Finite Group Databasebeta

← #49130902

Subgroups — #49130902

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
1C22×#17985379C211yesmaximal, characteristic, complemented
2C2×#22583617C211yesmaximal, characteristic, complemented
3#31827029C211yesmaximal, characteristic
4#31826713C214yesmaximal, complemented
5#31826696C214yesmaximal, complemented
6#31826501C211yesmaximal, characteristic, complemented
7#31826474C211yesmaximal, characteristic, complemented
8#31826469C211yesmaximal, characteristic, complemented
9#536×C283C211yesmaximal, characteristic, complemented
10C22×D1132C2211yescharacteristic
11C2×#17985379—24no—
12C2×#17985379C2212yes—
13C2×#17985379C2212yes—
14#22583617—24no—
15C2×#17985376C2211yescharacteristic
16C2×#17985376C2212yescomplemented
17C22×C283⋊C8C2211yescharacteristic
18C22×C283⋊C8C2212yescomplemented
19#22583606—21no—
20#22583599—21no—
21#22583584C2214yes—
22#22583578—22no—
23#22583569C2211yescharacteristic
24#22583543C2212yescomplemented
25#22583541C2212yescomplemented
26#22583534C2214yescomplemented
27#22583530C2214yes—
28C2×#41×C283C2211yescharacteristic
29C22×Q8×C283C2211yescharacteristic
30C4⋊Q8×C283—21no—
31#124×C283—21no—
32#123×C283—22no—
33C22⋊Q8×C283C2214yescomplemented
34#117×C283C2211yescharacteristic
35C23×D283—21no—
36C2×D1132—22no—
37C2×D1132—21no—
38C2×D1132—22no—
39C2×D1132C2312yes—
40C2×C22⋊D283—24no—
41#17985379—24no—
42#17985379—24no—
43#17985376—24no—
44#17985376—22no—
45C2×C283⋊C8—24no—
46C2×C283⋊C8D414yescomplemented
47C2×C283⋊C8C2312yes—
48C2×C283⋊C8C2311yescharacteristic
49C2×C283⋊C8C2311yescharacteristic
50C4⋊Dic283C2312yes—
51C22⋊Dic283—21no—
52(C2×D283)⋊C4—24no—
53C4×Dic283—21no—
54#41×C283—22no—
55#41×C283—22no—
56C2×Q8×C283—21no—
57C2×Q8×C283—22no—
58C2×Q8×C283—22no—
59C2×Q8×C283D411yescharacteristic
60C2×Q8×C283C2312yes—
61C2×D4×C283D412yes—
62C2×D4×C283D411yescharacteristic
63C22×C4×C283—21no—
64C22×C4×C283C2312yes—
65C22×C4×C283C2311yescharacteristic
66C4⋊C4×C283—24no—
67C4⋊C4×C283C2312yes—
68C22⋊C4×C283—21no—
69C22⋊C4×C283—24no—
70C42×C283—21no—
71C22×D283—22no—
72C22×D283—42no—
73C22×D283—82no—
74D1132—22no—
75D1132—22no—
76D1132—42no—
77C22⋊D283—84no—
78C2×Dic283—22no—
79C283⋊C8—22no—
80C283⋊C8C2×D412yes—
81C283⋊C8C2×D412yes—
82C23×C283C2×D412yes—
83C23×C283C2×D411yescharacteristic
84Q8×C283—22no—
85Q8×C283—22no—
86Q8×C283—22no—
87Q8×C283—42no—
88D4×C283—24no—
89D4×C283—22no—
90C2×C4×C283—22no—
91C2×C4×C283—22no—
92C2×C4×C283—22no—
93C2×C4×C283—22no—
94C2×C4×C283—42no—
95C2×C4×C283C2×D412yes—
96C2×C4×C283C2×D412yes—
97C2×C4×C283C2×D411yescharacteristic
98C2×C4×C283#4112yes—
99C2×C4×C283C2411yescharacteristic
100C22×C283—22no—
101C22×C283—22no—
102C22×C283—24no—
103C22×C283#12112yes—
104C22×C283C22×D411yescharacteristic
105C2×D283—42no—
106C2×D283—44no—
107C2×D283—84no—
108C4×C283—22no—
109C4×C283—42no—
110C4×C283—42no—
111C4×C283#12112yes—
112C4×C283C22×D411yescharacteristic
113C4×C283C2×#4111yescharacteristic
114Dic283—42no—
115C2×C283—22no—
116C2×C283—42no—
117C2×C283C2×#12111yescharacteristic
118C2×C283#57712yes—
119D283—82no—
120C283#305711yescharacteristic, complemented, Sylow
