Finite Group Databasebeta

← C2×#14521297 #16855301

Subgroups — C2×#14521297 #16855301

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×#92481C211yesmaximal, characteristic, complemented
2C22×#92474C211yesmaximal, characteristic, complemented
3C2×#11758507C211yesmaximal, characteristic
4#14521297C218yesmaximal, direct product factor
5C2×#11758395C211yesmaximal, characteristic, complemented
6C2×#11758423C211yesmaximal, characteristic, complemented
7C2×#11758397C211yesmaximal, characteristic, complemented
8C2×C31×C22⋊Q8C211yesmaximal, characteristic, complemented
9C22×Q8×C31C2211yescharacteristic
10C23×C4×C31C2211yescharacteristic
11C22×C22⋊D31—21no—
12C22×D124C2211yescharacteristic
13C31×C22⋊Q8—22no—
14C31×C22⋊Q8C2214yescomplemented
15C2×C4⋊C4×C31—21no—
16C2×C4⋊C4×C31C2211yescharacteristic
17C2×C22⋊C4×C31—21no—
18C2×#92481—24no—
19C2×#92481C2214yescomplemented
20#11758507—22no—
21#11758507C2214yes—
22C2×(C2×D31)⋊C4—21no—
23C2×C4⋊Dic31C2211yescharacteristic
24C2×#92474—24no—
25C2×#92474C2214yescomplemented
26C22×C31⋊C8C2211yescharacteristic
27C22×C31⋊C8C2211yescharacteristic
28#11758423C2214yescomplemented
29#11758397C2214yescomplemented
30#11758395C2214yescomplemented
31C24×C31D411yescharacteristic
32C23×D31—21no—
33C2×Q8×C31—21no—
34C2×Q8×C31—22no—
35C2×Q8×C31—22no—
36C2×Q8×C31C2312yes—
37C22×C4×C31—22no—
38C22×C4×C31—22no—
39C22×C4×C31—21no—
40C22×C4×C31—21no—
41C22×C4×C31D411yescharacteristic
42C22×C4×C31D412yes—
43C22×C4×C31C2312yes—
44C22×C4×C31C2311yescharacteristic
45C2×C22⋊D31—24no—
46C2×C22⋊D31—44no—
47C22×Dic31—21no—
48C2×D124—22no—
49C2×D124—22no—
50C2×D124—21no—
51C2×D124C2312yes—
52C4⋊C4×C31—24no—
53C4⋊C4×C31—21no—
54C4⋊C4×C31C2312yes—
55C22⋊C4×C31—24no—
56#92481—28no—
57(C2×D31)⋊C4—24no—
58C4⋊Dic31—21no—
59C4⋊Dic31C2312yes—
60#92474—28no—
61C2×C31⋊C8—22no—
62C2×C31⋊C8D414yescomplemented
63C2×C31⋊C8C2312yes—
64C2×C31⋊C8C2312yes—
65C23×C31—22no—
66C23×C31—22no—
67C23×C31—22no—
68C23×C31C2×D412yes—
69C23×C31C2×D411yescharacteristic
70C22×D31—22no—
71C22×D31—42no—
72C22×D31—42no—
73C22×D31—42no—
74Q8×C31—22no—
75Q8×C31—22no—
76Q8×C31—42no—
77C2×C4×C31—22no—
78C2×C4×C31—24no—
79C2×C4×C31—22no—
80C2×C4×C31—22no—
81C2×C4×C31—22no—
82C2×C4×C31—22no—
83C2×C4×C31—42no—
84C2×C4×C31—42no—
85C2×C4×C31C2×D412yes—
86C2×C4×C31C2×D412yes—
87C2×C4×C31C2×D411yescharacteristic
88C2×C4×C31#4112yes—
89C2×C4×C31C2411yescharacteristic
90C22⋊D31—48no—
91C2×Dic31—22no—
92C2×Dic31—42no—
93D124—22no—
94D124—22no—
95D124—42no—
96C31⋊C8—22no—
97C31⋊C8C2×D414yescomplemented
98C2×#468—311nomaximal, Sylow
99C22×C31—22no—
100C22×C31—22no—
101C22×C31—22no—
102C22×C31—44no—
103C22×C31#12112yes—
104C22×C31AGL(1,ℤ/8)12yes—
105C22×C31#13712yes—
106C22×C31C22×D411yescharacteristic
107C2×D31—42no—
108C2×D31—42no—
109C2×D31—42no—
110C2×D31—84no—
111C4×C31—22no—
112C4×C31—42no—
113C4×C31—42no—
114C4×C31#12112yes—
115C4×C31C22×D411yescharacteristic
116C4×C31C2×#4111yescharacteristic
117Dic31—42no—
118C22×SD16—311no—
119C22×M16—311no—
120C2×C22⋊Q8D3111yescharacteristic, complemented
121C2×#121—311no—
122#468—318no—
123C2×#107—311no—
124C2×#103—311no—
125C2×#102—311no—
126C2×C31—42no—
127C2×C31#46814yescomplemented
128C2×C31C2×#12111yescharacteristic
