Finite Group Databasebeta

← C2×#23757520 #34109725

Subgroups — C2×#23757520 #34109725

Order 20096.

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×#14578943C211yesmaximal, characteristic, complemented
2C22×#14578937C211yesmaximal, characteristic, complemented
3C2×#19097751C211yesmaximal, characteristic, complemented
4C2×#19097746C211yesmaximal, characteristic
5#23757520C218yesmaximal, direct product factor
6C2×#19097694C211yesmaximal, characteristic, complemented
7C2×#19097691C211yesmaximal, characteristic, complemented
8C2×#107×C157C211yesmaximal, characteristic, complemented
9C22×Dic314C2211yescharacteristic
10C22×D628—21no—
11C22×D628C2211yescharacteristic
12C22×C4×D157C2211yescharacteristic
13C2×#14578943—24no—
14C2×#14578943C2214yescomplemented
15C2×#14578937—24no—
16C2×#14578937C2214yescomplemented
17C22×#11929434C2211yescharacteristic
18#19097751—22no—
19#19097751C2214yescomplemented
20#19097746—22no—
21#19097746C2214yes—
22C2×C4⋊Dic157—21no—
23C2×#14578931—21no—
24C2×#14578931—21no—
25#19097694C2214yescomplemented
26#19097691C2214yescomplemented
27C22×C8×C157C2211yescharacteristic
28C2×C4⋊C4×C157C2211yescharacteristic
29C2×C4⋊C4×C157C2211yescharacteristic
30#107×C157C2214yescomplemented
31C23×D157—21no—
32C23×D157D411yescharacteristic
33C2×Dic314—21no—
34C2×Dic314—22no—
35C2×Dic314—22no—
36C2×Dic314C2312yes—
37C2×D628—24no—
38C2×D628—22no—
39C2×D628—21no—
40C2×D628—22no—
41C2×D628—44no—
42C2×D628C2312yes—
43C22×Dic157—21no—
44C22×Dic157D411yescharacteristic
45C2×C4×D157—22no—
46C2×C4×D157—22no—
47C2×C4×D157D412yes—
48C2×C4×D157C2312yes—
49#14578943—28no—
50#14578937—28no—
51C2×#11929434—22no—
52C2×#11929434C2312yes—
53C4⋊Dic157—24no—
54#14578931—24no—
55#14578931—24no—
56C22×C4×C157—21no—
57C22×C4×C157—21no—
58C22×C4×C157C2311yescharacteristic
59C2×C8×C157D414yescomplemented
60C2×C8×C157C2312yes—
61C4⋊C4×C157—21no—
62C4⋊C4×C157—21no—
63C4⋊C4×C157C2312yes—
64C4⋊C4×C157C2312yes—
65C22×D157—22no—
66C22×D157—22no—
67C22×D157—22no—
68C22×D157—22no—
69C22×D157—42no—
70C22×D157—42no—
71C22×D157—42no—
72C22×D157C2×D412yes—
73Dic314—22no—
74Dic314—22no—
75Dic314—42no—
76D628—22no—
77D628—22no—
78D628—48no—
79D628—42no—
80C2×Dic157—22no—
81C2×Dic157—22no—
82C2×Dic157—42no—
83C2×Dic157C2×D412yes—
84C4×D157—24no—
85C4×D157—22no—
86C4×D157—22no—
87#11929434—22no—
88C23×C157C2×D411yescharacteristic
89C2×C4×C157—22no—
90C2×C4×C157—22no—
91C2×C4×C157—42no—
92C2×C4×C157—42no—
93C2×C4×C157C2×D411yescharacteristic
94C2×C4×C157C2×D412yes—
95C2×C4×C157#4112yes—
96C2×C4×C157C2411yescharacteristic
97C8×C157C2×D414yescomplemented
98C22×C157#12112yes—
99C22×C157AGL(1,ℤ/8)12yes—
100C22×C157#13712yes—
101C22×C157C22×D411yescharacteristic
102C2×D157—22no—
103C2×D157—22no—
104C2×D157—22no—
105C2×D157—44no—
106C2×D157—42no—
107C2×D157—42no—
108C2×D157—42no—
109C2×D157—84no—
110C4×C157—42no—
111C4×C157—42no—
112C4×C157#12112yes—
113C4×C157C22×D411yescharacteristic
114C4×C157C2×#4111yescharacteristic
115Dic157—22no—
116Dic157—42no—
117C2×C157#46814yescomplemented
118C2×C157C2×#12111yescharacteristic
119C2×C157C2×AGL(1,ℤ/8)11yescharacteristic
120C2×C157C2×#13711yescharacteristic
121D157—42no—
122D157—82no—
123C157C2×#46811yescharacteristic, complemented, Sylow
124C2×#468—1571nomaximal, Sylow
125C22×SD16—1571no—
126C22×M16—1571no—
127C2×C22⋊Q8—1571no—
128C2×#121—1571no—
129#468—1578no—
