Finite Group Databasebeta

← #28400519

Subgroups — #28400519

Order 14464.

410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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⋊Q8×D113C211yesmaximal, characteristic
2C2×#16813580C211yesmaximal, characteristic
3#20298941C212yesmaximal, complemented
4#20298937C212yesmaximal, complemented
5#20298933C211yesmaximal, characteristic, complemented
6#20298929C211yesmaximal, characteristic, complemented
7#20298926C211yesmaximal, characteristic, complemented
8#20298639C212yesmaximal, complemented
9#20298605C212yesmaximal, complemented
10#20298560C211yesmaximal, characteristic
11#484×C113C211yesmaximal, characteristic, complemented
12C2×Q8×D113C2211yescharacteristic
13C22×C4×D113C2211yescharacteristic
14C2×#14268630C2212yes—
15#16813602C2211yescharacteristic
16#16813601C2211yescharacteristic
17#16813600—21no—
18#16813599—21no—
19#16813598C2211yescharacteristic
20#16813580—21no—
21#16813580—21no—
22#16813580C2212yes—
23#16813580C2212yes—
24C2×C4⋊Dic113C2211yescharacteristic
25C4⋊C4×D113—21no—
26C4⋊C4×D113C2211yescharacteristic
27C2×#14268624—21no—
28C22⋊C4×D113—21no—
29C2×C4×Dic113—21no—
30#16813555C2212yescomplemented
31#16813554C2212yescomplemented
32#16813553C2212yescomplemented
33#16813547C2212yescomplemented
34#16813546C2212yescomplemented
35#16813545C2212yescomplemented
36C22⋊#11744751C2211yescharacteristic
37#16813534C2212yes—
38C22⋊Q8×C113C2211yescharacteristic
39C2×C4⋊C4×C113C2211yescharacteristic
40#107×C113C2212yescomplemented
41#103×C113C2212yescomplemented
42C22⋊C8×C113C2211yescharacteristic
43C23×D113D411yescharacteristic
44C2×Dic226—21no—
45C2×Dic226C2311yescharacteristic
46Q8×D113—24no—
47C22×Dic113—21no—
48C22×Dic113D411yescharacteristic
49C2×C4×D113—24no—
50C2×C4×D113—21no—
51C2×C4×D113—21no—
52C2×C4×D113D411yescharacteristic
53C2×C4×D113D411yescharacteristic
54C2×C4×D113C2311yescharacteristic
55C2×C4×D113C2311yescharacteristic
56#14268630—24no—
57C2×#11744751C2312yes—
58C4⋊Dic113—21no—
59C4⋊Dic113—21no—
60C4⋊Dic113C2311yescharacteristic
61C4⋊Dic113C2312yes—
62#14268626—21no—
63#14268626—21no—
64#14268626—21no—
65C22⋊Dic113—21no—
66#14268624—21no—
67#14268624—21no—
68#14268624—22no—
69#14268624—22no—
70C4×Dic113—22no—
71C4×Dic113—22no—
72C2×Q8×C113C2311yescharacteristic
73C22×C4×C113—21no—
74C22×C4×C113C2311yescharacteristic
75C2×C8×C113C2312yes—
76C4⋊C4×C113—21no—
77C4⋊C4×C113—21no—
78C4⋊C4×C113C2311yescharacteristic
79C4⋊C4×C113C2312yes—
80C22⋊C4×C113—21no—
81C23×C113C2×D411yescharacteristic
82C22×D113—22no—
83C22×D113—22no—
84C22×D113—41no—
85C22×D113C2×D411yescharacteristic
86C22×D113C2×D411yescharacteristic
87Q8×C113—22no—
88C2×C4×C113—22no—
89C2×C4×C113—21no—
90C2×C4×C113—21no—
91C2×C4×C113—22no—
92C2×C4×C113—42no—
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2411yescharacteristic
95C2×Dic113—22no—
96C2×Dic113—22no—
97C2×Dic113—21no—
98C2×Dic113—21no—
99C2×Dic113—42no—
100C2×Dic113C2×D411yescharacteristic
101C2×Dic113C2×D411yescharacteristic
102C4×D113—22no—
103C4×D113—22no—
104C4×D113—22no—
105C4×D113—42no—
106C4×D113—42no—
107C4×D113#4114yes—
108Dic226—22no—
109Dic226—42no—
110C8×C113—22no—
111#11744751—22no—
112C22×C113—21no—
113C22×C113—21no—
114C22×C113#13712yes—
115C22×C113C22×D411yescharacteristic
116C2×D113—21no—
117C2×D113—21no—
118C2×D113—21no—
119C2×D113—21no—
120C2×D113—21no—
121C2×D113—44no—
122C2×D113#12312yes—
123C4×C113—21no—
124C4×C113—41no—
125C4×C113—41no—
126C4×C113—42no—
127C4×C113C2×#4112yes—
128Dic113—21no—
129Dic113—41no—
130Dic113—42no—
131Dic113—41no—
132Dic113#12312yes—
133C2×C113—22no—
134C2×C113C2×#12311yescharacteristic
