Finite Group Databasebeta

← #28345503

Subgroups — #28345503

Order 13696.

412 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293136C211yesmaximal, characteristic
2#20292706C211yesmaximal, characteristic, complemented
3#20292702C211yesmaximal, characteristic, complemented
4#20292699C211yesmaximal, characteristic, complemented
5#20292698C211yesmaximal, characteristic, complemented
6#20292697C211yesmaximal, characteristic, complemented
7#20292695C211yesmaximal, characteristic, complemented
8C8×C22⋊D107C211yesmaximal, characteristic, complemented
9#20292687C211yesmaximal, characteristic, complemented
10#20292686C211yesmaximal, characteristic, complemented
11#20292593C211yesmaximal, characteristic, complemented
12#20292592C211yesmaximal, characteristic, complemented
13#20292589C211yesmaximal, characteristic, complemented
14C2×(C2×D107)⋊C8C211yesmaximal, characteristic, complemented
15C8×D4×C107C211yesmaximal, characteristic, complemented
16C2×#13133818C2211yescharacteristic
17C22×C4×D107C2211yescharacteristic
18C2×#13133802C2211yescharacteristic, complemented
19C2×#13133801C2211yescharacteristic
20C2×#13133801C2211yescharacteristic
21C2×#13133801C2211yescharacteristic, complemented
22C22×C107⋊C8C2211yescharacteristic
23C2×C8×D107C2211yescharacteristic, complemented
24#16812094C411yescharacteristic
25#16812091C411yescharacteristic
26#16812087C411yescharacteristic
27#16812086C411yescharacteristic
28#16812082C411yescharacteristic
29#16812081C411yescharacteristic
30#16812079C411yescharacteristic
31#16812077C411yescharacteristic
32C4×D428C2211yescharacteristic
33C4×C22⋊D107C2211yescharacteristic
34C4×C22⋊D107C2211yescharacteristic
35#16812066C2211yescharacteristic
36C4⋊(C107⋊C8)C2211yescharacteristic, complemented
37Dic107⋊C8C2211yescharacteristic, complemented
38Dic107⋊C8C2211yescharacteristic, complemented
39C22⋊(C107⋊C8)C2211yescharacteristic
40C22⋊(C107⋊C8)C2211yescharacteristic, complemented
41(C2×D107)⋊C8C2211yescharacteristic
42(C2×D107)⋊C8C2211yescharacteristic
43(C2×D107)⋊C8C2211yescharacteristic
44(C2×D107)⋊C8C2211yescharacteristic
45(C2×D107)⋊C8C2211yescharacteristic
46(C2×D107)⋊C8C2211yescharacteristic
47(C2×D107)⋊C8C2211yescharacteristic, complemented
48(C2×D107)⋊C8C2211yescharacteristic, complemented
49#16812020C2211yescharacteristic, complemented
50#16812019C2211yescharacteristic, complemented
51C8×Dic107C2211yescharacteristic, complemented
52C22×C8×C107C2211yescharacteristic
53C22×C8×C107C2211yescharacteristic, complemented
54C4×D4×C107C2211yescharacteristic
55C4⋊C8×C107C2211yescharacteristic, complemented
56C22⋊C8×C107C2211yescharacteristic
57C22⋊C8×C107C2211yescharacteristic, complemented
58C4×C8×C107C2211yescharacteristic, complemented
59C23×D107C2×C411yescharacteristic
60#13133818—41no—
61#13133818—41no—
62C2×Dic214C2×C411yescharacteristic
63C2×D428C2×C411yescharacteristic
64C2×D428C2×C411yescharacteristic
65C2×C22⋊D107C2×C411yescharacteristic
