Finite Group Databasebeta

← C2×#20298738 #28399763

Subgroups — C2×#20298738 #28399763

Order 14464.

792 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 173 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×Q8×D113C211yesmaximal, characteristic, complemented
2C22×#14268636C211yesmaximal, characteristic, complemented
3C22×#14268634C211yesmaximal, characteristic, complemented
4C2×#16813597C211yesmaximal, characteristic
5#20298738C218yesmaximal, direct product factor
6C2×#16813545C211yesmaximal, characteristic, complemented
7C2×#16813534C211yesmaximal, characteristic, complemented
8C2×#103×C113C211yesmaximal, characteristic, complemented
9C22×Dic226—21no—
10C22×Dic226C2211yescharacteristic
11C2×Q8×D113—24no—
12C2×Q8×D113—22no—
13C2×Q8×D113—24no—
14C2×Q8×D113C2214yescomplemented
15C22×D452—21no—
16C22×D452C2211yescharacteristic
17C22×C4×D113—21no—
18C22×C4×D113C2211yescharacteristic
19C2×#14268636—24no—
20C2×#14268636C2214yescomplemented
21C2×#14268634—24no—
22C2×#14268634C2214yescomplemented
23C22×#11744751C2211yescharacteristic
24#16813597—22no—
25#16813597C2214yes—
26C2×#14268624—21no—
27#16813545C2214yescomplemented
28#16813534C2214yescomplemented
29C22×Q8×C113C2211yescharacteristic
30C22×C8×C113C2211yescharacteristic
31C2×C4⋊C4×C113C2211yescharacteristic
32#103×C113C2214yescomplemented
33C23×D113—21no—
34C23×D113D411yescharacteristic
35C2×Dic226—28no—
36C2×Dic226—21no—
37C2×Dic226—22no—
38C2×Dic226—24no—
39C2×Dic226D414yescomplemented
40C2×Dic226C2312yes—
41Q8×D113—216no—
42Q8×D113—28no—
43Q8×D113—28no—
44C2×D452—22no—
45C2×D452—22no—
46C2×D452—24no—
47C2×D452—21no—
48C2×D452—44no—
49C2×D452C2312yes—
50C22×Dic113—21no—
51C22×Dic113D411yescharacteristic
52C2×C4×D113—28no—
53C2×C4×D113—24no—
54C2×C4×D113—22no—
55C2×C4×D113—22no—
56C2×C4×D113D412yes—
57C2×C4×D113C2312yes—
58#14268636—28no—
59#14268634—28no—
60C2×#11744751—22no—
61C2×#11744751C2312yes—
62#14268624—24no—
63C2×Q8×C113—22no—
64C2×Q8×C113—21no—
65C2×Q8×C113D414yescomplemented
66C2×Q8×C113C2312yes—
67C22×C4×C113—21no—
68C22×C4×C113—21no—
69C22×C4×C113C2311yescharacteristic
70C2×C8×C113—22no—
71C2×C8×C113C2312yes—
72C4⋊C4×C113—21no—
73C4⋊C4×C113C2312yes—
74C23×C113C2×D411yescharacteristic
75C22×D113—22no—
76C22×D113—22no—
77C22×D113—22no—
78C22×D113—42no—
79C22×D113—42no—
80C22×D113—42no—
81C22×D113SD1614yescomplemented
82C22×D113C2×D412yes—
83Q8×C113—24no—
84Q8×C113—22no—
85Q8×C113C2×D414yescomplemented
86C2×C4×C113—24no—
87C2×C4×C113—22no—
88C2×C4×C113—22no—
89C2×C4×C113—42no—
90C2×C4×C113C2×D411yescharacteristic
91C2×C4×C113C2×D412yes—
92C2×C4×C113C2×D412yes—
93C2×C4×C113C2411yescharacteristic
94C2×Dic113—24no—
95C2×Dic113—22no—
96C2×Dic113—22no—
97C2×Dic113C2×D412yes—
98D452—22no—
99D452—22no—
100D452—48no—
101D452—42no—
102C4×D113—216no—
103C4×D113—24no—
104C4×D113—22no—
105C4×D113—22no—
106Dic226—216no—
107Dic226—24no—
108Dic226—22no—
109Dic226C2×D414yescomplemented
110C8×C113—22no—
111#11744751—22no—
112C22×C113#12012yes—
113C22×C113C2×SD1612yes—
114C22×C113#13712yes—
115C22×C113C22×D411yescharacteristic
116C2×D113—22no—
117C2×D113—22no—
118C2×D113—28no—
119C2×D113—42no—
120C2×D113—42no—
121C2×D113—42no—
122C2×D113—84no—
123C2×D113C2×SD1614yescomplemented
124C4×C113—24no—
125C4×C113—42no—
126C4×C113#12012yes—
127C4×C113C22×D411yescharacteristic
128C4×C113C22×D411yescharacteristic
129Dic113—22no—
130Dic113—24no—
131C2×C113#44814yescomplemented
132C2×C113C2×#12011yescharacteristic
133C2×C113C22×SD1611yescharacteristic
134C2×C113C2×#13711yescharacteristic
135D113—24no—
136D113—82no—
137C2×#448—1131nomaximal, Sylow
138C113C2×#44811yescharacteristic, complemented, Sylow
139C23×Q8—1131no—
140C22×SD16—1131no—
141C22×SD16—1131no—
142C2×#121—1131no—
