Finite Group Databasebeta

← C2×#19132539 #25005748

Subgroups — C2×#19132539 #25005748

Order 11008.

510 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C2×#14582625C212yesmaximal
2#19132539C214yesmaximal, direct product factor
3C2×C43×#382C211yesmaximal, characteristic
4C2×C22⋊(C43⋊C8)—22no—
5#14582625—22no—
6#14582625C2214yes—
7C22×C4⋊C4×C43C411yescharacteristic
8C22×C4⋊C4×C43C2211yescharacteristic
9C22×C42×C43C411yescharacteristic
10C43×#382—22no—
11C43×#382C412yes—
12C43×#382C2212yes—
13C2×#95×C43—22no—
14C22×C43⋊C8—42no—
15C22⋊(C43⋊C8)—24no—
16C22⋊(C43⋊C8)—42no—
17C23×C4×C43—21no—
18C23×C4×C43—21no—
19C23×C4×C43C2×C411yescharacteristic
20C23×C4×C43D412yes—
21C2×C4⋊C4×C43—21no—
22C2×C4⋊C4×C43—41no—
23C2×C4⋊C4×C43—41no—
24C2×C4⋊C4×C43—41no—
25C2×C4⋊C4×C43—41no—
26C2×C4⋊C4×C43C2×C412yes—
27C2×C4⋊C4×C43C2×C411yescharacteristic
28C2×C4⋊C4×C43D412yes—
29C2×C4⋊C4×C43C2311yescharacteristic
30C2×C42×C43—21no—
31C2×C42×C43—22no—
32C2×C42×C43C814yescomplemented
33C2×C42×C43C2×C412yes—
34#95×C43—24no—
35#95×C43—24no—
36C24×C43C22⋊C411yescharacteristic
37C22×C4×C43—24no—
38C22×C4×C43—21no—
39C22×C4×C43—21no—
40C22×C4×C43—22no—
41C22×C4×C43—22no—
42C22×C4×C43—22no—
43C22×C4×C43—22no—
44C22×C4×C43—22no—
45C22×C4×C43—42no—
46C22×C4×C43—42no—
47C22×C4×C43—44no—
48C22×C4×C43—44no—
49C22×C4×C43—41no—
50C22×C4×C43—41no—
51C22×C4×C43C22⋊C411yescharacteristic
52C22×C4×C43C22⋊C412yes—
53C22×C4×C43C2×C812yes—
54C22×C4×C43M1612yes—
55C22×C4×C43C22×C411yescharacteristic
56C22×C4×C43C2×D412yes—
57C4⋊C4×C43—41no—
58C4⋊C4×C43—42no—
59C4⋊C4×C43—41no—
60C4⋊C4×C43—42no—
61C4⋊C4×C43—42no—
62C42×C43—24no—
63C42×C43—22no—
64C42×C43C2×C814yescomplemented
65C2×C43⋊C8—44no—
66C2×C43⋊C8—84no—
67C23×C43—22no—
68C23×C43—22no—
69C23×C43C22⋊C812yes—
70C23×C43#9911yescharacteristic
71C23×C43#9911yescharacteristic
72C23×C43#10112yes—
73C23×C43C2×C22⋊C411yescharacteristic
74C2×C4×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—21no—
79C2×C4×C43—21no—
80C2×C4×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43—24no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—48no—
86C2×C4×C43—42no—
87C2×C4×C43—42no—
88C2×C4×C43—44no—
89C2×C4×C43—42no—
90C2×C4×C43—42no—
91C2×C4×C43—44no—
92C2×C4×C43—42no—
93C2×C4×C43—82no—
94C2×C4×C43—82no—
95C2×C4×C43—82no—
96C2×C4×C43C22⋊C812yes—
97C2×C4×C43C22×C811yescharacteristic
98C2×C4×C43C2×M1611yescharacteristic
99C43⋊C8—84no—
100C2×#1324—431nomaximal, Sylow
101C22×C43—24no—
102C22×C43—24no—
103C22×C43—21no—
104C22×C43—21no—
105C22×C43—21no—
106C22×C43—21no—
107C22×C43#32412yes—
108C22×C43#32412yes—
109C22×C43#35412yes—
110C22×C43#35512yes—
111C22×C43C2×C22⋊C811yescharacteristic
112C22×C43C2×#9911yescharacteristic
113C22×C43C2×#10111yescharacteristic
114C4×C43—22no—
115C4×C43—21no—
116C4×C43—21no—
117C4×C43—44no—
118C4×C43—42no—
119C4×C43—42no—
120C4×C43—82no—
121C2×#382D4311yescharacteristic
122C2×#324—432no—
123#1324—434no—
124C2×C43—21no—
125C2×C43—22no—
126C2×C43—21no—
127C2×C43#132414yescomplemented
128C2×C43C2×#32411yescharacteristic
