Finite Group Databasebeta

← #34112093

Subgroups — #34112093

Order 20096.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757924C211yesmaximal, characteristic, complemented
2#23757917C211yesmaximal, characteristic, complemented
3#23757631C211yesmaximal, characteristic, complemented
4#23757603C211yesmaximal, characteristic, complemented
5#23757590C211yesmaximal, characteristic, complemented
6#23757561C211yesmaximal, characteristic, complemented
7#23757525C211yesmaximal, characteristic, complemented
8#23757502C211yesmaximal, characteristic, complemented
9#23757487C211yesmaximal, characteristic, complemented
10#23757419C211yesmaximal, characteristic, complemented
11#23757407C211yesmaximal, characteristic, complemented
12#23757382C211yesmaximal, characteristic, complemented
13#23757344C211yesmaximal, characteristic, complemented
14#23757271C211yesmaximal, characteristic, complemented
15C2×#102×C157C211yesmaximal, characteristic, complemented
16C2×#14578954—21no—
17C2×#14578953C2211yescharacteristic
18C2×#14578943C2211yescharacteristic, complemented
19C2×#14578939C2211yescharacteristic
20C2×#14578939C2211yescharacteristic
21C2×#14578937C2211yescharacteristic, complemented
22#19097770C2211yescharacteristic, complemented
23#19097758C2211yescharacteristic
24#19097756—21no—
25#19097754—21no—
26#19097752—21no—
27#19097750C2211yescharacteristic
28#19097749—21no—
29#19097746C2211yescharacteristic, complemented
30#19097745C2211yescharacteristic
31#19097743—21no—
32#19097742C2211yescharacteristic
33#19097740—21no—
34D4×Dic157C2211yescharacteristic
35#19097733C2211yescharacteristic, complemented
36C4×C22⋊D157C2211yescharacteristic
37C4⋊C4×D157C2211yescharacteristic, complemented
38C2×C22⋊Dic157—21no—
39#19097703C2211yescharacteristic, complemented
40#19097702C2211yescharacteristic, complemented
41#19097702C2211yescharacteristic, complemented
42#19097700C2211yescharacteristic, complemented
43#19097696C2211yescharacteristic, complemented
44#19097694C2211yescharacteristic, complemented
45#19097694C2211yescharacteristic, complemented
46#19097693C2211yescharacteristic, complemented
47#19097692C2211yescharacteristic
48#19097692C2211yescharacteristic
49C22⋊#11929434C2211yescharacteristic
50#19097683C2211yescharacteristic, complemented
51#19097681C2211yescharacteristic, complemented
52C22×D4×C157C2211yescharacteristic
53C22×C8×C157C2211yescharacteristic
54C2×C4⋊C4×C157C2211yescharacteristic
55#102×C157C2211yescharacteristic
56#102×C157C2211yescharacteristic
57#102×C157C2211yescharacteristic
58#102×C157C2211yescharacteristic
59#14578954—44no—
60#14578953—22no—
61#14578953—41no—
62C2×Dic314—21no—
63C2×Dic314C2311yescharacteristic
64C2×D628—21no—
65C2×D628C2311yescharacteristic
66C2×C22⋊D157—21no—
67C2×C22⋊D157—21no—
68C2×C22⋊D157—21no—
69C2×C22⋊D157D411yescharacteristic
70C22×Dic157—21no—
71C22×Dic157—21no—
72C2×C4×D157—21no—
73C2×C4×D157—21no—
74C2×C4×D157C2311yescharacteristic
75#14578943—41no—
76#14578939—22no—
77#14578939—41no—
78#14578937—41no—
79C2×#11929434C2311yescharacteristic
80C2×#11929434C2311yescharacteristic
81C4⋊Dic157C2311yescharacteristic
82C4⋊Dic157C2311yescharacteristic
83#14578933—21no—
84#14578933—21no—
85#14578933—21no—
86#14578933D411yescharacteristic
87C22⋊Dic157—21no—
88C22⋊Dic157—21no—
89C22⋊Dic157—21no—
90C22⋊Dic157—21no—
91C22⋊Dic157—21no—
92C22⋊Dic157D411yescharacteristic
93#14578931—21no—
94#14578931—21no—
95#14578931—21no—
96#14578931D411yescharacteristic
97C4×Dic157C2311yescharacteristic
98C24×C157—21no—
