Finite Group Databasebeta

← #16848478

Subgroups — #16848478

Order 3968.

596 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 217 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#14520952C212yesmaximal, complemented
2#14520942C212yesmaximal, complemented
3#14520935C212yesmaximal, complemented
4#14520929C212yesmaximal, complemented
5#14520929C212yesmaximal, complemented
6#14520912C211yesmaximal, characteristic, complemented
7C22⋊C4×Dic31C212yesmaximal, complemented
8C4×C22⋊Dic31C211yesmaximal, characteristic, complemented
9C2×C31×#121C211yesmaximal, characteristic
10C22×D4×C31C2211yescharacteristic
11C22×D4×C31C2212yes—
12C23×C4×C31C2211yescharacteristic
13C23×Dic31C2212yes—
14C31×#121C418yescomplemented
15C2×C4⋊C4×C31C2211yescharacteristic
16C2×C22⋊C4×C31C2212yes—
17C2×C22⋊Dic31C2212yes—
18C2×C22⋊Dic31C2212yes—
19C2×C22⋊Dic31C2211yescharacteristic
20C2×C22⋊Dic31C2211yescharacteristic
21C2×C22⋊Dic31C2212yes—
22C2×C22⋊Dic31C2212yes—
23C2×C4⋊Dic31C2212yes—
24C2×C4×Dic31C2211yescharacteristic
25C2×C4×Dic31C2211yescharacteristic
26C2×C4×Dic31C2212yes—
27C31⋊#95C2212yes—
28C31⋊#95C2212yes—
29C31⋊#95C2212yes—
30C31⋊#95C2212yes—
31C31⋊#95C2212yes—
32C24×C31C2311yescharacteristic
33C24×C31C2312yes—
34C2×D4×C31—42no—
35C2×D4×C31—42no—
36C2×D4×C31—41no—
37C2×D4×C31—41no—
38C2×D4×C31C2×C414yes—
39C2×D4×C31C2×C418yescomplemented
40C22×C4×C31—41no—
41C22×C4×C31—41no—
42C22×C4×C31C2×C414yescomplemented
43C22×C4×C31C2311yescharacteristic
44C22×C4×C31C2311yescharacteristic
45C22×C4×C31C2312yes—
46C22×Dic31—24no—
47C22×Dic31—42no—
48C22×Dic31—42no—
49C22×Dic31C2312yes—
50C22×Dic31C2312yes—
51C22×Dic31C2312yes—
52C22×Dic31C2312yes—
53C4⋊C4×C31C2×C414yescomplemented
54C22⋊C4×C31C2×C418yescomplemented
55C22⋊Dic31—24no—
56C22⋊Dic31—24no—
57C22⋊Dic31—42no—
58C22⋊Dic31—42no—
59C22⋊Dic31—41no—
60C22⋊Dic31—41no—
61C4⋊Dic31—42no—
62C4×Dic31—41no—
63C4×Dic31—42no—
64C4×Dic31—41no—
65C23×C31—22no—
66C23×C31—22no—
67C23×C31—22no—
68C23×C31—21no—
69C23×C31—21no—
70C23×C31—22no—
71C23×C31—22no—
72C23×C31—22no—
73C23×C31—22no—
74C23×C31—22no—
75C23×C31C22×C414yes—
76C23×C31C22×C412yes—
77C23×C31C2411yescharacteristic
78D4×C31—44no—
79D4×C31—48no—
80C2×C4×C31—21no—
81C2×C4×C31—21no—
82C2×C4×C31—22no—
83C2×C4×C31—22no—
84C2×C4×C31—21no—
85C2×C4×C31—21no—
86C2×C4×C31—44no—
87C2×C4×C31C22×C412yes—
88C2×C4×C31C22×C414yes—
89C2×C4×C31C22×C412yes—
90C2×Dic31—22no—
91C2×Dic31—22no—
92C2×Dic31—22no—
93C2×Dic31—22no—
94C2×Dic31—22no—
95C2×Dic31—22no—
96C2×Dic31—22no—
97C2×Dic31—22no—
98C2×Dic31—22no—
99C2×Dic31—22no—
100C2×Dic31—22no—
101C2×Dic31—48no—
102C2×Dic31#4114yes—
103#2333—311nomaximal, Sylow
104C22×C31—22no—
105C22×C31—24no—
106C22×C31—22no—
107C22×C31—22no—
108C22×C31—24no—
109C22×C31—24no—
110C22×C31—42no—
111C22×C31—42no—
112C22×C31—42no—
113C22×C31—42no—
114C22×C31—42no—
115C22×C31—42no—
116C22×C31C23×C411yescharacteristic
117C22×C31C2×#4112yes—
118C22×C31H(5,𝔽2)11yescharacteristic
119C22×C31H(5,𝔽2)12yes—
120C22×C31H(5,𝔽2)11yescharacteristic
121C4×C31—22no—
122C4×C31—22no—
123C4×C31—24no—
124Dic31—24no—
125Dic31—42no—
126Dic31—42no—
127Dic31—42no—
128C2×#121D3111yescharacteristic
129#390—312no—
130#388—312no—
131#387—312no—
132#386—312no—
133#386—312no—
134#381—311no—
135C4×C22⋊C4—311no—
136C4×C22⋊C4—312no—
137C2×C31—42no—
138C2×C31—44no—
139C2×C31C4×#4111yescharacteristic
