Group #21425903 — subgroups

Subgroups — #21425903

Order 7552.

138 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₄⋊(C₅₉⋊C₁₆)	C₂	1	2	yes	maximal, complemented
2	C₂²⋊(C₅₉⋊C₁₆)	C₂	1	2	yes	maximal
3	#16837178	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#405	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅₉⋊C₁₆	C₂²	1	2	yes	—
7	C₂×C₅₉⋊C₁₆	C₂²	1	2	yes	—
8	C₂×M₁₆×C₅₉	C₄	1	1	yes	characteristic
9	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
10	#117×C₅₉	C₄	1	1	yes	characteristic
11	#97×C₅₉	C₄	1	1	yes	characteristic
12	#97×C₅₉	C₄	1	1	yes	characteristic
13	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
16	M₁₆×C₅₉	—	2	2	no	—
17	C₂×C₈×C₅₉	—	2	2	no	—
18	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₅₉	C₈	1	2	yes	—
23	C₂²⋊C₄×C₅₉	C₈	1	2	yes	—
24	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
25	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
26	C₅₉⋊C₁₆	—	2	2	no	—
27	C₅₉⋊C₁₆	—	2	2	no	—
28	C₂³×C₅₉	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₅₉	—	2	1	no	—
30	C₂×C₄×C₅₉	—	2	1	no	—
31	C₂×C₄×C₅₉	C₂×C₈	1	2	yes	—
32	C₂×C₄×C₅₉	C₂×C₈	1	2	yes	—
33	C₂×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
34	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₅₉	—	2	1	no	—
36	C₈×C₅₉	—	2	1	no	—
37	C₈×C₅₉	M₁₆	1	2	yes	—
38	C₈×C₅₉	#41	1	2	yes	—
39	C₂²×C₅₉	—	2	1	no	—
40	C₂²×C₅₉	—	2	2	no	—
41	C₂²×C₅₉	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₅₉	—	2	1	no	—
43	C₄×C₅₉	—	2	2	no	—
44	C₄×C₅₉	—	2	2	no	—
45	C₄×C₅₉	#117	1	1	yes	characteristic
46	C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
47	#2164	—	59	1	no	maximal, Sylow
48	C₂×C₅₉	—	4	1	no	—
49	C₂×C₅₉	#431	1	1	yes	characteristic
50	C₂×C₅₉	#504	1	2	yes	—
51	#405	D₅₉	1	1	yes	characteristic
52	C₄⋊C₁₆	—	59	2	no	—
53	C₂²⋊C₁₆	—	59	2	no	—
54	#346	—	59	1	no	—
55	C₄×C₁₆	—	59	1	no	—
56	C₅₉	#2164	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₁₆	Dic₅₉	1	1	yes	characteristic
58	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
59	#117	Dic₅₉	1	1	yes	characteristic
60	C₂×C₁₆	—	59	2	no	—
61	C₂×C₁₆	—	59	2	no	—
62	#97	Dic₅₉	1	1	yes	characteristic
63	#97	Dic₅₉	1	1	yes	characteristic
64	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
65	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
66	C₂²×C₄	C₂×Dic₅₉	1	1	yes	characteristic
67	M₁₆	—	2	2	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂×C₈	C₂×Dic₅₉	1	1	yes	characteristic
70	C₂×C₈	C₂×Dic₅₉	1	1	yes	characteristic
71	C₂×C₈	C₂×Dic₅₉	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
73	C₄⋊C₄	C₅₉⋊C₈	1	2	yes	—
74	C₂²⋊C₄	C₅₉⋊C₈	1	2	yes	—
75	C₄²	C₂×Dic₅₉	1	1	yes	characteristic
76	C₄²	C₂×Dic₅₉	1	1	yes	characteristic
77	C₁₆	—	118	2	no	—
78	C₁₆	—	118	2	no	—
79	C₂³	C₂×C₅₉⋊C₈	1	1	yes	characteristic
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	C₂×C₅₉⋊C₈	1	2	yes	—
83	C₂×C₄	C₂×C₅₉⋊C₈	1	2	yes	—
84	C₂×C₄	C₂×C₅₉⋊C₈	1	1	yes	characteristic
85	C₂×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	2	1	no	—
88	C₈	#11745664	1	2	yes	—
89	C₈	#11745685	1	2	yes	—
90	C₂²	—	2	1	no	—
91	C₂²	—	2	2	no	—
92	C₂²	C₂²×C₅₉⋊C₈	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	2	2	no	—
96	C₄	#14273686	1	1	yes	characteristic
97	C₄	C₂×#11745664	1	1	yes	characteristic
98	C₂	—	4	1	no	—
99	C₂	#16837455	1	1	yes	characteristic
100	C₂	#16837819	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊(C₅₉⋊C₁₆)

