Finite Group Databasebeta

← #49132882

Subgroups — #49132882

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×#22583637C212yesmaximal, complemented
2#31827137C211yesmaximal, characteristic, complemented
3D4×D1132C211yesmaximal, characteristic, complemented
4#31826842C211yesmaximal, characteristic, complemented
5#31826719C212yesmaximal, complemented
6#31826665C211yesmaximal, characteristic, complemented
7#31826660C211yesmaximal, characteristic, complemented
8#31826613C212yesmaximal, complemented
9#31826600C212yesmaximal, complemented
10#31826544C211yesmaximal, characteristic, complemented
11C4×SD16×C283C211yesmaximal, characteristic, complemented
12C2×#17985393C2212yescomplemented
13C22×D1132—21no—
14C2×D4×D283C2212yes—
15#22583637—28no—
16C2×#17985379C2212yescomplemented
17C2×D2264C2212yescomplemented
18C2×D2264C2212yescomplemented
19C2×#17985377C2212yes—
20C2×#17985375C2212yescomplemented
21#22583607—21no—
22#22583607C2211yescharacteristic
23#22583607C2211yescharacteristic, complemented
24#22583585—22no—
25#22583585C2212yes—
26#22583585C2212yescomplemented
27#22583584—21no—
28#22583580—22no—
29C4×D1132—21no—
30C4×D1132C2211yescharacteristic
31C4⋊(C283⋊C8)C2211yescharacteristic, complemented
32#22583530C2212yescomplemented
33#22583530C2212yescomplemented
34(C2×D283)⋊C8C2212yescomplemented
35C2×SD16×C283C2211yescharacteristic
36C4×Q8×C283C2211yescharacteristic, complemented
37C4×D4×C283C2211yescharacteristic
38#106×C283C2211yescharacteristic, complemented
39#103×C283C2211yescharacteristic, complemented
40#102×C283C2211yescharacteristic
41C4×C8×C283C2211yescharacteristic, complemented
42C23×D283—22no—
43#17985393—24no—
44#17985393—42no—
45C2×D1132—22no—
46C2×D1132—22no—
47C2×D1132—22no—
48C2×D1132—21no—
49C2×D1132—21no—
50C2×D1132—21no—
51C2×D1132—21no—
52C2×D1132—44no—
53C2×D1132D411yescharacteristic
54C2×D1132C2312yes—
55C2×D1132C2312yes—
56C2×C22⋊D283—22no—
57D4×D283—24no—
58D4×D283—42no—
59C2×C4×D283—22no—
60C2×C4×D283C2312yes—
61#17985379—24no—
62D2264—24no—
63D2264—42no—
64#17985377—24no—
65#17985375—24no—
66C2×C283⋊C8C2312yes—
67C4⋊Dic283D411yescharacteristic
68(C2×D283)⋊C4—22no—
69(C2×D283)⋊C4—22no—
70(C2×D283)⋊C4D412yes—
71C2×Q8×C283C2311yescharacteristic
72C2×D4×C283C2311yescharacteristic
73C22×C4×C283—21no—
74SD16×C283D414yescomplemented
75C2×C8×C283C2311yescharacteristic
76C2×C8×C283C2311yescharacteristic
77C4⋊C4×C283—21no—
78C4⋊C4×C283C2311yescharacteristic
79C4⋊C4×C283C2311yescharacteristic
80C22⋊C4×C283—21no—
81C42×C283—21no—
82C42×C283C2311yescharacteristic
83C22×D283—22no—
84C22×D283—22no—
85C22×D283—44no—
86C22×D283—44no—
87C22×D283—82no—
88C22×D283C2×D412yes—
89D1132—22no—
90D1132—22no—
91D1132—22no—
92D1132—22no—
93D1132—22no—
94D1132—44no—
95D1132—44no—
96D1132—42no—
97D1132—42no—
98D1132—81no—
99D1132—81no—
100D1132—82no—
101C22⋊D283—44no—
102C2×Dic283C2×D412yes—
103C4×D283—22no—
104C4×D283—22no—
105C4×D283—44no—
106C283⋊C8—22no—
107C23×C283—21no—
108Q8×C283—21no—
109Q8×C283C2×D412yescomplemented
110D4×C283—21no—
111D4×C283C2×D412yes—
112C2×C4×C283—21no—
113C2×C4×C283—21no—
114C2×C4×C283—21no—
115C2×C4×C283—42no—
116C2×C4×C283C2×D411yescharacteristic
117C2×C4×C283C2×D411yescharacteristic
118C2×C4×C283C2411yescharacteristic
119C8×C283—21no—
120C8×C283C2×D412yescomplemented
121C22×C283—22no—
122C22×C283—41no—
123C22×C283—41no—
124C22×C283C22×D411yescharacteristic
125C2×D283—22no—
126C2×D283—22no—
127C2×D283—22no—
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×C283—41no—
138C4×C283—41no—
139C4×C283AGL(1,ℤ/8)12yescomplemented
140C4×C283C22×D411yescharacteristic
141C4×C283H(5,𝔽2)11yescharacteristic
142Dic283—22no—
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×SD16D28311yescharacteristic, complemented
162#436—2831no—
163C2×#41—2832no—
164C22×D4—2832no—
165C22×D4—5661no—
166AGL(1,ℤ/8)—5668no—
167C2×SD16—2832no—
168C2×SD16C2×D28311yescharacteristic
169C2×D8—2832no—
170C2×D8—2832no—
171C2×D8—2832no—
172C2×M16—2832no—
173#127—2831no—
174#127—2831no—
