Finite Group Databasebeta

← #28349214

Subgroups — #28349214

Order 13696.

358 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293362C211yesmaximal, characteristic, complemented
2#20292993C211yesmaximal, characteristic, complemented
3#20292989C211yesmaximal, characteristic, complemented
4#20292984C211yesmaximal, characteristic, complemented
5#20292931C211yesmaximal, characteristic, complemented
6#20292924C211yesmaximal, characteristic, complemented
7#20292904C211yesmaximal, characteristic, complemented
8#20292842C211yesmaximal, characteristic, complemented
9#20292842C211yesmaximal, characteristic, complemented
10#20292822C211yesmaximal, characteristic
11#20292758C211yesmaximal, characteristic, complemented
12#20292737C211yesmaximal, characteristic, complemented
13#20292727C211yesmaximal, characteristic, complemented
14C4×#13133803C211yesmaximal, characteristic, complemented
15#554×C107C211yesmaximal, characteristic, complemented
16C2×#13133806C2211yescharacteristic
17C2×#13133803C2211yescharacteristic
18C2×#13133803C2211yescharacteristic
19#16812106C2211yescharacteristic
20#16812098—21no—
21#16812097C2211yescharacteristic
22#16812097C2211yescharacteristic
23#16812094—21no—
24#16812094—21no—
25C4×Dic214C2211yescharacteristic
26C4×D428C2211yescharacteristic
27C4×D428C2211yescharacteristic
28#16812071—21no—
29#16812042C2211yescharacteristic
30#16812042C2211yescharacteristic
31#16812040C2211yescharacteristic
32C4⋊(C107⋊C8)C2211yescharacteristic
33C4⋊(C107⋊C8)C2211yescharacteristic
34C4⋊(C107⋊C8)C2211yescharacteristic
35#16812032C2211yescharacteristic
36#16812032C2211yescharacteristic
37#16812032C2211yescharacteristic
38#16812030C2211yescharacteristic
39#16812029C2211yescharacteristic
40#16812029C2211yescharacteristic
41#16812029C2211yescharacteristic
42#16812029C2211yescharacteristic
43#16812029C2211yescharacteristic
44#16812029C2211yescharacteristic
45#16812020C2211yescharacteristic
46#16812020C2211yescharacteristic
47C4×C107⋊C8C2211yescharacteristic
48C4⋊Q8×C107C2211yescharacteristic
49#125×C107C2211yescharacteristic
50#125×C107C2211yescharacteristic
51C22⋊Q8×C107—21no—
52C22⋊Q8×C107—21no—
53C22⋊Q8×C107—21no—
54C4×Q8×C107C2211yescharacteristic
55C4×D4×C107C2211yescharacteristic
56C4×D4×C107C2211yescharacteristic
57C4×D4×C107C2211yescharacteristic
58C2×C4⋊C4×C107—21no—
59C2×Dic214C2311yescharacteristic
60C2×D428—21no—
61C2×D428—21no—
62C2×D428C2311yescharacteristic
63C2×D428C2311yescharacteristic
64C2×C4×D107—21no—
65C2×C4×D107—21no—
66#13133806—22no—
67#13133803—22no—
68#13133803—22no—
69C2×C107⋊C8C2311yescharacteristic
70C2×C107⋊C8C2311yescharacteristic
71C2×C107⋊C8C2311yescharacteristic
72C2×C107⋊C8C2311yescharacteristic
73C4⋊Dic107C2311yescharacteristic
74Dic107⋊C4—21no—
75(C2×D107)⋊C4—21no—
76(C2×D107)⋊C4—21no—
77(C2×D107)⋊C4—21no—
78(C2×D107)⋊C4—21no—
79(C2×D107)⋊C4—21no—
80(C2×D107)⋊C4—21no—
81C4×Dic107—21no—
82C2×Q8×C107—21no—
83C2×Q8×C107D411yescharacteristic
84C2×D4×C107C2311yescharacteristic
