Finite Group Databasebeta

← C29×#19946 #20314846

Subgroups — C29×#19946 #20314846

Order 7424.

622 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×#3397C211yesmaximal, characteristic, complemented
2C29×#3354C211yesmaximal, characteristic, complemented
3C29×#3305C211yesmaximal, characteristic, complemented
4C29×#3302C211yesmaximal, characteristic, complemented
5C29×#1708C211yesmaximal, characteristic, complemented
6C29×#1692C211yesmaximal, characteristic, complemented
7C29×#1685C211yesmaximal, characteristic, complemented
8C29×#1679C211yesmaximal, characteristic, complemented
9C29×#1677C211yesmaximal, characteristic, complemented
10C29×#1646C211yesmaximal, characteristic, complemented
11C29×#1641C211yesmaximal, characteristic, complemented
12C29×#1638C211yesmaximal, characteristic, complemented
13C29×#1625C211yesmaximal, characteristic, complemented
14C29×#1590C211yesmaximal, characteristic, complemented
15C8×D8×C29C211yesmaximal, characteristic, complemented
16C29×#556C2211yescharacteristic
17C29×#555C2211yescharacteristic
18C29×#550C2211yescharacteristic
19C29×#547C2211yescharacteristic
20C29×#498C2211yescharacteristic
21C29×#496—21no—
22C29×#492C2211yescharacteristic
23C29×#487C2211yescharacteristic
24C29×#487C2211yescharacteristic
25C29×#486C2211yescharacteristic
26C29×#486C2211yescharacteristic
27C29×#485—21no—
28C29×#482—21no—
29C29×#482—21no—
30C29×#481—21no—
31C29×#477C2211yescharacteristic
32C29×#476C2211yescharacteristic
33C29×#474C2211yescharacteristic
34C29×#474C2211yescharacteristic
35C29×#469—21no—
36C29×#467—21no—
37C29×#466—21no—
38C29×#463—21no—
39C29×#462C2211yescharacteristic
40C29×#461C2211yescharacteristic
41C29×#460—21no—
42C29×#459C2211yescharacteristic
43C29×#459C2211yescharacteristic
44C29×#452—21no—
45C29×#449—21no—
46C29×#446C2211yescharacteristic
47C29×#440—21no—
48C4×SD16×C29C2211yescharacteristic
49C4×D8×C29C2211yescharacteristic
50C29×#436C2211yescharacteristic
51C8×D4×C29C2211yescharacteristic
52C8×D4×C29C2211yescharacteristic
53C29×#428—21no—
54C29×#416—21no—
55C29×#416—21no—
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×D4⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C82×C29C2211yescharacteristic
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C2×Q16×C29—21no—
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29D411yescharacteristic
74C2×D8×C29—21no—
75C2×D8×C29—21no—
76C2×D8×C29D411yescharacteristic
77C2×M16×C29—21no—
78C22×C8×C29—21no—
79C22×C8×C29—21no—
80C29×C4⋊Q8C2311yescharacteristic
81C29×C4⋊Q8C2311yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×#127—21no—
84C29×#127C2311yescharacteristic
85C29×#126—41no—
86C29×#124—21no—
87C29×#124—41no—
88C29×#123—41no—
89C29×C22⋊Q8—21no—
90C29×C22⋊Q8—21no—
91C29×#121—21no—
92C29×#121—21no—
93C29×#121—21no—
94C29×#121—21no—
95C29×#121—41no—
96C4×Q8×C29—21no—
97C4×Q8×C29C2311yescharacteristic
98C4×D4×C29—21no—
99C4×D4×C29C2311yescharacteristic
100C4×D4×C29C2311yescharacteristic
101C4×D4×C29C2311yescharacteristic
102C29×#117—21no—
103C29×#117—21no—
104C29×#117—21no—
105C2×C4⋊C4×C29—21no—
106C29×#107—21no—
107C29×#107—21no—
108C29×#107—21no—
109C29×#107D411yescharacteristic
110C29×#106—21no—
111C29×#106—21no—
112C29×#106—21no—
113C29×#106D411yescharacteristic
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—41no—
