Group #23763570 — subgroups

Subgroups — #23763570

Order 10112.

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

normal subgroups only

This group has 220 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	C₂×#14579097	C₂	1	1	yes	maximal, characteristic
2	C₂×#14579096	C₂	1	2	yes	maximal
3	#19098586	C₂	1	2	yes	maximal
4	C₂×C₈×Dic₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#108×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#11929608	C₂²	1	2	yes	—
7	C₂²×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
9	#14579097	—	2	2	no	—
10	#14579096	—	2	4	no	—
11	Dic₇₉⋊C₈	—	2	4	no	—
12	C₈×Dic₇₉	C₄	1	2	yes	—
13	C₈×Dic₇₉	C₄	1	2	yes	—
14	C₂×M₁₆×C₇₉	C₂²	1	2	yes	—
15	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
16	#108×C₇₉	—	2	2	no	—
17	C₂²×Dic₇₉	Q₈	1	2	yes	—
18	#11929608	—	2	2	no	—
19	#11929608	—	2	2	no	—
20	C₂×C₇₉⋊C₈	—	2	2	no	—
21	C₂×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
22	C₂×C₇₉⋊C₈	D₄	1	2	yes	—
23	C₂×C₇₉⋊C₈	Q₈	1	2	yes	—
24	C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
26	C₄×Dic₇₉	D₄	1	2	yes	—
27	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
28	M₁₆×C₇₉	—	2	2	no	—
29	M₁₆×C₇₉	—	2	2	no	—
30	C₂×C₈×C₇₉	—	2	2	no	—
31	C₂×C₈×C₇₉	C₂×C₄	1	2	yes	—
32	C₂×C₈×C₇₉	D₄	1	2	yes	—
33	C₂×C₈×C₇₉	Q₈	1	2	yes	—
34	C₂³×C₇₉	C₂×Q₈	1	1	yes	characteristic
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×D₄	1	1	yes	characteristic
38	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
41	C₂×Dic₇₉	—	2	4	no	—
42	C₂×Dic₇₉	C₄⋊C₄	1	2	yes	—
43	C₂×Dic₇₉	C₄⋊C₄	1	2	yes	—
44	C₈×C₇₉	—	4	2	no	—
45	C₈×C₇₉	C₄⋊C₄	1	4	yes	—
46	C₇₉⋊C₈	—	4	2	no	—
47	C₇₉⋊C₈	C₄⋊C₄	1	4	yes	—
48	C₂²×C₇₉	—	2	2	no	—
49	C₂²×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂²×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
51	C₂²×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
52	C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₄×C₇₉	#127	1	1	yes	characteristic
55	C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
56	Dic₇₉	—	2	2	no	—
57	Dic₇₉	#108	1	4	yes	complemented
58	C₂×C₇₉	—	2	1	no	—
59	C₂×C₇₉	—	2	1	no	—
60	C₂×C₇₉	#384	1	1	yes	characteristic
61	C₂×C₇₉	C₂×#108	1	2	yes	—
62	#1848	—	79	1	no	maximal, Sylow
63	C₇₉	#1848	1	1	yes	characteristic, complemented, Sylow
64	C₂×#108	—	79	2	no	—
65	C₂×#108	—	79	1	no	—
66	C₂×#108	D₇₉	1	1	yes	characteristic
67	#423	—	79	2	no	—
68	C₂×C₄×C₈	—	79	1	no	—
69	C₂×M₁₆	—	79	2	no	—
70	C₂×M₁₆	C₂×D₇₉	1	2	yes	—
71	C₂²×C₈	—	79	1	no	—
72	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
73	C₂×C₄²	—	79	1	no	—
74	#108	—	2	2	no	—
75	#108	—	158	4	no	—
76	#108	—	158	2	no	—
77	C₄⋊C₈	—	158	4	no	—
78	C₄×C₈	—	79	2	no	—
79	C₄×C₈	—	79	2	no	—
80	C₂²×C₄	—	79	2	no	—
81	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
82	M₁₆	—	2	2	no	—
83	M₁₆	—	2	2	no	—
84	M₁₆	—	158	2	no	—
85	M₁₆	—	158	2	no	—
86	C₂×C₈	—	2	2	no	—
87	C₂×C₈	—	79	2	no	—
88	C₂×C₈	—	79	2	no	—
89	C₂×C₈	—	79	2	no	—
90	C₂×C₈	—	158	2	no	—
91	C₂×C₈	Dic₁₅₈	1	2	yes	—
92	C₂×C₈	C₄×D₇₉	1	2	yes	—
93	C₂×C₈	C₂²⋊D₇₉	1	2	yes	—
94	C₄²	—	79	1	no	—
95	C₄²	—	79	1	no	—
96	C₄²	—	79	2	no	—
97	C₂³	Q₈×D₇₉	1	1	yes	characteristic
98	C₂×C₄	—	79	2	no	—
99	C₂×C₄	—	79	2	no	—
100	C₂×C₄	—	158	4	no	—
101	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
102	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
103	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
104	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
105	C₂×C₄	Q₈×D₇₉	1	1	yes	characteristic
106	C₂×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
107	C₈	—	4	2	no	—
108	C₈	—	316	2	no	—
109	C₈	—	79	4	no	—
110	C₈	Dic₇₉⋊C₄	1	4	yes	—
111	C₂²	—	2	2	no	—
112	C₂²	C₄⋊C₄×D₇₉	1	1	yes	characteristic
113	C₂²	#14579159	1	1	yes	characteristic
114	C₂²	#14579160	1	1	yes	characteristic
115	C₄	—	79	4	no	—
116	C₄	—	158	2	no	—
117	C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
118	C₄	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
119	C₄	#14579157	1	1	yes	characteristic
120	C₄	#14579160	1	1	yes	characteristic
121	C₂	—	2	1	no	—
122	C₂	—	2	1	no	—
123	C₂	#19098432	1	1	yes	characteristic
124	C₂	#108×D₇₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579097

