Finite Group Databasebeta

← C29×#19863 #20314763

Subgroups — C29×#19863 #20314763

Order 7424.

594 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3393C211yesmaximal, characteristic, complemented
2C29×#3353C211yesmaximal, characteristic, complemented
3C29×#3340C211yesmaximal, characteristic, complemented
4C29×#3303C211yesmaximal, characteristic
5C29×#1723C211yesmaximal, characteristic, complemented
6C29×#1691C211yesmaximal, characteristic, complemented
7C29×#1684C211yesmaximal, characteristic, complemented
8C29×#1673C211yesmaximal, characteristic, complemented
9C29×#1669C211yesmaximal, characteristic, complemented
10C29×#1650C211yesmaximal, characteristic, complemented
11C29×#1647C211yesmaximal, characteristic, complemented
12C29×#1646C211yesmaximal, characteristic, complemented
13C29×#1638C211yesmaximal, characteristic, complemented
14C29×#1581C211yesmaximal, characteristic, complemented
15C29×SD16⋊C8C211yesmaximal, characteristic, complemented
16C29×#556C2211yescharacteristic
17C29×#556C2211yescharacteristic
18C29×#555C2211yescharacteristic
19C29×#547C2211yescharacteristic
20C29×#500C2211yescharacteristic
21C29×#500C2211yescharacteristic
22C29×#498C2211yescharacteristic
23C29×#495—21no—
24C29×#494C2211yescharacteristic
25C29×#487C2211yescharacteristic
26C29×#487C2211yescharacteristic
27C29×#485—21no—
28C29×#485—21no—
29C29×#484—21no—
30C29×#482—21no—
31C29×#482—21no—
32C29×#477C2211yescharacteristic
33C29×#476C2211yescharacteristic
34C29×#475C2211yescharacteristic
35C29×#474C2211yescharacteristic
36C29×#474C2211yescharacteristic
37C29×#468—21no—
38C29×#465—21no—
39C29×#465—21no—
40C29×#464—21no—
41C29×#464—21no—
42C29×#461C2211yescharacteristic
43C29×#461C2211yescharacteristic
44C29×#461C2211yescharacteristic
45C29×#449—21no—
46C8×Q8×C29C2211yescharacteristic
47C4×Q16×C29—21no—
48C4×SD16×C29C2211yescharacteristic
49C4×D8×C29C2211yescharacteristic
50C29×#436C2211yescharacteristic
51C8×D4×C29C2211yescharacteristic
52C8×D4×C29C2211yescharacteristic
53C29×#428—21no—
54C29×#427—21no—
55C29×#416—21no—
56C29×#335C2211yescharacteristic
57C29×#335C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×D4⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C29×#322C2211yescharacteristic
67C2×#41×C29—21no—
68C2×Q16×C29—21no—
69C2×Q16×C29—21no—
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29D411yescharacteristic
74C2×D8×C29D411yescharacteristic
75C2×M16×C29—21no—
76C22×C8×C29—21no—
77C22×C8×C29—21no—
78C29×C4⋊Q8C2311yescharacteristic
79C29×C4⋊Q8C2311yescharacteristic
80C29×C4⋊Q8C2311yescharacteristic
81C29×C4⋊Q8C2311yescharacteristic
82C29×#126—41no—
83C29×#126—41no—
84C29×#124—21no—
85C29×#124—21no—
86C29×#124—41no—
87C29×#123—41no—
88C29×C22⋊Q8—21no—
89C29×C22⋊Q8—21no—
90C29×C22⋊Q8—21no—
91C29×#121—21no—
92C29×#121—21no—
93C29×#121—21no—
94C4×Q8×C29—21no—
95C4×Q8×C29—21no—
96C4×Q8×C29C2311yescharacteristic
97C4×D4×C29C2311yescharacteristic
98C4×D4×C29C2311yescharacteristic
99C4×D4×C29C2311yescharacteristic
100C29×#117—21no—
101C29×#117—21no—
102C29×#117—21no—
103C29×#117—21no—
104C2×C4⋊C4×C29—21no—
105C29×#107—21no—
106C29×#107—21no—
107C29×#107—21no—
108C29×#107—21no—
109C29×#107—21no—
110C29×#107—41no—
111C29×#107D411yescharacteristic
112C29×#106—21no—
113C29×#106—21no—
114C29×#106—21no—
115C29×#106—21no—
116C29×#106D411yescharacteristic
