Finite Group Databasebeta

← D29×#471 #16829187

Subgroups — D29×#471 #16829187

Order 3712.

468 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#137×D29C211yesmaximal, characteristic, complemented
2AGL(1,ℤ/8)×D29C211yesmaximal, characteristic
3C2×SD16×D29C211yesmaximal, characteristic, complemented
4#131×D29C211yesmaximal, characteristic, complemented
5#14271429C211yesmaximal, characteristic, complemented
6#14271428C211yesmaximal, characteristic, complemented
7#14271427C211yesmaximal, characteristic, complemented
8#14271426C211yesmaximal, characteristic, complemented
9#14271425C211yesmaximal, characteristic, complemented
10#14271424C211yesmaximal, characteristic, complemented
11#14271423C211yesmaximal, characteristic, complemented
12#108×D29C211yesmaximal, characteristic, complemented
13#101×D29C211yesmaximal, characteristic, complemented
14#100×D29C211yesmaximal, characteristic, complemented
15C29×#471C211yesmaximal, characteristic, complemented
16#41×D29C2211yescharacteristic
17C2×Q8×D29C2211yescharacteristic
18C2×D4×D29C2211yescharacteristic
19C29×#137C2211yescharacteristic, complemented
20C29×AGL(1,ℤ/8)C2211yescharacteristic
21C2×SD16×C29C2211yescharacteristic, complemented
22C29×#131C2211yescharacteristic, complemented
23#11745313C2211yescharacteristic, complemented
24#11745311C2211yescharacteristic
25#11745310C2211yescharacteristic, complemented
26#11745304C2211yescharacteristic, complemented
27C2×#90784C2211yescharacteristic, complemented
28C2×#90783C2211yescharacteristic, complemented
29#11745294C2211yescharacteristic
30#11745280—21no—
31Q16×D29—21no—
32#11745277—21no—
33#11745276—21no—
34SD16×D29—21no—
35SD16×D29—21no—
36SD16×D29—21no—
37SD16×D29—21no—
38SD16×D29—21no—
39SD16×D29—21no—
40#11745273—21no—
41D8×D29—21no—
42#11745271C2211yescharacteristic, complemented
43#11745270C2211yescharacteristic
44#11745269—21no—
45#11745269C2211yescharacteristic, complemented
46M16×D29—21no—
47M16×D29C2211yescharacteristic
48M16×D29C2211yescharacteristic
49M16×D29C2211yescharacteristic
50C2×#90773C2211yescharacteristic, complemented
51#11745263—21no—
52#11745263C2211yescharacteristic, complemented
53C2×C8×D29—21no—
54C2×C8×D29C2211yescharacteristic
55C29×#108C2211yescharacteristic, complemented
56C29×#101C2211yescharacteristic, complemented
57C29×#100C2211yescharacteristic, complemented
58#11745184C2211yescharacteristic, complemented
59#11745181C2211yescharacteristic, complemented
60#11745172C2211yescharacteristic, complemented
61#11745172C2211yescharacteristic, complemented
62#11745171C2211yescharacteristic, complemented
63#11745171C2211yescharacteristic, complemented
64#11745170C2211yescharacteristic, complemented
65#11745170C2211yescharacteristic, complemented
66#11745167C2211yescharacteristic, complemented
67C23×D29—21no—
68#41×C29C2311yescharacteristic
69C2×Q8×C29C2311yescharacteristic
70C2×D4×C29C2311yescharacteristic
71C2×C22⋊D29—21no—
72#90809D411yescharacteristic
73Q8×D29—21no—
74Q8×D29—21no—
75Q8×D29—21no—
