Finite Group Databasebeta

← #28348283

Subgroups — #28348283

Order 13696.

462 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#20293332C211yesmaximal, characteristic, complemented
2#20293261C211yesmaximal, characteristic
3#20292972C211yesmaximal, characteristic, complemented
4#20292947C211yesmaximal, characteristic, complemented
5#20292916C211yesmaximal, characteristic, complemented
6#20292857C211yesmaximal, characteristic, complemented
7#20292854C211yesmaximal, characteristic, complemented
8#20292826C211yesmaximal, characteristic, complemented
9#20292780C211yesmaximal, characteristic, complemented
10#20292779C211yesmaximal, characteristic, complemented
11#20292714C211yesmaximal, characteristic, complemented
12(C22⋊D107)⋊C8C211yesmaximal, characteristic, complemented
13C2×#16812029C211yesmaximal, characteristic, complemented
14#102×D107C211yesmaximal, characteristic, complemented
15#481×C107C211yesmaximal, characteristic, complemented
16C22×D428C2211yescharacteristic
17C2×D4×D107—21no—
18C2×D4×D107C2211yescharacteristic
19C2×#13133807C2211yescharacteristic
20C2×#13133807C2211yescharacteristic, complemented
21C2×#13133806C2211yescharacteristic, complemented
22C22×C107⋊C8C2211yescharacteristic, complemented
23C2×C8×D107C2211yescharacteristic, complemented
24#16812108C2211yescharacteristic, complemented
25#16812105C2211yescharacteristic
26#16812099—21no—
27#16812089C2211yescharacteristic, complemented
28#16812088—21no—
29#16812088C2211yescharacteristic, complemented
30#16812087—21no—
31#16812084C2211yescharacteristic
32#16812082—21no—
33#16812079—21no—
34#16812077—21no—
35#16812074C2211yescharacteristic, complemented
36#16812071C2211yescharacteristic
37C4×C22⋊D107—21no—
38C4×C22⋊D107C2211yescharacteristic
39C4⋊C4×D107C2211yescharacteristic, complemented
40#16812040C2211yescharacteristic, complemented
41Dic107⋊C8C2211yescharacteristic, complemented
42#16812032C2211yescharacteristic, complemented
43#16812031C2211yescharacteristic
44#16812031C2211yescharacteristic, complemented
45#16812030C2211yescharacteristic, complemented
46#16812029C2211yescharacteristic
47#16812029C2211yescharacteristic
48#16812029C2211yescharacteristic, complemented
49#16812029C2211yescharacteristic, complemented
50(C2×D107)⋊C8C2211yescharacteristic, complemented
51C8×Dic107C2211yescharacteristic, complemented
52#121×C107C2211yescharacteristic
53C2×C4⋊C4×C107C2211yescharacteristic, complemented
54#106×C107C2211yescharacteristic, complemented
55#106×C107C2211yescharacteristic, complemented
56#102×C107C2211yescharacteristic, complemented
57#102×C107C2211yescharacteristic, complemented
58C22⋊C8×C107C2211yescharacteristic, complemented
59C23×D107—21no—
60C23×D107—21no—
61C2×Dic214—21no—
62C2×Dic214C2311yescharacteristic
63C2×D428—22no—
64C2×D428—21no—
65C2×D428—21no—
66C2×D428—41no—
67C2×D428C2311yescharacteristic
68C2×D428C2311yescharacteristic
69C2×C22⋊D107—21no—
70C2×C22⋊D107—21no—
71C2×C22⋊D107—21no—
72C2×C22⋊D107D411yescharacteristic
73D4×D107—22no—
74D4×D107—41no—
75D4×D107—44no—
76C2×C4×D107—21no—
77C2×C4×D107—21no—
78C2×C4×D107C2311yescharacteristic
79#13133807—22no—
80#13133807—41no—
81#13133806—41no—
82C2×C107⋊C8—41no—
83C2×C107⋊C8C2311yescharacteristic
84C2×C107⋊C8C2311yescharacteristic
85C8×D107—41no—
86C4⋊Dic107—21no—
87C4⋊Dic107C2311yescharacteristic
88Dic107⋊C4—21no—
89Dic107⋊C4—21no—
90Dic107⋊C4—21no—
91Dic107⋊C4—21no—
92Dic107⋊C4D411yescharacteristic
93C22⋊Dic107—21no—
94C22⋊Dic107D411yescharacteristic
95(C2×D107)⋊C4—21no—
96(C2×D107)⋊C4—21no—
97(C2×D107)⋊C4—21no—
98(C2×D107)⋊C4D411yescharacteristic
99C4×Dic107—21no—
100C4×Dic107C2311yescharacteristic
101C2×D4×C107—21no—
102C2×D4×C107C2311yescharacteristic
103C22×C4×C107—21no—
104C22×C4×C107C2311yescharacteristic
