Finite Group Databasebeta

← C29×#18968 #20313868

Subgroups — C29×#18968 #20313868

Order 7424.

874 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3547C211yesmaximal, characteristic
2C29×#3239C211yesmaximal, characteristic, complemented
3C29×#3229C211yesmaximal, characteristic, complemented
4C29×#3206C211yesmaximal, characteristic, complemented
5C29×#1654C212yesmaximal, complemented
6C29×#1651C212yesmaximal, complemented
7C29×#1646C212yesmaximal, complemented
8C29×#1643C212yesmaximal, complemented
9C29×#1554C211yesmaximal, characteristic, complemented
10C29×#1496C211yesmaximal, characteristic, complemented
11C29×#1482C211yesmaximal, characteristic, complemented
12C29×#562—22no—
13C29×#555—21no—
14C29×#555C2211yescharacteristic
15C29×#554C2211yescharacteristic
16C29×#553—21no—
17C29×#552—21no—
18D4×Q8×C29C2211yescharacteristic
19C29×#548—21no—
20C29×#547C2211yescharacteristic
21C29×#544—21no—
22C29×#542—22no—
23C29×#540—21no—
24C29×#537—21no—
25C29×#536—21no—
26C29×#533C2211yescharacteristic
27C29×#532C2211yescharacteristic
28C2×C29×C4⋊Q8C2211yescharacteristic
29C29×#529C2211yescharacteristic
30C29×#501—21no—
31C29×#498C2212yes—
32C29×#492—21no—
33C29×#489—21no—
34C29×#487—21no—
35C29×#487C2212yes—
36C29×#484—21no—
37C29×#483—22no—
38C29×#481—21no—
39C29×#475—22no—
40C29×#475C2212yes—
41C29×#474C2212yes—
42C29×#461C2212yes—
43C29×#461C2212yes—
44C29×#448—21no—
45C29×#448—21no—
46C29×#432C2211yescharacteristic
47C29×#431C2211yescharacteristic
48C29×#431C2211yescharacteristic
49C29×#333C2212yes—
50C29×#332C2212yes—
51C29×Q8⋊C8C2212yes—
52C29×D4⋊C8C2212yes—
53C29×D4⋊C8C2212yes—
54C29×D4⋊C8C2212yes—
55C2×#41×C29—21no—
56C2×#41×C29—21no—
57C22×Q8×C29—21no—
58C22×Q8×C29—21no—
59C2×SD16×C29—22no—
60C2×SD16×C29—22no—
61C29×C4⋊Q8—22no—
62C29×C4⋊Q8—21no—
63C29×C4⋊Q8—21no—
64C29×C4⋊Q8—21no—
65C29×C4⋊Q8—21no—
66C29×C4⋊Q8D411yescharacteristic
67C29×C4⋊Q8C2312yes—
68C29×C4⋊Q8C2311yescharacteristic
69C29×C4⋊Q8C2311yescharacteristic
70C29×#127D411yescharacteristic
71C29×#126—22no—
72C29×#126—21no—
73C29×#125—22no—
74C29×#125—21no—
75C29×#125—21no—
76C29×#125D411yescharacteristic
77C29×#124—22no—
78C29×#124—22no—
79C29×#124—22no—
80C29×#124—21no—
81C29×#124D411yescharacteristic
82C29×#123—22no—
83C29×#123—22no—
84C29×#123—22no—
85C29×#123—21no—
86C29×#123—22no—
87C29×C22⋊Q8—22no—
88C29×C22⋊Q8—22no—
89C29×C22⋊Q8—21no—
90C29×C22⋊Q8—22no—
91C29×C22⋊Q8—21no—
92C29×C22⋊Q8—21no—
93C29×C22⋊Q8—21no—
94C29×C22⋊Q8—22no—
95C29×C22⋊Q8D412yes—
96C29×C22⋊Q8D411yescharacteristic
97C29×#121—22no—
98C29×#121—22no—
99C29×#121—22no—
100C29×#121—22no—
101C29×#121—21no—
102C29×#121—21no—
103C29×#121—21no—
104C29×#121—21no—
105C29×#121D411yescharacteristic
106C29×#121D411yescharacteristic
107C29×#121D411yescharacteristic
108C4×Q8×C29—21no—
109C4×Q8×C29D412yes—
110C4×Q8×C29C2311yescharacteristic
111C4×D4×C29—22no—
112C4×D4×C29—21no—
113C4×D4×C29—21no—
114C4×D4×C29—21no—
115C4×D4×C29—21no—
116C4×D4×C29C2311yescharacteristic
117C4×D4×C29C2311yescharacteristic
118C4×D4×C29C2311yescharacteristic
119C29×#117—22no—
120C29×#117—21no—
121C29×#117—21no—
122C29×#117—21no—
123C29×#117—21no—
124C2×C4⋊C4×C29—21no—
125C2×C4⋊C4×C29—21no—
126C2×C4⋊C4×C29—21no—
127C2×C4⋊C4×C29—21no—
128C2×C42×C29C2311yescharacteristic
129C29×#107—22no—
