Finite Group Databasebeta

← #548×D269 #46824347

Subgroups — #548×D269 #46824347

Order 34432.

1620 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D269C211yesmaximal, characteristic, complemented
2C22×Q8×D269C211yesmaximal, characteristic, complemented
3#31771267C211yesmaximal, characteristic, complemented
4#31771266C211yesmaximal, characteristic, complemented
5#31771265C213yesmaximal, complemented
6#31771264C213yesmaximal, complemented
7#31771263C213yesmaximal, complemented
8#31771262C211yesmaximal, characteristic, complemented
9#31771261C213yesmaximal, complemented
10#124×D269C213yesmaximal, complemented
11C22⋊Q8×D269C213yesmaximal, complemented
12#121×D269C213yesmaximal, complemented
13C4×Q8×D269C211yesmaximal, characteristic, complemented
14C4×D4×D269C213yesmaximal, complemented
15#548×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic, complemented
17C2×#16864402C2213yescomplemented
18C2×#16864401C2213yescomplemented
19#41×D269—28no—
20C22×Dic538C2213yescomplemented
21C2×Q8×D269—28no—
22C2×Q8×D269C2213yes—
23C2×Q8×D269C2211yescharacteristic
24C2×Q8×D269C2211yescharacteristic, complemented
25C2×Q8×D269C2213yescomplemented
26C2×D4×D269C2213yes—
27C2×D4×D269C2213yes—
28C22×C4×D269C2213yes—
29C22×C4×D269C2213yes—
30#22575442C2213yescomplemented
31#22575441C2213yescomplemented
32#22575440C2213yescomplemented
33#22575439C2216yescomplemented
34#22575439C2216yescomplemented
35#22575433C2213yescomplemented
36#22575432C2213yescomplemented
37#22575431C2216yescomplemented
38#22575430C2216yescomplemented
39#22575429C2213yescomplemented
40#22575428C2213yescomplemented
41#22575427C2213yescomplemented
42#22575426C2216yescomplemented
43#22575425C2216yescomplemented
44#22575424C2213yescomplemented
45Q8×Dic269C2211yescharacteristic, complemented
46C4×Dic538C2213yescomplemented
47#22575418C2213yescomplemented
48C4×D1076C2213yescomplemented
49D4×Dic269C2213yescomplemented
50#22575415C2213yescomplemented
51C4×C22⋊D269C2213yescomplemented
52C4×C22⋊D269C2213yescomplemented
53#22575413C2213yescomplemented
54#22575413C2213yescomplemented
55C4⋊C4×D269C2213yes—
56C4⋊C4×D269C2213yes—
57C22⋊C4×D269C2211yescharacteristic
58C22⋊C4×D269C2213yes—
59C22⋊C4×D269C2216yes—
60C42×D269C2213yes—
61C2×#41×C269C2211yescharacteristic, complemented
62C22×Q8×C269C2211yescharacteristic, complemented
63#124×C269C2213yescomplemented
64C22⋊Q8×C269C2213yescomplemented
65#121×C269C2213yescomplemented
66C4×Q8×C269C2211yescharacteristic, complemented
67C4×D4×C269C2213yescomplemented
68C23×D269C2313yes—
69C23×D269C2311yescharacteristic
70#16864403—24no—
71#16864402—212no—
72#16864401—212no—
73C2×Dic538—212no—
74C2×Dic538C2316yes—
75C2×Dic538C2313yes—
76C2×Dic538C2313yes—
77Q8×D269—212no—
78Q8×D269—212no—
79Q8×D269—24no—
80Q8×D269D418yescomplemented
81C2×D1076C2313yes—
82C2×D1076C2313yes—
83C2×C22⋊D269C2313yes—
84C2×C22⋊D269C2313yes—
85C2×C22⋊D269C2316yes—
86D4×D269—212no—
87D4×D269—212no—
88C22×Dic269C2313yes—
89C22×Dic269C2313yes—
90C2×C4×D269—212no—
91C2×C4×D269—212no—
92C2×C4×D269C2311yescharacteristic
93C2×C4×D269C2313yes—
