Finite Group Databasebeta

← C29×#18853 #20313753

Subgroups — C29×#18853 #20313753

Order 7424.

874 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3518C211yesmaximal, characteristic
2C29×#3238C211yesmaximal, characteristic, complemented
3C29×#3209C211yesmaximal, characteristic, complemented
4C29×#3079C211yesmaximal, characteristic, complemented
5C29×#1638C212yesmaximal, complemented
6C29×#1637C212yesmaximal, complemented
7C29×#1634C212yesmaximal, complemented
8C29×#1633C212yesmaximal, complemented
9C29×#1559C211yesmaximal, characteristic, complemented
10C29×#1495C211yesmaximal, characteristic, complemented
11C29×#1488C211yesmaximal, characteristic, complemented
12Q82×C29C2211yescharacteristic
13C29×#556—21no—
14C29×#556—22no—
15C29×#556—21no—
16C29×#556C2211yescharacteristic
17C29×#555—21no—
18C29×#555C2211yescharacteristic
19D4×Q8×C29C2211yescharacteristic
20C29×#548—21no—
21C29×#542—22no—
22C29×#542—21no—
23C29×#533—21no—
24C29×#533C2211yescharacteristic
25C2×C29×C4⋊Q8C2211yescharacteristic
26C29×#529—21no—
27C29×#529C2211yescharacteristic
28C29×#519—21no—
29C4×#41×C29C2211yescharacteristic
30C29×#501—21no—
31C29×#494C2212yes—
32C29×#489—21no—
33C29×#487C2212yes—
34C29×#483—21no—
35C29×#480—21no—
36C29×#477C2212yes—
37C29×#477C2212yes—
38C29×#476C2212yes—
39C29×#476C2212yes—
40C29×#475—21no—
41C29×#474—21no—
42C29×#462—22no—
43C29×#451—22no—
44C29×#432C2211yescharacteristic
45C29×#431C2211yescharacteristic
46C29×#428—21no—
47C29×#423C2211yescharacteristic
48C29×#417—21no—
49C29×#333C2212yes—
50C29×#332C2212yes—
51C29×Q8⋊C8C2212yes—
52C29×Q8⋊C8C2212yes—
53C29×D4⋊C8C2212yes—
54C29×D4⋊C8C2212yes—
55C2×#41×C29D411yescharacteristic
56C22×Q8×C29—21no—
57C22×Q8×C29—21no—
58C2×Q16×C29—24no—
59C2×M16×C29—21no—
60C29×C4⋊Q8—22no—
61C29×C4⋊Q8—21no—
62C29×C4⋊Q8—21no—
63C29×C4⋊Q8—21no—
64C29×C4⋊Q8—21no—
65C29×C4⋊Q8—21no—
66C29×C4⋊Q8—21no—
67C29×C4⋊Q8C2312yes—
68C29×C4⋊Q8C2311yescharacteristic
69C29×C4⋊Q8C2311yescharacteristic
70C29×#126—22no—
71C29×#126—22no—
72C29×#126—22no—
73C29×#126—22no—
74C29×#126—21no—
75C29×#125—21no—
76C29×#125D411yescharacteristic
77C29×#124—22no—
78C29×#124—22no—
79C29×#124—22no—
80C29×#124—22no—
81C29×#124—21no—
82C29×#124D411yescharacteristic
83C29×#123—22no—
84C29×#123—21no—
85C29×C22⋊Q8—22no—
86C29×C22⋊Q8—22no—
87C29×C22⋊Q8—21no—
88C29×C22⋊Q8—21no—
89C29×C22⋊Q8—21no—
90C29×C22⋊Q8—22no—
91C29×C22⋊Q8D412yes—
92C29×C22⋊Q8D411yescharacteristic
93C29×#121—22no—
94C29×#121—21no—
95C29×#121—21no—
96C29×#121D411yescharacteristic
97C4×Q8×C29—22no—
98C4×Q8×C29—22no—
99C4×Q8×C29—22no—
100C4×Q8×C29—21no—
101C4×Q8×C29—21no—
102C4×Q8×C29—21no—
103C4×Q8×C29—21no—
104C4×Q8×C29D412yes—
105C4×Q8×C29D411yescharacteristic
106C4×Q8×C29C2311yescharacteristic
107C4×Q8×C29C2311yescharacteristic
108C4×D4×C29—22no—
109C4×D4×C29—21no—
110C4×D4×C29—21no—
111C4×D4×C29—21no—
112C4×D4×C29—21no—
113C4×D4×C29D411yescharacteristic
114C4×D4×C29C2311yescharacteristic
115C4×D4×C29C2311yescharacteristic
116C29×#117—22no—
117C29×#117—22no—
118C29×#117—21no—
119C29×#117—21no—
120C29×#117—21no—
121C29×#117—21no—
122C29×#117—21no—
123C29×#117—21no—
124C29×#117D411yescharacteristic
125C2×C4⋊C4×C29—21no—
126C2×C4⋊C4×C29—21no—
127C2×C42×C29—21no—