C₂

yes

maximal, characteristic

C₂×#14579096

C₂

yes

maximal

#19098586

C₂

yes

maximal

C₂×C₈×Dic₇₉

C₂

yes

maximal, characteristic

C₂×#108×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929608

C₂²

yes

—

C₂²×C₇₉⋊C₈

C₂²

yes

characteristic

C₂×C₄×Dic₇₉

C₂²

yes

characteristic

#14579097

—

#14579096

—

Dic₇₉⋊C₈

—

C₈×Dic₇₉

C₄

yes

—

C₈×Dic₇₉

C₄

yes

—

C₂×M₁₆×C₇₉

C₂²

yes

—

C₂²×C₈×C₇₉

C₂²

yes

characteristic

#108×C₇₉

—

C₂²×Dic₇₉

Q₈

yes

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

—

C₂×C₇₉⋊C₈

D₄

yes

—

C₂×C₇₉⋊C₈

Q₈

yes

—

C₄×Dic₇₉

C₂×C₄

yes

characteristic

C₄×Dic₇₉

C₂×C₄

yes

characteristic

C₄×Dic₇₉

D₄

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

—

C₂×C₈×C₇₉

D₄

yes

—

C₂×C₈×C₇₉

Q₈

yes

—

C₂³×C₇₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₈

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

C₄⋊C₄

yes

—

C₂×Dic₇₉

C₄⋊C₄

yes

—

C₈×C₇₉

—

C₈×C₇₉

C₄⋊C₄

yes

—

C₇₉⋊C₈

—

C₇₉⋊C₈

C₄⋊C₄

yes

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₇₉

C₄⋊Q₈

yes

characteristic

C₂²×C₇₉

C₄⋊Q₈

yes

characteristic

C₄×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₉

#127

yes

characteristic

C₄×C₇₉

C₄⋊Q₈

yes

characteristic

Dic₇₉

—

Dic₇₉

#108

yes

complemented

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#384

yes

characteristic

C₂×C₇₉

C₂×#108

yes

—

#1848

—

maximal, Sylow

C₇₉

#1848

yes

characteristic, complemented, Sylow

C₂×#108

—

C₂×#108

—

C₂×#108

D₇₉

yes

characteristic

#423

—

C₂×C₄×C₈

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₉

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₇₉

yes

characteristic

C₂×C₄²

—

#108

—

#108

—

158

—

#108

—

158

—

C₄⋊C₈

—

158

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

158

—

M₁₆

—

158

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

Dic₁₅₈

yes

—

C₂×C₈

C₄×D₇₉

yes

—

C₂×C₈

C₂²⋊D₇₉

yes

—

C₄²

—

C₄²

—

C₄²

—

C₂³

Q₈×D₇₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

158

—

101

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

102

C₂×C₄

D₄×D₇₉

yes

characteristic

103

C₂×C₄

D₄×D₇₉

yes

characteristic

104

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

105

C₂×C₄

Q₈×D₇₉

yes

characteristic

106

C₂×C₄

C₂×Dic₁₅₈

yes

characteristic

107

C₈

—

108

C₈

—

316

—

109

C₈

—

110

C₈

Dic₇₉⋊C₄

yes

—

111

C₂²

—

112

C₂²

C₄⋊C₄×D₇₉

yes

characteristic

113

C₂²

#14579159

yes

characteristic

114

C₂²

#14579160

yes

characteristic

115

C₄

—

116

C₄

—

158

—

117

C₄

C₄⋊C₄×D₇₉

yes

characteristic

118

C₄

C₂×Dic₇₉⋊C₄

yes

characteristic

119

C₄

#14579157

yes

characteristic

120

C₄

#14579160

yes

characteristic

121

C₂

—

122

C₂

—

123

C₂

#19098432

yes

characteristic

124

C₂

#108×D₇₉

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	C₂×#108×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₄⋊C₄
prime radical	C₂³×C₇₉	C₂×Q₈
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	C₂×#108	D₇₉
hypocenter	C₇₉	#1848
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₇₉

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

C₂×#108×C₇₉

C₂

socle

C₂²×C₇₉

C₂×C₄⋊C₄

prime radical

C₂³×C₇₉

C₂×Q₈

cosocle

C₂²×C₄×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
57. Dic₇₉	#108	semidirect
63. C₇₉	#1848	semidirect

H ≅ G/N

type

57. Dic₇₉

#108

semidirect

63. C₇₉

#1848

semidirect

Subgroups — #23763570

Conjugacy classes of subgroups

Complements