Finite Group Databasebeta

← C2×#10621365 #13061578

Subgroups — C2×#10621365 #13061578

Order 1344.

1324 conjugacy classes of subgroups; only the 219 normal subgroups are shown.

normal subgroups only

This group has 1324 conjugacy classes of subgroups — too many to draw. Only its 219 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
1C24×D21C211yesmaximal, characteristic, complemented
2C22×#4268C211yesmaximal, characteristic, complemented
3C22×D84C212yesmaximal, complemented
4C2×C3×C7×C22⋊C4C211yesmaximal, characteristic, complemented
5C2×#66631C212yesmaximal, complemented
6#10621365C218yesmaximal, direct product factor
7C2×#6445—31nomaximal, Hall
8C24×C3×C7C2211yescharacteristic
9C23×D21—24no—
10C23×D21—28no—
11C23×D21C2212yes—
12C23×D21C2214yescomplemented
13C23×D21C2211yescharacteristic, complemented
14C22×C3×C4×C7C2212yescomplemented
15C2×#4268—24no—
16C2×#4268C2214yescomplemented
17C22×Dic21C2211yescharacteristic, complemented
18C2×D84—28no—
19C2×D84C2218yescomplemented
20C3×C7×C22⋊C4C2214yescomplemented
21#66631C2218yescomplemented
22C24×D7—31no—
23C22×C22⋊D7—31no—
24C22×D28—32no—
25C2×C7×C22⋊C4D311yescharacteristic, complemented
26C2×(C2×D7)⋊C4—32no—
27#6445—38no—
28C2×#882—71nomaximal, Hall
29C23×C3×C7—24no—
30C23×C3×C7D414yescomplemented
31C23×C3×C7C2312yes—
32C23×C3×C7C2311yescharacteristic
33C22×D21—232no—
34C22×D21—24no—
35C22×D21—24no—
36C22×D21—28no—
37C22×D21—216no—
38C22×D21—24no—
39C22×D21—22no—
40C22×D21D418yescomplemented
41C22×D21C2314yes—
42C22×D21C2312yescomplemented
43C2×C3×C4×C7—24no—
44C2×C3×C4×C7C2314yescomplemented
45#4268—28no—
46C2×Dic21—22no—
47C2×Dic21C2312yescomplemented
48D84—216no—
49C24×C7C2×D311yescharacteristic
50C23×D7—32no—
51C23×D7—34no—
52C23×D7—31no—
53C23×D7—68no—
54C23×D7—64no—
55C22×C4×C7C2×D312yescomplemented
56C2×C22⋊D7—34no—
57C2×C22⋊D7—64no—
58C22×Dic7—31no—
59C2×D28—38no—
60C2×D28—68no—
61C7×C22⋊C4C2×D314yescomplemented
62(C2×D7)⋊C4—38no—
63C24×D3—71no—
64C22×#67—71no—
65C22×D12—72no—
66C2×C3×C22⋊C4D711yescharacteristic, complemented
67C2×(C2×D3)⋊C4—72no—
68#882—78no—
69C22×C3×C7—28no—
70C22×C3×C7—24no—
71C22×C3×C7C2×D412yes—
72C22×C3×C7C2×D414yes—
73C22×C3×C7C2×D414yescomplemented
74C22×C3×C7C2411yescharacteristic
75C2×D21—232no—
76C2×D21—216no—
77C2×D21—24no—
78C2×D21—24no—
79C2×D21—24no—
80C2×D21—22no—
81C2×D21—44no—
82C2×D21C2×D418yescomplemented
83C3×C4×C7—24no—
84Dic21—22no—
85C2×#120—211noSylow
86C23×C7—24no—
87C23×C7D1214yescomplemented
88C23×C7C22×D312yes—
89C23×C7C22×D311yescharacteristic
90C22×D7—38no—
91C22×D7—34no—
92C22×D7—32no—
93C22×D7—616no—
94C22×D7—632no—
95C22×D7—64no—
96C22×D7—68no—
97C22×D7—64no—
98C22×D7—62no—
99C22×D7—64no—
100C2×C4×C7—24no—
101C2×C4×C7C22×D314yescomplemented
102C22⋊D7—68no—
103C2×Dic7—32no—
104C2×Dic7—62no—
105D28—616no—
106C24×C3C2×D711yescharacteristic
107C23×D3—72no—
108C23×D3—74no—
109C23×D3—71no—
110C23×D3—148no—
111C23×D3—144no—
112C22×C3×C4C2×D712yescomplemented
113C2×#67—74no—
114C2×#67—144no—
115C22×Dic3—71no—
116C2×D12—78no—
117C2×D12—148no—
118C3×C22⋊C4C2×D714yescomplemented
119(C2×D3)⋊C4—78no—
120C2×C3×C7—24no—
121C2×C3×C7#12014yescomplemented
122C2×C3×C7C22×D411yescharacteristic
123C2×C3×C7C22×D412yes—
124D21—28no—
125D21—42no—
126C25—211no—
127C22×D4—211no—
128C22×D4—212no—
129#120—218no—
130C2×C22⋊C4—212no—
131C2×C22⋊C4D2111yescharacteristic, complemented
132C22×C7—28no—
133C22×C7—24no—
134C22×C7C2×D1212yes—
135C22×C7C2×D1214yescomplemented
136C22×C7D3×D414yes—
137C22×C7C23×D311yescharacteristic
138C2×D7—38no—
139C2×D7—632no—
140C2×D7—616no—
141C2×D7—64no—
142C2×D7—64no—
143C2×D7—62no—
144C2×D7—64no—
145C2×D7—124no—
146C4×C7—24no—
147Dic7—62no—
148C23×C3—24no—
149C23×C3D2814yescomplemented
