Finite Group Databasebeta

← #49132863

Subgroups — #49132863

Order 36224.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#22583638C212yesmaximal, complemented
2#31827120C211yesmaximal, characteristic, complemented
3D4×D1132C211yesmaximal, characteristic, complemented
4#31826838C211yesmaximal, characteristic, complemented
5#31826711C212yesmaximal, complemented
6#31826671C211yesmaximal, characteristic, complemented
7#31826661C211yesmaximal, characteristic, complemented
8#31826618C212yesmaximal, complemented
9#31826612C212yesmaximal, complemented
10C4×D2264C211yesmaximal, characteristic, complemented
11#436×C283C211yesmaximal, characteristic, complemented
12C2×#17985392C2212yescomplemented
13C22×D1132C2212yes—
14C2×D4×D283—21no—
15#22583638—28no—
16C2×#17985381C2212yes—
17C2×#17985381C2212yescomplemented
18C2×#17985381C2212yescomplemented
19C2×D2264C2211yescharacteristic
20C2×D2264C2212yescomplemented
21#22583610C2211yescharacteristic, complemented
22#22583607C2211yescharacteristic
23#22583592—22no—
24#22583589C2212yescomplemented
25#22583585—21no—
26#22583584C2212yes—
27#22583581—21no—
28#22583580—22no—
29C4×D1132C2211yescharacteristic
30C4×D1132C2211yescharacteristic, complemented
31C4⋊C4×D283—21no—
32#22583544C2211yescharacteristic, complemented
33#22583535C2212yescomplemented
34#22583532C2211yescharacteristic
35#22583532C2212yescomplemented
36#22583532C2211yescharacteristic, complemented
37C2×M16×C283C2212yescomplemented
38C4×D4×C283C2211yescharacteristic
39C4⋊C8×C283C2211yescharacteristic, complemented
40C22⋊C8×C283C2212yescomplemented
41C4×C8×C283C2211yescharacteristic, complemented
42C23×D283—22no—
43#17985392—24no—
44#17985392—42no—
45C2×Dic566C2312yes—
46C2×D1132—24no—
47C2×D1132—22no—
48C2×D1132—21no—
49C2×D1132—21no—
50C2×D1132—42no—
51C2×D1132C2312yes—
52C2×D1132C2311yescharacteristic
53C2×D1132C2311yescharacteristic
54C2×C22⋊D283—22no—
55C2×C22⋊D283—22no—
56D4×D283—44no—
57C2×C4×D283—21no—
58C2×C4×D283—22no—
59C2×C4×D283—21no—
60#17985381—24no—
61#17985381—24no—
62#17985381—42no—
63D2264—24no—
64D2264D414yescomplemented
65C4⋊Dic283—21no—
66C4⋊Dic283—21no—
67C4⋊Dic283C2311yescharacteristic
68C4⋊Dic283C2311yescharacteristic
69Dic283⋊C4—22no—
70C22⋊Dic283—22no—
71(C2×D283)⋊C4—21no—
72(C2×D283)⋊C4—21no—
73(C2×D283)⋊C4—22no—
74C2×D4×C283D411yescharacteristic
75C22×C4×C283C2312yes—
76M16×C283—24no—
77C2×C8×C283C2312yes—
78C2×C8×C283C2311yescharacteristic
79C2×C8×C283C2311yescharacteristic
80C4⋊C4×C283D411yescharacteristic
81C22⋊C4×C283D412yes—
82C42×C283C2311yescharacteristic
83C22×D283—21no—
84C22×D283—21no—
85C22×D283—22no—
86C22×D283—44no—
87C22×D283—44no—
88C22×D283—82no—
89Dic566—22no—
90Dic566—22no—
91D1132—22no—
92D1132—21no—
93D1132—21no—
94D1132—22no—
95D1132—44no—
