Finite Group Databasebeta

← #34111919

Subgroups — #34111919

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#23758089C211yesmaximal, characteristic, complemented
2#23758085C211yesmaximal, characteristic, complemented
3#23758079C211yesmaximal, characteristic, complemented
4#23758077C211yesmaximal, characteristic, complemented
5#23757654C211yesmaximal, characteristic, complemented
6#23757547C211yesmaximal, characteristic, complemented
7#23757542C211yesmaximal, characteristic, complemented
8#23757537C211yesmaximal, characteristic, complemented
9#23757453C211yesmaximal, characteristic, complemented
10#23757449C211yesmaximal, characteristic, complemented
11#23757448C211yesmaximal, characteristic, complemented
12#23757444C211yesmaximal, characteristic, complemented
13#23757389C211yesmaximal, characteristic, complemented
14#23757388C211yesmaximal, characteristic, complemented
15#471×C157C211yesmaximal, characteristic, complemented
16#19097819C2211yescharacteristic, complemented
17#19097818C2211yescharacteristic, complemented
18#19097817C2211yescharacteristic
19#19097816C2211yescharacteristic
20#19097804—21no—
21#19097804C2211yescharacteristic
22#19097804C2211yescharacteristic, complemented
23#19097803—21no—
24#19097802C2211yescharacteristic
25#19097800—21no—
26#19097800—21no—
27#19097799—21no—
28#19097799C2211yescharacteristic
29#19097799C2211yescharacteristic, complemented
30#19097798—21no—
31#19097798—21no—
32#19097797C2211yescharacteristic, complemented
33#19097795—21no—
34#19097793—21no—
35#19097793C2211yescharacteristic
36#19097792—21no—
37#19097792—21no—
38#19097792—21no—
39#19097791C2211yescharacteristic
40C2×#14578944C2211yescharacteristic, complemented
41Q16×D157—21no—
42C2×#14578943—21no—
43C2×#14578943C2211yescharacteristic, complemented
44SD16×D157—21no—
45C2×#14578939C2211yescharacteristic
46D8×D157—21no—
47#19097779C2211yescharacteristic
48#19097779C2211yescharacteristic, complemented
49#19097777C2211yescharacteristic, complemented
50#19097760C2211yescharacteristic, complemented
51#19097758C2211yescharacteristic, complemented
52#19097706C2211yescharacteristic, complemented
53#19097698C2211yescharacteristic, complemented
54#19097697C2211yescharacteristic
55#19097697C2211yescharacteristic, complemented
56#19097697C2211yescharacteristic, complemented
57#19097689C2211yescharacteristic, complemented
58#19097687C2211yescharacteristic, complemented
59C8×Dic157C2211yescharacteristic, complemented
60#137×C157C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C157C2211yescharacteristic
62C2×SD16×C157C2211yescharacteristic, complemented
63#131×C157C2211yescharacteristic, complemented
64#108×C157C2211yescharacteristic, complemented
65#101×C157C2211yescharacteristic, complemented
66#100×C157C2211yescharacteristic, complemented
67#14578955—21no—
68#14578955—21no—
69#14578955—21no—
70#14578954—21no—
71#14578954—21no—
72#14578954—41no—
73#14578954C2311yescharacteristic
74#14578954C2311yescharacteristic
75#14578954C2311yescharacteristic
76#14578953—21no—
77#14578953—21no—
78#14578953—21no—
79#14578953—41no—
80C2×Dic314—21no—
81C2×Dic314C2311yescharacteristic
82Q8×D157—21no—
83Q8×D157—21no—
84Q8×D157—21no—
85C2×D628—21no—
86C2×D628C2311yescharacteristic
87C2×C22⋊D157—41no—
88D4×D157—21no—
89D4×D157—21no—
90D4×D157—21no—
91D4×D157—41no—
92Dic628—21no—
93Dic628—21no—
94Dic628D411yescharacteristic
95#14578944—21no—
96#14578944—21no—
97#14578944—21no—
98#14578944D411yescharacteristic
99#14578943—21no—
100#14578943—21no—
101#14578943—21no—
102#14578943—21no—
103#14578943—21no—
104#14578943—21no—
105#14578943D411yescharacteristic
106#14578943D411yescharacteristic
107#14578942—21no—
108#14578942D411yescharacteristic
109#14578941—21no—
110#14578941D411yescharacteristic
111D1256—21no—
112D1256—21no—
113D1256D411yescharacteristic
