Group #23761489 — subgroups

Subgroups — #23761489

Order 10112.

136 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 81 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×#14579101	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#405×C₇₉	C₂	1	1	yes	maximal, characteristic
4	#14579101	—	2	1	no	—
5	#14579101	C₄	1	2	yes	complemented
6	C₂×C₇₉⋊C₁₆	—	2	1	no	—
7	C₂×C₇₉⋊C₁₆	—	2	1	no	—
8	C₂×C₇₉⋊C₁₆	—	2	1	no	—
9	C₂×C₇₉⋊C₁₆	C₄	1	2	yes	complemented
10	C₂×M₁₆×C₇₉	C₄	1	1	yes	characteristic
11	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
12	#117×C₇₉	C₄	1	1	yes	characteristic
13	#97×C₇₉	—	2	1	no	—
14	C₄×C₈×C₇₉	—	2	1	no	—
15	C₇₉⋊C₁₆	—	2	2	no	—
16	C₇₉⋊C₁₆	—	2	2	no	—
17	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
18	M₁₆×C₇₉	—	2	1	no	—
19	M₁₆×C₇₉	C₈	1	2	yes	—
20	C₂×C₈×C₇₉	—	2	1	no	—
21	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
25	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
26	C₂×C₈×C₇₉	Q₈	1	1	yes	characteristic
27	C₄⋊C₄×C₇₉	C₈	1	2	yes	—
28	C₂²⋊C₄×C₇₉	—	2	1	no	—
29	C₄²×C₇₉	—	2	1	no	—
30	C₂³×C₇₉	M₁₆	1	1	yes	characteristic
31	C₂×C₄×C₇₉	—	2	2	no	—
32	C₂×C₄×C₇₉	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
37	C₂×C₄×C₇₉	M₁₆	1	1	yes	characteristic
38	C₈×C₇₉	—	2	2	no	—
39	C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
41	C₈×C₇₉	C₄⋊C₄	1	1	yes	characteristic
42	C₈×C₇₉	C₄⋊C₄	1	1	yes	characteristic
43	C₂²×C₇₉	—	2	2	no	—
44	C₂²×C₇₉	#97	1	1	yes	characteristic
45	C₂²×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
46	C₂²×C₇₉	C₄⋊C₈	1	1	yes	characteristic
47	C₄×C₇₉	—	4	2	no	—
48	C₄×C₇₉	#95	1	1	yes	characteristic
49	C₄×C₇₉	C₄×C₈	1	1	yes	characteristic
50	C₄×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
51	C₄×C₇₉	C₄⋊C₈	1	1	yes	characteristic
52	C₂×C₇₉	—	2	1	no	—
53	C₂×C₇₉	—	2	1	no	—
54	C₂×C₇₉	#336	1	1	yes	characteristic
55	C₂×C₇₉	#350	1	2	yes	—
56	#1379	—	79	1	no	maximal, Sylow
57	C₇₉	#1379	1	1	yes	characteristic, complemented, Sylow
58	C₂×M₃₂	—	79	1	no	—
59	C₂²×C₁₆	—	79	1	no	—
60	#405	D₇₉	1	1	yes	characteristic
61	C₂×M₁₆	Dic₇₉	1	1	yes	characteristic
62	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
63	#117	Dic₇₉	1	1	yes	characteristic
64	M₃₂	—	79	2	no	—
65	M₃₂	—	158	1	no	—
66	C₂×C₁₆	—	79	2	no	—
67	C₂×C₁₆	—	158	1	no	—
68	C₂×C₁₆	—	158	1	no	—
69	C₂×C₁₆	—	158	1	no	—
70	#97	—	2	1	no	—
71	C₄×C₈	—	2	1	no	—
72	C₂²×C₄	C₂×Dic₇₉	1	1	yes	characteristic
73	M₁₆	—	2	1	no	—
74	M₁₆	C₇₉⋊C₈	1	2	yes	—
75	C₂×C₈	—	2	1	no	—
76	C₂×C₈	Dic₁₅₈	1	1	yes	characteristic
77	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
78	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
79	C₂×C₈	D₃₁₆	1	1	yes	characteristic
80	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
81	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
82	C₄⋊C₄	C₇₉⋊C₈	1	2	yes	—
83	C₂²⋊C₄	—	2	1	no	—
84	C₄²	—	2	1	no	—
85	C₁₆	—	158	2	no	—
86	C₁₆	—	158	2	no	—
87	C₂³	#11929608	1	1	yes	characteristic
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	C₄×Dic₇₉	1	1	yes	characteristic
90	C₂×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
91	C₂×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
92	C₂×C₄	C₂×C₇₉⋊C₈	1	1	yes	characteristic
93	C₂×C₄	C₂×C₇₉⋊C₈	1	1	yes	characteristic
94	C₂×C₄	#11929608	1	1	yes	characteristic
95	C₈	—	2	2	no	—
96	C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
97	C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
98	C₈	Dic₇₉⋊C₄	1	1	yes	characteristic
99	C₈	Dic₇₉⋊C₄	1	1	yes	characteristic
100	C₂²	—	2	2	no	—
101	C₂²	#14579072	1	1	yes	characteristic
102	C₂²	C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
103	C₂²	C₄⋊(C₇₉⋊C₈)	1	1	yes	characteristic
104	C₄	—	4	2	no	—
105	C₄	C₇₉⋊#95	1	1	yes	characteristic
106	C₄	C₄×C₇₉⋊C₈	1	1	yes	characteristic
107	C₄	C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
108	C₄	C₄⋊(C₇₉⋊C₈)	1	1	yes	characteristic
109	C₂	—	2	1	no	—
110	C₂	—	2	1	no	—
111	C₂	#19098318	1	1	yes	characteristic
112	C₂	#19098347	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579101

