Finite Group Databasebeta

← #41×C22⋊D107 #28349946

Subgroups — #41×C22⋊D107 #28349946

Order 13696.

1648 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D107C211yesmaximal, characteristic, complemented
2#20293296C211yesmaximal, characteristic, complemented
3Q8×C22⋊D107C211yesmaximal, characteristic, complemented
4#20293288C211yesmaximal, characteristic, complemented
5#20293284C211yesmaximal, characteristic, complemented
6#20293276C213yesmaximal, complemented
7#20293271C213yesmaximal, complemented
8#20293265C213yesmaximal, complemented
9D4×C22⋊D107C213yesmaximal, complemented
10#20293173C213yesmaximal, complemented
11#20293138C213yesmaximal, complemented
12#20293134C213yesmaximal, complemented
13#41×Dic107C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊D107C213yesmaximal, complemented
15C22×#41×C107C211yesmaximal, characteristic, complemented
16C2×#13133819C2211yescharacteristic, complemented
17C2×#13133818C2213yescomplemented
18C2×#13133817C2213yescomplemented
19#41×D107—28no—
20C2×Q8×D107C2211yescharacteristic, complemented
21C22×C22⋊D107C2213yes—
22C2×D4×D107C2213yescomplemented
23C22×C4×D107C2213yescomplemented
24#16812107C2213yescomplemented
25#16812105C2213yescomplemented
26#16812098C2213yescomplemented
27#16812096C2213yescomplemented
28#16812092C2216yescomplemented
29#16812090C2216yescomplemented
30#16812088C2213yescomplemented
31#16812088C2213yescomplemented
32#16812085C2213yescomplemented
33#16812085C2213yescomplemented
34#16812083C2213yescomplemented
35#16812083C2213yescomplemented
36#16812081C2216yescomplemented
37#16812081C2216yescomplemented
38#16812080C2213yescomplemented
39#16812080C2213yescomplemented
40#16812078C2216yescomplemented
41#16812077C2216yescomplemented
42Q8×Dic107C2211yescharacteristic, complemented
43Q8×Dic107C2211yescharacteristic, complemented
44D4×Dic107C2213yescomplemented
45D4×Dic107C2213yescomplemented
46C4×C22⋊D107C2213yes—
47C4×C22⋊D107C2211yescharacteristic
48C4×C22⋊D107C2213yescomplemented
49C4×C22⋊D107C2216yescomplemented
50C4×C22⋊D107C2213yescomplemented
51C4×C22⋊D107C2213yescomplemented
52C4×C22⋊D107C2213yescomplemented
53C4×C22⋊D107C2213yescomplemented
54C4×C22⋊D107C2213yescomplemented
55#16812068C2213yescomplemented
56C2×Dic107⋊C4C2213yescomplemented
57C2×C22⋊Dic107C2213yescomplemented
58C2×(C2×D107)⋊C4C2213yescomplemented
59C2×C4×Dic107C2213yescomplemented
60C2×#41×C107—28no—
61C2×#41×C107C2211yescharacteristic
62C2×#41×C107C2213yescomplemented
63C2×#41×C107C2213yescomplemented
64C2×#41×C107C2211yescharacteristic, complemented
65C22×Q8×C107C2211yescharacteristic, complemented
66C22×D4×C107C2213yescomplemented
67C23×C4×C107C2213yescomplemented
68C23×D107C2313yes—
69#13133819—24no—
70#13133818—212no—
71#13133817—212no—
72C2×Dic214C2313yes—
73Q8×D107—24no—
74C2×D428C2313yes—
75C2×C22⋊D107—212no—
76C2×C22⋊D107C2313yes—
77C2×C22⋊D107C2313yes—
78C2×C22⋊D107C2313yes—
79C2×C22⋊D107C2316yes—
80C2×C22⋊D107C2316yes—
81C2×C22⋊D107C2311yescharacteristic
82D4×D107—212no—
83C22×Dic107C2313yes—
84C22×Dic107C2313yes—
85C22×Dic107C2313yes—
86C2×C4×D107—212no—
87C2×C4×D107C2311yescharacteristic
88C2×C4×D107C2313yes—
89C2×C4×D107C2313yes—
90C2×C4×D107C2313yes—
91C4⋊Dic107C2313yes—
92C4⋊Dic107C2313yes—
