Finite Group Databasebeta

← C29×#19956 #20314856

Subgroups — C29×#19956 #20314856

Order 7424.

588 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×#3360C211yesmaximal, characteristic, complemented
2C29×#3357C211yesmaximal, characteristic, complemented
3C29×#3353C211yesmaximal, characteristic, complemented
4C29×#3303C211yesmaximal, characteristic
5C29×#1710C211yesmaximal, characteristic, complemented
6C29×#1695C211yesmaximal, characteristic, complemented
7C29×#1693C211yesmaximal, characteristic, complemented
8C29×#1684C211yesmaximal, characteristic, complemented
9C29×#1683C211yesmaximal, characteristic, complemented
10C29×#1646C211yesmaximal, characteristic, complemented
11C29×#1643C211yesmaximal, characteristic, complemented
12C29×#1638C211yesmaximal, characteristic, complemented
13C29×#1635C211yesmaximal, characteristic, complemented
14C29×#1589C211yesmaximal, characteristic, complemented
15C8×SD16×C29C211yesmaximal, characteristic, complemented
16C29×#556C2211yescharacteristic
17C29×#555C2211yescharacteristic
18C29×#554C2211yescharacteristic
19C29×#547C2211yescharacteristic
20C29×#500C2211yescharacteristic
21C29×#500C2211yescharacteristic
22C29×#488—21no—
23C29×#487C2211yescharacteristic
24C29×#487C2211yescharacteristic
25C29×#487C2211yescharacteristic
26C29×#487C2211yescharacteristic
27C29×#485—21no—
28C29×#485—21no—
29C29×#484—21no—
30C29×#482—21no—
31C29×#480—21no—
32C29×#479—21no—
33C29×#477C2211yescharacteristic
34C29×#476C2211yescharacteristic
35C29×#476C2211yescharacteristic
36C29×#476C2211yescharacteristic
37C29×#475C2211yescharacteristic
38C29×#474C2211yescharacteristic
39C29×#468—21no—
40C29×#468—21no—
41C29×#465—21no—
42C29×#463—21no—
43C29×#461C2211yescharacteristic
44C29×#461C2211yescharacteristic
45C29×#449—21no—
46C8×Q8×C29C2211yescharacteristic
47C4×SD16×C29—21no—
48C4×SD16×C29C2211yescharacteristic
49C4×D8×C29C2211yescharacteristic
50C29×#436C2211yescharacteristic
51C29×#436C2211yescharacteristic
52C8×D4×C29C2211yescharacteristic
53C29×#428—21no—
54C29×#428—21no—
55C29×#416—21no—
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×D4⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C82×C29C2211yescharacteristic
67C2×#41×C29—21no—
68C2×SD16×C29—21no—
69C2×SD16×C29—21no—
70C2×SD16×C29D411yescharacteristic
71C2×D8×C29D411yescharacteristic
72C2×M16×C29—21no—
73C2×M16×C29—21no—
74C22×C8×C29—21no—
75C29×C4⋊Q8C2311yescharacteristic
76C29×C4⋊Q8C2311yescharacteristic
77C29×C4⋊Q8C2311yescharacteristic
78C29×C4⋊Q8C2311yescharacteristic
79C29×#126—41no—
80C29×#125—21no—
81C29×#124—21no—
82C29×#124—41no—
83C29×#123—41no—
84C29×C22⋊Q8—21no—
85C29×C22⋊Q8—21no—
86C29×C22⋊Q8—21no—
87C29×C22⋊Q8—41no—
88C29×#121—21no—
89C29×#121—21no—
90C29×#121—21no—
91C4×Q8×C29—21no—
92C4×Q8×C29C2311yescharacteristic
93C4×D4×C29—21no—
94C4×D4×C29C2311yescharacteristic
95C4×D4×C29C2311yescharacteristic
96C4×D4×C29C2311yescharacteristic
97C29×#117—21no—
98C29×#117—21no—
99C29×#117—21no—
100C2×C4⋊C4×C29—21no—
101C2×C4⋊C4×C29—21no—
102C29×#107—21no—
103C29×#107—21no—
104C29×#107—21no—
105C29×#107—21no—
106C29×#107—21no—
107C29×#107—21no—
108C29×#107D411yescharacteristic
