Finite Group Databasebeta

← #16844047

Subgroups — #16844047

Order 3968.

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

normal subgroups only

This group has 316 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
1C2×C4×C22⋊D31C211yesmaximal, characteristic
2#14521013C211yesmaximal, characteristic, complemented
3#14520774C212yesmaximal, complemented
4#14520772C212yesmaximal, complemented
5C31×#407C211yesmaximal, characteristic, complemented
6C23×C4×C31C2211yescharacteristic
7C22×C22⋊D31C411yescharacteristic
8C22×C4×D31C411yescharacteristic
9C2×M16×C31—21no—
10C2×C22⋊Dic31C411yescharacteristic
11C4×C22⋊D31—21no—
12C4×C22⋊D31—21no—
13C4×C22⋊D31—21no—
14C4×C22⋊D31—21no—
15C2×(C2×D31)⋊C4C2211yescharacteristic
16C2×Dic31⋊C4C2211yescharacteristic
17C2×C4×Dic31C411yescharacteristic
18C2×#92474—21no—
19C31×C22⋊C8—21no—
20C31×C22⋊C8C2212yes—
21C22⋊(C31⋊C8)—21no—
22C22⋊(C31⋊C8)C2212yes—
23C24×C31C2×C411yescharacteristic
24C23×D31C2×C411yescharacteristic
25C22×C4×C31—42no—
26C22×C4×C31C2×C411yescharacteristic
27C22×C4×C31D411yescharacteristic
28C22×C4×C31D411yescharacteristic
29C22×C4×C31D411yescharacteristic
30C22×C4×C31D411yescharacteristic
31C22×C4×C31C2311yescharacteristic
32C2×C22⋊D31—21no—
33C2×C22⋊D31—21no—
34C2×C22⋊D31—22no—
35C2×C22⋊D31—22no—
36C22×Dic31C2×C411yescharacteristic
37C22×Dic31C2×C411yescharacteristic
38C22×Dic31C2×C411yescharacteristic
39C2×C4×D31—21no—
40C2×C4×D31—21no—
41C2×C4×D31—42no—
42M16×C31—42no—
43C2×C8×C31—22no—
44C22⋊Dic31—21no—
45C22⋊Dic31—21no—
46(C2×D31)⋊C4—21no—
47(C2×D31)⋊C4—21no—
48Dic31⋊C4—21no—
49Dic31⋊C4—21no—
50C4×Dic31—21no—
51C4×Dic31—21no—
52#92474—42no—
53C2×C31⋊C8—22no—
54C23×C31—21no—
55C23×C31—21no—
56C23×C31—41no—
57C23×C31—41no—
58C23×C31C22⋊C411yescharacteristic
59C23×C31C22⋊C411yescharacteristic
60C23×C31C22×C411yescharacteristic
61C22×D31—21no—
62C22×D31—21no—
63C22×D31—41no—
64C22×D31—41no—
65C22×D31M1612yescomplemented
66C2×C4×C31—22no—
67C2×C4×C31—22no—
68C2×C4×C31—22no—
69C2×C4×C31—41no—
70C2×C4×C31—41no—
71C2×C4×C31—41no—
72C2×C4×C31C22⋊C411yescharacteristic
73C2×C4×C31C22⋊C411yescharacteristic
74C2×C4×C31C2×D411yescharacteristic
75C2×C4×C31C2×D411yescharacteristic
76C22⋊D31—24no—
77C22⋊D31—24no—
78C2×Dic31—21no—
79C2×Dic31—21no—
80C2×Dic31—21no—
81C2×Dic31—21no—
82C2×Dic31—41no—
83C2×Dic31—41no—
84C2×Dic31M1612yescomplemented
85C4×D31—42no—
86C4×D31—42no—
87C8×C31—42no—
88C31⋊C8—42no—
89#1465—311nomaximal, Sylow
90C22×C31—21no—
91C22×C31—21no—
92C22×C31—21no—
93C22×C31—21no—
94C22×C31—21no—
95C22×C31—21no—
96C22×C31—21no—
97C22×C31—21no—
98C22×C31—42no—
99C22×C31—42no—
100C22×C31C2×C22⋊C411yescharacteristic
101C22×C31C2×M1611yescharacteristic
102C22×C31C2×M1611yescharacteristic
103C2×D31—22no—
104C2×D31—42no—
105C2×D31—41no—
106C2×D31—41no—
107C2×D31—42no—
108C4×C31—21no—
109C4×C31—21no—
110C4×C31—21no—
111C4×C31#9912yes—
112Dic31—22no—
113Dic31—41no—
114Dic31—41no—
115C2×C4×D4—311no—
116#407—311no—
117#407D3111yescharacteristic, complemented