93Dic107⋊C4C2311yescharacteristic
94Dic107⋊C4C2313yes—
95Dic107⋊C4C2313yes—
96Dic107⋊C4C2313yes—
97Dic107⋊C4C2316yes—
98C22⋊Dic107C2311yescharacteristic
99C22⋊Dic107C2313yes—
100C22⋊Dic107C2313yes—
101C22⋊Dic107C2313yes—
102C22⋊Dic107C2316yes—
103C22⋊Dic107C2316yes—
104(C2×D107)⋊C4C2311yescharacteristic
105(C2×D107)⋊C4C2313yes—
106(C2×D107)⋊C4C2313yes—
107(C2×D107)⋊C4C2313yes—
108(C2×D107)⋊C4C2316yes—
109C4×Dic107C2311yescharacteristic
110C4×Dic107C2313yes—
111C4×Dic107C2313yes—
112C4×Dic107C2313yes—
113C24×C107C2313yes—
114#41×C107—24no—
115#41×C107—212no—
116#41×C107—212no—
117#41×C107D418yescomplemented
118C2×Q8×C107—24no—
119C2×Q8×C107C2313yes—
120C2×Q8×C107C2311yescharacteristic
121C2×D4×C107—212no—
122C2×D4×C107C2316yes—
123C2×D4×C107C2313yes—
124C2×D4×C107C2313yes—
125C22×C4×C107—212no—
126C22×C4×C107C2313yes—
127C22×C4×C107C2311yescharacteristic
128C22×C4×C107C2313yes—
129C22×C4×C107C2313yes—
130C22×C4×C107C2313yes—
131C22×C4×C107C2313yes—
132C23×C107—26no—
133C23×C107—26no—
134C23×C107—43no—
135C23×C107C2413yes—
136C23×C107C2413yes—
137C23×C107C2411yescharacteristic
138C22×D107—26no—
139C22×D107—26no—
140C22×D107—43no—
141C22×D107C2413yes—
142C22×D107C2411yescharacteristic
143Q8×C107—26no—
144Q8×C107C2×D414yescomplemented
145D4×C107—212no—
146D4×C107—26no—
147D4×C107C2×D4112yescomplemented
148C2×C4×C107—26no—
149C2×C4×C107—22no—
150C2×C4×C107—26no—
151C2×C4×C107—26no—
152C2×C4×C107—26no—
153C2×C4×C107C2×D4112yescomplemented
154C2×C4×C107C2411yescharacteristic
155C2×C4×C107C2413yes—
156C2×C4×C107C2413yes—
157C2×C4×C107C2411yescharacteristic
158C22⋊D107—212no—
159C22⋊D107—26no—
160C22⋊D107—26no—
161C22⋊D107—26no—
162C22⋊D107—46no—
163C22⋊D107#4114yesdirect product factor
164C2×Dic107—26no—
165C2×Dic107—26no—
166C2×Dic107—43no—
167C2×Dic107C2411yescharacteristic
168C2×Dic107C2413yes—
169C2×Dic107C2413yes—
170C2×Dic107C2411yescharacteristic
171C2×Dic107C2413yes—
172C2×Dic107C2411yescharacteristic
173D428—26no—
174C4×D107—22no—
175C4×D107—26no—
176C4×D107—26no—
177C4×D107—26no—
178Dic214—26no—
179C22×C107—21no—
180C22×C107—23no—
181C22×C107—23no—
182C22×C107—21no—
183C22×C107—23no—
184C22×C107—23no—
185C22×C107—23no—
186C22×C107—412no—
187C22×C107C22×D416yes—
188C22×C107C2×#4112yescomplemented
189C22×C107C2511yescharacteristic
190C2×D107—21no—
191C2×D107—21no—
192C2×D107—23no—
193C2×D107—23no—
194C2×D107—23no—
195C2×D107—412no—
196C2×D107C2×#4112yescomplemented
197C4×C107—21no—
198C4×C107—23no—
199C4×C107C22×D416yes—
200C4×C107C22×D412yes—
201Dic107—23no—
202Dic107—21no—
203Dic107—23no—
204Dic107—21no—
205Dic107—23no—
206Dic107C2×#4112yescomplemented
207C2×C107—26no—
208C2×C107—22no—
209C2×C107—43no—
210C2×C107C23×D411yescharacteristic
211C2×C107C22×#4111yescharacteristic
212C2×C107#58511yescharacteristic
213D107—22no—
214D107—43no—
215D4×#41—1071nomaximal, Sylow
216C107D4×#4111yescharacteristic, complemented, Sylow
217C22×#41—1071no—
218C22×#41D10711yescharacteristic, complemented
219#550—1071no—
220D4×Q8—1071no—
221#548—1071no—
222#548—1071no—
223#547—1073no—
224#546—1073no—
225#546—1073no—
226D42—1073no—
227#532—1073no—
228#525—1073no—
229#525—1073no—
230C4×#41—1071no—
231C2×C4×D4—1073no—
232C2×#41—28no—
233C2×#41—1071no—
234C2×#41—1073no—