C₂

yes

maximal, complemented

C₂²⋊(C₅₉⋊C₁₆)

C₂

yes

maximal

#16837178

C₂

yes

maximal, characteristic, complemented

C₄×C₅₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₅₉×#405

C₂

yes

maximal, characteristic

C₂×C₅₉⋊C₁₆

C₂²

yes

—

C₂×C₅₉⋊C₁₆

C₂²

yes

—

C₂×M₁₆×C₅₉

C₄

yes

characteristic

C₂²×C₈×C₅₉

C₂²

yes

characteristic

#117×C₅₉

C₄

yes

characteristic

#97×C₅₉

C₄

yes

characteristic

#97×C₅₉

C₄

yes

characteristic

C₄×C₈×C₅₉

C₂²

yes

characteristic

C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂²×C₄×C₅₉

C₂×C₄

yes

characteristic

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₄⋊C₄×C₅₉

C₈

yes

—

C₂²⋊C₄×C₅₉

C₈

yes

—

C₄²×C₅₉

C₂×C₄

yes

characteristic

C₄²×C₅₉

C₂×C₄

yes

characteristic

C₅₉⋊C₁₆

—

C₅₉⋊C₁₆

—

C₂³×C₅₉

C₂×C₈

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×C₈

yes

—

C₂×C₄×C₅₉

C₂×C₈

yes

—

C₂×C₄×C₅₉

C₂×C₈

yes

characteristic

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

M₁₆

yes

—

C₈×C₅₉

#41

yes

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂²×C₈

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

#117

yes

characteristic

C₄×C₅₉

C₂×M₁₆

yes

characteristic

#2164

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

#431

yes

characteristic

C₂×C₅₉

#504

yes

—

#405

D₅₉

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

C₄×C₁₆

—

C₅₉

#2164

yes

characteristic, complemented, Sylow

C₂×M₁₆

Dic₅₉

yes

characteristic

C₂²×C₈

C₂×D₅₉

yes

characteristic

#117

Dic₅₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

#97

Dic₅₉

yes

characteristic

#97

Dic₅₉

yes

characteristic

C₄×C₈

C₂×D₅₉

yes

characteristic

C₄×C₈

C₂×D₅₉

yes

characteristic

C₂²×C₄

C₂×Dic₅₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂×Dic₅₉

yes

characteristic

C₂×C₈

C₂×Dic₅₉

yes

characteristic

C₂×C₈

C₂×Dic₅₉

yes

characteristic

C₂×C₈

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

C₅₉⋊C₈

yes

—

C₂²⋊C₄

C₅₉⋊C₈

yes

—

C₄²

C₂×Dic₅₉

yes

characteristic

C₄²

C₂×Dic₅₉

yes

characteristic

C₁₆

—

118

—

C₁₆

—

118

—

C₂³

C₂×C₅₉⋊C₈

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₅₉⋊C₈

yes

—

C₂×C₄

C₂×C₅₉⋊C₈

yes

—

C₂×C₄

C₂×C₅₉⋊C₈

yes

characteristic

C₂×C₄

C₂²×Dic₅₉

yes

characteristic

C₈

—

C₈

—

C₈

#11745664

yes

—

C₈

#11745685

yes

—

C₂²

—

C₂²

—

C₂²

C₂²×C₅₉⋊C₈

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

C₂

#16837455

yes

characteristic

100

C₂

#16837819

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₅₉
commutator, socle	C₂²×C₅₉	C₂²×C₈
Fitting	C₅₉×#405	C₂
hypercenter	#405	D₅₉
hypocenter	C₅₉	#2164
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ #405

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₅₉

commutator, socle

C₂²×C₅₉

C₂²×C₈

Fitting

C₅₉×#405

C₂

D₅₉

C₅₉

G ▷ C₂²×C₅₉ ▷ C₅₉

C₁ ◁ C₂×C₈ ◁ #405

N	H ≅ G/N	type
1. C₄⋊(C₅₉⋊C₁₆)	C₂	semidirect
3. #16837178	C₂	semidirect
4. C₄×C₅₉⋊C₁₆	C₂	semidirect
56. C₅₉	#2164	semidirect

H ≅ G/N

type

1. C₄⋊(C₅₉⋊C₁₆)

C₂

semidirect

3. #16837178

C₂

semidirect

4. C₄×C₅₉⋊C₁₆

C₂

semidirect

56. C₅₉

#2164

semidirect

Subgroups — #21425903

Conjugacy classes of subgroups

Complements