Finite Group Databasebeta

← #46822650

Subgroups — #46822650

Order 34432.

464 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771414C211yesmaximal, characteristic, complemented
2#31771411C211yesmaximal, characteristic, complemented
3#31771410C211yesmaximal, characteristic, complemented
4#31771409C211yesmaximal, characteristic, complemented
5#31770991C211yesmaximal, characteristic, complemented
6#31770876C211yesmaximal, characteristic, complemented
7#31770874C211yesmaximal, characteristic, complemented
8#31770871C211yesmaximal, characteristic, complemented
9#31770781C211yesmaximal, characteristic, complemented
10#31770780C211yesmaximal, characteristic, complemented
11#31770775C211yesmaximal, characteristic, complemented
12#31770771C211yesmaximal, characteristic, complemented
13#31770726C211yesmaximal, characteristic, complemented
14#31770725C211yesmaximal, characteristic, complemented
15#471×C269C211yesmaximal, characteristic, complemented
16#22575501C2211yescharacteristic, complemented
17#22575499C2211yescharacteristic
18#22575499C2211yescharacteristic, complemented
19#22575498C2211yescharacteristic, complemented
20#22575485—21no—
21#22575484C2211yescharacteristic, complemented
22#22575482—21no—
23#22575481—21no—
24#22575481—21no—
25#22575481C2211yescharacteristic
26#22575481C2211yescharacteristic, complemented
27#22575481C2211yescharacteristic, complemented
28#22575481C2211yescharacteristic, complemented
29#22575480—21no—
30#22575480—21no—
31#22575480—21no—
32#22575479C2211yescharacteristic, complemented
33#22575477—21no—
34#22575476—21no—
35#22575475—21no—
36#22575475C2211yescharacteristic
37#22575474—21no—
38#22575474—21no—
39#22575473C2211yescharacteristic
40C2×#16864389C2211yescharacteristic, complemented
41SD16×D269—21no—
42SD16×D269—21no—
43C2×D2152—21no—
44C2×D2152C2211yescharacteristic, complemented
45C2×#16864387C2211yescharacteristic, complemented
46D8×D269—21no—
47#22575461C2211yescharacteristic, complemented
48#22575461C2211yescharacteristic, complemented
49#22575459C2211yescharacteristic, complemented
50#22575449C2211yescharacteristic, complemented
51#22575442C2211yescharacteristic, complemented
52#22575388C2211yescharacteristic, complemented
53#22575380C2211yescharacteristic, complemented
54#22575379C2211yescharacteristic, complemented
55#22575379C2211yescharacteristic, complemented
56#22575379C2211yescharacteristic, complemented
57#22575369C2211yescharacteristic, complemented
58#22575369C2211yescharacteristic, complemented
59#22575363C2211yescharacteristic, complemented
60#137×C269C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C269C2211yescharacteristic
62C2×SD16×C269C2211yescharacteristic, complemented
63#131×C269C2211yescharacteristic, complemented
64#108×C269C2211yescharacteristic, complemented
65#101×C269C2211yescharacteristic, complemented
66#100×C269C2211yescharacteristic, complemented
67#16864403—21no—
68#16864403—21no—
69#16864403—21no—
70#16864403—21no—
71#16864402—21no—
72#16864402—21no—
73#16864402—41no—
74#16864402C2311yescharacteristic
75#16864402C2311yescharacteristic
76#16864402C2311yescharacteristic
77#16864401—21no—
78#16864401—21no—
79Q8×D269—21no—
80Q8×D269—21no—
81C2×D1076—21no—
