Finite Group Databasebeta

← C29×#19922 #20314822

Subgroups — C29×#19922 #20314822

Order 7424.

674 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3392C211yesmaximal, characteristic, complemented
2C29×#3368C211yesmaximal, characteristic, complemented
3C29×#3332C211yesmaximal, characteristic, complemented
4C29×#3284C211yesmaximal, characteristic, complemented
5C29×#1706C211yesmaximal, characteristic, complemented
6C29×#1702C211yesmaximal, characteristic, complemented
7C29×#1701C211yesmaximal, characteristic, complemented
8C29×#1666C211yesmaximal, characteristic, complemented
9C29×#1665C211yesmaximal, characteristic, complemented
10C29×#1648C211yesmaximal, characteristic, complemented
11C29×#1647C211yesmaximal, characteristic, complemented
12C29×#1621C211yesmaximal, characteristic, complemented
13C29×#1621C211yesmaximal, characteristic, complemented
14C29×#1590C211yesmaximal, characteristic, complemented
15C8×SD16×C29C211yesmaximal, characteristic, complemented
16C2×C29×#135—21no—
17C29×#557C2211yescharacteristic
18C29×#550C2211yescharacteristic
19C29×#550C2211yescharacteristic
20C29×#547C2211yescharacteristic
21C29×#500C2211yescharacteristic
22C29×#493C2211yescharacteristic
23C29×#492—21no—
24C29×#492C2211yescharacteristic
25C29×#492C2211yescharacteristic
26C29×#490—21no—
27C29×#486C2211yescharacteristic
28C29×#486C2211yescharacteristic
29C29×#481—21no—
30C29×#478—21no—
31C29×#475C2211yescharacteristic
32C29×#474C2211yescharacteristic
33C29×#469—21no—
34C29×#465—21no—
35C29×#462C2211yescharacteristic
36C29×#461—21no—
37C29×#461C2211yescharacteristic
38C29×#460—21no—
39C29×#460—21no—
40C29×#460C2211yescharacteristic
41C29×#460C2211yescharacteristic
42C29×#459C2211yescharacteristic
43C29×#459C2211yescharacteristic
44C29×#452—21no—
45C29×#449—21no—
46C29×#449—21no—
47C29×#446C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C29×#440—21no—
50C4×SD16×C29—21no—
51C4×SD16×C29C2211yescharacteristic
52C4×SD16×C29C2211yescharacteristic
53C29×#436C2211yescharacteristic
54C8×D4×C29C2211yescharacteristic
55C29×#417—21no—
56C29×#334C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#332C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#331C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C82×C29C2211yescharacteristic
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C2×#41×C29—21no—
70C29×#135—44no—
71C2×Q16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×SD16×C29—21no—
75C2×SD16×C29—21no—
76C2×SD16×C29—21no—
77C2×SD16×C29—21no—
78C2×SD16×C29—21no—
79C2×SD16×C29D411yescharacteristic
80C2×SD16×C29D411yescharacteristic
81C2×D8×C29—21no—
82C2×D8×C29—21no—
83C2×D8×C29—41no—
84C2×M16×C29—21no—
85C22×C8×C29—21no—
86C29×C4⋊Q8—21no—
87C29×C4⋊Q8C2311yescharacteristic
88C29×C4⋊Q8C2311yescharacteristic
89C29×#127—21no—
90C29×#127—21no—
91C29×#127C2311yescharacteristic
92C29×#127C2311yescharacteristic
93C29×#125—21no—
94C29×#125—41no—
95C29×#123—41no—
96C29×C22⋊Q8—21no—
97C29×#121—21no—
98C29×#121—21no—
99C29×#121—21no—
100C29×#121—41no—
101C29×#121—41no—
102C4×Q8×C29—21no—
103C4×Q8×C29—21no—
104C4×Q8×C29C2311yescharacteristic
105C4×Q8×C29C2311yescharacteristic
106C4×D4×C29—21no—
107C4×D4×C29—21no—
108C4×D4×C29C2311yescharacteristic
109C4×D4×C29C2311yescharacteristic
110C2×C4⋊C4×C29—21no—
111C29×#107—21no—
112C29×#107—41no—
113C29×#106—21no—
114C29×#106D411yescharacteristic
115C29×#106D411yescharacteristic
116C29×C4⋊C8—21no—
117C29×C4⋊C8—21no—
