Finite Group Databasebeta

← #28349069

Subgroups — #28349069

Order 13696.

342 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#20293348C211yesmaximal, characteristic
2#20293332C211yesmaximal, characteristic
3#20293024C211yesmaximal, characteristic, complemented
4#20292971C211yesmaximal, characteristic, complemented
5#20292969C211yesmaximal, characteristic, complemented
6#20292956C211yesmaximal, characteristic, complemented
7#20292920C211yesmaximal, characteristic, complemented
8#20292911C211yesmaximal, characteristic, complemented
9#20292884C211yesmaximal, characteristic, complemented
10#20292883C211yesmaximal, characteristic, complemented
11#20292719C211yesmaximal, characteristic, complemented
12#20292702C211yesmaximal, characteristic
13#20292667C211yesmaximal, characteristic, complemented
14#20292666C211yesmaximal, characteristic, complemented
15#483×C107C211yesmaximal, characteristic, complemented
16C2×#13133808C2211yescharacteristic
17C2×#13133802C2211yescharacteristic
18C2×#13133801C2211yescharacteristic
19#16812108C2211yescharacteristic
20#16812108C2211yescharacteristic
21#16812104—21no—
22#16812102—21no—
23#16812099—21no—
24#16812095—21no—
25#16812089C2211yescharacteristic
26#16812088—21no—
27#16812088C2211yescharacteristic
28#16812087—21no—
29#16812085C2211yescharacteristic
30Q8×Dic107C2211yescharacteristic
31#16812074—21no—
32#16812074C2211yescharacteristic
33C4×C22⋊D107—21no—
34C4×C22⋊D107C2211yescharacteristic
35#16812068C2211yescharacteristic
36#16812067C2211yescharacteristic
37C4⋊C4×D107C2211yescharacteristic
38#16812043C2211yescharacteristic
39#16812042C2211yescharacteristic
40#16812042C2211yescharacteristic
41#16812041C2211yescharacteristic
42#16812040C2211yescharacteristic
43#16812040C2211yescharacteristic
44#16812040C2211yescharacteristic
45Dic107⋊C8C2211yescharacteristic
46#16812034C2211yescharacteristic
47#16812034C2211yescharacteristic
48#16812033C2211yescharacteristic
49#16812032C2211yescharacteristic
50(C2×D107)⋊C8C2211yescharacteristic
51C8×Dic107C2211yescharacteristic
52C22⋊Q8×C107C2211yescharacteristic
53C2×C4⋊C4×C107C2211yescharacteristic
54#106×C107C2211yescharacteristic
55#106×C107C2211yescharacteristic
56#103×C107C2211yescharacteristic
57#103×C107C2211yescharacteristic
58C22⋊C8×C107C2211yescharacteristic
59C2×Dic214—21no—
60C2×Dic214—21no—
61C2×Dic214C2311yescharacteristic
62C2×C22⋊D107D411yescharacteristic
63C2×C4×D107—21no—
64C2×C4×D107C2311yescharacteristic
65#13133808—22no—
66#13133802—22no—
67#13133801—22no—
68C2×C107⋊C8C2311yescharacteristic
69C2×C107⋊C8C2311yescharacteristic
70C4⋊Dic107—21no—
71C4⋊Dic107—21no—
72C4⋊Dic107C2311yescharacteristic
73C4⋊Dic107C2311yescharacteristic
74C4⋊Dic107C2311yescharacteristic
75Dic107⋊C4—21no—
76Dic107⋊C4—21no—
77Dic107⋊C4—21no—
78Dic107⋊C4—21no—
79Dic107⋊C4—21no—
80Dic107⋊C4—21no—
81Dic107⋊C4D411yescharacteristic
82C22⋊Dic107—21no—
