Finite Group Databasebeta

← #49123930

Subgroups — #49123930

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×C4×C22⋊D283C211yesmaximal, characteristic
3#31826360C212yesmaximal, complemented
4#31826355C212yesmaximal, complemented
5#31826346C212yesmaximal, complemented
6#31826344C211yesmaximal, characteristic
7#31826338C211yesmaximal, characteristic, complemented
8#31826336C212yesmaximal, complemented
9#31826328C211yesmaximal, characteristic, complemented
10C4×C22⋊Dic283C211yesmaximal, characteristic, complemented
11C22×C4⋊C4×C283C211yesmaximal, characteristic, complemented
12C22×C22⋊D283C2211yescharacteristic
13C22×C4×D283C2211yescharacteristic
14#22583593C418yescomplemented
15C4×C22⋊D283—24no—
16C2×Dic283⋊C4C2211yescharacteristic
17C2×Dic283⋊C4C2212yes—
18C2×Dic283⋊C4C2212yes—
19C2×C22⋊Dic283C2211yescharacteristic
20C2×C22⋊Dic283C2211yescharacteristic
21C2×C22⋊Dic283C2211yescharacteristic
22C2×(C2×D283)⋊C4C2211yescharacteristic
23C2×(C2×D283)⋊C4C2212yes—
24C2×(C2×D283)⋊C4C2212yes—
25C2×C4×Dic283C2211yescharacteristic
26C2×C4×Dic283C2212yes—
27C283⋊#95C2212yes—
28C283⋊#95C2212yes—
29C283⋊#95C2212yes—
30C283⋊#95C2212yes—
31C283⋊#95C2212yes—
32C23×C4×C283C2211yescharacteristic
33C23×C4×C283C2211yescharacteristic
34C23×C4×C283C2211yescharacteristic
35C2×C4⋊C4×C283—24no—
36C2×C4⋊C4×C283C2212yes—
37C2×C4⋊C4×C283C2212yes—
38C23×D283C2311yescharacteristic
39C2×C22⋊D283—22no—
40C2×C22⋊D283—22no—
41C2×C22⋊D283C2×C414yes—
42C22×Dic283C2311yescharacteristic
43C22×Dic283C2312yes—
44C22×Dic283C2311yescharacteristic
45C22×Dic283C2312yes—
46C22×Dic283C2311yescharacteristic
47C2×C4×D283—22no—
48C2×C4×D283—42no—
49Dic283⋊C4—22no—
50Dic283⋊C4—42no—
51Dic283⋊C4C2×C418yescomplemented
52C22⋊Dic283—22no—
53C22⋊Dic283—22no—
54C22⋊Dic283C2×C414yescomplemented
55(C2×D283)⋊C4—22no—
56(C2×D283)⋊C4—42no—
57(C2×D283)⋊C4C2×C418yescomplemented
58C4×Dic283—22no—
59C4×Dic283—42no—
60C24×C283C2311yescharacteristic
61C22×C4×C283—22no—
62C22×C4×C283—22no—
63C22×C4×C283—22no—
64C22×C4×C283—42no—
65C22×C4×C283—42no—
66C22×C4×C283C2×C414yescomplemented
67C22×C4×C283D414yes—
68C22×C4×C283C2312yes—
69C22×C4×C283C2312yes—
70C22×C4×C283C2311yescharacteristic
71C22×C4×C283C2311yescharacteristic
72C4⋊C4×C283—24no—
73C4⋊C4×C283—24no—
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—21no—
85C2×Dic283—21no—
86C2×Dic283—22no—
87C2×Dic283—22no—
88C2×Dic283—22no—
89C2×Dic283—22no—
90C2×Dic283—22no—
91C2×Dic283C22×C414yes—
92C2×Dic283C22×C412yes—
93C4×D283—44no—
94C23×C283—22no—
95C23×C283—22no—
96C23×C283C22×C412yes—
97C23×C283C2×D412yes—
98C23×C283#4112yes—
99C23×C283C2411yescharacteristic
100C2×C4×C283—28no—
101C2×C4×C283—22no—
102C2×C4×C283—22no—
103C2×C4×C283—22no—
104C2×C4×C283—22no—
105C2×C4×C283—22no—
106C2×C4×C283—22no—
107C2×C4×C283—22no—
108C2×C4×C283—44no—
109C2×C4×C283—44no—
110C2×C4×C283C22×C414yes—
111C2×C4×C283C2×D412yes—
112C2×C4×C283C2×D412yes—
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—22no—
130C4×C283—22no—
131C4×C283—42no—
132Dic283—22no—
133Dic283—24no—
134Dic283—41no—
135Dic283—41no—
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⋊C4D28311yescharacteristic, complemented
149#389—2832no—
150#388—2832no—
151#387—2832no—
152#386—2831no—
153#385—2831no—
