Finite Group Databasebeta

← #541×D107 #28349823

Subgroups — #541×D107 #28349823

Order 13696.

1004 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293240C211yesmaximal, characteristic, complemented
2#20293239C211yesmaximal, characteristic, complemented
3#20293238C211yesmaximal, characteristic, complemented
4#20293237C212yesmaximal, complemented
5#20293236C214yesmaximal, complemented
6#20293235C212yesmaximal, complemented
7#20293234C214yesmaximal, complemented
8C4⋊Q8×D107C211yesmaximal, characteristic, complemented
9#126×D107C214yesmaximal
10#125×D107C214yesmaximal, complemented
11#125×D107C211yesmaximal, characteristic, complemented
12C22⋊Q8×D107C212yesmaximal
13C4×Q8×D107C212yesmaximal, complemented
14#117×D107C211yesmaximal, characteristic
15#541×C107C211yesmaximal, characteristic, complemented
16C2×Q8×D107C2212yes—
17C22×C4×D107C2211yescharacteristic
18#16812109C2211yescharacteristic, complemented
19#16812108C2214yescomplemented
20#16812107C2212yescomplemented
21#16812104C2214yes—
22#16812104C2214yes—
23#16812104C2214yes—
24#16812103C2214yes—
25#16812102C2214yes—
26#16812102C2214yes—
27#16812102C2214yes—
28#16812101C2214yescomplemented
29#16812101C2211yescharacteristic, complemented
30#16812100C2214yescomplemented
31#16812100C2212yescomplemented
32#16812100C2214yescomplemented
33#16812099C2214yescomplemented
34#16812099C2214yescomplemented
35#16812099C2214yescomplemented
36#16812099C2214yescomplemented
37#16812099C2214yescomplemented
38#16812089C2212yes—
39#16812088C2212yes—
40#16812087C2214yes—
41#16812086C2214yes—
42#16812085C2212yes—
43Q8×Dic107C2212yescomplemented
44C4×Dic214C2214yescomplemented
45C4×Dic214C2212yescomplemented
46#16812074C2214yescomplemented
47#16812074C2212yescomplemented
48#16812068C2211yescharacteristic
49#16812067C2212yes—
50#16812066C2211yescharacteristic
51#16812066C2211yescharacteristic
52#16812065C2212yes—
53C4⋊C4×D107C2214yes—
54C4⋊C4×D107C2212yes—
55C4⋊C4×D107C2214yes—
56C4⋊C4×D107C2212yes—
57C4⋊C4×D107C2214yes—
58C4⋊C4×D107C2214yes—
59C22⋊C4×D107C2214yes—
60C22⋊C4×D107C2212yes—
61C42×D107C2214yes—
62C42×D107C2211yescharacteristic
63C42×D107C2211yescharacteristic
64C4⋊Q8×C107C2211yescharacteristic, complemented
65#126×C107C2214yes—
66#125×C107C2214yescomplemented
67#125×C107C2211yescharacteristic, complemented
68C22⋊Q8×C107C2212yes—
69C4×Q8×C107C2212yescomplemented
70#117×C107C2211yescharacteristic
71C23×D107C2311yescharacteristic
72C2×Dic214C2314yes—
73C2×Dic214C2312yes—
74Q8×D107—28no—
75C22×Dic107C2311yescharacteristic
76C2×C4×D107—24no—
77C2×C4×D107C2312yes—
78C2×C4×D107C2314yes—
79C2×C4×D107C2312yes—
80C2×C4×D107C2314yes—
81C2×C4×D107C2311yescharacteristic
82C2×C4×D107C2311yescharacteristic
83C2×C4×D107C2311yescharacteristic
84C2×C4×D107C2311yescharacteristic
85C4⋊Dic107C2312yes—
86C4⋊Dic107C2312yes—
87C4⋊Dic107C2314yes—
88C4⋊Dic107C2314yes—
89C4⋊Dic107C2314yes—
90C4⋊Dic107C2314yes—
91Dic107⋊C4C2312yes—
92Dic107⋊C4C2312yes—
93Dic107⋊C4C2314yes—
94Dic107⋊C4C2314yes—
95Dic107⋊C4C2314yes—
96Dic107⋊C4C2314yes—
97Dic107⋊C4C2314yes—
98Dic107⋊C4C2314yes—
99Dic107⋊C4C2314yes—
100Dic107⋊C4C2314yes—
101Dic107⋊C4C2314yes—
102C22⋊Dic107C2312yes—
103C22⋊Dic107C2314yes—
104(C2×D107)⋊C4C2312yes—
105(C2×D107)⋊C4C2312yes—
106(C2×D107)⋊C4C2314yes—
107(C2×D107)⋊C4C2314yes—
108C4×Dic107C2312yes—
109C4×Dic107C2312yes—
110C4×Dic107C2311yescharacteristic
111C4×Dic107C2311yescharacteristic
112C4×Dic107C2314yes—
113C4×Dic107C2314yes—
114C4×Dic107C2314yes—
115C2×Q8×C107C2312yes—
116C22×C4×C107C2311yescharacteristic
117C4⋊C4×C107C2312yes—
118C4⋊C4×C107C2312yes—
119C4⋊C4×C107C2314yes—
120C4⋊C4×C107C2314yes—
121C4⋊C4×C107C2314yes—
122C4⋊C4×C107C2314yes—
123C22⋊C4×C107C2312yes—
124C22⋊C4×C107C2314yes—
125C42×C107C2311yescharacteristic
126C42×C107C2311yescharacteristic
127C42×C107C2314yes—
128C23×C107C2411yescharacteristic
129C22×D107—22no—
130C22×D107—24no—
131C22×D107C2411yescharacteristic
132C22×D107C2411yescharacteristic
133Q8×C107—24no—
134C2×C4×C107—22no—
135C2×C4×C107C2412yes—
136C2×C4×C107C2412yes—
137C2×C4×C107C2414yes—
138C2×C4×C107C2414yes—
139C2×C4×C107C2411yescharacteristic
140C2×C4×C107C2411yescharacteristic
141C2×Dic107—22no—
142C2×Dic107C2412yes—
143C2×Dic107C2412yes—
144C2×Dic107C2414yes—
145C2×Dic107C2414yes—
146C2×Dic107C2411yescharacteristic
147C2×Dic107C2411yescharacteristic
148C4×D107—22no—
149C4×D107—28no—
150C4×D107—24no—