83C22⋊Dic107—21no—
84C22⋊Dic107D411yescharacteristic
85(C2×D107)⋊C4—21no—
86(C2×D107)⋊C4—21no—
87(C2×D107)⋊C4—21no—
88(C2×D107)⋊C4D411yescharacteristic
89C4×Dic107—21no—
90C4×Dic107—21no—
91C4×Dic107—21no—
92C4×Dic107—21no—
93C4×Dic107C2311yescharacteristic
94C2×Q8×C107C2311yescharacteristic
95C22×C4×C107—21no—
96C22×C4×C107C2311yescharacteristic
97C2×C8×C107C2311yescharacteristic
98C2×C8×C107C2311yescharacteristic
99C4⋊C4×C107—21no—
100C4⋊C4×C107—21no—
101C4⋊C4×C107C2311yescharacteristic
102C4⋊C4×C107C2311yescharacteristic
103C4⋊C4×C107C2311yescharacteristic
104C22⋊C4×C107—21no—
105C23×C107C2×D411yescharacteristic
106C22×D107C2×D411yescharacteristic
107Q8×C107—21no—
108Q8×C107—21no—
109C2×C4×C107—21no—
110C2×C4×C107—21no—
111C2×C4×C107—21no—
112C2×C4×C107—21no—
113C2×C4×C107—21no—
114C2×C4×C107—21no—
115C2×C4×C107—81no—
116C2×C4×C107C2×D411yescharacteristic
117C2×C4×C107C2411yescharacteristic
118C22⋊D107—22no—
119C2×Dic107—21no—
120C2×Dic107—21no—
121C2×Dic107—21no—
122C2×Dic107—21no—
123C2×Dic107C2×D411yescharacteristic
124C2×Dic107C2×D411yescharacteristic
125C2×Dic107C2×D411yescharacteristic
126C4×D107—21no—
127C4×D107—21no—
128C4×D107—81no—
129Dic214—21no—
130Dic214—21no—
131Dic214—42no—
132Dic214—81no—
133C8×C107—21no—
134C8×C107—21no—
135C107⋊C8—21no—
136C107⋊C8#4112yes—
137C22×C107—21no—
138C22×C107—21no—
139C22×C107—21no—
140C22×C107C22×D411yescharacteristic
141C2×D107—21no—
142C2×D107—21no—
143C2×D107—21no—
144C4×C107—21no—
145C4×C107—41no—
146C4×C107—41no—
147C4×C107—41no—
148C4×C107—41no—
149C4×C107C2×#4111yescharacteristic
150C4×C1072−1+411yescharacteristic
151Dic107—21no—
152Dic107—21no—
153Dic107—41no—
154Dic107—41no—
155Dic107—41no—
156Dic107—41no—
157Dic107#13712yes—
158C2×C107—41no—
159C2×C107#54711yescharacteristic
160C2×C107C2×#13711yescharacteristic
161C2×C107#57711yescharacteristic
162D107—41no—
163#3356—1071nomaximal, Sylow
164C107#335611yescharacteristic, complemented, Sylow
165#556—1071no—
166#554—1071no—
167#498—1071no—
168#485—1071no—
169#485—1071no—
170#483—1071no—
171#483D10711yescharacteristic, complemented
172#477—1071no—
173#475—1071no—
174#470—1071no—
175#470—1071no—
176C4×Q16—1071no—
177#436—1071no—
178#428—1071no—
179#428—1071no—
180C2×Q16—1071no—
181C2×M16—1071no—
182C2×M16—1071no—
183C4⋊Q8—1071no—
184C4⋊Q8—1071no—
185#126—2141no—
186#126—2141no—
187#125—2141no—
188#124—2141no—
189C22⋊Q8—1071no—
190C22⋊Q8—1071no—
191C22⋊Q8—1071no—
192C22⋊Q8—2141no—
193C22⋊Q8—2141no—
194C22⋊Q8C2×D10711yescharacteristic
195C4×Q8—1071no—
196C4×Q8—1071no—
197C4×Q8—2141no—
198C4×D4—1071no—
199C4×D4—2141no—
200#117—1071no—
201#117—1071no—
202C2×C4⋊C4—1071no—
203C2×C4⋊C4C2×D10711yescharacteristic
204#107—1071no—
205#107—1071no—
206#107—1071no—
207#106—1071no—
208#106—1071no—
209#106—1071no—
210#106—1071no—
211#106C2×D10711yescharacteristic
212#106C2×D10711yescharacteristic
213C4⋊C8—1071no—
