Finite Group Databasebeta

← C2×#20298758 #28399781

Subgroups — C2×#20298758 #28399781

Order 14464.

760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14268647C211yesmaximal, characteristic
2C22×#14268637C211yesmaximal, characteristic, complemented
3C22×#14268634C211yesmaximal, characteristic, complemented
4#20298758C218yesmaximal, direct product factor
5C2×#16813545C211yesmaximal, characteristic, complemented
6C2×#16813542C211yesmaximal, characteristic, complemented
7C2×C22⋊#11744751C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C113C211yesmaximal, characteristic, complemented
9C2×#14268647—24no—
10C2×#14268647—24no—
11C2×#14268647—22no—
12C2×#14268647C2214yes—
13C22×Dic226C2211yescharacteristic
14C22×D452C2211yescharacteristic
15C22×C22⋊D113—21no—
16C22×C4×D113—21no—
17C2×#14268637—24no—
18C2×#14268637C2214yescomplemented
19C2×#14268634—24no—
20C2×#14268634C2214yescomplemented
21C22×#11744751C2211yescharacteristic
22C22×#11744751C2211yescharacteristic
23#16813545C2214yescomplemented
24#16813542C2214yescomplemented
25C22⋊#11744751C2214yescomplemented
26C22×Q8×C113C2211yescharacteristic
27C23×C4×C113C2211yescharacteristic
28C22⋊Q8×C113—22no—
29C22⋊Q8×C113C2214yescomplemented
30C2×C4⋊C4×C113—21no—
31C2×C4⋊C4×C113C2211yescharacteristic
32C2×C22⋊C4×C113—21no—
33C23×D113—21no—
34#14268647—216no—
35#14268647—28no—
36#14268647—28no—
37C2×Dic226—22no—
38C2×Dic226—21no—
39C2×Dic226D414yes—
40C2×Dic226C2312yes—
41C2×D452—22no—
42C2×D452—21no—
43C2×D452D414yes—
44C2×D452C2312yes—
45C2×C22⋊D113—28no—
46C2×C22⋊D113—24no—
47C22×Dic113—21no—
48C2×C4×D113—28no—
49C2×C4×D113—24no—
50#14268637—28no—
51#14268634—28no—
52C2×#11744751—22no—
53C2×#11744751—22no—
54C2×#11744751C2312yes—
55C2×#11744751C2312yes—
56C24×C113D411yescharacteristic
57C2×Q8×C113—21no—
58C2×Q8×C113—22no—
59C2×Q8×C113—22no—
60C2×Q8×C113C2312yes—
61C22×C4×C113—22no—
62C22×C4×C113—22no—
63C22×C4×C113—21no—
64C22×C4×C113—21no—
65C22×C4×C113D411yescharacteristic
66C22×C4×C113D412yes—
67C22×C4×C113C2312yes—
68C22×C4×C113C2311yescharacteristic
69C4⋊C4×C113—24no—
70C4⋊C4×C113—21no—
71C4⋊C4×C113C2312yes—
72C22⋊C4×C113—24no—
73C23×C113—22no—
74C23×C113—22no—
75C23×C113—22no—
76C23×C113C2×D412yes—
77C23×C113C2×D411yescharacteristic
78C22×D113—24no—
79C22×D113—22no—
80C22×D113—42no—
81C22×D113—42no—
82Q8×C113—22no—
83Q8×C113—22no—
84Q8×C113—42no—
85C2×C4×C113—22no—
86C2×C4×C113—24no—
87C2×C4×C113—22no—
88C2×C4×C113—22no—
89C2×C4×C113—22no—
90C2×C4×C113—22no—
91C2×C4×C113—42no—
92C2×C4×C113—42no—
93C2×C4×C113C2×D412yes—
94C2×C4×C113C2×D412yes—
95C2×C4×C113C2×D412yes—
96C2×C4×C113C2×D411yescharacteristic
97C2×C4×C113C2411yescharacteristic
98C22⋊D113—216no—
99C2×Dic113—24no—
100C2×Dic113—22no—
101D452—24no—
102D452—22no—
103D452C2×D414yes—
104C4×D113—216no—
105Dic226—24no—
106Dic226—22no—
107Dic226C2×D414yes—
108#11744751—22no—
109#11744751—22no—
110C22×C113—22no—
111C22×C113—22no—
112C22×C113—22no—
113C22×C113—44no—
114C22×C113#12012yes—
115C22×C113#13512yes—
116C22×C113#13712yes—
117C22×C113C22×D411yescharacteristic
118C2×D113—24no—
119C2×D113—42no—
120C2×D113—42no—
121C2×D113—48no—
122C4×C113—22no—
123C4×C113—42no—
124C4×C113—42no—
125C4×C113#12012yes—
126C4×C113C22×D411yescharacteristic
127C4×C113C22×D411yescharacteristic
128Dic113—24no—
129C2×C113—42no—
130C2×C113#45214yescomplemented
131C2×C113C2×#12011yescharacteristic
132C2×C113C2×#13511yescharacteristic