140C2×C31#51811yescharacteristic
141C2×C31#51811yescharacteristic
142C2×C31#53812yes—
143C2×C31#54012yes—
144C22×D4C2×D3111yescharacteristic
145C22×D4C2×D3112yes—
146C23×C4—312no—
147C23×C4C2×D3111yescharacteristic
148#121Dic3118yescomplemented
149C2×C4⋊C4—312no—
150C2×C4⋊C4C2×D3111yescharacteristic
151C2×C22⋊C4—312no—
152C2×C22⋊C4—312no—
153C2×C22⋊C4—311no—
154C2×C22⋊C4—311no—
155C2×C22⋊C4—312no—
156C2×C22⋊C4—312no—
157C2×C22⋊C4C2×D3112yes—
158C2×C42—311no—
159C2×C42—312no—
160C2×C42—311no—
161#95—312no—
162#95—312no—
163#95—312no—
164#95—312no—
165#95—312no—
166C31#233311yescharacteristic, complemented, Sylow
167C24C22×D3111yescharacteristic
168C24C22×D3112yes—
169C2×D4—42no—
170C2×D4—42no—
171C2×D4—41no—
172C2×D4—41no—
173C2×D4C2×Dic3114yes—
174C2×D4C2×Dic3118yescomplemented
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—312no—
178C22×C4—312no—
179C22×C4—312no—
180C22×C4—312no—
181C22×C4—624no—
182C22×C4—1242no—
183C22×C4—1242no—
184C22×C4C2×Dic3114yescomplemented
185C22×C4C22×D3111yescharacteristic
186C22×C4C22×D3111yescharacteristic
187C22×C4C22×D3112yes—
188C4⋊C4—1242no—
189C4⋊C4C2×Dic3114yescomplemented
190C22⋊C4—624no—
191C22⋊C4—624no—
192C22⋊C4—1242no—
193C22⋊C4—1241no—
194C22⋊C4—1242no—
195C22⋊C4—1241no—
196C22⋊C4C2×Dic3118yescomplemented
197C42—1241no—
198C42—1241no—
199C42—1242no—
200C23—21no—
201C23—21no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—22no—
209C23—22no—
210C23C22×Dic3114yes—
211C23C22×Dic3112yes—
212C23C23×D3111yescharacteristic
213D4—44no—
214D4—48no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—44no—
222C2×C4—314no—
223C2×C4—622no—
224C2×C4—622no—
225C2×C4—622no—
226C2×C4—622no—
227C2×C4—622no—
228C2×C4—622no—
229C2×C4—622no—
230C2×C4—622no—
231C2×C4—622no—
232C2×C4—622no—
233C2×C4—622no—
234C2×C4—1248no—
235C2×C4C22×Dic3112yes—
236C2×C4C22×Dic3114yes—
237C2×C4C22×Dic3112yes—
238C22—22no—
239C22—24no—
240C22—22no—
241C22—22no—
242C22—24no—
243C22—24no—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22#1175856111yescharacteristic
251C22#1175856112yes—
252C22#1175856111yescharacteristic
253C22#41×D3112yes—
254C22C23×Dic3111yescharacteristic
255C4—22no—
256C4—22no—
257C4—24no—
258C4—624no—
259C4—1242no—
260C4—1242no—
261C4—1242no—
262C2—42no—
263C2—44no—
264C2#41×Dic3111yescharacteristic
265C2#1452152411yescharacteristic
266C2#1452152411yescharacteristic
267C2#1452163112yes—
268C2#1452164912yes—
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
Fitting, prime radicalC2×C31×#121C2
socle, cosocleC23×C31C24
hypercenterC2×#121D31
hypocenterC31#2333
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #14520952C2semidirect
2. #14520942C2semidirect
3. #14520935C2semidirect
4. #14520929C2semidirect
5. #14520929C2semidirect
6. #14520912C2semidirect
7. C22⋊C4×Dic31C2semidirect
8. C4×C22⋊Dic31C2semidirect
14. C31×#121C4semidirect
39. C2×D4×C31C2×C4semidirect
42. C22×C4×C31C2×C4semidirect
53. C4⋊C4×C31C2×C4semidirect
54. C22⋊C4×C31C2×C4semidirect
148. #121Dic31semidirect
166. C31#2333semidirect
174. C2×D4C2×Dic31semidirect
184. C22×C4C2×Dic31semidirect
189. C4⋊C4C2×Dic31semidirect
196. C22⋊C4C2×Dic31semidirect

Maximal subgroups

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

subgroupindex
#145209522
#145209422
#145209352
#145209292
#145209122
C22⋊C4×Dic312
C4×C22⋊Dic312
C2×C31×#1212
#233331