Finite Group Databasebeta

← #49123955

Subgroups — #49123955

Order 36224.

668 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583585C211yesmaximal, characteristic
2C2×C4×D1132C211yesmaximal, characteristic, complemented
3C2×#22583567C211yesmaximal, characteristic, complemented
4#31826367C212yesmaximal, complemented
5#31826366C211yesmaximal, characteristic, complemented
6#31826364C211yesmaximal, characteristic, complemented
7#31826356C212yesmaximal, complemented
8#31826343C212yesmaximal, complemented
9#31826339C212yesmaximal, complemented
10#31826322C211yesmaximal, characteristic, complemented
11C4×C4⋊C4×C283C211yesmaximal, characteristic, complemented
12C22×D1132C2211yescharacteristic
13C22×D1132C2212yes—
14C22×C4×D283C2211yescharacteristic
15C22×C4×D283C2212yes—
16#22583585C418yescomplemented
17C4×D1132—24no—
18#22583567—24no—
19C2×C4⋊Dic283C2211yescharacteristic
20C2×C4⋊Dic283C2212yes—
21C2×Dic283⋊C4C2211yescharacteristic
22C2×Dic283⋊C4C2211yescharacteristic
23C2×(C2×D283)⋊C4C2211yescharacteristic
24C2×(C2×D283)⋊C4C2212yes—
25C2×(C2×D283)⋊C4C2211yescharacteristic
26C2×(C2×D283)⋊C4C2212yes—
27C2×(C2×D283)⋊C4C2212yes—
28C2×(C2×D283)⋊C4C2212yes—
29C2×(C2×D283)⋊C4C2212yes—
30C2×C4×Dic283C2211yescharacteristic
31C283⋊#95C2212yes—
32C283⋊#95C2212yes—
33C2×C4⋊C4×C283C2211yescharacteristic
34C2×C4⋊C4×C283C2211yescharacteristic
35C2×C42×C283C2212yes—
36C2×C42×C283C2211yescharacteristic
37#95×C283C2212yes—
38C23×D283C2311yescharacteristic
39C23×D283C2312yes—
40C2×D1132—22no—
41C2×D1132—22no—
42C2×D1132—42no—
43C2×D1132—42no—
44C2×D1132C2×C414yes—
45C2×D1132C2×C418yescomplemented
46C22×Dic283C2311yescharacteristic
47C22×Dic283C2311yescharacteristic
48C22×Dic283C2312yes—
49C22×Dic283C2311yescharacteristic
50C2×C4×D283—22no—
51C2×C4×D283—24no—
52C2×C4×D283—22no—
53C2×C4×D283—42no—
54C2×C4×D283—42no—
55C2×C4×D283C2×C414yescomplemented
56C4⋊Dic283—22no—
57C4⋊Dic283—42no—
58Dic283⋊C4—22no—
59Dic283⋊C4—22no—
60(C2×D283)⋊C4—22no—
61(C2×D283)⋊C4—22no—
62(C2×D283)⋊C4—24no—
63(C2×D283)⋊C4—42no—
64(C2×D283)⋊C4—42no—
65(C2×D283)⋊C4—42no—
66(C2×D283)⋊C4C2×C418yescomplemented
67C4×Dic283—22no—
68C22×C4×C283C2312yes—
69C22×C4×C283C2312yes—
70C22×C4×C283C2311yescharacteristic
71C22×C4×C283C2311yescharacteristic
72C22×C4×C283C2311yescharacteristic
73C4⋊C4×C283—22no—
74C4⋊C4×C283C2×C414yescomplemented
75C42×C283—42no—
76C42×C283D414yescomplemented
77C22×D283—21no—
78C22×D283—22no—
79C22×D283—21no—
80C22×D283—22no—
81C22×D283—21no—
82C22×D283—22no—
83C22×D283—22no—
84C22×D283—22no—
85C22×D283—21no—
86C22×D283—21no—
87C22×D283—21no—
88C22×D283—22no—
89C22×D283C22×C414yes—
90C22×D283C22×C412yes—
91D1132—28no—
92D1132—48no—
93C2×Dic283—21no—
94C2×Dic283—21no—
95C2×Dic283—21no—
96C2×Dic283—21no—
97C2×Dic283—22no—
98C2×Dic283—21no—
99C2×Dic283—21no—
100C2×Dic283—22no—