128C2×C42×C29C2311yescharacteristic
129C29×#107—22no—
130C29×#107—22no—
131C29×#106—22no—
132C29×#106—22no—
133C29×C4⋊C8—21no—
134C29×C4⋊C8—21no—
135C29×C4⋊C8C2312yes—
136C29×C4⋊C8C2312yes—
137C29×#103—22no—
138C29×#103—22no—
139C29×#103—24no—
140C29×#102—22no—
141C29×#102—22no—
142C29×C22⋊C8—21no—
143C29×C22⋊C8—21no—
144C29×#97—21no—
145C4×C8×C29C2312yes—
146#41×C29—22no—
147#41×C29—41no—
148C2×Q8×C29—22no—
149C2×Q8×C29—22no—
150C2×Q8×C29—21no—
151C2×Q8×C29—22no—
152C2×Q8×C29—42no—
153C2×Q8×C29—42no—
154C2×Q8×C29—41no—
155C2×Q8×C29—82no—
156C2×Q8×C29C2×D411yescharacteristic
157C2×Q8×C29C2×D411yescharacteristic
158C2×Q8×C29C2×D412yes—
159C2×D4×C29—21no—
160C2×D4×C29—22no—
161C2×D4×C29—21no—
162C2×D4×C29C2×D411yescharacteristic
163C2×D4×C29C2×D411yescharacteristic
164C22×C4×C29—22no—
165C22×C4×C29—21no—
166C22×C4×C29—21no—
167C22×C4×C29—21no—
168C22×C4×C29—21no—
169C22×C4×C29—41no—
170C22×C4×C29C2×D411yescharacteristic
171C22×C4×C29C2×D411yescharacteristic
172C22×C4×C29C2×D411yescharacteristic
173Q16×C29—84no—
174M16×C29—42no—
175C2×C8×C29—22no—
176C2×C8×C29—22no—
177C2×C8×C29—22no—
178C4⋊C4×C29—22no—
179C4⋊C4×C29—22no—
180C4⋊C4×C29—22no—
181C4⋊C4×C29—22no—
182C4⋊C4×C29—21no—
183C4⋊C4×C29—21no—
184C4⋊C4×C29—22no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—22no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—22no—
194C4⋊C4×C29—22no—
195C4⋊C4×C29—41no—
196C4⋊C4×C29—41no—
197C4⋊C4×C29C2×D411yescharacteristic
198C4⋊C4×C29C2×D411yescharacteristic
199C4⋊C4×C29C2×D411yescharacteristic
200C4⋊C4×C29C2×D411yescharacteristic
201C4⋊C4×C29C2×D412yes—
202C22⋊C4×C29—22no—
203C22⋊C4×C29—22no—
204C22⋊C4×C29—22no—
205C22⋊C4×C29—22no—
206C22⋊C4×C29—22no—
207C22⋊C4×C29—22no—
208C22⋊C4×C29—21no—
209C22⋊C4×C29—21no—
210C22⋊C4×C29—21no—
211C22⋊C4×C29—21no—
212C22⋊C4×C29—21no—
213C22⋊C4×C29—21no—
214C22⋊C4×C29—21no—
215C22⋊C4×C29—21no—
216C42×C29—22no—
217C42×C29—22no—
218C42×C29—22no—
219C42×C29—21no—
220C42×C29—21no—
221C42×C29—22no—
222C42×C29—21no—
223C42×C29—21no—
224C42×C29C2×D411yescharacteristic
225C42×C29C2×D411yescharacteristic
226C42×C29C2×D411yescharacteristic
227C42×C29C2411yescharacteristic
228#18853C2911yesmaximal, characteristic, direct product factor, Sylow
229C23×C29—21no—
230C23×C29—21no—
231C23×C29#12011yescharacteristic
232Q8×C29—21no—
233Q8×C29—22no—
234Q8×C29—42no—
235Q8×C29—44no—
236Q8×C29—44no—
237Q8×C29—41no—
238Q8×C29—41no—
239Q8×C29—82no—
240Q8×C29—82no—
241Q8×C29#13712yes—
242D4×C29—21no—
243D4×C29—21no—
244D4×C29—22no—
245D4×C29—42no—
246D4×C29—81no—
247D4×C29—82no—
248C2×C4×C29—21no—
249C2×C4×C29—21no—
250C2×C4×C29—21no—
251C2×C4×C29—22no—
252C2×C4×C29—21no—
253C2×C4×C29—21no—
254C2×C4×C29—22no—
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—44no—
262C2×C4×C29—41no—
263C2×C4×C29—41no—
264C2×C4×C29—42no—
265C2×C4×C29—42no—
266C2×C4×C29—81no—
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#3518C2×C2911yescharacteristic
278#3238C2×C2911yescharacteristic, complemented
279#3209C2×C2911yescharacteristic, complemented
280#3079C2×C2911yescharacteristic, complemented
281#1638C2×C2912yescomplemented
282#1637C2×C2912yescomplemented
283#1634C2×C2912yescomplemented
284#1633C2×C2912yescomplemented
