Finite Group Databasebeta

← #49123927

Subgroups — #49123927

Order 36224.

632 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583593C211yesmaximal, characteristic
2C2×(C22⋊D283)⋊C4C211yesmaximal, characteristic
3C22×C4⋊Dic283C211yesmaximal, characteristic, complemented
4#31826362C212yesmaximal, complemented
5#31826357C212yesmaximal, complemented
6#31826352C212yesmaximal, complemented
7#31826342C211yesmaximal, characteristic
8#31826339C212yesmaximal, complemented
9#31826337C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic283C211yesmaximal, characteristic, complemented
11#381×C283C211yesmaximal, characteristic, complemented
12C22×C22⋊D283C2211yescharacteristic
13C23×Dic283C2211yescharacteristic
14C23×Dic283C2211yescharacteristic
15C22×C4×D283C2211yescharacteristic
16#22583593C418yescomplemented
17(C22⋊D283)⋊C4—24no—
18C2×C4⋊Dic283—24no—
19C2×C4⋊Dic283C2212yes—
20C2×C4⋊Dic283C2212yes—
21C2×Dic283⋊C4C2211yescharacteristic
22C2×Dic283⋊C4C2212yes—
23C2×Dic283⋊C4C2212yes—
24C2×C22⋊Dic283C2211yescharacteristic
25C2×(C2×D283)⋊C4C2211yescharacteristic
26C2×(C2×D283)⋊C4C2212yes—
27C2×(C2×D283)⋊C4C2212yes—
28C2×C4×Dic283C2211yescharacteristic
29C2×C4×Dic283C2212yes—
30C283⋊#95C2212yes—
31C283⋊#95C2212yes—
32C283⋊#95C2212yes—
33C23×C4×C283C2211yescharacteristic
34C2×C22⋊C4×C283C2211yescharacteristic
35C2×C22⋊C4×C283C2211yescharacteristic
36#95×C283C2212yes—
37#95×C283C2212yes—
38C23×D283C2311yescharacteristic
39C2×C22⋊D283—22no—
40C2×C22⋊D283—22no—
41C2×C22⋊D283C2×C414yes—
42C22×Dic283—22no—
43C22×Dic283—42no—
44C22×Dic283—42no—
45C22×Dic283D414yes—
46C22×Dic283C2312yes—
47C22×Dic283C2312yes—
48C22×Dic283C2311yescharacteristic
49C22×Dic283C2311yescharacteristic
50C22×Dic283C2311yescharacteristic
51C2×C4×D283—22no—
52C2×C4×D283—42no—
53C4⋊Dic283—24no—
54C4⋊Dic283—24no—
55Dic283⋊C4—22no—
56Dic283⋊C4—42no—
57Dic283⋊C4C2×C418yescomplemented
58C22⋊Dic283C2×C414yescomplemented
59(C2×D283)⋊C4—22no—
60(C2×D283)⋊C4—42no—
61(C2×D283)⋊C4C2×C418yescomplemented
62C4×Dic283—22no—
63C4×Dic283—42no—
64C24×C283C2311yescharacteristic
65C22×C4×C283—22no—
66C22×C4×C283—22no—
67C22×C4×C283C2×C414yescomplemented
68C22×C4×C283C2311yescharacteristic
69C22×C4×C283C2312yes—
70C22×C4×C283C2311yescharacteristic
71C22×C4×C283C2312yes—
72C22⋊C4×C283—22no—
73C22⋊C4×C283—22no—
74C22×D283—21no—
75C22×D283—21no—
76C22×D283—22no—
77C22×D283—22no—
78C22×D283C22×C412yes—
79C22⋊D283—28no—
80C2×Dic283—21no—
81C2×Dic283—21no—
82C2×Dic283—22no—
83C2×Dic283—22no—
84C2×Dic283—22no—
85C2×Dic283—22no—
86C2×Dic283—22no—
87C2×Dic283—22no—
88C2×Dic283—22no—
89C2×Dic283—44no—
90C2×Dic283—44no—
91C2×Dic283C22×C414yes—
92C2×Dic283C22×C412yes—
93C2×Dic283C2×D412yes—
94C2×Dic283C2×D412yes—
95C4×D283—44no—
96C23×C283—22no—
97C23×C283—22no—
98C23×C283C22×C412yes—
99C23×C283C2×D412yes—
100C23×C283#4112yes—
101C23×C283C2411yescharacteristic
102C2×C4×C283—28no—
103C2×C4×C283—22no—
104C2×C4×C283—22no—
105C2×C4×C283—21no—
106C2×C4×C283—21no—
107C2×C4×C283—22no—
108C2×C4×C283—22no—
109C2×C4×C283—22no—
110C2×C4×C283—22no—
111C2×C4×C283—22no—
112C2×C4×C283C22×C414yes—
113C22×C283—24no—
114C22×C283—22no—
115C22×C283—22no—
116C22×C283—24no—
117C22×C283C4×D414yes—
118C22×C283C23×C411yescharacteristic
119C22×C283C22×D411yescharacteristic
120C22×C283C2×#4111yescharacteristic
121C22×C283H(5,𝔽2)12yes—
122C22×C2832−1+412yes—
123C2×D283—22no—
124C2×D283—24no—
125C2×D283—41no—
126C2×D283—41no—
127C2×D283—42no—
128C4×C283—24no—
129C4×C283—41no—
130C4×C283—41no—
131C4×C283—42no—
132Dic283—22no—
133Dic283—24no—
134Dic283—22no—
135Dic283—22no—
136Dic283—42no—
137C2×C283—24no—
138C2×C283C2×C4×D411yescharacteristic
139C2×C283#52012yes—
140C2×C283#53411yescharacteristic
