Finite Group Databasebeta

← #49130662

Subgroups — #49130662

Order 36224.

772 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 145 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
1#31827301C211yesmaximal, characteristic, complemented
2#31827032C212yesmaximal, complemented
3#31826651C218yesmaximal, complemented
4#31826439C211yesmaximal, characteristic, complemented
5#31826438C212yesmaximal, complemented
6#535×C283C211yesmaximal, characteristic, complemented
7#22583658—21no—
8#22583657—22no—
9#22583656—22no—
10#22583655—21no—
11#22583655C2214yes—
12C2×#17985392—22no—
13C2×#17985392C2212yes—
14#41×D283—24no—
15#22583606—22no—
16#22583597—22no—
17#22583581—24no—
18#22583579C2218yescomplemented
19#22583569C2212yescomplemented
20#22583525C2214yescomplemented
21#22583524C2218yescomplemented
22C2×#41×C283C2211yescharacteristic
23C22×D4×C283C2211yescharacteristic, complemented
24#127×C283—21no—
25#124×C283—21no—
26#121×C283—22no—
27#120×C283C2214yescomplemented
28#117×C283C2211yescharacteristic, complemented
29#17985393—24no—
30#17985392—24no—
31#17985392—24no—
32#17985392—22no—
33#17985392—22no—
34#17985392—24no—
35#17985392—22no—
36#17985392—22no—
37#17985391—24no—
38#17985391—28no—
39C2×Dic566—22no—
40C2×Dic566D412yescomplemented
41Q8×D283—24no—
42C2×D1132—22no—
43C2×D1132D412yescomplemented
44C2×C22⋊D283—28no—
45C2×C22⋊D283—24no—
46C2×C22⋊D283C2314yes—
47D4×D283—24no—
48D4×D283—28no—
49C2×C4×D283—24no—
50C2×C4×D283D414yescomplemented
51C4⋊Dic283—22no—
52C22⋊Dic283—28no—
53C22⋊Dic283C2314yes—
54C4×Dic283—22no—
55C24×C283C2312yes—
56#41×C283—22no—
57#41×C283—22no—
58C2×Q8×C283D411yescharacteristic, complemented
59C2×D4×C283—24no—
60C2×D4×C283—22no—
61C2×D4×C283—22no—
62C2×D4×C283—21no—
63C2×D4×C283—21no—
64C2×D4×C283D411yescharacteristic, complemented
65C2×D4×C283C2312yes—
66C22×C4×C283D412yescomplemented
67C22×C4×C283C2311yescharacteristic
68C4⋊C4×C283—21no—
69C22⋊C4×C283—24no—
70C22⋊C4×C283C2312yes—
71C42×C283—21no—
72C22×D283—24no—
73C22×D283C2×D414yes—
74Dic566—24no—
75Dic566—22no—
76Dic566—22no—
77D1132—24no—
78D1132—22no—
79D1132—22no—
80C22⋊D283—28no—
81C22⋊D283—24no—
82C22⋊D283—24no—
83C22⋊D283—88no—
84C2×Dic283—24no—
85C2×Dic283—24no—
86C2×Dic283C2×D414yes—
87C4×D283—28no—
88C4×D283—24no—
89C4×D283—24no—
90C23×C283—22no—
91C23×C283—24no—
92C23×C283—82no—
93C23×C283C2×D412yes—
94C23×C283C2411yescharacteristic
95Q8×C283—22no—
96D4×C283—24no—
97D4×C283—22no—
98D4×C283—41no—
99D4×C283—41no—
100D4×C283—42no—
101D4×C283—84no—
102C2×C4×C283—22no—
103C2×C4×C283—22no—
104C2×C4×C283—22no—
105C2×C4×C283C2×D412yes—
106C2×C4×C283C2×D412yes—
107C2×C4×C283C2×D412yes—
108C2×C4×C283C2×D411yescharacteristic
109C2×C4×C283C2×D411yescharacteristic
110C22×C283—22no—
111C22×C283—41no—
112C22×C283—42no—
113C22×C283—44no—
114C22×C283—48no—
115C22×C283—42no—
116C22×C283C22×D412yes—
117C22×C283C22×D411yescharacteristic
118C2×D283—24no—
119C2×D283—44no—
120C2×D283—84no—
121C4×C283—22no—
122C4×C283—42no—
123C4×C283#12011yescharacteristic
124C4×C283#12011yescharacteristic
125C4×C283#12012yes—
126Dic283—24no—
127Dic283—44no—
128C2×C283—22no—
129C2×C283—21no—
130C2×C283—42no—
131C2×C283—82no—
132C2×C283C2×#12011yescharacteristic
133D283—44no—
134C283#302711yescharacteristic, complemented, Sylow
135#3027—2831nomaximal, Sylow
136#585—2831no—
137#535—2832no—
138#535D28311yescharacteristic, complemented
139B(4,𝔽2)—2838no—
140#410—2831no—
141#410—2832no—