105C2×C8×C107C2311yescharacteristic
106C2×C8×C107C2311yescharacteristic
107C4⋊C4×C107—21no—
108C4⋊C4×C107C2311yescharacteristic
109C4⋊C4×C107C2311yescharacteristic
110C4⋊C4×C107C2311yescharacteristic
111C22⋊C4×C107—21no—
112C23×C107—21no—
113C23×C107C2×D411yescharacteristic
114C22×D107—21no—
115C22×D107—21no—
116C22×D107—42no—
117C22×D107—42no—
118C22×D107—42no—
119C22×D107—42no—
120C22×D107—81no—
121C22×D107—81no—
122C22×D107C2×D411yescharacteristic
123D4×C107—21no—
124D4×C107—21no—
125D4×C107—42no—
126C2×C4×C107—21no—
127C2×C4×C107—21no—
128C2×C4×C107—21no—
129C2×C4×C107—21no—
130C2×C4×C107—21no—
131C2×C4×C107—81no—
132C2×C4×C107C2×D411yescharacteristic
133C2×C4×C107C2411yescharacteristic
134C22⋊D107—42no—
135C22⋊D107—42no—
136C22⋊D107—81no—
137C22⋊D107SD1614yescomplemented
138C2×Dic107—21no—
139C2×Dic107—21no—
140C2×Dic107C2×D411yescharacteristic
141C2×Dic107C2×D411yescharacteristic
142C2×Dic107C2×D411yescharacteristic
143D428—21no—
144D428—21no—
145D428—21no—
146D428—42no—
147D428—42no—
148D428#4112yes—
149C4×D107—21no—
150C4×D107—21no—
151C4×D107—42no—
152C4×D107—81no—
153Dic214—21no—
154Dic214—21no—
155Dic214—81no—
156C8×C107—21no—
157C8×C107—21no—
158C107⋊C8—21no—
159C107⋊C8—21no—
160C22×C107—21no—
161C22×C107—21no—
162C22×C107—41no—
163C22×C107—41no—
164C22×C107—41no—
165C22×C107C2×SD1612yes—
166C22×C107C22×D411yescharacteristic
167C2×D107—21no—
168C2×D107—21no—
169C2×D107—22no—
170C2×D107—41no—
171C2×D107—41no—
172C2×D107—41no—
173C2×D107—41no—
174C2×D107—41no—
175C2×D107—84no—
176C2×D107—84no—
177C2×D107C2×SD1612yes—
178C4×C107—21no—
179C4×C107—41no—
180C4×C107—41no—
181C4×C107—41no—
182C4×C107C2×#4111yescharacteristic
183C4×C107H(5,𝔽2)11yescharacteristic
184Dic107—21no—
185Dic107—21no—
186Dic107—41no—
187Dic107—41no—
188Dic107C2×SD1612yes—
189C2×C107—22no—
190C2×C107—81no—
191C2×C107#54611yescharacteristic
192C2×C107C22×SD1611yescharacteristic
193C2×C107#57611yescharacteristic
194D107—22no—
195D107—42no—
196D107—81no—
197#3295—1071nomaximal, Sylow
198C107#329511yescharacteristic, complemented, Sylow
199#554—1071no—
200D42—1071no—
201#486—1071no—
202#481—1071no—
203#481D10711yescharacteristic, complemented
204#476—1071no—
205#465—1071no—
206#465—1071no—
207#460—1071no—
208#450—1071no—
209#450—1071no—
210C4×SD16—1071no—
211C8×D4—1071no—
212C2×#102—1071no—
213C2×#102—1071no—
214C22×D4—1071no—
215C22×D4—1071no—
216C22×D4—2141no—
217C2×SD16—1071no—
218C2×SD16—1071no—
219C2×SD16—1071no—
220C22×C8—1071no—
221C22×C8—1071no—
222C4⋊Q8—1071no—
223#127—1071no—
224#125—2141no—
225C22⋊Q8—1071no—
226C22⋊Q8—1071no—
227C22⋊Q8—2141no—
228C22⋊Q8—2141no—
229#121—1071no—
230#121—2141no—
231#121C2×D10711yescharacteristic
232#120—2141no—
233#120—2141no—
234C4×Q8—1071no—
235C4×D4—1071no—
236C4×D4—1071no—
237C4×D4—2141no—
238C2×C4⋊C4—1071no—
239C2×C4⋊C4C2×D10711yescharacteristic, complemented
240#106—1071no—
241#106C2×D10711yescharacteristic, complemented
242#106C2×D10711yescharacteristic, complemented
243C4⋊C8—1071no—
244#103—1071no—
245#102—1071no—
246#102—1071no—
247#102—1071no—
248#102—1071no—
249#102—1071no—
250#102—1071no—
251#102—1071no—
252#102C2×D10711yescharacteristic, complemented
253#102C2×D10711yescharacteristic, complemented
254C22⋊C8—1071no—
255C22⋊C8C2×D10711yescharacteristic, complemented
256C4×C8—1071no—
257C24—2141no—
258C24—2141no—
259C2×Q8—1071no—
260C2×Q8—2141no—
261C2×D4—21no—
262C2×D4—1071no—
263C2×D4—1071no—
264C2×D4—1071no—
265C2×D4—4281no—
266C2×D4—4284no—
267C2×D4—4281no—
268C2×D4—2142no—
269C2×D4—2141no—
270C2×D4—2141no—
271C2×D4—2141no—
272C2×D4—2141no—
273C2×D4—2142no—
274C2×D4—2141no—
275C2×D4C22×D10711yescharacteristic
276C22×C4—21no—
277C22×C4—1071no—
278C22×C4—2141no—
279C22×C4—2141no—