82C2×D1076—21no—
83C2×D1076C2311yescharacteristic
84C2×D1076C2311yescharacteristic
85C2×C22⋊D269—41no—
86C2×C22⋊D269—41no—
87D4×D269—21no—
88D4×D269—21no—
89D4×D269—21no—
90D4×D269—21no—
91D4×D269—41no—
92D4×D269—41no—
93Dic1076D411yescharacteristic, complemented
94#16864392—21no—
95#16864392D411yescharacteristic, complemented
96#16864391—21no—
97#16864391—21no—
98#16864391—21no—
99#16864391—21no—
100#16864391D411yescharacteristic, complemented
101#16864391D411yescharacteristic, complemented
102#16864390—21no—
103#16864390D411yescharacteristic, complemented
104#16864389—21no—
105#16864389—21no—
106#16864389—21no—
107#16864389D411yescharacteristic, complemented
108D2152—21no—
109D2152—21no—
110D2152—21no—
111D2152—21no—
112D2152—21no—
113D2152—21no—
114D2152D411yescharacteristic, complemented
115#16864387—21no—
116#16864387—21no—
117#16864387—21no—
118#16864387D411yescharacteristic, complemented
119#16864386C2311yescharacteristic
120#16864385—21no—
121#16864385—21no—
122#16864385—21no—
123C2×#14524130C2311yescharacteristic
124C8×D269—21no—
125C8×D269—21no—
126C8×D269—21no—
127#16864379—41no—
128C4×Dic269C2311yescharacteristic
129#41×C269C2311yescharacteristic
130C2×Q8×C269C2311yescharacteristic
131C2×D4×C269C2311yescharacteristic
132Q16×C269—21no—
133SD16×C269—21no—
134SD16×C269—21no—
135SD16×C269—21no—
136SD16×C269—21no—
137D8×C269—21no—
138M16×C269—21no—
139M16×C269C2311yescharacteristic
140M16×C269C2311yescharacteristic
141M16×C269C2311yescharacteristic
142C2×C8×C269—21no—
143C2×C8×C269C2311yescharacteristic
144C22×D269—21no—
145C22×D269—21no—
146C22×D269—41no—
147C22×D269—41no—
148C22×D269—41no—
149Dic538—41no—
150Dic538C2×D411yescharacteristic
151Dic538C2×D411yescharacteristic
152Dic538C2×D411yescharacteristic
153D1076—21no—
154D1076—21no—
155D1076—21no—
156D1076—21no—
157D1076—41no—
158D1076—41no—
159D1076—41no—
160D1076C2×D411yescharacteristic
161D1076C2×D411yescharacteristic
162D1076C2×D411yescharacteristic
163C22⋊D269—21no—
164C22⋊D269—21no—
165C22⋊D269—21no—
166C22⋊D269—41no—
167C22⋊D269—41no—
168C22⋊D269—41no—
169C22⋊D269—41no—
170C22⋊D269—82no—
171C2×Dic269—21no—
172C2×Dic269—41no—
173C4×D269—21no—
174C4×D269—21no—
175C4×D269—21no—
176C4×D269—41no—
177C4×D269—41no—
178C4×D269—41no—
179C4×D269—41no—
180#14524130—21no—
181#14524130C2×D411yescharacteristic
182#14524130C2×D411yescharacteristic
183C23×C269—21no—
184Q8×C269—21no—
185Q8×C269—21no—
186Q8×C269C2×D411yescharacteristic
187D4×C269—21no—
188D4×C269—21no—
189D4×C269—21no—
190D4×C269C2×D411yescharacteristic
191C2×C4×C269—21no—
192C2×C4×C269—21no—
193C2×C4×C269C2411yescharacteristic
194C8×C269—21no—
195C8×C269—21no—
196C8×C269—21no—
197C8×C269C2×D411yescharacteristic
198C8×C269C2×D411yescharacteristic
199C22×C269—21no—
200C22×C269—41no—
201C22×C269—81no—
202C22×C269H(5,𝔽2)11yescharacteristic
203C2×D269—21no—
204C2×D269—21no—
205C2×D269—21no—
206C2×D269—41no—
207C2×D269—41no—
208C2×D269—81no—
209C2×D269—81no—
210C2×D269—161no—
211C2×D269—161no—
212C2×D269—161no—
213C4×C269—21no—
214C4×C269—41no—
215C4×C269C22×D411yescharacteristic
216C4×C269C22×D411yescharacteristic
217Dic269—21no—
218Dic269—21no—
219Dic269—21no—
220Dic269—41no—
221C2×C269—21no—
222C2×C269—41no—
