Finite Group Databasebeta

← C29×#19899 #20314799

Subgroups — C29×#19899 #20314799

Order 7424.

666 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3330C211yesmaximal, characteristic, complemented
2C29×#3325C211yesmaximal, characteristic, complemented
3C29×#3303C211yesmaximal, characteristic, complemented
4C29×#3294C211yesmaximal, characteristic, complemented
5C29×#1711C211yesmaximal, characteristic, complemented
6C29×#1699C211yesmaximal, characteristic, complemented
7C29×#1697C211yesmaximal, characteristic, complemented
8C29×#1683C211yesmaximal, characteristic, complemented
9C29×#1681C211yesmaximal, characteristic, complemented
10C29×#1646C211yesmaximal, characteristic, complemented
11C29×#1639C211yesmaximal, characteristic, complemented
12C29×#1635C211yesmaximal, characteristic, complemented
13C29×#1625C211yesmaximal, characteristic, complemented
14C29×#1589C211yesmaximal, characteristic, complemented
15C8×D8×C29C211yesmaximal, characteristic, complemented
16C29×#555C2211yescharacteristic
17C29×#547C2211yescharacteristic
18C29×#547C2211yescharacteristic, complemented
19D42×C29C2211yescharacteristic
20C29×#487C2211yescharacteristic, complemented
21C29×#487C2211yescharacteristic, complemented
22C29×#487C2211yescharacteristic, complemented
23C29×#486C2211yescharacteristic
24C29×#486C2211yescharacteristic
25C29×#486C2211yescharacteristic
26C29×#485—21no—
27C29×#484—21no—
28C29×#482—21no—
29C29×#480—21no—
30C29×#476C2211yescharacteristic
31C29×#476C2211yescharacteristic, complemented
32C29×#474C2211yescharacteristic
33C29×#474C2211yescharacteristic
34C29×#469—21no—
35C29×#468—21no—
36C29×#466—21no—
37C29×#465—21no—
38C29×#461C2211yescharacteristic
39C29×#461C2211yescharacteristic, complemented
40C29×#459C2211yescharacteristic
41C29×#459C2211yescharacteristic
42C29×#449—21no—
43C29×#449—21no—
44C29×#447—21no—
45C29×#447—21no—
46C4×D8×C29C2211yescharacteristic
47C4×D8×C29C2211yescharacteristic
48C29×#436C2211yescharacteristic
49C29×#436C2211yescharacteristic, complemented
50C8×D4×C29C2211yescharacteristic
51C8×D4×C29C2211yescharacteristic, complemented
52C29×#418—21no—
53C29×#417—21no—
54C29×#416—21no—
55C2×C29×#102—21no—
56C29×#335C2211yescharacteristic, complemented
57C29×#335C2211yescharacteristic, complemented
58C29×#333C2211yescharacteristic, complemented
59C29×#332C2211yescharacteristic, complemented
60C29×#332C2211yescharacteristic, complemented
61C29×#331C2211yescharacteristic
62C29×D4⋊C8C2211yescharacteristic
63C29×D4⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic, complemented
65C29×D4⋊C8C2211yescharacteristic, complemented
66C82×C29C2211yescharacteristic, complemented
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C22×D4×C29—21no—
70C22×D4×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×D8×C29—21no—
74C2×D8×C29—21no—
75C2×D8×C29D411yescharacteristic
76C2×D8×C29D411yescharacteristic
77C2×M16×C29—21no—
78C2×M16×C29—21no—
79C22×C8×C29—21no—
80C22×C8×C29—21no—
81C29×C4⋊Q8C2311yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×C4⋊Q8C2311yescharacteristic
84C29×#127C2311yescharacteristic
85C29×#124—41no—
86C29×#123—41no—
87C29×#123—41no—
88C29×C22⋊Q8—21no—
89C29×C22⋊Q8—21no—
90C29×#121—21no—
91C29×#121—21no—
92C29×#121—21no—
93C29×#121—21no—
94C29×#121—21no—
95C29×#121—21no—
96C29×#120—41no—
97C4×D4×C29C2311yescharacteristic
98C4×D4×C29C2311yescharacteristic
99C4×D4×C29C2311yescharacteristic
100C4×D4×C29C2311yescharacteristic
101C29×#117—21no—
102C29×#117—21no—
103C2×C4⋊C4×C29—21no—
104C2×C4⋊C4×C29—21no—
105C29×#107—21no—
106C29×#107—21no—
107C29×#107D411yescharacteristic
108C29×#107D411yescharacteristic
109C29×#106—21no—
110C29×#106—21no—
111C29×C4⋊C8C2311yescharacteristic
112C29×C4⋊C8C2311yescharacteristic
