Finite Group Databasebeta

← #28399814

Subgroups — #28399814

Order 14464.

758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 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, complemented
2C2×#16813652C211yesmaximal, characteristic, complemented
3C2×#16813647C211yesmaximal, characteristic, complemented
4#20298758C214yesmaximal, complemented
5#20298741C214yesmaximal, complemented
6#20298606C211yesmaximal, characteristic, complemented
7#20298602C211yesmaximal, characteristic, complemented
8#20298562C211yesmaximal, characteristic, complemented
9#525×C113C211yesmaximal, characteristic, complemented
10C2×#14268647—24no—
11C2×#14268647—24no—
12C2×#14268647—22no—
13C2×#14268647C2214yes—
14C22×Dic226C2211yescharacteristic
15C22×D452C2211yescharacteristic
16C22×C22⋊D113—21no—
17C22×C4×D113—21no—
18#16813652—24no—
19#16813647—24no—
20C2×#14268637C2212yescomplemented
21C2×#14268635C2212yescomplemented
22C2×#14268634C2212yescomplemented
23C2×#14268632C2212yescomplemented
24C2×#14268631C2211yescharacteristic
25C2×#14268631C2211yescharacteristic
26#16813545C2214yescomplemented
27#16813542C2214yescomplemented
28C22⋊#11744751C2214yescomplemented
29C2×#41×C113C2211yescharacteristic
30C23×C4×C113C2211yescharacteristic
31#123×C113—21no—
32C22⋊Q8×C113C2212yescomplemented
33#121×C113C2212yescomplemented
34#120×C113—21no—
35C4×D4×C113—22no—
36#117×C113C2211yescharacteristic
37C23×D113—21no—
38#14268647—216no—
39#14268647—28no—
40#14268647—28no—
41C2×Dic226—22no—
42C2×Dic226—21no—
43C2×Dic226D414yescomplemented
44C2×Dic226C2312yes—
45C2×D452—22no—
46C2×D452—21no—
47C2×D452D414yescomplemented
48C2×D452C2312yes—
49C2×C22⋊D113—28no—
50C2×C22⋊D113—24no—
51C22×Dic113—21no—
52C2×C4×D113—28no—
53C2×C4×D113—24no—
54#14268637—24no—
55#14268635—24no—
56#14268634—24no—
57#14268632—24no—
58#14268631—22no—
59#14268631—22no—
60C2×#11744751C2312yes—
61C2×#11744751C2312yes—
62C24×C113D411yescharacteristic
63#41×C113—22no—
64#41×C113—22no—
65C2×Q8×C113C2311yescharacteristic
66C2×D4×C113—22no—
67C2×D4×C113—21no—
68C2×D4×C113C2311yescharacteristic
69C22×C4×C113—22no—
70C22×C4×C113—22no—
71C22×C4×C113—21no—
72C22×C4×C113D411yescharacteristic
73C22×C4×C113D412yes—
74C22×C4×C113C2312yes—
75C22×C4×C113C2311yescharacteristic
76C4⋊C4×C113—22no—
77C4⋊C4×C113C2312yes—
78C22⋊C4×C113—21no—
79C22⋊C4×C113—22no—
80C22⋊C4×C113—22no—
81C42×C113—21no—
82C23×C113—22no—
83C23×C113—21no—
84C23×C113—42no—
85C23×C113C2×D412yes—
86C23×C113C2×D411yescharacteristic
87C22×D113—24no—
88C22×D113—22no—
89C22×D113—44no—
90Q8×C113—21no—
91Q8×C113—21no—
92D4×C113—21no—
93D4×C113—21no—
94D4×C113—44no—
95D4×C113—42no—
96C2×C4×C113—22no—
97C2×C4×C113—24no—
98C2×C4×C113—22no—
99C2×C4×C113—22no—
100C2×C4×C113—22no—
101C2×C4×C113—21no—
102C2×C4×C113—42no—
103C2×C4×C113C2×D412yes—
104C2×C4×C113C2×D412yes—
105C2×C4×C113C2×D412yes—
106C2×C4×C113C2×D411yescharacteristic
107C2×C4×C113C2411yescharacteristic
108C22⋊D113—216no—
109C2×Dic113—24no—
110C2×Dic113—22no—
111D452—24no—
112D452—22no—
113D452C2×D414yes—
114C4×D113—216no—
115Dic226—24no—
116Dic226—22no—
117Dic226C2×D414yes—
118#11744751—22no—
119#11744751—22no—
120C22×C113—22no—
121C22×C113—22no—
122C22×C113—22no—
123C22×C113—22no—
124C22×C113—44no—
125C22×C113—41no—
126C22×C113—42no—
127C22×C113#12012yes—
128C22×C113C22×D411yescharacteristic
129C2×D113—24no—
130C2×D113—48no—
131C2×D113—44no—
132C4×C113—22no—
133C4×C113—41no—
134C4×C113—42no—
135C4×C113#12012yes—
136C4×C113C22×D411yescharacteristic
137C4×C113C22×D411yescharacteristic
138Dic113—24no—
139C2×C113—22no—
140C2×C113—42no—
141C2×C113—81no—
142C2×C113C2×#12011yescharacteristic
143C2×C113#57512yes—
144D113—44no—
145#3005—1131nomaximal, Sylow
