Finite Group Databasebeta

← #16848476

Subgroups — #16848476

Order 3968.

596 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 181 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×#11758507C211yesmaximal, characteristic
2#14520949C212yesmaximal, complemented
3#14520940C212yesmaximal, complemented
4#14520932C212yesmaximal, complemented
5#14520927C212yesmaximal, complemented
6#14520925C212yesmaximal, complemented
7#14520912C211yesmaximal, characteristic, complemented
8C4×(C2×D31)⋊C4C212yesmaximal, complemented
9C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
10C23×C4×C31C2211yescharacteristic
11C22×C22⋊D31C2212yes—
12C22×D124C2211yescharacteristic
13C22×C4×D31C2212yes—
14C2×C22⋊C4×C31C2212yes—
15C2×C42×C31C2211yescharacteristic
16C2×C42×C31C2211yescharacteristic
17C2×C22⋊Dic31C2211yescharacteristic
18C2×C22⋊Dic31C2211yescharacteristic
19#11758507C418yescomplemented
20C2×(C2×D31)⋊C4C2212yes—
21C2×(C2×D31)⋊C4C2212yes—
22C2×(C2×D31)⋊C4C2212yes—
23C2×(C2×D31)⋊C4C2212yes—
24C2×C4⋊Dic31C2211yescharacteristic
25C2×Dic31⋊C4C2212yes—
26C2×C4×Dic31C2212yes—
27C31×#95C2212yes—
28C31⋊#95C2212yes—
29C31⋊#95C2212yes—
30C31⋊#95C2212yes—
31C31⋊#95C2212yes—
32C24×C31C2311yescharacteristic
33C23×D31C2312yes—
34C22×C4×C31—41no—
35C22×C4×C31—41no—
36C22×C4×C31C2×C414yescomplemented
37C22×C4×C31C2312yes—
38C22×C4×C31C2311yescharacteristic
39C22×C4×C31C2311yescharacteristic
40C22×C4×C31C2312yes—
41C2×C22⋊D31—42no—
42C2×C22⋊D31—42no—
43C2×C22⋊D31C2×C418yescomplemented
44C22×Dic31C2312yes—
45C22×Dic31C2312yes—
46C22×Dic31C2312yes—
47C2×D124—41no—
48C2×D124—41no—
49C2×D124C2×C414yes—
50C2×C4×D31—24no—
51C2×C4×D31—42no—
52C2×C4×D31—42no—
53C22⋊C4×C31—24no—
54C42×C31—41no—
55C42×C31—41no—
56C22⋊Dic31—41no—
57C22⋊Dic31—41no—
58(C2×D31)⋊C4—24no—
59(C2×D31)⋊C4—42no—
60(C2×D31)⋊C4—42no—
61(C2×D31)⋊C4C2×C418yescomplemented
62C4⋊Dic31C2×C414yescomplemented
63Dic31⋊C4—42no—
64C4×Dic31—42no—
65C23×C31—22no—
66C23×C31—21no—
67C23×C31—21no—
68C23×C31—22no—
69C23×C31C22×C412yes—
70C23×C31C2411yescharacteristic
71C22×D31—22no—
72C22×D31—22no—
73C22×D31—22no—
74C22×D31—22no—
75C22×D31—22no—
76C22×D31—22no—
77C22×D31C22×C414yes—
78C2×C4×C31—22no—
79C2×C4×C31—22no—
80C2×C4×C31—21no—
81C2×C4×C31—21no—
82C2×C4×C31—21no—
83C2×C4×C31—21no—
84C2×C4×C31—22no—
85C2×C4×C31—22no—
86C2×C4×C31—22no—
87C2×C4×C31—44no—
88C2×C4×C31C22×C412yes—
89C2×C4×C31C22×C412yes—
90C2×C4×C31#4114yes—
91C22⋊D31—48no—
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×Dic31C22×C414yes—
101D124—44no—
102C4×D31—48no—
103#2333—311nomaximal, Sylow
104C22×C31—22no—
105C22×C31—22no—
106C22×C31—22no—
107C22×C31—42no—
108C22×C31—42no—
109C22×C31C23×C411yescharacteristic
110C22×C31C2×#4112yes—
111C22×C31H(5,𝔽2)11yescharacteristic
112C22×C31H(5,𝔽2)11yescharacteristic
113C22×C31H(5,𝔽2)12yes—
114C2×D31—24no—
115C2×D31—24no—
116C2×D31—24no—
117C2×D31—42no—
118C2×D31—42no—
119C2×D31—42no—
120C2×D31—42no—
121C4×C31—22no—
122C4×C31—22no—
123C4×C31—24no—
124C4×C31—42no—
125Dic31—24no—
126Dic31—42no—
127Dic31—42no—
128C2×#121—311no—
129#390—312no—
130#388—312no—
131#387—312no—
132#386—312no—
133#386—312no—
