Finite Group Databasebeta

← C29×#19911 #20314811

Subgroups — C29×#19911 #20314811

Order 7424.

666 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3366C211yesmaximal, characteristic, complemented
2C29×#3325C211yesmaximal, characteristic, complemented
3C29×#3305C211yesmaximal, characteristic, complemented
4C29×#3295C211yesmaximal, characteristic, complemented
5C29×#1709C211yesmaximal, characteristic, complemented
6C29×#1698C211yesmaximal, characteristic, complemented
7C29×#1697C211yesmaximal, characteristic, complemented
8C29×#1677C211yesmaximal, characteristic, complemented
9C29×#1677C211yesmaximal, characteristic, complemented
10C29×#1634C211yesmaximal, characteristic, complemented
11C29×#1632C211yesmaximal, characteristic, complemented
12C29×#1621C211yesmaximal, characteristic, complemented
13C29×#1619C211yesmaximal, characteristic, complemented
14C29×#1590C211yesmaximal, characteristic, complemented
15C8×D8×C29C211yesmaximal, characteristic, complemented
16C29×#555C2211yescharacteristic
17C29×#554C2211yescharacteristic
18C29×#550C2211yescharacteristic, complemented
19D42×C29C2211yescharacteristic
20C29×#494C2211yescharacteristic, complemented
21C29×#493C2211yescharacteristic
22C29×#490—21no—
23C29×#486C2211yescharacteristic
24C29×#486C2211yescharacteristic
25C29×#486C2211yescharacteristic, complemented
26C29×#486C2211yescharacteristic, complemented
27C29×#482—21no—
28C29×#482—21no—
29C29×#481—21no—
30C29×#478—21no—
31C29×#477C2211yescharacteristic, complemented
32C29×#476C2211yescharacteristic
33C29×#476C2211yescharacteristic
34C29×#476C2211yescharacteristic, complemented
35C29×#469—21no—
36C29×#466—21no—
37C29×#465—21no—
38C29×#460C2211yescharacteristic
39C29×#459—21no—
40C29×#459C2211yescharacteristic
41C29×#459C2211yescharacteristic
42C29×#459C2211yescharacteristic
43C29×#450—21no—
44C29×#449—21no—
45C29×#447—21no—
46C29×#446C2211yescharacteristic, complemented
47C29×#442—21no—
48C4×SD16×C29C2211yescharacteristic
49C4×D8×C29C2211yescharacteristic
50C29×#436C2211yescharacteristic
51C8×D4×C29C2211yescharacteristic
52C8×D4×C29C2211yescharacteristic, complemented
53C29×#418—21no—
54C29×#416—21no—
55C2×C29×#102—21no—
56C29×#335C2211yescharacteristic, complemented
57C29×#334C2211yescharacteristic, complemented
58C29×#333C2211yescharacteristic, complemented
59C29×#333C2211yescharacteristic, complemented
60C29×#331C2211yescharacteristic
61C29×#331C2211yescharacteristic, complemented
62C29×Q8⋊C8C2211yescharacteristic, complemented
63C29×D4⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic, complemented
66C82×C29C2211yescharacteristic, complemented
67C2×#41×C29—21no—
68C22×D4×C29—21no—
69C22×D4×C29—21no—
70C2×Q16×C29—41no—
71C2×SD16×C29—21no—
72C2×SD16×C29D411yescharacteristic
73C2×D8×C29—21no—
74C2×D8×C29—21no—
75C2×D8×C29—21no—
76C2×D8×C29—41no—
77C2×D8×C29D411yescharacteristic
78C2×M16×C29—21no—
79C22×C8×C29—21no—
80C22×C8×C29—21no—
81C29×C4⋊Q8C2311yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×#127—21no—
84C29×#127C2311yescharacteristic
