Finite Group Databasebeta

← #28400868

Subgroups — #28400868

Order 14464.

358 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299208C211yesmaximal, characteristic
2#20299076C211yesmaximal, characteristic
3#20298940C211yesmaximal, characteristic
4#20298936C211yesmaximal, characteristic
5#20298907C211yesmaximal, characteristic, complemented
6#20298903C211yesmaximal, characteristic, complemented
7#20298806C211yesmaximal, characteristic, complemented
8#20298806C211yesmaximal, characteristic, complemented
9#20298754C211yesmaximal, characteristic
10#20298705C211yesmaximal, characteristic, complemented
11#20298702C211yesmaximal, characteristic, complemented
12Q16×Dic113C211yesmaximal, characteristic, complemented
13#20298690C211yesmaximal, characteristic, complemented
14#20298656C211yesmaximal, characteristic
15#451×C113C211yesmaximal, characteristic
16C2×#14268637C2211yescharacteristic
17C2×#14268637C2211yescharacteristic
18#16813620C2211yescharacteristic
19#16813615—21no—
20#16813615—21no—
21#16813613—21no—
22#16813613C2211yescharacteristic
23#16813612—21no—
24#16813601C2211yescharacteristic
25Q8×Dic113—21no—
26Q8×Dic113—21no—
27Q8×Dic113C2211yescharacteristic
28Q8×Dic113C2211yescharacteristic
29Q8×Dic113C2211yescharacteristic
30Q8×Dic113C2211yescharacteristic
31Q8×Dic113C2211yescharacteristic
32#16813587C2211yescharacteristic
33#16813581—21no—
34#16813581—21no—
35#16813581C2211yescharacteristic
36#16813581C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813546C2211yescharacteristic
48#16813546C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C22×Q8×C113C2211yescharacteristic
53C2×Q16×C113C2211yescharacteristic
54C2×Q16×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59C2×Dic226C2311yescharacteristic
60#14268637—22no—
61#14268637—22no—
62C2×#11744751C2311yescharacteristic
63C2×#11744751C2311yescharacteristic
64C4⋊Dic113—21no—
65C4⋊Dic113—21no—
66C4⋊Dic113—21no—
67C4⋊Dic113—21no—
68C4⋊Dic113—21no—
69C4⋊Dic113—21no—
70C4⋊Dic113D411yescharacteristic
71C4⋊Dic113D411yescharacteristic
72C4⋊Dic113C2311yescharacteristic
73C4⋊Dic113C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75#14268626—21no—
76#14268626—21no—
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80C22⋊Dic113—21no—
81C22⋊Dic113—21no—
82C22⋊Dic113D411yescharacteristic
83C22⋊Dic113D411yescharacteristic
84C4×Dic113—21no—
85C4×Dic113—21no—
86C4×Dic113—21no—
87C4×Dic113—21no—
88C4×Dic113—21no—
89C4×Dic113—21no—
90C4×Dic113—21no—
91C4×Dic113C2311yescharacteristic
92C4×Dic113C2311yescharacteristic
93C2×Q8×C113—22no—
94C2×Q8×C113—22no—
95C2×Q8×C113—21no—
96C2×Q8×C113C2311yescharacteristic
97C2×Q8×C113C2311yescharacteristic
98C2×Q8×C113C2311yescharacteristic
99C22×C4×C113—21no—
100C22×C4×C113C2311yescharacteristic
101Q16×C113—22no—
102Q16×C113—22no—
103C2×C8×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C4⋊C4×C113—21no—
106C4⋊C4×C113C2311yescharacteristic
107C22⋊C4×C113—21no—
108C23×C113C2×D411yescharacteristic
109Q8×C113—24no—
110Q8×C113—21no—
111Q8×C113—21no—
112Q8×C113—21no—
113Q8×C113—21no—
114Q8×C113#4112yes—
115Q8×C113#4112yes—
116C2×C4×C113—24no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2411yescharacteristic
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113C2×D411yescharacteristic
130C2×Dic113C2×D411yescharacteristic
131C2×Dic113C2×D411yescharacteristic
132C2×Dic113C2×D411yescharacteristic
133Dic226—21no—
134Dic226—21no—
135C8×C113—21no—
136C8×C113—21no—
137#11744751—21no—
138#11744751—21no—
139C22×C113—21no—
140C22×C113—21no—
141C22×C113—21no—
142C22×C113C22×D411yescharacteristic
143C4×C113—22no—
144C4×C113—22no—
145C4×C113—21no—
146C4×C113—41no—
147C4×C113—41no—
148C4×C113C2×#4111yescharacteristic
149C4×C113C2×#4111yescharacteristic
150Dic113—21no—
151Dic113—21no—
152Dic113—21no—
153Dic113—21no—
154Dic113—41no—
155Dic113—41no—
