Finite Group Databasebeta

← #34110485

Subgroups — #34110485

Order 20096.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757900C211yesmaximal, characteristic, complemented
2#23757836C211yesmaximal, characteristic
3#23757637C211yesmaximal, characteristic, complemented
4#23757636C211yesmaximal, characteristic, complemented
5#23757635C211yesmaximal, characteristic, complemented
6#23757631C211yesmaximal, characteristic, complemented
7#23757628C211yesmaximal, characteristic, complemented
8#23757626C211yesmaximal, characteristic, complemented
9#23757618C211yesmaximal, characteristic, complemented
10#23757276C211yesmaximal, characteristic, complemented
11#23757271C211yesmaximal, characteristic, complemented
12#23757266C211yesmaximal, characteristic, complemented
13#102×D157C211yesmaximal, characteristic, complemented
14#23757227C211yesmaximal, characteristic, complemented
15#486×C157C211yesmaximal, characteristic, complemented
16C2×#14578953C2211yescharacteristic
17C2×D4×D157C2211yescharacteristic
18C2×#14578937C2211yescharacteristic
19C2×C8×D157C2211yescharacteristic
20#19097770C2211yescharacteristic, complemented
21#19097769—21no—
22#19097767C2211yescharacteristic
23#19097763C2211yescharacteristic, complemented
24#19097762C2211yescharacteristic, complemented
25#19097761—21no—
26#19097759C2211yescharacteristic
27#19097758C2211yescharacteristic
28#19097749—21no—
29#19097747—21no—
30#19097743—21no—
31#19097743—21no—
32#19097739—21no—
33#19097739—21no—
34#19097729C2211yescharacteristic
35#19097728C2211yescharacteristic
36C4⋊C4×D157C2211yescharacteristic
37#19097696C2211yescharacteristic, complemented
38#19097696C2211yescharacteristic, complemented
39#19097694C2211yescharacteristic, complemented
40#19097694C2211yescharacteristic, complemented
41#19097693C2211yescharacteristic
42#19097693C2211yescharacteristic
43#19097692C2211yescharacteristic
44#19097692C2211yescharacteristic
45#19097692C2211yescharacteristic, complemented
46#19097692C2211yescharacteristic, complemented
47#19097691C2211yescharacteristic
48#19097691C2211yescharacteristic
49#19097682C2211yescharacteristic, complemented
50#19097681C2211yescharacteristic, complemented
51C8×Dic157C2211yescharacteristic, complemented
52C4⋊Q8×C157C2211yescharacteristic, complemented
53#127×C157C2211yescharacteristic
54#102×C157C2211yescharacteristic
55#102×C157C2211yescharacteristic
56#102×C157C2211yescharacteristic, complemented
57#102×C157C2211yescharacteristic, complemented
58C4×C8×C157C2211yescharacteristic, complemented
59C23×D157—21no—
60#14578953—22no—
61#14578953—22no—
62C2×Dic314—21no—
63C2×Dic314C2311yescharacteristic
64C2×D628C2311yescharacteristic
65C2×C22⋊D157—21no—
66C2×C22⋊D157—21no—
67C2×C22⋊D157—21no—
68C2×C22⋊D157—21no—
69D4×D157—22no—
70D4×D157—22no—
71C22×Dic157—21no—
72C2×C4×D157—21no—
73C2×C4×D157C2311yescharacteristic
74#14578937—22no—
75C2×#11929434C2311yescharacteristic
76C2×#11929434C2311yescharacteristic
77C8×D157—22no—
78C4⋊Dic157—21no—
79C4⋊Dic157C2311yescharacteristic
80C4⋊Dic157C2311yescharacteristic
81#14578933—21no—
82#14578933—21no—
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#14578931D411yescharacteristic
94#14578931D411yescharacteristic
95C4×Dic157—21no—
96C4×Dic157C2311yescharacteristic
97C2×Q8×C157—21no—
98C2×D4×C157—21no—
99C2×D4×C157—21no—
