Finite Group Databasebeta

← #49130896

Subgroups — #49130896

Order 36224.

492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22583616C211yesmaximal, characteristic, complemented
2#31827039C211yesmaximal, characteristic, complemented
3#31827032C211yesmaximal, characteristic
4#31826708C214yesmaximal, complemented
5#31826691C214yesmaximal, complemented
6#31826503C211yesmaximal, characteristic, complemented
7#31826474C211yesmaximal, characteristic, complemented
8#31826470C211yesmaximal, characteristic, complemented
9C22×SD16×C283C211yesmaximal, characteristic, complemented
10C2×#17985392C2211yescharacteristic
11#22583616—24no—
12C2×#17985376C2211yescharacteristic
13C2×#17985375C2212yescomplemented
14C2×C8×D283C2212yescomplemented
15#22583608—21no—
16#22583606—21no—
17#22583599—21no—
18#22583597—21no—
19#22583593—22no—
20#22583586C2214yescomplemented
21#22583581C2214yes—
22#22583579—22no—
23#22583569C2211yescharacteristic
24#22583569C2211yescharacteristic
25#22583544C2212yescomplemented
26#22583542C2212yescomplemented
27#22583534C2214yescomplemented
28#22583531C2214yes—
29C22×Q8×C283C2211yescharacteristic
30C22×D4×C283C2211yescharacteristic
31C2×SD16×C283—24no—
32C2×SD16×C283C2212yes—
33C2×SD16×C283C2212yes—
34C22×C8×C283C2211yescharacteristic
35#17985392—22no—
36#17985392—22no—
37C2×Dic566D411yescharacteristic
38C2×D1132D411yescharacteristic
39C2×C22⋊D283—24no—
40C2×C22⋊D283D412yes—
41C2×C4×D283C2312yes—
42#17985376—22no—
43#17985375—24no—
44C2×C283⋊C8C2312yes—
45C8×D283—24no—
46C4⋊Dic283C2312yes—
47C4⋊Dic283C2312yes—
48Dic283⋊C4—24no—
49C22⋊Dic283—24no—
50C22⋊Dic283—21no—
51C22⋊Dic283—21no—
52(C2×D283)⋊C4—24no—
53C4×Dic283—21no—
54C4×Dic283—21no—
55C24×C283—21no—
56C2×Q8×C283—21no—
57C2×Q8×C283—22no—
58C2×Q8×C283—22no—
59C2×Q8×C283C2312yes—
60C2×D4×C283—22no—
61C2×D4×C283—21no—
62C2×D4×C283—22no—
63C2×D4×C283C2312yes—
64C22×C4×C283—21no—
65C22×C4×C283C2311yescharacteristic
66SD16×C283—24no—
67SD16×C283—24no—
68C2×C8×C283D414yescomplemented
69C2×C8×C283C2311yescharacteristic
70C2×C8×C283C2311yescharacteristic
71C22×D283C2×D412yes—
72Dic566—22no—
73D1132—22no—
74C22⋊D283—24no—
75C22⋊D283—84no—
76C2×Dic283—22no—
77C2×Dic283—22no—
78C2×Dic283C2×D412yes—
79C4×D283—22no—
80C4×D283—22no—
81C283⋊C8—22no—
82C23×C283—22no—
83C23×C283—42no—
84C23×C283—82no—
85C23×C283C2×D411yescharacteristic
86Q8×C283—22no—
87Q8×C283—22no—
88Q8×C283—42no—
89D4×C283—22no—
90D4×C283—22no—
91D4×C283—42no—
92C2×C4×C283—22no—
93C2×C4×C283—42no—
94C2×C4×C283C2×D411yescharacteristic
95C2×C4×C283C2×D412yes—
96C2×C4×C283#4112yes—
97C2×C4×C283C2411yescharacteristic
98C8×C283C2×D412yes—
99C8×C283C2×D412yes—
100C22×C283—22no—
101C22×C283—42no—
102C22×C283—44no—
103C22×C283—84no—
104C22×C283#12112yes—
105C22×C283C22×D411yescharacteristic
106C2×D283—22no—
107C2×D283—24no—
108C4×C283—42no—
109C4×C283#12112yes—
110C4×C283C22×D411yescharacteristic
111C4×C283C2×#4111yescharacteristic
112Dic283—22no—
113Dic283—42no—
114Dic283—42no—
115C2×C283—22no—
116C2×C283—82no—
117C2×C283C2×#12111yescharacteristic
118C2×C283#57712yes—
119D283—42no—
120C283#305711yescharacteristic, complemented, Sylow