101C2×Dic283—21no—
102C2×Dic283—22no—
103C2×Dic283—21no—
104C2×Dic283C22×C412yes—
105C4×D283—28no—
106C4×D283—48no—
107C23×C283C2411yescharacteristic
108C2×C4×C283—21no—
109C2×C4×C283—22no—
110C2×C4×C283—22no—
111C2×C4×C283—21no—
112C2×C4×C283—21no—
113C2×C4×C283—21no—
114C2×C4×C283—22no—
115C2×C4×C283—22no—
116C2×C4×C283—22no—
117C2×C4×C283C22×C414yes—
118C2×C4×C283C22×C412yes—
119C2×C4×C283C2×D412yes—
120C2×C4×C283C2×D412yes—
121C2×C4×C283C2×D412yes—
122C2×C4×C283#4112yes—
123C22×C283C23×C411yescharacteristic
124C22×C283C22×D411yescharacteristic
125C22×C283C2×#4111yescharacteristic
126C22×C283H(5,𝔽2)11yescharacteristic
127C22×C283H(5,𝔽2)11yescharacteristic
128C22×C283H(5,𝔽2)11yescharacteristic
129C22×C2832−1+411yescharacteristic
130C2×D283—22no—
131C2×D283—24no—
132C2×D283—22no—
133C2×D283—24no—
134C2×D283—22no—
135C2×D283—24no—
136C2×D283—42no—
137C2×D283—41no—
138C2×D283—41no—
139C2×D283—42no—
140C2×D283—41no—
141C2×D283—42no—
142C2×D283—41no—
143C2×D283—42no—
144C4×C283—24no—
145C4×C283—22no—
146C4×C283—22no—
147C4×C283—42no—
148C4×C283C4×D414yes—
149Dic283—22no—
150Dic283—42no—
151Dic283—41no—
152Dic283—41no—
153C2×C283C2×C4×D411yescharacteristic
154C2×C283#51811yescharacteristic
155C2×C283#52011yescharacteristic
156C2×C283#53511yescharacteristic
157C2×C283#53711yescharacteristic
158C2×C283#54011yescharacteristic
159C2×C283#54211yescharacteristic
160D283—42no—
161D283—44no—
162C283#232411yescharacteristic, complemented, Sylow
163#2324—2831nomaximal, Sylow
164C2×#121—2831no—
165C2×C4×D4—2831no—
166C2×#117—2831no—
167#390—2831no—
168#390—2832no—
169#389—2831no—
170#388—2832no—
171#386—2832no—
172#385—2832no—
173#380—2831no—
174C4×C4⋊C4D28311yescharacteristic, complemented
175C22×D4—2831no—
176C22×D4—2832no—
177C23×C4—2831no—
178C23×C4—2832no—
179#121—2838no—
180C4×D4—5664no—
181#117—5664no—
182C2×C4⋊C4—2831no—
183C2×C4⋊C4—2831no—
184C2×C4⋊C4—2831no—
185C2×C4⋊C4—2832no—
186C2×C4⋊C4C2×D28311yescharacteristic
187C2×C4⋊C4C2×D28311yescharacteristic
188C2×C22⋊C4—2832no—
189C2×C22⋊C4—2831no—
190C2×C22⋊C4—2831no—
191C2×C22⋊C4—2832no—
192C2×C22⋊C4—2832no—
193C2×C22⋊C4—2832no—
194C2×C22⋊C4—2832no—
195C2×C42—2831no—
196C2×C42C2×D28312yes—
197C2×C42C2×D28311yescharacteristic
198#95—2832no—
199#95—2832no—
200#95C2×D28312yes—
201C24—2832no—
202C24—2831no—
203C2×D4—2834no—
204C2×D4—2838no—
205C2×D4—5662no—
206C2×D4—5662no—
207C2×D4—11322no—
208C2×D4—11322no—
209C22×C4—2831no—
210C22×C4—2834no—
211C22×C4—2831no—
212C22×C4—2832no—
213C22×C4—2831no—
214C22×C4—5662no—
215C22×C4—5662no—
216C22×C4—5664no—
217C22×C4—11322no—
218C22×C4—11322no—
219C22×C4C22×D28312yes—
220C22×C4C22×D28312yes—
221C22×C4C22×D28311yescharacteristic
222C22×C4C22×D28311yescharacteristic
223C22×C4C22×D28311yescharacteristic
224C4⋊C4—22no—
225C4⋊C4—5662no—
226C4⋊C4—5662no—
