Finite Group Databasebeta

← #28345486

Subgroups — #28345486

Order 13696.

456 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×D107C211yesmaximal, characteristic
2#20292701C211yesmaximal, characteristic, complemented
3#20292700C211yesmaximal, characteristic, complemented
4#20292699C211yesmaximal, characteristic, complemented
5#20292698C211yesmaximal, characteristic, complemented
6#20292697C211yesmaximal, characteristic, complemented
7#20292696C211yesmaximal, characteristic, complemented
8#20292695C211yesmaximal, characteristic, complemented
9#20292683C211yesmaximal, characteristic, complemented
10#20292682C211yesmaximal, characteristic, complemented
11#20292590C211yesmaximal, characteristic, complemented
12#20292589C211yesmaximal, characteristic, complemented
13C2×(C2×D107)⋊C8C211yesmaximal, characteristic, complemented
14C22⋊C8×D107C211yesmaximal, characteristic, complemented
15#435×C107C211yesmaximal, characteristic, complemented
16C2×D4×D107C411yescharacteristic
17C22×C4×D107C2211yescharacteristic
18C22×C4×D107C2211yescharacteristic
19C2×#13133802C2211yescharacteristic, complemented
20C2×#13133801C2211yescharacteristic, complemented
21C2×#13133801C2211yescharacteristic, complemented
22C22×C107⋊C8C2211yescharacteristic, complemented
23C2×C8×D107C2211yescharacteristic, complemented
24C2×C8×D107C2211yescharacteristic, complemented
25C4×D428C2211yescharacteristic
26D4×Dic107C411yescharacteristic
27#16812071C411yescharacteristic
28C4×C22⋊D107C2211yescharacteristic
29C4×C22⋊D107C2211yescharacteristic
30(C22⋊D107)⋊C4C411yescharacteristic
31(C22⋊D107)⋊C4C411yescharacteristic
32C4⋊C4×D107C411yescharacteristic
33C22⋊C4×D107C411yescharacteristic
34C22⋊C4×D107C411yescharacteristic
35C42×D107C2211yescharacteristic
36C4⋊(C107⋊C8)C2211yescharacteristic, complemented
37Dic107⋊C8C2211yescharacteristic, complemented
38Dic107⋊C8C2211yescharacteristic, complemented
39C22⋊(C107⋊C8)C2211yescharacteristic, complemented
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, complemented
46(C2×D107)⋊C8C2211yescharacteristic, complemented
47(C2×D107)⋊C8C2211yescharacteristic, complemented
48(C2×D107)⋊C8C2211yescharacteristic, complemented
49#16812020C2211yescharacteristic, complemented
50#16812019C2211yescharacteristic, complemented
51#16812019C2211yescharacteristic, complemented
52C2×M16×C107C2211yescharacteristic, complemented
53C22×C8×C107C2211yescharacteristic, complemented
54C4×D4×C107C2211yescharacteristic
55C4⋊C8×C107C2211yescharacteristic, complemented
56C22⋊C8×C107C2211yescharacteristic, complemented
57C22⋊C8×C107C2211yescharacteristic, complemented
58#97×C107C2211yescharacteristic, complemented
59C23×D107C2×C411yescharacteristic
60C23×D107C2×C411yescharacteristic
61C2×D428C2×C411yescharacteristic
62C2×C22⋊D107C2×C411yescharacteristic
63C2×C22⋊D107C2×C411yescharacteristic
64D4×D107—24no—
65C22×Dic107C2×C411yescharacteristic
66C22×Dic107C2×C411yescharacteristic
67C2×C4×D107—41no—
68C2×C4×D107—41no—
69C2×C4×D107—41no—
70C2×C4×D107—41no—
71C2×C4×D107C2×C411yescharacteristic
72C2×C4×D107C2×C411yescharacteristic
