Group #23774143 — subgroups

Subgroups — #23774143

Order 10112.

358 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 125 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	#19099118	C₂	1	2	yes	maximal
2	#19098961	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098913	C₂	1	2	yes	maximal, complemented
4	#19098818	C₂	1	4	yes	maximal
5	#19098670	C₂	1	4	yes	maximal, complemented
6	C₄×#11929607	C₂	1	1	yes	maximal, characteristic
7	#494×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11929607	C₂²	1	2	yes	—
9	#14579161	C₂²	1	2	yes	—
10	#14579152	—	2	2	no	—
11	#14579141	—	2	2	no	—
12	#14579137	C₂²	1	4	yes	—
13	Q₈×Dic₇₉	C₂²	1	4	yes	—
14	#14579126	—	2	2	no	—
15	#14579119	—	2	2	no	—
16	C₄²×D₇₉	C₂²	1	1	yes	characteristic
17	#14579093	C₂²	1	4	yes	—
18	#14579085	C₂²	1	8	yes	—
19	#14579071	C₂²	1	2	yes	—
20	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Q₁₆×C₇₉	C₂²	1	4	yes	—
22	C₄⋊Q₈×C₇₉	C₂²	1	2	yes	—
23	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×Dic₁₅₈	—	2	2	no	—
25	C₂×C₄×D₇₉	D₄	1	2	yes	—
26	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
27	#11929607	—	2	4	no	—
28	C₂×C₇₉⋊C₈	C₂³	1	2	yes	—
29	C₄⋊Dic₇₉	—	2	4	no	—
30	C₄⋊Dic₇₉	—	2	2	no	—
31	C₄⋊Dic₇₉	C₂³	1	4	yes	—
32	Dic₇₉⋊C₄	—	2	4	no	—
33	(C₂×D₇₉)⋊C₄	—	2	4	no	—
34	C₄×Dic₇₉	—	2	4	no	—
35	C₄×Dic₇₉	D₄	1	2	yes	—
36	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
37	C₂×Q₈×C₇₉	C₂³	1	4	yes	—
38	Q₁₆×C₇₉	—	2	8	no	—
39	C₂×C₈×C₇₉	C₂³	1	2	yes	—
40	C₄⋊C₄×C₇₉	—	2	2	no	—
41	C₄⋊C₄×C₇₉	—	2	2	no	—
42	C₄²×C₇₉	C₂³	1	1	yes	characteristic
43	C₂²×D₇₉	C₂×D₄	1	1	yes	characteristic
44	Q₈×C₇₉	—	2	8	no	—
45	C₂×C₄×C₇₉	—	2	4	no	—
46	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
48	C₂×Dic₇₉	—	2	4	no	—
49	C₂×Dic₇₉	C₂×D₄	1	2	yes	—
50	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
51	C₄×D₇₉	—	2	4	no	—
52	C₄×D₇₉	—	2	2	no	—
53	Dic₁₅₈	—	4	4	no	—
54	C₈×C₇₉	#41	1	4	yes	—
55	C₇₉⋊C₈	—	2	2	no	—
56	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
57	C₂×D₇₉	—	2	1	no	—
58	C₂×D₇₉	—	2	2	no	—
59	C₄×C₇₉	—	4	4	no	—