214#103—1071no—
215#103—1071no—
216#103—1071no—
217#103—1071no—
218#103C2×D10711yescharacteristic
219#103C2×D10711yescharacteristic
220C22⋊C8—1071no—
221C22⋊C8C2×D10711yescharacteristic
222C4×C8—1071no—
223C2×Q8—1071no—
224C2×Q8—2141no—
225C2×Q8—2141no—
226C2×Q8C22×D10711yescharacteristic
227C2×D4—1071no—
228C22×C4—21no—
229C22×C4—1071no—
230C22×C4—2141no—
231C22×C4C22×D10711yescharacteristic
232Q16—2142no—
233M16—2142no—
234M16—2142no—
235C2×C8—1071no—
236C2×C8—1071no—
237C2×C8C22×D10711yescharacteristic
238C2×C8C22×D10711yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—1071no—
242C4⋊C4—1071no—
243C4⋊C4—1071no—
244C4⋊C4—1071no—
245C4⋊C4—2141no—
246C4⋊C4—2141no—
247C4⋊C4—2141no—
248C4⋊C4—2141no—
249C4⋊C4—2141no—
250C4⋊C4—2141no—
251C4⋊C4—2141no—
252C4⋊C4—2141no—
253C4⋊C4C22×D10711yescharacteristic
254C4⋊C4C22×D10711yescharacteristic
255C4⋊C4C22×D10711yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—1071no—
258C22⋊C4—1071no—
259C22⋊C4—2141no—
260C22⋊C4—2141no—
261C22⋊C4—2141no—
262C22⋊C4—2141no—
263C22⋊C4—2141no—
264C42—1071no—
265C42—2141no—
266C42—2141no—
267C42—2141no—
268C42—2141no—
269C23—1071no—
270C23D4×D10711yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—8561no—
274Q8—4282no—
275Q8—2141no—
276Q8—2141no—
277D4—2142no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—81no—
285C2×C4—8561no—
286C2×C4—1071no—
287C2×C4—1071no—
288C2×C4—1071no—
289C2×C4—2141no—
290C2×C4—2141no—
291C2×C4—2141no—
292C2×C4—2141no—
293C2×C4—2141no—
294C2×C4—2141no—
295C2×C4D4×D10711yescharacteristic
296C2×C4C23×D10711yescharacteristic
297C8—21no—
298C8—21no—
299C8—1072no—
300C8—2141no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—2141no—
305C22—2141no—
306C22—2141no—
307C22C2×D4×D10711yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—1072no—
314C4—4281no—
315C4—4281no—
316C4—4281no—
317C4—4281no—
318C4—2141no—
319C4—2141no—
320C4#41×D10711yescharacteristic
321C4#1681215611yescharacteristic
322C2—41no—
323C2—4281no—
324C2#2029327511yescharacteristic
325C2#137×D10711yescharacteristic
326C2#2029343311yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#483×C107C2
socleC22×C107C22×D4
prime radicalC2×C22⋊D107D4
hypercenter#483D107
hypocenterC107#3356
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #20293024C2semidirect
4. #20292971C2semidirect
5. #20292969C2semidirect
6. #20292956C2semidirect
7. #20292920C2semidirect
8. #20292911C2semidirect
9. #20292884C2semidirect
10. #20292883C2semidirect
11. #20292719C2semidirect
13. #20292667C2semidirect
14. #20292666C2semidirect
15. #483×C107C2semidirect
164. C107#3356semidirect
171. #483D107semidirect

Maximal subgroups

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

subgroupindex
#202933482
#202933322
#202930242
#202929712
#202929692
#202929562
#202929202
#202929112
#202928842
#202928832
#202927192
#202927022
#202926672
#202926662
#483×C1072
#3356107