114#14578939—21no—
115#14578939—21no—
116#14578939—21no—
117#14578939D411yescharacteristic
118#14578938C2311yescharacteristic
119#14578937—21no—
120#14578937—21no—
121#14578937—21no—
122C2×#11929434C2311yescharacteristic
123C8×D157—21no—
124C8×D157—21no—
125C8×D157—21no—
126C22⋊Dic157—41no—
127#14578931—41no—
128C4×Dic157C2311yescharacteristic
129#41×C157C2311yescharacteristic
130C2×Q8×C157C2311yescharacteristic
131C2×D4×C157C2311yescharacteristic
132Q16×C157—21no—
133SD16×C157—21no—
134SD16×C157—21no—
135SD16×C157—21no—
136SD16×C157—21no—
137D8×C157—21no—
138M16×C157—21no—
139M16×C157C2311yescharacteristic
140M16×C157C2311yescharacteristic
141M16×C157C2311yescharacteristic
142C2×C8×C157—21no—
143C2×C8×C157C2311yescharacteristic
144C22×D157—21no—
145C22×D157—41no—
146C22×D157—41no—
147Dic314—21no—
148Dic314—21no—
149Dic314—41no—
150Dic314—41no—
151Dic314C2×D411yescharacteristic
152Dic314C2×D411yescharacteristic
153Dic314C2×D411yescharacteristic
154D628—21no—
155D628—21no—
156D628—41no—
157D628—41no—
158D628C2×D411yescharacteristic
159D628C2×D411yescharacteristic
160D628C2×D411yescharacteristic
161C22⋊D157—21no—
162C22⋊D157—21no—
163C22⋊D157—21no—
164C22⋊D157—41no—
165C22⋊D157—41no—
166C22⋊D157—41no—
167C22⋊D157—41no—
168C2×Dic157—21no—
169C2×Dic157—21no—
170C2×Dic157—41no—
171C2×Dic157—41no—
172C4×D157—21no—
173C4×D157—21no—
174C4×D157—21no—
175C4×D157—41no—
176C4×D157—41no—
177C4×D157—41no—
178C4×D157—41no—
179#11929434—21no—
180#11929434C2×D411yescharacteristic
181#11929434C2×D411yescharacteristic
182C23×C157—21no—
183Q8×C157—21no—
184Q8×C157—21no—
185Q8×C157C2×D411yescharacteristic
186D4×C157—21no—
187D4×C157—21no—
188D4×C157—21no—
189D4×C157C2×D411yescharacteristic
190C2×C4×C157—21no—
191C2×C4×C157—21no—
192C2×C4×C157C2411yescharacteristic
193C8×C157—21no—
194C8×C157—21no—
195C8×C157—21no—
196C8×C157C2×D411yescharacteristic
197C8×C157C2×D411yescharacteristic
198C22×C157—21no—
199C22×C157—41no—
200C22×C157—81no—
201C22×C157H(5,𝔽2)11yescharacteristic
202C2×D157—21no—
203C2×D157—21no—
204C2×D157—21no—
205C2×D157—41no—
206C2×D157—81no—
207C2×D157—161no—
208C2×D157—161no—
209C4×C157—21no—
210C4×C157—41no—
211C4×C157C22×D411yescharacteristic
212C4×C157C22×D411yescharacteristic
213Dic157—21no—
214Dic157—21no—
215Dic157—21no—
216Dic157—41no—
217Dic157—41no—
218C2×C157—21no—
219C2×C157—41no—
220C2×C157—81no—
221C2×C157D4211yescharacteristic
222D157—41no—
223D157—41no—
224D157—41no—
225D157—81no—
226C157#329011yescharacteristic, complemented, Sylow
227#3290—1571nomaximal, Sylow
228#578—1571no—
229#577—1571no—
230#577—1571no—
231#576—1571no—
232#495—1571no—
233#473—1571no—
234#472—1571no—
235#471—1571no—
236#471D15711yescharacteristic, complemented
237#455—1571no—
238#455—1571no—
239#454—1571no—
240#454—1571no—
241#443—1571no—
242#443—1571no—
2432−1+4—1571no—
2442−1+4—1571no—
245H(5,𝔽2)—1571no—
246H(5,𝔽2)—1571no—
247#137—3141no—
248#137—3141no—
249#137—3141no—
250#137—3141no—
251#137—1571no—
252#137—1571no—
253#137—1571no—
254#137C2×D15711yescharacteristic, complemented
255AGL(1,ℤ/8)—3141no—
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
263#135—3141no—
264#135—3141no—
265#135—3141no—
266#135—3141no—
267#135—1571no—
268#135—1571no—
269C2×Q16—3141no—
270C2×Q16—1571no—
271C2×SD16—3141no—
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#108C2×D15711yescharacteristic, complemented
285#104—1571no—
286#104—1571no—
287#104—1571no—
288#104—1571no—
289#101—1571no—
290#101C2×D15711yescharacteristic, complemented
291#100—1571no—
292#100C2×D15711yescharacteristic, complemented
293C4×C8—1571no—
294#41—3141no—
295#41—3141no—
296#41—3141no—
297#41—3141no—
298#41—3141no—
299#41—3141no—
300#41—3141no—
301#41—3141no—
302#41—6281no—
303#41—6281no—
304#41—1571no—
305#41—1571no—
306#41—1571no—
307#41C22×D15711yescharacteristic
