Group #23762061 — subgroups

Subgroups — #23762061

Order 10112.

246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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	#19099114	C₂	1	1	yes	maximal, characteristic
2	#19098615	C₂	1	2	yes	maximal, complemented
3	#19098312	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098306	C₂	1	2	yes	maximal, complemented
5	#333×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11929625	C₄	1	2	yes	—
7	#14579158	C₂²	1	1	yes	characteristic
8	#14579150	C₄	1	2	yes	—
9	#14579136	—	2	2	no	—
10	#14579123	—	2	2	no	—
11	C₄²×D₇₉	C₂²	1	1	yes	characteristic
12	C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
13	(C₂×D₇₉)⋊C₈	—	2	2	no	—
14	C₈×Dic₇₉	—	2	2	no	—
15	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
17	#11929625	—	4	4	no	—
18	C₂×D₃₁₆	—	2	2	no	—
19	C₂×D₃₁₆	—	2	2	no	—
20	C₂×D₃₁₆	C₂×C₄	1	2	yes	—
21	C₂×C₄×D₇₉	—	2	2	no	—
22	C₂×C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×D₇₉	D₄	1	2	yes	—
24	C₂×C₇₉⋊C₈	—	2	2	no	—
25	(C₂×D₇₉)⋊C₄	—	2	4	no	—
26	C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₇₉	D₄	1	2	yes	—
28	C₂×Q₈×C₇₉	C₂×C₄	1	2	yes	—
29	C₂×C₈×C₇₉	—	2	2	no	—
30	C₄⋊C₄×C₇₉	—	2	2	no	—
31	C₄²×C₇₉	C₂³	1	1	yes	characteristic
32	C₂²×D₇₉	—	2	2	no	—
33	C₂²×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
34	Q₈×C₇₉	—	4	2	no	—
35	C₂×C₄×C₇₉	—	2	2	no	—
36	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
38	C₂×Dic₇₉	C₂²⋊C₄	1	2	yes	—
39	C₂×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
40	D₃₁₆	—	4	2	no	—
41	D₃₁₆	—	4	4	no	—
42	D₃₁₆	—	4	2	no	—
43	D₃₁₆	—	4	2	no	—
44	C₄×D₇₉	—	2	2	no	—
45	C₄×D₇₉	—	2	2	no	—
46	C₄×D₇₉	—	2	2	no	—
47	C₄×D₇₉	—	4	4	no	—
48	C₈×C₇₉	—	4	2	no	—
49	C₇₉⋊C₈	—	4	2	no	—
50	C₂²×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
51	C₂×D₇₉	—	2	1	no	—
52	C₂×D₇₉	—	2	2	no	—
53	C₂×D₇₉	—	4	2	no	—
54	C₂×D₇₉	—	4	4	no	—
55	C₄×C₇₉	—	2	1	no	—
56	C₄×C₇₉	—	4	2	no	—
57	C₄×C₇₉	#135	1	2	yes	—
58	C₄×C₇₉	#135	1	2	yes	—
59	Dic₇₉	—	2	2	no	—
60	Dic₇₉	#100	1	2	yes	—
61	C₂×C₇₉	C₂×#100	1	1	yes	characteristic
62	C₂×C₇₉	#416	1	2	yes	—
63	D₇₉	—	4	1	no	—
64	D₇₉	—	8	2	no	—
65	#1543	—	79	1	no	maximal, Sylow
66	C₇₉	#1543	1	1	yes	characteristic, complemented, Sylow
67	#532	—	79	1	no	—
68	#431	—	79	2	no	—
69	#333	—	79	1	no	—
70	#333	D₇₉	1	1	yes	characteristic, complemented
71	#331	—	79	2	no	—
72	C₂×#41	—	79	2	no	—
73	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
74	#127	—	79	1	no	—
75	#124	—	79	2	no	—
76	#121	—	158	2	no	—
77	C₄×D₄	—	158	2	no	—
78	C₂×C₄²	—	79	1	no	—
79	C₄⋊C₈	—	79	2	no	—
80	C₄⋊C₈	C₂×D₇₉	1	2	yes	—
81	C₂²⋊C₈	—	158	2	no	—
82	C₄×C₈	—	158	2	no	—
83	#41	—	316	4	no	—
84	C₂×Q₈	C₄×D₇₉	1	2	yes	—
85	C₂×D₄	—	79	2	no	—
86	C₂×D₄	—	158	2	no	—
87	C₂×D₄	—	158	2	no	—
88	C₂²×C₄	—	79	1	no	—
89	C₂²×C₄	—	79	2	no	—
90	C₂²×C₄	—	158	2	no	—
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	158	2	no	—
93	C₄⋊C₄	—	2	2	no	—
94	C₂²⋊C₄	—	158	4	no	—
95	C₄²	—	79	1	no	—
96	C₄²	—	79	2	no	—
97	C₄²	C₂²×D₇₉	1	1	yes	characteristic
98	C₂³	—	79	1	no	—
99	C₂³	—	158	2	no	—
100	Q₈	—	4	2	no	—
101	D₄	—	316	2	no	—
102	D₄	—	316	4	no	—
103	D₄	—	316	2	no	—
104	D₄	—	316	2	no	—
105	C₂×C₄	—	2	2	no	—
106	C₂×C₄	—	316	4	no	—
107	C₂×C₄	—	79	1	no	—
108	C₂×C₄	—	79	2	no	—
109	C₂×C₄	—	158	2	no	—
110	C₂×C₄	—	158	2	no	—
111	C₂×C₄	—	158	2	no	—
112	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
113	C₂×C₄	D₄×D₇₉	1	2	yes	—
114	C₈	—	4	2	no	—
115	C₈	—	316	2	no	—
116	C₂²	—	316	2	no	—
117	C₂²	—	316	4	no	—
118	C₂²	—	158	1	no	—
119	C₂²	—	158	2	no	—
120	C₂²	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
121	C₄	—	2	1	no	—
122	C₄	—	4	2	no	—
123	C₄	—	79	2	no	—
124	C₄	—	158	2	no	—
125	C₄	#14579182	1	2	yes	—
126	C₄	#14579184	1	2	yes	—
127	C₂	—	316	1	no	—
128	C₂	—	632	2	no	—
129	C₂	#100×D₇₉	1	1	yes	characteristic
130	C₂	#19098558	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19099114