76Q8×D29—21no—
77Q8×D29D411yescharacteristic
78#90807—21no—
79#90807D411yescharacteristic
80D4×D29—21no—
81D4×D29—21no—
82D4×D29—21no—
83D4×D29—21no—
84D4×D29—21no—
85D4×D29D411yescharacteristic
86#90805—21no—
87#90805C2311yescharacteristic
88C2×D116C2311yescharacteristic
89C2×C4×D29—21no—
90C2×C4×D29—21no—
91C2×C4×D29C2311yescharacteristic
92C2×Dic58—21no—
93C2×Dic58C2311yescharacteristic
94Q16×C29—21no—
95SD16×C29—21no—
96SD16×C29—21no—
97SD16×C29—21no—
98SD16×C29—21no—
99D8×C29—21no—
100M16×C29—21no—
101M16×C29C2311yescharacteristic
102M16×C29C2311yescharacteristic
103M16×C29C2311yescharacteristic
104C2×C8×C29—21no—
105C2×C8×C29C2311yescharacteristic
106#90785—21no—
107#90785—21no—
108#90784—21no—
109#90784—21no—
110#90784—21no—
111#90784—21no—
112#90783—21no—
113#90783—21no—
114#90783—21no—
115#90783—21no—
116#90782—21no—
117#90782—21no—
118#90777—21no—
119#90777C2311yescharacteristic
120#90777C2311yescharacteristic
121#90777C2311yescharacteristic
122C2×#6597—21no—
123C2×#6597C2311yescharacteristic
124Dic116—21no—
125D232—21no—
126#90773—21no—
127#90773—21no—
128#90773—21no—
129#90773—21no—
130#90772—21no—
131#90772—21no—
132#90772—21no—
133#90772—21no—
134#90772—21no—
135C8×D29—21no—
136C8×D29—21no—
137C8×D29—21no—
138C8×D29—21no—
139C8×D29—21no—
140C8×D29D411yescharacteristic
141C8×D29D411yescharacteristic
142C8×D29D411yescharacteristic
143C8×D29D411yescharacteristic
144C23×C29—21no—
145C22×D29—21no—
146C22×D29—21no—
147C22×D29—41no—
148C22×D29—41no—
149C22×D29—82no—
150C22×D29#4111yescharacteristic
151Q8×C29—21no—
152Q8×C29—21no—
153Q8×C29C2×D411yescharacteristic
154D4×C29—21no—
155D4×C29—21no—
156D4×C29—21no—
157D4×C29C2×D411yescharacteristic
158C2×C4×C29—21no—
159C2×C4×C29—21no—
160C2×C4×C29C2411yescharacteristic
161C22⋊D29—21no—
162C22⋊D29—21no—
163C22⋊D29—21no—
164C22⋊D29—41no—
165C22⋊D29—41no—
166C2×Dic29—21no—
167C2×Dic29—21no—
168C2×Dic29#4111yescharacteristic
169D116—21no—
170D116—21no—
171D116—21no—
172D116C2×D411yescharacteristic
173C4×D29—21no—
174C4×D29—21no—
175C4×D29—21no—
176C4×D29—41no—
177C4×D29—41no—
178C4×D29C2×D411yescharacteristic
179C4×D29C2×D411yescharacteristic
180C4×D29C2×D411yescharacteristic
181C4×D29C2×D411yescharacteristic
182Dic58—21no—
183Dic58—21no—
184Dic58—21no—
185Dic58—41no—
186Dic58—41no—
187Dic58C2×D411yescharacteristic
188C8×C29—21no—
189C8×C29—21no—
190C8×C29—21no—
191C8×C29C2×D411yescharacteristic
192C8×C29C2×D411yescharacteristic
193#6597—21no—
194#6597—21no—
195#6597—21no—
196#6597C2×D411yescharacteristic
197#6597C2×D411yescharacteristic
198C2×#471—291nomaximal, Sylow
199C22×C29—21no—
200C22×C29—41no—
201C22×C29—81no—
202C22×C29C2×#4111yescharacteristic
203C2×D29—22no—
204C2×D29—21no—
205C2×D29—42no—
206C2×D29—41no—
207C2×D29—82no—
208C2×D29—82no—
209C2×D29—81no—
210C2×D29#12111yescharacteristic
211C2×D29#12111yescharacteristic
212C4×C29—21no—
213C4×C29—41no—
214C4×C29C22×D411yescharacteristic
215C4×C29C22×D411yescharacteristic
216Dic29—21no—
217Dic29—41no—