227C4⋊C4—5662no—
228C4⋊C4—11322no—
229C4⋊C4C4×D28314yescomplemented
230C22⋊C4—2838no—
231C22⋊C4—5662no—
232C22⋊C4—5662no—
233C22⋊C4—5664no—
234C22⋊C4—11322no—
235C22⋊C4—11322no—
236C22⋊C4—11322no—
237C42—42no—
238C42—5662no—
239C42D113214yescomplemented
240C23—2834no—
241C23—2832no—
242C23—5661no—
243C23—5662no—
244C23—5661no—
245C23—5662no—
246C23—5662no—
247C23—5661no—
248C23—5661no—
249C23—5662no—
250C23—5662no—
251C23—5661no—
252C23—5662no—
253C23—5661no—
254C23C23×D28311yescharacteristic
255D4—5668no—
256D4—11328no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—2832no—
267C2×C4—5661no—
268C2×C4—5661no—
269C2×C4—5668no—
270C2×C4—5661no—
271C2×C4—5661no—
272C2×C4—5662no—
273C2×C4—5661no—
274C2×C4—5661no—
275C2×C4—5662no—
276C2×C4—5661no—
277C2×C4—5662no—
278C2×C4—5661no—
279C2×C4—11328no—
280C2×C4C2×C4×D28314yes—
281C2×C4C2×C4×D28312yes—
282C2×C4C2×D113212yes—
283C2×C4C2×D113212yes—
284C2×C4C2×D113212yes—
285C2×C4#1798539212yes—
286C22—5664no—
287C22—5662no—
288C22—5662no—
289C22—5664no—
290C22—5662no—
291C22—5664no—
292C22—11322no—
293C22—11321no—
294C22—11321no—
295C22—11322no—
296C22—11321no—
297C22—11322no—
298C22—11321no—
299C22—11322no—
300C22C22×C4×D28311yescharacteristic
301C22C22×D113211yescharacteristic
302C22C2×#1798539211yescharacteristic
303C22#2258365511yescharacteristic
304C22#2258365611yescharacteristic
305C22#2258365611yescharacteristic
306C22#2258365811yescharacteristic
307C4—22no—
308C4—22no—
309C4—24no—
310C4—42no—
311C4—5662no—
312C4—11322no—
313C4—11321no—
314C4—11321no—
315C4C4×D113214yes—
316C2—11322no—
317C2—11324no—
318C2C2×C4×D113211yescharacteristic
319C2#3182693711yescharacteristic
320C2#3182694711yescharacteristic
321C2#3182703411yescharacteristic
322C2#3182704611yescharacteristic
323C2#3182706611yescharacteristic
324C2#3182708711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
FittingC4×C4⋊C4×C283C2
socle, cosocleC23×C283C24
prime radicalC2×#22583585C2
hypercenterC4×C4⋊C4D283
hypocenterC283#2324
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D1132C2semidirect
3. C2×#22583567C2semidirect
4. #31826367C2semidirect
5. #31826366C2semidirect
6. #31826364C2semidirect
7. #31826356C2semidirect
8. #31826343C2semidirect
9. #31826339C2semidirect
10. #31826322C2semidirect
11. C4×C4⋊C4×C283C2semidirect
16. #22583585C4semidirect
45. C2×D1132C2×C4semidirect
55. C2×C4×D283C2×C4semidirect
66. (C2×D283)⋊C4C2×C4semidirect
74. C4⋊C4×C283C2×C4semidirect
76. C42×C283D4semidirect
162. C283#2324semidirect
174. C4×C4⋊C4D283semidirect
229. C4⋊C4C4×D283semidirect
239. C42D1132semidirect

Maximal subgroups

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

subgroupindex
C2×#225835852
C2×C4×D11322
C2×#225835672
#318263672
#318263662
#318263642
#318263562
#318263432
#318263392
#318263222
C4×C4⋊C4×C2832
#2324283