Finite Group Databasebeta

← #16846164

Subgroups — #16846164

Order 3968.

598 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 101 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×#11758530C211yesmaximal, characteristic
2C2×#11758394C212yesmaximal, complemented
3#14520905C211yesmaximal, characteristic, complemented
4#14520815C212yesmaximal, complemented
5C22×C22⋊C4×C31C211yesmaximal, characteristic, complemented
6C25×C31C2211yescharacteristic
7C23×C4×C31—21no—
8C22×C22⋊D31C412yescomplemented
9C22×C22⋊D31C2211yescharacteristic
10C2×C22⋊C4×C31—21no—
11C2×C22⋊C4×C31—24no—
12C2×C22⋊C4×C31C2212yes—
13#11758530—21no—
14#11758530—22no—
15#11758530—21no—
16C2×C22⋊Dic31—22no—
17C2×C22⋊Dic31C412yescomplemented
18C2×C22⋊Dic31C2212yes—
19C2×C22⋊Dic31C2211yescharacteristic
20#11758394—24no—
21C24×C31—22no—
22C24×C31—22no—
23C24×C31—44no—
24C24×C31C2×C412yes—
25C24×C31D411yescharacteristic
26C24×C31D412yes—
27C24×C31D411yescharacteristic
28C24×C31C2311yescharacteristic
29C23×D31C2×C411yescharacteristic, complemented
30C22×C4×C31—24no—
31C22×C4×C31—22no—
32C22×C4×C31—44no—
33C2×C22⋊D31—22no—
34C2×C22⋊D31—22no—
35C2×C22⋊D31—22no—
36C2×C22⋊D31—21no—
37C2×C22⋊D31—21no—
38C2×C22⋊D31—22no—
39C2×C22⋊D31—44no—
40C22×Dic31—22no—
41C22×Dic31C2×C411yescharacteristic, complemented
42C22×Dic31C2×C412yescomplemented
43C22⋊C4×C31—24no—
44C22⋊C4×C31—22no—
45C22⋊C4×C31D414yescomplemented
46C22⋊Dic31—22no—
47C22⋊Dic31—22no—
48C22⋊Dic31—21no—
49C22⋊Dic31—21no—
50C22⋊Dic31—22no—
51C22⋊Dic31—22no—
52C22⋊Dic31—44no—
53C23×C31—24no—
54C23×C31—21no—
55C23×C31—21no—
56C23×C31—24no—
57C23×C31—24no—
58C23×C31—24no—
59C23×C31—21no—
60C23×C31—24no—
61C23×C31—21no—
62C23×C31—42no—
63C23×C31—42no—
64C23×C31—42no—
65C23×C31—42no—
66C23×C31—48no—
67C23×C31—48no—
68C23×C31C22⋊C412yes—
69C23×C31C22⋊C412yes—
70C23×C31C22×C411yescharacteristic
71C23×C31C2×D411yescharacteristic
72C23×C31C2×D411yescharacteristic
73C23×C31C2×D412yes—
74C23×C31#4112yes—
75C22×D31—21no—
76C22×D31—22no—
77C22×D31—42no—
78C2×C4×C31—24no—
79C2×C4×C31—48no—
80C2×C4×C31—44no—
81C22⋊D31—44no—
82C22⋊D31—44no—
83C22⋊D31—41no—
84C22⋊D31—42no—
85C22⋊D31—41no—
86C2×Dic31—21no—
87C2×Dic31—22no—
88C2×Dic31—22no—
89C2×Dic31—42no—
90C2×Dic31—44no—
91C2×Dic31—42no—
92#1898—311nomaximal, Sylow
93C22×C31—24no—
94C22×C31—24no—
95C22×C31—22no—
96C22×C31—22no—
97C22×C31—22no—
98C22×C31—22no—
99C22×C31—22no—
100C22×C31—22no—
101C22×C31—22no—
102C22×C31—22no—
103C22×C31—42no—
104C22×C31—42no—
105C22×C31—48no—
106C22×C31—48no—
107C22×C31—42no—
108C22×C31—42no—
109C22×C31#9914yescomplemented
110C22×C31C2×C22⋊C411yescharacteristic
111C22×C31C4×D412yes—
112C22×C31#12011yescharacteristic
113C22×C31#12112yes—
114C22×C31#12311yescharacteristic
115C2×D31—41no—
116C2×D31—42no—
117C2×D31—82no—
118C4×C31—44no—
119Dic31—41no—
120Dic31—42no—
121Dic31—82no—
122C2×#120—311no—
123C22×C22⋊C4D3111yescharacteristic, complemented
124C2×#99—312no—
125#379—311no—
126#342—312no—
127C2×C31—22no—
128C2×C31—21no—
129C2×C31—22no—
130C2×C31—24no—
131C2×C31—21no—
132C2×C31—42no—
133C2×C31#38611yescharacteristic
