Finite Group Databasebeta

← #28399836

Subgroups — #28399836

Order 14464.

754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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
2C2×#16813655C212yesmaximal, complemented
3C2×#16813601C211yesmaximal, characteristic, complemented
4#20298762C214yesmaximal, complemented
5#20298756C212yesmaximal, complemented
6#20298751C212yesmaximal, complemented
7#20298600C212yesmaximal, complemented
8#407×C113C211yesmaximal, characteristic, complemented
9C2×#14268647—28no—
10C2×#14268647—21no—
11C2×#14268647—21no—
12C2×#14268647C2212yes—
13C2×#14268647C2212yes—
14C22×Dic226C2211yescharacteristic
15C22×Dic226C2211yescharacteristic, complemented
16C22×D452C2211yescharacteristic
17C22×C22⋊D113—21no—
18C22×C4×D113—21no—
19#16813655—28no—
20C2×Dic452C2214yescomplemented
21C2×#14268636C2214yescomplemented
22#16813601—21no—
23#16813601—21no—
24#16813601C2212yes—
25#16813601C2212yescomplemented
26C2×C4⋊Dic113C2211yescharacteristic, complemented
27C2×#14268626—21no—
28C2×C22⋊Dic113—21no—
29#16813547C2214yescomplemented
30#16813544C2214yescomplemented
31C23×C4×C113C2211yescharacteristic
32C2×M16×C113C2212yescomplemented
33C22⋊C8×C113C2212yes—
34C22⋊C8×C113C2212yescomplemented
35C23×D113—21no—
36#14268647—28no—
37#14268647—28no—
38#14268647—24no—
39#14268647—24no—
40#14268647—24no—
41#14268647D418yes—
42C2×Dic226—21no—
43C2×Dic226—24no—
44C2×Dic226—24no—
45C2×Dic226—21no—
46C2×Dic226C2312yes—
47C2×Dic226C2312yes—
48C2×D452—21no—
49C2×D452—24no—
50C2×D452C2312yes—
51C2×C22⋊D113—28no—
52C2×C22⋊D113—22no—
53C2×C22⋊D113—22no—
54C22×Dic113—21no—
55C22×Dic113—21no—
56C22×Dic113—21no—
57C2×C4×D113—28no—
58C2×C4×D113—22no—
59C2×C4×D113—22no—
60Dic452—28no—
61#14268636—28no—
62C4⋊Dic113—21no—
63C4⋊Dic113C2312yes—
64#14268626—22no—
65#14268626—22no—
66C22⋊Dic113—22no—
67C22⋊Dic113—22no—
68C24×C113D411yescharacteristic
69C22×C4×C113—24no—
70C22×C4×C113D411yescharacteristic
71C22×C4×C113D411yescharacteristic
72C22×C4×C113D411yescharacteristic
73C22×C4×C113C2311yescharacteristic
74C22×C4×C113C2311yescharacteristic
75C22×C4×C113C2311yescharacteristic
76M16×C113—24no—
77C2×C8×C113C2314yes—
78C23×C113—22no—
79C23×C113—22no—
80C23×C113—41no—
81C23×C113C2×D411yescharacteristic
82C23×C113C2×D411yescharacteristic
83C23×C113C2×D411yescharacteristic
84C22×D113—24no—
85C22×D113—22no—
86C22×D113—42no—
87C22×D113—42no—
88C2×C4×C113—22no—
89C2×C4×C113—22no—
90C2×C4×C113—22no—
91C2×C4×C113—22no—
92C2×C4×C113—22no—
93C2×C4×C113C2×D414yes—
94C2×C4×C113C2×D411yescharacteristic
95C2×C4×C113C2×D411yescharacteristic
96C2×C4×C113C2×D411yescharacteristic
97C2×C4×C113C2411yescharacteristic
98C22⋊D113—28no—
99C22⋊D113—28no—
100C2×Dic113—24no—
101C2×Dic113—22no—
102C2×Dic113—22no—
103C2×Dic113—22no—
104C2×Dic113—42no—
105C2×Dic113—42no—
106D452—24no—
107D452—22no—
108D452C2×D414yes—
109C4×D113—28no—
110C4×D113—28no—
111Dic226—24no—
112Dic226—22no—
113Dic226—24no—
114Dic226—42no—
115Dic226C2×D414yes—
116C8×C113—24no—
117C22×C113—21no—
118C22×C113—21no—
119C22×C113—21no—
120C22×C113—21no—
121C22×C113—21no—
122C22×C113—21no—
123C22×C113—21no—
124C22×C113—44no—
125C22×C113#12012yes—
126C22×C113#13712yescomplemented
127C22×C113C22×D411yescharacteristic
128C2×D113—24no—
129C2×D113—48no—
130C2×D113—42no—
131C2×D113—42no—
132C4×C113—21no—
133C4×C113—21no—
134C4×C113#12012yes—
135C4×C113C22×D412yes—
136Dic113—24no—
137Dic113—42no—
138Dic113—42no—
139C2×C113—22no—
140C2×C113—22no—
141C2×C113—41no—
142C2×C113C2×#12011yescharacteristic
143C2×C113C2×#13711yescharacteristic
144C2×C113#57511yescharacteristic
145D113—44no—
146#3007—1131nomaximal, Sylow
147C113#300711yescharacteristic, complemented, Sylow
148C22×#41—1131no—
