Finite Group Databasebeta

← #394×D283 #49124463

Subgroups — #394×D283 #49124463

Order 36224.

1252 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
1C22×D4×D283C211yesmaximal, characteristic
2C2×C4⋊C4×D283C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D283C212yesmaximal, complemented
4C2×C22⋊C4×D283C212yesmaximal, complemented
5#31826383C211yesmaximal, characteristic, complemented
6#31826382C211yesmaximal, characteristic, complemented
7#31826381C212yesmaximal, complemented
8#31826380C212yesmaximal, complemented
9#31826379C211yesmaximal, characteristic, complemented
10#95×D283C211yesmaximal, characteristic, complemented
11#394×C283C211yesmaximal, characteristic, complemented
12C24×D283C2212yes—
13C22×D1132C2211yescharacteristic
14C22×C22⋊D283C2212yes—
15C2×D4×D283—28no—
16C2×D4×D283—24no—
17C22×C4×D283C2212yes—
18C22×C4×D283C2211yescharacteristic
19C22×C4×D283C2211yescharacteristic
20C22×C4×D283C2211yescharacteristic
21C2×C4⋊Dic283C2211yescharacteristic, complemented
22C2×Dic283⋊C4C2211yescharacteristic, complemented
23C2×Dic283⋊C4C2211yescharacteristic, complemented
24C4⋊C4×D283—24no—
25C2×C22⋊Dic283C2212yescomplemented
26C2×C22⋊Dic283C2212yescomplemented
27C2×(C2×D283)⋊C4C2212yescomplemented
28C2×(C2×D283)⋊C4C2212yescomplemented
29C2×(C2×D283)⋊C4C2212yescomplemented
30C2×(C2×D283)⋊C4C2212yescomplemented
31C22⋊C4×D283—28no—
32C22⋊C4×D283—28no—
33C283⋊#95C2211yescharacteristic, complemented
34C283⋊#95C2212yescomplemented
35C22×D4×C283C2211yescharacteristic
36C2×C4⋊C4×C283C2211yescharacteristic, complemented
37C2×C22⋊C4×C283C2212yescomplemented
38C2×C22⋊C4×C283C2212yescomplemented
39#95×C283C2211yescharacteristic, complemented
40C23×D283—24no—
41C23×D283—24no—
42C23×D283—24no—
43C23×D283—24no—
44C23×D283—24no—
45C23×D283—24no—
46C23×D283D418yes—
47C23×D283C2312yes—
48C23×D283C2311yescharacteristic
49C2×D1132—24no—
50C2×D1132—22no—
51C2×C22⋊D283—24no—
52C2×C22⋊D283—24no—
53C2×C22⋊D283—24no—
54D4×D283—232no—
55C22×Dic283C2311yescharacteristic
56C22×Dic283C2312yes—
57C22×Dic283C2311yescharacteristic
58C22×Dic283C2311yescharacteristic
59C2×C4×D283—22no—
60C2×C4×D283—24no—
61C2×C4×D283—22no—
62C2×C4×D283—24no—
63C2×C4×D283—24no—
64C2×C4×D283—24no—
65C2×C4×D283—22no—
66C2×C4×D283—24no—
67C2×C4×D283D414yes—
68C2×C4×D283D414yescomplemented
69C4⋊Dic283—22no—
70Dic283⋊C4—22no—
71Dic283⋊C4—22no—
72C22⋊Dic283—24no—
73C22⋊Dic283—24no—
74(C2×D283)⋊C4—24no—
75(C2×D283)⋊C4—24no—
76(C2×D283)⋊C4—24no—
77(C2×D283)⋊C4—24no—
78C24×C283C2312yes—
79C2×D4×C283—24no—
80C2×D4×C283—22no—
81C22×C4×C283C2311yescharacteristic
82C22×C4×C283C2312yes—
83C22×C4×C283C2311yescharacteristic
84C22×C4×C283C2311yescharacteristic
85C4⋊C4×C283—22no—
86C22⋊C4×C283—24no—
87C22⋊C4×C283—24no—
88C22×D283—22no—
89C22×D283—22no—
90C22×D283—22no—
91C22×D283—22no—
92C22×D283—22no—
93C22×D283—22no—
94C22×D283—216no—
95C22×D283—216no—
96C22×D283—216no—
97C22×D283—48no—
98C22×D283—48no—
99C22×D283—48no—
100C22×D283—48no—
101C22×D283C2×D414yes—
102C22×D283C2×D414yes—
103C22×D283C2×D412yes—
104C22×D283C2×D412yes—
105C22×D283#4112yes—
106C22×D283#4114yes—
107D1132—28no—
108C22⋊D283—216no—
109C2×Dic283—21no—
110C2×Dic283—22no—
111C2×Dic283—21no—
