Finite Group Databasebeta

← #28345445

Subgroups — #28345445

Order 13696.

362 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293164C211yesmaximal, characteristic
2#20292758C211yesmaximal, characteristic, complemented
3#20292706C211yesmaximal, characteristic, complemented
4#20292704C211yesmaximal, characteristic, complemented
5#20292700C211yesmaximal, characteristic, complemented
6#20292700C211yesmaximal, characteristic, complemented
7#20292697C211yesmaximal, characteristic, complemented
8#20292697C211yesmaximal, characteristic, complemented
9#20292687C211yesmaximal, characteristic, complemented
10#20292687C211yesmaximal, characteristic, complemented
11#20292683C211yesmaximal, characteristic, complemented
12#20292584C211yesmaximal, characteristic, complemented
13#20292581C211yesmaximal, characteristic, complemented
14#20292579C211yesmaximal, characteristic, complemented
15#446×C107C211yesmaximal, characteristic, complemented
16C2×#13133801C2211yescharacteristic
17C2×#13133801C2211yescharacteristic
18C2×#13133801C2211yescharacteristic
19C2×#13133801C2211yescharacteristic
20C2×C8×D107C2211yescharacteristic
21C2×C8×D107C2211yescharacteristic
22#16812104C411yescharacteristic
23#16812104C411yescharacteristic
24#16812100C411yescharacteristic
25#16812098C411yescharacteristic
26#16812094C411yescharacteristic
27#16812094C411yescharacteristic
28#16812085C411yescharacteristic
29#16812084C411yescharacteristic
30C4×D428C2211yescharacteristic
31C4×D428C2211yescharacteristic
32C4×D428C2211yescharacteristic
33#16812066C2211yescharacteristic
34#16812066C2211yescharacteristic
35C42×D107C2211yescharacteristic
36C4⋊(C107⋊C8)C2211yescharacteristic
37C4⋊(C107⋊C8)C2211yescharacteristic
38C4⋊(C107⋊C8)C2211yescharacteristic
39(C2×D107)⋊C8C2211yescharacteristic
40(C2×D107)⋊C8C2211yescharacteristic
41(C2×D107)⋊C8C2211yescharacteristic
42(C2×D107)⋊C8C2211yescharacteristic
43(C2×D107)⋊C8C2211yescharacteristic
44(C2×D107)⋊C8C2211yescharacteristic
45#16812020C2211yescharacteristic
46#16812020C2211yescharacteristic
47#16812019C2211yescharacteristic
48#16812019C2211yescharacteristic
49C4×C107⋊C8C2211yescharacteristic
50C8×Dic107C2211yescharacteristic
51C8×Dic107C2211yescharacteristic
52C4×Q8×C107C2211yescharacteristic
53C4⋊C8×C107C2211yescharacteristic
54C4⋊C8×C107C2211yescharacteristic
55C4⋊C8×C107C2211yescharacteristic
56#97×C107C2211yescharacteristic
57#97×C107C2211yescharacteristic
58C4×C8×C107C2211yescharacteristic
59C2×D428C2×C411yescharacteristic
60C2×D428C2×C411yescharacteristic
61C2×D428C2×C411yescharacteristic
62C2×C4×D107C2×C411yescharacteristic
63C2×C4×D107C2×C411yescharacteristic
64C2×C4×D107C2311yescharacteristic
65C2×C4×D107C2311yescharacteristic
66C2×C4×D107C2311yescharacteristic
67#13133801—22no—
68#13133801—22no—
69#13133801—22no—
70#13133801—22no—
71C2×C107⋊C8C2311yescharacteristic
72C2×C107⋊C8C2311yescharacteristic
73C2×C107⋊C8C2311yescharacteristic
74C2×C107⋊C8C2311yescharacteristic
75C8×D107—22no—
76C8×D107—22no—
77C4⋊Dic107C2×C411yescharacteristic
78C4⋊Dic107C2×C411yescharacteristic
79C4⋊Dic107C2×C411yescharacteristic
80Dic107⋊C4C2×C411yescharacteristic
81Dic107⋊C4C2×C411yescharacteristic
82Dic107⋊C4C2×C411yescharacteristic
83Dic107⋊C4C2×C411yescharacteristic
84(C2×D107)⋊C4C2×C411yescharacteristic
85(C2×D107)⋊C4C2×C411yescharacteristic
86(C2×D107)⋊C4C2×C411yescharacteristic
