Finite Group Databasebeta

← #410×D283 #49129715

Subgroups — #410×D283 #49129715

Order 36224.

788 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D283C211yesmaximal, characteristic
2#117×D283C212yesmaximal, complemented
3#31826439C211yesmaximal, characteristic, complemented
4#31826438C212yesmaximal, complemented
5#31826437C214yesmaximal, complemented
6#99×D283C214yesmaximal, complemented
7#410×C283C211yesmaximal, characteristic, complemented
8C2×#17985393C411yescharacteristic, complemented
9C2×#17985392C412yescomplemented
10C2×#17985392C2211yescharacteristic
11C2×#17985391C411yescharacteristic, complemented
12C2×#17985391C2212yes—
13#41×D283—22no—
14#41×D283—22no—
15#41×D283—22no—
16#41×D283—22no—
17C2×Q8×D283C411yescharacteristic, complemented
18C2×D4×D283C411yescharacteristic, complemented
19C2×D4×D283C2212yes—
20C22×C4×D283C412yescomplemented
21C22×C4×D283C2211yescharacteristic
22#22583569C2212yescomplemented
23#22583568—22no—
24#22583567—22no—
25#22583566C2214yescomplemented
26C4⋊C4×D283—22no—
27C22⋊C4×D283C2214yes—
28C42×D283—22no—
29#22583525C2214yescomplemented
30#22583524C2218yescomplemented
31C2×#41×C283C2211yescharacteristic
32#117×C283C2212yescomplemented
33#99×C283C2214yescomplemented
34C23×D283C2×C412yes—
35C23×D283C2311yescharacteristic
36#17985393—22no—
37#17985393—22no—
38#17985392—24no—
39#17985392—24no—
40#17985392—22no—
41#17985392—22no—
42#17985391—24no—
43#17985391—24no—
44#17985391—22no—
45#17985391—22no—
46C2×Dic566C2×C411yescharacteristic, complemented
47C2×Dic566C2×C412yescomplemented
48Q8×D283—22no—
49Q8×D283—22no—
50C2×D1132C2×C412yes—
51C2×D1132C2×C411yescharacteristic, complemented
52C2×C22⋊D283C2×C412yes—
53C2×C22⋊D283C2×C412yescomplemented
54C2×C22⋊D283C2312yes—
55D4×D283—24no—
56D4×D283—24no—
57D4×D283—22no—
58D4×D283—22no—
59C22×Dic283C2×C412yescomplemented
60C22×Dic283C2311yescharacteristic
61C2×C4×D283—22no—
62C2×C4×D283—22no—
63C2×C4×D283—22no—
64C2×C4×D283—22no—
65C2×C4×D283—24no—
66C2×C4×D283C2×C412yes—
67C2×C4×D283C2×C411yescharacteristic
68C2×C4×D283C2×C411yescharacteristic
69C2×C4×D283C2×C411yescharacteristic
70C2×C4×D283C2×C411yescharacteristic
71C2×C4×D283C2×C412yescomplemented
72C2×C4×D283C2×C412yescomplemented
73C2×C4×D283D412yes—
74C2×C4×D283D412yes—
75C2×C4×D283D412yes—
76C2×C4×D283D412yes—
77C4⋊Dic283—22no—
78Dic283⋊C4—24no—
79C22⋊Dic283C2314yes—
80(C2×D283)⋊C4—24no—
81C4×Dic283—24no—
82C4×Dic283—22no—
83#41×C283—22no—
84#41×C283—22no—
85C2×Q8×C283C2×C411yescharacteristic, complemented
86C2×D4×C283C2×C411yescharacteristic, complemented
87C2×D4×C283C2312yes—
88C22×C4×C283C2×C412yescomplemented
89C22×C4×C283C2311yescharacteristic
90C4⋊C4×C283—22no—
91C22⋊C4×C283C2314yes—
92C42×C283—22no—
93C22×D283—22no—
94C22×D283—22no—
95C22×D283—42no—
96C22×D283—44no—
97C22×D283C22×C411yescharacteristic
98C22×D283C22×C412yes—
99C22×D283C22×C411yescharacteristic
100C22×D283C2×D412yes—
101C22×D283C2×D412yes—
102Dic566—22no—
103Dic566—24no—
104D1132—24no—
105D1132—22no—
106C22⋊D283—24no—
107C22⋊D283—24no—
108C22⋊D283—24no—
109C2×Dic283—22no—
110C2×Dic283—22no—
111C2×Dic283—24no—
112C2×Dic283C22×C412yes—
113C2×Dic283C22×C411yescharacteristic
114C2×Dic283C22×C411yescharacteristic