112C2×Dic283—22no—
113C2×Dic283—22no—
114C2×Dic283—22no—
115C2×Dic283—21no—
116C2×Dic283—22no—
117C2×Dic283C2×D412yes—
118C2×Dic283C2×D412yescomplemented
119C4×D283—28no—
120C4×D283—28no—
121C4×D283—44no—
122C4×D283—48no—
123C23×C283—22no—
124C23×C283—22no—
125C23×C283—22no—
126C23×C283—22no—
127C23×C283—22no—
128C23×C283—22no—
129C23×C283C2×D414yes—
130C23×C283C2411yescharacteristic
131D4×C283—28no—
132C2×C4×C283—21no—
133C2×C4×C283—22no—
134C2×C4×C283—21no—
135C2×C4×C283—22no—
136C2×C4×C283—22no—
137C2×C4×C283—22no—
138C2×C4×C283—21no—
139C2×C4×C283—22no—
140C2×C4×C283C2×D412yes—
141C2×C4×C283C2×D412yescomplemented
142C22×C283—24no—
143C22×C283—24no—
144C22×C283—24no—
145C22×C283—42no—
146C22×C283—42no—
147C22×C283—42no—
148C22×C283—42no—
149C22×C283C22×D412yes—
150C22×C283C22×D411yescharacteristic
151C22×C283C22×D411yescharacteristic
152C22×C283C2×#4111yescharacteristic
153C22×C283C2×#4112yes—
154C2×D283—24no—
155C2×D283—24no—
156C2×D283—24no—
157C2×D283—42no—
158C2×D283—42no—
159C2×D283—42no—
160C2×D283—42no—
161C2×D283—432no—
162C2×D283#12014yes—
163C2×D283#12114yes—
164C2×D283#12118yes—
165C2×D283#12318yes—
166C2×D283#12414yes—
167C4×C283—22no—
168C4×C283—22no—
169C4×C283—41no—
170C4×C283—42no—
171Dic283—22no—
172Dic283—22no—
173Dic283—41no—
174Dic283—42no—
175C2×C283—44no—
176C2×C283C2×#12011yescharacteristic
177C2×C283C2×#12111yescharacteristic
178C2×C283C2×#12112yes—
179C2×C283C2×#12312yes—
180C2×C283C2×#12411yescharacteristic
181D283—44no—
182D283#39418yesdirect product factor
183C283C2×#39411yescharacteristic, complemented, Sylow
184C2×#394—2831nomaximal, Sylow
185C23×D4—2831no—
186C22×C4⋊C4—2831no—
187C22×C22⋊C4—2832no—
188C22×C22⋊C4—2832no—
189#394—2831no—
190#394—2831no—
191#394—2832no—
192#394—2832no—
193#394—2831no—
194#394D28311yescharacteristic, direct product factor
195C2×#95—2831no—
196C25—2832no—
197C22×D4—2832no—
198C22×D4—2831no—
199C22×D4—5664no—
200C22×D4—5668no—
201C22×D4C2×D28311yescharacteristic
202C23×C4—2831no—
203C23×C4—2831no—
204C23×C4—2831no—
205C23×C4—2832no—
206C2×C4⋊C4—2831no—
207C2×C4⋊C4—2831no—
208C2×C4⋊C4—2831no—
209C2×C4⋊C4—5664no—
210C2×C4⋊C4C2×D28311yescharacteristic, complemented
211C2×C22⋊C4—2832no—
212C2×C22⋊C4—2832no—
213C2×C22⋊C4—2832no—
214C2×C22⋊C4—2832no—
215C2×C22⋊C4—2832no—
216C2×C22⋊C4—2832no—
217C2×C22⋊C4—5668no—
218C2×C22⋊C4—5668no—
219C2×C22⋊C4C2×D28312yescomplemented
220C2×C22⋊C4C2×D28312yescomplemented
221#95—2832no—
222#95—2831no—
223#95C2×D28311yescharacteristic, complemented
224C24—2831no—
225C24—2838no—
226C24—2832no—
227C24—5664no—
228C24—5664no—
229C24—5664no—
230C24—5664no—
231C24—5664no—
232C24—5664no—
233C24C22×D28312yes—
234C2×D4—24no—
235C2×D4—22no—
236C2×D4—5664no—
237C2×D4—5664no—
238C2×D4—56632no—
239C2×D4—5664no—
240C2×D4—5664no—
241C2×D4—5662no—
242C22×C4—2831no—
243C22×C4—2831no—
244C22×C4—2834no—
245C22×C4—2834no—
246C22×C4—2832no—
247C22×C4—2831no—
248C22×C4—5662no—
249C22×C4—5662no—
250C22×C4—5664no—
251C22×C4—5664no—
252C22×C4—5664no—
253C22×C4—5664no—
254C22×C4—5662no—
255C22×C4—5664no—
256C22×C4C22×D28312yes—
257C22×C4C22×D28311yescharacteristic
258C22×C4C22×D28311yescharacteristic
259C22×C4C22×D28311yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—5662no—
