Finite Group Databasebeta

← C2×#14521212 #16854921

Subgroups — C2×#14521212 #16854921

Order 3968.

760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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×#92497C211yesmaximal, characteristic
2C22×Dic124C211yesmaximal, characteristic, complemented
3C22×#92480C211yesmaximal, characteristic, complemented
4C2×#11758474C211yesmaximal, characteristic, complemented
5#14521212C218yesmaximal, direct product factor
6C2×#11758398C211yesmaximal, characteristic, complemented
7C2×(C2×D31)⋊C8C211yesmaximal, characteristic, complemented
8C2×C31×#102C211yesmaximal, characteristic, complemented
9C22×D4×C31C2211yescharacteristic
10C22×C22⋊D31—21no—
11C23×Dic31—21no—
12C2×#92497—24no—
13C2×#92497—22no—
14C2×#92497—24no—
15C2×#92497C2214yes—
16C22×C4×D31C2211yescharacteristic
17C22×Dic62C2211yescharacteristic
18C22×Dic62C2211yescharacteristic
19C22×C8×C31C2211yescharacteristic
20C2×C4⋊C4×C31C2211yescharacteristic
21C2×#92480—24no—
22C2×#92480C2214yescomplemented
23C2×(C2×D31)⋊C4—21no—
24C2×C4⋊Dic31—21no—
25C22×C31⋊C8C2211yescharacteristic
26C2×Dic124—24no—
27C2×Dic124C2214yescomplemented
28#11758474—22no—
29#11758474C2214yescomplemented
30C31×#102C2214yescomplemented
31(C2×D31)⋊C8C2214yescomplemented
32#11758398C2214yescomplemented
33C24×C31—21no—
34C23×D31D411yescharacteristic
35C2×D4×C31—21no—
36C2×D4×C31—22no—
37C2×D4×C31D414yes—
38C2×D4×C31C2312yes—
39C22×C4×C31—21no—
40C22×C4×C31C2311yescharacteristic
41C2×C22⋊D31—28no—
42C2×C22⋊D31—24no—
43C22×Dic31—28no—
44C22×Dic31—21no—
45C22×Dic31—24no—
46C22×Dic31—21no—
47C22×Dic31D411yescharacteristic
48#92497—216no—
49#92497—28no—
50#92497—28no—
51C2×C4×D31—22no—
52C2×C4×D31—22no—
53C2×C4×D31D412yes—
54C2×C4×D31C2312yes—
55C2×Dic62—21no—
56C2×Dic62—22no—
57C2×Dic62—22no—
58C2×Dic62—22no—
59C2×Dic62—21no—
60C2×Dic62D414yes—
61C2×Dic62C2312yes—
62C2×Dic62C2312yes—
63C2×C8×C31—22no—
64C2×C8×C31C2312yes—
65C4⋊C4×C31—21no—
66C4⋊C4×C31C2312yes—
67#92480—28no—
68(C2×D31)⋊C4—24no—
69C4⋊Dic31—24no—
70C2×C31⋊C8—22no—
71C2×C31⋊C8C2312yes—
72Dic124—28no—
73C23×C31—24no—
74C23×C31—22no—
75C23×C31—42no—
76C23×C31—42no—
77C23×C31C2×D411yescharacteristic
78C22×D31—22no—
79C22×D31—22no—
80C22×D31—22no—
81C22×D31C2×D412yes—
82D4×C31—24no—
83D4×C31—22no—
84D4×C31C2×D414yes—
85C2×C4×C31—22no—
86C2×C4×C31—42no—
87C2×C4×C31C2×D412yes—
88C2×C4×C31C2×D411yescharacteristic
89C2×C4×C31C2×D412yes—
90C2×C4×C31C2411yescharacteristic
91C22⋊D31—216no—
92C2×Dic31—216no—
93C2×Dic31—24no—
94C2×Dic31—22no—
95C2×Dic31—22no—
96C2×Dic31—22no—
97C2×Dic31—42no—
98C2×Dic31C2×D412yes—
99C4×D31—24no—
100C4×D31—22no—
101C4×D31—22no—
102Dic62—24no—
103Dic62—22no—
104Dic62—22no—
105Dic62—22no—
106Dic62—42no—
107Dic62C2×D414yes—
108C8×C31—22no—
109C31⋊C8—22no—
110C2×#452—311nomaximal, Sylow
111C22×C31—24no—
112C22×C31—42no—
113C22×C31—42no—
114C22×C31—48no—
115C22×C31#12012yes—
116C22×C31#13512yes—
117C22×C31#13712yes—
118C22×C31C22×D411yescharacteristic
119C2×D31—22no—
120C2×D31—22no—
121C2×D31—22no—
122C2×D31—44no—
123C4×C31—42no—
124C4×C31#12012yes—
125C4×C31C22×D411yescharacteristic
126C4×C31C22×D411yescharacteristic
127Dic31—24no—
128Dic31—22no—
129Dic31—42no—
130C22×#41—311no—
131C22×Q16—311no—
132C22×SD16—311no—
133C2×C22⋊Q8—311no—
134#452—318no—
135C2×#103—311no—
136C2×#102D3111yescharacteristic, complemented
137C2×C22⋊C8—311no—
