Finite Group Databasebeta

← C29×#19366 #20314266

Subgroups — C29×#19366 #20314266

Order 7424.

592 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×#3252C211yesmaximal, characteristic, complemented
2C29×#3251C211yesmaximal, characteristic
3C29×#3131C211yesmaximal, characteristic, complemented
4C29×#2966C211yesmaximal, characteristic, complemented
5C29×#1704C211yesmaximal, characteristic, complemented
6C29×#1703C211yesmaximal, characteristic, complemented
7C29×#1702C211yesmaximal, characteristic, complemented
8C29×#1701C211yesmaximal, characteristic, complemented
9C29×#1680C211yesmaximal, characteristic, complemented
10C29×#1679C211yesmaximal, characteristic, complemented
11C29×#1678C211yesmaximal, characteristic, complemented
12C29×#1677C211yesmaximal, characteristic, complemented
13C29×#1566C211yesmaximal, characteristic, complemented
14C29×#1559C211yesmaximal, characteristic, complemented
15C29×#1557C211yesmaximal, characteristic, complemented
16C29×#533C2211yescharacteristic
17C29×#532C2211yescharacteristic
18C29×#529C2211yescharacteristic
19C29×#488—21no—
20C29×#488—21no—
21C29×#487C2211yescharacteristic
22C29×#487C2211yescharacteristic
23C29×#486C2211yescharacteristic
24C29×#486C2211yescharacteristic
25C29×#479—21no—
26C29×#478—21no—
27C29×#477C2211yescharacteristic
28C29×#476C2211yescharacteristic
29C29×#475C2211yescharacteristic
30C29×#474C2211yescharacteristic
31C29×#470—21no—
32C29×#469—21no—
33C29×#468—21no—
34C29×#468—21no—
35C29×#464—21no—
36C29×#463—21no—
37C29×#462C2211yescharacteristic
38C29×#461C2211yescharacteristic
39C29×#460C2211yescharacteristic
40C29×#459C2211yescharacteristic
41C29×#446C2211yescharacteristic
42C8×Q8×C29C2211yescharacteristic
43C29×#436C2211yescharacteristic
44C29×#435—21no—
45C8×D4×C29—21no—
46C8×D4×C29C2211yescharacteristic
47C29×#433—21no—
48C29×#432C2211yescharacteristic
49C29×#423C2211yescharacteristic
50C29×#423C2211yescharacteristic
51C29×#416—21no—
52C29×#416—21no—
53C29×#405—21no—
54C2×C4×C8×C29C2211yescharacteristic
55C29×#334C2211yescharacteristic
56C29×#334C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×#332C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#331C2211yescharacteristic
66C29×#331C2211yescharacteristic
67C2×#41×C29—21no—
68C2×Q16×C29—21no—
69C2×SD16×C29—21no—
70C2×SD16×C29—21no—
71C2×D8×C29—21no—
72C2×M16×C29—21no—
73C2×M16×C29—21no—
74C2×M16×C29—21no—
75C22×C8×C29—21no—
76C22×C8×C29D411yescharacteristic
77C22×C8×C29D411yescharacteristic
78C29×C4⋊Q8C2311yescharacteristic
79C29×C4⋊Q8C2311yescharacteristic
80C29×C4⋊Q8C2311yescharacteristic
81C29×#127C2311yescharacteristic
82C29×#126—21no—
83C29×#125—21no—
84C29×#125D411yescharacteristic
85C29×#124—21no—
86C29×#124D411yescharacteristic
87C29×#123—21no—
88C29×C22⋊Q8—21no—
89C29×C22⋊Q8—21no—
90C29×C22⋊Q8D411yescharacteristic
91C29×#121—21no—
92C29×#121—21no—
93C29×#121D411yescharacteristic
94C4×Q8×C29—21no—
95C4×Q8×C29—21no—
96C4×Q8×C29C2311yescharacteristic
97C4×D4×C29—21no—
98C4×D4×C29—21no—
99C4×D4×C29—21no—
100C4×D4×C29C2311yescharacteristic
101C29×#117—21no—
102C29×#117—21no—
103C2×C42×C29C2311yescharacteristic
104C29×#107—21no—
105C29×#107—21no—
106C29×#106—21no—
107C29×#106—21no—
108C29×C4⋊C8—21no—
109C29×C4⋊C8—21no—
110C29×C4⋊C8—21no—
