Group #10628818 — subgroups

Subgroups — C₃×#10211 #10628818

Order 768.

406 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 94 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	C₃×#3237	C₂	1	3	yes	maximal
2	C₃×#1515	C₂	1	3	yes	maximal
3	C₃×#1308	C₂	1	1	yes	maximal, characteristic
4	#10211	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×#533	C₂²	1	3	yes	—
6	C₃×#501	—	2	3	no	—
7	C₃×#491	—	2	3	no	—
8	C₃×#485	—	2	6	no	—
9	C₃×#477	—	2	3	no	—
10	C₃×#475	—	2	3	no	—
11	C₃×#432	C₂²	1	3	yes	—
12	C₃×#383	C₂²	1	1	yes	characteristic
13	C₃×#328	—	2	6	no	—
14	#3237	C₂×C₃	1	3	yes	—
15	#1515	C₂×C₃	1	3	yes	—
16	#1308	C₂×C₃	1	1	yes	characteristic
17	C₃×C₄⋊Q₈	D₄	1	3	yes	—
18	C₃×C₄⋊Q₈	D₄	1	3	yes	—
19	C₃×#125	—	2	3	no	—
20	C₃×C₂²⋊Q₈	—	2	3	no	—
21	C₃×C₂²⋊Q₈	—	2	3	no	—
22	C₃×C₄×Q₈	—	2	3	no	—
23	C₃×C₄×Q₈	—	2	3	no	—
24	C₃×#117	—	2	3	no	—
25	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
26	C₃×#107	—	2	6	no	—
27	C₃×#106	—	2	6	no	—
28	C₃×C₄⋊C₈	—	2	3	no	—
29	C₃×#103	—	2	6	no	—
30	C₃×#103	—	2	6	no	—
31	C₃×C₂²⋊C₈	D₄	1	6	yes	—
32	C₃×#97	—	2	3	no	—
33	C₃×#95	—	2	3	no	—
34	#533	C₂²×C₃	1	3	yes	—
35	#501	—	2	3	no	—
36	#491	—	2	3	no	—
37	#485	—	2	6	no	—
38	#477	—	2	3	no	—
39	#475	—	2	3	no	—
40	#432	C₂²×C₃	1	3	yes	—
41	#383	C₂²×C₃	1	1	yes	characteristic
42	#328	—	2	6	no	—
43	C₂×C₃×Q₈	—	2	3	no	—
44	C₂×C₃×Q₈	—	2	3	no	—
45	C₂²×C₃×C₄	—	4	1	no	—
46	C₂²×C₃×C₄	C₂×D₄	1	3	yes	—
47	C₂×C₃×C₈	—	2	6	no	—
48	C₃×C₄⋊C₄	—	2	3	no	—
49	C₃×C₄⋊C₄	—	2	3	no	—
50	C₃×C₄⋊C₄	—	2	3	no	—
51	C₃×C₄⋊C₄	—	2	3	no	—
52	C₃×C₄⋊C₄	—	4	3	no	—
53	C₃×C₄⋊C₄	—	4	3	no	—
54	C₃×C₂²⋊C₄	—	4	3	no	—
55	C₃×C₄²	—	4	3	no	—
56	C₃×C₄²	C₂×D₄	1	3	yes	—
57	C₃×C₄²	#41	1	1	yes	characteristic
58	C₄⋊Q₈	C₃×D₄	1	3	yes	—
59	C₄⋊Q₈	C₃×D₄	1	3	yes	—
60	#125	—	2	3	no	—
61	C₂²⋊Q₈	—	2	3	no	—
62	C₂²⋊Q₈	—	2	3	no	—
63	C₄×Q₈	—	2	3	no	—
64	C₄×Q₈	—	2	3	no	—
65	#117	—	2	3	no	—
66	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
67	#107	—	2	6	no	—
68	#106	—	2	6	no	—
69	C₄⋊C₈	—	2	3	no	—
70	#103	—	2	6	no	—
71	#103	—	2	6	no	—
72	C₂²⋊C₈	C₃×D₄	1	6	yes	—
73	#97	—	2	3	no	—
74	#95	—	2	3	no	—
75	C₂³×C₃	#127	1	1	yes	characteristic
76	C₃×Q₈	—	4	6	no	—
77	C₃×Q₈	—	8	3	no	—
78	C₂×C₃×C₄	—	4	3	no	—
79	C₂×C₃×C₄	—	4	3	no	—
80	C₂×C₃×C₄	—	4	3	no	—
81	C₂×C₃×C₄	—	8	3	no	—
82	C₂×C₃×C₄	#120	1	3	yes	—
83	C₂×C₃×C₄	#121	1	3	yes	—
84	C₃×C₈	—	4	6	no	—
85	C₂×Q₈	—	2	3	no	—
86	C₂×Q₈	—	2	3	no	—
87	C₂²×C₄	—	4	1	no	—
88	C₂²×C₄	C₂×C₃×D₄	1	3	yes	—
89	C₂×C₈	—	2	6	no	—
90	C₄⋊C₄	—	2	3	no	—
91	C₄⋊C₄	—	2	3	no	—
92	C₄⋊C₄	—	2	3	no	—
93	C₄⋊C₄	—	2	3	no	—
94	C₄⋊C₄	—	4	3	no	—
95	C₄⋊C₄	—	4	3	no	—
96	C₂²⋊C₄	—	4	3	no	—
97	C₄²	—	4	3	no	—
98	C₄²	C₂×C₃×D₄	1	3	yes	—
99	C₄²	C₃×#41	1	1	yes	characteristic
100	C₂²×C₃	—	2	3	no	—
101	C₂²×C₃	#392	1	1	yes	characteristic
102	C₃×C₄	—	2	3	no	—
103	C₃×C₄	—	2	3	no	—
104	C₃×C₄	—	8	3	no	—
105	C₃×C₄	—	8	3	no	—
106	C₃×C₄	—	16	1	no	—
107	C₂³	C₃×#127	1	1	yes	characteristic
108	Q₈	—	4	6	no	—
109	Q₈	—	8	3	no	—
110	C₂×C₄	—	4	3	no	—
111	C₂×C₄	—	4	3	no	—
112	C₂×C₄	—	4	3	no	—
113	C₂×C₄	—	8	3	no	—
114	C₂×C₄	C₃×#120	1	3	yes	—
115	C₂×C₄	C₃×#121	1	3	yes	—
116	C₈	—	4	6	no	—
117	C₂×C₃	—	4	1	no	—
118	C₂×C₃	#2009	1	3	yes	—
119	C₂²	—	2	3	no	—
120	C₂²	C₃×#392	1	1	yes	characteristic
121	C₄	—	2	3	no	—
122	C₄	—	2	3	no	—
123	C₄	—	8	3	no	—
124	C₄	—	8	3	no	—
125	C₄	—	16	1	no	—
126	C₃	#10211	1	1	yes	characteristic, direct product factor, Sylow
127	C₂	—	4	1	no	—
128	C₂	C₃×#2009	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×#3237

