Finite Group Databasebeta

← C29×#19949 #20314849

Subgroups — C29×#19949 #20314849

Order 7424.

622 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3399C211yesmaximal, characteristic, complemented
2C29×#3361C211yesmaximal, characteristic, complemented
3C29×#3357C211yesmaximal, characteristic, complemented
4C29×#3305C211yesmaximal, characteristic, complemented
5C29×#1706C211yesmaximal, characteristic, complemented
6C29×#1696C211yesmaximal, characteristic, complemented
7C29×#1687C211yesmaximal, characteristic, complemented
8C29×#1678C211yesmaximal, characteristic, complemented
9C29×#1677C211yesmaximal, characteristic, complemented
10C29×#1631C211yesmaximal, characteristic, complemented
11C29×#1630C211yesmaximal, characteristic, complemented
12C29×#1624C211yesmaximal, characteristic, complemented
13C29×#1622C211yesmaximal, characteristic, complemented
14C29×#1590C211yesmaximal, characteristic, complemented
15C8×SD16×C29C211yesmaximal, characteristic, complemented
16C29×#559C2211yescharacteristic
17C29×#555C2211yescharacteristic
18C29×#554C2211yescharacteristic
19C29×#550C2211yescharacteristic
20C29×#500C2211yescharacteristic
21C29×#496—21no—
22C29×#493C2211yescharacteristic
23C29×#492C2211yescharacteristic
24C29×#492C2211yescharacteristic
25C29×#488—21no—
26C29×#486C2211yescharacteristic
27C29×#486C2211yescharacteristic
28C29×#485—21no—
29C29×#482—21no—
30C29×#480—21no—
31C29×#478—21no—
32C29×#477C2211yescharacteristic
33C29×#477C2211yescharacteristic
34C29×#477C2211yescharacteristic
35C29×#476C2211yescharacteristic
36C29×#468—21no—
37C29×#466—21no—
38C29×#463—21no—
39C29×#463—21no—
40C29×#460C2211yescharacteristic
41C29×#459—21no—
42C29×#459C2211yescharacteristic
43C29×#459C2211yescharacteristic
44C29×#459C2211yescharacteristic
45C29×#449—21no—
46C29×#446C2211yescharacteristic
47C8×Q8×C29C2211yescharacteristic
48C29×#442—21no—
49C4×SD16×C29C2211yescharacteristic
50C4×SD16×C29C2211yescharacteristic
51C4×D8×C29—21no—
52C29×#436C2211yescharacteristic
53C8×D4×C29C2211yescharacteristic
54C29×#428—21no—
55C29×#416—21no—
56C29×#334C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#331C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C82×C29C2211yescharacteristic
67C2×#41×C29—21no—
68C2×SD16×C29—21no—
69C2×SD16×C29—41no—
70C2×SD16×C29—41no—
71C2×SD16×C29D411yescharacteristic
72C2×SD16×C29D411yescharacteristic
73C2×D8×C29—21no—
74C2×D8×C29—21no—
75C2×D8×C29—21no—
76C2×D8×C29—21no—
77C2×D8×C29—21no—
78C2×M16×C29—21no—
79C22×C8×C29—21no—
80C29×C4⋊Q8C2311yescharacteristic
81C29×C4⋊Q8C2311yescharacteristic
82C29×#127—21no—
83C29×#127C2311yescharacteristic
84C29×#127C2311yescharacteristic
85C29×#125—21no—
86C29×#124—21no—
87C29×#124—21no—
88C29×#124—41no—
89C29×#123—41no—
90C29×C22⋊Q8—21no—
91C29×C22⋊Q8—41no—
92C29×#121—21no—
93C29×#121—21no—
94C29×#121—21no—
95C29×#121—41no—
96C4×Q8×C29C2311yescharacteristic
97C4×Q8×C29C2311yescharacteristic
98C4×D4×C29—21no—
99C4×D4×C29—21no—
100C4×D4×C29—21no—
101C4×D4×C29—21no—
102C4×D4×C29C2311yescharacteristic
103C4×D4×C29C2311yescharacteristic
104C29×#117—21no—
105C29×#117—21no—
106C2×C4⋊C4×C29—21no—
107C29×#107—21no—
108C29×#107—21no—
109C29×#107—21no—
110C29×#107—21no—
111C29×#107—21no—
112C29×#106—21no—
113C29×#106D411yescharacteristic
114C29×#106D411yescharacteristic
115C29×C4⋊C8—21no—
116C29×C4⋊C8—21no—
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×#103—21no—
122C29×#103—21no—
123C29×#103—21no—
