Finite Group Databasebeta

← #28401608

Subgroups — #28401608

Order 14464.

396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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#20299149C211yesmaximal, characteristic, complemented
2#20299127C211yesmaximal, characteristic, complemented
3#20298988C211yesmaximal, characteristic, complemented
4#20298966C211yesmaximal, characteristic, complemented
5#20298963C211yesmaximal, characteristic, complemented
6#20298822C212yesmaximal, complemented
7#20298815C212yesmaximal, complemented
8#20298759C212yesmaximal, complemented
9#20298742C212yesmaximal, complemented
10#20298653C211yesmaximal, characteristic, complemented
11#497×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2212yes—
13C2×#14268634C2212yes—
14C2×#14268632C2212yes—
15#16813619C2211yescharacteristic
16#16813615—21no—
17#16813614C2211yescharacteristic
18#16813611C2212yes—
19#16813604—21no—
20#16813598C2211yescharacteristic
21#16813597—21no—
22#16813597—21no—
23#16813593C2211yescharacteristic
24Q8×Dic113C2211yescharacteristic
25D4×Dic113C2211yescharacteristic
26#16813584—21no—
27#16813584—21no—
28#16813582—21no—
29#16813578—21no—
30C42×D113C2211yescharacteristic
31#16813551C2212yes—
32#16813546C2212yes—
33#16813546C2212yes—
34#16813544C2212yes—
35#16813544C2212yes—
36#16813534C2212yes—
37#16813533C2211yescharacteristic
38C2×Q16×C113C2212yes—
39C2×SD16×C113C2212yes—
40C4⋊Q8×C113C2211yescharacteristic
41#124×C113C2211yescharacteristic
42#97×C113C2211yescharacteristic
43#14268648—42no—
44#14268648—42no—
45C2×D452—22no—
46C2×D452—21no—
47C2×D452—21no—
48C2×D452C2312yes—
49C2×C22⋊D113—21no—
50C22×Dic113—21no—
51C2×C4×D113—22no—
52C2×C4×D113D411yescharacteristic
53C2×C4×D113D411yescharacteristic
54C2×C4×D113C2311yescharacteristic
55#14268634—42no—
56#14268632—42no—
57C2×#11744751C2312yes—
58C4⋊Dic113—21no—
59C4⋊Dic113C2311yescharacteristic
60C4⋊Dic113C2311yescharacteristic
61#14268626—21no—
62#14268626—21no—
63#14268626—21no—
64C22⋊Dic113—21no—
65C22⋊Dic113—21no—
66#14268624—21no—
67#14268624—22no—
68#14268624—22no—
69C4×Dic113—21no—
70C4×Dic113D411yescharacteristic
71C4×Dic113D411yescharacteristic
72C4×Dic113C2311yescharacteristic
73C2×Q8×C113C2311yescharacteristic
74C2×Q8×C113C2312yes—
75C2×D4×C113C2311yescharacteristic
76Q16×C113—42no—
77SD16×C113—42no—
78C2×C8×C113C2312yes—
79C4⋊C4×C113—21no—
80C4⋊C4×C113—21no—
81C22⋊C4×C113—21no—
82C22⋊C4×C113—21no—
83C42×C113C2311yescharacteristic
84C23×C113—21no—
85C22×D113—22no—
86C22×D113C2×D411yescharacteristic
87Q8×C113—22no—
88Q8×C113—22no—
89Q8×C113—22no—
90D4×C113—22no—
91C2×C4×C113—21no—
92C2×C4×C113—22no—
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2×D411yescharacteristic
95C2×C4×C113C2411yescharacteristic
96C22⋊D113—42no—
97C2×Dic113—21no—
98C2×Dic113—21no—
99C2×Dic113—42no—
100C2×Dic113C2×D411yescharacteristic
101C2×Dic113C2×D411yescharacteristic
102C2×Dic113C2×D411yescharacteristic
103D452—22no—
104D452—22no—
105D452—42no—
106D452—42no—
107D452—44no—
108C4×D113—22no—
109C4×D113—41no—
110C4×D113—41no—
111C4×D113—44no—
112C8×C113—22no—
113#11744751—22no—
114C22×C113—41no—
115C22×C113—41no—
116C22×C113—41no—
117C22×C113C22×D411yescharacteristic
118C2×D113—21no—
119C2×D113—21no—
120C2×D113—21no—
121C2×D113—42no—
122C2×D113—42no—
123C2×D113—42no—
124C4×C113—21no—
125C4×C113—21no—
126C4×C113—42no—
127C4×C113—41no—
128C4×C113H(5,𝔽2)12yes—
129Dic113—21no—
130Dic113—21no—
131Dic113—21no—
132Dic113—41no—
133Dic113—41no—
