Finite Group Databasebeta

← #389×D283 #49123708

Subgroups — #389×D283 #49123708

Order 36224.

800 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D283C211yesmaximal, characteristic
2C2×C4⋊C4×D283C212yesmaximal
3C2×C4⋊C4×D283C211yesmaximal, characteristic
4C2×C42×D283C211yesmaximal, characteristic
5#31826364C211yesmaximal, characteristic, complemented
6#31826363C211yesmaximal, characteristic, complemented
7#31826362C212yesmaximal, complemented
8#31826361C211yesmaximal, characteristic, complemented
9#31826360C212yesmaximal, complemented
10#95×D283C212yesmaximal
11#389×C283C211yesmaximal, characteristic, complemented
12C22×C4×D283C2212yes—
13C22×C4×D283C2212yes—
14C22×C4×D283C2211yescharacteristic
15C22×C4×D283C2211yescharacteristic
16C22×C4×D283C2211yescharacteristic
17C2×C4⋊Dic283C2212yes—
18C2×C4⋊Dic283C2211yescharacteristic
19C2×C4⋊Dic283C2211yescharacteristic
20C2×Dic283⋊C4C2212yes—
21C2×Dic283⋊C4C2212yes—
22C2×Dic283⋊C4C2212yes—
23C2×Dic283⋊C4C2212yes—
24C4⋊C4×D283—24no—
25C4⋊C4×D283—28no—
26C4⋊C4×D283C418yescomplemented
27C2×C4×Dic283C2211yescharacteristic
28C2×C4×Dic283C2211yescharacteristic
29C2×C4×Dic283C2211yescharacteristic
30C42×D283—24no—
31C283⋊#95C2212yes—
32C283⋊#95C2212yes—
33C283⋊#95C2212yes—
34C2×C4⋊C4×C283C2212yes—
35C2×C4⋊C4×C283C2211yescharacteristic
36C2×C4⋊C4×C283C2211yescharacteristic
37C2×C42×C283C2211yescharacteristic
38#95×C283C2212yes—
39C23×D283C2311yescharacteristic
40C22×Dic283C2312yes—
41C22×Dic283C2312yes—
42C22×Dic283C2311yescharacteristic
43C22×Dic283C2311yescharacteristic
44C22×Dic283C2311yescharacteristic
45C2×C4×D283—22no—
46C2×C4×D283—22no—
47C2×C4×D283—24no—
48C2×C4×D283—24no—
49C2×C4×D283—22no—
50C2×C4×D283—22no—
51C2×C4×D283—24no—
52C2×C4×D283—24no—
53C2×C4×D283—24no—
54C2×C4×D283C2×C418yes—
55C2×C4×D283C2×C414yes—
56C2×C4×D283D414yes—
57C2×C4×D283D414yes—
58C2×C4×D283Q814yes—
59C2×C4×D283Q814yes—
60C4⋊Dic283—24no—
61C4⋊Dic283—22no—
62C4⋊Dic283C2×C414yescomplemented
63Dic283⋊C4—24no—
64Dic283⋊C4—24no—
65Dic283⋊C4—24no—
66Dic283⋊C4C2×C418yescomplemented
67C4×Dic283—22no—
68C4×Dic283—22no—
69C4×Dic283—22no—
70C22×C4×C283C2312yes—
71C22×C4×C283C2312yes—
72C22×C4×C283C2311yescharacteristic
73C22×C4×C283C2311yescharacteristic
74C22×C4×C283C2311yescharacteristic
75C4⋊C4×C283—24no—
76C4⋊C4×C283—22no—
77C4⋊C4×C283C2×C414yescomplemented
78C42×C283—22no—
79C22×D283C22×C412yes—
80C22×D283C2×D412yes—
81C22×D283C2×D412yes—
82C22×D283C2×Q812yes—
83C22×D283C2×Q812yes—
84C22×D283#4112yes—
85C22×D283#4112yes—
86C2×Dic283—21no—
87C2×Dic283—21no—
88C2×Dic283—22no—
89C2×Dic283—22no—
90C2×Dic283—21no—
91C2×Dic283—21no—
92C2×Dic283—22no—
93C2×Dic283—22no—
94C2×Dic283—22no—
95C2×Dic283C22×C414yes—
96C2×Dic283C22×C412yes—
