Finite Group Databasebeta

← C29×#19835 #20314735

Subgroups — C29×#19835 #20314735

Order 7424.

652 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3367C211yesmaximal, characteristic, complemented
2C29×#3358C211yesmaximal, characteristic
3C29×#3304C211yesmaximal, characteristic, complemented
4D4×Q16×C29C211yesmaximal, characteristic, complemented
5C29×#1720C211yesmaximal, characteristic, complemented
6C29×#1702C211yesmaximal, characteristic, complemented
7C29×#1681C211yesmaximal, characteristic, complemented
8C29×#1680C211yesmaximal, characteristic, complemented
9C29×#1669C211yesmaximal, characteristic, complemented
10C29×#1652C211yesmaximal, characteristic, complemented
11C29×#1651C211yesmaximal, characteristic, complemented
12C29×#1641C211yesmaximal, characteristic, complemented
13C29×#1627C211yesmaximal, characteristic, complemented
14C29×#1584C211yesmaximal, characteristic, complemented
15C29×#1580C211yesmaximal, characteristic, complemented
16C22×Q16×C29—21no—
17C29×#556C2211yescharacteristic
18C29×#550C2211yescharacteristic
19D4×Q8×C29C2211yescharacteristic
20D4×Q8×C29C2211yescharacteristic
21C29×#498C2211yescharacteristic
22C29×#494C2211yescharacteristic
23C29×#489—21no—
24C29×#487C2211yescharacteristic
25C29×#486—21no—
26C29×#486C2211yescharacteristic
27C29×#486C2211yescharacteristic
28C29×#486C2211yescharacteristic
29C29×#482—21no—
30C29×#477—21no—
31C29×#475C2211yescharacteristic
32C29×#474—21no—
33C29×#474C2211yescharacteristic
34C29×#474C2211yescharacteristic
35C29×#467—21no—
36C29×#465—21no—
37C29×#463—21no—
38C29×#462C2211yescharacteristic
39C29×#462C2211yescharacteristic
40C29×#461C2211yescharacteristic
41C29×#460C2211yescharacteristic
42C29×#459—21no—
43C29×#459C2211yescharacteristic
44C29×#452—21no—
45C29×#451—21no—
46C29×#451—21no—
47C29×#446C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C29×#440—21no—
50C4×Q16×C29C2211yescharacteristic
51C4×D8×C29—21no—
52C4×D8×C29C2211yescharacteristic
53C8×D4×C29C2211yescharacteristic
54C8×D4×C29C2211yescharacteristic
55C29×#416—21no—
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#332C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C29×#322C2211yescharacteristic
67C2×#41×C29—21no—
68C22×Q8×C29—21no—
69C22×Q8×C29—21no—
70C2×Q16×C29—21no—
71C2×Q16×C29—21no—
72C2×Q16×C29—21no—
73C2×Q16×C29—21no—
74C2×Q16×C29—44no—
75C2×Q16×C29D411yescharacteristic
76C2×SD16×C29—21no—
77C2×SD16×C29—21no—
78C2×D8×C29—21no—
79C2×D8×C29D411yescharacteristic
80C22×C8×C29—21no—
81C22×C8×C29—21no—
82C29×C4⋊Q8—21no—
83C29×C4⋊Q8—21no—
84C29×C4⋊Q8C2311yescharacteristic
85C29×C4⋊Q8C2311yescharacteristic
86C29×C4⋊Q8C2311yescharacteristic
87C29×#127—21no—
88C29×#127C2311yescharacteristic
89C29×#126—41no—
90C29×#124—21no—
91C29×C22⋊Q8—21no—
92C29×C22⋊Q8—21no—
93C29×C22⋊Q8—21no—
94C29×C22⋊Q8—41no—
95C29×C22⋊Q8—41no—
96C29×#121—21no—
97C29×#121—41no—
98C4×Q8×C29—21no—
99C4×Q8×C29C2311yescharacteristic
100C4×Q8×C29C2311yescharacteristic
101C4×D4×C29—21no—
102C4×D4×C29—21no—
103C4×D4×C29—21no—
104C4×D4×C29C2311yescharacteristic
105C4×D4×C29C2311yescharacteristic
106C29×#117—21no—
107C29×#107—21no—
108C29×#107—21no—
109C29×#107D411yescharacteristic
110C29×#107D411yescharacteristic
111C29×#106—21no—
112C29×#106—41no—
113C29×C4⋊C8—21no—
114C29×C4⋊C8—21no—
115C29×C4⋊C8C2311yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×#103—21no—
120C29×#103—21no—
121C29×#103—21no—
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103D411yescharacteristic
126C29×#103D411yescharacteristic