285#1559C2×C2911yescharacteristic, complemented
286#1495C2×C2911yescharacteristic, complemented
287#1488C2×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×C29C2×#12011yescharacteristic
298C4×C29—21no—
299C4×C29—22no—
300C4×C29—21no—
301C4×C29—21no—
302C4×C29—21no—
303C4×C29—42no—
304C4×C29—41no—
305C4×C29—41no—
306C4×C29—41no—
307C4×C29—41no—
308C4×C29—42no—
309C4×C29—41no—
310C4×C29—82no—
311C4×C29C2×#13711yescharacteristic
312C4×C29#57511yescharacteristic
313C4×C29#57812yes—
314Q82C22×C2911yescharacteristic
315#556—21no—
316#556—22no—
317#556—21no—
318#556C22×C2911yescharacteristic
319#555—21no—
320#555C22×C2911yescharacteristic
321D4×Q8C22×C2911yescharacteristic
322#548—21no—
323#542—22no—
324#542—21no—
325#533—21no—
326#533C22×C2911yescharacteristic
327C2×C4⋊Q8C22×C2911yescharacteristic
328#529—21no—
329#529C22×C2911yescharacteristic
330#519—21no—
331C4×#41C22×C2911yescharacteristic
332#501—21no—
333#494C22×C2912yes—
334#489—21no—
335#487C22×C2912yes—
336#483—21no—
337#480—21no—
338#477C22×C2912yes—
339#477C22×C2912yes—
340#476C22×C2912yes—
341#476C22×C2912yes—
342#475—21no—
343#474—21no—
344#462—22no—
345#451—22no—
346#432C22×C2911yescharacteristic
347#431C22×C2911yescharacteristic
348#428—21no—
349#423C22×C2911yescharacteristic
350#417—21no—
351#333C22×C2912yes—
352#332C22×C2912yes—
353Q8⋊C8C22×C2912yes—
354Q8⋊C8C22×C2912yes—
355D4⋊C8C22×C2912yes—
356D4⋊C8C22×C2912yes—
357C2×C29—41no—
358C2×C29—81no—
359C2×C29—81no—
360C2×C29#300711yescharacteristic
361C2×C29#301111yescharacteristic
362C2×C29#302111yescharacteristic
363C2×#41D4×C2911yescharacteristic
364C22×Q8—21no—
365C22×Q8—21no—
366C2×Q16—24no—
367C2×M16—21no—
368C4⋊Q8—22no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8C23×C2912yes—
376C4⋊Q8C23×C2911yescharacteristic
377C4⋊Q8C23×C2911yescharacteristic
378#126—22no—
379#126—22no—
380#126—22no—
381#126—22no—
382#126—21no—
383#125—21no—
384#125D4×C2911yescharacteristic
385#124—22no—
386#124—22no—
387#124—22no—
388#124—22no—
389#124—21no—
390#124D4×C2911yescharacteristic
391#123—22no—
392#123—21no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—22no—
399C22⋊Q8D4×C2911yescharacteristic
400C22⋊Q8D4×C2912yes—
401#121—22no—
402#121—21no—
403#121—21no—
404#121D4×C2911yescharacteristic
405C4×Q8—22no—
406C4×Q8—22no—
407C4×Q8—22no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—21no—
412C4×Q8D4×C2911yescharacteristic
413C4×Q8D4×C2912yes—
414C4×Q8C23×C2911yescharacteristic
415C4×Q8C23×C2911yescharacteristic
416C4×D4—22no—
417C4×D4—21no—
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—21no—
421C4×D4D4×C2911yescharacteristic
422C4×D4C23×C2911yescharacteristic
423C4×D4C23×C2911yescharacteristic
424#117—22no—
425#117—22no—
426#117—21no—
427#117—21no—
428#117—21no—
429#117—21no—
430#117—21no—
431#117—21no—
432#117D4×C2911yescharacteristic
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C42—21no—
436C2×C42C23×C2911yescharacteristic
437#107—22no—
438#107—22no—
439#106—22no—
440#106—22no—
441C4⋊C8—21no—
442C4⋊C8—21no—
443C4⋊C8C23×C2912yes—
444C4⋊C8C23×C2912yes—
445#103—22no—
446#103—22no—
447#103—24no—
448#102—22no—
449#102—22no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452#97—21no—
453C4×C8C23×C2912yes—