223C2×C269—81no—
224C2×C269D4211yescharacteristic
225D269—41no—
226D269—41no—
227D269—41no—
228D269—81no—
229D269—81no—
230C269#328811yescharacteristic, complemented, Sylow
231#3288—2691nomaximal, Sylow
232#577—2691no—
233#577—2691no—
234#576—2691no—
235#576—2691no—
236#496—2691no—
237#472—2691no—
238#472—2691no—
239#471—2691no—
240#471D26911yescharacteristic, complemented
241#455—2691no—
242#454—2691no—
243#453—2691no—
244#453—2691no—
245#444—2691no—
246#444—2691no—
2472−1+4—2691no—
248H(5,𝔽2)—2691no—
249H(5,𝔽2)—2691no—
250H(5,𝔽2)—2691no—
251#137—2691no—
252#137—5381no—
253#137—5381no—
254#137C2×D26911yescharacteristic, complemented
255AGL(1,ℤ/8)—2691no—
256AGL(1,ℤ/8)—2691no—
257AGL(1,ℤ/8)—2691no—
258AGL(1,ℤ/8)—2691no—
259AGL(1,ℤ/8)—2691no—
260AGL(1,ℤ/8)—5381no—
261AGL(1,ℤ/8)—5381no—
262AGL(1,ℤ/8)—5381no—
263AGL(1,ℤ/8)—5381no—
264AGL(1,ℤ/8)—5381no—
265AGL(1,ℤ/8)—5381no—
266AGL(1,ℤ/8)C2×D26911yescharacteristic
267#135—2691no—
268#135—2691no—
269#135—5381no—
270#135—5381no—
271#135—5381no—
272#135—5381no—
273C2×SD16—2691no—
274C2×SD16—5381no—
275C2×SD16—5381no—
276C2×SD16C2×D26911yescharacteristic, complemented
277C2×D8—2691no—
278C2×D8—2691no—
279C2×D8—5381no—
280C2×D8—5381no—
281#131—2691no—
282#131—2691no—
283#131—2691no—
284#131C2×D26911yescharacteristic, complemented
285#127—2691no—
286#124—2691no—
287#108—2691no—
288#108C2×D26911yescharacteristic, complemented
289#104—2691no—
290#104—2691no—
291#104—2691no—
292#104—2691no—
293#101C2×D26911yescharacteristic, complemented
294#100—2691no—
295#100—2691no—
296#100C2×D26911yescharacteristic, complemented
297#97—2691no—
298#41—2691no—
299#41—2691no—
300#41—2691no—
301#41—5381no—
302#41—5381no—
303#41—5381no—
304#41—5381no—
305#41—5381no—
306#41—5381no—
307#41—5381no—
308#41—5381no—
309#41—10761no—
310#41C22×D26911yescharacteristic
311C2×Q8—5381no—
312C2×Q8—5381no—
313C2×Q8C22×D26911yescharacteristic
314C2×D4—2691no—
315C2×D4—2691no—
316C2×D4—5381no—
317C2×D4—5381no—
318C2×D4—5381no—
319C2×D4—5381no—
320C2×D4—5381no—
321C2×D4—5381no—
322C2×D4—10761no—
323C2×D4—10761no—
324C2×D4—10761no—
325C2×D4—10761no—
326C2×D4C22×D26911yescharacteristic
327Q16—21no—
328Q16—2691no—
329Q16—2691no—
330Q16—5381no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—21no—
335SD16—2691no—
336SD16—2691no—
337SD16—2691no—
338SD16—2691no—
339SD16—5381no—
340SD16—5381no—
341SD16—5381no—
342SD16—5381no—
343SD16—5381no—
344SD16—5381no—
345SD16—5381no—
346SD16—5381no—
347D8—21no—
348D8—2691no—
349D8—2691no—
350D8—5381no—
351D8—5381no—
352D8—5381no—
353D8—5381no—
354D8—5381no—
355D8—5381no—
356D8—5381no—
357D8—5381no—
358D8—5381no—
359M16—21no—
360M16—2691no—
361M16—5381no—
362M16—5381no—
363M16—5381no—
364M16C22×D26911yescharacteristic
365M16C22×D26911yescharacteristic
366M16C22×D26911yescharacteristic
367C2×C8—21no—
368C2×C8—2691no—
369C2×C8—5381no—
370C2×C8—5381no—
371C2×C8—5381no—
372C2×C8C22×D26911yescharacteristic
373C22⋊C4—10761no—
374C42—2691no—
375C23—21no—
376C23—5381no—
377C23—5381no—
378C23—10761no—
379C23—10761no—
380C23—10761no—
381Q8—21no—
382Q8—21no—
383Q8—2691no—
384Q8—2691no—
385Q8—2691no—
386Q8—10761no—
387Q8D4×D26911yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—2691no—
392D4—2691no—
