Finite Group Databasebeta

← #41×C22⋊D269 #46824370

Subgroups — #41×C22⋊D269 #46824370

Order 34432.

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×D269C211yesmaximal, characteristic, complemented
2#31771274C211yesmaximal, characteristic, complemented
3Q8×C22⋊D269C211yesmaximal, characteristic, complemented
4#31771266C211yesmaximal, characteristic, complemented
5#31771262C211yesmaximal, characteristic, complemented
6#31771254C213yesmaximal, complemented
7#31771249C213yesmaximal, complemented
8#31771243C213yesmaximal, complemented
9D4×C22⋊D269C213yesmaximal, complemented
10#31771151C213yesmaximal, complemented
11#31771116C213yesmaximal, complemented
12#31771112C213yesmaximal, complemented
13#41×Dic269C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊D269C213yesmaximal, complemented
15C22×#41×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic, complemented
17C2×#16864402C2213yescomplemented
18C2×#16864401C2213yescomplemented
19#41×D269—28no—
20C2×Q8×D269C2211yescharacteristic, complemented
21C22×C22⋊D269C2213yes—
22C2×D4×D269C2213yescomplemented
23C22×C4×D269C2213yescomplemented
24#22575451C2213yescomplemented
25#22575449C2213yescomplemented
26#22575442C2213yescomplemented
27#22575440C2213yescomplemented
28#22575436C2216yescomplemented
29#22575434C2216yescomplemented
30#22575432C2213yescomplemented
31#22575432C2213yescomplemented
32#22575429C2213yescomplemented
33#22575429C2213yescomplemented
34#22575427C2213yescomplemented
35#22575427C2213yescomplemented
36#22575425C2216yescomplemented
37#22575425C2216yescomplemented
38#22575424C2213yescomplemented
39#22575424C2213yescomplemented
40#22575422C2216yescomplemented
41#22575421C2216yescomplemented
42Q8×Dic269C2211yescharacteristic, complemented
43Q8×Dic269C2211yescharacteristic, complemented
44D4×Dic269C2213yescomplemented
45D4×Dic269C2213yescomplemented
46C4×C22⋊D269C2213yes—
47C4×C22⋊D269C2211yescharacteristic
48C4×C22⋊D269C2213yescomplemented
49C4×C22⋊D269C2216yescomplemented
50C4×C22⋊D269C2213yescomplemented
51C4×C22⋊D269C2213yescomplemented
52C4×C22⋊D269C2213yescomplemented
53C4×C22⋊D269C2213yescomplemented
54C4×C22⋊D269C2213yescomplemented
55#22575412C2213yescomplemented
56C2×#16864381C2213yescomplemented
57C2×C22⋊Dic269C2213yescomplemented
58C2×#16864379C2213yescomplemented
59C2×C4×Dic269C2213yescomplemented
60C2×#41×C269—28no—
61C2×#41×C269C2211yescharacteristic
62C2×#41×C269C2213yescomplemented
63C2×#41×C269C2213yescomplemented
64C2×#41×C269C2211yescharacteristic, complemented
65C22×Q8×C269C2211yescharacteristic, complemented
66C22×D4×C269C2213yescomplemented
67C23×C4×C269C2213yescomplemented
68C23×D269C2313yes—
69#16864403—24no—
70#16864402—212no—
71#16864401—212no—
72C2×Dic538C2313yes—
73Q8×D269—24no—
74C2×D1076C2313yes—
75C2×C22⋊D269—212no—
76C2×C22⋊D269C2313yes—
77C2×C22⋊D269C2313yes—
78C2×C22⋊D269C2313yes—
79C2×C22⋊D269C2316yes—
80C2×C22⋊D269C2316yes—
81C2×C22⋊D269C2311yescharacteristic
82D4×D269—212no—
83C22×Dic269C2313yes—
84C22×Dic269C2313yes—
85C22×Dic269C2313yes—
86C2×C4×D269—212no—
87C2×C4×D269C2311yescharacteristic
88C2×C4×D269C2313yes—
89C2×C4×D269C2313yes—
90C2×C4×D269C2313yes—
91C4⋊Dic269C2313yes—
92C4⋊Dic269C2313yes—
93#16864381C2311yescharacteristic