124C29×#103D411yescharacteristic
125C29×#103D411yescharacteristic
126C29×#102—21no—
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×#102D411yescharacteristic
136C29×#102D411yescharacteristic
137C29×C22⋊C8—21no—
138C29×C22⋊C8—21no—
139C29×#97—21no—
140C4×C8×C29—21no—
141C4×C8×C29C2311yescharacteristic
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144#41×C29—42no—
145#41×C29—81no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29C2×D411yescharacteristic
149C2×Q8×C29C2×D411yescharacteristic
150C2×D4×C29—21no—
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—41no—
157C2×D4×C29—41no—
158C2×D4×C29—41no—
159C2×D4×C29C2×D411yescharacteristic
160C2×D4×C29C2×D411yescharacteristic
161C22×C4×C29—21no—
162C22×C4×C29—21no—
163C22×C4×C29—41no—
164C22×C4×C29—41no—
165C22×C4×C29—41no—
166SD16×C29—22no—
167SD16×C29—41no—
168SD16×C29—82no—
169SD16×C29—82no—
170SD16×C29—81no—
171D8×C29—42no—
172D8×C29—42no—
173D8×C29—81no—
174D8×C29—81no—
175D8×C29—81no—
176M16×C29—42no—
177C2×C8×C29—21no—
178C2×C8×C29—21no—
179C2×C8×C29—21no—
180C2×C8×C29—21no—
181C2×C8×C29—21no—
182C2×C8×C29—81no—
183C2×C8×C29C2×D411yescharacteristic
184C2×C8×C29C2×D411yescharacteristic
185C2×C8×C29C2×D411yescharacteristic
186C2×C8×C29C2×D411yescharacteristic
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—41no—
194C4⋊C4×C29—41no—
195C4⋊C4×C29C2×D411yescharacteristic
196C4⋊C4×C29C2×D411yescharacteristic
197C4⋊C4×C29C2×D411yescharacteristic
198C4⋊C4×C29C2×D411yescharacteristic
199C22⋊C4×C29—21no—
200C22⋊C4×C29—21no—
201C22⋊C4×C29—41no—
202C22⋊C4×C29—41no—
203C22⋊C4×C29—41no—
204C22⋊C4×C29—41no—
205C22⋊C4×C29—41no—
206C22⋊C4×C29—41no—
207C22⋊C4×C29—41no—
208C42×C29—21no—
209C42×C29—21no—
210C42×C29—41no—
211C42×C29C2411yescharacteristic
212#19949C2911yesmaximal, characteristic, direct product factor, Sylow
213C23×C29—21no—
214C23×C29—21no—
215C23×C29—41no—
216C23×C29—41no—
217Q8×C29—21no—
218Q8×C29—21no—
219Q8×C29—21no—
220Q8×C29—21no—
221Q8×C29—81no—
222Q8×C29—81no—
223D4×C29—21no—
224D4×C29—21no—
225D4×C29—21no—
226D4×C29—21no—
227D4×C29—41no—
228D4×C29—41no—
229D4×C29—41no—
230D4×C29—41no—
231D4×C29—41no—
232D4×C29—41no—
233D4×C29—41no—
234D4×C29—41no—
235D4×C29—81no—
236D4×C29—81no—
237D4×C29—82no—
238D4×C29—161no—
239D4×C29—161no—
240C2×C4×C29—21no—
241C2×C4×C29—21no—
242C2×C4×C29—21no—
243C2×C4×C29—21no—
244C2×C4×C29—21no—
245C2×C4×C29—21no—
246C2×C4×C29—41no—
247C2×C4×C29—41no—
248C2×C4×C29—41no—
249C2×C4×C29—41no—
250C2×C4×C29—41no—
251C2×C4×C29—41no—
252C2×C4×C29—82no—
253C2×C4×C29—161no—
254C2×C4×C29—161no—
255C2×C4×C29C22×D411yescharacteristic
256C2×C4×C29C22×D411yescharacteristic
257C2×C4×C29H(5,𝔽2)11yescharacteristic
258C8×C29—22no—
259C8×C29—21no—
260C8×C29—21no—
261C8×C29—21no—
262C8×C29—41no—
263C8×C29—41no—
264C8×C29—41no—
265C8×C29—41no—
266C8×C29#13512yes—
267#3399C2×C2911yescharacteristic, complemented
268#3361C2×C2911yescharacteristic, complemented
269#3357C2×C2911yescharacteristic, complemented
270#3305C2×C2911yescharacteristic, complemented
271#1706C2×C2911yescharacteristic, complemented
272#1696C2×C2911yescharacteristic, complemented
273#1687C2×C2911yescharacteristic, complemented
274#1678C2×C2911yescharacteristic, complemented
275#1677C2×C2911yescharacteristic, complemented
276#1631C2×C2911yescharacteristic, complemented
277#1630C2×C2911yescharacteristic, complemented
278#1624C2×C2911yescharacteristic, complemented