111C29×C4⋊C8—21no—
112C29×C4⋊C8C2311yescharacteristic
113C29×C4⋊C8C2311yescharacteristic
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×#102—21no—
127C29×#102—21no—
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×C22⋊C8—21no—
135C29×C22⋊C8—21no—
136C29×C22⋊C8—21no—
137C29×#97—21no—
138C29×#97—21no—
139C4×C8×C29—21no—
140C4×C8×C29D411yescharacteristic
141C4×C8×C29D411yescharacteristic
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144#41×C29—42no—
145#41×C29—42no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29C2×D411yescharacteristic
150C2×D4×C29—21no—
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—41no—
155C2×D4×C29C2×D411yescharacteristic
156C22×C4×C29—21no—
157C22×C4×C29—41no—
158C22×C4×C29C2×D411yescharacteristic
159C22×C4×C29C2×D411yescharacteristic
160C22×C4×C29#4111yescharacteristic
161Q16×C29—81no—
162SD16×C29—81no—
163SD16×C29—81no—
164D8×C29—81no—
165M16×C29—42no—
166M16×C29—81no—
167M16×C29—81no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C2×C8×C29—21no—
173C2×C8×C29—21no—
174C2×C8×C29—41no—
175C2×C8×C29—41no—
176C2×C8×C29—42no—
177C2×C8×C29C2×D411yescharacteristic
178C2×C8×C29C2×D411yescharacteristic
179C2×C8×C29C2×D411yescharacteristic
180C2×C8×C29C2×D411yescharacteristic
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—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—41no—
192C4⋊C4×C29—41no—
193C4⋊C4×C29C2×D411yescharacteristic
194C4⋊C4×C29C2×D411yescharacteristic
195C22⋊C4×C29—21no—
196C22⋊C4×C29—21no—
197C22⋊C4×C29—21no—
198C22⋊C4×C29—21no—
199C22⋊C4×C29—21no—
200C22⋊C4×C29—41no—
201C22⋊C4×C29—41no—
202C22⋊C4×C29—41no—
203C42×C29—21no—
204C42×C29—41no—
205C42×C29C2×D411yescharacteristic
206C42×C29C2×D411yescharacteristic
207C42×C29#4111yescharacteristic
208C42×C29C2411yescharacteristic
209#19366C2911yesmaximal, characteristic, direct product factor, Sylow
210C23×C29—21no—
211C23×C29—41no—
212C23×C29#12111yescharacteristic
213Q8×C29—21no—
214Q8×C29—21no—
215Q8×C29—41no—
216Q8×C29—41no—
217Q8×C29—41no—
218Q8×C29—41no—
219Q8×C29—81no—
220D4×C29—21no—
221D4×C29—21no—
222D4×C29—42no—
223D4×C29—41no—
224D4×C29—41no—
225D4×C29—41no—
226D4×C29—41no—
227D4×C29—81no—
228D4×C29—82no—
229C2×C4×C29—21no—
230C2×C4×C29—21no—
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—82no—
243C2×C4×C29#12111yescharacteristic
244C2×C4×C29#12111yescharacteristic
245C2×C4×C29#12111yescharacteristic
246C2×C4×C29C22×D411yescharacteristic
247C2×C4×C29C22×D411yescharacteristic
248C2×C4×C29C2×#4111yescharacteristic
249C8×C29—21no—
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—41no—
259#3252C2×C2911yescharacteristic, complemented
260#3251C2×C2911yescharacteristic
261#3131C2×C2911yescharacteristic, complemented
262#2966C2×C2911yescharacteristic, complemented
263#1704C2×C2911yescharacteristic, complemented
264#1703C2×C2911yescharacteristic, complemented
265#1702C2×C2911yescharacteristic, complemented
266#1701C2×C2911yescharacteristic, complemented
267#1680C2×C2911yescharacteristic, complemented
268#1679C2×C2911yescharacteristic, complemented
269#1678C2×C2911yescharacteristic, complemented
270#1677C2×C2911yescharacteristic, complemented
271#1566C2×C2911yescharacteristic, complemented
272#1559C2×C2911yescharacteristic, complemented
