Group #10795567 — subgroups

Subgroups — D₃×#1843 #10795567

Order 768.

1230 conjugacy classes of subgroups; only the 427 normal subgroups are shown.

normal subgroups only

This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 427 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×D₃×C₄⋊C₈	C₂	1	6	yes	maximal
2	D₃×#376	C₂	1	1	yes	maximal, characteristic
3	C₃×#1843	C₂	1	1	yes	maximal, characteristic, complemented
4	#70446	C₂	1	6	yes	maximal, complemented
5	#69439	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#1843	—	3	1	no	maximal, Sylow
7	C₂²×D₃×C₈	C₂²	1	4	yes	—
8	C₂×C₄²×D₃	C₂²	1	3	yes	—
9	C₂×C₃×C₄⋊C₈	C₂²	1	6	yes	—
10	C₃×#376	C₂²	1	1	yes	characteristic
11	C₂×Dic₃⋊C₈	C₂²	1	12	yes	—
12	#4932	C₂²	1	3	yes	—
13	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	6	yes	—
14	D₃×C₄⋊C₈	—	2	24	no	—
15	D₃×#95	C₄	1	4	yes	—
16	#4648	C₄	1	4	yes	—
17	C₂²×C₄⋊C₈	—	3	6	no	—
18	C₂×#376	—	3	1	no	—
19	#1843	—	3	6	no	—
20	#1843	—	3	1	no	—
21	#1843	D₃	1	1	yes	characteristic, direct product factor
22	C₂²×C₄×D₃	C₂×C₄	1	6	yes	—
23	C₂²×C₄×D₃	C₂³	1	1	yes	characteristic
24	C₂²×C₃×C₈	C₂³	1	4	yes	—
25	C₂×C₃×C₄²	C₂³	1	3	yes	—
26	C₂×C₄×Dic₃	C₂×C₄	1	6	yes	—
27	C₂×C₄×Dic₃	C₂³	1	3	yes	—
28	C₂²×C₃⋊C₈	C₂³	1	4	yes	—
29	C₂×D₃×C₈	—	2	24	no	—
30	C₄²×D₃	D₄	1	12	yes	—
31	C₄²×D₃	Q₈	1	12	yes	—
32	C₃×C₄⋊C₈	—	2	12	no	—
33	C₃×#95	C₂×C₄	1	4	yes	—
34	C₃⋊#95	C₂×C₄	1	12	yes	—
35	Dic₃⋊C₈	—	2	24	no	—
36	C₄⋊(C₃⋊C₈)	—	2	12	no	—
37	C₂³×C₈	—	3	4	no	—
38	C₂²×C₄²	—	3	3	no	—
39	C₂×C₄⋊C₈	—	3	12	no	—
40	C₂×C₄⋊C₈	—	3	6	no	—
41	C₂×C₄⋊C₈	—	6	24	no	—
42	C₂×C₄⋊C₈	C₂×D₃	1	6	yes	—
43	#376	—	3	3	no	—
44	#376	—	3	4	no	—
45	#376	C₂×D₃	1	1	yes	characteristic
46	C₂×#95	—	3	4	no	—
47	C₂³×D₃	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₃×C₄	C₂²×C₄	1	6	yes	—
49	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
50	C₂²×Dic₃	C₂²×C₄	1	6	yes	—
51	C₂²×Dic₃	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₄×D₃	—	2	24	no	—
53	C₂×C₄×D₃	C₄⋊C₄	1	24	yes	—
54	C₂×C₄×D₃	C₂×D₄	1	6	yes	—
55	C₂×C₄×D₃	C₂×Q₈	1	6	yes	—
56	C₂×C₃×C₈	—	2	12	no	—
57	C₃×C₄²	C₂×D₄	1	6	yes	—
58	C₃×C₄²	C₂×Q₈	1	6	yes	—
59	C₄×Dic₃	C₄⋊C₄	1	24	yes	—
60	C₄×Dic₃	C₂×D₄	1	6	yes	—
61	C₄×Dic₃	C₂×Q₈	1	6	yes	—
62	C₂×C₃⋊C₈	—	2	12	no	—
63	D₃×C₈	—	4	16	no	—
64	C₂³×C₄	—	3	1	no	—
65	C₂³×C₄	—	3	6	no	—