393D4—2691no—
394D4—5381no—
395D4—5381no—
396D4—5381no—
397D4—5381no—
398D4—5381no—
399D4—5381no—
400D4—5381no—
401D4—10761no—
402D4—10761no—
403D4—10761no—
404D4—10761no—
405D4—10761no—
406D4—10761no—
407D4—10761no—
408D4—21522no—
409D4D4×D26911yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—5381no—
413C2×C4—5381no—
414C2×C4—5381no—
415C2×C4—5381no—
416C2×C4—10761no—
417C2×C4—10761no—
418C2×C4—10761no—
419C2×C4—10761no—
420C2×C4—10761no—
421C2×C4C23×D26911yescharacteristic
422C8—21no—
423C8—21no—
424C8—21no—
425C8—2691no—
426C8—2691no—
427C8—5381no—
428C8D4×D26911yescharacteristic
429C8D4×D26911yescharacteristic
430C22—21no—
431C22—41no—
432C22—81no—
433C22—5381no—
434C22—5381no—
435C22—5381no—
436C22—10761no—
437C22—10761no—
438C22—21521no—
439C22—21521no—
440C22—43041no—
441C22—43041no—
442C22—43041no—
443C22#2257549911yescharacteristic
444C4—21no—
445C4—41no—
446C4—5381no—
447C4—5381no—
448C4—5381no—
449C4—10761no—
450C4C2×D4×D26911yescharacteristic
451C4C2×D4×D26911yescharacteristic
452C2—21no—
453C2—41no—
454C2—81no—
455C2—10761no—
456C2—10761no—
457C2—10761no—
458C2—21521no—
459C2—21521no—
460C2#3177123911yescharacteristic
subgroupG/H
centerC2#31771239
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#471×C269C2
socleC2×C269D42
hypercenter#471D269
hypocenterC269#3288
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #31771414C2semidirect
2. #31771411C2semidirect
3. #31771410C2semidirect
4. #31771409C2semidirect
5. #31770991C2semidirect
6. #31770876C2semidirect
7. #31770874C2semidirect
8. #31770871C2semidirect
9. #31770781C2semidirect
10. #31770780C2semidirect
11. #31770775C2semidirect
12. #31770771C2semidirect
13. #31770726C2semidirect
14. #31770725C2semidirect
15. #471×C269C2semidirect
16. #22575501C22semidirect
18. #22575499C22semidirect
19. #22575498C22semidirect
21. #22575484C22semidirect
26. #22575481C22semidirect
27. #22575481C22semidirect
28. #22575481C22semidirect
32. #22575479C22semidirect
40. C2×#16864389C22semidirect
44. C2×D2152C22semidirect
45. C2×#16864387C22semidirect
47. #22575461C22semidirect
48. #22575461C22semidirect
49. #22575459C22semidirect
50. #22575449C22semidirect
51. #22575442C22semidirect
52. #22575388C22semidirect
53. #22575380C22semidirect
54. #22575379C22semidirect
55. #22575379C22semidirect
56. #22575379C22semidirect
57. #22575369C22semidirect
58. #22575369C22semidirect
59. #22575363C22semidirect
60. #137×C269C22semidirect
62. C2×SD16×C269C22semidirect
63. #131×C269C22semidirect
64. #108×C269C22semidirect
65. #101×C269C22semidirect
66. #100×C269C22semidirect
93. Dic1076D4semidirect
95. #16864392D4semidirect
100. #16864391D4semidirect
101. #16864391D4semidirect
103. #16864390D4semidirect
107. #16864389D4semidirect
114. D2152D4semidirect
118. #16864387D4semidirect
230. C269#3288semidirect
240. #471D269semidirect
254. #137C2×D269semidirect
276. C2×SD16C2×D269semidirect
284. #131C2×D269semidirect
288. #108C2×D269semidirect
293. #101C2×D269semidirect
296. #100C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317714142
#317714112
#317714102
#317714092
#317709912
#317708762
#317708742
#317708712
#317707812
#317707802
#317707752
#317707712
#317707262
#317707252
#471×C2692
#3288269