Finite Group Databasebeta

← #49133049

Subgroups — #49133049

Order 36224.

454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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#31827279C211yesmaximal, characteristic, complemented
2#31827277C212yesmaximal, complemented
3#31827267C211yesmaximal, characteristic, complemented
4#31826849C211yesmaximal, characteristic, complemented
5#31826741C211yesmaximal, characteristic, complemented
6#31826736C211yesmaximal, characteristic, complemented
7#31826728C212yesmaximal, complemented
8#31826644C212yesmaximal, complemented
9#31826639C212yesmaximal, complemented
10#31826583C211yesmaximal, characteristic, complemented
11#443×C283C211yesmaximal, characteristic, complemented
12#22583657C2212yescomplemented
13#22583656C2212yes—
14#22583643—22no—
15#22583643C2212yes—
16#22583640C2212yescomplemented
17#22583639—22no—
18#22583638—22no—
19#22583638C2212yescomplemented
20#22583637—22no—
21#22583635C2212yes—
22#22583633—21no—
23#22583632—22no—
24#22583632C2211yescharacteristic
25#22583629—21no—
26C2×Dic1132C2211yescharacteristic, complemented
27Q16×D283—21no—
28C2×#17985381—22no—
29C2×#17985381C2212yescomplemented
30C2×D2264C2211yescharacteristic
31D8×D283—21no—
32#22583616C2211yescharacteristic
33#22583616C2211yescharacteristic, complemented
34#22583598C2212yescomplemented
35#22583546C2211yescharacteristic, complemented
36#22583538C2211yescharacteristic
37#22583538C2211yescharacteristic, complemented
38#22583528C2212yescomplemented
39#22583526C2212yescomplemented
40#135×C283C2211yescharacteristic
41#131×C283C2212yescomplemented
42#108×C283C2211yescharacteristic, complemented
43#104×C283C2212yescomplemented
44C4×C8×C283C2211yescharacteristic, complemented
45#17985393—22no—
46#17985392—22no—
47#17985392—22no—
48#17985392C2311yescharacteristic
49#17985392C2311yescharacteristic
50#17985391—22no—
51#17985391—42no—
52C2×Dic566—22no—
53C2×Dic566C2312yes—
54Q8×D283—22no—
55C2×D1132—22no—
56C2×D1132C2312yes—
57D4×D283—22no—
58D4×D283—42no—
59Dic1132—22no—
60Dic1132—21no—
61Dic1132—21no—
62Dic1132D411yescharacteristic
63#17985382—22no—
64#17985381—22no—
65#17985381—22no—
66#17985381—22no—
67#17985381—22no—
68#17985381D411yescharacteristic
69#17985381D411yescharacteristic
70#17985380—22no—
71#17985379—22no—
72D2264—22no—
73D2264—21no—
74D2264—21no—
75D2264D411yescharacteristic
76#17985377—22no—
77#17985376C2311yescharacteristic
78#17985376C2311yescharacteristic
79#17985375—21no—
80#17985375—21no—
81C8×D283—21no—
82C8×D283—21no—
83(C2×D283)⋊C4—42no—
84#41×C283C2312yes—
85Q16×C283D411yescharacteristic
86SD16×C283D412yes—
87D8×C283D411yescharacteristic
88M16×C283—22no—
89M16×C283C2312yes—
90C2×C8×C283—22no—
91C2×C8×C283C2311yescharacteristic
92C2×C8×C283C2311yescharacteristic
93C42×C283C2311yescharacteristic
94C22×D283—22no—
95C22×D283—42no—
96Dic566—22no—
97Dic566—22no—
98Dic566—42no—
99Dic566C2×D411yescharacteristic
100Dic566C2×D411yescharacteristic
101D1132—22no—
102D1132—22no—
103D1132—42no—
104D1132C2×D411yescharacteristic
105D1132C2×D411yescharacteristic
106C22⋊D283—21no—
107C22⋊D283—21no—
108C22⋊D283—42no—
109C22⋊D283—42no—
110C2×Dic283—22no—
111C2×Dic283—42no—
112C4×D283—21no—
113C4×D283—21no—
114C4×D283—42no—
115C4×D283—42no—
116C283⋊C8—21no—
117C283⋊C8—21no—
118Q8×C283C2×D412yes—
119D4×C283—22no—
120D4×C283C2×D412yes—
121C2×C4×C283—22no—
122C2×C4×C283—21no—
123C2×C4×C283C2411yescharacteristic
124C8×C283—22no—
125C8×C283C2×D411yescharacteristic
126C8×C283C2×D411yescharacteristic
127C8×C283C2×D411yescharacteristic
128C8×C283C2×D411yescharacteristic
129C22×C283—22no—
130C22×C283H(5,𝔽2)11yescharacteristic
131C2×D283—21no—
132C2×D283—21no—
133C2×D283—42no—
134C2×D283—82no—
135C2×D283—162no—
136C4×C283—22no—
137C4×C283—41no—
138C4×C283C22×D411yescharacteristic
139C4×C283C22×D411yescharacteristic
140Dic283—21no—
141Dic283—21no—
142Dic283—42no—
143C2×C283—21no—
144C2×C283—42no—
145C2×C283D4211yescharacteristic
146D283—41no—
147D283—41no—
148D283—82no—
149C283#329011yescharacteristic, complemented, Sylow