85C22×C4×C107—21no—
86C22×C4×C107—21no—
87C22×C4×C107—21no—
88C4⋊C4×C107—21no—
89C4⋊C4×C107—21no—
90C4⋊C4×C107—21no—
91C4⋊C4×C107—21no—
92C4⋊C4×C107—21no—
93C4⋊C4×C107D411yescharacteristic
94C4⋊C4×C107D411yescharacteristic
95C4⋊C4×C107D411yescharacteristic
96C4⋊C4×C107C2311yescharacteristic
97C4⋊C4×C107C2311yescharacteristic
98C4⋊C4×C107C2311yescharacteristic
99C22⋊C4×C107—21no—
100C22⋊C4×C107—21no—
101C22⋊C4×C107—21no—
102C42×C107C2311yescharacteristic
103C42×C107C2311yescharacteristic
104C42×C107C2311yescharacteristic
105C23×C107—21no—
106C22×D107—21no—
107C22×D107—21no—
108Q8×C107—41no—
109Q8×C107—81no—
110D4×C107—21no—
111D4×C107#4112yes—
112C2×C4×C107—21no—
113C2×C4×C107—21no—
114C2×C4×C107—21no—
115C2×C4×C107—42no—
116C2×C4×C107—81no—
117C2×C4×C107—81no—
118C2×C4×C107C2×D411yescharacteristic
119C2×C4×C107C2×D411yescharacteristic
120C2×C4×C107C2×D411yescharacteristic
121C2×C4×C107C2×D411yescharacteristic
122C2×C4×C107C2×D411yescharacteristic
123C2×C4×C107C2×D411yescharacteristic
124C2×C4×C107C2411yescharacteristic
125C2×Dic107—21no—
126C2×Dic107—21no—
127D428—21no—
128D428—21no—
129D428—21no—
130D428—21no—
131D428—42no—
132D428—81no—
133C4×D107—81no—
134C4×D107—81no—
135Dic214—21no—
136Dic214—21no—
137C107⋊C8—21no—
138C107⋊C8—21no—
139C107⋊C8—21no—
140C107⋊C8—21no—
141C22×C107—22no—
142C22×C107—41no—
143C22×C107—41no—
144C22×C107C22×D411yescharacteristic
145C2×D107—41no—
146C2×D107—41no—
147C2×D107—41no—
148C2×D107—41no—
149C2×D107—41no—
150C2×D107—41no—
151C4×C107—21no—
152C4×C107—21no—
153C4×C107—21no—
154C4×C107—21no—
155C4×C107—21no—
156C4×C107—21no—
157C4×C107—41no—
158C4×C107—41no—
159C4×C107—41no—
160C4×C107C2×#4111yescharacteristic
161C4×C1072−1+411yescharacteristic
162Dic107—41no—
163Dic107—41no—
164C2×C107—42no—
165C2×C107#54811yescharacteristic
166C2×C107#57511yescharacteristic
167C2×C107#57611yescharacteristic
168D107—81no—
169D107—81no—
170#3370—1071nomaximal, Sylow
171C107#337011yescharacteristic, complemented, Sylow
172#559—1071no—
173#554D10711yescharacteristic, complemented
174#490—1071no—
175#489—1071no—
176#488—1071no—
177#479—1071no—
178#478—1071no—
179#474—1071no—
180#463—1071no—
181#463—1071no—
182#459—1071no—
183#446—1071no—
184#442—1071no—
185#440—1071no—
186C4×D8—1071no—
187C2×SD16—1071no—
188C2×D8—1071no—
189C2×D8—1071no—
190C4⋊Q8C2×D10711yescharacteristic
191#127—1071no—
192#125C2×D10711yescharacteristic
193#125C2×D10711yescharacteristic
194#124—1071no—
195#124—1071no—
196#124—2141no—
197#123—2141no—
198#123—2141no—
199C22⋊Q8—21no—
200C22⋊Q8—21no—
201C22⋊Q8—21no—
202C4×Q8—1071no—
203C4×Q8C2×D10711yescharacteristic
204C4×D4—1071no—
205C4×D4—1071no—
206C4×D4—2141no—
207C4×D4C2×D10711yescharacteristic
208C4×D4C2×D10711yescharacteristic
209C4×D4C2×D10711yescharacteristic
210C2×C4⋊C4—21no—
211#107—1071no—
212#107—1071no—
213#106—1071no—
214C4⋊C8—1071no—
215C4⋊C8—1071no—
216C4⋊C8—1071no—
217#103—1071no—
218#103—1071no—
219#103—1071no—
220#102—1071no—
221#102—1071no—
222#102—1071no—
