Finite Group Databasebeta

← #28402813

Subgroups — #28402813

Order 14464.

460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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#20299314C211yesmaximal, characteristic, complemented
2D4×D452C211yesmaximal, characteristic, complemented
3#20298946C211yesmaximal, characteristic, complemented
4#20298924C212yesmaximal, complemented
5#20298852C212yesmaximal, complemented
6#20298794C211yesmaximal, characteristic, complemented
7#20298733C212yesmaximal, complemented
8C4×#14268632C211yesmaximal, characteristic, complemented
9#20298675C211yesmaximal, characteristic, complemented
10#20298601C212yesmaximal, complemented
11#476×C113C211yesmaximal, characteristic, complemented
12C22×D452—21no—
13C2×D4×D113C2212yes—
14C2×D904C2212yescomplemented
15C2×#14268632C2211yescharacteristic
16C2×#14268630C2212yescomplemented
17#16813619C2211yescharacteristic
18#16813611—22no—
19#16813597—21no—
20#16813597C2212yes—
21#16813597C2212yescomplemented
22#16813596—21no—
23#16813592—22no—
24C4×D452C2211yescharacteristic
25C4×D452C2211yescharacteristic, complemented
26#16813580—21no—
27#16813580C2212yescomplemented
28#16813555C2211yescharacteristic, complemented
29#16813544C2212yescomplemented
30#16813543C2211yescharacteristic
31#16813542C2211yescharacteristic, complemented
32#16813542C2212yescomplemented
33#16813542C2212yescomplemented
34#16813534C2212yescomplemented
35C4×#11744751C2211yescharacteristic, complemented
36C4⋊Q8×C113C2211yescharacteristic, complemented
37C4×D4×C113C2211yescharacteristic
38#106×C113C2212yescomplemented
39C4⋊C8×C113C2211yescharacteristic, complemented
40#102×C113C2212yes—
41C23×D113—22no—
42C2×D452—22no—
43C2×D452—21no—
44C2×D452—22no—
45C2×D452—21no—
46C2×D452—44no—
47C2×D452D411yescharacteristic
48C2×D452C2311yescharacteristic
49C2×D452C2312yes—
50C2×C22⋊D113—22no—
51D4×D113—24no—
52D4×D113—42no—
53C2×C4×D113—21no—
54C2×C4×D113C2312yes—
55D904—42no—
56#14268632—22no—
57#14268630—42no—
58C2×#11744751C2311yescharacteristic
59C2×#11744751C2311yescharacteristic
60C4⋊Dic113D411yescharacteristic
61C4⋊Dic113C2311yescharacteristic
62#14268624—22no—
63#14268624—21no—
64#14268624—22no—
65#14268624—22no—
66#14268624D412yes—
67C4×Dic113—22no—
68C2×Q8×C113—21no—
69C2×D4×C113C2311yescharacteristic
70C22×C4×C113—21no—
71C2×C8×C113C2312yes—
72C4⋊C4×C113—21no—
73C4⋊C4×C113C2312yes—
74C4⋊C4×C113C2311yescharacteristic
75C22⋊C4×C113—21no—
76C42×C113C2311yescharacteristic
77C23×C113—21no—
78C22×D113—21no—
79C22×D113—22no—
80C22×D113—44no—
81C22×D113—44no—
82C22×D113—82no—
83C22×D113C2×D412yes—
84Q8×C113—81no—
85D4×C113—21no—
86D4×C113#4112yes—
87C2×C4×C113—21no—
88C2×C4×C113—22no—
89C2×C4×C113—42no—
90C2×C4×C113C2×D411yescharacteristic
91C2×C4×C113C2×D411yescharacteristic
92C2×C4×C113C2411yescharacteristic
93C22⋊D113—44no—
94C2×Dic113—21no—
95C2×Dic113C2×D412yes—
96D452—22no—
97D452—21no—
98D452—22no—
99D452—21no—
100D452—22no—
101D452—44no—
102D452—42no—
103D452—81no—
104D452—82no—
105C4×D113—22no—
106C4×D113—22no—
107C4×D113—42no—
108C8×C113—22no—
109#11744751—21no—
110#11744751—21no—
111C22×C113—22no—
112C22×C113—41no—
113C22×C113—41no—
114C22×C113C22×D411yescharacteristic
115C2×D113—22no—
116C2×D113—22no—
117C2×D113—22no—
118C2×D113—42no—
119C2×D113—41no—
120C2×D113—41no—
121C2×D113—42no—
122C2×D113—41no—
123C2×D113—42no—
124C2×D113—88no—
125C4×C113—21no—
126C4×C113—41no—
127C4×C113—42no—
128C4×C113AGL(1,ℤ/8)12yes—
129C4×C113C2×#4111yescharacteristic
130C4×C113H(5,𝔽2)11yescharacteristic
131Dic113—22no—
132Dic113—41no—
133C2×C113—42no—
