Finite Group Databasebeta

← #34111916

Subgroups — #34111916

Order 20096.

454 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23758088C211yesmaximal, characteristic, complemented
2#23758080C211yesmaximal, characteristic, complemented
3#23758076C211yesmaximal, characteristic, complemented
4#23757654C211yesmaximal, characteristic, complemented
5#23757546C211yesmaximal, characteristic, complemented
6#23757541C211yesmaximal, characteristic, complemented
7#23757536C211yesmaximal, characteristic, complemented
8#23757533C211yesmaximal, characteristic, complemented
9#23757451C211yesmaximal, characteristic, complemented
10#23757449C211yesmaximal, characteristic, complemented
11#23757446C211yesmaximal, characteristic, complemented
12#23757444C211yesmaximal, characteristic, complemented
13#23757390C211yesmaximal, characteristic, complemented
14#23757388C211yesmaximal, characteristic, complemented
15#577×C157C211yesmaximal, characteristic, complemented
16#19097818C2211yescharacteristic, complemented
17#19097817C2211yescharacteristic
18#19097803—21no—
19#19097802—21no—
20#19097802C2211yescharacteristic, complemented
21#19097801—21no—
22#19097801C2211yescharacteristic
23#19097801C2211yescharacteristic, complemented
24#19097797—21no—
25#19097797C2211yescharacteristic
26#19097796—21no—
27#19097796C2211yescharacteristic
28#19097796C2211yescharacteristic, complemented
29#19097795—21no—
30#19097792—21no—
31#19097791—21no—
32#19097791—21no—
33#19097791C2211yescharacteristic
34C2×#14578944—21no—
35C2×#14578944C2211yescharacteristic, complemented
36C2×#14578943C2211yescharacteristic, complemented
37SD16×D157—21no—
38C2×#14578939—21no—
39C2×#14578939C2211yescharacteristic
40#19097778C2211yescharacteristic
41#19097778C2211yescharacteristic, complemented
42#19097777C2211yescharacteristic, complemented
43#19097760C2211yescharacteristic, complemented
44#19097758C2211yescharacteristic, complemented
45#19097707C2211yescharacteristic, complemented
46#19097706C2211yescharacteristic, complemented
47#19097698C2211yescharacteristic
48#19097698C2211yescharacteristic, complemented
49#19097698C2211yescharacteristic, complemented
50#19097697C2211yescharacteristic, complemented
51#19097690C2211yescharacteristic, complemented
52#19097689C2211yescharacteristic, complemented
53#19097688C2211yescharacteristic, complemented
54#19097687C2211yescharacteristic, complemented
55C8×Dic157C2211yescharacteristic, complemented
562−1+4×C157C2211yescharacteristic, complemented
57H(5,𝔽2)×C157C2211yescharacteristic
58#137×C157—21no—
59#137×C157C2211yescharacteristic
60AGL(1,ℤ/8)×C157—21no—
61AGL(1,ℤ/8)×C157C2211yescharacteristic, complemented
62#135×C157—21no—
63#135×C157C2211yescharacteristic
64C2×SD16×C157—21no—
65C2×SD16×C157C2211yescharacteristic, complemented
66#131×C157C2211yescharacteristic, complemented
67#14578955—21no—
68#14578954—21no—
69#14578954—21no—
70#14578954C2311yescharacteristic
71#14578953—21no—
72#14578953—41no—
73C2×Dic314—21no—
74C2×Dic314C2311yescharacteristic
75Q8×D157—21no—
