Finite Group Databasebeta

← #49130664

Subgroups — #49130664

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#31827034C212yesmaximal, complemented
3#31827029C211yesmaximal, characteristic, complemented
4#31826653C218yesmaximal, complemented
5#31826438C212yesmaximal, complemented
6#410×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—
15C22×D1132C2211yescharacteristic, complemented
16#22583607—22no—
17#22583606—21no—
18#22583599—21no—
19#22583598—22no—
20#22583585—24no—
21#22583584—22no—
22#22583580C2218yescomplemented
23#22583578C2214yescomplemented
24#22583569C2211yescharacteristic, complemented
25#22583524C2218yescomplemented
26C2×#41×C283C2211yescharacteristic
27#117×C283C2212yescomplemented
28#99×C283C2214yescomplemented
29C23×D283C2312yes—
30#17985393—24no—
31#17985392—24no—
32#17985392—24no—
33#17985392—22no—
34#17985392—22no—
35#17985392—24no—
36#17985392—22no—
37#17985392—22no—
38#17985391—24no—
39#17985391—28no—
40C2×Dic566—22no—
41C2×Dic566D412yescomplemented
42Q8×D283—24no—
43C2×D1132—22no—
44C2×D1132—28no—
45C2×D1132—21no—
46C2×D1132—22no—
47C2×D1132—22no—
48C2×D1132—21no—
49C2×D1132D412yescomplemented
50C2×C22⋊D283—24no—
51C2×C22⋊D283—24no—
52C2×C22⋊D283C2314yes—
53D4×D283—24no—
54D4×D283—28no—
55C2×C4×D283—24no—
56C2×C4×D283D414yescomplemented
57C4⋊Dic283—21no—
58C22⋊Dic283C2312yes—
59(C2×D283)⋊C4—28no—
60(C2×D283)⋊C4—24no—
61C4×Dic283—21no—
62#41×C283—22no—
63#41×C283—22no—
64C2×Q8×C283D411yescharacteristic, complemented
65C2×D4×C283D411yescharacteristic, complemented
66C2×D4×C283C2312yes—
67C22×C4×C283D412yescomplemented
68C22×C4×C283C2311yescharacteristic
69C4⋊C4×C283—22no—
70C22⋊C4×C283C2314yes—
71C42×C283—22no—
72C22×D283—24no—
73C22×D283—22no—
74C22×D283—24no—
75C22×D283—82no—
76C22×D283C2×D414yes—
77Dic566—24no—
78Dic566—22no—
79Dic566—22no—
80D1132—24no—
81D1132—22no—
82D1132—22no—
83D1132—41no—
84D1132—41no—
85D1132—42no—
86D1132—88no—
87C22⋊D283—28no—
88C22⋊D283—24no—
89C22⋊D283—24no—
90C22⋊D283—84no—
91C2×Dic283—24no—
92C2×Dic283—22no—
93C2×Dic283C2×D414yes—
94C4×D283—28no—
95C4×D283—24no—
96C4×D283—24no—
97C23×C283C2×D412yes—
98C23×C283C2411yescharacteristic
99Q8×C283—22no—
100D4×C283—24no—
101D4×C283—22no—
102C2×C4×C283—22no—
103C2×C4×C283—22no—
104C2×C4×C283—24no—
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×C283C22×D412yes—
114C22×C283C22×D411yescharacteristic
115C2×D283—24no—
116C2×D283—44no—
117C2×D283—44no—
118C2×D283—48no—
119C2×D283—42no—
120C2×D283—84no—
121C4×C283—22no—
122C4×C283—44no—
123C4×C283#12011yescharacteristic
124C4×C283#12011yescharacteristic
125C4×C283#12012yes—
126Dic283—24no—
127Dic283—42no—
128C2×C283—21no—
129C2×C283—22no—
130C2×C283—42no—
131C2×C283C2×#12011yescharacteristic
132D283—44no—
133D283—82no—
134C283#302711yescharacteristic, complemented, Sylow
135#3027—2831nomaximal, Sylow
136#585—2831no—
137#535—2831no—
138#535—2832no—
139B(4,𝔽2)—2838no—
140#410—2832no—
141#410D28311yescharacteristic, complemented
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×D4—2831no—
152#127—5662no—
