Finite Group Databasebeta

← #28403030

Subgroups — #28403030

Order 14464.

344 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299303C211yesmaximal, characteristic
2#20299287C211yesmaximal, characteristic
3#20299006C211yesmaximal, characteristic, complemented
4#20298939C211yesmaximal, characteristic, complemented
5#20298935C211yesmaximal, characteristic, complemented
6#20298930C211yesmaximal, characteristic, complemented
7#20298928C211yesmaximal, characteristic, complemented
8#20298904C211yesmaximal, characteristic, complemented
9#20298882C211yesmaximal, characteristic, complemented
10#20298856C211yesmaximal, characteristic, complemented
11#20298840C211yesmaximal, characteristic, complemented
12#20298704C211yesmaximal, characteristic, complemented
13#20298667C211yesmaximal, characteristic
14#106×D113C211yesmaximal, characteristic, complemented
15#428×C113C211yesmaximal, characteristic, complemented
16C2×Dic452C2211yescharacteristic
17C2×C8×D113C2211yescharacteristic
18#16813621C2211yescharacteristic
19#16813615—21no—
20#16813614—21no—
21#16813613C2211yescharacteristic
22#16813612—21no—
23#16813604—21no—
24#16813602C2211yescharacteristic
25#16813602C2211yescharacteristic
26#16813601—21no—
27#16813601C2211yescharacteristic
28#16813601C2211yescharacteristic
29#16813600—21no—
30#16813587C2211yescharacteristic
31#16813587C2211yescharacteristic
32C4×C22⋊D113—21no—
33C4×C22⋊D113C2211yescharacteristic
34#16813579—21no—
35C4⋊C4×D113C2211yescharacteristic
36C4⋊C4×D113C2211yescharacteristic
37#16813555C2211yescharacteristic
38#16813554C2211yescharacteristic
39#16813553C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813545C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813532C2211yescharacteristic
52C2×M16×C113C2211yescharacteristic
53#117×C113C2211yescharacteristic
54C2×C4⋊C4×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56#107×C113C2211yescharacteristic
57#106×C113C2211yescharacteristic
58#106×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×Dic226C2311yescharacteristic
62C2×C22⋊D113D411yescharacteristic
63C2×C4×D113—21no—
64C2×C4×D113—21no—
65C2×C4×D113C2311yescharacteristic
66Dic452—22no—
67C2×#11744751C2311yescharacteristic
68C2×#11744751C2311yescharacteristic
69C8×D113—22no—
70C4⋊Dic113—21no—
71C4⋊Dic113—21no—
72C4⋊Dic113—21no—
73C4⋊Dic113C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75#14268626—21no—
76#14268626—21no—
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626D411yescharacteristic
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113D411yescharacteristic
87#14268624—21no—
88#14268624—21no—
89#14268624D411yescharacteristic
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113C2311yescharacteristic
93C22×C4×C113—21no—
94C22×C4×C113C2311yescharacteristic
95M16×C113—22no—
96C2×C8×C113C2311yescharacteristic
97C2×C8×C113C2311yescharacteristic
98C4⋊C4×C113—21no—
99C4⋊C4×C113C2311yescharacteristic
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C22⋊C4×C113—21no—
104C42×C113—21no—
105C23×C113C2×D411yescharacteristic
106C22×D113C2×D411yescharacteristic
107C2×C4×C113—21no—
108C2×C4×C113—21no—
109C2×C4×C113—21no—
110C2×C4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—81no—
114C2×C4×C113C2×D411yescharacteristic
115C2×C4×C113C2411yescharacteristic
116C22⋊D113—22no—
117C2×Dic113—21no—
118C2×Dic113—21no—
119C2×Dic113—21no—
120C2×Dic113—21no—
121C2×Dic113C2×D411yescharacteristic
122C2×Dic113C2×D411yescharacteristic
123C2×Dic113C2×D411yescharacteristic
124C4×D113—21no—
125C4×D113—21no—
126C4×D113—42no—
127C4×D113—81no—
128Dic226—21no—
129Dic226—21no—
130Dic226—21no—
131Dic226—21no—
132Dic226—81no—
133C8×C113—21no—
134C8×C113#4112yes—
135#11744751—21no—
136#11744751—21no—
137C22×C113—21no—
138C22×C113—21no—
139C22×C113—21no—
140C22×C113C22×D411yescharacteristic
141C2×D113—21no—
142C2×D113—21no—
143C2×D113#13712yes—
144C4×C113—21no—
145C4×C113—41no—
146C4×C113—41no—
147C4×C113—41no—
148C4×C113—41no—
149C4×C113C2×#4111yescharacteristic
150C4×C1132−1+411yescharacteristic
151Dic113—21no—