73C2×C4×D107C2×C411yescharacteristic
74C2×C4×D107C2×C411yescharacteristic
75C2×C4×D107C2×C411yescharacteristic
76C2×C4×D107C2×C411yescharacteristic
77C2×C4×D107C2311yescharacteristic
78C2×C4×D107C2311yescharacteristic
79C2×C4×D107C2311yescharacteristic
80#13133802—41no—
81#13133801—41no—
82#13133801—41no—
83C2×C107⋊C8—41no—
84C2×C107⋊C8C2311yescharacteristic
85C2×C107⋊C8C2311yescharacteristic
86C2×C107⋊C8C2311yescharacteristic
87C2×C107⋊C8C2311yescharacteristic
88C8×D107—41no—
89C8×D107—41no—
90C4⋊Dic107C2×C411yescharacteristic
91Dic107⋊C4C2×C411yescharacteristic
92Dic107⋊C4C2×C411yescharacteristic
93C22⋊Dic107C2×C411yescharacteristic
94C22⋊Dic107C2×C411yescharacteristic
95(C2×D107)⋊C4C2×C411yescharacteristic
96(C2×D107)⋊C4C2×C411yescharacteristic
97(C2×D107)⋊C4C2×C411yescharacteristic
98(C2×D107)⋊C4C2×C411yescharacteristic
99C4×Dic107C2×C411yescharacteristic
100C4×Dic107C2×C411yescharacteristic
101C4×Dic107C2311yescharacteristic
102C2×D4×C107C2×C411yescharacteristic
103C22×C4×C107C2311yescharacteristic
104C22×C4×C107C2311yescharacteristic
105M16×C107—41no—
106C2×C8×C107—41no—
107C2×C8×C107C2311yescharacteristic
108C2×C8×C107C2311yescharacteristic
109C2×C8×C107C2311yescharacteristic
110C2×C8×C107C2311yescharacteristic
111C4⋊C4×C107C2×C411yescharacteristic
112C22⋊C4×C107C2×C411yescharacteristic
113C22⋊C4×C107C2×C411yescharacteristic
114C42×C107C2311yescharacteristic
115C23×C107C22×C411yescharacteristic
116C23×C107C22×C411yescharacteristic
117C22×D107—22no—
118C22×D107—41no—
119C22×D107—41no—
120C22×D107—41no—
121C22×D107—41no—
122C22×D107M1614yescomplemented
123C22×D107C22×C411yescharacteristic
124C22×D107C22×C411yescharacteristic
125C22×D107C22×C411yescharacteristic
126D4×C107—22no—
127C2×C4×C107—21no—
128C2×C4×C107—21no—
129C2×C4×C107—21no—
130C2×C4×C107—21no—
131C2×C4×C107C22×C411yescharacteristic
132C2×C4×C107C22×C411yescharacteristic
133C2×C4×C107C22×C411yescharacteristic
134C2×C4×C107C22×C411yescharacteristic
135C2×C4×C107C2411yescharacteristic
136C22⋊D107—22no—
137C22⋊D107—22no—
138C2×Dic107—41no—
139C2×Dic107—41no—
140C2×Dic107C22×C411yescharacteristic
141C2×Dic107C22×C411yescharacteristic
142C2×Dic107C22×C411yescharacteristic
143C2×Dic107C22×C411yescharacteristic
144C2×Dic107C22×C411yescharacteristic
145D428—22no—
146C4×D107—22no—
147C4×D107—21no—
148C4×D107—21no—
149C4×D107—21no—
150C4×D107—21no—
151C4×D107—21no—
152C4×D107—21no—
153C4×D107—41no—
154C4×D107—41no—
155C4×D107—41no—
156C4×D107—41no—
157C4×D107—41no—
158C8×C107—21no—
159C8×C107—21no—
160C8×C107—21no—
161C8×C107—21no—
162C107⋊C8—21no—
163C107⋊C8—21no—
164C107⋊C8—21no—
165C107⋊C8—21no—
166C22×C107—21no—
167C22×C107—21no—
168C22×C107—21no—
169C22×C107—21no—
170C22×C107—21no—
171C22×C107C2×M1612yes—
172C22×C107C23×C411yescharacteristic
173C2×D107—21no—
174C2×D107—21no—
175C2×D107—21no—
176C2×D107—21no—
177C2×D107—21no—
178C2×D107—21no—
179C2×D107—21no—
180C2×D107—44no—
181C2×D107—44no—
182C2×D107C2×M1612yes—
183C2×D107C2×M1612yes—
184C4×C107—21no—
185C4×C107—21no—
186C4×C107—21no—
187C4×C107—21no—
188C4×C107H(5,𝔽2)11yescharacteristic
