Finite Group Databasebeta

← #28401497

Subgroups — #28401497

Order 14464.

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

normal subgroups only

This group has 428 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#20299143C211yesmaximal, characteristic
2C2×#16813620C211yesmaximal, characteristic, complemented
3#20298969C212yesmaximal, complemented
4#20298947C212yesmaximal, complemented
5#20298802C212yesmaximal, complemented
6#20298801C212yesmaximal, complemented
7#20298739C211yesmaximal, characteristic, complemented
8#20298737C211yesmaximal, characteristic, complemented
9#20298736C211yesmaximal, characteristic, complemented
10#20298648C211yesmaximal, characteristic, complemented
11#448×C113C211yesmaximal, characteristic, complemented
12C2×#14268646—21no—
13C22×Dic226C2211yescharacteristic
14C2×#14268636C2212yes—
15C2×#14268635C2212yes—
16C2×#14268634C2212yes—
17#16813621C2211yescharacteristic
18#16813620—21no—
19#16813620—21no—
20#16813620C2212yes—
21#16813620C2212yes—
22#16813618C2211yescharacteristic
23#16813608—21no—
24#16813596C2211yescharacteristic
25#16813594—21no—
26D4×Dic113C2211yescharacteristic
27#16813584C2211yescharacteristic
28#16813582—21no—
29C2×#14268626—21no—
30C2×#14268626—21no—
31C2×C4×Dic113C2211yescharacteristic
32#16813551C2212yes—
33#16813547C2212yes—
34#16813546C2212yes—
35#16813545C2212yes—
36C22⋊#11744751C2211yescharacteristic
37C8×Dic113C2212yes—
38C22×Q8×C113C2211yescharacteristic
39C2×SD16×C113C2212yes—
40#121×C113C2211yescharacteristic
41#103×C113C2212yes—
42C22⋊C8×C113C2211yescharacteristic
43#14268646—44no—
44C2×Dic226—21no—
45C2×Dic226—21no—
46C2×Dic226—42no—
47C2×Dic226C2312yes—
48C2×D452C2311yescharacteristic
49C2×C22⋊D113—21no—
50C2×C22⋊D113—21no—
51C2×C22⋊D113—21no—
52C22×Dic113—21no—
53C22×Dic113—21no—
54C22×Dic113D411yescharacteristic
55C22×Dic113D411yescharacteristic
56C2×C4×D113—21no—
57#14268636—42no—
58#14268635—42no—
59#14268634—42no—
60C2×#11744751C2312yes—
61C4⋊Dic113C2311yescharacteristic
62#14268626—22no—
63#14268626—22no—
64#14268626—22no—
65#14268626—22no—
66#14268626—21no—
67C22⋊Dic113—21no—
68#14268624—21no—
69#14268624—21no—
70C4×Dic113D411yescharacteristic
71C4×Dic113D411yescharacteristic
72C4×Dic113C2311yescharacteristic
73C4×Dic113C2311yescharacteristic
74C2×Q8×C113—21no—
75C2×Q8×C113—42no—
76C2×Q8×C113C2312yes—
77C2×D4×C113—21no—
78C2×D4×C113C2311yescharacteristic
79C22×C4×C113—21no—
80C22×C4×C113C2311yescharacteristic
81SD16×C113—42no—
82C2×C8×C113C2312yes—
83C4⋊C4×C113C2311yescharacteristic
84C22⋊C4×C113—21no—
85C23×C113—21no—
86C23×C113C2×D411yescharacteristic
87C22×D113—21no—
88Q8×C113—22no—
89Q8×C113—22no—
90Q8×C113—42no—
91D4×C113—22no—
92D4×C113—42no—
93C2×C4×C113—22no—
94C2×C4×C113—21no—
95C2×C4×C113—22no—
96C2×C4×C113—42no—
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2411yescharacteristic
99C22⋊D113—42no—
100C22⋊D113—42no—
101C22⋊D113—42no—
102C2×Dic113—22no—
103C2×Dic113—21no—
104C2×Dic113—22no—
105C2×Dic113—42no—
106C2×Dic113—42no—
107C2×Dic113SD1614yescomplemented
108C2×Dic113C2×D411yescharacteristic
109C2×Dic113C2×D411yescharacteristic
110C2×Dic113C2×D411yescharacteristic
111C2×Dic113C2×D411yescharacteristic
112D452—22no—
113C4×D113—42no—
114Dic226—22no—
115Dic226—22no—
116Dic226—42no—
117Dic226—42no—
118C8×C113—22no—
119#11744751—22no—
120C22×C113—21no—
121C22×C113—21no—
122C22×C113—41no—
123C22×C113—41no—
124C22×C113—41no—
125C22×C113C2×SD1612yes—
126C22×C113C22×D411yescharacteristic
127C2×D113—41no—
128C2×D113—41no—
129C2×D113—41no—
130C4×C113—21no—
131C4×C113—42no—
132C4×C113—41no—
133C4×C113H(5,𝔽2)12yes—
134Dic113—21no—
135Dic113—42no—
136Dic113—41no—
