Finite Group Databasebeta

← C2×#23757533 #34109832

Subgroups — C2×#23757533 #34109832

Order 20096.

468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#19097802C211yesmaximal, characteristic, complemented
2C2×#19097797C211yesmaximal, characteristic
3C2×#19097777C211yesmaximal, characteristic, complemented
4#23757533C218yesmaximal, direct product factor
5C2×#19097707C211yesmaximal, characteristic, complemented
6C2×#19097690C211yesmaximal, characteristic, complemented
7C2×#19097688C211yesmaximal, characteristic, complemented
8C22×SD16×C157C211yesmaximal, characteristic, complemented
9C2×#14578954C2211yescharacteristic
10#19097802—22no—
11#19097802C2214yescomplemented
12#19097797—22no—
13#19097797C2214yes—
14C2×#14578944—21no—
15C2×#14578942—21no—
16C2×#14578941—21no—
17C2×#14578939—21no—
18#19097777—22no—
19#19097777C2214yescomplemented
20C2×#14578938C2211yescharacteristic
21C2×#14578938C2211yescharacteristic
22C2×#14578938C2211yescharacteristic
23C2×#14578937—21no—
24C2×C8×D157—21no—
25#19097707C2214yescomplemented
26#19097690C2214yescomplemented
27#19097688C2214yescomplemented
28C22×Q8×C157C2211yescharacteristic
29C22×D4×C157C2211yescharacteristic
30C2×SD16×C157—21no—
31C2×SD16×C157—21no—
32C2×SD16×C157—22no—
33C2×SD16×C157C2214yescomplemented
34C22×C8×C157C2211yescharacteristic
35#14578954—21no—
36#14578954—21no—
37#14578954D412yes—
38#14578954C2312yes—
39C2×Dic314D411yescharacteristic
40C2×D628D411yescharacteristic
41C2×C22⋊D157—21no—
42C2×C4×D157—21no—
43#14578944—24no—
44#14578942—24no—
45#14578941—24no—
46#14578939—24no—
47#14578938—21no—
48#14578938—21no—
49#14578938—21no—
50#14578938C2312yes—
51#14578938C2312yes—
52#14578938C2312yes—
53#14578937—24no—
54C2×#11929434—21no—
55C2×#11929434—21no—
56C2×#11929434—21no—
57C8×D157—24no—
58C24×C157—21no—
59C2×Q8×C157—21no—
60C2×Q8×C157—21no—
61C2×Q8×C157—21no—
62C2×Q8×C157—21no—
63C2×Q8×C157—21no—
64C2×Q8×C157C2312yes—
65C2×D4×C157—21no—
66C2×D4×C157—21no—
67C2×D4×C157—21no—
68C2×D4×C157—21no—
69C2×D4×C157—21no—
70C2×D4×C157C2312yes—
71C22×C4×C157—21no—
72C22×C4×C157C2311yescharacteristic
73SD16×C157—24no—
74SD16×C157—24no—
75C2×C8×C157D411yescharacteristic
76C2×C8×C157D411yescharacteristic
77C2×C8×C157D412yes—
78C2×C8×C157C2312yes—
79C22×D157—21no—
80Dic314—21no—
81Dic314C2×D412yes—
82D628—21no—
83D628C2×D412yes—
84C22⋊D157—22no—
85C22⋊D157—22no—
86C2×Dic157—21no—
87C4×D157—22no—
88C4×D157—22no—
89#11929434—22no—
90#11929434—22no—
91#11929434—22no—
92C23×C157—22no—
93C23×C157—41no—
94C23×C157—41no—
95C23×C157—82no—
96C23×C157#4111yescharacteristic
97Q8×C157—22no—
98Q8×C157—22no—
99Q8×C157—41no—
100Q8×C157—41no—
101D4×C157—22no—
102D4×C157—22no—
103D4×C157—41no—
104D4×C157—41no—
105C2×C4×C157—22no—
106C2×C4×C157—41no—
107C2×C4×C157—41no—
108C2×C4×C157C2×D411yescharacteristic
109C2×C4×C157C2×D411yescharacteristic
110C2×C4×C157C2×D411yescharacteristic
111C2×C4×C157C2×D411yescharacteristic
112C2×C4×C157#4111yescharacteristic
113C2×C4×C157C2411yescharacteristic
114C8×C157C2×D412yes—
115C8×C157C2×D412yes—
116C22×C157—22no—
117C22×C157—42no—
118C22×C157—82no—
119C22×C157—82no—
120C22×C157—82no—
121C22×C157#12111yescharacteristic
122C22×C157#12111yescharacteristic
123C22×C157C2×#4111yescharacteristic
124C2×D157—22no—
125C2×D157—42no—
126C4×C157—42no—
127C4×C157#12111yescharacteristic
128C4×C157#12111yescharacteristic
129C4×C157C22×D411yescharacteristic
130C4×C157C22×D411yescharacteristic
131Dic157—22no—
132C2×C157—21no—
133C2×C157—21no—
134C2×C157—82no—
135C2×C157#47112yescomplemented
136C2×C157C2×#12111yescharacteristic
137D157—42no—
138C157C2×#47111yescharacteristic, complemented, Sylow
