Finite Group Databasebeta

← C29×#19910 #20314810

Subgroups — C29×#19910 #20314810

Order 7424.

668 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3367C211yesmaximal, characteristic, complemented
2C29×#3340C211yesmaximal, characteristic, complemented
3C29×#3325C211yesmaximal, characteristic
4D4×SD16×C29C211yesmaximal, characteristic, complemented
5C29×#1708C211yesmaximal, characteristic, complemented
6C29×#1699C211yesmaximal, characteristic, complemented
7C29×#1698C211yesmaximal, characteristic, complemented
8C29×#1671C211yesmaximal, characteristic, complemented
9C29×#1665C211yesmaximal, characteristic, complemented
10C29×#1646C211yesmaximal, characteristic, complemented
11C29×#1639C211yesmaximal, characteristic, complemented
12C29×#1637C211yesmaximal, characteristic, complemented
13C29×#1628C211yesmaximal, characteristic, complemented
14C29×#1590C211yesmaximal, characteristic, complemented
15C8×D8×C29C211yesmaximal, characteristic, complemented
16C22×SD16×C29—21no—
17C29×#556C2211yescharacteristic, complemented
18C29×#555C2211yescharacteristic
19D4×Q8×C29C2211yescharacteristic
20D42×C29C2211yescharacteristic
21C29×#498C2211yescharacteristic, complemented
22C29×#492C2211yescharacteristic
23C29×#489—21no—
24C29×#487C2211yescharacteristic, complemented
25C29×#487C2211yescharacteristic, complemented
26C29×#486C2211yescharacteristic
27C29×#486C2211yescharacteristic
28C29×#485—21no—
29C29×#482—21no—
30C29×#482—21no—
31C29×#477—21no—
32C29×#477C2211yescharacteristic, complemented
33C29×#476C2211yescharacteristic
34C29×#474C2211yescharacteristic
35C29×#474C2211yescharacteristic, complemented
36C29×#469—21no—
37C29×#465—21no—
38C29×#465—21no—
39C29×#463—21no—
40C29×#461C2211yescharacteristic
41C29×#461C2211yescharacteristic
42C29×#460C2211yescharacteristic
43C29×#459C2211yescharacteristic
44C29×#450—21no—
45C29×#448—21no—
46C29×#447—21no—
47C29×#446C2211yescharacteristic, complemented
48C29×#440—21no—
49C4×SD16×C29C2211yescharacteristic
50C4×D8×C29C2211yescharacteristic
51C29×#436C2211yescharacteristic
52C8×D4×C29C2211yescharacteristic
53C8×D4×C29C2211yescharacteristic, complemented
54C29×#427—21no—
55C29×#418—21no—
56C29×#335C2211yescharacteristic, complemented
57C29×#334C2211yescharacteristic, complemented
58C29×#333C2211yescharacteristic, complemented
59C29×#332C2211yescharacteristic, complemented
60C29×#332C2211yescharacteristic, complemented
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic, complemented
63C29×D4⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic, complemented
66C82×C29C2211yescharacteristic, complemented
67C22×Q8×C29—21no—
68C22×D4×C29—21no—
69C22×D4×C29—21no—
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×SD16×C29—21no—
75C2×SD16×C29—44no—
76C2×SD16×C29D411yescharacteristic
77C2×D8×C29—21no—
78C2×D8×C29D411yescharacteristic
79C2×M16×C29—21no—
80C22×C8×C29—21no—
81C22×C8×C29—21no—
82C29×C4⋊Q8—21no—
83C29×C4⋊Q8C2311yescharacteristic
84C29×C4⋊Q8C2311yescharacteristic
85C29×C4⋊Q8C2311yescharacteristic
86C29×#127C2311yescharacteristic
87C29×#126—41no—
88C29×#124—21no—
89C29×#124—41no—
90C29×C22⋊Q8—21no—
91C29×C22⋊Q8—21no—
92C29×C22⋊Q8—41no—
93C29×#121—21no—
94C29×#121—21no—
95C29×#121—21no—
96C29×#121—21no—
97C29×#120—41no—
98C4×Q8×C29—21no—
99C4×Q8×C29C2311yescharacteristic
100C4×D4×C29—21no—
101C4×D4×C29C2311yescharacteristic
102C4×D4×C29C2311yescharacteristic
103C4×D4×C29C2311yescharacteristic
104C29×#117—21no—
105C29×#117—21no—
106C29×#117—21no—
107C29×#107—21no—
108C29×#107—21no—
109C29×#107—21no—
110C29×#107D411yescharacteristic
111C29×#106—21no—
112C29×#106—21no—
113C29×#106—21no—
114C29×#106D411yescharacteristic
115C29×C4⋊C8—21no—
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×#103—21no—