C₂

yes

maximal

C₃×#1515

C₂

yes

maximal

C₃×#1308

C₂

yes

maximal, characteristic

#10211

C₃

yes

maximal, characteristic, direct product factor, Sylow

C₃×#533

C₂²

yes

—

—

—

—

—

—

C₂²

yes

—

C₃×#383

C₂²

yes

characteristic

C₃×#328

—

#3237

C₂×C₃

yes

—

#1515

C₂×C₃

yes

—

#1308

C₂×C₃

yes

characteristic

C₃×C₄⋊Q₈

D₄

yes

—

C₃×C₄⋊Q₈

D₄

yes

—

C₃×#125

—

C₃×C₂²⋊Q₈

—

C₃×C₂²⋊Q₈

—

C₃×C₄×Q₈

—

C₃×C₄×Q₈

—

C₃×#117

—

C₂×C₃×C₄²

C₂³

yes

characteristic

C₃×#107

—

C₃×#106

—

C₃×C₄⋊C₈

—

C₃×#103

—

C₃×#103

—

C₃×C₂²⋊C₈

D₄

yes

—

C₃×#97

—

C₃×#95

—

#533

C₂²×C₃

yes

—

—

—

—

—

—

C₂²×C₃

yes

—

#383

C₂²×C₃

yes

characteristic

#328

—

C₂×C₃×Q₈

—

C₂×C₃×Q₈

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

C₂×D₄

yes

—

C₂×C₃×C₈

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₂²⋊C₄

—

C₃×C₄²

—

C₃×C₄²

C₂×D₄

yes

—

C₃×C₄²

#41

yes

characteristic

C₄⋊Q₈

C₃×D₄

yes

—

C₄⋊Q₈

C₃×D₄

yes

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

C₂³×C₃

yes

characteristic

#107

—

#106

—

C₄⋊C₈

—

#103

—

#103

—

C₂²⋊C₈

C₃×D₄

yes

—

#97

—

#95

—

C₂³×C₃

#127

yes

characteristic

C₃×Q₈

—

C₃×Q₈

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

#120

yes

—

C₂×C₃×C₄

#121

yes

—

C₃×C₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂×C₃×D₄

yes

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂×C₃×D₄

yes

—

C₄²

C₃×#41

yes

characteristic

100

C₂²×C₃

—

101

C₂²×C₃

#392

yes

characteristic

102

C₃×C₄

—

103

C₃×C₄

—

104

C₃×C₄

—

105

C₃×C₄

—

106

C₃×C₄

—

107

C₂³

C₃×#127

yes

characteristic

108

Q₈

—

109

Q₈

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

C₃×#120

yes

—

115

C₂×C₄

C₃×#121

yes

—

116

C₈

—

117

C₂×C₃

—

118

C₂×C₃

#2009

yes

—

119

C₂²

—

120

C₂²

C₃×#392

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

126

C₃

#10211

yes

characteristic, direct product factor, Sylow

127

C₂

—

128

C₂

C₃×#2009

yes

—

	subgroup	G/H
center, socle	C₂²×C₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₃
prime radical	C₂³×C₃	#127
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ G

subgroup

G/H

center, socle

C₂²×C₃

#392

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₃

prime radical

C₂³×C₃

#127

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ G

N	H ≅ G/N	type
4. #10211	C₃	direct (N × H)
126. C₃	#10211	direct (N × H)

H ≅ G/N

type

4. #10211

C₃

direct (N × H)

126. C₃

#10211

direct (N × H)

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

subgroup	index
C₃×#3237	2
C₃×#1515	2
C₃×#1308	2
#10211	3

subgroup

index

Subgroups — C₃×#10211 #10628818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×#10211 #10628818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10211 #10628818