Finite Group Databasebeta

← #49124191

Subgroups — #49124191

Order 36224.

660 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D283C211yesmaximal, characteristic
2C2×C4⋊C4×D283C211yesmaximal, characteristic, complemented
3#31826359C212yesmaximal, complemented
4#31826349C212yesmaximal, complemented
5#31826341C212yesmaximal
6#31826330C211yesmaximal, characteristic, complemented
7#31826325C211yesmaximal, characteristic, complemented
8#31826322C211yesmaximal, characteristic, complemented
9C4⋊C4×Dic283C211yesmaximal, characteristic, complemented
10C4×(C2×D283)⋊C4C212yesmaximal, complemented
11C2×#117×C283C211yesmaximal, characteristic, complemented
12C22×C22⋊D283C2211yescharacteristic
13C22×C4×D283C2212yes—
14C22×C4×D283C2211yescharacteristic
15C4×C22⋊D283C418yescomplemented
16C2×C4⋊Dic283C2211yescharacteristic
17C2×C4⋊Dic283C2211yescharacteristic
18C2×Dic283⋊C4C2212yes—
19C2×Dic283⋊C4C2211yescharacteristic
20C4⋊C4×D283—24no—
21C2×C22⋊Dic283C2212yes—
22C2×C22⋊Dic283C2211yescharacteristic
23C2×(C2×D283)⋊C4C2212yes—
24C2×(C2×D283)⋊C4C2211yescharacteristic
25C2×C4×Dic283C2212yes—
26C2×C4×Dic283C2211yescharacteristic
27C283⋊#95C2212yes—
28C283⋊#95C2212yes—
29C283⋊#95C2212yes—
30C283⋊#95C2212yes—
31C283⋊#95C2212yes—
32C23×C4×C283C2211yescharacteristic
33#117×C283—24no—
34C2×C4⋊C4×C283C2211yescharacteristic
35C2×C4⋊C4×C283C2211yescharacteristic
36C2×C22⋊C4×C283C2212yes—
37C2×C42×C283C2212yes—
38C23×D283C2311yescharacteristic
39C2×C22⋊D283—22no—
40C2×C22⋊D283—22no—
41C2×C22⋊D283C2×C414yes—
42C22×Dic283C2312yes—
43C22×Dic283C2312yes—
44C22×Dic283C2311yescharacteristic
45C22×Dic283C2311yescharacteristic
46C22×Dic283C2311yescharacteristic
47C2×C4×D283—24no—
48C2×C4×D283—22no—
49C2×C4×D283—24no—
50C2×C4×D283—22no—
51C2×C4×D283—42no—
52C2×C4×D283C2×C414yes—
53C4⋊Dic283—22no—
54C4⋊Dic283—22no—
55Dic283⋊C4—24no—
56Dic283⋊C4C2×C414yescomplemented
57C22⋊Dic283—42no—
58C22⋊Dic283C2×C414yescomplemented
59(C2×D283)⋊C4—24no—
60(C2×D283)⋊C4C2×C414yes—
61C4×Dic283—42no—
62C4×Dic283C2×C414yescomplemented
63C24×C283C2311yescharacteristic
64C22×C4×C283—22no—
65C22×C4×C283—22no—
66C22×C4×C283C2×C414yescomplemented
67C22×C4×C283C2312yes—
68C22×C4×C283C2311yescharacteristic
69C22×C4×C283C2312yes—
70C22×C4×C283C2311yescharacteristic
71C4⋊C4×C283—22no—
72C4⋊C4×C283D414yescomplemented
73C22⋊C4×C283—24no—
74C42×C283—24no—
75C22×D283—21no—
76C22×D283—21no—
77C22×D283—21no—
78C22×D283—21no—
79C22×D283C22×C412yes—
80C22×D283#4112yes—
81C22×D283#4112yes—
82C22⋊D283—28no—
83C2×Dic283—21no—
84C2×Dic283—21no—
85C2×Dic283—21no—
86C2×Dic283—21no—
87C2×Dic283—21no—
88C2×Dic283—21no—
89C2×Dic283—22no—
90C2×Dic283—22no—
91C2×Dic283—22no—
92C2×Dic283—22no—
93C2×Dic283—22no—
94C2×Dic283—22no—
95C2×Dic283C22×C412yes—
96C2×Dic283C22×C412yes—
97C2×Dic283C22×C412yes—
