Finite Group Databasebeta

← #16831283

Subgroups — #16831283

Order 3712.

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#14271974C211yesmaximal, characteristic, complemented
2#14271971C211yesmaximal, characteristic, complemented
3#14271970C211yesmaximal, characteristic, complemented
4#14271534C211yesmaximal, characteristic, complemented
5#14271428C211yesmaximal, characteristic, complemented
6#14271426C211yesmaximal, characteristic, complemented
7#14271424C211yesmaximal, characteristic, complemented
8#14271423C211yesmaximal, characteristic, complemented
9#14271346C211yesmaximal, characteristic, complemented
10#14271344C211yesmaximal, characteristic, complemented
11#14271331C211yesmaximal, characteristic, complemented
12#14271329C211yesmaximal, characteristic, complemented
13#14271280C211yesmaximal, characteristic, complemented
14#14271278C211yesmaximal, characteristic, complemented
15C29×#577C211yesmaximal, characteristic, complemented
16C29×2−1+4C2211yescharacteristic
17C29×H(5,𝔽2)C2211yescharacteristic, complemented
18#11745365C2211yescharacteristic
19#11745364C2211yescharacteristic, complemented
20C29×#137—21no—
21C29×#137C2211yescharacteristic, complemented
22C29×AGL(1,ℤ/8)—21no—
23C29×AGL(1,ℤ/8)C2211yescharacteristic
24C29×#135—21no—
25C29×#135C2211yescharacteristic
26C2×SD16×C29—21no—
27C2×SD16×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
38#11745310C2211yescharacteristic, complemented
39#11745310C2211yescharacteristic, complemented
40#11745306C2211yescharacteristic, complemented
41#11745304—21no—
42#11745304C2211yescharacteristic, complemented
43C2×#90784—21no—
44C2×#90784C2211yescharacteristic, complemented
45#11745302C2211yescharacteristic
46C2×#90783—21no—
47C2×#90783C2211yescharacteristic, complemented
48#11745294—21no—
49#11745294C2211yescharacteristic
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#11745184C2211yescharacteristic, complemented
60#11745181C2211yescharacteristic, complemented
61#11745173C2211yescharacteristic, complemented
62#11745172C2211yescharacteristic, complemented
63#11745171C2211yescharacteristic, complemented
64#11745170C2211yescharacteristic, complemented
65#11745167C2211yescharacteristic, complemented
66C8×Dic29C2211yescharacteristic, complemented
67#41×C29—21no—
68#41×C29—21no—
69#41×C29—21no—
70#41×C29—21no—
71#41×C29—41no—
72#41×C29C2311yescharacteristic
73#41×C29C2311yescharacteristic
74#41×C29C2311yescharacteristic
75C2×Q8×C29—21no—
76C2×Q8×C29—21no—
77C2×Q8×C29C2311yescharacteristic
78C2×D4×C29—21no—
79C2×D4×C29—21no—
80C2×D4×C29—41no—
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×C29—21no—
97Q16×C29D411yescharacteristic, complemented
98SD16×C29—21no—
99SD16×C29—21no—
100SD16×C29—21no—
101SD16×C29—21no—
102SD16×C29D411yescharacteristic, complemented
103SD16×C29D411yescharacteristic, complemented
104D8×C29—21no—
105D8×C29D411yescharacteristic, complemented
106M16×C29—21no—
107M16×C29C2311yescharacteristic
108C2×C8×C29—21no—
109C2×C8×C29C2311yescharacteristic
110#90785—21no—
111#90785—21no—
112#90785—21no—
113#90785D411yescharacteristic, complemented
114#90784—21no—
115#90784—21no—
116#90784—21no—
117#90784—21no—
118#90784—21no—
119#90784D411yescharacteristic, complemented
120#90783—21no—
121#90783—21no—
122#90783—21no—
123#90783—21no—
124#90783—21no—
125#90783D411yescharacteristic, complemented
126#90782—21no—
127#90782—21no—
128#90782—21no—
129#90782D411yescharacteristic, complemented
130#90779—41no—
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—41no—