273#1557C2×C2911yescharacteristic, complemented
274C22×C29—21no—
275C22×C29—21no—
276C22×C29—21no—
277C22×C29—41no—
278C22×C29—41no—
279C22×C29—41no—
280C22×C29—81no—
281C22×C29—81no—
282C22×C29—81no—
283C22×C29C2×#12111yescharacteristic
284C4×C29—21no—
285C4×C29—21no—
286C4×C29—21no—
287C4×C29—21no—
288C4×C29—41no—
289C4×C29—41no—
290C4×C29—41no—
291C4×C29—81no—
292C4×C29—81no—
293C4×C29—81no—
294C4×C29#57511yescharacteristic
295C4×C29#57511yescharacteristic
296C4×C29#57711yescharacteristic
297C4×C29#57711yescharacteristic
298#533C22×C2911yescharacteristic
299#532C22×C2911yescharacteristic
300#529C22×C2911yescharacteristic
301#488—21no—
302#488—21no—
303#487C22×C2911yescharacteristic
304#487C22×C2911yescharacteristic
305#486C22×C2911yescharacteristic
306#486C22×C2911yescharacteristic
307#479—21no—
308#478—21no—
309#477C22×C2911yescharacteristic
310#476C22×C2911yescharacteristic
311#475C22×C2911yescharacteristic
312#474C22×C2911yescharacteristic
313#470—21no—
314#469—21no—
315#468—21no—
316#468—21no—
317#464—21no—
318#463—21no—
319#462C22×C2911yescharacteristic
320#461C22×C2911yescharacteristic
321#460C22×C2911yescharacteristic
322#459C22×C2911yescharacteristic
323#446C22×C2911yescharacteristic
324C8×Q8C22×C2911yescharacteristic
325#436C22×C2911yescharacteristic
326#435—21no—
327C8×D4—21no—
328C8×D4C22×C2911yescharacteristic
329#433—21no—
330#432C22×C2911yescharacteristic
331#423C22×C2911yescharacteristic
332#423C22×C2911yescharacteristic
333#416—21no—
334#416—21no—
335#405—21no—
336C2×C4×C8C22×C2911yescharacteristic
337#334C22×C2911yescharacteristic
338#334C22×C2911yescharacteristic
339#334C22×C2911yescharacteristic
340#334C22×C2911yescharacteristic
341#333C22×C2911yescharacteristic
342#333C22×C2911yescharacteristic
343#332C22×C2911yescharacteristic
344#332C22×C2911yescharacteristic
345#332C22×C2911yescharacteristic
346#332C22×C2911yescharacteristic
347#331C22×C2911yescharacteristic
348#331C22×C2911yescharacteristic
349C2×C29—41no—
350C2×C29—81no—
351C2×C29—161no—
352C2×C29#304011yescharacteristic
353C2×C29#306011yescharacteristic
354C2×C29#306711yescharacteristic
355C2×#41—21no—
356C2×Q16—21no—
357C2×SD16—21no—
358C2×SD16—21no—
359C2×D8—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C22×C8—21no—
364C22×C8D4×C2911yescharacteristic
365C22×C8D4×C2911yescharacteristic
366C4⋊Q8C23×C2911yescharacteristic
367C4⋊Q8C23×C2911yescharacteristic
368C4⋊Q8C23×C2911yescharacteristic
369#127C23×C2911yescharacteristic
370#126—21no—
371#125—21no—
372#125D4×C2911yescharacteristic
373#124—21no—
374#124D4×C2911yescharacteristic
375#123—21no—
376C22⋊Q8—21no—
377C22⋊Q8—21no—
378C22⋊Q8D4×C2911yescharacteristic
379#121—21no—
380#121—21no—
381#121D4×C2911yescharacteristic
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8C23×C2911yescharacteristic
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4C23×C2911yescharacteristic
389#117—21no—
390#117—21no—
391C2×C42C23×C2911yescharacteristic
392#107—21no—
393#107—21no—
394#106—21no—
395#106—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8C23×C2911yescharacteristic
401C4⋊C8C23×C2911yescharacteristic
402C4⋊C8C23×C2911yescharacteristic
403C4⋊C8C23×C2911yescharacteristic
404C4⋊C8C23×C2911yescharacteristic
405C4⋊C8C23×C2911yescharacteristic
