Finite Group Databasebeta

← #49131171

Subgroups — #49131171

Order 36224.

420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31826975C211yesmaximal, characteristic
2C2×#22583568C211yesmaximal, characteristic, complemented
3#31826809C212yesmaximal, complemented
4#31826800C211yesmaximal, characteristic, complemented
5#31826796C211yesmaximal, characteristic, complemented
6#31826788C212yesmaximal, complemented
7#31826776C211yesmaximal, characteristic, complemented
8#31826500C212yesmaximal, complemented
9#31826458C212yesmaximal, complemented
10C22⋊C8×D283C211yesmaximal, characteristic, complemented
11#481×C283C211yesmaximal, characteristic, complemented
12C2×#17985391C2211yescharacteristic
13C22×C4×D283C2211yescharacteristic
14C2×C8×D283C2212yes—
15#22583592—21no—
16#22583590C2211yescharacteristic
17#22583589C2211yescharacteristic
18#22583581C2211yescharacteristic
19#22583578—21no—
20D4×Dic283—21no—
21(C22⋊D283)⋊C4—21no—
22#22583568—21no—
23#22583568—21no—
24#22583568C2212yes—
25#22583568C2211yescharacteristic
26#22583568C2212yes—
27C2×C4⋊Dic283C2211yescharacteristic
28C2×(C2×D283)⋊C4—21no—
29C2×C4×Dic283—21no—
30#22583543C2212yescomplemented
31#22583543C2212yescomplemented
32#22583542C2212yescomplemented
33#22583535C2212yescomplemented
34#22583533C2212yescomplemented
35#22583531C2212yescomplemented
36C22⋊(C283⋊C8)C2211yescharacteristic
37(C2×D283)⋊C8C2212yes—
38#121×C283C2211yescharacteristic
39C2×C4⋊C4×C283C2211yescharacteristic
40#106×C283C2212yescomplemented
41#102×C283C2212yescomplemented
42C22⋊C8×C283C2211yescharacteristic
43C23×D283D411yescharacteristic
44#17985391—24no—
45C2×Dic566C2311yescharacteristic
46C2×C22⋊D283—21no—
47C2×C22⋊D283—21no—
48C22×Dic283—21no—
49C22×Dic283—21no—
50C22×Dic283D411yescharacteristic
51C2×C4×D283—24no—
52C2×C4×D283D411yescharacteristic
53C2×C4×D283D411yescharacteristic
54C2×C4×D283C2311yescharacteristic
55C2×C4×D283C2311yescharacteristic
56C2×C283⋊C8C2312yes—
57C8×D283—24no—
58C4⋊Dic283—21no—
59C4⋊Dic283—21no—
60C4⋊Dic283C2312yes—
61C4⋊Dic283C2311yescharacteristic
62Dic283⋊C4—21no—
63C22⋊Dic283—21no—
64C22⋊Dic283—21no—
65(C2×D283)⋊C4—22no—
66(C2×D283)⋊C4—22no—
67(C2×D283)⋊C4—21no—
68(C2×D283)⋊C4—21no—
69C4×Dic283—22no—
70C4×Dic283—22no—
71C4×Dic283—21no—
72C2×D4×C283—21no—
73C2×D4×C283C2311yescharacteristic
74C22×C4×C283—21no—
75C22×C4×C283C2311yescharacteristic
76C2×C8×C283C2312yes—
77C4⋊C4×C283—21no—
78C4⋊C4×C283C2312yes—
79C4⋊C4×C283C2311yescharacteristic
80C22⋊C4×C283—21no—
81C22×D283—22no—
82C22×D283—22no—
83C22×D283—41no—
84C22×D283C2×D411yescharacteristic
85C22×D283C2×D411yescharacteristic
86Dic566—22no—
87C22⋊D283—42no—
88C22⋊D283—42no—
89C2×Dic283—22no—
90C2×Dic283—22no—
91C2×Dic283—21no—
92C2×Dic283—21no—
93C2×Dic283—42no—
94C2×Dic283—42no—
95C2×Dic283C2×D411yescharacteristic
96C2×Dic283C2×D411yescharacteristic
97C4×D283—22no—
98C4×D283—22no—
99C4×D283—22no—
100C4×D283#4114yes—
101C283⋊C8—22no—
102C23×C283—21no—
103C23×C283C2×D411yescharacteristic
104D4×C283—22no—
105D4×C283—42no—
106C2×C4×C283—22no—
107C2×C4×C283—21no—
108C2×C4×C283—22no—
109C2×C4×C283—42no—
110C2×C4×C283C2×D411yescharacteristic
111C2×C4×C283C2411yescharacteristic
112C8×C283—22no—
113C22×C283—21no—
114C22×C283—21no—
115C22×C283—41no—
116C22×C283—41no—
117C22×C283—41no—
118C22×C283#13512yes—
119C22×C283C22×D411yescharacteristic
120C2×D283—21no—
121C2×D283—21no—
122C2×D283—21no—
123C2×D283—21no—
124C2×D283—21no—
125C2×D283—44no—
126C2×D283#12312yes—
127C4×C283—21no—
128C4×C283—41no—
129C4×C283—42no—
130C4×C283C2×#4112yes—
131Dic283—21no—
132Dic283—41no—
133Dic283—42no—
134Dic283—41no—
135Dic283#12312yes—
136C2×C283—22no—
137C2×C283—81no—
138C2×C283C2×#12311yescharacteristic
139C2×C283C2×#13511yescharacteristic