94#16864381C2313yes—
95#16864381C2313yes—
96#16864381C2313yes—
97#16864381C2316yes—
98C22⋊Dic269C2311yescharacteristic
99C22⋊Dic269C2313yes—
100C22⋊Dic269C2313yes—
101C22⋊Dic269C2313yes—
102C22⋊Dic269C2316yes—
103C22⋊Dic269C2316yes—
104#16864379C2311yescharacteristic
105#16864379C2313yes—
106#16864379C2313yes—
107#16864379C2313yes—
108#16864379C2316yes—
109C4×Dic269C2311yescharacteristic
110C4×Dic269C2313yes—
111C4×Dic269C2313yes—
112C4×Dic269C2313yes—
113C24×C269C2313yes—
114#41×C269—24no—
115#41×C269—212no—
116#41×C269—212no—
117#41×C269D418yescomplemented
118C2×Q8×C269—24no—
119C2×Q8×C269C2313yes—
120C2×Q8×C269C2311yescharacteristic
121C2×D4×C269—212no—
122C2×D4×C269C2316yes—
123C2×D4×C269C2313yes—
124C2×D4×C269C2313yes—
125C22×C4×C269—212no—
126C22×C4×C269C2313yes—
127C22×C4×C269C2311yescharacteristic
128C22×C4×C269C2313yes—
129C22×C4×C269C2313yes—
130C22×C4×C269C2313yes—
131C22×C4×C269C2313yes—
132C22×D269—26no—
133C22×D269—26no—
134C22×D269—43no—
135C22×D269C2413yes—
136C22×D269C2411yescharacteristic
137Dic538—26no—
138D1076—26no—
139C22⋊D269—212no—
140C22⋊D269—26no—
141C22⋊D269—26no—
142C22⋊D269—26no—
143C22⋊D269—46no—
144C22⋊D269#4114yesdirect product factor
145C2×Dic269—26no—
146C2×Dic269—26no—
147C2×Dic269—43no—
148C2×Dic269C2411yescharacteristic
149C2×Dic269C2413yes—
150C2×Dic269C2413yes—
151C2×Dic269C2411yescharacteristic
152C2×Dic269C2413yes—
153C2×Dic269C2411yescharacteristic
154C4×D269—22no—
155C4×D269—26no—
156C4×D269—26no—
157C4×D269—26no—
158C23×C269—26no—
159C23×C269—26no—
160C23×C269—43no—
161C23×C269C2413yes—
162C23×C269C2413yes—
163C23×C269C2411yescharacteristic
164Q8×C269—26no—
165Q8×C269C2×D414yescomplemented
166D4×C269—212no—
167D4×C269—26no—
168D4×C269C2×D4112yescomplemented
169C2×C4×C269—26no—
170C2×C4×C269—22no—
171C2×C4×C269—26no—
172C2×C4×C269—26no—
173C2×C4×C269—26no—
174C2×C4×C269C2×D4112yescomplemented
175C2×C4×C269C2411yescharacteristic
176C2×C4×C269C2413yes—
177C2×C4×C269C2413yes—
178C2×C4×C269C2411yescharacteristic
179C22×C269—21no—
180C22×C269—23no—
181C22×C269—21no—
182C22×C269—23no—
183C22×C269—23no—
184C22×C269—23no—
185C22×C269—23no—
186C22×C269—412no—
187C22×C269C22×D416yes—
188C22×C269C2×#4112yescomplemented
189C22×C269C2511yescharacteristic
190C2×D269—21no—
191C2×D269—21no—
192C2×D269—23no—
193C2×D269—23no—
194C2×D269—23no—
195C2×D269—412no—
196C2×D269C2×#4112yescomplemented
197C4×C269—21no—
198C4×C269—23no—
199C4×C269C22×D412yes—
200C4×C269C22×D416yes—
201Dic269—21no—
202Dic269—23no—
203Dic269—23no—
204Dic269—21no—
205Dic269—23no—
206Dic269C2×#4112yescomplemented
207C2×C269—26no—
208C2×C269—22no—
209C2×C269—43no—
210C2×C269C23×D411yescharacteristic
211C2×C269C22×#4111yescharacteristic
212C2×C269#58511yescharacteristic
213D269—22no—
214D269—43no—
215C269D4×#4111yescharacteristic, complemented, Sylow
216D4×#41—2691nomaximal, Sylow
217C22×#41—2691no—
218C22×#41D26911yescharacteristic, complemented
219#550—2691no—
220D4×Q8—2691no—
221#548—2691no—
222#548—2691no—
223#547—2693no—
224#546—2693no—
225#546—2693no—
226D42—2693no—
227#532—2693no—
228#525—2693no—
229#525—2693no—
230C4×#41—2691no—
231C2×C4×D4—2693no—
232C2×#41—28no—
233C2×#41—2691no—
234C2×#41—2693no—
235C2×#41—2693no—
236C2×#41—5388no—
237C2×#41C2×D26911yescharacteristic