151C4×D107—28no—
152C4×D107—24no—
153C4×D107—22no—
154C4×D107—22no—
155C4×D107#4114yes—
156Dic214—24no—
157Dic214—28no—
158C22×C107—21no—
159C22×C107—22no—
160C22×C107C2511yescharacteristic
161C2×D107—21no—
162C2×D107—22no—
163C2×D107—44no—
164C2×D107C2×#4112yes—
165C2×D1072−1+414yes—
166C4×C107—24no—
167C4×C107—21no—
168C4×C107—22no—
169C4×C107—22no—
170C4×C107—24no—
171C4×C107C2×#4112yes—
172Dic107—24no—
173Dic107—21no—
174Dic107—22no—
175Dic107—22no—
176Dic107—24no—
177Dic107C2×#4112yes—
178C2×C107—41no—
179C2×C107C22×#4111yescharacteristic
180C2×C107C2×2−1+412yes—
181D107—41no—
182D107#54114yesdirect product factor
183C2×#541—1071nomaximal, Sylow
184C107C2×#54111yescharacteristic, complemented, Sylow
185#541—1071no—
186#541—1074no—
187#541—1074no—
188#541—1071no—
189#541—1072no—
190#541—1072no—
191#541—1071no—
192#541D10711yescharacteristic, direct product factor
193C2×C4⋊Q8—1071no—
194C2×#126—1074no—
195C2×#125—1071no—
196C2×#125—1074no—
197C2×C22⋊Q8—1072no—
198C2×C4×Q8—1072no—
199C2×#117—1071no—
200C22×Q8—1072no—
201C23×C4—1071no—
202C4⋊Q8—1072no—
203C4⋊Q8—1074no—
204C4⋊Q8—1071no—
205C4⋊Q8C2×D10711yescharacteristic, complemented
206#126—1074no—
207#126—1074no—
208#126—1074no—
209#126—1074no—
210#126—1074no—
211#126—1074no—
212#126—1074no—
213#126C2×D10714yes—
214#125—1074no—
215#125—1074no—
216#125—1074no—
217#125—1074no—
218#125—1074no—
219#125—1072no—
220#125—1074no—
221#125—1074no—
222#125—1071no—
223#125—1074no—
224#125C2×D10711yescharacteristic, complemented
225#125C2×D10714yescomplemented
226C22⋊Q8—1072no—
227C22⋊Q8—1072no—
228C22⋊Q8—1074no—
229C22⋊Q8—1072no—
230C22⋊Q8—1074no—
231C22⋊Q8C2×D10712yes—
232C4×Q8—1072no—
233C4×Q8—1074no—
234C4×Q8—1072no—
235C4×Q8—1074no—
236C4×Q8—1072no—
237C4×Q8C2×D10712yescomplemented
238#117—1071no—
239#117—1072no—
240#117—1072no—
241#117—1071no—
242#117—1071no—
243#117C2×D10711yescharacteristic
244C2×C4⋊C4—1072no—
245C2×C4⋊C4—1072no—
246C2×C4⋊C4—1074no—
247C2×C4⋊C4—1074no—
248C2×C4⋊C4—1074no—
249C2×C4⋊C4—1074no—
250C2×C22⋊C4—1072no—
251C2×C22⋊C4—1074no—
252C2×C42—1071no—
253C2×C42—1071no—
254C2×C42—1074no—
255C24—1071no—
256C2×Q8—1074no—
257C2×Q8—1072no—
258C2×Q8—2148no—
259C2×Q8C22×D10712yes—
260C22×C4—1071no—
261C22×C4—1071no—
262C22×C4—1072no—
263C22×C4—1072no—
264C22×C4—1074no—
265C22×C4—1074no—
266C22×C4—1071no—
267C22×C4—1071no—
268C22×C4—1071no—
269C22×C4—2144no—
270C22×C4C22×D10711yescharacteristic
271C4⋊C4—1072no—
272C4⋊C4—1072no—
273C4⋊C4—1072no—
274C4⋊C4—1074no—
275C4⋊C4—1072no—
276C4⋊C4—1074no—
277C4⋊C4—1074no—
278C4⋊C4—1074no—
279C4⋊C4—1074no—
280C4⋊C4—1074no—
281C4⋊C4—1074no—
282C4⋊C4—1074no—
283C4⋊C4—1074no—
284C4⋊C4—1074no—
285C4⋊C4—1074no—
286C4⋊C4—1074no—
287C4⋊C4—1074no—
288C4⋊C4C22×D10712yes—
289C4⋊C4C22×D10712yes—
290C4⋊C4C22×D10714yes—
291C4⋊C4C22×D10714yes—
292C4⋊C4C22×D10714yes—
293C4⋊C4C22×D10714yes—
294C22⋊C4—1072no—
295C22⋊C4—1074no—
296C22⋊C4—1072no—
297C22⋊C4—1072no—
298C22⋊C4—1074no—
299C22⋊C4—1074no—
300C22⋊C4C22×D10712yes—
301C22⋊C4C22×D10714yes—
302C42—1072no—
303C42—1071no—
304C42—1072no—
305C42—1071no—
306C42—1074no—
307C42—1074no—
308C42—1074no—
309C42C22×D10711yescharacteristic
310C42C22×D10711yescharacteristic
311C42C22×D10714yes—
312C23—1071no—
313C23—1071no—
314C23—2142no—
315C23—2144no—
316C23C23×D10711yescharacteristic
317Q8—24no—
318Q8—2148no—
319Q8—2144no—
320C2×C4—22no—
321C2×C4—1071no—
322C2×C4—1074no—
323C2×C4—1072no—
324C2×C4—1072no—
325C2×C4—1074no—
326C2×C4—1074no—
327C2×C4—1071no—
328C2×C4—2142no—
329C2×C4—2142no—
330C2×C4—2148no—
331C2×C4—2144no—
332C2×C4—2144no—
333C2×C4—2148no—
334C2×C4—2142no—
335C2×C4—2142no—
336C2×C4C23×D10712yes—
337C2×C4C23×D10712yes—
338C2×C4C23×D10714yes—
339C2×C4C23×D10714yes—
340C2×C4C23×D10711yescharacteristic
341C2×C4C23×D10711yescharacteristic
342C22—21no—
343C22—22no—
344C22—1072no—
345C22—1074no—
346C22—4284no—
347C22—2141no—
348C22—2142no—
349C22C24×D10711yescharacteristic
350C4—21no—
351C4—24no—
352C4—22no—
353C4—22no—
354C4—24no—
355C4—1072no—
356C4—2141no—
357C4—2144no—
358C4—2142no—
359C4—2142no—
360C4—2144no—
361C4#41×D10712yes—
362C2—41no—
363C2—1074no—
364C2—4281no—
365C2C2×#41×D10711yescharacteristic
366C22−1+4×D10712yes—
subgroupG/H
center, FrattiniC22C24×D107
commutator, socle, cosocleC22×C107C25
Fitting#541×C107C2
prime radicalC23×D107C23
hypercenter#541D107
hypocenterC107C2×#541
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ #541

