Finite Group Databasebeta

← #16844217

Subgroups — #16844217

Order 3968.

272 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 63 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#14521594C211yesmaximal, characteristic
2#14521103C211yesmaximal, characteristic, complemented
3#14520894C211yesmaximal, characteristic, complemented
4#14520784C211yesmaximal, characteristic, complemented
5#14520783C211yesmaximal, characteristic, complemented
6#14520782C211yesmaximal, characteristic, complemented
7C31×#327C211yesmaximal, characteristic, complemented
8C2×#92497—21no—
9C31×#121C2211yescharacteristic
10#11758517C411yescharacteristic, complemented
11#11758516—21no—
12D4×Dic31C411yescharacteristic, complemented
13#11758507C2211yescharacteristic
14C2×C4×Dic31—21no—
15C2×C4×Dic31C2211yescharacteristic
16#11758470C411yescharacteristic, complemented
17#11758465C411yescharacteristic, complemented
18#11758462—21no—
19(C22⋊D31)⋊C4—21no—
20C31×C22⋊C8C2211yescharacteristic
21C31×#95C2211yescharacteristic
22C31⋊#95—21no—
23C31⋊#95C2211yescharacteristic
24C22⋊(C31⋊C8)C2211yescharacteristic
25#11758403—21no—
26Dic31⋊C8—21no—
27C2×D4×C31—21no—
28C2×D4×C31C2×C411yescharacteristic
29C22×C4×C31—21no—
30C22×C4×C31C2311yescharacteristic
31C2×C22⋊D31—21no—
32C2×C22⋊D31—21no—
33C2×C22⋊D31—21no—
34C22×Dic31—21no—
35C22×Dic31—21no—
36C22×Dic31D411yescharacteristic
37C22×Dic31D411yescharacteristic
38#92497—42no—
39#92497—42no—
40C2×D124C2×C411yescharacteristic
41C2×C4×D31—21no—
42C2×Dic62—21no—
43C2×C8×C31—21no—
44C4⋊C4×C31C2×C411yescharacteristic
45C22⋊C4×C31—21no—
46C22⋊Dic31—21no—
47(C2×D31)⋊C4—21no—
48(C2×D31)⋊C4—21no—
49C4⋊Dic31C2×C411yescharacteristic
50Dic31⋊C4—21no—
51C4×Dic31—24no—
52C4×Dic31C2×C411yescharacteristic
53C4×Dic31C2×C411yescharacteristic
54C4×Dic31D411yescharacteristic
55C4×Dic31D411yescharacteristic
56C2×C31⋊C8—21no—
57C23×C31—21no—
58C23×C31C2×D411yescharacteristic
59C22×D31—21no—
60D4×C31—41no—
61D4×C31—41no—
62D4×C31—41no—
63C2×C4×C31—22no—
64C2×C4×C31—21no—
65C2×C4×C31—41no—
66C2×C4×C31—41no—
67C2×C4×C31—41no—
68C2×C4×C31C22×C411yescharacteristic
69C2×C4×C31C2×D411yescharacteristic
70C22⋊D31—42no—
71C22⋊D31—41no—
72C22⋊D31—41no—
73C22⋊D31—42no—
74C2×Dic31—21no—
75C2×Dic31—21no—
76C2×Dic31—22no—
77C2×Dic31—22no—
78C2×Dic31—21no—
79C2×Dic31—42no—
80C2×Dic31—41no—
81C2×Dic31—41no—
82C2×Dic31C22⋊C411yescharacteristic
83C2×Dic31C22⋊C411yescharacteristic
84C2×Dic31C22⋊C411yescharacteristic
85C2×Dic31C22⋊C411yescharacteristic
86D124—41no—
87C4×D31—42no—
88Dic62—42no—
89C8×C31—41no—
90C31⋊C8—41no—
91#1505—311nomaximal, Sylow
92C22×C31—21no—
93C22×C31—21no—
94C22×C31—41no—
95C22×C31—41no—
96C22×C31—41no—
97C22×C31C2×C22⋊C411yescharacteristic
98C22×C31AGL(1,ℤ/8)11yescharacteristic
99C22×C31AGL(1,ℤ/8)11yescharacteristic
100C2×D31—41no—
101C2×D31—41no—
102C2×D31—41no—
103C4×C31—21no—
104C4×C31—21no—
105C4×C31—42no—
106C4×C31—41no—
107Dic31—21no—
108Dic31—21no—
109Dic31—21no—
110Dic31—42no—