85C29×#127C2311yescharacteristic
86C29×#125—21no—
87C29×#124—41no—
88C29×C22⋊Q8—21no—
89C29×C22⋊Q8—41no—
90C29×#121—21no—
91C29×#121—21no—
92C29×#121—21no—
93C29×#121—21no—
94C29×#121—21no—
95C29×#121—41no—
96C29×#120—41no—
97C4×Q8×C29C2311yescharacteristic
98C4×D4×C29—21no—
99C4×D4×C29—21no—
100C4×D4×C29C2311yescharacteristic
101C4×D4×C29C2311yescharacteristic
102C4×D4×C29C2311yescharacteristic
103C29×#117—21no—
104C29×#117—21no—
105C2×C4⋊C4×C29—21no—
106C29×#107—21no—
107C29×#107D411yescharacteristic
108C29×#106—21no—
109C29×#106—21no—
110C29×#106—21no—
111C29×#106D411yescharacteristic
112C29×C4⋊C8—21no—
113C29×C4⋊C8C2311yescharacteristic
114C29×C4⋊C8C2311yescharacteristic
115C29×C4⋊C8C2311yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×#103—21no—
118C29×#103D411yescharacteristic
119C29×#102—21no—
120C29×#102—21no—
121C29×#102—21no—
122C29×#102—21no—
123C29×#102—21no—
124C29×#102—21no—
125C29×#102—21no—
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×#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
144C24×C29—41no—
145#41×C29—42no—
146#41×C29—81no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29C2×D411yescharacteristic
150C2×D4×C29—21no—
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—41no—
157C2×D4×C29—41no—
158C2×D4×C29—41no—
159C2×D4×C29—41no—
160C2×D4×C29—42no—
161C2×D4×C29—42no—
162C2×D4×C29—41no—
163C2×D4×C29—81no—
164C2×D4×C29—81no—
165C2×D4×C29C2×D411yescharacteristic
166C2×D4×C29C2×D411yescharacteristic
167C2×D4×C29C2×D411yescharacteristic
168C22×C4×C29—21no—
169C22×C4×C29—21no—
170C22×C4×C29—21no—
171C22×C4×C29—41no—
172C22×C4×C29—41no—
173Q16×C29—82no—
174SD16×C29—41no—
175SD16×C29—81no—
176D8×C29—22no—
177D8×C29—42no—
178D8×C29—82no—
179D8×C29—81no—
180D8×C29—81no—
181M16×C29—81no—
182C2×C8×C29—21no—
183C2×C8×C29—21no—
184C2×C8×C29—21no—
185C2×C8×C29—21no—
186C2×C8×C29—21no—
187C2×C8×C29—81no—
188C2×C8×C29—81no—
189C2×C8×C29C2×D411yescharacteristic
190C2×C8×C29C2×D411yescharacteristic
191C2×C8×C29C2×D411yescharacteristic
192C2×C8×C29C2×D411yescharacteristic
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×C29C2×D411yescharacteristic
201C4⋊C4×C29C2×D411yescharacteristic
202C4⋊C4×C29C2×D411yescharacteristic
203C4⋊C4×C29C2×D411yescharacteristic
204C22⋊C4×C29—21no—
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—41no—
214C42×C29C2411yescharacteristic
215#19911C2911yesmaximal, characteristic, direct product factor, Sylow
216C23×C29—21no—
217C23×C29—21no—
218C23×C29—21no—
219C23×C29—41no—
220C23×C29—41no—
221C23×C29—82no—
222C23×C29—82no—
223C23×C29—161no—
224Q8×C29—21no—
225Q8×C29—21no—
226Q8×C29—81no—
227Q8×C29—81no—
228D4×C29—21no—
229D4×C29—21no—
230D4×C29—21no—
231D4×C29—21no—
232D4×C29—21no—
233D4×C29—41no—
234D4×C29—41no—
235D4×C29—41no—
236D4×C29—41no—
237D4×C29—41no—
238D4×C29—41no—
239D4×C29—41no—
240D4×C29—41no—
241D4×C29—81no—
242D4×C29—81no—
243D4×C29—82no—
244D4×C29—82no—
245D4×C29—82no—
246D4×C29—161no—
247D4×C29—161no—
248D4×C29#13512yes—
249C2×C4×C29—21no—
250C2×C4×C29—21no—
