Finite Group Databasebeta

← #34110322

Subgroups — #34110322

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#23757894C211yesmaximal, characteristic, complemented
2#23757747C211yesmaximal, characteristic, complemented
3#23757615C211yesmaximal, characteristic, complemented
4#23757598C211yesmaximal, characteristic, complemented
5#23757564C211yesmaximal, characteristic, complemented
6#23757554C211yesmaximal, characteristic, complemented
7#23757489C211yesmaximal, characteristic, complemented
8#23757489C211yesmaximal, characteristic, complemented
9#23757426C211yesmaximal, characteristic, complemented
10#23757409C211yesmaximal, characteristic
11#23757386C211yesmaximal, characteristic, complemented
12#23757375C211yesmaximal, characteristic, complemented
13C4×#14578943C211yesmaximal, characteristic, complemented
14C4×D1256C211yesmaximal, characteristic, complemented
15#433×C157C211yesmaximal, characteristic, complemented
16C22×D628C2211yescharacteristic
17C2×#14578943C2211yescharacteristic
18C2×#14578943C2211yescharacteristic
19C2×D1256C2211yescharacteristic
20C2×D1256C2211yescharacteristic
21#19097771C2211yescharacteristic, complemented
22#19097766—21no—
23#19097759C2211yescharacteristic, complemented
24#19097757—21no—
25#19097753—21no—
26#19097750C2211yescharacteristic
27#19097749—21no—
28#19097745C2211yescharacteristic
29C4×Dic314C2211yescharacteristic, complemented
30C4×D628C2211yescharacteristic
31C4×D628C2211yescharacteristic
32C4×D628C2211yescharacteristic
33C4×D628C2211yescharacteristic
34C4×D628C2211yescharacteristic, complemented
35#19097733—21no—
36#19097733—21no—
37#19097730C2211yescharacteristic
38C22⋊C4×D157—21no—
39C22⋊C4×D157—21no—
40#19097705C2211yescharacteristic, complemented
41#19097705C2211yescharacteristic, complemented
42#19097703C2211yescharacteristic, complemented
43#19097703C2211yescharacteristic, complemented
44#19097696C2211yescharacteristic, complemented
45#19097696C2211yescharacteristic, complemented
46#19097693C2211yescharacteristic
47#19097693C2211yescharacteristic
48#19097693C2211yescharacteristic
49#19097693C2211yescharacteristic
50#19097693C2211yescharacteristic, complemented
51#19097693C2211yescharacteristic, complemented
52#117×C157C2211yescharacteristic
53C4⋊C8×C157C2211yescharacteristic, complemented
54C4⋊C8×C157C2211yescharacteristic, complemented
55C22⋊C8×C157C2211yescharacteristic
56C22⋊C8×C157C2211yescharacteristic
57#97×C157C2211yescharacteristic, complemented
58C4×C8×C157C2211yescharacteristic, complemented
59C23×D157—21no—
60C2×Dic314—21no—
61C2×Dic314C2311yescharacteristic
62C2×D628—22no—
63C2×D628—22no—
64C2×D628—21no—
65C2×D628C2311yescharacteristic
66C2×D628C2311yescharacteristic
67C2×D628C2311yescharacteristic
68C2×C22⋊D157—21no—
69C2×C4×D157—21no—
70C2×C4×D157—21no—
71C2×C4×D157—21no—
72C2×C4×D157—21no—
73C2×C4×D157—21no—
74#14578943—22no—
75#14578943—22no—
76D1256—22no—
77D1256—22no—
78C4⋊Dic157—21no—
79C4⋊Dic157C2311yescharacteristic
80C4⋊Dic157C2311yescharacteristic
81C4⋊Dic157C2311yescharacteristic
82C4⋊Dic157C2311yescharacteristic
83#14578933—21no—
84#14578933—21no—
85C22⋊Dic157—21no—
86C22⋊Dic157—21no—
87#14578931—21no—
88#14578931—21no—