115C2×Dic283C2×D412yes—
116C2×Dic283C2×D412yes—
117C4×D283—22no—
118C4×D283—22no—
119C4×D283—22no—
120C4×D283—22no—
121C4×D283—22no—
122C4×D283—22no—
123C4×D283—48no—
124C4×D283C22⋊C411yescharacteristic
125C4×D283C22⋊C411yescharacteristic
126C4×D283C22⋊C411yescharacteristic
127C4×D283C22⋊C411yescharacteristic
128C4×D283C22⋊C412yes—
129C4×D283C22⋊C412yes—
130C4×D283C22⋊C412yes—
131C4×D283C22⋊C412yes—
132C4×D283C22⋊C412yes—
133C4×D283C22⋊C412yes—
134C23×C283C22×C412yes—
135C23×C283C2411yescharacteristic
136Q8×C283—22no—
137D4×C283—24no—
138D4×C283—22no—
139C2×C4×C283—22no—
140C2×C4×C283—22no—
141C2×C4×C283—24no—
142C2×C4×C283C22×C412yes—
143C2×C4×C283C22×C411yescharacteristic
144C2×C4×C283C22×C411yescharacteristic
145C2×C4×C283C2×D412yes—
146C2×C4×C283C2×D412yes—
147C22×C283—22no—
148C22×C283—41no—
149C22×C283—42no—
150C22×C283C23×C411yescharacteristic
151C22×C283C22×D412yes—
152C2×D283—24no—
153C2×D283—22no—
154C2×D283—22no—
155C2×D283—41no—
156C2×D283—42no—
157C2×D283—44no—
158C2×D283—44no—
159C2×D283—42no—
160C2×D283C2×C22⋊C411yescharacteristic
161C2×D283C2×C22⋊C412yes—
162C2×D283C2×C22⋊C411yescharacteristic
163C4×C283—22no—
164C4×C283—44no—
165C4×C283C2×C22⋊C411yescharacteristic
166C4×C283C2×C22⋊C412yes—
167C4×C283C2×C22⋊C411yescharacteristic
168Dic283—22no—
169Dic283—44no—
170Dic283C2×C22⋊C411yescharacteristic
171Dic283C2×C22⋊C411yescharacteristic
172Dic283C2×C22⋊C412yes—
173C2×C283—22no—
174C2×C283—21no—
175C2×C283—42no—
176C2×C283C22×C22⋊C411yescharacteristic
177D283—21no—
178D283—22no—
179D283—42no—
180D283#41012yesdirect product factor
181C283C2×#41011yescharacteristic, complemented, Sylow
182C2×#410—2831nomaximal, Sylow
183C22×#41—2831no—
184C2×#117—2832no—
185#410—2831no—
186#410—2832no—
187#410—2834no—
188#410D28311yescharacteristic, direct product factor
189C2×#99—2834no—
190C2×#41—2831no—
191C2×#41—2831no—
192C2×#41—2832no—
193C2×#41—2832no—
194C2×#41—2831no—
195C2×#41—5662no—
196C2×#41—5662no—
197C2×#41—5662no—
198C2×#41—5662no—
199C2×#41C2×D28311yescharacteristic
200C22×Q8—2831no—
201C22×D4—2831no—
202C22×D4—2832no—
203C23×C4—2831no—
204C23×C4—2832no—
205#117—2832no—
206#117—2834no—
207#117—5662no—
208#117—5662no—
209#117C2×D28312yescomplemented
210C2×C4⋊C4—5662no—
211C2×C22⋊C4—2834no—
212C2×C42—5662no—
213#99—2834no—
214#99—2838no—
215#99C2×D28314yescomplemented
216C24—2831no—
217C24—2832no—
218#41—22no—
219#41—22no—
220#41—5664no—
221#41—5664no—
222#41—5664no—
223#41—5664no—
224#41—5662no—
225#41—5662no—
226#41—5662no—
227#41—5662no—
228#41—5662no—
229#41—5662no—
230C2×Q8—2832no—
231C2×Q8—2831no—
232C2×Q8—5662no—
233C2×Q8—5662no—
234C2×Q8C4×D28311yescharacteristic, complemented
235C2×D4—2832no—
236C2×D4—2832no—
237C2×D4—2832no—
238C2×D4—2832no—
239C2×D4—2831no—
240C2×D4—5662no—
241C2×D4—5662no—
242C2×D4—5664no—
243C2×D4—5664no—
244C2×D4C4×D28311yescharacteristic, complemented
245C2×D4C22×D28312yes—
246C22×C4—2831no—
247C22×C4—2831no—
248C22×C4—2831no—
249C22×C4—2831no—
250C22×C4—2831no—
251C22×C4—2832no—
252C22×C4—2832no—
253C22×C4—2832no—
254C22×C4—2832no—
255C22×C4—2832no—
256C22×C4—2832no—
257C22×C4—2832no—
258C22×C4—2832no—
259C22×C4—5662no—
260C22×C4—5662no—
261C22×C4—5662no—
262C22×C4—5662no—