121#3057—2831nomaximal, Sylow
122C22×SD16—2831no—
123C2×#131—2831no—
124#536D28311yescharacteristic, complemented
125#535—2831no—
126#468—2834no—
127#465—2834no—
128#427—2831no—
129#419—2831no—
130#418—2831no—
131C2×#41C2×D28311yescharacteristic
132C22×Q8C2×D28311yescharacteristic
133C22×D4—2831no—
134C2×SD16—2832no—
135C2×SD16—2832no—
136C2×SD16—5664no—
137#131—5664no—
138C2×M16—2831no—
139C2×M16—2832no—
140C22×C8—2831no—
141C22×C8—2832no—
142C4⋊Q8—21no—
143#127—5661no—
144#124—21no—
145#124—5661no—
146#123—22no—
147C22⋊Q8C2×D28314yescomplemented
148#121—2834no—
149#120—5662no—
150#117—2831no—
151#117C2×D28311yescharacteristic
152#107—2832no—
153#106—2832no—
154#103—2834no—
155#102—2834no—
156C24—5661no—
157#41—22no—
158#41—22no—
159C2×Q8—21no—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8C22⋊D28311yescharacteristic
163C2×Q8C22×D28312yes—
164C2×D4—2832no—
165C2×D4—5664no—
166C2×D4—5662no—
167C2×D4—5661no—
168C2×D4—5662no—
169C2×D4C22⋊D28312yes—
170C2×D4C22⋊D28311yescharacteristic
171C22×C4—21no—
172C22×C4C22×D28312yes—
173C22×C4C22×D28311yescharacteristic
174SD16—5664no—
175SD16—5664no—
176M16—5664no—
177M16—5662no—
178C2×C8—2834no—
179C2×C8—2831no—
180C2×C8—2831no—
181C2×C8—2832no—
182C2×C8—5664no—
183C4⋊C4—24no—
184C4⋊C4—2832no—
185C4⋊C4C22×D28312yes—
186C22⋊C4—21no—
187C22⋊C4—24no—
188C22⋊C4—5661no—
189C22⋊C4—5664no—
190C42—21no—
191C42—5661no—
192C23—5662no—
193C23—11322no—
194C23—22642no—
195C23C2×C22⋊D28312yes—
196C23C2×C22⋊D28311yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—24no—
202D4—22no—
203D4—5662no—
204D4—5662no—
205D4—11322no—
206D4—22644no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—5662no—
213C2×C4D4×D28312yes—
214C2×C4C2×C22⋊D28312yes—
215C2×C4C2×C22⋊D28311yescharacteristic
216C2×C4#1798539112yes—
217C2×C4C23×D28311yescharacteristic
218C8—2832no—
219C8—2832no—
220C8—5662no—
221C22—22no—
222C22—22no—
223C22—24no—
224C22—11322no—
225C22—11324no—
226C22—22644no—
227C22#2258358212yes—
228C22C22×C22⋊D28311yescharacteristic
229C4—22no—
230C4—42no—
231C4—42no—
232C4—11322no—
233C4#2258358212yes—
234C4C2×D4×D28311yescharacteristic
235C4C2×#1798539111yescharacteristic
236C2—22no—
237C2—42no—
238C2—22642no—
239C2C2×#2258358211yescharacteristic
240C2#3182727312yes—
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#536×C283C2
socleC22×C283C22×D4
prime radical#31827029C2
hypercenter#536D283
hypocenterC283#3057
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C22×#17985379C2semidirect
2. C2×#22583617C2semidirect
4. #31826713C2semidirect
5. #31826696C2semidirect
6. #31826501C2semidirect
7. #31826474C2semidirect
8. #31826469C2semidirect
9. #536×C283C2semidirect
16. C2×#17985376C22semidirect
18. C22×C283⋊C8C22semidirect
24. #22583543C22semidirect
25. #22583541C22semidirect
26. #22583534C22semidirect
33. C22⋊Q8×C283C22semidirect
46. C2×C283⋊C8D4semidirect
120. C283#3057semidirect
124. #536D283semidirect
147. C22⋊Q8C2×D283semidirect

Maximal subgroups

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

subgroupindex
C22×#179853792
C2×#225836172
#318270292
#318267132
#318266962
#318265012
#318264742
#318264692
#536×C2832
#3057283