Finite Group Databasebeta

← C29×#19843 #20314743

Subgroups — C29×#19843 #20314743

Order 7424.

644 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3368C211yesmaximal, characteristic, complemented
2C29×#3363C211yesmaximal, characteristic, complemented
3C29×#3362C211yesmaximal, characteristic, complemented
4C29×#3287C211yesmaximal, characteristic
5C29×#1717C211yesmaximal, characteristic, complemented
6C29×#1698C211yesmaximal, characteristic, complemented
7C29×#1683C211yesmaximal, characteristic, complemented
8C29×#1682C211yesmaximal, characteristic, complemented
9C29×#1668C211yesmaximal, characteristic, complemented
10C29×#1641C211yesmaximal, characteristic, complemented
11C29×#1631C211yesmaximal, characteristic, complemented
12C29×#1626C211yesmaximal, characteristic, complemented
13C29×#1623C211yesmaximal, characteristic, complemented
14C29×#1584C211yesmaximal, characteristic, complemented
15C29×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×C29×#135—21no—
17Q82×C29C2211yescharacteristic
18C29×#557C2211yescharacteristic
19C29×#550C2211yescharacteristic
20C29×#550C2211yescharacteristic
21C29×#493C2211yescharacteristic
22C29×#492C2211yescharacteristic
23C29×#490—21no—
24C29×#487—21no—
25C29×#487C2211yescharacteristic
26C29×#486—21no—
27C29×#486C2211yescharacteristic
28C29×#486C2211yescharacteristic
29C29×#486C2211yescharacteristic
30C29×#478—21no—
31C29×#477—21no—
32C29×#477C2211yescharacteristic
33C29×#476—21no—
34C29×#476C2211yescharacteristic
35C29×#474C2211yescharacteristic
36C29×#466—21no—
37C29×#462—21no—
38C29×#462C2211yescharacteristic
39C29×#460—21no—
40C29×#460—21no—
41C29×#460C2211yescharacteristic
42C29×#460C2211yescharacteristic
43C29×#460C2211yescharacteristic
44C29×#460C2211yescharacteristic
45C29×#449—21no—
46C29×#449—21no—
47C29×#446C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C8×Q8×C29C2211yescharacteristic
50C29×#440—21no—
51C4×Q16×C29—21no—
52C4×Q16×C29C2211yescharacteristic
53C4×SD16×C29—21no—
54C4×SD16×C29C2211yescharacteristic
55C8×D4×C29C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#335C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#331C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×Q8⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C29×#322C2211yescharacteristic
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C29×#135—44no—
70C2×Q16×C29—21no—
71C2×Q16×C29D411yescharacteristic
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×SD16×C29—21no—
75C2×SD16×C29—21no—
76C2×SD16×C29—41no—
77C2×SD16×C29D411yescharacteristic
78C2×D8×C29—21no—
79C2×D8×C29—21no—
80C22×C8×C29—21no—
81C29×C4⋊Q8—21no—
82C29×C4⋊Q8—21no—
83C29×C4⋊Q8—21no—
84C29×C4⋊Q8—41no—
85C29×C4⋊Q8C2311yescharacteristic
86C29×C4⋊Q8C2311yescharacteristic
87C29×#127—21no—
88C29×#127—21no—
89C29×#127C2311yescharacteristic
90C29×#127C2311yescharacteristic
91C29×#125—21no—
92C29×#125—41no—
93C29×#121—21no—
94C29×#121—21no—
95C29×#121—41no—
96C29×#121—41no—
97C4×Q8×C29—21no—
98C4×Q8×C29—21no—
99C4×Q8×C29—21no—
100C4×Q8×C29—21no—
101C4×Q8×C29C2311yescharacteristic
102C4×Q8×C29C2311yescharacteristic
103C4×Q8×C29C2311yescharacteristic
104C4×D4×C29—21no—
105C4×D4×C29—21no—
106C4×D4×C29C2311yescharacteristic
107C29×#107—21no—
108C29×#107—21no—
109C29×#107D411yescharacteristic
110C29×#106—21no—
111C29×#106D411yescharacteristic
112C29×C4⋊C8—21no—
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×#103D411yescharacteristic