121C29×#103—21no—
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—41no—
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—41no—
135C29×#102D411yescharacteristic
136C29×#102D411yescharacteristic
137C29×#102D411yescharacteristic
138C29×C22⋊C8—21no—
139C29×C22⋊C8—21no—
140C29×C22⋊C8—21no—
141C29×#97—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C4×C8×C29C2311yescharacteristic
145C24×C29—41no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—41no—
150C2×Q8×C29—42no—
151C2×Q8×C29—81no—
152C2×Q8×C29C2×D411yescharacteristic
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—41no—
157C2×D4×C29—41no—
158C2×D4×C29—42no—
159C2×D4×C29—42no—
160C2×D4×C29—41no—
161C2×D4×C29—81no—
162C2×D4×C29—81no—
163C2×D4×C29C2×D411yescharacteristic
164C2×D4×C29C2×D411yescharacteristic
165C2×D4×C29C2×D411yescharacteristic
166C22×C4×C29—21no—
167C22×C4×C29—21no—
168C22×C4×C29—21no—
169C22×C4×C29—41no—
170SD16×C29—22no—
171SD16×C29—42no—
172SD16×C29—42no—
173SD16×C29—42no—
174SD16×C29—42no—
175SD16×C29—81no—
176D8×C29—22no—
177D8×C29—81no—
178M16×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×C29—42no—
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—41no—
198C4⋊C4×C29—41no—
199C4⋊C4×C29C2×D411yescharacteristic
200C4⋊C4×C29C2×D411yescharacteristic
201C4⋊C4×C29C2×D411yescharacteristic
202C4⋊C4×C29C2×D411yescharacteristic
203C22⋊C4×C29—21no—
204C22⋊C4×C29—21no—
205C22⋊C4×C29—21no—
206C22⋊C4×C29—41no—
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×C29—41no—
215C42×C29C2411yescharacteristic
216#19910C2911yesmaximal, characteristic, direct product factor, Sylow
217C23×C29—21no—
218C23×C29—21no—
219C23×C29—21no—
220C23×C29—41no—
221C23×C29—82no—
222C23×C29—82no—
223C23×C29—161no—
224Q8×C29—21no—
225Q8×C29—21no—
226Q8×C29—41no—
227Q8×C29—41no—
228Q8×C29—41no—
229Q8×C29—41no—
230Q8×C29—81no—
231Q8×C29—82no—
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—161no—
245D4×C29#13512yes—
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—41no—
256C2×C4×C29—41no—
257C2×C4×C29—41no—
258C2×C4×C29—41no—
259C2×C4×C29—41no—
260C2×C4×C29—82no—
261C2×C4×C29C22×D411yescharacteristic
262C2×C4×C29C22×D411yescharacteristic
263C2×C4×C29H(5,𝔽2)11yescharacteristic
264C8×C29—21no—
265C8×C29—21no—
266C8×C29—21no—
267C8×C29—41no—
268C8×C29—41no—
269C8×C29—41no—
270C8×C29—41no—
271C8×C29—41no—
272C8×C29AGL(1,ℤ/8)12yes—
273#3367C2×C2911yescharacteristic, complemented
274#3340C2×C2911yescharacteristic, complemented
275#3325C2×C2911yescharacteristic
276D4×SD16C2×C2911yescharacteristic, complemented
277#1708C2×C2911yescharacteristic, complemented
278#1699C2×C2911yescharacteristic, complemented
279#1698C2×C2911yescharacteristic, complemented
280#1671C2×C2911yescharacteristic, complemented
281#1665C2×C2911yescharacteristic, complemented
282#1646C2×C2911yescharacteristic, complemented
283#1639C2×C2911yescharacteristic, complemented
284#1637C2×C2911yescharacteristic, complemented
285#1628C2×C2911yescharacteristic, complemented
286#1590C2×C2911yescharacteristic, complemented
287C8×D8C2×C2911yescharacteristic, complemented
288C22×C29—22no—
289C22×C29—41no—
290C22×C29—41no—
291C22×C29—41no—
292C22×C29—41no—
293C22×C29—41no—
294C22×C29—41no—
295C22×C29—41no—
296C22×C29—41no—
297C22×C29—81no—
298C22×C29—81no—
299C22×C29—81no—
300C22×C29—164no—
301C22×C29D4211yescharacteristic
302C4×C29—21no—
303C4×C29—41no—
304C4×C29—41no—
305C4×C29—41no—
306C4×C29—41no—
307C4×C29—41no—
308C4×C29—81no—
309C4×C29—81no—
310C4×C29—81no—
311C4×C29C2×#13511yescharacteristic
312C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
313C4×C29#57711yescharacteristic
314C4×C29#57711yescharacteristic
315C22×SD16—21no—
316#556C22×C2911yescharacteristic, complemented