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×C4⋊C8C2311yescharacteristic
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103D411yescharacteristic
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—21no—
135C29×#102—21no—
136C29×#102D411yescharacteristic
137C29×#102D411yescharacteristic
138C29×C22⋊C8—21no—
139C29×C22⋊C8—21no—
140C29×#97—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—42no—
148#41×C29—81no—
149#41×C29—81no—
150#41×C29—81no—
151C2×Q8×C29—21no—
152C2×Q8×C29—21no—
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×C29—41no—
166C2×D4×C29C2×D411yescharacteristic
167C2×D4×C29C2×D411yescharacteristic
168C22×C4×C29—21no—
169C22×C4×C29—21no—
170C22×C4×C29—41no—
171C22×C4×C29—41no—
172C22×C4×C29—41no—
173Q16×C29—42no—
174SD16×C29—22no—
175SD16×C29—22no—
176SD16×C29—42no—
177SD16×C29—42no—
178SD16×C29—42no—
179SD16×C29—81no—
180SD16×C29—81no—
181SD16×C29—81no—
182SD16×C29—81no—
183D8×C29—42no—
184D8×C29—82no—
185D8×C29—81no—
186M16×C29—81no—
187C2×C8×C29—21no—
188C2×C8×C29—21no—
189C2×C8×C29—21no—
190C2×C8×C29—21no—
191C2×C8×C29—21no—
192C2×C8×C29—42no—
193C2×C8×C29C2×D411yescharacteristic
194C2×C8×C29C2×D411yescharacteristic
195C2×C8×C29C2×D411yescharacteristic
196C2×C8×C29C2×D411yescharacteristic
197C4⋊C4×C29—21no—
198C4⋊C4×C29—21no—
199C4⋊C4×C29—21no—
200C4⋊C4×C29—21no—
201C4⋊C4×C29—21no—
202C4⋊C4×C29—21no—
203C4⋊C4×C29—41no—
204C4⋊C4×C29—41no—
205C4⋊C4×C29—41no—
206C4⋊C4×C29—41no—
207C4⋊C4×C29C2×D411yescharacteristic
208C4⋊C4×C29C2×D411yescharacteristic
209C4⋊C4×C29C2×D411yescharacteristic
210C4⋊C4×C29C2×D411yescharacteristic
211C22⋊C4×C29—21no—
212C22⋊C4×C29—21no—
213C22⋊C4×C29—41no—
214C22⋊C4×C29—41no—
215C22⋊C4×C29—41no—
216C42×C29—21no—
217C42×C29—21no—
218C42×C29—41no—
219C42×C29C2411yescharacteristic
220#19922C2911yesmaximal, characteristic, direct product factor, Sylow
221C23×C29—21no—
222C23×C29—21no—
223C23×C29—41no—
224C23×C29—41no—
225Q8×C29—21no—
226Q8×C29—21no—
227Q8×C29—21no—
228Q8×C29—41no—
229Q8×C29—41no—
230Q8×C29—41no—
231Q8×C29—41no—
232Q8×C29#13512yescomplemented
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—41no—
242D4×C29—41no—
243D4×C29—41no—
244D4×C29—41no—
245D4×C29—82no—
246D4×C29—81no—
247D4×C29—81no—
248D4×C29—82no—
249D4×C29—82no—
250D4×C29—161no—
251D4×C29—161no—
252C2×C4×C29—21no—
253C2×C4×C29—21no—
254C2×C4×C29—21no—
255C2×C4×C29—21no—
256C2×C4×C29—21no—
257C2×C4×C29—21no—
258C2×C4×C29—41no—
259C2×C4×C29—41no—
260C2×C4×C29—41no—
261C2×C4×C29—41no—
262C2×C4×C29—41no—
263C2×C4×C29—41no—
264C2×C4×C29—82no—
265C2×C4×C29—82no—
266C2×C4×C29—82no—
267C2×C4×C29C22×D411yescharacteristic
268C2×C4×C29C22×D411yescharacteristic
269C2×C4×C29H(5,𝔽2)11yescharacteristic
270C8×C29—22no—
271C8×C29—21no—
272C8×C29—21no—
273C8×C29—21no—
274C8×C29—41no—
275C8×C29—41no—
276C8×C29—41no—
277C8×C29—41no—
278C8×C29AGL(1,ℤ/8)12yes—
279#3392C2×C2911yescharacteristic, complemented
280#3368C2×C2911yescharacteristic, complemented
281#3332C2×C2911yescharacteristic, complemented
282#3284C2×C2911yescharacteristic, complemented
283#1706C2×C2911yescharacteristic, complemented
284#1702C2×C2911yescharacteristic, complemented
285#1701C2×C2911yescharacteristic, complemented
286#1666C2×C2911yescharacteristic, complemented
287#1665C2×C2911yescharacteristic, complemented
288#1648C2×C2911yescharacteristic, complemented
289#1647C2×C2911yescharacteristic, complemented
290#1621C2×C2911yescharacteristic, complemented
291#1621C2×C2911yescharacteristic, complemented