130C29×#106—24no—
131C29×#106—22no—
132C29×C4⋊C8—21no—
133C29×C4⋊C8C2312yes—
134C29×C4⋊C8C2312yes—
135C29×#103—24no—
136C29×#103—22no—
137C29×#103—22no—
138C29×#103—22no—
139C29×#102—22no—
140C29×C22⋊C8—21no—
141C29×C22⋊C8—21no—
142C29×C22⋊C8—21no—
143C29×#97—21no—
144C4×C8×C29—21no—
145C4×C8×C29C2312yes—
146#41×C29—82no—
147#41×C29—82no—
148C2×Q8×C29—22no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×Q8×C29—22no—
152C2×Q8×C29—41no—
153C2×Q8×C29—82no—
154C2×Q8×C29—82no—
155C2×Q8×C29C2×D411yescharacteristic
156C2×Q8×C29C2×D412yes—
157C2×D4×C29—22no—
158C2×D4×C29—22no—
159C2×D4×C29—21no—
160C2×D4×C29—21no—
161C2×D4×C29—21no—
162C2×D4×C29—21no—
163C2×D4×C29—21no—
164C2×D4×C29C2×D411yescharacteristic
165C2×D4×C29C2×D411yescharacteristic
166C2×D4×C29C2×D411yescharacteristic
167C22×C4×C29—22no—
168C22×C4×C29—22no—
169C22×C4×C29—22no—
170C22×C4×C29—21no—
171C22×C4×C29—21no—
172C22×C4×C29—21no—
173C22×C4×C29—41no—
174C22×C4×C29C2×D411yescharacteristic
175C22×C4×C29C2×D411yescharacteristic
176C22×C4×C29C2×D411yescharacteristic
177SD16×C29—82no—
178SD16×C29—82no—
179C2×C8×C29—22no—
180C2×C8×C29—22no—
181C2×C8×C29—22no—
182C4⋊C4×C29—22no—
183C4⋊C4×C29—22no—
184C4⋊C4×C29—22no—
185C4⋊C4×C29—22no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—22no—
191C4⋊C4×C29—22no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—21no—
194C4⋊C4×C29—21no—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—22no—
197C4⋊C4×C29—22no—
198C4⋊C4×C29—41no—
199C4⋊C4×C29—41no—
200C4⋊C4×C29C2×D411yescharacteristic
201C4⋊C4×C29C2×D411yescharacteristic
202C4⋊C4×C29C2×D411yescharacteristic
203C4⋊C4×C29C2×D411yescharacteristic
204C4⋊C4×C29C2×D412yes—
205C22⋊C4×C29—22no—
206C22⋊C4×C29—22no—
207C22⋊C4×C29—22no—
208C22⋊C4×C29—22no—
209C22⋊C4×C29—22no—
210C22⋊C4×C29—22no—
211C22⋊C4×C29—21no—
212C22⋊C4×C29—21no—
213C22⋊C4×C29—21no—
214C22⋊C4×C29—21no—
215C22⋊C4×C29—21no—
216C22⋊C4×C29—21no—
217C22⋊C4×C29—21no—
218C22⋊C4×C29—21no—
219C22⋊C4×C29—21no—
220C42×C29—22no—
221C42×C29—22no—
222C42×C29—21no—
223C42×C29C2×D411yescharacteristic
224C42×C29C2×D411yescharacteristic
225C42×C29C2×D411yescharacteristic
226C42×C29C2411yescharacteristic
227#18968C2911yesmaximal, characteristic, direct product factor, Sylow
228C23×C29—21no—
229C23×C29—21no—
230C23×C29—21no—
231C23×C29#12011yescharacteristic
232Q8×C29—22no—
233Q8×C29—42no—
234Q8×C29—42no—
235Q8×C29—42no—
236Q8×C29—42no—
237Q8×C29—81no—
238Q8×C29—82no—
239Q8×C29—82no—
240D4×C29—22no—
241D4×C29—22no—
242D4×C29—22no—
243D4×C29—81no—
244D4×C29—81no—
245D4×C29—81no—
246D4×C29—81no—
247D4×C29—81no—
248D4×C29—82no—
249D4×C29—82no—
250C2×C4×C29—22no—
251C2×C4×C29—22no—
252C2×C4×C29—21no—
253C2×C4×C29—22no—
254C2×C4×C29—21no—
255C2×C4×C29—21no—
256C2×C4×C29—21no—
257C2×C4×C29—22no—
258C2×C4×C29—21no—
259C2×C4×C29—41no—
260C2×C4×C29—42no—
261C2×C4×C29—42no—
262C2×C4×C29—42no—
263C2×C4×C29—42no—
264C2×C4×C29—82no—
265C2×C4×C29—82no—
266C2×C4×C29—82no—
267C2×C4×C29—82no—
268C2×C4×C29#12011yescharacteristic
269C2×C4×C29#12011yescharacteristic
270C2×C4×C29#12011yescharacteristic
271C2×C4×C29C22×D411yescharacteristic
272C2×C4×C29C22×D411yescharacteristic
273C2×C4×C29C22×D411yescharacteristic
274C8×C29—42no—
275C8×C29—42no—
276C8×C29—42no—
277#3547C2×C2911yescharacteristic
278#3239C2×C2911yescharacteristic, complemented
