Finite Group Databasebeta

← C2×#14521189 #16854900

Subgroups — C2×#14521189 #16854900

Order 3968.

792 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C22×Q8×D31C211yesmaximal, characteristic, complemented
2C22×#92470C211yesmaximal, characteristic, complemented
3C22×#92481C211yesmaximal, characteristic, complemented
4C2×#11758472C211yesmaximal, characteristic
5#14521189C218yesmaximal, direct product factor
6C2×#11758398C211yesmaximal, characteristic, complemented
7C2×(C2×D31)⋊C8C211yesmaximal, characteristic, complemented
8C2×C31×#103C211yesmaximal, characteristic, complemented
9C22×Q8×C31C2211yescharacteristic
10C2×Q8×D31—24no—
11C2×Q8×D31—22no—
12C2×Q8×D31—24no—
13C2×Q8×D31C2214yescomplemented
14C22×D124—21no—
15C22×D124C2211yescharacteristic
16C22×C4×D31—21no—
17C22×C4×D31C2211yescharacteristic
18C22×Dic62—21no—
19C22×Dic62C2211yescharacteristic
20C22×C8×C31C2211yescharacteristic
21C2×C4⋊C4×C31C2211yescharacteristic
22C2×#92481—24no—
23C2×#92481C2214yescomplemented
24C2×(C2×D31)⋊C4—21no—
25C22×C31⋊C8C2211yescharacteristic
26C2×#92470—24no—
27C2×#92470C2214yescomplemented
28#11758472—22no—
29#11758472C2214yes—
30C31×#103C2214yescomplemented
31(C2×D31)⋊C8C2214yescomplemented
32#11758398C2214yescomplemented
33C23×D31—21no—
34C23×D31D411yescharacteristic
35C2×Q8×C31—22no—
36C2×Q8×C31—21no—
37C2×Q8×C31D414yescomplemented
38C2×Q8×C31C2312yes—
39C22×C4×C31—21no—
40C22×C4×C31—21no—
41C22×C4×C31C2311yescharacteristic
42C22×Dic31—21no—
43C22×Dic31D411yescharacteristic
44Q8×D31—216no—
45Q8×D31—28no—
46Q8×D31—28no—
47C2×D124—22no—
48C2×D124—22no—
49C2×D124—24no—
50C2×D124—21no—
51C2×D124—44no—
52C2×D124C2312yes—
53C2×C4×D31—28no—
54C2×C4×D31—24no—
55C2×C4×D31—22no—
56C2×C4×D31—22no—
57C2×C4×D31D412yes—
58C2×C4×D31C2312yes—
59C2×Dic62—28no—
60C2×Dic62—21no—
61C2×Dic62—22no—
62C2×Dic62—24no—
63C2×Dic62D414yescomplemented
64C2×Dic62C2312yes—
65C2×C8×C31—22no—
66C2×C8×C31C2312yes—
67C4⋊C4×C31—21no—
68C4⋊C4×C31C2312yes—
69#92481—28no—
70(C2×D31)⋊C4—24no—
71C2×C31⋊C8—22no—
72C2×C31⋊C8C2312yes—
73#92470—28no—
74C23×C31C2×D411yescharacteristic
75C22×D31—22no—
76C22×D31—22no—
77C22×D31—22no—
78C22×D31—42no—
79C22×D31—42no—
80C22×D31—42no—
81C22×D31SD1614yescomplemented
82C22×D31C2×D412yes—
83Q8×C31—24no—
84Q8×C31—22no—
85Q8×C31C2×D414yescomplemented
86C2×C4×C31—24no—
87C2×C4×C31—22no—
88C2×C4×C31—22no—
89C2×C4×C31—42no—
90C2×C4×C31C2×D412yes—
91C2×C4×C31C2×D411yescharacteristic
92C2×C4×C31C2×D412yes—
93C2×C4×C31C2411yescharacteristic
94C2×Dic31—22no—
95C2×Dic31—24no—
96C2×Dic31—22no—
97C2×Dic31C2×D412yes—
98D124—22no—
99D124—22no—
100D124—48no—
101D124—42no—
102C4×D31—216no—
103C4×D31—24no—
104C4×D31—22no—
105C4×D31—22no—
106Dic62—216no—
107Dic62—24no—
108Dic62—22no—
109Dic62C2×D414yescomplemented
110C8×C31—22no—
111C31⋊C8—22no—
112C2×#448—311nomaximal, Sylow
113C22×C31#12012yes—
114C22×C31C2×SD1612yes—
115C22×C31#13712yes—
116C22×C31C22×D411yescharacteristic
117C2×D31—22no—
118C2×D31—22no—
119C2×D31—28no—
120C2×D31—42no—
121C2×D31—42no—
122C2×D31—42no—
123C2×D31—84no—
124C2×D31C2×SD1614yescomplemented
125C4×C31—24no—
126C4×C31—42no—
127C4×C31#12012yes—
128C4×C31C22×D411yescharacteristic
129C4×C31C22×D411yescharacteristic
130Dic31—22no—
131Dic31—24no—
132C23×Q8—311no—
133C22×SD16—311no—
134C22×SD16—311no—
135C2×#121—311no—
136#448—318no—
137C2×#103—311no—
138C2×#103D3111yescharacteristic, complemented
139C2×C22⋊C8—311no—
140C2×C31#44814yescomplemented
141C2×C31C2×#12011yescharacteristic
142C2×C31C22×SD1611yescharacteristic
143C2×C31C2×#13711yescharacteristic
