Finite Group Databasebeta

← C29×#19801 #20314701

Subgroups — C29×#19801 #20314701

Order 7424.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3392C211yesmaximal, characteristic
2C29×#3374C211yesmaximal, characteristic, complemented
3C29×#3364C211yesmaximal, characteristic, complemented
4C29×#3304C211yesmaximal, characteristic
5C29×#1719C211yesmaximal, characteristic, complemented
6C29×#1702C211yesmaximal, characteristic, complemented
7C29×#1680C211yesmaximal, characteristic, complemented
8C29×#1679C211yesmaximal, characteristic, complemented
9C29×#1666C211yesmaximal, characteristic, complemented
10C29×#1650C211yesmaximal, characteristic, complemented
11C29×#1648C211yesmaximal, characteristic, complemented
12C29×#1641C211yesmaximal, characteristic
13C29×#1626C211yesmaximal, characteristic, complemented
14C29×#1582C211yesmaximal, characteristic, complemented
15C29×#1579C211yesmaximal, characteristic, complemented
16C29×#557C2211yescharacteristic
17C29×#557C2211yescharacteristic
18C29×#556C2211yescharacteristic
19C29×#550C2211yescharacteristic
20C29×#500C2211yescharacteristic
21C29×#492—21no—
22C29×#492C2211yescharacteristic
23C29×#491—21no—
24C29×#488—21no—
25C29×#487C2211yescharacteristic
26C29×#487C2211yescharacteristic
27C29×#486C2211yescharacteristic
28C29×#486C2211yescharacteristic
29C29×#482—21no—
30C29×#479—21no—
31C29×#479—21no—
32C29×#475C2211yescharacteristic
33C29×#475C2211yescharacteristic
34C29×#474C2211yescharacteristic
35C29×#465—21no—
36C29×#464—21no—
37C29×#462—21no—
38C29×#462C2211yescharacteristic
39C29×#462C2211yescharacteristic
40C29×#461—21no—
41C29×#461C2211yescharacteristic
42C29×#460—21no—
43C29×#460C2211yescharacteristic
44C29×#460C2211yescharacteristic
45C29×#452—21no—
46C29×#446C2211yescharacteristic
47C8×Q8×C29C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C29×#441—21no—
50C4×Q16×C29—21no—
51C4×Q16×C29C2211yescharacteristic
52C4×SD16×C29—21no—
53C4×SD16×C29C2211yescharacteristic
54C8×D4×C29C2211yescharacteristic
55C29×#416—21no—
56C29×#334C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#332C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×Q8⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C29×#322C2211yescharacteristic
67C2×#41×C29—21no—
68C2×Q16×C29—21no—
69C2×Q16×C29—21no—
70C2×Q16×C29D411yescharacteristic
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×SD16×C29—21no—
75C2×SD16×C29—21no—
76C2×SD16×C29D411yescharacteristic
77C22×C8×C29—21no—
78C29×C4⋊Q8—21no—
79C29×C4⋊Q8—21no—
80C29×C4⋊Q8C2311yescharacteristic
81C29×C4⋊Q8C2311yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×#127—21no—
84C29×#127C2311yescharacteristic
85C29×#126—41no—
86C29×#125—21no—
87C29×#125—21no—
88C29×#125—41no—
89C29×#125—41no—
90C29×#124—21no—
91C29×C22⋊Q8—21no—
92C29×#121—21no—
93C29×#121—41no—
94C4×Q8×C29—21no—
95C4×Q8×C29—21no—
96C4×Q8×C29—21no—
97C4×Q8×C29—21no—
98C4×Q8×C29—21no—
99C4×Q8×C29C2311yescharacteristic
100C4×Q8×C29C2311yescharacteristic
101C4×Q8×C29C2311yescharacteristic
102C4×D4×C29—21no—
103C4×D4×C29C2311yescharacteristic
104C29×#117—21no—
105C29×#107—21no—
106C29×#107—41no—
107C29×#107D411yescharacteristic
108C29×#106—21no—
109C29×#106—21no—
110C29×#106D411yescharacteristic
111C29×C4⋊C8—21no—
112C29×C4⋊C8—21no—
113C29×C4⋊C8—21no—
114C29×C4⋊C8C2311yescharacteristic
115C29×C4⋊C8C2311yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×#103—21no—
119C29×#103—21no—
120C29×#103—21no—
121C29×#103—21no—
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—21no—
126C29×#103—21no—
127C29×#103D411yescharacteristic
128C29×#103D411yescharacteristic
129C29×#103D411yescharacteristic
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×#102—41no—
136C29×#102D411yescharacteristic
137C29×C22⋊C8—21no—
138C29×#97—21no—
139C4×C8×C29—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×C29C2×D411yescharacteristic
150C2×Q8×C29C2×D411yescharacteristic
151C2×Q8×C29C2×D411yescharacteristic
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—41no—
156C2×D4×C29—41no—
157C2×D4×C29C2×D411yescharacteristic
158C22×C4×C29—21no—