137Dic113C2×SD1612yes—
138Dic113C2×SD1612yes—
139Dic113#13712yes—
140C2×C113—22no—
141C2×C113—81no—
142C2×C113#53511yescharacteristic
143C2×C113C22×SD1611yescharacteristic
144C2×C113C2×#13711yescharacteristic
145D113—81no—
146#3206—1131nomaximal, Sylow
147C113#320611yescharacteristic, complemented, Sylow
148#532—1131no—
149C2×C4⋊Q8—1131no—
150#492—1132no—
151#487—1132no—
152#461—1132no—
153#461—1132no—
154#448—1131no—
155#448—1131no—
156#448—1131no—
157#448D11311yescharacteristic, complemented
158#431—1131no—
159C2×#41—2261no—
160C22×Q8—1131no—
161C22×Q8C2×D11311yescharacteristic
162C2×SD16—1132no—
163C2×SD16—1132no—
164C2×SD16—1132no—
165C2×SD16C2×D11312yes—
166C4⋊Q8—1131no—
167C4⋊Q8—1132no—
168C4⋊Q8—1132no—
169C4⋊Q8—2261no—
170C4⋊Q8—2261no—
171#127—1131no—
172#124—2261no—
173#121—1131no—
174#121—2261no—
175#121C2×D11311yescharacteristic
176C4×D4—1131no—
177C4×D4—1131no—
178C4×D4—2261no—
179C2×C4⋊C4—2261no—
180C2×C4⋊C4—2261no—
181C2×C42—1131no—
182C4⋊C8—1132no—
183#103—1132no—
184#103—1132no—
185#103—1132no—
186#103C2×D11312yes—
187C22⋊C8—1131no—
188C22⋊C8C2×D11311yescharacteristic
189C4×C8—1132no—
190#41—4524no—
191C2×Q8—21no—
192C2×Q8—42no—
193C2×Q8—1132no—
194C2×Q8—4522no—
195C2×Q8—2261no—
196C2×Q8—2261no—
197C2×Q8C22×D11312yes—
198C2×D4—21no—
199C2×D4—1131no—
200C2×D4—2261no—
201C2×D4—2261no—
202C2×D4—2261no—
203C2×D4C22×D11311yescharacteristic
204C22×C4—21no—
205C22×C4—1131no—
206C22×C4—1131no—
207C22×C4—2261no—
208C22×C4—2261no—
209C22×C4—2261no—
210C22×C4C22×D11311yescharacteristic
211SD16—42no—
212SD16—4522no—
213SD16—4522no—
214SD16—4522no—
215C2×C8—1132no—
216C2×C8C22×D11312yes—
217C4⋊C4—1131no—
218C4⋊C4—2262no—
219C4⋊C4—2262no—
220C4⋊C4—2262no—
221C4⋊C4—2262no—
222C4⋊C4—2261no—
223C4⋊C4C22×D11311yescharacteristic
224C22⋊C4—21no—
225C22⋊C4—2261no—
226C22⋊C4—2261no—
227C22⋊C4—2261no—
228C42—1131no—
229C42—1131no—
230C42—1131no—
231C42—1131no—
232C23—21no—
233C23—2261no—
234C23D4×D11311yescharacteristic
235Q8—22no—
236Q8—22no—
237Q8—42no—
238Q8—4522no—
239Q8—4522no—
240Q8—2262no—
241Q8—2262no—
242D4—22no—
243D4—42no—
244D4—4522no—
245D4—4522no—
246D4—4522no—
247D4—2262no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—1134no—
253C2×C4—1131no—
254C2×C4—1131no—
255C2×C4—1131no—
256C2×C4—1131no—
257C2×C4—4522no—
258C2×C4—4522no—
259C2×C4—4522no—
260C2×C4—2262no—
261C2×C4—2261no—
262C2×C4—2262no—
263C2×C4D4×D11311yescharacteristic
264C2×C4C23×D11311yescharacteristic
265C8—22no—
266C8—2262no—
267C22—21no—
268C22—21no—
269C22—41no—
270C22—41no—
271C22—41no—
272C22—4521no—
273C22—4521no—
274C22—4521no—
275C22SD16×D11312yes—
276C22C2×D4×D11311yescharacteristic
277C4—21no—
278C4—41no—
279C4—42no—
280C4—1132no—
281C4—1132no—
282C4—1132no—
283C4—4521no—
284C4—4522no—
285C4—2261no—
286C4#1681366712yes—
287C2—22no—
288C2—81no—
289C2—9041no—
290C2#2029916311yescharacteristic
291C2C2×SD16×D11311yescharacteristic
292C2#137×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#448×C113C2
socleC22×C113C22×D4
prime radical#20299143C2
hypercenter#448D113
hypocenterC113#3206
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. C2×#16813620C2semidirect
3. #20298969C2semidirect
4. #20298947C2semidirect
5. #20298802C2semidirect
6. #20298801C2semidirect
7. #20298739C2semidirect
8. #20298737C2semidirect
9. #20298736C2semidirect
10. #20298648C2semidirect
11. #448×C113C2semidirect
107. C2×Dic113SD16semidirect
147. C113#3206semidirect
157. #448D113semidirect

Maximal subgroups

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

subgroupindex
#202991432
C2×#168136202
#202989692
#202989472
#202988022
#202988012
#202987392
#202987372
#202987362
#202986482
#448×C1132
#3206113