218Dic29#12111yescharacteristic
219Dic29#12111yescharacteristic
220C2×#137—291no—
221C2×AGL(1,ℤ/8)—291no—
222C22×SD16—291no—
223C2×#131—291no—
224#471—291no—
225#471—291no—
226#471—291no—
227#471—291no—
228#471—291no—
229#471—291no—
230#471—291no—
231#471D2911yescharacteristic, direct product factor
232C2×#108—291no—
233C2×#101—291no—
234C2×#100—291no—
235C2×C29—21no—
236C2×C29—41no—
237C2×C29—81no—
238C2×C29C2×#12111yescharacteristic
239D29—21no—
240D29—41no—
241D29—81no—
242D29#47112yesdirect product factor
243C2×#41—291no—
244C22×Q8—291no—
245C22×D4—291no—
246#137—291no—
247#137—291no—
248#137—291no—
249#137—581no—
250#137—581no—
251#137C2×D2911yescharacteristic, complemented
252AGL(1,ℤ/8)—291no—
253AGL(1,ℤ/8)—291no—
254AGL(1,ℤ/8)—291no—
255AGL(1,ℤ/8)—581no—
256AGL(1,ℤ/8)—581no—
257AGL(1,ℤ/8)C2×D2911yescharacteristic
258C2×Q16—581no—
259C2×SD16—291no—
260C2×SD16—291no—
261C2×SD16—291no—
262C2×SD16—581no—
263C2×SD16—581no—
264C2×SD16—581no—
265C2×SD16—581no—
266C2×SD16—581no—
267C2×SD16—581no—
268C2×SD16C2×D2911yescharacteristic, complemented
269C2×D8—581no—
270#131—291no—
271#131—291no—
272#131—291no—
273#131—581no—
274#131—581no—
275#131C2×D2911yescharacteristic, complemented
276C2×M16—291no—
277C2×M16—291no—
278C2×M16—291no—
279C2×M16—581no—
280C22×C8—291no—
281C22×C8—581no—
282#108—291no—
283#108—291no—
284#108—291no—
285#108C2×D2911yescharacteristic, complemented
286#101—291no—
287#101—291no—
288#101—291no—
289#101C2×D2911yescharacteristic, complemented
290#100—291no—
291#100—291no—
292#100—291no—
293#100C2×D2911yescharacteristic, complemented
294C29C2×#47111yescharacteristic, complemented, Sylow
295C24—581no—
296#41—291no—
297#41—291no—
298#41—291no—
299#41—581no—
300#41—581no—
301#41C22×D2911yescharacteristic
302C2×Q8—291no—
303C2×Q8—291no—
304C2×Q8—581no—
305C2×Q8—581no—
306C2×Q8—581no—
307C2×Q8—581no—
308C2×Q8—581no—
309C2×Q8C22×D2911yescharacteristic
310C2×D4—291no—
311C2×D4—291no—
312C2×D4—581no—
313C2×D4—581no—
314C2×D4—581no—
315C2×D4—581no—
316C2×D4—581no—
317C2×D4—581no—
318C2×D4C22×D2911yescharacteristic
319C22×C4—291no—
320C22×C4—581no—
321C22×C4—581no—
322Q16—21no—
323Q16—581no—
324Q16—581no—
325Q16—581no—
326SD16—21no—
327SD16—21no—
328SD16—21no—
329SD16—21no—
330SD16—581no—
331SD16—581no—
332SD16—581no—
333SD16—581no—
334SD16—581no—
335SD16—581no—
336SD16—581no—
337SD16—581no—
338SD16—581no—
339SD16—581no—
340SD16—581no—
341SD16—581no—
342D8—21no—
343D8—581no—
344D8—581no—
345D8—581no—
346M16—21no—
347M16—291no—
348M16—291no—
349M16—291no—
350M16—581no—
351M16—581no—
352M16—581no—
353M16—581no—
354M16—581no—
355M16—581no—
356M16C22×D2911yescharacteristic
357M16C22×D2911yescharacteristic
358M16C22×D2911yescharacteristic
359C2×C8—21no—
360C2×C8—291no—
361C2×C8—291no—
362C2×C8—291no—
363C2×C8—291no—
364C2×C8—291no—
365C2×C8—581no—
366C2×C8—581no—
367C2×C8—581no—
368C2×C8—581no—
369C2×C8—581no—
370C2×C8—581no—
371C2×C8C22×D2911yescharacteristic
372C23—21no—
373C23—291no—
374C23—581no—
375C23—581no—
376C23—1161no—
