Finite Group Databasebeta

← #34111927

Subgroups — #34111927

Order 20096.

460 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23758084C211yesmaximal, characteristic, complemented
2#23758081C211yesmaximal, characteristic, complemented
3#23758080C211yesmaximal, characteristic, complemented
4#23757644C211yesmaximal, characteristic, complemented
5#23757538C211yesmaximal, characteristic, complemented
6#23757536C211yesmaximal, characteristic, complemented
7#23757534C211yesmaximal, characteristic, complemented
8#23757533C211yesmaximal, characteristic, complemented
9#23757456C211yesmaximal, characteristic, complemented
10#23757454C211yesmaximal, characteristic, complemented
11#23757441C211yesmaximal, characteristic, complemented
12#23757439C211yesmaximal, characteristic, complemented
13#23757390C211yesmaximal, characteristic, complemented
14#23757388C211yesmaximal, characteristic, complemented
15#577×C157C211yesmaximal, characteristic, complemented
16#19097818C2211yescharacteristic
17#19097817C2211yescharacteristic, complemented
18#19097803—21no—
19#19097802—21no—
20#19097802C2211yescharacteristic, complemented
21#19097801—21no—
22#19097801C2211yescharacteristic, complemented
23#19097801C2211yescharacteristic, complemented
24#19097797—21no—
25#19097797C2211yescharacteristic
26#19097796—21no—
27#19097796C2211yescharacteristic
28#19097796C2211yescharacteristic
29#19097795—21no—
30#19097792—21no—
31#19097791—21no—
32#19097791—21no—
33#19097791C2211yescharacteristic
34C2×#14578943C2211yescharacteristic, complemented
35C2×#14578942—21no—
36C2×#14578942C2211yescharacteristic, complemented
37C2×#14578941—21no—
38C2×#14578941C2211yescharacteristic, complemented
39SD16×D157—21no—
40#19097778C2211yescharacteristic, complemented
41#19097778C2211yescharacteristic, complemented
42#19097777C2211yescharacteristic, complemented
43#19097769C2211yescharacteristic, complemented
44#19097767C2211yescharacteristic
45#19097707C2211yescharacteristic, complemented
46#19097706C2211yescharacteristic, complemented
47#19097698C2211yescharacteristic, complemented
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
57H(5,𝔽2)×C157C2211yescharacteristic, complemented
58#137×C157—21no—
59#137×C157C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C157—21no—
61AGL(1,ℤ/8)×C157C2211yescharacteristic
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
78C2×C22⋊D157—41no—
79D4×D157—21no—
80D4×D157—41no—
81#14578944—21no—
82#14578944—21no—
83#14578944—21no—
84#14578944D411yescharacteristic, complemented
85#14578943—21no—
86#14578943—21no—
87#14578942—21no—
88#14578942—21no—
89#14578942—21no—
90#14578942—21no—
91#14578942—21no—
92#14578942D411yescharacteristic, complemented
93#14578941—21no—
94#14578941—21no—
95#14578941—21no—
96#14578941—21no—
97#14578941—21no—
98#14578941D411yescharacteristic, complemented
99#14578939—21no—
100#14578939—21no—
101#14578939—21no—
102#14578939D411yescharacteristic, complemented
103#14578938—21no—
104#14578938—21no—
105#14578938C2311yescharacteristic
106#14578938C2311yescharacteristic
107#14578938C2311yescharacteristic
108#14578937—21no—
109C2×#11929434—21no—
110C2×#11929434—21no—
111C2×#11929434C2311yescharacteristic
112C8×D157—21no—
113#14578933—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, complemented
132SD16×C157—21no—
133SD16×C157—21no—
134SD16×C157—21no—
135SD16×C157—21no—
136SD16×C157D411yescharacteristic, complemented
137SD16×C157D411yescharacteristic, complemented
138D8×C157—21no—
139D8×C157D411yescharacteristic, complemented
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—
157C22⋊D157—82no—
158C2×Dic157—21no—
159C2×Dic157—21no—
160C2×Dic157—41no—
161C4×D157—21no—
162C4×D157—41no—
163C4×D157—41no—
