Finite Group Databasebeta

← #28400498

Subgroups — #28400498

Order 14464.

458 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 123 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#20299111C211yesmaximal, characteristic
2C2×C4⋊C4×D113C211yesmaximal, characteristic, complemented
3#20298932C212yesmaximal, complemented
4#20298926C211yesmaximal, characteristic, complemented
5#20298918C212yesmaximal, complemented
6#20298912C211yesmaximal, characteristic, complemented
7#20298911C211yesmaximal, characteristic, complemented
8#20298637C212yesmaximal, complemented
9#20298598C212yesmaximal, complemented
10#20298560C211yesmaximal, characteristic, complemented
11#483×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2211yescharacteristic
13C22×C4×D113—21no—
14C22×C4×D113C2211yescharacteristic
15C2×#14268630C2212yes—
16#16813607—21no—
17#16813598C2211yescharacteristic
18#16813597C2211yescharacteristic
19#16813596C2211yescharacteristic
20#16813592—21no—
21#16813584—21no—
22#16813582—21no—
23#16813580C2211yescharacteristic
24C2×C4⋊Dic113C2211yescharacteristic
25C2×#14268626—21no—
26C4⋊C4×D113—21no—
27C4⋊C4×D113—21no—
28C4⋊C4×D113C2212yes—
29C4⋊C4×D113C2212yes—
30#16813556C2212yescomplemented
31#16813555C2212yescomplemented
32#16813553C2212yescomplemented
33#16813546C2212yescomplemented
34#16813544C2212yescomplemented
35#16813542C2212yescomplemented
36C22⋊#11744751C2211yescharacteristic
37#16813534C2212yes—
38C22⋊Q8×C113C2211yescharacteristic
39C2×C4⋊C4×C113C2211yescharacteristic
40#106×C113C2212yescomplemented
41#103×C113C2212yescomplemented
42C22⋊C8×C113C2211yescharacteristic
43C23×D113D411yescharacteristic
44#14268648—24no—
45C2×D452—21no—
46C2×D452—21no—
47C2×D452C2311yescharacteristic
48C2×C22⋊D113—21no—
49C22×Dic113—21no—
50C22×Dic113D411yescharacteristic
51C2×C4×D113—24no—
52C2×C4×D113—22no—
53C2×C4×D113—22no—
54C2×C4×D113—21no—
55C2×C4×D113—44no—
56C2×C4×D113D411yescharacteristic
57C2×C4×D113D411yescharacteristic
58C2×C4×D113C2311yescharacteristic
59C2×C4×D113C2311yescharacteristic
60#14268630—24no—
61C2×#11744751C2312yes—
62C4⋊Dic113—21no—
63C4⋊Dic113C2312yes—
64C4⋊Dic113C2311yescharacteristic
65#14268626—22no—
66#14268626—22no—
67#14268626—21no—
68#14268624—21no—
69#14268624—21no—
70#14268624—21no—
71#14268624—21no—
72C4×Dic113—21no—
73C2×Q8×C113C2311yescharacteristic
74C22×C4×C113—21no—
75C22×C4×C113C2311yescharacteristic
76C2×C8×C113C2312yes—
77C4⋊C4×C113—21no—
78C4⋊C4×C113—21no—
79C4⋊C4×C113C2312yes—
80C4⋊C4×C113C2311yescharacteristic
81C22⋊C4×C113—21no—
82C23×C113C2×D411yescharacteristic
83C22×D113—22no—
84C22×D113—22no—
85C22×D113—22no—
86C22×D113—21no—
87C22×D113C2×D411yescharacteristic
88C22×D113C2×D411yescharacteristic
89Q8×C113—22no—
90C2×C4×C113—22no—
91C2×C4×C113—21no—
92C2×C4×C113—21no—
93C2×C4×C113—22no—
94C2×C4×C113—42no—
95C2×C4×C113C2×D411yescharacteristic
96C2×C4×C113C2411yescharacteristic
97C22⋊D113—42no—
98C2×Dic113—22no—
99C2×Dic113—21no—
100C2×Dic113—22no—
101C2×Dic113—42no—
102C2×Dic113C2×D411yescharacteristic
103C2×Dic113C2×D411yescharacteristic
104D452—22no—
105D452—42no—
106D452—42no—
107C4×D113—22no—
108C4×D113—22no—
109C4×D113—22no—
110C4×D113—44no—
111C4×D113—44no—
112C4×D113—42no—
113C4×D113#4114yes—
114C8×C113—22no—
115#11744751—22no—
116C22×C113—21no—
117C22×C113—21no—
118C22×C113AGL(1,ℤ/8)12yes—
119C22×C113C22×D411yescharacteristic
120C2×D113—28no—
121C2×D113—21no—
122C2×D113—21no—
123C2×D113—21no—
124C2×D113—21no—
125C2×D113—41no—
126C2×D113—41no—
127C2×D113—41no—
128C2×D113#12312yes—
129C2×D113#13712yes—
130C4×C113—21no—
131C4×C113—41no—
132C4×C113—42no—
133C4×C113—41no—
134C4×C113C2×#4112yes—
135Dic113—21no—
136Dic113—42no—
137Dic113—41no—
138Dic113#12312yes—
139C2×C113—22no—
140C2×C113C2×#12311yescharacteristic
141C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