138C2×C31—44no—
139C2×C31#45214yescomplemented
140C2×C31C2×#12011yescharacteristic
141C2×C31C2×#13511yescharacteristic
142C2×C31C2×#13711yescharacteristic
143D31—42no—
144C2×#41—314no—
145C2×#41—622no—
146C2×#41—624no—
147C2×#41—624no—
148C22×Q8—311no—
149C22×Q8—311no—
150C22×D4—621no—
151C22×D4C2×D3111yescharacteristic
152C23×C4—311no—
153C23×C4—621no—
154C2×Q16—314no—
155C2×Q16—624no—
156C2×SD16—314no—
157C2×SD16—624no—
158C22×C8—311no—
159C22×C8C2×D3111yescharacteristic
160C22⋊Q8—314no—
161C22⋊Q8—622no—
162C2×C4⋊C4—621no—
163C2×C4⋊C4C2×D3111yescharacteristic
164C2×C22⋊C4—621no—
165#103—314no—
166#102C2×D3114yescomplemented
167C22⋊C8—314no—
168C31C2×#45211yescharacteristic, complemented, Sylow
169C24—21no—
170C24—311no—
171#41—628no—
172#41—6216no—
173#41—628no—
174C2×Q8—314no—
175C2×Q8—312no—
176C2×Q8—312no—
177C2×Q8—622no—
178C2×Q8—621no—
179C2×Q8—621no—
180C2×Q8—622no—
181C2×Q8—622no—
182C2×D4—21no—
183C2×D4—22no—
184C2×D4—624no—
185C2×D4—628no—
186C2×D4D12414yes—
187C2×D4C22×D3112yes—
188C22×C4—21no—
189C22×C4—311no—
190C22×C4—312no—
191C22×C4—312no—
192C22×C4—624no—
193C22×C4—628no—
194C22×C4—621no—
195C22×C4—622no—
196C22×C4—622no—
197C22×C4—621no—
198C22×C4C22×D3111yescharacteristic
199Q16—628no—
200SD16—628no—
201C2×C8—22no—
202C2×C8—312no—
203C2×C8—622no—
204C2×C8C22×D3112yes—
205C4⋊C4—21no—
206C4⋊C4—624no—
207C4⋊C4C22×D3112yes—
208C22⋊C4—624no—
209C23—24no—
210C23—22no—
211C23—42no—
212C23—42no—
213C23—312no—
214C23—622no—
215C23—622no—
216C23—622no—
217C23D4×D3111yescharacteristic
218Q8—314no—
219Q8—624no—
220Q8—622no—
221Q8—622no—
222Q8—622no—
223Q8—1242no—
224D4—24no—
225D4—22no—
226D4—6216no—
227D4C2×D12414yes—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—312no—
231C2×C4—6216no—
232C2×C4—622no—
233C2×C4—624no—
234C2×C4—622no—
235C2×C4—624no—
236C2×C4—622no—
237C2×C4—622no—
238C2×C4—622no—
239C2×C4—1242no—
240C2×C4C2×D12412yes—
241C2×C4D4×D3111yescharacteristic
242C2×C4D4×D3112yes—
243C2×C4C23×D3111yescharacteristic
244C8—22no—
245C8—622no—
246C22—24no—
247C22—48no—
248C22—42no—
249C22—42no—
250C22—622no—
251C22—622no—
252C22—622no—
253C22—1244no—
254C22#1175845912yes—
255C22#1175848912yes—
256C22#1175849212yes—
257C22C2×D4×D3111yescharacteristic
258C4—42no—
259C4—622no—
260C4—624no—
261C4—1242no—
262C4#1175845912yes—
263C4C22×D12411yescharacteristic
264C4C2×D4×D3111yescharacteristic
265C2—44no—
266C2—1242no—
267C2#1452121214yesdirect product factor
268C2C2×#1175845911yescharacteristic
269C2C2×#1175848911yescharacteristic
270C2C2×#1175849211yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#102C2
socleC23×C31C2×D4
prime radicalC22×#92497C2
hypercenterC2×#102D31
hypocenterC31C2×#452
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C22×Dic124C2semidirect
3. C22×#92480C2semidirect
4. C2×#11758474C2semidirect
5. #14521212C2direct (N × H)
6. C2×#11758398C2semidirect
7. C2×(C2×D31)⋊C8C2semidirect
8. C2×C31×#102C2semidirect
22. C2×#92480C22semidirect
27. C2×Dic124C22semidirect
29. #11758474C22semidirect
30. C31×#102C22semidirect
31. (C2×D31)⋊C8C22semidirect
32. #11758398C22semidirect
136. C2×#102D31semidirect
139. C2×C31#452semidirect
166. #102C2×D31semidirect
168. C31C2×#452semidirect
267. C2#14521212direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#924972
C22×Dic1242
C22×#924802
C2×#117584742
#145212122
C2×#117583982
C2×(C2×D31)⋊C82
C2×C31×#1022
C2×#45231