150#3290—2831nomaximal, Sylow
151#578—2831no—
152#577—2832no—
153#576—2831no—
154#495—2831no—
155#473—2831no—
156#472—2831no—
157#471—2832no—
158#455—2832no—
159#454—2832no—
160#443—2831no—
161#443D28311yescharacteristic, complemented
1622−1+4—2832no—
163H(5,𝔽2)—2832no—
164#137—2832no—
165#137—2832no—
166#137—5662no—
167#137—5662no—
168AGL(1,ℤ/8)—2832no—
169AGL(1,ℤ/8)—2832no—
170AGL(1,ℤ/8)—5662no—
171AGL(1,ℤ/8)—5662no—
172#135—2831no—
173#135—5662no—
174#135—5661no—
175#135—5661no—
176#135C2×D28311yescharacteristic
177C2×Q16—2831no—
178C2×Q16—5661no—
179C2×SD16—2832no—
180C2×SD16—5662no—
181C2×D8—2831no—
182C2×D8—5661no—
183#131—2831no—
184#131—2831no—
185#131C2×D28312yescomplemented
186#124—2832no—
187#108—2831no—
188#108C2×D28311yescharacteristic, complemented
189#104—2831no—
190#104—2831no—
191#104C2×D28312yescomplemented
192#101—2832no—
193#100—2832no—
194C4×C8C2×D28311yescharacteristic, complemented
195#41—2831no—
196#41—2831no—
197#41—5662no—
198#41—5662no—
199#41—5662no—
200#41—5662no—
201#41—11322no—
202#41C22×D28312yes—
203C2×Q8—2832no—
204C2×Q8—5662no—
205C2×Q8—5662no—
206C2×D4—2832no—
207C2×D4—5662no—
208C2×D4—5662no—
209C2×D4—11322no—
210Q16—2831no—
211Q16—5662no—
212Q16—5662no—
213Q16—5661no—
214Q16—5661no—
215Q16D113211yescharacteristic
216SD16—2831no—
217SD16—2831no—
218SD16—5662no—
219SD16—5662no—
220SD16—5662no—
221SD16—5662no—
222SD16—5662no—
223SD16—5662no—
224SD16D113212yes—
225D8—2831no—
226D8—5662no—
227D8—5662no—
228D8—5661no—
229D8—5661no—
230D8D113211yescharacteristic
231M16—22no—
232M16—2831no—
233M16—2831no—
234M16—5661no—
235M16—5661no—
236M16C22×D28312yes—
237C2×C8—22no—
238C2×C8—5661no—
239C2×C8—5661no—
240C2×C8C22×D28311yescharacteristic
241C2×C8C22×D28311yescharacteristic
242C22⋊C4—11322no—
243C42C22×D28311yescharacteristic
244C23—5662no—
245C23—11322no—
246Q8—2831no—
247Q8—2831no—
248Q8—5662no—
249Q8—5662no—
250Q8—11322no—
251Q8C2×D113212yes—
252D4—22no—
253D4—2831no—
254D4—2831no—
255D4—5661no—
256D4—5661no—
257D4—5662no—
258D4—5662no—
259D4—11322no—
260D4—11322no—
261D4—11322no—
262D4C2×D113212yes—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—5661no—
266C2×C4—5661no—
267C2×C4—5662no—
268C2×C4—11322no—
269C2×C4—11322no—
270C2×C4—11322no—
271C2×C4C23×D28311yescharacteristic
272C8—22no—
273C8—5661no—
274C8—5661no—
275C8D4×D28311yescharacteristic
276C8D4×D28311yescharacteristic
277C8C2×D113211yescharacteristic
278C8C2×D113211yescharacteristic
279C22—22no—
280C22—5661no—
281C22—5661no—
282C22—11322no—
283C22—45282no—
284C22—22642no—
285C22#2258365611yescharacteristic
286C4—22no—
287C4—41no—
288C4—5661no—
289C4—5661no—
290C4—11322no—
291C4C2×D4×D28311yescharacteristic
292C4C22×D113211yescharacteristic
293C2—21no—
294C2—42no—
295C2—11321no—
296C2—11321no—
297C2—22642no—
298C2D4×D113211yescharacteristic
subgroupG/H
centerC2D4×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#443×C283C2
socleC2×C283D42
hypercenter#443D283
hypocenterC283#3290
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #31827279C2semidirect
2. #31827277C2semidirect
3. #31827267C2semidirect
4. #31826849C2semidirect
5. #31826741C2semidirect
6. #31826736C2semidirect
7. #31826728C2semidirect
8. #31826644C2semidirect
9. #31826639C2semidirect
10. #31826583C2semidirect
11. #443×C283C2semidirect
12. #22583657C22semidirect
16. #22583640C22semidirect
19. #22583638C22semidirect
26. C2×Dic1132C22semidirect
29. C2×#17985381C22semidirect
33. #22583616C22semidirect
34. #22583598C22semidirect
35. #22583546C22semidirect
37. #22583538C22semidirect
38. #22583528C22semidirect
39. #22583526C22semidirect
41. #131×C283C22semidirect
42. #108×C283C22semidirect
43. #104×C283C22semidirect
44. C4×C8×C283C22semidirect
149. C283#3290semidirect
161. #443D283semidirect
185. #131C2×D283semidirect
188. #108C2×D283semidirect
191. #104C2×D283semidirect
194. C4×C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318272792
#318272772
#318272672
#318268492
#318267412
#318267362
#318267282
#318266442
#318266392
#318265832
#443×C2832
#3290283