127C29×#102—21no—
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×#102—41no—
136C29×#102D411yescharacteristic
137C29×#102D411yescharacteristic
138C29×C22⋊C8—21no—
139C29×C22⋊C8—21no—
140C29×#97—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C4×C8×C29C2311yescharacteristic
145#41×C29—42no—
146#41×C29—81no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29—41no—
151C2×Q8×C29—41no—
152C2×Q8×C29—42no—
153C2×Q8×C29—42no—
154C2×Q8×C29—81no—
155C2×Q8×C29—81no—
156C2×Q8×C29C2×D411yescharacteristic
157C2×Q8×C29C2×D411yescharacteristic
158C2×D4×C29—21no—
159C2×D4×C29—21no—
160C2×D4×C29—21no—
161C2×D4×C29—41no—
162C2×D4×C29—41no—
163C2×D4×C29C2×D411yescharacteristic
164C2×D4×C29C2×D411yescharacteristic
165C22×C4×C29—21no—
166C22×C4×C29—21no—
167C22×C4×C29—41no—
168C22×C4×C29—41no—
169C22×C4×C29—41no—
170Q16×C29—22no—
171Q16×C29—42no—
172Q16×C29—42no—
173Q16×C29—42no—
174Q16×C29—81no—
175SD16×C29—42no—
176SD16×C29—81no—
177D8×C29—22no—
178D8×C29—42no—
179C2×C8×C29—21no—
180C2×C8×C29—21no—
181C2×C8×C29—21no—
182C2×C8×C29—21no—
183C2×C8×C29—21no—
184C2×C8×C29—42no—
185C2×C8×C29—81no—
186C2×C8×C29C2×D411yescharacteristic
187C2×C8×C29C2×D411yescharacteristic
188C2×C8×C29C2×D411yescharacteristic
189C2×C8×C29C2×D411yescharacteristic
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—21no—
194C4⋊C4×C29—21no—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—21no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29—41no—
199C4⋊C4×C29—41no—
200C4⋊C4×C29—41no—
201C4⋊C4×C29C2×D411yescharacteristic
202C4⋊C4×C29C2×D411yescharacteristic
203C4⋊C4×C29C2×D411yescharacteristic
204C4⋊C4×C29C2×D411yescharacteristic
205C22⋊C4×C29—21no—
206C22⋊C4×C29—21no—
207C22⋊C4×C29—41no—
208C22⋊C4×C29—41no—
209C22⋊C4×C29—41no—
210C22⋊C4×C29—41no—
211C22⋊C4×C29—41no—
212C42×C29—21no—
213C42×C29—21no—
214C42×C29—41no—
215C42×C29C2411yescharacteristic
216#19835C2911yesmaximal, characteristic, direct product factor, Sylow
217C23×C29—21no—
218C23×C29—21no—
219C23×C29—41no—
220Q8×C29—21no—
221Q8×C29—21no—
222Q8×C29—21no—
223Q8×C29—41no—
224Q8×C29—41no—
225Q8×C29—41no—
226Q8×C29—41no—
227Q8×C29—41no—
228Q8×C29—41no—
229Q8×C29—82no—
230Q8×C29—82no—
231Q8×C29AGL(1,ℤ/8)12yes—
232D4×C29—21no—
233D4×C29—21no—
234D4×C29—21no—
235D4×C29—41no—
236D4×C29—41no—
237D4×C29—41no—
238D4×C29—41no—
239D4×C29—82no—
240D4×C29—81no—
241D4×C29—161no—
242D4×C29#13512yes—
243C2×C4×C29—21no—
244C2×C4×C29—21no—
245C2×C4×C29—21no—
246C2×C4×C29—21no—
247C2×C4×C29—21no—
248C2×C4×C29—21no—
249C2×C4×C29—41no—
250C2×C4×C29—41no—
251C2×C4×C29—41no—
252C2×C4×C29—41no—
253C2×C4×C29—41no—
254C2×C4×C29—41no—
255C2×C4×C29—41no—
256C2×C4×C29—82no—
257C2×C4×C29—82no—
258C2×C4×C29—82no—
259C2×C4×C29C22×D411yescharacteristic
260C2×C4×C29C22×D411yescharacteristic
261C2×C4×C29H(5,𝔽2)11yescharacteristic
262C8×C29—21no—
263C8×C29—21no—
264C8×C29—21no—
265C8×C29—21no—
266C8×C29—41no—
267C8×C29—41no—
268C8×C29—41no—
269C8×C29—41no—
270C8×C29—41no—
271#3367C2×C2911yescharacteristic, complemented
272#3358C2×C2911yescharacteristic
273#3304C2×C2911yescharacteristic, complemented
274D4×Q16C2×C2911yescharacteristic, complemented
275#1720C2×C2911yescharacteristic, complemented
276#1702C2×C2911yescharacteristic, complemented
277#1681C2×C2911yescharacteristic, complemented
278#1680C2×C2911yescharacteristic, complemented
279#1669C2×C2911yescharacteristic, complemented
280#1652C2×C2911yescharacteristic, complemented
281#1651C2×C2911yescharacteristic, complemented
282#1641C2×C2911yescharacteristic, complemented
