Finite Group Databasebeta

← #49130545

Subgroups — #49130545

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×#22583657C211yesmaximal, characteristic, complemented
2C2×#22583636C211yesmaximal, characteristic, complemented
3C22×#17985380C211yesmaximal, characteristic, complemented
4#31826608C214yesmaximal, complemented
5#31826603C214yesmaximal, complemented
6#31826473C211yesmaximal, characteristic, complemented
7#31826459C211yesmaximal, characteristic, complemented
8#31826432C211yesmaximal, characteristic, complemented
9#535×C283C211yesmaximal, characteristic, complemented
10#22583657—24no—
11#22583657—24no—
12C2×#17985392C2211yescharacteristic
13C2×#17985392C2212yescomplemented
14C2×#17985391—22no—
15C2×#17985391—21no—
16C22×Dic566C2211yescharacteristic
17C22×Dic566C2212yescomplemented
18C2×Q8×D283—21no—
19#22583636—24no—
20C2×#17985380—24no—
21C2×#17985380C2214yes—
22C2×#17985380C2212yes—
23C2×#17985377C2212yes—
24C2×#17985376C2211yescharacteristic
25C22×C283⋊C8C2211yescharacteristic
26#22583533C2212yescomplemented
27#22583533C2214yescomplemented
28#22583530C2212yescomplemented
29C22⋊(C283⋊C8)C2214yescomplemented
30C2×#41×C283C2211yescharacteristic
31C22×D4×C283C2211yescharacteristic
32#127×C283—21no—
33#124×C283—21no—
34#121×C283C2214yes—
35#120×C283—22no—
36#117×C283C2211yescharacteristic
37#17985392—24no—
38#17985392—24no—
39#17985392—22no—
40#17985392D414yescomplemented
41#17985391—216no—
42#17985391—28no—
43C2×Dic566—24no—
44C2×Dic566—24no—
45C2×Dic566—21no—
46C2×Dic566—22no—
47C2×Dic566—22no—
48C2×Dic566D414yescomplemented
49C2×Dic566C2312yes—
50C2×Dic566C2311yescharacteristic
51Q8×D283—28no—
52C2×D1132C2311yescharacteristic
53C2×C22⋊D283—21no—
54C2×C22⋊D283—22no—
55C22×Dic283—21no—
56C22×Dic283—22no—
57C2×C4×D283—21no—
58C2×C4×D283—22no—
59#17985380—28no—
60#17985380—24no—
61#17985377—24no—
62#17985376—22no—
63C2×C283⋊C8—22no—
64C2×C283⋊C8C2312yes—
65C2×C283⋊C8C2312yes—
66C24×C283—21no—
67#41×C283—22no—
68#41×C283—22no—
69C2×Q8×C283D411yescharacteristic
70C2×D4×C283—24no—
71C2×D4×C283—22no—
72C2×D4×C283—22no—
73C2×D4×C283—21no—
74C2×D4×C283D412yes—
75C2×D4×C283D411yescharacteristic
76C2×D4×C283C2312yes—
77C22×C4×C283C2312yes—
78C22×C4×C283C2311yescharacteristic
79C4⋊C4×C283C2312yes—
80C22⋊C4×C283—21no—
81C22⋊C4×C283—24no—
82C42×C283—21no—
83C22×D283—21no—
84Dic566—28no—
85Dic566—24no—
86Dic566—21no—
87Dic566—22no—
88Dic566C2×D412yes—
89Dic566C2×D414yes—
90D1132—21no—
91D1132C2×D412yes—
92C22⋊D283—28no—
93C22⋊D283—24no—
94C2×Dic283—28no—
95C2×Dic283—24no—
96C2×Dic283—21no—
97C2×Dic283—22no—
98C4×D283—28no—
99C4×D283—24no—
100C283⋊C8—22no—
101C283⋊C8—22no—
102C23×C283—22no—
103C23×C283—42no—
104C23×C283—82no—
105C23×C283C2×D412yes—
106C23×C283C2×D411yescharacteristic
107Q8×C283—22no—
108D4×C283—24no—
109D4×C283—22no—
110D4×C283—22no—
111D4×C283—22no—
112D4×C283—42no—
113D4×C283—84no—
114C2×C4×C283—22no—
115C2×C4×C283—22no—
116C2×C4×C283—22no—
117C2×C4×C283C2×D412yes—
118C2×C4×C283C2×D412yes—
119C2×C4×C283C2×D412yes—
120C2×C4×C283C2×D411yescharacteristic
121C2×C4×C283C2411yescharacteristic
122C22×C283—22no—
123C22×C283—22no—
124C22×C283—24no—
125C22×C283—42no—
126C22×C283—44no—
127C22×C283—84no—
128C22×C283#12012yes—
129C22×C283C22×D411yescharacteristic
130C2×D283—22no—
131C2×D283—42no—
132C4×C283—22no—
133C4×C283—42no—
134C4×C283#12012yes—
135C4×C283C22×D411yescharacteristic
136C4×C283C22×D411yescharacteristic
137Dic283—24no—
138Dic283—22no—
139C2×C283—22no—
140C2×C283—42no—
141C2×C283—82no—
142C2×C283C2×#12011yescharacteristic