121#3057—2831nomaximal, Sylow
122C22×SD16D28311yescharacteristic, complemented
123C2×#131—2831no—
124#536—2831no—
125#535—2831no—
126#468—2834no—
127#465—2834no—
128#427—2831no—
129#419—2831no—
130#418—2831no—
131C2×#41—2831no—
132C22×Q8C2×D28311yescharacteristic
133C22×D4C2×D28311yescharacteristic
134C2×SD16—24no—
135C2×SD16C2×D28312yes—
136C2×SD16C2×D28312yes—
137#131—5664no—
138C2×M16—2831no—
139C2×M16—2832no—
140C22×C8—2832no—
141C22×C8C2×D28311yescharacteristic
142C4⋊Q8—5661no—
143#127—5661no—
144#124—5661no—
145#124—5661no—
146#123—5662no—
147C22⋊Q8—2834no—
148#121—2834no—
149#120—5662no—
150#117—2831no—
151#117—2831no—
152#107—2832no—
153#106—2832no—
154#103—2834no—
155#102—2834no—
156C24—21no—
157#41—5662no—
158#41—5662no—
159C2×Q8—21no—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—2831no—
163C2×Q8C22×D28312yes—
164C2×D4—21no—
165C2×D4—22no—
166C2×D4—22no—
167C2×D4—2832no—
168C2×D4—2831no—
169C2×D4—5664no—
170C2×D4C22×D28312yes—
171C22×C4—21no—
172C22×C4—2832no—
173C22×C4C22×D28311yescharacteristic
174SD16—24no—
175SD16—24no—
176M16—5662no—
177M16—5664no—
178C2×C8—2832no—
179C2×C8—5664no—
180C2×C8C22⋊D28314yescomplemented
181C2×C8C22×D28311yescharacteristic
182C2×C8C22×D28311yescharacteristic
183C4⋊C4—2832no—
184C4⋊C4—2832no—
185C4⋊C4—5664no—
186C22⋊C4—5664no—
187C22⋊C4—5664no—
188C22⋊C4—5661no—
189C22⋊C4—5661no—
190C42—5661no—
191C42—5661no—
192C23—22no—
193C23—42no—
194C23—82no—
195C23—2832no—
196C23D4×D28311yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—42no—
200Q8—5662no—
201D4—22no—
202D4—22no—
203D4—42no—
204D4—5664no—
205D4—5662no—
206D4—22644no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—2832no—
210C2×C4—5662no—
211C2×C4—5662no—
212C2×C4—5662no—
213C2×C4—5662no—
214C2×C4D4×D28311yescharacteristic
215C2×C4C2×C22⋊D28312yes—
216C2×C4#1798539112yes—
217C2×C4C23×D28311yescharacteristic
218C8—5662no—
219C8C2×C22⋊D28312yes—
220C8C2×C22⋊D28312yes—
221C22—22no—
222C22—42no—
223C22—44no—
224C22—84no—
225C22—5662no—
226C22—5664no—
227C22#2258358112yes—
228C22C2×D4×D28311yescharacteristic
229C4—42no—
230C4—5662no—
231C4—11322no—
232C4—11322no—
233C4#2258358112yes—
234C4C22×C22⋊D28311yescharacteristic
235C4C2×#1798539111yescharacteristic
236C2—22no—
237C2—82no—
238C2—11322no—
239C2C2×#2258358111yescharacteristic
240C2#3182727112yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC22×SD16×C283C2
socleC22×C283C22×D4
prime radical#31827032C2
hypercenterC22×SD16D283
hypocenterC283#3057
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#22583616C2semidirect
2. #31827039C2semidirect
4. #31826708C2semidirect
5. #31826691C2semidirect
6. #31826503C2semidirect
7. #31826474C2semidirect
8. #31826470C2semidirect
9. C22×SD16×C283C2semidirect
13. C2×#17985375C22semidirect
14. C2×C8×D283C22semidirect
20. #22583586C22semidirect
25. #22583544C22semidirect
26. #22583542C22semidirect
27. #22583534C22semidirect
68. C2×C8×C283D4semidirect
120. C283#3057semidirect
122. C22×SD16D283semidirect
180. C2×C8C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836162
#318270392
#318270322
#318267082
#318266912
#318265032
#318264742
#318264702
C22×SD16×C2832
#3057283