149C2×#137—1132no—
150C2×C22⋊Q8—1131no—
151#452—1134no—
152#451—1132no—
153#450—1132no—
154#417—1132no—
155#407D11311yescharacteristic, complemented
156C2×#41—1132no—
157C2×#41—1132no—
158C2×#41—2268no—
159C2×#41—2261no—
160C2×#41—2261no—
161C22×Q8—1131no—
162C22×Q8—1131no—
163C22×D4—1131no—
164C22×D4—2261no—
165C23×C4—2261no—
166C23×C4C2×D11311yescharacteristic
167#137—2268no—
168C2×Q16—1134no—
169C2×SD16—1134no—
170C2×M16C2×D11312yescomplemented
171C22⋊Q8—1132no—
172C22⋊Q8—1132no—
173C22⋊Q8—2261no—
174C22⋊Q8—2261no—
175C2×C4⋊C4—1131no—
176C2×C4⋊C4—2261no—
177C2×C22⋊C4—2261no—
178#103—1134no—
179#102—1134no—
180C22⋊C8C2×D11312yes—
181C22⋊C8C2×D11312yescomplemented
182C24—2261no—
183C24D45211yescharacteristic
184#41—1138no—
185#41—2264no—
186#41—2264no—
187#41—2268no—
188#41—2268no—
189#41—2264no—
190C2×Q8—1132no—
191C2×Q8—1132no—
192C2×Q8—2264no—
193C2×Q8—2264no—
194C2×Q8—2261no—
195C2×Q8—2261no—
196C2×D4—1132no—
197C2×D4—2264no—
198C2×D4—2268no—
199C2×D4—2262no—
200C2×D4—2262no—
201C2×D4—2261no—
202C22×C4—24no—
203C22×C4—2268no—
204C22×C4—2261no—
205C22×C4—2261no—
206C22×C4—2261no—
207C22×C4—2262no—
208C22×C4—2262no—
209C22×C4D45211yescharacteristic
210C22×C4D45211yescharacteristic
211C22×C4D45211yescharacteristic
212C22×C4C22×D11311yescharacteristic
213C22×C4C22×D11311yescharacteristic
214C22×C4C22×D11311yescharacteristic
215Q16—2268no—
216SD16—2268no—
217M16—24no—
218C2×C8C22×D11314yes—
219C4⋊C4—1132no—
220C4⋊C4—2261no—
221C4⋊C4—2262no—
222C4⋊C4—2262no—
223C22⋊C4—2262no—
224C22⋊C4—2262no—
225C23—22no—
226C23—22no—
227C23—41no—
228C23—4522no—
229C23—4522no—
230C23—2264no—
231C23—2262no—
232C23C2×D45211yescharacteristic
233C23C2×D45211yescharacteristic
234C23C2×D45211yescharacteristic
235Q8—1134no—
236Q8—4522no—
237Q8—2264no—
238Q8—2264no—
239Q8—2262no—
240D4—1134no—
241D4—2264no—
242D4—2268no—
243D4—2268no—
244D4—2262no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—4522no—
251C2×C4—4522no—
252C2×C4—2268no—
253C2×C4—2262no—
254C2×C4—2262no—
255C2×C4—2264no—
256C2×C4—2262no—
257C2×C4—2268no—
258C2×C4D4×D11314yes—
259C2×C4C2×D45211yescharacteristic
260C2×C4C2×D45211yescharacteristic
261C2×C4C2×D45211yescharacteristic
262C2×C4C23×D11311yescharacteristic
263C8—24no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—44no—
272C22—4528no—
273C22—4522no—
274C22—4522no—
275C22—2264no—
276C22#1681359212yes—
277C22#1681365512yescomplemented
278C22C22×D45211yescharacteristic
279C4—21no—
280C4—21no—
281C4—4522no—
282C4—4522no—
283C4—2264no—
284C4#1681359212yes—
285C4C2×D4×D11312yes—
286C2—22no—
287C2—22no—
288C2—41no—
289C2—4524no—
290C2C2×#1681359211yescharacteristic
291C2C2×#1681365511yescharacteristic
292C2#2029939811yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#407×C113C2
socleC22×C113C22×D4
prime radicalC22×#14268647C2
hypercenter#407D113
hypocenterC113#3007
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#16813655C2semidirect
3. C2×#16813601C2semidirect
4. #20298762C2semidirect
5. #20298756C2semidirect
6. #20298751C2semidirect
7. #20298600C2semidirect
8. #407×C113C2semidirect
15. C22×Dic226C22semidirect
20. C2×Dic452C22semidirect
21. C2×#14268636C22semidirect
25. #16813601C22semidirect
26. C2×C4⋊Dic113C22semidirect
29. #16813547C22semidirect
30. #16813544C22semidirect
32. C2×M16×C113C22semidirect
34. C22⋊C8×C113C22semidirect
126. C22×C113#137semidirect
147. C113#3007semidirect
155. #407D113semidirect
170. C2×M16C2×D113semidirect
181. C22⋊C8C2×D113semidirect
277. C22#16813655semidirect

Maximal subgroups

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

subgroupindex
C22×#142686472
C2×#168136552
C2×#168136012
#202987622
#202987562
#202987512
#202986002
#407×C1132
#3007113