109C29×#106—21no—
110C29×#106—21no—
111C29×#106—21no—
112C29×#106—21no—
113C29×#106D411yescharacteristic
114C29×C4⋊C8—21no—
115C29×C4⋊C8C2311yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
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×#103—41no—
128C29×#103—41no—
129C29×#103D411yescharacteristic
130C29×#102—21no—
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—
160C22×C4×C29—41no—
161SD16×C29—22no—
162SD16×C29—42no—
163SD16×C29—81no—
164D8×C29—41no—
165M16×C29—42no—
166M16×C29—42no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C2×C8×C29—81no—
173C2×C8×C29C2×D411yescharacteristic
174C2×C8×C29C2×D411yescharacteristic
175C2×C8×C29C2×D411yescharacteristic
176C2×C8×C29C2×D411yescharacteristic
177C4⋊C4×C29—21no—
178C4⋊C4×C29—21no—
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—41no—
187C4⋊C4×C29—41no—
188C4⋊C4×C29—41no—
189C4⋊C4×C29—41no—
190C4⋊C4×C29C2×D411yescharacteristic
191C4⋊C4×C29C2×D411yescharacteristic
192C4⋊C4×C29C2×D411yescharacteristic
193C4⋊C4×C29C2×D411yescharacteristic
194C22⋊C4×C29—21no—
195C22⋊C4×C29—21no—
196C22⋊C4×C29—21no—
197C22⋊C4×C29—41no—
198C22⋊C4×C29—41no—
199C22⋊C4×C29—41no—
200C22⋊C4×C29—41no—
201C22⋊C4×C29—41no—
202C22⋊C4×C29—41no—
203C42×C29—21no—
204C42×C29—41no—
205C42×C29—41no—
206C42×C29C2411yescharacteristic
207#19956C2911yesmaximal, characteristic, direct product factor, Sylow
208C23×C29—21no—
209C23×C29—21no—
210C23×C29—21no—
211Q8×C29—21no—
212Q8×C29—21no—
213Q8×C29—41no—
214Q8×C29—41no—
215Q8×C29—41no—
216Q8×C29—41no—
217Q8×C29—81no—
218Q8×C29—81no—
219D4×C29—21no—
220D4×C29—21no—
221D4×C29—21no—
222D4×C29—21no—
223D4×C29—21no—
224D4×C29—21no—
225D4×C29—82no—
226D4×C29—161no—
227C2×C4×C29—21no—
228C2×C4×C29—21no—
229C2×C4×C29—21no—
230C2×C4×C29—21no—
231C2×C4×C29—21no—
232C2×C4×C29—41no—
233C2×C4×C29—41no—
234C2×C4×C29—41no—
235C2×C4×C29—41no—
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—82no—
243C2×C4×C29—161no—
244C2×C4×C29C22×D411yescharacteristic
245C2×C4×C29C22×D411yescharacteristic
246C2×C4×C29H(5,𝔽2)11yescharacteristic
247C8×C29—21no—
248C8×C29—21no—
249C8×C29—21no—
250C8×C29—41no—
251C8×C29—41no—
252C8×C29—41no—
253C8×C29—41no—
254C8×C29—41no—
255C8×C29#13512yes—
256#3360C2×C2911yescharacteristic, complemented
257#3357C2×C2911yescharacteristic, complemented
258#3353C2×C2911yescharacteristic, complemented
259#3303C2×C2911yescharacteristic
260#1710C2×C2911yescharacteristic, complemented
261#1695C2×C2911yescharacteristic, complemented
262#1693C2×C2911yescharacteristic, complemented
263#1684C2×C2911yescharacteristic, complemented
264#1683C2×C2911yescharacteristic, complemented
265#1646C2×C2911yescharacteristic, complemented
266#1643C2×C2911yescharacteristic, complemented
267#1638C2×C2911yescharacteristic, complemented
268#1635C2×C2911yescharacteristic, complemented
269#1589C2×C2911yescharacteristic, complemented
270C8×SD16C2×C2911yescharacteristic, complemented
271C22×C29—41no—
272C22×C29—41no—
273C22×C29—41no—
274C22×C29—41no—
275C22×C29—41no—
276C22×C29—41no—
277C22×C29—41no—
278C22×C29—41no—
279C22×C29—41no—
280C22×C29D4211yescharacteristic
281C4×C29—21no—
282C4×C29—41no—
283C4×C29—41no—
