Finite Group Databasebeta

← #16846013

Subgroups — #16846013

Order 3968.

376 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 97 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×#11758413C212yesmaximal, complemented
3C4×C22⋊Dic31C211yesmaximal, characteristic, complemented
4#14520810C212yesmaximal, complemented
5C22×M16×C31C211yesmaximal, characteristic, complemented
6C23×C4×C31C2211yescharacteristic
7C2×#92495C2211yescharacteristic
8C2×M16×C31—21no—
9C2×M16×C31—24no—
10C2×M16×C31C2212yes—
11C22×C8×C31—21no—
12#11758530—21no—
13C2×C22⋊Dic31—21no—
14#11758507C411yescharacteristic, complemented
15#11758507C411yescharacteristic, complemented
16#11758506—21no—
17C4×C22⋊D31—21no—
18C4×C22⋊D31—21no—
19#11758503C2211yescharacteristic
20#11758501C411yescharacteristic, complemented
21#11758501C411yescharacteristic, complemented
22C2×C4×Dic31C2212yes—
23C31⋊#95—21no—
24#11758413—24no—
25C24×C31D411yescharacteristic
26C22×C4×C31—22no—
27C22×C4×C31—22no—
28C22×C4×C31C2×C411yescharacteristic
29C22×C4×C31C2×C411yescharacteristic
30C22×C4×C31D411yescharacteristic
31C22×C4×C31D411yescharacteristic
32C22×C4×C31D411yescharacteristic
33C22×C4×C31C2311yescharacteristic
34C2×C22⋊D31—21no—
35C2×C22⋊D31—21no—
36C2×C22⋊D31—21no—
37C22×Dic31—22no—
38#92495—22no—
39#92495—22no—
40C2×D124C2×C411yescharacteristic
41C2×C4×D31—21no—
42C2×Dic62C2×C411yescharacteristic
43M16×C31—24no—
44M16×C31—22no—
45M16×C31D414yescomplemented
46C2×C8×C31—24no—
47C2×C8×C31—22no—
48C22⋊Dic31—24no—
49C22⋊Dic31—21no—
50C22⋊Dic31—21no—
51C22⋊Dic31—21no—
52(C2×D31)⋊C4—21no—
53(C2×D31)⋊C4—21no—
54C4⋊Dic31C2×C411yescharacteristic
55C4⋊Dic31C2×C411yescharacteristic
56Dic31⋊C4—21no—
57Dic31⋊C4—21no—
58C4×Dic31—21no—
59C4×Dic31—22no—
60C4×Dic31—22no—
61C23×C31—22no—
62C23×C31—22no—
63C23×C31—41no—
64C23×C31C22⋊C411yescharacteristic
65C23×C31C22⋊C411yescharacteristic
66C23×C31C2×D411yescharacteristic
67C22×D31—21no—
68C2×C4×C31—22no—
69C2×C4×C31—22no—
70C2×C4×C31—22no—
71C2×C4×C31—21no—
72C2×C4×C31—21no—
73C2×C4×C31—21no—
74C2×C4×C31—21no—
75C2×C4×C31C22⋊C411yescharacteristic
76C2×C4×C31C22⋊C411yescharacteristic
77C2×C4×C31C22×C411yescharacteristic
78C2×C4×C31C2×D412yes—
79C2×C4×C31C2×D411yescharacteristic
80C2×C4×C31#4112yes—
81C22⋊D31—42no—
82C22⋊D31—42no—
83C22⋊D31—42no—
84C2×Dic31—24no—
85C2×Dic31—21no—
86C2×Dic31—21no—
87C2×Dic31—21no—
88C2×Dic31—42no—
89C2×Dic31—42no—
90D124—22no—
91C4×D31—41no—
92C4×D31—41no—
93Dic62—22no—
94C8×C31—24no—
95#1871—311nomaximal, Sylow
96C22×C31—21no—
97C22×C31—21no—
98C22×C31—21no—
99C22×C31—21no—
100C22×C31—21no—
101C22×C31—21no—
102C22×C31—21no—
103C22×C31—44no—
104C22×C31#10412yescomplemented
105C22×C31C2×C22⋊C411yescharacteristic
106C22×C31#12112yes—
107C2×D31—41no—
108C2×D31—41no—
109C2×D31—41no—
110C4×C31—21no—
111C4×C31—21no—
112C4×C31C4×D412yes—
113C4×C31#12011yescharacteristic
114C4×C31#12311yescharacteristic
115Dic31—44no—
116Dic31—41no—
117Dic31—41no—
118Dic31—41no—
119C22×M16D3111yescharacteristic, complemented
120#525—311no—
121C2×#104—312no—
122C4×C22⋊C4—311no—
123#339—312no—
124C2×C31—22no—
125C2×C31—22no—
126C2×C31—41no—