129C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
130C2×C31C2×#13711yescharacteristic
131D31—82no—
132C22×Q8C2×D3111yescharacteristic
133C22×D4—311no—
134C22×D4—621no—
135C23×C4C2×D3111yescharacteristic
136C2×SD16—314no—
137C2×SD16—624no—
138C2×M16—314no—
139C2×M16—624no—
140C22×C8—311no—
141C22×C8—311no—
142C22⋊Q8—22no—
143C22⋊Q8C2×D3114yescomplemented
144#121—314no—
145#121—622no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—311no—
148C2×C4⋊C4C2×D3111yescharacteristic
149C2×C22⋊C4—21no—
150C2×C22⋊C4—621no—
151#107—314no—
152#103—314no—
153#102—314no—
154C31C2×#46811yescharacteristic, complemented, Sylow
155C24—621no—
156C24C22⋊D3111yescharacteristic
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D3112yes—
161C2×D4—312no—
162C2×D4—624no—
163C2×D4—622no—
164C2×D4—622no—
165C2×D4—621no—
166C2×D4—1244no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—621no—
172C22×C4C22⋊D3112yes—
173C22×C4C22⋊D3111yescharacteristic
174C22×C4C22×D3112yes—
175C22×C4C22×D3111yescharacteristic
176SD16—628no—
177M16—628no—
178C2×C8—314no—
179C2×C8—312no—
180C2×C8—312no—
181C2×C8—622no—
182C4⋊C4—24no—
183C4⋊C4—21no—
184C4⋊C4—312no—
185C4⋊C4—621no—
186C4⋊C4C22×D3112yes—
187C22⋊C4—24no—
188C22⋊C4—624no—
189C23—22no—
190C23—22no—
191C23—22no—
192C23—622no—
193C23—1242no—
194C23—1242no—
195C23—1242no—
196C23C2×C22⋊D3112yes—
197C23C2×C22⋊D3111yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—622no—
202D4—622no—
203D4—1248no—
204D4—1242no—
205C2×C4—22no—
206C2×C4—24no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—622no—
214C2×C4—1242no—
215C2×C4D4×D3112yes—
216C2×C4#9249712yes—
217C2×C4C2×C22⋊D3112yes—
218C2×C4C2×C22⋊D3111yescharacteristic
219C2×C4C23×D3111yescharacteristic
220C8—314no—
221C8—622no—
222C22—22no—
223C22—22no—
224C22—22no—
225C22—44no—
226C22—1242no—
227C22—1242no—
228C22—1242no—
229C22—2484no—
230C22#1175851612yes—
231C22#1175851912yes—
232C22#1175852612yes—
233C22C22×C22⋊D3111yescharacteristic
234C4—22no—
235C4—42no—
236C4—42no—
237C4—1242no—
238C4#1175851612yes—
239C4C2×D4×D3111yescharacteristic
240C4C2×#9249711yescharacteristic
241C2—42no—
242C2—2482no—
243C2#1452129714yesdirect product factor
244C2C2×#1175851611yescharacteristic
245C2C2×#1175852611yescharacteristic
246C2C2×#1175851911yescharacteristic
subgroupG/H
centerC23C2×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×C22⋊Q8C2
socleC23×C31C2×D4
prime radicalC2×#11758507C2
hypercenterC2×C22⋊Q8D31
hypocenterC31C2×#468
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#92481C2semidirect
2. C22×#92474C2semidirect
4. #14521297C2direct (N × H)
5. C2×#11758395C2semidirect
6. C2×#11758423C2semidirect
7. C2×#11758397C2semidirect
8. C2×C31×C22⋊Q8C2semidirect
14. C31×C22⋊Q8C22semidirect
19. C2×#92481C22semidirect
25. C2×#92474C22semidirect
28. #11758423C22semidirect
29. #11758397C22semidirect
30. #11758395C22semidirect
62. C2×C31⋊C8D4semidirect
97. C31⋊C8C2×D4semidirect
120. C2×C22⋊Q8D31semidirect
127. C2×C31#468semidirect
143. C22⋊Q8C2×D31semidirect
154. C31C2×#468semidirect
243. C2#14521297direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#924812
C22×#924742
C2×#117585072
#145212972
C2×#117583952
C2×#117584232
C2×#117583972
C2×C31×C22⋊Q82
C2×#46831