Group #23764378 — subgroups

Subgroups — #23764378

Order 10112.

284 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 105 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	#19098587	C₂	1	1	yes	maximal, characteristic
2	C₄²×Dic₇₉	C₂	1	1	yes	maximal, characteristic
3	#19098322	C₂	1	4	yes	maximal
4	#533×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#11929608	C₂²	1	2	yes	—
6	C₂×C₄×Dic₇₉	—	2	2	no	—
7	C₂×C₄×Dic₇₉	C₂²	1	2	yes	—
8	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
9	C₄⋊Q₈×C₇₉	C₄	1	2	yes	complemented
10	#125×C₇₉	C₄	1	2	yes	complemented
11	C₂²⋊Q₈×C₇₉	—	2	2	no	—
12	C₄×Q₈×C₇₉	—	2	2	no	—
13	#117×C₇₉	C₂²	1	2	yes	—
14	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
15	C₂²×Dic₇₉	—	2	2	no	—
16	#11929608	—	2	4	no	—
17	C₂×C₇₉⋊C₈	—	2	2	no	—
18	C₄×Dic₇₉	—	2	8	no	—
19	C₄×Dic₇₉	—	2	2	no	—
20	C₄×Dic₇₉	Q₈	1	4	yes	complemented
21	C₂×Q₈×C₇₉	—	2	2	no	—
22	C₂²×C₄×C₇₉	D₄	1	2	yes	—
23	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₇₉	—	2	4	no	—
25	C₄⋊C₄×C₇₉	—	2	2	no	—
26	C₄⋊C₄×C₇₉	C₂×C₄	1	4	yes	—
27	C₂²⋊C₄×C₇₉	—	2	2	no	—
28	C₄²×C₇₉	—	2	2	no	—
29	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
30	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
31	C₄²×C₇₉	D₄	1	2	yes	—
32	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
33	Q₈×C₇₉	—	4	4	no	—
34	C₂×C₄×C₇₉	—	2	4	no	—
35	C₂×C₄×C₇₉	—	2	4	no	—
36	C₂×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
38	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
41	C₂×C₄×C₇₉	#41	1	2	yes	—
42	C₂×Dic₇₉	—	2	8	no	—
43	C₂×Dic₇₉	—	2	4	no	—
44	C₇₉⋊C₈	—	4	2	no	—
45	C₂²×C₇₉	—	2	2	no	—
46	C₂²×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₇₉	C₂²⋊Q₈	1	2	yes	—
48	C₄×C₇₉	—	2	2	no	—
49	C₄×C₇₉	—	4	4	no	—
50	C₄×C₇₉	#104	1	4	yes	—
51	C₄×C₇₉	C₄×Q₈	1	2	yes	—
52	C₄×C₇₉	#124	1	1	yes	characteristic
53	C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
54	Dic₇₉	—	2	8	no	—
55	C₂×C₇₉	—	2	2	no	—
56	C₂×C₇₉	#391	1	1	yes	characteristic
57	C₂×C₇₉	C₂×#104	1	2	yes	—
58	#1994	—	79	1	no	maximal, Sylow
59	C₇₉	#1994	1	1	yes	characteristic, complemented, Sylow
60	#533	D₇₉	1	1	yes	characteristic
61	#423	—	79	1	no	—
62	C₄³	—	79	1	no	—
63	#339	—	79	4	no	—
64	C₂×M₁₆	—	79	2	no	—
65	C₄⋊Q₈	Dic₇₉	1	2	yes	complemented
66	#125	Dic₇₉	1	2	yes	complemented
67	C₂²⋊Q₈	—	2	2	no	—
68	C₄×Q₈	—	2	2	no	—
69	#117	C₂×D₇₉	1	2	yes	—
70	C₂×C₄²	—	79	2	no	—
71	C₂×C₄²	—	158	2	no	—
72	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
73	C₄⋊C₈	—	158	2	no	—
74	C₂×Q₈	—	2	2	no	—
75	C₂²×C₄	—	158	2	no	—
76	C₂²×C₄	C₂²⋊D₇₉	1	2	yes	—
77	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
78	M₁₆	—	158	4	no	—
79	C₂×C₈	—	158	2	no	—
80	C₄⋊C₄	—	2	4	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	C₂×Dic₇₉	1	4	yes	—
83	C₂²⋊C₄	—	2	2	no	—
84	C₄²	—	2	2	no	—
85	C₄²	—	79	4	no	—
86	C₄²	—	158	8	no	—
87	C₄²	—	158	2	no	—
88	C₄²	C₂×Dic₇₉	1	1	yes	characteristic
89	C₄²	C₂×Dic₇₉	1	1	yes	characteristic
90	C₄²	C₂²⋊D₇₉	1	2	yes	—
91	C₂³	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
92	Q₈	—	4	4	no	—
93	C₂×C₄	—	2	4	no	—
94	C₂×C₄	—	2	4	no	—
95	C₂×C₄	—	158	8	no	—
96	C₂×C₄	—	158	4	no	—
97	C₂×C₄	C₂²⋊Dic₇₉	1	2	yes	—
98	C₂×C₄	C₂²⋊Dic₇₉	1	2	yes	—
99	C₂×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
100	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
101	C₂×C₄	Q₈×D₇₉	1	2	yes	—
102	C₂×C₄	#11929625	1	2	yes	—
103	C₈	—	316	2	no	—
104	C₂²	—	2	2	no	—
105	C₂²	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
106	C₂²	#14579137	1	2	yes	—
107	C₄	—	2	2	no	—
108	C₄	—	4	4	no	—
109	C₄	—	158	8	no	—
110	C₄	#14579088	1	4	yes	—
111	C₄	Q₈×Dic₇₉	1	2	yes	—
112	C₄	#14579150	1	1	yes	characteristic
113	C₄	#14579159	1	1	yes	characteristic
114	C₂	—	2	2	no	—
115	C₂	#19098470	1	1	yes	characteristic
116	C₂	C₂×#14579088	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19098587