124C29×#103D411yescharacteristic
125C29×#103D411yescharacteristic
126C29×#102—21no—
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—21no—
136C29×#102—41no—
137C29×#102D411yescharacteristic
138C29×C22⋊C8—21no—
139C29×#97—21no—
140C4×C8×C29—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C4×C8×C29C2311yescharacteristic
145#41×C29—42no—
146#41×C29—42no—
147#41×C29—81no—
148#41×C29—81no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×Q8×C29—41no—
152C2×Q8×C29C2×D411yescharacteristic
153C2×Q8×C29C2×D411yescharacteristic
154C2×Q8×C29C2×D411yescharacteristic
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29—21no—
158C2×D4×C29—21no—
159C2×D4×C29—21no—
160C2×D4×C29—21no—
161C2×D4×C29—41no—
162C2×D4×C29—41no—
163C2×D4×C29—41no—
164C2×D4×C29—41no—
165C2×D4×C29C2×D411yescharacteristic
166C22×C4×C29—21no—
167C22×C4×C29—41no—
168C22×C4×C29—41no—
169Q16×C29—22no—
170Q16×C29—42no—
171SD16×C29—22no—
172SD16×C29—42no—
173SD16×C29—42no—
174SD16×C29—42no—
175SD16×C29—42no—
176SD16×C29—82no—
177D8×C29—42no—
178D8×C29—81no—
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×C29C2×D411yescharacteristic
186C2×C8×C29C2×D411yescharacteristic
187C2×C8×C29C2×D411yescharacteristic
188C2×C8×C29C2×D411yescharacteristic
189C4⋊C4×C29—21no—
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—41no—
197C4⋊C4×C29—41no—
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—41no—
207C22⋊C4×C29—41no—
208C42×C29—21no—
209C42×C29—21no—
210C42×C29—21no—
211C42×C29—41no—
212C42×C29—41no—
213C42×C29C2411yescharacteristic
214#19843C2911yesmaximal, characteristic, direct product factor, Sylow
215C23×C29—21no—
216C23×C29—41no—
217C23×C29—41no—
218Q8×C29—21no—
219Q8×C29—21no—
220Q8×C29—21no—
221Q8×C29—21no—
222Q8×C29—41no—
223Q8×C29—41no—
224Q8×C29—81no—
225Q8×C29—161no—
226Q8×C29#13512yescomplemented
227Q8×C29AGL(1,ℤ/8)12yes—
228D4×C29—21no—
229D4×C29—21no—
230D4×C29—41no—
231D4×C29—41no—
232D4×C29—41no—
233D4×C29—41no—
234D4×C29—41no—
235D4×C29—41no—
236D4×C29—41no—
237D4×C29—41no—
238D4×C29—82no—
239D4×C29—81no—
240D4×C29—81no—
241D4×C29—82no—
242D4×C29—161no—
243D4×C29—161no—
244C2×C4×C29—21no—
245C2×C4×C29—21no—
246C2×C4×C29—21no—
247C2×C4×C29—21no—
248C2×C4×C29—21no—
249C2×C4×C29—21no—
250C2×C4×C29—21no—
251C2×C4×C29—41no—
252C2×C4×C29—41no—
253C2×C4×C29—41no—
254C2×C4×C29—41no—
255C2×C4×C29—82no—
256C2×C4×C29—82no—
257C2×C4×C29C22×D411yescharacteristic
258C2×C4×C29C22×D411yescharacteristic
259C2×C4×C29H(5,𝔽2)11yescharacteristic
260C8×C29—21no—
261C8×C29—21no—
262C8×C29—21no—
263C8×C29—21no—
264C8×C29—41no—
265C8×C29—41no—
266C8×C29—41no—
267C8×C29—41no—
268C8×C29—41no—
269#3368C2×C2911yescharacteristic, complemented
270#3363C2×C2911yescharacteristic, complemented
271#3362C2×C2911yescharacteristic, complemented
272#3287C2×C2911yescharacteristic
273#1717C2×C2911yescharacteristic, complemented
274#1698C2×C2911yescharacteristic, complemented
275#1683C2×C2911yescharacteristic, complemented
276#1682C2×C2911yescharacteristic, complemented
277#1668C2×C2911yescharacteristic, complemented
278#1641C2×C2911yescharacteristic, complemented
279#1631C2×C2911yescharacteristic, complemented
280#1626C2×C2911yescharacteristic, complemented
281#1623C2×C2911yescharacteristic, complemented
282#1584C2×C2911yescharacteristic, complemented
283SD16⋊C8C2×C2911yescharacteristic, complemented
284C22×C29—41no—
285C22×C29—41no—