99C2×D4×C157—22no—
100C2×D4×C157—21no—
101C2×D4×C157—41no—
102C2×D4×C157C2311yescharacteristic
103C2×D4×C157C2311yescharacteristic
104C22×C4×C157—21no—
105C22×C4×C157C2311yescharacteristic
106C2×C8×C157—41no—
107C2×C8×C157C2311yescharacteristic
108C2×C8×C157C2311yescharacteristic
109C4⋊C4×C157—21no—
110C4⋊C4×C157C2311yescharacteristic
111C4⋊C4×C157C2311yescharacteristic
112C22×D157—21no—
113C22×D157C2×D411yescharacteristic
114Dic314—21no—
115Dic314—21no—
116Dic314—42no—
117D628—21no—
118D628—21no—
119D628—42no—
120C22⋊D157—22no—
121C22⋊D157—42no—
122C22⋊D157—42no—
123C22⋊D157—81no—
124C2×Dic157—21no—
125C2×Dic157—21no—
126C2×Dic157—21no—
127C2×Dic157—42no—
128C2×Dic157—81no—
129C2×Dic157C2×D411yescharacteristic
130C2×Dic157C2×D411yescharacteristic
131C2×Dic157C2×D411yescharacteristic
132C4×D157—21no—
133C4×D157—21no—
134C4×D157—42no—
135C4×D157—42no—
136#11929434—21no—
137#11929434—21no—
138C23×C157—21no—
139C23×C157—21no—
140C23×C157—42no—
141C23×C157—42no—
142C23×C157—81no—
143C23×C157C2×D411yescharacteristic
144D4×C157—21no—
145D4×C157—21no—
146D4×C157—21no—
147D4×C157—42no—
148D4×C157#4112yescomplemented
149C2×C4×C157—21no—
150C2×C4×C157—21no—
151C2×C4×C157—21no—
152C2×C4×C157—21no—
153C2×C4×C157—42no—
154C2×C4×C157C2×D411yescharacteristic
155C2×C4×C157C2411yescharacteristic
156C8×C157—21no—
157C8×C157—21no—
158C22×C157—21no—
159C22×C157—21no—
160C22×C157—22no—
161C22×C157—41no—
162C22×C157—41no—
163C22×C157—41no—
164C22×C157—41no—
165C22×C157—41no—
166C22×C157—84no—
167C22×C157AGL(1,ℤ/8)12yes—
168C22×C157C22×D411yescharacteristic
169C2×D157—21no—
170C2×D157—21no—
171C2×D157—21no—
172C2×D157—41no—
173C2×D157—41no—
174C2×D157—41no—
175C4×C157—21no—
176C4×C157—41no—
177C4×C157—41no—
178C4×C157C2×#4111yescharacteristic
179C4×C157H(5,𝔽2)11yescharacteristic
180Dic157—21no—
181Dic157—21no—
182Dic157—21no—
183Dic157—41no—
184Dic157—41no—
185Dic157—41no—
186C2×C157—22no—
187C2×C157—42no—
188C2×C157—81no—
189C2×C157#54611yescharacteristic
190C2×C157C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C157#57711yescharacteristic
192D157—41no—
193D157—81no—
194C157#330611yescharacteristic, complemented, Sylow
195#3306—1571nomaximal, Sylow
196#547—1571no—
197#546—1571no—
198#489—1571no—
199#483—1571no—
200#481—1571no—
201#476—1571no—
202#469—1571no—
203#465—1571no—
204#463—1571no—
205#449—1571no—
206#447—1571no—
207#442—1571no—
208#435—1571no—
209#417—1571no—
210C2×#102D15711yescharacteristic, complemented
211C2×#41—3141no—
212C2×#41—1571no—
213C22×D4C2×D15711yescharacteristic
214C2×SD16—1571no—
215C2×D8—1571no—
216C2×D8—1571no—
217C2×M16—1571no—
218C22×C8C2×D15711yescharacteristic
219C4⋊Q8—1571no—
220#124—1571no—
221#123—3141no—
222#123—3141no—
223#123—3141no—
224C22⋊Q8—3141no—
225C22⋊Q8—1571no—
226#121—3141no—
227#121—1571no—
228#121—1571no—
229#121—1571no—
230#120—3141no—
231C4×D4—1571no—
232C4×D4—1571no—
233C4×D4—1571no—
234C2×C4⋊C4—1571no—
235C2×C4⋊C4C2×D15711yescharacteristic
236C2×C22⋊C4—3141no—
237#106—1571no—
238#106—1571no—
239#106—1571no—
240C4⋊C8—1571no—
241#103—1571no—
242#103—1571no—
243#103—1571no—
244#102—1571no—
245#102—1571no—
246#102—1571no—
247#102C2×D15711yescharacteristic
248#102C2×D15711yescharacteristic
249#102C2×D15711yescharacteristic
250#102C2×D15711yescharacteristic
251C22⋊C8—1571no—
252C22⋊C8—1571no—
253#97—1571no—
254C24—21no—
255#41—3142no—
256#41—6284no—
257#41—6281no—
258C2×Q8—3141no—
259C2×Q8—1571no—
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—3141no—
264C2×D4—3141no—
265C2×D4—3141no—