156Dic113—41no—
157Dic113—41no—
158C2×C113—41no—
159C2×C113#52511yescharacteristic
160C2×C113#57811yescharacteristic
161C2×C113#57811yescharacteristic
162#3127—1131nomaximal, Sylow
163C113#312711yescharacteristic, complemented, Sylow
164#541—1131no—
165#519—1131no—
166#485—1131no—
167#485—1131no—
168#479—1131no—
169#479—1131no—
170#462—1131no—
171#462—1131no—
172#451—1131no—
173#451D11311yescharacteristic
174#441—1131no—
175#441—1131no—
176C4×Q16—1131no—
177C4×Q16—1131no—
178#433—1131no—
179C22×Q8C2×D11311yescharacteristic
180C2×Q16—1131no—
181C2×Q16—1131no—
182C2×Q16C2×D11311yescharacteristic
183C2×Q16C2×D11311yescharacteristic
184C4⋊Q8—1131no—
185#126—2261no—
186#126—2261no—
187#125—1131no—
188#125—2261no—
189#125—2261no—
190C22⋊Q8—1131no—
191C22⋊Q8C2×D11311yescharacteristic
192C4×Q8—1131no—
193C4×Q8—1131no—
194C4×Q8—1131no—
195C4×Q8—1131no—
196C4×Q8—1131no—
197C4×Q8—1131no—
198C4×Q8—2261no—
199C4×Q8—2261no—
200#117—1131no—
201#117—1131no—
202#117—2261no—
203#117—2261no—
204#107—1131no—
205#107—1131no—
206#106—1131no—
207#106—1131no—
208C4⋊C8—1131no—
209C4⋊C8—1131no—
210#103—1131no—
211#103—1131no—
212#103—1131no—
213#103—1131no—
214#103—1131no—
215#103—1131no—
216#103C2×D11311yescharacteristic
217#103C2×D11311yescharacteristic
218C22⋊C8—1131no—
219C22⋊C8C2×D11311yescharacteristic
220#97—1131no—
221C4×C8—1131no—
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—21no—
225C2×Q8—1131no—
226C2×Q8C22×D11311yescharacteristic
227C2×Q8C22×D11311yescharacteristic
228C2×Q8C22×D11311yescharacteristic
229C22×C4—21no—
230C22×C4C22×D11311yescharacteristic
231Q16—22no—
232Q16—22no—
233Q16—2262no—
234Q16—2262no—
235C2×C8—1131no—
236C2×C8—1131no—
237C2×C8C22×D11311yescharacteristic
238C2×C8C22×D11311yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—1131no—
241C4⋊C4—1131no—
242C4⋊C4—1131no—
243C4⋊C4—1131no—
244C4⋊C4—1131no—
245C4⋊C4—2261no—
246C4⋊C4—2261no—
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⋊C4—2261no—
256C4⋊C4C22×D11311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—1131no—
259C22⋊C4—1131no—
260C22⋊C4—2261no—
261C22⋊C4—2261no—
262C42—1131no—
263C42—1131no—
264C42—2261no—
265C42—2261no—
266C42—2261no—
267C42—2261no—
268C42—2261no—
269C42—2261no—
270C42—2261no—
271C23D4×D11311yescharacteristic
272Q8—24no—
273Q8—21no—
274Q8—21no—
275Q8—21no—
276Q8—21no—
277Q8—2261no—
278Q8—2261no—
279Q8#1426864612yes—
280Q8#1426864612yes—
281C2×C4—24no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—1131no—
289C2×C4—1131no—
290C2×C4—1131no—
291C2×C4—1131no—
292C2×C4—2261no—
293C2×C4—2261no—
294C2×C4—2261no—
295C2×C4—2261no—
296C2×C4D4×D11311yescharacteristic
297C2×C4C23×D11311yescharacteristic
298C8—21no—
299C8—21no—
300C8—2261no—
301C8—2261no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22C2×D4×D11311yescharacteristic
306C4—22no—
307C4—22no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—4521no—
312C4—4521no—
313C4—4521no—
314C4—4521no—
315C4—2261no—
316C4—2261no—
317C4—2261no—
318C4—2261no—
319C4C2×#1426864611yescharacteristic
320C4C2×#1426864611yescharacteristic
321C2—41no—
322C2#2029910411yescharacteristic
323C2#2029941111yescharacteristic
324C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#451×C113C2
socleC22×C113C22×D4
prime radicalC23×C113C2×D4
hypercenter#451D113
hypocenterC113#3127
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
5. #20298907C2semidirect
6. #20298903C2semidirect
7. #20298806C2semidirect
8. #20298806C2semidirect
10. #20298705C2semidirect
11. #20298702C2semidirect
12. Q16×Dic113C2semidirect
13. #20298690C2semidirect
163. C113#3127semidirect

Maximal subgroups

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

subgroupindex
#202992082
#202990762
#202989402
#202989362
#202989072
#202989032
#202988062
#202987542
#202987052
#202987022
Q16×Dic1132
#202986902
#202986562
#451×C1132
#3127113