Finite Group Databasebeta

← #16848975

Subgroups — #16848975

Order 3968.

560 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 147 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×#11758470C211yesmaximal, characteristic
2C2×#11758469C211yesmaximal, characteristic, complemented
3#14520988C211yesmaximal, characteristic, complemented
4#14520986C211yesmaximal, characteristic, complemented
5#14520976C212yesmaximal, complemented
6#14520975C211yesmaximal, characteristic, complemented
7#14520966C212yesmaximal
8C4⋊C4×Dic31C212yesmaximal, complemented
9#14520896C211yesmaximal, characteristic, complemented
10#14520896C212yesmaximal, complemented
11C31×#398C211yesmaximal, characteristic, complemented
12C22×D124C2211yescharacteristic
13C22×C4×D31C2211yescharacteristic
14C22×C4×D31C2211yescharacteristic
15C2×C4⋊C4×C31C2212yes—
16C2×C4⋊C4×C31C2211yescharacteristic
17C2×C4⋊C4×C31C2211yescharacteristic
18C2×(C2×D31)⋊C4C2212yes—
19C2×(C2×D31)⋊C4C2212yes—
20C2×(C2×D31)⋊C4C2212yes—
21C2×(C2×D31)⋊C4C2212yes—
22C2×(C2×D31)⋊C4C2211yescharacteristic
23C2×(C2×D31)⋊C4C2211yescharacteristic
24C2×C4⋊Dic31C2212yes—
25C2×C4⋊Dic31C2211yescharacteristic
26C2×C4×Dic31C2212yes—
27C2×C4×Dic31C2212yes—
28C2×C4×Dic31C2211yescharacteristic
29#11758470—24no—
30#11758469—24no—
31C31×#95C2212yes—
32C31×#95C2211yescharacteristic
33C31⋊#95C2211yescharacteristic
34C31⋊#95C2212yes—
35C31⋊#95C2212yes—
36C31⋊#95C2212yes—
37C23×D31C2311yescharacteristic
38C23×D31C2311yescharacteristic
39C22×C4×C31C2311yescharacteristic
40C22×C4×C31C2312yes—
41C22×C4×C31C2311yescharacteristic
42C22×C4×C31C2311yescharacteristic
43C22×C4×C31C2312yes—
44C22×Dic31C2312yes—
45C22×Dic31C2312yes—
46C22×Dic31C2311yescharacteristic
47C22×Dic31C2311yescharacteristic
48C2×D124—22no—
49C2×D124—22no—
50C2×D124—22no—
51C2×C4×D31—24no—
52C2×C4×D31—22no—
53C2×C4×D31—24no—
54C2×C4×D31D414yes—
55C4⋊C4×C31—22no—
56C4⋊C4×C31—22no—
57C4⋊C4×C31—24no—
58(C2×D31)⋊C4—24no—
59(C2×D31)⋊C4—22no—
60(C2×D31)⋊C4—24no—
61(C2×D31)⋊C4—22no—
62(C2×D31)⋊C4—24no—
63(C2×D31)⋊C4—24no—
64C4⋊Dic31—22no—
65C4⋊Dic31—24no—
66C4×Dic31—24no—
67C4×Dic31—22no—
68C4×Dic31—24no—
69C23×C31C2411yescharacteristic
70C22×D31—21no—
71C22×D31—22no—
72C22×D31—22no—
73C22×D31—22no—
74C22×D31—22no—
75C22×D31—21no—
76C22×D31—21no—
77C22×D31—21no—
78C22×D31C2×D412yes—
79C22×D31#4112yes—
80C2×C4×C31—21no—
81C2×C4×C31—22no—
82C2×C4×C31—22no—
83C2×C4×C31—22no—
84C2×C4×C31—21no—
85C2×C4×C31—22no—
86C2×C4×C31—21no—
87C2×C4×C31—22no—
88C2×C4×C31—22no—
89C2×C4×C31—22no—
90C2×C4×C31C2×D412yes—
91C2×C4×C31#4112yes—
92C2×C4×C31#4114yes—
93C2×Dic31—22no—
94C2×Dic31—21no—
95C2×Dic31—22no—
96C2×Dic31—22no—
97C2×Dic31—22no—
98C2×Dic31—22no—
99C2×Dic31—22no—
100C2×Dic31—22no—
101C2×Dic31C2×D412yes—
102C2×Dic31#4114yes—
103D124—28no—
104C4×D31—28no—
105C4×D31—44no—
106#2395—311nomaximal, Sylow
107C22×C31C22×D411yescharacteristic
108C22×C31C2×#4111yescharacteristic
109C22×C31C2×#4112yes—
110C22×C31C2×#4112yes—
111C22×C31C2×#4111yescharacteristic
112C2×D31—22no—
113C2×D31—22no—
114C2×D31—22no—
115C2×D31—24no—
116C2×D31—22no—
117C2×D31—41no—
118C2×D31—42no—
119C2×D31—42no—
120C2×D31—42no—
121C2×D31—41no—
122C4×C31—22no—
123C4×C31—22no—
124C4×C31—24no—
125C4×C31—41no—
126C4×C31—42no—
127Dic31—42no—
128Dic31—42no—
129Dic31—41no—
130Dic31#12314yes—
131C2×C4×D4—311no—