154#385—2832no—
155#381—2831no—
156C4×C22⋊C4—2831no—
157C22×D4—2831no—
158C23×C4—2831no—
159C23×C4C2×D28311yescharacteristic
160C23×C4C2×D28311yescharacteristic
161C23×C4C2×D28311yescharacteristic
162#123—2838no—
163C4×D4—5664no—
164C2×C4⋊C4—24no—
165C2×C4⋊C4—2832no—
166C2×C4⋊C4—2831no—
167C2×C4⋊C4—2832no—
168C2×C4⋊C4C2×D28312yes—
169C2×C4⋊C4C2×D28312yes—
170C2×C22⋊C4—2831no—
171C2×C22⋊C4—2832no—
172C2×C22⋊C4—2831no—
173C2×C22⋊C4—2831no—
174C2×C22⋊C4—2831no—
175C2×C22⋊C4—2832no—
176C2×C42—2831no—
177C2×C42—2832no—
178#95—2832no—
179#95—2832no—
180#95—2832no—
181#95—2832no—
182#95—2832no—
183C24—2831no—
184C24C22×D28311yescharacteristic
185C2×D4—2834no—
186C2×D4—5662no—
187C2×D4—5662no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—42no—
192C22×C4—42no—
193C22×C4—2832no—
194C22×C4—2831no—
195C22×C4—2831no—
196C22×C4—2832no—
197C22×C4—2831no—
198C22×C4—5662no—
199C22×C4—11322no—
200C22×C4C4×D28314yescomplemented
201C22×C4C22⋊D28314yes—
202C22×C4C22×D28312yes—
203C22×C4C22×D28312yes—
204C22×C4C22×D28311yescharacteristic
205C22×C4C22×D28311yescharacteristic
206C4⋊C4—24no—
207C4⋊C4—24no—
208C4⋊C4—2838no—
209C4⋊C4—5662no—
210C4⋊C4—11322no—
211C22⋊C4—2834no—
212C22⋊C4—2838no—
213C22⋊C4—5662no—
214C22⋊C4—5662no—
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—
227C23C2×C22⋊D28312yes—
228C23#1798539212yes—
229C23C23×D28311yescharacteristic
230D4—5668no—
231C2×C4—28no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—44no—
240C2×C4—44no—
241C2×C4—2834no—
242C2×C4—2832no—
243C2×C4—5661no—
244C2×C4—5661no—
245C2×C4—5662no—
246C2×C4—5662no—
247C2×C4—5661no—
248C2×C4—5661no—
249C2×C4—5662no—
250C2×C4—5662no—
251C2×C4—5662no—
252C2×C4—5662no—
253C2×C4—5662no—
254C2×C4—11324no—
255C2×C4C2×C4×D28314yes—
256C2×C4C2×C22⋊D28312yes—
257C2×C4C2×C22⋊D28312yes—
258C22—24no—
259C22—22no—
260C22—22no—
261C22—24no—
262C22—5664no—
263C22—5662no—
264C22—11321no—
265C22—11321no—
266C22—11322no—
267C22C4×C22⋊D28314yes—
268C22C22×C4×D28311yescharacteristic
269C22C22×C22⋊D28311yescharacteristic
270C22C2×#1798539211yescharacteristic
271C22#2258365512yes—
272C22#2258365812yes—
273C4—22no—
274C4—22no—
275C4—24no—
276C4—42no—
277C4—5664no—
278C4—5662no—
279C4—11321no—
280C4—11321no—
281C4—11322no—
282C2—24no—
283C2—11322no—
284C2C2×C4×C22⋊D28311yescharacteristic
285C2#3182694612yes—
286C2#3182702411yescharacteristic
287C2#3182703911yescharacteristic
288C2#3182706212yes—
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
FittingC22×C4⋊C4×C283C2
socle, cosocleC23×C283C24
prime radicalC22×C22⋊D283C22
hypercenterC22×C4⋊C4D283
hypocenterC283#2322
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #31826360C2semidirect
4. #31826355C2semidirect
5. #31826346C2semidirect
7. #31826338C2semidirect
8. #31826336C2semidirect
9. #31826328C2semidirect
10. C4×C22⋊Dic283C2semidirect
11. C22×C4⋊C4×C283C2semidirect
14. #22583593C4semidirect
51. Dic283⋊C4C2×C4semidirect
54. C22⋊Dic283C2×C4semidirect
57. (C2×D283)⋊C4C2×C4semidirect
66. C22×C4×C283C2×C4semidirect
144. C283#2322semidirect
148. C22×C4⋊C4D283semidirect
200. 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×C4×C22⋊D2832
#318263602
#318263552
#318263462
#318263442
#318263382
#318263362
#318263282
C4×C22⋊Dic2832
C22×C4⋊C4×C2832
#2322283