87(C2×D107)⋊C4C2×C411yescharacteristic
88(C2×D107)⋊C4C2×C411yescharacteristic
89(C2×D107)⋊C4C2×C411yescharacteristic
90(C2×D107)⋊C4C2×C411yescharacteristic
91(C2×D107)⋊C4C2×C411yescharacteristic
92(C2×D107)⋊C4C2×C411yescharacteristic
93(C2×D107)⋊C4C2×C411yescharacteristic
94C4×Dic107C2×C411yescharacteristic
95C4×Dic107C2×C411yescharacteristic
96C4×Dic107C2311yescharacteristic
97C2×Q8×C107C2×C411yescharacteristic
98C2×C8×C107C2311yescharacteristic
99C2×C8×C107C2311yescharacteristic
100C2×C8×C107C2311yescharacteristic
101C2×C8×C107C2311yescharacteristic
102C4⋊C4×C107C2×C411yescharacteristic
103C4⋊C4×C107C2×C411yescharacteristic
104C4⋊C4×C107C2×C411yescharacteristic
105C42×C107C2311yescharacteristic
106C42×C107C2311yescharacteristic
107C42×C107C2311yescharacteristic
108C22×D107C22×C411yescharacteristic
109C22×D107C22×C411yescharacteristic
110C22×D107C22×C411yescharacteristic
111Q8×C107—41no—
112C2×C4×C107C22×C411yescharacteristic
113C2×C4×C107C22×C411yescharacteristic
114C2×C4×C107C22×C411yescharacteristic
115C2×C4×C107C22×C411yescharacteristic
116C2×C4×C107C22×C411yescharacteristic
117C2×C4×C107C22×C411yescharacteristic
118C2×C4×C107C2411yescharacteristic
119C2×Dic107C22×C411yescharacteristic
120C2×Dic107C22×C411yescharacteristic
121C2×Dic107C22×C411yescharacteristic
122C2×Dic107C22×C411yescharacteristic
123C2×Dic107C22×C411yescharacteristic
124D428—41no—
125D428—41no—
126D428—41no—
127C4×D107—21no—
128C4×D107—21no—
129C4×D107—21no—
130C4×D107—21no—
131C4×D107—21no—
132C4×D107—21no—
133C4×D107—41no—
134C4×D107—41no—
135C8×C107—21no—
136C8×C107—21no—
137C8×C107—21no—
138C8×C107#4112yes—
139C107⋊C8—21no—
140C107⋊C8—21no—
141C107⋊C8—21no—
142C107⋊C8#4112yes—
143C22×C107C23×C411yescharacteristic
144C2×D107—21no—
145C2×D107—21no—
146C2×D107—21no—
147C2×D107—21no—
148C2×D107—21no—
149C2×D107—21no—
150C2×D107—21no—
151C2×D107—21no—
152C2×D107—21no—
153C4×C107—21no—
154C4×C107—21no—
155C4×C107—21no—
156C4×C107—21no—
157C4×C107—21no—
158C4×C107—21no—
159C4×C107C2×#4111yescharacteristic
160C4×C107C2×#4111yescharacteristic
161Dic107—21no—
162Dic107—21no—
163Dic107—21no—
164Dic107—21no—
165Dic107—21no—
166C2×C107C4×#4111yescharacteristic
167C2×C107#56811yescharacteristic
168C2×C107#56811yescharacteristic
169D107—41no—
170D107—41no—
171D107—41no—
172#2967—1071nomaximal, Sylow
173C107#296711yescharacteristic, complemented, Sylow
174#529—1071no—
175#446—1071no—
176#446D10711yescharacteristic, complemented
177#436—1071no—
178#436—1071no—
179#435—1071no—
180#435—1071no—
181#435—1071no—
182#435—1071no—
183#433—1071no—
184#433—1071no—
185#432—1071no—
186#405—1071no—
187#405—1071no—
188C4×M16—1071no—
189C2×M16—1071no—
190C2×M16—1071no—
191C2×M16—1071no—
192C2×M16—1071no—
193C22×C8—1071no—
194C22×C8—1071no—
195#126—1071no—
196#126—1071no—
197#125—1071no—
198#124—1071no—
199#123—1071no—
200#123—1071no—
201C22⋊Q8—1071no—
202#121—1071no—
203C4×Q8C2×D10711yescharacteristic
204C4×D4—1071no—
205C4×D4—1071no—
206C4×D4—1071no—
207#117—1071no—
208#117—1071no—
209C2×C42—1071no—
210C4⋊C8—1071no—
211C4⋊C8—1071no—
212C4⋊C8—1071no—
213C4⋊C8C2×D10711yescharacteristic
214C4⋊C8C2×D10711yescharacteristic
215C4⋊C8C2×D10711yescharacteristic
216C22⋊C8—1071no—
217C22⋊C8—1071no—
218C22⋊C8—1071no—
219C22⋊C8—1071no—
220C22⋊C8—1071no—
221C22⋊C8—1071no—
222#97—1071no—
223#97—1071no—
224#97—1071no—
225#97—1071no—