146C22×D29—21no—
147C22×D29—41no—
148Q8×C29—21no—
149Q8×C29—21no—
150Q8×C29—41no—
151Q8×C29C2×D411yescharacteristic
152Q8×C29C2×D411yescharacteristic
153Q8×C29C2×D411yescharacteristic
154D4×C29—21no—
155D4×C29—21no—
156D4×C29—21no—
157D4×C29—21no—
158D4×C29—21no—
159D4×C29—41no—
160D4×C29—41no—
161D4×C29—41no—
162D4×C29C2×D411yescharacteristic
163D4×C29C2×D411yescharacteristic
164D4×C29C2×D411yescharacteristic
165C2×C4×C29—21no—
166C2×C4×C29—21no—
167C2×C4×C29—21no—
168C2×C4×C29—21no—
169C2×C4×C29—41no—
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#3291—291nomaximal, Sylow
200C22×C29—21no—
201C22×C29—21no—
202C22×C29—21no—
203C22×C29—41no—
204C22×C29—81no—
205C22×C29—161no—
206C22×C29H(5,𝔽2)11yescharacteristic
207C2×D29—21no—
208C2×D29—41no—
209C2×D29—81no—
210C2×D29—161no—
211C4×C29—21no—
212C4×C29—21no—
213C4×C29—21no—
214C4×C29—41no—
215C4×C29C22×D411yescharacteristic
216C4×C29C22×D411yescharacteristic
217Dic29—22no—
218Dic29—21no—
219Dic29—41no—
220#577—291no—
221#577—291no—
222#577—291no—
223#577D2911yescharacteristic, complemented
224#492—291no—
225#471—291no—
226#471—291no—
227#471—291no—
228#471—291no—
229#456—291no—
230#456—291no—
231#453—291no—
232#453—291no—
233#443—291no—
234#443—291no—
235C2×C29—21no—
236C2×C29—41no—
237C2×C29—41no—
238C2×C29—41no—
239C2×C29—81no—
240C2×C29D4211yescharacteristic
241D29—41no—
242D29—81no—
2432−1+4—291no—
2442−1+4C2×D2911yescharacteristic
245H(5,𝔽2)—291no—
246H(5,𝔽2)C2×D2911yescharacteristic, complemented
247#137—21no—
248#137—291no—
249#137—291no—
250#137—291no—
251#137—581no—
252#137—581no—
253#137—581no—
254#137C2×D2911yescharacteristic, complemented
255AGL(1,ℤ/8)—21no—
256AGL(1,ℤ/8)—291no—
257AGL(1,ℤ/8)—291no—
258AGL(1,ℤ/8)—291no—
259AGL(1,ℤ/8)—581no—
260AGL(1,ℤ/8)—581no—
261AGL(1,ℤ/8)—581no—
262AGL(1,ℤ/8)C2×D2911yescharacteristic
263#135—21no—
264#135—291no—
265#135—581no—
266#135—581no—
267#135—581no—
268#135C2×D2911yescharacteristic
269C2×SD16—21no—
270C2×SD16—291no—
271C2×SD16—291no—
272C2×SD16—291no—
273C2×SD16—581no—
274C2×SD16—581no—
275C2×SD16—581no—
276C2×SD16C2×D2911yescharacteristic, complemented
277#131—291no—
278#131—291no—
279#131—291no—
280#131C2×D2911yescharacteristic, complemented
281C4⋊Q8—291no—
282#127—291no—
283#108—291no—
284#108—291no—
285#104—291no—
286#104—291no—
287#104—291no—
288#104—291no—
289#101—291no—
290#101—291no—
291#100—291no—
292#100—291no—
293C4×C8—291no—
294C29#329111yescharacteristic, complemented, Sylow
295#41—21no—
296#41—21no—
297#41—21no—
298#41—21no—
299#41—41no—
300#41—291no—
301#41—581no—
302#41—581no—
303#41—581no—
304#41—581no—
305#41—1161no—
306#41C22×D2911yescharacteristic
307#41C22×D2911yescharacteristic
308#41C22×D2911yescharacteristic
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—291no—
312C2×Q8—581no—
313C2×Q8—581no—
314C2×Q8C22×D2911yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—291no—
319C2×D4—581no—
320C2×D4—581no—
321C2×D4—1161no—
322C2×D4—1161no—
323C2×D4C22×D2911yescharacteristic
324Q16—21no—
325Q16—291no—
326Q16—581no—
327Q16—581no—
328Q16—581no—
329Q16C22⋊D2911yescharacteristic, complemented
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—291no—
335SD16—291no—
336SD16—581no—
337SD16—581no—
338SD16—581no—
339SD16—581no—
340SD16—581no—
341SD16—581no—
342SD16—581no—
343SD16—581no—
344SD16—581no—
345SD16—581no—
346SD16—581no—
347SD16—581no—
348SD16C22⋊D2911yescharacteristic, complemented
349SD16C22⋊D2911yescharacteristic, complemented
350D8—21no—
351D8—291no—
352D8—581no—
353D8—581no—
354D8—581no—
