Finite Group Databasebeta

← #34109680

Subgroups — #34109680

Order 20096.

504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19097797C211yesmaximal, characteristic, complemented
2C2×#19097793C211yesmaximal, characteristic, complemented
3#23757840C211yesmaximal, characteristic, complemented
4#23757754C211yesmaximal, characteristic, complemented
5#23757494C212yesmaximal, complemented
6#23757487C212yesmaximal, complemented
7#23757472C212yesmaximal, complemented
8#23757467C212yesmaximal, complemented
9#23757299C211yesmaximal, characteristic, complemented
10#23757272C211yesmaximal, characteristic, complemented
11C2×#102×C157C211yesmaximal, characteristic, complemented
12C2×#14578954C2211yescharacteristic
13C2×#14578954C2211yescharacteristic
14#19097797—24no—
15#19097793—24no—
16C2×Dic628C2211yescharacteristic, complemented
17C2×#14578943C2211yescharacteristic, complemented
18C2×#14578943C2211yescharacteristic, complemented
19C2×#14578942C2212yes—
20C2×D1256C2211yescharacteristic, complemented
21C2×#14578939C2212yes—
22C2×#14578938C2211yescharacteristic
23#19097767C2212yes—
24#19097758C2212yes—
25#19097742—21no—
26#19097742—21no—
27#19097740—22no—
28#19097736C2212yescomplemented
29#19097733C2212yescomplemented
30C4×C22⋊D157—22no—
31#19097730C2211yescharacteristic
32#19097729—21no—
33C4⋊C4×D157—21no—
34#19097700C2212yescomplemented
35#19097700C2212yescomplemented
36#19097694C2212yescomplemented
37#19097691C2212yescomplemented
38C22×D4×C157C2211yescharacteristic
39C22×C8×C157C2211yescharacteristic
40C2×C4⋊C4×C157C2211yescharacteristic
41#102×C157C2212yes—
42#102×C157C2212yes—
43#14578954—22no—
44#14578954—22no—
45#14578954—22no—
46#14578954D414yescomplemented
47C2×Dic314C2311yescharacteristic
48C2×Dic314C2311yescharacteristic
49C2×D628C2311yescharacteristic
50C2×D628C2311yescharacteristic
51C2×C22⋊D157—22no—
52C2×C22⋊D157—22no—
53C2×C22⋊D157—21no—
54C2×C22⋊D157—21no—
55C2×C4×D157—22no—
56C2×C4×D157—21no—
57C2×C4×D157—21no—
58Dic628—22no—
59#14578943—22no—
60#14578943—22no—
61#14578942—24no—
62D1256—22no—
63#14578939—24no—
64#14578938—22no—
65C2×#11929434C2312yes—
66C4⋊Dic157D411yescharacteristic
67C4⋊Dic157D411yescharacteristic
68#14578933—22no—
69C22⋊Dic157—22no—
70C22⋊Dic157—22no—
71C22⋊Dic157D412yes—
72#14578931—22no—
73C4×Dic157—22no—
74C4×Dic157C2312yes—
75C24×C157—21no—
76C2×D4×C157—22no—
77C2×D4×C157—21no—
78C2×D4×C157—22no—
79C2×D4×C157C2312yes—
80C22×C4×C157—21no—
81C22×C4×C157C2311yescharacteristic
82C2×C8×C157—22no—
83C2×C8×C157C2311yescharacteristic
84C2×C8×C157C2311yescharacteristic
85C4⋊C4×C157—21no—
86C4⋊C4×C157C2312yes—
87C22×D157—21no—
88C22×D157—21no—
89Dic314—21no—
90Dic314—21no—
91Dic314—21no—
92Dic314C2×D412yes—
93D628—21no—
94D628—21no—
95D628—21no—
96D628C2×D412yes—
97C22⋊D157—24no—
98C22⋊D157—42no—
99C22⋊D157—82no—
100C22⋊D157—82no—
101C2×Dic157—21no—
102C2×Dic157—21no—
103C2×Dic157C2×D412yes—
104C2×Dic157C2×D412yes—
105C4×D157—24no—
106C4×D157—42no—
107C4×D157—82no—
108#11929434—22no—
109C23×C157—22no—
110C23×C157—42no—
111C23×C157—81no—
112C23×C157—81no—
113C23×C157C2×D411yescharacteristic
114D4×C157—22no—
115D4×C157—22no—
116D4×C157—42no—
117C2×C4×C157—22no—
118C2×C4×C157—81no—
119C2×C4×C157C2×D411yescharacteristic
120C2×C4×C157C2×D412yes—
121C2×C4×C157#4112yes—
122C2×C4×C157C2411yescharacteristic
123C8×C157—21no—
124C8×C157—21no—
125C22×C157—21no—
126C22×C157—21no—
127C22×C157—42no—
128C22×C157—42no—
129C22×C157—42no—
130C22×C157—84no—
131C22×C157#12112yes—
132C22×C157C22×D411yescharacteristic
133C2×D157—22no—
134C2×D157—41no—
135C2×D157—41no—
136C2×D157—41no—
137C2×D157—41no—
138C2×D157—41no—
139C4×C157—42no—
140C4×C157#12112yes—
141C4×C157C22×D411yescharacteristic
142C4×C157C2×#4111yescharacteristic
143Dic157—22no—
144Dic157—22no—
145Dic157—22no—
146Dic157—41no—
147C2×C157—22no—
148C2×C157—82no—
149C2×C157C2×#12111yescharacteristic
150C2×C157#57611yescharacteristic
151C2×C157#57711yescharacteristic