139C2×#471—1571nomaximal, Sylow
140C2×#137—1571no—
141C2×AGL(1,ℤ/8)—1571no—
142C22×SD16D15711yescharacteristic, complemented
143C2×#131—1571no—
144#471—1578no—
145C2×#108—1571no—
146C2×#101—1571no—
147C2×#100—1571no—
148C2×#41—1571no—
149C22×Q8C2×D15711yescharacteristic
150C22×D4C2×D15711yescharacteristic
151#137—3142no—
152#137—1574no—
153AGL(1,ℤ/8)—3142no—
154AGL(1,ℤ/8)—1574no—
155C2×Q16—3141no—
156C2×SD16—21no—
157C2×SD16—21no—
158C2×SD16—22no—
159C2×SD16—3141no—
160C2×SD16—3141no—
161C2×SD16C2×D15714yescomplemented
162C2×D8—3141no—
163#131—3142no—
164#131—1574no—
165C2×M16—3141no—
166C2×M16—1571no—
167C2×M16—1571no—
168C2×M16—1571no—
169C22×C8—3141no—
170C22×C8C2×D15711yescharacteristic
171#108—1574no—
172#101—1574no—
173#100—1574no—
174C24—21no—
175#41—3141no—
176#41—3141no—
177#41—1572no—
178#41—1572no—
179C2×Q8—21no—
180C2×Q8—21no—
181C2×Q8—21no—
182C2×Q8—21no—
183C2×Q8—21no—
184C2×Q8—1571no—
185C2×Q8C22×D15712yes—
186C2×D4—21no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—21no—
190C2×D4—21no—
191C2×D4—3141no—
192C2×D4—1571no—
193C2×D4C22×D15712yes—
194C22×C4—21no—
195C22×C4—3141no—
196C22×C4C22×D15711yescharacteristic
197Q16—3144no—
198SD16—24no—
199SD16—24no—
200SD16—3144no—
201SD16—3144no—
202D8—3144no—
203M16—3141no—
204M16—3141no—
205M16—3141no—
206M16—3144no—
207M16—1572no—
208M16—1572no—
209M16—1572no—
210C2×C8—3141no—
211C2×C8—3141no—
212C2×C8—3141no—
213C2×C8—3144no—
214C2×C8C22⋊D15711yescharacteristic
215C2×C8C22⋊D15711yescharacteristic
216C2×C8C22⋊D15712yes—
217C2×C8C22×D15712yes—
218C23—22no—
219C23—41no—
220C23—41no—
221C23—82no—
222C23—3141no—
223C23#1457895311yescharacteristic
224Q8—22no—
225Q8—22no—
226Q8—41no—
227Q8—41no—
228Q8—3141no—
229Q8—1572no—
230D4—22no—
231D4—22no—
232D4—41no—
233D4—41no—
234D4—3142no—
235D4—3142no—
236D4—3141no—
237D4—1572no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—3141no—
242C2×C4—3142no—
243C2×C4—3142no—
244C2×C4D4×D15711yescharacteristic
245C2×C4D4×D15711yescharacteristic
246C2×C4C2×C22⋊D15711yescharacteristic
247C2×C4C2×C22⋊D15711yescharacteristic
248C2×C4#1457895311yescharacteristic
249C2×C4C23×D15711yescharacteristic
250C8—3142no—
251C8—3142no—
252C8—3142no—
253C8C2×C22⋊D15712yes—
254C8C2×C22⋊D15712yes—
255C22—22no—
256C22—42no—
257C22—82no—
258C22—82no—
259C22—82no—
260C22—3142no—
261C22—6282no—
262C22#1909774211yescharacteristic
263C22#1909774211yescharacteristic
264C22C2×#1457895311yescharacteristic
265C4—42no—
266C4—3142no—
267C4#1909774211yescharacteristic
268C4#1909774211yescharacteristic
269C4C2×D4×D15711yescharacteristic
270C4C22×C22⋊D15711yescharacteristic
271C2—21no—
272C2—21no—
273C2—82no—
274C2—6282no—
275C2#2375753312yesdirect product factor
276C2C2×#1909774211yescharacteristic
subgroupG/H
centerC22#19097742
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC22×SD16×C157C2
socleC22×C157#121
prime radicalC2×#19097797C2
hypercenterC22×SD16D157
hypocenterC157C2×#471
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#19097802C2semidirect
3. C2×#19097777C2semidirect
4. #23757533C2direct (N × H)
5. C2×#19097707C2semidirect
6. C2×#19097690C2semidirect
7. C2×#19097688C2semidirect
8. C22×SD16×C157C2semidirect
11. #19097802C22semidirect
19. #19097777C22semidirect
25. #19097707C22semidirect
26. #19097690C22semidirect
27. #19097688C22semidirect
33. C2×SD16×C157C22semidirect
135. C2×C157#471semidirect
138. C157C2×#471semidirect
142. C22×SD16D157semidirect
161. C2×SD16C2×D157semidirect
275. C2#23757533direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190978022
C2×#190977972
C2×#190977772
#237575332
C2×#190977072
C2×#190976902
C2×#190976882
C22×SD16×C1572
C2×#471157