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×#103—21no—
126C29×#103—21no—
127C29×#103—21no—
128C29×#103—21no—
129C29×#103—41no—
130C29×#103D411yescharacteristic
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102D411yescharacteristic
135C29×#102D411yescharacteristic
136C29×#102D411yescharacteristic
137C29×C22⋊C8—21no—
138C29×C22⋊C8—21no—
139C29×C22⋊C8—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×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29C2×D411yescharacteristic
151C2×D4×C29—41no—
152C2×D4×C29—41no—
153C2×D4×C29C2×D411yescharacteristic
154C2×D4×C29C2×D411yescharacteristic
155C2×D4×C29C2×D411yescharacteristic
156C22×C4×C29—21no—
157C22×C4×C29—21no—
158C22×C4×C29—21no—
159C22×C4×C29—41no—
160Q16×C29—42no—
161Q16×C29—81no—
162SD16×C29—22no—
163SD16×C29—81no—
164SD16×C29—81no—
165SD16×C29—81no—
166D8×C29—41no—
167M16×C29—42no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C2×C8×C29—21no—
173C2×C8×C29—42no—
174C2×C8×C29—81no—
175C2×C8×C29C2×D411yescharacteristic
176C2×C8×C29C2×D411yescharacteristic
177C2×C8×C29C2×D411yescharacteristic
178C2×C8×C29C2×D411yescharacteristic
179C4⋊C4×C29—21no—
180C4⋊C4×C29—21no—
181C4⋊C4×C29—21no—
182C4⋊C4×C29—21no—
183C4⋊C4×C29—21no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—41no—
189C4⋊C4×C29—41no—
190C4⋊C4×C29—41no—
191C4⋊C4×C29C2×D411yescharacteristic
192C4⋊C4×C29C2×D411yescharacteristic
193C4⋊C4×C29C2×D411yescharacteristic
194C4⋊C4×C29C2×D411yescharacteristic
195C22⋊C4×C29—21no—
196C22⋊C4×C29—21no—
197C22⋊C4×C29—21no—
198C22⋊C4×C29—41no—
199C22⋊C4×C29—41no—
200C22⋊C4×C29—41no—
201C22⋊C4×C29—41no—
202C22⋊C4×C29—41no—
203C22⋊C4×C29—41no—
204C22⋊C4×C29—41no—
205C42×C29—21no—
206C42×C29—41no—
207C42×C29—41no—
208C42×C29—41no—
209C42×C29C2411yescharacteristic
210#19863C2911yesmaximal, characteristic, direct product factor, Sylow
211C23×C29—21no—
212C23×C29—21no—
213C23×C29—21no—
214Q8×C29—21no—
215Q8×C29—21no—
216Q8×C29—41no—
217Q8×C29—41no—
218Q8×C29—41no—
219Q8×C29—41no—
220Q8×C29—41no—
221Q8×C29—41no—
222Q8×C29—81no—
223D4×C29—21no—
224D4×C29—21no—
225D4×C29—21no—
226D4×C29—21no—
227D4×C29—21no—
228D4×C29—21no—
229D4×C29—82no—
230D4×C29—161no—
231C2×C4×C29—21no—
232C2×C4×C29—21no—
233C2×C4×C29—21no—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—41no—
237C2×C4×C29—41no—
238C2×C4×C29—41no—
239C2×C4×C29—41no—
240C2×C4×C29—41no—
241C2×C4×C29—41no—
242C2×C4×C29—41no—
243C2×C4×C29—41no—
244C2×C4×C29—41no—
245C2×C4×C29—41no—
246C2×C4×C29—82no—
247C2×C4×C29C22×D411yescharacteristic
248C2×C4×C29C22×D411yescharacteristic
249C2×C4×C29H(5,𝔽2)11yescharacteristic
250C8×C29—21no—
251C8×C29—21no—
252C8×C29—21no—
253C8×C29—41no—
254C8×C29—41no—
255C8×C29—41no—
256C8×C29—41no—
257C8×C29—41no—
258C8×C29#13512yes—
259#3393C2×C2911yescharacteristic, complemented
260#3353C2×C2911yescharacteristic, complemented
261#3340C2×C2911yescharacteristic, complemented
262#3303C2×C2911yescharacteristic
263#1723C2×C2911yescharacteristic, complemented
264#1691C2×C2911yescharacteristic, complemented
265#1684C2×C2911yescharacteristic, complemented
266#1673C2×C2911yescharacteristic, complemented
267#1669C2×C2911yescharacteristic, complemented
268#1650C2×C2911yescharacteristic, complemented
269#1647C2×C2911yescharacteristic, complemented
270#1646C2×C2911yescharacteristic, complemented
271#1638C2×C2911yescharacteristic, complemented