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—41no—
134C29×#102D411yescharacteristic
135C29×#102D411yescharacteristic
136C29×#102D411yescharacteristic
137C29×C22⋊C8—21no—
138C29×C22⋊C8—21no—
139C29×C22⋊C8—21no—
140C29×#97—21no—
141C4×C8×C29C2311yescharacteristic
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144#41×C29—42no—
145#41×C29—42no—
146#41×C29—81no—
147#41×C29—81no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×Q8×C29C2×D411yescharacteristic
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—41no—
156C2×D4×C29—41no—
157C2×D4×C29—41no—
158C2×D4×C29—41no—
159C2×D4×C29C2×D411yescharacteristic
160C2×D4×C29C2×D411yescharacteristic
161C2×D4×C29C2×D411yescharacteristic
162C22×C4×C29—21no—
163C22×C4×C29—21no—
164C22×C4×C29—21no—
165C22×C4×C29—41no—
166C22×C4×C29—41no—
167Q16×C29—81no—
168SD16×C29—41no—
169SD16×C29—42no—
170SD16×C29—81no—
171SD16×C29—81no—
172D8×C29—22no—
173D8×C29—81no—
174D8×C29—81no—
175M16×C29—42no—
176C2×C8×C29—21no—
177C2×C8×C29—21no—
178C2×C8×C29—21no—
179C2×C8×C29—21no—
180C2×C8×C29—21no—
181C2×C8×C29—81no—
182C2×C8×C29—81no—
183C2×C8×C29C2×D411yescharacteristic
184C2×C8×C29C2×D411yescharacteristic
185C2×C8×C29C2×D411yescharacteristic
186C2×C8×C29C2×D411yescharacteristic
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—21no—
194C4⋊C4×C29—41no—
195C4⋊C4×C29—41no—
196C4⋊C4×C29C2×D411yescharacteristic
197C4⋊C4×C29C2×D411yescharacteristic
198C4⋊C4×C29C2×D411yescharacteristic
199C4⋊C4×C29C2×D411yescharacteristic
200C22⋊C4×C29—21no—
201C22⋊C4×C29—21no—
202C22⋊C4×C29—21no—
203C22⋊C4×C29—41no—
204C22⋊C4×C29—41no—
205C22⋊C4×C29—41no—
206C22⋊C4×C29—41no—
207C22⋊C4×C29—41no—
208C22⋊C4×C29—41no—
209C42×C29—21no—
210C42×C29—41no—
211C42×C29—41no—
212C42×C29C2411yescharacteristic
213#19946C2911yesmaximal, characteristic, direct product factor, Sylow
214C23×C29—21no—
215C23×C29—21no—
216C23×C29—21no—
217C23×C29—41no—
218Q8×C29—21no—
219Q8×C29—21no—
220Q8×C29—41no—
221Q8×C29—41no—
222Q8×C29—41no—
223Q8×C29—41no—
224Q8×C29—81no—
225D4×C29—21no—
226D4×C29—21no—
227D4×C29—21no—
228D4×C29—21no—
229D4×C29—21no—
230D4×C29—21no—
231D4×C29—41no—
232D4×C29—41no—
233D4×C29—41no—
234D4×C29—41no—
235D4×C29—81no—
236D4×C29—82no—
237D4×C29—82no—
238D4×C29—161no—
239D4×C29—161no—
240C2×C4×C29—21no—
241C2×C4×C29—21no—
242C2×C4×C29—21no—
243C2×C4×C29—21no—
244C2×C4×C29—21no—
245C2×C4×C29—41no—
246C2×C4×C29—41no—
247C2×C4×C29—41no—
248C2×C4×C29—41no—
249C2×C4×C29—41no—
250C2×C4×C29—41no—
251C2×C4×C29—41no—
252C2×C4×C29—41no—
253C2×C4×C29—41no—
254C2×C4×C29—82no—
255C2×C4×C29—82no—
256C2×C4×C29C22×D411yescharacteristic
257C2×C4×C29C22×D411yescharacteristic
258C2×C4×C29H(5,𝔽2)11yescharacteristic
259C8×C29—21no—
260C8×C29—21no—
261C8×C29—21no—
262C8×C29—41no—
263C8×C29—41no—
264C8×C29—41no—
265C8×C29—41no—
266C8×C29—41no—
267C8×C29#13512yes—
268#3397C2×C2911yescharacteristic, complemented
269#3354C2×C2911yescharacteristic, complemented
270#3305C2×C2911yescharacteristic, complemented
271#3302C2×C2911yescharacteristic, complemented
272#1708C2×C2911yescharacteristic, complemented
273#1692C2×C2911yescharacteristic, complemented
274#1685C2×C2911yescharacteristic, complemented
275#1679C2×C2911yescharacteristic, complemented
276#1677C2×C2911yescharacteristic, complemented
277#1646C2×C2911yescharacteristic, complemented