Complements

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

NH ≅ G/Ntype
1. #20293240C2semidirect
2. #20293239C2semidirect
3. #20293238C2semidirect
4. #20293237C2semidirect
5. #20293236C2semidirect
6. #20293235C2semidirect
7. #20293234C2semidirect
8. C4⋊Q8×D107C2semidirect
10. #125×D107C2semidirect
11. #125×D107C2semidirect
13. C4×Q8×D107C2semidirect
15. #541×C107C2semidirect
18. #16812109C22semidirect
19. #16812108C22semidirect
20. #16812107C22semidirect
28. #16812101C22semidirect
29. #16812101C22semidirect
30. #16812100C22semidirect
31. #16812100C22semidirect
32. #16812100C22semidirect
33. #16812099C22semidirect
34. #16812099C22semidirect
35. #16812099C22semidirect
36. #16812099C22semidirect
37. #16812099C22semidirect
43. Q8×Dic107C22semidirect
44. C4×Dic214C22semidirect
45. C4×Dic214C22semidirect
46. #16812074C22semidirect
47. #16812074C22semidirect
64. C4⋊Q8×C107C22semidirect
66. #125×C107C22semidirect
67. #125×C107C22semidirect
69. C4×Q8×C107C22semidirect
182. D107#541direct (N × H)
184. C107C2×#541semidirect
192. #541D107direct (N × H)
205. C4⋊Q8C2×D107semidirect
224. #125C2×D107semidirect
225. #125C2×D107semidirect
237. C4×Q8C2×D107semidirect

Maximal subgroups

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

subgroupindex
#202932402
#202932392
#202932382
#202932372
#202932362
#202932352
#202932342
C4⋊Q8×D1072
#126×D1072
#125×D1072
C22⋊Q8×D1072
C4×Q8×D1072
#117×D1072
#541×C1072
C2×#541107