134C2×C113#54611yescharacteristic
135C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
136C2×C113#57611yescharacteristic
137D113—42no—
138D113—81no—
139D113—82no—
140#3325—1131nomaximal, Sylow
141C113#332511yescharacteristic, complemented, Sylow
142#555—1131no—
143D42—1131no—
144#486—1131no—
145#482—1132no—
146#476D11311yescharacteristic, complemented
147#469—1132no—
148#459—1131no—
149#447—1132no—
150C4×D8—1131no—
151#436—1131no—
152#418—1132no—
153C22×D4—1132no—
154C22×D4—2261no—
155C2×D8—1131no—
156C2×D8—1132no—
157C2×M16—1132no—
158C4⋊Q8C2×D11311yescharacteristic, complemented
159#127—1131no—
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
169#117—1132no—
170#117—2261no—
171#107—1131no—
172#106C2×D11312yescomplemented
173C4⋊C8C2×D11311yescharacteristic, complemented
174#102—1131no—
175#102—1132no—
176#102—1132no—
177#102—1131no—
178#102—1132no—
179#102C2×D11312yes—
180C22⋊C8—1132no—
181C4×C8—1131no—
182C24—2262no—
183C2×Q8—21no—
184C2×D4—1131no—
185C2×D4—1132no—
186C2×D4—1131no—
187C2×D4—4524no—
188C2×D4—4522no—
189C2×D4—2262no—
190C2×D4—2262no—
191C2×D4—2262no—
192C2×D4—2264no—
193C2×D4—2261no—
194C2×D4—2261no—
195C2×D4C22×D11311yescharacteristic
196C22×C4—21no—
197C22×C4—1132no—
198C22×C4—2261no—
199D8—4522no—
200D8—2262no—
201M16—4522no—
202C2×C8—1131no—
203C2×C8—1131no—
204C2×C8C22×D11312yes—
205C4⋊C4—21no—
206C4⋊C4—1131no—
207C4⋊C4—1131no—
208C4⋊C4C22×D11312yes—
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—1132no—
220C23—9042no—
221C23—4524no—
222C23—4524no—
223C23—2261no—
224C23—2262no—
225Q8—81no—
226D4—21no—
227D4—9041no—
228D4—9042no—
229D4—4524no—
230D4—4524no—
231D4—4522no—
232D4—2262no—
233D4—2261no—
234D4—2262no—
235D4—2261no—
236D4—2262no—
237D4#1426864812yes—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—42no—
241C2×C4—1132no—
242C2×C4—4522no—
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—22no—
253C22—41no—
254C22—41no—
255C22—9048no—
256C22—4521no—
257C22—4522no—
258C22—4521no—
259C22—4522no—
260C22—4522no—
261C22—4521no—
262C22—2262no—
263C22—2262no—
264C22—2262no—
265C22C2×D4×D11311yescharacteristic
266C4—21no—
267C4—41no—
268C4—42no—
269C4—4521no—
270C4—2262no—
271C4#1681364912yes—
272C4C2×#1426864811yescharacteristic
273C4#1681366811yescharacteristic
274C2—42no—
275C2—9042no—
276C2—9041no—
277C2—4522no—
278C2#2029923911yescharacteristic
279C2C2×#1681364911yescharacteristic
280C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#476×C113C2
socleC22×C113C22×D4
hypercenter#476D113
hypocenterC113#3325
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #20299314C2semidirect
2. D4×D452C2semidirect
3. #20298946C2semidirect
4. #20298924C2semidirect
5. #20298852C2semidirect
6. #20298794C2semidirect
7. #20298733C2semidirect
8. C4×#14268632C2semidirect
9. #20298675C2semidirect
10. #20298601C2semidirect
11. #476×C113C2semidirect
14. C2×D904C22semidirect
16. C2×#14268630C22semidirect
21. #16813597C22semidirect
25. C4×D452C22semidirect
27. #16813580C22semidirect
28. #16813555C22semidirect
29. #16813544C22semidirect
31. #16813542C22semidirect
32. #16813542C22semidirect
33. #16813542C22semidirect
34. #16813534C22semidirect
35. C4×#11744751C22semidirect
36. C4⋊Q8×C113C22semidirect
38. #106×C113C22semidirect
39. C4⋊C8×C113C22semidirect
141. C113#3325semidirect
146. #476D113semidirect
158. C4⋊Q8C2×D113semidirect
172. #106C2×D113semidirect
173. C4⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993142
D4×D4522
#202989462
#202989242
#202988522
#202987942
#202987332
C4×#142686322
#202986752
#202986012
#476×C1132
#3325113