94C2×C4×D269C2313yes—
95C2×C4×D269C2311yescharacteristic
96C2×C4×D269C2313yes—
97C2×C4×D269C2313yes—
98C2×C4×D269C2313yes—
99C2×C4×D269C2313yes—
100C2×C4×D269C2313yes—
101C4⋊Dic269C2313yes—
102C4⋊Dic269C2313yes—
103#16864381C2313yes—
104#16864381C2313yes—
105#16864381C2316yes—
106C22⋊Dic269C2311yescharacteristic
107C22⋊Dic269C2313yes—
108C22⋊Dic269C2316yes—
109#16864379C2311yescharacteristic
110#16864379C2313yes—
111#16864379C2311yescharacteristic
112#16864379C2313yes—
113#16864379C2316yes—
114#16864379C2316yes—
115C4×Dic269C2313yes—
116C4×Dic269C2313yes—
117C4×Dic269C2313yes—
118#41×C269—24no—
119C2×Q8×C269—24no—
120C2×Q8×C269C2313yes—
121C2×Q8×C269C2311yescharacteristic
122C2×D4×C269C2313yes—
123C2×D4×C269C2313yes—
124C22×C4×C269C2313yes—
125C22×C4×C269C2313yes—
126C4⋊C4×C269C2313yes—
127C4⋊C4×C269C2313yes—
128C22⋊C4×C269C2311yescharacteristic
129C22⋊C4×C269C2313yes—
130C22⋊C4×C269C2316yes—
131C42×C269C2313yes—
132C22×D269—22no—
133C22×D269—22no—
134C22×D269—26no—
135C22×D269—26no—
136C22×D269—26no—
137C22×D269#4114yescomplemented
138C22×D269C2413yes—
139C22×D269C2411yescharacteristic
140C22×D269C2411yescharacteristic
141Dic538—26no—
142Dic538—212no—
143Dic538C2×D4112yescomplemented
144D1076—26no—
145D1076—26no—
146C22⋊D269—26no—
147C22⋊D269—26no—
148C22⋊D269—212no—
149C2×Dic269—26no—
150C2×Dic269—26no—
151C2×Dic269C2411yescharacteristic
152C2×Dic269C2413yes—
153C2×Dic269C2413yes—
154C2×Dic269C2411yescharacteristic
155C2×Dic269C2413yes—
156C4×D269—22no—
157C4×D269—26no—
158C4×D269—26no—
159C4×D269—22no—
160C4×D269—26no—
161C4×D269—26no—
162C4×D269—26no—
163C4×D269—26no—
164C4×D269C2×D4112yes—
165C23×C269C2413yes—
166C23×C269C2411yescharacteristic
167Q8×C269—26no—
168Q8×C269C2×D414yescomplemented
169D4×C269—26no—
170D4×C269—26no—
171C2×C4×C269—26no—
172C2×C4×C269—26no—
173C2×C4×C269C2411yescharacteristic
174C2×C4×C269C2413yes—
175C2×C4×C269C2413yes—
176C2×C4×C269C2411yescharacteristic
177C2×C4×C269C2413yes—
178C22×C269—21no—
179C22×C269—21no—
180C22×C269—23no—
181C22×C269—23no—
182C22×C269—23no—
183C22×C269C2×#4112yescomplemented
184C22×C269C2511yescharacteristic
185C2×D269—21no—
186C2×D269—21no—
187C2×D269—28no—
188C2×D269—23no—
189C2×D269—23no—
190C2×D269—23no—
191C2×D269—412no—
192C2×D269C22×D412yes—
193C2×D269C2×#4112yes—
194C2×D269C2×#4112yescomplemented
195C2×D2692−1+412yes—
196C4×C269—21no—
197C4×C269—23no—
198C4×C269—23no—
199C4×C269—21no—
200C4×C269C22×D416yes—
201Dic269—21no—
202Dic269—23no—
203Dic269—23no—
204Dic269—21no—
205Dic269C22×D416yes—
206C2×C269—22no—
207C2×C269—43no—
208C2×C269C23×D411yescharacteristic
209C2×C269C22×#4111yescharacteristic
210C2×C269C2×2−1+411yescharacteristic
211D269—22no—
212D269—43no—
213D269#54814yesdirect product factor
214C269C2×#54811yescharacteristic, complemented, Sylow
215C2×#548—2691nomaximal, Sylow
216C22×#41—2691no—
217C23×Q8—2691no—
218#548—2691no—
219#548—2691no—
220#548—2693no—
221#548—2693no—
222#548—2693no—
223#548—2691no—
224#548—2693no—
225#548D26911yescharacteristic, direct product factor
226C2×#124—2693no—
227C2×C22⋊Q8—2693no—
