Finite Group Databasebeta

← #28348299

Subgroups — #28348299

Order 13696.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293316C211yesmaximal, characteristic, complemented
2#20293274C211yesmaximal, characteristic
3#20292980C211yesmaximal, characteristic, complemented
4#20292959C211yesmaximal, characteristic, complemented
5#20292930C211yesmaximal, characteristic, complemented
6#20292869C211yesmaximal, characteristic, complemented
7#20292854C211yesmaximal, characteristic, complemented
8#20292848C211yesmaximal, characteristic, complemented
9#20292791C211yesmaximal, characteristic, complemented
10#20292779C211yesmaximal, characteristic, complemented
11#20292714C211yesmaximal, characteristic, complemented
12(C22⋊D107)⋊C8C211yesmaximal, characteristic, complemented
13#20292621C211yesmaximal, characteristic, complemented
14#102×D107C211yesmaximal, characteristic, complemented
15#482×C107C211yesmaximal, characteristic, complemented
16C2×#13133818C2211yescharacteristic
17C2×D4×D107C2211yescharacteristic
18C2×Dic428C2211yescharacteristic, complemented
19C2×#13133807C2211yescharacteristic
20C2×#13133806C2211yescharacteristic
21C22×C107⋊C8C2211yescharacteristic, complemented
22C2×C8×D107C2211yescharacteristic
23#16812102—21no—
24#16812101—21no—
25#16812100C2211yescharacteristic, complemented
26#16812096C2211yescharacteristic
27#16812091—21no—
28#16812091—21no—
29#16812089C2211yescharacteristic
30#16812089C2211yescharacteristic
31#16812088C2211yescharacteristic, complemented
32#16812080—21no—
33#16812077—21no—
34#16812074C2211yescharacteristic, complemented
35#16812071C2211yescharacteristic
36C4×C22⋊D107C2211yescharacteristic
37#16812066—21no—
38C4⋊C4×D107C2211yescharacteristic
39C22⋊C4×D107—21no—
40#16812040C2211yescharacteristic, complemented
41Dic107⋊C8C2211yescharacteristic, complemented
42#16812034C2211yescharacteristic, complemented
43#16812032C2211yescharacteristic, complemented
44#16812032C2211yescharacteristic, complemented
45#16812032C2211yescharacteristic, complemented
46#16812031C2211yescharacteristic
47#16812030C2211yescharacteristic
48#16812029C2211yescharacteristic
49#16812029C2211yescharacteristic
50(C2×D107)⋊C8C2211yescharacteristic
51C8×Dic107C2211yescharacteristic, complemented
52#121×C107C2211yescharacteristic
53#117×C107C2211yescharacteristic, complemented
54#107×C107C2211yescharacteristic, complemented
55#106×C107C2211yescharacteristic, complemented
56#102×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic
58C22⋊C8×C107C2211yescharacteristic, complemented
59C23×D107—21no—
60#13133818—22no—
61#13133818—41no—
62C2×Dic214C2311yescharacteristic
63C2×Dic214C2311yescharacteristic
64C2×D428C2311yescharacteristic
65C2×C22⋊D107—21no—
66C2×C22⋊D107—21no—
67C2×C22⋊D107D411yescharacteristic
68D4×D107—22no—
69D4×D107—41no—
70C2×C4×D107—21no—
71C2×C4×D107—21no—
72C2×C4×D107—21no—
73C2×C4×D107C2311yescharacteristic
74Dic428—41no—
75#13133807—22no—
76#13133806—41no—
77C2×C107⋊C8—41no—
78C2×C107⋊C8C2311yescharacteristic
79C2×C107⋊C8C2311yescharacteristic
80C8×D107—41no—
81C4⋊Dic107—21no—
82C4⋊Dic107—21no—
83C4⋊Dic107—21no—
84C4⋊Dic107C2311yescharacteristic
85Dic107⋊C4—21no—
86Dic107⋊C4—21no—
87Dic107⋊C4—21no—
88Dic107⋊C4—21no—
89Dic107⋊C4D411yescharacteristic
90C22⋊Dic107—21no—
91C22⋊Dic107—21no—
92C22⋊Dic107—21no—
93C22⋊Dic107D411yescharacteristic
94(C2×D107)⋊C4—21no—
95(C2×D107)⋊C4—21no—
96(C2×D107)⋊C4—21no—
