Group #23764380 — subgroups

Subgroups — #23764380

Order 10112.

244 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 89 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	#19099120	C₂	1	1	yes	maximal, characteristic
2	#19098409	C₂	1	1	yes	maximal, characteristic
3	#19098324	C₂	1	4	yes	maximal
4	#423×C₇₉	C₂	1	1	yes	maximal, characteristic
5	#14579161	C₄	1	2	yes	complemented
6	#14579153	C₄	1	2	yes	complemented
7	#14579140	—	2	2	no	—
8	C₄×Dic₁₅₈	—	2	2	no	—
9	#14579120	C₂²	1	2	yes	—
10	C₂×C₄×Dic₇₉	C₂²	1	2	yes	—
11	C₇₉⋊#95	—	2	2	no	—
12	C₂×M₁₆×C₇₉	C₂²	1	2	yes	—
13	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₇₉	—	2	2	no	—
15	C₂×Dic₁₅₈	—	2	2	no	—
16	C₂²×Dic₇₉	—	2	2	no	—
17	C₄⋊Dic₇₉	—	2	2	no	—
18	C₄⋊Dic₇₉	C₂×C₄	1	4	yes	—
19	Dic₇₉⋊C₄	—	2	4	no	—
20	C₂²⋊Dic₇₉	—	2	2	no	—
21	C₄×Dic₇₉	—	2	2	no	—
22	C₄×Dic₇₉	—	2	2	no	—
23	C₄×Dic₇₉	Q₈	1	4	yes	complemented
24	C₂²×C₄×C₇₉	D₄	1	2	yes	—
25	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
26	M₁₆×C₇₉	—	2	4	no	—
27	C₂×C₈×C₇₉	—	2	2	no	—
28	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
29	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
30	C₄²×C₇₉	D₄	1	2	yes	—
31	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₇₉	—	4	2	no	—
33	C₂×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
34	C₂×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
35	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
38	C₂×C₄×C₇₉	#41	1	2	yes	—
39	C₂×Dic₇₉	—	2	4	no	—
40	C₂×Dic₇₉	—	2	4	no	—
41	C₂×Dic₇₉	—	4	4	no	—
42	Dic₁₅₈	—	4	4	no	—
43	C₈×C₇₉	—	4	2	no	—
44	C₂²×C₇₉	—	2	2	no	—
45	C₂²×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₇₉	C₂²⋊Q₈	1	2	yes	—
47	C₄×C₇₉	—	2	2	no	—
48	C₄×C₇₉	—	2	2	no	—
49	C₄×C₇₉	C₄×Q₈	1	2	yes	—
50	C₄×C₇₉	#124	1	1	yes	characteristic
51	C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
52	Dic₇₉	—	4	4	no	—
53	Dic₇₉	—	4	4	no	—
54	C₂×C₇₉	—	2	2	no	—
55	C₂×C₇₉	#391	1	1	yes	characteristic
56	C₂×C₇₉	#421	1	2	yes	—
57	#1995	—	79	1	no	maximal, Sylow
58	C₇₉	#1995	1	1	yes	characteristic, complemented, Sylow
59	#533	—	79	1	no	—
60	#423	D₇₉	1	1	yes	characteristic
61	#376	—	79	1	no	—
62	#339	—	79	4	no	—
63	C₂×M₁₆	C₂×D₇₉	1	2	yes	—
64	C₄⋊Q₈	—	79	2	no	—
65	#125	—	79	2	no	—
66	C₂²⋊Q₈	—	158	2	no	—
67	C₄×Q₈	—	158	2	no	—
68	#117	—	79	2	no	—
69	C₂×C₄²	—	79	2	no	—
70	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
71	C₄⋊C₈	—	2	2	no	—
72	#95	—	158	2	no	—
73	C₂×Q₈	—	158	2	no	—
74	C₂²×C₄	—	158	2	no	—
75	C₂²×C₄	D₃₁₆	1	2	yes	—
76	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
77	M₁₆	—	2	4	no	—
78	C₂×C₈	—	2	2	no	—
79	C₄⋊C₄	—	79	4	no	—
80	C₄⋊C₄	—	158	4	no	—
81	C₄⋊C₄	—	158	2	no	—
82	C₂²⋊C₄	—	158	2	no	—
83	C₄²	—	79	4	no	—
84	C₄²	—	158	2	no	—
85	C₄²	—	158	2	no	—
86	C₄²	C₄×D₇₉	1	1	yes	characteristic
87	C₄²	C₄×D₇₉	1	1	yes	characteristic
88	C₄²	C₂²⋊D₇₉	1	2	yes	—
89	C₂³	C₂×D₃₁₆	1	1	yes	characteristic
90	Q₈	—	316	4	no	—
91	C₂×C₄	—	4	2	no	—
92	C₂×C₄	—	316	4	no	—
93	C₂×C₄	—	158	4	no	—
94	C₂×C₄	—	158	4	no	—
95	C₂×C₄	(C₂×D₇₉)⋊C₄	1	2	yes	—
96	C₂×C₄	(C₂×D₇₉)⋊C₄	1	2	yes	—
97	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
98	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
99	C₂×C₄	Q₈×D₇₉	1	2	yes	—
100	C₂×C₄	#11929623	1	2	yes	—
101	C₈	—	4	2	no	—
102	C₂²	—	2	2	no	—
103	C₂²	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
104	C₂²	#14579141	1	2	yes	—
105	C₄	—	2	2	no	—
106	C₄	—	2	2	no	—
107	C₄	—	316	4	no	—
108	C₄	—	316	4	no	—
109	C₄	#14579126	1	2	yes	—
110	C₄	#14579148	1	1	yes	characteristic
111	C₄	#14579159	1	1	yes	characteristic
112	C₂	—	2	2	no	—
113	C₂	#19098468	1	1	yes	characteristic
114	C₂	#19098579	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19099120