146C113#300511yescharacteristic, complemented, Sylow
147C22×#41—1131no—
148C2×#137—1131no—
149C2×AGL(1,ℤ/8)—1131no—
150#525D11311yescharacteristic, complemented
151#452—1134no—
152#449—1134no—
153#419—1131no—
154#418—1131no—
155#407—1131no—
156C2×#41—1134no—
157C2×#41—2264no—
158C2×#41—2264no—
159C2×#41—2262no—
160C2×#41C2×D11311yescharacteristic
161C22×Q8—1131no—
162C22×D4—1131no—
163C22×D4—2261no—
164C23×C4—2261no—
165C23×C4C2×D11311yescharacteristic
166#137—2264no—
167AGL(1,ℤ/8)—2264no—
168C2×Q16—1132no—
169C2×SD16—1132no—
170C2×SD16—1132no—
171C2×D8—1132no—
172C2×M16—1131no—
173C2×M16—1131no—
174#123—21no—
175C22⋊Q8C2×D11312yescomplemented
176#121C2×D11312yescomplemented
177#120—21no—
178C4×D4—22no—
179#117C2×D11311yescharacteristic
180#103—1134no—
181#102—1134no—
182C22⋊C8—1134no—
183C24—2261no—
184C24C22⋊D11311yescharacteristic
185#41—22no—
186#41—22no—
187#41—2268no—
188#41—2268no—
189#41—22616no—
190C2×Q8—1134no—
191C2×Q8—1132no—
192C2×Q8—2262no—
193C2×Q8—2261no—
194C2×Q8C22×D11311yescharacteristic
195C2×D4—22no—
196C2×D4—21no—
197C2×D4—1134no—
198C2×D4—1132no—
199C2×D4—2268no—
200C2×D4—2264no—
201C2×D4—2262no—
202C2×D4—2261no—
203C2×D4C22×D11311yescharacteristic
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—21no—
207C22×C4—2268no—
208C22×C4—2261no—
209C22×C4—2264no—
210C22×C4C22⋊D11312yes—
211C22×C4C22⋊D11311yescharacteristic
212C22×C4C22×D11312yes—
213C22×C4C22×D11311yescharacteristic
214Q16—2264no—
215SD16—2264no—
216SD16—2264no—
217D8—2264no—
218M16—2262no—
219M16—2262no—
220C2×C8—1132no—
221C2×C8—1132no—
222C4⋊C4—22no—
223C4⋊C4C22×D11312yes—
224C22⋊C4—21no—
225C22⋊C4—22no—
226C22⋊C4—22no—
227C42—21no—
228C23—22no—
229C23—21no—
230C23—42no—
231C23—4524no—
232C23—2264no—
233C23—2262no—
234C23C2×C22⋊D11312yes—
235C23C2×C22⋊D11311yescharacteristic
236Q8—21no—
237Q8—21no—
238Q8—1134no—
239Q8—2264no—
240Q8—2262no—
241D4—21no—
242D4—21no—
243D4—44no—
244D4—42no—
245D4—1134no—
246D4—22616no—
247D4—2264no—
248D4—2262no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—22616no—
257C2×C4—2264no—
258C2×C4—2262no—
259C2×C4D4×D11312yes—
260C2×C4D4×D11312yes—
261C2×C4C2×C22⋊D11312yes—
262C2×C4C2×C22⋊D11311yescharacteristic
263C2×C4C23×D11311yescharacteristic
264C8—2262no—
265C8—2262no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—44no—
271C22—41no—
272C22—42no—
273C22—4528no—
274C22—4524no—
275C22—2264no—
276C22#1681359012yes—
277C22C22×C22⋊D11311yescharacteristic
278C4—22no—
279C4—41no—
280C4—42no—
281C4—2264no—
282C4#1681359012yes—
283C4C2×D4×D11311yescharacteristic
284C4C2×D4×D11311yescharacteristic
285C2—22no—
286C2—42no—
287C2—81no—
288C2—4524no—
289C2C2×#1681359011yescharacteristic
290C2#2029939612yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#525×C113C2
socleC22×C113C22×D4
hypercenter#525D113
hypocenterC113#3005
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C22×#14268647C2semidirect
2. C2×#16813652C2semidirect
3. C2×#16813647C2semidirect
4. #20298758C2semidirect
5. #20298741C2semidirect
6. #20298606C2semidirect
7. #20298602C2semidirect
8. #20298562C2semidirect
9. #525×C113C2semidirect
20. C2×#14268637C22semidirect
21. C2×#14268635C22semidirect
22. C2×#14268634C22semidirect
23. C2×#14268632C22semidirect
26. #16813545C22semidirect
27. #16813542C22semidirect
28. C22⋊#11744751C22semidirect
32. C22⋊Q8×C113C22semidirect
33. #121×C113C22semidirect
43. C2×Dic226D4semidirect
47. C2×D452D4semidirect
146. C113#3005semidirect
150. #525D113semidirect
175. C22⋊Q8C2×D113semidirect
176. #121C2×D113semidirect

Maximal subgroups

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

subgroupindex
C22×#142686472
C2×#168136522
C2×#168136472
#202987582
#202987412
#202986062
#202986022
#202985622
#525×C1132
#3005113