134#381—311no—
135C4×C22⋊C4—312no—
136C4×C22⋊C4D3111yescharacteristic, complemented
137C2×C31—42no—
138C2×C31C4×#4111yescharacteristic
139C2×C31#51811yescharacteristic
140C2×C31#51811yescharacteristic
141C2×C31#53812yes—
142C2×C31#54012yes—
143D31—44no—
144C22×D4—312no—
145C22×D4—311no—
146C23×C4—312no—
147C23×C4C2×D3111yescharacteristic
148#121—318no—
149C2×C4⋊C4—311no—
150C2×C4⋊C4—312no—
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—312no—
159C2×C42C2×D3111yescharacteristic
160C2×C42C2×D3111yescharacteristic
161#95—312no—
162#95—312no—
163#95—312no—
164#95—312no—
165#95C2×D3112yes—
166C31#233311yescharacteristic, complemented, Sylow
167C24—312no—
168C24C22×D3111yescharacteristic
169C2×D4—318no—
170C2×D4—314no—
171C2×D4—1241no—
172C2×D4—1241no—
173C2×D4—1242no—
174C2×D4—1242no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—312no—
178C22×C4—312no—
179C22×C4—312no—
180C22×C4—624no—
181C22×C4—1242no—
182C22×C4—1242no—
183C22×C4C4×D3114yescomplemented
184C22×C4C22×D3112yes—
185C22×C4C22×D3111yescharacteristic
186C22×C4C22×D3111yescharacteristic
187C22×C4C22×D3112yes—
188C4⋊C4—314no—
189C4⋊C4—1242no—
190C22⋊C4—24no—
191C22⋊C4—318no—
192C22⋊C4—624no—
193C22⋊C4—1242no—
194C22⋊C4—1242no—
195C22⋊C4—1241no—
196C22⋊C4—1241no—
197C42—41no—
198C42—41no—
199C42—1242no—
200C23—22no—
201C23—21no—
202C23—21no—
203C23—22no—
204C23—314no—
205C23—622no—
206C23—622no—
207C23—622no—
208C23—622no—
209C23—622no—
210C23—622no—
211C23C2×C4×D3112yes—
212C23C23×D3111yescharacteristic
213D4—1244no—
214D4—1248no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—44no—
225C2×C4—314no—
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×C4C2×C4×D3112yes—
236C2×C4C2×C4×D3112yes—
237C2×C4#9249514yes—
238C22—22no—
239C22—22no—
240C22—22no—
241C22—42no—
242C22—42no—
243C22—624no—
244C22—624no—
245C22—624no—
246C22—1242no—
247C22—1242no—
248C22—1242no—
249C22—1242no—
250C22C22×C4×D3111yescharacteristic
251C22C2×#9249512yes—
252C22#1175856111yescharacteristic
253C22#1175856111yescharacteristic
254C22#1175856612yes—
255C4—24no—
256C4—22no—
257C4—22no—
258C4—42no—
259C4—624no—
260C4—1242no—
261C4—1242no—
262C2—42no—
263C2—1244no—
264C2C4×#9249511yescharacteristic
265C2#1452152211yescharacteristic
266C2#1452152311yescharacteristic
267C2#1452163212yes—
268C2#1452165012yes—
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC4×C22⋊C4×C31C2
socle, cosocleC23×C31C24
prime radicalC2×#11758507C2
hypercenterC4×C22⋊C4D31
hypocenterC31#2333
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #14520949C2semidirect
3. #14520940C2semidirect
4. #14520932C2semidirect
5. #14520927C2semidirect
6. #14520925C2semidirect
7. #14520912C2semidirect
8. C4×(C2×D31)⋊C4C2semidirect
9. C4×C22⋊C4×C31C2semidirect
19. #11758507C4semidirect
36. C22×C4×C31C2×C4semidirect
43. C2×C22⋊D31C2×C4semidirect
61. (C2×D31)⋊C4C2×C4semidirect
62. C4⋊Dic31C2×C4semidirect
136. C4×C22⋊C4D31semidirect
166. C31#2333semidirect
183. C22×C4C4×D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117585072
#145209492
#145209402
#145209322
#145209272
#145209252
#145209122
C4×(C2×D31)⋊C42
C4×C22⋊C4×C312
#233331