Finite Group Databasebeta

← C2×#20298760 #28399783

Subgroups — C2×#20298760 #28399783

Order 14464.

760 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C22×#14268637C211yesmaximal, characteristic, complemented
2C22×#14268635C211yesmaximal, characteristic, complemented
3C2×#16813601C211yesmaximal, characteristic, complemented
4#20298760C218yesmaximal, direct product factor
5C2×#16813546C211yesmaximal, characteristic, complemented
6C2×#16813543C211yesmaximal, characteristic, complemented
7C2×C22⋊#11744751C211yesmaximal, characteristic, complemented
8C22×#41×C113C211yesmaximal, characteristic
9C22×Dic226C2211yescharacteristic
10C2×#14268637—24no—
11C2×#14268637C2214yescomplemented
12C2×#14268635—24no—
13C2×#14268635C2214yescomplemented
14C22×#11744751C2211yescharacteristic
15C22×#11744751C2211yescharacteristic
16#16813601—22no—
17#16813601C2214yescomplemented
18C2×C4⋊Dic113C2211yescharacteristic
19C2×#14268626—21no—
20C2×C22⋊Dic113—21no—
21#16813546C2214yescomplemented
22#16813543C2214yescomplemented
23C22⋊#11744751C2214yescomplemented
24C2×#41×C113—24no—
25C2×#41×C113—24no—
26C2×#41×C113—22no—
27C2×#41×C113C2214yes—
28C22×Q8×C113C2211yescharacteristic
29C22×D4×C113—21no—
30C22×D4×C113C2211yescharacteristic
31C23×C4×C113—21no—
32C23×C4×C113C2211yescharacteristic
33C2×Dic226—22no—
34C2×Dic226—22no—
35C2×Dic226—21no—
36C2×Dic226C2312yes—
37C22×Dic113—21no—
38C22×Dic113—21no—
39#14268637—28no—
40#14268635—28no—
41C2×#11744751—22no—
42C2×#11744751—22no—
43C2×#11744751C2312yes—
44C2×#11744751C2312yes—
45C4⋊Dic113—21no—
46C4⋊Dic113C2312yes—
47#14268626—24no—
48C22⋊Dic113—24no—
49C24×C113—21no—
50C24×C113D411yescharacteristic
51#41×C113—216no—
52#41×C113—28no—
53#41×C113—28no—
54C2×Q8×C113—22no—
55C2×Q8×C113—21no—
56C2×Q8×C113D414yes—
57C2×Q8×C113C2312yes—
58C2×D4×C113—28no—
59C2×D4×C113—24no—
60C2×D4×C113—21no—
61C2×D4×C113—22no—
62C2×D4×C113D414yes—
63C2×D4×C113C2312yes—
64C22×C4×C113—28no—
65C22×C4×C113—21no—
66C22×C4×C113—24no—
67C22×C4×C113—22no—
68C22×C4×C113—22no—
69C22×C4×C113D411yescharacteristic
70C22×C4×C113D412yes—
71C22×C4×C113C2312yes—
72C22×C4×C113C2311yescharacteristic
73C23×C113—22no—
74C23×C113—24no—
75C23×C113—22no—
76C23×C113—22no—
77C23×C113—22no—
78C23×C113—42no—
79C23×C113—42no—
80C23×C113C2×D412yes—
81C23×C113C2×D411yescharacteristic
82Q8×C113—24no—
83Q8×C113—22no—
84Q8×C113C2×D414yes—
85D4×C113—216no—
86D4×C113—24no—
87D4×C113—22no—
88D4×C113C2×D414yes—
89C2×C4×C113—216no—
90C2×C4×C113—22no—
91C2×C4×C113—24no—
92C2×C4×C113—22no—
93C2×C4×C113—24no—
94C2×C4×C113—22no—
95C2×C4×C113—22no—
96C2×C4×C113C2×D412yes—
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2×D412yes—
99C2×C4×C113C2×D412yes—
100C2×C4×C113C2411yescharacteristic
101C2×Dic113—22no—
102C2×Dic113—22no—
103C2×Dic113—42no—
104C2×Dic113—42no—
105Dic226—22no—
106Dic226—22no—
107Dic226—42no—
108#11744751—22no—
109#11744751—22no—
110C22×C113—22no—
111C22×C113—24no—
112C22×C113—22no—
113C22×C113—22no—
114C22×C113—42no—
115C22×C113—42no—
116C22×C113—44no—
117C22×C113—48no—
118C22×C113#12012yes—
119C22×C113#13512yes—
120C22×C113#13712yes—
121C22×C113C22×D411yescharacteristic
122C4×C113—22no—
123C4×C113—24no—
124C4×C113#12012yes—
125C4×C113C22×D411yescharacteristic
126C4×C113C22×D411yescharacteristic
127Dic113—42no—
128Dic113—42no—
129C2×C113—42no—
130C2×C113—44no—
131C2×C113#45214yescomplemented
132C2×C113C2×#12011yescharacteristic
133C2×C113C2×#13511yescharacteristic
134C2×C113C2×#13711yescharacteristic
135C2×#452—1131nomaximal, Sylow