113C29×C4⋊C8C2311yescharacteristic
114C29×C4⋊C8C2311yescharacteristic
115C29×#103—21no—
116C29×#103—21no—
117C29×#103—21no—
118C29×#103—21no—
119C29×#103—21no—
120C29×#103—21no—
121C29×#103—41no—
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—41no—
133C29×#102D411yescharacteristic
134C29×#102D411yescharacteristic
135C29×#102D411yescharacteristic
136C29×#102D411yescharacteristic
137C29×C22⋊C8—21no—
138C29×C22⋊C8—21no—
139C29×C22⋊C8—21no—
140C29×C22⋊C8—21no—
141C4×C8×C29C2311yescharacteristic
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C24×C29—41no—
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—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—41no—
156C2×D4×C29—41no—
157C2×D4×C29—42no—
158C2×D4×C29—42no—
159C2×D4×C29—41no—
160C2×D4×C29—41no—
161C2×D4×C29—41no—
162C2×D4×C29—81no—
163C2×D4×C29—81no—
164C2×D4×C29C2×D411yescharacteristic
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—21no—
172C22×C4×C29—41no—
173C22×C4×C29—41no—
174SD16×C29—81no—
175SD16×C29—81no—
176D8×C29—22no—
177D8×C29—41no—
178D8×C29—81no—
179D8×C29—81no—
180M16×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—21no—
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—21no—
208C22⋊C4×C29—21no—
209C22⋊C4×C29—41no—
210C22⋊C4×C29—41no—
211C22⋊C4×C29—41no—
212C22⋊C4×C29—41no—
213C22⋊C4×C29—41no—
214C42×C29—41no—
215C42×C29C2411yescharacteristic
216#19899C2911yesmaximal, characteristic, direct product factor, Sylow
217C23×C29—21no—
218C23×C29—21no—
219C23×C29—21no—
220C23×C29—21no—
221C23×C29—41no—
222C23×C29—82no—
223C23×C29—82no—
224C23×C29—161no—
225Q8×C29—41no—
226Q8×C29—41no—
227Q8×C29—41no—
228Q8×C29—41no—
229Q8×C29—81no—
230D4×C29—21no—
231D4×C29—21no—
232D4×C29—21no—
233D4×C29—21no—
234D4×C29—21no—
235D4×C29—21no—
236D4×C29—21no—
237D4×C29—41no—
238D4×C29—41no—
239D4×C29—41no—
240D4×C29—41no—
241D4×C29—81no—
242D4×C29—82no—
243D4×C29—82no—
244D4×C29—82no—
245D4×C29—82no—
246D4×C29—161no—
247D4×C29#13512yes—
248C2×C4×C29—21no—
249C2×C4×C29—21no—
250C2×C4×C29—21no—
251C2×C4×C29—21no—
252C2×C4×C29—41no—
253C2×C4×C29—41no—
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—41no—
263C2×C4×C29—82no—
264C2×C4×C29—82no—
265C2×C4×C29C22×D411yescharacteristic
266C2×C4×C29C22×D411yescharacteristic
267C2×C4×C29H(5,𝔽2)11yescharacteristic
268C8×C29—21no—
269C8×C29—21no—
270C8×C29—21no—
271C8×C29—21no—
272C8×C29—41no—
273C8×C29—41no—
274C8×C29—41no—
275C8×C29—41no—
276C8×C29—41no—
277#3330C2×C2911yescharacteristic, complemented
278#3325C2×C2911yescharacteristic, complemented
279#3303C2×C2911yescharacteristic, complemented
280#3294C2×C2911yescharacteristic, complemented
281#1711C2×C2911yescharacteristic, complemented
282#1699C2×C2911yescharacteristic, complemented
283#1697C2×C2911yescharacteristic, complemented
284#1683C2×C2911yescharacteristic, complemented
285#1681C2×C2911yescharacteristic, complemented
286#1646C2×C2911yescharacteristic, complemented
287#1639C2×C2911yescharacteristic, complemented
288#1635C2×C2911yescharacteristic, complemented
289#1625C2×C2911yescharacteristic, complemented
290#1589C2×C2911yescharacteristic, complemented
291C8×D8C2×C2911yescharacteristic, complemented
292C22×C29—22no—
293C22×C29—41no—
294C22×C29—41no—
295C22×C29—41no—
296C22×C29—41no—
297C22×C29—41no—
298C22×C29—41no—
299C22×C29—41no—
300C22×C29—41no—
301C22×C29—41no—
302C22×C29—41no—
303C22×C29—41no—
304C22×C29—81no—
305C22×C29—81no—
306C22×C29—81no—
307C22×C29—164no—
308C22×C29D4211yescharacteristic
309C4×C29—21no—
310C4×C29—41no—
311C4×C29—41no—
312C4×C29—41no—
313C4×C29—41no—
314C4×C29—81no—
315C4×C29—81no—
316C4×C29—81no—
317C4×C29C2×#13511yescharacteristic
318C4×C29#57511yescharacteristic
319C4×C29#57611yescharacteristic