280C22×C4C22×D10711yescharacteristic
281SD16—4281no—
282SD16—4281no—
283SD16—2142no—
284C2×C8—1071no—
285C2×C8—1071no—
286C2×C8—4281no—
287C2×C8—4281no—
288C2×C8C22×D10711yescharacteristic
289C2×C8C22×D10711yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—1071no—
292C4⋊C4—1071no—
293C4⋊C4—2141no—
294C4⋊C4—2141no—
295C4⋊C4—2141no—
296C4⋊C4—2141no—
297C4⋊C4—2141no—
298C4⋊C4C22×D10711yescharacteristic
299C4⋊C4C22×D10711yescharacteristic
300C4⋊C4C22×D10711yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—1071no—
303C22⋊C4—1071no—
304C22⋊C4—2141no—
305C22⋊C4—2141no—
306C22⋊C4—2141no—
307C22⋊C4—2141no—
308C42—1071no—
309C42—2141no—
310C23—21no—
311C23—8561no—
312C23—8561no—
313C23—1071no—
314C23—4282no—
315C23—4282no—
316C23—4282no—
317C23—4282no—
318C23—2141no—
319C23—2141no—
320C23D4×D10711yescharacteristic
321Q8—8561no—
322Q8—2141no—
323Q8—2141no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—8561no—
328D4—1074no—
329D4—1072no—
330D4—4282no—
331D4—4282no—
332D4—4282no—
333D4—4282no—
334D4—2141no—
335D4—2141no—
336D4—2141no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—81no—
343C2×C4—8561no—
344C2×C4—1071no—
345C2×C4—1071no—
346C2×C4—1071no—
347C2×C4—4282no—
348C2×C4—2141no—
349C2×C4—2141no—
350C2×C4—2141no—
351C2×C4—2141no—
352C2×C4D4×D10711yescharacteristic
353C2×C4C23×D10711yescharacteristic
354C8—21no—
355C8—21no—
356C8—2141no—
357C8—2141no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—8564no—
364C22—8564no—
365C22—1072no—
366C22—4281no—
367C22—4281no—
368C22—4281no—
369C22—4281no—
370C22—4281no—
371C22—2142no—
372C22—2141no—
373C22—2141no—
374C22SD16×D10712yes—
375C22C2×D4×D10711yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—1072no—
381C4—4281no—
382C4—4281no—
383C4—2141no—
384C4—2141no—
385C4#41×D10711yescharacteristic
386C4#1681215511yescharacteristic
387C2—22no—
388C2—81no—
389C2—8561no—
390C2—4282no—
391C2—2142no—
392C2#2029326911yescharacteristic
393C2C2×SD16×D10711yescharacteristic
394C2#2029343111yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#481×C107C2
socleC22×C107C22×D4
prime radical#20293261C2
hypercenter#481D107
hypocenterC107#3295
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #20293332C2semidirect
3. #20292972C2semidirect
4. #20292947C2semidirect
5. #20292916C2semidirect
6. #20292857C2semidirect
7. #20292854C2semidirect
8. #20292826C2semidirect
9. #20292780C2semidirect
10. #20292779C2semidirect
11. #20292714C2semidirect
12. (C22⋊D107)⋊C8C2semidirect
13. C2×#16812029C2semidirect
14. #102×D107C2semidirect
15. #481×C107C2semidirect
20. C2×#13133807C22semidirect
21. C2×#13133806C22semidirect
22. C22×C107⋊C8C22semidirect
23. C2×C8×D107C22semidirect
24. #16812108C22semidirect
27. #16812089C22semidirect
29. #16812088C22semidirect
35. #16812074C22semidirect
39. C4⋊C4×D107C22semidirect
40. #16812040C22semidirect
41. Dic107⋊C8C22semidirect
42. #16812032C22semidirect
44. #16812031C22semidirect
45. #16812030C22semidirect
48. #16812029C22semidirect
49. #16812029C22semidirect
50. (C2×D107)⋊C8C22semidirect
51. C8×Dic107C22semidirect
53. C2×C4⋊C4×C107C22semidirect
54. #106×C107C22semidirect
55. #106×C107C22semidirect
56. #102×C107C22semidirect
57. #102×C107C22semidirect
58. C22⋊C8×C107C22semidirect
137. C22⋊D107SD16semidirect
198. C107#3295semidirect
203. #481D107semidirect
239. C2×C4⋊C4C2×D107semidirect
241. #106C2×D107semidirect
242. #106C2×D107semidirect
252. #102C2×D107semidirect
253. #102C2×D107semidirect
255. C22⋊C8C2×D107semidirect

Maximal subgroups

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

subgroupindex
#202933322
#202932612
#202929722
#202929472
#202929162
#202928572
#202928542
#202928262
#202927802
#202927792
#202927142
(C22⋊D107)⋊C82
C2×#168120292
#102×D1072
#481×C1072
#3295107