Finite Group Databasebeta

← #49132861

Subgroups — #49132861

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×#22583635C212yesmaximal, complemented
2D4×D1132C211yesmaximal, characteristic, complemented
3#31826839C211yesmaximal, characteristic, complemented
4#31826713C212yesmaximal, complemented
5#31826667C211yesmaximal, characteristic, complemented
6#31826660C211yesmaximal, characteristic, complemented
7#31826615C212yesmaximal, complemented
8#31826610C212yesmaximal, complemented
9C4×#17985377C211yesmaximal, characteristic, complemented
10#31826543C211yesmaximal, characteristic, complemented
11#547×C283C211yesmaximal, characteristic, complemented
12C22×D1132C2212yes—
13C2×D4×D283—21no—
14#22583635—28no—
15C2×#17985379C2212yes—
16C2×#17985379C2212yescomplemented
17C2×#17985379C2212yescomplemented
18C2×#17985377C2211yescharacteristic
19C2×#17985377C2212yescomplemented
20C2×#17985376C2212yescomplemented
21#22583607C2211yescharacteristic
22#22583585—21no—
23#22583584C2212yes—
24#22583580—22no—
25C4×D1132C2211yescharacteristic
26#22583543C2211yescharacteristic, complemented
27C4⋊(C283⋊C8)C2211yescharacteristic, complemented
28#22583534C2212yescomplemented
29#22583531C2211yescharacteristic, complemented
30#22583530C2211yescharacteristic
31#22583530C2212yescomplemented
32C22⋊(C283⋊C8)C2212yescomplemented
33C4×C283⋊C8C2211yescharacteristic, complemented
34C2×#41×C283C2212yescomplemented
35C4⋊Q8×C283C2211yescharacteristic, complemented
36#123×C283—22no—
37C22⋊Q8×C283C2212yescomplemented
38#121×C283—21no—
39C4×D4×C283C2211yescharacteristic
40C4×D4×C283C2211yescharacteristic, complemented
41C2×C4⋊C4×C283—21no—
42C23×D283—22no—
43C2×D1132—24no—
44C2×D1132—22no—
45C2×D1132—21no—
46C2×D1132—21no—
47C2×D1132—42no—
48C2×D1132C2312yes—
49C2×D1132C2311yescharacteristic
50C2×C22⋊D283—22no—
51D4×D283—44no—
52C2×C4×D283—21no—
53#17985379—24no—
54#17985379—24no—
55#17985379—42no—
56#17985377—24no—
57#17985377D414yescomplemented
58#17985376—24no—
59C2×C283⋊C8C2312yes—
60C2×C283⋊C8C2311yescharacteristic
61C2×C283⋊C8C2311yescharacteristic
62C4⋊Dic283C2311yescharacteristic
63(C2×D283)⋊C4—21no—
64(C2×D283)⋊C4—22no—
65#41×C283—24no—
66#41×C283—42no—
67C2×Q8×C283C2312yes—
68C2×D4×C283—22no—
69C2×D4×C283D411yescharacteristic
70C2×D4×C283C2311yescharacteristic
71C22×C4×C283—21no—
72C22×C4×C283—22no—
73C22×C4×C283C2312yes—
74C4⋊C4×C283—21no—
75C4⋊C4×C283—22no—
76C4⋊C4×C283—21no—
77C4⋊C4×C283D411yescharacteristic
78C4⋊C4×C283C2311yescharacteristic
79C22⋊C4×C283—22no—
80C22⋊C4×C283—21no—
81C22⋊C4×C283D412yes—
82C42×C283C2311yescharacteristic
83C22×D283—21no—
84C22×D283—22no—
85C22×D283—44no—
86C22×D283—44no—
87C22×D283—82no—
88D1132—22no—
89D1132—21no—
90D1132—22no—
91D1132—44no—
92D1132—42no—
93D1132—81no—
94D1132C2×D412yes—
95C22⋊D283—44no—
96C2×Dic283—21no—
97C4×D283—42no—
98C283⋊C8—22no—
99C283⋊C8—21no—
100C283⋊C8C2×D412yescomplemented
101C23×C283—21no—
102C23×C283C2×D412yes—
103Q8×C283—22no—
104Q8×C283—22no—
105D4×C283—22no—
106D4×C283—21no—
107D4×C283—44no—
108D4×C283C2×D412yescomplemented
109C2×C4×C283—22no—
110C2×C4×C283—22no—
111C2×C4×C283—21no—
112C2×C4×C283—22no—
113C2×C4×C283—44no—
114C2×C4×C283—42no—
115C2×C4×C283C2×D411yescharacteristic
116C2×C4×C283C2×D412yes—
117C2×C4×C283C2×D411yescharacteristic
118C2×C4×C283C2411yescharacteristic
119C22×C283—22no—
120C22×C283—22no—
121C22×C283—22no—
122C22×C283—22no—
123C22×C283—41no—
124C22×C283—41no—
125C22×C283C22×D411yescharacteristic
126C2×D283—22no—
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×C283—42no—
136C4×C283—41no—
137C4×C283AGL(1,ℤ/8)12yescomplemented
138C4×C283C22×D411yescharacteristic
139C4×C283H(5,𝔽2)11yescharacteristic
140Dic283—41no—
141C2×C283—42no—
142C2×C283—42no—
143C2×C283D4211yescharacteristic
144C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
145C2×C283#57711yescharacteristic
146D283—42no—
147D283—82no—
148C283#327211yescharacteristic, complemented, Sylow
149#3272—2831nomaximal, Sylow
150C2×AGL(1,ℤ/8)—2832no—
151#547D28311yescharacteristic, complemented
152D42—2831no—
153#492—2831no—
