Finite Group Databasebeta

← #397×D283 #49124484

Subgroups — #397×D283 #49124484

Order 36224.

820 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D283C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D283C212yesmaximal
3C2×C22⋊C4×D283C211yesmaximal, characteristic
4#31826394C212yesmaximal, complemented
5#31826393C212yesmaximal, complemented
6#31826392C211yesmaximal, characteristic, complemented
7#31826391C211yesmaximal, characteristic, complemented
8#31826390C211yesmaximal, characteristic, complemented
9#95×D283C212yesmaximal, complemented
10#95×D283C211yesmaximal, characteristic, complemented
11#397×C283C211yesmaximal, characteristic, complemented
12C24×D283C2211yescharacteristic
13C22×C4×D283C2212yes—
14C22×C4×D283C2211yescharacteristic
15C22×C4×D283C2212yes—
16C22×C4×D283C2211yescharacteristic
17C2×C4⋊Dic283C2211yescharacteristic, complemented
18C2×Dic283⋊C4C2212yescomplemented
19C4⋊C4×D283—24no—
20C2×C22⋊Dic283C2212yes—
21C2×C22⋊Dic283C2211yescharacteristic
22C2×(C2×D283)⋊C4C2211yescharacteristic
23C2×(C2×D283)⋊C4C2212yes—
24C2×(C2×D283)⋊C4C2212yes—
25C2×(C2×D283)⋊C4C2211yescharacteristic
26C22⋊C4×D283—28no—
27C22⋊C4×D283—24no—
28C283⋊#95C2211yescharacteristic, complemented
29C283⋊#95C2212yescomplemented
30C283⋊#95C2212yescomplemented
31C283⋊#95C2212yescomplemented
32C283⋊#95C2212yescomplemented
33C2×C4⋊C4×C283C2211yescharacteristic, complemented
34C2×C22⋊C4×C283C2211yescharacteristic
35C2×C22⋊C4×C283C2212yes—
36#95×C283C2211yescharacteristic, complemented
37#95×C283C2212yescomplemented
38C23×D283—22no—
39C23×D283—22no—
40C23×D283—24no—
41C23×D283—24no—
42C23×D283D414yes—
43C23×D283C2311yescharacteristic
44C23×D283C2311yescharacteristic
45C22×Dic283C2312yes—
46C22×Dic283C2311yescharacteristic
47C22×Dic283C2312yes—
48C22×Dic283C2311yescharacteristic
49C2×C4×D283—24no—
50C2×C4×D283—24no—
51C2×C4×D283—24no—
52C2×C4×D283—22no—
53C2×C4×D283—24no—
54C2×C4×D283—24no—
55C2×C4×D283—24no—
56C2×C4×D283—24no—
57C2×C4×D283—24no—
58C2×C4×D283D414yes—
59C4⋊Dic283—22no—
60Dic283⋊C4—24no—
61C22⋊Dic283—22no—
62C22⋊Dic283—24no—
63(C2×D283)⋊C4—24no—
64(C2×D283)⋊C4—24no—
65(C2×D283)⋊C4—22no—
66(C2×D283)⋊C4—22no—
67C24×C283C2311yescharacteristic
68C22×C4×C283C2312yes—
69C22×C4×C283C2312yes—
70C22×C4×C283C2311yescharacteristic
71C22×C4×C283C2311yescharacteristic
72C4⋊C4×C283—22no—
73C22⋊C4×C283—24no—
74C22⋊C4×C283—22no—
75C22×D283—21no—
76C22×D283—21no—
77C22×D283—22no—
78C22×D283—22no—
79C22×D283—28no—
80C22×D283—216no—
81C22×D283—44no—
82C22×D283—44no—
83C22×D283—48no—
84C22×D283C2×D412yes—
85C22×D283C2×D412yes—
86C22×D283C2×D412yes—
87C22×D283#4112yes—
88C22×D283#4114yes—
89C22×D283#4114yes—
90C2×Dic283—22no—
91C2×Dic283—22no—
