Finite Group Databasebeta

← #28399816

Subgroups — #28399816

Order 14464.

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

normal subgroups only

This group has 758 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
1C2×#16813653C211yesmaximal, characteristic, complemented
2C2×#16813648C211yesmaximal, characteristic, complemented
3#20299109C211yesmaximal, characteristic, complemented
4#20298760C214yesmaximal, complemented
5#20298743C214yesmaximal, complemented
6#20298607C211yesmaximal, characteristic, complemented
7#20298603C211yesmaximal, characteristic, complemented
8#20298562C211yesmaximal, characteristic, complemented
9C22×#41×C113C211yesmaximal, characteristic, complemented
10C2×#14268647C2211yescharacteristic
11#16813653—24no—
12#16813648—24no—
13C2×#14268637C2212yescomplemented
14C2×#14268635C2212yescomplemented
15C2×#14268634C2212yescomplemented
16C2×#14268632C2212yescomplemented
17C2×#14268631C2211yescharacteristic
18C2×#14268631C2211yescharacteristic
19#16813605—21no—
20#16813601C2212yescomplemented
21#16813596C2212yescomplemented
22#16813591—21no—
23C4×C22⋊D113—22no—
24#16813581C2211yescharacteristic
25#16813546C2214yescomplemented
26#16813543C2214yescomplemented
27C22⋊#11744751C2214yescomplemented
28C2×#41×C113—24no—
29C2×#41×C113—24no—
30C2×#41×C113—22no—
31C2×#41×C113C2214yes—
32C22×Q8×C113C2211yescharacteristic
33C22×D4×C113—21no—
34C22×D4×C113C2211yescharacteristic
35C23×C4×C113—21no—
36C23×C4×C113C2211yescharacteristic
37#14268647—22no—
38#14268647—22no—
39C2×Dic226C2311yescharacteristic
40C2×D452C2311yescharacteristic
41C2×C22⋊D113—22no—
42C2×C22⋊D113—21no—
43C2×C4×D113—21no—
44#14268637—24no—
45#14268635—24no—
46#14268634—24no—
47#14268632—24no—
48#14268631—22no—
49#14268631—22no—
50C2×#11744751C2312yes—
51C2×#11744751C2312yes—
52C4⋊Dic113C2312yes—
53#14268626—22no—
54C22⋊Dic113—21no—
55C22⋊Dic113—22no—
56#14268624—22no—
57C4×Dic113—21no—
58C24×C113—21no—
59C24×C113D411yescharacteristic
60#41×C113—216no—
61#41×C113—28no—
62#41×C113—28no—
63C2×Q8×C113—22no—
64C2×Q8×C113—21no—
65C2×Q8×C113D414yescomplemented
66C2×Q8×C113C2312yes—
67C2×D4×C113—28no—
68C2×D4×C113—24no—
69C2×D4×C113—21no—
70C2×D4×C113—22no—
71C2×D4×C113D414yescomplemented
72C2×D4×C113C2312yes—
73C22×C4×C113—28no—
74C22×C4×C113—21no—
75C22×C4×C113—24no—
76C22×C4×C113—22no—
77C22×C4×C113—22no—
78C22×C4×C113D412yes—
79C22×C4×C113D411yescharacteristic
80C22×C4×C113C2312yes—
81C22×C4×C113C2311yescharacteristic
82C23×C113—22no—
83C23×C113—24no—
84C23×C113—22no—
85C23×C113—42no—
86C23×C113—44no—
87C23×C113C2×D412yes—
88C23×C113C2×D411yescharacteristic
89C22×D113—21no—
90Q8×C113—24no—
91Q8×C113—22no—
92Q8×C113C2×D414yes—
93D4×C113—216no—
94D4×C113—24no—
95D4×C113—22no—
96D4×C113C2×D414yes—
97C2×C4×C113—216no—
98C2×C4×C113—22no—
99C2×C4×C113—24no—
100C2×C4×C113—22no—
101C2×C4×C113—24no—
102C2×C4×C113—22no—
103C2×C4×C113—22no—
104C2×C4×C113C2×D412yes—
105C2×C4×C113C2×D411yescharacteristic
106C2×C4×C113C2×D412yes—
107C2×C4×C113C2×D412yes—
108C2×C4×C113C2411yescharacteristic
109C22⋊D113—44no—
110C22⋊D113—42no—
111C2×Dic113—22no—
112C2×Dic113—21no—
113D452—21no—
114D452—21no—
115C4×D113—42no—
116Dic226—21no—
117Dic226—21no—
118#11744751—22no—
119#11744751—22no—
120C22×C113—22no—
121C22×C113—22no—
122C22×C113—24no—
123C22×C113—22no—
124C22×C113—22no—
125C22×C113—44no—
126C22×C113—48no—
127C22×C113—44no—
128C22×C113#12012yes—
129C22×C113C22×D411yescharacteristic
130C2×D113—41no—
131C2×D113—42no—
132C4×C113—22no—
133C4×C113—24no—
134C4×C113#12012yes—
135C4×C113C22×D411yescharacteristic
