Finite Group Databasebeta

← #28349149

Subgroups — #28349149

Order 13696.

336 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293354C211yesmaximal, characteristic, complemented
2#20293349C211yesmaximal, characteristic
3#20292984C211yesmaximal, characteristic
4#20292983C211yesmaximal, characteristic
5#20292976C211yesmaximal, characteristic, complemented
6#20292937C211yesmaximal, characteristic, complemented
7#20292906C211yesmaximal, characteristic
8#20292852C211yesmaximal, characteristic
9#20292850C211yesmaximal, characteristic
10#20292836C211yesmaximal, characteristic, complemented
11#20292751C211yesmaximal, characteristic, complemented
12#20292721C211yesmaximal, characteristic, complemented
13C4×#13133808C211yesmaximal, characteristic, complemented
14#20292714C211yesmaximal, characteristic
15#479×C107C211yesmaximal, characteristic, complemented
16C2×Dic428C2211yescharacteristic
17C2×#13133808C2211yescharacteristic
18C2×#13133807C2211yescharacteristic
19#16812108—21no—
20#16812108C2211yescharacteristic
21#16812107C2211yescharacteristic
22#16812104—21no—
23#16812103—21no—
24#16812100C2211yescharacteristic
25#16812099—21no—
26#16812099—21no—
27#16812098C2211yescharacteristic
28#16812097C2211yescharacteristic
29#16812087—21no—
30C4×Dic214C2211yescharacteristic
31C4×Dic214C2211yescharacteristic
32#16812074—21no—
33#16812074C2211yescharacteristic
34#16812074C2211yescharacteristic
35#16812074C2211yescharacteristic
36#16812071C2211yescharacteristic
37#16812066—21no—
38#16812042C2211yescharacteristic
39Dic107⋊C8C2211yescharacteristic
40Dic107⋊C8C2211yescharacteristic
41#16812034C2211yescharacteristic
42#16812033C2211yescharacteristic
43#16812032C2211yescharacteristic
44#16812032C2211yescharacteristic
45#16812032C2211yescharacteristic
46#16812031C2211yescharacteristic
47#16812029C2211yescharacteristic
48#16812029C2211yescharacteristic
49C4×C107⋊C8C2211yescharacteristic
50C8×Dic107C2211yescharacteristic
51C8×Dic107C2211yescharacteristic
52#125×C107C2211yescharacteristic
53C4×Q8×C107C2211yescharacteristic
54#107×C107C2211yescharacteristic
55#106×C107C2211yescharacteristic
56C4⋊C8×C107C2211yescharacteristic
57#103×C107C2211yescharacteristic
58#103×C107C2211yescharacteristic
59C2×Dic214—21no—
60C2×Dic214D411yescharacteristic
61C2×Dic214C2311yescharacteristic
62C2×Dic214C2311yescharacteristic
63C2×D428C2311yescharacteristic
64C2×C4×D107—21no—
65Dic428—22no—
66#13133808—22no—
67#13133807—22no—
68C2×C107⋊C8C2311yescharacteristic
69C2×C107⋊C8C2311yescharacteristic
70C4⋊Dic107—21no—
71C4⋊Dic107D411yescharacteristic
72C4⋊Dic107C2311yescharacteristic
73Dic107⋊C4—21no—
74Dic107⋊C4—21no—
75Dic107⋊C4—21no—
76Dic107⋊C4—21no—
77Dic107⋊C4—21no—
78Dic107⋊C4—21no—
79Dic107⋊C4—21no—
80Dic107⋊C4—21no—
81Dic107⋊C4D411yescharacteristic
82Dic107⋊C4D411yescharacteristic
83(C2×D107)⋊C4—21no—
84(C2×D107)⋊C4—21no—
85(C2×D107)⋊C4—21no—
86(C2×D107)⋊C4—21no—
87(C2×D107)⋊C4—21no—
88C4×Dic107—21no—
89C4×Dic107—21no—
90C4×Dic107—21no—
91C4×Dic107—21no—
92C4×Dic107C2311yescharacteristic
93C4×Dic107C2311yescharacteristic
94C2×Q8×C107C2311yescharacteristic
95C2×C8×C107C2311yescharacteristic
96C2×C8×C107C2311yescharacteristic
97C4⋊C4×C107—21no—
98C4⋊C4×C107—21no—
99C4⋊C4×C107—21no—
100C4⋊C4×C107C2311yescharacteristic
101C4⋊C4×C107C2311yescharacteristic
102C4⋊C4×C107C2311yescharacteristic
103C42×C107—21no—
104C42×C107C2311yescharacteristic
105C22×D107—21no—
106Q8×C107—21no—
107Q8×C107—21no—
108C2×C4×C107—21no—
109C2×C4×C107—21no—
110C2×C4×C107—21no—
111C2×C4×C107—21no—
112C2×C4×C107C2×D411yescharacteristic
113C2×C4×C107C2×D411yescharacteristic
114C2×C4×C107C2411yescharacteristic
115C2×Dic107—21no—
116C2×Dic107—21no—
117C2×Dic107—21no—
118C2×Dic107C2×D411yescharacteristic
119C2×Dic107C2×D411yescharacteristic
120C2×Dic107C2×D411yescharacteristic
121C2×Dic107C2×D411yescharacteristic
122D428—21no—
123D428—21no—
124C4×D107—42no—
125Dic214—21no—
126Dic214—22no—
127Dic214—21no—
128Dic214—21no—
129Dic214—42no—
130Dic214#4112yes—
131C8×C107—21no—
132C8×C107—21no—
133C107⋊C8—21no—
134C107⋊C8—21no—
135C22×C107C22×D411yescharacteristic
136C2×D107—41no—
137C2×D107—41no—