C₂

yes

maximal, characteristic

#19098615

C₂

yes

maximal, complemented

#19098312

C₂

yes

maximal, characteristic, complemented

#19098306

C₂

yes

maximal, complemented

#333×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929625

C₄

yes

—

#14579158

C₂²

yes

characteristic

#14579150

C₄

yes

—

#14579136

—

#14579123

—

C₄²×D₇₉

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

(C₂×D₇₉)⋊C₈

—

C₈×Dic₇₉

—

C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

C₂²

yes

—

#11929625

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

C₂×C₄

yes

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

C₂×C₄

yes

characteristic

C₂×C₄×D₇₉

D₄

yes

—

C₂×C₇₉⋊C₈

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

C₂×C₄

yes

characteristic

C₄×Dic₇₉

D₄

yes

—

C₂×Q₈×C₇₉

C₂×C₄

yes

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

C₂²⋊C₄

yes

characteristic

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×Dic₇₉

C₂²⋊C₄

yes

—

C₂×Dic₇₉

C₂²⋊C₄

yes

characteristic

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

C₄×D₇₉

—

C₄×D₇₉

—

C₄×D₇₉

—

C₄×D₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#135

yes

—

C₄×C₇₉

#135

yes

—

Dic₇₉

—

Dic₇₉

#100

yes

—

C₂×C₇₉

C₂×#100

yes

characteristic

C₂×C₇₉

#416

yes

—

D₇₉

—

D₇₉

—

#1543

—

maximal, Sylow

C₇₉

#1543

yes

characteristic, complemented, Sylow

—

—

—

D₇₉

yes

characteristic, complemented

#331

—

C₂×#41

—

C₄⋊Q₈

C₂×D₇₉

yes

—

—

—

158

—

C₄×D₄

—

158

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₇₉

yes

—

C₂²⋊C₈

—

158

—

C₄×C₈

—

158

—

#41

—

316

—

C₂×Q₈

C₄×D₇₉

yes

—

C₂×D₄

—

C₂×D₄

—

158

—

C₂×D₄

—

158

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

158

—

C₂×C₈

—

C₂×C₈

—

158

—

C₄⋊C₄

—

C₂²⋊C₄

—

158

—

C₄²

—

C₄²

—

C₄²

C₂²×D₇₉

yes

characteristic

C₂³

—

C₂³

—

158

—

100

Q₈

—

101

D₄

—

316

—

102

D₄

—

316

—

103

D₄

—

316

—

104

D₄

—

316

—

105

C₂×C₄

—

106

C₂×C₄

—

316

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

158

—

110

C₂×C₄

—

158

—

111

C₂×C₄

—

158

—

112

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

113

C₂×C₄

D₄×D₇₉

yes

—

114

C₈

—

115

C₈

—

316

—

116

C₂²

—

316

—

117

C₂²

—

316

—

118

C₂²

—

158

—

119

C₂²

—

158

—

120

C₂²

C₂²⋊C₄×D₇₉

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

158

—

125

C₄

#14579182

yes

—

126

C₄

#14579184

yes

—

127

C₂

—

316

—

128

C₂

—

632

—

129

C₂

#100×D₇₉

yes

characteristic

130

C₂

#19098558

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₄²	C₂²×D₇₉
Fitting	#333×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₂²⋊C₄
prime radical	#19099114	C₂
cosocle	C₄²×C₇₉	C₂³
hypercenter	#333	D₇₉
hypocenter	C₇₉	#1543
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₇₉

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₄²

C₂²×D₇₉

Fitting

#333×C₇₉

C₂

socle

C₂²×C₇₉

C₂×C₂²⋊C₄

prime radical

#19099114

C₂

cosocle

C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #333

N	H ≅ G/N	type
2. #19098615	C₂	semidirect
3. #19098312	C₂	semidirect
4. #19098306	C₂	semidirect
5. #333×C₇₉	C₂	semidirect
66. C₇₉	#1543	semidirect
70. #333	D₇₉	semidirect

H ≅ G/N

type

2. #19098615

C₂

semidirect

3. #19098312

C₂

semidirect

4. #19098306

C₂

semidirect

5. #333×C₇₉

C₂

semidirect

66. C₇₉

#1543

semidirect

70. #333

D₇₉

semidirect

Subgroups — #23762061

Conjugacy classes of subgroups

Complements