355D8C22⋊D2911yescharacteristic, complemented
356M16—21no—
357M16—291no—
358M16—291no—
359M16—291no—
360M16—581no—
361M16—581no—
362M16—581no—
363M16C22×D2911yescharacteristic
364C2×C8—21no—
365C2×C8—291no—
366C2×C8—581no—
367C2×C8—581no—
368C2×C8—581no—
369C2×C8C22×D2911yescharacteristic
370C4⋊C4—1161no—
371C42—291no—
372C23—21no—
373C23—41no—
374C23—581no—
375C23—1161no—
376Q8—21no—
377Q8—21no—
378Q8—41no—
379Q8—291no—
380Q8—581no—
381Q8—581no—
382Q8—1161no—
383Q8D4×D2911yescharacteristic
384Q8C2×C22⋊D2911yescharacteristic
385Q8C2×C22⋊D2911yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—291no—
395D4—581no—
396D4—581no—
397D4—581no—
398D4—1161no—
399D4—1161no—
400D4—1161no—
401D4—2322no—
402D4D4×D2911yescharacteristic
403D4C2×C22⋊D2911yescharacteristic
404D4C2×C22⋊D2911yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—581no—
413C2×C4—581no—
414C2×C4—581no—
415C2×C4—1161no—
416C2×C4—1161no—
417C2×C4—1161no—
418C2×C4C23×D2911yescharacteristic
419C8—21no—
420C8—291no—
421C8—291no—
422C8—581no—
423C8—581no—
424C8—581no—
425C8C2×C22⋊D2911yescharacteristic
426C8C2×C22⋊D2911yescharacteristic
427C22—21no—
428C22—21no—
429C22—21no—
430C22—41no—
431C22—81no—
432C22—161no—
433C22—581no—
434C22—1161no—
435C22—4641no—
436C22—2321no—
437C22#1174535911yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—41no—
442C4—582no—
443C4—581no—
444C4—1161no—
445C4C2×D4×D2911yescharacteristic
446C4C22×C22⋊D2911yescharacteristic
447C2—21no—
448C2—41no—
449C2—41no—
450C2—41no—
451C2—81no—
452C2—1161no—
453C2—2321no—
454C2D4×C22⋊D2911yescharacteristic
subgroupG/H
centerC2D4×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#577C2
socleC2×C29D42
hypercenter#577D29
hypocenterC29#3291
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #14271974C2semidirect
2. #14271971C2semidirect
3. #14271970C2semidirect
4. #14271534C2semidirect
5. #14271428C2semidirect
6. #14271426C2semidirect
7. #14271424C2semidirect
8. #14271423C2semidirect
9. #14271346C2semidirect
10. #14271344C2semidirect
11. #14271331C2semidirect
12. #14271329C2semidirect
13. #14271280C2semidirect
14. #14271278C2semidirect
15. C29×#577C2semidirect
17. C29×H(5,𝔽2)C22semidirect
19. #11745364C22semidirect
21. C29×#137C22semidirect
27. C2×SD16×C29C22semidirect
28. C29×#131C22semidirect
30. #11745313C22semidirect
31. #11745313C22semidirect
38. #11745310C22semidirect
39. #11745310C22semidirect
40. #11745306C22semidirect
42. #11745304C22semidirect
44. C2×#90784C22semidirect
47. C2×#90783C22semidirect
54. C2×#90773C22semidirect
55. #11745263C22semidirect
56. #11745185C22semidirect
57. #11745185C22semidirect
58. #11745185C22semidirect
59. #11745184C22semidirect
60. #11745181C22semidirect
61. #11745173C22semidirect
62. #11745172C22semidirect
63. #11745171C22semidirect
64. #11745170C22semidirect
65. #11745167C22semidirect
66. C8×Dic29C22semidirect
97. Q16×C29D4semidirect
102. SD16×C29D4semidirect
103. SD16×C29D4semidirect
105. D8×C29D4semidirect
113. #90785D4semidirect
119. #90784D4semidirect
125. #90783D4semidirect
129. #90782D4semidirect
223. #577D29semidirect
246. H(5,𝔽2)C2×D29semidirect
254. #137C2×D29semidirect
276. C2×SD16C2×D29semidirect
280. #131C2×D29semidirect
294. C29#3291semidirect
329. Q16C22⋊D29semidirect
348. SD16C22⋊D29semidirect
349. SD16C22⋊D29semidirect
355. D8C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
#142719742
#142719712
#142719702
#142715342
#142714282
#142714262
#142714242
#142714232
#142713462
#142713442
#142713312
#142713292
#142712802
#142712782
C29×#5772
#329129