153#127—5661no—
154#124—5662no—
155#124—5661no—
156#121—5664no—
157#121—5662no—
158#120—2834no—
159#120—2838no—
160#117—2831no—
161#117C2×D28312yescomplemented
162#99—2838no—
163#99C2×D28314yescomplemented
164C24—2832no—
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×Q8D113211yescharacteristic, complemented
181C2×D4—2834no—
182C2×D4—2832no—
183C2×D4—5662no—
184C2×D4—5668no—
185C2×D4—5668no—
186C2×D4—5664no—
187C2×D4—5664no—
188C2×D4—5664no—
189C2×D4—5662no—
190C2×D4—5662no—
191C2×D4—5661no—
192C2×D4—5661no—
193C2×D4D113211yescharacteristic, complemented
194C2×D4C22×D28312yes—
195C22×C4—2834no—
196C22×C4—5664no—
197C22×C4D113212yescomplemented
198C22×C4C22×D28311yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—5661no—
201C22⋊C4—2832no—
202C22⋊C4—5668no—
203C22⋊C4—5664no—
204C22⋊C4C22×D28314yes—
205C42—22no—
206C42—5661no—
207C23—2834no—
208C23—5664no—
209C23—5664no—
210C23—5662no—
211C23—22642no—
212C23C2×D113212yes—
213C23C23×D28311yescharacteristic
214Q8—22no—
215Q8—5664no—
216Q8—5662no—
217Q8—5662no—
218D4—24no—
219D4—22no—
220D4—5664no—
221D4—5668no—
222D4—5664no—
223D4—5664no—
224D4—5662no—
225D4—5662no—
226D4—11321no—
227D4—11321no—
228D4—11322no—
229D4—22648no—
230D4—22644no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—24no—
234C2×C4—2834no—
235C2×C4—5668no—
236C2×C4—5664no—
237C2×C4—5664no—
238C2×C4—5664no—
239C2×C4—5662no—
240C2×C4D4×D28312yes—
241C2×C4D4×D28312yes—
242C2×C4C2×D113212yes—
243C2×C4C2×D113211yescharacteristic
244C2×C4C2×D113211yescharacteristic
245C22—22no—
246C22—41no—
247C22—42no—
248C22—5664no—
249C22—11324no—
250C22—11328no—
251C22—11324no—
252C22—11322no—
253C22—22644no—
254C22C2×D4×D28312yes—
255C22C22×D113211yescharacteristic
256C4—22no—
257C4—44no—
258C4—5664no—
259C4—11322no—
260C4#2258358011yescharacteristic
261C4#2258358011yescharacteristic
262C4#2258358012yes—
263C2—22no—
264C2—21no—
265C2—42no—
266C2—11324no—
267C2—22642no—
268C2C2×#2258358011yescharacteristic
subgroupG/H
centerC2C2×#22583580
commutator, cosocleC23×C283C24
FrattiniC23C23×D283
Fitting#410×C283C2
socleC2×C283C2×#120
hypercenter#410D283
hypocenterC283#3027
LCSG ▷ C23×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #31827301C2semidirect
2. #31827034C2semidirect
3. #31827029C2semidirect
4. #31826653C2semidirect
5. #31826438C2semidirect
6. #410×C283C2semidirect
15. C22×D1132C22semidirect
22. #22583580C22semidirect
23. #22583578C22semidirect
24. #22583569C22semidirect
25. #22583524C22semidirect
27. #117×C283C22semidirect
28. #99×C283C22semidirect
41. C2×Dic566D4semidirect
49. C2×D1132D4semidirect
56. C2×C4×D283D4semidirect
64. C2×Q8×C283D4semidirect
65. C2×D4×C283D4semidirect
67. C22×C4×C283D4semidirect
134. C283#3027semidirect
141. #410D283semidirect
161. #117C2×D283semidirect
163. #99C2×D283semidirect
180. C2×Q8D1132semidirect
193. C2×D4D1132semidirect
197. C22×C4D1132semidirect

Maximal subgroups

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

subgroupindex
#318273012
#318270342
#318270292
#318266532
#318264382
#410×C2832
#3027283