164#11929434—21no—
165#11929434—21no—
166#11929434—21no—
167#11929434C2×D411yescharacteristic
168#11929434C2×D411yescharacteristic
169C23×C157—21no—
170C23×C157—41no—
171Q8×C157—21no—
172Q8×C157—21no—
173Q8×C157—41no—
174Q8×C157C2×D411yescharacteristic
175Q8×C157C2×D411yescharacteristic
176Q8×C157C2×D411yescharacteristic
177D4×C157—21no—
178D4×C157—21no—
179D4×C157—21no—
180D4×C157—21no—
181D4×C157—21no—
182D4×C157—41no—
183D4×C157—41no—
184D4×C157—41no—
185D4×C157C2×D411yescharacteristic
186D4×C157C2×D411yescharacteristic
187D4×C157C2×D411yescharacteristic
188C2×C4×C157—21no—
189C2×C4×C157—21no—
190C2×C4×C157—21no—
191C2×C4×C157—21no—
192C2×C4×C157—41no—
193C2×C4×C157—41no—
194C2×C4×C157—41no—
195C2×C4×C157C2411yescharacteristic
196C8×C157—21no—
197C8×C157C2×D411yescharacteristic
198C8×C157C2×D411yescharacteristic
199C22×C157—21no—
200C22×C157—21no—
201C22×C157—21no—
202C22×C157—41no—
203C22×C157—81no—
204C22×C157—161no—
205C22×C157H(5,𝔽2)11yescharacteristic
206C2×D157—21no—
207C2×D157—41no—
208C2×D157—81no—
209C2×D157—161no—
210C4×C157—21no—
211C4×C157—21no—
212C4×C157—21no—
213C4×C157—41no—
214C4×C157C22×D411yescharacteristic
215C4×C157C22×D411yescharacteristic
216Dic157—22no—
217Dic157—21no—
218Dic157—41no—
219C2×C157—21no—
220C2×C157—41no—
221C2×C157—41no—
222C2×C157—41no—
223C2×C157—81no—
224C2×C157D4211yescharacteristic
225D157—41no—
226D157—81no—
227C157#329111yescharacteristic, complemented, Sylow
228#3291—1571nomaximal, Sylow
229#577—1571no—
230#577—1571no—
231#577—1571no—
232#577D15711yescharacteristic, complemented
233#492—1571no—
234#471—1571no—
235#471—1571no—
236#471—1571no—
237#471—1571no—
238#456—1571no—
239#456—1571no—
240#453—1571no—
241#453—1571no—
242#443—1571no—
243#443—1571no—
2442−1+4—1571no—
2452−1+4C2×D15711yescharacteristic
246H(5,𝔽2)—1571no—
247H(5,𝔽2)C2×D15711yescharacteristic, complemented
248#137—21no—
249#137—3141no—
250#137—3141no—
251#137—3141no—
252#137—1571no—
253#137—1571no—
254#137—1571no—
255#137C2×D15711yescharacteristic, complemented
256AGL(1,ℤ/8)—21no—
257AGL(1,ℤ/8)—3141no—
258AGL(1,ℤ/8)—3141no—
259AGL(1,ℤ/8)—3141no—
260AGL(1,ℤ/8)—1571no—
261AGL(1,ℤ/8)—1571no—
262AGL(1,ℤ/8)—1571no—
263AGL(1,ℤ/8)C2×D15711yescharacteristic
264#135—21no—
265#135—3141no—
266#135—3141no—
267#135—3141no—
268#135—1571no—
269#135C2×D15711yescharacteristic
270C2×SD16—21no—
271C2×SD16—3141no—
272C2×SD16—3141no—
273C2×SD16—3141no—
274C2×SD16—1571no—
275C2×SD16—1571no—
276C2×SD16—1571no—
277C2×SD16C2×D15711yescharacteristic, complemented
278#131—1571no—
279#131—1571no—
280#131—1571no—
281#131C2×D15711yescharacteristic, complemented
282C4⋊Q8—1571no—
283#127—1571no—
284#108—1571no—
285#108—1571no—
286#104—1571no—
287#104—1571no—
288#104—1571no—
289#104—1571no—
290#101—1571no—
291#101—1571no—
292#100—1571no—
293#100—1571no—
294C4×C8—1571no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—21no—
299#41—41no—
300#41—3141no—
301#41—3141no—
302#41—3141no—
303#41—3141no—
304#41—6281no—
305#41—1571no—
306#41C22×D15711yescharacteristic
307#41C22×D15711yescharacteristic
308#41C22×D15711yescharacteristic
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—3141no—
312C2×Q8—3141no—
313C2×Q8—1571no—
314C2×Q8C22×D15711yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—3141no—
319C2×D4—3141no—
320C2×D4—6281no—
321C2×D4—6281no—
322C2×D4—1571no—
323C2×D4C22×D15711yescharacteristic
324Q16—21no—
325Q16—3141no—
326Q16—3141no—
327Q16—3141no—
328Q16—1571no—
329Q16C22⋊D15711yescharacteristic, complemented
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—3141no—
343SD16—3141no—
344SD16—3141no—
345SD16—3141no—
346SD16—1571no—
347SD16—1571no—
348SD16C22⋊D15711yescharacteristic, complemented
349SD16C22⋊D15711yescharacteristic, complemented
