Finite Group Databasebeta

← #16848868

Subgroups — #16848868

Order 3968.

576 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 213 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#14520924C212yesmaximal, complemented
7#14520912C211yesmaximal, characteristic, complemented
8#14520909C211yesmaximal, 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⋊Dic31C2211yescharacteristic
18C2×C22⋊Dic31C2211yescharacteristic
19C2×C22⋊Dic31C2212yes—
20C2×C22⋊Dic31C2212yes—
21C2×C22⋊Dic31C2212yes—
22C2×C22⋊Dic31C2212yes—
23C2×C4⋊Dic31C2212yes—
24C2×C4⋊Dic31C2212yes—
25C2×C4×Dic31C2212yes—
26C31⋊#95C2212yes—
27C31⋊#95C2211yescharacteristic
28C31⋊#95C2212yes—
29C31⋊#95C2211yescharacteristic
30C31⋊#95C2212yes—
31C31⋊#95C2212yes—
32C24×C31C2311yescharacteristic
33C24×C31C2312yes—
34C2×D4×C31—42no—
35C2×D4×C31—42no—
36C2×D4×C31—42no—
37C2×D4×C31C2×C414yes—
38C2×D4×C31C2×C418yescomplemented
39C22×C4×C31—42no—
40C22×C4×C31C2×C414yescomplemented
41C22×C4×C31C2311yescharacteristic
42C22×C4×C31C2312yes—
43C22×C4×C31C2311yescharacteristic
44C22×Dic31—42no—
45C22×Dic31—42no—
46C22×Dic31—42no—
47C22×Dic31C2312yes—
48C22×Dic31C2312yes—
49C22×Dic31C2312yes—
50C22×Dic31C2312yes—
51C4⋊C4×C31C2×C414yescomplemented
52C22⋊C4×C31C2×C418yescomplemented
53C22⋊Dic31—42no—
54C22⋊Dic31—42no—
55C22⋊Dic31—41no—
56C22⋊Dic31—42no—
57C22⋊Dic31—42no—
58C22⋊Dic31—41no—
59C4⋊Dic31—42no—
60C4⋊Dic31—42no—
61C4×Dic31—42no—
62C23×C31—21no—
63C23×C31—22no—
64C23×C31—22no—
65C23×C31—22no—
66C23×C31—22no—
67C23×C31—22no—
68C23×C31—22no—
69C23×C31—22no—
70C23×C31—21no—
71C23×C31—22no—
72C23×C31C22×C414yes—
73C23×C31C22×C412yes—
74C23×C31C2411yescharacteristic
75D4×C31—44no—
76D4×C31—48no—
77C2×C4×C31—22no—
78C2×C4×C31—22no—
79C2×C4×C31—22no—
80C2×C4×C31—22no—
81C2×C4×C31—44no—
82C2×C4×C31C22×C412yes—
83C2×C4×C31C22×C414yes—
84C2×C4×C31C22×C412yes—
85C2×Dic31—22no—
86C2×Dic31—22no—
87C2×Dic31—22no—
88C2×Dic31—22no—
89C2×Dic31—22no—
90C2×Dic31—22no—
91C2×Dic31—22no—
92C2×Dic31—22no—
93C2×Dic31—22no—
94C2×Dic31—22no—
95C2×Dic31—22no—
96C2×Dic31—22no—
97C2×Dic31—48no—
98#2377—311nomaximal, Sylow
99C22×C31—22no—
100C22×C31—22no—
101C22×C31—24no—
102C22×C31—24no—
103C22×C31—22no—
104C22×C31—24no—
105C22×C31—42no—
106C22×C31—42no—
107C22×C31—42no—
108C22×C31—42no—
109C22×C31—42no—
110C22×C31—42no—
111C22×C31C23×C411yescharacteristic
112C22×C31H(5,𝔽2)12yes—
113C22×C31H(5,𝔽2)12yes—
114C22×C31H(5,𝔽2)11yescharacteristic
115C22×C312−1+411yescharacteristic
116C4×C31—22no—
117C4×C31—22no—
118C4×C31—24no—
119Dic31—42no—
120Dic31—42no—
121Dic31—42no—
122Dic31—42no—
123C2×#121D3111yescharacteristic
124#390—312no—
125#388—312no—
126#387—312no—
127#386—312no—
128#386—312no—
129#385—312no—
130#381—311no—
131#380—311no—
132C2×C31—42no—
133C2×C31—44no—
134C2×C31#51811yescharacteristic
135C2×C31#51811yescharacteristic
136C2×C31#52011yescharacteristic
137C2×C31#56012yes—
138C2×C31#56212yes—
139C22×D4C2×D3111yescharacteristic