60	C₄×C₇₉	#137	1	4	yes	—
61	C₄×C₇₉	C₂×#41	1	2	yes	—
62	Dic₇₉	—	2	1	no	—
63	Dic₇₉	—	2	2	no	—
64	Dic₇₉	—	4	4	no	—
65	C₂×C₇₉	#532	1	1	yes	characteristic
66	C₂×C₇₉	C₂×#137	1	2	yes	—
67	D₇₉	—	4	1	no	—
68	#3185	—	79	1	no	maximal, Sylow
69	C₇₉	#3185	1	1	yes	characteristic, complemented, Sylow
70	#533	—	79	2	no	—
71	#498	—	79	1	no	—
72	#494	D₇₉	1	1	yes	characteristic, complemented
73	#487	—	79	2	no	—
74	#470	—	79	4	no	—
75	#441	—	79	4	no	—
76	C₄×M₁₆	—	79	1	no	—
77	C₂×Q₁₆	C₂×D₇₉	1	4	yes	—
78	C₂×M₁₆	—	79	2	no	—
79	C₄⋊Q₈	—	79	2	no	—
80	C₄⋊Q₈	C₂×D₇₉	1	2	yes	—
81	#125	—	158	2	no	—
82	C₂²⋊Q₈	—	79	4	no	—
83	C₂²⋊Q₈	—	158	2	no	—
84	C₄×Q₈	—	79	4	no	—
85	C₄×Q₈	—	158	2	no	—
86	#117	—	158	2	no	—
87	C₂×C₄²	—	79	1	no	—
88	#106	—	79	4	no	—
89	#103	—	79	8	no	—
90	#97	—	79	2	no	—
91	C₄×C₈	—	79	1	no	—
92	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
93	C₂×Q₈	—	158	2	no	—
94	C₂×Q₈	C₂²×D₇₉	1	4	yes	—
95	C₂²×C₄	—	79	2	no	—
96	C₂²×C₄	—	79	1	no	—
97	Q₁₆	—	2	8	no	—
98	M₁₆	—	158	4	no	—
99	C₂×C₈	—	79	2	no	—
100	C₂×C₈	C₂²×D₇₉	1	2	yes	—
101	C₄⋊C₄	—	2	2	no	—
102	C₄⋊C₄	—	2	2	no	—
103	C₄⋊C₄	—	79	4	no	—
104	C₄⋊C₄	—	158	4	no	—
105	C₄⋊C₄	—	158	4	no	—
106	C₄⋊C₄	—	158	2	no	—
107	C₂²⋊C₄	—	158	4	no	—
108	C₄²	—	79	2	no	—
109	C₄²	—	79	1	no	—
110	C₄²	—	158	4	no	—
111	C₄²	C₂²×D₇₉	1	1	yes	characteristic
112	C₂³	—	79	1	no	—
113	Q₈	—	2	8	no	—
114	Q₈	—	316	4	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	79	2	no	—
117	C₂×C₄	—	79	1	no	—
118	C₂×C₄	—	158	4	no	—
119	C₂×C₄	—	158	2	no	—
120	C₂×C₄	—	158	4	no	—
121	C₂×C₄	D₄×D₇₉	1	2	yes	—
122	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
123	C₈	—	158	2	no	—
124	C₈	#11929623	1	4	yes	—
125	C₂²	—	158	2	no	—
126	C₂²	—	158	1	no	—
127	C₂²	C₂×D₄×D₇₉	1	1	yes	characteristic
128	C₄	—	4	4	no	—
129	C₄	—	316	4	no	—
130	C₄	—	158	2	no	—
131	C₄	—	158	1	no	—
132	C₄	#14579193	1	4	yes	—
133	C₄	C₂×#11929623	1	2	yes	—
134	C₂	—	316	1	no	—
135	C₂	#19099111	1	1	yes	characteristic
136	C₂	C₂×#14579193	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19099118