350D8—21no—
351D8—3141no—
352D8—3141no—
353D8—3141no—
354D8—1571no—
355D8C22⋊D15711yescharacteristic, complemented
356M16—21no—
357M16—3141no—
358M16—3141no—
359M16—3141no—
360M16—1571no—
361M16—1571no—
362M16—1571no—
363M16C22×D15711yescharacteristic
364C2×C8—21no—
365C2×C8—3141no—
366C2×C8—3141no—
367C2×C8—3141no—
368C2×C8—1571no—
369C2×C8C22×D15711yescharacteristic
370C4⋊C4—6281no—
371C42—1571no—
372C23—21no—
373C23—41no—
374C23—3141no—
375C23—6281no—
376Q8—21no—
377Q8—21no—
378Q8—41no—
379Q8—3141no—
380Q8—3141no—
381Q8—6281no—
382Q8—1571no—
383Q8D4×D15711yescharacteristic
384Q8C2×C22⋊D15711yescharacteristic
385Q8C2×C22⋊D15711yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—3141no—
395D4—3141no—
396D4—3141no—
397D4—6281no—
398D4—6281no—
399D4—6281no—
400D4—1571no—
401D4—12562no—
402D4D4×D15711yescharacteristic
403D4C2×C22⋊D15711yescharacteristic
404D4C2×C22⋊D15711yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—3141no—
413C2×C4—3141no—
414C2×C4—3141no—
415C2×C4—6281no—
416C2×C4—6281no—
417C2×C4—6281no—
418C2×C4C23×D15711yescharacteristic
419C8—21no—
420C8—3141no—
421C8—3141no—
422C8—3141no—
423C8—1571no—
424C8—1571no—
425C8C2×C22⋊D15711yescharacteristic
426C8C2×C22⋊D15711yescharacteristic
427C22—21no—
428C22—21no—
429C22—21no—
430C22—41no—
431C22—81no—
432C22—161no—
433C22—3141no—
434C22—6281no—
435C22—25121no—
436C22—12561no—
437C22#1909781611yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—41no—
442C4—3142no—
443C4—3141no—
444C4—6281no—
445C4C2×D4×D15711yescharacteristic
446C4C22×C22⋊D15711yescharacteristic
447C2—21no—
448C2—41no—
449C2—41no—
450C2—41no—
451C2—81no—
452C2—6281no—
453C2—12561no—
454C2D4×C22⋊D15711yescharacteristic
subgroupG/H
centerC2D4×C22⋊D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#577×C157C2
socleC2×C157D42
hypercenter#577D157
hypocenterC157#3291
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. #23758084C2semidirect
2. #23758081C2semidirect
3. #23758080C2semidirect
4. #23757644C2semidirect
5. #23757538C2semidirect
6. #23757536C2semidirect
7. #23757534C2semidirect
8. #23757533C2semidirect
9. #23757456C2semidirect
10. #23757454C2semidirect
11. #23757441C2semidirect
12. #23757439C2semidirect
13. #23757390C2semidirect
14. #23757388C2semidirect
15. #577×C157C2semidirect
17. #19097817C22semidirect
20. #19097802C22semidirect
22. #19097801C22semidirect
23. #19097801C22semidirect
34. C2×#14578943C22semidirect
36. C2×#14578942C22semidirect
38. C2×#14578941C22semidirect
40. #19097778C22semidirect
41. #19097778C22semidirect
42. #19097777C22semidirect
43. #19097769C22semidirect
45. #19097707C22semidirect
46. #19097706C22semidirect
47. #19097698C22semidirect
48. #19097698C22semidirect
49. #19097698C22semidirect
50. #19097697C22semidirect
51. #19097690C22semidirect
52. #19097689C22semidirect
53. #19097688C22semidirect
54. #19097687C22semidirect
55. C8×Dic157C22semidirect
57. H(5,𝔽2)×C157C22semidirect
59. #137×C157C22semidirect
65. C2×SD16×C157C22semidirect
66. #131×C157C22semidirect
84. #14578944D4semidirect
92. #14578942D4semidirect
98. #14578941D4semidirect
102. #14578939D4semidirect
131. Q16×C157D4semidirect
136. SD16×C157D4semidirect
137. SD16×C157D4semidirect
139. D8×C157D4semidirect
227. C157#3291semidirect
232. #577D157semidirect
247. H(5,𝔽2)C2×D157semidirect
255. #137C2×D157semidirect
277. C2×SD16C2×D157semidirect
281. #131C2×D157semidirect
329. Q16C22⋊D157semidirect
348. SD16C22⋊D157semidirect
349. SD16C22⋊D157semidirect
355. D8C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
#237580842
#237580812
#237580802
#237576442
#237575382
#237575362
#237575342
#237575332
#237574562
#237574542
#237574412
#237574392
#237573902
#237573882
#577×C1572
#3291157