Finite Group Databasebeta

← C2×#14521243 #16855122

Subgroups — C2×#14521243 #16855122

Order 3968.

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

normal subgroups only

This group has 648 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×D248C211yesmaximal, characteristic, complemented
2C22×#92479C211yesmaximal, characteristic, complemented
3C2×#11758517C211yesmaximal, characteristic, complemented
4C2×#11758470C211yesmaximal, characteristic, complemented
5#14521243C218yesmaximal, direct product factor
6C2×Dic31⋊C8C211yesmaximal, characteristic, complemented
7C2×#11758397C211yesmaximal, characteristic, complemented
8C2×C31×#102C211yesmaximal, characteristic, complemented
9C22×D4×C31C2211yescharacteristic
10C22×C22⋊D31—21no—
11C22×C22⋊D31—21no—
12C22×D124C2211yescharacteristic
13C22×D124C2211yescharacteristic
14C22×C4×D31—21no—
15C22×C8×C31C2211yescharacteristic
16C2×C4⋊C4×C31C2211yescharacteristic
17#11758517—22no—
18#11758517C2214yescomplemented
19C2×#92479—24no—
20C2×#92479C2214yescomplemented
21C2×(C2×D31)⋊C4—21no—
22C2×C4×Dic31C2211yescharacteristic
23C22×C31⋊C8C2211yescharacteristic
24C2×D248—24no—
25C2×D248C2214yescomplemented
26#11758470—22no—
27#11758470C2214yescomplemented
28C31×#102C2214yescomplemented
29Dic31⋊C8C2214yescomplemented
30#11758397C2214yescomplemented
31C24×C31—21no—
32C23×D31—21no—
33C23×D31—21no—
34C2×D4×C31—22no—
35C2×D4×C31—21no—
36C2×D4×C31—22no—
37C2×D4×C31C2312yes—
38C22×C4×C31—21no—
39C22×C4×C31C2311yescharacteristic
40C2×C22⋊D31—24no—
41C2×C22⋊D31—24no—
42C2×C22⋊D31—44no—
43C2×C22⋊D31—44no—
44C22×Dic31D411yescharacteristic
45C22×Dic31D411yescharacteristic
46C2×D124—21no—
47C2×D124—22no—
48C2×D124—22no—
49C2×D124—22no—
50C2×D124—21no—
51C2×D124D414yescomplemented
52C2×D124C2312yes—
53C2×D124C2312yes—
54C2×C4×D31—24no—
55C2×C4×D31—44no—
56C2×C8×C31—22no—
57C2×C8×C31C2312yes—
58C4⋊C4×C31—21no—
59C4⋊C4×C31C2312yes—
60#92479—28no—
61(C2×D31)⋊C4—24no—
62C4×Dic31D412yes—
63C4×Dic31C2312yes—
64C2×C31⋊C8—22no—
65C2×C31⋊C8C2312yes—
66D248—28no—
67C23×C31—22no—
68C23×C31—42no—
69C23×C31—42no—
70C23×C31—42no—
71C23×C31C2×D411yescharacteristic
72C22×D31—24no—
73C22×D31—22no—
74C22×D31—22no—
75C22×D31—42no—
76C22×D31—42no—
77C22×D31—42no—
78C22×D31—42no—
79C22×D31—42no—
80D4×C31—22no—
81D4×C31—22no—
82D4×C31—42no—
83C2×C4×C31—22no—
84C2×C4×C31—42no—
85C2×C4×C31C2×D411yescharacteristic
86C2×C4×C31C2×D412yes—
87C2×C4×C31#4112yes—
88C2×C4×C31C2411yescharacteristic
89C22⋊D31—48no—
90C22⋊D31—48no—
91C2×Dic31—22no—
92C2×Dic31D814yescomplemented
93C2×Dic31C2×D412yes—
94C2×Dic31C2×D412yes—
95D124—24no—
96D124—22no—
97D124—22no—
98D124—22no—
99D124—42no—
100D124C2×D414yescomplemented
101C4×D31—48no—
102C8×C31—22no—
103C31⋊C8—22no—
104C2×#459—311nomaximal, Sylow
105C22×C31—42no—
106C22×C31—42no—
107C22×C31—42no—
108C22×C31—84no—
109C22×C31#12112yes—
110C22×C31C2×D812yes—
111C22×C31AGL(1,ℤ/8)12yes—
112C22×C31C22×D411yescharacteristic
113C2×D31—24no—
114C2×D31—42no—
115C2×D31—42no—
116C2×D31—48no—
117C2×D31—42no—
118C2×D31—42no—
119C2×D31—42no—
120C2×D31—84no—
121C4×C31—42no—
122C4×C31#12112yes—
123C4×C31C22×D411yescharacteristic
124C4×C31C2×#4111yescharacteristic
125Dic31—22no—
126Dic31C2×D814yescomplemented
127C22×D8—311no—
128C22×D8—311no—
129C2×#127—311no—
130C2×C4×D4—311no—
131#459—318no—
132C2×C4⋊C8—311no—
133C2×#102—311no—
134C2×#102D3111yescharacteristic, complemented
135C2×C31—82no—