135C2×C113C2×#13711yescharacteristic
136C2×C113#57511yescharacteristic
137D113—22no—
138D113—41no—
139#3095—1131nomaximal, Sylow
140C113#309511yescharacteristic, complemented, Sylow
141C2×C22⋊Q8—1131no—
142C2×#117—1131no—
143#485—1132no—
144#485—1132no—
145#484—1131no—
146#484D11311yescharacteristic, complemented
147#483—1131no—
148#483—1131no—
149#428—1132no—
150#419—1132no—
151#407—1131no—
152C22×Q8—1131no—
153C23×C4—1131no—
154C2×M16—1132no—
155C22⋊Q8—1131no—
156C22⋊Q8—1131no—
157C22⋊Q8—1131no—
158C22⋊Q8—2261no—
159C22⋊Q8—2261no—
160C22⋊Q8C2×D11311yescharacteristic
161#117—1132no—
162#117—1132no—
163#117—2261no—
164#117—2261no—
165C2×C4⋊C4—1131no—
166C2×C4⋊C4—1131no—
167C2×C4⋊C4—2261no—
168C2×C4⋊C4C2×D11311yescharacteristic
169C2×C22⋊C4—2261no—
170C2×C22⋊C4—2261no—
171C2×C42—2261no—
172#107—1132no—
173#107C2×D11312yescomplemented
174#106—1132no—
175#106—1132no—
176#103—1132no—
177#103—1132no—
178#103—1132no—
179#103C2×D11312yescomplemented
180C22⋊C8—1131no—
181C22⋊C8—1132no—
182C22⋊C8C2×D11311yescharacteristic
183C24—1131no—
184C2×Q8—1131no—
185C2×Q8—2261no—
186C2×Q8—2264no—
187C2×Q8C22×D11311yescharacteristic
188C22×C4—21no—
189C22×C4—1131no—
190C22×C4—1131no—
191C22×C4—1131no—
192C22×C4—1131no—
193C22×C4—1131no—
194C22×C4—2264no—
195C22×C4—2261no—
196C22×C4—2261no—
197C22×C4—2261no—
198C22×C4C22×D11311yescharacteristic
199M16—2264no—
200C2×C8—1132no—
201C2×C8C22×D11312yes—
202C4⋊C4—21no—
203C4⋊C4—21no—
204C4⋊C4—1132no—
205C4⋊C4—1131no—
206C4⋊C4—2261no—
207C4⋊C4—2261no—
208C4⋊C4—2261no—
209C4⋊C4—2261no—
210C4⋊C4—2261no—
211C4⋊C4C22×D11312yes—
212C4⋊C4C22×D11311yescharacteristic
213C22⋊C4—21no—
214C22⋊C4—2262no—
215C22⋊C4—2262no—
216C22⋊C4—2261no—
217C22⋊C4—2261no—
218C22⋊C4—2261no—
219C42—2262no—
220C42—2262no—
221C23—1131no—
222C23—1131no—
223C23—4521no—
224C23—2262no—
225C23—2262no—
226C23D4×D11311yescharacteristic
227Q8—22no—
228Q8—4522no—
229Q8—2262no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—1131no—
236C2×C4—1134no—
237C2×C4—1131no—
238C2×C4—4522no—
239C2×C4—4522no—
240C2×C4—4522no—
241C2×C4—2262no—
242C2×C4—2262no—
243C2×C4—2262no—
244C2×C4—2262no—
245C2×C4—2261no—
246C2×C4—2261no—
247C2×C4—2262no—
248C2×C4D4×D11311yescharacteristic
249C2×C4C23×D11311yescharacteristic
250C8—22no—
251C8—2262no—
252C22—21no—
253C22—21no—
254C22—1132no—
255C22—4524no—
256C22—2261no—
257C22—2261no—
258C22—2261no—
259C22—2261no—
260C22—2261no—
261C22#1681365412yes—
262C22C2×D4×D11311yescharacteristic
263C4—21no—
264C4—41no—
265C4—42no—
266C4—41no—
267C4—1132no—
268C4—4521no—
269C4—4522no—
270C4—4521no—
271C4—2261no—
272C4#41×D11312yes—
273C2—22no—
274C2—4521no—
275C2—2262no—
276C2#123×D11311yescharacteristic
277C2C2×#1681365411yescharacteristic
278C2#2029939411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#484×C113C2
socleC22×C113C22×D4
prime radicalC23×D113D4
hypercenter#484D113
hypocenterC113#3095
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #20298941C2semidirect
4. #20298937C2semidirect
5. #20298933C2semidirect
6. #20298929C2semidirect
7. #20298926C2semidirect
8. #20298639C2semidirect
9. #20298605C2semidirect
11. #484×C113C2semidirect
30. #16813555C22semidirect
31. #16813554C22semidirect
32. #16813553C22semidirect
33. #16813547C22semidirect
34. #16813546C22semidirect
35. #16813545C22semidirect
40. #107×C113C22semidirect
41. #103×C113C22semidirect
140. C113#3095semidirect
146. #484D113semidirect
173. #107C2×D113semidirect
179. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D1132
C2×#168135802
#202989412
#202989372
#202989332
#202989292
#202989262
#202986392
#202986052
#202985602
#484×C1132
#3095113