138C2×D107—41no—
139C4×C107—21no—
140C4×C107—21no—
141C4×C107—41no—
142C4×C107—41no—
143C4×C107—41no—
144C4×C107—41no—
145C4×C107C2×#4111yescharacteristic
146C4×C1072−1+411yescharacteristic
147Dic107—22no—
148Dic107—21no—
149Dic107—21no—
150Dic107—21no—
151Dic107—41no—
152Dic107—41no—
153Dic107#13512yes—
154C2×C107#54811yescharacteristic
155C2×C107C2×#13511yescharacteristic
156C2×C107#57811yescharacteristic
157D107—81no—
158#3364—1071nomaximal, Sylow
159C107#336411yescharacteristic, complemented, Sylow
160#557—1071no—
161#556—1071no—
162#488—1071no—
163#488—1071no—
164#487—1071no—
165#479—1071no—
166#479D10711yescharacteristic, complemented
167#474—1071no—
168#464—1071no—
169#464—1071no—
170#462—1071no—
171C8×Q8—1071no—
172C4×Q16—1071no—
173C4×Q16—1071no—
174C4×SD16—1071no—
175C2×Q16—1071no—
176C2×Q16—1071no—
177C2×SD16—1071no—
178C4⋊Q8—1071no—
179C4⋊Q8—1071no—
180C4⋊Q8—2141no—
181#126—2141no—
182#126—2141no—
183#125—1071no—
184#125—2141no—
185#125—2141no—
186#125C2×D10711yescharacteristic
187#124—1071no—
188#124—1071no—
189C22⋊Q8—2141no—
190C4×Q8—1071no—
191C4×Q8—1071no—
192C4×Q8—1071no—
193C4×Q8—1071no—
194C4×Q8—1071no—
195C4×Q8—2141no—
196C4×Q8C2×D10711yescharacteristic
197C4×D4—1071no—
198#117—2141no—
199#107—1071no—
200#107C2×D10711yescharacteristic
201#106C2×D10711yescharacteristic
202C4⋊C8—1071no—
203C4⋊C8—1071no—
204C4⋊C8C2×D10711yescharacteristic
205#103—1071no—
206#103—1071no—
207#103—1071no—
208#103—1071no—
209#103—1071no—
210#103C2×D10711yescharacteristic
211#103C2×D10711yescharacteristic
212#102—1071no—
213#102—1071no—
214#102—1071no—
215C4×C8—1071no—
216C4×C8—1071no—
217C4×C8—1071no—
218C2×Q8—1071no—
219C2×Q8—1071no—
220C2×Q8—1071no—
221C2×Q8—2141no—
222C2×Q8C22×D10711yescharacteristic
223C2×D4—1071no—
224C22×C4—2141no—
225Q16—2142no—
226Q16—2142no—
227SD16—2142no—
228C2×C8—1071no—
229C2×C8—1071no—
230C2×C8C22×D10711yescharacteristic
231C2×C8C22×D10711yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—1071no—
236C4⋊C4—1071no—
237C4⋊C4—1071no—
238C4⋊C4—1071no—
239C4⋊C4—2141no—
240C4⋊C4—2141no—
241C4⋊C4—2141no—
242C4⋊C4—2141no—
243C4⋊C4—2141no—
244C4⋊C4—2141no—
245C4⋊C4—2141no—
246C4⋊C4—2141no—
247C4⋊C4—2141no—
248C4⋊C4C22×D10711yescharacteristic
249C4⋊C4C22×D10711yescharacteristic
250C4⋊C4C22×D10711yescharacteristic
251C22⋊C4—2141no—
252C22⋊C4—2141no—
253C22⋊C4—2141no—
254C22⋊C4—2141no—
255C22⋊C4—2141no—
256C42—21no—
257C42—1071no—
258C42—1071no—
259C42—2141no—
260C42—2141no—
261C42—2141no—
262C42—2141no—
263C42C22×D10711yescharacteristic
264C23—2141no—
265Q8—21no—
266Q8—21no—
267Q8—1072no—
268Q8—4282no—
269Q8—2142no—
270Q8—2141no—
271Q8—2141no—
272Q8—2141no—
273D4—2141no—
274D4—2141no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—1071no—
280C2×C4—1071no—
281C2×C4—1071no—
282C2×C4—1071no—
283C2×C4—4282no—
284C2×C4—2141no—
285C2×C4—2141no—
286C2×C4—2141no—
287C2×C4D4×D10711yescharacteristic
288C2×C4D4×D10711yescharacteristic
289C2×C4C23×D10711yescharacteristic
290C8—21no—
291C8—21no—
292C8—2141no—
293C8—2141no—
294C22—4281no—
295C22—4281no—
296C22—4281no—
297C22C2×D4×D10711yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—1072no—
305C4—4281no—
306C4—4281no—
307C4—2141no—
308C4—2141no—
309C4—2141no—
310C4—2142no—
311C4#41×D10711yescharacteristic
312C4#1681215711yescharacteristic
313C2—8561no—
314C2#2029328711yescharacteristic
315C2#135×D10711yescharacteristic
316C2#2029344311yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#479×C107C2
socleC22×C107C22×D4
prime radicalC2×D428C23
hypercenter#479D107
hypocenterC107#3364
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #20293354C2semidirect
5. #20292976C2semidirect
6. #20292937C2semidirect
10. #20292836C2semidirect
11. #20292751C2semidirect
12. #20292721C2semidirect
13. C4×#13133808C2semidirect
15. #479×C107C2semidirect
159. C107#3364semidirect
166. #479D107semidirect

Maximal subgroups

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

subgroupindex
#202933542
#202933492
#202929842
#202929832
#202929762
#202929372
#202929062
#202928522
#202928502
#202928362
#202927512
#202927212
C4×#131338082
#202927142
#479×C1072
#3364107