Finite Group Databasebeta

← C2×#14521296 #16855300

Subgroups — C2×#14521296 #16855300

Order 3968.

544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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×#92470C211yesmaximal, characteristic, complemented
2C22×#92469C211yesmaximal, characteristic, complemented
3C2×#11758474C211yesmaximal, characteristic, complemented
4C2×#11758472C211yesmaximal, characteristic
5#14521296C218yesmaximal, direct product factor
6C2×#11758398C211yesmaximal, characteristic, complemented
7C2×#11758397C211yesmaximal, characteristic, complemented
8C2×C31×#107C211yesmaximal, characteristic, complemented
9C22×D124—21no—
10C22×D124C2211yescharacteristic
11C22×C4×D31C2211yescharacteristic
12C22×Dic62C2211yescharacteristic
13C22×C8×C31C2211yescharacteristic
14C2×C4⋊C4×C31C2211yescharacteristic
15C2×C4⋊C4×C31C2211yescharacteristic
16C2×(C2×D31)⋊C4—21no—
17C2×(C2×D31)⋊C4—21no—
18C2×C4⋊Dic31—21no—
19C22×C31⋊C8C2211yescharacteristic
20C2×#92470—24no—
21C2×#92470C2214yescomplemented
22C2×#92469—24no—
23C2×#92469C2214yescomplemented
24#11758474—22no—
25#11758474C2214yescomplemented
26#11758472—22no—
27#11758472C2214yes—
28C31×#107C2214yescomplemented
29#11758398C2214yescomplemented
30#11758397C2214yescomplemented
31C23×D31—21no—
32C23×D31D411yescharacteristic
33C22×C4×C31—21no—
34C22×C4×C31—21no—
35C22×C4×C31C2311yescharacteristic
36C22×Dic31—21no—
37C22×Dic31D411yescharacteristic
38C2×D124—22no—
39C2×D124—22no—
40C2×D124—24no—
41C2×D124—21no—
42C2×D124—44no—
43C2×D124C2312yes—
44C2×C4×D31—22no—
45C2×C4×D31—22no—
46C2×C4×D31D412yes—
47C2×C4×D31C2312yes—
48C2×Dic62—22no—
49C2×Dic62—22no—
50C2×Dic62—21no—
51C2×Dic62C2312yes—
52C2×C8×C31D414yescomplemented
53C2×C8×C31C2312yes—
54C4⋊C4×C31—21no—
55C4⋊C4×C31—21no—
56C4⋊C4×C31C2312yes—
57C4⋊C4×C31C2312yes—
58(C2×D31)⋊C4—24no—
59(C2×D31)⋊C4—24no—
60C4⋊Dic31—24no—
61C2×C31⋊C8—22no—
62C2×C31⋊C8C2312yes—
63#92470—28no—
64#92469—28no—
65C23×C31C2×D411yescharacteristic
66C22×D31—22no—
67C22×D31—22no—
68C22×D31—22no—
69C22×D31—22no—
70C22×D31—42no—
71C22×D31—42no—
72C22×D31—42no—
73C22×D31C2×D412yes—
74C2×C4×C31—22no—
75C2×C4×C31—22no—
76C2×C4×C31—42no—
77C2×C4×C31—42no—
78C2×C4×C31C2×D412yes—
79C2×C4×C31C2×D411yescharacteristic
80C2×C4×C31#4112yes—
81C2×C4×C31C2411yescharacteristic
82C2×Dic31—22no—
83C2×Dic31—22no—
84C2×Dic31—42no—
85C2×Dic31C2×D412yes—
86D124—22no—
87D124—22no—
88D124—48no—
89D124—42no—
90C4×D31—24no—
91C4×D31—22no—
92C4×D31—22no—
93Dic62—22no—
94Dic62—22no—
95Dic62—42no—
96C8×C31C2×D414yescomplemented
97C31⋊C8—22no—
98C2×#468—311nomaximal, Sylow
99C22×C31#12112yes—
100C22×C31AGL(1,ℤ/8)12yes—
101C22×C31#13712yes—
102C22×C31C22×D411yescharacteristic
103C2×D31—22no—
104C2×D31—22no—
105C2×D31—22no—
106C2×D31—44no—
107C2×D31—42no—
108C2×D31—42no—
109C2×D31—42no—
110C2×D31—84no—
111C4×C31—42no—
112C4×C31—42no—
113C4×C31#12112yes—
114C4×C31C22×D411yescharacteristic
115C4×C31C2×#4111yescharacteristic
116Dic31—22no—
117Dic31—42no—
118C22×SD16—311no—
119C22×M16—311no—
120C2×C22⋊Q8—311no—
121C2×#121—311no—
122#468—318no—
123C2×#107D3111yescharacteristic, complemented
124C2×#103—311no—
125C2×#102—311no—
126C2×C31#46814yescomplemented
127C2×C31C2×#12111yescharacteristic
128C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