235C2×#41—1073no—
236C2×#41—2148no—
237C2×#41C2×D10711yescharacteristic
238C2×#41C2×D10713yescomplemented
239C2×#41C2×D10713yescomplemented
240C2×#41C2×D10711yescharacteristic, complemented
241C22×Q8—1071no—
242C22×Q8C2×D10711yescharacteristic, complemented
243C22×D4—1073no—
244C22×D4—1073no—
245C22×D4C2×D10713yescomplemented
246C23×C4—1073no—
247C23×C4C2×D10713yescomplemented
248C4⋊Q8—1073no—
249#127—1073no—
250#124—1073no—
251#124—1073no—
252#123—1076no—
253#123—1076no—
254C22⋊Q8—1073no—
255C22⋊Q8—1073no—
256C22⋊Q8—1073no—
257C22⋊Q8—1073no—
258#121—1073no—
259#121—1073no—
260#121—1076no—
261#121—1076no—
262#121—1073no—
263#121—1073no—
264#120—1076no—
265#120—1076no—
266C4×Q8—1071no—
267C4×Q8—1071no—
268C4×D4—1073no—
269C4×D4—1073no—
270C4×D4—1071no—
271C4×D4—1073no—
272C4×D4—1073no—
273C4×D4—1073no—
274C4×D4—1073no—
275C4×D4—1073no—
276C4×D4—1073no—
277C4×D4—1073no—
278C4×D4—1076no—
279#117—1073no—
280C2×C4⋊C4—1073no—
281C2×C22⋊C4—1073no—
282C2×C22⋊C4—1073no—
283C2×C42—1073no—
284C24—1073no—
285C24C22×D10713yes—
286#41—24no—
287#41—212no—
288#41—212no—
289#41—2144no—
290#41—21412no—
291#41—21412no—
292#41C22⋊D10718yesdirect product factor
293C2×Q8—24no—
294C2×Q8—1073no—
295C2×Q8—2144no—
296C2×Q8C22×D10713yes—
297C2×Q8C22×D10711yescharacteristic
298C2×D4—212no—
299C2×D4—1071no—
300C2×D4—1076no—
301C2×D4—1073no—
302C2×D4—1073no—
303C2×D4—1073no—
304C2×D4—1076no—
305C2×D4—1073no—
306C2×D4—21412no—
307C2×D4—21412no—
308C2×D4C22×D10716yes—
309C2×D4C22×D10713yes—
310C2×D4C22×D10713yes—
311C22×C4—212no—
312C22×C4—1073no—
313C22×C4—1073no—
314C22×C4—1073no—
315C22×C4—1073no—
316C22×C4—1073no—
317C22×C4—1071no—
318C22×C4—1073no—
319C22×C4—21412no—
320C22×C4C22×D10713yes—
321C22×C4C22×D10713yes—
322C22×C4C22×D10713yes—
323C22×C4C22×D10711yescharacteristic
324C22×C4C22×D10713yes—
325C22×C4C22×D10713yes—
326C4⋊C4—1071no—
327C4⋊C4—1073no—
328C4⋊C4—1073no—
329C4⋊C4—1073no—
330C4⋊C4—1073no—
331C4⋊C4—1073no—
332C4⋊C4—1076no—
333C22⋊C4—1071no—
334C22⋊C4—1073no—
335C22⋊C4—1073no—
336C22⋊C4—1073no—
337C22⋊C4—1076no—
338C22⋊C4—1076no—
339C22⋊C4—1071no—
340C22⋊C4—1073no—
341C22⋊C4—1073no—
342C22⋊C4—1073no—
343C22⋊C4—1076no—
344C42—1073no—
345C42—1073no—
346C42—1071no—
347C42—1073no—
348C23—26no—
349C23—26no—
350C23—43no—
351C23—1071no—
352C23—1073no—
353C23—4283no—
354C23—2146no—
355C23—2146no—
356C23C23×D10713yes—
357C23C23×D10713yes—
358C23C23×D10711yescharacteristic
359Q8—26no—
360Q8—2146no—
361Q8C2×C22⋊D10714yescomplemented
362D4—212no—
363D4—26no—
364D4—1074no—
365D4—4286no—
366D4—2146no—
367D4—2146no—
368D4—21412no—
369D4—2146no—
370D4—2146no—
371D4C2×C22⋊D107112yescomplemented
372C2×C4—26no—
373C2×C4—22no—
374C2×C4—26no—
375C2×C4—26no—
376C2×C4—26no—
377C2×C4—1071no—
378C2×C4—1071no—
379C2×C4—1073no—
380C2×C4—1073no—
381C2×C4—1071no—
382C2×C4—1073no—
383C2×C4—4283no—
384C2×C4—2146no—
385C2×C4—2146no—
386C2×C4—2142no—
387C2×C4—2146no—
388C2×C4—2146no—
389C2×C4—2146no—
390C2×C4C2×C22⋊D107112yescomplemented
391C2×C4C23×D10711yescharacteristic
392C2×C4C23×D10713yes—
393C2×C4C23×D10713yes—
394C2×C4C23×D10711yescharacteristic
395C22—21no—
396C22—23no—
397C22—23no—
398C22—21no—
399C22—23no—
400C22—23no—
401C22—23no—
402C22—412no—
403C22—1072no—
404C22—42812no—
405C22—2143no—