141C2×C283#53611yescharacteristic
142C2×C283#53912yes—
143D283—42no—
144C283#232211yescharacteristic, complemented, Sylow
145#2322—2831nomaximal, Sylow
146C2×#123—2831no—
147C2×C4×D4—2831no—
148C22×C4⋊C4—2831no—
149#389—2832no—
150#388—2832no—
151#387—2832no—
152#386—2831no—
153#385—2831no—
154#385—2832no—
155#381D28311yescharacteristic, complemented
156C4×C22⋊C4—2831no—
157C22×D4—2831no—
158C23×C4—2831no—
159C23×C4—2831no—
160C23×C4—2831no—
161C23×C4C2×D28311yescharacteristic
162#123—2838no—
163C4×D4—5664no—
164C2×C4⋊C4—2832no—
165C2×C4⋊C4—2832no—
166C2×C4⋊C4—2832no—
167C2×C4⋊C4—2831no—
168C2×C4⋊C4—2832no—
169C2×C4⋊C4—5664no—
170C2×C22⋊C4—2831no—
171C2×C22⋊C4—2832no—
172C2×C22⋊C4—2831no—
173C2×C22⋊C4—2832no—
174C2×C22⋊C4C2×D28311yescharacteristic
175C2×C22⋊C4C2×D28311yescharacteristic
176C2×C42—2831no—
177C2×C42—2832no—
178#95—2832no—
179#95—2832no—
180#95—2832no—
181#95C2×D28312yes—
182#95C2×D28312yes—
183C24—2831no—
184C24C22×D28311yescharacteristic
185C2×D4—2834no—
186C2×D4—5662no—
187C2×D4—5662no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—2832no—
191C22×C4—2831no—
192C22×C4—2831no—
193C22×C4—2831no—
194C22×C4—2834no—
195C22×C4—2832no—
196C22×C4—5662no—
197C22×C4—5662no—
198C22×C4—11322no—
199C22×C4—11322no—
200C22×C4—11322no—
201C22×C4C4×D28314yescomplemented
202C22×C4C22×D28311yescharacteristic
203C22×C4C22×D28312yes—
204C22×C4C22×D28311yescharacteristic
205C22×C4C22×D28312yes—
206C4⋊C4—2838no—
207C4⋊C4—5662no—
208C4⋊C4—5664no—
209C4⋊C4—5664no—
210C4⋊C4—11322no—
211C22⋊C4—22no—
212C22⋊C4—22no—
213C22⋊C4—2834no—
214C22⋊C4—2838no—
215C22⋊C4—5662no—
216C22⋊C4—11322no—
217C42—5662no—
218C42—11322no—
219C23—22no—
220C23—22no—
221C23—2832no—
222C23—5661no—
223C23—5661no—
224C23—5662no—
225C23—5662no—
226C23C2×C4×D28312yes—
227C23D4×D28312yes—
228C23#1798539112yes—
229C23C23×D28311yescharacteristic
230D4—5668no—
231C2×C4—28no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—2834no—
242C2×C4—2832no—
243C2×C4—2832no—
244C2×C4—2832no—
245C2×C4—5661no—
246C2×C4—5661no—
247C2×C4—5662no—
248C2×C4—5662no—
249C2×C4—5662no—
250C2×C4—5662no—
251C2×C4—5662no—
252C2×C4—5662no—
253C2×C4—5662no—
254C2×C4—11324no—
255C2×C4—11324no—
256C2×C4—11324no—
257C2×C4C2×C4×D28314yes—
258C22—24no—
259C22—22no—
260C22—22no—
261C22—24no—
262C22—5664no—
263C22—5662no—
264C22—11321no—
265C22—11321no—
266C22—11322no—
267C22(C22⋊D283)⋊C414yes—
268C22C22×C4×D28311yescharacteristic
269C22C2×D4×D28311yescharacteristic
270C22C2×#1798539111yescharacteristic
271C22#2258365612yes—
272C22#2258365712yes—
273C4—24no—
274C4—41no—
275C4—41no—
276C4—42no—
277C4—5664no—
278C4—5662no—
279C4—5662no—
280C4—5662no—
281C4—11322no—
282C2—24no—
283C2—11322no—
284C2C2×(C22⋊D283)⋊C411yescharacteristic
285C2#3182694512yes—
286C2#3182702611yescharacteristic
287C2#3182703711yescharacteristic
288C2#3182705912yes—
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#381×C283C2
socle, cosocleC23×C283C24
prime radicalC22×C22⋊D283C22
hypercenter#381D283
hypocenterC283#2322
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊Dic283C2semidirect
4. #31826362C2semidirect
5. #31826357C2semidirect
6. #31826352C2semidirect
8. #31826339C2semidirect
9. #31826337C2semidirect
10. C22⋊C4×Dic283C2semidirect
11. #381×C283C2semidirect
16. #22583593C4semidirect
57. Dic283⋊C4C2×C4semidirect
58. C22⋊Dic283C2×C4semidirect
61. (C2×D283)⋊C4C2×C4semidirect
67. C22×C4×C283C2×C4semidirect
144. C283#2322semidirect
155. #381D283semidirect
201. C22×C4C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835932
C2×(C22⋊D283)⋊C42
C22×C4⋊Dic2832
#318263622
#318263572
#318263522
#318263422
#318263392
#318263372
C22⋊C4×Dic2832
#381×C2832
#2322283