96D1132—42no—
97D1132—81no—
98D1132C2×D412yes—
99D1132C2×D412yescomplemented
100C22⋊D283—44no—
101C22⋊D283—44no—
102C2×Dic283—21no—
103C2×Dic283—21no—
104C2×Dic283—22no—
105C4×D283—44no—
106C4×D283—42no—
107C4×D283—42no—
108C23×C283C2×D412yes—
109D4×C283—22no—
110C2×C4×C283—22no—
111C2×C4×C283—22no—
112C2×C4×C283C2×D411yescharacteristic
113C2×C4×C283C2×D412yes—
114C2×C4×C283C2×D411yescharacteristic
115C2×C4×C283C2411yescharacteristic
116C8×C283—22no—
117C8×C283—21no—
118C8×C283C2×D412yescomplemented
119C22×C283—22no—
120C22×C283—22no—
121C22×C283—22no—
122C22×C283C22×D411yescharacteristic
123C2×D283—22no—
124C2×D283—22no—
125C2×D283—41no—
126C2×D283—41no—
127C2×D283—41no—
128C2×D283—41no—
129C2×D283—42no—
130C2×D283—42no—
131C2×D283—42no—
132C2×D283—88no—
133C4×C283—22no—
134C4×C283—21no—
135C4×C283AGL(1,ℤ/8)12yescomplemented
136C4×C283C22×D411yescharacteristic
137C4×C283H(5,𝔽2)11yescharacteristic
138Dic283—42no—
139Dic283—41no—
140Dic283—41no—
141C2×C283—42no—
142C2×C283D4211yescharacteristic
143C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
144C2×C283#57711yescharacteristic
145D283—42no—
146D283—42no—
147D283—82no—
148C283#327211yescharacteristic, complemented, Sylow
149#3272—2831nomaximal, Sylow
150C2×AGL(1,ℤ/8)—2832no—
151#547—2831no—
152D42—2831no—
153#492—2831no—
154#468—2832no—
155#461—2831no—
156#459—2831no—
157#450—2832no—
158#449—2832no—
159C4×D8—2831no—
160#436D28311yescharacteristic, complemented
161C2×#41—2832no—
162C22×D4—2832no—
163C22×D4—5661no—
164AGL(1,ℤ/8)—5668no—
165C2×SD16—2832no—
166C2×SD16—2832no—
167C2×SD16—2832no—
168C2×D8—2831no—
169C2×D8—2832no—
170C2×M16C2×D28312yescomplemented
171C4⋊Q8—2831no—
172#127—2831no—
173#123—5662no—
174C22⋊Q8—2832no—
175#121—2832no—
176#121—5661no—
177#121—5661no—
178#120—5662no—
179C4×D4—2831no—
180C4×D4—2831no—
181C4×D4C2×D28311yescharacteristic
182C2×C4⋊C4—5661no—
183#107—2831no—
184C4⋊C8C2×D28311yescharacteristic, complemented
185#103—2832no—
186#102—2831no—
187#102—2831no—
188#102—2832no—
189C22⋊C8C2×D28312yescomplemented
190C4×C8C2×D28311yescharacteristic, complemented
191C24—5662no—
192#41—5664no—
193#41—11322no—
194C2×Q8—2832no—
195C2×D4—2831no—
196C2×D4—2831no—
197C2×D4—2832no—
198C2×D4—5664no—
199C2×D4—5662no—
200C2×D4—5662no—
201C2×D4—5662no—
202C2×D4—5661no—
203C2×D4—5661no—
204C2×D4—11322no—
205C2×D4—11324no—
206C2×D4D113211yescharacteristic
207C22×C4—5661no—
208C22×C4—5662no—
209C22×C4—5661no—
210C22×C4C22×D28312yes—
211SD16—5664no—
212SD16—5664no—
213SD16—11322no—
214D8—2834no—
215D8—5664no—
216M16—24no—
217C2×C8C22×D28311yescharacteristic
218C2×C8C22×D28312yes—
219C2×C8C22×D28311yescharacteristic
220C4⋊C4—2831no—
221C4⋊C4—2831no—
222C4⋊C4—5662no—
223C4⋊C4—5661no—
224C4⋊C4—5661no—
225C4⋊C4D113211yescharacteristic
