Finite Group Databasebeta

← #16844216

Subgroups — #16844216

Order 3968.

334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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#14521560C211yesmaximal, characteristic
2C2×C31⋊#95C211yesmaximal, characteristic, complemented
3#14520787C212yesmaximal, complemented
4#14520784C212yesmaximal, complemented
5C31×#407C211yesmaximal, characteristic, complemented
6C23×C4×C31C2211yescharacteristic
7C23×Dic31—21no—
8C2×#92495C411yescharacteristic, complemented
9C2×M16×C31—21no—
10#11758530—21no—
11#11758507C411yescharacteristic, complemented
12#11758507C2211yescharacteristic
13#11758506—21no—
14C4×C22⋊D31—21no—
15C4×C22⋊D31—21no—
16#11758503C411yescharacteristic, complemented
17#11758501C411yescharacteristic, complemented
18#11758501C2211yescharacteristic
19C31×C22⋊C8—21no—
20C31×C22⋊C8C2212yes—
21C31⋊#95—21no—
22C31⋊#95C2212yes—
23C24×C31D411yescharacteristic
24C22×C4×C31—42no—
25C22×C4×C31C2×C411yescharacteristic
26C22×C4×C31C2×C411yescharacteristic
27C22×C4×C31D411yescharacteristic
28C22×C4×C31D411yescharacteristic
29C22×C4×C31D411yescharacteristic
30C22×C4×C31C2311yescharacteristic
31C2×C22⋊D31—21no—
32C2×C22⋊D31—21no—
33C2×C22⋊D31—21no—
34C22×Dic31—24no—
35C22×Dic31—22no—
36C22×Dic31—42no—
37C22×Dic31—42no—
38#92495—42no—
39C2×D124C2×C411yescharacteristic, complemented
40C2×C4×D31—21no—
41C2×Dic62C2×C411yescharacteristic, complemented
42M16×C31—42no—
43C2×C8×C31—22no—
44C22⋊Dic31—21no—
45C22⋊Dic31—21no—
46C22⋊Dic31—21no—
47(C2×D31)⋊C4—21no—
48(C2×D31)⋊C4—21no—
49C4⋊Dic31C2×C411yescharacteristic, complemented
50C4⋊Dic31C2×C411yescharacteristic, complemented
51Dic31⋊C4—21no—
52Dic31⋊C4—21no—
53C4×Dic31—21no—
54C23×C31—22no—
55C23×C31—22no—
56C23×C31—21no—
57C23×C31—21no—
58C23×C31C22⋊C411yescharacteristic
59C23×C31C22⋊C411yescharacteristic
60C23×C31C2×D411yescharacteristic
61C22×D31—21no—
62C2×C4×C31—22no—
63C2×C4×C31—22no—
64C2×C4×C31—41no—
65C2×C4×C31—41no—
66C2×C4×C31—41no—
67C2×C4×C31—41no—
68C2×C4×C31C22⋊C411yescharacteristic
69C2×C4×C31C22⋊C411yescharacteristic
70C2×C4×C31C22×C411yescharacteristic
71C2×C4×C31C2×D411yescharacteristic
72C22⋊D31—42no—
73C22⋊D31—42no—
74C22⋊D31—41no—
75C22⋊D31—41no—
76C2×Dic31—24no—
77C2×Dic31—21no—
78C2×Dic31—21no—
79C2×Dic31—21no—
80C2×Dic31—48no—
81C2×Dic31—42no—
82C2×Dic31—42no—
83D124—41no—
84C4×D31—42no—
85Dic62—41no—
86C8×C31—42no—
87#1504—311nomaximal, Sylow
88C22×C31—24no—
89C22×C31—24no—
90C22×C31—21no—
91C22×C31—21no—
92C22×C31—21no—
93C22×C31—21no—
94C22×C31—21no—
95C22×C31—21no—
96C22×C31#9912yes—
97C22×C31#10412yes—
98C22×C31C2×C22⋊C411yescharacteristic
99C22×C31AGL(1,ℤ/8)11yescharacteristic
100C22×C31#13711yescharacteristic
101C2×D31—41no—
102C2×D31—41no—
103C2×D31—41no—
104C4×C31—21no—
105C4×C31—21no—
106C4×C31—21no—
107C4×C31—21no—
108Dic31—44no—
109Dic31—41no—
110Dic31—41no—
111Dic31—41no—
112#525—311no—
113#407D3111yescharacteristic, complemented
114C2×#95—311no—
115#328—312no—
116#327—312no—
117C2×C31—21no—
118C2×C31—22no—
