Finite Group Databasebeta

← #49130536

Subgroups — #49130536

Order 36224.

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

normal subgroups only

This group has 752 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×#22583656C211yesmaximal, characteristic
2C2×#22583641C211yesmaximal, characteristic, complemented
3C22×#17985379C211yesmaximal, characteristic, complemented
4#31826625C214yesmaximal, complemented
5#31826615C214yesmaximal, complemented
6#31826469C211yesmaximal, characteristic, complemented
7#31826459C211yesmaximal, characteristic, complemented
8#31826432C211yesmaximal, characteristic, complemented
9#536×C283C211yesmaximal, characteristic, complemented
10#22583656—24no—
11#22583656—24no—
12C2×#17985393—21no—
13C2×#17985392C2212yes—
14C2×#17985392C2211yescharacteristic
15C22×D1132C2212yes—
16C22×D1132C2211yescharacteristic
17C2×D4×D283—22no—
18C2×D4×D283—21no—
19#22583641—24no—
20C2×#17985382C2212yescomplemented
21C2×#17985379—24no—
22C2×#17985379C2214yescomplemented
23C2×#17985379C2212yescomplemented
24C2×#17985376C2211yescharacteristic, complemented
25C22×C283⋊C8C2211yescharacteristic, complemented
26#22583533C2212yescomplemented
27#22583530C2212yescomplemented
28#22583530C2214yescomplemented
29C22⋊(C283⋊C8)C2214yescomplemented
30C2×#41×C283C2211yescharacteristic
31C22×Q8×C283C2211yescharacteristic, complemented
32C4⋊Q8×C283—21no—
33#124×C283—21no—
34#123×C283—22no—
35C22⋊Q8×C283C2214yescomplemented
36#117×C283C2211yescharacteristic, complemented
37C23×D283—22no—
38C23×D283—21no—
39#17985393—28no—
40#17985392—24no—
41#17985392—24no—
42#17985392—22no—
43#17985392D414yes—
44C2×Dic566C2311yescharacteristic
45C2×D1132—24no—
46C2×D1132—24no—
47C2×D1132—22no—
48C2×D1132—21no—
49C2×D1132—22no—
50C2×D1132D414yes—
51C2×D1132C2311yescharacteristic
52C2×D1132C2312yes—
53C2×C22⋊D283—22no—
54C2×C22⋊D283—21no—
55D4×D283—216no—
56D4×D283—28no—
57C2×C4×D283—22no—
58C2×C4×D283—21no—
59#17985382—24no—
60#17985379—28no—
61#17985379—24no—
62#17985376—22no—
63C2×C283⋊C8—22no—
64C2×C283⋊C8C2312yes—
65C2×C283⋊C8C2312yes—
66#41×C283—22no—
67#41×C283—22no—
68C2×Q8×C283—21no—
69C2×Q8×C283—22no—
70C2×Q8×C283—22no—
71C2×Q8×C283D411yescharacteristic
72C2×Q8×C283C2312yes—
73C2×D4×C283D412yes—
74C2×D4×C283D411yescharacteristic
75C22×C4×C283—21no—
76C22×C4×C283C2312yes—
77C22×C4×C283C2311yescharacteristic
78C4⋊C4×C283—24no—
79C4⋊C4×C283C2312yes—
80C22⋊C4×C283—21no—
81C22⋊C4×C283—24no—
82C42×C283—21no—
83C22×D283—22no—
84C22×D283—21no—
85C22×D283—28no—
86C22×D283—24no—
87C22×D283—82no—
88C22×D283—84no—
89Dic566—21no—
90Dic566C2×D412yes—
91D1132—28no—
92D1132—24no—
93D1132—22no—
94D1132—21no—
95D1132C2×D412yes—
96D1132C2×D414yes—
97C22⋊D283—28no—
98C22⋊D283—24no—
99C2×Dic283—21no—
100C4×D283—28no—
101C4×D283—24no—
102C283⋊C8—22no—
103C283⋊C8—22no—
104C23×C283C2×D412yes—
105C23×C283C2×D411yescharacteristic
106Q8×C283—22no—
107Q8×C283—22no—
108Q8×C283—22no—
109Q8×C283—42no—
110D4×C283—24no—
111D4×C283—22no—
112C2×C4×C283—22no—
113C2×C4×C283—22no—
114C2×C4×C283—22no—
115C2×C4×C283—22no—
116C2×C4×C283—42no—
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#12012yes—
126C22×C283C22×D411yescharacteristic
127C2×D283—24no—
128C2×D283—22no—
129C2×D283—44no—
130C2×D283—42no—
131C2×D283—84no—
132C2×D283—88no—
133C4×C283—22no—
134C4×C283—42no—
135C4×C283—42no—
136C4×C283#12012yes—
137C4×C283C22×D411yescharacteristic
138C4×C283C22×D411yescharacteristic
139Dic283—22no—
140C2×C283—22no—
141C2×C283—42no—
142C2×C283C2×#12011yescharacteristic
143C2×C283#57712yes—
144D283—44no—
145D283—42no—
146C283#300911yescharacteristic, complemented, Sylow
147#3009—2831nomaximal, Sylow
148C2×H(5,𝔽2)—2831no—
149C2×#137—2831no—
150C22×SD16—2831no—
