Finite Group Databasebeta

← #49123866

Subgroups — #49123866

Order 36224.

484 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583567C211yesmaximal, characteristic
2#31826356C212yesmaximal
3#31826354C212yesmaximal
4#31826349C212yesmaximal, complemented
5#31826347C212yesmaximal, complemented
6#31826334C211yesmaximal, characteristic, complemented
7#31826330C211yesmaximal, characteristic, complemented
8#31826322C211yesmaximal, characteristic
9#31826322C211yesmaximal, characteristic
10C4×C4⋊Dic283C211yesmaximal, characteristic, complemented
11C4×C4⋊C4×C283C211yesmaximal, characteristic, complemented
12C22×C4×D283C2211yescharacteristic
13#22583567C418yescomplemented
14C2×C4⋊Dic283C2211yescharacteristic
15C2×C4⋊Dic283C2211yescharacteristic
16C2×Dic283⋊C4C2212yes—
17C2×Dic283⋊C4C2212yes—
18C2×Dic283⋊C4C2211yescharacteristic
19C2×Dic283⋊C4C2211yescharacteristic
20C2×(C2×D283)⋊C4C2212yes—
21C2×(C2×D283)⋊C4C2212yes—
22C2×(C2×D283)⋊C4C2211yescharacteristic
23C2×(C2×D283)⋊C4C2211yescharacteristic
24C2×C4×Dic283C2212yes—
25C2×C4×Dic283C2211yescharacteristic
26C283⋊#95C2212yes—
27C283⋊#95C2212yes—
28C283⋊#95C2212yes—
29C283⋊#95C2212yes—
30C283⋊#95C2212yes—
31C2×C4⋊C4×C283C2211yescharacteristic
32C2×C4⋊C4×C283C2211yescharacteristic
33C2×C42×C283C2212yes—
34C2×C42×C283C2211yescharacteristic
35#95×C283C2212yes—
36C23×D283C2311yescharacteristic
37C22×Dic283C2312yes—
38C22×Dic283C2312yes—
39C22×Dic283C2311yescharacteristic
40C22×Dic283C2311yescharacteristic
41C22×Dic283C2311yescharacteristic
42C2×C4×D283—22no—
43C2×C4×D283—22no—
44C2×C4×D283C2×C414yes—
45C4⋊Dic283—22no—
46C4⋊Dic283—22no—
47Dic283⋊C4—42no—
48Dic283⋊C4—42no—
49Dic283⋊C4C2×C414yes—
50Dic283⋊C4C2×C414yes—
51(C2×D283)⋊C4—42no—
52(C2×D283)⋊C4—42no—
53(C2×D283)⋊C4C2×C414yes—
54(C2×D283)⋊C4C2×C414yes—
55C4×Dic283—42no—
56C4×Dic283C2×C414yes—
57C22×C4×C283C2312yes—
58C22×C4×C283C2312yes—
59C22×C4×C283C2311yescharacteristic
60C22×C4×C283C2311yescharacteristic
61C22×C4×C283C2311yescharacteristic
62C4⋊C4×C283—22no—
63C4⋊C4×C283—22no—
64C42×C283—42no—
65C42×C283C2×C414yes—
66C22×D283—21no—
67C22×D283—21no—
68C22×D283—21no—
69C22×D283—21no—
70C22×D283—21no—
71C22×D283—21no—
72C22×D283C22×C412yes—
73C2×Dic283—21no—
74C2×Dic283—21no—
75C2×Dic283—21no—
76C2×Dic283—21no—
77C2×Dic283—21no—
78C2×Dic283—21no—
79C2×Dic283—22no—
80C2×Dic283—22no—
81C2×Dic283—22no—
82C2×Dic283—22no—
83C2×Dic283—22no—
84C2×Dic283—22no—
85C2×Dic283C22×C412yes—
86C2×Dic283C22×C412yes—
87C2×Dic283C22×C412yes—
88C4×D283—28no—
89C23×C283C2411yescharacteristic
90C2×C4×C283—21no—
91C2×C4×C283—21no—
92C2×C4×C283—21no—
93C2×C4×C283—21no—
94C2×C4×C283—22no—
95C2×C4×C283—22no—
96C2×C4×C283—22no—
97C2×C4×C283—22no—
98C2×C4×C283—22no—
99C2×C4×C283—22no—
100C2×C4×C283C22×C412yes—
101C2×C4×C283C22×C412yes—
102C2×C4×C283C22×C412yes—
103C2×C4×C283#4112yes—
104C2×C4×C283#4112yes—
105C22×C283C23×C411yescharacteristic
106C22×C283C2×#4111yescharacteristic
107C22×C283C2×#4111yescharacteristic
108C22×C283H(5,𝔽2)11yescharacteristic
109C22×C283H(5,𝔽2)11yescharacteristic
110C22×C2832−1+411yescharacteristic
111C22×C2832−1+411yescharacteristic
112C2×D283—22no—
113C2×D283—22no—
114C2×D283—22no—
115C2×D283—41no—
116C2×D283—41no—
117C2×D283—41no—
118C2×D283—41no—
119C4×C283—22no—
120C4×C283—22no—
121C4×C283—42no—
122C4×C283—42no—
123C4×C283#11714yes—
124Dic283—22no—
125Dic283—22no—
126Dic283—22no—
127Dic283—42no—
128Dic283—42no—
129C2×C283C2×#11711yescharacteristic
130C2×C283#52011yescharacteristic
131C2×C283#52011yescharacteristic