266C2×D4—3141no—
267C2×D4—1571no—
268C2×D4—1571no—
269C2×D4C22×D15711yescharacteristic
270C2×D4C22×D15711yescharacteristic
271C22×C4—21no—
272C22×C4—3141no—
273C22×C4—3141no—
274C22×C4—3141no—
275C22×C4—3141no—
276C22×C4—1571no—
277C22×C4C22×D15711yescharacteristic
278SD16—6281no—
279D8—3142no—
280D8—6281no—
281M16—6281no—
282C2×C8—41no—
283C2×C8—1571no—
284C2×C8—1571no—
285C2×C8C22×D15711yescharacteristic
286C2×C8C22×D15711yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—3141no—
289C4⋊C4—3141no—
290C4⋊C4—3141no—
291C4⋊C4—1571no—
292C4⋊C4—1571no—
293C4⋊C4—1571no—
294C4⋊C4C22×D15711yescharacteristic
295C4⋊C4C22×D15711yescharacteristic
296C22⋊C4—3141no—
297C22⋊C4—3141no—
298C22⋊C4—3141no—
299C22⋊C4—3141no—
300C22⋊C4—3141no—
301C22⋊C4—3141no—
302C22⋊C4—3141no—
303C22⋊C4—3141no—
304C22⋊C4—1571no—
305C22⋊C4—1571no—
306C42—1571no—
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—3141no—
313C23—1571no—
314C23D4×D15711yescharacteristic
315Q8—3141no—
316Q8—3141no—
317Q8—6282no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—3142no—
323D4—3141no—
324D4—3141no—
325D4—6282no—
326D4—6282no—
327D4—6282no—
328D4—12561no—
329D4#1457895412yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—3141no—
336C2×C4—3141no—
337C2×C4—3141no—
338C2×C4—3141no—
339C2×C4—3141no—
340C2×C4—6282no—
341C2×C4—6282no—
342C2×C4—6282no—
343C2×C4—1571no—
344C2×C4—1571no—
345C2×C4—1571no—
346C2×C4—12561no—
347C2×C4D4×D15711yescharacteristic
348C2×C4C23×D15711yescharacteristic
349C8—21no—
350C8—21no—
351C8—3141no—
352C8—3141no—
353C22—21no—
354C22—21no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—84no—
362C22—3141no—
363C22—3141no—
364C22—3141no—
365C22—6281no—
366C22—6281no—
367C22—6281no—
368C22#1909779512yes—
369C22C2×D4×D15711yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—3141no—
374C4—3141no—
375C4—3141no—
376C4—6281no—
377C4—6281no—
378C4—6281no—
379C4C2×#1457895411yescharacteristic
380C4#1909781611yescharacteristic
381C2—22no—
382C2—42no—
383C2—81no—
384C2—6281no—
385C2—12561no—
386C2#2375791311yescharacteristic
387C2C2×#1909779511yescharacteristic
388C2#2375807911yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC2×#102×C157C2
socleC22×C157C22×D4
hypercenterC2×#102D157
hypocenterC157#3306
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. #23757924C2semidirect
2. #23757917C2semidirect
3. #23757631C2semidirect
4. #23757603C2semidirect
5. #23757590C2semidirect
6. #23757561C2semidirect
7. #23757525C2semidirect
8. #23757502C2semidirect
9. #23757487C2semidirect
10. #23757419C2semidirect
11. #23757407C2semidirect
12. #23757382C2semidirect
13. #23757344C2semidirect
14. #23757271C2semidirect
15. C2×#102×C157C2semidirect
18. C2×#14578943C22semidirect
21. C2×#14578937C22semidirect
22. #19097770C22semidirect
29. #19097746C22semidirect
35. #19097733C22semidirect
37. C4⋊C4×D157C22semidirect
39. #19097703C22semidirect
40. #19097702C22semidirect
41. #19097702C22semidirect
42. #19097700C22semidirect
43. #19097696C22semidirect
44. #19097694C22semidirect
45. #19097694C22semidirect
46. #19097693C22semidirect
50. #19097683C22semidirect
51. #19097681C22semidirect
148. D4×C157#41semidirect
194. C157#3306semidirect
210. C2×#102D157semidirect
329. D4#14578954semidirect

Maximal subgroups

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

subgroupindex
#237579242
#237579172
#237576312
#237576032
#237575902
#237575612
#237575252
#237575022
#237574872
#237574192
#237574072
#237573822
#237573442
#237572712
C2×#102×C1572
#3306157