89#14578931—21no—
90#14578931—21no—
91#14578931—21no—
92#14578931—21no—
93#14578931—21no—
94#14578931—21no—
95C4×Dic157—21no—
96C4×Dic157—21no—
97C22×C4×C157C2311yescharacteristic
98C2×C8×C157C2311yescharacteristic
99C2×C8×C157C2311yescharacteristic
100C2×C8×C157C2311yescharacteristic
101C2×C8×C157C2311yescharacteristic
102C4⋊C4×C157D411yescharacteristic
103C4⋊C4×C157D411yescharacteristic
104C22⋊C4×C157D411yescharacteristic
105C22⋊C4×C157D411yescharacteristic
106C42×C157C2311yescharacteristic
107C42×C157C2311yescharacteristic
108C22×D157—21no—
109C22×D157—21no—
110C22×D157—24no—
111C22×D157—21no—
112C22×D157—81no—
113C22×D157—81no—
114Dic314—21no—
115Dic314—21no—
116Dic314—81no—
117D628—24no—
118D628—21no—
119D628—21no—
120D628—21no—
121D628—21no—
122D628#4112yes—
123D628#4112yes—
124C22⋊D157—81no—
125C2×Dic157—21no—
126C2×Dic157—21no—
127C2×Dic157—21no—
128C2×Dic157—21no—
129C2×Dic157—21no—
130C4×D157—81no—
131C4×D157—81no—
132C4×D157—81no—
133C4×D157—81no—
134C4×D157—81no—
135C23×C157C2×D411yescharacteristic
136C2×C4×C157—21no—
137C2×C4×C157—21no—
138C2×C4×C157C2×D411yescharacteristic
139C2×C4×C157C2×D411yescharacteristic
140C2×C4×C157C2×D411yescharacteristic
141C2×C4×C157C2×D411yescharacteristic
142C2×C4×C157C2×D411yescharacteristic
143C2×C4×C157C2411yescharacteristic
144C8×C157—21no—
145C8×C157—21no—
146C8×C157—21no—
147C8×C157—21no—
148C22×C157—21no—
149C22×C157—21no—
150C22×C157—21no—
151C22×C157C22×D411yescharacteristic
152C2×D157—22no—
153C2×D157—22no—
154C2×D157—41no—
155C2×D157—41no—
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—21no—
165C4×C157—21no—
166C4×C157—21no—
167C4×C157C2×#4111yescharacteristic
168C4×C157C2×#4111yescharacteristic
169Dic157—41no—
170Dic157—41no—
171Dic157—41no—
172Dic157—41no—
173Dic157—41no—
174C2×C157—41no—
175C2×C157#52511yescharacteristic
176C2×C157#57611yescharacteristic
177C2×C157#57711yescharacteristic
178D157—42no—
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×SD16—1571no—
196C4×D8—1571no—
197#433D15711yescharacteristic, complemented
198C22×D4—1571no—
199C2×SD16—1571no—
200C2×SD16—1571no—
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×Q8—1571no—
212C4×D4—3141no—
213C4×D4—3141no—
214C4×D4—1571no—
215C4×D4—1571no—
216C4×D4—1571no—
217C4×D4—1571no—
218C4×D4—1571no—
219#117—1571no—
220#117C2×D15711yescharacteristic
221C2×C22⋊C4—3141no—
222C2×C22⋊C4—3141no—
223#107—1571no—
224#107—1571no—
225#106—1571no—
226#106—1571no—
227C4⋊C8C2×D15711yescharacteristic, complemented
228C4⋊C8C2×D15711yescharacteristic, complemented
229#103—1571no—
230#103—1571no—
231#102—1571no—
232#102—1571no—
233#102—1571no—
234#102—1571no—
235#102—1571no—
236#102—1571no—
237C22⋊C8C2×D15711yescharacteristic
238C22⋊C8C2×D15711yescharacteristic
239#97C2×D15711yescharacteristic, complemented
240C4×C8C2×D15711yescharacteristic, complemented
241C24—3141no—
242C2×Q8—3141no—
243C2×Q8—1571no—
244C2×D4—3142no—
245C2×D4—3142no—
246C2×D4—3141no—
247C2×D4—3141no—
248C2×D4—1571no—
249C2×D4—1571no—
250C2×D4—1571no—
251C22×C4—3141no—
252C22×C4—3141no—
253C22×C4—3141no—
254C22×C4—3141no—
255C22×C4—3141no—
256C22×C4C22×D15711yescharacteristic
257SD16—3142no—
258SD16—3142no—
259D8—3142no—
260D8—3142no—