262C4⋊C4—5662no—
263C4⋊C4—5662no—
264C22⋊C4—24no—
265C22⋊C4—24no—
266C22⋊C4—5664no—
267C22⋊C4—5664no—
268C22⋊C4—5664no—
269C22⋊C4—5664no—
270C22⋊C4—5664no—
271C22⋊C4—5664no—
272C23—22no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—22no—
278C23—2832no—
279C23—2832no—
280C23—2834no—
281C23—2832no—
282C23—2834no—
283C23—2834no—
284C23—56616no—
285C23—56616no—
286C23—56616no—
287C23—5662no—
288C23—5662no—
289C23—5662no—
290C23—5662no—
291C23—5662no—
292C23—5662no—
293C23—11328no—
294C23—11328no—
295C23—11328no—
296C23—11328no—
297C23D4×D28314yes—
298C23C23×D28311yescharacteristic
299D4—28no—
300D4—5668no—
301D4—56616no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—2832no—
311C2×C4—2832no—
312C2×C4—5668no—
313C2×C4—5668no—
314C2×C4—5661no—
315C2×C4—5662no—
316C2×C4—5661no—
317C2×C4—5662no—
318C2×C4—5662no—
319C2×C4—5662no—
320C2×C4—5661no—
321C2×C4—5662no—
322C2×C4—11324no—
323C2×C4—11328no—
324C2×C4D4×D28312yes—
325C2×C4D4×D28312yescomplemented
326C22—24no—
327C22—24no—
328C22—24no—
329C22—42no—
330C22—42no—
331C22—42no—
332C22—42no—
333C22—2834no—
334C22—2834no—
335C22—2838no—
336C22—2838no—
337C22—2834no—
338C22—5664no—
339C22—5664no—
340C22—5664no—
341C22—113232no—
342C22—11322no—
343C22—11322no—
344C22—11322no—
345C22—11322no—
346C22C2×D4×D28312yes—
347C22C2×D4×D28311yescharacteristic
348C22C2×D4×D28311yescharacteristic
349C22#41×D28311yescharacteristic
350C22#41×D28312yes—
351C4—22no—
352C4—22no—
353C4—41no—
354C4—42no—
355C4—5662no—
356C4—5662no—
357C4—11321no—
358C4—11322no—
359C2—44no—
360C2—2838no—
361C2—11324no—
362C2#120×D28311yescharacteristic
363C2#121×D28311yescharacteristic
364C2#121×D28312yes—
365C2#123×D28312yes—
366C2#124×D28311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutator, socle, cosocleC23×C283C24
Fitting#394×C283C2
prime radicalC22×D4×D283C2
hypercenter#394D283
hypocenterC283C2×#394
LCSG ▷ C23×C283 ▷ C283
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D283C2semidirect
3. C2×C22⋊C4×D283C2semidirect
4. C2×C22⋊C4×D283C2semidirect
5. #31826383C2semidirect
6. #31826382C2semidirect
7. #31826381C2semidirect
8. #31826380C2semidirect
9. #31826379C2semidirect
10. #95×D283C2semidirect
11. #394×C283C2semidirect
21. C2×C4⋊Dic283C22semidirect
22. C2×Dic283⋊C4C22semidirect
23. C2×Dic283⋊C4C22semidirect
25. C2×C22⋊Dic283C22semidirect
26. C2×C22⋊Dic283C22semidirect
27. C2×(C2×D283)⋊C4C22semidirect
28. C2×(C2×D283)⋊C4C22semidirect
29. C2×(C2×D283)⋊C4C22semidirect
30. C2×(C2×D283)⋊C4C22semidirect
33. C283⋊#95C22semidirect
34. C283⋊#95C22semidirect
36. C2×C4⋊C4×C283C22semidirect
37. C2×C22⋊C4×C283C22semidirect
38. C2×C22⋊C4×C283C22semidirect
39. #95×C283C22semidirect
68. C2×C4×D283D4semidirect
118. C2×Dic283C2×D4semidirect
141. C2×C4×C283C2×D4semidirect
182. D283#394direct (N × H)
183. C283C2×#394semidirect
194. #394D283direct (N × H)
210. C2×C4⋊C4C2×D283semidirect
219. C2×C22⋊C4C2×D283semidirect
220. C2×C22⋊C4C2×D283semidirect
223. #95C2×D283semidirect
325. C2×C4D4×D283semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D2832
C2×C4⋊C4×D2832
C2×C22⋊C4×D2832
#318263832
#318263822
#318263812
#318263802
#318263792
#95×D2832
#394×C2832
C2×#394283