C₂

yes

maximal, characteristic

C₄²×Dic₇₉

C₂

yes

maximal, characteristic

#19098322

C₂

yes

maximal

#533×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929608

C₂²

yes

—

C₂×C₄×Dic₇₉

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊Q₈×C₇₉

C₄

yes

complemented

#125×C₇₉

C₄

yes

complemented

C₂²⋊Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

#117×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂²×Dic₇₉

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

Q₈

yes

complemented

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

D₄

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₂×C₄

yes

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂×C₄

yes

characteristic

C₄²×C₇₉

C₂×C₄

yes

characteristic

C₄²×C₇₉

D₄

yes

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

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

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₇₉

C₂²⋊Q₈

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#104

yes

—

C₄×C₇₉

C₄×Q₈

yes

—

C₄×C₇₉

#124

yes

characteristic

C₄×C₇₉

C₄⋊Q₈

yes

characteristic

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#391

yes

characteristic

C₂×C₇₉

C₂×#104

yes

—

#1994

—

maximal, Sylow

C₇₉

#1994

yes

characteristic, complemented, Sylow

#533

D₇₉

yes

characteristic

#423

—

C₄³

—

#339

—

C₂×M₁₆

—

C₄⋊Q₈

Dic₇₉

yes

complemented

#125

Dic₇₉

yes

complemented

C₂²⋊Q₈

—

C₄×Q₈

—

#117

C₂×D₇₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

158

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

C₄⋊C₈

—

158

—

C₂×Q₈

—

C₂²×C₄

—

158

—

C₂²×C₄

C₂²⋊D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

M₁₆

—

158

—

C₂×C₈

—

158

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×Dic₇₉

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

158

—

C₄²

—

158

—

C₄²

C₂×Dic₇₉

yes

characteristic

C₄²

C₂×Dic₇₉

yes

characteristic

C₄²

C₂²⋊D₇₉

yes

—

C₂³

C₂×C₂²⋊D₇₉

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

C₂²⋊Dic₇₉

yes

—

C₂×C₄

C₂²⋊Dic₇₉

yes

—

C₂×C₄

C₂²×Dic₇₉

yes

characteristic

100

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

101

C₂×C₄

Q₈×D₇₉

yes

—

102

C₂×C₄

#11929625

yes

—

103

C₈

—

316

—

104

C₂²

—

105

C₂²

C₂×C₂²⋊Dic₇₉

yes

characteristic

106

C₂²

#14579137

yes

—

107

C₄

—

108

C₄

—

109

C₄

—

158

—

110

C₄

#14579088

yes

—

111

C₄

Q₈×Dic₇₉

yes

—

112

C₄

#14579150

yes

characteristic

113

C₄

#14579159

yes

characteristic

114

C₂

—

115

C₂

#19098470

yes

characteristic

116

C₂

C₂×#14579088

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#533×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₂²⋊C₄
prime radical	C₂³×C₇₉	C₂×D₄
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	#533	D₇₉
hypocenter	C₇₉	#1994
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #533

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₇₉

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

#533×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 ◁ #533

N	H ≅ G/N	type
9. C₄⋊Q₈×C₇₉	C₄	semidirect
10. #125×C₇₉	C₄	semidirect
20. C₄×Dic₇₉	Q₈	semidirect
59. C₇₉	#1994	semidirect
65. C₄⋊Q₈	Dic₇₉	semidirect
66. #125	Dic₇₉	semidirect

H ≅ G/N

type

9. C₄⋊Q₈×C₇₉

C₄

semidirect

10. #125×C₇₉

C₄

semidirect

20. C₄×Dic₇₉

Q₈

semidirect

59. C₇₉

#1994

semidirect

65. C₄⋊Q₈

Dic₇₉

semidirect

66. #125

Dic₇₉

semidirect

Subgroups — #23764378

Conjugacy classes of subgroups

Complements