Finite Group Databasebeta

← #34110068

Subgroups — #34110068

Order 20096.

414 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757786C211yesmaximal, characteristic
2#117×D157C211yesmaximal, characteristic, complemented
3#23757613C211yesmaximal, characteristic, complemented
4#23757612C211yesmaximal, characteristic, complemented
5#23757611C211yesmaximal, characteristic, complemented
6#23757600C211yesmaximal, characteristic, complemented
7#23757599C211yesmaximal, characteristic, complemented
8#23757598C211yesmaximal, characteristic, complemented
9#23757597C211yesmaximal, characteristic, complemented
10#23757314C211yesmaximal, characteristic, complemented
11#23757312C211yesmaximal, characteristic, complemented
12#23757273C211yesmaximal, characteristic, complemented
13#23757273C211yesmaximal, characteristic, complemented
14#23757235C211yesmaximal, characteristic, complemented
15#485×C157C211yesmaximal, characteristic, complemented
16C2×#14578955C2211yescharacteristic
17C22×C4×D157C2211yescharacteristic
18C2×#14578937C2211yescharacteristic
19C2×#14578937C2211yescharacteristic
20#19097756—21no—
21#19097747C2211yescharacteristic
22#19097746C2211yescharacteristic
23#19097745C2211yescharacteristic
24#19097741—21no—
25#19097733—21no—
26#19097731—21no—
27#19097730C2211yescharacteristic
28#19097729C2211yescharacteristic
29#19097729C2211yescharacteristic
30#19097729C2211yescharacteristic
31#19097728—21no—
32#19097727—21no—
33C4⋊C4×D157C2211yescharacteristic
34C4⋊C4×D157C2211yescharacteristic
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#19097695C2211yescharacteristic, complemented
44#19097695C2211yescharacteristic, complemented
45#19097693C2211yescharacteristic, complemented
46#19097693C2211yescharacteristic, complemented
47#19097691C2211yescharacteristic, complemented
48#19097691C2211yescharacteristic, complemented
49C22⋊#11929434C2211yescharacteristic
50#19097683C2211yescharacteristic
51#19097683C2211yescharacteristic
52C22⋊Q8×C157C2211yescharacteristic
53#117×C157C2211yescharacteristic
54#107×C157C2211yescharacteristic, complemented
55#106×C157C2211yescharacteristic, complemented
56#103×C157C2211yescharacteristic, complemented
57#103×C157C2211yescharacteristic, complemented
58C22⋊C8×C157C2211yescharacteristic
59C23×D157D411yescharacteristic
60#14578955—22no—
61#14578955—22no—
62C2×D628—21no—
63C2×D628—21no—
64C2×D628C2311yescharacteristic
65C2×C22⋊D157—21no—
66C22×Dic157D411yescharacteristic
67C2×C4×D157—22no—
68C2×C4×D157—22no—
69C2×C4×D157—21no—
70C2×C4×D157—21no—
71C2×C4×D157—21no—
72C2×C4×D157D411yescharacteristic
73C2×C4×D157D411yescharacteristic
74C2×C4×D157C2311yescharacteristic
75C2×C4×D157C2311yescharacteristic
76#14578937—22no—
77#14578937—22no—
78C2×#11929434C2311yescharacteristic
79C2×#11929434C2311yescharacteristic
80C4⋊Dic157C2311yescharacteristic
81C4⋊Dic157C2311yescharacteristic
82C4⋊Dic157C2311yescharacteristic
83#14578933—21no—
84#14578933—21no—
85#14578933—21no—
86C22⋊Dic157—21no—
87#14578931—21no—
88#14578931—21no—
89#14578931—21no—
90#14578931—21no—
91#14578931—21no—
92#14578931—21no—
93C4×Dic157—21no—
94C4×Dic157—21no—
95C4×Dic157—21no—
96C4×Dic157—21no—
97C2×Q8×C157C2311yescharacteristic
98C22×C4×C157C2311yescharacteristic
99C2×C8×C157C2311yescharacteristic