272#1581C2×C2911yescharacteristic, complemented
273SD16⋊C8C2×C2911yescharacteristic, complemented
274C22×C29—41no—
275C22×C29—41no—
276C22×C29—41no—
277C22×C29—41no—
278C22×C29—41no—
279C22×C29—41no—
280C22×C29—41no—
281C22×C29—41no—
282C22×C29—41no—
283C22×C29D4211yescharacteristic
284C4×C29—21no—
285C4×C29—41no—
286C4×C29—41no—
287C4×C29—41no—
288C4×C29—41no—
289C4×C29—41no—
290C4×C29—81no—
291C4×C29—81no—
292C4×C29—81no—
293C4×C29—81no—
294C4×C29C2×#13511yescharacteristic
295C4×C29#57511yescharacteristic
296C4×C29#57611yescharacteristic
297C4×C29#57811yescharacteristic
298#556C22×C2911yescharacteristic
299#556C22×C2911yescharacteristic
300#555C22×C2911yescharacteristic
301#547C22×C2911yescharacteristic
302#500C22×C2911yescharacteristic
303#500C22×C2911yescharacteristic
304#498C22×C2911yescharacteristic
305#495—21no—
306#494C22×C2911yescharacteristic
307#487C22×C2911yescharacteristic
308#487C22×C2911yescharacteristic
309#485—21no—
310#485—21no—
311#484—21no—
312#482—21no—
313#482—21no—
314#477C22×C2911yescharacteristic
315#476C22×C2911yescharacteristic
316#475C22×C2911yescharacteristic
317#474C22×C2911yescharacteristic
318#474C22×C2911yescharacteristic
319#468—21no—
320#465—21no—
321#465—21no—
322#464—21no—
323#464—21no—
324#461C22×C2911yescharacteristic
325#461C22×C2911yescharacteristic
326#461C22×C2911yescharacteristic
327#449—21no—
328C8×Q8C22×C2911yescharacteristic
329C4×Q16—21no—
330C4×SD16C22×C2911yescharacteristic
331C4×D8C22×C2911yescharacteristic
332#436C22×C2911yescharacteristic
333C8×D4C22×C2911yescharacteristic
334C8×D4C22×C2911yescharacteristic
335#428—21no—
336#427—21no—
337#416—21no—
338#335C22×C2911yescharacteristic
339#335C22×C2911yescharacteristic
340#333C22×C2911yescharacteristic
341#332C22×C2911yescharacteristic
342#332C22×C2911yescharacteristic
343#332C22×C2911yescharacteristic
344Q8⋊C8C22×C2911yescharacteristic
345D4⋊C8C22×C2911yescharacteristic
346D4⋊C8C22×C2911yescharacteristic
347D4⋊C8C22×C2911yescharacteristic
348#322C22×C2911yescharacteristic
349C2×C29—81no—
350C2×C29—81no—
351C2×C29—81no—
352C2×C29#326811yescharacteristic
353C2×C29#328311yescharacteristic
354C2×C29#328911yescharacteristic
355C2×#41—21no—
356C2×Q16—21no—
357C2×Q16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16D4×C2911yescharacteristic
362C2×D8D4×C2911yescharacteristic
363C2×M16—21no—
364C22×C8—21no—
365C22×C8—21no—
366C4⋊Q8C23×C2911yescharacteristic
367C4⋊Q8C23×C2911yescharacteristic
368C4⋊Q8C23×C2911yescharacteristic
369C4⋊Q8C23×C2911yescharacteristic
370#126—41no—
371#126—41no—
372#124—21no—
373#124—21no—
374#124—41no—
375#123—41no—
376C22⋊Q8—21no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379#121—21no—
380#121—21no—
381#121—21no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8C23×C2911yescharacteristic
385C4×D4C23×C2911yescharacteristic
386C4×D4C23×C2911yescharacteristic
387C4×D4C23×C2911yescharacteristic
388#117—21no—
389#117—21no—
390#117—21no—
391#117—21no—
392C2×C4⋊C4—21no—
393#107—21no—
394#107—21no—
395#107—21no—
396#107—21no—
397#107—21no—
398#107—41no—
399#107D4×C2911yescharacteristic
400#106—21no—
401#106—21no—
402#106—21no—
403#106—21no—
404#106D4×C2911yescharacteristic
405C4⋊C8—21no—
406C4⋊C8C23×C2911yescharacteristic
407C4⋊C8C23×C2911yescharacteristic
408C4⋊C8C23×C2911yescharacteristic
409C4⋊C8C23×C2911yescharacteristic