140C22×D4C2×D3112yes—
141C23×C4—312no—
142C23×C4C2×D3111yescharacteristic
143#121Dic3118yescomplemented
144C2×C4⋊C4—312no—
145C2×C4⋊C4—312no—
146C2×C4⋊C4C2×D3111yescharacteristic
147C2×C22⋊C4—311no—
148C2×C22⋊C4—311no—
149C2×C22⋊C4—312no—
150C2×C22⋊C4—312no—
151C2×C22⋊C4—312no—
152C2×C22⋊C4—312no—
153C2×C22⋊C4C2×D3112yes—
154C2×C42—312no—
155#95—312no—
156#95—311no—
157#95—312no—
158#95—311no—
159#95—312no—
160#95—312no—
161C31#237711yescharacteristic, complemented, Sylow
162C24C22×D3111yescharacteristic
163C24C22×D3112yes—
164C2×D4—42no—
165C2×D4—42no—
166C2×D4—42no—
167C2×D4C2×Dic3114yes—
168C2×D4C2×Dic3118yescomplemented
169C22×C4—42no—
170C22×C4—312no—
171C22×C4—312no—
172C22×C4—312no—
173C22×C4—312no—
174C22×C4—1242no—
175C22×C4—1242no—
176C22×C4—1242no—
177C22×C4C2×Dic3114yescomplemented
178C22×C4C22×D3111yescharacteristic
179C22×C4C22×D3112yes—
180C22×C4C22×D3111yescharacteristic
181C4⋊C4—1242no—
182C4⋊C4—1242no—
183C4⋊C4C2×Dic3114yescomplemented
184C22⋊C4—1242no—
185C22⋊C4—1242no—
186C22⋊C4—1242no—
187C22⋊C4—1241no—
188C22⋊C4—1242no—
189C22⋊C4—1241no—
190C22⋊C4C2×Dic3118yescomplemented
191C42—1242no—
192C23—22no—
193C23—22no—
194C23—22no—
195C23—22no—
196C23—22no—
197C23—22no—
198C23—21no—
199C23—22no—
200C23—21no—
201C23—22no—
202C23C22×Dic3114yes—
203C23C22×Dic3112yes—
204C23C23×D3111yescharacteristic
205D4—44no—
206D4—48no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—44no—
212C2×C4—622no—
213C2×C4—622no—
214C2×C4—622no—
215C2×C4—622no—
216C2×C4—622no—
217C2×C4—622no—
218C2×C4—622no—
219C2×C4—622no—
220C2×C4—622no—
221C2×C4—622no—
222C2×C4—622no—
223C2×C4—622no—
224C2×C4—1248no—
225C2×C4C22×Dic3112yes—
226C2×C4C22×Dic3114yes—
227C2×C4C22×Dic3112yes—
228C22—22no—
229C22—22no—
230C22—24no—
231C22—24no—
232C22—22no—
233C22—24no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22#1175856112yes—
241C22#1175856112yes—
242C22#1175856611yescharacteristic
243C22#1175856711yescharacteristic
244C22C23×Dic3111yescharacteristic
245C4—22no—
246C4—22no—
247C4—24no—
248C4—1242no—
249C4—1242no—
250C4—1242no—
251C4—1242no—
252C2—42no—
253C2—44no—
254C2#1452152411yescharacteristic
255C2#1452152411yescharacteristic
256C2#1452153211yescharacteristic
257C2#1452178712yes—
258C2#1452179412yes—
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
Fitting, prime radicalC2×C31×#121C2
socle, cosocleC23×C31C24
hypercenterC2×#121D31
hypocenterC31#2377
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. #14520924C2semidirect
7. #14520912C2semidirect
8. #14520909C2semidirect
14. C31×#121C4semidirect
38. C2×D4×C31C2×C4semidirect
40. C22×C4×C31C2×C4semidirect
51. C4⋊C4×C31C2×C4semidirect
52. C22⋊C4×C31C2×C4semidirect
143. #121Dic31semidirect
161. C31#2377semidirect
168. C2×D4C2×Dic31semidirect
177. C22×C4C2×Dic31semidirect
183. C4⋊C4C2×Dic31semidirect
190. 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
#145209242
#145209122
#145209092
C2×C31×#1212
#237731