132C2×C283#54011yescharacteristic
133C2×C283#54111yescharacteristic
134C2×C283#54211yescharacteristic
135C2×C283#54211yescharacteristic
136D283—42no—
137C283#231411yescharacteristic, complemented, Sylow
138#2314—2831nomaximal, Sylow
139C2×#117—2831no—
140#388—2832no—
141#388—2832no—
142#387—2832no—
143#387—2832no—
144#384—2831no—
145#382—2831no—
146#380—2831no—
147#380—2831no—
148C4×C4⋊C4—2831no—
149C4×C4⋊C4D28311yescharacteristic, complemented
150C23×C4—2831no—
151#117—2838no—
152C2×C4⋊C4—2831no—
153C2×C4⋊C4—2831no—
154C2×C4⋊C4—2831no—
155C2×C4⋊C4—2831no—
156C2×C4⋊C4—2832no—
157C2×C4⋊C4—2832no—
158C2×C4⋊C4C2×D28311yescharacteristic
159C2×C4⋊C4C2×D28311yescharacteristic
160C2×C22⋊C4—2831no—
161C2×C22⋊C4—2831no—
162C2×C22⋊C4—2832no—
163C2×C22⋊C4—2832no—
164C2×C42—2831no—
165C2×C42—2832no—
166C2×C42C2×D28312yes—
167C2×C42C2×D28311yescharacteristic
168#95—2832no—
169#95—2832no—
170#95—2832no—
171#95—2832no—
172#95—2832no—
173#95C2×D28312yes—
174C24—2831no—
175C22×C4—2831no—
176C22×C4—2831no—
177C22×C4—2831no—
178C22×C4—2834no—
179C22×C4—2832no—
180C22×C4—2832no—
181C22×C4—5662no—
182C22×C4—5662no—
183C22×C4C22×D28312yes—
184C22×C4C22×D28312yes—
185C22×C4C22×D28311yescharacteristic
186C22×C4C22×D28311yescharacteristic
187C22×C4C22×D28311yescharacteristic
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—2834no—
191C4⋊C4—2834no—
192C4⋊C4—5662no—
193C4⋊C4—5662no—
194C4⋊C4—11322no—
195C4⋊C4—11322no—
196C22⋊C4—2834no—
197C22⋊C4—2834no—
198C22⋊C4—11322no—
199C22⋊C4—11322no—
200C42—42no—
201C42—2834no—
202C42—11322no—
203C42C4×D28314yes—
204C23—2832no—
205C23—5661no—
206C23—5661no—
207C23—5661no—
208C23—5661no—
209C23—5661no—
210C23—5661no—
211C23C23×D28311yescharacteristic
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—2832no—
223C2×C4—2832no—
224C2×C4—2832no—
225C2×C4—5661no—
226C2×C4—5661no—
227C2×C4—5661no—
228C2×C4—5661no—
229C2×C4—5661no—
230C2×C4—5661no—
231C2×C4—5668no—
232C2×C4—5662no—
233C2×C4—5662no—
234C2×C4—5662no—
235C2×C4—5662no—
236C2×C4—5662no—
237C2×C4—5662no—
238C2×C4C2×C4×D28312yes—
239C2×C4C2×C4×D28312yes—
240C2×C4C2×C4×D28312yes—
241C2×C4#1798539212yes—
242C2×C4#1798539212yes—
243C22—5662no—
244C22—5662no—
245C22—5662no—
246C22—11321no—
247C22—11321no—
248C22—11321no—
249C22—11321no—
250C22C22×C4×D28311yescharacteristic
251C22C2×#1798539211yescharacteristic
252C22C2×#1798539211yescharacteristic
253C22#2258365511yescharacteristic
254C22#2258365611yescharacteristic
255C22#2258365711yescharacteristic
256C22#2258365811yescharacteristic
257C4—22no—
258C4—22no—
259C4—42no—
260C4—42no—
261C4—5662no—
262C4—5662no—
263C4—5662no—
264C4—11322no—
265C4—11322no—
266C4#2258356714yes—
267C2—11322no—
268C2C2×#2258356711yescharacteristic
269C2#3182694511yescharacteristic
270C2#3182694611yescharacteristic
271C2#3182706611yescharacteristic
272C2#3182707311yescharacteristic
273C2#3182708011yescharacteristic
274C2#3182708711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
FittingC4×C4⋊C4×C283C2
socle, cosocleC23×C283C24
prime radicalC23×D283C23
hypercenterC4×C4⋊C4D283
hypocenterC283#2314
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #31826349C2semidirect
5. #31826347C2semidirect
6. #31826334C2semidirect
7. #31826330C2semidirect
10. C4×C4⋊Dic283C2semidirect
11. C4×C4⋊C4×C283C2semidirect
13. #22583567C4semidirect
137. C283#2314semidirect
149. C4×C4⋊C4D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835672
#318263562
#318263542
#318263492
#318263472
#318263342
#318263302
#318263222
C4×C4⋊Dic2832
C4×C4⋊C4×C2832
#2314283