228C2×#121—2693no—
229C2×C4×Q8—2691no—
230C2×C4×D4—2693no—
231C2×#41—2691no—
232C2×#41—2693no—
233C2×#41—2693no—
234C2×#41—5388no—
235C2×#41C2×D26911yescharacteristic, complemented
236C22×Q8—2691no—
237C22×Q8—2693no—
238C22×Q8—2693no—
239C22×Q8—2691no—
240C22×Q8—2693no—
241C22×Q8—5388no—
242C22×Q8C2×D26911yescharacteristic, complemented
243C22×D4—2693no—
244C22×D4—2693no—
245C23×C4—2693no—
246C23×C4—2693no—
247#124—2693no—
248#124—2693no—
249#124—2696no—
250#124—2696no—
251#124—2693no—
252#124C2×D26913yescomplemented
253C22⋊Q8—2693no—
254C22⋊Q8—2693no—
255C22⋊Q8—2696no—
256C22⋊Q8—2693no—
257C22⋊Q8—2696no—
258C22⋊Q8C2×D26913yescomplemented
259#121—2693no—
260#121—2696no—
261#121—2693no—
262#121—2693no—
263#121—2696no—
264#121C2×D26913yescomplemented
265C4×Q8—2691no—
266C4×Q8—2693no—
267C4×Q8—2693no—
268C4×Q8C2×D26911yescharacteristic, complemented
269C4×D4—2693no—
270C4×D4—2693no—
271C4×D4—2693no—
272C4×D4—2693no—
273C4×D4—2693no—
274C4×D4—2693no—
275C4×D4—2693no—
276C4×D4C2×D26913yescomplemented
277C2×C4⋊C4—2693no—
278C2×C4⋊C4—2693no—
279C2×C22⋊C4—2691no—
280C2×C22⋊C4—2693no—
281C2×C22⋊C4—2696no—
282C2×C42—2693no—
283C24—2691no—
284C24—2693no—
285#41—24no—
286#41—53812no—
287#41—53812no—
288#41—5384no—
289C2×Q8—24no—
290C2×Q8—2698no—
291C2×Q8—2693no—
292C2×Q8—2696no—
293C2×Q8—2693no—
294C2×Q8—53812no—
295C2×Q8—53812no—
296C2×Q8—53812no—
297C2×Q8—5384no—
298C2×Q8C22×D26913yes—
299C2×Q8C22×D26911yescharacteristic
300C2×D4—2693no—
301C2×D4—2693no—
302C2×D4—2696no—
303C2×D4—2693no—
304C2×D4—2693no—
305C2×D4—53812no—
306C2×D4—53812no—
307C2×D4C22×D26913yes—
308C2×D4C22×D26913yes—
309C22×C4—2693no—
310C22×C4—2693no—
311C22×C4—2693no—
312C22×C4—2691no—
313C22×C4—2693no—
314C22×C4—2693no—
315C22×C4—2691no—
316C22×C4—2693no—
317C22×C4—2693no—
318C22×C4—2693no—
319C22×C4—2693no—
320C22×C4—53812no—
321C22×C4—53812no—
322C22×C4C22×D26913yes—
323C22×C4C22×D26913yes—
324C4⋊C4—2693no—
325C4⋊C4—2693no—
326C4⋊C4—2693no—
327C4⋊C4—2696no—
328C4⋊C4—2693no—
329C4⋊C4C22×D26913yes—
330C4⋊C4C22×D26913yes—
331C22⋊C4—2691no—
332C22⋊C4—2693no—
333C22⋊C4—2696no—
334C22⋊C4—2691no—
335C22⋊C4—2691no—
336C22⋊C4—2693no—
337C22⋊C4—2693no—
338C22⋊C4—2696no—
339C22⋊C4—2696no—
340C22⋊C4C22×D26911yescharacteristic
341C22⋊C4C22×D26913yes—
342C22⋊C4C22×D26916yes—
343C42—2693no—
344C42—2693no—
345C42—2693no—
346C42C22×D26913yes—
347C23—2691no—
348C23—2694no—
349C23—2691no—
350C23—2693no—
351C23—5382no—
352C23—5382no—
353C23—5386no—
354C23—5386no—
355C23—5386no—
356C23C23×D26913yes—
357C23C23×D26911yescharacteristic
358Q8—26no—
359Q8—26912no—
360Q8—53812no—
361Q8—5386no—
362Q8D4×D26914yescomplemented
363D4—26no—
364D4—26no—
365D4—5386no—
366D4—53812no—
367D4—5386no—
368D4—5386no—
369D4—5386no—
370C2×C4—26no—
371C2×C4—26no—
372C2×C4—2693no—
373C2×C4—26912no—
374C2×C4—2691no—
375C2×C4—2693no—
376C2×C4—2693no—
377C2×C4—2691no—
378C2×C4—5386no—
379C2×C4—5386no—
380C2×C4—5382no—
381C2×C4—5386no—
382C2×C4—5386no—
383C2×C4—5382no—
384C2×C4—5386no—
385C2×C4—5386no—
386C2×C4—5386no—
387C2×C4—5386no—
388C2×C4C23×D26911yescharacteristic