284C4×C29—41no—
285C4×C29—41no—
286C4×C29—41no—
287C4×C29—81no—
288C4×C29—81no—
289C4×C29—81no—
290C4×C29—81no—
291C4×C29C2×#13511yescharacteristic
292C4×C29#57511yescharacteristic
293C4×C29#57711yescharacteristic
294C4×C29#57811yescharacteristic
295#556C22×C2911yescharacteristic
296#555C22×C2911yescharacteristic
297#554C22×C2911yescharacteristic
298#547C22×C2911yescharacteristic
299#500C22×C2911yescharacteristic
300#500C22×C2911yescharacteristic
301#488—21no—
302#487C22×C2911yescharacteristic
303#487C22×C2911yescharacteristic
304#487C22×C2911yescharacteristic
305#487C22×C2911yescharacteristic
306#485—21no—
307#485—21no—
308#484—21no—
309#482—21no—
310#480—21no—
311#479—21no—
312#477C22×C2911yescharacteristic
313#476C22×C2911yescharacteristic
314#476C22×C2911yescharacteristic
315#476C22×C2911yescharacteristic
316#475C22×C2911yescharacteristic
317#474C22×C2911yescharacteristic
318#468—21no—
319#468—21no—
320#465—21no—
321#463—21no—
322#461C22×C2911yescharacteristic
323#461C22×C2911yescharacteristic
324#449—21no—
325C8×Q8C22×C2911yescharacteristic
326C4×SD16—21no—
327C4×SD16C22×C2911yescharacteristic
328C4×D8C22×C2911yescharacteristic
329#436C22×C2911yescharacteristic
330#436C22×C2911yescharacteristic
331C8×D4C22×C2911yescharacteristic
332#428—21no—
333#428—21no—
334#416—21no—
335#335C22×C2911yescharacteristic
336#334C22×C2911yescharacteristic
337#333C22×C2911yescharacteristic
338#333C22×C2911yescharacteristic
339#332C22×C2911yescharacteristic
340#332C22×C2911yescharacteristic
341Q8⋊C8C22×C2911yescharacteristic
342D4⋊C8C22×C2911yescharacteristic
343D4⋊C8C22×C2911yescharacteristic
344D4⋊C8C22×C2911yescharacteristic
345C82C22×C2911yescharacteristic
346C2×C29—81no—
347C2×C29—81no—
348C2×C29—81no—
349C2×C29#327511yescharacteristic
350C2×C29#328311yescharacteristic
351C2×C29#329011yescharacteristic
352C2×#41—21no—
353C2×SD16—21no—
354C2×SD16—21no—
355C2×SD16D4×C2911yescharacteristic
356C2×D8D4×C2911yescharacteristic
357C2×M16—21no—
358C2×M16—21no—
359C22×C8—21no—
360C4⋊Q8C23×C2911yescharacteristic
361C4⋊Q8C23×C2911yescharacteristic
362C4⋊Q8C23×C2911yescharacteristic
363C4⋊Q8C23×C2911yescharacteristic
364#126—41no—
365#125—21no—
366#124—21no—
367#124—41no—
368#123—41no—
369C22⋊Q8—21no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—41no—
373#121—21no—
374#121—21no—
375#121—21no—
376C4×Q8—21no—
377C4×Q8C23×C2911yescharacteristic
378C4×D4—21no—
379C4×D4C23×C2911yescharacteristic
380C4×D4C23×C2911yescharacteristic
381C4×D4C23×C2911yescharacteristic
382#117—21no—
383#117—21no—
384#117—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387#107—21no—
388#107—21no—
389#107—21no—
390#107—21no—
391#107—21no—
392#107—21no—
393#107D4×C2911yescharacteristic
394#106—21no—
395#106—21no—
396#106—21no—
397#106—21no—
398#106D4×C2911yescharacteristic
399C4⋊C8—21no—
400C4⋊C8C23×C2911yescharacteristic
401C4⋊C8C23×C2911yescharacteristic
402C4⋊C8C23×C2911yescharacteristic
403C4⋊C8C23×C2911yescharacteristic
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#103—41no—
413#103—41no—
414#103D4×C2911yescharacteristic
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102D4×C2911yescharacteristic
