Finite Group Databasebeta

← #541×D283 #49134623

Subgroups — #541×D283 #49134623

Order 36224.

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#31827078C211yesmaximal, characteristic, complemented
2#31827077C211yesmaximal, characteristic, complemented
3#31827076C211yesmaximal, characteristic, complemented
4#31827075C212yesmaximal, complemented
5#31827074C214yesmaximal, complemented
6#31827073C212yesmaximal, complemented
7#31827072C214yesmaximal, complemented
8C4⋊Q8×D283C211yesmaximal, characteristic, complemented
9#126×D283C214yesmaximal
10#125×D283C214yesmaximal, complemented
11#125×D283C211yesmaximal, characteristic, complemented
12C22⋊Q8×D283C212yesmaximal
13C4×Q8×D283C212yesmaximal, complemented
14#117×D283C211yesmaximal, characteristic
15#541×C283C211yesmaximal, characteristic, complemented
16C2×Q8×D283C2212yes—
17C22×C4×D283C2211yescharacteristic
18#22583610C2211yescharacteristic, complemented
19#22583609C2214yescomplemented
20#22583608C2212yescomplemented
21#22583605C2214yes—
22#22583605C2214yes—
23#22583605C2214yes—
24#22583604C2214yes—
25#22583603C2214yes—
26#22583603C2214yes—
27#22583603C2214yes—
28#22583602C2214yescomplemented
29#22583602C2211yescharacteristic, complemented
30#22583601C2214yescomplemented
31#22583601C2212yescomplemented
32#22583601C2214yescomplemented
33#22583600C2214yescomplemented
34#22583600C2214yescomplemented
35#22583600C2214yescomplemented
36#22583600C2214yescomplemented
37#22583600C2214yescomplemented
38#22583590C2212yes—
39#22583589C2212yes—
40#22583588C2214yes—
41#22583587C2214yes—
42#22583586C2212yes—
43Q8×Dic283C2212yescomplemented
44C4×Dic566C2214yescomplemented
45C4×Dic566C2212yescomplemented
46#22583575C2214yescomplemented
47#22583575C2212yescomplemented
48#22583569C2211yescharacteristic
49#22583568C2212yes—
50#22583567C2211yescharacteristic
51#22583567C2211yescharacteristic
52#22583566C2212yes—
53C4⋊C4×D283C2214yes—
54C4⋊C4×D283C2212yes—
55C4⋊C4×D283C2214yes—
56C4⋊C4×D283C2212yes—
57C4⋊C4×D283C2214yes—
58C4⋊C4×D283C2214yes—
59C22⋊C4×D283C2214yes—
60C22⋊C4×D283C2212yes—
61C42×D283C2214yes—
62C42×D283C2211yescharacteristic
63C42×D283C2211yescharacteristic
64C4⋊Q8×C283C2211yescharacteristic, complemented
65#126×C283C2214yes—
66#125×C283C2214yescomplemented
67#125×C283C2211yescharacteristic, complemented
68C22⋊Q8×C283C2212yes—
69C4×Q8×C283C2212yescomplemented
70#117×C283C2211yescharacteristic
71C23×D283C2311yescharacteristic
72C2×Dic566C2314yes—
73C2×Dic566C2312yes—
74Q8×D283—28no—
75C22×Dic283C2311yescharacteristic
76C2×C4×D283—24no—
77C2×C4×D283C2312yes—
78C2×C4×D283C2314yes—
79C2×C4×D283C2312yes—
80C2×C4×D283C2314yes—
81C2×C4×D283C2311yescharacteristic
82C2×C4×D283C2311yescharacteristic
83C2×C4×D283C2311yescharacteristic
84C2×C4×D283C2311yescharacteristic
85C4⋊Dic283C2312yes—
86C4⋊Dic283C2312yes—
87C4⋊Dic283C2314yes—
88C4⋊Dic283C2314yes—
89C4⋊Dic283C2314yes—
90C4⋊Dic283C2314yes—
91Dic283⋊C4C2312yes—
92Dic283⋊C4C2312yes—
93Dic283⋊C4C2314yes—
94Dic283⋊C4C2314yes—
95Dic283⋊C4C2314yes—
96Dic283⋊C4C2314yes—
97Dic283⋊C4C2314yes—
98Dic283⋊C4C2314yes—
99Dic283⋊C4C2314yes—
100Dic283⋊C4C2314yes—
101Dic283⋊C4C2314yes—
102C22⋊Dic283C2312yes—
103C22⋊Dic283C2314yes—
104(C2×D283)⋊C4C2312yes—
105(C2×D283)⋊C4C2312yes—
106(C2×D283)⋊C4C2314yes—
107(C2×D283)⋊C4C2314yes—
108C4×Dic283C2312yes—
109C4×Dic283C2312yes—
110C4×Dic283C2311yescharacteristic
111C4×Dic283C2311yescharacteristic
112C4×Dic283C2314yes—
113C4×Dic283C2314yes—
114C4×Dic283C2314yes—
115C2×Q8×C283C2312yes—
116C22×C4×C283C2311yescharacteristic
117C4⋊C4×C283C2312yes—
118C4⋊C4×C283C2312yes—
119C4⋊C4×C283C2314yes—
120C4⋊C4×C283C2314yes—
121C4⋊C4×C283C2314yes—
122C4⋊C4×C283C2314yes—
123C22⋊C4×C283C2312yes—
124C22⋊C4×C283C2314yes—
125C42×C283C2311yescharacteristic
126C42×C283C2311yescharacteristic
127C42×C283C2314yes—
128C22×D283—22no—
129C22×D283—24no—
130C22×D283C2411yescharacteristic
131C22×D283C2411yescharacteristic
132Dic566—24no—
133Dic566—28no—
134C2×Dic283—22no—
135C2×Dic283C2412yes—
136C2×Dic283C2412yes—
137C2×Dic283C2414yes—
138C2×Dic283C2414yes—
139C2×Dic283C2411yescharacteristic
140C2×Dic283C2411yescharacteristic
141C4×D283—22no—
142C4×D283—28no—
143C4×D283—24no—
144C4×D283—28no—
145C4×D283—24no—
146C4×D283—22no—
147C4×D283—22no—
148C4×D283#4114yes—
149C23×C283C2411yescharacteristic
150Q8×C283—24no—
151C2×C4×C283—22no—
152C2×C4×C283C2412yes—
153C2×C4×C283C2412yes—