279#1622C2×C2911yescharacteristic, complemented
280#1590C2×C2911yescharacteristic, complemented
281C8×SD16C2×C2911yescharacteristic, complemented
282C22×C29—41no—
283C22×C29—41no—
284C22×C29—41no—
285C22×C29—41no—
286C22×C29—41no—
287C22×C29—41no—
288C22×C29—81no—
289C22×C29—81no—
290C22×C29—81no—
291C22×C29—81no—
292C22×C29—81no—
293C22×C29—81no—
294C22×C29D4211yescharacteristic
295C4×C29—21no—
296C4×C29—41no—
297C4×C29—41no—
298C4×C29—41no—
299C4×C29—41no—
300C4×C29—41no—
301C4×C29—41no—
302C4×C29—81no—
303C4×C29—81no—
304C4×C29C2×#13511yescharacteristic
305C4×C29#57511yescharacteristic
306C4×C29#57711yescharacteristic
307C4×C29#57711yescharacteristic
308#559C22×C2911yescharacteristic
309#555C22×C2911yescharacteristic
310#554C22×C2911yescharacteristic
311#550C22×C2911yescharacteristic
312#500C22×C2911yescharacteristic
313#496—21no—
314#493C22×C2911yescharacteristic
315#492C22×C2911yescharacteristic
316#492C22×C2911yescharacteristic
317#488—21no—
318#486C22×C2911yescharacteristic
319#486C22×C2911yescharacteristic
320#485—21no—
321#482—21no—
322#480—21no—
323#478—21no—
324#477C22×C2911yescharacteristic
325#477C22×C2911yescharacteristic
326#477C22×C2911yescharacteristic
327#476C22×C2911yescharacteristic
328#468—21no—
329#466—21no—
330#463—21no—
331#463—21no—
332#460C22×C2911yescharacteristic
333#459—21no—
334#459C22×C2911yescharacteristic
335#459C22×C2911yescharacteristic
336#459C22×C2911yescharacteristic
337#449—21no—
338#446C22×C2911yescharacteristic
339C8×Q8C22×C2911yescharacteristic
340#442—21no—
341C4×SD16C22×C2911yescharacteristic
342C4×SD16C22×C2911yescharacteristic
343C4×D8—21no—
344#436C22×C2911yescharacteristic
345C8×D4C22×C2911yescharacteristic
346#428—21no—
347#416—21no—
348#334C22×C2911yescharacteristic
349#334C22×C2911yescharacteristic
350#333C22×C2911yescharacteristic
351#333C22×C2911yescharacteristic
352#331C22×C2911yescharacteristic
353#331C22×C2911yescharacteristic
354Q8⋊C8C22×C2911yescharacteristic
355Q8⋊C8C22×C2911yescharacteristic
356D4⋊C8C22×C2911yescharacteristic
357D4⋊C8C22×C2911yescharacteristic
358C82C22×C2911yescharacteristic
359C2×C29—81no—
360C2×C29—81no—
361C2×C29—161no—
362C2×C29—161no—
363C2×C29#327511yescharacteristic
364C2×C29#328411yescharacteristic
365C2×C29#329211yescharacteristic
366C2×#41—21no—
367C2×SD16—21no—
368C2×SD16—41no—
369C2×SD16—41no—
370C2×SD16D4×C2911yescharacteristic
371C2×SD16D4×C2911yescharacteristic
372C2×D8—21no—
373C2×D8—21no—
374C2×D8—21no—
375C2×D8—21no—
376C2×D8—21no—
377C2×M16—21no—
378C22×C8—21no—
379C4⋊Q8C23×C2911yescharacteristic
380C4⋊Q8C23×C2911yescharacteristic
381#127—21no—
382#127C23×C2911yescharacteristic
383#127C23×C2911yescharacteristic
384#125—21no—
385#124—21no—
386#124—21no—
387#124—41no—
388#123—41no—
389C22⋊Q8—21no—
390C22⋊Q8—41no—
391#121—21no—
392#121—21no—
393#121—21no—
394#121—41no—
395C4×Q8C23×C2911yescharacteristic
396C4×Q8C23×C2911yescharacteristic
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4C23×C2911yescharacteristic
402C4×D4C23×C2911yescharacteristic
403#117—21no—
404#117—21no—
405C2×C4⋊C4—21no—
406#107—21no—
407#107—21no—
408#107—21no—
409#107—21no—
410#107—21no—
411#106—21no—
412#106D4×C2911yescharacteristic
413#106D4×C2911yescharacteristic
414C4⋊C8—21no—
415C4⋊C8—21no—
416C4⋊C8C23×C2911yescharacteristic
417C4⋊C8C23×C2911yescharacteristic
418C4⋊C8C23×C2911yescharacteristic
419C4⋊C8C23×C2911yescharacteristic
420#103—21no—
421#103—21no—
422#103—21no—