66C2×C22⋊D107C2×C411yescharacteristic
67C2×C22⋊D107C2×C411yescharacteristic
68C2×C22⋊D107C2×C411yescharacteristic
69C22×Dic107C2×C411yescharacteristic
70C2×C4×D107—41no—
71C2×C4×D107—41no—
72C2×C4×D107C2×C411yescharacteristic
73C2×C4×D107C2×C411yescharacteristic
74C2×C4×D107C2311yescharacteristic
75C2×C4×D107C2311yescharacteristic
76C2×C4×D107C2311yescharacteristic
77#13133802—41no—
78#13133801—41no—
79#13133801—41no—
80#13133801—41no—
81C2×C107⋊C8—41no—
82C2×C107⋊C8C2311yescharacteristic
83C2×C107⋊C8C2311yescharacteristic
84C2×C107⋊C8C2311yescharacteristic
85C2×C107⋊C8C2311yescharacteristic
86C8×D107—41no—
87C4⋊Dic107C2×C411yescharacteristic
88Dic107⋊C4C2×C411yescharacteristic
89Dic107⋊C4C2×C411yescharacteristic
90Dic107⋊C4C2×C411yescharacteristic
91Dic107⋊C4C2×C411yescharacteristic
92C22⋊Dic107C2×C411yescharacteristic
93C22⋊Dic107C2×C411yescharacteristic
94(C2×D107)⋊C4C2×C411yescharacteristic
95(C2×D107)⋊C4C2×C411yescharacteristic
96(C2×D107)⋊C4C2×C411yescharacteristic
97(C2×D107)⋊C4C2×C411yescharacteristic
98(C2×D107)⋊C4C2×C411yescharacteristic
99(C2×D107)⋊C4C2×C411yescharacteristic
100C4×Dic107C2311yescharacteristic
101C2×D4×C107C2×C411yescharacteristic
102C22×C4×C107C2311yescharacteristic
103C22×C4×C107C2311yescharacteristic
104C2×C8×C107—41no—
105C2×C8×C107—41no—
106C2×C8×C107C2311yescharacteristic
107C2×C8×C107C2311yescharacteristic
108C2×C8×C107C2311yescharacteristic
109C2×C8×C107C2311yescharacteristic
110C4⋊C4×C107C2×C411yescharacteristic
111C22⋊C4×C107C2×C411yescharacteristic
112C22⋊C4×C107C2×C411yescharacteristic
113C42×C107C2311yescharacteristic
114C23×C107C22×C411yescharacteristic
115C23×C107C22×C411yescharacteristic
116C22×D107—22no—
117C22×D107—41no—
118C22×D107—41no—
119C22×D107C22×C411yescharacteristic
120C22×D107C22×C411yescharacteristic
121C22×D107C22×C411yescharacteristic
122D4×C107—22no—
123C2×C4×C107—21no—
124C2×C4×C107—21no—
125C2×C4×C107—21no—
126C2×C4×C107—21no—
127C2×C4×C107C22×C411yescharacteristic
128C2×C4×C107C22×C411yescharacteristic
129C2×C4×C107C22×C411yescharacteristic
130C2×C4×C107C22×C411yescharacteristic
131C2×C4×C107C2411yescharacteristic
132C22⋊D107—22no—
133C22⋊D107—41no—
134C22⋊D107—41no—
135C22⋊D107—41no—
136C2×Dic107—41no—
137C2×Dic107C22×C411yescharacteristic
138C2×Dic107C22×C411yescharacteristic
139C2×Dic107C22×C411yescharacteristic
140C2×Dic107C22×C411yescharacteristic
141C2×Dic107C22×C411yescharacteristic
142D428—41no—
143D428—41no—
144C4×D107—21no—
145C4×D107—21no—
146C4×D107—21no—
147C4×D107—21no—
148C4×D107—21no—
149C4×D107—21no—
150C4×D107—41no—
151C4×D107—41no—
152Dic214—41no—
153C8×C107—21no—
154C8×C107—21no—
155C8×C107—21no—
156C8×C107—21no—
157C107⋊C8—21no—
158C107⋊C8—21no—
159C107⋊C8—21no—
160C107⋊C8—21no—
161C22×C107—21no—
162C22×C107—21no—
163C22×C107—21no—
164C22×C107—21no—
165C22×C107—21no—
166C22×C107#13112yes—
167C22×C107C23×C411yescharacteristic
168C2×D107—21no—
169C2×D107—21no—
170C2×D107—21no—
171C2×D107—21no—
172C2×D107—21no—
