Finite Group Databasebeta

← #16844126

Subgroups — #16844126

Order 3968.

262 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 67 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#14521596C211yesmaximal, characteristic
2#14521101C211yesmaximal, characteristic, complemented
3C4×#92469C211yesmaximal, characteristic, complemented
4#14520778C211yesmaximal, characteristic, complemented
5D4⋊(C31⋊C8)C211yesmaximal, characteristic, complemented
6#14520776C211yesmaximal, characteristic, complemented
7C31×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#92495—21no—
9C4×D4×C31C2211yescharacteristic
10#11758517C411yescharacteristic
11#11758515C411yescharacteristic
12C4×C22⋊D31—21no—
13C2×#92469—21no—
14#11758472C411yescharacteristic
15#11758465C411yescharacteristic
16#11758462—21no—
17#11758461—21no—
18C4×D124C2211yescharacteristic
19C42×D31C2211yescharacteristic
20C31×C4⋊C8C2211yescharacteristic
21C4×C8×C31C2211yescharacteristic
22(C2×D31)⋊C8—21no—
23#11758403—21no—
24C8×Dic31—21no—
25C4⋊(C31⋊C8)C2211yescharacteristic
26C4×C31⋊C8C2211yescharacteristic
27C2×D4×C31C2×C411yescharacteristic
28C22×C4×C31—21no—
29C2×C22⋊D31—21no—
30C2×C22⋊D31—21no—
31C2×C22⋊D31—21no—
32#92495—42no—
33#92495—42no—
34C2×D124—21no—
35C2×D124C2×C411yescharacteristic
36C2×C4×D31—21no—
37C2×C4×D31C2×C411yescharacteristic
38C2×C4×D31D411yescharacteristic
39C2×C4×D31D411yescharacteristic
40C2×Dic62—21no—
41C2×C8×C31—21no—
42C2×C8×C31—21no—
43C4⋊C4×C31C2×C411yescharacteristic
44C22⋊C4×C31—21no—
45C42×C31C2311yescharacteristic
46C22⋊Dic31—21no—
47(C2×D31)⋊C4—21no—
48(C2×D31)⋊C4—21no—
49C4⋊Dic31C2×C411yescharacteristic
50Dic31⋊C4—21no—
51C4×Dic31C2×C411yescharacteristic
52C4×Dic31D411yescharacteristic
53C4×Dic31D411yescharacteristic
54C2×C31⋊C8—21no—
55C2×C31⋊C8—21no—
56#92469—24no—
57C23×C31—21no—
58C22×D31—21no—
59C22×D31C22⋊C411yescharacteristic
60D4×C31—21no—
61D4×C31—21no—
62C2×C4×C31—21no—
63C2×C4×C31—41no—
64C2×C4×C31—41no—
65C2×C4×C31C22×C411yescharacteristic
66C2×C4×C31C2×D411yescharacteristic
67C2×C4×C31C2×D411yescharacteristic
68C22⋊D31—42no—
69C22⋊D31—42no—
70C22⋊D31—42no—
71C2×Dic31—21no—
72C2×Dic31C22⋊C411yescharacteristic
73C2×Dic31C22⋊C411yescharacteristic
74C2×Dic31C22⋊C411yescharacteristic
75D124—21no—
76D124—21no—
77D124—42no—
78C4×D31—21no—
79C4×D31—21no—
80C4×D31—21no—
81C4×D31—21no—
82C4×D31—22no—
83C4×D31—41no—
84C4×D31—41no—
85Dic62—42no—
86C8×C31—22no—
87C8×C31—41no—
88C31⋊C8—22no—
89C31⋊C8—41no—
90#1484—311nomaximal, Sylow
91C22×C31—41no—
92C22×C31—41no—
93C22×C31—41no—
94C22×C31C2×C22⋊C411yescharacteristic
95C2×D31—21no—
96C2×D31—21no—
97C2×D31—21no—
98C2×D31—41no—
99C2×D31—41no—
100C2×D31—41no—
101C4×C31—21no—
102C4×C31—41no—
103C4×C31#13111yescharacteristic
104C4×C31#13111yescharacteristic
105C4×C31AGL(1,ℤ/8)11yescharacteristic
106C4×C31AGL(1,ℤ/8)11yescharacteristic
107Dic31—21no—
108Dic31—21no—
109Dic31—41no—
110Dic31#10412yes—
111#532—311no—