127C2×C31#38611yescharacteristic
128C2×C31C2×#10411yescharacteristic
129C2×C31#42111yescharacteristic
130D31—81no—
131C2×#41—311no—
132C23×C4C2×D3111yescharacteristic
133C2×M16—21no—
134C2×M16—24no—
135C2×M16C2×D3112yes—
136C22×C8—21no—
137#123—621no—
138C22⋊Q8—311no—
139C22⋊Q8—311no—
140#121—311no—
141#121—311no—
142#120—621no—
143C4×D4—621no—
144C4×D4—621no—
145#117—311no—
146C2×C22⋊C4—621no—
147C2×C42—312no—
148#104—624no—
149#95—621no—
150C31#187111yescharacteristic, complemented, Sylow
151C24D12411yescharacteristic
152#41—622no—
153#41—622no—
154C2×Q8—311no—
155C2×D4—311no—
156C2×D4—621no—
157C2×D4—621no—
158C2×D4—621no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—622no—
162C22×C4—621no—
163C22×C4C4×D3111yescharacteristic
164C22×C4C4×D3111yescharacteristic
165C22×C4D12411yescharacteristic
166C22×C4C22⋊D3111yescharacteristic
167C22×C4C22⋊D3111yescharacteristic
168C22×C4C22×D3111yescharacteristic
169M16—24no—
170M16—22no—
171M16C22⋊D3114yescomplemented
172C2×C8—24no—
173C2×C8—22no—
174C4⋊C4—311no—
175C4⋊C4—311no—
176C4⋊C4—621no—
177C4⋊C4—621no—
178C22⋊C4—624no—
179C22⋊C4—621no—
180C22⋊C4—621no—
181C22⋊C4—621no—
182C22⋊C4—621no—
183C22⋊C4—621no—
184C42—621no—
185C42—622no—
186C42—622no—
187C23—22no—
188C23—22no—
189C23—41no—
190C23—621no—
191C23(C2×D31)⋊C411yescharacteristic
192C23(C2×D31)⋊C411yescharacteristic
193C23C2×D12411yescharacteristic
194Q8—622no—
195D4—622no—
196D4—1242no—
197D4—1242no—
198D4—1242no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—624no—
207C2×C4—621no—
208C2×C4—621no—
209C2×C4—621no—
210C2×C4—1242no—
211C2×C4—1242no—
212C2×C4—1241no—
213C2×C4—1241no—
214C2×C4(C2×D31)⋊C411yescharacteristic
215C2×C4(C2×D31)⋊C411yescharacteristic
216C2×C4C2×C4×D3111yescharacteristic
217C2×C4#9249512yes—
218C2×C4C2×C22⋊D3112yes—
219C2×C4C2×C22⋊D3111yescharacteristic
220C8—24no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—44no—
229C22—1241no—
230C22—1241no—
231C22—1241no—
232C22#1175841312yescomplemented
233C22C2×(C2×D31)⋊C411yescharacteristic
234C22#1175850712yes—
235C4—21no—
236C4—21no—
237C4—1244no—
238C4—1241no—
239C4—1241no—
240C4—1241no—
241C4C4×C22⋊D3112yes—
242C4#1175850611yescharacteristic
243C4#1175853011yescharacteristic
244C2—22no—
245C2—22no—
246C2—41no—
247C2—2481no—
248C2#1452092811yescharacteristic
249C2C2×#1175841311yescharacteristic
250C2#1452106511yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC22×M16×C31C2
socleC22×C31C2×C22⋊C4
prime radical#14521560C2
cosocleC22×C4×C31C23
hypercenterC22×M16D31
hypocenterC31#1871
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. C2×#11758413C2semidirect
3. C4×C22⋊Dic31C2semidirect
4. #14520810C2semidirect
5. C22×M16×C31C2semidirect
14. #11758507C4semidirect
15. #11758507C4semidirect
20. #11758501C4semidirect
21. #11758501C4semidirect
45. M16×C31D4semidirect
104. C22×C31#104semidirect
119. C22×M16D31semidirect
150. C31#1871semidirect
171. M16C22⋊D31semidirect
232. C22#11758413semidirect

Maximal subgroups

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

subgroupindex
#145215602
C2×#117584132
C4×C22⋊Dic312
#145208102
C22×M16×C312
#187131