173C2×D107—21no—
174C2×D107—21no—
175C2×D107—21no—
176C2×D107—21no—
177C2×D107—44no—
178C4×C107—21no—
179C4×C107—21no—
180C4×C107—21no—
181C4×C107—21no—
182C4×C107H(5,𝔽2)11yescharacteristic
183C4×C107H(5,𝔽2)11yescharacteristic
184Dic107—21no—
185Dic107—21no—
186Dic107—21no—
187Dic107—21no—
188Dic107—21no—
189C2×C107—22no—
190C2×C107—41no—
191C2×C107#51811yescharacteristic
192C2×C107C2×#13111yescharacteristic
193C2×C107#56811yescharacteristic
194D107—41no—
195D107—41no—
196D107—41no—
197#2976—1071nomaximal, Sylow
198C107#297611yescharacteristic, complemented, Sylow
199#525—1071no—
200#436—1071no—
201#436—1071no—
202#435—1071no—
203#435—1071no—
204#435—1071no—
205#435—1071no—
206C8×D4—1071no—
207C8×D4D10711yescharacteristic, complemented
208#433—1071no—
209#433—1071no—
210#408—1071no—
211#408—1071no—
212#407—1071no—
213C2×C22⋊C8—1071no—
214C2×#41—1071no—
215C23×C4—1071no—
216C2×M16—1071no—
217C2×M16—1071no—
218C2×M16—1071no—
219C2×M16—1071no—
220C22×C8—1071no—
221C22×C8—1071no—
222C22×C8C2×D10711yescharacteristic
223C22×C8C2×D10711yescharacteristic, complemented
224#123—1071no—
225#123—1071no—
226C22⋊Q8—1071no—
227C22⋊Q8—1071no—
228#121—1071no—
229#121—1071no—
230#120—1071no—
231#120—1071no—
232C4×D4—1071no—
233C4×D4—1071no—
234C4×D4—1071no—
235C4×D4C2×D10711yescharacteristic
236#117—1071no—
237C4⋊C8—1071no—
238C4⋊C8—1071no—
239C4⋊C8—1071no—
240C4⋊C8C2×D10711yescharacteristic, complemented
241C22⋊C8—1071no—
242C22⋊C8—1071no—
243C22⋊C8—1071no—
244C22⋊C8—1071no—
245C22⋊C8—1071no—
246C22⋊C8—1071no—
247C22⋊C8—1071no—
248C22⋊C8—1071no—
249C22⋊C8—1071no—
250C22⋊C8—1071no—
251C22⋊C8C2×D10711yescharacteristic
252C22⋊C8C2×D10711yescharacteristic, complemented
253#97—1071no—
254#97—1071no—
255C4×C8—1071no—
256C4×C8C2×D10711yescharacteristic, complemented
257C24—1071no—
258#41—4281no—
259#41—4281no—
260C2×Q8—1071no—
261C2×D4—1071no—
262C2×D4—1071no—
263C2×D4—1071no—
264C2×D4—1071no—
265C2×D4—1071no—
266C2×D4—1071no—
267C2×D4C4×D10711yescharacteristic
268C22×C4—1071no—
269C22×C4—1071no—
270C22×C4—1071no—
271C22×C4—1071no—
272C22×C4—1071no—
273C22×C4—1071no—
274C22×C4—4281no—
275C22×C4—4281no—
276C22×C4C22×D10711yescharacteristic
277C22×C4C22×D10711yescharacteristic
278M16—4281no—
279M16—4281no—
280M16—4281no—
281M16—4281no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—1071no—
285C2×C8—1071no—
286C2×C8—1071no—
287C2×C8—1071no—
288C2×C8—4281no—
289C2×C8—4281no—
290C2×C8C22×D10711yescharacteristic
291C2×C8C22×D10711yescharacteristic
292C2×C8C22×D10711yescharacteristic
293C2×C8C22×D10711yescharacteristic
294C4⋊C4—1071no—
295C4⋊C4—1071no—
296C4⋊C4—1071no—
297C4⋊C4—1071no—
298C4⋊C4—1071no—
299C4⋊C4C4×D10711yescharacteristic
300C22⋊C4—1071no—
301C22⋊C4—1071no—
302C22⋊C4—1071no—
303C22⋊C4—1071no—
304C22⋊C4—1071no—
305C22⋊C4—1071no—
306C22⋊C4—1071no—
307C22⋊C4—1071no—
308C22⋊C4C4×D10711yescharacteristic
309C22⋊C4C4×D10711yescharacteristic
310C42—1071no—
311C42C22×D10711yescharacteristic