143#448—1138no—
144C2×#103—1131no—
145C2×#103D11311yescharacteristic, complemented
146C2×C22⋊C8—1131no—
147C22×Q8—1134no—
148C22×Q8—1131no—
149C22×Q8—2261no—
150C22×Q8—2262no—
151C22×Q8—2264no—
152C22×Q8—2264no—
153C22×Q8C2×D11311yescharacteristic
154C22×D4—1131no—
155C22×D4—2261no—
156C23×C4—1131no—
157C23×C4—2261no—
158C2×SD16—1134no—
159C2×SD16—1134no—
160C2×SD16—2264no—
161C2×SD16—2264no—
162C22×C8—1131no—
163C22×C8C2×D11311yescharacteristic
164#121—1134no—
165#121—2262no—
166C2×C4⋊C4C2×D11311yescharacteristic
167C2×C22⋊C4—2261no—
168#103—1134no—
169#103C2×D11314yescomplemented
170C22⋊C8—1134no—
171C24—1131no—
172C24—2261no—
173C2×Q8—22no—
174C2×Q8—21no—
175C2×Q8—1134no—
176C2×Q8—1132no—
177C2×Q8—2264no—
178C2×Q8—2268no—
179C2×Q8—2268no—
180C2×Q8—22616no—
181C2×Q8—2268no—
182C2×Q8—2261no—
183C2×Q8—2262no—
184C2×Q8D45214yescomplemented
185C2×Q8C22×D11312yes—
186C2×D4—1132no—
187C2×D4—4524no—
188C2×D4—2264no—
189C2×D4—2261no—
190C2×D4—2262no—
191C2×D4—2262no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—1131no—
195C22×C4—1132no—
196C22×C4—1132no—
197C22×C4—2264no—
198C22×C4—2268no—
199C22×C4—2261no—
200C22×C4—2262no—
201C22×C4—2262no—
202C22×C4C22×D11311yescharacteristic
203SD16—2268no—
204SD16—2268no—
205C2×C8—22no—
206C2×C8—1132no—
207C2×C8—2262no—
208C2×C8C22×D11312yes—
209C4⋊C4—21no—
210C4⋊C4C22×D11312yes—
211C22⋊C4—2264no—
212C23—1134no—
213C23—1132no—
214C23—4522no—
215C23—4522no—
216C23—4522no—
217C23—2262no—
218C23—2262no—
219C23—2262no—
220C23D4×D11311yescharacteristic
221Q8—24no—
222Q8—22no—
223Q8—1134no—
224Q8—22616no—
225Q8—2264no—
226Q8—2262no—
227Q8C2×D45214yescomplemented
228D4—4528no—
229D4—4522no—
230D4—2262no—
231D4—2262no—
232C2×C4—24no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—42no—
236C2×C4—1132no—
237C2×C4—22616no—
238C2×C4—2262no—
239C2×C4—2264no—
240C2×C4—2262no—
241C2×C4—2264no—
242C2×C4—2262no—
243C2×C4—2262no—
244C2×C4D4×D11311yescharacteristic
245C2×C4D4×D11312yes—
246C2×C4C2×D45212yes—
247C2×C4C23×D11311yescharacteristic
248C8—22no—
249C8—2262no—
250C22—1134no—
251C22—9044no—
252C22—4522no—
253C22—4522no—
254C22—4522no—
255C22—2262no—
256C22—2262no—
257C22—2268no—
258C22#1681359212yes—
259C22SD16×D11312yes—
260C22#1681365412yes—
261C22C2×D4×D11311yescharacteristic
262C4—24no—
263C4—42no—
264C4—2262no—
265C4—2264no—
266C4#1681359212yes—
267C4C2×D4×D11311yescharacteristic
268C4C22×D45211yescharacteristic
269C2—9042no—
270C2—2264no—
271C2#2029873814yesdirect product factor
272C2C2×#1681359211yescharacteristic
273C2C2×SD16×D11311yescharacteristic
274C2C2×#1681365411yescharacteristic
subgroupG/H
centerC23D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#103×C113C2
socleC23×C113C2×D4
prime radicalC2×#16813597C2
hypercenterC2×#103D113
hypocenterC113C2×#448
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D113C2semidirect
2. C22×#14268636C2semidirect
3. C22×#14268634C2semidirect
5. #20298738C2direct (N × H)
6. C2×#16813545C2semidirect
7. C2×#16813534C2semidirect
8. C2×#103×C113C2semidirect
14. C2×Q8×D113C22semidirect
20. C2×#14268636C22semidirect
22. C2×#14268634C22semidirect
27. #16813545C22semidirect
28. #16813534C22semidirect
32. #103×C113C22semidirect
39. C2×Dic226D4semidirect
65. C2×Q8×C113D4semidirect
81. C22×D113SD16semidirect
85. Q8×C113C2×D4semidirect
109. Dic226C2×D4semidirect
123. C2×D113C2×SD16semidirect
131. C2×C113#448semidirect
138. C113C2×#448semidirect
145. C2×#103D113semidirect
169. #103C2×D113semidirect
184. C2×Q8D452semidirect
227. Q8C2×D452semidirect
271. C2#20298738direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D1132
C22×#142686362
C22×#142686342
C2×#168135972
#202987382
C2×#168135452
C2×#168135342
C2×#103×C1132
C2×#448113