98C4×D283—28no—
99C4×D283—48no—
100C23×C283—21no—
101C23×C283—21no—
102C23×C283—21no—
103C23×C283—21no—
104C23×C283—21no—
105C23×C283—21no—
106C23×C283C22×C412yes—
107C23×C283C2411yescharacteristic
108C2×C4×C283—21no—
109C2×C4×C283—21no—
110C2×C4×C283—22no—
111C2×C4×C283—22no—
112C2×C4×C283—28no—
113C2×C4×C283—22no—
114C2×C4×C283—22no—
115C2×C4×C283—22no—
116C2×C4×C283C22×C412yes—
117C2×C4×C283C22×C412yes—
118C2×C4×C283C2×D414yes—
119C2×C4×C283C2×D412yes—
120C2×C4×C283#4112yes—
121C22×C283—22no—
122C22×C283—22no—
123C22×C283—22no—
124C22×C283—41no—
125C22×C283—41no—
126C22×C283—41no—
127C22×C283—41no—
128C22×C283C23×C411yescharacteristic
129C22×C283C22×D411yescharacteristic
130C22×C283C2×#4111yescharacteristic
131C22×C283C2×#4111yescharacteristic
132C22×C283C2×#4111yescharacteristic
133C22×C283H(5,𝔽2)11yescharacteristic
134C22×C2832−1+411yescharacteristic
135C2×D283—22no—
136C2×D283—22no—
137C2×D283—22no—
138C2×D283—22no—
139C2×D283—22no—
140C2×D283—22no—
141C2×D283#11714yescomplemented
142C4×C283—22no—
143C4×C283—24no—
144C4×C283—42no—
145C4×C283C4×D414yes—
146Dic283—22no—
147Dic283—22no—
148Dic283—22no—
149Dic283—42no—
150Dic283—42no—
151C2×C283—42no—
152C2×C283C2×#11711yescharacteristic
153C2×C283C2×C4×D411yescharacteristic
154C2×C283#52011yescharacteristic
155C2×C283#54611yescharacteristic
156C2×C283#54811yescharacteristic
157C2×C283#55211yescharacteristic
158C2×C283#55311yescharacteristic
159D283—24no—
160C283#235211yescharacteristic, complemented, Sylow
161#2352—2831nomaximal, Sylow
162C2×C4×D4—2831no—
163C2×#117D28311yescharacteristic, complemented
164C22×C4⋊C4—2831no—
165#388—2832no—
166#387—2832no—
167#386—2832no—
168#382—2831no—
169#380—2831no—
170#380—2831no—
171C4×C4⋊C4—2831no—
172C4×C22⋊C4—2832no—
173C22×D4—2831no—
174C23×C4—2831no—
175C23×C4—2832no—
176C23×C4C2×D28311yescharacteristic
177C4×D4—2838no—
178#117—24no—
179C2×C4⋊C4—2831no—
180C2×C4⋊C4—2832no—
181C2×C4⋊C4—2831no—
182C2×C4⋊C4—2831no—
183C2×C4⋊C4—5664no—
184C2×C4⋊C4C2×D28311yescharacteristic
185C2×C4⋊C4C2×D28311yescharacteristic
186C2×C22⋊C4—2831no—
187C2×C22⋊C4—2831no—
188C2×C22⋊C4—2832no—
189C2×C22⋊C4—2832no—
190C2×C22⋊C4C2×D28312yes—
191C2×C42—2831no—
192C2×C42—2832no—
193C2×C42C2×D28312yes—
194#95—2832no—
195#95—2832no—
196#95—2832no—
197#95—2832no—
198#95—2832no—
199C24—2831no—
200C24C22×D28311yescharacteristic
201C2×D4—2834no—
202C2×D4—5662no—
203C2×D4—5662no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—2831no—
207C22×C4—2831no—
208C22×C4—2831no—
209C22×C4—2834no—
210C22×C4—2832no—
211C22×C4—2832no—
212C22×C4—5664no—
213C22×C4—5662no—
214C22×C4—5662no—
215C22×C4—5664no—
216C22×C4—11322no—
217C22×C4C4×D28314yescomplemented
218C22×C4C22×D28312yes—
219C22×C4C22×D28311yescharacteristic
220C22×C4C22×D28312yes—
