Finite Group Databasebeta

← #34110326

Subgroups — #34110326

Order 20096.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757895C211yesmaximal, characteristic, complemented
2#23757745C211yesmaximal, characteristic, complemented
3#23757613C211yesmaximal, characteristic, complemented
4#23757599C211yesmaximal, characteristic, complemented
5#23757562C211yesmaximal, characteristic, complemented
6#23757551C211yesmaximal, characteristic, complemented
7#23757491C211yesmaximal, characteristic, complemented
8#23757490C211yesmaximal, characteristic, complemented
9#23757422C211yesmaximal, characteristic, complemented
10#23757408C211yesmaximal, characteristic
11#23757383C211yesmaximal, characteristic, complemented
12#23757371C211yesmaximal, characteristic, complemented
13C4×D1256C211yesmaximal, characteristic, complemented
14#23757332C211yesmaximal, characteristic, complemented
15C4×SD16×C157C211yesmaximal, characteristic, complemented
16C2×D4×D157C2211yescharacteristic
17C2×#14578941C2211yescharacteristic
18C2×D1256C2211yescharacteristic
19C2×#14578939C2211yescharacteristic
20#19097770C2211yescharacteristic, complemented
21#19097765—21no—
22#19097760C2211yescharacteristic, complemented
23#19097759—21no—
24#19097756—21no—
25#19097749—21no—
26#19097747C2211yescharacteristic
27#19097746C2211yescharacteristic
28C4×D628C2211yescharacteristic
29C4×D628C2211yescharacteristic, complemented
30D4×Dic157C2211yescharacteristic
31#19097733C2211yescharacteristic
32C4×C22⋊D157—21no—
33#19097731—21no—
34#19097729C2211yescharacteristic
35#19097728C2211yescharacteristic
36C2×#14578931—21no—
37C22⋊C4×D157—21no—
38#19097705C2211yescharacteristic, complemented
39#19097704C2211yescharacteristic, complemented
40#19097702C2211yescharacteristic, complemented
41#19097700C2211yescharacteristic, complemented
42#19097700C2211yescharacteristic, complemented
43#19097695C2211yescharacteristic, complemented
44#19097693C2211yescharacteristic
45#19097693C2211yescharacteristic, complemented
46#19097692C2211yescharacteristic
47#19097691C2211yescharacteristic
48#19097691C2211yescharacteristic, complemented
49#19097683C2211yescharacteristic
50#19097683C2211yescharacteristic
51#19097682C2211yescharacteristic, complemented
52C2×SD16×C157C2211yescharacteristic
53C4×Q8×C157C2211yescharacteristic, complemented
54C4×D4×C157C2211yescharacteristic
55#106×C157C2211yescharacteristic, complemented
56#103×C157C2211yescharacteristic, complemented
57#102×C157C2211yescharacteristic
58C4×C8×C157C2211yescharacteristic, complemented
59C23×D157—21no—
60C2×Dic314—21no—
61C2×D628—21no—
62C2×D628C2311yescharacteristic
63C2×D628C2311yescharacteristic
64C2×C22⋊D157—21no—
65D4×D157—22no—
66D4×D157—22no—
67C22×Dic157—21no—
68C2×C4×D157—21no—
69C2×C4×D157—21no—
70C2×C4×D157—21no—
71C2×C4×D157C2311yescharacteristic
72#14578941—22no—
73D1256—22no—
74#14578939—22no—
75C2×#11929434C2311yescharacteristic
76C2×#11929434C2311yescharacteristic
77C4⋊Dic157C2311yescharacteristic
78C4⋊Dic157C2311yescharacteristic
79#14578933—21no—
80#14578933—21no—
81#14578933D411yescharacteristic
82#14578933D411yescharacteristic
83C22⋊Dic157—21no—
84#14578931—21no—
85#14578931—21no—
86#14578931—21no—
87#14578931—21no—
88#14578931—21no—
89#14578931—21no—
90#14578931—21no—
91#14578931—21no—
92#14578931D411yescharacteristic
93#14578931D411yescharacteristic
94C4×Dic157—21no—
