Finite Group Databasebeta

← #49130543

Subgroups — #49130543

Order 36224.

732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22583658C211yesmaximal, characteristic, complemented
2C2×#22583636C211yesmaximal, characteristic, complemented
3#31827032C211yesmaximal, characteristic, complemented
4#31826609C214yesmaximal, complemented
5#31826602C214yesmaximal, complemented
6#31826474C211yesmaximal, characteristic, complemented
7#31826462C211yesmaximal, characteristic, complemented
8#31826431C211yesmaximal, characteristic, complemented
9C22×SD16×C283C211yesmaximal, characteristic, complemented
10#22583658—24no—
11#22583658—24no—
12C2×#17985393—21no—
13C2×#17985393C2212yescomplemented
14C2×#17985392—22no—
15C2×#17985392C2211yescharacteristic
16C2×#17985392C2211yescharacteristic
17C2×Q8×D283—21no—
18C2×Q8×D283C2212yescomplemented
19#22583636—24no—
20C2×#17985380C2212yes—
21C2×#17985377C2212yes—
22C2×#17985376C2211yescharacteristic
23#22583606—21no—
24#22583597—21no—
25#22583581C2214yes—
26#22583579—22no—
27#22583569C2211yescharacteristic
28#22583535C2212yescomplemented
29#22583534C2214yescomplemented
30#22583532C2212yescomplemented
31(C2×D283)⋊C8C2214yescomplemented
32C22×Q8×C283C2211yescharacteristic
33C22×D4×C283C2211yescharacteristic
34C2×SD16×C283—24no—
35C2×SD16×C283C2214yes—
36C22×C8×C283C2211yescharacteristic
37#17985393—28no—
38#17985393—24no—
39#17985393—24no—
40#17985392—216no—
41#17985392—22no—
42#17985392—22no—
43#17985392—22no—
44#17985392D414yescomplemented
45C2×Dic566—22no—
46C2×Dic566D411yescharacteristic
47C2×Dic566C2311yescharacteristic
48Q8×D283—28no—
49Q8×D283—24no—
50Q8×D283—24no—
51C2×D1132—22no—
52C2×D1132D411yescharacteristic
53C2×D1132C2311yescharacteristic
54C2×C22⋊D283—24no—
55C2×C22⋊D283—21no—
56C2×C22⋊D283D412yes—
57C2×C4×D283—22no—
58C2×C4×D283—22no—
59C2×C4×D283—21no—
60C2×C4×D283C2312yes—
61#17985380—24no—
62#17985377—24no—
63#17985376—22no—
64C2×C283⋊C8C2312yes—
65C4⋊Dic283C2312yes—
66C22⋊Dic283—24no—
67C22⋊Dic283—21no—
68C4×Dic283—21no—
69C24×C283—21no—
70C2×Q8×C283—21no—
71C2×Q8×C283—22no—
72C2×Q8×C283D414yescomplemented
73C2×Q8×C283C2312yes—
74C2×D4×C283—22no—
75C2×D4×C283—22no—
76C2×D4×C283—21no—
77C2×D4×C283C2312yes—
78C22×C4×C283—21no—
79C22×C4×C283C2311yescharacteristic
80SD16×C283—28no—
81C2×C8×C283—22no—
82C2×C8×C283C2312yes—
83C22×D283—21no—
84C22×D283C2×D412yes—
85Dic566—28no—
86Dic566—22no—
87Dic566—21no—
88Dic566C2×D412yes—
89D1132—28no—
90D1132—22no—
91D1132—21no—
92D1132C2×D412yes—
93C22⋊D283—24no—
94C22⋊D283—24no—
95C22⋊D283—84no—
96C2×Dic283—21no—
97C2×Dic283—22no—
98C2×Dic283C2×D412yes—
99C4×D283—28no—
100C4×D283—28no—
101C4×D283—24no—
102C4×D283—22no—
103C4×D283—22no—
104C283⋊C8—22no—
105C23×C283—22no—
106C23×C283—42no—
107C23×C283—82no—
108C23×C283C2×D411yescharacteristic
109Q8×C283—24no—
110Q8×C283—22no—
111Q8×C283C2×D414yes—
112D4×C283—22no—
113D4×C283—22no—
114D4×C283—42no—
115C2×C4×C283—24no—
116C2×C4×C283—22no—
117C2×C4×C283C2×D411yescharacteristic
118C2×C4×C283C2×D412yes—
119C2×C4×C283C2×D412yes—
120C2×C4×C283C2411yescharacteristic
121C8×C283—22no—
122C22×C283—22no—
123C22×C283—42no—
124C22×C283—44no—
125C22×C283—84no—
126C22×C283#12012yes—
127C22×C283C22×D411yescharacteristic
128C2×D283—22no—
129C2×D283—22no—
130C2×D283—24no—
131C2×D283—42no—
132C4×C283—24no—
133C4×C283#12012yes—
134C4×C283C22×D411yescharacteristic
135C4×C283C22×D411yescharacteristic
136Dic283—22no—
137Dic283—22no—
138Dic283—42no—
139C2×C283—22no—
140C2×C283—82no—
141C2×C283C2×#12011yescharacteristic
142C2×C283#57712yes—
143D283—42no—
144D283—42no—