189C4×C107H(5,𝔽2)11yescharacteristic
190Dic107—21no—
191Dic107—21no—
192Dic107—21no—
193Dic107—21no—
194Dic107—21no—
195C2×C107—22no—
196C2×C107—41no—
197C2×C107#51811yescharacteristic
198C2×C107C22×M1611yescharacteristic
199C2×C107#56811yescharacteristic
200D107—22no—
201D107—22no—
202D107—41no—
203#2973—1071nomaximal, Sylow
204C107#297311yescharacteristic, complemented, Sylow
205C2×C4×D4—1071no—
206#435—1071no—
207#435—1071no—
208#435—1071no—
209#435—1071no—
210#435—1071no—
211#435—1071no—
212#435—1071no—
213#435D10711yescharacteristic, complemented
214#432—1071no—
215#432—1071no—
216#407—1071no—
217#407—1071no—
218C2×C22⋊C8—1071no—
219C2×C22⋊C8—1071no—
220C22×D4—1071no—
221C23×C4—1071no—
222C23×C4—1071no—
223C2×M16—1071no—
224C2×M16—1071no—
225C2×M16—1071no—
226C2×M16C2×D10711yescharacteristic, complemented
227C22×C8—1071no—
228C22×C8—1071no—
229C22×C8—1071no—
230C22×C8C2×D10711yescharacteristic, complemented
231C4×D4—1071no—
232C4×D4—1071no—
233C4×D4—1071no—
234C4×D4—1071no—
235C4×D4—1071no—
236C4×D4—1071no—
237C4×D4—1071no—
238C4×D4C2×D10711yescharacteristic
239C2×C4⋊C4—1071no—
240C2×C22⋊C4—1071no—
241C2×C22⋊C4—1071no—
242C2×C42—1071no—
243C4⋊C8—1071no—
244C4⋊C8—1071no—
245C4⋊C8—1071no—
246C4⋊C8C2×D10711yescharacteristic, complemented
247C22⋊C8—1071no—
248C22⋊C8—1071no—
249C22⋊C8—1071no—
250C22⋊C8—1071no—
251C22⋊C8—1071no—
252C22⋊C8—1071no—
253C22⋊C8—1071no—
254C22⋊C8—1071no—
255C22⋊C8—1071no—
256C22⋊C8—1071no—
257C22⋊C8C2×D10711yescharacteristic, complemented
258C22⋊C8C2×D10711yescharacteristic, complemented
259#97—1071no—
260#97—1071no—
261#97—1071no—
262#97C2×D10711yescharacteristic, complemented
263C24—1071no—
264C24—1071no—
265C2×D4—1071no—
266C2×D4—1071no—
267C2×D4—1071no—
268C2×D4—2144no—
269C2×D4C4×D10711yescharacteristic
270C22×C4—1071no—
271C22×C4—1071no—
272C22×C4—1071no—
273C22×C4—1071no—
274C22×C4—1071no—
275C22×C4—1071no—
276C22×C4—1071no—
277C22×C4—1071no—
278C22×C4—1071no—
279C22×C4—1071no—
280C22×C4—1071no—
281C22×C4—4281no—
282C22×C4—4281no—
283C22×C4—4281no—
284C22×C4—4281no—
285C22×C4C22×D10711yescharacteristic
286C22×C4C22×D10711yescharacteristic
287M16—41no—
288M16—4281no—
289M16—4281no—
290M16—4281no—
291C2×C8—41no—
292C2×C8—1071no—
293C2×C8—1071no—
294C2×C8—1071no—
295C2×C8—1071no—
296C2×C8—4281no—
297C2×C8—4281no—
298C2×C8—4281no—
299C2×C8C22×D10711yescharacteristic
300C2×C8C22×D10711yescharacteristic
301C2×C8C22×D10711yescharacteristic
302C2×C8C22×D10711yescharacteristic
303C4⋊C4—1071no—
304C4⋊C4—1071no—
305C4⋊C4—1071no—
306C4⋊C4C4×D10711yescharacteristic
307C22⋊C4—1071no—
308C22⋊C4—1071no—
309C22⋊C4—1071no—
310C22⋊C4—1071no—
311C22⋊C4—1071no—
312C22⋊C4—1071no—
313C22⋊C4C4×D10711yescharacteristic
314C22⋊C4C4×D10711yescharacteristic
315C42—1071no—
316C42—1071no—
317C42—1071no—
318C42C22×D10711yescharacteristic
319C23—1074no—
320C23—1071no—
321C23—1071no—
322C23—1071no—
323C23—4281no—
324C23—4281no—
325C23—4281no—
326C23—4281no—
327C23—2142no—
328C23C2×C4×D10711yescharacteristic
329C23C2×C4×D10711yescharacteristic
330D4—22no—
331D4—2142no—
332D4—2142no—