95C4×Dic157C2311yescharacteristic
96C2×Q8×C157C2311yescharacteristic
97C2×D4×C157C2311yescharacteristic
98C22×C4×C157—21no—
99SD16×C157—22no—
100C2×C8×C157C2311yescharacteristic
101C2×C8×C157C2311yescharacteristic
102C4⋊C4×C157—21no—
103C4⋊C4×C157C2311yescharacteristic
104C4⋊C4×C157C2311yescharacteristic
105C22⋊C4×C157—21no—
106C42×C157—21no—
107C42×C157C2311yescharacteristic
108C22×D157—21no—
109C22×D157—24no—
110C22×D157—21no—
111C22×D157—81no—
112C22×D157—81no—
113C22×D157C2×D411yescharacteristic
114Dic314—81no—
115D628—21no—
116D628—21no—
117D628—21no—
118D628—81no—
119D628#4112yes—
120C22⋊D157—24no—
121C2×Dic157—21no—
122C2×Dic157—21no—
123C2×Dic157—81no—
124C2×Dic157C2×D411yescharacteristic
125C2×Dic157C2×D411yescharacteristic
126C2×Dic157C2×D411yescharacteristic
127C4×D157—21no—
128C4×D157—21no—
129C4×D157—81no—
130C4×D157—81no—
131C4×D157—81no—
132#11929434—21no—
133#11929434—21no—
134C23×C157—21no—
135Q8×C157—21no—
136Q8×C157—21no—
137D4×C157—21no—
138D4×C157#4112yes—
139C2×C4×C157—21no—
140C2×C4×C157—21no—
141C2×C4×C157—21no—
142C2×C4×C157—81no—
143C2×C4×C157C2×D411yescharacteristic
144C2×C4×C157C2×D411yescharacteristic
145C2×C4×C157C2411yescharacteristic
146C8×C157—21no—
147C8×C157—21no—
148C22×C157—22no—
149C22×C157—41no—
150C22×C157—41no—
151C22×C157C22×D411yescharacteristic
152C2×D157—21no—
153C2×D157—22no—
154C2×D157—21no—
155C2×D157—21no—
156C2×D157—41no—
157C2×D157—41no—
158C2×D157—41no—
159C2×D157—41no—
160C2×D157—41no—
161C2×D157—84no—
162C4×C157—21no—
163C4×C157—21no—
164C4×C157—41no—
165C4×C157—41no—
166C4×C157—41no—
167C4×C157C2×#4111yescharacteristic
168C4×C157C2×#4111yescharacteristic
169Dic157—21no—
170Dic157—21no—
171Dic157—21no—
172Dic157—41no—
173Dic157—41no—
174C2×C157—42no—
175C2×C157#52511yescharacteristic
176C2×C157#57611yescharacteristic
177C2×C157#57711yescharacteristic
178D157—41no—
179D157—42no—
180D157—81no—
181C157#311811yescharacteristic, complemented, Sylow
182#3118—1571nomaximal, Sylow
183#542—1571no—
184#518—1571no—
185#485—1571no—
186#482—1571no—
187#476—1571no—
188#474—1571no—
189#463—1571no—
190#463—1571no—
191#450—1571no—
192#447—1571no—
193#442—1571no—
194#440—1571no—
195C4×SD16D15711yescharacteristic, complemented
196C4×D8—1571no—
197#433—1571no—
198C22×D4—1571no—
199C2×SD16—1571no—
200C2×SD16C2×D15711yescharacteristic
201C2×D8—1571no—
202C2×D8—1571no—
203C4⋊Q8—1571no—
204#126—3141no—
205#124—3141no—
206#124—1571no—
207#123—3141no—
208C22⋊Q8—3141no—
209C22⋊Q8—1571no—
210#121—1571no—
211C4×Q8C2×D15711yescharacteristic, complemented
212C4×D4—3141no—
213C4×D4—3141no—
214C4×D4—1571no—
215C4×D4—1571no—
216C4×D4—1571no—
217C4×D4—1571no—
218C4×D4C2×D15711yescharacteristic
219#117—1571no—
220#117—1571no—
221C2×C22⋊C4—3141no—
222C2×C22⋊C4—3141no—
223#107—1571no—
224#107—1571no—
225#106—1571no—
226#106C2×D15711yescharacteristic, complemented
227C4⋊C8—1571no—
228C4⋊C8—1571no—
229#103—1571no—
230#103C2×D15711yescharacteristic, complemented
231#102—1571no—
232#102—1571no—
233#102—1571no—
234#102—1571no—
235#102—1571no—
236#102C2×D15711yescharacteristic
237C22⋊C8—1571no—
238C22⋊C8—1571no—
239#97—1571no—
240C4×C8C2×D15711yescharacteristic, complemented
241C24—3141no—
242C2×Q8—3141no—
243C2×Q8C22×D15711yescharacteristic
244C2×D4—3141no—
245C2×D4—3142no—
246C2×D4—3142no—
247C2×D4—3141no—
248C2×D4—1571no—
249C2×D4—1571no—
250C2×D4C22×D15711yescharacteristic