C₂

yes

maximal, characteristic

C₂²×C₇₉⋊C₁₆

C₂

yes

maximal, characteristic

#405×C₇₉

C₂

yes

maximal, characteristic

#14579101

—

#14579101

C₄

yes

complemented

C₂×C₇₉⋊C₁₆

—

C₂×C₇₉⋊C₁₆

—

C₂×C₇₉⋊C₁₆

—

C₂×C₇₉⋊C₁₆

C₄

yes

complemented

C₂×M₁₆×C₇₉

C₄

yes

characteristic

C₂²×C₈×C₇₉

C₂²

yes

characteristic

#117×C₇₉

C₄

yes

characteristic

#97×C₇₉

—

C₄×C₈×C₇₉

—

C₇₉⋊C₁₆

—

C₇₉⋊C₁₆

—

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

M₁₆×C₇₉

—

M₁₆×C₇₉

C₈

yes

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

Q₈

yes

characteristic

C₄⋊C₄×C₇₉

C₈

yes

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₂³×C₇₉

M₁₆

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄²

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×C₈

yes

characteristic

C₂×C₄×C₇₉

C₂×C₈

yes

characteristic

C₂×C₄×C₇₉

M₁₆

yes

characteristic

C₈×C₇₉

—

C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₈×C₇₉

C₄⋊C₄

yes

characteristic

C₈×C₇₉

C₄⋊C₄

yes

characteristic

C₂²×C₇₉

—

C₂²×C₇₉

#97

yes

characteristic

C₂²×C₇₉

C₂²⋊C₈

yes

characteristic

C₂²×C₇₉

C₄⋊C₈

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

#95

yes

characteristic

C₄×C₇₉

C₄×C₈

yes

characteristic

C₄×C₇₉

C₂²⋊C₈

yes

characteristic

C₄×C₇₉

C₄⋊C₈

yes

characteristic

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#336

yes

characteristic

C₂×C₇₉

#350

yes

—

#1379

—

maximal, Sylow

C₇₉

#1379

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂²×C₁₆

—

#405

D₇₉

yes

characteristic

C₂×M₁₆

Dic₇₉

yes

characteristic

C₂²×C₈

C₂×D₇₉

yes

characteristic

#117

Dic₇₉

yes

characteristic

M₃₂

—

M₃₂

—

158

—

C₂×C₁₆

—

C₂×C₁₆

—

158

—

C₂×C₁₆

—

158

—

C₂×C₁₆

—

158

—

#97

—

C₄×C₈

—

C₂²×C₄

C₂×Dic₇₉

yes

characteristic

M₁₆

—

M₁₆

C₇₉⋊C₈

yes

—

C₂×C₈

—

C₂×C₈

Dic₁₅₈

yes

characteristic

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

D₃₁₆

yes

characteristic

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₄⋊C₄

C₇₉⋊C₈

yes

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

158

—

C₁₆

—

158

—

C₂³

#11929608

yes

characteristic

C₂×C₄

—

C₂×C₄

C₄×Dic₇₉

yes

characteristic

C₂×C₄

C₂²⋊Dic₇₉

yes

characteristic

C₂×C₄

C₄⋊Dic₇₉

yes

characteristic

C₂×C₄

C₂×C₇₉⋊C₈

yes

characteristic

C₂×C₄

C₂×C₇₉⋊C₈

yes

characteristic

C₂×C₄

#11929608

yes

characteristic

C₈

—

C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

C₈

Dic₇₉⋊C₄

yes

characteristic

C₈

Dic₇₉⋊C₄

yes

characteristic

100

C₂²

—

101

C₂²

#14579072

yes

characteristic

102

C₂²

C₂²⋊(C₇₉⋊C₈)

yes

characteristic

103

C₂²

C₄⋊(C₇₉⋊C₈)

yes

characteristic

104

C₄

—

105

C₄

C₇₉⋊#95

yes

characteristic

106

C₄

C₄×C₇₉⋊C₈

yes

characteristic

107

C₄

C₂²⋊(C₇₉⋊C₈)

yes

characteristic

108

C₄

C₄⋊(C₇₉⋊C₈)

yes

characteristic

109

C₂

—

110

C₂

—

111

C₂

#19098318

yes

characteristic

112

C₂

#19098347

yes

—

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₇₉
commutator	C₄×C₇₉	C₄×C₈
Frattini	C₂²×C₈	C₂×D₇₉
Fitting	#405×C₇₉	C₂
socle	C₂²×C₇₉	C₂²⋊C₈
prime radical	C₂³×C₇₉	M₁₆
cosocle	C₂²×C₈×C₇₉	C₂²
hypercenter	#405	D₇₉
hypocenter	C₇₉	#1379
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #405

subgroup

G/H

center

C₂×C₈

C₂²⋊D₇₉

commutator

C₄×C₇₉

C₄×C₈

Frattini

C₂²×C₈

C₂×D₇₉

Fitting

#405×C₇₉

C₂

socle

C₂²×C₇₉

C₂²⋊C₈

prime radical

C₂³×C₇₉

M₁₆

cosocle

C₂²×C₈×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #405

N	H ≅ G/N	type
5. #14579101	C₄	semidirect
9. C₂×C₇₉⋊C₁₆	C₄	semidirect
57. C₇₉	#1379	semidirect

H ≅ G/N

type

5. #14579101

C₄

semidirect

9. C₂×C₇₉⋊C₁₆

C₄

semidirect

57. C₇₉

#1379

semidirect

Subgroups — #23761489

Conjugacy classes of subgroups

Complements