Finite Group Databasebeta

← C2×#14521275 #16855268

Subgroups — C2×#14521275 #16855268

Order 3968.

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

normal subgroups only

This group has 564 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×C8×D31C211yesmaximal, characteristic, complemented
2C2×#11758523C211yesmaximal, characteristic, complemented
3C2×#11758515C211yesmaximal, characteristic
4#14521275C218yesmaximal, direct product factor
5C2×#11758405C211yesmaximal, characteristic, complemented
6C2×#11758423C211yesmaximal, characteristic, complemented
7C2×#11758420C211yesmaximal, characteristic, complemented
8C22×SD16×C31C211yesmaximal, characteristic, complemented
9C22×Q8×C31C2211yescharacteristic
10C22×D4×C31C2211yescharacteristic
11C22×C22⋊D31—21no—
12C22×C4×D31C2211yescharacteristic
13C2×SD16×C31—24no—
14C2×SD16×C31C2214yescomplemented
15C22×C8×C31C2211yescharacteristic
16C2×C22⋊Dic31—21no—
17#11758523—22no—
18#11758523C2214yescomplemented
19#11758515—22no—
20#11758515C2214yes—
21C2×(C2×D31)⋊C4—21no—
22C2×C4⋊Dic31C2211yescharacteristic
23C2×C4⋊Dic31C2211yescharacteristic
24C2×Dic31⋊C4—21no—
25C22×C31⋊C8C2211yescharacteristic
26C2×C8×D31—24no—
27C2×C8×D31C2214yescomplemented
28#11758423C2214yescomplemented
29#11758420C2214yescomplemented
30#11758405C2214yescomplemented
31C24×C31—21no—
32C23×D31D411yescharacteristic
33C2×Q8×C31—21no—
34C2×Q8×C31—22no—
35C2×Q8×C31—22no—
36C2×Q8×C31C2312yes—
37C2×D4×C31—22no—
38C2×D4×C31—21no—
39C2×D4×C31—22no—
40C2×D4×C31C2312yes—
41C22×C4×C31—21no—
42C22×C4×C31C2311yescharacteristic
43C2×C22⋊D31—24no—
44C2×C22⋊D31—44no—
45C22×Dic31—21no—
46C22×Dic31—21no—
47C22×Dic31D411yescharacteristic
48C2×C4×D31—22no—
49C2×C4×D31—22no—
50C2×C4×D31D412yes—
51C2×C4×D31C2312yes—
52SD16×C31—28no—
53C2×C8×C31D414yescomplemented
54C2×C8×C31C2312yes—
55C22⋊Dic31—24no—
56(C2×D31)⋊C4—24no—
57C4⋊Dic31—21no—
58C4⋊Dic31—21no—
59C4⋊Dic31C2312yes—
60C4⋊Dic31C2312yes—
61Dic31⋊C4—24no—
62C2×C31⋊C8—22no—
63C2×C31⋊C8C2312yes—
64C8×D31—28no—
65C23×C31—22no—
66C23×C31—42no—
67C23×C31—42no—
68C23×C31—42no—
69C23×C31C2×D411yescharacteristic
70C22×D31—22no—
71C22×D31—22no—
72C22×D31SD1614yescomplemented
73C22×D31C2×D412yes—
74Q8×C31—22no—
75Q8×C31—22no—
76Q8×C31—42no—
77D4×C31—22no—
78D4×C31—22no—
79D4×C31—42no—
80C2×C4×C31—22no—
81C2×C4×C31—42no—
82C2×C4×C31C2×D411yescharacteristic
83C2×C4×C31C2×D412yes—
84C2×C4×C31#4112yes—
85C2×C4×C31C2411yescharacteristic
86C22⋊D31—48no—
87C2×Dic31—22no—
88C2×Dic31—22no—
89C2×Dic31—22no—
90C2×Dic31—42no—
91C2×Dic31—42no—
92C2×Dic31C2×D412yes—
93C4×D31—24no—
94C4×D31—22no—
95C4×D31—22no—
96C8×C31C2×D414yescomplemented
97C31⋊C8—22no—
98C2×#465—311nomaximal, Sylow
99C22×C31—42no—
100C22×C31—42no—
101C22×C31—42no—
102C22×C31—84no—
103C22×C31#12112yes—
104C22×C31C2×SD1612yes—
105C22×C31#13512yes—
106C22×C31C22×D411yescharacteristic
107C2×D31—22no—
108C2×D31—22no—
109C2×D31—28no—
110C2×D31C2×SD1614yescomplemented
111C4×C31—42no—
112C4×C31#12112yes—
113C4×C31C22×D411yescharacteristic
114C4×C31C2×#4111yescharacteristic
115Dic31—22no—
116Dic31—42no—
117Dic31—42no—
118C22×SD16D3111yescharacteristic, complemented
119C23×C8—311no—
120C2×C22⋊Q8—311no—
121C2×#121—311no—
122#465—318no—
123C2×#106—311no—
124C2×#103—311no—
125C2×#102—311no—
126C2×C31—82no—
127C2×C31#46514yescomplemented
128C2×C31C2×#12111yescharacteristic