317#555C22×C2911yescharacteristic
318D4×Q8C22×C2911yescharacteristic
319D42C22×C2911yescharacteristic
320#498C22×C2911yescharacteristic, complemented
321#492C22×C2911yescharacteristic
322#489—21no—
323#487C22×C2911yescharacteristic, complemented
324#487C22×C2911yescharacteristic, complemented
325#486C22×C2911yescharacteristic
326#486C22×C2911yescharacteristic
327#485—21no—
328#482—21no—
329#482—21no—
330#477—21no—
331#477C22×C2911yescharacteristic, complemented
332#476C22×C2911yescharacteristic
333#474C22×C2911yescharacteristic
334#474C22×C2911yescharacteristic, complemented
335#469—21no—
336#465—21no—
337#465—21no—
338#463—21no—
339#461C22×C2911yescharacteristic
340#461C22×C2911yescharacteristic
341#460C22×C2911yescharacteristic
342#459C22×C2911yescharacteristic
343#450—21no—
344#448—21no—
345#447—21no—
346#446C22×C2911yescharacteristic, complemented
347#440—21no—
348C4×SD16C22×C2911yescharacteristic
349C4×D8C22×C2911yescharacteristic
350#436C22×C2911yescharacteristic
351C8×D4C22×C2911yescharacteristic
352C8×D4C22×C2911yescharacteristic, complemented
353#427—21no—
354#418—21no—
355#335C22×C2911yescharacteristic, complemented
356#334C22×C2911yescharacteristic, complemented
357#333C22×C2911yescharacteristic, complemented
358#332C22×C2911yescharacteristic, complemented
359#332C22×C2911yescharacteristic, complemented
360#331C22×C2911yescharacteristic
361Q8⋊C8C22×C2911yescharacteristic, complemented
362D4⋊C8C22×C2911yescharacteristic
363D4⋊C8C22×C2911yescharacteristic
364D4⋊C8C22×C2911yescharacteristic, complemented
365C82C22×C2911yescharacteristic, complemented
366C2×C29—42no—
367C2×C29—81no—
368C2×C29—81no—
369C2×C29—161no—
370C2×C29#327211yescharacteristic
371C2×C29#328211yescharacteristic
372C2×C29#329011yescharacteristic
373C22×Q8—21no—
374C22×D4—21no—
375C22×D4—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—44no—
382C2×SD16D4×C2911yescharacteristic
383C2×D8—21no—
384C2×D8D4×C2911yescharacteristic
385C2×M16—21no—
386C22×C8—21no—
387C22×C8—21no—
388C4⋊Q8—21no—
389C4⋊Q8C23×C2911yescharacteristic
390C4⋊Q8C23×C2911yescharacteristic
391C4⋊Q8C23×C2911yescharacteristic
392#127C23×C2911yescharacteristic
393#126—41no—
394#124—21no—
395#124—41no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—41no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121—21no—
403#120—41no—
404C4×Q8—21no—
405C4×Q8C23×C2911yescharacteristic
406C4×D4—21no—
407C4×D4C23×C2911yescharacteristic
408C4×D4C23×C2911yescharacteristic
409C4×D4C23×C2911yescharacteristic
410#117—21no—
411#117—21no—
412#117—21no—
413#107—21no—
414#107—21no—
415#107—21no—
416#107D4×C2911yescharacteristic
417#106—21no—
418#106—21no—
419#106—21no—
420#106D4×C2911yescharacteristic
421C4⋊C8—21no—
422C4⋊C8C23×C2911yescharacteristic
423C4⋊C8C23×C2911yescharacteristic
424C4⋊C8C23×C2911yescharacteristic
425C4⋊C8C23×C2911yescharacteristic
426#103—21no—
427#103—21no—
428#103—21no—
429#103—21no—
430#103—21no—
431#103—41no—
432#103D4×C2911yescharacteristic
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—41no—
441#102D4×C2911yescharacteristic
442#102D4×C2911yescharacteristic
443#102D4×C2911yescharacteristic
444C22⋊C8—21no—
445C22⋊C8—21no—
446C22⋊C8—21no—
447#97—21no—
448C4×C8C23×C2911yescharacteristic
449C4×C8C23×C2911yescharacteristic
450C4×C8C23×C2911yescharacteristic
451C29#1991011yescharacteristic, direct product factor, Sylow
452C24—41no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—41no—
457C2×Q8—42no—
458C2×Q8—81no—
459C2×Q8C2×D4×C2911yescharacteristic
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—41no—
468C2×D4—81no—
469C2×D4—81no—
470C2×D4C2×D4×C2911yescharacteristic
471C2×D4C2×D4×C2911yescharacteristic
472C2×D4C2×D4×C2911yescharacteristic