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—41no—
418#103D4×C2911yescharacteristic
419#102—21no—
420#102—21no—
421#102—21no—
422#102D4×C2911yescharacteristic
423#102D4×C2911yescharacteristic
424#102D4×C2911yescharacteristic
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C4×C8—21no—
429C4×C8C23×C2911yescharacteristic
430C4×C8C23×C2911yescharacteristic
431C4×C8C23×C2911yescharacteristic
432C29#1986311yescharacteristic, direct product factor, Sylow
433#41—42no—
434#41—81no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8C2×D4×C2911yescharacteristic
440C2×D4—41no—
441C2×D4—41no—
442C2×D4C2×D4×C2911yescharacteristic
443C2×D4C2×D4×C2911yescharacteristic
444C2×D4C2×D4×C2911yescharacteristic
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—41no—
449Q16—42no—
450Q16—81no—
451SD16—22no—
452SD16—81no—
453SD16—81no—
454SD16—81no—
455D8—41no—
456M16—42no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—42no—
463C2×C8—81no—
464C2×C8C2×D4×C2911yescharacteristic
465C2×C8C2×D4×C2911yescharacteristic
466C2×C8C2×D4×C2911yescharacteristic
467C2×C8C2×D4×C2911yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4C2×D4×C2911yescharacteristic
481C4⋊C4C2×D4×C2911yescharacteristic
482C4⋊C4C2×D4×C2911yescharacteristic
483C4⋊C4C2×D4×C2911yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C42—21no—
495C42—41no—
496C42—41no—
497C42—41no—
498C42C24×C2911yescharacteristic
499C23—21no—
500C23—21no—
501C23—21no—
502Q8—21no—
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—81no—
511D4—21no—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—21no—
517D4—82no—
518D4—161no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—82no—
535C2×C4C22×D4×C2911yescharacteristic
536C2×C4C22×D4×C2911yescharacteristic
537C2×C4C29×H(5,𝔽2)11yescharacteristic
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8C29×#13512yes—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22D42×C2911yescharacteristic
557C4—21no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4C2×C29×#13511yescharacteristic
568C4C29×#57511yescharacteristic
569C4C29×#57611yescharacteristic
570C4C29×#57811yescharacteristic
571C2—81no—
572C2—81no—
573C2—81no—
574C2C29×#326811yescharacteristic
575C2C29×#328311yescharacteristic
576C2C29×#328911yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3303C2
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×#3393C2semidirect
2. C29×#3353C2semidirect
3. C29×#3340C2semidirect
5. C29×#1723C2semidirect
6. C29×#1691C2semidirect
7. C29×#1684C2semidirect
8. C29×#1673C2semidirect
9. C29×#1669C2semidirect
10. C29×#1650C2semidirect
11. C29×#1647C2semidirect
12. C29×#1646C2semidirect
13. C29×#1638C2semidirect
14. C29×#1581C2semidirect
15. C29×SD16⋊C8C2semidirect
210. #19863C29direct (N × H)
259. #3393C2×C29semidirect
260. #3353C2×C29semidirect
261. #3340C2×C29semidirect
263. #1723C2×C29semidirect
264. #1691C2×C29semidirect
265. #1684C2×C29semidirect
266. #1673C2×C29semidirect
267. #1669C2×C29semidirect
268. #1650C2×C29semidirect
269. #1647C2×C29semidirect
270. #1646C2×C29semidirect
271. #1638C2×C29semidirect
272. #1581C2×C29semidirect
273. SD16⋊C8C2×C29semidirect
432. C29#19863direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33932
C29×#33532
C29×#33402
C29×#33032
C29×#17232
C29×#16912
C29×#16842
C29×#16732
C29×#16692
C29×#16502
C29×#16472
C29×#16462
C29×#16382
C29×#15812
C29×SD16⋊C82
#1986329