308C2×Q8—3141no—
309C2×Q8—3141no—
310C2×Q8—3141no—
311C2×Q8—3141no—
312C2×Q8—1571no—
313C2×Q8C22×D15711yescharacteristic
314C2×D4—3141no—
315C2×D4—3141no—
316C2×D4—3141no—
317C2×D4—3141no—
318C2×D4—6281no—
319C2×D4—6281no—
320C2×D4—1571no—
321C2×D4C22×D15711yescharacteristic
322Q16—21no—
323Q16—3141no—
324Q16—3141no—
325Q16—3141no—
326Q16—3141no—
327Q16—3141no—
328Q16—1571no—
329Q16—1571no—
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—
344SD16—1571no—
345SD16—1571no—
346D8—21no—
347D8—3141no—
348D8—3141no—
349D8—3141no—
350D8—3141no—
351D8—3141no—
352D8—1571no—
353D8—1571no—
354M16—21no—
355M16—3141no—
356M16—3141no—
357M16—3141no—
358M16—1571no—
359M16C22×D15711yescharacteristic
360M16C22×D15711yescharacteristic
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—3141no—
373C23—6281no—
374C23—6281no—
375Q8—21no—
376Q8—21no—
377Q8—3141no—
378Q8—3141no—
379Q8—6281no—
380Q8—6281no—
381Q8—1571no—
382Q8—1571no—
383Q8—1571no—
384Q8D4×D15711yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—3141no—
389D4—3141no—
390D4—3141no—
391D4—3141no—
392D4—3141no—
393D4—6281no—
394D4—6281no—
395D4—6281no—
396D4—6281no—
397D4—6281no—
398D4—6281no—
399D4—1571no—
400D4—1571no—
401D4—1571no—
402D4D4×D15711yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—3141no—
406C2×C4—3141no—
407C2×C4—3141no—
408C2×C4—3141no—
409C2×C4—3141no—
410C2×C4—6281no—
411C2×C4—6281no—
412C2×C4—6281no—
413C2×C4—6281no—
414C2×C4—6281no—
415C2×C4—6281no—
416C2×C4C23×D15711yescharacteristic
417C8—21no—
418C8—21no—
419C8—21no—
420C8—3141no—
421C8—1571no—
422C8—1571no—
423C8D4×D15711yescharacteristic
424C8D4×D15711yescharacteristic
425C22—21no—
426C22—41no—
427C22—81no—
428C22—3141no—
429C22—3141no—
430C22—3141no—
431C22—6281no—
432C22—25121no—
433C22—25121no—
434C22—12561no—
435C22#1909781711yescharacteristic
436C4—21no—
437C4—41no—
438C4—3141no—
439C4—3141no—
440C4—3141no—
441C4—6281no—
442C4—6281no—
443C4C2×D4×D15711yescharacteristic
444C4C2×D4×D15711yescharacteristic
445C2—21no—
446C2—41no—
447C2—81no—
448C2—6281no—
449C2—6281no—
450C2—6281no—
451C2—12561no—
452C2#2375790711yescharacteristic
subgroupG/H
centerC2#23757907
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#471×C157C2
socleC2×C157D42
hypercenter#471D157
hypocenterC157#3290
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #23758089C2semidirect
2. #23758085C2semidirect
3. #23758079C2semidirect
4. #23758077C2semidirect
5. #23757654C2semidirect
6. #23757547C2semidirect
7. #23757542C2semidirect
8. #23757537C2semidirect
9. #23757453C2semidirect
10. #23757449C2semidirect
11. #23757448C2semidirect
12. #23757444C2semidirect
13. #23757389C2semidirect
14. #23757388C2semidirect
15. #471×C157C2semidirect
16. #19097819C22semidirect
17. #19097818C22semidirect
22. #19097804C22semidirect
29. #19097799C22semidirect
32. #19097797C22semidirect
40. C2×#14578944C22semidirect
43. C2×#14578943C22semidirect
48. #19097779C22semidirect
49. #19097777C22semidirect
50. #19097760C22semidirect
51. #19097758C22semidirect
52. #19097706C22semidirect
53. #19097698C22semidirect
55. #19097697C22semidirect
56. #19097697C22semidirect
57. #19097689C22semidirect
58. #19097687C22semidirect
59. C8×Dic157C22semidirect
60. #137×C157C22semidirect
62. C2×SD16×C157C22semidirect
63. #131×C157C22semidirect
64. #108×C157C22semidirect
65. #101×C157C22semidirect
66. #100×C157C22semidirect
226. C157#3290semidirect
236. #471D157semidirect
254. #137C2×D157semidirect
274. C2×SD16C2×D157semidirect
280. #131C2×D157semidirect
284. #108C2×D157semidirect
290. #101C2×D157semidirect
292. #100C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237580892
#237580852
#237580792
#237580772
#237576542
#237575472
#237575422
#237575372
#237574532
#237574492
#237574482
#237574442
#237573892
#237573882
#471×C1572
#3290157