279#3229C2×C2911yescharacteristic, complemented
280#3206C2×C2911yescharacteristic, complemented
281#1654C2×C2912yescomplemented
282#1651C2×C2912yescomplemented
283#1646C2×C2912yescomplemented
284#1643C2×C2912yescomplemented
285#1554C2×C2911yescharacteristic, complemented
286#1496C2×C2911yescharacteristic, complemented
287#1482C2×C2911yescharacteristic, complemented
288C22×C29—21no—
289C22×C29—21no—
290C22×C29—21no—
291C22×C29—41no—
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×C29C2×#12011yescharacteristic
301C4×C29—21no—
302C4×C29—21no—
303C4×C29—21no—
304C4×C29—21no—
305C4×C29—41no—
306C4×C29—41no—
307C4×C29—42no—
308C4×C29—41no—
309C4×C29—41no—
310C4×C29—41no—
311C4×C29—42no—
312C4×C29—82no—
313C4×C29#57712yes—
314C4×C29#57712yes—
315#562—22no—
316#555—21no—
317#555C22×C2911yescharacteristic
318#554C22×C2911yescharacteristic
319#553—21no—
320#552—21no—
321D4×Q8C22×C2911yescharacteristic
322#548—21no—
323#547C22×C2911yescharacteristic
324#544—21no—
325#542—22no—
326#540—21no—
327#537—21no—
328#536—21no—
329#533C22×C2911yescharacteristic
330#532C22×C2911yescharacteristic
331C2×C4⋊Q8C22×C2911yescharacteristic
332#529C22×C2911yescharacteristic
333#501—21no—
334#498C22×C2912yes—
335#492—21no—
336#489—21no—
337#487—21no—
338#487C22×C2912yes—
339#484—21no—
340#483—22no—
341#481—21no—
342#475—22no—
343#475C22×C2912yes—
344#474C22×C2912yes—
345#461C22×C2912yes—
346#461C22×C2912yes—
347#448—21no—
348#448—21no—
349#432C22×C2911yescharacteristic
350#431C22×C2911yescharacteristic
351#431C22×C2911yescharacteristic
352#333C22×C2912yes—
353#332C22×C2912yes—
354Q8⋊C8C22×C2912yes—
355D4⋊C8C22×C2912yes—
356D4⋊C8C22×C2912yes—
357D4⋊C8C22×C2912yes—
358C2×C29—41no—
359C2×C29—81no—
360C2×C29—81no—
361C2×C29—81no—
362C2×C29#300911yescharacteristic
363C2×C29#301011yescharacteristic
364C2×C29#302211yescharacteristic
365C2×#41—21no—
366C2×#41—21no—
367C22×Q8—21no—
368C22×Q8—21no—
369C2×SD16—22no—
370C2×SD16—22no—
371C4⋊Q8—22no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376C4⋊Q8D4×C2911yescharacteristic
377C4⋊Q8C23×C2912yes—
378C4⋊Q8C23×C2911yescharacteristic
379C4⋊Q8C23×C2911yescharacteristic
380#127D4×C2911yescharacteristic
381#126—22no—
382#126—21no—
383#125—22no—
384#125—21no—
385#125—21no—
386#125D4×C2911yescharacteristic
387#124—22no—
388#124—22no—
389#124—22no—
390#124—21no—
391#124D4×C2911yescharacteristic
392#123—22no—
393#123—22no—
394#123—22no—
395#123—21no—
396#123—22no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—21no—
400C22⋊Q8—22no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8—22no—
405C22⋊Q8D4×C2911yescharacteristic
406C22⋊Q8D4×C2912yes—
407#121—22no—
408#121—22no—
409#121—22no—
410#121—22no—
411#121—21no—
412#121—21no—
413#121—21no—
414#121—21no—
415#121D4×C2911yescharacteristic
416#121D4×C2911yescharacteristic
417#121D4×C2911yescharacteristic
418C4×Q8—21no—
419C4×Q8D4×C2912yes—
420C4×Q8C23×C2911yescharacteristic
421C4×D4—22no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4C23×C2911yescharacteristic
427C4×D4C23×C2911yescharacteristic
428C4×D4C23×C2911yescharacteristic
429#117—22no—
430#117—21no—
431#117—21no—
432#117—21no—
433#117—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C42C23×C2911yescharacteristic
439#107—22no—
440#106—24no—