144D31—24no—
145D31—82no—
146C22×Q8—314no—
147C22×Q8—311no—
148C22×Q8—621no—
149C22×Q8—622no—
150C22×Q8—624no—
151C22×Q8—624no—
152C22×Q8C2×D3111yescharacteristic
153C22×D4—311no—
154C22×D4—621no—
155C23×C4—311no—
156C23×C4—621no—
157C2×SD16—314no—
158C2×SD16—314no—
159C2×SD16—624no—
160C2×SD16—624no—
161C22×C8—311no—
162C22×C8C2×D3111yescharacteristic
163#121—314no—
164#121—622no—
165C2×C4⋊C4C2×D3111yescharacteristic
166C2×C22⋊C4—621no—
167#103—314no—
168#103C2×D3114yescomplemented
169C22⋊C8—314no—
170C31C2×#44811yescharacteristic, complemented, Sylow
171C24—311no—
172C24—621no—
173C2×Q8—22no—
174C2×Q8—21no—
175C2×Q8—314no—
176C2×Q8—312no—
177C2×Q8—624no—
178C2×Q8—628no—
179C2×Q8—628no—
180C2×Q8—6216no—
181C2×Q8—628no—
182C2×Q8—622no—
183C2×Q8—621no—
184C2×Q8D12414yescomplemented
185C2×Q8C22×D3112yes—
186C2×D4—312no—
187C2×D4—624no—
188C2×D4—622no—
189C2×D4—622no—
190C2×D4—621no—
191C2×D4—1244no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—311no—
195C22×C4—312no—
196C22×C4—312no—
197C22×C4—624no—
198C22×C4—628no—
199C22×C4—621no—
200C22×C4—622no—
201C22×C4—622no—
202C22×C4C22×D3111yescharacteristic
203SD16—628no—
204SD16—628no—
205C2×C8—22no—
206C2×C8—312no—
207C2×C8—622no—
208C2×C8C22×D3112yes—
209C4⋊C4—21no—
210C4⋊C4C22×D3112yes—
211C22⋊C4—624no—
212C23—314no—
213C23—312no—
214C23—622no—
215C23—622no—
216C23—622no—
217C23—1242no—
218C23—1242no—
219C23—1242no—
220C23D4×D3111yescharacteristic
221Q8—24no—
222Q8—22no—
223Q8—314no—
224Q8—6216no—
225Q8—624no—
226Q8—622no—
227Q8C2×D12414yescomplemented
228D4—622no—
229D4—622no—
230D4—1248no—
231D4—1242no—
232C2×C4—24no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—42no—
236C2×C4—312no—
237C2×C4—6216no—
238C2×C4—622no—
239C2×C4—624no—
240C2×C4—622no—
241C2×C4—624no—
242C2×C4—622no—
243C2×C4—622no—
244C2×C4C2×D12412yes—
245C2×C4D4×D3111yescharacteristic
246C2×C4D4×D3112yes—
247C2×C4C23×D3111yescharacteristic
248C8—22no—
249C8—622no—
250C22—314no—
251C22—628no—
252C22—622no—
253C22—622no—
254C22—1242no—
255C22—1242no—
256C22—1242no—
257C22—2484no—
258C22#1175845912yes—
259C22SD16×D3112yes—
260C22#1175849512yes—
261C22C2×D4×D3111yescharacteristic
262C4—24no—
263C4—42no—
264C4—622no—
265C4—624no—
266C4#1175845912yes—
267C4C22×D12411yescharacteristic
268C4C2×D4×D3111yescharacteristic
269C2—624no—
270C2—2482no—
271C2#1452118914yesdirect product factor
272C2C2×#1175845911yescharacteristic
273C2C2×SD16×D3111yescharacteristic
274C2C2×#1175849511yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#103C2
socleC23×C31C2×D4
prime radicalC2×#11758472C2
hypercenterC2×#103D31
hypocenterC31C2×#448
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D31C2semidirect
2. C22×#92470C2semidirect
3. C22×#92481C2semidirect
5. #14521189C2direct (N × H)
6. C2×#11758398C2semidirect
7. C2×(C2×D31)⋊C8C2semidirect
8. C2×C31×#103C2semidirect
13. C2×Q8×D31C22semidirect
23. C2×#92481C22semidirect
27. C2×#92470C22semidirect
30. C31×#103C22semidirect
31. (C2×D31)⋊C8C22semidirect
32. #11758398C22semidirect
37. C2×Q8×C31D4semidirect
63. C2×Dic62D4semidirect
81. C22×D31SD16semidirect
85. Q8×C31C2×D4semidirect
109. Dic62C2×D4semidirect
124. C2×D31C2×SD16semidirect
138. C2×#103D31semidirect
140. C2×C31#448semidirect
168. #103C2×D31semidirect
170. C31C2×#448semidirect
184. C2×Q8D124semidirect
227. Q8C2×D124semidirect
271. C2#14521189direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D312
C22×#924702
C22×#924812
C2×#117584722
#145211892
C2×#117583982
C2×(C2×D31)⋊C82
C2×C31×#1032
C2×#44831