Finite Group Databasebeta

← #34111944

Subgroups — #34111944

Order 20096.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757923C211yesmaximal, characteristic, complemented
2#23757907C211yesmaximal, characteristic, complemented
3#23757618C211yesmaximal, characteristic, complemented
4#23757588C211yesmaximal, characteristic, complemented
5#23757584C211yesmaximal, characteristic, complemented
6#23757552C211yesmaximal, characteristic, complemented
7#23757508C211yesmaximal, characteristic, complemented
8#23757466C211yesmaximal, characteristic, complemented
9#23757406C211yesmaximal, characteristic, complemented
10#23757405C211yesmaximal, characteristic, complemented
11#23757353C211yesmaximal, characteristic, complemented
12C8×C22⋊D157C211yesmaximal, characteristic, complemented
13C2×#19097693C211yesmaximal, characteristic, complemented
14#102×D157C211yesmaximal, characteristic, complemented
15#466×C157C211yesmaximal, characteristic, complemented
16C2×#14578953—21no—
17C22×D628C2211yescharacteristic
18C2×D4×D157—21no—
19C2×D4×D157C2211yescharacteristic
20C2×#14578939C2211yescharacteristic
21C2×#14578939C2211yescharacteristic, complemented
22C2×C8×D157C2211yescharacteristic, complemented
23#19097770C2211yescharacteristic, complemented
24#19097767C2211yescharacteristic
25#19097753—21no—
26#19097752—21no—
27#19097748—21no—
28#19097746C2211yescharacteristic
29#19097744—21no—
30#19097742C2211yescharacteristic, complemented
31#19097741—21no—
32#19097739—21no—
33D4×Dic157C2211yescharacteristic, complemented
34#19097733C2211yescharacteristic
35C4×C22⋊D157C2211yescharacteristic
36C2×C4⋊Dic157C2211yescharacteristic, complemented
37C4⋊C4×D157C2211yescharacteristic, complemented
38#19097704C2211yescharacteristic, complemented
39#19097704C2211yescharacteristic, complemented
40#19097700C2211yescharacteristic, complemented
41#19097693C2211yescharacteristic
42#19097693C2211yescharacteristic
43#19097693C2211yescharacteristic, complemented
44#19097693C2211yescharacteristic, complemented
45#19097692C2211yescharacteristic, complemented
46#19097692C2211yescharacteristic, complemented
47#19097691C2211yescharacteristic
48#19097691C2211yescharacteristic, complemented
49C22⋊#11929434C2211yescharacteristic, complemented
50#19097683C2211yescharacteristic, complemented
51C8×Dic157C2211yescharacteristic, complemented
52C2×D8×C157C2211yescharacteristic, complemented
53C22×C8×C157C2211yescharacteristic, complemented
54#121×C157C2211yescharacteristic
55#121×C157C2211yescharacteristic, complemented
56#107×C157C2211yescharacteristic, complemented
57#102×C157C2211yescharacteristic, complemented
58#102×C157C2211yescharacteristic, complemented
59C23×D157—21no—
60C23×D157—21no—
61#14578953—44no—
62C2×Dic314—21no—
63C2×D628—22no—
64C2×D628—21no—
65C2×D628—21no—
66C2×D628—41no—
67C2×D628C2311yescharacteristic
68C2×D628C2311yescharacteristic
69C2×C22⋊D157—21no—
70C2×C22⋊D157—21no—
71C2×C22⋊D157—21no—
72C2×C22⋊D157—21no—
73C2×C22⋊D157D411yescharacteristic
74D4×D157—22no—
75D4×D157—41no—
76D4×D157—44no—
77C22×Dic157—21no—
78C22×Dic157—21no—
79C2×C4×D157—21no—
80C2×C4×D157—21no—
81C2×C4×D157C2311yescharacteristic
82#14578939—22no—
83#14578939—41no—
84C2×#11929434C2311yescharacteristic
85C2×#11929434C2311yescharacteristic
86C8×D157—41no—
87C4⋊Dic157—21no—
88C4⋊Dic157C2311yescharacteristic
89C4⋊Dic157C2311yescharacteristic
90#14578933—21no—
91#14578933—21no—
92#14578933D411yescharacteristic
93C22⋊Dic157—21no—
94C22⋊Dic157—21no—
95C22⋊Dic157D411yescharacteristic
96#14578931—21no—
97#14578931—21no—
98#14578931D411yescharacteristic
99C4×Dic157C2311yescharacteristic
100C2×D4×C157—21no—
101C2×D4×C157—21no—
102C2×D4×C157C2311yescharacteristic
103C2×D4×C157C2311yescharacteristic
104C22×C4×C157C2311yescharacteristic
105D8×C157—41no—