320C4×C29#57611yescharacteristic
321#555C22×C2911yescharacteristic
322#547C22×C2911yescharacteristic
323#547C22×C2911yescharacteristic, complemented
324D42C22×C2911yescharacteristic
325#487C22×C2911yescharacteristic, complemented
326#487C22×C2911yescharacteristic, complemented
327#487C22×C2911yescharacteristic, complemented
328#486C22×C2911yescharacteristic
329#486C22×C2911yescharacteristic
330#486C22×C2911yescharacteristic
331#485—21no—
332#484—21no—
333#482—21no—
334#480—21no—
335#476C22×C2911yescharacteristic
336#476C22×C2911yescharacteristic, complemented
337#474C22×C2911yescharacteristic
338#474C22×C2911yescharacteristic
339#469—21no—
340#468—21no—
341#466—21no—
342#465—21no—
343#461C22×C2911yescharacteristic
344#461C22×C2911yescharacteristic, complemented
345#459C22×C2911yescharacteristic
346#459C22×C2911yescharacteristic
347#449—21no—
348#449—21no—
349#447—21no—
350#447—21no—
351C4×D8C22×C2911yescharacteristic
352C4×D8C22×C2911yescharacteristic
353#436C22×C2911yescharacteristic
354#436C22×C2911yescharacteristic, complemented
355C8×D4C22×C2911yescharacteristic
356C8×D4C22×C2911yescharacteristic, complemented
357#418—21no—
358#417—21no—
359#416—21no—
360C2×#102—21no—
361#335C22×C2911yescharacteristic, complemented
362#335C22×C2911yescharacteristic, complemented
363#333C22×C2911yescharacteristic, complemented
364#332C22×C2911yescharacteristic, complemented
365#332C22×C2911yescharacteristic, complemented
366#331C22×C2911yescharacteristic
367D4⋊C8C22×C2911yescharacteristic
368D4⋊C8C22×C2911yescharacteristic
369D4⋊C8C22×C2911yescharacteristic, complemented
370D4⋊C8C22×C2911yescharacteristic, complemented
371C82C22×C2911yescharacteristic, complemented
372C2×C29—42no—
373C2×C29—81no—
374C2×C29—81no—
375C2×C29—81no—
376C2×C29—161no—
377C2×C29#327311yescharacteristic
378C2×C29#328011yescharacteristic
379C2×C29#329011yescharacteristic
380C2×#41—21no—
381C2×#41—21no—
382C22×D4—21no—
383C22×D4—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×D8D4×C2911yescharacteristic
389C2×D8D4×C2911yescharacteristic
390C2×M16—21no—
391C2×M16—21no—
392C22×C8—21no—
393C22×C8—21no—
394C4⋊Q8C23×C2911yescharacteristic
395C4⋊Q8C23×C2911yescharacteristic
396C4⋊Q8C23×C2911yescharacteristic
397#127C23×C2911yescharacteristic
398#124—41no—
399#123—41no—
400#123—41no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403#121—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—21no—
409#120—41no—
410C4×D4C23×C2911yescharacteristic
411C4×D4C23×C2911yescharacteristic
412C4×D4C23×C2911yescharacteristic
413C4×D4C23×C2911yescharacteristic
414#117—21no—
415#117—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418#107—21no—
419#107—21no—
420#107D4×C2911yescharacteristic
421#107D4×C2911yescharacteristic
422#106—21no—
423#106—21no—
424C4⋊C8C23×C2911yescharacteristic
425C4⋊C8C23×C2911yescharacteristic
426C4⋊C8C23×C2911yescharacteristic
427C4⋊C8C23×C2911yescharacteristic
428#103—21no—
429#103—21no—
430#103—21no—
431#103—21no—
432#103—21no—
433#103—21no—
434#103—41no—
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—41no—
446#102D4×C2911yescharacteristic
447#102D4×C2911yescharacteristic
448#102D4×C2911yescharacteristic
449#102D4×C2911yescharacteristic
450C22⋊C8—21no—
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454C4×C8C23×C2911yescharacteristic
455C4×C8C23×C2911yescharacteristic
456C4×C8C23×C2911yescharacteristic
457C29#1989911yescharacteristic, direct product factor, Sylow
458C24—41no—
459#41—42no—
460#41—42no—
461#41—81no—
462#41—81no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—81no—
477C2×D4—81no—
478C2×D4C2×D4×C2911yescharacteristic
479C2×D4C2×D4×C2911yescharacteristic
480C2×D4C2×D4×C2911yescharacteristic
481C2×D4C2×D4×C2911yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—41no—