312C23—1071no—
313C23—1071no—
314C23—1071no—
315C23—4281no—
316C23—4281no—
317C23—2142no—
318C23C2×C4×D10711yescharacteristic
319C23C2×C4×D10711yescharacteristic
320Q8—4281no—
321D4—22no—
322D4—4281no—
323D4—4281no—
324D4—4281no—
325D4—4281no—
326D4—4281no—
327D4—2142no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—1071no—
333C2×C4—1071no—
334C2×C4—1071no—
335C2×C4—1071no—
336C2×C4—1071no—
337C2×C4—4281no—
338C2×C4—4281no—
339C2×C4—4281no—
340C2×C4—2141no—
341C2×C4—2141no—
342C2×C4—2141no—
343C2×C4—2141no—
344C2×C4—2141no—
345C2×C4—2141no—
346C2×C4C2×C4×D10711yescharacteristic
347C2×C4C2×C4×D10711yescharacteristic
348C2×C4C2×C4×D10711yescharacteristic
349C2×C4C2×C4×D10711yescharacteristic
350C2×C4C23×D10711yescharacteristic
351C8—21no—
352C8—21no—
353C8—21no—
354C8—21no—
355C8—2141no—
356C8—2141no—
357C8—2141no—
358C8—2141no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—4284no—
365C22—2141no—
366C22—2141no—
367C22—2141no—
368C22—2141no—
369C22—2141no—
370C22—2141no—
371C22—2141no—
372C22—2141no—
373C22—2141no—
374C22#1681211512yes—
375C22C22×C4×D10711yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—2141no—
381C4—2141no—
382C4—2141no—
383C4—2141no—
384C4—2141no—
385C4#1681215411yescharacteristic
386C4#1681215511yescharacteristic
387C2—22no—
388C2—41no—
389C2—4281no—
390C2—4281no—
391C2—4281no—
392C2#2029309911yescharacteristic
393C2C2×#1681211511yescharacteristic
394C2#2029339211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D107
commutator, socleC22×C107C23×C4
FittingC8×D4×C107C2
prime radical#20293136C2
cosocleC2×C4×C107C24
hypercenterC8×D4D107
hypocenterC107#2976
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. #20292706C2semidirect
3. #20292702C2semidirect
4. #20292699C2semidirect
5. #20292698C2semidirect
6. #20292697C2semidirect
7. #20292695C2semidirect
8. C8×C22⋊D107C2semidirect
9. #20292687C2semidirect
10. #20292686C2semidirect
11. #20292593C2semidirect
12. #20292592C2semidirect
13. #20292589C2semidirect
14. C2×(C2×D107)⋊C8C2semidirect
15. C8×D4×C107C2semidirect
18. C2×#13133802C22semidirect
21. C2×#13133801C22semidirect
23. C2×C8×D107C22semidirect
36. C4⋊(C107⋊C8)C22semidirect
37. Dic107⋊C8C22semidirect
38. Dic107⋊C8C22semidirect
40. C22⋊(C107⋊C8)C22semidirect
47. (C2×D107)⋊C8C22semidirect
48. (C2×D107)⋊C8C22semidirect
49. #16812020C22semidirect
50. #16812019C22semidirect
51. C8×Dic107C22semidirect
53. C22×C8×C107C22semidirect
55. C4⋊C8×C107C22semidirect
57. C22⋊C8×C107C22semidirect
58. C4×C8×C107C22semidirect
198. C107#2976semidirect
207. C8×D4D107semidirect
223. C22×C8C2×D107semidirect
240. C4⋊C8C2×D107semidirect
252. C22⋊C8C2×D107semidirect
256. C4×C8C2×D107semidirect

Maximal subgroups

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

subgroupindex
#202931362
#202927062
#202927022
#202926992
#202926982
#202926972
#202926952
C8×C22⋊D1072
#202926872
#202926862
#202925932
#202925922
#202925892
C2×(C2×D107)⋊C82
C8×D4×C1072
#2976107