152Dic113—21no—
153Dic113—21no—
154Dic113—41no—
155Dic113—41no—
156Dic113—41no—
157Dic113—41no—
158C2×C113—41no—
159C2×C113#54711yescharacteristic
160C2×C113C2×#13711yescharacteristic
161C2×C113#57711yescharacteristic
162D113—22no—
163#3344—1131nomaximal, Sylow
164C113#334411yescharacteristic, complemented, Sylow
165#554—1131no—
166#552—1131no—
167#501—1131no—
168#485—1131no—
169#484—1131no—
170#483—1131no—
171#483—1131no—
172#479—1131no—
173#475—1131no—
174#470—1131no—
175#467—1131no—
176#441—1131no—
177#435—1131no—
178#428D11311yescharacteristic, complemented
179C2×#106—1131no—
180C2×Q16—1131no—
181C2×M16C2×D11311yescharacteristic
182C22×C8—1131no—
183C4⋊Q8—1131no—
184#126—2261no—
185#125—1131no—
186#125—2261no—
187#125—2261no—
188#123—2261no—
189C22⋊Q8—1131no—
190C22⋊Q8—1131no—
191C22⋊Q8—1131no—
192C22⋊Q8—1131no—
193C22⋊Q8—2261no—
194C22⋊Q8—2261no—
195C4×Q8—1131no—
196C4×Q8—1131no—
197C4×D4—1131no—
198C4×D4—2261no—
199#117—2261no—
200#117C2×D11311yescharacteristic
201C2×C4⋊C4—1131no—
202C2×C4⋊C4—1131no—
203C2×C4⋊C4C2×D11311yescharacteristic
204#107—1131no—
205#107C2×D11311yescharacteristic
206#107C2×D11311yescharacteristic
207#106—1131no—
208#106—1131no—
209#106—1131no—
210#106—1131no—
211#106C2×D11311yescharacteristic
212#106C2×D11311yescharacteristic
213C4⋊C8—1131no—
214#103—1131no—
215#103—1131no—
216#103—1131no—
217#103—1131no—
218#103—1131no—
219#103—1131no—
220C22⋊C8—1131no—
221C22⋊C8—1131no—
222#97—1131no—
223C2×Q8—1131no—
224C2×Q8—1131no—
225C2×Q8—2261no—
226C2×D4—1131no—
227C22×C4—21no—
228C22×C4—1131no—
229C22×C4—2261no—
230C22×C4—2261no—
231C22×C4C22×D11311yescharacteristic
232Q16—2262no—
233M16—22no—
234C2×C8—1131no—
235C2×C8—1131no—
236C2×C8—2262no—
237C2×C8C22×D11311yescharacteristic
238C2×C8C22×D11311yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—1131no—
241C4⋊C4—1131no—
242C4⋊C4—1131no—
243C4⋊C4—2261no—
244C4⋊C4—2261no—
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⋊C4C22×D11311yescharacteristic
255C4⋊C4C22×D11311yescharacteristic
256C4⋊C4C22×D11311yescharacteristic
257C4⋊C4C22×D11311yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—1131no—
260C22⋊C4—1131no—
261C22⋊C4—2261no—
262C22⋊C4—2261no—
263C22⋊C4—2261no—
264C22⋊C4—2261no—
265C42—21no—
266C42—1131no—
267C42—2261no—
268C42—2261no—
269C23—1131no—
270C23D4×D11311yescharacteristic
271Q8—9041no—
272Q8—2261no—
273Q8—2261no—
274Q8—2261no—
275Q8—2261no—
276D4—2262no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—81no—
284C2×C4—1131no—
285C2×C4—1131no—
286C2×C4—1131no—
287C2×C4—9041no—
288C2×C4—4522no—
289C2×C4—2261no—
290C2×C4—2261no—
291C2×C4—2261no—
292C2×C4—2261no—
293C2×C4—2261no—
294C2×C4—2261no—
295C2×C4D4×D11311yescharacteristic
296C2×C4C23×D11311yescharacteristic
297C8—21no—
298C8—2261no—
299C8—2261no—
300C8#1426864712yes—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—1132no—
305C22—2261no—
306C22—2261no—
307C22C2×D4×D11311yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—4521no—
314C4—4521no—
315C4—4521no—
316C4—4521no—
317C4—2261no—
318C4—2261no—
319C4—2261no—
320C4C2×#1426864711yescharacteristic
321C4#1681367011yescharacteristic
322C2—41no—
323C2—2262no—
324C2#2029924911yescharacteristic
325C2#137×D11311yescharacteristic
326C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#428×C113C2
socleC22×C113C22×D4
prime radicalC2×C22⋊D113D4
hypercenter#428D113
hypocenterC113#3344
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #20299006C2semidirect
4. #20298939C2semidirect
5. #20298935C2semidirect
6. #20298930C2semidirect
7. #20298928C2semidirect
8. #20298904C2semidirect
9. #20298882C2semidirect
10. #20298856C2semidirect
11. #20298840C2semidirect
12. #20298704C2semidirect
14. #106×D113C2semidirect
15. #428×C113C2semidirect
164. C113#3344semidirect
178. #428D113semidirect

Maximal subgroups

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

subgroupindex
#202993032
#202992872
#202990062
#202989392
#202989352
#202989302
#202989282
#202989042
#202988822
#202988562
#202988402
#202987042
#202986672
#106×D1132
#428×C1132
#3344113