132C2×#117—311no—
133#400—311no—
134#399—311no—
135#398D3111yescharacteristic, complemented
136#397—311no—
137#397—312no—
138#394—312no—
139C4×C4⋊C4—312no—
140C4×C22⋊C4—312no—
141C4×C22⋊C4—311no—
142C2×C31C2×#12311yescharacteristic
143C2×C31#52511yescharacteristic
144C2×C31#52912yes—
145C2×C31#52912yes—
146C2×C31#53211yescharacteristic
147D31—42no—
148D31—42no—
149C22×D4—311no—
150C23×C4—311no—
151C23×C4—311no—
152C4×D4—624no—
153#117—624no—
154C2×C4⋊C4—311no—
155C2×C4⋊C4—312no—
156C2×C4⋊C4C2×D3111yescharacteristic
157C2×C4⋊C4C2×D3111yescharacteristic
158C2×C4⋊C4C2×D3112yes—
159C2×C22⋊C4—312no—
160C2×C22⋊C4—311no—
161C2×C22⋊C4—311no—
162C2×C22⋊C4—312no—
163C2×C22⋊C4—312no—
164C2×C22⋊C4—312no—
165C2×C42—312no—
166C2×C42—311no—
167C2×C42—312no—
168#95—311no—
169#95—312no—
170#95—312no—
171#95—312no—
172#95C2×D3112yes—
173#95C2×D3111yescharacteristic
174C31#239511yescharacteristic, complemented, Sylow
175C24—311no—
176C24—311no—
177C2×D4—622no—
178C2×D4—622no—
179C2×D4—622no—
180C22×C4—311no—
181C22×C4—314no—
182C22×C4—312no—
183C22×C4—311no—
184C22×C4—312no—
185C22×C4—624no—
186C22×C4—622no—
187C22×C4—624no—
188C22×C4C22×D3111yescharacteristic
189C22×C4C22×D3112yes—
190C22×C4C22×D3111yescharacteristic
191C22×C4C22×D3111yescharacteristic
192C22×C4C22×D3112yes—
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—24no—
196C4⋊C4—622no—
197C4⋊C4—624no—
198C22⋊C4—624no—
199C22⋊C4—624no—
200C22⋊C4—622no—
201C22⋊C4—622no—
202C22⋊C4—624no—
203C22⋊C4—624no—
204C42—624no—
205C42—624no—
206C42—622no—
207C23—312no—
208C23—312no—
209C23—621no—
210C23—621no—
211C23—621no—
212C23—622no—
213C23—622no—
214C23—622no—
215C23—622no—
216C23—621no—
217C23C23×D3111yescharacteristic
218D4—628no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—312no—
230C2×C4—314no—
231C2×C4—628no—
232C2×C4—621no—
233C2×C4—622no—
234C2×C4—622no—
235C2×C4—622no—
236C2×C4—622no—
237C2×C4—622no—
238C2×C4—622no—
239C2×C4—622no—
240C2×C4—1244no—
241C2×C4D4×D3112yes—
242C2×C4#9249712yes—
243C2×C4#9249914yes—
244C22—622no—
245C22—622no—
246C22—622no—
247C22—622no—
248C22—624no—
249C22—1241no—
250C22—1241no—
251C22—1242no—
252C22—1242no—
253C22—1242no—
254C22C2×D4×D3111yescharacteristic
255C22C2×#9249711yescharacteristic
256C22C2×#9249912yes—
257C22#41×D3112yes—
258C22#41×D3111yescharacteristic
259C4—22no—
260C4—22no—
261C4—24no—
262C4—41no—
263C4—42no—
264C4—314no—
265C4—1241no—
266C4—1242no—
267C4—1242no—
268C2—1242no—
269C2—1242no—
270C2#123×D3111yescharacteristic
271C2#1452155911yescharacteristic
272C2#1452158412yes—
273C2#1452158512yes—
274C2#1452160011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutator, socle, cosocleC23×C31C24
FittingC31×#398C2
prime radicalC22×D124C22
hypercenter#398D31
hypocenterC31#2395
LCSG ▷ C23×C31 ▷ C31
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×#11758469C2semidirect
3. #14520988C2semidirect
4. #14520986C2semidirect
5. #14520976C2semidirect
6. #14520975C2semidirect
8. C4⋊C4×Dic31C2semidirect
9. #14520896C2semidirect
10. #14520896C2semidirect
11. C31×#398C2semidirect
135. #398D31semidirect
174. C31#2395semidirect

Maximal subgroups

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

subgroupindex
C2×#117584702
C2×#117584692
#145209882
#145209862
#145209762
#145209752
#145209662
C4⋊C4×Dic312
#145208962
C31×#3982
#239531