97C2×Dic283C2×D412yes—
98C2×Dic283C2×D412yes—
99C2×Dic283C2×Q812yes—
100C2×Dic283C2×Q812yes—
101C4×D283—216no—
102C4×D283—28no—
103C4×D283—28no—
104C4×D283—48no—
105C4×D283C4⋊C4116yescomplemented
106C23×C283C2411yescharacteristic
107C2×C4×C283—21no—
108C2×C4×C283—21no—
109C2×C4×C283—22no—
110C2×C4×C283—22no—
111C2×C4×C283—21no—
112C2×C4×C283—21no—
113C2×C4×C283—22no—
114C2×C4×C283—22no—
115C2×C4×C283—22no—
116C2×C4×C283C22×C414yes—
117C2×C4×C283C22×C412yes—
118C2×C4×C283C2×D412yes—
119C2×C4×C283C2×D412yes—
120C2×C4×C283C2×Q812yes—
121C2×C4×C283C2×Q812yes—
122C22×C283C23×C411yescharacteristic
123C22×C283C22×D411yescharacteristic
124C22×C283C22×D411yescharacteristic
125C22×C283C22×Q811yescharacteristic
126C22×C283C22×Q811yescharacteristic
127C22×C283C2×#4111yescharacteristic
128C22×C283C2×#4111yescharacteristic
129C2×D283C2×C4⋊C414yes—
130C2×D283C4×D414yes—
131C2×D283C4×Q814yes—
132C2×D283#12114yes—
133C2×D283C22⋊Q814yes—
134C2×D283#12514yes—
135C2×D283C4⋊Q814yes—
136C4×C283—24no—
137C4×C283—22no—
138C4×C283—22no—
139C4×C283—42no—
140C4×C283C2×C4⋊C414yescomplemented
141Dic283—24no—
142Dic283—22no—
143Dic283—22no—
144Dic283—42no—
145Dic283C2×C4⋊C414yescomplemented
146C2×C283C22×C4⋊C411yescharacteristic
147C2×C283C2×C4×D411yescharacteristic
148C2×C283C2×C4×Q811yescharacteristic
149C2×C283C2×#12111yescharacteristic
150C2×C283C2×C22⋊Q811yescharacteristic
151C2×C283C2×#12511yescharacteristic
152C2×C283C2×C4⋊Q811yescharacteristic
153D283#38918yesdirect product factor
154C283C2×#38911yescharacteristic, complemented, Sylow
155C2×#389—2831nomaximal, Sylow
156C22×C4⋊C4—2831no—
157C22×C4⋊C4—2831no—
158C22×C4⋊C4—2832no—
159C22×C42—2831no—
160#389—2832no—
161#389—2831no—
162#389—2831no—
163#389—2831no—
164#389—2832no—
165#389D28311yescharacteristic, direct product factor
166C2×#95—2832no—
167C23×C4—2831no—
168C23×C4—2832no—
169C23×C4—2831no—
170C23×C4—2831no—
171C23×C4—2832no—
172C2×C4⋊C4—2832no—
173C2×C4⋊C4—2831no—
174C2×C4⋊C4—2838no—
175C2×C4⋊C4—2832no—
176C2×C4⋊C4—2832no—
177C2×C4⋊C4—2832no—
178C2×C4⋊C4—2832no—
179C2×C4⋊C4—2831no—
180C2×C4⋊C4—5664no—
181C2×C4⋊C4—5668no—
182C2×C4⋊C4C2×D28311yescharacteristic
183C2×C4⋊C4C2×D28312yes—
184C2×C4⋊C4C2×D28311yescharacteristic
185C2×C42—2831no—
186C2×C42—2831no—
187C2×C42—2831no—
188C2×C42—5664no—
189C2×C42C2×D28311yescharacteristic
190#95—2832no—
191#95—2832no—
192#95—2832no—
193#95C2×D28312yes—
194C24—2831no—
195C22×C4—2831no—
196C22×C4—2834no—
197C22×C4—2834no—
198C22×C4—2834no—
199C22×C4—2831no—
200C22×C4—2832no—
201C22×C4—2831no—
202C22×C4—2838no—
203C22×C4—2834no—
204C22×C4—2834no—
205C22×C4—2832no—
206C22×C4—5662no—
207C22×C4—5662no—
208C22×C4—5664no—
209C22×C4—5664no—
210C22×C4—5662no—
211C22×C4—5662no—
212C22×C4—5664no—
