Finite Group Databasebeta

← #16831256

Subgroups — #16831256

Order 3712.

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#14271974C211yesmaximal, characteristic, complemented
2#14271970C211yesmaximal, characteristic, complemented
3#14271966C211yesmaximal, characteristic, complemented
4#14271551C211yesmaximal, characteristic, complemented
5#14271431C211yesmaximal, characteristic, complemented
6#14271430C211yesmaximal, characteristic, complemented
7#14271426C211yesmaximal, characteristic, complemented
8#14271424C211yesmaximal, characteristic, complemented
9#14271341C211yesmaximal, characteristic, complemented
10#14271334C211yesmaximal, characteristic, complemented
11#14271331C211yesmaximal, characteristic, complemented
12#14271329C211yesmaximal, characteristic, complemented
13#14271285C211yesmaximal, characteristic, complemented
14#14271283C211yesmaximal, characteristic, complemented
15C29×#576C211yesmaximal, characteristic, complemented
16C29×H(5,𝔽2)C2211yescharacteristic
17C29×H(5,𝔽2)C2211yescharacteristic, complemented
18#11745365C2211yescharacteristic, complemented
19#11745364C2211yescharacteristic, complemented
20C29×AGL(1,ℤ/8)—21no—
21C29×AGL(1,ℤ/8)—21no—
22C29×AGL(1,ℤ/8)C2211yescharacteristic
23C29×AGL(1,ℤ/8)C2211yescharacteristic, complemented
24C29×#135—21no—
25C29×#135C2211yescharacteristic
26C2×D8×C29—21no—
27C2×D8×C29C2211yescharacteristic, complemented
28C29×#131C2211yescharacteristic, complemented
29#11745313—21no—
30#11745313C2211yescharacteristic, complemented
31#11745313C2211yescharacteristic, complemented
32#11745312—21no—
33#11745312—21no—
34#11745312C2211yescharacteristic
35#11745311—21no—
36#11745311C2211yescharacteristic
37#11745311C2211yescharacteristic, complemented
38#11745310C2211yescharacteristic, complemented
39#11745310C2211yescharacteristic, complemented
40#11745302C2211yescharacteristic, complemented
41#11745298C2211yescharacteristic, complemented
42C2×#90783—21no—
43C2×#90783C2211yescharacteristic, complemented
44#11745294—21no—
45#11745294—21no—
46#11745294C2211yescharacteristic, complemented
47#11745294C2211yescharacteristic, complemented
48C2×#90782—21no—
49C2×#90782C2211yescharacteristic, complemented
50#11745280—21no—
51#11745278—21no—
52SD16×D29—21no—
53#11745273—21no—
54C2×#90773C2211yescharacteristic, complemented
55#11745263C2211yescharacteristic, complemented
56#11745185C2211yescharacteristic, complemented
57#11745185C2211yescharacteristic, complemented
58#11745185C2211yescharacteristic, complemented
59#11745181C2211yescharacteristic, complemented
60#11745181C2211yescharacteristic, complemented
61#11745173C2211yescharacteristic, complemented
62#11745172C2211yescharacteristic, complemented
63#11745171C2211yescharacteristic, complemented
64#11745170C2211yescharacteristic, complemented
65#11745167C2211yescharacteristic, complemented
66#11745163C2211yescharacteristic, complemented
67#41×C29—21no—
68#41×C29—21no—
69#41×C29—21no—
70#41×C29—21no—
71#41×C29C2311yescharacteristic
72#41×C29C2311yescharacteristic
73#41×C29C2311yescharacteristic
74C2×D4×C29—21no—
75C2×D4×C29—21no—
76C2×D4×C29—21no—
77C2×D4×C29—21no—
78C2×D4×C29—41no—
79C2×D4×C29—41no—
80C2×D4×C29C2311yescharacteristic
81C2×D4×C29C2311yescharacteristic
82C2×C22⋊D29—41no—
83#90809—21no—
84Q8×D29—21no—
85#90807—21no—
86#90807—41no—
87D4×D29—21no—
88D4×D29—41no—
89#90805—21no—
90#90805—21no—
91#90805C2311yescharacteristic
92C2×D116—21no—
93C2×D116C2311yescharacteristic
94C2×Dic58—21no—
95C2×Dic58C2311yescharacteristic
96Q16×C29D411yescharacteristic, complemented