406C22—2143no—
407C22—2143no—
408C22—2141no—
409C22—2141no—
410C22C22×C22⋊D10716yes—
411C22#41×D10712yescomplemented
412C22C24×D10711yescharacteristic
413C4—21no—
414C4—23no—
415C4—1072no—
416C4—2141no—
417C4—2143no—
418C4—2143no—
419C4—2141no—
420C4—2143no—
421C4C22×C22⋊D10712yes—
422C4C22×C22⋊D10716yes—
423C2—22no—
424C2—26no—
425C2—43no—
426C2—4283no—
427C2—2142no—
428C2C23×C22⋊D10711yescharacteristic
429C2C2×#41×D10711yescharacteristic
430C2#2029346311yescharacteristic
subgroupG/H
centerC2×C4C23×D107
commutator, socle, cosocleC22×C107C25
FrattiniC22C24×D107
FittingC22×#41×C107C2
hypercenterC22×#41D107
hypocenterC107D4×#41
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×D107C2semidirect
2. #20293296C2semidirect
3. Q8×C22⋊D107C2semidirect
4. #20293288C2semidirect
5. #20293284C2semidirect
6. #20293276C2semidirect
7. #20293271C2semidirect
8. #20293265C2semidirect
9. D4×C22⋊D107C2semidirect
10. #20293173C2semidirect
11. #20293138C2semidirect
12. #20293134C2semidirect
13. #41×Dic107C2semidirect
14. C2×C4×C22⋊D107C2semidirect
15. C22×#41×C107C2semidirect
16. C2×#13133819C22semidirect
17. C2×#13133818C22semidirect
18. C2×#13133817C22semidirect
20. C2×Q8×D107C22semidirect
22. C2×D4×D107C22semidirect
23. C22×C4×D107C22semidirect
24. #16812107C22semidirect
25. #16812105C22semidirect
26. #16812098C22semidirect
27. #16812096C22semidirect
28. #16812092C22semidirect
29. #16812090C22semidirect
30. #16812088C22semidirect
31. #16812088C22semidirect
32. #16812085C22semidirect
33. #16812085C22semidirect
34. #16812083C22semidirect
35. #16812083C22semidirect
36. #16812081C22semidirect
37. #16812081C22semidirect
38. #16812080C22semidirect
39. #16812080C22semidirect
40. #16812078C22semidirect
41. #16812077C22semidirect
42. Q8×Dic107C22semidirect
43. Q8×Dic107C22semidirect
44. D4×Dic107C22semidirect
45. D4×Dic107C22semidirect
48. C4×C22⋊D107C22semidirect
49. C4×C22⋊D107C22semidirect
50. C4×C22⋊D107C22semidirect
51. C4×C22⋊D107C22semidirect
52. C4×C22⋊D107C22semidirect
53. C4×C22⋊D107C22semidirect
54. C4×C22⋊D107C22semidirect
55. #16812068C22semidirect
56. C2×Dic107⋊C4C22semidirect
57. C2×C22⋊Dic107C22semidirect
58. C2×(C2×D107)⋊C4C22semidirect
59. C2×C4×Dic107C22semidirect
62. C2×#41×C107C22semidirect
63. C2×#41×C107C22semidirect
64. C2×#41×C107C22semidirect
65. C22×Q8×C107C22semidirect
66. C22×D4×C107C22semidirect
67. C23×C4×C107C22semidirect
117. #41×C107D4semidirect
144. Q8×C107C2×D4semidirect
147. D4×C107C2×D4semidirect
153. C2×C4×C107C2×D4semidirect
163. C22⋊D107#41direct (N × H)
188. C22×C107C2×#41semidirect
196. C2×D107C2×#41semidirect
206. Dic107C2×#41semidirect
216. C107D4×#41semidirect
218. C22×#41D107semidirect
238. C2×#41C2×D107semidirect
239. C2×#41C2×D107semidirect
240. C2×#41C2×D107semidirect
242. C22×Q8C2×D107semidirect
245. C22×D4C2×D107semidirect
247. C23×C4C2×D107semidirect
292. #41C22⋊D107direct (N × H)
361. Q8C2×C22⋊D107semidirect
371. D4C2×C22⋊D107semidirect
390. C2×C4C2×C22⋊D107semidirect
411. C22#41×D107semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D1072
#202932962
Q8×C22⋊D1072
#202932882
#202932842
#202932762
#202932712
#202932652
D4×C22⋊D1072
#202931732
#202931382
#202931342
#41×Dic1072
C2×C4×C22⋊D1072
C22×#41×C1072
D4×#41107