238C2×#41C2×D26913yescomplemented
239C2×#41C2×D26913yescomplemented
240C2×#41C2×D26911yescharacteristic, complemented
241C22×Q8—2691no—
242C22×Q8C2×D26911yescharacteristic, complemented
243C22×D4—2693no—
244C22×D4—2693no—
245C22×D4C2×D26913yescomplemented
246C23×C4—2693no—
247C23×C4C2×D26913yescomplemented
248C4⋊Q8—2693no—
249#127—2693no—
250#124—2693no—
251#124—2693no—
252#123—2696no—
253#123—2696no—
254C22⋊Q8—2693no—
255C22⋊Q8—2693no—
256C22⋊Q8—2693no—
257C22⋊Q8—2693no—
258#121—2693no—
259#121—2693no—
260#121—2696no—
261#121—2696no—
262#121—2693no—
263#121—2693no—
264#120—2696no—
265#120—2696no—
266C4×Q8—2691no—
267C4×Q8—2691no—
268C4×D4—2693no—
269C4×D4—2693no—
270C4×D4—2691no—
271C4×D4—2693no—
272C4×D4—2693no—
273C4×D4—2693no—
274C4×D4—2693no—
275C4×D4—2693no—
276C4×D4—2693no—
277C4×D4—2693no—
278C4×D4—2696no—
279#117—2693no—
280C2×C4⋊C4—2693no—
281C2×C22⋊C4—2693no—
282C2×C22⋊C4—2693no—
283C2×C42—2693no—
284C24—2693no—
285C24C22×D26913yes—
286#41—24no—
287#41—212no—
288#41—212no—
289#41—5384no—
290#41—53812no—
291#41—53812no—
292#41C22⋊D26918yesdirect product factor
293C2×Q8—24no—
294C2×Q8—2693no—
295C2×Q8—5384no—
296C2×Q8C22×D26913yes—
297C2×Q8C22×D26911yescharacteristic
298C2×D4—212no—
299C2×D4—2691no—
300C2×D4—2693no—
301C2×D4—2693no—
302C2×D4—2693no—
303C2×D4—2696no—
304C2×D4—2696no—
305C2×D4—2693no—
306C2×D4—53812no—
307C2×D4—53812no—
308C2×D4C22×D26916yes—
309C2×D4C22×D26913yes—
310C2×D4C22×D26913yes—
311C22×C4—212no—
312C22×C4—2693no—
313C22×C4—2693no—
314C22×C4—2693no—
315C22×C4—2693no—
316C22×C4—2693no—
317C22×C4—2691no—
318C22×C4—2693no—
319C22×C4—53812no—
320C22×C4C22×D26913yes—
321C22×C4C22×D26913yes—
322C22×C4C22×D26913yes—
323C22×C4C22×D26911yescharacteristic
324C22×C4C22×D26913yes—
325C22×C4C22×D26913yes—
326C4⋊C4—2691no—
327C4⋊C4—2693no—
328C4⋊C4—2693no—
329C4⋊C4—2693no—
330C4⋊C4—2693no—
331C4⋊C4—2693no—
332C4⋊C4—2696no—
333C22⋊C4—2691no—
334C22⋊C4—2693no—
335C22⋊C4—2693no—
336C22⋊C4—2693no—
337C22⋊C4—2696no—
338C22⋊C4—2696no—
339C22⋊C4—2691no—
340C22⋊C4—2693no—
341C22⋊C4—2693no—
342C22⋊C4—2693no—
343C22⋊C4—2696no—
344C42—2693no—
345C42—2693no—
346C42—2691no—
347C42—2693no—
348C23—26no—
349C23—26no—
350C23—43no—
351C23—2691no—
352C23—2693no—
353C23—5386no—
354C23—5386no—
355C23—10763no—
356C23C23×D26913yes—
357C23C23×D26913yes—
358C23C23×D26911yescharacteristic
359Q8—26no—
360Q8—5386no—
361Q8C2×C22⋊D26914yescomplemented
362D4—212no—
363D4—26no—
364D4—2694no—
365D4—5386no—
366D4—5386no—
367D4—53812no—
368D4—5386no—
369D4—5386no—
370D4—10766no—
371D4C2×C22⋊D269112yescomplemented
372C2×C4—26no—
373C2×C4—22no—
374C2×C4—26no—
375C2×C4—26no—
376C2×C4—26no—
377C2×C4—2691no—
378C2×C4—2691no—
379C2×C4—2693no—
380C2×C4—2693no—
381C2×C4—2691no—
382C2×C4—2693no—
383C2×C4—5386no—
384C2×C4—5386no—
385C2×C4—5382no—
386C2×C4—5386no—
387C2×C4—5386no—
388C2×C4—5386no—
389C2×C4—10763no—
390C2×C4C2×C22⋊D269112yescomplemented
391C2×C4C23×D26911yescharacteristic
392C2×C4C23×D26913yes—
393C2×C4C23×D26913yes—
394C2×C4C23×D26911yescharacteristic
395C22—21no—
396C22—23no—
397C22—23no—
398C22—21no—
399C22—23no—
400C22—23no—
401C22—23no—
402C22—412no—
403C22—2692no—
404C22—5381no—
405C22—5381no—
406C22—5383no—
407C22—5383no—
408C22—5383no—
