₄₇	1	1	yes	characteristic
77	Q₈	—	188	4	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	2	3	no	—
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	3	no	—
82	C₂×C₄	—	94	6	no	—
83	C₂×C₄	—	94	12	no	—
84	C₂×C₄	—	94	6	no	—
85	C₂×C₄	C₂×Dic₉₄	1	6	yes	—
86	C₂×C₄	#10625350	1	6	yes	—
87	C₂×C₄	#10625350	1	6	yes	—
88	C₂²	C₂²×Dic₉₄	1	1	yes	characteristic
89	C₂²	C₂×#10625350	1	3	yes	—
90	C₂²	C₂×#10625350	1	3	yes	—
91	C₄	—	2	6	no	—
92	C₄	—	2	6	no	—
93	C₄	—	188	2	no	—
94	C₄	—	188	6	no	—
95	C₄	#13094018	1	4	yes	—
96	C₂	C₂×#13094018	1	1	yes	characteristic
97	C₂	#15689657	1	3	yes	—
98	C₂	#15689680	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689029

C₂

yes

maximal

#15689021

C₂

yes

maximal

#15689007

C₂

yes

maximal

#15688991

C₂

yes

maximal

C₄³×C₄₇

C₂

yes

maximal, characteristic

C₂²×Dic₉₄

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂×Dic₉₄

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

Q₈

yes

complemented

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

C₂²×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

C₂×#41

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#126

yes

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#533

yes

—

—

—

—

—

C₄³

D₄₇

yes

characteristic

C₄₇

#2863

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₇

yes

—

C₂×C₄²

C₂×D₄₇

yes

—

C₂×C₄²

C₂×D₄₇

yes

—

—

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

Dic₉₄

yes

complemented

C₂³

C₂³×D₄₇

yes

characteristic

Q₈

—

188

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₉₄

yes

—

C₂×C₄

#10625350

yes

—

C₂×C₄

#10625350

yes

—

C₂²

C₂²×Dic₉₄

yes

characteristic

C₂²

C₂×#10625350

yes

—

C₂²

C₂×#10625350

yes

—

C₄

—

C₄

—

C₄

—

188

—

C₄

—

188

—

C₄

#13094018

yes

—

C₂

C₂×#13094018

yes

characteristic

C₂

#15689657

yes

—

C₂

#15689680

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄³×C₄₇	C₂
hypercenter	C₄³	D₄₇
hypocenter	C₄₇	#2863
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄³

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄³×C₄₇

C₂

hypercenter

C₄³

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ C₄³

N	H ≅ G/N	type
23. C₄²×C₄₇	Q₈	semidirect
55. C₄₇	#2863	semidirect
75. C₄²	Dic₉₄	semidirect

H ≅ G/N

type

23. C₄²×C₄₇

Q₈

semidirect

55. C₄₇

#2863

semidirect

75. C₄²

Dic₉₄

semidirect

Subgroups — #20251770

Conjugacy classes of subgroups

Complements