129C2×C31C22×SD1611yescharacteristic
130C2×C31C2×#13511yescharacteristic
131D31—24no—
132C22×Q8C2×D3111yescharacteristic
133C22×D4—621no—
134C22×D4C2×D3111yescharacteristic
135C23×C4—311no—
136C2×SD16—24no—
137C2×SD16C2×D3114yescomplemented
138C22×C8—311no—
139C22×C8—314no—
140C22×C8—624no—
141C22×C8C2×D3111yescharacteristic
142C22⋊Q8—314no—
143C22⋊Q8—622no—
144#121—314no—
145#121—622no—
146C2×C4⋊C4—311no—
147C2×C4⋊C4—311no—
148C2×C4⋊C4—621no—
149C2×C22⋊C4—621no—
150C2×C22⋊C4—621no—
151#106—314no—
152#103—314no—
153#102—314no—
154C31C2×#46511yescharacteristic, complemented, Sylow
155C24—21no—
156C24—311no—
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D3112yes—
161C2×D4—21no—
162C2×D4—22no—
163C2×D4—22no—
164C2×D4—624no—
165C2×D4—1244no—
166C2×D4C22×D3112yes—
167C22×C4—21no—
168C22×C4—311no—
169C22×C4—312no—
170C22×C4—312no—
171C22×C4—622no—
172C22×C4—622no—
173C22×C4—621no—
174C22×C4—621no—
175C22×C4C22×D3111yescharacteristic
176SD16—28no—
177C2×C8—312no—
178C2×C8—622no—
179C2×C8—628no—
180C2×C8C22⋊D3114yescomplemented
181C2×C8C22×D3112yes—
182C4⋊C4—312no—
183C4⋊C4—312no—
184C4⋊C4—624no—
185C4⋊C4—621no—
186C4⋊C4—621no—
187C22⋊C4—624no—
188C22⋊C4—624no—
189C23—22no—
190C23—42no—
191C23—42no—
192C23—42no—
193C23—314no—
194C23—312no—
195C23—622no—
196C23—622no—
197C23D4×D3111yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—22no—
202D4—22no—
203D4—42no—
204D4—1248no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—312no—
208C2×C4—622no—
209C2×C4—624no—
210C2×C4—622no—
211C2×C4—622no—
212C2×C4—622no—
213C2×C4—622no—
214C2×C4—1242no—
215C2×C4—1242no—
216C2×C4D4×D3111yescharacteristic
217C2×C4#9249712yes—
218C2×C4C2×C22⋊D3112yes—
219C2×C4C23×D3111yescharacteristic
220C8—622no—
221C8C2×C22⋊D3114yescomplemented
222C22—42no—
223C22—42no—
224C22—42no—
225C22—84no—
226C22—314no—
227C22—628no—
228C22—622no—
229C22—622no—
230C22SD16×D3112yes—
231C22#1175849312yes—
232C22#1175851512yes—
233C22C2×D4×D3111yescharacteristic
234C4—42no—
235C4—622no—
236C4—1242no—
237C4—1242no—
238C4#1175851512yes—
239C4C2×#9249711yescharacteristic
240C4C22×C22⋊D3111yescharacteristic
241C2—82no—
242C2—624no—
243C2#1452127514yesdirect product factor
244C2C2×#1175851511yescharacteristic
245C2C2×SD16×D3111yescharacteristic
246C2C2×#1175849311yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC22×SD16×C31C2
socleC23×C31C2×D4
prime radicalC2×#11758515C2
hypercenterC22×SD16D31
hypocenterC31C2×#465
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×C8×D31C2semidirect
2. C2×#11758523C2semidirect
4. #14521275C2direct (N × H)
5. C2×#11758405C2semidirect
6. C2×#11758423C2semidirect
7. C2×#11758420C2semidirect
8. C22×SD16×C31C2semidirect
14. C2×SD16×C31C22semidirect
18. #11758523C22semidirect
27. C2×C8×D31C22semidirect
28. #11758423C22semidirect
29. #11758420C22semidirect
30. #11758405C22semidirect
53. C2×C8×C31D4semidirect
72. C22×D31SD16semidirect
96. C8×C31C2×D4semidirect
110. C2×D31C2×SD16semidirect
118. C22×SD16D31semidirect
127. C2×C31#465semidirect
137. C2×SD16C2×D31semidirect
154. C31C2×#465semidirect
180. C2×C8C22⋊D31semidirect
221. C8C2×C22⋊D31semidirect
243. C2#14521275direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C8×D312
C2×#117585232
C2×#117585152
#145212752
C2×#117584052
C2×#117584232
C2×#117584202
C22×SD16×C312
C2×#46531