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—41no—
477SD16—22no—
478SD16—42no—
479SD16—42no—
480SD16—42no—
481SD16—42no—
482SD16—81no—
483D8—22no—
484D8—81no—
485M16—81no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—42no—
492C2×C8—42no—
493C2×C8C2×D4×C2911yescharacteristic
494C2×C8C2×D4×C2911yescharacteristic
495C2×C8C2×D4×C2911yescharacteristic
496C2×C8C2×D4×C2911yescharacteristic
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4C2×D4×C2911yescharacteristic
507C4⋊C4C2×D4×C2911yescharacteristic
508C4⋊C4C2×D4×C2911yescharacteristic
509C4⋊C4C2×D4×C2911yescharacteristic
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C42—21no—
520C42—41no—
521C42—41no—
522C42C24×C2911yescharacteristic
523C23—21no—
524C23—21no—
525C23—21no—
526C23—41no—
527C23—82no—
528C23—82no—
529C23—161no—
530Q8—21no—
531Q8—21no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—81no—
537Q8—82no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—81no—
548D4—82no—
549D4—82no—
550D4—161no—
551D4C29×#13512yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—82no—
567C2×C4C22×D4×C2911yescharacteristic
568C2×C4C22×D4×C2911yescharacteristic
569C2×C4C29×H(5,𝔽2)11yescharacteristic
570C8—21no—
571C8—21no—
572C8—21no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8C29×AGL(1,ℤ/8)12yes—
579C22—22no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—164no—
592C22D42×C2911yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4C2×C29×#13511yescharacteristic
603C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
604C4C29×#57711yescharacteristic
605C4C29×#57711yescharacteristic
606C2—42no—
607C2—81no—
608C2—81no—
609C2—161no—
610C2C29×#327211yescharacteristic
611C2C29×#328211yescharacteristic
612C2C29×#329011yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3325C2
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
2. C29×#3340C2semidirect
4. D4×SD16×C29C2semidirect
5. C29×#1708C2semidirect
6. C29×#1699C2semidirect
7. C29×#1698C2semidirect
8. C29×#1671C2semidirect
9. C29×#1665C2semidirect
10. C29×#1646C2semidirect
11. C29×#1639C2semidirect
12. C29×#1637C2semidirect
13. C29×#1628C2semidirect
14. C29×#1590C2semidirect
15. C8×D8×C29C2semidirect
17. C29×#556C22semidirect
21. C29×#498C22semidirect
24. C29×#487C22semidirect
25. C29×#487C22semidirect
32. C29×#477C22semidirect
35. C29×#474C22semidirect
47. C29×#446C22semidirect
53. C8×D4×C29C22semidirect
56. C29×#335C22semidirect
57. C29×#334C22semidirect
58. C29×#333C22semidirect
59. C29×#332C22semidirect
60. C29×#332C22semidirect
62. C29×Q8⋊C8C22semidirect
65. C29×D4⋊C8C22semidirect
66. C82×C29C22semidirect
216. #19910C29direct (N × H)
273. #3367C2×C29semidirect
274. #3340C2×C29semidirect
276. D4×SD16C2×C29semidirect
277. #1708C2×C29semidirect
278. #1699C2×C29semidirect
279. #1698C2×C29semidirect
280. #1671C2×C29semidirect
281. #1665C2×C29semidirect
282. #1646C2×C29semidirect
283. #1639C2×C29semidirect
284. #1637C2×C29semidirect
285. #1628C2×C29semidirect
286. #1590C2×C29semidirect
287. C8×D8C2×C29semidirect
316. #556C22×C29semidirect
320. #498C22×C29semidirect
323. #487C22×C29semidirect
324. #487C22×C29semidirect
331. #477C22×C29semidirect
334. #474C22×C29semidirect
346. #446C22×C29semidirect
352. C8×D4C22×C29semidirect
355. #335C22×C29semidirect
356. #334C22×C29semidirect
357. #333C22×C29semidirect
358. #332C22×C29semidirect
359. #332C22×C29semidirect
361. Q8⋊C8C22×C29semidirect
364. D4⋊C8C22×C29semidirect
365. C82C22×C29semidirect
451. C29#19910direct (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×#33402
C29×#33252
D4×SD16×C292
C29×#17082
C29×#16992
C29×#16982
C29×#16712
C29×#16652
C29×#16462
C29×#16392
C29×#16372
C29×#16282
C29×#15902
C8×D8×C292
#1991029