150C23×C3C22×D712yes—
151C23×C3C22×D711yescharacteristic
152C22×D3—78no—
153C22×D3—74no—
154C22×D3—72no—
155C22×D3—1416no—
156C22×D3—1432no—
157C22×D3—144no—
158C22×D3—148no—
159C22×D3—144no—
160C22×D3—142no—
161C22×D3—144no—
162C2×C3×C4—24no—
163C2×C3×C4C22×D714yescomplemented
164#67—148no—
165C2×Dic3—72no—
166C2×Dic3—142no—
167D12—1416no—
168C3×C7C2×#12011yescharacteristic, complemented, Hall
169C24—212no—
170C24—214no—
171C24—211no—
172C24—428no—
173C24—424no—
174C24C2×D2111yescharacteristic
175C2×D4—214no—
176C2×D4—218no—
177C2×D4—428no—
178C2×D4—424no—
179C22×C4—211no—
180C22×C4C2×D2112yescomplemented
181C22⋊C4—218no—
182C22⋊C4C2×D2114yescomplemented
183C2×C7—24no—
184C2×C7#88214yescomplemented
185C2×C7C22×D1211yescharacteristic
186C2×C7C2×D3×D412yes—
187D7—68no—
188D7—122no—
189C22×C3—28no—
190C22×C3—24no—
191C22×C3C2×D2812yes—
192C22×C3C2×D2814yescomplemented
193C22×C3D4×D714yes—
194C22×C3C23×D711yescharacteristic
195C2×D3—78no—
196C2×D3—1432no—
197C2×D3—1416no—
198C2×D3—144no—
199C2×D3—144no—
200C2×D3—142no—
201C2×D3—144no—
202C2×D3—284no—
203C3×C4—24no—
204Dic3—142no—
205C23—24no—
206C23—218no—
207C23—214no—
208C23—212no—
209C23—4216no—
210C23—4232no—
211C23—424no—
212C23—428no—
213C23—424no—
214C23—422no—
215C23—424no—
216C23D8414yescomplemented
217C23C22×D2112yes—
218C23C22×D2111yescharacteristic
219D4—4216no—
220D4—428no—
221C2×C4—24no—
222C2×C4—212no—
223C2×C4—422no—
224C2×C4C22×D2114yescomplemented
225C7C2×#88211yescharacteristic, complemented, Sylow
226C2×C3—24no—
227C2×C3#644514yescomplemented
228C2×C3C22×D2811yescharacteristic
229C2×C3C2×D4×D712yes—
230D3—148no—
231D3—282no—
232C22—28no—
233C22—24no—
234C22—218no—
235C22—4232no—
236C22—4216no—
237C22—424no—
238C22—424no—
239C22—422no—
240C22—424no—
241C22—844no—
242C22C2×D8412yes—
243C22C2×D8414yescomplemented
244C22D4×D2114yes—
245C22C23×D2111yescharacteristic
246C4—24no—
247C4—422no—
248C3C2×#644511yescharacteristic, complemented, Sylow
249C2—24no—
250C2—428no—
251C2—842no—
252C2#1062136514yesdirect product factor
253C2C22×D8411yescharacteristic
254C2C2×D4×D2112yes—
subgroupG/H
centerC23C22×D21
commutator, cosocleC22×C3×C7C24
FrattiniC22C23×D21
FittingC2×C3×C7×C22⋊C4C2
socleC23×C3×C7C23
hypercenterC2×C22⋊C4D21
hypocenterC3×C7C2×#120
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C24×D21C2semidirect
2. C22×#4268C2semidirect
3. C22×D84C2semidirect
4. C2×C3×C7×C22⋊C4C2semidirect
5. C2×#66631C2semidirect
6. #10621365C2direct (N × H)
12. C23×D21C22semidirect
13. C23×D21C22semidirect
14. C22×C3×C4×C7C22semidirect
16. C2×#4268C22semidirect
17. C22×Dic21C22semidirect
19. C2×D84C22semidirect
20. C3×C7×C22⋊C4C22semidirect
21. #66631C22semidirect
25. C2×C7×C22⋊C4D3semidirect
30. C23×C3×C7D4semidirect
40. C22×D21D4semidirect
42. C22×D21C23semidirect
44. C2×C3×C4×C7C23semidirect
47. C2×Dic21C23semidirect
55. C22×C4×C7C2×D3semidirect
61. C7×C22⋊C4C2×D3semidirect
66. C2×C3×C22⋊C4D7semidirect
73. C22×C3×C7C2×D4semidirect
82. C2×D21C2×D4semidirect
87. C23×C7D12semidirect
101. C2×C4×C7C22×D3semidirect
112. C22×C3×C4C2×D7semidirect
118. C3×C22⋊C4C2×D7semidirect
121. C2×C3×C7#120semidirect
131. C2×C22⋊C4D21semidirect
135. C22×C7C2×D12semidirect
149. C23×C3D28semidirect
163. C2×C3×C4C22×D7semidirect
168. C3×C7C2×#120semidirect
180. C22×C4C2×D21semidirect
182. C22⋊C4C2×D21semidirect
184. C2×C7#882semidirect
192. C22×C3C2×D28semidirect
216. C23D84semidirect
224. C2×C4C22×D21semidirect
225. C7C2×#882semidirect
227. C2×C3#6445semidirect
243. C22C2×D84semidirect
248. C3C2×#6445semidirect
252. C2#10621365direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D212
C22×#42682
C22×D842
C2×C3×C7×C22⋊C42
C2×#666312
#106213652
C2×#64453
C2×#8827