423#103D4×C2911yescharacteristic
424#103D4×C2911yescharacteristic
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102D4×C2911yescharacteristic
435#102D4×C2911yescharacteristic
436C22⋊C8—21no—
437C22⋊C8—21no—
438#97—21no—
439C4×C8—21no—
440C4×C8C23×C2911yescharacteristic
441C4×C8C23×C2911yescharacteristic
442C4×C8C23×C2911yescharacteristic
443C29#1994911yescharacteristic, direct product factor, Sylow
444#41—42no—
445#41—81no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8C2×D4×C2911yescharacteristic
449C2×Q8C2×D4×C2911yescharacteristic
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4C2×D4×C2911yescharacteristic
460C2×D4C2×D4×C2911yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466SD16—22no—
467SD16—41no—
468SD16—82no—
469SD16—82no—
470SD16—81no—
471D8—42no—
472D8—42no—
473D8—81no—
474D8—81no—
475D8—81no—
476M16—42no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—81no—
483C2×C8C2×D4×C2911yescharacteristic
484C2×C8C2×D4×C2911yescharacteristic
485C2×C8C2×D4×C2911yescharacteristic
486C2×C8C2×D4×C2911yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4C2×D4×C2911yescharacteristic
496C4⋊C4C2×D4×C2911yescharacteristic
497C4⋊C4C2×D4×C2911yescharacteristic
498C4⋊C4C2×D4×C2911yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C42—21no—
509C42—21no—
510C42—41no—
511C42C24×C2911yescharacteristic
512C23—21no—
513C23—21no—
514C23—41no—
515C23—41no—
516Q8—21no—
517Q8—21no—
518Q8—21no—
519Q8—21no—
520Q8—81no—
521Q8—81no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—81no—
535D4—81no—
536D4—82no—
537D4—161no—
538D4—161no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—82no—
552C2×C4—161no—
553C2×C4—161no—
554C2×C4C22×D4×C2911yescharacteristic
555C2×C4C22×D4×C2911yescharacteristic
556C2×C4C29×H(5,𝔽2)11yescharacteristic
557C8—22no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8C29×#13512yes—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22D42×C2911yescharacteristic
579C4—21no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—81no—
587C4—81no—
588C4C2×C29×#13511yescharacteristic
589C4C29×#57511yescharacteristic
590C4C29×#57711yescharacteristic
591C4C29×#57711yescharacteristic
592C2—81no—
593C2—81no—
594C2—161no—
595C2—161no—
596C2C29×#327511yescharacteristic
597C2C29×#328411yescharacteristic
598C2C29×#329211yescharacteristic
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×#3399C2semidirect
2. C29×#3361C2semidirect
3. C29×#3357C2semidirect
4. C29×#3305C2semidirect
5. C29×#1706C2semidirect
6. C29×#1696C2semidirect
7. C29×#1687C2semidirect
8. C29×#1678C2semidirect
9. C29×#1677C2semidirect
10. C29×#1631C2semidirect
11. C29×#1630C2semidirect
12. C29×#1624C2semidirect
13. C29×#1622C2semidirect
14. C29×#1590C2semidirect
15. C8×SD16×C29C2semidirect
212. #19949C29direct (N × H)
267. #3399C2×C29semidirect
268. #3361C2×C29semidirect
269. #3357C2×C29semidirect
270. #3305C2×C29semidirect
271. #1706C2×C29semidirect
272. #1696C2×C29semidirect
273. #1687C2×C29semidirect
274. #1678C2×C29semidirect
275. #1677C2×C29semidirect
276. #1631C2×C29semidirect
277. #1630C2×C29semidirect
278. #1624C2×C29semidirect
279. #1622C2×C29semidirect
280. #1590C2×C29semidirect
281. C8×SD16C2×C29semidirect
443. C29#19949direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33992
C29×#33612
C29×#33572
C29×#33052
C29×#17062
C29×#16962
C29×#16872
C29×#16782
C29×#16772
C29×#16312
C29×#16302
C29×#16242
C29×#16222
C29×#15902
C8×SD16×C292
#1994929