441#106—22no—
442C4⋊C8—21no—
443C4⋊C8C23×C2912yes—
444C4⋊C8C23×C2912yes—
445#103—24no—
446#103—22no—
447#103—22no—
448#103—22no—
449#102—22no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452C22⋊C8—21no—
453#97—21no—
454C4×C8—21no—
455C4×C8C23×C2912yes—
456C29#1896811yescharacteristic, direct product factor, Sylow
457#41—82no—
458#41—82no—
459C2×Q8—22no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—22no—
463C2×Q8—41no—
464C2×Q8—82no—
465C2×Q8—82no—
466C2×Q8C2×D4×C2911yescharacteristic
467C2×Q8C2×D4×C2912yes—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4C2×D4×C2911yescharacteristic
476C2×D4C2×D4×C2911yescharacteristic
477C2×D4C2×D4×C2911yescharacteristic
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485C22×C4C2×D4×C2911yescharacteristic
486C22×C4C2×D4×C2911yescharacteristic
487C22×C4C2×D4×C2911yescharacteristic
488SD16—82no—
489SD16—82no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4C2×D4×C2911yescharacteristic
512C4⋊C4C2×D4×C2911yescharacteristic
513C4⋊C4C2×D4×C2911yescharacteristic
514C4⋊C4C2×D4×C2912yes—
515C4⋊C4C2×D4×C2911yescharacteristic
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C42—22no—
532C42—22no—
533C42—21no—
534C42C2×D4×C2911yescharacteristic
535C42C2×D4×C2911yescharacteristic
536C42C2×D4×C2911yescharacteristic
537C42C24×C2911yescharacteristic
538C23—21no—
539C23—21no—
540C23—21no—
541C23C29×#12011yescharacteristic
542Q8—22no—
543Q8—42no—
544Q8—42no—
545Q8—42no—
546Q8—42no—
547Q8—81no—
548Q8—82no—
549Q8—82no—
550D4—22no—
551D4—22no—
552D4—22no—
553D4—81no—
554D4—81no—
555D4—81no—
556D4—81no—
557D4—81no—
558D4—82no—
559D4—82no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—82no—
575C2×C4—82no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4C29×#12011yescharacteristic
579C2×C4C29×#12011yescharacteristic
580C2×C4C29×#12011yescharacteristic
581C2×C4C22×D4×C2911yescharacteristic
582C2×C4C22×D4×C2911yescharacteristic
583C2×C4C22×D4×C2911yescharacteristic
584C8—42no—
585C8—42no—
586C8—42no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22C2×C29×#12011yescharacteristic
600C4—21no—
601C4—21no—
602C4—21no—
603C4—21no—
604C4—41no—
605C4—41no—
606C4—42no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—42no—
611C4—82no—
612C4C29×#57712yes—
613C4C29×#57712yes—
614C2—41no—
615C2—81no—
616C2—81no—
617C2—81no—
618C2C29×#300911yescharacteristic
619C2C29×#301011yescharacteristic
620C2C29×#302211yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3547C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C29×#3239C2semidirect
3. C29×#3229C2semidirect
4. C29×#3206C2semidirect
5. C29×#1654C2semidirect
6. C29×#1651C2semidirect
7. C29×#1646C2semidirect
8. C29×#1643C2semidirect
9. C29×#1554C2semidirect
10. C29×#1496C2semidirect
11. C29×#1482C2semidirect
227. #18968C29direct (N × H)
278. #3239C2×C29semidirect
279. #3229C2×C29semidirect
280. #3206C2×C29semidirect
281. #1654C2×C29semidirect
282. #1651C2×C29semidirect
283. #1646C2×C29semidirect
284. #1643C2×C29semidirect
285. #1554C2×C29semidirect
286. #1496C2×C29semidirect
287. #1482C2×C29semidirect
456. C29#18968direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35472
C29×#32392
C29×#32292
C29×#32062
C29×#16542
C29×#16512
C29×#16462
C29×#16432
C29×#15542
C29×#14962
C29×#14822
#1896829