251C2×C4×C29—21no—
252C2×C4×C29—21no—
253C2×C4×C29—21no—
254C2×C4×C29—41no—
255C2×C4×C29—41no—
256C2×C4×C29—41no—
257C2×C4×C29—41no—
258C2×C4×C29—41no—
259C2×C4×C29—41no—
260C2×C4×C29—41no—
261C2×C4×C29—41no—
262C2×C4×C29—82no—
263C2×C4×C29—161no—
264C2×C4×C29C22×D411yescharacteristic
265C2×C4×C29C22×D411yescharacteristic
266C2×C4×C29H(5,𝔽2)11yescharacteristic
267C8×C29—22no—
268C8×C29—21no—
269C8×C29—21no—
270C8×C29—21no—
271C8×C29—21no—
272C8×C29—41no—
273C8×C29—41no—
274C8×C29—41no—
275C8×C29—41no—
276#3366C2×C2911yescharacteristic, complemented
277#3325C2×C2911yescharacteristic, complemented
278#3305C2×C2911yescharacteristic, complemented
279#3295C2×C2911yescharacteristic, complemented
280#1709C2×C2911yescharacteristic, complemented
281#1698C2×C2911yescharacteristic, complemented
282#1697C2×C2911yescharacteristic, complemented
283#1677C2×C2911yescharacteristic, complemented
284#1677C2×C2911yescharacteristic, complemented
285#1634C2×C2911yescharacteristic, complemented
286#1632C2×C2911yescharacteristic, complemented
287#1621C2×C2911yescharacteristic, complemented
288#1619C2×C2911yescharacteristic, complemented
289#1590C2×C2911yescharacteristic, complemented
290C8×D8C2×C2911yescharacteristic, complemented
291C22×C29—22no—
292C22×C29—41no—
293C22×C29—41no—
294C22×C29—41no—
295C22×C29—41no—
296C22×C29—41no—
297C22×C29—41no—
298C22×C29—41no—
299C22×C29—41no—
300C22×C29—81no—
301C22×C29—81no—
302C22×C29—81no—
303C22×C29—81no—
304C22×C29—81no—
305C22×C29—81no—
306C22×C29—164no—
307C22×C29D4211yescharacteristic
308C4×C29—21no—
309C4×C29—41no—
310C4×C29—41no—
311C4×C29—41no—
312C4×C29—41no—
313C4×C29—41no—
314C4×C29—81no—
315C4×C29—81no—
316C4×C29C2×#13511yescharacteristic
317C4×C29#57511yescharacteristic
318C4×C29#57611yescharacteristic
319C4×C29#57711yescharacteristic
320#555C22×C2911yescharacteristic
321#554C22×C2911yescharacteristic
322#550C22×C2911yescharacteristic, complemented
323D42C22×C2911yescharacteristic
324#494C22×C2911yescharacteristic, complemented
325#493C22×C2911yescharacteristic
326#490—21no—
327#486C22×C2911yescharacteristic
328#486C22×C2911yescharacteristic
329#486C22×C2911yescharacteristic, complemented
330#486C22×C2911yescharacteristic, complemented
331#482—21no—
332#482—21no—
333#481—21no—
334#478—21no—
335#477C22×C2911yescharacteristic, complemented
336#476C22×C2911yescharacteristic
337#476C22×C2911yescharacteristic
338#476C22×C2911yescharacteristic, complemented
339#469—21no—
340#466—21no—
341#465—21no—
342#460C22×C2911yescharacteristic
343#459—21no—
344#459C22×C2911yescharacteristic
345#459C22×C2911yescharacteristic
346#459C22×C2911yescharacteristic
347#450—21no—
348#449—21no—
349#447—21no—
350#446C22×C2911yescharacteristic, complemented
351#442—21no—
352C4×SD16C22×C2911yescharacteristic
353C4×D8C22×C2911yescharacteristic
354#436C22×C2911yescharacteristic
355C8×D4C22×C2911yescharacteristic
356C8×D4C22×C2911yescharacteristic, complemented
357#418—21no—
358#416—21no—
359C2×#102—21no—
360#335C22×C2911yescharacteristic, complemented
