Finite Group Databasebeta

← #28402819

Subgroups — #28402819

Order 14464.

460 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#20299313C211yesmaximal, characteristic, complemented
2#20299233C211yesmaximal, characteristic, complemented
3#20298944C211yesmaximal, characteristic, complemented
4#20298921C212yesmaximal, complemented
5#20298889C211yesmaximal, characteristic, complemented
6#20298848C212yesmaximal, complemented
7#20298730C212yesmaximal, complemented
8C4×#14268632C211yesmaximal, characteristic, complemented
9#20298675C211yesmaximal, characteristic, complemented
10#20298601C212yesmaximal, complemented
11#459×C113C211yesmaximal, characteristic, complemented
12C2×D4×D113—21no—
13C2×D4×D113C2212yes—
14C2×#14268632C2211yescharacteristic
15C2×#14268630C2212yescomplemented
16#16813622C2211yescharacteristic, complemented
17#16813608—22no—
18#16813596—21no—
19#16813593—21no—
20#16813593C2212yes—
21#16813593C2212yescomplemented
22#16813590—22no—
23C4×D452C2211yescharacteristic
24C4×D452C2211yescharacteristic
25#16813581—21no—
26#16813580C2212yescomplemented
27#16813555C2211yescharacteristic, complemented
28#16813554C2212yescomplemented
29#16813544C2212yes—
30#16813543C2211yescharacteristic, complemented
31#16813543C2212yescomplemented
32#16813543C2212yescomplemented
33#16813542C2211yescharacteristic
34#16813534C2212yescomplemented
35C4×#11744751C2211yescharacteristic, complemented
36C2×D8×C113C2212yescomplemented
37#127×C113C2211yescharacteristic
38C4×D4×C113C2211yescharacteristic, complemented
39C4⋊C8×C113C2211yescharacteristic, complemented
40#102×C113C2212yescomplemented
41C23×D113—22no—
42C2×Dic226—21no—
43C2×D452D411yescharacteristic
44C2×D452C2311yescharacteristic
45C2×C22⋊D113—22no—
46C2×C22⋊D113—22no—
47C2×C22⋊D113—22no—
48D4×D113—24no—
49D4×D113—42no—
50D4×D113—44no—
51C2×C4×D113—21no—
52C2×C4×D113C2312yes—
53#14268632—22no—
54#14268630—42no—
55C2×#11744751C2311yescharacteristic
56C2×#11744751C2311yescharacteristic
57C4⋊Dic113—21no—
58C4⋊Dic113D411yescharacteristic
59C4⋊Dic113C2312yes—
60C4⋊Dic113C2311yescharacteristic
61C22⋊Dic113—22no—
62C22⋊Dic113—22no—
63#14268624—22no—
64#14268624—21no—
65#14268624D412yes—
66C4×Dic113—22no—
67C2×D4×C113—21no—
68C2×D4×C113—21no—
69C2×D4×C113C2312yes—
70C2×D4×C113C2311yescharacteristic
71C22×C4×C113—21no—
72D8×C113—42no—
73C2×C8×C113C2312yes—
74C4⋊C4×C113C2311yescharacteristic
75C22⋊C4×C113—21no—
76C42×C113C2311yescharacteristic
77C23×C113—21no—
78C23×C113—22no—
79C22×D113—21no—
80C22×D113—44no—
81C22×D113—44no—
82C22×D113—82no—
83C22×D113C2×D412yes—
84D4×C113—21no—
85D4×C113—22no—
86D4×C113—21no—
87D4×C113—22no—
88D4×C113—42no—
89D4×C113—81no—
90C2×C4×C113—21no—
91C2×C4×C113—42no—
92C2×C4×C113C2×D411yescharacteristic
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2411yescharacteristic
95C22⋊D113—44no—
96C22⋊D113—44no—
97C22⋊D113—82no—
98C2×Dic113—22no—
99C2×Dic113—21no—
100C2×Dic113C2×D412yes—
101D452—22no—
102D452—21no—
103D452#4112yes—
104C4×D113—22no—
105C4×D113—22no—
106C4×D113—42no—
107Dic226—81no—
108C8×C113—22no—
109#11744751—21no—
110#11744751—21no—
111C22×C113—42no—
112C22×C113—41no—
113C22×C113—42no—
114C22×C113—41no—
115C22×C113—41no—
116C22×C113—42no—
117C22×C113C22×D411yescharacteristic
118C2×D113—22no—
119C2×D113—22no—
120C2×D113—22no—
121C2×D113—22no—
122C2×D113—41no—
123C2×D113—41no—
124C2×D113—88no—
125C4×C113—21no—
126C4×C113—41no—
127C4×C113AGL(1,ℤ/8)12yes—
128C4×C113C2×#4111yescharacteristic
129C4×C113H(5,𝔽2)11yescharacteristic
130Dic113—22no—
131Dic113—41no—
132Dic113—42no—
133C2×C113—82no—
134C2×C113—81no—
135C2×C113#54611yescharacteristic
136C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C113#57611yescharacteristic
138D113—42no—
139D113—42no—
140#3325—1131nomaximal, Sylow
141C113#332511yescharacteristic, complemented, Sylow