454C29#1885311yescharacteristic, direct product factor, Sylow
455#41—22no—
456#41—41no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—21no—
460C2×Q8—22no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—41no—
464C2×Q8—82no—
465C2×Q8C2×D4×C2911yescharacteristic
466C2×Q8C2×D4×C2911yescharacteristic
467C2×Q8C2×D4×C2912yes—
468C2×D4—21no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4C2×D4×C2911yescharacteristic
472C2×D4C2×D4×C2911yescharacteristic
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—41no—
479C22×C4C2×D4×C2911yescharacteristic
480C22×C4C2×D4×C2911yescharacteristic
481C22×C4C2×D4×C2911yescharacteristic
482Q16—84no—
483M16—42no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—22no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4C2×D4×C2912yes—
507C4⋊C4C2×D4×C2911yescharacteristic
508C4⋊C4C2×D4×C2911yescharacteristic
509C4⋊C4C2×D4×C2911yescharacteristic
510C4⋊C4C2×D4×C2911yescharacteristic
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C42—22no—
526C42—22no—
527C42—22no—
528C42—21no—
529C42—21no—
530C42—22no—
531C42—21no—
532C42—21no—
533C42C2×D4×C2911yescharacteristic
534C42C2×D4×C2911yescharacteristic
535C42C2×D4×C2911yescharacteristic
536C42C24×C2911yescharacteristic
537C23—21no—
538C23—21no—
539C23C29×#12011yescharacteristic
540Q8—21no—
541Q8—22no—
542Q8—42no—
543Q8—44no—
544Q8—44no—
545Q8—41no—
546Q8—41no—
547Q8—82no—
548Q8—82no—
549Q8C29×#13712yes—
550D4—21no—
551D4—21no—
552D4—22no—
553D4—42no—
554D4—81no—
555D4—82no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—44no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—81no—
575C2×C4—82no—
576C2×C4C29×#12011yescharacteristic
577C2×C4C29×#12011yescharacteristic
578C2×C4C29×#12011yescharacteristic
579C2×C4C22×D4×C2911yescharacteristic
580C2×C4C22×D4×C2911yescharacteristic
581C2×C4C22×D4×C2911yescharacteristic
582C8—42no—
583C8—42no—
584C8—42no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22C2×C29×#12011yescharacteristic
595C4—21no—
596C4—22no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—42no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—42no—
606C4—41no—
607C4—82no—
608C4C2×C29×#13711yescharacteristic
609C4C29×#57511yescharacteristic
610C4C29×#57812yes—
611C2—41no—
612C2—81no—
613C2—81no—
614C2C29×#300711yescharacteristic
615C2C29×#301111yescharacteristic
616C2C29×#302111yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3518C2
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×#3238C2semidirect
3. C29×#3209C2semidirect
4. C29×#3079C2semidirect
5. C29×#1638C2semidirect
6. C29×#1637C2semidirect
7. C29×#1634C2semidirect
8. C29×#1633C2semidirect
9. C29×#1559C2semidirect
10. C29×#1495C2semidirect
11. C29×#1488C2semidirect
228. #18853C29direct (N × H)
278. #3238C2×C29semidirect
279. #3209C2×C29semidirect
280. #3079C2×C29semidirect
281. #1638C2×C29semidirect
282. #1637C2×C29semidirect
283. #1634C2×C29semidirect
284. #1633C2×C29semidirect
285. #1559C2×C29semidirect
286. #1495C2×C29semidirect
287. #1488C2×C29semidirect
454. C29#18853direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35182
C29×#32382
C29×#32092
C29×#30792
C29×#16382
C29×#16372
C29×#16342
C29×#16332
C29×#15592
C29×#14952
C29×#14882
#1885329