Finite Group Databasebeta

← #49132883

Subgroups — #49132883

Order 36224.

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

normal subgroups only

This group has 556 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#31827136C211yesmaximal, characteristic, complemented
3D4×D1132C211yesmaximal, characteristic, complemented
4#31826842C211yesmaximal, characteristic, complemented
5#31826718C212yesmaximal, complemented
6#31826666C211yesmaximal, characteristic, complemented
7#31826661C211yesmaximal, characteristic, complemented
8#31826612C212yesmaximal, complemented
9#31826601C212yesmaximal, complemented
10C4×#17985381C211yesmaximal, characteristic, complemented
11#436×C283C211yesmaximal, characteristic, complemented
12C2×#17985392C2212yescomplemented
13C22×D1132C2212yes—
14C2×D4×D283—21no—
15#22583638—28no—
16C2×#17985381C2211yescharacteristic
17C2×#17985381C2212yescomplemented
18C2×D2264C2212yes—
19C2×D2264C2212yescomplemented
20C2×D2264C2212yescomplemented
21#22583607C2211yescharacteristic
22#22583607C2211yescharacteristic, complemented
23#22583606—21no—
24#22583585—21no—
25#22583584C2212yes—
26#22583584C2212yescomplemented
27#22583583—22no—
28#22583580—22no—
29C4×Dic566C2211yescharacteristic, complemented
30C4×D1132C2211yescharacteristic
31#22583572—21no—
32#22583542C2211yescharacteristic, complemented
33#22583535C2211yescharacteristic, complemented
34#22583532C2211yescharacteristic
35#22583532C2212yescomplemented
36#22583532C2212yescomplemented
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×Dic566C2311yescharacteristic
46C2×D1132—24no—
47C2×D1132—21no—
48C2×D1132—22no—
49C2×D1132—21no—
50C2×D1132—21no—
51C2×D1132—21no—
52C2×D1132—42no—
53C2×D1132C2312yes—
54C2×D1132C2312yes—
55C2×D1132C2311yescharacteristic
56C2×C22⋊D283—22no—
57C2×C22⋊D283—22no—
58C2×C22⋊D283—22no—
59D4×D283—44no—
60C2×C4×D283—22no—
61C2×C4×D283—21no—
62#17985381—24no—
63#17985381D414yescomplemented
64D2264—24no—
65D2264—24no—
66D2264—42no—
67C4⋊Dic283C2311yescharacteristic
68C4⋊Dic283C2311yescharacteristic
69Dic283⋊C4—21no—
70(C2×D283)⋊C4—22no—
71(C2×D283)⋊C4—21no—
72(C2×D283)⋊C4—22no—
73C4×Dic283—21no—
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—22no—
85C22×D283—22no—
86C22×D283—44no—
87C22×D283—44no—
88C22×D283—82no—
89Dic566—21no—
90Dic566C2×D412yescomplemented
91D1132—22no—
92D1132—22no—
93D1132—21no—
94D1132—22no—
95D1132—22no—
96D1132—44no—
97D1132—42no—
98D1132—42no—
99D1132—81no—
100D1132—81no—
101D1132C2×D412yes—
102C22⋊D283—44no—
103C22⋊D283—44no—
104C22⋊D283—82no—
105C2×Dic283—21no—
106C2×Dic283—21no—
107C2×Dic283—21no—
108C4×D283—44no—
109C4×D283—42no—
110C23×C283C2×D412yes—
111D4×C283—22no—
112C2×C4×C283—22no—
113C2×C4×C283—22no—
114C2×C4×C283C2×D411yescharacteristic
115C2×C4×C283C2×D412yes—
116C2×C4×C283C2×D411yescharacteristic
117C2×C4×C283C2411yescharacteristic
118C8×C283—22no—
119C8×C283—21no—
120C8×C283C2×D412yescomplemented
121C22×C283—22no—
122C22×C283—22no—
123C22×C283—22no—
124C22×C283C22×D411yescharacteristic
125C2×D283—22no—
126C2×D283—41no—
127C2×D283—41no—
128C2×D283—42no—
129C2×D283—42no—
130C2×D283—42no—
131C2×D283—42no—
132C2×D283—42no—
133C2×D283—42no—
134C2×D283—88no—
135C4×C283—22no—
136C4×C283—21no—
137C4×C283AGL(1,ℤ/8)12yescomplemented
138C4×C283C22×D411yescharacteristic
139C4×C283H(5,𝔽2)11yescharacteristic
140Dic283—22no—
141Dic283—41no—
142Dic283—41no—
143C2×C283—42no—
144C2×C283D4211yescharacteristic
145C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
146C2×C283#57611yescharacteristic
147D283—42no—
148D283—82no—
149D283—82no—
150C283#327411yescharacteristic, complemented, Sylow
151#3274—2831nomaximal, Sylow
152C2×AGL(1,ℤ/8)—2832no—
153#550—2831no—
154D42—2831no—
155#493—2831no—
156#469—2832no—
157#460—2831no—
158#459—2831no—
159#449—2832no—
160#447—2832no—
161C4×SD16—2831no—
162#436D28311yescharacteristic, complemented
163C2×#41—2832no—
164C22×D4—2832no—
165C22×D4—5661no—
166AGL(1,ℤ/8)—5668no—
167C2×SD16—2831no—