118#324—312no—
119#323—312no—
120C2×C31—21no—
121C2×C31—21no—
122C2×C31—41no—
123C2×C31—41no—
124C2×C31#40711yescharacteristic
125C2×C31C2×#9911yescharacteristic
126C2×C31#41311yescharacteristic
127D31—42no—
128C22×D4—311no—
129C23×C4—311no—
130C23×C4C2×D3111yescharacteristic
131C2×M16—21no—
132C2×M16—621no—
133C4×D4—621no—
134C4×D4—621no—
135C4×D4—621no—
136C4×D4—621no—
137C2×C4⋊C4—311no—
138C2×C22⋊C4—311no—
139C2×C22⋊C4—311no—
140C2×C42—311no—
141C22⋊C8—21no—
142C22⋊C8—312no—
143C22⋊C8—621no—
144C22⋊C8C2×D3112yes—
145C31#146511yescharacteristic, complemented, Sylow
146C24—311no—
147C24C4×D3111yescharacteristic
148C2×D4—622no—
149C2×D4—622no—
150C2×D4—621no—
151C2×D4—621no—
152C22×C4—42no—
153C22×C4—311no—
154C22×C4—311no—
155C22×C4—311no—
156C22×C4—621no—
157C22×C4—621no—
158C22×C4—1242no—
159C22×C4C4×D3111yescharacteristic
160C22×C4D12411yescharacteristic
161C22×C4D12411yescharacteristic
162C22×C4C22⋊D3111yescharacteristic
163C22×C4C22⋊D3111yescharacteristic
164C22×C4C22×D3111yescharacteristic
165M16—42no—
166M16—1242no—
167C2×C8—22no—
168C2×C8—622no—
169C4⋊C4—621no—
170C4⋊C4—621no—
171C22⋊C4—621no—
172C22⋊C4—621no—
173C22⋊C4—621no—
174C22⋊C4—621no—
175C42—621no—
176C42—621no—
177C23—21no—
178C23—21no—
179C23—41no—
180C23—41no—
181C23—312no—
182C23—621no—
183C23—621no—
184C23—1241no—
185C23—1241no—
186C23(C2×D31)⋊C411yescharacteristic
187C23(C2×D31)⋊C411yescharacteristic
188C23C2×C4×D3111yescharacteristic
189D4—624no—
190D4—624no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—312no—
198C2×C4—621no—
199C2×C4—621no—
200C2×C4—621no—
201C2×C4—621no—
202C2×C4—1242no—
203C2×C4—1242no—
204C2×C4—1241no—
205C2×C4—1241no—
206C2×C4(C2×D31)⋊C411yescharacteristic
207C2×C4(C2×D31)⋊C411yescharacteristic
208C2×C4C2×D12411yescharacteristic
209C2×C4C2×C22⋊D3111yescharacteristic
210C8—42no—
211C8—1242no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—21no—
218C22—21no—
219C22—21no—
220C22—42no—
221C22—42no—
222C22—622no—
223C22—1242no—
224C22—1242no—
225C22—1241no—
226C22—1241no—
227C22M16×D3111yescharacteristic
228C22M16×D3111yescharacteristic
229C22C2×(C2×D31)⋊C411yescharacteristic
230C4—21no—
231C4—21no—
232C4—21no—
233C4—622no—
234C4—1241no—
235C4—1241no—
236C4#1175839412yes—
237C2—21no—
238C2—21no—
239C2—41no—
240C2—41no—
241C2—1242no—
242C2#1452101211yescharacteristic
243C2C2×#1175839411yescharacteristic
244C2#1452103111yescharacteristic
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC23×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#407C2
socleC22×C31C2×C22⋊C4
prime radicalC22×C22⋊D31C4
cosocleC22×C4×C31C23
hypercenter#407D31
hypocenterC31#1465
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. #14521013C2semidirect
3. #14520774C2semidirect
4. #14520772C2semidirect
5. C31×#407C2semidirect
65. C22×D31M16semidirect
84. C2×Dic31M16semidirect
117. #407D31semidirect
145. C31#1465semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D312
#145210132
#145207742
#145207722
C31×#4072
#146531