292#1590C2×C2911yescharacteristic, complemented
293C8×SD16C2×C2911yescharacteristic, complemented
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×C29D4211yescharacteristic
307C4×C29—22no—
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×C29C2×AGL(1,ℤ/8)11yescharacteristic
318C4×C29#57611yescharacteristic
319C4×C29#57711yescharacteristic
320C2×#135—21no—
321#557C22×C2911yescharacteristic
322#550C22×C2911yescharacteristic
323#550C22×C2911yescharacteristic
324#547C22×C2911yescharacteristic
325#500C22×C2911yescharacteristic
326#493C22×C2911yescharacteristic
327#492—21no—
328#492C22×C2911yescharacteristic
329#492C22×C2911yescharacteristic
330#490—21no—
331#486C22×C2911yescharacteristic
332#486C22×C2911yescharacteristic
333#481—21no—
334#478—21no—
335#475C22×C2911yescharacteristic
336#474C22×C2911yescharacteristic
337#469—21no—
338#465—21no—
339#462C22×C2911yescharacteristic
340#461—21no—
341#461C22×C2911yescharacteristic
342#460—21no—
343#460—21no—
344#460C22×C2911yescharacteristic
345#460C22×C2911yescharacteristic
346#459C22×C2911yescharacteristic
347#459C22×C2911yescharacteristic
348#452—21no—
349#449—21no—
350#449—21no—
351#446C22×C2911yescharacteristic
352C8×Q8C22×C2911yescharacteristic
353#440—21no—
354C4×SD16—21no—
355C4×SD16C22×C2911yescharacteristic
356C4×SD16C22×C2911yescharacteristic
357#436C22×C2911yescharacteristic
358C8×D4C22×C2911yescharacteristic
359#417—21no—
360#334C22×C2911yescharacteristic
361#334C22×C2911yescharacteristic
362#332C22×C2911yescharacteristic
363#332C22×C2911yescharacteristic
364#331C22×C2911yescharacteristic
365#331C22×C2911yescharacteristic
366Q8⋊C8C22×C2911yescharacteristic
367Q8⋊C8C22×C2911yescharacteristic
368D4⋊C8C22×C2911yescharacteristic
369D4⋊C8C22×C2911yescharacteristic
370C82C22×C2911yescharacteristic
371C2×C29—81no—
372C2×C29—81no—
373C2×C29—161no—
374C2×C29—161no—
375C2×C29#327411yescharacteristic
376C2×C29#328211yescharacteristic
377C2×C29#329111yescharacteristic
378C2×#41—21no—
379C2×#41—21no—
380C2×#41—21no—
381#135—44no—
382C2×Q16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16—21no—
390C2×SD16D4×C2911yescharacteristic
391C2×SD16D4×C2911yescharacteristic
392C2×D8—21no—
393C2×D8—21no—
394C2×D8—41no—
395C2×M16—21no—
396C22×C8—21no—
397C4⋊Q8—21no—
398C4⋊Q8C23×C2911yescharacteristic
399C4⋊Q8C23×C2911yescharacteristic
400#127—21no—
401#127—21no—
402#127C23×C2911yescharacteristic
403#127C23×C2911yescharacteristic
404#125—21no—
405#125—41no—
406#123—41no—
407C22⋊Q8—21no—
408#121—21no—
409#121—21no—
410#121—21no—
411#121—41no—
412#121—41no—
413C4×Q8—21no—
414C4×Q8—21no—
415C4×Q8C23×C2911yescharacteristic
416C4×Q8C23×C2911yescharacteristic
417C4×D4—21no—
418C4×D4—21no—
419C4×D4C23×C2911yescharacteristic
420C4×D4C23×C2911yescharacteristic
421C2×C4⋊C4—21no—
422#107—21no—
423#107—41no—
424#106—21no—
425#106D4×C2911yescharacteristic
426#106D4×C2911yescharacteristic
427C4⋊C8—21no—
428C4⋊C8—21no—
429C4⋊C8C23×C2911yescharacteristic
430C4⋊C8C23×C2911yescharacteristic
431C4⋊C8C23×C2911yescharacteristic
432C4⋊C8C23×C2911yescharacteristic
433#103—21no—
434#103—21no—
435#103—21no—
436#103D4×C2911yescharacteristic
437#103D4×C2911yescharacteristic
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#102—21no—
447#102D4×C2911yescharacteristic
448#102D4×C2911yescharacteristic
449C22⋊C8—21no—
450C22⋊C8—21no—
451#97—21no—
452C4×C8—21no—
453C4×C8C23×C2911yescharacteristic
454C4×C8C23×C2911yescharacteristic