100C2×C8×C157C2311yescharacteristic
101C4⋊C4×C157—21no—
102C4⋊C4×C157C2311yescharacteristic
103C4⋊C4×C157C2311yescharacteristic
104C4⋊C4×C157C2311yescharacteristic
105C22⋊C4×C157—21no—
106C22⋊C4×C157—21no—
107C42×C157—21no—
108C22×D157—22no—
109C22×D157—21no—
110C22×D157—41no—
111C22×D157—41no—
112C22×D157C2×D411yescharacteristic
113C22×D157C2×D411yescharacteristic
114D628—21no—
115D628—21no—
116D628—42no—
117D628—42no—
118C22⋊D157—42no—
119C2×Dic157—22no—
120C2×Dic157—21no—
121C2×Dic157—21no—
122C2×Dic157—21no—
123C2×Dic157C2×D411yescharacteristic
124C2×Dic157C2×D411yescharacteristic
125C4×D157—22no—
126C4×D157—21no—
127C4×D157—21no—
128C4×D157—22no—
129C4×D157—42no—
130C4×D157—42no—
131C4×D157—42no—
132C4×D157#4112yes—
133C4×D157#4112yes—
134#11929434—21no—
135#11929434—21no—
136C23×C157C2×D411yescharacteristic
137Q8×C157—21no—
138Q8×C157—21no—
139C2×C4×C157—21no—
140C2×C4×C157—21no—
141C2×C4×C157—21no—
142C2×C4×C157—21no—
143C2×C4×C157—21no—
144C2×C4×C157—21no—
145C2×C4×C157C2×D411yescharacteristic
146C2×C4×C157C2411yescharacteristic
147C8×C157—21no—
148C8×C157—21no—
149C22×C157—21no—
150C22×C157—21no—
151C22×C157—21no—
152C22×C157C22×D411yescharacteristic
153C2×D157—21no—
154C2×D157—21no—
155C2×D157—21no—
156C2×D157—21no—
157C2×D157—21no—
158C2×D157—44no—
159C2×D157—41no—
160C2×D157—41no—
161C2×D157—41no—
162C2×D157#12312yes—
163C4×C157—21no—
164C4×C157—41no—
165C4×C157—41no—
166C4×C157—41no—
167C4×C157—41no—
168C4×C157C2×#4111yescharacteristic
169C4×C157C2×#4111yescharacteristic
170Dic157—21no—
171Dic157—41no—
172Dic157—41no—
173Dic157—41no—
174Dic157#12312yes—
175C2×C157—41no—
176C2×C157C2×#12311yescharacteristic
177C2×C157#57511yescharacteristic
178C2×C157#57511yescharacteristic
179D157—22no—
180D157—41no—
181D157—81no—
182C157#309311yescharacteristic, complemented, Sylow
183#3093—1571nomaximal, Sylow
184#525—1571no—
185C2×#117—1571no—
186#485—1571no—
187#485—1571no—
188#485—1571no—
189#485D15711yescharacteristic, complemented
190#482—1571no—
191#482—1571no—
192#482—1571no—
193#482—1571no—
194#428—1571no—
195#428—1571no—
196#417—1571no—
197#417—1571no—
198#407—1571no—
199C2×#41—1571no—
200C23×C4—1571no—
201C2×M16—1571no—
202C2×M16—1571no—
203#123—3141no—
204C22⋊Q8—1571no—
205C22⋊Q8C2×D15711yescharacteristic
206#121—1571no—
207#121—1571no—
208#120—3141no—
209C4×D4—3141no—
210C4×D4—3141no—
211#117—3141no—
212#117—3141no—
213#117—1571no—
214#117—1571no—
215#117—1571no—
216#117—1571no—
217#117C2×D15711yescharacteristic
218C2×C4⋊C4—1571no—
219C2×C4⋊C4—1571no—
220C2×C22⋊C4—3141no—
221C2×C42—3141no—
222#107—1571no—
223#107—1571no—
224#107—1571no—
225#107C2×D15711yescharacteristic, complemented
226#106—1571no—
227#106—1571no—
228#106—1571no—
229#106C2×D15711yescharacteristic, complemented
230#103—1571no—
231#103—1571no—
232#103C2×D15711yescharacteristic, complemented
233#103C2×D15711yescharacteristic, complemented
234#102—1571no—
235#102—1571no—
236#102—1571no—
237#102—1571no—
238C22⋊C8—1571no—
239C22⋊C8—1571no—
240C22⋊C8—1571no—
241C22⋊C8C2×D15711yescharacteristic
242C24—1571no—
243#41—3142no—
244#41—3142no—
245C2×Q8C22×D15711yescharacteristic
246C2×D4—3141no—
247C2×D4—3141no—
248C2×D4—3141no—
249C2×D4—1571no—
250C22×C4—3142no—
251C22×C4—3142no—
252C22×C4—3141no—
253C22×C4—3141no—
254C22×C4—3141no—
