Finite Group Databasebeta

← #34113151

Subgroups — #34113151

Order 20096.

406 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757995C211yesmaximal, characteristic, complemented
2#23757943C211yesmaximal, characteristic, complemented
3#23757660C211yesmaximal, characteristic, complemented
4#23757659C211yesmaximal, characteristic, complemented
5#23757644C211yesmaximal, characteristic, complemented
6#23757490C211yesmaximal, characteristic, complemented
7#23757489C211yesmaximal, characteristic, complemented
8#23757476C211yesmaximal, characteristic, complemented
9#23757472C211yesmaximal, characteristic, complemented
10#23757467C211yesmaximal, characteristic, complemented
11#23757402C211yesmaximal, characteristic, complemented
12#23757371C211yesmaximal, characteristic, complemented
13#23757370C211yesmaximal, characteristic, complemented
14#23757353C211yesmaximal, characteristic, complemented
15#460×C157C211yesmaximal, characteristic, complemented
16C2×#14578953—21no—
17C2×#14578943C2211yescharacteristic
18C2×#14578942C2211yescharacteristic
19C2×#14578942C2211yescharacteristic
20C2×#14578941C2211yescharacteristic
21C2×D1256C2211yescharacteristic
22C2×#14578939C2211yescharacteristic
23C2×#14578939C2211yescharacteristic
24#19097769C2211yescharacteristic
25#19097767C2211yescharacteristic
26#19097767C2211yescharacteristic
27#19097766—21no—
28#19097765—21no—
29#19097760C2211yescharacteristic
30#19097759C2211yescharacteristic
31#19097749—21no—
32#19097743—21no—
33#19097743—21no—
34#19097742—21no—
35C4×Dic314C2211yescharacteristic
36#19097736C2211yescharacteristic
37C4×D628C2211yescharacteristic
38D4×Dic157C2211yescharacteristic
39D4×Dic157C2211yescharacteristic
40#19097733C2211yescharacteristic
41#19097728—21no—
42#19097704C2211yescharacteristic
43#19097700C2211yescharacteristic
44#19097700C2211yescharacteristic
45#19097696C2211yescharacteristic
46#19097695C2211yescharacteristic
47#19097693C2211yescharacteristic
48#19097691C2211yescharacteristic
49#19097682C2211yescharacteristic
50#19097681C2211yescharacteristic
51C8×Dic157C2211yescharacteristic
52C2×SD16×C157C2211yescharacteristic
53C2×SD16×C157C2211yescharacteristic
54#127×C157C2211yescharacteristic
55C4×Q8×C157C2211yescharacteristic
56C4⋊C8×C157C2211yescharacteristic
57#102×C157C2211yescharacteristic
58#102×C157C2211yescharacteristic
59#14578953—44no—
60C2×Dic314D411yescharacteristic
61C2×Dic314C2311yescharacteristic
62C2×D628C2311yescharacteristic
63C2×D628C2311yescharacteristic
64C2×C22⋊D157—21no—
65C2×C22⋊D157—21no—
66C2×C22⋊D157—21no—
67C2×C22⋊D157—21no—
68C22×Dic157—21no—
69C22×Dic157—21no—
70C2×C4×D157—21no—
71C2×C4×D157—21no—
72#14578943—41no—
73#14578942—22no—
74#14578942—41no—
75#14578941—22no—
76D1256—41no—
77#14578939—22no—
78#14578939—41no—
79C2×#11929434C2311yescharacteristic
80C2×#11929434C2311yescharacteristic
81C4⋊Dic157D411yescharacteristic
82C4⋊Dic157C2311yescharacteristic
83#14578933—21no—
84#14578933—21no—
85#14578933—21no—
86#14578933D411yescharacteristic
87#14578933D411yescharacteristic
88C22⋊Dic157—21no—
89C22⋊Dic157—21no—
90#14578931—21no—
91#14578931—21no—
92#14578931—21no—
93#14578931—21no—
94#14578931—21no—
95#14578931—21no—