168C2×SD16—2832no—
169C2×D8—2832no—
170C2×D8—2832no—
171C2×D8—2832no—
172C2×M16C2×D28312yescomplemented
173#127—2831no—
174#127—2831no—
175#127—5661no—
176#121—2832no—
177#121—2832no—
178#121—5661no—
179#121—5662no—
180#120—5662no—
181C4×Q8—2831no—
182C4×D4—2831no—
183C4×D4—5661no—
184C4×D4C2×D28311yescharacteristic
185#106—2831no—
186C4⋊C8C2×D28311yescharacteristic, complemented
187#103—2831no—
188#102—2831no—
189#102—2832no—
190#102—2832no—
191C22⋊C8C2×D28312yescomplemented
192C4×C8C2×D28311yescharacteristic, complemented
193C24—5662no—
194#41—5664no—
195#41—11322no—
196C2×Q8—2831no—
197C2×D4—2831no—
198C2×D4—2832no—
199C2×D4—2832no—
200C2×D4—5664no—
201C2×D4—5662no—
202C2×D4—5662no—
203C2×D4—5662no—
204C2×D4—5661no—
205C2×D4—5662no—
206C2×D4—5661no—
207C2×D4—5661no—
208C2×D4—5661no—
209C2×D4—11322no—
210C2×D4—11324no—
211C2×D4D113211yescharacteristic
212C22×C4—5661no—
213C22×C4—5662no—
214C22×C4C22×D28312yes—
215SD16—2834no—
216SD16—5664no—
217D8—5664no—
218D8—5664no—
219D8—11322no—
220M16—24no—
221C2×C8C22×D28311yescharacteristic
222C2×C8C22×D28312yes—
223C2×C8C22×D28311yescharacteristic
224C4⋊C4—2831no—
225C4⋊C4—2831no—
226C4⋊C4—5661no—
227C4⋊C4D113211yescharacteristic
228C22⋊C4—5661no—
229C22⋊C4—5662no—
230C22⋊C4—5662no—
231C22⋊C4D113212yes—
232C42—5661no—
233C42C22×D28311yescharacteristic
234C23—5661no—
235C23—5662no—
236C23—5662no—
237C23—11324no—
238C23—11324no—
239C23—22642no—
240C23C2×D113212yes—
241Q8—2832no—
242Q8—5661no—
243D4—22no—
244D4—2832no—
245D4—5662no—
246D4—5662no—
247D4—5661no—
248D4—5662no—
249D4—5662no—
250D4—11324no—
251D4—11324no—
252D4—11324no—
253D4—11322no—
254D4—11322no—
255D4—22641no—
256D4—22641no—
257D4—22642no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—5661no—
261C2×C4—5661no—
262C2×C4—5661no—
263C2×C4—11324no—
264C2×C4—11322no—
265C2×C4C2×D113211yescharacteristic
266C2×C4C2×D113212yes—
267C2×C4C2×D113211yescharacteristic
268C2×C4C23×D28311yescharacteristic
269C8—22no—
270C8—21no—
271C8D4×D28312yescomplemented
272C22—22no—
273C22—22no—
274C22—22no—
275C22—5662no—
276C22—11321no—
277C22—11321no—
278C22—11322no—
279C22—11322no—
280C22—11322no—
281C22—11322no—
282C22—11322no—
283C22—11322no—
284C22—22648no—
285C22C22×D113211yescharacteristic
286C4—21no—
287C4—22no—
288C4—5662no—
289C4—11321no—
290C4—11321no—
291C4#2258363812yescomplemented
292C4C2×D4×D28311yescharacteristic
293C4#2258365611yescharacteristic
294C2—42no—
295C2—11322no—
296C2—22642no—
297C2—22642no—
298C2D4×D113211yescharacteristic
299C2C2×#2258363811yescharacteristic
300C2#3182727011yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#436×C283C2
socleC22×C283C22×D4
hypercenter#436D283
hypocenterC283#3274
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. #31827136C2semidirect
3. D4×D1132C2semidirect
4. #31826842C2semidirect
5. #31826718C2semidirect
6. #31826666C2semidirect
7. #31826661C2semidirect
8. #31826612C2semidirect
9. #31826601C2semidirect
10. C4×#17985381C2semidirect
11. #436×C283C2semidirect
12. C2×#17985392C22semidirect
17. C2×#17985381C22semidirect
19. C2×D2264C22semidirect
20. C2×D2264C22semidirect
22. #22583607C22semidirect
26. #22583584C22semidirect
29. C4×Dic566C22semidirect
32. #22583542C22semidirect
33. #22583535C22semidirect
35. #22583532C22semidirect
36. #22583532C22semidirect
37. C2×M16×C283C22semidirect
39. C4⋊C8×C283C22semidirect
40. C22⋊C8×C283C22semidirect
41. C4×C8×C283C22semidirect
63. #17985381D4semidirect
90. Dic566C2×D4semidirect
120. C8×C283C2×D4semidirect
137. C4×C283AGL(1,ℤ/8)semidirect
150. C283#3274semidirect
162. #436D283semidirect
172. C2×M16C2×D283semidirect
186. C4⋊C8C2×D283semidirect
191. C22⋊C8C2×D283semidirect
192. C4×C8C2×D283semidirect
271. C8D4×D283semidirect
291. C4#22583638semidirect

Maximal subgroups

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

subgroupindex
C2×#225836382
#318271362
D4×D11322
#318268422
#318267182
#318266662
#318266612
#318266122
#318266012
C4×#179853812
#436×C2832
#3274283