100C2×D4×C157C2311yescharacteristic
101C2×D4×C157C2311yescharacteristic
102C2×C8×C157C2311yescharacteristic
103C2×C8×C157C2311yescharacteristic
104C4⋊C4×C157—21no—
105C4⋊C4×C157C2311yescharacteristic
106C4⋊C4×C157C2311yescharacteristic
107C42×C157C2311yescharacteristic
108C22×D157—21no—
109C22×D157—42no—
110C22×D157—81no—
111C22×D157—81no—
112C22×D157C2×D411yescharacteristic
113Dic314—21no—
114Dic314—21no—
115Dic314—81no—
116D628—21no—
117D628—21no—
118C22⋊D157—42no—
119C22⋊D157—42no—
120C22⋊D157—81no—
121C22⋊D157—81no—
122C2×Dic157—21no—
123C2×Dic157—21no—
124C2×Dic157—21no—
125C2×Dic157—42no—
126C2×Dic157C2×D411yescharacteristic
127C2×Dic157C2×D411yescharacteristic
128C2×Dic157C2×D411yescharacteristic
129C4×D157—81no—
130C4×D157#4112yes—
131C4×D157#4112yes—
132#11929434—21no—
133#11929434—21no—
134C23×C157—21no—
135C23×C157—21no—
136Q8×C157—81no—
137D4×C157—21no—
138D4×C157—21no—
139D4×C157—21no—
140D4×C157—21no—
141D4×C157—81no—
142D4×C157—81no—
143C2×C4×C157—21no—
144C2×C4×C157—21no—
145C2×C4×C157C2×D411yescharacteristic
146C2×C4×C157C2×D411yescharacteristic
147C2×C4×C157C2411yescharacteristic
148C8×C157—21no—
149C8×C157—21no—
150C22×C157—41no—
151C22×C157—41no—
152C22×C157—41no—
153C22×C157—41no—
154C22×C157—41no—
155C22×C157—41no—
156C22×C157C22×D411yescharacteristic
157C2×D157—21no—
158C2×D157—21no—
159C2×D157—41no—
160C2×D157—41no—
161C2×D157—41no—
162C2×D157—84no—
163C2×D157#12412yes—
164C4×C157—21no—
165C4×C157—21no—
166C4×C157—41no—
167C4×C157—41no—
168C4×C157C2×#4111yescharacteristic
169C4×C157C2×#4111yescharacteristic
170Dic157—21no—
171Dic157—21no—
172Dic157—41no—
173Dic157—41no—
174Dic157—41no—
175Dic157#12412yes—
176C2×C157—81no—
177C2×C157—81no—
178C2×C157C2×#12411yescharacteristic
179C2×C157#57611yescharacteristic
180C2×C157#57711yescharacteristic
181D157—22no—
182D157—81no—
183C157#313611yescharacteristic, complemented, Sylow
184#3136—1571nomaximal, Sylow
185#544—1571no—
186#535—1571no—
187#490—1571no—
188#490—1571no—
189#489—1571no—
190#489—1571no—
191#488—1571no—
192#488—1571no—
193#486—1571no—
194#486D15711yescharacteristic, complemented
195#418—1571no—
196#417—1571no—
197#416—1571no—
198C2×#102—1571no—
199#405—1571no—
200C2×#41—1571no—
201C22×D4—1571no—
202C2×M16—1571no—
203C22×C8—1571no—
204C4⋊Q8—3141no—
205C4⋊Q8—1571no—
206C4⋊Q8C2×D15711yescharacteristic, complemented
207#127—1571no—
208#127C2×D15711yescharacteristic
209#125—3141no—
210#125—1571no—
211#125—1571no—
212#124—1571no—
213#124—1571no—
214C22⋊Q8—3141no—
215C22⋊Q8—3141no—
216#121—3141no—
217#121—3141no—
218#120—3141no—
219#120—3141no—
220#117—1571no—
221#117—1571no—
222C2×C4⋊C4—1571no—
223#103—1571no—
224#103—1571no—
225#103—1571no—
226#103—1571no—
227#102—1571no—
228#102—1571no—
229#102—1571no—
230#102—1571no—
231#102—1571no—
232#102—1571no—
233#102—1571no—
234#102—1571no—
235#102C2×D15711yescharacteristic
236#102C2×D15711yescharacteristic
237#102C2×D15711yescharacteristic, complemented
238#102C2×D15711yescharacteristic, complemented
239#97—1571no—
240#97—1571no—
241C4×C8—1571no—
242C4×C8C2×D15711yescharacteristic, complemented
243C24—3141no—
244#41—3142no—
245#41—3142no—
246C2×Q8—21no—
247C2×Q8—3141no—
248C2×Q8—1571no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—3141no—
252C2×D4—3142no—
253C2×D4—3142no—
254C2×D4—3141no—
255C2×D4—3141no—
