Finite Group Databasebeta

← #416×D283 #49129753

Subgroups — #416×D283 #49129753

Order 36224.

792 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D283C211yesmaximal, characteristic
2C22×C8×D283C211yesmaximal, characteristic, complemented
3#117×D283C211yesmaximal, characteristic, complemented
4#31826462C211yesmaximal, characteristic, complemented
5#31826461C211yesmaximal, characteristic, complemented
6#31826460C212yesmaximal, complemented
7#31826459C211yesmaximal, characteristic, complemented
8#31826458C212yesmaximal, complemented
9#103×D283C212yesmaximal, complemented
10#102×D283C212yesmaximal, complemented
11#416×C283C211yesmaximal, characteristic, complemented
12C2×#17985393C2211yescharacteristic
13C2×#17985392—21no—
14C2×#17985392C2211yescharacteristic
15C2×#17985391—21no—
16C2×#17985391C2211yescharacteristic
17#41×D283—24no—
18#41×D283C418yescomplemented
19C2×Q8×D283C2211yescharacteristic
20C2×D4×D283—21no—
21C2×D4×D283C2211yescharacteristic
22C22×C4×D283—21no—
23C22×C4×D283C2211yescharacteristic
24C22×C283⋊C8C2211yescharacteristic, complemented
25C2×C8×D283—24no—
26C2×C8×D283C2212yes—
27C2×C8×D283C2212yescomplemented
28#22583569C2211yescharacteristic, complemented
29#22583568C2212yescomplemented
30#22583567—21no—
31#22583566—21no—
32C4⋊C4×D283C2212yes—
33C22⋊C4×D283—21no—
34C42×D283—21no—
35#22583535C2212yescomplemented
36#22583534C2212yescomplemented
37#22583533C2212yescomplemented
38#22583532C2212yescomplemented
39#22583531C2212yescomplemented
40#22583530C2212yescomplemented
41C2×#41×C283C2211yescharacteristic
42C22×C8×C283C2211yescharacteristic, complemented
43#117×C283C2211yescharacteristic, complemented
44#103×C283C2212yescomplemented
45#102×C283C2212yescomplemented
46C23×D283—21no—
47C23×D283D411yescharacteristic
48#17985393—22no—
49#17985393C2×C414yescomplemented
50#17985392—28no—
51#17985392—22no—
52#17985392C2×C414yescomplemented
53#17985391—28no—
54#17985391—22no—
55#17985391C2×C414yescomplemented
56C2×Dic566—21no—
57C2×Dic566C2311yescharacteristic
58Q8×D283—22no—
59Q8×D283C2×C414yes—
60C2×D1132—21no—
61C2×D1132C2311yescharacteristic
62C2×C22⋊D283—21no—
63C2×C22⋊D283—21no—
64C2×C22⋊D283—21no—
65D4×D283—28no—
66D4×D283—22no—
67D4×D283C2×C414yes—
68C22×Dic283—21no—
69C22×Dic283D411yescharacteristic
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—28no—
73C2×C4×D283—22no—
74C2×C4×D283—21no—
75C2×C4×D283C2×C414yes—
76C2×C4×D283D411yescharacteristic
77C2×C4×D283D411yescharacteristic
78C2×C4×D283D414yes—
79C2×C4×D283C2311yescharacteristic
80C2×C4×D283C2311yescharacteristic
81C2×C283⋊C8—22no—
82C2×C283⋊C8C2312yes—
83C8×D283—24no—
84C8×D283—24no—
85C4⋊Dic283C2312yes—
86Dic283⋊C4—22no—
87C22⋊Dic283—21no—
88(C2×D283)⋊C4—22no—
89C4×Dic283—22no—
90C4×Dic283—21no—
91#41×C283—22no—
92#41×C283C2×C414yescomplemented
93C2×Q8×C283C2311yescharacteristic
94C2×D4×C283—21no—
95C2×D4×C283C2311yescharacteristic
96C22×C4×C283—21no—
97C22×C4×C283C2311yescharacteristic
98C2×C8×C283—22no—
99C2×C8×C283C2312yes—
100C4⋊C4×C283C2312yes—
101C22⋊C4×C283—21no—
102C42×C283—21no—
103C22×D283—24no—
104C22×D283—21no—
105C22×D283—24no—
106C22×D283—44no—
107C22×D283C22⋊C414yes—
108C22×D283C2×D411yescharacteristic
109C22×D283C2×D411yescharacteristic