76C2×D628—21no—
77C2×D628C2311yescharacteristic
78D4×D157—21no—
79D4×D157—41no—
80#14578944—21no—
81#14578944—21no—
82#14578944—21no—
83#14578944—21no—
84#14578944—21no—
85#14578944D411yescharacteristic
86#14578943—21no—
87#14578943—21no—
88#14578942—21no—
89#14578942—21no—
90#14578942—21no—
91#14578942D411yescharacteristic
92#14578941—21no—
93#14578941—21no—
94#14578941—21no—
95#14578941D411yescharacteristic
96#14578939—21no—
97#14578939—21no—
98#14578939—21no—
99#14578939—21no—
100#14578939—21no—
101#14578939D411yescharacteristic
102#14578938—21no—
103#14578938—21no—
104#14578938C2311yescharacteristic
105#14578938C2311yescharacteristic
106#14578938C2311yescharacteristic
107#14578937—21no—
108C2×#11929434—21no—
109C2×#11929434—21no—
110C2×#11929434C2311yescharacteristic
111C8×D157—21no—
112C22⋊Dic157—41no—
113#14578931—41no—
114C4×Dic157C2311yescharacteristic
115#41×C157—21no—
116#41×C157—21no—
117#41×C157—21no—
118#41×C157—21no—
119#41×C157—41no—
120#41×C157C2311yescharacteristic
121#41×C157C2311yescharacteristic
122#41×C157C2311yescharacteristic
123C2×Q8×C157—21no—
124C2×Q8×C157—21no—
125C2×Q8×C157C2311yescharacteristic
126C2×D4×C157—21no—
127C2×D4×C157—21no—
128C2×D4×C157—41no—
129C2×D4×C157C2311yescharacteristic
130Q16×C157—21no—
131Q16×C157D411yescharacteristic
132SD16×C157—21no—
133SD16×C157—21no—
134SD16×C157—21no—
135SD16×C157—21no—
136SD16×C157D411yescharacteristic
137SD16×C157D411yescharacteristic
138D8×C157—21no—
139D8×C157D411yescharacteristic
140M16×C157—21no—
141M16×C157C2311yescharacteristic
142C2×C8×C157—21no—
143C2×C8×C157C2311yescharacteristic
144C22×D157—21no—
145C22×D157—41no—
146Dic314—21no—
147Dic314—21no—
148Dic314—41no—
149Dic314C2×D411yescharacteristic
150D628—21no—
151D628—21no—
152D628—41no—
153D628C2×D411yescharacteristic
154C22⋊D157—21no—
155C22⋊D157—41no—
156C22⋊D157—41no—
157C2×Dic157—21no—
158C2×Dic157—21no—
159C2×Dic157—41no—
160C4×D157—21no—
161C4×D157—41no—
162C4×D157—41no—
163#11929434—21no—
164#11929434—21no—
165#11929434—21no—
166#11929434C2×D411yescharacteristic
167#11929434C2×D411yescharacteristic
168C23×C157—21no—
169C23×C157—41no—
170Q8×C157—21no—
171Q8×C157—21no—
172Q8×C157—41no—
173Q8×C157C2×D411yescharacteristic
174Q8×C157C2×D411yescharacteristic
175Q8×C157C2×D411yescharacteristic
176D4×C157—21no—
177D4×C157—21no—
178D4×C157—21no—
179D4×C157—21no—
180D4×C157—21no—
181D4×C157—41no—
182D4×C157—41no—
183D4×C157—41no—
184D4×C157C2×D411yescharacteristic
185D4×C157C2×D411yescharacteristic
186D4×C157C2×D411yescharacteristic
187C2×C4×C157—21no—
188C2×C4×C157—21no—
189C2×C4×C157—21no—
190C2×C4×C157—21no—
191C2×C4×C157—41no—
192C2×C4×C157—41no—
193C2×C4×C157—41no—
194C2×C4×C157C2411yescharacteristic
195C8×C157—21no—
196C8×C157C2×D411yescharacteristic
197C8×C157C2×D411yescharacteristic
198C22×C157—21no—
199C22×C157—21no—
200C22×C157—21no—
201C22×C157—41no—
202C22×C157—81no—
203C22×C157—161no—
204C22×C157H(5,𝔽2)11yescharacteristic
205C2×D157—21no—
206C2×D157—41no—
207C2×D157—81no—
208C2×D157—161no—
209C4×C157—21no—
