Finite Group Databasebeta

← #34110075

Subgroups — #34110075

Order 20096.

462 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×D157C211yesmaximal, characteristic
2#117×D157C211yesmaximal, characteristic, complemented
3#23757598C211yesmaximal, characteristic, complemented
4#23757597C211yesmaximal, characteristic, complemented
5#23757594C211yesmaximal, characteristic, complemented
6#23757593C211yesmaximal, characteristic, complemented
7#23757590C211yesmaximal, characteristic, complemented
8#23757588C211yesmaximal, characteristic, complemented
9#23757585C211yesmaximal, characteristic, complemented
10#23757314C211yesmaximal, characteristic, complemented
11#23757312C211yesmaximal, characteristic, complemented
12#23757276C211yesmaximal, characteristic, complemented
13#23757276C211yesmaximal, characteristic, complemented
14#23757235C211yesmaximal, characteristic, complemented
15#482×C157C211yesmaximal, characteristic, complemented
16C2×D4×D157—21no—
17C2×D4×D157C2211yescharacteristic
18C22×C4×D157C2211yescharacteristic
19C2×#14578937C2211yescharacteristic
20C2×#14578937C2211yescharacteristic
21#19097746C2211yescharacteristic
22#19097745C2211yescharacteristic
23#19097744—21no—
24#19097743—21no—
25#19097742C2211yescharacteristic
26#19097730C2211yescharacteristic, complemented
27#19097729C2211yescharacteristic
28#19097729C2211yescharacteristic
29#19097728—21no—
30#19097727—21no—
31C4⋊C4×D157C2211yescharacteristic
32C4⋊C4×D157C2211yescharacteristic, complemented
33C4⋊C4×D157C2211yescharacteristic, complemented
34C22⋊C4×D157—21no—
35C22⋊C4×D157—21no—
36C42×D157—21no—
37#19097705C2211yescharacteristic, complemented
38#19097704C2211yescharacteristic, complemented
39#19097704C2211yescharacteristic, complemented
40#19097703C2211yescharacteristic, complemented
41#19097702C2211yescharacteristic, complemented
42#19097702C2211yescharacteristic, complemented
43#19097693C2211yescharacteristic, complemented
44#19097693C2211yescharacteristic, complemented
45#19097692C2211yescharacteristic, complemented
46#19097692C2211yescharacteristic, complemented
47#19097691C2211yescharacteristic, complemented
48#19097691C2211yescharacteristic, complemented
49C22⋊#11929434C2211yescharacteristic, complemented
50#19097683C2211yescharacteristic, complemented
51#19097683C2211yescharacteristic, complemented
52#121×C157C2211yescharacteristic
53#117×C157C2211yescharacteristic, complemented
54#107×C157C2211yescharacteristic, complemented
55#106×C157C2211yescharacteristic, complemented
56#102×C157C2211yescharacteristic, complemented
57#102×C157C2211yescharacteristic, complemented
58C22⋊C8×C157C2211yescharacteristic, complemented
59C23×D157—21no—
60C23×D157D411yescharacteristic
61C2×D628—21no—
62C2×D628C2311yescharacteristic
63C2×C22⋊D157—21no—
64C2×C22⋊D157—21no—
65C2×C22⋊D157—21no—
66D4×D157—22no—
67D4×D157—22no—
68D4×D157—44no—
69C22×Dic157D411yescharacteristic
70C2×C4×D157—22no—
71C2×C4×D157—22no—
72C2×C4×D157—21no—
73C2×C4×D157—21no—
74C2×C4×D157—21no—
75C2×C4×D157D411yescharacteristic
76C2×C4×D157D411yescharacteristic
77C2×C4×D157C2311yescharacteristic
78C2×C4×D157C2311yescharacteristic
79#14578937—22no—
80#14578937—22no—
81C2×#11929434C2311yescharacteristic
82C2×#11929434C2311yescharacteristic
83C4⋊Dic157C2311yescharacteristic
84C4⋊Dic157C2311yescharacteristic
85C4⋊Dic157C2311yescharacteristic
86#14578933—21no—
87#14578933—21no—
88#14578933—21no—
89C22⋊Dic157—21no—
90C22⋊Dic157—21no—
91#14578931—21no—
92#14578931—21no—
93#14578931—21no—
94#14578931—21no—
95C4×Dic157—21no—
96C4×Dic157—21no—
97C4×Dic157—21no—
98C2×D4×C157—21no—
99C2×D4×C157C2311yescharacteristic
100C22×C4×C157C2311yescharacteristic