154C2×C4×C283C2414yes—
155C2×C4×C283C2414yes—
156C2×C4×C283C2411yescharacteristic
157C2×C4×C283C2411yescharacteristic
158C22×C283—21no—
159C22×C283—22no—
160C22×C283C2511yescharacteristic
161C2×D283—21no—
162C2×D283—22no—
163C2×D283—44no—
164C2×D283C2×#4112yes—
165C2×D2832−1+414yes—
166C4×C283—21no—
167C4×C283—24no—
168C4×C283—22no—
169C4×C283—22no—
170C4×C283—24no—
171C4×C283C2×#4112yes—
172Dic283—21no—
173Dic283—24no—
174Dic283—22no—
175Dic283—22no—
176Dic283—24no—
177Dic283C2×#4112yes—
178C2×C283—41no—
179C2×C283C22×#4111yescharacteristic
180C2×C283C2×2−1+412yes—
181D283—41no—
182D283#54114yesdirect product factor
183C283C2×#54111yescharacteristic, complemented, Sylow
184C2×#541—2831nomaximal, Sylow
185#541—2831no—
186#541—2834no—
187#541—2834no—
188#541—2831no—
189#541—2832no—
190#541—2832no—
191#541—2831no—
192#541D28311yescharacteristic, direct product factor
193C2×C4⋊Q8—2831no—
194C2×#126—2834no—
195C2×#125—2831no—
196C2×#125—2834no—
197C2×C22⋊Q8—2832no—
198C2×C4×Q8—2832no—
199C2×#117—2831no—
200C22×Q8—2832no—
201C23×C4—2831no—
202C4⋊Q8—2832no—
203C4⋊Q8—2834no—
204C4⋊Q8—2831no—
205C4⋊Q8C2×D28311yescharacteristic, complemented
206#126—2834no—
207#126—2834no—
208#126—2834no—
209#126—2834no—
210#126—2834no—
211#126—2834no—
212#126—2834no—
213#126C2×D28314yes—
214#125—2834no—
215#125—2834no—
216#125—2834no—
217#125—2834no—
218#125—2834no—
219#125—2832no—
220#125—2834no—
221#125—2834no—
222#125—2831no—
223#125—2834no—
224#125C2×D28311yescharacteristic, complemented
225#125C2×D28314yescomplemented
226C22⋊Q8—2832no—
227C22⋊Q8—2832no—
228C22⋊Q8—2834no—
229C22⋊Q8—2832no—
230C22⋊Q8—2834no—
231C22⋊Q8C2×D28312yes—
232C4×Q8—2832no—
233C4×Q8—2834no—
234C4×Q8—2832no—
235C4×Q8—2834no—
236C4×Q8—2832no—
237C4×Q8C2×D28312yescomplemented
238#117—2831no—
239#117—2832no—
240#117—2832no—
241#117—2831no—
242#117—2831no—
243#117C2×D28311yescharacteristic
244C2×C4⋊C4—2832no—
245C2×C4⋊C4—2832no—
246C2×C4⋊C4—2834no—
247C2×C4⋊C4—2834no—
248C2×C4⋊C4—2834no—
249C2×C4⋊C4—2834no—
250C2×C22⋊C4—2832no—
251C2×C22⋊C4—2834no—
252C2×C42—2831no—
253C2×C42—2831no—
254C2×C42—2834no—
255C24—2831no—
256C2×Q8—2834no—
257C2×Q8—2832no—
258C2×Q8—5668no—
259C2×Q8C22×D28312yes—
260C22×C4—2831no—
261C22×C4—2831no—
262C22×C4—2832no—
263C22×C4—2832no—
264C22×C4—2834no—
265C22×C4—2834no—
266C22×C4—2831no—
267C22×C4—2831no—
268C22×C4—2831no—
269C22×C4—5664no—
270C22×C4C22×D28311yescharacteristic
271C4⋊C4—2832no—
272C4⋊C4—2832no—
273C4⋊C4—2834no—
274C4⋊C4—2834no—
275C4⋊C4—2834no—
276C4⋊C4—2834no—
277C4⋊C4—2834no—
278C4⋊C4—2834no—
279C4⋊C4—2834no—
280C4⋊C4—2834no—
281C4⋊C4—2834no—
282C4⋊C4—2832no—
283C4⋊C4—2832no—
284C4⋊C4—2834no—
285C4⋊C4—2834no—
286C4⋊C4—2834no—
287C4⋊C4—2834no—
288C4⋊C4C22×D28312yes—
289C4⋊C4C22×D28312yes—
290C4⋊C4C22×D28314yes—
291C4⋊C4C22×D28314yes—
292C4⋊C4C22×D28314yes—
293C4⋊C4C22×D28314yes—
294C22⋊C4—2832no—
295C22⋊C4—2834no—
296C22⋊C4—2832no—
297C22⋊C4—2832no—
298C22⋊C4—2834no—
299C22⋊C4—2834no—
300C22⋊C4C22×D28312yes—
301C22⋊C4C22×D28314yes—
302C42—2832no—
303C42—2831no—
304C42—2832no—
305C42—2831no—
306C42—2834no—
307C42—2834no—
308C42—2834no—
309C42C22×D28311yescharacteristic
310C42C22×D28311yescharacteristic
311C42C22×D28314yes—
312C23—2831no—
313C23—2831no—
314C23—5662no—
315C23—5664no—
316C23C23×D28311yescharacteristic
317Q8—24no—
318Q8—5668no—
319Q8—5664no—
320C2×C4—22no—
321C2×C4—2831no—
322C2×C4—2834no—
323C2×C4—2832no—
324C2×C4—2832no—
325C2×C4—2834no—
326C2×C4—2834no—
327C2×C4—2831no—
328C2×C4—5662no—
329C2×C4—5662no—
330C2×C4—5668no—
331C2×C4—5664no—
332C2×C4—5664no—
333C2×C4—5668no—
334C2×C4—5662no—
335C2×C4—5662no—
336C2×C4C23×D28312yes—
337C2×C4C23×D28312yes—
338C2×C4C23×D28314yes—
339C2×C4C23×D28314yes—
340C2×C4C23×D28311yescharacteristic
341C2×C4C23×D28311yescharacteristic
342C22—21no—
343C22—22no—
344C22—2832no—
345C22—2834no—
346C22—5661no—
347C22—5662no—
348C22—11324no—
349C22C24×D28311yescharacteristic
350C4—21no—
351C4—24no—
352C4—22no—
353C4—22no—
354C4—24no—
355C4—2832no—
356C4—5661no—
357C4—5664no—
358C4—5662no—
359C4—5662no—
360C4—5664no—
361C4#41×D28312yes—
362C2—41no—
363C2—2834no—
364C2—11321no—
365C2C2×#41×D28311yescharacteristic
366C22−1+4×D28312yes—
subgroupG/H
center, FrattiniC22C24×D283
commutator, socle, cosocleC22×C283C25
Fitting#541×C283C2
prime radicalC23×D283C23
hypercenter#541D283
hypocenterC283C2×#541
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ #541