136C4×C113C22×D411yescharacteristic
137Dic113—41no—
138Dic113—42no—
139C2×C113—22no—
140C2×C113—42no—
141C2×C113—44no—
142C2×C113C2×#12011yescharacteristic
143C2×C113#57512yes—
144D113—81no—
145#3005—1131nomaximal, Sylow
146C113#300511yescharacteristic, complemented, Sylow
147C22×#41D11311yescharacteristic, complemented
148C2×#137—1131no—
149C2×AGL(1,ℤ/8)—1131no—
150#525—1131no—
151#452—1134no—
152#449—1134no—
153#419—1131no—
154#418—1131no—
155#407—1131no—
156C2×#41—24no—
157C2×#41—24no—
158C2×#41—22no—
159C2×#41—1131no—
160C2×#41C2×D11314yes—
161C22×Q8C2×D11311yescharacteristic
162C22×D4—21no—
163C22×D4C2×D11311yescharacteristic
164C23×C4—21no—
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—2261no—
175C22⋊Q8—1132no—
176#121—1132no—
177#120—2261no—
178C4×D4—2262no—
179#117—1131no—
180#103—1134no—
181#102—1134no—
182C22⋊C8—1134no—
183C24—21no—
184C24C22⋊D11311yescharacteristic
185#41—216no—
186#41—28no—
187#41—28no—
188#41—2262no—
189#41—2262no—
190C2×Q8—22no—
191C2×Q8—21no—
192C2×Q8—1131no—
193C2×Q8C22⋊D11314yescomplemented
194C2×Q8C22×D11312yes—
195C2×D4—28no—
196C2×D4—24no—
197C2×D4—21no—
198C2×D4—22no—
199C2×D4—1131no—
200C2×D4—2262no—
201C2×D4—2261no—
202C2×D4C22⋊D11314yescomplemented
203C2×D4C22×D11312yes—
204C22×C4—28no—
205C22×C4—21no—
206C22×C4—24no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—2261no—
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—1132no—
223C4⋊C4—2262no—
224C22⋊C4—2261no—
225C22⋊C4—2262no—
226C22⋊C4—2262no—
227C42—2261no—
228C23—22no—
229C23—24no—
230C23—22no—
231C23—42no—
232C23—44no—
233C23—2261no—
234C23C2×C22⋊D11312yes—
235C23C2×C22⋊D11311yescharacteristic
236Q8—24no—
237Q8—22no—
238Q8—2261no—
239Q8—2261no—
240Q8C2×C22⋊D11314yes—
241D4—216no—
242D4—24no—
243D4—22no—
244D4—4524no—
245D4—4522no—
246D4—2261no—
247D4—2261no—
248D4C2×C22⋊D11314yes—
249C2×C4—216no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—4522no—
257C2×C4—2262no—
258C2×C4—2261no—
259C2×C4C2×C22⋊D11312yes—
260C2×C4C2×C22⋊D11311yescharacteristic
261C2×C4C2×C22⋊D11312yes—
262C2×C4C2×C22⋊D11312yes—
263C2×C4C23×D11311yescharacteristic
264C8—2262no—
265C8—2262no—
266C22—22no—
267C22—22no—
268C22—24no—
269C22—22no—
270C22—22no—
271C22—44no—
272C22—48no—
273C22—44no—
274C22—4521no—
275C22—4522no—
276C22#1681359112yes—
277C22C22×C22⋊D11311yescharacteristic
278C4—22no—
279C4—24no—
280C4—4521no—
281C4—4522no—
282C4#1681359112yes—
283C4C22×C22⋊D11311yescharacteristic
284C4C22×C22⋊D11311yescharacteristic
285C2—22no—
286C2—42no—
287C2—44no—
288C2—9041no—
289C2C2×#1681359111yescharacteristic
290C2#2029939612yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC22×#41×C113C2
socleC22×C113C22×D4
hypercenterC22×#41D113
hypocenterC113#3005
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#16813653C2semidirect
2. C2×#16813648C2semidirect
3. #20299109C2semidirect
4. #20298760C2semidirect
5. #20298743C2semidirect
6. #20298607C2semidirect
7. #20298603C2semidirect
8. #20298562C2semidirect
9. C22×#41×C113C2semidirect
13. C2×#14268637C22semidirect
14. C2×#14268635C22semidirect
15. C2×#14268634C22semidirect
16. C2×#14268632C22semidirect
20. #16813601C22semidirect
21. #16813596C22semidirect
25. #16813546C22semidirect
26. #16813543C22semidirect
27. C22⋊#11744751C22semidirect
65. C2×Q8×C113D4semidirect
71. C2×D4×C113D4semidirect
146. C113#3005semidirect
147. C22×#41D113semidirect
193. C2×Q8C22⋊D113semidirect
202. C2×D4C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136532
C2×#168136482
#202991092
#202987602
#202987432
#202986072
#202986032
#202985622
C22×#41×C1132
#3005113