136C2×C31#45914yescomplemented
137C2×C31C2×#12111yescharacteristic
138C2×C31C22×D811yescharacteristic
139C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
140D31—44no—
141D31—82no—
142C22×D4—311no—
143C22×D4—311no—
144C22×D4—621no—
145C22×D4—621no—
146C22×D4C2×D3111yescharacteristic
147C23×C4—621no—
148C2×D8—314no—
149C2×D8—314no—
150C2×D8—624no—
151C2×D8—624no—
152C22×C8—311no—
153C22×C8C2×D3111yescharacteristic
154#127—314no—
155#127—622no—
156C4×D4—314no—
157C4×D4—622no—
158C2×C4⋊C4C2×D3111yescharacteristic
159C2×C22⋊C4—621no—
160C2×C42—311no—
161C4⋊C8—314no—
162#102—314no—
163#102C2×D3114yescomplemented
164C31C2×#45911yescharacteristic, complemented, Sylow
165C24—21no—
166C24—621no—
167C24—621no—
168C2×D4—22no—
169C2×D4—22no—
170C2×D4—21no—
171C2×D4—314no—
172C2×D4—312no—
173C2×D4—312no—
174C2×D4—624no—
175C2×D4—624no—
176C2×D4—622no—
177C2×D4—622no—
178C2×D4—621no—
179C2×D4—622no—
180C2×D4—621no—
181C2×D4—1244no—
182C2×D4—1244no—
183C2×D4C22×D3112yes—
184C22×C4—21no—
185C22×C4—311no—
186C22×C4—311no—
187C22×C4—624no—
188C22×C4—1244no—
189C22×C4C22×D3111yescharacteristic
190D8—628no—
191D8—628no—
192C2×C8—22no—
193C2×C8—312no—
194C2×C8—622no—
195C2×C8C22×D3112yes—
196C4⋊C4—21no—
197C4⋊C4C22×D3112yes—
198C22⋊C4—624no—
199C42—312no—
200C42—312no—
201C23—22no—
202C23—42no—
203C23—42no—
204C23—42no—
205C23—624no—
206C23—622no—
207C23—622no—
208C23—1242no—
209C23—1242no—
210C23—1242no—
211C23—1242no—
212C23—1242no—
213C23D4×D3111yescharacteristic
214D4—22no—
215D4—22no—
216D4—42no—
217D4—314no—
218D4—624no—
219D4—622no—
220D4—622no—
221D4—622no—
222D4—1248no—
223D4—1248no—
224D4—1242no—
225C2×C4—22no—
226C2×C4—42no—
227C2×C4—314no—
228C2×C4—312no—
229C2×C4—312no—
230C2×C4—622no—
231C2×C4—1248no—
232C2×C4#9249512yes—
233C2×C4D4×D3111yescharacteristic
234C2×C4D4×D3112yes—
235C2×C4C23×D3111yescharacteristic
236C8—22no—
237C8—622no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—84no—
242C22—624no—
243C22—1248no—
244C22—1242no—
245C22—1242no—
246C22—1242no—
247C22—1242no—
248C22—1242no—
249C22—2484no—
250C22#1175846112yes—
251C22D8×D3112yes—
252C22#1175849112yes—
253C22C2×D4×D3111yescharacteristic
254C4—42no—
255C4—314no—
256C4—622no—
257C4#1175846112yes—
258C4C2×#9249511yescharacteristic
259C4C2×D4×D3111yescharacteristic
260C2—82no—
261C2—1244no—
262C2—2482no—
263C2#1452124314yesdirect product factor
264C2C2×#1175846111yescharacteristic
265C2C2×D8×D3111yescharacteristic
266C2C2×#1175849111yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#102C2
socleC23×C31C2×D4
hypercenterC2×#102D31
hypocenterC31C2×#459
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
1. C22×D248C2semidirect
2. C22×#92479C2semidirect
3. C2×#11758517C2semidirect
4. C2×#11758470C2semidirect
5. #14521243C2direct (N × H)
6. C2×Dic31⋊C8C2semidirect
7. C2×#11758397C2semidirect
8. C2×C31×#102C2semidirect
18. #11758517C22semidirect
20. C2×#92479C22semidirect
25. C2×D248C22semidirect
27. #11758470C22semidirect
28. C31×#102C22semidirect
29. Dic31⋊C8C22semidirect
30. #11758397C22semidirect
51. C2×D124D4semidirect
92. C2×Dic31D8semidirect
100. D124C2×D4semidirect
126. Dic31C2×D8semidirect
134. C2×#102D31semidirect
136. C2×C31#459semidirect
163. #102C2×D31semidirect
164. C31C2×#459semidirect
263. C2#14521243direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D2482
C22×#924792
C2×#117585172
C2×#117584702
#145212432
C2×Dic31⋊C82
C2×#117583972
C2×C31×#1022
C2×#45931