Finite Group Databasebeta

← #16844178

Subgroups — #16844178

Order 3968.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#14521105C211yesmaximal, characteristic, complemented
3#14521100C211yesmaximal, 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—
13#11758472C411yescharacteristic
14#11758465C411yescharacteristic
15#11758462—21no—
16#11758461—21no—
17C4×D124C2211yescharacteristic
18C42×D31C2211yescharacteristic
19C31×C4⋊C8C2211yescharacteristic
20C4×C8×C31C2211yescharacteristic
21(C2×D31)⋊C8—21no—
22(C2×D31)⋊C8—21no—
23#11758403—21no—
24Dic31⋊C8—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—
56C23×C31—21no—
57C22×D31—21no—
58C22×D31C22⋊C411yescharacteristic
59D4×C31—21no—
60D4×C31—21no—
61C2×C4×C31—21no—
62C2×C4×C31—41no—
63C2×C4×C31—41no—
64C2×C4×C31C22×C411yescharacteristic
65C2×C4×C31C2×D411yescharacteristic
66C2×C4×C31C2×D411yescharacteristic
67C22⋊D31—42no—
68C22⋊D31—42no—
69C22⋊D31—42no—
70C2×Dic31—21no—
71C2×Dic31C22⋊C411yescharacteristic
72C2×Dic31C22⋊C411yescharacteristic
73C2×Dic31C22⋊C411yescharacteristic
74D124—21no—
75D124—21no—
76D124—42no—
77C4×D31—21no—
78C4×D31—21no—
79C4×D31—21no—
80C4×D31—21no—
81C4×D31—41no—
82C4×D31—41no—
83C4×D31—41no—
84Dic62—42no—
85C8×C31—41no—
86C8×C31—41no—
87C31⋊C8—41no—
88C31⋊C8—41no—
89#1496—311nomaximal, Sylow
90C22×C31—41no—
91C22×C31—41no—
92C22×C31—41no—
93C22×C31C2×C22⋊C411yescharacteristic
94C2×D31—21no—
95C2×D31—21no—
96C2×D31—21no—
97C2×D31—41no—
98C2×D31—41no—
99C2×D31—41no—
100C4×C31—21no—
101C4×C31—41no—
102C4×C31#13111yescharacteristic
103C4×C31#13111yescharacteristic
104C4×C31AGL(1,ℤ/8)11yescharacteristic
105C4×C31AGL(1,ℤ/8)11yescharacteristic
106Dic31—21no—
107Dic31—21no—
108Dic31—21no—
109Dic31—41no—
110#532—311no—
111#432—311no—
112#431—311no—
113D4⋊C8—311no—
114D4⋊C8—311no—
115D4⋊C8—311no—
116D4⋊C8D3111yescharacteristic, complemented
117C2×C31—81no—
118C2×C31#40811yescharacteristic
119C2×C31#41811yescharacteristic
120C2×C31#42111yescharacteristic
121D31—41no—
122D31—81no—
123C2×#41—621no—
124C4⋊Q8—311no—
125#127—311no—
126#124—621no—
127#121—311no—
128#121—311no—
129#121—621no—
130C4×D4—311no—
131C4×D4—621no—
132C4×D4C2×D3111yescharacteristic
133C2×C42—311no—
134C4⋊C8—311no—
135C4⋊C8—621no—
136C4⋊C8C2×D3111yescharacteristic
137C22⋊C8—621no—
138C22⋊C8—621no—
139#97—621no—
140C4×C8—311no—
141C4×C8C2×D3111yescharacteristic
142C31#149611yescharacteristic, complemented, Sylow
143#41—1242no—
144#41—1242no—
145C2×Q8—621no—
146C2×D4—311no—
147C2×D4—621no—
148C2×D4—621no—
149C2×D4—621no—
150C2×D4—621no—
151C2×D4C4×D3111yescharacteristic
152C22×C4—21no—
153C22×C4—311no—
154C22×C4—311no—
155C22×C4—311no—
156C22×C4—621no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—621no—
160C2×C8—621no—
161C4⋊C4—311no—
162C4⋊C4—621no—
163C4⋊C4C4×D3111yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—621no—
166C22⋊C4—621no—
167C22⋊C4—621no—
168C42—311no—
169C42—311no—
170C42—311no—
171C42C22×D3111yescharacteristic
172C23—21no—
173C23—311no—
174C23—621no—
175Q8—1242no—
176D4—21no—
177D4—21no—
178D4—621no—
179D4—621no—
180D4—1242no—
181D4—1242no—
182D4—1242no—
183D4—1242no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—311no—
188C2×C4—311no—
189C2×C4—311no—
190C2×C4—621no—
191C2×C4—621no—
192C2×C4—621no—
193C2×C4—621no—
194C2×C4—621no—
195C2×C4—1241no—
196C2×C4—1241no—
197C2×C4—1241no—
198C2×C4C2×C4×D3111yescharacteristic
199C2×C4D4×D3111yescharacteristic
200C2×C4D4×D3111yescharacteristic
201C8—41no—
202C8—41no—
203C8—1241no—
204C8—1241no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—621no—
209C22—621no—
210C22—621no—
211C22—1241no—
212C22—1241no—
213C22—1241no—
214C22C22⋊C4×D3111yescharacteristic
215C4—21no—
216C4—41no—
217C4—621no—
218C4—621no—
219C4—621no—
220C4—1241no—
221C4#1175847811yescharacteristic
222C4#1175848411yescharacteristic
223C4#1175848811yescharacteristic
224C4#1175849111yescharacteristic
225C2—81no—
226C2—1241no—
227C2—2481no—
228C2#1452101411yescharacteristic
229C2#1452105211yescharacteristic
230C2#1452106411yescharacteristic
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#1496
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. #14521105C2semidirect
3. #14521100C2semidirect
4. #14520778C2semidirect
5. D4⋊(C31⋊C8)C2semidirect
6. #14520776C2semidirect
7. C31×D4⋊C8C2semidirect
116. D4⋊C8D31semidirect
142. C31#1496semidirect

Maximal subgroups

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

subgroupindex
#145215962
#145211052
#145211002
#145207782
D4⋊(C31⋊C8)2
#145207762
C31×D4⋊C82
#149631