361#334C22×C2911yescharacteristic, complemented
362#333C22×C2911yescharacteristic, complemented
363#333C22×C2911yescharacteristic, complemented
364#331C22×C2911yescharacteristic
365#331C22×C2911yescharacteristic, complemented
366Q8⋊C8C22×C2911yescharacteristic, complemented
367D4⋊C8C22×C2911yescharacteristic
368D4⋊C8C22×C2911yescharacteristic
369D4⋊C8C22×C2911yescharacteristic, complemented
370C82C22×C2911yescharacteristic, complemented
371C2×C29—42no—
372C2×C29—81no—
373C2×C29—81no—
374C2×C29—161no—
375C2×C29—161no—
376C2×C29#327311yescharacteristic
377C2×C29#328211yescharacteristic
378C2×C29#329211yescharacteristic
379C2×#41—21no—
380C22×D4—21no—
381C22×D4—21no—
382C2×Q16—41no—
383C2×SD16—21no—
384C2×SD16D4×C2911yescharacteristic
385C2×D8—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×D8—41no—
389C2×D8D4×C2911yescharacteristic
390C2×M16—21no—
391C22×C8—21no—
392C22×C8—21no—
393C4⋊Q8C23×C2911yescharacteristic
394C4⋊Q8C23×C2911yescharacteristic
395#127—21no—
396#127C23×C2911yescharacteristic
397#127C23×C2911yescharacteristic
398#125—21no—
399#124—41no—
400C22⋊Q8—21no—
401C22⋊Q8—41no—
402#121—21no—
403#121—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—41no—
408#120—41no—
409C4×Q8C23×C2911yescharacteristic
410C4×D4—21no—
411C4×D4—21no—
412C4×D4C23×C2911yescharacteristic
413C4×D4C23×C2911yescharacteristic
414C4×D4C23×C2911yescharacteristic
415#117—21no—
416#117—21no—
417C2×C4⋊C4—21no—
418#107—21no—
419#107D4×C2911yescharacteristic
420#106—21no—
421#106—21no—
422#106—21no—
423#106D4×C2911yescharacteristic
424C4⋊C8—21no—
425C4⋊C8C23×C2911yescharacteristic
426C4⋊C8C23×C2911yescharacteristic
427C4⋊C8C23×C2911yescharacteristic
428C4⋊C8C23×C2911yescharacteristic
429#103—21no—
430#103D4×C2911yescharacteristic
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102D4×C2911yescharacteristic
447#102D4×C2911yescharacteristic
448#102D4×C2911yescharacteristic
449C22⋊C8—21no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452#97—21no—
453C4×C8C23×C2911yescharacteristic
454C4×C8C23×C2911yescharacteristic
455C4×C8C23×C2911yescharacteristic
456C29#1991111yescharacteristic, direct product factor, Sylow
457C24—41no—
458#41—42no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8C2×D4×C2911yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—41no—
476C2×D4—81no—
477C2×D4—81no—
478C2×D4C2×D4×C2911yescharacteristic
479C2×D4C2×D4×C2911yescharacteristic
480C2×D4C2×D4×C2911yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485C22×C4—41no—
486Q16—82no—
487SD16—41no—
488SD16—81no—
489D8—22no—
490D8—42no—
491D8—82no—
492D8—81no—
493D8—81no—
494M16—81no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—81no—
501C2×C8—81no—
502C2×C8C2×D4×C2911yescharacteristic
503C2×C8C2×D4×C2911yescharacteristic
504C2×C8C2×D4×C2911yescharacteristic
505C2×C8C2×D4×C2911yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4C2×D4×C2911yescharacteristic
514C4⋊C4C2×D4×C2911yescharacteristic
515C4⋊C4C2×D4×C2911yescharacteristic
516C4⋊C4C2×D4×C2911yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C42—21no—