129C2×C43C2×#35411yescharacteristic
130C2×C43C2×#35511yescharacteristic
131C22×C4⋊C4Dic4311yescharacteristic
132C22×C4⋊C4C2×D4311yescharacteristic
133C22×C42Dic4311yescharacteristic
134C2×C22⋊C8—862no—
135#382—22no—
136#382Dic4312yes—
137#382C2×D4312yes—
138C2×#95—22no—
139#324—434no—
140#324—862no—
141C43C2×#132411yescharacteristic, complemented, Sylow
142C23×C4—21no—
143C23×C4—21no—
144C23×C4C2×Dic4311yescharacteristic
145C23×C4C22⋊D4312yes—
146C22×C8—1722no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4C2×Dic4312yes—
153C2×C4⋊C4C2×Dic4311yescharacteristic
154C2×C4⋊C4C22⋊D4312yes—
155C2×C4⋊C4C22×D4311yescharacteristic
156C2×C42—22no—
157C2×C42—21no—
158C2×C42C43⋊C814yescomplemented
159C2×C42C2×Dic4312yes—
160C22⋊C8—864no—
161C22⋊C8—1722no—
162#95—24no—
163#95—24no—
164C24C22⋊Dic4311yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—22no—
168C22×C4—24no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4—44no—
176C22×C4—44no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4C2×C43⋊C812yes—
180C22×C4#1062187712yes—
181C22×C4C22⋊Dic4311yescharacteristic
182C22×C4C22⋊Dic4312yes—
183C22×C4C22×Dic4311yescharacteristic
184C22×C4C2×C22⋊D4312yes—
185C2×C8—3444no—
186C2×C8—1724no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C42—24no—
193C42—22no—
194C42C2×C43⋊C814yescomplemented
195C23—22no—
196C23—22no—
197C23C22⋊(C43⋊C8)12yes—
198C23#1306324011yescharacteristic
199C23#1306324011yescharacteristic
200C23#1306324412yes—
201C23C2×C22⋊Dic4311yescharacteristic
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—24no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—48no—
216C2×C4—44no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—44no—
220C2×C4—42no—
221C2×C4—82no—
222C2×C4—82no—
223C2×C4—82no—
224C2×C4C22⋊(C43⋊C8)12yes—
225C2×C4C22×C43⋊C811yescharacteristic
226C2×C4C2×#1062187711yescharacteristic
227C8—3444no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22—21no—
232C22—24no—
233C22—24no—
234C22#1458262512yes—
235C22#1458262512yes—
236C22#1458269412yes—
237C22#1458269612yes—
238C22C2×C22⋊(C43⋊C8)11yescharacteristic
239C22C2×#1306324011yescharacteristic
240C22C2×#1306324411yescharacteristic
241C4—22no—
242C4—21no—
243C4—21no—
244C4—44no—
245C4—42no—
246C4—42no—
247C4—82no—
248C2—21no—
249C2—21no—
250C2—22no—
251C2#1913253914yesdirect product factor
252C2C2×#1458262511yescharacteristic
253C2C2×#1458269411yescharacteristic
254C2C2×#1458269611yescharacteristic
subgroupG/H
centerC23#13063240
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC2×C43×#382C2
socleC23×C43#99
prime radicalC24×C43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenterC2×#382D43
hypocenterC43C2×#1324
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. #19132539C2direct (N × H)
32. C2×C42×C43C8semidirect
64. C42×C43C2×C8semidirect
127. C2×C43#1324semidirect
141. C43C2×#1324semidirect
158. C2×C42C43⋊C8semidirect
194. C42C2×C43⋊C8semidirect
251. C2#19132539direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145826252
#191325392
C2×C43×#3822
C2×#132443