Finite Group Databasebeta

← #49133055

Subgroups — #49133055

Order 36224.

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

normal subgroups only

This group has 460 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#31827277C212yesmaximal, complemented
2#31827272C212yesmaximal, complemented
3#31826838C211yesmaximal, characteristic, complemented
4#31826729C212yesmaximal, complemented
5#31826728C212yesmaximal, complemented
6#31826649C212yesmaximal, complemented
7#31826634C212yesmaximal, complemented
8#31826583C211yesmaximal, characteristic, complemented
9#443×C283C211yesmaximal, characteristic, complemented
10#22583657C2212yes—
11#22583656C2212yescomplemented
12#22583643—22no—
13#22583643C2212yescomplemented
14#22583642—22no—
15#22583640C2212yescomplemented
16#22583638—22no—
17#22583638C2212yes—
18#22583635C2212yes—
19#22583634—22no—
20#22583632—22no—
21#22583632C2211yescharacteristic
22#22583631—22no—
23C2×#17985381—22no—
24C2×#17985381C2212yescomplemented
25C2×#17985381C2212yescomplemented
26SD16×D283—22no—
27#22583616C2212yescomplemented
28#22583610C2211yescharacteristic, complemented
29#22583607C2211yescharacteristic
30#22583546C2211yescharacteristic, complemented
31#22583538C2212yescomplemented
32#22583528C2212yescomplemented
33#22583526C2212yescomplemented
34#135×C283C2211yescharacteristic
35#131×C283C2212yescomplemented
36#108×C283C2211yescharacteristic, complemented
37#104×C283C2212yescomplemented
38C4×C8×C283C2211yescharacteristic, complemented
39#17985393—22no—
40#17985392—22no—
41#17985392—22no—
42#17985392C2312yes—
43#17985391—22no—
44#17985391—42no—
45C2×Dic566—22no—
46C2×Dic566C2312yes—
47Q8×D283—22no—
48C2×D1132—22no—
49C2×D1132—41no—
50C2×D1132C2312yes—
51D4×D283—22no—
52D4×D283—42no—
53Dic1132—22no—
54Dic1132D411yescharacteristic, complemented
55#17985382—22no—
56#17985381—22no—
57#17985381—22no—
58#17985381—22no—
59#17985381—22no—
60#17985381—22no—
61#17985381—22no—
62#17985381D412yescomplemented
63#17985380—22no—
64#17985379—22no—
65D2264—22no—
66D2264D411yescharacteristic, complemented
67#17985377—22no—
68#17985376C2312yes—
69#17985375—22no—
70C8×D283—22no—
71C4⋊Dic283—41no—
72#41×C283C2312yes—
73Q16×C283D411yescharacteristic, complemented
74SD16×C283D412yescomplemented
75D8×C283D411yescharacteristic, complemented
76M16×C283—22no—
77M16×C283C2312yes—
78C2×C8×C283—22no—
79C2×C8×C283C2311yescharacteristic
80C2×C8×C283C2311yescharacteristic
81C42×C283C2311yescharacteristic
82C22×D283—22no—
83C22×D283—42no—
84Dic566—22no—
85Dic566—22no—
86Dic566—42no—
87Dic566C2×D412yes—
88D1132—22no—
89D1132—22no—
90D1132—42no—
91D1132—82no—
92D1132C2×D412yes—
93C22⋊D283—22no—
94C22⋊D283—42no—
95C22⋊D283—42no—
96C2×Dic283—22no—
97C2×Dic283—42no—
98C4×D283—22no—
99C4×D283—42no—
100C4×D283—42no—
101C283⋊C8—22no—
102Q8×C283C2×D412yes—
103D4×C283—22no—
104D4×C283C2×D412yes—
105C2×C4×C283—21no—
106C2×C4×C283—22no—
107C2×C4×C283C2411yescharacteristic
108C8×C283—22no—
109C8×C283C2×D411yescharacteristic
110C8×C283C2×D411yescharacteristic
111C8×C283C2×D411yescharacteristic
112C8×C283C2×D411yescharacteristic
113C22×C283—22no—
114C22×C283H(5,𝔽2)11yescharacteristic
115C2×D283—22no—
116C2×D283—42no—
117C2×D283—82no—
118C2×D283—162no—
119C4×C283—22no—
120C4×C283—22no—
121C4×C283C22×D411yescharacteristic
122C4×C283C22×D411yescharacteristic
123Dic283—22no—
124Dic283—42no—
125C2×C283—21no—
126C2×C283—42no—
127C2×C283D4211yescharacteristic
128D283—42no—
129D283—82no—
130C283#329111yescharacteristic, complemented, Sylow
131#3291—2831nomaximal, Sylow
132#577—2832no—
133#577—2832no—
134#492—2831no—
135#471—2832no—
136#471—2832no—
137#456—2832no—
138#453—2832no—
139#443—2831no—
140#443D28311yescharacteristic, complemented
1412−1+4—2832no—
142H(5,𝔽2)—2832no—