97SD16×C29—21no—
98SD16×C29—21no—
99SD16×C29D411yescharacteristic, complemented
100SD16×C29D411yescharacteristic, complemented
101D8×C29—21no—
102D8×C29—21no—
103D8×C29—21no—
104D8×C29—21no—
105D8×C29D411yescharacteristic, complemented
106M16×C29—21no—
107M16×C29C2311yescharacteristic
108C2×C8×C29—21no—
109C2×C8×C29C2311yescharacteristic
110C22⋊Dic29—41no—
111#90785—21no—
112#90785—21no—
113#90785D411yescharacteristic, complemented
114#90784—21no—
115#90784—21no—
116#90784D411yescharacteristic, complemented
117#90783—21no—
118#90783—21no—
119#90783—21no—
120#90783—21no—
121#90783—21no—
122#90783—21no—
123#90783D411yescharacteristic, complemented
124#90782—21no—
125#90782—21no—
126#90782—21no—
127#90782—21no—
128#90782—21no—
129#90782—21no—
130#90782D411yescharacteristic, complemented
131C4×Dic29C2311yescharacteristic
132#90777—21no—
133#90777—21no—
134#90777C2311yescharacteristic
135#90777C2311yescharacteristic
136#90777C2311yescharacteristic
137C2×#6597—21no—
138C2×#6597—21no—
139C2×#6597C2311yescharacteristic
140#90773—21no—
141#90773—21no—
142#90772—21no—
143C8×D29—21no—
144C23×C29—21no—
145C23×C29—21no—
146C23×C29—41no—
147C23×C29—41no—
148C22×D29—21no—
149C22×D29—41no—
150Q8×C29C2×D411yescharacteristic
151Q8×C29C2×D411yescharacteristic
152Q8×C29C2×D411yescharacteristic
153D4×C29—21no—
154D4×C29—21no—
155D4×C29—21no—
156D4×C29—21no—
157D4×C29—21no—
158D4×C29—21no—
159D4×C29—21no—
160D4×C29—41no—
161D4×C29—41no—
162D4×C29—41no—
163D4×C29—41no—
164D4×C29C2×D411yescharacteristic
165D4×C29C2×D411yescharacteristic
166D4×C29C2×D411yescharacteristic
167C2×C4×C29—21no—
168C2×C4×C29—21no—
169C2×C4×C29—21no—
170C2×C4×C29—41no—
171C2×C4×C29—41no—
172C2×C4×C29C2411yescharacteristic
173C22⋊D29—21no—
174C22⋊D29—41no—
175C22⋊D29—41no—
176C22⋊D29—82no—
177C2×Dic29—21no—
178C2×Dic29—21no—
179C2×Dic29—41no—
180D116—21no—
181D116—21no—
182D116—41no—
183D116C2×D411yescharacteristic
184C4×D29—21no—
185C4×D29—41no—
186C4×D29—41no—
187Dic58—21no—
188Dic58—21no—
189Dic58—41no—
190Dic58C2×D411yescharacteristic
191C8×C29—21no—
192C8×C29C2×D411yescharacteristic
193C8×C29C2×D411yescharacteristic
194#6597—21no—
195#6597—21no—
196#6597—21no—
197#6597C2×D411yescharacteristic
198#6597C2×D411yescharacteristic
199#3288—291nomaximal, Sylow
200C22×C29—21no—
201C22×C29—21no—
202C22×C29—21no—
203C22×C29—41no—
204C22×C29—41no—
205C22×C29—81no—
206C22×C29—81no—
207C22×C29—161no—
208C22×C29—161no—
209C22×C29H(5,𝔽2)11yescharacteristic
210C2×D29—21no—
211C2×D29—41no—
212C2×D29—81no—
213C2×D29—161no—
214C4×C29—21no—
215C4×C29—21no—
216C4×C29—21no—
217C4×C29C22×D411yescharacteristic
218C4×C29C22×D411yescharacteristic
219Dic29—21no—
220Dic29—41no—
221Dic29—41no—
222#577—291no—
223#577—291no—
224#576—291no—
225#576D2911yescharacteristic, complemented
226#496—291no—
227#472—291no—
228#472—291no—
229#471—291no—
230#471—291no—
231#455—291no—
232#454—291no—
233#453—291no—
234#453—291no—
235#444—291no—
236#444—291no—
237C2×C29—21no—
238C2×C29—41no—
239C2×C29—41no—
240C2×C29—41no—
241C2×C29—81no—
242C2×C29—81no—
243C2×C29D4211yescharacteristic
244D29—41no—
245D29—81no—
2462−1+4—291no—
247H(5,𝔽2)—291no—
248H(5,𝔽2)C2×D2911yescharacteristic
249H(5,𝔽2)C2×D2911yescharacteristic, complemented
250#137—291no—
251#137—291no—
252#137—581no—
253#137—581no—
254AGL(1,ℤ/8)—21no—
255AGL(1,ℤ/8)—21no—
256AGL(1,ℤ/8)—291no—
257AGL(1,ℤ/8)—291no—
258AGL(1,ℤ/8)—291no—
259AGL(1,ℤ/8)—291no—
260AGL(1,ℤ/8)—581no—
261AGL(1,ℤ/8)—581no—
262AGL(1,ℤ/8)—581no—
263AGL(1,ℤ/8)—581no—
264AGL(1,ℤ/8)C2×D2911yescharacteristic