159C22×C4×C29—41no—
160Q16×C29—22no—
161Q16×C29—42no—
162Q16×C29—42no—
163SD16×C29—41no—
164SD16×C29—42no—
165SD16×C29—81no—
166SD16×C29—81no—
167SD16×C29—81no—
168SD16×C29—81no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C2×C8×C29—21no—
173C2×C8×C29—21no—
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×C29—41no—
192C4⋊C4×C29—41no—
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—41no—
201C22⋊C4×C29—41no—
202C22⋊C4×C29—41no—
203C42×C29—21no—
204C42×C29—21no—
205C42×C29—21no—
206C42×C29—41no—
207C42×C29—41no—
208C42×C29—41no—
209C42×C29C2411yescharacteristic
210#19801C2911yesmaximal, characteristic, direct product factor, Sylow
211C23×C29—21no—
212C23×C29—41no—
213Q8×C29—21no—
214Q8×C29—21no—
215Q8×C29—21no—
216Q8×C29—21no—
217Q8×C29—21no—
218Q8×C29—41no—
219Q8×C29—41no—
220Q8×C29—41no—
221Q8×C29—41no—
222Q8×C29—41no—
223Q8×C29—41no—
224Q8×C29#13512yes—
225D4×C29—21no—
226D4×C29—21no—
227D4×C29—41no—
228D4×C29—41no—
229D4×C29—41no—
230D4×C29—41no—
231D4×C29—82no—
232D4×C29—81no—
233D4×C29—161no—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—21no—
239C2×C4×C29—21no—
240C2×C4×C29—21no—
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—21no—
254C8×C29—41no—
255C8×C29—41no—
256C8×C29—41no—
257C8×C29—41no—
258C8×C29—41no—
259#3392C2×C2911yescharacteristic
260#3374C2×C2911yescharacteristic, complemented
261#3364C2×C2911yescharacteristic, complemented
262#3304C2×C2911yescharacteristic
263#1719C2×C2911yescharacteristic, complemented
264#1702C2×C2911yescharacteristic, complemented
265#1680C2×C2911yescharacteristic, complemented
266#1679C2×C2911yescharacteristic, complemented
267#1666C2×C2911yescharacteristic, complemented
268#1650C2×C2911yescharacteristic, complemented
269#1648C2×C2911yescharacteristic, complemented
270#1641C2×C2911yescharacteristic
271#1626C2×C2911yescharacteristic, complemented
272#1582C2×C2911yescharacteristic, complemented
273#1579C2×C2911yescharacteristic, complemented
274C22×C29—41no—
275C22×C29—41no—
276C22×C29—41no—
277C22×C29—81no—
278C22×C29—81no—
279C22×C29—81no—
280C22×C29D4211yescharacteristic
281C4×C29—22no—
282C4×C29—21no—
283C4×C29—41no—
284C4×C29—41no—
285C4×C29—41no—
286C4×C29—41no—
287C4×C29—41no—
288C4×C29—41no—
289C4×C29—81no—
290C4×C29—81no—
291C4×C29—81no—
292C4×C29C2×#13511yescharacteristic
293C4×C29#57511yescharacteristic
294C4×C29#57711yescharacteristic
295C4×C29#57711yescharacteristic
296#557C22×C2911yescharacteristic
297#557C22×C2911yescharacteristic
298#556C22×C2911yescharacteristic
299#550C22×C2911yescharacteristic
300#500C22×C2911yescharacteristic
301#492—21no—
302#492C22×C2911yescharacteristic
303#491—21no—
304#488—21no—
305#487C22×C2911yescharacteristic
306#487C22×C2911yescharacteristic
307#486C22×C2911yescharacteristic
308#486C22×C2911yescharacteristic
309#482—21no—
310#479—21no—
311#479—21no—
312#475C22×C2911yescharacteristic
313#475C22×C2911yescharacteristic
314#474C22×C2911yescharacteristic
315#465—21no—
316#464—21no—
317#462—21no—
318#462C22×C2911yescharacteristic
319#462C22×C2911yescharacteristic
320#461—21no—
321#461C22×C2911yescharacteristic
322#460—21no—
323#460C22×C2911yescharacteristic
324#460C22×C2911yescharacteristic
325#452—21no—
326#446C22×C2911yescharacteristic
327C8×Q8C22×C2911yescharacteristic
328C8×Q8C22×C2911yescharacteristic
329#441—21no—
330C4×Q16—21no—
331C4×Q16C22×C2911yescharacteristic
332C4×SD16—21no—
333C4×SD16C22×C2911yescharacteristic
334C8×D4C22×C2911yescharacteristic
335#416—21no—
336#334C22×C2911yescharacteristic
337#334C22×C2911yescharacteristic
338#332C22×C2911yescharacteristic
339#332C22×C2911yescharacteristic
340#332C22×C2911yescharacteristic
341#331C22×C2911yescharacteristic
342Q8⋊C8C22×C2911yescharacteristic
343Q8⋊C8C22×C2911yescharacteristic
344Q8⋊C8C22×C2911yescharacteristic
345D4⋊C8C22×C2911yescharacteristic
346#322C22×C2911yescharacteristic
347C2×C29—81no—
348C2×C29—161no—
349C2×C29#327111yescharacteristic
350C2×C29#328211yescharacteristic
351C2×C29#328911yescharacteristic
352C2×#41—21no—
353C2×Q16—21no—
354C2×Q16—21no—
355C2×Q16D4×C2911yescharacteristic
356C2×SD16—21no—