143#137—2832no—
144#137—2832no—
145#137—5662no—
146#137—5662no—
147AGL(1,ℤ/8)—2832no—
148AGL(1,ℤ/8)—2832no—
149AGL(1,ℤ/8)—5662no—
150AGL(1,ℤ/8)—5662no—
151#135—2831no—
152#135—5662no—
153#135—5662no—
154#135C2×D28311yescharacteristic
155C2×SD16—2832no—
156C2×SD16—2832no—
157C2×SD16—5662no—
158C2×SD16—5662no—
159#131—2832no—
160#131C2×D28312yescomplemented
161C4⋊Q8—2831no—
162#127—2831no—
163#108—2831no—
164#108C2×D28311yescharacteristic, complemented
165#104—2832no—
166#104C2×D28312yescomplemented
167#101—2832no—
168#100—2832no—
169C4×C8C2×D28311yescharacteristic, complemented
170#41—2832no—
171#41—5662no—
172#41—5662no—
173#41—5662no—
174#41—5662no—
175#41—11322no—
176#41C22×D28312yes—
177C2×Q8—2832no—
178C2×Q8—5662no—
179C2×Q8—5662no—
180C2×D4—2832no—
181C2×D4—5662no—
182C2×D4—5662no—
183C2×D4—11321no—
184C2×D4—11322no—
185Q16—2831no—
186Q16—5662no—
187Q16—5662no—
188Q16D113211yescharacteristic, complemented
189SD16—2832no—
190SD16—5662no—
191SD16—5662no—
192SD16—5662no—
193SD16—5662no—
194SD16—5662no—
195SD16—5662no—
196SD16—5662no—
197SD16—5662no—
198SD16D113212yescomplemented
199D8—2831no—
200D8—5662no—
201D8—5662no—
202D8D113211yescharacteristic, complemented
203M16—22no—
204M16—2832no—
205M16—5662no—
206M16C22×D28312yes—
207C2×C8—22no—
208C2×C8—5662no—
209C2×C8C22×D28311yescharacteristic
210C2×C8C22×D28311yescharacteristic
211C4⋊C4—11321no—
212C42C22×D28311yescharacteristic
213C23—5662no—
214C23—11322no—
215Q8—2832no—
216Q8—5662no—
217Q8—5662no—
218Q8—11322no—
219Q8C2×D113212yes—
220D4—22no—
221D4—2832no—
222D4—5662no—
223D4—5662no—
224D4—5662no—
225D4—11322no—
226D4—11322no—
227D4—11322no—
228D4—22642no—
229D4C2×D113212yes—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—5662no—
233C2×C4—5662no—
234C2×C4—11322no—
235C2×C4—11322no—
236C2×C4—11322no—
237C2×C4C23×D28311yescharacteristic
238C8—22no—
239C8—5662no—
240C8D4×D28311yescharacteristic
241C8D4×D28311yescharacteristic
242C8C2×D113211yescharacteristic
243C8C2×D113211yescharacteristic
244C22—22no—
245C22—5662no—
246C22—11322no—
247C22—45282no—
248C22—22642no—
249C22#2258365611yescharacteristic
250C4—22no—
251C4—22no—
252C4—5662no—
253C4—11322no—
254C4C2×D4×D28311yescharacteristic
255C4C22×D113211yescharacteristic
256C2—21no—
257C2—42no—
258C2—11322no—
259C2—22642no—
260C2D4×D113211yescharacteristic
subgroupG/H
centerC2D4×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#443×C283C2
socleC2×C283D42
hypercenter#443D283
hypocenterC283#3291
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. #31827277C2semidirect
2. #31827272C2semidirect
3. #31826838C2semidirect
4. #31826729C2semidirect
5. #31826728C2semidirect
6. #31826649C2semidirect
7. #31826634C2semidirect
8. #31826583C2semidirect
9. #443×C283C2semidirect
11. #22583656C22semidirect
13. #22583643C22semidirect
15. #22583640C22semidirect
24. C2×#17985381C22semidirect
25. C2×#17985381C22semidirect
27. #22583616C22semidirect
28. #22583610C22semidirect
30. #22583546C22semidirect
31. #22583538C22semidirect
32. #22583528C22semidirect
33. #22583526C22semidirect
35. #131×C283C22semidirect
36. #108×C283C22semidirect
37. #104×C283C22semidirect
38. C4×C8×C283C22semidirect
54. Dic1132D4semidirect
62. #17985381D4semidirect
66. D2264D4semidirect
73. Q16×C283D4semidirect
74. SD16×C283D4semidirect
75. D8×C283D4semidirect
130. C283#3291semidirect
140. #443D283semidirect
160. #131C2×D283semidirect
164. #108C2×D283semidirect
166. #104C2×D283semidirect
169. C4×C8C2×D283semidirect
188. Q16D1132semidirect
198. SD16D1132semidirect
202. D8D1132semidirect

Maximal subgroups

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

subgroupindex
#318272772
#318272722
#318268382
#318267292
#318267282
#318266492
#318266342
#318265832
#443×C2832
#3291283