96C4×Dic157—21no—
97C4×Dic157C2311yescharacteristic
98C4×Dic157C2311yescharacteristic
99C2×Q8×C157C2311yescharacteristic
100C2×D4×C157—21no—
101C2×D4×C157—21no—
102C2×D4×C157C2311yescharacteristic
103C2×D4×C157C2311yescharacteristic
104SD16×C157—41no—
105SD16×C157—41no—
106C2×C8×C157C2311yescharacteristic
107C2×C8×C157C2311yescharacteristic
108C4⋊C4×C157—21no—
109C4⋊C4×C157C2311yescharacteristic
110C42×C157—21no—
111C42×C157C2311yescharacteristic
112C22×D157—21no—
113C22×D157—21no—
114Dic314—22no—
115Dic314—21no—
116Dic314—21no—
117D628—21no—
118D628—21no—
119D628—21no—
120D628—21no—
121C22⋊D157—42no—
122C22⋊D157—42no—
123C22⋊D157—81no—
124C22⋊D157—81no—
125C2×Dic157—21no—
126C2×Dic157—21no—
127C2×Dic157—42no—
128C2×Dic157—42no—
129C2×Dic157C2×D411yescharacteristic
130C2×Dic157C2×D411yescharacteristic
131C2×Dic157C2×D411yescharacteristic
132C2×Dic157C2×D411yescharacteristic
133C4×D157—42no—
134C4×D157—42no—
135#11929434—21no—
136#11929434#4112yescomplemented
137C23×C157—21no—
138C23×C157—21no—
139Q8×C157—21no—
140Q8×C157—21no—
141D4×C157—21no—
142D4×C157—21no—
143D4×C157—21no—
144D4×C157—21no—
145D4×C157—42no—
146D4×C157—81no—
147C2×C4×C157—21no—
148C2×C4×C157—21no—
149C2×C4×C157C2×D411yescharacteristic
150C2×C4×C157C2×D411yescharacteristic
151C2×C4×C157C2411yescharacteristic
152C8×C157—21no—
153C8×C157—21no—
154C22×C157—41no—
155C22×C157—41no—
156C22×C157—41no—
157C22×C157—41no—
158C22×C157—41no—
159C22×C157—41no—
160C22×C157C22×D411yescharacteristic
161C2×D157—41no—
162C2×D157—41no—
163C2×D157—41no—
164C2×D157—41no—
165C2×D157—41no—
166C2×D157—41no—
167C4×C157—21no—
168C4×C157—21no—
169C4×C157—41no—
170C4×C157—41no—
171C4×C157C2×#4111yescharacteristic
172C4×C157H(5,𝔽2)11yescharacteristic
173Dic157—21no—
174Dic157—21no—
175Dic157—21no—
176Dic157—41no—
177Dic157—41no—
178Dic157AGL(1,ℤ/8)12yes—
179C2×C157—81no—
180C2×C157—81no—
181C2×C157#55011yescharacteristic
182C2×C157C2×AGL(1,ℤ/8)11yescharacteristic
183C2×C157#57711yescharacteristic
184D157—81no—
185D157—81no—
186C157#339711yescharacteristic, complemented, Sylow
187#3397—1571nomaximal, Sylow
188#556—1571no—
189#550—1571no—
190#496—1571no—
191#496—1571no—
192#492—1571no—
193#463—1571no—
194#463—1571no—
195#461—1571no—
196#460—1571no—
197#460D15711yescharacteristic, complemented
198#459—1571no—
199#446—1571no—
200#440—1571no—
201#440—1571no—
202C4×D8—1571no—
203C2×#41—3141no—
204C2×SD16—1571no—
205C2×SD16—1571no—
206C2×SD16—1571no—
207C2×SD16—1571no—
208C2×SD16C2×D15711yescharacteristic
209C2×SD16C2×D15711yescharacteristic
210C2×D8—1571no—
211C2×D8—1571no—
212C2×D8—1571no—
213C4⋊Q8—1571no—
214#127—1571no—
215#127—1571no—
216#127C2×D15711yescharacteristic
217#126—3141no—
218#126—3141no—
219#124—1571no—
220#124—1571no—
221C22⋊Q8—3141no—
222#121—3141no—
223#121—3141no—
224#121—3141no—
225C4×Q8—1571no—
226C4×Q8—1571no—
227C4×Q8C2×D15711yescharacteristic
228C4×D4—1571no—
229C4×D4—1571no—
230C4×D4—1571no—
231C4×D4—1571no—
232#117—3141no—
233#107—1571no—
234C4⋊C8—1571no—
235C4⋊C8—1571no—
236C4⋊C8C2×D15711yescharacteristic
237#103—1571no—
238#103—1571no—
239#102—1571no—
240#102—1571no—
241#102C2×D15711yescharacteristic
242#102C2×D15711yescharacteristic