142#555—1131no—
143D42—1131no—
144#486—1131no—
145#482—1132no—
146#476—1131no—
147#469—1132no—
148#459D11311yescharacteristic, complemented
149#447—1132no—
150C4×D8—1131no—
151#436—1131no—
152#418—1132no—
153C22×D4—1132no—
154C22×D4—2261no—
155C2×D8—1131no—
156C2×D8C2×D11312yescomplemented
157C2×M16—1132no—
158C4⋊Q8—1131no—
159#127C2×D11311yescharacteristic
160#124—2262no—
161#121—1132no—
162#121—1132no—
163#121—2261no—
164#121—2261no—
165#120—2262no—
166C4×D4—1131no—
167C4×D4—1131no—
168C4×D4C2×D11311yescharacteristic, complemented
169#117—1132no—
170#117—2261no—
171#107—1131no—
172#106—1132no—
173C4⋊C8C2×D11311yescharacteristic, complemented
174#102—1132no—
175#102—1131no—
176#102—1132no—
177#102—1132no—
178#102—1131no—
179#102C2×D11312yescomplemented
180C22⋊C8—1132no—
181C4×C8—1131no—
182C24—2262no—
183C2×Q8—2261no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—1131no—
187C2×D4—1131no—
188C2×D4—4524no—
189C2×D4—4522no—
190C2×D4—2262no—
191C2×D4—2264no—
192C2×D4—2262no—
193C2×D4—2262no—
194C2×D4C22×D11312yes—
195C2×D4C22×D11311yescharacteristic
196C22×C4—21no—
197C22×C4—1132no—
198C22×C4—2261no—
199D8—42no—
200D8—2262no—
201M16—4522no—
202C2×C8—1131no—
203C2×C8—1131no—
204C2×C8C22×D11312yes—
205C4⋊C4—1131no—
206C4⋊C4—1132no—
207C4⋊C4—1131no—
208C4⋊C4—2261no—
209C4⋊C4C22×D11311yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—1132no—
212C22⋊C4—2262no—
213C22⋊C4—2262no—
214C22⋊C4—2262no—
215C22⋊C4—2261no—
216C42—2262no—
217C42C22×D11311yescharacteristic
218C23—21no—
219C23—22no—
220C23—1132no—
221C23—9042no—
222C23—4524no—
223C23—4524no—
224C23—2261no—
225Q8—9041no—
226D4—21no—
227D4—22no—
228D4—21no—
229D4—22no—
230D4—42no—
231D4—81no—
232D4—1132no—
233D4—9042no—
234D4—4524no—
235D4—4524no—
236D4—2262no—
237D4—2261no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—1132no—
241C2×C4—4522no—
242C2×C4—2262no—
243C2×C4—2261no—
244C2×C4—2262no—
245C2×C4—2262no—
246C2×C4D4×D11311yescharacteristic
247C2×C4D4×D11311yescharacteristic
248C2×C4C23×D11311yescharacteristic
249C8—22no—
250C8—2261no—
251C8—2261no—
252C22—41no—
253C22—42no—
254C22—42no—
255C22—41no—
256C22—42no—
257C22—41no—
258C22—9048no—
259C22—4521no—
260C22—4521no—
261C22—2262no—
262C22—2262no—
263C22—2262no—
264C22—2262no—
265C22C2×D4×D11311yescharacteristic
266C4—21no—
267C4—41no—
268C4—4521no—
269C4—4522no—
270C4—2262no—
271C4#1681364612yes—
272C4#41×D11311yescharacteristic
273C4#1681366711yescharacteristic
274C2—82no—
275C2—81no—
276C2—4522no—
277C2—4522no—
278C2#2029924511yescharacteristic
279C2C2×#1681364611yescharacteristic
280C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#459×C113C2
socleC22×C113C22×D4
hypercenter#459D113
hypocenterC113#3325
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #20299313C2semidirect
2. #20299233C2semidirect
3. #20298944C2semidirect
4. #20298921C2semidirect
5. #20298889C2semidirect
6. #20298848C2semidirect
7. #20298730C2semidirect
8. C4×#14268632C2semidirect
9. #20298675C2semidirect
10. #20298601C2semidirect
11. #459×C113C2semidirect
15. C2×#14268630C22semidirect
16. #16813622C22semidirect
21. #16813593C22semidirect
26. #16813580C22semidirect
27. #16813555C22semidirect
28. #16813554C22semidirect
30. #16813543C22semidirect
31. #16813543C22semidirect
32. #16813543C22semidirect
34. #16813534C22semidirect
35. C4×#11744751C22semidirect
36. C2×D8×C113C22semidirect
38. C4×D4×C113C22semidirect
39. C4⋊C8×C113C22semidirect
40. #102×C113C22semidirect
141. C113#3325semidirect
148. #459D113semidirect
156. C2×D8C2×D113semidirect
168. C4×D4C2×D113semidirect
173. C4⋊C8C2×D113semidirect
179. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993132
#202992332
#202989442
#202989212
#202988892
#202988482
#202987302
C4×#142686322
#202986752
#202986012
#459×C1132
#3325113