145C283#301011yescharacteristic, complemented, Sylow
146#3010—2831nomaximal, Sylow
147C2×2−1+4—2831no—
148C2×AGL(1,ℤ/8)—2831no—
149C22×SD16D28311yescharacteristic, complemented
150#535—2831no—
151#449—2834no—
152#448—2834no—
153#419—2831no—
154#416—2831no—
155#408—2831no—
1562−1+4—5664no—
1572−1+4—5664no—
158C2×#41—2831no—
159C2×#41—2832no—
160C2×#41—2831no—
161C2×#41—5662no—
162C2×#41—5661no—
163C22×Q8—2832no—
164C22×Q8—5661no—
165C22×Q8C2×D28311yescharacteristic
166C22×D4C2×D28311yescharacteristic
167AGL(1,ℤ/8)—5664no—
168C2×SD16—24no—
169C2×SD16—2832no—
170C2×SD16C2×D28314yes—
171C2×D8—2832no—
172C2×M16—2831no—
173C22×C8C2×D28311yescharacteristic
174#127—5661no—
175#124—5661no—
176#121—2834no—
177#120—5662no—
178#117—2831no—
179#103—2834no—
180#103—2832no—
181#102—2832no—
182C22⋊C8—2834no—
183C24—21no—
184#41—2834no—
185#41—56616no—
186#41—5664no—
187#41—5668no—
188#41—5664no—
189#41—5662no—
190#41—5662no—
191#41—5662no—
192C2×Q8—21no—
193C2×Q8—22no—
194C2×Q8—2831no—
195C2×Q8—2831no—
196C2×Q8—5662no—
197C2×Q8—5664no—
198C2×Q8—5668no—
199C2×Q8—5664no—
200C2×Q8C22⋊D28314yescomplemented
201C2×Q8C22×D28312yes—
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—22no—
205C2×D4—2832no—
206C2×D4—2831no—
207C2×D4—2831no—
208C2×D4—5662no—
209C2×D4—5661no—
210C2×D4—5664no—
211C2×D4C22×D28312yes—
212C22×C4—21no—
213C22×C4—2832no—
214C22×C4—5662no—
215C22×C4—5662no—
216C22×C4—5661no—
217C22×C4C22×D28311yescharacteristic
218SD16—28no—
219SD16—5664no—
220D8—5664no—
221M16—5662no—
222C2×C8—22no—
223C2×C8—2832no—
224C2×C8C22×D28312yes—
225C4⋊C4—2832no—
226C22⋊C4—5664no—
227C22⋊C4—5661no—
228C42—5661no—
229C23—22no—
230C23—42no—
231C23—82no—
232C23—2832no—
233C23—5661no—
234C23D4×D28311yescharacteristic
235Q8—24no—
236Q8—22no—
237Q8—2832no—
238Q8—5668no—
239Q8—5662no—
240Q8—5661no—
241Q8C2×C22⋊D28314yes—
242D4—22no—
243D4—22no—
244D4—42no—
245D4—2832no—
246D4—5668no—
247D4—5664no—
248D4—5664no—
249D4—5662no—
250D4—5661no—
251D4—22644no—
252C2×C4—24no—
253C2×C4—22no—
254C2×C4—2832no—
255C2×C4—5668no—
256C2×C4—5668no—
257C2×C4—5661no—
258C2×C4—5664no—
259C2×C4—5662no—
260C2×C4—5662no—
261C2×C4—5662no—
262C2×C4D4×D28311yescharacteristic
263C2×C4D4×D28312yes—
264C2×C4C2×C22⋊D28312yes—
265C2×C4C23×D28311yescharacteristic
266C8—22no—
267C8—5662no—
268C22—22no—
269C22—42no—
270C22—44no—
271C22—84no—
272C22—5662no—
273C22—5662no—
274C22—5664no—
275C22—11322no—
276C22#2258357812yes—
277C22C2×D4×D28311yescharacteristic
278C4—24no—
279C4—5662no—
280C4—5662no—
281C4—11322no—
282C4#2258357812yes—
283C4C2×D4×D28311yescharacteristic
284C4C22×C22⋊D28311yescharacteristic
285C2—22no—
286C2—82no—
287C2—11322no—
288C2—11322no—
289C2C2×#2258357811yescharacteristic
290C2#3182727112yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC22×SD16×C283C2
socleC22×C283C22×D4
hypercenterC22×SD16D283
hypocenterC283#3010
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#22583658C2semidirect
2. C2×#22583636C2semidirect
3. #31827032C2semidirect
4. #31826609C2semidirect
5. #31826602C2semidirect
6. #31826474C2semidirect
7. #31826462C2semidirect
8. #31826431C2semidirect
9. C22×SD16×C283C2semidirect
13. C2×#17985393C22semidirect
18. C2×Q8×D283C22semidirect
28. #22583535C22semidirect
29. #22583534C22semidirect
30. #22583532C22semidirect
31. (C2×D283)⋊C8C22semidirect
44. #17985392D4semidirect
72. C2×Q8×C283D4semidirect
145. C283#3010semidirect
149. C22×SD16D283semidirect
200. C2×Q8C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836582
C2×#225836362
#318270322
#318266092
#318266022
#318264742
#318264622
#318264312
C22×SD16×C2832
#3010283