133C2×C113C2×#13711yescharacteristic
134D113—44no—
135C2×#452—1131nomaximal, Sylow
136C113C2×#45211yescharacteristic, complemented, Sylow
137C22×#41—1131no—
138C22×Q16—1131no—
139C22×SD16—1131no—
140C2×C22⋊Q8D11311yescharacteristic, complemented
141#452—1138no—
142C2×#103—1131no—
143C2×#102—1131no—
144C2×C22⋊C8—1131no—
145C2×#41—1134no—
146C2×#41—2264no—
147C2×#41—2264no—
148C2×#41—2262no—
149C22×Q8—1131no—
150C22×Q8C2×D11311yescharacteristic
151C22×D4—1131no—
152C22×D4—2261no—
153C23×C4—2261no—
154C23×C4C2×D11311yescharacteristic
155C2×Q16—1134no—
156C2×Q16—2264no—
157C2×SD16—1134no—
158C2×SD16—2264no—
159C22×C8—1131no—
160C22×C8—1131no—
161C22⋊Q8—22no—
162C22⋊Q8C2×D11314yescomplemented
163C2×C4⋊C4—21no—
164C2×C4⋊C4C2×D11311yescharacteristic
165C2×C22⋊C4—21no—
166#103—1134no—
167#102—1134no—
168C22⋊C8—1134no—
169C24—2261no—
170C24C22⋊D11311yescharacteristic
171#41—2268no—
172#41—2268no—
173#41—22616no—
174C2×Q8—21no—
175C2×Q8—22no—
176C2×Q8—22no—
177C2×Q8—1134no—
178C2×Q8—1132no—
179C2×Q8—2262no—
180C2×Q8—2261no—
181C2×Q8C22×D11312yes—
182C2×D4—1134no—
183C2×D4—1132no—
184C2×D4—2268no—
185C2×D4—2264no—
186C2×D4—2262no—
187C2×D4—2261no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—2268no—
193C22×C4—2261no—
194C22×C4—2264no—
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—24no—
206C4⋊C4—21no—
207C4⋊C4C22×D11312yes—
208C22⋊C4—24no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—4522no—
213C23—4522no—
214C23—2264no—
215C23—2262no—
216C23C2×C22⋊D11312yes—
217C23C2×C22⋊D11311yescharacteristic
218Q8—22no—
219Q8—22no—
220Q8—42no—
221Q8—1134no—
222Q8—2264no—
223Q8—2262no—
224D4—1134no—
225D4—22616no—
226D4—2264no—
227D4—2262no—
228C2×C4—22no—
229C2×C4—24no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—22616no—
237C2×C4—2264no—
238C2×C4—2262no—
239C2×C4D4×D11312yes—
240C2×C4D4×D11312yes—
241C2×C4C2×C22⋊D11312yes—
242C2×C4C2×C22⋊D11311yescharacteristic
243C2×C4C23×D11311yescharacteristic
244C8—2262no—
245C8—2262no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—44no—
250C22—4528no—
251C22—4522no—
252C22—4522no—
253C22—2264no—
254C22#1681359012yes—
255C22#1681364212yes—
256C22#1681365312yes—
257C22C22×C22⋊D11311yescharacteristic
258C4—22no—
259C4—42no—
260C4—42no—
261C4—2264no—
262C4#1681359012yes—
263C4C2×D4×D11311yescharacteristic
264C4C2×D4×D11311yescharacteristic
265C2—42no—
266C2—4524no—
267C2#2029875814yesdirect product factor
268C2C2×#1681359011yescharacteristic
269C2C2×#1681364211yescharacteristic
270C2C2×#1681365311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×C22⋊Q8×C113C2
socleC23×C113C2×D4
prime radicalC22×#14268647C2
hypercenterC2×C22⋊Q8D113
hypocenterC113C2×#452
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C22×#14268637C2semidirect
3. C22×#14268634C2semidirect
4. #20298758C2direct (N × H)
5. C2×#16813545C2semidirect
6. C2×#16813542C2semidirect
7. C2×C22⋊#11744751C2semidirect
8. C2×C22⋊Q8×C113C2semidirect
18. C2×#14268637C22semidirect
20. C2×#14268634C22semidirect
23. #16813545C22semidirect
24. #16813542C22semidirect
25. C22⋊#11744751C22semidirect
29. C22⋊Q8×C113C22semidirect
130. C2×C113#452semidirect
136. C113C2×#452semidirect
140. C2×C22⋊Q8D113semidirect
162. C22⋊Q8C2×D113semidirect
267. C2#20298758direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142686472
C22×#142686372
C22×#142686342
#202987582
C2×#168135452
C2×#168135422
C2×C22⋊#117447512
C2×C22⋊Q8×C1132
C2×#452113