154#468—2832no—
155#461—2831no—
156#459—2831no—
157#450—2832no—
158#449—2832no—
159C4×D8—2831no—
160#436—2831no—
161C2×#41C2×D28312yescomplemented
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×M16—2832no—
171C4⋊Q8C2×D28311yescharacteristic, complemented
172#127—2831no—
173#123—22no—
174C22⋊Q8C2×D28312yescomplemented
175#121—21no—
176#121—2832no—
177#121—5661no—
178#120—5662no—
179C4×D4—2831no—
180C4×D4C2×D28311yescharacteristic
181C4×D4C2×D28311yescharacteristic, complemented
182C2×C4⋊C4—21no—
183#107—2831no—
184C4⋊C8—2831no—
185#103—2832no—
186#102—2831no—
187#102—2831no—
188#102—2832no—
189C22⋊C8—2832no—
190C4×C8—2831no—
191C24—5662no—
192#41—24no—
193#41—42no—
194C2×Q8C22×D28312yes—
195C2×D4—22no—
196C2×D4—2831no—
197C2×D4—2832no—
198C2×D4—5664no—
199C2×D4—5662no—
200C2×D4—5662no—
201C2×D4—5661no—
202C2×D4—5661no—
203C2×D4—11322no—
204C2×D4—11324no—
205C2×D4C22⋊D28311yescharacteristic
206C2×D4C22×D28311yescharacteristic
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—5661no—
210C22×C4C22×D28312yes—
211SD16—5664no—
212SD16—5664no—
213SD16—11322no—
214D8—2834no—
215D8—5664no—
216M16—5664no—
217C2×C8—2831no—
218C2×C8—2831no—
219C2×C8—2832no—
220C4⋊C4—21no—
221C4⋊C4—22no—
222C4⋊C4—21no—
223C4⋊C4—2831no—
224C4⋊C4C22⋊D28311yescharacteristic
225C4⋊C4C22×D28311yescharacteristic
226C22⋊C4—22no—
227C22⋊C4—21no—
228C22⋊C4—5661no—
229C22⋊C4—5662no—
230C22⋊C4C22⋊D28312yes—
231C42C22×D28311yescharacteristic
232C23—21no—
233C23—5661no—
234C23—5662no—
235C23—11324no—
236C23—11324no—
237C23—22642no—
238C23C2×C22⋊D28312yes—
239Q8—22no—
240Q8—22no—
241D4—22no—
242D4—21no—
243D4—44no—
244D4—2832no—
245D4—5662no—
246D4—5661no—
247D4—5662no—
248D4—11324no—
249D4—11324no—
250D4—11322no—
251D4—22641no—
252D4D4×D28312yescomplemented
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—44no—
258C2×C4—42no—
259C2×C4—5661no—
260C2×C4—11322no—
261C2×C4C2×C22⋊D28311yescharacteristic
262C2×C4C2×C22⋊D28312yes—
263C2×C4C2×C22⋊D28311yescharacteristic
264C2×C4C23×D28311yescharacteristic
265C8—2832no—
266C8—5662no—
267C8—5661no—
268C22—22no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—41no—
273C22—41no—
274C22—5662no—
275C22—11321no—
276C22—11321no—
277C22—11322no—
278C22—11322no—
279C22—11322no—
280C22—22648no—
281C22C22×C22⋊D28311yescharacteristic
282C4—21no—
283C4—22no—
284C4—41no—
285C4—42no—
286C4—11321no—
287C4#2258363512yescomplemented
288C4C2×D4×D28311yescharacteristic
289C4#2258365511yescharacteristic
290C2—42no—
291C2—42no—
292C2—11322no—
293C2—22642no—
294C2D4×C22⋊D28311yescharacteristic
295C2C2×#2258363511yescharacteristic
296C2#3182727311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#547×C283C2
socleC22×C283C22×D4
hypercenter#547D283
hypocenterC283#3272
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C2×#22583635C2semidirect
2. D4×D1132C2semidirect
3. #31826839C2semidirect
4. #31826713C2semidirect
5. #31826667C2semidirect
6. #31826660C2semidirect
7. #31826615C2semidirect
8. #31826610C2semidirect
9. C4×#17985377C2semidirect
10. #31826543C2semidirect
11. #547×C283C2semidirect
16. C2×#17985379C22semidirect
17. C2×#17985379C22semidirect
19. C2×#17985377C22semidirect
20. C2×#17985376C22semidirect
26. #22583543C22semidirect
27. C4⋊(C283⋊C8)C22semidirect
28. #22583534C22semidirect
29. #22583531C22semidirect
31. #22583530C22semidirect
32. C22⋊(C283⋊C8)C22semidirect
33. C4×C283⋊C8C22semidirect
34. C2×#41×C283C22semidirect
35. C4⋊Q8×C283C22semidirect
37. C22⋊Q8×C283C22semidirect
40. C4×D4×C283C22semidirect
57. #17985377D4semidirect
100. C283⋊C8C2×D4semidirect
108. D4×C283C2×D4semidirect
137. C4×C283AGL(1,ℤ/8)semidirect
148. C283#3272semidirect
151. #547D283semidirect
161. C2×#41C2×D283semidirect
171. C4⋊Q8C2×D283semidirect
174. C22⋊Q8C2×D283semidirect
181. C4×D4C2×D283semidirect
252. D4D4×D283semidirect
287. C4#22583635semidirect

Maximal subgroups

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

subgroupindex
C2×#225836352
D4×D11322
#318268392
#318267132
#318266672
#318266602
#318266152
#318266102
C4×#179853772
#318265432
#547×C2832
#3272283