261C2×C8C22×D15711yescharacteristic
262C2×C8C22×D15711yescharacteristic
263C2×C8C22×D15711yescharacteristic
264C2×C8C22×D15711yescharacteristic
265C4⋊C4—3141no—
266C4⋊C4—3141no—
267C4⋊C4—3141no—
268C4⋊C4—1571no—
269C4⋊C4—1571no—
270C4⋊C4—1571no—
271C4⋊C4—1571no—
272C4⋊C4D62811yescharacteristic
273C4⋊C4D62811yescharacteristic
274C22⋊C4—3141no—
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⋊C4D62811yescharacteristic
285C22⋊C4D62811yescharacteristic
286C42—3141no—
287C42—3141no—
288C42C22×D15711yescharacteristic
289C42C22×D15711yescharacteristic
290C23—3144no—
291C23—3141no—
292C23—3141no—
293C23—3141no—
294C23—12561no—
295C23—12561no—
296C23C2×D62811yescharacteristic
297Q8—3141no—
298Q8—3141no—
299Q8—12561no—
300D4—3144no—
301D4—3141no—
302D4—3141no—
303D4—3141no—
304D4—3141no—
305D4—1572no—
306D4—1572no—
307D4—12561no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—3141no—
311C2×C4—3141no—
312C2×C4—3141no—
313C2×C4—3141no—
314C2×C4—3141no—
315C2×C4—12561no—
316C2×C4—12561no—
317C2×C4—12561no—
318C2×C4—12561no—
319C2×C4—12561no—
320C2×C4C2×D62811yescharacteristic
321C2×C4C2×D62811yescharacteristic
322C2×C4C2×D62811yescharacteristic
323C2×C4C2×D62811yescharacteristic
324C2×C4C2×D62811yescharacteristic
325C2×C4C23×D15711yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—3142no—
334C22—3142no—
335C22—6281no—
336C22—6281no—
337C22—6281no—
338C22—6281no—
339C22—6281no—
340C22—6281no—
341C22—6281no—
342C22—12564no—
343C22C22×D62811yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—6281no—
350C4—6281no—
351C4—6281no—
352C4—6281no—
353C4—6281no—
354C4#41×D15711yescharacteristic
355C4#41×D15711yescharacteristic
356C2—41no—
357C2—6282no—
358C2—6282no—
359C2—12561no—
360C2#2375778511yescharacteristic
361C2#2375807811yescharacteristic
362C2#2375808511yescharacteristic
subgroupG/H
centerC22C22×D628
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#433×C157C2
socleC22×C157C22×D4
prime radical#23757409C2
hypercenter#433D157
hypocenterC157#3118
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23757894C2semidirect
2. #23757747C2semidirect
3. #23757615C2semidirect
4. #23757598C2semidirect
5. #23757564C2semidirect
6. #23757554C2semidirect
7. #23757489C2semidirect
8. #23757489C2semidirect
9. #23757426C2semidirect
11. #23757386C2semidirect
12. #23757375C2semidirect
13. C4×#14578943C2semidirect
14. C4×D1256C2semidirect
15. #433×C157C2semidirect
21. #19097771C22semidirect
23. #19097759C22semidirect
29. C4×Dic314C22semidirect
34. C4×D628C22semidirect
40. #19097705C22semidirect
41. #19097705C22semidirect
42. #19097703C22semidirect
43. #19097703C22semidirect
44. #19097696C22semidirect
45. #19097696C22semidirect
50. #19097693C22semidirect
51. #19097693C22semidirect
53. C4⋊C8×C157C22semidirect
54. C4⋊C8×C157C22semidirect
57. #97×C157C22semidirect
58. C4×C8×C157C22semidirect
181. C157#3118semidirect
197. #433D157semidirect
227. C4⋊C8C2×D157semidirect
228. C4⋊C8C2×D157semidirect
239. #97C2×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
#237578942
#237577472
#237576152
#237575982
#237575642
#237575542
#237574892
#237574262
#237574092
#237573862
#237573752
C4×#145789432
C4×D12562
#433×C1572
#3118157