226C22⋊C4—5662no—
227C22⋊C4—5661no—
228C22⋊C4—5661no—
229C22⋊C4—5662no—
230C22⋊C4D113212yes—
231C42C22×D28311yescharacteristic
232C23—5661no—
233C23—5661no—
234C23—5662no—
235C23—11324no—
236C23—11324no—
237C23—22642no—
238C23C2×D113212yes—
239Q8—5662no—
240Q8—5662no—
241D4—22no—
242D4—2832no—
243D4—2832no—
244D4—5662no—
245D4—5661no—
246D4—5661no—
247D4—5662no—
248D4—11324no—
249D4—11324no—
250D4—11324no—
251D4—11322no—
252D4—22641no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—5661no—
256C2×C4—5661no—
257C2×C4—5662no—
258C2×C4—11324no—
259C2×C4—11322no—
260C2×C4—11322no—
261C2×C4C2×D113211yescharacteristic
262C2×C4C2×D113212yes—
263C2×C4C2×D113211yescharacteristic
264C2×C4C23×D28311yescharacteristic
265C8—22no—
266C8—21no—
267C8D4×D28312yescomplemented
268C22—22no—
269C22—22no—
270C22—22no—
271C22—5662no—
272C22—5662no—
273C22—11321no—
274C22—11321no—
275C22—11321no—
276C22—11321no—
277C22—11322no—
278C22—11322no—
279C22—11322no—
280C22—22648no—
281C22C22×D113211yescharacteristic
282C4—21no—
283C4—22no—
284C4—11321no—
285C4—11321no—
286C4—11322no—
287C4#2258363812yescomplemented
288C4C2×D4×D28311yescharacteristic
289C4#2258365611yescharacteristic
290C2—42no—
291C2—11322no—
292C2—11322no—
293C2—22642no—
294C2D4×D113211yescharacteristic
295C2C2×#2258363811yescharacteristic
296C2#3182727711yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#436×C283C2
socleC22×C283C22×D4
hypercenter#436D283
hypocenterC283#3272
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#22583638C2semidirect
2. #31827120C2semidirect
3. D4×D1132C2semidirect
4. #31826838C2semidirect
5. #31826711C2semidirect
6. #31826671C2semidirect
7. #31826661C2semidirect
8. #31826618C2semidirect
9. #31826612C2semidirect
10. C4×D2264C2semidirect
11. #436×C283C2semidirect
12. C2×#17985392C22semidirect
17. C2×#17985381C22semidirect
18. C2×#17985381C22semidirect
20. C2×D2264C22semidirect
21. #22583610C22semidirect
24. #22583589C22semidirect
30. C4×D1132C22semidirect
32. #22583544C22semidirect
33. #22583535C22semidirect
35. #22583532C22semidirect
36. #22583532C22semidirect
37. C2×M16×C283C22semidirect
39. C4⋊C8×C283C22semidirect
40. C22⋊C8×C283C22semidirect
41. C4×C8×C283C22semidirect
64. D2264D4semidirect
99. D1132C2×D4semidirect
118. C8×C283C2×D4semidirect
135. C4×C283AGL(1,ℤ/8)semidirect
148. C283#3272semidirect
160. #436D283semidirect
170. C2×M16C2×D283semidirect
184. C4⋊C8C2×D283semidirect
189. C22⋊C8C2×D283semidirect
190. C4×C8C2×D283semidirect
267. C8D4×D283semidirect
287. C4#22583638semidirect

Maximal subgroups

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

subgroupindex
C2×#225836382
#318271202
D4×D11322
#318268382
#318267112
#318266712
#318266612
#318266182
#318266122
C4×D22642
#436×C2832
#3272283