Finite Group Databasebeta

← #28399819

Subgroups — #28399819

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×#16813655C211yesmaximal, characteristic, complemented
3C2×#16813650C211yesmaximal, characteristic, complemented
4#20299109C211yesmaximal, characteristic, complemented
5#20298762C214yesmaximal, complemented
6#20298745C214yesmaximal, complemented
7#20298608C211yesmaximal, characteristic, complemented
8#20298604C211yesmaximal, characteristic, complemented
9#407×C113C211yesmaximal, characteristic, complemented
10C2×#14268647—24no—
11C2×#14268647—24no—
12C2×#14268647—22no—
13C2×#14268647C2214yes—
14C2×#14268647C2211yescharacteristic
15C22×Dic226C2211yescharacteristic
16C22×D452C2211yescharacteristic
17C22×C22⋊D113—21no—
18C22×C4×D113—21no—
19#16813655—24no—
20#16813650—24no—
21C2×Dic452C2212yescomplemented
22C2×#14268636C2212yescomplemented
23C2×#14268636C2212yescomplemented
24C2×D904C2212yescomplemented
25#16813605—21no—
26#16813601C2212yescomplemented
27#16813596C2212yescomplemented
28#16813591—21no—
29C4×C22⋊D113—22no—
30#16813581C2211yescharacteristic
31#16813547C2214yescomplemented
32#16813544C2214yescomplemented
33C23×C4×C113C2211yescharacteristic
34C2×M16×C113C2211yescharacteristic
35C2×M16×C113C2211yescharacteristic
36C22⋊C8×C113C2214yescomplemented
37C23×D113—21no—
38#14268647—216no—
39#14268647—28no—
40#14268647—22no—
41#14268647—22no—
42#14268647—28no—
43C2×Dic226—22no—
44C2×Dic226—21no—
45C2×Dic226D414yescomplemented
46C2×Dic226C2311yescharacteristic
47C2×Dic226C2312yes—
48C2×D452—22no—
49C2×D452—21no—
50C2×D452D414yescomplemented
51C2×D452C2311yescharacteristic
52C2×D452C2312yes—
53C2×C22⋊D113—28no—
54C2×C22⋊D113—24no—
55C2×C22⋊D113—22no—
56C2×C22⋊D113—21no—
57C22×Dic113—21no—
58C2×C4×D113—28no—
59C2×C4×D113—24no—
60C2×C4×D113—21no—
61Dic452—24no—
62#14268636—24no—
63#14268636—24no—
64D904—24no—
65C4⋊Dic113C2312yes—
66#14268626—22no—
67C22⋊Dic113—21no—
68C22⋊Dic113—22no—
69#14268624—22no—
70C4×Dic113—21no—
71C24×C113D411yescharacteristic
72C22×C4×C113—22no—
73C22×C4×C113—22no—
74C22×C4×C113D412yes—
75C22×C4×C113D411yescharacteristic
76C22×C4×C113C2312yes—
77C22×C4×C113C2311yescharacteristic
78M16×C113—22no—
79M16×C113—22no—
80C2×C8×C113C2312yes—
81C2×C8×C113C2312yes—
82C23×C113—22no—
83C23×C113—42no—
84C23×C113C2×D412yes—
85C23×C113C2×D411yescharacteristic
86C22×D113—24no—
87C22×D113—22no—
88C22×D113—21no—
89C22×D113—44no—
90C2×C4×C113—22no—
91C2×C4×C113—24no—
92C2×C4×C113—22no—
93C2×C4×C113—22no—
94C2×C4×C113C2×D412yes—
95C2×C4×C113C2×D412yes—
96C2×C4×C113C2×D412yes—
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2411yescharacteristic
99C22⋊D113—216no—
100C22⋊D113—44no—
101C22⋊D113—42no—
102C2×Dic113—24no—
103C2×Dic113—22no—
104C2×Dic113—22no—
105C2×Dic113—21no—
106D452—24no—
107D452—22no—
108D452—21no—
109D452—21no—
110D452C2×D414yes—
111C4×D113—216no—
112C4×D113—42no—
113Dic226—24no—
114Dic226—22no—
115Dic226—21no—
116Dic226—21no—
117Dic226C2×D414yes—
118C8×C113—22no—
119C8×C113—22no—
120C22×C113—22no—
121C22×C113—22no—
122C22×C113—22no—
123C22×C113—22no—
124C22×C113—44no—
125C22×C113#12012yes—
126C22×C113C22×D411yescharacteristic
127C2×D113—24no—
128C2×D113—48no—
129C2×D113—44no—
130C2×D113—41no—
131C2×D113—42no—
132C4×C113—22no—
133C4×C113#12012yes—
134C4×C113C22×D411yescharacteristic
135C4×C113C22×D411yescharacteristic
136Dic113—24no—
137Dic113—41no—
138Dic113—42no—
139C2×C113—22no—
140C2×C113—42no—