142C2×C113C2×#13711yescharacteristic
143D113—22no—
144D113—22no—
145D113—81no—
146#3092—1131nomaximal, Sylow
147C113#309211yescharacteristic, complemented, Sylow
148#525—1131no—
149C22×C4⋊C4—1131no—
150#484—1132no—
151#483—1131no—
152#483D11311yescharacteristic, complemented
153#481—1132no—
154#480—1131no—
155#480—1131no—
156#428—1132no—
157#417—1132no—
158#407—1131no—
159C2×#41—1131no—
160C23×C4—1131no—
161C23×C4—2261no—
162C2×M16—1132no—
163#123—2261no—
164C22⋊Q8—1131no—
165C22⋊Q8C2×D11311yescharacteristic
166#121—1131no—
167#121—1131no—
168#120—2261no—
169C4×D4—2261no—
170C4×D4—2261no—
171#117—1131no—
172C2×C4⋊C4—1131no—
173C2×C4⋊C4—1132no—
174C2×C4⋊C4—1132no—
175C2×C4⋊C4—2261no—
176C2×C4⋊C4—2261no—
177C2×C4⋊C4—2261no—
178C2×C4⋊C4C2×D11311yescharacteristic
179#107—1132no—
180#107—1132no—
181#106—1132no—
182#106C2×D11312yescomplemented
183#103—1132no—
184#103C2×D11312yescomplemented
185#102—1132no—
186#102—1132no—
187C22⋊C8—1131no—
188C22⋊C8—1132no—
189C22⋊C8C2×D11311yescharacteristic
190C24—1131no—
191#41—2264no—
192C2×Q8C22×D11311yescharacteristic
193C2×D4—1131no—
194C2×D4—2261no—
195C2×D4—2261no—
196C2×D4—2261no—
197C22×C4—21no—
198C22×C4—1131no—
199C22×C4—1131no—
200C22×C4—1131no—
201C22×C4—1131no—
202C22×C4—1131no—
203C22×C4—4524no—
204C22×C4—2261no—
205C22×C4—2264no—
206C22×C4—2262no—
207C22×C4—2262no—
208C22×C4—2261no—
209C22×C4C22×D11311yescharacteristic
210M16—2264no—
211C2×C8—1132no—
212C2×C8C22×D11312yes—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—1132no—
216C4⋊C4—1131no—
217C4⋊C4—2262no—
218C4⋊C4—2262no—
219C4⋊C4—2261no—
220C4⋊C4—2261no—
221C4⋊C4C22×D11312yes—
222C4⋊C4C22×D11311yescharacteristic
223C22⋊C4—21no—
224C22⋊C4—2261no—
225C22⋊C4—2261no—
226C22⋊C4—2261no—
227C22⋊C4—2261no—
228C42—2261no—
229C23—1131no—
230C23—1131no—
231C23—2262no—
232C23—2262no—
233C23—2261no—
234C23—2262no—
235C23D4×D11311yescharacteristic
236Q8—22no—
237D4—4522no—
238D4—4522no—
239D4—4522no—
240D4—2262no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—42no—
246C2×C4—1131no—
247C2×C4—1134no—
248C2×C4—1131no—
249C2×C4—4522no—
250C2×C4—4524no—
251C2×C4—4524no—
252C2×C4—4522no—
253C2×C4—2262no—
254C2×C4—2262no—
255C2×C4—2262no—
256C2×C4—2261no—
257C2×C4—2262no—
258C2×C4—2262no—
259C2×C4D4×D11311yescharacteristic
260C2×C4C23×D11311yescharacteristic
261C8—22no—
262C8—2262no—
263C22—21no—
264C22—21no—
265C22—1132no—
266C22—1132no—
267C22—4521no—
268C22—4521no—
269C22—4521no—
270C22—2268no—
271C22—2261no—
272C22—2261no—
273C22—2261no—
274C22—2261no—
275C22#1681364912yes—
276C22C2×D4×D11311yescharacteristic
277C4—21no—
278C4—41no—
279C4—42no—
280C4—41no—
281C4—1132no—
282C4—4522no—
283C4—4521no—
284C4—2261no—
285C4#41×D11312yes—
286C2—22no—
287C2—9041no—
288C2—2262no—
289C2—2262no—
290C2#123×D11311yescharacteristic
291C2C2×#1681364911yescharacteristic
292C2#137×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#483×C113C2
socleC22×C113C22×D4
prime radical#20299111C2
hypercenter#483D113
hypocenterC113#3092
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D113C2semidirect
3. #20298932C2semidirect
4. #20298926C2semidirect
5. #20298918C2semidirect
6. #20298912C2semidirect
7. #20298911C2semidirect
8. #20298637C2semidirect
9. #20298598C2semidirect
10. #20298560C2semidirect
11. #483×C113C2semidirect
30. #16813556C22semidirect
31. #16813555C22semidirect
32. #16813553C22semidirect
33. #16813546C22semidirect
34. #16813544C22semidirect
35. #16813542C22semidirect
40. #106×C113C22semidirect
41. #103×C113C22semidirect
147. C113#3092semidirect
152. #483D113semidirect
182. #106C2×D113semidirect
184. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991112
C2×C4⋊C4×D1132
#202989322
#202989262
#202989182
#202989122
#202989112
#202986372
#202985982
#202985602
#483×C1132
#3092113