92C2×Dic283—22no—
93C2×Dic283—21no—
94C2×Dic283—22no—
95C2×Dic283—22no—
96C2×Dic283—22no—
97C2×Dic283—22no—
98C2×Dic283—22no—
99C2×Dic283C2×D412yes—
100C4×D283—28no—
101C4×D283—48no—
102C4×D283—48no—
103C4×D283—44no—
104C23×C283—21no—
105C23×C283—21no—
106C23×C283—22no—
107C23×C283—22no—
108C23×C283C2×D412yes—
109C23×C283C2411yescharacteristic
110C2×C4×C283—22no—
111C2×C4×C283—22no—
112C2×C4×C283—22no—
113C2×C4×C283—21no—
114C2×C4×C283—22no—
115C2×C4×C283—22no—
116C2×C4×C283—22no—
117C2×C4×C283—22no—
118C2×C4×C283—22no—
119C2×C4×C283C2×D412yes—
120C22×C283—22no—
121C22×C283—24no—
122C22×C283—41no—
123C22×C283—41no—
124C22×C283—42no—
125C22×C283C22×D411yescharacteristic
126C22×C283C22×D411yescharacteristic
127C22×C283C2×#4111yescharacteristic
128C22×C283C2×#4112yes—
129C22×C283C2×#4112yes—
130C2×D283—22no—
131C2×D283—24no—
132C2×D283—41no—
133C2×D283—41no—
134C2×D283—42no—
135C2×D283—416no—
136C2×D283#12114yes—
137C2×D283#12314yes—
138C2×D283#12318yes—
139C2×D283#12414yes—
140C2×D283#12618yes—
141C4×C283—22no—
142C4×C283—42no—
143C4×C283—42no—
144C4×C283—41no—
145Dic283—22no—
146Dic283—42no—
147Dic283—42no—
148Dic283—41no—
149C2×C283—42no—
150C2×C283C2×#12111yescharacteristic
151C2×C283C2×#12311yescharacteristic
152C2×C283C2×#12312yes—
153C2×C283C2×#12411yescharacteristic
154C2×C283C2×#12612yes—
155D283—42no—
156D283#39718yesdirect product factor
157C283C2×#39711yescharacteristic, complemented, Sylow
158C2×#397—2831nomaximal, Sylow
159C22×C4⋊C4—2831no—
160C22×C22⋊C4—2831no—
161C22×C22⋊C4—2832no—
162#397—2831no—
163#397—2831no—
164#397—2832no—
165#397—2831no—
166#397—2832no—
167#397D28311yescharacteristic, direct product factor
168C2×#95—2831no—
169C2×#95—2832no—
170C25—2831no—
171C23×C4—2831no—
172C23×C4—2832no—
173C23×C4—2831no—
174C23×C4—2832no—
175C2×C4⋊C4—2832no—
176C2×C4⋊C4—2831no—
177C2×C4⋊C4—5664no—
178C2×C4⋊C4C2×D28311yescharacteristic, complemented
179C2×C22⋊C4—2831no—
180C2×C22⋊C4—2832no—
181C2×C22⋊C4—2831no—
182C2×C22⋊C4—2832no—
183C2×C22⋊C4—2832no—
184C2×C22⋊C4—2831no—
185C2×C22⋊C4—5664no—
186C2×C22⋊C4—5668no—
187C2×C22⋊C4C2×D28312yes—
188C2×C22⋊C4C2×D28311yescharacteristic
189#95—2832no—
190#95—2832no—
191#95—2831no—
192#95—2832no—
193#95—2832no—
194#95C2×D28312yescomplemented
195#95C2×D28311yescharacteristic, complemented
196C24—2831no—
197C24—2834no—
198C24—2831no—
199C24—5662no—
200C24—5662no—
201C24—5664no—
202C24—5664no—
203C24C22×D28311yescharacteristic
204C22×C4—2831no—
205C22×C4—2834no—
206C22×C4—2832no—
207C22×C4—2831no—
208C22×C4—2832no—
209C22×C4—5664no—
210C22×C4—5662no—
211C22×C4—5664no—
212C22×C4—5664no—
213C22×C4—5664no—
214C22×C4—5664no—
215C22×C4—5664no—
216C22×C4—5664no—
217C22×C4—5664no—