255C22×C4—1571no—
256C22×C4—1571no—
257C22×C4—1571no—
258C22×C4—1571no—
259C22×C4—1571no—
260C22×C4C22×D15711yescharacteristic
261M16—3142no—
262M16—3142no—
263C2×C8—1571no—
264C2×C8—1571no—
265C2×C8C22×D15711yescharacteristic
266C2×C8C22×D15711yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—3141no—
269C4⋊C4—3141no—
270C4⋊C4—3141no—
271C4⋊C4—1571no—
272C4⋊C4—1571no—
273C4⋊C4—1571no—
274C4⋊C4C22×D15711yescharacteristic
275C4⋊C4C22×D15711yescharacteristic
276C4⋊C4C22×D15711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—3141no—
280C22⋊C4—3141no—
281C22⋊C4—3141no—
282C22⋊C4—3141no—
283C22⋊C4—3141no—
284C22⋊C4—3141no—
285C22⋊C4—3141no—
286C42—21no—
287C42—3141no—
288C42—3141no—
289C42—3141no—
290C42—3141no—
291C23—3142no—
292C23—3141no—
293C23—6281no—
294C23—6281no—
295C23—1571no—
296C23—1571no—
297C23D4×D15711yescharacteristic
298Q8—21no—
299Q8—21no—
300D4—3141no—
301D4—3141no—
302D4—6282no—
303D4—6282no—
304D4—6282no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—3142no—
312C2×C4—3142no—
313C2×C4—3142no—
314C2×C4—3141no—
315C2×C4—3141no—
316C2×C4—3141no—
317C2×C4—3141no—
318C2×C4—3141no—
319C2×C4—6282no—
320C2×C4—6282no—
321C2×C4—6282no—
322C2×C4—1571no—
323C2×C4—1571no—
324C2×C4—1572no—
325C2×C4—1572no—
326C2×C4D4×D15711yescharacteristic
327C2×C4C23×D15711yescharacteristic
328C8—21no—
329C8—21no—
330C8—3141no—
331C8—3141no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—3141no—
336C22—3141no—
337C22—3141no—
338C22—3141no—
339C22—3141no—
340C22—6284no—
341C22—6281no—
342C22—6281no—
343C22—6281no—
344C22—1572no—
345C22C2×D4×D15711yescharacteristic
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—3141no—
352C4—6281no—
353C4—6281no—
354C4—6281no—
355C4—1572no—
356C4#41×D15711yescharacteristic
357C4#41×D15711yescharacteristic
358C2—41no—
359C2—3142no—
360C2—6281no—
361C2—12561no—
362C2#123×D15711yescharacteristic
363C2#2375807011yescharacteristic
364C2#2375807211yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#485×C157C2
socleC22×C157C22×D4
prime radical#23757786C2
hypercenter#485D157
hypocenterC157#3093
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. #117×D157C2semidirect
3. #23757613C2semidirect
4. #23757612C2semidirect
5. #23757611C2semidirect
6. #23757600C2semidirect
7. #23757599C2semidirect
8. #23757598C2semidirect
9. #23757597C2semidirect
10. #23757314C2semidirect
11. #23757312C2semidirect
12. #23757273C2semidirect
13. #23757273C2semidirect
14. #23757235C2semidirect
15. #485×C157C2semidirect
37. #19097705C22semidirect
38. #19097704C22semidirect
39. #19097704C22semidirect
40. #19097703C22semidirect
41. #19097702C22semidirect
42. #19097702C22semidirect
43. #19097695C22semidirect
44. #19097695C22semidirect
45. #19097693C22semidirect
46. #19097693C22semidirect
47. #19097691C22semidirect
48. #19097691C22semidirect
54. #107×C157C22semidirect
55. #106×C157C22semidirect
56. #103×C157C22semidirect
57. #103×C157C22semidirect
182. C157#3093semidirect
189. #485D157semidirect
225. #107C2×D157semidirect
229. #106C2×D157semidirect
232. #103C2×D157semidirect
233. #103C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237577862
#117×D1572
#237576132
#237576122
#237576112
#237576002
#237575992
#237575982
#237575972
#237573142
#237573122
#237572732
#237572352
#485×C1572
#3093157