278#1641C2×C2911yescharacteristic, complemented
279#1638C2×C2911yescharacteristic, complemented
280#1625C2×C2911yescharacteristic, complemented
281#1590C2×C2911yescharacteristic, complemented
282C8×D8C2×C2911yescharacteristic, complemented
283C22×C29—41no—
284C22×C29—41no—
285C22×C29—41no—
286C22×C29—41no—
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—21no—
297C4×C29—41no—
298C4×C29—41no—
299C4×C29—41no—
300C4×C29—41no—
301C4×C29—41no—
302C4×C29—81no—
303C4×C29—81no—
304C4×C29—81no—
305C4×C29C2×#13511yescharacteristic
306C4×C29#57511yescharacteristic
307C4×C29#57611yescharacteristic
308C4×C29#57711yescharacteristic
309#556C22×C2911yescharacteristic
310#555C22×C2911yescharacteristic
311#550C22×C2911yescharacteristic
312#547C22×C2911yescharacteristic
313#498C22×C2911yescharacteristic
314#496—21no—
315#492C22×C2911yescharacteristic
316#487C22×C2911yescharacteristic
317#487C22×C2911yescharacteristic
318#486C22×C2911yescharacteristic
319#486C22×C2911yescharacteristic
320#485—21no—
321#482—21no—
322#482—21no—
323#481—21no—
324#477C22×C2911yescharacteristic
325#476C22×C2911yescharacteristic
326#474C22×C2911yescharacteristic
327#474C22×C2911yescharacteristic
328#469—21no—
329#467—21no—
330#466—21no—
331#463—21no—
332#462C22×C2911yescharacteristic
333#461C22×C2911yescharacteristic
334#460—21no—
335#459C22×C2911yescharacteristic
336#459C22×C2911yescharacteristic
337#452—21no—
338#449—21no—
339#446C22×C2911yescharacteristic
340#440—21no—
341C4×SD16C22×C2911yescharacteristic
342C4×D8C22×C2911yescharacteristic
343#436C22×C2911yescharacteristic
344C8×D4C22×C2911yescharacteristic
345C8×D4C22×C2911yescharacteristic
346#428—21no—
347#416—21no—
348#416—21no—
349#335C22×C2911yescharacteristic
350#334C22×C2911yescharacteristic
351#333C22×C2911yescharacteristic
352#332C22×C2911yescharacteristic
353#332C22×C2911yescharacteristic
354#331C22×C2911yescharacteristic
355Q8⋊C8C22×C2911yescharacteristic
356D4⋊C8C22×C2911yescharacteristic
357D4⋊C8C22×C2911yescharacteristic
358D4⋊C8C22×C2911yescharacteristic
359C82C22×C2911yescharacteristic
360C2×C29—81no—
361C2×C29—81no—
362C2×C29—81no—
363C2×C29—161no—
364C2×C29#327311yescharacteristic
365C2×C29#328411yescharacteristic
366C2×C29#329011yescharacteristic
367C2×#41—21no—
368C2×#41—21no—
369C2×Q16—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16D4×C2911yescharacteristic
374C2×D8—21no—
375C2×D8—21no—
376C2×D8D4×C2911yescharacteristic
377C2×M16—21no—
378C22×C8—21no—
379C22×C8—21no—
380C4⋊Q8C23×C2911yescharacteristic
381C4⋊Q8C23×C2911yescharacteristic
382C4⋊Q8C23×C2911yescharacteristic
383#127—21no—
384#127C23×C2911yescharacteristic
385#126—41no—
386#124—21no—
387#124—41no—
388#123—41no—
389C22⋊Q8—21no—
390C22⋊Q8—21no—
391#121—21no—
392#121—21no—
393#121—21no—
394#121—21no—
395#121—41no—
396C4×Q8—21no—
397C4×Q8C23×C2911yescharacteristic
398C4×D4—21no—
399C4×D4C23×C2911yescharacteristic
400C4×D4C23×C2911yescharacteristic
401C4×D4C23×C2911yescharacteristic
402#117—21no—
403#117—21no—
404#117—21no—
405C2×C4⋊C4—21no—
406#107—21no—
407#107—21no—
408#107—21no—
409#107D4×C2911yescharacteristic
410#106—21no—
411#106—21no—
412#106—21no—
413#106D4×C2911yescharacteristic
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—41no—
425#103D4×C2911yescharacteristic