134C2×C113—81no—
135C2×C113#53511yescharacteristic
136C2×C113#57511yescharacteristic
137C2×C113#57511yescharacteristic
138D113—41no—
139D113—82no—
140#3219—1131nomaximal, Sylow
141C113#321911yescharacteristic, complemented, Sylow
142#532—1131no—
143#529—1131no—
144#497D11311yescharacteristic, complemented
145#496—1131no—
146#491—1131no—
147#490—1131no—
148#464—1132no—
149#463—1132no—
150#452—1132no—
151#449—1132no—
152#432—1131no—
153C2×#41—1132no—
154C2×Q16C2×D11312yes—
155C2×SD16—1132no—
156C2×SD16C2×D11312yes—
157C2×D8—1132no—
158C4⋊Q8C2×D11311yescharacteristic
159#127—1131no—
160#126—2261no—
161#125—1131no—
162#124—1132no—
163#124C2×D11311yescharacteristic
164#123—2261no—
165C22⋊Q8—1131no—
166#121—1131no—
167#121—2261no—
168#121—2261no—
169C4×Q8—1131no—
170C4×D4—1131no—
171C4×D4—2261no—
172C4×D4—2261no—
173C4×D4—2261no—
174#117—2261no—
175C2×C42—1131no—
176C4⋊C8—1132no—
177#103—1132no—
178#103—1132no—
179#102—1132no—
180#102—1132no—
181C22⋊C8—1132no—
182#97—1131no—
183#97C2×D11311yescharacteristic
184#41—4522no—
185#41—4522no—
186C2×Q8C22×D11312yes—
187C2×Q8C22×D11311yescharacteristic
188C2×D4—1132no—
189C2×D4—2262no—
190C2×D4—2261no—
191C2×D4—2261no—
192C2×D4—2261no—
193C2×D4C22×D11311yescharacteristic
194C22×C4—1131no—
195C22×C4—1131no—
196C22×C4—1131no—
197C22×C4—2262no—
198C22×C4—2261no—
199Q16—42no—
200SD16—42no—
201SD16—4522no—
202D8—4522no—
203C2×C8—1132no—
204C2×C8C22×D11312yes—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—1131no—
208C4⋊C4—1131no—
209C4⋊C4—2261no—
210C4⋊C4—2261no—
211C4⋊C4—2261no—
212C4⋊C4—2261no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—2262no—
216C22⋊C4—2262no—
217C22⋊C4—2261no—
218C22⋊C4—2261no—
219C22⋊C4—2261no—
220C42—1131no—
221C42—1131no—
222C42—1131no—
223C42—2261no—
224C42C22×D11311yescharacteristic
225C23—21no—
226C23—1131no—
227C23—2262no—
228Q8—22no—
229Q8—22no—
230Q8—22no—
231D4—22no—
232D4—4522no—
233D4—4522no—
234D4—4524no—
235D4—4522no—
236D4—2262no—
237D4—2262no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—1131no—
241C2×C4—1131no—
242C2×C4—1131no—
243C2×C4—4521no—
244C2×C4—4521no—
245C2×C4—4524no—
246C2×C4—4522no—
247C2×C4—2261no—
248C2×C4—2261no—
249C2×C4—2262no—
250C2×C4D4×D11311yescharacteristic
251C2×C4D4×D11311yescharacteristic
252C2×C4C23×D11311yescharacteristic
253C8—22no—
254C8—2262no—
255C22—41no—
256C22—41no—
257C22—41no—
258C22—4522no—
259C22—4522no—
260C22—4522no—
261C22—2261no—
262C22—2261no—
263C22—2261no—
264C22C2×D4×D11311yescharacteristic
265C4—21no—
266C4—21no—
267C4—42no—
268C4—41no—
269C4—4521no—
270C4—4521no—
271C4—2261no—
272C4—2261no—
273C4—2261no—
274C4#1681366712yes—
275C2—81no—
276C2—9042no—
277C2—4521no—
278C2#2029916111yescharacteristic
279C2#2029939711yescharacteristic
280C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#497×C113C2
socleC22×C113C22×D4
hypercenter#497D113
hypocenterC113#3219
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #20299149C2semidirect
2. #20299127C2semidirect
3. #20298988C2semidirect
4. #20298966C2semidirect
5. #20298963C2semidirect
6. #20298822C2semidirect
7. #20298815C2semidirect
8. #20298759C2semidirect
9. #20298742C2semidirect
10. #20298653C2semidirect
11. #497×C113C2semidirect
141. C113#3219semidirect
144. #497D113semidirect

Maximal subgroups

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

subgroupindex
#202991492
#202991272
#202989882
#202989662
#202989632
#202988222
#202988152
#202987592
#202987422
#202986532
#497×C1132
#3219113