141C2×C113C2×#12011yescharacteristic
142C2×C113#57512yes—
143D113—44no—
144D113—81no—
145#3005—1131nomaximal, Sylow
146C113#300511yescharacteristic, complemented, Sylow
147C22×#41—1131no—
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#407D11311yescharacteristic, complemented
156C2×#41—1131no—
157C2×#41—1134no—
158C2×#41—2264no—
159C2×#41—2264no—
160C2×#41—2262no—
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×M16C2×D11311yescharacteristic
173C2×M16C2×D11311yescharacteristic
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⋊C8C2×D11314yescomplemented
183C24—2261no—
184C24D45211yescharacteristic
185#41—2268no—
186#41—2268no—
187#41—22616no—
188#41—2262no—
189#41—2262no—
190C2×Q8—1134no—
191C2×Q8—1132no—
192C2×Q8—1131no—
193C2×Q8—2262no—
194C2×Q8—2261no—
195C2×D4—1134no—
196C2×D4—1132no—
197C2×D4—1131no—
198C2×D4—2262no—
199C2×D4—2261no—
200C2×D4—2268no—
201C2×D4—2264no—
202C2×D4—2262no—
203C2×D4—2261no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—2268no—
207C22×C4—2261no—
208C22×C4—2261no—
209C22×C4—2264no—
210C22×C4D45212yes—
211C22×C4D45211yescharacteristic
212C22×C4C22×D11312yes—
213C22×C4C22×D11311yescharacteristic
214Q16—2264no—
215SD16—2264no—
216SD16—2264no—
217D8—2264no—
218M16—22no—
219M16—22no—
220C2×C8C22×D11312yes—
221C2×C8C22×D11312yes—
222C4⋊C4—1132no—
223C4⋊C4—2262no—
224C22⋊C4—2261no—
225C22⋊C4—2262no—
226C22⋊C4—2262no—
227C42—2261no—
228C23—22no—
229C23—42no—
230C23—4524no—
231C23—2261no—
232C23—2264no—
233C23—2262no—
234C23C2×D45212yes—
235C23C2×D45211yescharacteristic
236Q8—1134no—
237Q8—2261no—
238Q8—2261no—
239Q8—2264no—
240Q8—2262no—
241D4—1134no—
242D4—4524no—
243D4—4522no—
244D4—22616no—
245D4—2264no—
246D4—2261no—
247D4—2261no—
248D4—2262no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—4522no—
254C2×C4—22616no—
255C2×C4—2262no—
256C2×C4—2261no—
257C2×C4—2264no—
258C2×C4—2262no—
259C2×C4D4×D11312yes—
260C2×C4D4×D11312yes—
261C2×C4C2×D45212yes—
262C2×C4C2×D45211yescharacteristic
263C2×C4C23×D11311yescharacteristic
264C8—22no—
265C8—22no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—44no—
271C22—4528no—
272C22—4521no—
273C22—4522no—
274C22—4524no—
275C22—2264no—
276C22#1681359212yes—
277C22C22×D45211yescharacteristic
278C4—22no—
279C4—4521no—
280C4—4522no—
281C4—2264no—
282C4#1681359212yes—
283C4C2×D4×D11311yescharacteristic
284C4C2×D4×D11311yescharacteristic
285C2—22no—
286C2—42no—
287C2—9041no—
288C2—4524no—
289C2C2×#1681359211yescharacteristic
290C2#2029939812yes—
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#407×C113C2
socleC22×C113C22×D4
hypercenter#407D113
hypocenterC113#3005
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
1. C22×#14268647C2semidirect
2. C2×#16813655C2semidirect
3. C2×#16813650C2semidirect
4. #20299109C2semidirect
5. #20298762C2semidirect
6. #20298745C2semidirect
7. #20298608C2semidirect
8. #20298604C2semidirect
9. #407×C113C2semidirect
21. C2×Dic452C22semidirect
22. C2×#14268636C22semidirect
23. C2×#14268636C22semidirect
24. C2×D904C22semidirect
26. #16813601C22semidirect
27. #16813596C22semidirect
31. #16813547C22semidirect
32. #16813544C22semidirect
36. C22⋊C8×C113C22semidirect
45. C2×Dic226D4semidirect
50. C2×D452D4semidirect
146. C113#3005semidirect
155. #407D113semidirect
182. C22⋊C8C2×D113semidirect

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×#168136502
#202991092
#202987622
#202987452
#202986082
#202986042
#407×C1132
#3005113