251C22×C4—21no—
252C22×C4—3141no—
253C22×C4—3141no—
254C22×C4—3141no—
255C22×C4—3141no—
256C22×C4—1571no—
257SD16—22no—
258SD16—3142no—
259D8—3142no—
260D8—3142no—
261C2×C8—1571no—
262C2×C8—1571no—
263C2×C8C22×D15711yescharacteristic
264C2×C8C22×D15711yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—3141no—
267C4⋊C4—3141no—
268C4⋊C4—1571no—
269C4⋊C4—1571no—
270C4⋊C4—1571no—
271C4⋊C4—1571no—
272C4⋊C4C22×D15711yescharacteristic
273C4⋊C4C22×D15711yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—3141no—
276C22⋊C4—3141no—
277C22⋊C4—3141no—
278C22⋊C4—3141no—
279C22⋊C4—3141no—
280C22⋊C4—3141no—
281C22⋊C4—3141no—
282C22⋊C4—3141no—
283C22⋊C4—3141no—
284C22⋊C4—1571no—
285C22⋊C4—1571no—
286C42—21no—
287C42—3141no—
288C42—1571no—
289C42C22×D15711yescharacteristic
290C23—21no—
291C23—3144no—
292C23—3141no—
293C23—3141no—
294C23—1571no—
295C23—12561no—
296C23—12561no—
297Q8—21no—
298Q8—21no—
299Q8—12561no—
300D4—21no—
301D4—3144no—
302D4—3141no—
303D4—3141no—
304D4—3141no—
305D4—1572no—
306D4—12561no—
307D4#1457895412yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—3141no—
313C2×C4—3141no—
314C2×C4—3141no—
315C2×C4—3141no—
316C2×C4—1571no—
317C2×C4—1571no—
318C2×C4—1571no—
319C2×C4—12561no—
320C2×C4—12561no—
321C2×C4—12561no—
322C2×C4—12561no—
323C2×C4D4×D15711yescharacteristic
324C2×C4D4×D15711yescharacteristic
325C2×C4C23×D15711yescharacteristic
326C8—21no—
327C8—21no—
328C8—3141no—
329C8—3141no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—3141no—
334C22—3142no—
335C22—3141no—
336C22—3141no—
337C22—6281no—
338C22—6281no—
339C22—6281no—
340C22—6281no—
341C22—6281no—
342C22—12564no—
343C22C2×D4×D15711yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—3141no—
350C4—3141no—
351C4—3141no—
352C4—6281no—
353C4—6281no—
354C4#41×D15711yescharacteristic
355C4C2×#1457895411yescharacteristic
356C2—42no—
357C2—6281no—
358C2—6282no—
359C2—12561no—
360C2#2375778211yescharacteristic
361C2#2375807511yescharacteristic
362C2#2375807911yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC4×SD16×C157C2
socleC22×C157C22×D4
prime radical#23757408C2
hypercenterC4×SD16D157
hypocenterC157#3118
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #23757895C2semidirect
2. #23757745C2semidirect
3. #23757613C2semidirect
4. #23757599C2semidirect
5. #23757562C2semidirect
6. #23757551C2semidirect
7. #23757491C2semidirect
8. #23757490C2semidirect
9. #23757422C2semidirect
11. #23757383C2semidirect
12. #23757371C2semidirect
13. C4×D1256C2semidirect
14. #23757332C2semidirect
15. C4×SD16×C157C2semidirect
20. #19097770C22semidirect
22. #19097760C22semidirect
29. C4×D628C22semidirect
38. #19097705C22semidirect
39. #19097704C22semidirect
40. #19097702C22semidirect
41. #19097700C22semidirect
42. #19097700C22semidirect
43. #19097695C22semidirect
45. #19097693C22semidirect
48. #19097691C22semidirect
51. #19097682C22semidirect
53. C4×Q8×C157C22semidirect
55. #106×C157C22semidirect
56. #103×C157C22semidirect
58. C4×C8×C157C22semidirect
181. C157#3118semidirect
195. C4×SD16D157semidirect
211. C4×Q8C2×D157semidirect
226. #106C2×D157semidirect
230. #103C2×D157semidirect
240. C4×C8C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237578952
#237577452
#237576132
#237575992
#237575622
#237575512
#237574912
#237574902
#237574222
#237574082
#237573832
#237573712
C4×D12562
#237573322
C4×SD16×C1572
#3118157