389C2×C4C23×D26913yes—
390C2×C4C23×D26913yes—
391C2×C4C23×D26911yescharacteristic
392C2×C4C23×D26913yes—
393C22—21no—
394C22—21no—
395C22—23no—
396C22—23no—
397C22—23no—
398C22—2692no—
399C22—2692no—
400C22—2692no—
401C22—2692no—
402C22—5388no—
403C22—5381no—
404C22—5381no—
405C22—5383no—
406C22—5383no—
407C22—5383no—
408C22—107612no—
409C22#41×D26912yescomplemented
410C22C24×D26911yescharacteristic
411C4—21no—
412C4—23no—
413C4—23no—
414C4—21no—
415C4—2696no—
416C4—5381no—
417C4—5383no—
418C4—5383no—
419C4—5381no—
420C4C2×D4×D26916yes—
421C2—22no—
422C2—43no—
423C2—2694no—
424C2—5382no—
425C2—10763no—
426C2C22×D4×D26911yescharacteristic
427C2C2×#41×D26911yescharacteristic
428C22−1+4×D26911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D269
commutator, socle, cosocleC22×C269C25
Fitting#548×C269C2
hypercenter#548D269
hypocenterC269C2×#548
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#41×D269C2semidirect
2. C22×Q8×D269C2semidirect
3. #31771267C2semidirect
4. #31771266C2semidirect
5. #31771265C2semidirect
6. #31771264C2semidirect
7. #31771263C2semidirect
8. #31771262C2semidirect
9. #31771261C2semidirect
10. #124×D269C2semidirect
11. C22⋊Q8×D269C2semidirect
12. #121×D269C2semidirect
13. C4×Q8×D269C2semidirect
14. C4×D4×D269C2semidirect
15. #548×C269C2semidirect
16. C2×#16864403C22semidirect
17. C2×#16864402C22semidirect
18. C2×#16864401C22semidirect
20. C22×Dic538C22semidirect
24. C2×Q8×D269C22semidirect
25. C2×Q8×D269C22semidirect
30. #22575442C22semidirect
31. #22575441C22semidirect
32. #22575440C22semidirect
33. #22575439C22semidirect
34. #22575439C22semidirect
35. #22575433C22semidirect
36. #22575432C22semidirect
37. #22575431C22semidirect
38. #22575430C22semidirect
39. #22575429C22semidirect
40. #22575428C22semidirect
41. #22575427C22semidirect
42. #22575426C22semidirect
43. #22575425C22semidirect
44. #22575424C22semidirect
45. Q8×Dic269C22semidirect
46. C4×Dic538C22semidirect
47. #22575418C22semidirect
48. C4×D1076C22semidirect
49. D4×Dic269C22semidirect
50. #22575415C22semidirect
51. C4×C22⋊D269C22semidirect
52. C4×C22⋊D269C22semidirect
53. #22575413C22semidirect
54. #22575413C22semidirect
61. C2×#41×C269C22semidirect
62. C22×Q8×C269C22semidirect
63. #124×C269C22semidirect
64. C22⋊Q8×C269C22semidirect
65. #121×C269C22semidirect
66. C4×Q8×C269C22semidirect
67. C4×D4×C269C22semidirect
80. Q8×D269D4semidirect
137. C22×D269#41semidirect
143. Dic538C2×D4semidirect
168. Q8×C269C2×D4semidirect
183. C22×C269C2×#41semidirect
194. C2×D269C2×#41semidirect
213. D269#548direct (N × H)
214. C269C2×#548semidirect
225. #548D269direct (N × H)
235. C2×#41C2×D269semidirect
242. C22×Q8C2×D269semidirect
252. #124C2×D269semidirect
258. C22⋊Q8C2×D269semidirect
264. #121C2×D269semidirect
268. C4×Q8C2×D269semidirect
276. C4×D4C2×D269semidirect
362. Q8D4×D269semidirect
409. 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
C22×Q8×D2692
#317712672
#317712662
#317712652
#317712642
#317712632
#317712622
#317712612
#124×D2692
C22⋊Q8×D2692
#121×D2692
C4×Q8×D2692
C4×D4×D2692
#548×C2692
C2×#548269