333D4—2142no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—1071no—
339C2×C4—1071no—
340C2×C4—1071no—
341C2×C4—1071no—
342C2×C4—1071no—
343C2×C4—4281no—
344C2×C4—4281no—
345C2×C4—4281no—
346C2×C4—4281no—
347C2×C4—4281no—
348C2×C4—4281no—
349C2×C4—4281no—
350C2×C4—2142no—
351C2×C4—2141no—
352C2×C4—2141no—
353C2×C4—2141no—
354C2×C4—2141no—
355C2×C4—2141no—
356C2×C4—2141no—
357C2×C4C2×C4×D10711yescharacteristic
358C2×C4C2×C4×D10711yescharacteristic
359C2×C4C2×C4×D10711yescharacteristic
360C2×C4C2×C4×D10711yescharacteristic
361C2×C4C23×D10711yescharacteristic
362C8—21no—
363C8—21no—
364C8—21no—
365C8—21no—
366C8—2141no—
367C8—2141no—
368C8—2141no—
369C8—2141no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—1072no—
376C22—1072no—
377C22—4284no—
378C22—4284no—
379C22—2141no—
380C22—2141no—
381C22—2141no—
382C22—2141no—
383C22—2141no—
384C22—2141no—
385C22—2141no—
386C22M16×D10712yes—
387C22C22×C4×D10711yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—2141no—
393C4—2141no—
394C4—2141no—
395C4—2141no—
396C4—2141no—
397C4#1681215411yescharacteristic
398C4#1681215511yescharacteristic
399C2—22no—
400C2—41no—
401C2—4281no—
402C2—2142no—
403C2—2142no—
404C2#2029309911yescharacteristic
405C2C2×M16×D10711yescharacteristic
406C2#2029339211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D107
commutator, socleC22×C107C23×C4
Fitting#435×C107C2
prime radicalC2×D4×D107C4
cosocleC2×C4×C107C24
hypercenter#435D107
hypocenterC107#2973
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #20292701C2semidirect
3. #20292700C2semidirect
4. #20292699C2semidirect
5. #20292698C2semidirect
6. #20292697C2semidirect
7. #20292696C2semidirect
8. #20292695C2semidirect
9. #20292683C2semidirect
10. #20292682C2semidirect
11. #20292590C2semidirect
12. #20292589C2semidirect
13. C2×(C2×D107)⋊C8C2semidirect
14. C22⋊C8×D107C2semidirect
15. #435×C107C2semidirect
19. C2×#13133802C22semidirect
20. C2×#13133801C22semidirect
21. C2×#13133801C22semidirect
22. C22×C107⋊C8C22semidirect
23. C2×C8×D107C22semidirect
24. C2×C8×D107C22semidirect
36. C4⋊(C107⋊C8)C22semidirect
37. Dic107⋊C8C22semidirect
38. Dic107⋊C8C22semidirect
39. C22⋊(C107⋊C8)C22semidirect
40. C22⋊(C107⋊C8)C22semidirect
45. (C2×D107)⋊C8C22semidirect
46. (C2×D107)⋊C8C22semidirect
47. (C2×D107)⋊C8C22semidirect
48. (C2×D107)⋊C8C22semidirect
49. #16812020C22semidirect
50. #16812019C22semidirect
51. #16812019C22semidirect
52. C2×M16×C107C22semidirect
53. C22×C8×C107C22semidirect
55. C4⋊C8×C107C22semidirect
56. C22⋊C8×C107C22semidirect
57. C22⋊C8×C107C22semidirect
58. #97×C107C22semidirect
122. C22×D107M16semidirect
204. C107#2973semidirect
213. #435D107semidirect
226. C2×M16C2×D107semidirect
230. C22×C8C2×D107semidirect
246. C4⋊C8C2×D107semidirect
257. C22⋊C8C2×D107semidirect
258. C22⋊C8C2×D107semidirect
262. #97C2×D107semidirect

Maximal subgroups

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

subgroupindex
C4×D4×D1072
#202927012
#202927002
#202926992
#202926982
#202926972
#202926962
#202926952
#202926832
#202926822
#202925902
#202925892
C2×(C2×D107)⋊C82
C22⋊C8×D1072
#435×C1072
#2973107