226#97C2×D10711yescharacteristic
227#97C2×D10711yescharacteristic
228C4×C8—1071no—
229C4×C8—1071no—
230C4×C8—1071no—
231C4×C8C2×D10711yescharacteristic
232C2×Q8C4×D10711yescharacteristic
233C2×D4—1071no—
234C2×D4—1071no—
235C2×D4—1071no—
236C22×C4—1071no—
237C22×C4—1071no—
238C22×C4—1071no—
239C22×C4—1071no—
240C22×C4—1071no—
241M16—2142no—
242M16—2142no—
243M16—2142no—
244M16—2142no—
245C2×C8—1071no—
246C2×C8—1071no—
247C2×C8—1071no—
248C2×C8—1071no—
249C2×C8—2142no—
250C2×C8—2142no—
251C2×C8C22×D10711yescharacteristic
252C2×C8C22×D10711yescharacteristic
253C2×C8C22×D10711yescharacteristic
254C2×C8C22×D10711yescharacteristic
255C4⋊C4—1071no—
256C4⋊C4—1071no—
257C4⋊C4—1071no—
258C4⋊C4—1071no—
259C4⋊C4—1071no—
260C4⋊C4—1071no—
261C4⋊C4—1071no—
262C4⋊C4C4×D10711yescharacteristic
263C4⋊C4C4×D10711yescharacteristic
264C4⋊C4C4×D10711yescharacteristic
265C22⋊C4—1071no—
266C22⋊C4—1071no—
267C22⋊C4—1071no—
268C22⋊C4—1071no—
269C22⋊C4—1071no—
270C22⋊C4—1071no—
271C22⋊C4—1071no—
272C22⋊C4—1071no—
273C22⋊C4—1071no—
274C22⋊C4—1071no—
275C42—1071no—
276C42—1071no—
277C42—1071no—
278C42C22×D10711yescharacteristic
279C42C22×D10711yescharacteristic
280C42C22×D10711yescharacteristic
281C23—1071no—
282C23—1071no—
283C23—1071no—
284Q8—41no—
285D4—4281no—
286D4—4281no—
287D4—4281no—
288C2×C4—1071no—
289C2×C4—1071no—
290C2×C4—1071no—
291C2×C4—1071no—
292C2×C4—1071no—
293C2×C4—4281no—
294C2×C4—4281no—
295C2×C4—2141no—
296C2×C4—2141no—
297C2×C4—2141no—
298C2×C4—2141no—
299C2×C4—2141no—
300C2×C4—2141no—
301C2×C4C2×C4×D10711yescharacteristic
302C2×C4C2×C4×D10711yescharacteristic
303C2×C4C2×C4×D10711yescharacteristic
304C2×C4C2×C4×D10711yescharacteristic
305C2×C4C2×C4×D10711yescharacteristic
306C2×C4C2×C4×D10711yescharacteristic
307C2×C4C23×D10711yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—1072no—
312C8—2141no—
313C8—2141no—
314C8—2141no—
315C8#1313381912yes—
316C22—2141no—
317C22—2141no—
318C22—2141no—
319C22—2141no—
320C22—2141no—
321C22—2141no—
322C22—2141no—
323C22—2141no—
324C22—2141no—
325C22C22×C4×D10711yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—2141no—
333C4—2141no—
334C4—2141no—
335C4—2141no—
336C4—2141no—
337C4#41×D10711yescharacteristic
338C4C2×#1313381911yescharacteristic
339C2—4281no—
340C2—4281no—
341C2—4281no—
342C2C4×#1313381911yescharacteristic
343C2#2029339211yescharacteristic
344C2#2029339311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D107
commutator, socleC22×C107C23×C4
Fitting#446×C107C2
prime radical#16812084C4
cosocleC2×C4×C107C24
hypercenter#446D107
hypocenterC107#2967
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ #446

Complements

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

NH ≅ G/Ntype
2. #20292758C2semidirect
3. #20292706C2semidirect
4. #20292704C2semidirect
5. #20292700C2semidirect
6. #20292700C2semidirect
7. #20292697C2semidirect
8. #20292697C2semidirect
9. #20292687C2semidirect
10. #20292687C2semidirect
11. #20292683C2semidirect
12. #20292584C2semidirect
13. #20292581C2semidirect
14. #20292579C2semidirect
15. #446×C107C2semidirect
173. C107#2967semidirect
176. #446D107semidirect

Maximal subgroups

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

subgroupindex
#202931642
#202927582
#202927062
#202927042
#202927002
#202926972
#202926872
#202926832
#202925842
#202925812
#202925792
#446×C1072
#2967107