283#1627C2×C2911yescharacteristic, complemented
284#1584C2×C2911yescharacteristic, complemented
285#1580C2×C2911yescharacteristic, complemented
286C22×C29—22no—
287C22×C29—41no—
288C22×C29—41no—
289C22×C29—41no—
290C22×C29—41no—
291C22×C29—41no—
292C22×C29—81no—
293C22×C29—81no—
294C22×C29—81no—
295C22×C29D4211yescharacteristic
296C4×C29—22no—
297C4×C29—21no—
298C4×C29—41no—
299C4×C29—41no—
300C4×C29—41no—
301C4×C29—41no—
302C4×C29—41no—
303C4×C29—81no—
304C4×C29—81no—
305C4×C29—81no—
306C4×C29C2×#13511yescharacteristic
307C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
308C4×C29#57611yescharacteristic
309C4×C29#57811yescharacteristic
310C22×Q16—21no—
311#556C22×C2911yescharacteristic
312#550C22×C2911yescharacteristic
313D4×Q8C22×C2911yescharacteristic
314D4×Q8C22×C2911yescharacteristic
315#498C22×C2911yescharacteristic
316#494C22×C2911yescharacteristic
317#489—21no—
318#487C22×C2911yescharacteristic
319#486—21no—
320#486C22×C2911yescharacteristic
321#486C22×C2911yescharacteristic
322#486C22×C2911yescharacteristic
323#482—21no—
324#477—21no—
325#475C22×C2911yescharacteristic
326#474—21no—
327#474C22×C2911yescharacteristic
328#474C22×C2911yescharacteristic
329#467—21no—
330#465—21no—
331#463—21no—
332#462C22×C2911yescharacteristic
333#462C22×C2911yescharacteristic
334#461C22×C2911yescharacteristic
335#460C22×C2911yescharacteristic
336#459—21no—
337#459C22×C2911yescharacteristic
338#452—21no—
339#451—21no—
340#451—21no—
341#446C22×C2911yescharacteristic
342C8×Q8C22×C2911yescharacteristic
343#440—21no—
344C4×Q16C22×C2911yescharacteristic
345C4×D8—21no—
346C4×D8C22×C2911yescharacteristic
347C8×D4C22×C2911yescharacteristic
348C8×D4C22×C2911yescharacteristic
349#416—21no—
350#335C22×C2911yescharacteristic
351#334C22×C2911yescharacteristic
352#332C22×C2911yescharacteristic
353#332C22×C2911yescharacteristic
354#332C22×C2911yescharacteristic
355#331C22×C2911yescharacteristic
356Q8⋊C8C22×C2911yescharacteristic
357Q8⋊C8C22×C2911yescharacteristic
358D4⋊C8C22×C2911yescharacteristic
359D4⋊C8C22×C2911yescharacteristic
360#322C22×C2911yescharacteristic
361C2×C29—42no—
362C2×C29—81no—
363C2×C29—161no—
364C2×C29#326411yescharacteristic
365C2×C29#328511yescharacteristic
366C2×C29#328911yescharacteristic
367C2×#41—21no—
368C22×Q8—21no—
369C22×Q8—21no—
370C2×Q16—21no—
371C2×Q16—21no—
372C2×Q16—21no—
373C2×Q16—21no—
374C2×Q16—44no—
375C2×Q16D4×C2911yescharacteristic
376C2×SD16—21no—
377C2×SD16—21no—
378C2×D8—21no—
379C2×D8D4×C2911yescharacteristic
380C22×C8—21no—
381C22×C8—21no—
382C4⋊Q8—21no—
383C4⋊Q8—21no—
384C4⋊Q8C23×C2911yescharacteristic
385C4⋊Q8C23×C2911yescharacteristic
386C4⋊Q8C23×C2911yescharacteristic
387#127—21no—
388#127C23×C2911yescharacteristic
389#126—41no—
390#124—21no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8—41no—
395C22⋊Q8—41no—
396#121—21no—
397#121—41no—
398C4×Q8—21no—
399C4×Q8C23×C2911yescharacteristic
400C4×Q8C23×C2911yescharacteristic
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4C23×C2911yescharacteristic
405C4×D4C23×C2911yescharacteristic
406#117—21no—
407#107—21no—
408#107—21no—
409#107D4×C2911yescharacteristic
410#107D4×C2911yescharacteristic
411#106—21no—
412#106—41no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8C23×C2911yescharacteristic
416C4⋊C8C23×C2911yescharacteristic
417C4⋊C8C23×C2911yescharacteristic
418C4⋊C8C23×C2911yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103D4×C2911yescharacteristic
426#103D4×C2911yescharacteristic