140C2×C283#57511yescharacteristic
141D283—22no—
142D283—41no—
143C283#309111yescharacteristic, complemented, Sylow
144#3091—2831nomaximal, Sylow
145#525—2831no—
146C2×#117—2831no—
147#485—2832no—
148#484—2831no—
149#483—2831no—
150#482—2832no—
151#481D28311yescharacteristic, complemented
152#480—2831no—
153#427—2832no—
154#416—2832no—
155C2×C22⋊C8—2831no—
156C2×#41—2831no—
157C23×C4—2831no—
158C22×C8—2832no—
159#123—5661no—
160C22⋊Q8—2831no—
161C22⋊Q8—2831no—
162#121—2831no—
163#121C2×D28311yescharacteristic
164#120—5661no—
165C4×D4—5661no—
166C4×D4—5661no—
167#117—2832no—
168#117—2832no—
169#117—2831no—
170#117—5661no—
171#117—5661no—
172C2×C4⋊C4—2831no—
173C2×C4⋊C4C2×D28311yescharacteristic
174C2×C22⋊C4—5661no—
175C2×C42—5661no—
176#107—2832no—
177#107—2832no—
178#106—2832no—
179#106C2×D28312yescomplemented
180#103—2832no—
181#103—2832no—
182#102—2832no—
183#102C2×D28312yescomplemented
184C22⋊C8—2831no—
185C22⋊C8—2832no—
186C22⋊C8C2×D28311yescharacteristic
187C24—2831no—
188#41—5664no—
189C2×Q8—2831no—
190C2×D4—21no—
191C2×D4—5661no—
192C2×D4—5661no—
193C2×D4C22×D28311yescharacteristic
194C22×C4—21no—
195C22×C4—2831no—
196C22×C4—2831no—
197C22×C4—2831no—
198C22×C4—2831no—
199C22×C4—2831no—
200C22×C4—5664no—
201C22×C4—5661no—
202C22×C4—5661no—
203C22×C4C22×D28311yescharacteristic
204C2×C8—2832no—
205C2×C8—5664no—
206C2×C8C22×D28312yes—
207C4⋊C4—21no—
208C4⋊C4—2832no—
209C4⋊C4—2831no—
210C4⋊C4—5661no—
211C4⋊C4—5661no—
212C4⋊C4—5661no—
213C4⋊C4C22×D28312yes—
214C4⋊C4C22×D28311yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—5662no—
217C22⋊C4—5662no—
218C22⋊C4—5661no—
219C22⋊C4—5661no—
220C22⋊C4—5661no—
221C22⋊C4—5661no—
222C42—5662no—
223C42—5662no—
224C42—5661no—
225C23—21no—
226C23—2831no—
227C23—2831no—
228C23—5662no—
229C23—5662no—
230C23—11321no—
231C23D4×D28311yescharacteristic
232Q8—5662no—
233D4—22no—
234D4—42no—
235D4—11322no—
236D4—11322no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—42no—
241C2×C4—2831no—
242C2×C4—2834no—
243C2×C4—2831no—
244C2×C4—5662no—
245C2×C4—5662no—
246C2×C4—5662no—
247C2×C4—5662no—
248C2×C4—5662no—
249C2×C4—5661no—
250C2×C4—5661no—
251C2×C4—11322no—
252C2×C4—11322no—
253C2×C4D4×D28311yescharacteristic
254C2×C4C23×D28311yescharacteristic
255C8—22no—
256C8—5662no—
257C22—21no—
258C22—21no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—2832no—
263C22—5661no—
264C22—5661no—
265C22—5661no—
266C22—5661no—
267C22—5661no—
268C22—11324no—
269C22#2258363112yes—
270C22C2×D4×D28311yescharacteristic
271C4—21no—
272C4—41no—
273C4—42no—
274C4—2832no—
275C4—5661no—
276C4—11321no—
277C4—11322no—
278C4—11321no—
279C4#41×D28312yes—
280C2—22no—
281C2—81no—
282C2—5662no—
283C2—11321no—
284C2#123×D28311yescharacteristic
285C2C2×#2258363111yescharacteristic
286C2#3182726111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#481×C283C2
socleC22×C283C22×D4
prime radical#31826975C2
hypercenter#481D283
hypocenterC283#3091
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#22583568C2semidirect
3. #31826809C2semidirect
4. #31826800C2semidirect
5. #31826796C2semidirect
6. #31826788C2semidirect
7. #31826776C2semidirect
8. #31826500C2semidirect
9. #31826458C2semidirect
10. C22⋊C8×D283C2semidirect
11. #481×C283C2semidirect
30. #22583543C22semidirect
31. #22583543C22semidirect
32. #22583542C22semidirect
33. #22583535C22semidirect
34. #22583533C22semidirect
35. #22583531C22semidirect
40. #106×C283C22semidirect
41. #102×C283C22semidirect
143. C283#3091semidirect
151. #481D283semidirect
179. #106C2×D283semidirect
183. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318269752
C2×#225835682
#318268092
#318268002
#318267962
#318267882
#318267762
#318265002
#318264582
C22⋊C8×D2832
#481×C2832
#3091283