1422−1+4—5662no—
1432−1+4—5661no—
144H(5,𝔽2)—2834no—
145H(5,𝔽2)—5662no—
146H(5,𝔽2)—5661no—
147C2×#41—2832no—
148C2×#41—5664no—
149C2×#41—5662no—
150C2×#41C2×D28311yescharacteristic
151C22×D4C2×D28311yescharacteristic, complemented
152#127—21no—
153#127—5662no—
154#124—21no—
155#124—5662no—
156#121—22no—
157#121—5664no—
158#120—2838no—
159#120C2×D28314yescomplemented
160#117—2832no—
161#117C2×D28311yescharacteristic, complemented
162#99—2834no—
163#99—2838no—
164C24C22×D28312yes—
165#41—22no—
166#41—22no—
167#41—5664no—
168#41—5664no—
169#41—5668no—
170#41—5664no—
171#41—5664no—
172#41—5662no—
173#41—5662no—
174#41—5662no—
175#41—5662no—
176#41—5664no—
177C2×Q8—2832no—
178C2×Q8—5662no—
179C2×Q8—5664no—
180C2×Q8C22⋊D28311yescharacteristic, complemented
181C2×D4—24no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—2834no—
187C2×D4—2832no—
188C2×D4—5662no—
189C2×D4—5668no—
190C2×D4—5664no—
191C2×D4—5664no—
192C2×D4—5668no—
193C2×D4C22⋊D28311yescharacteristic, complemented
194C2×D4C22×D28312yes—
195C22×C4—2834no—
196C22×C4—5664no—
197C22×C4C22⋊D28312yescomplemented
198C22×C4C22×D28311yescharacteristic
199C4⋊C4—21no—
200C4⋊C4—5662no—
201C22⋊C4—24no—
202C22⋊C4—2834no—
203C22⋊C4—5668no—
204C22⋊C4C22×D28312yes—
205C42—21no—
206C42—5662no—
207C23—24no—
208C23—22no—
209C23—82no—
210C23—2834no—
211C23—5664no—
212C23C2×C22⋊D28312yes—
213C23C23×D28311yescharacteristic
214Q8—22no—
215Q8—5664no—
216Q8—5662no—
217Q8—5662no—
218D4—24no—
219D4—22no—
220D4—41no—
221D4—41no—
222D4—42no—
223D4—84no—
224D4—5664no—
225D4—5668no—
226D4—5664no—
227D4—5664no—
228D4—5662no—
229D4—5662no—
230D4—22648no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—2834no—
235C2×C4—5668no—
236C2×C4—5664no—
237C2×C4—5664no—
238C2×C4—5664no—
239C2×C4—5664no—
240C2×C4D4×D28312yes—
241C2×C4D4×D28312yes—
242C2×C4C2×C22⋊D28312yes—
243C2×C4C2×C22⋊D28311yescharacteristic
244C2×C4C2×C22⋊D28311yescharacteristic
245C22—22no—
246C22—41no—
247C22—42no—
248C22—44no—
249C22—48no—
250C22—42no—
251C22—5664no—
252C22—11324no—
253C22—22644no—
254C22C2×D4×D28312yes—
255C22C22×C22⋊D28311yescharacteristic
256C4—22no—
257C4—42no—
258C4—5664no—
259C4—11324no—
260C4#2258357811yescharacteristic
261C4#2258357811yescharacteristic
262C4#2258357812yes—
263C2—21no—
264C2—22no—
265C2—42no—
266C2—82no—
267C2—11324no—
268C2C2×#2258357811yescharacteristic
subgroupG/H
centerC2C2×#22583578
commutator, cosocleC23×C283C24
FrattiniC23C23×D283
Fitting#535×C283C2
socleC2×C283C2×#120
hypercenter#535D283
hypocenterC283#3027
LCSG ▷ C23×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #31827301C2semidirect
2. #31827032C2semidirect
3. #31826651C2semidirect
4. #31826439C2semidirect
5. #31826438C2semidirect
6. #535×C283C2semidirect
18. #22583579C22semidirect
19. #22583569C22semidirect
20. #22583525C22semidirect
21. #22583524C22semidirect
23. C22×D4×C283C22semidirect
27. #120×C283C22semidirect
28. #117×C283C22semidirect
40. C2×Dic566D4semidirect
43. C2×D1132D4semidirect
50. C2×C4×D283D4semidirect
58. C2×Q8×C283D4semidirect
64. C2×D4×C283D4semidirect
66. C22×C4×C283D4semidirect
134. C283#3027semidirect
138. #535D283semidirect
151. C22×D4C2×D283semidirect
159. #120C2×D283semidirect
161. #117C2×D283semidirect
180. C2×Q8C22⋊D283semidirect
193. C2×D4C22⋊D283semidirect
197. C22×C4C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
#318273012
#318270322
#318266512
#318264392
#318264382
#535×C2832
#3027283