210C4×C157—21no—
211C4×C157—21no—
212C4×C157—41no—
213C4×C157C22×D411yescharacteristic
214C4×C157C22×D411yescharacteristic
215Dic157—21no—
216Dic157—41no—
217Dic157—41no—
218C2×C157—21no—
219C2×C157—41no—
220C2×C157—41no—
221C2×C157—41no—
222C2×C157—81no—
223C2×C157D4211yescharacteristic
224D157—41no—
225D157—81no—
226C157#329011yescharacteristic, complemented, Sylow
227#3290—1571nomaximal, Sylow
228#578—1571no—
229#577—1571no—
230#577D15711yescharacteristic, complemented
231#576—1571no—
232#495—1571no—
233#473—1571no—
234#472—1571no—
235#471—1571no—
236#471—1571no—
237#455—1571no—
238#455—1571no—
239#454—1571no—
240#454—1571no—
241#443—1571no—
242#443—1571no—
2432−1+4—1571no—
2442−1+4C2×D15711yescharacteristic, complemented
245H(5,𝔽2)—1571no—
246H(5,𝔽2)C2×D15711yescharacteristic
247#137—21no—
248#137—3141no—
249#137—3141no—
250#137—3141no—
251#137—1571no—
252#137—1571no—
253#137—1571no—
254#137C2×D15711yescharacteristic
255AGL(1,ℤ/8)—21no—
256AGL(1,ℤ/8)—3141no—
257AGL(1,ℤ/8)—3141no—
258AGL(1,ℤ/8)—3141no—
259AGL(1,ℤ/8)—1571no—
260AGL(1,ℤ/8)—1571no—
261AGL(1,ℤ/8)—1571no—
262AGL(1,ℤ/8)C2×D15711yescharacteristic, complemented
263#135—21no—
264#135—3141no—
265#135—3141no—
266#135—3141no—
267#135—1571no—
268#135C2×D15711yescharacteristic
269C2×Q16—3141no—
270C2×Q16—1571no—
271C2×SD16—21no—
272C2×SD16—3141no—
273C2×SD16—1571no—
274C2×SD16C2×D15711yescharacteristic, complemented
275C2×D8—3141no—
276C2×D8—1571no—
277#131—1571no—
278#131—1571no—
279#131—1571no—
280#131C2×D15711yescharacteristic, complemented
281#124—1571no—
282#124—1571no—
283#108—1571no—
284#108—1571no—
285#104—1571no—
286#104—1571no—
287#104—1571no—
288#104—1571no—
289#101—1571no—
290#101—1571no—
291#100—1571no—
292#100—1571no—
293C4×C8—1571no—
294#41—21no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—41no—
299#41—3141no—
300#41—3141no—
301#41—3141no—
302#41—3141no—
303#41—6281no—
304#41—1571no—
305#41C22×D15711yescharacteristic
306#41C22×D15711yescharacteristic
307#41C22×D15711yescharacteristic
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—3141no—
311C2×Q8—3141no—
312C2×Q8—1571no—
313C2×Q8C22×D15711yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—3141no—
318C2×D4—3141no—
319C2×D4—6281no—
320C2×D4—1571no—
321C2×D4C22×D15711yescharacteristic
322Q16—21no—
323Q16—3141no—
324Q16—3141no—
325Q16—3141no—
326Q16—3141no—
327Q16—3141no—
328Q16—1571no—
329Q16C22⋊D15711yescharacteristic
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—3141no—
335SD16—3141no—
336SD16—3141no—
337SD16—3141no—
338SD16—3141no—
339SD16—3141no—
340SD16—3141no—
341SD16—3141no—
342SD16—1571no—
343SD16—1571no—
344SD16C22⋊D15711yescharacteristic
345SD16C22⋊D15711yescharacteristic
346D8—21no—
347D8—3141no—
348D8—3141no—
349D8—3141no—
350D8—3141no—
351D8—3141no—
352D8—1571no—
353D8C22⋊D15711yescharacteristic
354M16—21no—
355M16—3141no—
356M16—3141no—
357M16—3141no—
358M16—1571no—
359M16—1571no—
360M16—1571no—
361M16C22×D15711yescharacteristic
362C2×C8—21no—
363C2×C8—3141no—
364C2×C8—3141no—
365C2×C8—3141no—