175#127—5661no—
176#121—2832no—
177#121—2832no—
178#121—5662no—
179#121—5661no—
180#120—5662no—
181C4×Q8C2×D28311yescharacteristic, complemented
182C4×D4—2831no—
183C4×D4—5661no—
184C4×D4C2×D28311yescharacteristic
185#106C2×D28311yescharacteristic, complemented
186C4⋊C8—2831no—
187#103C2×D28311yescharacteristic, complemented
188#102—2832no—
189#102—2832no—
190#102C2×D28311yescharacteristic
191C22⋊C8—2832no—
192C4×C8C2×D28311yescharacteristic, complemented
193C24—5662no—
194#41—5664no—
195#41—11322no—
196C2×Q8C22×D28311yescharacteristic
197C2×D4—2831no—
198C2×D4—2832no—
199C2×D4—2832no—
200C2×D4—5662no—
201C2×D4—5662no—
202C2×D4—5662no—
203C2×D4—5662no—
204C2×D4—5664no—
205C2×D4—5661no—
206C2×D4—5661no—
207C2×D4—5661no—
208C2×D4—5661no—
209C2×D4—11324no—
210C2×D4—11322no—
211C2×D4C22×D28311yescharacteristic
212C22×C4—21no—
213C22×C4—2832no—
214C22×C4—5662no—
215SD16—5664no—
216SD16D113214yescomplemented
217D8—5664no—
218D8—5664no—
219D8—11322no—
220M16—5664no—
221C2×C8—2832no—
222C2×C8C22×D28311yescharacteristic
223C2×C8C22×D28311yescharacteristic
224C4⋊C4—21no—
225C4⋊C4—2831no—
226C4⋊C4C22×D28311yescharacteristic
227C4⋊C4C22×D28311yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—2832no—
230C22⋊C4—5662no—
231C22⋊C4—5662no—
232C42—21no—
233C42C22×D28311yescharacteristic
234C23—21no—
235C23—2832no—
236C23—5662no—
237C23—5662no—
238C23—11324no—
239C23—11324no—
240C23—22642no—
241Q8—21no—
242Q8C2×D113212yescomplemented
243D4—21no—
244D4—5662no—
245D4—5662no—
246D4—5662no—
247D4—5662no—
248D4—5662no—
249D4—11324no—
250D4—11324no—
251D4—11324no—
252D4—11322no—
253D4—11322no—
254D4—22641no—
255D4—22641no—
256D4—22642no—
257D4C2×D113212yes—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—2832no—
263C2×C4—5662no—
264C2×C4—5662no—
265C2×C4—11324no—
266C2×C4D4×D28311yescharacteristic
267C2×C4D4×D28311yescharacteristic
268C2×C4C23×D28311yescharacteristic
269C8—21no—
270C8—5662no—
271C8C2×D113212yescomplemented
272C22—22no—
273C22—41no—
274C22—41no—
275C22—5662no—
276C22—5662no—
277C22—5662no—
278C22—11322no—
279C22—11322no—
280C22—11322no—
281C22—11322no—
282C22—11322no—
283C22—11322no—
284C22—22648no—
285C22C2×D4×D28311yescharacteristic
286C4—21no—
287C4—22no—
288C4—41no—
289C4—41no—
290C4—5662no—
291C4#2258363712yescomplemented
292C4C22×D113211yescharacteristic
293C4#2258365611yescharacteristic
294C2—42no—
295C2—11322no—
296C2—22642no—
297C2—22642no—
298C2D4×D113211yescharacteristic
299C2C2×#2258363711yescharacteristic
300C2#3182726711yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC4×SD16×C283C2
socleC22×C283C22×D4
hypercenterC4×SD16D283
hypocenterC283#3274
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#22583637C2semidirect
2. #31827137C2semidirect
3. D4×D1132C2semidirect
4. #31826842C2semidirect
5. #31826719C2semidirect
6. #31826665C2semidirect
7. #31826660C2semidirect
8. #31826613C2semidirect
9. #31826600C2semidirect
10. #31826544C2semidirect
11. C4×SD16×C283C2semidirect
12. C2×#17985393C22semidirect
16. C2×#17985379C22semidirect
17. C2×D2264C22semidirect
18. C2×D2264C22semidirect
20. C2×#17985375C22semidirect
23. #22583607C22semidirect
26. #22583585C22semidirect
31. C4⋊(C283⋊C8)C22semidirect
32. #22583530C22semidirect
33. #22583530C22semidirect
34. (C2×D283)⋊C8C22semidirect
36. C4×Q8×C283C22semidirect
38. #106×C283C22semidirect
39. #103×C283C22semidirect
41. C4×C8×C283C22semidirect
74. SD16×C283D4semidirect
109. Q8×C283C2×D4semidirect
120. C8×C283C2×D4semidirect
139. C4×C283AGL(1,ℤ/8)semidirect
150. C283#3274semidirect
161. C4×SD16D283semidirect
181. C4×Q8C2×D283semidirect
185. #106C2×D283semidirect
187. #103C2×D283semidirect
192. C4×C8C2×D283semidirect
216. SD16D1132semidirect
242. Q8C2×D1132semidirect
271. C8C2×D1132semidirect
291. C4#22583637semidirect

Maximal subgroups

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

subgroupindex
C2×#225836372
#318271372
D4×D11322
#318268422
#318267192
#318266652
#318266602
#318266132
#318266002
#318265442
C4×SD16×C2832
#3274283