221C22×C4C22×D28311yescharacteristic
222C4⋊C4—22no—
223C4⋊C4—2834no—
224C4⋊C4—5664no—
225C4⋊C4—5662no—
226C4⋊C4—5662no—
227C4⋊C4C22⋊D28314yescomplemented
228C22⋊C4—24no—
229C22⋊C4—2834no—
230C22⋊C4—2834no—
231C22⋊C4—5664no—
232C22⋊C4—11322no—
233C42—24no—
234C42—2834no—
235C42—11322no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23—2832no—
243C23—2832no—
244C23—2832no—
245C23—5661no—
246C23—5661no—
247C23—5661no—
248C23—5661no—
249C23C2×C4×D28312yes—
250C23C23×D28311yescharacteristic
251D4—5668no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—28no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—2832no—
261C2×C4—2832no—
262C2×C4—2832no—
263C2×C4—5661no—
264C2×C4—5661no—
265C2×C4—5661no—
266C2×C4—5661no—
267C2×C4—5661no—
268C2×C4—5661no—
269C2×C4—5668no—
270C2×C4—5662no—
271C2×C4—5662no—
272C2×C4—5662no—
273C2×C4—5662no—
274C2×C4—5662no—
275C2×C4—5662no—
276C2×C4—11328no—
277C2×C4C2×C4×D28312yes—
278C2×C4C2×C4×D28312yes—
279C2×C4C2×C22⋊D28314yes—
280C2×C4C2×C22⋊D28312yes—
281C2×C4#1798539212yes—
282C22—22no—
283C22—22no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—2834no—
290C22—5662no—
291C22—5662no—
292C22—5662no—
293C22—5662no—
294C22—5662no—
295C22—5662no—
296C22C22×C4×D28311yescharacteristic
297C22C22×C22⋊D28311yescharacteristic
298C22#41×D28311yescharacteristic
299C22#41×D28311yescharacteristic
300C22C2×#1798539211yescharacteristic
301C22#2258365611yescharacteristic
302C22#2258365711yescharacteristic
303C4—24no—
304C4—22no—
305C4—42no—
306C4—5662no—
307C4—5662no—
308C4—5662no—
309C4—11322no—
310C4—11322no—
311C4C4×C22⋊D28314yes—
312C2—42no—
313C2—5664no—
314C2#117×D28311yescharacteristic
315C2C2×C4×C22⋊D28311yescharacteristic
316C2#3182694511yescharacteristic
317C2#3182710311yescharacteristic
318C2#3182712211yescharacteristic
319C2#3182715411yescharacteristic
320C2#3182715911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
FittingC2×#117×C283C2
socle, cosocleC23×C283C24
prime radicalC22×C22⋊D283C22
hypercenterC2×#117D283
hypocenterC283#2352
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D283C2semidirect
3. #31826359C2semidirect
4. #31826349C2semidirect
6. #31826330C2semidirect
7. #31826325C2semidirect
8. #31826322C2semidirect
9. C4⋊C4×Dic283C2semidirect
10. C4×(C2×D283)⋊C4C2semidirect
11. C2×#117×C283C2semidirect
15. C4×C22⋊D283C4semidirect
56. Dic283⋊C4C2×C4semidirect
58. C22⋊Dic283C2×C4semidirect
62. C4×Dic283C2×C4semidirect
66. C22×C4×C283C2×C4semidirect
72. C4⋊C4×C283D4semidirect
141. C2×D283#117semidirect
160. C283#2352semidirect
163. C2×#117D283semidirect
217. C22×C4C4×D283semidirect
227. C4⋊C4C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D2832
C2×C4⋊C4×D2832
#318263592
#318263492
#318263412
#318263302
#318263252
#318263222
C4⋊C4×Dic2832
C4×(C2×D283)⋊C42
C2×#117×C2832
#2352283