487C22×C4—41no—
488SD16—81no—
489SD16—81no—
490D8—22no—
491D8—41no—
492D8—81no—
493D8—81no—
494M16—81no—
495M16—81no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—81no—
502C2×C8—81no—
503C2×C8C2×D4×C2911yescharacteristic
504C2×C8C2×D4×C2911yescharacteristic
505C2×C8C2×D4×C2911yescharacteristic
506C2×C8C2×D4×C2911yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4C2×D4×C2911yescharacteristic
516C4⋊C4C2×D4×C2911yescharacteristic
517C4⋊C4C2×D4×C2911yescharacteristic
518C4⋊C4C2×D4×C2911yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C42—41no—
529C42C24×C2911yescharacteristic
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—41no—
535C23—82no—
536C23—82no—
537C23—161no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—81no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—81no—
555D4—82no—
556D4—82no—
557D4—82no—
558D4—82no—
559D4—161no—
560D4C29×#13512yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
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—41no—
575C2×C4—41no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4C22×D4×C2911yescharacteristic
579C2×C4C22×D4×C2911yescharacteristic
580C2×C4C29×H(5,𝔽2)11yescharacteristic
581C8—21no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8—41no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—164no—
606C22D42×C2911yescharacteristic
607C4—21no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—81no—
613C4—81no—
614C4—81no—
615C4C2×C29×#13511yescharacteristic
616C4C29×#57511yescharacteristic
617C4C29×#57611yescharacteristic
618C4C29×#57611yescharacteristic
619C2—42no—
620C2—81no—
621C2—81no—
622C2—81no—
623C2—161no—
624C2C29×#327311yescharacteristic
625C2C29×#328011yescharacteristic
626C2C29×#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×#3330C2semidirect
2. C29×#3325C2semidirect
3. C29×#3303C2semidirect
4. C29×#3294C2semidirect
5. C29×#1711C2semidirect
6. C29×#1699C2semidirect
7. C29×#1697C2semidirect
8. C29×#1683C2semidirect
9. C29×#1681C2semidirect
10. C29×#1646C2semidirect
11. C29×#1639C2semidirect
12. C29×#1635C2semidirect
13. C29×#1625C2semidirect
14. C29×#1589C2semidirect
15. C8×D8×C29C2semidirect
18. C29×#547C22semidirect
20. C29×#487C22semidirect
21. C29×#487C22semidirect
22. C29×#487C22semidirect
31. C29×#476C22semidirect
39. C29×#461C22semidirect
49. C29×#436C22semidirect
51. C8×D4×C29C22semidirect
56. C29×#335C22semidirect
57. C29×#335C22semidirect
58. C29×#333C22semidirect
59. C29×#332C22semidirect
60. C29×#332C22semidirect
64. C29×D4⋊C8C22semidirect
65. C29×D4⋊C8C22semidirect
66. C82×C29C22semidirect
216. #19899C29direct (N × H)
277. #3330C2×C29semidirect
278. #3325C2×C29semidirect
279. #3303C2×C29semidirect
280. #3294C2×C29semidirect
281. #1711C2×C29semidirect
282. #1699C2×C29semidirect
283. #1697C2×C29semidirect
284. #1683C2×C29semidirect
285. #1681C2×C29semidirect
286. #1646C2×C29semidirect
287. #1639C2×C29semidirect
288. #1635C2×C29semidirect
289. #1625C2×C29semidirect
290. #1589C2×C29semidirect
291. C8×D8C2×C29semidirect
323. #547C22×C29semidirect
325. #487C22×C29semidirect
326. #487C22×C29semidirect
327. #487C22×C29semidirect
336. #476C22×C29semidirect
344. #461C22×C29semidirect
354. #436C22×C29semidirect
356. C8×D4C22×C29semidirect
361. #335C22×C29semidirect
362. #335C22×C29semidirect
363. #333C22×C29semidirect
364. #332C22×C29semidirect
365. #332C22×C29semidirect
369. D4⋊C8C22×C29semidirect
370. D4⋊C8C22×C29semidirect
371. C82C22×C29semidirect
457. C29#19899direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33302
C29×#33252
C29×#33032
C29×#32942
C29×#17112
C29×#16992
C29×#16972
C29×#16832
C29×#16812
C29×#16462
C29×#16392
C29×#16352
C29×#16252
C29×#15892
C8×D8×C292
#1989929