66	C₂²×C₈	—	3	4	no	—
67	C₂²×C₈	—	6	24	no	—
68	C₂²×C₈	C₂²×D₃	1	4	yes	—
69	C₂×C₄²	—	3	6	no	—
70	C₂×C₄²	—	3	3	no	—
71	C₂×C₄²	—	3	12	no	—
72	C₂×C₄²	—	3	12	no	—
73	C₂×C₄²	C₂²×D₃	1	3	yes	—
74	C₄⋊C₈	—	2	12	no	—
75	C₄⋊C₈	—	6	24	no	—
76	C₄⋊C₈	—	6	12	no	—
77	#95	—	3	12	no	—
78	#95	C₄×D₃	1	4	yes	—
79	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
80	C₂²×D₃	C₂×C₄⋊C₄	1	6	yes	—
81	C₂²×D₃	#131	1	8	yes	—
82	C₂×C₃×C₄	—	2	12	no	—
83	C₂×C₃×C₄	C₂×C₄⋊C₄	1	12	yes	—
84	C₂×C₃×C₄	C₂²×D₄	1	3	yes	—
85	C₂×C₃×C₄	C₂²×Q₈	1	3	yes	—
86	C₂×Dic₃	—	2	12	no	—
87	C₂×Dic₃	C₂×C₄⋊C₄	1	12	yes	—
88	C₂×Dic₃	C₂×C₄⋊C₄	1	6	yes	—
89	C₄×D₃	—	2	48	no	—
90	C₄×D₃	#127	1	4	yes	—
91	C₄×D₃	C₄⋊Q₈	1	12	yes	—
92	C₃×C₈	—	4	4	no	—
93	C₃⋊C₈	—	4	4	no	—
94	C₂⁴	—	3	1	no	—
95	C₂²×C₄	—	3	1	no	—
96	C₂²×C₄	—	3	6	no	—
97	C₂²×C₄	—	3	6	no	—
98	C₂²×C₄	—	3	6	no	—
99	C₂²×C₄	—	3	24	no	—
100	C₂²×C₄	—	6	24	no	—
101	C₂²×C₄	C₂×C₄×D₃	1	6	yes	—
102	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
103	C₂×C₈	—	2	12	no	—
104	C₂×C₈	—	6	12	no	—
105	C₂×C₈	—	12	16	no	—
106	C₄²	—	3	24	no	—
107	C₄²	—	3	6	no	—
108	C₄²	—	3	6	no	—
109	C₄²	D₃×D₄	1	6	yes	—
110	C₄²	D₃×Q₈	1	6	yes	—
111	C₂²×C₃	C₂²×C₄⋊C₄	1	3	yes	—
112	C₂²×C₃	C₂×#131	1	4	yes	—
113	C₂×D₃	#384	1	4	yes	—
114	C₂×D₃	#424	1	24	yes	—
115	C₃×C₄	—	2	12	no	—
116	C₃×C₄	C₂×#127	1	1	yes	characteristic
117	C₃×C₄	C₂×C₄⋊Q₈	1	3	yes	—
118	Dic₃	—	2	12	no	—
119	Dic₃	#384	1	4	yes	—
120	C₂³	—	3	8	no	—
121	C₂³	—	3	6	no	—
122	C₂³	C₂²×C₄×D₃	1	1	yes	characteristic
123	C₂×C₄	—	2	12	no	—
124	C₂×C₄	—	3	6	no	—
125	C₂×C₄	—	3	4	no	—
126	C₂×C₄	—	3	12	no	—
127	C₂×C₄	—	3	12	no	—
128	C₂×C₄	—	6	48	no	—
129	C₂×C₄	—	6	12	no	—
130	C₂×C₄	D₃×C₄⋊C₄	1	12	yes	—
131	C₂×C₄	C₂×D₃×D₄	1	3	yes	—
132	C₂×C₄	C₂×D₃×Q₈	1	3	yes	—
133	C₈	—	4	4	no	—
134	C₈	—	12	4	no	—
135	C₂×C₃	C₂×#384	1	1	yes	characteristic
136	C₂×C₃	C₂×#424	1	6	yes	—
137	D₃	#1843	1	8	yes	direct product factor
138	C₂²	—	3	4	no	—
139	C₂²	—	3	24	no	—
140	C₂²	C₂×D₃×C₄⋊C₄	1	3	yes	—
141	C₂²	D₃×#131	1	4	yes	—
142	C₄	—	2	12	no	—
143	C₄	—	3	4	no	—
144	C₄	—	6	12	no	—
145	C₄	D₃×#127	1	1	yes	characteristic
146	C₄	D₃×C₄⋊Q₈	1	3	yes	—
147	C₃	C₂×#1843	1	1	yes	characteristic, complemented, Sylow
148	C₂	—	3	8	no	—
149	C₂	D₃×#384	1	1	yes	characteristic
150	C₂	D₃×#424	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₃×C₄⋊C₈