143C2×C283#57712yes—
144D283—42no—
145C283#301011yescharacteristic, complemented, Sylow
146#3010—2831nomaximal, Sylow
147C2×2−1+4—2831no—
148C2×AGL(1,ℤ/8)—2831no—
149C22×SD16—2831no—
150#535D28311yescharacteristic, complemented
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—5662no—
161C2×#41—5661no—
162C2×#41C2×D28311yescharacteristic
163C22×Q8—2831no—
164C22×Q8—2832no—
165C22×Q8—5661no—
166C22×D4C2×D28311yescharacteristic
167AGL(1,ℤ/8)—5664no—
168C2×SD16—2834no—
169C2×SD16—2832no—
170C2×SD16—5664no—
171C2×D8—2832no—
172C2×M16—2831no—
173C22×C8—2831no—
174#127—21no—
175#124—21no—
176#121C2×D28314yes—
177#120—22no—
178#117C2×D28311yescharacteristic
179#103—2832no—
180#103—2834no—
181#102—2832no—
182C22⋊C8—2834no—
183C24—21no—
184#41—22no—
185#41—22no—
186#41—2834no—
187#41—5664no—
188#41—5664no—
189#41—56616no—
190#41—5668no—
191#41—5662no—
192C2×Q8—2834no—
193C2×Q8—2832no—
194C2×Q8—2831no—
195C2×Q8—5664no—
196C2×Q8—5664no—
197C2×Q8—5668no—
198C2×Q8—5662no—
199C2×Q8—5662no—
200C2×Q8—5661no—
201C2×Q8C22⋊D28311yescharacteristic
202C2×D4—24no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—21no—
206C2×D4—2831no—
207C2×D4—5662no—
208C2×D4—5661no—
209C2×D4C22⋊D28312yes—
210C2×D4C22⋊D28311yescharacteristic
211C2×D4C22×D28312yes—
212C22×C4—5662no—
213C22×C4—5661no—
214C22×C4—5662no—
215C22×C4—5661no—
216C22×C4C22×D28312yes—
217C22×C4C22×D28311yescharacteristic
218SD16—5668no—
219SD16—5664no—
220D8—5664no—
221M16—5662no—
222C2×C8—2832no—
223C2×C8—2832no—
224C2×C8—5662no—
225C4⋊C4C22×D28312yes—
226C22⋊C4—21no—
227C22⋊C4—24no—
228C42—21no—
229C23—22no—
230C23—42no—
231C23—82no—
232C23—5661no—
233C23C2×C22⋊D28312yes—
234C23C2×C22⋊D28311yescharacteristic
235Q8—22no—
236Q8—2834no—
237Q8—2832no—
238Q8—5668no—
239Q8—5664no—
240Q8—5662no—
241Q8—5661no—
242D4—24no—
243D4—22no—
244D4—22no—
245D4—22no—
246D4—42no—
247D4—84no—
248D4—2832no—
249D4—5668no—
250D4—5664no—
251D4—5661no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—5668no—
256C2×C4—5668no—
257C2×C4—5664no—
258C2×C4—5662no—
259C2×C4—5661no—
260C2×C4—5664no—
261C2×C4D4×D28312yes—
262C2×C4D4×D28312yes—
263C2×C4C2×C22⋊D28312yes—
264C2×C4C2×C22⋊D28311yescharacteristic
265C2×C4C23×D28311yescharacteristic
266C8—5662no—
267C8—5662no—
268C22—22no—
269C22—22no—
270C22—24no—
271C22—42no—
272C22—44no—
273C22—84no—
274C22—5662no—
275C22—11322no—
276C22#2258357812yes—
277C22C22×C22⋊D28311yescharacteristic
278C4—22no—
279C4—42no—
280C4—5664no—
281C4—5662no—
282C4#2258357812yes—
283C4C2×D4×D28311yescharacteristic
284C4C2×D4×D28311yescharacteristic
285C2—22no—
286C2—42no—
287C2—82no—
288C2—11322no—
289C2C2×#2258357811yescharacteristic
290C2#3182727612yes—
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#535×C283C2
socleC22×C283C22×D4
hypercenter#535D283
hypocenterC283#3010
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#22583657C2semidirect
2. C2×#22583636C2semidirect
3. C22×#17985380C2semidirect
4. #31826608C2semidirect
5. #31826603C2semidirect
6. #31826473C2semidirect
7. #31826459C2semidirect
8. #31826432C2semidirect
9. #535×C283C2semidirect
13. C2×#17985392C22semidirect
17. C22×Dic566C22semidirect
26. #22583533C22semidirect
27. #22583533C22semidirect
28. #22583530C22semidirect
29. C22⋊(C283⋊C8)C22semidirect
40. #17985392D4semidirect
48. C2×Dic566D4semidirect
145. C283#3010semidirect
150. #535D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836572
C2×#225836362
C22×#179853802
#318266082
#318266032
#318264732
#318264592
#318264322
#535×C2832
#3010283