223#102—1071no—
224#102—1071no—
225#102—1071no—
226#102—1071no—
227#97—1071no—
228#97—1071no—
229C4×C8—1071no—
230C2×Q8—21no—
231C2×Q8—1071no—
232C2×Q8C22⋊D10711yescharacteristic
233C2×D4—1071no—
234C2×D4—1071no—
235C2×D4—2141no—
236C2×D4—2141no—
237C2×D4C22×D10711yescharacteristic
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—2141no—
242C22×C4—2141no—
243SD16—2142no—
244D8—2142no—
245D8—2142no—
246C2×C8—1071no—
247C2×C8—1071no—
248C2×C8—1071no—
249C2×C8—1071no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—1071no—
256C4⋊C4—2141no—
257C4⋊C4C22⋊D10711yescharacteristic
258C4⋊C4C22⋊D10711yescharacteristic
259C4⋊C4C22⋊D10711yescharacteristic
260C4⋊C4C22×D10711yescharacteristic
261C4⋊C4C22×D10711yescharacteristic
262C4⋊C4C22×D10711yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—2141no—
267C22⋊C4—2141no—
268C22⋊C4—2141no—
269C22⋊C4—2141no—
270C22⋊C4—2141no—
271C22⋊C4—2141no—
272C42—2141no—
273C42C22×D10711yescharacteristic
274C42C22×D10711yescharacteristic
275C42C22×D10711yescharacteristic
276C23—21no—
277C23—2141no—
278C23—2141no—
279Q8—41no—
280Q8—81no—
281Q8—2141no—
282Q8—2141no—
283D4—21no—
284D4—8561no—
285D4—4282no—
286D4—2141no—
287D4—2141no—
288D4—2141no—
289D4—2141no—
290D4#1313381912yes—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—8561no—
298C2×C4—8561no—
299C2×C4—2141no—
300C2×C4—2141no—
301C2×C4C2×C22⋊D10711yescharacteristic
302C2×C4C2×C22⋊D10711yescharacteristic
303C2×C4C2×C22⋊D10711yescharacteristic
304C2×C4C2×C22⋊D10711yescharacteristic
305C2×C4C2×C22⋊D10711yescharacteristic
306C2×C4C2×C22⋊D10711yescharacteristic
307C2×C4C23×D10711yescharacteristic
308C8—2141no—
309C8—2141no—
310C8—2141no—
311C8—2141no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—4281no—
316C22—4281no—
317C22—4281no—
318C22—4281no—
319C22—4281no—
320C22—4281no—
321C22C22×C22⋊D10711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—4281no—
332C4—4281no—
333C4C2×#1313381911yescharacteristic
334C4#1681215711yescharacteristic
335C2—42no—
336C2—8561no—
337C2—8561no—
338C2#2029328811yescharacteristic
339C2#2029342511yescharacteristic
340C2#2029343011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#554×C107C2
socleC22×C107C22×D4
prime radical#20292822C2
hypercenter#554D107
hypocenterC107#3370
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #20293362C2semidirect
2. #20292993C2semidirect
3. #20292989C2semidirect
4. #20292984C2semidirect
5. #20292931C2semidirect
6. #20292924C2semidirect
7. #20292904C2semidirect
8. #20292842C2semidirect
9. #20292842C2semidirect
11. #20292758C2semidirect
12. #20292737C2semidirect
13. #20292727C2semidirect
14. C4×#13133803C2semidirect
15. #554×C107C2semidirect
171. C107#3370semidirect
173. #554D107semidirect

Maximal subgroups

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

subgroupindex
#202933622
#202929932
#202929892
#202929842
#202929312
#202929242
#202929042
#202928422
#202928222
#202927582
#202927372
#202927272
C4×#131338032
#554×C1072
#3370107