256C2×D4—3141no—
257C2×D4—1571no—
258C2×D4C22×D15711yescharacteristic
259C2×D4C22×D15711yescharacteristic
260C22×C4—3141no—
261C22×C4—3141no—
262C22×C4—1571no—
263M16—3142no—
264C2×C8—3142no—
265C2×C8—1571no—
266C2×C8—1571no—
267C2×C8C22×D15711yescharacteristic
268C2×C8C22×D15711yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—3141no—
271C4⋊C4—3141no—
272C4⋊C4—3141no—
273C4⋊C4—3141no—
274C4⋊C4—3141no—
275C4⋊C4—3141no—
276C4⋊C4—1571no—
277C4⋊C4—1571no—
278C4⋊C4—1571no—
279C4⋊C4—1571no—
280C4⋊C4C22×D15711yescharacteristic
281C4⋊C4C22×D15711yescharacteristic
282C22⋊C4—3141no—
283C22⋊C4—3141no—
284C22⋊C4—3141no—
285C22⋊C4—3141no—
286C22⋊C4—3141no—
287C22⋊C4—1571no—
288C22⋊C4—1571no—
289C42—3141no—
290C42—1571no—
291C42C22×D15711yescharacteristic
292C23—21no—
293C23—21no—
294C23—3141no—
295C23—6282no—
296C23—1571no—
297C23—12561no—
298C23—12561no—
299Q8—81no—
300Q8—3141no—
301Q8—3141no—
302Q8—12561no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—81no—
309D4—3141no—
310D4—3141no—
311D4—6282no—
312D4—6282no—
313D4—12561no—
314D4—12561no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—3141no—
318C2×C4—3141no—
319C2×C4—3141no—
320C2×C4—6282no—
321C2×C4—1571no—
322C2×C4—1571no—
323C2×C4—1571no—
324C2×C4—1572no—
325C2×C4—1572no—
326C2×C4—12561no—
327C2×C4D4×D15711yescharacteristic
328C2×C4D4×D15711yescharacteristic
329C2×C4C23×D15711yescharacteristic
330C8—21no—
331C8—21no—
332C8—3141no—
333C8—3141no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—3141no—
341C22—3141no—
342C22—6281no—
343C22—6281no—
344C22—6281no—
345C22—1572no—
346C22—12564no—
347C22C2×D4×D15711yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—3141no—
353C4—3141no—
354C4—6281no—
355C4—6281no—
356C4—6281no—
357C4—1572no—
358C4#41×D15711yescharacteristic
359C4#41×D15711yescharacteristic
360C2—81no—
361C2—81no—
362C2—3142no—
363C2—12561no—
364C2#124×D15711yescharacteristic
365C2#2375807411yescharacteristic
366C2#2375807911yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#486×C157C2
socleC22×C157C22×D4
prime radical#23757836C2
hypercenter#486D157
hypocenterC157#3136
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #23757900C2semidirect
3. #23757637C2semidirect
4. #23757636C2semidirect
5. #23757635C2semidirect
6. #23757631C2semidirect
7. #23757628C2semidirect
8. #23757626C2semidirect
9. #23757618C2semidirect
10. #23757276C2semidirect
11. #23757271C2semidirect
12. #23757266C2semidirect
13. #102×D157C2semidirect
14. #23757227C2semidirect
15. #486×C157C2semidirect
20. #19097770C22semidirect
23. #19097763C22semidirect
24. #19097762C22semidirect
37. #19097696C22semidirect
38. #19097696C22semidirect
39. #19097694C22semidirect
40. #19097694C22semidirect
45. #19097692C22semidirect
46. #19097692C22semidirect
49. #19097682C22semidirect
50. #19097681C22semidirect
51. C8×Dic157C22semidirect
52. C4⋊Q8×C157C22semidirect
56. #102×C157C22semidirect
57. #102×C157C22semidirect
58. C4×C8×C157C22semidirect
183. C157#3136semidirect
194. #486D157semidirect
206. C4⋊Q8C2×D157semidirect
237. #102C2×D157semidirect
238. #102C2×D157semidirect
242. C4×C8C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237579002
#237578362
#237576372
#237576362
#237576352
#237576312
#237576282
#237576262
#237576182
#237572762
#237572712
#237572662
#102×D1572
#237572272
#486×C1572
#3136157