C₂

yes

maximal, characteristic

#19098409

C₂

yes

maximal, characteristic

#19098324

C₂

yes

maximal

#423×C₇₉

C₂

yes

maximal, characteristic

#14579161

C₄

yes

complemented

#14579153

C₄

yes

complemented

#14579140

—

C₄×Dic₁₅₈

—

#14579120

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₇₉⋊#95

—

C₂×M₁₆×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₂×C₄

yes

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

Q₈

yes

complemented

C₂²×C₄×C₇₉

D₄

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₄²×C₇₉

C₂×C₄

yes

characteristic

C₄²×C₇₉

C₂×C₄

yes

characteristic

C₄²×C₇₉

D₄

yes

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

C₈×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₇₉

C₂²⋊Q₈

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₄×Q₈

yes

—

C₄×C₇₉

#124

yes

characteristic

C₄×C₇₉

C₄⋊Q₈

yes

characteristic

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#391

yes

characteristic

C₂×C₇₉

#421

yes

—

#1995

—

maximal, Sylow

C₇₉

#1995

yes

characteristic, complemented, Sylow

#533

—

#423

D₇₉

yes

characteristic

#376

—

#339

—

C₂×M₁₆

C₂×D₇₉

yes

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

158

—

C₄×Q₈

—

158

—

#117

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

C₄⋊C₈

—

#95

—

158

—

C₂×Q₈

—

158

—

C₂²×C₄

—

158

—

C₂²×C₄

D₃₁₆

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₂²⋊C₄

—

158

—

C₄²

—

C₄²

—

158

—

C₄²

—

158

—

C₄²

C₄×D₇₉

yes

characteristic

C₄²

C₄×D₇₉

yes

characteristic

C₄²

C₂²⋊D₇₉

yes

—

C₂³

C₂×D₃₁₆

yes

characteristic

Q₈

—

316

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

—

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

—

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

C₂×C₄

Q₈×D₇₉

yes

—

100

C₂×C₄

#11929623

yes

—

101

C₈

—

102

C₂²

—

103

C₂²

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

104

C₂²

#14579141

yes

—

105

C₄

—

106

C₄

—

107

C₄

—

316

—

108

C₄

—

316

—

109

C₄

#14579126

yes

—

110

C₄

#14579148

yes

characteristic

111

C₄

#14579159

yes

characteristic

112

C₂

—

113

C₂

#19098468

yes

characteristic

114

C₂

#19098579

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#423×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₂²⋊C₄
prime radical	C₂³×C₇₉	C₂×D₄
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	#423	D₇₉
hypocenter	C₇₉	#1995
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₇₉

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

#423×C₇₉

C₂

socle

C₂²×C₇₉

C₂×C₂²⋊C₄

prime radical

C₂³×C₇₉

C₂×D₄

cosocle

C₂²×C₄×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
5. #14579161	C₄	semidirect
6. #14579153	C₄	semidirect
23. C₄×Dic₇₉	Q₈	semidirect
58. C₇₉	#1995	semidirect

H ≅ G/N

type

5. #14579161

C₄

semidirect

6. #14579153

C₄

semidirect

23. C₄×Dic₇₉

Q₈

semidirect

58. C₇₉

#1995

semidirect

Subgroups — #23764380

Conjugacy classes of subgroups

Complements