357C2×SD16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16D4×C2911yescharacteristic
362C22×C8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8C23×C2911yescharacteristic
366C4⋊Q8C23×C2911yescharacteristic
367C4⋊Q8C23×C2911yescharacteristic
368#127—21no—
369#127C23×C2911yescharacteristic
370#126—41no—
371#125—21no—
372#125—21no—
373#125—41no—
374#125—41no—
375#124—21no—
376C22⋊Q8—21no—
377#121—21no—
378#121—41no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8C23×C2911yescharacteristic
385C4×Q8C23×C2911yescharacteristic
386C4×Q8C23×C2911yescharacteristic
387C4×D4—21no—
388C4×D4C23×C2911yescharacteristic
389#117—21no—
390#107—21no—
391#107—41no—
392#107D4×C2911yescharacteristic
393#106—21no—
394#106—21no—
395#106D4×C2911yescharacteristic
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8C23×C2911yescharacteristic
400C4⋊C8C23×C2911yescharacteristic
401C4⋊C8C23×C2911yescharacteristic
402C4⋊C8C23×C2911yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103D4×C2911yescharacteristic
413#103D4×C2911yescharacteristic
414#103D4×C2911yescharacteristic
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—41no—
421#102D4×C2911yescharacteristic
422C22⋊C8—21no—
423#97—21no—
424C4×C8—21no—
425C4×C8—21no—
426C4×C8C23×C2911yescharacteristic
427C4×C8C23×C2911yescharacteristic
428C4×C8C23×C2911yescharacteristic
429C29#1980111yescharacteristic, direct product factor, Sylow
430#41—42no—
431#41—81no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8C2×D4×C2911yescharacteristic
436C2×Q8C2×D4×C2911yescharacteristic
437C2×Q8C2×D4×C2911yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4C2×D4×C2911yescharacteristic
444C22×C4—21no—
445C22×C4—41no—
446Q16—22no—
447Q16—42no—
448Q16—42no—
449SD16—41no—
450SD16—42no—
451SD16—81no—
452SD16—81no—
453SD16—81no—
454SD16—81no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—81no—
461C2×C8C2×D4×C2911yescharacteristic
462C2×C8C2×D4×C2911yescharacteristic
463C2×C8C2×D4×C2911yescharacteristic
464C2×C8C2×D4×C2911yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4C2×D4×C2911yescharacteristic
482C4⋊C4C2×D4×C2911yescharacteristic
483C4⋊C4C2×D4×C2911yescharacteristic
484C4⋊C4C2×D4×C2911yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—41no—
493C42—41no—
494C42—41no—
495C42C24×C2911yescharacteristic
496C23—21no—
497C23—41no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8C29×#13512yes—
510D4—21no—
511D4—21no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—82no—
517D4—81no—
518D4—161no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—82no—
532C2×C4C22×D4×C2911yescharacteristic
533C2×C4C22×D4×C2911yescharacteristic
534C2×C4C29×H(5,𝔽2)11yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22D42×C2911yescharacteristic
551C4—22no—
552C4—21no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4C2×C29×#13511yescharacteristic
563C4C29×#57511yescharacteristic
564C4C29×#57711yescharacteristic
565C4C29×#57711yescharacteristic
566C2—81no—
567C2—161no—
568C2C29×#327111yescharacteristic
569C2C29×#328211yescharacteristic
570C2C29×#328911yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#550C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3374C2semidirect
3. C29×#3364C2semidirect
5. C29×#1719C2semidirect
6. C29×#1702C2semidirect
7. C29×#1680C2semidirect
8. C29×#1679C2semidirect
9. C29×#1666C2semidirect
10. C29×#1650C2semidirect
11. C29×#1648C2semidirect
13. C29×#1626C2semidirect
14. C29×#1582C2semidirect
15. C29×#1579C2semidirect
210. #19801C29direct (N × H)
260. #3374C2×C29semidirect
261. #3364C2×C29semidirect
263. #1719C2×C29semidirect
264. #1702C2×C29semidirect
265. #1680C2×C29semidirect
266. #1679C2×C29semidirect
267. #1666C2×C29semidirect
268. #1650C2×C29semidirect
269. #1648C2×C29semidirect
271. #1626C2×C29semidirect
272. #1582C2×C29semidirect
273. #1579C2×C29semidirect
429. C29#19801direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33922
C29×#33742
C29×#33642
C29×#33042
C29×#17192
C29×#17022
C29×#16802
C29×#16792
C29×#16662
C29×#16502
C29×#16482
C29×#16412
C29×#16262
C29×#15822
C29×#15792
#1980129