130C2×#107D15711yescharacteristic, complemented
131C2×#103—1571no—
132C2×#102—1571no—
133C22×Q8—1571no—
134C22×D4—3141no—
135C22×D4—1571no—
136C23×C4—1571no—
137C2×SD16—3144no—
138C2×SD16—1574no—
139C2×M16—3144no—
140C2×M16—1574no—
141C22×C8—1571no—
142C22×C8C2×D15711yescharacteristic
143C22⋊Q8—3142no—
144C22⋊Q8—1574no—
145#121—3142no—
146#121—1574no—
147C2×C4⋊C4—3141no—
148C2×C4⋊C4C2×D15711yescharacteristic
149C2×C4⋊C4C2×D15711yescharacteristic
150C2×C22⋊C4—3141no—
151C2×C22⋊C4—3141no—
152#107C2×D15714yescomplemented
153#103—1574no—
154#102—1574no—
155C24—3141no—
156C24—1571no—
157C2×Q8—3141no—
158C2×Q8—3142no—
159C2×Q8—3142no—
160C2×Q8—1572no—
161C2×D4—3144no—
162C2×D4—3141no—
163C2×D4—3142no—
164C2×D4—3142no—
165C2×D4—6284no—
166C2×D4—1572no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—3142no—
170C22×C4—3142no—
171C22×C4—3141no—
172C22×C4—1571no—
173C22×C4—1572no—
174C22×C4—1572no—
175C22×C4C22×D15711yescharacteristic
176SD16—3148no—
177M16—3148no—
178C2×C8—3142no—
179C2×C8—1572no—
180C2×C8D62814yescomplemented
181C2×C8C22×D15712yes—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—3144no—
185C4⋊C4C22×D15712yes—
186C4⋊C4C22×D15712yes—
187C22⋊C4—3144no—
188C22⋊C4—3144no—
189C23—3142no—
190C23—3142no—
191C23—3142no—
192C23—3142no—
193C23—6282no—
194C23—6282no—
195C23—6282no—
196C23—1572no—
197C23D4×D15711yescharacteristic
198Q8—3142no—
199Q8—3142no—
200Q8—6282no—
201D4—3142no—
202D4—3142no—
203D4—6288no—
204D4—6282no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—3142no—
210C2×C4—3144no—
211C2×C4—3142no—
212C2×C4—3142no—
213C2×C4—3142no—
214C2×C4—6282no—
215C2×C4—1572no—
216C2×C4D4×D15711yescharacteristic
217C2×C4C2×D62812yes—
218C2×C4#1457895512yes—
219C2×C4C23×D15711yescharacteristic
220C8—3142no—
221C8C2×D62814yescomplemented
222C22—3142no—
223C22—3142no—
224C22—3142no—
225C22—6284no—
226C22—6282no—
227C22—6282no—
228C22—6282no—
229C22—12564no—
230C22#1909774612yes—
231C22#1909779512yes—
232C22#1909780312yes—
233C22C2×D4×D15711yescharacteristic
234C4—42no—
235C4—42no—
236C4—3142no—
237C4—6282no—
238C4#1909774612yes—
239C4C22×D62811yescharacteristic
240C4C2×#1457895511yescharacteristic
241C2—6282no—
242C2—12562no—
243C2#2375752014yesdirect product factor
244C2C2×#1909774611yescharacteristic
245C2C2×#1909779511yescharacteristic
246C2C2×#1909780311yescharacteristic
subgroupG/H
centerC23D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC2×#107×C157C2
socleC23×C157C2×D4
prime radicalC2×#19097746C2
hypercenterC2×#107D157
hypocenterC157C2×#468
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C22×#14578943C2semidirect
2. C22×#14578937C2semidirect
3. C2×#19097751C2semidirect
5. #23757520C2direct (N × H)
6. C2×#19097694C2semidirect
7. C2×#19097691C2semidirect
8. C2×#107×C157C2semidirect
14. C2×#14578943C22semidirect
16. C2×#14578937C22semidirect
19. #19097751C22semidirect
25. #19097694C22semidirect
26. #19097691C22semidirect
30. #107×C157C22semidirect
59. C2×C8×C157D4semidirect
97. C8×C157C2×D4semidirect
117. C2×C157#468semidirect
123. C157C2×#468semidirect
130. C2×#107D157semidirect
152. #107C2×D157semidirect
180. C2×C8D628semidirect
221. C8C2×D628semidirect
243. C2#23757520direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145789432
C22×#145789372
C2×#190977512
C2×#190977462
#237575202
C2×#190976942
C2×#190976912
C2×#107×C1572
C2×#468157