106C2×C8×C157—41no—
107C2×C8×C157C2311yescharacteristic
108C2×C8×C157C2311yescharacteristic
109C4⋊C4×C157C2311yescharacteristic
110C4⋊C4×C157C2311yescharacteristic
111C22⋊C4×C157—21no—
112C22⋊C4×C157—21no—
113C22×D157—21no—
114C22×D157—21no—
115C22×D157—42no—
116C22×D157—42no—
117C22×D157—42no—
118C22×D157—42no—
119C22×D157—81no—
120C22×D157—81no—
121C22×D157C2×D411yescharacteristic
122Dic314—42no—
123D628—21no—
124D628—21no—
125D628—21no—
126D628—42no—
127D628—42no—
128D628#4112yescomplemented
129C22⋊D157—42no—
130C22⋊D157—42no—
131C22⋊D157—42no—
132C22⋊D157—81no—
133C22⋊D157D814yescomplemented
134C2×Dic157—21no—
135C2×Dic157—21no—
136C2×Dic157—42no—
137C2×Dic157—42no—
138C2×Dic157C2×D411yescharacteristic
139C2×Dic157C2×D411yescharacteristic
140C2×Dic157C2×D411yescharacteristic
141C4×D157—21no—
142C4×D157—21no—
143C4×D157—42no—
144C4×D157—42no—
145#11929434—21no—
146#11929434—21no—
147C23×C157—21no—
148C23×C157—21no—
149C23×C157C2×D411yescharacteristic
150D4×C157—21no—
151D4×C157—21no—
152D4×C157—21no—
153D4×C157—21no—
154D4×C157—42no—
155D4×C157—42no—
156C2×C4×C157—21no—
157C2×C4×C157—21no—
158C2×C4×C157—21no—
159C2×C4×C157—21no—
160C2×C4×C157C2×D411yescharacteristic
161C2×C4×C157C2411yescharacteristic
162C8×C157—21no—
163C8×C157—21no—
164C22×C157—21no—
165C22×C157—21no—
166C22×C157—41no—
167C22×C157—41no—
168C22×C157—41no—
169C22×C157—41no—
170C22×C157—41no—
171C22×C157—41no—
172C22×C157C2×D812yes—
173C22×C157C22×D411yescharacteristic
174C2×D157—21no—
175C2×D157—21no—
176C2×D157—22no—
177C2×D157—41no—
178C2×D157—41no—
179C2×D157—41no—
180C2×D157—41no—
181C2×D157—41no—
182C2×D157—84no—
183C2×D157—84no—
184C2×D157C2×D812yes—
185C4×C157—21no—
186C4×C157—41no—
187C4×C157—41no—
188C4×C157C2×#4111yescharacteristic
189C4×C157H(5,𝔽2)11yescharacteristic
190Dic157—21no—
191Dic157—21no—
192Dic157—41no—
193Dic157—41no—
194Dic157C2×D812yes—
195C2×C157—22no—
196C2×C157—81no—
197C2×C157—81no—
198C2×C157#54611yescharacteristic
199C2×C157C22×D811yescharacteristic
200C2×C157#57711yescharacteristic
201D157—22no—
202D157—42no—
203D157—81no—
204C157#329411yescharacteristic, complemented, Sylow
205#3294—1571nomaximal, Sylow
206#547—1571no—
207D42—1571no—
208#486—1571no—
209#480—1571no—
210#480—1571no—
211#474—1571no—
212#466—1571no—
213#466D15711yescharacteristic, complemented
214#459—1571no—
215#447—1571no—
216#447—1571no—
217C4×D8—1571no—
218C8×D4—1571no—
219C2×#102—1571no—
220C2×#102—1571no—
221C2×#41—3141no—
222C22×D4—3141no—
223C22×D4—1571no—
224C22×D4—1571no—
225C2×D8—1571no—
226C2×D8—1571no—
227C2×D8C2×D15711yescharacteristic, complemented
228C22×C8—1571no—
229C22×C8C2×D15711yescharacteristic, complemented
230C4⋊Q8—1571no—
231#127—1571no—
232#123—3141no—
233#123—3141no—
234C22⋊Q8—3141no—
235#121—3141no—
236#121—1571no—
237#121—1571no—
238#121C2×D15711yescharacteristic
239#121C2×D15711yescharacteristic, complemented
240#120—3141no—
241#120—3141no—
242C4×D4—1571no—
243C4×D4—1571no—
244C4×D4—1571no—
245C2×C4⋊C4—1571no—
246C2×C4⋊C4—1571no—
247#107—1571no—
248#107—1571no—
249#107C2×D15711yescharacteristic, complemented
250C4⋊C8—1571no—
251#102—1571no—
252#102—1571no—
253#102—1571no—
254#102—1571no—
255#102—1571no—
256#102—1571no—
257#102—1571no—
258#102—1571no—
259#102C2×D15711yescharacteristic, complemented
260#102C2×D15711yescharacteristic, complemented
261C22⋊C8—1571no—
262C22⋊C8—1571no—
263C4×C8—1571no—
264C24—3141no—
265C24—3141no—
266#41—6284no—
267C2×Q8—3141no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—3142no—
271C2×D4—3141no—
272C2×D4—3142no—
273C2×D4—3141no—
274C2×D4—3141no—
275C2×D4—3141no—
276C2×D4—3141no—
277C2×D4—3141no—
278C2×D4—6281no—
279C2×D4—6281no—
280C2×D4—6284no—
281C2×D4—1571no—
282C2×D4—1571no—
283C2×D4—1571no—
284C2×D4C22×D15711yescharacteristic