129C2×C31C2×#13711yescharacteristic
130D31—42no—
131D31—82no—
132C22×Q8—311no—
133C22×D4—311no—
134C22×D4—621no—
135C23×C4—311no—
136C2×SD16—314no—
137C2×SD16—624no—
138C2×M16—314no—
139C2×M16—624no—
140C22×C8—311no—
141C22×C8C2×D3111yescharacteristic
142C22⋊Q8—314no—
143C22⋊Q8—622no—
144#121—314no—
145#121—622no—
146C2×C4⋊C4—621no—
147C2×C4⋊C4C2×D3111yescharacteristic
148C2×C4⋊C4C2×D3111yescharacteristic
149C2×C22⋊C4—621no—
150C2×C22⋊C4—621no—
151#107C2×D3114yescomplemented
152#103—314no—
153#102—314no—
154C31C2×#46811yescharacteristic, complemented, Sylow
155C24—311no—
156C24—621no—
157C2×Q8—312no—
158C2×Q8—621no—
159C2×Q8—622no—
160C2×Q8—622no—
161C2×D4—312no—
162C2×D4—624no—
163C2×D4—622no—
164C2×D4—621no—
165C2×D4—622no—
166C2×D4—1244no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—311no—
170C22×C4—312no—
171C22×C4—312no—
172C22×C4—622no—
173C22×C4—622no—
174C22×C4—621no—
175C22×C4C22×D3111yescharacteristic
176SD16—628no—
177M16—628no—
178C2×C8—312no—
179C2×C8—622no—
180C2×C8D12414yescomplemented
181C2×C8C22×D3112yes—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—624no—
185C4⋊C4C22×D3112yes—
186C4⋊C4C22×D3112yes—
187C22⋊C4—624no—
188C22⋊C4—624no—
189C23—312no—
190C23—622no—
191C23—622no—
192C23—622no—
193C23—622no—
194C23—1242no—
195C23—1242no—
196C23—1242no—
197C23D4×D3111yescharacteristic
198Q8—622no—
199Q8—622no—
200Q8—1242no—
201D4—622no—
202D4—622no—
203D4—1248no—
204D4—1242no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—312no—
210C2×C4—622no—
211C2×C4—624no—
212C2×C4—622no—
213C2×C4—622no—
214C2×C4—622no—
215C2×C4—1242no—
216C2×C4C2×D12412yes—
217C2×C4D4×D3111yescharacteristic
218C2×C4#9249912yes—
219C2×C4C23×D3111yescharacteristic
220C8—622no—
221C8C2×D12414yescomplemented
222C22—622no—
223C22—622no—
224C22—622no—
225C22—1244no—
226C22—1242no—
227C22—1242no—
228C22—1242no—
229C22—2484no—
230C22#1175847212yes—
231C22#1175848812yes—
232C22#1175849512yes—
233C22C2×D4×D3111yescharacteristic
234C4—42no—
235C4—42no—
236C4—622no—
237C4—1242no—
238C4#1175847212yes—
239C4C22×D12411yescharacteristic
240C4C2×#9249911yescharacteristic
241C2—1242no—
242C2—2482no—
243C2#1452129614yesdirect product factor
244C2C2×#1175847211yescharacteristic
245C2C2×#1175848811yescharacteristic
246C2C2×#1175849511yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#107C2
socleC23×C31C2×D4
prime radicalC2×#11758472C2
hypercenterC2×#107D31
hypocenterC31C2×#468
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C22×#92470C2semidirect
2. C22×#92469C2semidirect
3. C2×#11758474C2semidirect
5. #14521296C2direct (N × H)
6. C2×#11758398C2semidirect
7. C2×#11758397C2semidirect
8. C2×C31×#107C2semidirect
21. C2×#92470C22semidirect
23. C2×#92469C22semidirect
25. #11758474C22semidirect
28. C31×#107C22semidirect
29. #11758398C22semidirect
30. #11758397C22semidirect
52. C2×C8×C31D4semidirect
96. C8×C31C2×D4semidirect
123. C2×#107D31semidirect
126. C2×C31#468semidirect
151. #107C2×D31semidirect
154. C31C2×#468semidirect
180. C2×C8D124semidirect
221. C8C2×D124semidirect
243. C2#14521296direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#924702
C22×#924692
C2×#117584742
C2×#117584722
#145212962
C2×#117583982
C2×#117583972
C2×C31×#1072
C2×#46831