265AGL(1,ℤ/8)C2×D2911yescharacteristic, complemented
266#135—21no—
267#135—291no—
268#135—581no—
269#135—581no—
270#135—581no—
271#135C2×D2911yescharacteristic
272C2×SD16—291no—
273C2×SD16—291no—
274C2×SD16—581no—
275C2×SD16—581no—
276C2×D8—21no—
277C2×D8—291no—
278C2×D8—581no—
279C2×D8C2×D2911yescharacteristic, complemented
280#131—291no—
281#131—291no—
282#131—291no—
283#131C2×D2911yescharacteristic, complemented
284#127—291no—
285#124—291no—
286#108—291no—
287#108—291no—
288#104—291no—
289#104—291no—
290#104—291no—
291#104—291no—
292#101—291no—
293#100—291no—
294#100—291no—
295#100—291no—
296#97—291no—
297C29#328811yescharacteristic, complemented, Sylow
298#41—21no—
299#41—21no—
300#41—21no—
301#41—21no—
302#41—291no—
303#41—581no—
304#41—581no—
305#41—581no—
306#41—581no—
307#41—1161no—
308#41C22×D2911yescharacteristic
309#41C22×D2911yescharacteristic
310#41C22×D2911yescharacteristic
311C2×Q8—291no—
312C2×Q8—581no—
313C2×Q8—581no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—291no—
321C2×D4—581no—
322C2×D4—581no—
323C2×D4—1161no—
324C2×D4—1161no—
325C2×D4C22×D2911yescharacteristic
326C2×D4C22×D2911yescharacteristic
327Q16—291no—
328Q16—581no—
329Q16—581no—
330Q16C22⋊D2911yescharacteristic, complemented
331SD16—21no—
332SD16—21no—
333SD16—291no—
334SD16—291no—
335SD16—581no—
336SD16—581no—
337SD16—581no—
338SD16—581no—
339SD16—581no—
340SD16—581no—
341SD16—581no—
342SD16—581no—
343SD16—581no—
344SD16—581no—
345SD16C22⋊D2911yescharacteristic, complemented
346SD16C22⋊D2911yescharacteristic, complemented
347D8—21no—
348D8—21no—
349D8—21no—
350D8—21no—
351D8—291no—
352D8—581no—
353D8—581no—
354D8—581no—
355D8—581no—
356D8—581no—
357D8—581no—
358D8C22⋊D2911yescharacteristic, complemented
359M16—21no—
360M16—291no—
361M16—291no—
362M16—291no—
363M16—581no—
364M16—581no—
365M16—581no—
366M16C22×D2911yescharacteristic
367C2×C8—21no—
368C2×C8—291no—
369C2×C8—581no—
370C2×C8—581no—
371C2×C8—581no—
372C2×C8C22×D2911yescharacteristic
373C22⋊C4—1161no—
374C42—291no—
375C23—21no—
376C23—21no—
377C23—41no—
378C23—41no—
379C23—581no—
380C23—1161no—
381Q8—291no—
382Q8—581no—
383Q8—581no—
384Q8—1161no—
385Q8D4×D2911yescharacteristic
386Q8C2×C22⋊D2911yescharacteristic
387Q8C2×C22⋊D2911yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—21no—
394D4—21no—
395D4—41no—
396D4—41no—
397D4—41no—
398D4—41no—
399D4—291no—
400D4—581no—
401D4—581no—
402D4—581no—
403D4—1161no—
404D4—1161no—
405D4—1161no—
406D4—2322no—
407D4D4×D2911yescharacteristic
408D4C2×C22⋊D2911yescharacteristic
409D4C2×C22⋊D2911yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—581no—
416C2×C4—581no—
417C2×C4—581no—
418C2×C4—1161no—
419C2×C4—1161no—
420C2×C4—1161no—
421C2×C4C23×D2911yescharacteristic
422C8—21no—
423C8—291no—
424C8—291no—
425C8—581no—
426C8—581no—
427C8—581no—
428C8C2×C22⋊D2911yescharacteristic
429C8C2×C22⋊D2911yescharacteristic
430C22—21no—
431C22—21no—
432C22—21no—
433C22—41no—
434C22—41no—
435C22—81no—
436C22—81no—
437C22—161no—
438C22—161no—
439C22—581no—
440C22—1161no—
441C22—4641no—
442C22—2321no—
443C22#1174535911yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—581no—
448C4—1161no—
449C4—1161no—
450C4C2×D4×D2911yescharacteristic
451C4C22×C22⋊D2911yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—41no—
456C2—81no—
457C2—81no—
458C2—1161no—
459C2—2321no—
460C2D4×C22⋊D2911yescharacteristic
subgroupG/H
centerC2D4×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#576C2
socleC2×C29D42
hypercenter#576D29
hypocenterC29#3288
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ #576