286C22×C29—41no—
287C22×C29—81no—
288C22×C29—81no—
289C22×C29—81no—
290C22×C29—81no—
291C22×C29—81no—
292C22×C29—81no—
293C22×C29D4211yescharacteristic
294C4×C29—22no—
295C4×C29—22no—
296C4×C29—21no—
297C4×C29—41no—
298C4×C29—41no—
299C4×C29—41no—
300C4×C29—41no—
301C4×C29—41no—
302C4×C29—81no—
303C4×C29—81no—
304C4×C29C2×#13511yescharacteristic
305C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
306C4×C29#57711yescharacteristic
307C4×C29#57811yescharacteristic
308C2×#135—21no—
309Q82C22×C2911yescharacteristic
310#557C22×C2911yescharacteristic
311#550C22×C2911yescharacteristic
312#550C22×C2911yescharacteristic
313#493C22×C2911yescharacteristic
314#492C22×C2911yescharacteristic
315#490—21no—
316#487—21no—
317#487C22×C2911yescharacteristic
318#486—21no—
319#486C22×C2911yescharacteristic
320#486C22×C2911yescharacteristic
321#486C22×C2911yescharacteristic
322#478—21no—
323#477—21no—
324#477C22×C2911yescharacteristic
325#476—21no—
326#476C22×C2911yescharacteristic
327#474C22×C2911yescharacteristic
328#466—21no—
329#462—21no—
330#462C22×C2911yescharacteristic
331#460—21no—
332#460—21no—
333#460C22×C2911yescharacteristic
334#460C22×C2911yescharacteristic
335#460C22×C2911yescharacteristic
336#460C22×C2911yescharacteristic
337#449—21no—
338#449—21no—
339#446C22×C2911yescharacteristic
340C8×Q8C22×C2911yescharacteristic
341C8×Q8C22×C2911yescharacteristic
342#440—21no—
343C4×Q16—21no—
344C4×Q16C22×C2911yescharacteristic
345C4×SD16—21no—
346C4×SD16C22×C2911yescharacteristic
347C8×D4C22×C2911yescharacteristic
348#335C22×C2911yescharacteristic
349#335C22×C2911yescharacteristic
350#333C22×C2911yescharacteristic
351#332C22×C2911yescharacteristic
352#331C22×C2911yescharacteristic
353#331C22×C2911yescharacteristic
354Q8⋊C8C22×C2911yescharacteristic
355Q8⋊C8C22×C2911yescharacteristic
356Q8⋊C8C22×C2911yescharacteristic
357D4⋊C8C22×C2911yescharacteristic
358#322C22×C2911yescharacteristic
359C2×C29—81no—
360C2×C29—161no—
361C2×C29—161no—
362C2×C29#326511yescharacteristic
363C2×C29#328511yescharacteristic
364C2×C29#328811yescharacteristic
365C2×#41—21no—
366C2×#41—21no—
367#135—44no—
368C2×Q16—21no—
369C2×Q16D4×C2911yescharacteristic
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16—41no—
375C2×SD16D4×C2911yescharacteristic
376C2×D8—21no—
377C2×D8—21no—
378C22×C8—21no—
379C4⋊Q8—21no—
380C4⋊Q8—21no—
381C4⋊Q8—21no—
382C4⋊Q8—41no—
383C4⋊Q8C23×C2911yescharacteristic
384C4⋊Q8C23×C2911yescharacteristic
385#127—21no—
386#127—21no—
387#127C23×C2911yescharacteristic
388#127C23×C2911yescharacteristic
389#125—21no—
390#125—41no—
391#121—21no—
392#121—21no—
393#121—41no—
394#121—41no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8C23×C2911yescharacteristic
400C4×Q8C23×C2911yescharacteristic
401C4×Q8C23×C2911yescharacteristic
402C4×D4—21no—
403C4×D4—21no—
404C4×D4C23×C2911yescharacteristic
405#107—21no—
406#107—21no—
407#107D4×C2911yescharacteristic
408#106—21no—
409#106D4×C2911yescharacteristic
410C4⋊C8—21no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8C23×C2911yescharacteristic
414C4⋊C8C23×C2911yescharacteristic
415C4⋊C8C23×C2911yescharacteristic
416C4⋊C8C23×C2911yescharacteristic
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103D4×C2911yescharacteristic
422#103D4×C2911yescharacteristic
423#103D4×C2911yescharacteristic
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—41no—
435#102D4×C2911yescharacteristic
436C22⋊C8—21no—