420#102D4×C2911yescharacteristic
421#102D4×C2911yescharacteristic
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C4×C8—21no—
426C4×C8C23×C2911yescharacteristic
427C4×C8C23×C2911yescharacteristic
428C4×C8C23×C2911yescharacteristic
429C29#1995611yescharacteristic, direct product factor, Sylow
430#41—42no—
431#41—81no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8C2×D4×C2911yescharacteristic
437C2×D4—41no—
438C2×D4—41no—
439C2×D4C2×D4×C2911yescharacteristic
440C2×D4C2×D4×C2911yescharacteristic
441C2×D4C2×D4×C2911yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—41no—
446C22×C4—41no—
447SD16—22no—
448SD16—42no—
449SD16—81no—
450D8—41no—
451M16—42no—
452M16—42no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—81no—
459C2×C8C2×D4×C2911yescharacteristic
460C2×C8C2×D4×C2911yescharacteristic
461C2×C8C2×D4×C2911yescharacteristic
462C2×C8C2×D4×C2911yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4C2×D4×C2911yescharacteristic
477C4⋊C4C2×D4×C2911yescharacteristic
478C4⋊C4C2×D4×C2911yescharacteristic
479C4⋊C4C2×D4×C2911yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C42—21no—
490C42—41no—
491C42—41no—
492C42C24×C2911yescharacteristic
493C23—21no—
494C23—21no—
495C23—21no—
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—81no—
503Q8—81no—
504D4—21no—
505D4—21no—
506D4—21no—
507D4—21no—
508D4—21no—
509D4—21no—
510D4—82no—
511D4—161no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—161no—
529C2×C4C22×D4×C2911yescharacteristic
530C2×C4C22×D4×C2911yescharacteristic
531C2×C4C29×H(5,𝔽2)11yescharacteristic
532C8—21no—
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8C29×#13512yes—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22D42×C2911yescharacteristic
551C4—21no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4—81no—
561C4C2×C29×#13511yescharacteristic
562C4C29×#57511yescharacteristic
563C4C29×#57711yescharacteristic
564C4C29×#57811yescharacteristic
565C2—81no—
566C2—81no—
567C2—81no—
568C2C29×#327511yescharacteristic
569C2C29×#328311yescharacteristic
570C2C29×#329011yescharacteristic
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×#3360C2semidirect
2. C29×#3357C2semidirect
3. C29×#3353C2semidirect
5. C29×#1710C2semidirect
6. C29×#1695C2semidirect
7. C29×#1693C2semidirect
8. C29×#1684C2semidirect
9. C29×#1683C2semidirect
10. C29×#1646C2semidirect
11. C29×#1643C2semidirect
12. C29×#1638C2semidirect
13. C29×#1635C2semidirect
14. C29×#1589C2semidirect
15. C8×SD16×C29C2semidirect
207. #19956C29direct (N × H)
256. #3360C2×C29semidirect
257. #3357C2×C29semidirect
258. #3353C2×C29semidirect
260. #1710C2×C29semidirect
261. #1695C2×C29semidirect
262. #1693C2×C29semidirect
263. #1684C2×C29semidirect
264. #1683C2×C29semidirect
265. #1646C2×C29semidirect
266. #1643C2×C29semidirect
267. #1638C2×C29semidirect
268. #1635C2×C29semidirect
269. #1589C2×C29semidirect
270. C8×SD16C2×C29semidirect
429. C29#19956direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33602
C29×#33572
C29×#33532
C29×#33032
C29×#17102
C29×#16952
C29×#16932
C29×#16842
C29×#16832
C29×#16462
C29×#16432
C29×#16382
C29×#16352
C29×#15892
C8×SD16×C292
#1995629