218C22×C4C22×D28312yes—
219C22×C4C22×D28311yescharacteristic
220C22×C4C22×D28312yes—
221C22×C4C22×D28311yescharacteristic
222C4⋊C4—22no—
223C4⋊C4—5664no—
224C4⋊C4—5662no—
225C22⋊C4—24no—
226C22⋊C4—22no—
227C22⋊C4—5662no—
228C22⋊C4—5664no—
229C22⋊C4—5664no—
230C22⋊C4—5662no—
231C22⋊C4—5664no—
232C22⋊C4—5662no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—22no—
237C23—2832no—
238C23—2832no—
239C23—2832no—
240C23—2834no—
241C23—2834no—
242C23—2832no—
243C23—5668no—
244C23—56616no—
245C23—5661no—
246C23—5661no—
247C23—5662no—
248C23—5662no—
249C23—11324no—
250C23—11324no—
251C23—11328no—
252C23D4×D28312yes—
253C23C23×D28311yescharacteristic
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—2832no—
264C2×C4—5668no—
265C2×C4—5662no—
266C2×C4—5662no—
267C2×C4—5662no—
268C2×C4—5661no—
269C2×C4—5662no—
270C2×C4—5662no—
271C2×C4—5662no—
272C2×C4—5662no—
273C2×C4—5662no—
274C2×C4—11328no—
275C2×C4—11328no—
276C2×C4—11324no—
277C2×C4D4×D28312yes—
278C22—22no—
279C22—24no—
280C22—41no—
281C22—41no—
282C22—42no—
283C22—2834no—
284C22—2834no—
285C22—2838no—
286C22—2834no—
287C22—2838no—
288C22—5662no—
289C22—5664no—
290C22—113216no—
291C22—11321no—
292C22—11321no—
293C22—11322no—
294C22C2×D4×D28311yescharacteristic
295C22C2×D4×D28311yescharacteristic
296C22#41×D28311yescharacteristic
297C22#41×D28312yes—
298C22#41×D28312yes—
299C4—22no—
300C4—42no—
301C4—42no—
302C4—41no—
303C4—5662no—
304C4—11322no—
305C4—11322no—
306C4—11321no—
307C2—42no—
308C2—2838no—
309C2—11322no—
310C2#121×D28311yescharacteristic
311C2#123×D28311yescharacteristic
312C2#123×D28312yes—
313C2#124×D28311yescharacteristic
314C2#126×D28312yes—
subgroupG/H
center, FrattiniC23C23×D283
commutator, socle, cosocleC23×C283C24
Fitting#397×C283C2
prime radicalC24×D283C22
hypercenter#397D283
hypocenterC283C2×#397
LCSG ▷ C23×C283 ▷ C283
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×D283C2semidirect
4. #31826394C2semidirect
5. #31826393C2semidirect
6. #31826392C2semidirect
7. #31826391C2semidirect
8. #31826390C2semidirect
9. #95×D283C2semidirect
10. #95×D283C2semidirect
11. #397×C283C2semidirect
17. C2×C4⋊Dic283C22semidirect
18. C2×Dic283⋊C4C22semidirect
28. C283⋊#95C22semidirect
29. C283⋊#95C22semidirect
30. C283⋊#95C22semidirect
31. C283⋊#95C22semidirect
32. C283⋊#95C22semidirect
33. C2×C4⋊C4×C283C22semidirect
36. #95×C283C22semidirect
37. #95×C283C22semidirect
156. D283#397direct (N × H)
157. C283C2×#397semidirect
167. #397D283direct (N × H)
178. C2×C4⋊C4C2×D283semidirect
194. #95C2×D283semidirect
195. #95C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D2832
C2×C22⋊C4×D2832
#318263942
#318263932
#318263922
#318263912
#318263902
#95×D2832
#397×C2832
C2×#397283