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—41no—
434#102D4×C2911yescharacteristic
435#102D4×C2911yescharacteristic
436#102D4×C2911yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—21no—
440#97—21no—
441C4×C8C23×C2911yescharacteristic
442C4×C8C23×C2911yescharacteristic
443C4×C8C23×C2911yescharacteristic
444C29#1994611yescharacteristic, direct product factor, Sylow
445#41—42no—
446#41—42no—
447#41—81no—
448#41—81no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8C2×D4×C2911yescharacteristic
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4C2×D4×C2911yescharacteristic
461C2×D4C2×D4×C2911yescharacteristic
462C2×D4C2×D4×C2911yescharacteristic
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—41no—
467C22×C4—41no—
468Q16—81no—
469SD16—41no—
470SD16—42no—
471SD16—81no—
472SD16—81no—
473D8—22no—
474D8—81no—
475D8—81no—
476M16—42no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—81no—
483C2×C8—81no—
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⋊C4C2×D4×C2911yescharacteristic
498C4⋊C4C2×D4×C2911yescharacteristic
499C4⋊C4C2×D4×C2911yescharacteristic
500C4⋊C4C2×D4×C2911yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C42—21no—
511C42—41no—
512C42—41no—
513C42C24×C2911yescharacteristic
514C23—21no—
515C23—21no—
516C23—21no—
517C23—41no—
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—81no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—81no—
536D4—82no—
537D4—82no—
538D4—161no—
539D4—161no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—82no—
555C2×C4—82no—
556C2×C4C22×D4×C2911yescharacteristic
557C2×C4C22×D4×C2911yescharacteristic
558C2×C4C29×H(5,𝔽2)11yescharacteristic
559C8—21no—
560C8—21no—
561C8—21no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8C29×#13512yes—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22D42×C2911yescharacteristic
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4C2×C29×#13511yescharacteristic
591C4C29×#57511yescharacteristic
592C4C29×#57611yescharacteristic
593C4C29×#57711yescharacteristic
594C2—81no—
595C2—81no—
596C2—81no—
597C2—161no—
598C2C29×#327311yescharacteristic
599C2C29×#328411yescharacteristic
600C2C29×#329011yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
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×#3397C2semidirect
2. C29×#3354C2semidirect
3. C29×#3305C2semidirect
4. C29×#3302C2semidirect
5. C29×#1708C2semidirect
6. C29×#1692C2semidirect
7. C29×#1685C2semidirect
8. C29×#1679C2semidirect
9. C29×#1677C2semidirect
10. C29×#1646C2semidirect
11. C29×#1641C2semidirect
12. C29×#1638C2semidirect
13. C29×#1625C2semidirect
14. C29×#1590C2semidirect
15. C8×D8×C29C2semidirect
213. #19946C29direct (N × H)
268. #3397C2×C29semidirect
269. #3354C2×C29semidirect
270. #3305C2×C29semidirect
271. #3302C2×C29semidirect
272. #1708C2×C29semidirect
273. #1692C2×C29semidirect
274. #1685C2×C29semidirect
275. #1679C2×C29semidirect
276. #1677C2×C29semidirect
277. #1646C2×C29semidirect
278. #1641C2×C29semidirect
279. #1638C2×C29semidirect
280. #1625C2×C29semidirect
281. #1590C2×C29semidirect
282. C8×D8C2×C29semidirect
444. C29#19946direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33972
C29×#33542
C29×#33052
C29×#33022
C29×#17082
C29×#16922
C29×#16852
C29×#16792
C29×#16772
C29×#16462
C29×#16412
C29×#16382
C29×#16252
C29×#15902
C8×D8×C292
#1994629