Complements

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

NH ≅ G/Ntype
1. #31827078C2semidirect
2. #31827077C2semidirect
3. #31827076C2semidirect
4. #31827075C2semidirect
5. #31827074C2semidirect
6. #31827073C2semidirect
7. #31827072C2semidirect
8. C4⋊Q8×D283C2semidirect
10. #125×D283C2semidirect
11. #125×D283C2semidirect
13. C4×Q8×D283C2semidirect
15. #541×C283C2semidirect
18. #22583610C22semidirect
19. #22583609C22semidirect
20. #22583608C22semidirect
28. #22583602C22semidirect
29. #22583602C22semidirect
30. #22583601C22semidirect
31. #22583601C22semidirect
32. #22583601C22semidirect
33. #22583600C22semidirect
34. #22583600C22semidirect
35. #22583600C22semidirect
36. #22583600C22semidirect
37. #22583600C22semidirect
43. Q8×Dic283C22semidirect
44. C4×Dic566C22semidirect
45. C4×Dic566C22semidirect
46. #22583575C22semidirect
47. #22583575C22semidirect
64. C4⋊Q8×C283C22semidirect
66. #125×C283C22semidirect
67. #125×C283C22semidirect
69. C4×Q8×C283C22semidirect
182. D283#541direct (N × H)
183. C283C2×#541semidirect
192. #541D283direct (N × H)
205. C4⋊Q8C2×D283semidirect
224. #125C2×D283semidirect
225. #125C2×D283semidirect
237. C4×Q8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270782
#318270772
#318270762
#318270752
#318270742
#318270732
#318270722
C4⋊Q8×D2832
#126×D2832
#125×D2832
C22⋊Q8×D2832
C4×Q8×D2832
#117×D2832
#541×C2832
C2×#541283