151#536D28311yescharacteristic, complemented
152#452—2834no—
153#450—2834no—
154#418—2831no—
155#416—2831no—
156#408—2831no—
157H(5,𝔽2)—5664no—
158H(5,𝔽2)—5664no—
159C2×#41—2831no—
160C2×#41—2832no—
161C2×#41—5661no—
162C2×#41C2×D28311yescharacteristic
163C22×Q8C2×D28311yescharacteristic, complemented
164C22×D4—2831no—
165C22×D4—2832no—
166C22×D4—5662no—
167C22×D4—5661no—
168#137—5664no—
169C2×Q16—2832no—
170C2×SD16—2834no—
171C2×SD16—2832no—
172C2×SD16—5664no—
173C2×M16—2831no—
174C22×C8—2831no—
175C4⋊Q8—21no—
176#124—21no—
177#123—22no—
178C22⋊Q8C2×D28314yescomplemented
179#117C2×D28311yescharacteristic, complemented
180#103—2832no—
181#102—2832no—
182#102—2834no—
183C22⋊C8—2834no—
184C24—5662no—
185C24—5661no—
186#41—22no—
187#41—22no—
188#41—2834no—
189#41—5664no—
190#41—5664no—
191#41—5668no—
192#41—5662no—
193C2×Q8—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—2831no—
197C2×Q8C22⋊D28311yescharacteristic
198C2×Q8C22×D28312yes—
199C2×D4—2834no—
200C2×D4—2832no—
201C2×D4—2831no—
202C2×D4—5664no—
203C2×D4—5664no—
204C2×D4—56616no—
205C2×D4—5668no—
206C2×D4—5662no—
207C2×D4—5661no—
208C2×D4—5662no—
209C2×D4—5662no—
210C2×D4—5661no—
211C2×D4C22⋊D28312yes—
212C2×D4C22⋊D28311yescharacteristic
213C22×C4—21no—
214C22×C4—5662no—
215C22×C4—5661no—
216C22×C4C22×D28312yes—
217C22×C4C22×D28311yescharacteristic
218Q16—5664no—
219SD16—5668no—
220SD16—5664no—
221M16—5662no—
222C2×C8—2832no—
223C2×C8—2832no—
224C2×C8—5662no—
225C4⋊C4—24no—
226C4⋊C4C22×D28312yes—
227C22⋊C4—21no—
228C22⋊C4—24no—
229C42—21no—
230C23—5668no—
231C23—5662no—
232C23—5661no—
233C23—5664no—
234C23—22642no—
235C23—22644no—
236C23C2×C22⋊D28312yes—
237C23C2×C22⋊D28311yescharacteristic
238Q8—22no—
239Q8—22no—
240Q8—22no—
241Q8—42no—
242Q8—2832no—
243Q8—5661no—
244D4—24no—
245D4—22no—
246D4—2834no—
247D4—2832no—
248D4—5668no—
249D4—5668no—
250D4—5664no—
251D4—5664no—
252D4—5661no—
253D4—5662no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—42no—
259C2×C4—5668no—
260C2×C4—5661no—
261C2×C4—5664no—
262C2×C4D4×D28312yes—
263C2×C4D4×D28312yes—
264C2×C4C2×C22⋊D28312yes—
265C2×C4C2×C22⋊D28311yescharacteristic
266C2×C4C23×D28311yescharacteristic
267C8—5662no—
268C8—5662no—
269C22—22no—
270C22—22no—
271C22—24no—
272C22—5664no—
273C22—5662no—
274C22—11324no—
275C22—11322no—
276C22—22644no—
277C22—22648no—
278C22#2258357812yes—
279C22C22×C22⋊D28311yescharacteristic
280C4—22no—
281C4—42no—
282C4—42no—
283C4—5662no—
284C4#2258357812yes—
285C4C2×D4×D28311yescharacteristic
286C4C2×D4×D28311yescharacteristic
287C2—22no—
288C2—42no—
289C2—11324no—
290C2—11322no—
291C2C2×#2258357811yescharacteristic
292C2#3182727312yes—
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#536×C283C2
socleC22×C283C22×D4
prime radicalC2×#22583656C2
hypercenter#536D283
hypocenterC283#3009
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C2×#22583641C2semidirect
3. C22×#17985379C2semidirect
4. #31826625C2semidirect
5. #31826615C2semidirect
6. #31826469C2semidirect
7. #31826459C2semidirect
8. #31826432C2semidirect
9. #536×C283C2semidirect
20. C2×#17985382C22semidirect
22. C2×#17985379C22semidirect
23. C2×#17985379C22semidirect
24. C2×#17985376C22semidirect
25. C22×C283⋊C8C22semidirect
26. #22583533C22semidirect
27. #22583530C22semidirect
28. #22583530C22semidirect
29. C22⋊(C283⋊C8)C22semidirect
31. C22×Q8×C283C22semidirect
35. C22⋊Q8×C283C22semidirect
36. #117×C283C22semidirect
146. C283#3009semidirect
151. #536D283semidirect
163. C22×Q8C2×D283semidirect
178. C22⋊Q8C2×D283semidirect
179. #117C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836562
C2×#225836412
C22×#179853792
#318266252
#318266152
#318264692
#318264592
#318264322
#536×C2832
#3009283