119C2×C31—22no—
120C2×C31—21no—
121C2×C31C2×#9911yescharacteristic
122C2×C31#41711yescharacteristic
123C2×C31C2×#10411yescharacteristic
124D31—81no—
125C2×#41—311no—
126C23×C4—621no—
127C23×C4C2×D3111yescharacteristic
128C2×M16—21no—
129#123—621no—
130C22⋊Q8—311no—
131C22⋊Q8—311no—
132#121—311no—
133#121—311no—
134#120—621no—
135C4×D4—621no—
136C4×D4—621no—
137#117—311no—
138C22⋊C8—21no—
139C22⋊C8C2×D3112yes—
140#95—312no—
141#95—621no—
142C31#150411yescharacteristic, complemented, Sylow
143C24D12411yescharacteristic
144#41—1242no—
145C2×Q8—311no—
146C2×D4—311no—
147C2×D4—621no—
148C2×D4—621no—
149C2×D4—621no—
150C22×C4—42no—
151C22×C4—624no—
152C22×C4—622no—
153C22×C4—621no—
154C22×C4—1242no—
155C22×C4—1242no—
156C22×C4C4×D3111yescharacteristic
157C22×C4C4×D3111yescharacteristic
158C22×C4D12411yescharacteristic
159C22×C4C22⋊D3111yescharacteristic
160C22×C4C22⋊D3111yescharacteristic
161C22×C4C22×D3111yescharacteristic
162M16—42no—
163C2×C8—22no—
164C4⋊C4—311no—
165C4⋊C4—311no—
166C4⋊C4—621no—
167C4⋊C4—621no—
168C22⋊C4—621no—
169C22⋊C4—621no—
170C22⋊C4—621no—
171C22⋊C4—621no—
172C22⋊C4—621no—
173C42—621no—
174C23—22no—
175C23—22no—
176C23—21no—
177C23—21no—
178C23—621no—
179C23(C2×D31)⋊C411yescharacteristic
180C23(C2×D31)⋊C411yescharacteristic
181C23C2×D12411yescharacteristic
182Q8—1241no—
183D4—1241no—
184D4—1242no—
185D4—1242no—
186D4—1241no—
187D4—1241no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—624no—
195C2×C4—621no—
196C2×C4—621no—
197C2×C4—621no—
198C2×C4—1242no—
199C2×C4—1248no—
200C2×C4—1242no—
201C2×C4—1242no—
202C2×C4(C2×D31)⋊C411yescharacteristic
203C2×C4(C2×D31)⋊C411yescharacteristic
204C2×C4C2×C4×D3111yescharacteristic
205C2×C4C2×C22⋊D3111yescharacteristic
206C8—42no—
207C22—24no—
208C22—24no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—1241no—
216C22—1241no—
217C22—1241no—
218C22#1175839412yes—
219C22#1175841312yes—
220C22#1175848511yescharacteristic
221C22#1175848611yescharacteristic
222C22C2×(C2×D31)⋊C411yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—21no—
227C4—1244no—
228C4—1241no—
229C4—1241no—
230C4—1241no—
231C2—21no—
232C2—22no—
233C2—22no—
234C2—21no—
235C2—2481no—
236C2C2×#1175839411yescharacteristic
237C2#1452105111yescharacteristic
238C2C2×#1175841311yescharacteristic
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#407C2
socleC22×C31C2×C22⋊C4
prime radical#14521560C2
cosocleC22×C4×C31C23
hypercenter#407D31
hypocenterC31#1504
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×C31⋊#95C2semidirect
3. #14520787C2semidirect
4. #14520784C2semidirect
5. C31×#407C2semidirect
8. C2×#92495C4semidirect
11. #11758507C4semidirect
16. #11758503C4semidirect
17. #11758501C4semidirect
39. C2×D124C2×C4semidirect
41. C2×Dic62C2×C4semidirect
49. C4⋊Dic31C2×C4semidirect
50. C4⋊Dic31C2×C4semidirect
113. #407D31semidirect
142. C31#1504semidirect

Maximal subgroups

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

subgroupindex
#145215602
C2×C31⋊#952
#145207872
#145207842
C31×#4072
#150431