C₂

yes

maximal

#19098961

C₂

yes

maximal, characteristic, complemented

#19098913

C₂

yes

maximal, complemented

#19098818

C₂

yes

maximal

#19098670

C₂

yes

maximal, complemented

C₄×#11929607

C₂

yes

maximal, characteristic

#494×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929607

C₂²

yes

—

#14579161

C₂²

yes

—

#14579152

—

#14579141

—

#14579137

C₂²

yes

—

Q₈×Dic₇₉

C₂²

yes

—

#14579126

—

#14579119

—

C₄²×D₇₉

C₂²

yes

characteristic

#14579093

C₂²

yes

—

#14579085

C₂²

yes

—

#14579071

C₂²

yes

—

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₂×Q₁₆×C₇₉

C₂²

yes

—

C₄⋊Q₈×C₇₉

C₂²

yes

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×C₄×D₇₉

D₄

yes

—

C₂×C₄×D₇₉

C₂³

yes

characteristic

#11929607

—

C₂×C₇₉⋊C₈

C₂³

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₂³

yes

—

Dic₇₉⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

D₄

yes

—

C₄×Dic₇₉

C₂³

yes

characteristic

C₂×Q₈×C₇₉

C₂³

yes

—

Q₁₆×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂²×D₇₉

C₂×D₄

yes

characteristic

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂×D₄

yes

—

C₂×Dic₇₉

C₂×D₄

yes

characteristic

C₄×D₇₉

—

C₄×D₇₉

—

Dic₁₅₈

—

C₈×C₇₉

#41

yes

—

C₇₉⋊C₈

—

C₂²×C₇₉

C₂²×D₄

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#137

yes

—

C₄×C₇₉

C₂×#41

yes

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

#532

yes

characteristic

C₂×C₇₉

C₂×#137

yes

—

D₇₉

—

#3185

—

maximal, Sylow

C₇₉

#3185

yes

characteristic, complemented, Sylow

#533

—

#498

—

#494

D₇₉

yes

characteristic, complemented

#487

—

#470

—

#441

—

C₄×M₁₆

—

C₂×Q₁₆

C₂×D₇₉

yes

—

C₂×M₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₇₉

yes

—

#125

—

158

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

158

—

C₄×Q₈

—

C₄×Q₈

—

158

—

#117

—

158

—

C₂×C₄²

—

#106

—

#103

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

158

—

C₂×Q₈

C₂²×D₇₉

yes

—

C₂²×C₄

—

C₂²×C₄

—

Q₁₆

—

M₁₆

—

158

—

C₂×C₈

—

100

C₂×C₈

C₂²×D₇₉

yes

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

158

—

105

C₄⋊C₄

—

158

—

106

C₄⋊C₄

—

158

—

107

C₂²⋊C₄

—

158

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

158

—

111

C₄²

C₂²×D₇₉

yes

characteristic

112

C₂³

—

113

Q₈

—

114

Q₈

—

316

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

158

—

119

C₂×C₄

—

158

—

120

C₂×C₄

—

158

—

121

C₂×C₄

D₄×D₇₉

yes

—

122

C₂×C₄

C₂³×D₇₉

yes

characteristic

123

C₈

—

158

—

124

C₈

#11929623

yes

—

125

C₂²

—

158

—

126

C₂²

—

158

—

127

C₂²

C₂×D₄×D₇₉

yes

characteristic

128

C₄

—

129

C₄

—

316

—

130

C₄

—

158

—

131

C₄

—

158

—

132

C₄

#14579193

yes

—

133

C₄

C₂×#11929623

yes

—

134

C₂

—

316

—

135

C₂

#19099111

yes

characteristic

136

C₂

C₂×#14579193

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	#494×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₄
prime radical	C₂²×D₇₉	C₂×D₄
hypercenter	#494	D₇₉
hypocenter	C₇₉	#3185
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

C₂×D₄×D₇₉

commutator, cosocle

C₂×C₄×C₇₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₉

Fitting

#494×C₇₉

C₂

socle

C₂²×C₇₉

C₂²×D₄

prime radical

C₂²×D₇₉

C₂×D₄

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
2. #19098961	C₂	semidirect
3. #19098913	C₂	semidirect
5. #19098670	C₂	semidirect
7. #494×C₇₉	C₂	semidirect
69. C₇₉	#3185	semidirect
72. #494	D₇₉	semidirect

H ≅ G/N

type

2. #19098961

C₂

semidirect

3. #19098913

C₂

semidirect

5. #19098670

C₂

semidirect

7. #494×C₇₉

C₂

semidirect

69. C₇₉

#3185

semidirect

72. #494

D₇₉

semidirect

Subgroups — #23774143

Conjugacy classes of subgroups

Complements