366C2×C8—1571no—
367C2×C8C22×D15711yescharacteristic
368C22⋊C4—6281no—
369C22⋊C4—6281no—
370C42—1571no—
371C23—21no—
372C23—41no—
373C23—3141no—
374C23—6281no—
375Q8—21no—
376Q8—21no—
377Q8—41no—
378Q8—3141no—
379Q8—3141no—
380Q8—6281no—
381Q8—1571no—
382Q8D4×D15711yescharacteristic
383Q8C2×C22⋊D15711yescharacteristic
384Q8C2×C22⋊D15711yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—41no—
391D4—41no—
392D4—41no—
393D4—3141no—
394D4—3141no—
395D4—3141no—
396D4—6281no—
397D4—6281no—
398D4—6281no—
399D4—1571no—
400D4D4×D15711yescharacteristic
401D4C2×C22⋊D15711yescharacteristic
402D4C2×C22⋊D15711yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—3141no—
411C2×C4—3141no—
412C2×C4—3141no—
413C2×C4—6281no—
414C2×C4—6281no—
415C2×C4—6281no—
416C2×C4C23×D15711yescharacteristic
417C8—21no—
418C8—3141no—
419C8—3141no—
420C8—3141no—
421C8—1571no—
422C8—1571no—
423C8C2×C22⋊D15711yescharacteristic
424C8C2×C22⋊D15711yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—41no—
429C22—81no—
430C22—161no—
431C22—3141no—
432C22—6281no—
433C22—25121no—
434C22—12561no—
435C22#1909781611yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—3141no—
441C4—6281no—
442C4—6281no—
443C4C2×D4×D15711yescharacteristic
444C4C22×C22⋊D15711yescharacteristic
445C2—21no—
446C2—41no—
447C2—41no—
448C2—41no—
449C2—81no—
450C2—6281no—
451C2—12561no—
452C2D4×C22⋊D15711yescharacteristic
subgroupG/H
centerC2D4×C22⋊D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#577×C157C2
socleC2×C157D42
hypercenter#577D157
hypocenterC157#3290
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #23758088C2semidirect
2. #23758080C2semidirect
3. #23758076C2semidirect
4. #23757654C2semidirect
5. #23757546C2semidirect
6. #23757541C2semidirect
7. #23757536C2semidirect
8. #23757533C2semidirect
9. #23757451C2semidirect
10. #23757449C2semidirect
11. #23757446C2semidirect
12. #23757444C2semidirect
13. #23757390C2semidirect
14. #23757388C2semidirect
15. #577×C157C2semidirect
16. #19097818C22semidirect
20. #19097802C22semidirect
23. #19097801C22semidirect
28. #19097796C22semidirect
35. C2×#14578944C22semidirect
36. C2×#14578943C22semidirect
41. #19097778C22semidirect
42. #19097777C22semidirect
43. #19097760C22semidirect
44. #19097758C22semidirect
45. #19097707C22semidirect
46. #19097706C22semidirect
48. #19097698C22semidirect
49. #19097698C22semidirect
50. #19097697C22semidirect
51. #19097690C22semidirect
52. #19097689C22semidirect
53. #19097688C22semidirect
54. #19097687C22semidirect
55. C8×Dic157C22semidirect
56. 2−1+4×C157C22semidirect
61. AGL(1,ℤ/8)×C157C22semidirect
65. C2×SD16×C157C22semidirect
66. #131×C157C22semidirect
226. C157#3290semidirect
230. #577D157semidirect
244. 2−1+4C2×D157semidirect
262. AGL(1,ℤ/8)C2×D157semidirect
274. C2×SD16C2×D157semidirect
280. #131C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237580882
#237580802
#237580762
#237576542
#237575462
#237575412
#237575362
#237575332
#237574512
#237574492
#237574462
#237574442
#237573902
#237573882
#577×C1572
#3290157