110Dic566—21no—
111Dic566—24no—
112Dic566C22×C412yes—
113D1132—24no—
114D1132—21no—
115D1132C22×C412yes—
116C22⋊D283—24no—
117C22⋊D283—24no—
118C22⋊D283—24no—
119C2×Dic283—21no—
120C2×Dic283—24no—
121C2×Dic283—22no—
122C2×Dic283C22⋊C414yes—
123C2×Dic283C2×D411yescharacteristic
124C2×Dic283C2×D411yescharacteristic
125C4×D283—24no—
126C4×D283—24no—
127C4×D283—24no—
128C4×D283—44no—
129C4×D283C22⋊C414yes—
130C4×D283C22⋊C414yes—
131C4×D283C22×C412yes—
132C4×D283C22×C412yes—
133C4×D283C2×D412yes—
134C4×D283C2×D412yes—
135C283⋊C8—22no—
136C23×C283—21no—
137C23×C283C2×D411yescharacteristic
138Q8×C283—21no—
139Q8×C283C22×C412yes—
140D4×C283—24no—
141D4×C283—21no—
142D4×C283C22×C412yes—
143C2×C4×C283—21no—
144C2×C4×C283—24no—
145C2×C4×C283—22no—
146C2×C4×C283C22×C412yes—
147C2×C4×C283C2×D412yes—
148C2×C4×C283C2×D411yescharacteristic
149C2×C4×C283C2411yescharacteristic
150C8×C283—22no—
151C22×C283—22no—
152C22×C283—22no—
153C22×C283—42no—
154C22×C283C2×C22⋊C412yes—
155C22×C283C22×D411yescharacteristic
156C2×D283—22no—
157C2×D283—28no—
158C2×D283—22no—
159C2×D283—42no—
160C2×D283—48no—
161C2×D283C2×C22⋊C412yes—
162C2×D283C2×C22⋊C412yes—
163C2×D283#13514yes—
164C4×C283—22no—
165C4×C283—42no—
166C4×C283C2×C22⋊C412yes—
167C4×C283C23×C411yescharacteristic
168C4×C283C22×D411yescharacteristic
169Dic283—22no—
170Dic283—42no—
171Dic283C2×C22⋊C412yes—
172Dic283C2×C22⋊C412yes—
173C2×C283—22no—
174C2×C283—42no—
175C2×C283C22×C22⋊C411yescharacteristic
176C2×C283C2×#13512yes—
177D283—22no—
178D283—42no—
179D283#41614yesdirect product factor
180C283C2×#41611yescharacteristic, complemented, Sylow
181C2×#416—2831nomaximal, Sylow
182C22×#41—2831no—
183C23×C8—2831no—
184C2×#117—2831no—
185#416—2831no—
186#416—2831no—
187#416—2831no—
188#416—2832no—
189#416—2832no—
190#416D28311yescharacteristic, direct product factor
191C2×#103—2832no—
192C2×#102—2832no—
193C2×#41—2838no—
194C2×#41—2831no—
195C2×#41—2831no—
196C2×#41—2831no—
197C2×#41—5661no—
198C2×#41—5661no—
199C2×#41—5664no—
200C2×#41C2×D28311yescharacteristic
201C22×Q8—2831no—
202C22×D4—2831no—
203C22×D4—5661no—
204C23×C4—2831no—
205C23×C4—5661no—
206C22×C8—2831no—
207C22×C8—2832no—
208C22×C8—2832no—
209C22×C8—5664no—
210C22×C8C2×D28311yescharacteristic, complemented
211#117—2831no—
212#117—2832no—
213#117—5661no—
214#117—5661no—
215#117C2×D28311yescharacteristic, complemented
216C2×C4⋊C4—2832no—
217C2×C22⋊C4—5661no—
218C2×C42—5661no—
219#103—2832no—
220#103—2832no—
221#103—2832no—
222#103C2×D28312yescomplemented
223#102—2832no—
224#102—2832no—
225#102—2832no—
226#102C2×D28312yescomplemented
227C24—2831no—
228C24—5661no—
229#41—22no—
230#41—2834no—
231#41—2834no—
232#41—2834no—
233#41—5668no—
234#41—5668no—
235#41—5662no—
236#41—5662no—
237#41—5662no—
238#41C4×D28314yescomplemented
239C2×Q8—2834no—
240C2×Q8—2831no—
241C2×Q8—5661no—
242C2×Q8—5662no—
243C2×Q8C22×D28311yescharacteristic
244C2×D4—21no—
245C2×D4—2834no—
246C2×D4—2831no—
247C2×D4—5661no—
248C2×D4—5662no—
249C2×D4—5661no—
250C2×D4—5668no—
251C2×D4—5661no—
252C2×D4—5661no—
253C2×D4C22×D28311yescharacteristic
254C22×C4—21no—
255C22×C4—2831no—
256C22×C4—2834no—
257C22×C4—2834no—
258C22×C4—2831no—
259C22×C4—2831no—
260C22×C4—2831no—