455C4×C8C23×C2911yescharacteristic
456C29#1992211yescharacteristic, direct product factor, Sylow
457#41—42no—
458#41—42no—
459#41—42no—
460#41—81no—
461#41—81no—
462#41—81no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8C2×D4×C2911yescharacteristic
466C2×Q8C2×D4×C2911yescharacteristic
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4C2×D4×C2911yescharacteristic
479C2×D4C2×D4×C2911yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485Q16—42no—
486SD16—22no—
487SD16—22no—
488SD16—42no—
489SD16—42no—
490SD16—42no—
491SD16—81no—
492SD16—81no—
493SD16—81no—
494SD16—81no—
495D8—42no—
496D8—82no—
497D8—81no—
498M16—81no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—42no—
505C2×C8C2×D4×C2911yescharacteristic
506C2×C8C2×D4×C2911yescharacteristic
507C2×C8C2×D4×C2911yescharacteristic
508C2×C8C2×D4×C2911yescharacteristic
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4C2×D4×C2911yescharacteristic
520C4⋊C4C2×D4×C2911yescharacteristic
521C4⋊C4C2×D4×C2911yescharacteristic
522C4⋊C4C2×D4×C2911yescharacteristic
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C42—21no—
529C42—21no—
530C42—41no—
531C42C24×C2911yescharacteristic
532C23—21no—
533C23—21no—
534C23—41no—
535C23—41no—
536Q8—21no—
537Q8—21no—
538Q8—21no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543Q8C29×#13512yescomplemented
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—82no—
557D4—81no—
558D4—81no—
559D4—82no—
560D4—82no—
561D4—161no—
562D4—161no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—82no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4C22×D4×C2911yescharacteristic
579C2×C4C22×D4×C2911yescharacteristic
580C2×C4C29×H(5,𝔽2)11yescharacteristic
581C8—22no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8C29×AGL(1,ℤ/8)12yes—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22D42×C2911yescharacteristic
603C4—22no—
604C4—21no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—81no—
612C4C2×C29×#13511yescharacteristic
613C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
614C4C29×#57611yescharacteristic
615C4C29×#57711yescharacteristic
616C2—81no—
617C2—81no—
618C2—161no—
619C2—161no—
620C2C29×#327411yescharacteristic
621C2C29×#328211yescharacteristic
622C2C29×#329111yescharacteristic
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×#3392C2semidirect
2. C29×#3368C2semidirect
3. C29×#3332C2semidirect
4. C29×#3284C2semidirect
5. C29×#1706C2semidirect
6. C29×#1702C2semidirect
7. C29×#1701C2semidirect
8. C29×#1666C2semidirect
9. C29×#1665C2semidirect
10. C29×#1648C2semidirect
11. C29×#1647C2semidirect
12. C29×#1621C2semidirect
13. C29×#1621C2semidirect
14. C29×#1590C2semidirect
15. C8×SD16×C29C2semidirect
220. #19922C29direct (N × H)
232. Q8×C29#135semidirect
279. #3392C2×C29semidirect
280. #3368C2×C29semidirect
281. #3332C2×C29semidirect
282. #3284C2×C29semidirect
283. #1706C2×C29semidirect
284. #1702C2×C29semidirect
285. #1701C2×C29semidirect
286. #1666C2×C29semidirect
287. #1665C2×C29semidirect
288. #1648C2×C29semidirect
289. #1647C2×C29semidirect
290. #1621C2×C29semidirect
291. #1621C2×C29semidirect
292. #1590C2×C29semidirect
293. C8×SD16C2×C29semidirect
456. C29#19922direct (N × H)
543. Q8C29×#135semidirect

Maximal subgroups

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

subgroupindex
C29×#33922
C29×#33682
C29×#33322
C29×#32842
C29×#17062
C29×#17022
C29×#17012
C29×#16662
C29×#16652
C29×#16482
C29×#16472
C29×#16212
C29×#15902
C8×SD16×C292
#1992229