243#97—1571no—
244#97—1571no—
245C4×C8—1571no—
246#41—6284no—
247C2×Q8—1571no—
248C2×Q8—1571no—
249C2×Q8C22×D15711yescharacteristic
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—3141no—
253C2×D4—3141no—
254C2×D4—3141no—
255C2×D4—3141no—
256C2×D4—1571no—
257C2×D4—1571no—
258C2×D4C22×D15711yescharacteristic
259C2×D4C22×D15711yescharacteristic
260C22×C4—3141no—
261C22×C4—3141no—
262C22×C4—3141no—
263C22×C4—3141no—
264SD16—41no—
265SD16—41no—
266SD16—3142no—
267SD16—3142no—
268SD16—6281no—
269SD16—6281no—
270D8—3142no—
271D8—6281no—
272D8—6281no—
273C2×C8—1571no—
274C2×C8—1571no—
275C2×C8C22×D15711yescharacteristic
276C2×C8C22×D15711yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—3141no—
279C4⋊C4—3141no—
280C4⋊C4—3141no—
281C4⋊C4—1571no—
282C4⋊C4—1571no—
283C4⋊C4—1571no—
284C4⋊C4—1571no—
285C4⋊C4C22×D15711yescharacteristic
286C22⋊C4—3141no—
287C22⋊C4—3141no—
288C22⋊C4—3141no—
289C22⋊C4—3141no—
290C22⋊C4—3141no—
291C22⋊C4—3141no—
292C22⋊C4—3141no—
293C22⋊C4—3141no—
294C42—21no—
295C42—3141no—
296C42—1571no—
297C42—1571no—
298C42C22×D15711yescharacteristic
299C23—21no—
300C23—21no—
301C23—3141no—
302C23—3141no—
303Q8—21no—
304Q8—21no—
305Q8—3142no—
306Q8—3141no—
307Q8—3141no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—81no—
314D4—3141no—
315D4—3141no—
316D4—3141no—
317D4—3141no—
318D4—6282no—
319D4—6282no—
320D4—12561no—
321D4—12561no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—3141no—
325C2×C4—3141no—
326C2×C4—6282no—
327C2×C4—6282no—
328C2×C4—6282no—
329C2×C4—6282no—
330C2×C4—1571no—
331C2×C4—1571no—
332C2×C4—1571no—
333C2×C4—1571no—
334C2×C4D4×D15711yescharacteristic
335C2×C4D4×D15711yescharacteristic
336C2×C4C23×D15711yescharacteristic
337C8—21no—
338C8—21no—
339C8—3141no—
340C8—1572no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—6281no—
348C22—6281no—
349C22—6281no—
350C22—6281no—
351C22—6281no—
352C22—6281no—
353C22C2×D4×D15711yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—3141no—
359C4—3141no—
360C4—3141no—
361C4—6281no—
362C4—6281no—
363C4—1572no—
364C4#41×D15711yescharacteristic
365C4#1909781611yescharacteristic
366C2—81no—
367C2—81no—
368C2—12561no—
369C2—12561no—
370C2#2375794111yescharacteristic
371C2AGL(1,ℤ/8)×D15711yescharacteristic
372C2#2375807911yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#460×C157C2
socleC22×C157C22×D4
hypercenter#460D157
hypocenterC157#3397
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #23757995C2semidirect
2. #23757943C2semidirect
3. #23757660C2semidirect
4. #23757659C2semidirect
5. #23757644C2semidirect
6. #23757490C2semidirect
7. #23757489C2semidirect
8. #23757476C2semidirect
9. #23757472C2semidirect
10. #23757467C2semidirect
11. #23757402C2semidirect
12. #23757371C2semidirect
13. #23757370C2semidirect
14. #23757353C2semidirect
15. #460×C157C2semidirect
136. #11929434#41semidirect
186. C157#3397semidirect
197. #460D157semidirect

Maximal subgroups

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

subgroupindex
#237579952
#237579432
#237576602
#237576592
#237576442
#237574902
#237574892
#237574762
#237574722
#237574672
#237574022
#237573712
#237573702
#237573532
#460×C1572
#3397157