112#431—311no—
113C4×M16—311no—
114D4⋊C8—311no—
115D4⋊C8—311no—
116D4⋊C8—311no—
117D4⋊C8D3111yescharacteristic, complemented
118C2×C31—81no—
119C2×C31#40811yescharacteristic
120C2×C31#41811yescharacteristic
121C2×C31C2×#10411yescharacteristic
122D31—41no—
123D31—81no—
124C2×#41—621no—
125C2×M16—621no—
126C4⋊Q8—311no—
127#127—311no—
128#124—621no—
129#121—311no—
130#121—311no—
131#121—621no—
132C4×D4—311no—
133C4×D4—621no—
134C4×D4C2×D3111yescharacteristic
135C2×C42—311no—
136C4⋊C8—311no—
137C4⋊C8C2×D3111yescharacteristic
138C22⋊C8—621no—
139#97—621no—
140C4×C8—311no—
141C4×C8—621no—
142C4×C8C2×D3111yescharacteristic
143C31#148411yescharacteristic, complemented, Sylow
144#41—1242no—
145#41—1242no—
146C2×Q8—621no—
147C2×D4—311no—
148C2×D4—621no—
149C2×D4—621no—
150C2×D4—621no—
151C2×D4—621no—
152C2×D4C4×D3111yescharacteristic
153C22×C4—21no—
154C22×C4—311no—
155C22×C4—311no—
156C22×C4—311no—
157C22×C4—621no—
158M16—624no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—621no—
162C2×C8—621no—
163C4⋊C4—311no—
164C4⋊C4—621no—
165C4⋊C4C4×D3111yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—621no—
168C22⋊C4—621no—
169C22⋊C4—621no—
170C42—311no—
171C42—311no—
172C42—311no—
173C42C22×D3111yescharacteristic
174C23—21no—
175C23—311no—
176C23—621no—
177Q8—1242no—
178D4—21no—
179D4—21no—
180D4—621no—
181D4—621no—
182D4—1242no—
183D4—1242no—
184D4—1242no—
185D4—1242no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—311no—
190C2×C4—311no—
191C2×C4—311no—
192C2×C4—622no—
193C2×C4—621no—
194C2×C4—621no—
195C2×C4—621no—
196C2×C4—621no—
197C2×C4—621no—
198C2×C4—1241no—
199C2×C4—1241no—
200C2×C4C2×C4×D3111yescharacteristic
201C2×C4D4×D3111yescharacteristic
202C2×C4D4×D3111yescharacteristic
203C8—22no—
204C8—41no—
205C8—622no—
206C8—1241no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—621no—
211C22—621no—
212C22—621no—
213C22—1241no—
214C22—1241no—
215C22—1241no—
216C22C22⋊C4×D3111yescharacteristic
217C4—21no—
218C4—41no—
219C4—312no—
220C4—621no—
221C4—621no—
222C4—1241no—
223C4#1175847811yescharacteristic
224C4#1175848411yescharacteristic
225C4#1175848811yescharacteristic
226C4#1175849111yescharacteristic
227C2—81no—
228C2—1241no—
229C2—2481no—
230C2#1452101411yescharacteristic
231C2#1452105211yescharacteristic
232C2#104×D3111yescharacteristic
subgroupG/H
centerC2×C4D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×D4⋊C8C2
socleC22×C31C2×C22⋊C4
prime radical#14521596C2
cosocleC42×C31C23
hypercenterD4⋊C8D31
hypocenterC31#1484
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #14521101C2semidirect
3. C4×#92469C2semidirect
4. #14520778C2semidirect
5. D4⋊(C31⋊C8)C2semidirect
6. #14520776C2semidirect
7. C31×D4⋊C8C2semidirect
117. D4⋊C8D31semidirect
143. C31#1484semidirect

Maximal subgroups

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

subgroupindex
#145215962
#145211012
C4×#924692
#145207782
D4⋊(C31⋊C8)2
#145207762
C31×D4⋊C82
#148431