285C2×D4C22×D15711yescharacteristic
286C22×C4—3141no—
287C22×C4—3141no—
288C22×C4—3141no—
289C22×C4—3141no—
290C22×C4—1571no—
291C22×C4C22×D15711yescharacteristic
292D8—41no—
293D8—3142no—
294D8—6281no—
295C2×C8—41no—
296C2×C8—6281no—
297C2×C8—1571no—
298C2×C8—1571no—
299C2×C8C22×D15711yescharacteristic
300C2×C8C22×D15711yescharacteristic
301C4⋊C4—3141no—
302C4⋊C4—3141no—
303C4⋊C4—3141no—
304C4⋊C4—1571no—
305C4⋊C4—1571no—
306C4⋊C4—1571no—
307C4⋊C4C22×D15711yescharacteristic
308C4⋊C4C22×D15711yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—3141no—
312C22⋊C4—3141no—
313C22⋊C4—3141no—
314C22⋊C4—3141no—
315C22⋊C4—1571no—
316C22⋊C4—1571no—
317C42—1571no—
318C23—21no—
319C23—21no—
320C23—3141no—
321C23—3141no—
322C23—6282no—
323C23—6282no—
324C23—6282no—
325C23—6282no—
326C23—1571no—
327C23—12561no—
328C23—12561no—
329C23D4×D15711yescharacteristic
330Q8—6282no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—42no—
336D4—42no—
337D4—3141no—
338D4—3141no—
339D4—3141no—
340D4—6282no—
341D4—6282no—
342D4—6282no—
343D4—6282no—
344D4—6282no—
345D4—1574no—
346D4—1572no—
347D4—12561no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—3141no—
353C2×C4—3141no—
354C2×C4—3141no—
355C2×C4—3141no—
356C2×C4—6282no—
357C2×C4—6282no—
358C2×C4—6282no—
359C2×C4—6282no—
360C2×C4—1571no—
361C2×C4—1571no—
362C2×C4—1571no—
363C2×C4D4×D15711yescharacteristic
364C2×C4C23×D15711yescharacteristic
365C8—21no—
366C8—21no—
367C8—3141no—
368C8—3141no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—3141no—
378C22—3141no—
379C22—3142no—
380C22—6281no—
381C22—6281no—
382C22—6281no—
383C22—6281no—
384C22—6281no—
385C22—1572no—
386C22—12564no—
387C22—12564no—
388C22D8×D15712yes—
389C22C2×D4×D15711yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—3141no—
394C4—3141no—
395C4—6281no—
396C4—6281no—
397C4—1572no—
398C4#41×D15711yescharacteristic
399C4#1909781611yescharacteristic
400C2—22no—
401C2—81no—
402C2—81no—
403C2—3142no—
404C2—6282no—
405C2—12561no—
406C2#2375791211yescharacteristic
407C2C2×D8×D15711yescharacteristic
408C2#2375808011yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#466×C157C2
socleC22×C157C22×D4
hypercenter#466D157
hypocenterC157#3294
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #23757923C2semidirect
2. #23757907C2semidirect
3. #23757618C2semidirect
4. #23757588C2semidirect
5. #23757584C2semidirect
6. #23757552C2semidirect
7. #23757508C2semidirect
8. #23757466C2semidirect
9. #23757406C2semidirect
10. #23757405C2semidirect
11. #23757353C2semidirect
12. C8×C22⋊D157C2semidirect
13. C2×#19097693C2semidirect
14. #102×D157C2semidirect
15. #466×C157C2semidirect
21. C2×#14578939C22semidirect
22. C2×C8×D157C22semidirect
23. #19097770C22semidirect
30. #19097742C22semidirect
33. D4×Dic157C22semidirect
36. C2×C4⋊Dic157C22semidirect
37. C4⋊C4×D157C22semidirect
38. #19097704C22semidirect
39. #19097704C22semidirect
40. #19097700C22semidirect
43. #19097693C22semidirect
44. #19097693C22semidirect
45. #19097692C22semidirect
46. #19097692C22semidirect
48. #19097691C22semidirect
49. C22⋊#11929434C22semidirect
50. #19097683C22semidirect
51. C8×Dic157C22semidirect
52. C2×D8×C157C22semidirect
53. C22×C8×C157C22semidirect
55. #121×C157C22semidirect
56. #107×C157C22semidirect
57. #102×C157C22semidirect
58. #102×C157C22semidirect
128. D628#41semidirect
133. C22⋊D157D8semidirect
204. C157#3294semidirect
213. #466D157semidirect
227. C2×D8C2×D157semidirect
229. C22×C8C2×D157semidirect
239. #121C2×D157semidirect
249. #107C2×D157semidirect
259. #102C2×D157semidirect
260. #102C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237579232
#237579072
#237576182
#237575882
#237575842
#237575522
#237575082
#237574662
#237574062
#237574052
#237573532
C8×C22⋊D1572
C2×#190976932
#102×D1572
#466×C1572
#3294157