Finite Group Databasebeta

← C2×#64139 #10596261

Subgroups — C2×#64139 #10596261

Order 576.

1278 conjugacy classes of subgroups; only the 327 normal subgroups are shown.

normal subgroups only

This group has 1278 conjugacy classes of subgroups — too many to draw. Only its 327 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×C4C211yesmaximal, characteristic, complemented
2C22×#638C212yesmaximal, complemented
3C22×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4#64139C218yesmaximal, direct product factor
5C2×#3752C212yesmaximal, complemented
6C2×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
7C2×#930—34nomaximal
8C24×C32C2211yescharacteristic
9C23×C3⋊D3C2212yes—
10C22×C32×C4—24no—
11C22×C32×C4C2211yescharacteristic
12C22×C32×C4C2211yescharacteristic
13C22×C32×C4C2214yescomplemented
14C2×#638—28no—
15C2×#638C2218yescomplemented
16C22×C3⋊Dic3C2212yes—
17C2×C4⋊(C3⋊D3)—24no—
18C2×C4⋊(C3⋊D3)C2214yescomplemented
19#3752C2218yescomplemented
20C4⋊(C3⋊Dic3)C2214yescomplemented
21C23×C3×C4D314yescomplemented
22C22×#67—38no—
23C22×D12—34no—
24#930—332no—
25C2×(C2×D3)⋊C4—38no—
26C2×C4⋊Dic3—34no—
27C23×C32—22no—
28C23×C32—22no—
29C23×C32D414yescomplemented
30C23×C32C2312yes—
31C23×C32C2311yescharacteristic
32C22×C3⋊D3—24no—
33C22×C3⋊D3—24no—
34C22×C3⋊D3—24no—
35C22×C3⋊D3C2314yes—
36C2×C32×C4—22no—
37C2×C32×C4—28no—
38C2×C32×C4D414yescomplemented
39C2×C32×C4C2312yes—
40C2×C32×C4C2312yes—
41#638—216no—
42C2×C3⋊Dic3—24no—
43C2×C3⋊Dic3C2314yes—
44C4⋊(C3⋊D3)—28no—
45C2×#121—91noSylow
46C24×C3C2×D314yes—
47C23×D3—38no—
48C22×C3×C4—216no—
49C22×C3×C4C2×D314yes—
50C22×C3×C4C2×D314yes—
51C22×C3×C4C2×D3116yescomplemented
52C2×#67—332no—
53C2×#67—632no—
54C22×Dic3—38no—
55C2×D12—316no—
56C2×D12—616no—
57(C2×D3)⋊C4—332no—
58C4⋊Dic3—316no—
59C22×C32—28no—
60C22×C32—22no—
61C22×C32—22no—
62C22×C32C2×D412yes—
63C22×C32C2×D412yes—
64C22×C32C2×D414yescomplemented
65C22×C32#4112yes—
66C22×C32C2411yescharacteristic
67C2×C3⋊D3—24no—
68C2×C3⋊D3—24no—
69C2×C3⋊D3—24no—
70C2×C3⋊D3—48no—
71C32×C4—22no—
72C32×C4C2×D414yescomplemented
73C3⋊Dic3—24no—
74C22×D4—92no—
75C22×D4—91no—
76C23×C4C3⋊D311yescharacteristic, complemented
77#121—98no—
78C2×C4⋊C4—91no—
79C2×C22⋊C4—92no—
80C23×C3—28no—
81C23×C3—28no—
82C23×C3D12116yescomplemented
83C23×C3C22×D318yes—
84C23×C3C22×D314yes—
85C22×D3—316no—
86C22×D3—616no—
87C22×D3—616no—
88C22×D3—616no—
89C2×C3×C4—28no—
90C2×C3×C4—232no—
91C2×C3×C4#67116yescomplemented
92C2×C3×C4C22×D318yes—
93C2×C3×C4C22×D318yes—
94#67—664no—
95C2×Dic3—316no—
96C2×Dic3—616no—
97D12—632no—
98C2×C32—24no—
99C2×C32#12114yescomplemented
100C2×C32C22×D411yescharacteristic
101C2×C32C22×D411yescharacteristic
102C2×C32C2×#4111yescharacteristic
103C3⋊D3—44no—
104C24—92no—
105C24C2×C3⋊D311yescharacteristic