261C22×C4—2831no—
262C22×C4—5661no—
263C22×C4—5668no—
264C22×C4—5661no—
265C22×C4—5662no—
266C22×C4—5661no—
267C22×C4—5661no—
268C22×C4C22×D28311yescharacteristic
269C2×C8—22no—
270C2×C8—2832no—
271C2×C8—5664no—
272C2×C8—5664no—
273C2×C8—5662no—
274C2×C8C22×D28312yes—
275C4⋊C4—2832no—
276C4⋊C4—5662no—
277C4⋊C4C22×D28312yes—
278C22⋊C4—21no—
279C22⋊C4—5662no—
280C22⋊C4—5661no—
281C42—21no—
282C42—5662no—
283C42—5661no—
284C23—21no—
285C23—2831no—
286C23—2834no—
287C23—2831no—
288C23—5664no—
289C23—5664no—
290C23—5661no—
291C23—11324no—
292C23D4×D28311yescharacteristic
293Q8—21no—
294Q8—2832no—
295Q8—5664no—
296Q8—5661no—
297Q8C2×C4×D28312yes—
298D4—24no—
299D4—21no—
300D4—2832no—
301D4—5664no—
302D4—5664no—
303D4—5664no—
304D4—5664no—
305D4—5661no—
306D4C2×C4×D28312yes—
307C2×C4—21no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—2834no—
311C2×C4—2831no—
312C2×C4—2831no—
313C2×C4—2834no—
314C2×C4—2834no—
315C2×C4—2832no—
316C2×C4—2832no—
317C2×C4—2832no—
318C2×C4—2832no—
319C2×C4—5664no—
320C2×C4—5664no—
321C2×C4—5664no—
322C2×C4—5661no—
323C2×C4—5664no—
324C2×C4—5662no—
325C2×C4—11324no—
326C2×C4C2×C4×D28312yes—
327C2×C4D4×D28312yes—
328C2×C4D4×D28311yescharacteristic
329C2×C4C23×D28311yescharacteristic
330C8—22no—
331C8—5662no—
332C22—22no—
333C22—22no—
334C22—42no—
335C22—2834no—
336C22—2832no—
337C22—2832no—
338C22—5668no—
339C22—5662no—
340C22—5662no—
341C22—11328no—
342C22—11322no—
343C22C22⋊C4×D28312yes—
344C22C2×D4×D28311yescharacteristic
345C4—22no—
346C4—42no—
347C4—2832no—
348C4—2832no—
349C4—5662no—
350C4—11322no—
351C4C22⋊C4×D28312yes—
352C4C22×C4×D28311yescharacteristic
353C4C2×D4×D28311yescharacteristic
354C2—22no—
355C2—42no—
356C2—2834no—
357C2—5662no—
358C2—11322no—
359C2C2×C22⋊C4×D28311yescharacteristic
360C2#135×D28312yes—
subgroupG/H
centerC2×C4D4×D283
commutatorC4×C283C23×C4
FrattiniC2×C4C23×D283
Fitting#416×C283C2
socleC22×C283C22×D4
prime radicalC2×#41×D283C2
cosocleC2×C4×C283C24
hypercenter#416D283
hypocenterC283C2×#416
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. C22×C8×D283C2semidirect
3. #117×D283C2semidirect
4. #31826462C2semidirect
5. #31826461C2semidirect
6. #31826460C2semidirect
7. #31826459C2semidirect
8. #31826458C2semidirect
9. #103×D283C2semidirect
10. #102×D283C2semidirect
11. #416×C283C2semidirect
18. #41×D283C4semidirect
24. C22×C283⋊C8C22semidirect
27. C2×C8×D283C22semidirect
28. #22583569C22semidirect
29. #22583568C22semidirect
35. #22583535C22semidirect
36. #22583534C22semidirect
37. #22583533C22semidirect
38. #22583532C22semidirect
39. #22583531C22semidirect
40. #22583530C22semidirect
42. C22×C8×C283C22semidirect
43. #117×C283C22semidirect
44. #103×C283C22semidirect
45. #102×C283C22semidirect
49. #17985393C2×C4semidirect
52. #17985392C2×C4semidirect
55. #17985391C2×C4semidirect
92. #41×C283C2×C4semidirect
179. D283#416direct (N × H)
180. C283C2×#416semidirect
190. #416D283direct (N × H)
210. C22×C8C2×D283semidirect
215. #117C2×D283semidirect
222. #103C2×D283semidirect
226. #102C2×D283semidirect
238. #41C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D2832
C22×C8×D2832
#117×D2832
#318264622
#318264612
#318264602
#318264592
#318264582
#103×D2832
#102×D2832
#416×C2832
C2×#416283