377C23—1161no—
378C23—2322no—
379Q8—21no—
380Q8—21no—
381Q8—291no—
382Q8—581no—
383Q8—581no—
384Q8—581no—
385Q8—1161no—
386Q8—1161no—
387Q8D4×D2911yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—291no—
392D4—581no—
393D4—581no—
394D4—581no—
395D4—581no—
396D4—581no—
397D4—581no—
398D4—1161no—
399D4—1161no—
400D4D4×D2911yescharacteristic
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—291no—
404C2×C4—291no—
405C2×C4—291no—
406C2×C4—291no—
407C2×C4—291no—
408C2×C4—581no—
409C2×C4—581no—
410C2×C4—581no—
411C2×C4—581no—
412C2×C4—581no—
413C2×C4—1161no—
414C2×C4—1161no—
415C2×C4C23×D2911yescharacteristic
416C8—21no—
417C8—21no—
418C8—21no—
419C8—291no—
420C8—291no—
421C8—581no—
422C8—581no—
423C8—581no—
424C8D4×D2911yescharacteristic
425C8D4×D2911yescharacteristic
426C22—21no—
427C22—41no—
428C22—81no—
429C22—291no—
430C22—291no—
431C22—582no—
432C22—581no—
433C22—1162no—
434C22—1161no—
435C22—2321no—
436C22—2322no—
437C22—2322no—
438C22#41×D2911yescharacteristic
439C4—21no—
440C4—41no—
441C4—291no—
442C4—291no—
443C4—581no—
444C4—1161no—
445C4C2×D4×D2911yescharacteristic
446C4C2×D4×D2911yescharacteristic
447C2—21no—
448C2—41no—
449C2—81no—
450C2—292no—
451C2—581no—
452C2—1161no—
453C2—2321no—
454C2#121×D2911yescharacteristic
subgroupG/H
centerC2#121×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#471C2
socleC2×C29C2×#121
prime radicalAGL(1,ℤ/8)×D29C2
hypercenter#471D29
hypocenterC29C2×#471
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #137×D29C2semidirect
3. C2×SD16×D29C2semidirect
4. #131×D29C2semidirect
5. #14271429C2semidirect
6. #14271428C2semidirect
7. #14271427C2semidirect
8. #14271426C2semidirect
9. #14271425C2semidirect
10. #14271424C2semidirect
11. #14271423C2semidirect
12. #108×D29C2semidirect
13. #101×D29C2semidirect
14. #100×D29C2semidirect
15. C29×#471C2semidirect
19. C29×#137C22semidirect
21. C2×SD16×C29C22semidirect
22. C29×#131C22semidirect
23. #11745313C22semidirect
25. #11745310C22semidirect
26. #11745304C22semidirect
27. C2×#90784C22semidirect
28. C2×#90783C22semidirect
42. #11745271C22semidirect
45. #11745269C22semidirect
50. C2×#90773C22semidirect
52. #11745263C22semidirect
55. C29×#108C22semidirect
56. C29×#101C22semidirect
57. C29×#100C22semidirect
58. #11745184C22semidirect
59. #11745181C22semidirect
60. #11745172C22semidirect
61. #11745172C22semidirect
62. #11745171C22semidirect
63. #11745171C22semidirect
64. #11745170C22semidirect
65. #11745170C22semidirect
66. #11745167C22semidirect
231. #471D29direct (N × H)
242. D29#471direct (N × H)
251. #137C2×D29semidirect
268. C2×SD16C2×D29semidirect
275. #131C2×D29semidirect
285. #108C2×D29semidirect
289. #101C2×D29semidirect
293. #100C2×D29semidirect
294. C29C2×#471semidirect

Maximal subgroups

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

subgroupindex
#137×D292
AGL(1,ℤ/8)×D292
C2×SD16×D292
#131×D292
#142714292
#142714282
#142714272
#142714262
#142714252
#142714242
#142714232
#108×D292
#101×D292
#100×D292
C29×#4712
C2×#47129