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—41no—
436#102D4×C2911yescharacteristic
437#102D4×C2911yescharacteristic
438C22⋊C8—21no—
439C22⋊C8—21no—
440#97—21no—
441C4×C8—21no—
442C4×C8C23×C2911yescharacteristic
443C4×C8C23×C2911yescharacteristic
444C4×C8C23×C2911yescharacteristic
445C29#1983511yescharacteristic, direct product factor, Sylow
446#41—42no—
447#41—81no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—41no—
452C2×Q8—41no—
453C2×Q8—42no—
454C2×Q8—42no—
455C2×Q8—81no—
456C2×Q8—81no—
457C2×Q8C2×D4×C2911yescharacteristic
458C2×Q8C2×D4×C2911yescharacteristic
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4C2×D4×C2911yescharacteristic
465C2×D4C2×D4×C2911yescharacteristic
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471Q16—22no—
472Q16—42no—
473Q16—42no—
474Q16—42no—
475Q16—81no—
476SD16—42no—
477SD16—81no—
478D8—22no—
479D8—42no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—42no—
486C2×C8—81no—
487C2×C8C2×D4×C2911yescharacteristic
488C2×C8C2×D4×C2911yescharacteristic
489C2×C8C2×D4×C2911yescharacteristic
490C2×C8C2×D4×C2911yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4C2×D4×C2911yescharacteristic
503C4⋊C4C2×D4×C2911yescharacteristic
504C4⋊C4C2×D4×C2911yescharacteristic
505C4⋊C4C2×D4×C2911yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C42—21no—
514C42—21no—
515C42—41no—
516C42C24×C2911yescharacteristic
517C23—21no—
518C23—21no—
519C23—41no—
520Q8—21no—
521Q8—21no—
522Q8—21no—
523Q8—41no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—82no—
530Q8—82no—
531Q8C29×AGL(1,ℤ/8)12yes—
532D4—21no—
533D4—21no—
534D4—21no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—82no—
540D4—81no—
541D4—161no—
542D4C29×#13512yes—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—82no—
557C2×C4—82no—
558C2×C4—82no—
559C2×C4C22×D4×C2911yescharacteristic
560C2×C4C22×D4×C2911yescharacteristic
561C2×C4C29×H(5,𝔽2)11yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—41no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22D42×C2911yescharacteristic
581C4—22no—
582C4—21no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4C2×C29×#13511yescharacteristic
592C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
593C4C29×#57611yescharacteristic
594C4C29×#57811yescharacteristic
595C2—42no—
596C2—81no—
597C2—161no—
598C2C29×#326411yescharacteristic
599C2C29×#328511yescharacteristic
600C2C29×#328911yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3358C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3367C2semidirect
3. C29×#3304C2semidirect
4. D4×Q16×C29C2semidirect
5. C29×#1720C2semidirect
6. C29×#1702C2semidirect
7. C29×#1681C2semidirect
8. C29×#1680C2semidirect
9. C29×#1669C2semidirect
10. C29×#1652C2semidirect
11. C29×#1651C2semidirect
12. C29×#1641C2semidirect
13. C29×#1627C2semidirect
14. C29×#1584C2semidirect
15. C29×#1580C2semidirect
216. #19835C29direct (N × H)
271. #3367C2×C29semidirect
273. #3304C2×C29semidirect
274. D4×Q16C2×C29semidirect
275. #1720C2×C29semidirect
276. #1702C2×C29semidirect
277. #1681C2×C29semidirect
278. #1680C2×C29semidirect
279. #1669C2×C29semidirect
280. #1652C2×C29semidirect
281. #1651C2×C29semidirect
282. #1641C2×C29semidirect
283. #1627C2×C29semidirect
284. #1584C2×C29semidirect
285. #1580C2×C29semidirect
445. C29#19835direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33672
C29×#33582
C29×#33042
D4×Q16×C292
C29×#17202
C29×#17022
C29×#16812
C29×#16802
C29×#16692
C29×#16522
C29×#16512
C29×#16412
C29×#16272
C29×#15842
C29×#15802
#1983529