134C2×C31C2×#9912yes—
135D31—81no—
136C25C2×D3111yescharacteristic
137C22×D4—311no—
138C22×D4—312no—
139C23×C4—21no—
140#120—622no—
141#120—621no—
142#120—621no—
143C2×C22⋊C4—21no—
144C2×C22⋊C4—24no—
145C2×C22⋊C4—312no—
146C2×C22⋊C4—311no—
147C2×C22⋊C4—312no—
148C2×C22⋊C4—622no—
149C2×C22⋊C4C2×D3112yes—
150#99—624no—
151C31#189811yescharacteristic, complemented, Sylow
152C24—22no—
153C24—22no—
154C24—44no—
155C24—311no—
156C24C4×D3112yes—
157C24D12412yes—
158C24C22⋊D3111yescharacteristic
159C24C22⋊D3111yescharacteristic
160C24C22×D3111yescharacteristic
161C2×D4—622no—
162C2×D4—622no—
163C2×D4—621no—
164C2×D4—622no—
165C2×D4—622no—
166C2×D4—621no—
167C2×D4—1244no—
168C22×C4—24no—
169C22×C4—22no—
170C22×C4—44no—
171C22×C4—311no—
172C22×C4—312no—
173C22×C4—622no—
174C22⋊C4—24no—
175C22⋊C4—22no—
176C22⋊C4—622no—
177C22⋊C4—622no—
178C22⋊C4—621no—
179C22⋊C4—621no—
180C22⋊C4—622no—
181C22⋊C4—622no—
182C22⋊C4—1244no—
183C22⋊C4C22⋊D3114yescomplemented
184C23—24no—
185C23—21no—
186C23—21no—
187C23—24no—
188C23—24no—
189C23—24no—
190C23—21no—
191C23—24no—
192C23—21no—
193C23—42no—
194C23—42no—
195C23—42no—
196C23—42no—
197C23—48no—
198C23—48no—
199C23—621no—
200C23—622no—
201C23—1242no—
202C23(C2×D31)⋊C412yes—
203C23(C2×D31)⋊C412yes—
204C23C2×C4×D3111yescharacteristic
205C23C2×D12411yescharacteristic
206C23#9249512yes—
207C23C2×C22⋊D3111yescharacteristic
208C23C2×C22⋊D3112yes—
209D4—1244no—
210D4—1244no—
211D4—1241no—
212D4—1242no—
213D4—1241no—
214C2×C4—24no—
215C2×C4—48no—
216C2×C4—44no—
217C2×C4—621no—
218C2×C4—622no—
219C2×C4—622no—
220C2×C4—1242no—
221C2×C4—1244no—
222C2×C4—1242no—
223C22—24no—
224C22—24no—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—42no—
234C22—42no—
235C22—48no—
236C22—48no—
237C22—42no—
238C22—42no—
239C22—1241no—
240C22—1242no—
241C22—2482no—
242C22#1175839414yescomplemented
243C22C2×(C2×D31)⋊C411yescharacteristic
244C22C4×C22⋊D3112yes—
245C22#1175850611yescharacteristic
246C22#1175850712yes—
247C22#1175853011yescharacteristic
248C4—44no—
249C4—1241no—
250C4—1242no—
251C4—2482no—
252C2—21no—
253C2—22no—
254C2—24no—
255C2—21no—
256C2—22no—
257C2—42no—
258C2—2481no—
259C2#1452092811yescharacteristic
260C2C2×#1175839412yes—
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC23×C31C22×C4
FrattiniC24C22×D31
FittingC22×C22⋊C4×C31C2
socleC22×C31C2×C22⋊C4
prime radicalC2×#11758530C2
cosocleC24×C31C23
hypercenterC22×C22⋊C4D31
hypocenterC31#1898
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11758394C2semidirect
3. #14520905C2semidirect
4. #14520815C2semidirect
5. C22×C22⋊C4×C31C2semidirect
8. C22×C22⋊D31C4semidirect
17. C2×C22⋊Dic31C4semidirect
29. C23×D31C2×C4semidirect
41. C22×Dic31C2×C4semidirect
42. C22×Dic31C2×C4semidirect
45. C22⋊C4×C31D4semidirect
109. C22×C31#99semidirect
123. C22×C22⋊C4D31semidirect
151. C31#1898semidirect
183. C22⋊C4C22⋊D31semidirect
242. C22#11758394semidirect

Maximal subgroups

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

subgroupindex
C2×#117585302
C2×#117583942
#145209052
#145208152
C22×C22⋊C4×C312
#189831