Complements

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

NH ≅ G/Ntype
1. #14271974C2semidirect
2. #14271970C2semidirect
3. #14271966C2semidirect
4. #14271551C2semidirect
5. #14271431C2semidirect
6. #14271430C2semidirect
7. #14271426C2semidirect
8. #14271424C2semidirect
9. #14271341C2semidirect
10. #14271334C2semidirect
11. #14271331C2semidirect
12. #14271329C2semidirect
13. #14271285C2semidirect
14. #14271283C2semidirect
15. C29×#576C2semidirect
17. C29×H(5,𝔽2)C22semidirect
18. #11745365C22semidirect
19. #11745364C22semidirect
23. C29×AGL(1,ℤ/8)C22semidirect
27. C2×D8×C29C22semidirect
28. C29×#131C22semidirect
30. #11745313C22semidirect
31. #11745313C22semidirect
37. #11745311C22semidirect
38. #11745310C22semidirect
39. #11745310C22semidirect
40. #11745302C22semidirect
41. #11745298C22semidirect
43. C2×#90783C22semidirect
46. #11745294C22semidirect
47. #11745294C22semidirect
49. C2×#90782C22semidirect
54. C2×#90773C22semidirect
55. #11745263C22semidirect
56. #11745185C22semidirect
57. #11745185C22semidirect
58. #11745185C22semidirect
59. #11745181C22semidirect
60. #11745181C22semidirect
61. #11745173C22semidirect
62. #11745172C22semidirect
63. #11745171C22semidirect
64. #11745170C22semidirect
65. #11745167C22semidirect
66. #11745163C22semidirect
96. Q16×C29D4semidirect
99. SD16×C29D4semidirect
100. SD16×C29D4semidirect
105. D8×C29D4semidirect
113. #90785D4semidirect
116. #90784D4semidirect
123. #90783D4semidirect
130. #90782D4semidirect
225. #576D29semidirect
249. H(5,𝔽2)C2×D29semidirect
265. AGL(1,ℤ/8)C2×D29semidirect
279. C2×D8C2×D29semidirect
283. #131C2×D29semidirect
297. C29#3288semidirect
330. Q16C22⋊D29semidirect
345. SD16C22⋊D29semidirect
346. SD16C22⋊D29semidirect
358. D8C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
#142719742
#142719702
#142719662
#142715512
#142714312
#142714302
#142714262
#142714242
#142713412
#142713342
#142713312
#142713292
#142712852
#142712832
C29×#5762
#328829