263C22×C4—5664no—
264C22×C4C4×D28312yescomplemented
265C22×C4C22×D28311yescharacteristic
266C4⋊C4—22no—
267C4⋊C4—5664no—
268C4⋊C4—5662no—
269C22⋊C4—2834no—
270C22⋊C4—5664no—
271C22⋊C4C22×D28314yes—
272C42—22no—
273C42—5664no—
274C42—5662no—
275C23—2831no—
276C23—2832no—
277C23—2831no—
278C23—2832no—
279C23—2832no—
280C23—5662no—
281C23—5662no—
282C23—11322no—
283C23—11324no—
284C23C2×C4×D28312yes—
285C23C23×D28311yescharacteristic
286Q8—22no—
287Q8—5664no—
288Q8—5662no—
289D4—24no—
290D4—22no—
291D4—5664no—
292D4—5664no—
293D4—5664no—
294D4—5664no—
295D4—5662no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—24no—
299C2×C4—2831no—
300C2×C4—2831no—
301C2×C4—2832no—
302C2×C4—2832no—
303C2×C4—2831no—
304C2×C4—2831no—
305C2×C4—2832no—
306C2×C4—2832no—
307C2×C4—2832no—
308C2×C4—2832no—
309C2×C4—2832no—
310C2×C4—2831no—
311C2×C4—2831no—
312C2×C4—2832no—
313C2×C4—2832no—
314C2×C4—5662no—
315C2×C4—5662no—
316C2×C4—5662no—
317C2×C4—5662no—
318C2×C4—5662no—
319C2×C4—5662no—
320C2×C4—5662no—
321C2×C4—5662no—
322C2×C4—5664no—
323C2×C4—11328no—
324C2×C4C2×C4×D28312yes—
325C2×C4C2×C4×D28311yescharacteristic
326C2×C4C2×C4×D28311yescharacteristic
327C2×C4D4×D28312yes—
328C2×C4D4×D28312yes—
329C22—22no—
330C22—41no—
331C22—42no—
332C22—2831no—
333C22—2831no—
334C22—2832no—
335C22—5664no—
336C22—5662no—
337C22—5662no—
338C22—11322no—
339C22—11321no—
340C22—11322no—
341C22—11324no—
342C22—11324no—
343C22C22×C4×D28311yescharacteristic
344C22C2×D4×D28312yes—
345C4—22no—
346C4—44no—
347C4—2831no—
348C4—2831no—
349C4—2832no—
350C4—5662no—
351C4—11324no—
352C4C22⋊C4×D28311yescharacteristic
353C4C22⋊C4×D28312yes—
354C4C22⋊C4×D28311yescharacteristic
355C2—22no—
356C2—21no—
357C2—42no—
358C2—2832no—
359C2—5661no—
360C2—5662no—
361C2—11322no—
362C2C2×C22⋊C4×D28311yescharacteristic
subgroupG/H
centerC4C22⋊C4×D283
commutatorC22×C283C23×C4
FrattiniC23C23×D283
Fitting#410×C283C2
socleC2×C283C22×C22⋊C4
prime radicalC2×#41×D283C2
cosocleC23×C283C24
hypercenter#410D283
hypocenterC283C2×#410
LCSG ▷ C22×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #117×D283C2semidirect
3. #31826439C2semidirect
4. #31826438C2semidirect
5. #31826437C2semidirect
6. #99×D283C2semidirect
7. #410×C283C2semidirect
8. C2×#17985393C4semidirect
9. C2×#17985392C4semidirect
11. C2×#17985391C4semidirect
17. C2×Q8×D283C4semidirect
18. C2×D4×D283C4semidirect
20. C22×C4×D283C4semidirect
22. #22583569C22semidirect
25. #22583566C22semidirect
29. #22583525C22semidirect
30. #22583524C22semidirect
32. #117×C283C22semidirect
33. #99×C283C22semidirect
46. C2×Dic566C2×C4semidirect
47. C2×Dic566C2×C4semidirect
51. C2×D1132C2×C4semidirect
53. C2×C22⋊D283C2×C4semidirect
59. C22×Dic283C2×C4semidirect
71. C2×C4×D283C2×C4semidirect
72. C2×C4×D283C2×C4semidirect
85. C2×Q8×C283C2×C4semidirect
86. C2×D4×C283C2×C4semidirect
88. C22×C4×C283C2×C4semidirect
180. D283#410direct (N × H)
181. C283C2×#410semidirect
188. #410D283direct (N × H)
209. #117C2×D283semidirect
215. #99C2×D283semidirect
234. C2×Q8C4×D283semidirect
244. C2×D4C4×D283semidirect
264. C22×C4C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D2832
#117×D2832
#318264392
#318264382
#318264372
#99×D2832
#410×C2832
C2×#410283