97(C2×D107)⋊C4D411yescharacteristic
98C4×Dic107—21no—
99C4×Dic107C2311yescharacteristic
100C2×D4×C107—21no—
101C2×D4×C107C2311yescharacteristic
102C22×C4×C107C2311yescharacteristic
103C2×C8×C107C2311yescharacteristic
104C2×C8×C107C2311yescharacteristic
105C4⋊C4×C107C2311yescharacteristic
106C4⋊C4×C107C2311yescharacteristic
107C4⋊C4×C107C2311yescharacteristic
108C22⋊C4×C107—21no—
109C22⋊C4×C107—21no—
110C42×C107—21no—
111C23×C107—21no—
112C23×C107C2×D411yescharacteristic
113C22×D107—21no—
114C22×D107—42no—
115C22×D107—42no—
116C22×D107—81no—
117C22×D107C2×D411yescharacteristic
118D4×C107—21no—
119D4×C107—21no—
120D4×C107—81no—
121C2×C4×C107—21no—
122C2×C4×C107—21no—
123C2×C4×C107—21no—
124C2×C4×C107—21no—
125C2×C4×C107—21no—
126C2×C4×C107C2×D411yescharacteristic
127C2×C4×C107C2411yescharacteristic
128C22⋊D107—22no—
129C22⋊D107—42no—
130C22⋊D107—42no—
131C2×Dic107—21no—
132C2×Dic107—21no—
133C2×Dic107—21no—
134C2×Dic107C2×D411yescharacteristic
135C2×Dic107C2×D411yescharacteristic
136C2×Dic107C2×D411yescharacteristic
137D428—21no—
138D428#4112yes—
139C4×D107—21no—
140C4×D107—21no—
141C4×D107—42no—
142C4×D107—42no—
143C4×D107—81no—
144Dic214—21no—
145Dic214—21no—
146Dic214—21no—
147Dic214—21no—
148C8×C107—21no—
149C8×C107—21no—
150C107⋊C8—21no—
151C107⋊C8—21no—
152C22×C107—21no—
153C22×C107—21no—
154C22×C107—21no—
155C22×C107—41no—
156C22×C107—41no—
157C22×C107—41no—
158C22×C107C22×D411yescharacteristic
159C2×D107—21no—
160C2×D107—21no—
161C2×D107—22no—
162C2×D107—41no—
163C2×D107—41no—
164C2×D107—84no—
165C2×D107#13512yes—
166C4×C107—21no—
167C4×C107—41no—
168C4×C107—41no—
169C4×C107—41no—
170C4×C107C2×#4111yescharacteristic
171C4×C107H(5,𝔽2)11yescharacteristic
172Dic107—21no—
173Dic107—21no—
174Dic107—21no—
175Dic107—41no—
176Dic107—41no—
177Dic107—41no—
178C2×C107—41no—
179C2×C107—81no—
180C2×C107#54611yescharacteristic
181C2×C107C2×#13511yescharacteristic
182C2×C107#57711yescharacteristic
183D107—22no—
184D107—42no—
185#3296—1071nomaximal, Sylow
186C107#329611yescharacteristic, complemented, Sylow
187#552—1071no—
188#546—1071no—
189#488—1071no—
190#483—1071no—
191#482D10711yescharacteristic, complemented
192#478—1071no—
193#467—1071no—
194#465—1071no—
195#464—1071no—
196#452—1071no—
197#450—1071no—
198C4×SD16—1071no—
199C8×D4—1071no—
200#416—1071no—
201C2×#102—1071no—
202C2×#41—1071no—
203C22×D4—1071no—
204C2×Q16—1071no—
205C2×SD16—1071no—
206C2×SD16—1071no—
207C22×C8—1071no—
208C22×C8—1071no—
209#126—2141no—
210#125—1071no—
211#125—2141no—
212#124—1071no—
213#123—2141no—
214#123—2141no—
215C22⋊Q8—1071no—
216C22⋊Q8—1071no—
217C22⋊Q8—1071no—
218#121—2141no—
219#121C2×D10711yescharacteristic
220#120—2141no—
221C4×Q8—1071no—
222C4×D4—1071no—
223C4×D4—1071no—
224#117—2141no—
225#117C2×D10711yescharacteristic, complemented
226C2×C4⋊C4—1071no—
227C2×C22⋊C4—2141no—
228#107C2×D10711yescharacteristic, complemented
229#106—1071no—
230#106C2×D10711yescharacteristic, complemented
231C4⋊C8—1071no—
232#103—1071no—
233#103—1071no—
234#103—1071no—
235#103—1071no—
236#102—1071no—
237#102—1071no—
238#102—1071no—
239#102—1071no—
240#102C2×D10711yescharacteristic
241#102C2×D10711yescharacteristic
242C22⋊C8—1071no—
243C22⋊C8C2×D10711yescharacteristic, complemented
244C4×C8—1071no—
245C24—2141no—
246#41—4281no—
247#41—2142no—
248C2×Q8—1071no—
249C2×Q8—1071no—
250C2×D4—21no—
251C2×D4—1071no—
252C2×D4—1071no—
253C2×D4—4281no—
254C2×D4—2141no—
255C2×D4—2142no—