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425#97—21no—
426#97—21no—
427C4×C8—21no—
428C4×C8D4×C2911yescharacteristic
429C4×C8D4×C2911yescharacteristic
430C4×C8C23×C2911yescharacteristic
431C4×C8C23×C2911yescharacteristic
432C29#1936611yescharacteristic, direct product factor, Sylow
433#41—42no—
434#41—42no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C2×D4×C2911yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4C2×D4×C2911yescharacteristic
445C22×C4—21no—
446C22×C4—41no—
447C22×C4C2×D4×C2911yescharacteristic
448C22×C4C2×D4×C2911yescharacteristic
449C22×C4#41×C2911yescharacteristic
450Q16—81no—
451SD16—81no—
452SD16—81no—
453D8—81no—
454M16—42no—
455M16—81no—
456M16—81no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—41no—
464C2×C8—41no—
465C2×C8—42no—
466C2×C8C2×D4×C2911yescharacteristic
467C2×C8C2×D4×C2911yescharacteristic
468C2×C8C2×D4×C2911yescharacteristic
469C2×C8C2×D4×C2911yescharacteristic
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4C2×D4×C2911yescharacteristic
483C4⋊C4C2×D4×C2911yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C42—21no—
493C42—41no—
494C42C2×D4×C2911yescharacteristic
495C42C2×D4×C2911yescharacteristic
496C42#41×C2911yescharacteristic
497C42C24×C2911yescharacteristic
498C23—21no—
499C23—41no—
500C23C29×#12111yescharacteristic
501Q8—21no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—81no—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—81no—
516D4—82no—
517C2×C4—21no—
518C2×C4—21no—
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—82no—
531C2×C4C29×#12111yescharacteristic
532C2×C4C29×#12111yescharacteristic
533C2×C4C29×#12111yescharacteristic
534C2×C4C22×D4×C2911yescharacteristic
535C2×C4C22×D4×C2911yescharacteristic
536C2×C4C2×#41×C2911yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22C2×C29×#12111yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4C29×#57511yescharacteristic
568C4C29×#57511yescharacteristic
569C4C29×#57711yescharacteristic
570C4C29×#57711yescharacteristic
571C2—41no—
572C2—81no—
573C2—161no—
574C2C29×#304011yescharacteristic
575C2C29×#306011yescharacteristic
576C2C29×#306711yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3251C2
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
1. C29×#3252C2semidirect
3. C29×#3131C2semidirect
4. C29×#2966C2semidirect
5. C29×#1704C2semidirect
6. C29×#1703C2semidirect
7. C29×#1702C2semidirect
8. C29×#1701C2semidirect
9. C29×#1680C2semidirect
10. C29×#1679C2semidirect
11. C29×#1678C2semidirect
12. C29×#1677C2semidirect
13. C29×#1566C2semidirect
14. C29×#1559C2semidirect
15. C29×#1557C2semidirect
209. #19366C29direct (N × H)
259. #3252C2×C29semidirect
261. #3131C2×C29semidirect
262. #2966C2×C29semidirect
263. #1704C2×C29semidirect
264. #1703C2×C29semidirect
265. #1702C2×C29semidirect
266. #1701C2×C29semidirect
267. #1680C2×C29semidirect
268. #1679C2×C29semidirect
269. #1678C2×C29semidirect
270. #1677C2×C29semidirect
271. #1566C2×C29semidirect
272. #1559C2×C29semidirect
273. #1557C2×C29semidirect
432. C29#19366direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32522
C29×#32512
C29×#31312
C29×#29662
C29×#17042
C29×#17032
C29×#17022
C29×#17012
C29×#16802
C29×#16792
C29×#16782
C29×#16772
C29×#15662
C29×#15592
C29×#15572
#1936629