101C2×C8×C157C2311yescharacteristic
102C2×C8×C157C2311yescharacteristic
103C4⋊C4×C157C2311yescharacteristic
104C4⋊C4×C157C2311yescharacteristic
105C4⋊C4×C157C2311yescharacteristic
106C22⋊C4×C157—21no—
107C22⋊C4×C157—21no—
108C42×C157—21no—
109C22×D157—22no—
110C22×D157—22no—
111C22×D157—21no—
112C22×D157—41no—
113C22×D157—42no—
114C22×D157—42no—
115C22×D157—42no—
116C22×D157C2×D411yescharacteristic
117C22×D157C2×D411yescharacteristic
118D628—21no—
119D628—21no—
120D628—42no—
121C22⋊D157—42no—
122C22⋊D157—42no—
123C22⋊D157—42no—
124C2×Dic157—22no—
125C2×Dic157—21no—
126C2×Dic157—21no—
127C2×Dic157—21no—
128C2×Dic157C2×D411yescharacteristic
129C2×Dic157C2×D411yescharacteristic
130C4×D157—22no—
131C4×D157—21no—
132C4×D157—21no—
133C4×D157—22no—
134C4×D157—42no—
135C4×D157—42no—
136C4×D157—42no—
137C4×D157#4112yes—
138C4×D157#4112yes—
139#11929434—21no—
140#11929434—21no—
141C23×C157—21no—
142C23×C157C2×D411yescharacteristic
143D4×C157—21no—
144D4×C157—21no—
145D4×C157—42no—
146C2×C4×C157—21no—
147C2×C4×C157—21no—
148C2×C4×C157—21no—
149C2×C4×C157—21no—
150C2×C4×C157—21no—
151C2×C4×C157C2×D411yescharacteristic
152C2×C4×C157C2411yescharacteristic
153C8×C157—21no—
154C8×C157—21no—
155C22×C157—21no—
156C22×C157—21no—
157C22×C157—21no—
158C22×C157—41no—
159C22×C157—41no—
160C22×C157—41no—
161C22×C157C22×D411yescharacteristic
162C2×D157—21no—
163C2×D157—21no—
164C2×D157—21no—
165C2×D157—21no—
166C2×D157—44no—
167C2×D157—41no—
168C2×D157—41no—
169C2×D157—41no—
170C2×D157—84no—
171C2×D157#12312yes—
172C2×D157AGL(1,ℤ/8)12yes—
173C4×C157—21no—
174C4×C157—41no—
175C4×C157—41no—
176C4×C157—41no—
177C4×C157C2×#4111yescharacteristic
178C4×C157C2×#4111yescharacteristic
179Dic157—21no—
180Dic157—41no—
181Dic157—41no—
182Dic157—41no—
183Dic157#12312yes—
184C2×C157—41no—
185C2×C157—81no—
186C2×C157C2×#12311yescharacteristic
187C2×C157C2×AGL(1,ℤ/8)11yescharacteristic
188C2×C157#57511yescharacteristic
189D157—22no—
190D157—22no—
191D157—81no—
192C157#309411yescharacteristic, complemented, Sylow
193#3094—1571nomaximal, Sylow
194C2×#121—1571no—
195C2×#117—1571no—
196#482—1571no—
197#482—1571no—
198#482—1571no—
199#482D15711yescharacteristic, complemented
200#481—1571no—
201#481—1571no—
202#480—1571no—
203#480—1571no—
204#428—1571no—
205#428—1571no—
206#418—1571no—
207#418—1571no—
208#407—1571no—
209C22×D4—3141no—
210C22×D4—1571no—
211C23×C4—1571no—
212C2×M16—1571no—
213C2×M16—1571no—
214#121—3141no—
215#121—3141no—
216#121—1571no—
217#121—1571no—
218#121—1571no—
219#121C2×D15711yescharacteristic
220#117—3141no—
221#117—3141no—
222#117—1571no—
223#117—1571no—
224#117—1571no—
225#117C2×D15711yescharacteristic, complemented
226C2×C4⋊C4—1571no—
227C2×C4⋊C4—1571no—
228C2×C4⋊C4—1571no—
229C2×C22⋊C4—3141no—
230C2×C22⋊C4—3141no—
231C2×C42—3141no—
232#107—1571no—
233#107—1571no—
234#107—1571no—
235#107C2×D15711yescharacteristic, complemented
236#106—1571no—
237#106—1571no—
238#106—1571no—
239#106C2×D15711yescharacteristic, complemented
240#102—1571no—
241#102—1571no—
242#102—1571no—
243#102—1571no—
244#102—1571no—
245#102—1571no—
246#102C2×D15711yescharacteristic, complemented
247#102C2×D15711yescharacteristic, complemented
248C22⋊C8—1571no—
249C22⋊C8—1571no—
250C22⋊C8—1571no—
251C22⋊C8C2×D15711yescharacteristic, complemented
252C24—3141no—
253C24—1571no—
254C2×D4—21no—
255C2×D4—3141no—
256C2×D4—3141no—
257C2×D4—3141no—
258C2×D4—3142no—
259C2×D4—3142no—
260C2×D4—3141no—
261C2×D4—6284no—
262C2×D4—1571no—
263C2×D4C22×D15711yescharacteristic
264C22×C4—3142no—
265C22×C4—3142no—
266C22×C4—3141no—
267C22×C4—3141no—
268C22×C4—3141no—
269C22×C4—1571no—
270C22×C4—1571no—