409C22—107612no—
410C22C22×C22⋊D26916yes—
411C22#41×D26912yescomplemented
412C22C24×D26911yescharacteristic
413C4—21no—
414C4—23no—
415C4—2692no—
416C4—5381no—
417C4—5383no—
418C4—5383no—
419C4—5381no—
420C4—5383no—
421C4C22×C22⋊D26912yes—
422C4C22×C22⋊D26916yes—
423C2—22no—
424C2—26no—
425C2—43no—
426C2—5382no—
427C2—10763no—
428C2C23×C22⋊D26911yescharacteristic
429C2C2×#41×D26911yescharacteristic
430C2#3177144111yescharacteristic
subgroupG/H
centerC2×C4C23×D269
commutator, socle, cosocleC22×C269C25
FrattiniC22C24×D269
FittingC22×#41×C269C2
hypercenterC22×#41D269
hypocenterC269D4×#41
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C2×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×D269C2semidirect
2. #31771274C2semidirect
3. Q8×C22⋊D269C2semidirect
4. #31771266C2semidirect
5. #31771262C2semidirect
6. #31771254C2semidirect
7. #31771249C2semidirect
8. #31771243C2semidirect
9. D4×C22⋊D269C2semidirect
10. #31771151C2semidirect
11. #31771116C2semidirect
12. #31771112C2semidirect
13. #41×Dic269C2semidirect
14. C2×C4×C22⋊D269C2semidirect
15. C22×#41×C269C2semidirect
16. C2×#16864403C22semidirect
17. C2×#16864402C22semidirect
18. C2×#16864401C22semidirect
20. C2×Q8×D269C22semidirect
22. C2×D4×D269C22semidirect
23. C22×C4×D269C22semidirect
24. #22575451C22semidirect
25. #22575449C22semidirect
26. #22575442C22semidirect
27. #22575440C22semidirect
28. #22575436C22semidirect
29. #22575434C22semidirect
30. #22575432C22semidirect
31. #22575432C22semidirect
32. #22575429C22semidirect
33. #22575429C22semidirect
34. #22575427C22semidirect
35. #22575427C22semidirect
36. #22575425C22semidirect
37. #22575425C22semidirect
38. #22575424C22semidirect
39. #22575424C22semidirect
40. #22575422C22semidirect
41. #22575421C22semidirect
42. Q8×Dic269C22semidirect
43. Q8×Dic269C22semidirect
44. D4×Dic269C22semidirect
45. D4×Dic269C22semidirect
48. C4×C22⋊D269C22semidirect
49. C4×C22⋊D269C22semidirect
50. C4×C22⋊D269C22semidirect
51. C4×C22⋊D269C22semidirect
52. C4×C22⋊D269C22semidirect
53. C4×C22⋊D269C22semidirect
54. C4×C22⋊D269C22semidirect
55. #22575412C22semidirect
56. C2×#16864381C22semidirect
57. C2×C22⋊Dic269C22semidirect
58. C2×#16864379C22semidirect
59. C2×C4×Dic269C22semidirect
62. C2×#41×C269C22semidirect
63. C2×#41×C269C22semidirect
64. C2×#41×C269C22semidirect
65. C22×Q8×C269C22semidirect
66. C22×D4×C269C22semidirect
67. C23×C4×C269C22semidirect
117. #41×C269D4semidirect
144. C22⋊D269#41direct (N × H)
165. Q8×C269C2×D4semidirect
168. D4×C269C2×D4semidirect
174. C2×C4×C269C2×D4semidirect
188. C22×C269C2×#41semidirect
196. C2×D269C2×#41semidirect
206. Dic269C2×#41semidirect
215. C269D4×#41semidirect
218. C22×#41D269semidirect
238. C2×#41C2×D269semidirect
239. C2×#41C2×D269semidirect
240. C2×#41C2×D269semidirect
242. C22×Q8C2×D269semidirect
245. C22×D4C2×D269semidirect
247. C23×C4C2×D269semidirect
292. #41C22⋊D269direct (N × H)
361. Q8C2×C22⋊D269semidirect
371. D4C2×C22⋊D269semidirect
390. C2×C4C2×C22⋊D269semidirect
411. C22#41×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D2692
#317712742
Q8×C22⋊D2692
#317712662
#317712622
#317712542
#317712492
#317712432
D4×C22⋊D2692
#317711512
#317711162
#317711122
#41×Dic2692
C2×C4×C22⋊D2692
C22×#41×C2692
D4×#41269