256C2×D4—2141no—
257C2×D4C22×D10711yescharacteristic
258C22×C4—1071no—
259C22×C4—2141no—
260C22×C4—2141no—
261C22×C4—2141no—
262C22×C4C22×D10711yescharacteristic
263Q16—4281no—
264SD16—4281no—
265SD16—2142no—
266C2×C8—1071no—
267C2×C8—1071no—
268C2×C8—4281no—
269C2×C8—4281no—
270C2×C8C22×D10711yescharacteristic
271C2×C8C22×D10711yescharacteristic
272C4⋊C4—1071no—
273C4⋊C4—1071no—
274C4⋊C4—2141no—
275C4⋊C4—2141no—
276C4⋊C4—2141no—
277C4⋊C4—2141no—
278C4⋊C4—2141no—
279C4⋊C4—2141no—
280C4⋊C4—2141no—
281C4⋊C4C22×D10711yescharacteristic
282C4⋊C4C22×D10711yescharacteristic
283C4⋊C4C22×D10711yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—1071no—
287C22⋊C4—1071no—
288C22⋊C4—2141no—
289C22⋊C4—2141no—
290C22⋊C4—2141no—
291C22⋊C4—2141no—
292C22⋊C4—2141no—
293C22⋊C4—2141no—
294C42—21no—
295C42—1071no—
296C42—2141no—
297C23—21no—
298C23—8561no—
299C23—1071no—
300C23—4282no—
301C23—4282no—
302C23—2141no—
303C23D4×D10711yescharacteristic
304Q8—2141no—
305Q8—2141no—
306Q8—2141no—
307Q8—2141no—
308D4—21no—
309D4—21no—
310D4—81no—
311D4—1072no—
312D4—4282no—
313D4—4282no—
314D4—2142no—
315D4—2141no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—8561no—
322C2×C4—1071no—
323C2×C4—1071no—
324C2×C4—1071no—
325C2×C4—4282no—
326C2×C4—4282no—
327C2×C4—2141no—
328C2×C4—2141no—
329C2×C4—2141no—
330C2×C4—2141no—
331C2×C4—2141no—
332C2×C4D4×D10711yescharacteristic
333C2×C4C23×D10711yescharacteristic
334C8—21no—
335C8—21no—
336C8—2141no—
337C8—2141no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—8564no—
345C22—1072no—
346C22—4281no—
347C22—4281no—
348C22—2142no—
349C22—2141no—
350C22—2141no—
351C22C2×D4×D10711yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—4281no—
357C4—4281no—
358C4—4281no—
359C4—2141no—
360C4—2141no—
361C4—2141no—
362C4#41×D10711yescharacteristic
363C4#1681215511yescharacteristic
364C2—41no—
365C2—81no—
366C2—4282no—
367C2—2142no—
368C2#2029326911yescharacteristic
369C2#135×D10711yescharacteristic
370C2#2029343711yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#482×C107C2
socleC22×C107C22×D4
prime radical#20293274C2
hypercenter#482D107
hypocenterC107#3296
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #20293316C2semidirect
3. #20292980C2semidirect
4. #20292959C2semidirect
5. #20292930C2semidirect
6. #20292869C2semidirect
7. #20292854C2semidirect
8. #20292848C2semidirect
9. #20292791C2semidirect
10. #20292779C2semidirect
11. #20292714C2semidirect
12. (C22⋊D107)⋊C8C2semidirect
13. #20292621C2semidirect
14. #102×D107C2semidirect
15. #482×C107C2semidirect
18. C2×Dic428C22semidirect
21. C22×C107⋊C8C22semidirect
25. #16812100C22semidirect
31. #16812088C22semidirect
34. #16812074C22semidirect
40. #16812040C22semidirect
41. Dic107⋊C8C22semidirect
42. #16812034C22semidirect
43. #16812032C22semidirect
44. #16812032C22semidirect
45. #16812032C22semidirect
51. C8×Dic107C22semidirect
53. #117×C107C22semidirect
54. #107×C107C22semidirect
55. #106×C107C22semidirect
58. C22⋊C8×C107C22semidirect
186. C107#3296semidirect
191. #482D107semidirect
225. #117C2×D107semidirect
228. #107C2×D107semidirect
230. #106C2×D107semidirect
243. C22⋊C8C2×D107semidirect

Maximal subgroups

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

subgroupindex
#202933162
#202932742
#202929802
#202929592
#202929302
#202928692
#202928542
#202928482
#202927912
#202927792
#202927142
(C22⋊D107)⋊C82
#202926212
#102×D1072
#482×C1072
#3296107