Finite Group Databasebeta

← #28403271

Subgroups — #28403271

Order 14464.

348 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299331C211yesmaximal, characteristic
2#20299324C211yesmaximal, characteristic, complemented
3#20298953C211yesmaximal, characteristic, complemented
4#20298951C211yesmaximal, characteristic, complemented
5#20298943C211yesmaximal, characteristic
6#20298898C211yesmaximal, characteristic, complemented
7#20298897C211yesmaximal, characteristic, complemented
8#20298882C211yesmaximal, characteristic, complemented
9#20298820C211yesmaximal, characteristic, complemented
10#20298818C211yesmaximal, characteristic, complemented
11#20298796C211yesmaximal, characteristic
12C8×Dic226C211yesmaximal, characteristic, complemented
13#20298690C211yesmaximal, characteristic, complemented
14#20298683C211yesmaximal, characteristic, complemented
15C4×SD16×C113C211yesmaximal, characteristic, complemented
16C2×#14268637C2211yescharacteristic
17C2×#14268634C2211yescharacteristic
18#16813621—21no—
19#16813621C2211yescharacteristic
20#16813618C2211yescharacteristic
21#16813614—21no—
22#16813614C2211yescharacteristic
23#16813613—21no—
24#16813613C2211yescharacteristic
25#16813610C2211yescharacteristic
26#16813609C2211yescharacteristic
27#16813608—21no—
28#16813605—21no—
29#16813604—21no—
30Q8×Dic113C2211yescharacteristic
31Q8×Dic113C2211yescharacteristic
32C4×Dic226—21no—
33C4×Dic226C2211yescharacteristic
34#16813587C2211yescharacteristic
35#16813584C2211yescharacteristic
36C4×C22⋊D113—21no—
37#16813555C2211yescharacteristic
38#16813553C2211yescharacteristic
39C4⋊#11744751C2211yescharacteristic
40#16813551C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813542C2211yescharacteristic
50C8×Dic113C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C4×C8×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226D411yescharacteristic
61C2×Dic226C2311yescharacteristic
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C2×C4×D113—21no—
66#14268637—22no—
67#14268634—22no—
68C2×#11744751C2311yescharacteristic
69C2×#11744751C2311yescharacteristic
70C4⋊Dic113—21no—
71C4⋊Dic113—21no—
72C4⋊Dic113—21no—
73C4⋊Dic113D411yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76#14268626—21no—
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626D411yescharacteristic
82#14268626D411yescharacteristic
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88C4×Dic113—21no—
89C4×Dic113—21no—
90C4×Dic113—21no—
91C4×Dic113C2311yescharacteristic
92C4×Dic113C2311yescharacteristic
93C2×Q8×C113C2311yescharacteristic
94C2×D4×C113C2311yescharacteristic
95C22×C4×C113—21no—
96SD16×C113—22no—
97C2×C8×C113C2311yescharacteristic
98C2×C8×C113C2311yescharacteristic
99C4⋊C4×C113—21no—
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C22⋊C4×C113—21no—
103C42×C113—21no—
104C42×C113C2311yescharacteristic
105C23×C113—21no—
106C22×D113—21no—
107Q8×C113—21no—
108Q8×C113#4112yes—
109D4×C113—21no—
110D4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—81no—
115C2×C4×C113C2×D411yescharacteristic
116C2×C4×C113C2×D411yescharacteristic
117C2×C4×C113C2411yescharacteristic
118C22⋊D113—42no—
119C22⋊D113—81no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113C2×D411yescharacteristic
124C2×Dic113C2×D411yescharacteristic
125C2×Dic113C2×D411yescharacteristic
126C2×Dic113C2×D411yescharacteristic
127D452—21no—
128D452—21no—
129C4×D113—81no—
130Dic226—22no—
131Dic226—21no—
132Dic226—21no—
133Dic226—42no—
134C8×C113—21no—
135C8×C113—21no—
136#11744751—21no—
137#11744751—21no—
138C22×C113—41no—
139C22×C113—41no—
140C22×C113—41no—
141C22×C113C22×D411yescharacteristic
142C2×D113—41no—
143C2×D113—41no—
144C2×D113—41no—
145C4×C113—22no—
146C4×C113—21no—
147C4×C113—21no—
148C4×C113—41no—
149C4×C113—41no—
150C4×C113C2×#4111yescharacteristic
151C4×C1132−1+411yescharacteristic
152Dic113—21no—
153Dic113—21no—
154Dic113—21no—
155Dic113—41no—
156Dic113—41no—
157Dic113—41no—
158Dic113#13512yes—
159C2×C113—81no—
160C2×C113#54811yescharacteristic
161C2×C113C2×#13511yescharacteristic