C₂

yes

maximal

D₃×#376

C₂

yes

maximal, characteristic

C₃×#1843

C₂

yes

maximal, characteristic, complemented

#70446

C₂

yes

maximal, complemented

#69439

C₂

yes

maximal, characteristic, complemented

C₂×#1843

—

maximal, Sylow

C₂²×D₃×C₈

C₂²

yes

—

C₂×C₄²×D₃

C₂²

yes

—

C₂×C₃×C₄⋊C₈

C₂²

yes

—

C₃×#376

C₂²

yes

characteristic

C₂×Dic₃⋊C₈

C₂²

yes

—

#4932

C₂²

yes

—

C₂×C₄⋊(C₃⋊C₈)

C₂²

yes

—

D₃×C₄⋊C₈

—

D₃×#95

C₄

yes

—

#4648

C₄

yes

—

C₂²×C₄⋊C₈

—

—

—

—

D₃

yes

characteristic, direct product factor

C₂²×C₄×D₃

C₂×C₄

yes

—

C₂²×C₄×D₃

C₂³

yes

characteristic

C₂²×C₃×C₈

C₂³

yes

—

C₂×C₃×C₄²

C₂³

yes

—

C₂×C₄×Dic₃

C₂×C₄

yes

—

C₂×C₄×Dic₃

C₂³

yes

—

C₂²×C₃⋊C₈

C₂³

yes

—

C₂×D₃×C₈

—

C₄²×D₃

D₄

yes

—

C₄²×D₃

Q₈

yes

—

C₃×C₄⋊C₈

—

C₃×#95

C₂×C₄

yes

—

C₃⋊#95

C₂×C₄

yes

—

Dic₃⋊C₈

—

C₄⋊(C₃⋊C₈)

—

C₂³×C₈

—

C₂²×C₄²

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

C₂×D₃

yes

—

#376

—

#376

—

#376

C₂×D₃

yes

characteristic

C₂×#95

—

C₂³×D₃

C₂²×C₄

yes

characteristic

C₂²×C₃×C₄

C₂²×C₄

yes

—

C₂²×C₃×C₄

C₂⁴

yes

characteristic

C₂²×Dic₃

C₂²×C₄

yes

—

C₂²×Dic₃

C₂²×C₄

yes

characteristic

C₂×C₄×D₃

—

C₂×C₄×D₃

C₄⋊C₄

yes

—

C₂×C₄×D₃

C₂×D₄

yes

—

C₂×C₄×D₃

C₂×Q₈

yes

—

C₂×C₃×C₈

—

C₃×C₄²

C₂×D₄

yes

—

C₃×C₄²

C₂×Q₈

yes

—

C₄×Dic₃

C₄⋊C₄

yes

—

C₄×Dic₃

C₂×D₄

yes

—

C₄×Dic₃

C₂×Q₈

yes

—

C₂×C₃⋊C₈

—

D₃×C₈

—

C₂³×C₄

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂²×D₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₃