152D157—42no—
153D157—81no—
154C157#304511yescharacteristic, complemented, Sylow
155#3045—1571nomaximal, Sylow
156C2×AGL(1,ℤ/8)—1571no—
157C2×#135—1571no—
158#535—1571no—
159#520—1571no—
160#464—1572no—
161#463—1572no—
162#460—1572no—
163#459—1572no—
164#424—1571no—
165#417—1571no—
166C2×#102D15711yescharacteristic, complemented
167C2×#41—1571no—
168C2×#41—1571no—
169C22×D4C2×D15711yescharacteristic
170AGL(1,ℤ/8)—3144no—
171#135—3144no—
172C2×Q16—1571no—
173C2×SD16—1572no—
174C2×SD16—1571no—
175C2×SD16—1571no—
176C2×D8—1572no—
177C2×D8—1571no—
178C2×M16—1571no—
179C22×C8C2×D15711yescharacteristic
180#127—1572no—
181#124—1572no—
182#121—3141no—
183#121—3141no—
184#120—3142no—
185C4×Q8—1572no—
186C4×D4—3142no—
187C4×D4—1572no—
188#117—3141no—
189#117—1571no—
190C2×C4⋊C4—3141no—
191C2×C4⋊C4C2×D15711yescharacteristic
192C4⋊C8—1572no—
193C4⋊C8—1572no—
194#103—1572no—
195#102—1572no—
196#102C2×D15712yes—
197#102C2×D15712yes—
198C24—21no—
199#41—3142no—
200#41—3142no—
201#41—3142no—
202#41—1574no—
203C2×Q8—1571no—
204C2×Q8—1571no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—22no—
208C2×D4—3141no—
209C2×D4—3141no—
210C2×D4—3142no—
211C2×D4—3142no—
212C2×D4—1571no—
213C2×D4—1571no—
214C2×D4C22×D15712yes—
215C22×C4—21no—
216C22×C4—3142no—
217C22×C4—3141no—
218C22×C4—3141no—
219C22×C4C22×D15711yescharacteristic
220Q16—3142no—
221SD16—3142no—
222SD16—3142no—
223SD16—3144no—
224D8—3142no—
225D8—3144no—
226M16—3142no—
227C2×C8—22no—
228C2×C8—1572no—
229C2×C8C22×D15711yescharacteristic
230C2×C8C22×D15711yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—3142no—
233C4⋊C4—1571no—
234C4⋊C4—1571no—
235C4⋊C4C22×D15712yes—
236C22⋊C4—3142no—
237C22⋊C4—3142no—
238C22⋊C4—3142no—
239C22⋊C4—1572no—
240C42—3142no—
241C42—1572no—
242C23—22no—
243C23—42no—
244C23—81no—
245C23—81no—
246C23—3141no—
247C23—3141no—
248C23D4×D15711yescharacteristic
249Q8—3141no—
250Q8—3141no—
251Q8—3141no—
252Q8—1572no—
253D4—22no—
254D4—22no—
255D4—42no—
256D4—3144no—
257D4—3141no—
258D4—3141no—
259D4—3141no—
260D4—6282no—
261D4—1572no—
262D4—12562no—
263D4—12562no—
264C2×C4—22no—
265C2×C4—81no—
266C2×C4—3141no—
267C2×C4—3144no—
268C2×C4—3141no—
269C2×C4—6282no—
270C2×C4—1572no—
271C2×C4—1572no—
272C2×C4—12562no—
273C2×C4D4×D15711yescharacteristic
274C2×C4D4×D15712yes—
275C2×C4#1457895412yes—
276C2×C4C23×D15711yescharacteristic
277C8—21no—
278C8—21no—
279C8—3142no—
280C22—21no—
281C22—21no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—84no—
286C22—3142no—
287C22—6281no—
288C22—6281no—
289C22—6281no—
290C22—6281no—
291C22—6281no—
292C22#1909774412yes—
293C22C2×D4×D15711yescharacteristic
294C4—42no—
295C4—3142no—
296C4—3142no—
297C4—3142no—
298C4—6281no—
299C4#1909774412yes—
300C4C2×D4×D15711yescharacteristic
301C4C2×#1457895411yescharacteristic
302C2—22no—
303C2—82no—
304C2—6282no—
305C2—12561no—
306C2C2×#1909774411yescharacteristic
307C2#2375807411yescharacteristic
308C2#2375807911yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC2×#102×C157C2
socleC22×C157C22×D4
hypercenterC2×#102D157
hypocenterC157#3045
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#19097797C2semidirect
2. C2×#19097793C2semidirect
3. #23757840C2semidirect
4. #23757754C2semidirect
5. #23757494C2semidirect
6. #23757487C2semidirect
7. #23757472C2semidirect
8. #23757467C2semidirect
9. #23757299C2semidirect
10. #23757272C2semidirect
11. C2×#102×C157C2semidirect
16. C2×Dic628C22semidirect
17. C2×#14578943C22semidirect
18. C2×#14578943C22semidirect
20. C2×D1256C22semidirect
28. #19097736C22semidirect
29. #19097733C22semidirect
34. #19097700C22semidirect
35. #19097700C22semidirect
36. #19097694C22semidirect
37. #19097691C22semidirect
46. #14578954D4semidirect
154. C157#3045semidirect
166. C2×#102D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977972
C2×#190977932
#237578402
#237577542
#237574942
#237574872
#237574722
#237574672
#237572992
#237572722
C2×#102×C1572
#3045157