162C2×C113#57711yescharacteristic
163D113—81no—
164#3365—1131nomaximal, Sylow
165C113#336511yescharacteristic, complemented, Sylow
166#559—1131no—
167#557—1131no—
168#488—1131no—
169#488—1131no—
170#486—1131no—
171#478—1131no—
172#478—1131no—
173#475—1131no—
174#464—1131no—
175#464—1131no—
176#460—1131no—
177C8×Q8—1131no—
178C4×Q16—1131no—
179C4×SD16—1131no—
180C4×SD16D11311yescharacteristic, complemented
181C2×Q16—1131no—
182C2×SD16—1131no—
183C2×SD16C2×D11311yescharacteristic
184C4⋊Q8—1131no—
185C4⋊Q8—2261no—
186#127—1131no—
187#125—1131no—
188#125—1131no—
189#125—2261no—
190#125—2261no—
191#124—1131no—
192#124—1131no—
193#124—2261no—
194#123—2261no—
195#123—2261no—
196C4×Q8—1131no—
197C4×Q8—1131no—
198C4×Q8—1131no—
199C4×Q8—1131no—
200C4×Q8—2261no—
201C4×Q8C2×D11311yescharacteristic
202C4×D4—1131no—
203C4×D4—2261no—
204C4×D4C2×D11311yescharacteristic
205#107—1131no—
206#106—1131no—
207#106C2×D11311yescharacteristic
208C4⋊C8—1131no—
209C4⋊C8—1131no—
210C4⋊C8—1131no—
211#103—1131no—
212#103—1131no—
213#103—1131no—
214#103C2×D11311yescharacteristic
215#102—1131no—
216#102—1131no—
217#102—1131no—
218#102—1131no—
219#102—1131no—
220#102C2×D11311yescharacteristic
221C4×C8—1131no—
222C4×C8—1131no—
223C4×C8C2×D11311yescharacteristic
224C2×Q8—1131no—
225C2×Q8—1131no—
226C2×Q8—2261no—
227C2×Q8C22×D11311yescharacteristic
228C2×D4—1131no—
229C2×D4—2261no—
230C2×D4—2261no—
231C2×D4C22×D11311yescharacteristic
232C22×C4—21no—
233C22×C4—2261no—
234Q16—2262no—
235SD16—22no—
236SD16—2262no—
237C2×C8—1131no—
238C2×C8—1131no—
239C2×C8C22×D11311yescharacteristic
240C2×C8C22×D11311yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—1131no—
243C4⋊C4—1131no—
244C4⋊C4—1131no—
245C4⋊C4—1131no—
246C4⋊C4—1131no—
247C4⋊C4—2261no—
248C4⋊C4—2261no—
249C4⋊C4—2261no—
250C4⋊C4—2261no—
251C4⋊C4—2261no—
252C4⋊C4—2261no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4C22×D11311yescharacteristic
256C4⋊C4C22×D11311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—2261no—
259C22⋊C4—2261no—
260C22⋊C4—2261no—
261C22⋊C4—2261no—
262C22⋊C4—2261no—
263C42—21no—
264C42—1131no—
265C42—1131no—
266C42—2261no—
267C42—2261no—
268C42—2261no—
269C42C22×D11311yescharacteristic
270C23—21no—
271C23—2261no—
272Q8—21no—
273Q8—4522no—
274Q8—2262no—
275Q8—2261no—
276Q8—2261no—
277Q8#1426864712yes—
278D4—21no—
279D4—21no—
280D4—9041no—
281D4—4522no—
282D4—2261no—
283D4—2261no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—81no—
288C2×C4—1131no—
289C2×C4—1131no—
290C2×C4—1131no—
291C2×C4—1131no—
292C2×C4—9041no—
293C2×C4—2261no—
294C2×C4—2261no—
295C2×C4—2261no—
296C2×C4D4×D11311yescharacteristic
297C2×C4D4×D11311yescharacteristic
298C2×C4C23×D11311yescharacteristic
299C8—21no—
300C8—21no—
301C8—2261no—
302C8—2261no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—4521no—
307C22—4521no—
308C22—4521no—
309C22C2×D4×D11311yescharacteristic
310C4—21no—
311C4—21no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—1132no—
316C4—4521no—
317C4—4521no—
318C4—4521no—
319C4—2261no—
320C4—2261no—
321C4—2261no—
322C4C2×#1426864711yescharacteristic
323C4#1681366911yescharacteristic
324C2—81no—
325C2—9041no—
326C2#2029925711yescharacteristic
327C2#135×D11311yescharacteristic
328C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC4×SD16×C113C2
socleC22×C113C22×D4
prime radical#16813618C22
hypercenterC4×SD16D113
hypocenterC113#3365
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #20299324C2semidirect
3. #20298953C2semidirect
4. #20298951C2semidirect
6. #20298898C2semidirect
7. #20298897C2semidirect
8. #20298882C2semidirect
9. #20298820C2semidirect
10. #20298818C2semidirect
12. C8×Dic226C2semidirect
13. #20298690C2semidirect
14. #20298683C2semidirect
15. C4×SD16×C113C2semidirect
165. C113#3365semidirect
180. C4×SD16D113semidirect

Maximal subgroups

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

subgroupindex
#202993312
#202993242
#202989532
#202989512
#202989432
#202988982
#202988972
#202988822
#202988202
#202988182
#202987962
C8×Dic2262
#202986902
#202986832
C4×SD16×C1132
#3365113