yes

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#95

—

#95

C₄×D₃

yes

—

C₂³×C₃

C₂³×C₄

yes

characteristic

C₂²×D₃

C₂×C₄⋊C₄

yes

—

C₂²×D₃

#131

yes

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₂×C₄⋊C₄

yes

—

C₂×C₃×C₄

C₂²×D₄

yes

—

C₂×C₃×C₄

C₂²×Q₈

yes

—

C₂×Dic₃

—

C₂×Dic₃

C₂×C₄⋊C₄

yes

—

C₂×Dic₃

C₂×C₄⋊C₄

yes

—

C₄×D₃

—

C₄×D₃

#127

yes

—

C₄×D₃

C₄⋊Q₈

yes

—

C₃×C₈

—

C₃⋊C₈

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

C₂×C₄×D₃

yes

—

102

C₂²×C₄

C₂³×D₃

yes

characteristic

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₄²

—

107

C₄²

—

108

C₄²

—

109

C₄²

D₃×D₄

yes

—

110

C₄²

D₃×Q₈

yes

—

111

C₂²×C₃

C₂²×C₄⋊C₄

yes

—

112

C₂²×C₃

C₂×#131

yes

—

113

C₂×D₃

#384

yes

—

114

C₂×D₃

#424

yes

—

115

C₃×C₄

—

116

C₃×C₄

C₂×#127

yes

characteristic

117

C₃×C₄

C₂×C₄⋊Q₈

yes

—

118

Dic₃

—

119

Dic₃

#384

yes

—

120

C₂³

—

121

C₂³

—

122

C₂³

C₂²×C₄×D₃

yes

characteristic

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

D₃×C₄⋊C₄

yes

—

131

C₂×C₄

C₂×D₃×D₄

yes

—

132

C₂×C₄

C₂×D₃×Q₈

yes

—

133

C₈

—

134

C₈

—

135

C₂×C₃

C₂×#384

yes

characteristic

136

C₂×C₃

C₂×#424

yes

—

137

D₃

#1843

yes

direct product factor

138

C₂²

—

139

C₂²

—

140

C₂²

C₂×D₃×C₄⋊C₄

yes

—

141

C₂²

D₃×#131

yes

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

D₃×#127

yes

characteristic

146

C₄

D₃×C₄⋊Q₈

yes

—

147

C₃

C₂×#1843

yes

characteristic, complemented, Sylow

148

C₂

—

149

C₂

D₃×#384

yes

characteristic

150

C₂

D₃×#424

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₃
commutator, socle	C₂³×C₃	C₂³×C₄
Fitting	C₃×#1843	C₂
prime radical	C₂³×D₃	C₂²×C₄
cosocle	C₂²×C₃×C₄	C₂⁴
hypercenter	#1843	D₃
hypocenter	C₃	C₂×#1843
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1843

subgroup

G/H

center, Frattini

C₂²×C₄

C₂³×D₃

commutator, socle

C₂³×C₃

C₂³×C₄

Fitting

C₃×#1843

C₂

prime radical

C₂³×D₃

C₂²×C₄

cosocle

C₂²×C₃×C₄

C₂⁴

D₃

C₃

G ▷ C₂³×C₃ ▷ C₃

C₁ ◁ C₂²×C₄ ◁ #1843

N	H ≅ G/N	type
3. C₃×#1843	C₂	semidirect
4. #70446	C₂	semidirect
5. #69439	C₂	semidirect
21. #1843	D₃	direct (N × H)
137. D₃	#1843	direct (N × H)
147. C₃	C₂×#1843	semidirect

H ≅ G/N

type

3. C₃×#1843

C₂

semidirect

4. #70446

C₂

semidirect

5. #69439

C₂

semidirect

21. #1843

D₃

direct (N × H)

137. D₃

#1843

direct (N × H)

147. C₃

C₂×#1843

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×D₃×C₄⋊C₈	2
D₃×#376	2
C₃×#1843	2
#70446	2
#69439	2
C₂×#1843	3

subgroup

index

C₂×D₃×C₄⋊C₈

Subgroups — D₃×#1843 #10795567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D3×#1843 #10795567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#1843 #10795567