136C113C2×#45211yescharacteristic, complemented, Sylow
137C22×#41D11311yescharacteristic
138C22×Q16—1131no—
139C22×SD16—1131no—
140C2×C22⋊Q8—1131no—
141#452—1138no—
142C2×#103—1131no—
143C2×#102—1131no—
144C2×C22⋊C8—1131no—
145C2×#41—24no—
146C2×#41—24no—
147C2×#41—22no—
148C2×#41C2×D11314yes—
149C22×Q8—1131no—
150C22×Q8C2×D11311yescharacteristic
151C22×D4—21no—
152C22×D4C2×D11311yescharacteristic
153C23×C4—21no—
154C23×C4C2×D11311yescharacteristic
155C2×Q16—1134no—
156C2×Q16—2264no—
157C2×SD16—1134no—
158C2×SD16—2264no—
159C22×C8—1131no—
160C22×C8—1131no—
161C22⋊Q8—1134no—
162C22⋊Q8—2262no—
163C2×C4⋊C4—1131no—
164C2×C4⋊C4—2261no—
165C2×C22⋊C4—2261no—
166#103—1134no—
167#102—1134no—
168C22⋊C8—1134no—
169C24—21no—
170C24C22⋊D11311yescharacteristic
171#41—216no—
172#41—28no—
173#41—28no—
174C2×Q8—22no—
175C2×Q8—21no—
176C2×Q8—1132no—
177C2×Q8—2262no—
178C2×Q8—2262no—
179C2×Q8—2261no—
180C2×Q8C22⋊D11314yes—
181C2×Q8C22×D11312yes—
182C2×D4—28no—
183C2×D4—24no—
184C2×D4—21no—
185C2×D4—22no—
186C2×D4C22⋊D11314yes—
187C2×D4C22×D11312yes—
188C22×C4—28no—
189C22×C4—21no—
190C22×C4—24no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—2261no—
194C22×C4—2261no—
195C22×C4C22⋊D11312yes—
196C22×C4C22⋊D11311yescharacteristic
197C22×C4C22×D11312yes—
198C22×C4C22×D11311yescharacteristic
199Q16—2268no—
200SD16—2268no—
201C2×C8—1132no—
202C2×C8—1132no—
203C2×C8—2262no—
204C2×C8—2262no—
205C4⋊C4—1132no—
206C4⋊C4—2261no—
207C4⋊C4—2264no—
208C22⋊C4—2264no—
209C23—22no—
210C23—24no—
211C23—22no—
212C23—22no—
213C23—22no—
214C23—42no—
215C23—42no—
216C23C2×C22⋊D11312yes—
217C23C2×C22⋊D11311yescharacteristic
218Q8—24no—
219Q8—22no—
220Q8—4522no—
221Q8—2262no—
222Q8—2262no—
223Q8C2×C22⋊D11314yes—
224D4—216no—
225D4—24no—
226D4—22no—
227D4C2×C22⋊D11314yes—
228C2×C4—216no—
229C2×C4—22no—
230C2×C4—24no—
231C2×C4—22no—
232C2×C4—24no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—4522no—
236C2×C4—4522no—
237C2×C4—2262no—
238C2×C4—2262no—
239C2×C4C2×C22⋊D11312yes—
240C2×C4C2×C22⋊D11311yescharacteristic
241C2×C4C2×C22⋊D11312yes—
242C2×C4C2×C22⋊D11312yes—
243C2×C4C23×D11311yescharacteristic
244C8—2262no—
245C8—2262no—
246C22—22no—
247C22—24no—
248C22—22no—
249C22—22no—
250C22—44no—
251C22—48no—
252C22—42no—
253C22—42no—
254C22#1681359112yes—
255C22#1681364212yes—
256C22#1681365212yes—
257C22C22×C22⋊D11311yescharacteristic
258C4—22no—
259C4—24no—
260C4—4522no—
261C4—4522no—
262C4#1681359112yes—
263C4C22×C22⋊D11311yescharacteristic
264C4C22×C22⋊D11311yescharacteristic
265C2—42no—
266C2—44no—
267C2#2029876014yesdirect product factor
268C2C2×#1681359111yescharacteristic
269C2C2×#1681364211yescharacteristic
270C2C2×#1681365211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting, prime radicalC22×#41×C113C2
socleC23×C113C2×D4
hypercenterC22×#41D113
hypocenterC113C2×#452
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×#14268637C2semidirect
2. C22×#14268635C2semidirect
3. C2×#16813601C2semidirect
4. #20298760C2direct (N × H)
5. C2×#16813546C2semidirect
6. C2×#16813543C2semidirect
7. C2×C22⋊#11744751C2semidirect
11. C2×#14268637C22semidirect
13. C2×#14268635C22semidirect
17. #16813601C22semidirect
21. #16813546C22semidirect
22. #16813543C22semidirect
23. C22⋊#11744751C22semidirect
131. C2×C113#452semidirect
136. C113C2×#452semidirect
267. C2#20298760direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142686372
C22×#142686352
C2×#168136012
#202987602
C2×#168135462
C2×#168135432
C2×C22⋊#117447512
C22×#41×C1132
C2×#452113