526C42—41no—
527C42C24×C2911yescharacteristic
528C23—21no—
529C23—21no—
530C23—21no—
531C23—41no—
532C23—41no—
533C23—82no—
534C23—82no—
535C23—161no—
536Q8—21no—
537Q8—21no—
538Q8—81no—
539Q8—81no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—81no—
554D4—81no—
555D4—82no—
556D4—82no—
557D4—82no—
558D4—161no—
559D4—161no—
560D4C29×#13512yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—82no—
575C2×C4—161no—
576C2×C4C22×D4×C2911yescharacteristic
577C2×C4C22×D4×C2911yescharacteristic
578C2×C4C29×H(5,𝔽2)11yescharacteristic
579C8—22no—
580C8—21no—
581C8—21no—
582C8—21no—
583C8—21no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—164no—
604C22D42×C2911yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4—81no—
613C4C2×C29×#13511yescharacteristic
614C4C29×#57511yescharacteristic
615C4C29×#57611yescharacteristic
616C4C29×#57711yescharacteristic
617C2—42no—
618C2—81no—
619C2—81no—
620C2—161no—
621C2—161no—
622C2C29×#327311yescharacteristic
623C2C29×#328211yescharacteristic
624C2C29×#329211yescharacteristic
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×#3366C2semidirect
2. C29×#3325C2semidirect
3. C29×#3305C2semidirect
4. C29×#3295C2semidirect
5. C29×#1709C2semidirect
6. C29×#1698C2semidirect
7. C29×#1697C2semidirect
8. C29×#1677C2semidirect
9. C29×#1677C2semidirect
10. C29×#1634C2semidirect
11. C29×#1632C2semidirect
12. C29×#1621C2semidirect
13. C29×#1619C2semidirect
14. C29×#1590C2semidirect
15. C8×D8×C29C2semidirect
18. C29×#550C22semidirect
20. C29×#494C22semidirect
25. C29×#486C22semidirect
26. C29×#486C22semidirect
31. C29×#477C22semidirect
34. C29×#476C22semidirect
46. C29×#446C22semidirect
52. C8×D4×C29C22semidirect
56. C29×#335C22semidirect
57. C29×#334C22semidirect
58. C29×#333C22semidirect
59. C29×#333C22semidirect
61. C29×#331C22semidirect
62. C29×Q8⋊C8C22semidirect
65. C29×D4⋊C8C22semidirect
66. C82×C29C22semidirect
215. #19911C29direct (N × H)
276. #3366C2×C29semidirect
277. #3325C2×C29semidirect
278. #3305C2×C29semidirect
279. #3295C2×C29semidirect
280. #1709C2×C29semidirect
281. #1698C2×C29semidirect
282. #1697C2×C29semidirect
283. #1677C2×C29semidirect
284. #1677C2×C29semidirect
285. #1634C2×C29semidirect
286. #1632C2×C29semidirect
287. #1621C2×C29semidirect
288. #1619C2×C29semidirect
289. #1590C2×C29semidirect
290. C8×D8C2×C29semidirect
322. #550C22×C29semidirect
324. #494C22×C29semidirect
329. #486C22×C29semidirect
330. #486C22×C29semidirect
335. #477C22×C29semidirect
338. #476C22×C29semidirect
350. #446C22×C29semidirect
356. C8×D4C22×C29semidirect
360. #335C22×C29semidirect
361. #334C22×C29semidirect
362. #333C22×C29semidirect
363. #333C22×C29semidirect
365. #331C22×C29semidirect
366. Q8⋊C8C22×C29semidirect
369. D4⋊C8C22×C29semidirect
370. C82C22×C29semidirect
456. C29#19911direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33662
C29×#33252
C29×#33052
C29×#32952
C29×#17092
C29×#16982
C29×#16972
C29×#16772
C29×#16342
C29×#16322
C29×#16212
C29×#16192
C29×#15902
C8×D8×C292
#1991129