111Dic31—41no—
112Dic31#10412yes—
113#532—311no—
114#432—311no—
115#376—311no—
116#327—311no—
117#327—311no—
118#327—311no—
119#327D3111yescharacteristic, complemented
120C2×C31—21no—
121C2×C31—21no—
122C2×C31—81no—
123C2×C31#41011yescharacteristic
124C2×C31#41811yescharacteristic
125C2×C31C2×#10411yescharacteristic
126D31—81no—
127C2×#41—621no—
128C4⋊Q8—311no—
129#127—311no—
130#124—621no—
131#121—311no—
132#121—621no—
133#121C2×D3111yescharacteristic
134C4×D4—311no—
135C4×D4—311no—
136C4×D4—621no—
137C2×C42—311no—
138C2×C42—621no—
139C4⋊C8—621no—
140C22⋊C8—311no—
141C22⋊C8C2×D3111yescharacteristic
142#97—621no—
143#95—311no—
144#95—621no—
145#95C2×D3111yescharacteristic
146C31#150511yescharacteristic, complemented, Sylow
147#41—1242no—
148#41—1242no—
149C2×Q8—621no—
150C2×D4—21no—
151C2×D4—311no—
152C2×D4—621no—
153C2×D4—621no—
154C2×D4—621no—
155C2×D4C4×D3111yescharacteristic
156C22×C4—21no—
157C22×C4—311no—
158C22×C4—311no—
159C22×C4—621no—
160C22×C4—621no—
161C22×C4—621no—
162C22×C4C22×D3111yescharacteristic
163C2×C8—21no—
164C2×C8—621no—
165C4⋊C4—311no—
166C4⋊C4—621no—
167C4⋊C4C4×D3111yescharacteristic
168C22⋊C4—21no—
169C22⋊C4—621no—
170C22⋊C4—621no—
171C22⋊C4—621no—
172C42—311no—
173C42—311no—
174C42—311no—
175C42—311no—
176C42—624no—
177C23—21no—
178C23—621no—
179C23D4×D3111yescharacteristic
180Q8—1242no—
181D4—41no—
182D4—41no—
183D4—41no—
184D4—1241no—
185D4—1242no—
186D4—1242no—
187D4—1241no—
188D4—1241no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—311no—
195C2×C4—311no—
196C2×C4—311no—
197C2×C4—311no—
198C2×C4—622no—
199C2×C4—621no—
200C2×C4—621no—
201C2×C4—622no—
202C2×C4—621no—
203C2×C4—1242no—
204C2×C4—1242no—
205C2×C4—1241no—
206C2×C4—1241no—
207C2×C4C2×C4×D3111yescharacteristic
208C2×C4D4×D3111yescharacteristic
209C8—41no—
210C8—1241no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—1241no—
217C22—1241no—
218C22—1241no—
219C22C22⋊C4×D3111yescharacteristic
220C22#1175848811yescharacteristic
221C22#1175849111yescharacteristic
222C4—21no—
223C4—21no—
224C4—42no—
225C4—41no—
226C4—312no—
227C4—621no—
228C4—621no—
229C4—621no—
230C4—1242no—
231C4—1241no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—2481no—
236C2#1452102111yescharacteristic
237C2#1452105211yescharacteristic
238C2#104×D3111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#327C2
socleC22×C31C2×C22⋊C4
prime radical#14521594C2
cosocleC22×C4×C31C23
hypercenter#327D31
hypocenterC31#1505
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14521103C2semidirect
3. #14520894C2semidirect
4. #14520784C2semidirect
5. #14520783C2semidirect
6. #14520782C2semidirect
7. C31×#327C2semidirect
10. #11758517C4semidirect
12. D4×Dic31C4semidirect
16. #11758470C4semidirect
17. #11758465C4semidirect
119. #327D31semidirect
146. C31#1505semidirect

Maximal subgroups

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

subgroupindex
#145215942
#145211032
#145208942
#145207842
#145207832
#145207822
C31×#3272
#150531