437#97—21no—
438C4×C8—21no—
439C4×C8—21no—
440C4×C8C23×C2911yescharacteristic
441C4×C8C23×C2911yescharacteristic
442C4×C8C23×C2911yescharacteristic
443C29#1984311yescharacteristic, direct product factor, Sylow
444#41—42no—
445#41—42no—
446#41—81no—
447#41—81no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—41no—
451C2×Q8C2×D4×C2911yescharacteristic
452C2×Q8C2×D4×C2911yescharacteristic
453C2×Q8C2×D4×C2911yescharacteristic
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4C2×D4×C2911yescharacteristic
465C22×C4—21no—
466C22×C4—41no—
467C22×C4—41no—
468Q16—22no—
469Q16—42no—
470SD16—22no—
471SD16—42no—
472SD16—42no—
473SD16—42no—
474SD16—42no—
475SD16—82no—
476D8—42no—
477D8—81no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—42no—
484C2×C8C2×D4×C2911yescharacteristic
485C2×C8C2×D4×C2911yescharacteristic
486C2×C8C2×D4×C2911yescharacteristic
487C2×C8C2×D4×C2911yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4C2×D4×C2911yescharacteristic
501C4⋊C4C2×D4×C2911yescharacteristic
502C4⋊C4C2×D4×C2911yescharacteristic
503C4⋊C4C2×D4×C2911yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—41no—
511C42—41no—
512C42C24×C2911yescharacteristic
513C23—21no—
514C23—41no—
515C23—41no—
516Q8—21no—
517Q8—21no—
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—81no—
523Q8—161no—
524Q8C29×#13512yescomplemented
525Q8C29×AGL(1,ℤ/8)12yes—
526D4—21no—
527D4—21no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—82no—
537D4—81no—
538D4—81no—
539D4—82no—
540D4—161no—
541D4—161no—
542C2×C4—21no—
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—82no—
554C2×C4—82no—
555C2×C4C22×D4×C2911yescharacteristic
556C2×C4C22×D4×C2911yescharacteristic
557C2×C4C29×H(5,𝔽2)11yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22D42×C2911yescharacteristic
577C4—22no—
578C4—22no—
579C4—21no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—81no—
587C4C2×C29×#13511yescharacteristic
588C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
589C4C29×#57711yescharacteristic
590C4C29×#57811yescharacteristic
591C2—81no—
592C2—161no—
593C2—161no—
594C2C29×#326511yescharacteristic
595C2C29×#328511yescharacteristic
596C2C29×#328811yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3287C2
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×#3368C2semidirect
2. C29×#3363C2semidirect
3. C29×#3362C2semidirect
5. C29×#1717C2semidirect
6. C29×#1698C2semidirect
7. C29×#1683C2semidirect
8. C29×#1682C2semidirect
9. C29×#1668C2semidirect
10. C29×#1641C2semidirect
11. C29×#1631C2semidirect
12. C29×#1626C2semidirect
13. C29×#1623C2semidirect
14. C29×#1584C2semidirect
15. C29×SD16⋊C8C2semidirect
214. #19843C29direct (N × H)
226. Q8×C29#135semidirect
269. #3368C2×C29semidirect
270. #3363C2×C29semidirect
271. #3362C2×C29semidirect
273. #1717C2×C29semidirect
274. #1698C2×C29semidirect
275. #1683C2×C29semidirect
276. #1682C2×C29semidirect
277. #1668C2×C29semidirect
278. #1641C2×C29semidirect
279. #1631C2×C29semidirect
280. #1626C2×C29semidirect
281. #1623C2×C29semidirect
282. #1584C2×C29semidirect
283. SD16⋊C8C2×C29semidirect
443. C29#19843direct (N × H)
524. Q8C29×#135semidirect

Maximal subgroups

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

subgroupindex
C29×#33682
C29×#33632
C29×#33622
C29×#32872
C29×#17172
C29×#16982
C29×#16832
C29×#16822
C29×#16682
C29×#16412
C29×#16312
C29×#16262
C29×#16232
C29×#15842
C29×SD16⋊C82
#1984329