106C2×D4—98no—
107C2×D4—94no—
108C2×D4—188no—
109C2×D4—184no—
110C22×C4—24no—
111C22×C4—92no—
112C22×C4C2×C3⋊D311yescharacteristic
113C22×C4C2×C3⋊D311yescharacteristic
114C22×C4C2×C3⋊D314yescomplemented
115C4⋊C4—94no—
116C22⋊C4—98no—
117C22×C3—232no—
118C22×C3—28no—
119C22×C3—28no—
120C22×C3C2×D1218yes—
121C22×C3C2×D12116yescomplemented
122C22×C3#23518yes—
123C22×C3C2×#6718yes—
124C22×C3C23×D314yes—
125C2×D3—616no—
126C2×D3—616no—
127C2×D3—616no—
128C2×D3—1232no—
129C3×C4—28no—
130C3×C4C2×#67116yescomplemented
131Dic3—616no—
132C32C2×#12111yescharacteristic, complemented, Sylow
133C23—22no—
134C23—22no—
135C23—94no—
136C23—184no—
137C23—184no—
138C23—184no—
139C23C4⋊(C3⋊D3)14yescomplemented
140C23C22×C3⋊D312yes—
141C23C22×C3⋊D311yescharacteristic
142D4—1816no—
143D4—188no—
144C2×C4—22no—
145C2×C4—28no—
146C2×C4—94no—
147C2×C4—184no—
148C2×C4#63814yescomplemented
149C2×C4C22×C3⋊D312yes—
150C2×C4C22×C3⋊D312yes—
151C2×C3—216no—
152C2×C3#930116yescomplemented
153C2×C3C22×D1214yes—
154C2×C3C2×#23514yes—
155C2×C3C22×#6714yes—
156D3—1216no—
157C22—22no—
158C22—22no—
159C22—28no—
160C22—184no—
161C22—184no—
162C22—184no—
163C22—368no—
164C22C2×C4⋊(C3⋊D3)12yes—
165C22C2×C4⋊(C3⋊D3)14yescomplemented
166C22#382812yes—
167C22C2×#63812yes—
168C22C23×C3⋊D311yescharacteristic
169C4—22no—
170C4—184no—
171C4C2×#63814yescomplemented
172C3C2×#93014yescomplemented
173C2—24no—
174C2—364no—
175C2#6413914yesdirect product factor
176C2C22×C4⋊(C3⋊D3)11yescharacteristic
177C2C2×#382811yescharacteristic
178C2C22×#63811yescharacteristic
subgroupG/H
centerC23C22×C3⋊D3
commutator, cosocleC22×C32C24
FrattiniC22C23×C3⋊D3
FittingC23×C32×C4C2
socleC23×C32C23
hypercenterC23×C4C3⋊D3
hypocenterC32C2×#121
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C23×C32×C4C2semidirect
2. C22×#638C2semidirect
3. C22×C4⋊(C3⋊D3)C2semidirect
4. #64139C2direct (N × H)
5. C2×#3752C2semidirect
6. C2×C4⋊(C3⋊Dic3)C2semidirect
13. C22×C32×C4C22semidirect
15. C2×#638C22semidirect
18. C2×C4⋊(C3⋊D3)C22semidirect
19. #3752C22semidirect
20. C4⋊(C3⋊Dic3)C22semidirect
21. C23×C3×C4D3semidirect
29. C23×C32D4semidirect
38. C2×C32×C4D4semidirect
51. C22×C3×C4C2×D3semidirect
64. C22×C32C2×D4semidirect
72. C32×C4C2×D4semidirect
76. C23×C4C3⋊D3semidirect
82. C23×C3D12semidirect
91. C2×C3×C4#67semidirect
99. C2×C32#121semidirect
114. C22×C4C2×C3⋊D3semidirect
121. C22×C3C2×D12semidirect
130. C3×C4C2×#67semidirect
132. C32C2×#121semidirect
139. C23C4⋊(C3⋊D3)semidirect
148. C2×C4#638semidirect
152. C2×C3#930semidirect
165. C22C2×C4⋊(C3⋊D3)semidirect
171. C4C2×#638semidirect
172. C3C2×#930semidirect
175. C2#64139direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C32×C42
C22×#6382
C22×C4⋊(C3⋊D3)2
#641392
C2×#37522
C2×C4⋊(C3⋊Dic3)2
C2×#9303