271C22×C4—1571no—
272C22×C4—1571no—
273C22×C4—1571no—
274C22×C4C22×D15711yescharacteristic
275M16—3142no—
276M16—3142no—
277C2×C8—1571no—
278C2×C8—1571no—
279C2×C8C22×D15711yescharacteristic
280C2×C8C22×D15711yescharacteristic
281C4⋊C4—3141no—
282C4⋊C4—3141no—
283C4⋊C4—3141no—
284C4⋊C4—1571no—
285C4⋊C4—1571no—
286C4⋊C4—1571no—
287C4⋊C4C22×D15711yescharacteristic
288C4⋊C4C22×D15711yescharacteristic
289C4⋊C4C22×D15711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—3141no—
293C22⋊C4—3141no—
294C22⋊C4—3141no—
295C22⋊C4—3141no—
296C22⋊C4—3141no—
297C22⋊C4—3141no—
298C42—21no—
299C42—3141no—
300C42—3141no—
301C42—3141no—
302C23—21no—
303C23—3142no—
304C23—3142no—
305C23—3141no—
306C23—6281no—
307C23—6282no—
308C23—6282no—
309C23—6282no—
310C23—1571no—
311C23—1571no—
312C23D4×D15711yescharacteristic
313D4—21no—
314D4—21no—
315D4—42no—
316D4—3141no—
317D4—3141no—
318D4—6282no—
319D4—6282no—
320D4—6282no—
321D4—6282no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—3142no—
328C2×C4—3142no—
329C2×C4—3142no—
330C2×C4—3141no—
331C2×C4—3141no—
332C2×C4—3141no—
333C2×C4—3141no—
334C2×C4—3141no—
335C2×C4—6282no—
336C2×C4—6282no—
337C2×C4—6282no—
338C2×C4—1571no—
339C2×C4—1571no—
340C2×C4—1572no—
341C2×C4—1572no—
342C2×C4D4×D15711yescharacteristic
343C2×C4C23×D15711yescharacteristic
344C8—21no—
345C8—21no—
346C8—3141no—
347C8—3141no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—3141no—
355C22—3141no—
356C22—3141no—
357C22—3141no—
358C22—6284no—
359C22—6281no—
360C22—6281no—
361C22—6281no—
362C22—1572no—
363C22—1572no—
364C22—12564no—
365C22C2×D4×D15711yescharacteristic
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—3141no—
371C4—6281no—
372C4—6281no—
373C4—6281no—
374C4—1572no—
375C4#41×D15711yescharacteristic
376C4#41×D15711yescharacteristic
377C2—41no—
378C2—81no—
379C2—3142no—
380C2—3142no—
381C2—12561no—
382C2#123×D15711yescharacteristic
383C2AGL(1,ℤ/8)×D15711yescharacteristic
384C2#2375807011yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#482×C157C2
socleC22×C157C22×D4
prime radical#121×D157C2
hypercenter#482D157
hypocenterC157#3094
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #117×D157C2semidirect
3. #23757598C2semidirect
4. #23757597C2semidirect
5. #23757594C2semidirect
6. #23757593C2semidirect
7. #23757590C2semidirect
8. #23757588C2semidirect
9. #23757585C2semidirect
10. #23757314C2semidirect
11. #23757312C2semidirect
12. #23757276C2semidirect
13. #23757276C2semidirect
14. #23757235C2semidirect
15. #482×C157C2semidirect
26. #19097730C22semidirect
32. C4⋊C4×D157C22semidirect
33. C4⋊C4×D157C22semidirect
37. #19097705C22semidirect
38. #19097704C22semidirect
39. #19097704C22semidirect
40. #19097703C22semidirect
41. #19097702C22semidirect
42. #19097702C22semidirect
43. #19097693C22semidirect
44. #19097693C22semidirect
45. #19097692C22semidirect
46. #19097692C22semidirect
47. #19097691C22semidirect
48. #19097691C22semidirect
49. C22⋊#11929434C22semidirect
50. #19097683C22semidirect
51. #19097683C22semidirect
53. #117×C157C22semidirect
54. #107×C157C22semidirect
55. #106×C157C22semidirect
56. #102×C157C22semidirect
57. #102×C157C22semidirect
58. C22⋊C8×C157C22semidirect
192. C157#3094semidirect
199. #482D157semidirect
225. #117C2×D157semidirect
235. #107C2×D157semidirect
239. #106C2×D157semidirect
246. #102C2×D157semidirect
247. #102C2×D157semidirect
251. C22⋊C8C2×D157semidirect

Maximal subgroups

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

subgroupindex
#121×D1572
#117×D1572
#237575982
#237575972
#237575942
#237575932
#237575902
#237575882
#237575852
#237573142
#237573122
#237572762
#237572352
#482×C1572
#3094157