213C22×C4—5664no—
214C22×C4—5664no—
215C22×C4C22×D28312yes—
216C22×C4C22×D28312yes—
217C22×C4C22×D28311yescharacteristic
218C22×C4C22×D28311yescharacteristic
219C22×C4C22×D28311yescharacteristic
220C4⋊C4—24no—
221C4⋊C4—22no—
222C4⋊C4—2838no—
223C4⋊C4—2834no—
224C4⋊C4—5664no—
225C4⋊C4—5664no—
226C4⋊C4—5664no—
227C4⋊C4—5664no—
228C4⋊C4—5662no—
229C4⋊C4C4×D28314yescomplemented
230C42—22no—
231C42—5662no—
232C42—5662no—
233C42—5662no—
234C23—2832no—
235C23—2832no—
236C23—2832no—
237C23—2832no—
238C23—2832no—
239C23—2832no—
240C23—2832no—
241C23C23×D28311yescharacteristic
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—2832no—
252C2×C4—2832no—
253C2×C4—2832no—
254C2×C4—28316no—
255C2×C4—2834no—
256C2×C4—2832no—
257C2×C4—2832no—
258C2×C4—5668no—
259C2×C4—5668no—
260C2×C4—56616no—
261C2×C4—5661no—
262C2×C4—5661no—
263C2×C4—5662no—
264C2×C4—5661no—
265C2×C4—5661no—
266C2×C4—5662no—
267C2×C4—5662no—
268C2×C4—5662no—
269C2×C4—5662no—
270C2×C4—11328no—
271C2×C4C2×C4×D28314yes—
272C2×C4C2×C4×D28312yes—
273C2×C4D4×D28312yes—
274C2×C4D4×D28312yes—
275C2×C4Q8×D28312yes—
276C2×C4Q8×D28312yes—
277C22—2834no—
278C22—2834no—
279C22—2834no—
280C22—2834no—
281C22—2834no—
282C22—2834no—
283C22—2834no—
284C22C22×C4×D28311yescharacteristic
285C22C2×D4×D28311yescharacteristic
286C22C2×D4×D28311yescharacteristic
287C22C2×Q8×D28311yescharacteristic
288C22C2×Q8×D28311yescharacteristic
289C22#41×D28311yescharacteristic
290C22#41×D28311yescharacteristic
291C4—22no—
292C4—22no—
293C4—24no—
294C4—42no—
295C4—2834no—
296C4—5662no—
297C4—5662no—
298C4—5664no—
299C4—11322no—
300C4C4⋊C4×D28314yescomplemented
301C2—2838no—
302C2C2×C4⋊C4×D28311yescharacteristic
303C2C4×D4×D28311yescharacteristic
304C2C4×Q8×D28311yescharacteristic
305C2#121×D28311yescharacteristic
306C2C22⋊Q8×D28311yescharacteristic
307C2#125×D28311yescharacteristic
308C2C4⋊Q8×D28311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#389×C283C2
socle, cosocleC23×C283C24
prime radicalC23×D283C23
hypercenter#389D283
hypocenterC283C2×#389
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
5. #31826364C2semidirect
6. #31826363C2semidirect
7. #31826362C2semidirect
8. #31826361C2semidirect
9. #31826360C2semidirect
11. #389×C283C2semidirect
26. C4⋊C4×D283C4semidirect
62. C4⋊Dic283C2×C4semidirect
66. Dic283⋊C4C2×C4semidirect
77. C4⋊C4×C283C2×C4semidirect
105. C4×D283C4⋊C4semidirect
140. C4×C283C2×C4⋊C4semidirect
145. Dic283C2×C4⋊C4semidirect
153. D283#389direct (N × H)
154. C283C2×#389semidirect
165. #389D283direct (N × H)
229. C4⋊C4C4×D283semidirect
300. C4C4⋊C4×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×C42×D2832
#318263642
#318263632
#318263622
#318263612
#318263602
#95×D2832
#389×C2832
C2×#389283