Finite Group Databasebeta

← C29×#19842 #20314742

Subgroups — C29×#19842 #20314742

Order 7424.

576 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3372C211yesmaximal, characteristic, complemented
2C29×#3365C211yesmaximal, characteristic, complemented
3C29×#3361C211yesmaximal, characteristic
4C29×#3338C211yesmaximal, characteristic, complemented
5C29×#1719C211yesmaximal, characteristic, complemented
6C29×#1698C211yesmaximal, characteristic, complemented
7C29×#1684C211yesmaximal, characteristic, complemented
8C29×#1681C211yesmaximal, characteristic
9C29×#1676C211yesmaximal, characteristic, complemented
10C29×#1643C211yesmaximal, characteristic, complemented
11C29×#1636C211yesmaximal, characteristic, complemented
12C29×#1630C211yesmaximal, characteristic, complemented
13C29×#1622C211yesmaximal, characteristic
14C29×#1584C211yesmaximal, characteristic, complemented
15C29×SD16⋊C8C211yesmaximal, characteristic, complemented
16C29×#559C2211yescharacteristic
17C29×#557C2211yescharacteristic
18C29×#554C2211yescharacteristic
19C29×#554C2211yescharacteristic
20C29×#500C2211yescharacteristic
21C29×#492C2211yescharacteristic
22C29×#491—21no—
23C29×#488—21no—
24C29×#488—21no—
25C29×#487C2211yescharacteristic
26C29×#487C2211yescharacteristic
27C29×#486C2211yescharacteristic
28C29×#486C2211yescharacteristic
29C29×#484—21no—
30C29×#484—21no—
31C29×#479—21no—
32C29×#478—21no—
33C29×#478—21no—
34C29×#477C2211yescharacteristic
35C29×#477C2211yescharacteristic
36C29×#477C2211yescharacteristic
37C29×#477C2211yescharacteristic
38C29×#475C2211yescharacteristic
39C29×#467—21no—
40C29×#464—21no—
41C29×#463—21no—
42C29×#461—21no—
43C29×#461C2211yescharacteristic
44C29×#460C2211yescharacteristic
45C29×#459C2211yescharacteristic
46C29×#446C2211yescharacteristic
47C8×Q8×C29C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C29×#440—21no—
50C4×Q16×C29C2211yescharacteristic
51C4×SD16×C29—21no—
52C4×SD16×C29C2211yescharacteristic
53C4×D8×C29—21no—
54C8×D4×C29C2211yescharacteristic
55C2×C29×#107—21no—
56C29×#335C2211yescharacteristic
57C29×#335C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×Q8⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C29×#322C2211yescharacteristic
67C2×Q16×C29D411yescharacteristic
68C2×SD16×C29—21no—
69C2×SD16×C29—21no—
70C2×SD16×C29—41no—
71C2×SD16×C29D411yescharacteristic
72C2×D8×C29—21no—
73C22×C8×C29—21no—
74C29×C4⋊Q8—21no—
75C29×C4⋊Q8C2311yescharacteristic
76C29×C4⋊Q8C2311yescharacteristic
77C29×C4⋊Q8C2311yescharacteristic
78C29×#127C2311yescharacteristic
79C29×#125—21no—
80C29×#125—21no—
81C29×#125—21no—
82C29×#125—41no—
83C29×#124—21no—
84C29×#124—21no—
85C29×#123—41no—
86C29×C22⋊Q8—21no—
87C29×C22⋊Q8—21no—
88C29×C22⋊Q8—41no—
89C29×C22⋊Q8—41no—
90C4×Q8×C29—21no—
91C4×Q8×C29—21no—
92C4×Q8×C29C2311yescharacteristic
93C4×Q8×C29C2311yescharacteristic
94C4×Q8×C29C2311yescharacteristic
95C4×D4×C29—21no—
96C4×D4×C29—21no—
97C4×D4×C29—21no—
98C4×D4×C29—21no—
99C4×D4×C29C2311yescharacteristic
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×#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—41no—
127C29×#103D411yescharacteristic
128C29×#103D411yescharacteristic
129C29×#103D411yescharacteristic
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×#102—21no—
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
144C2×Q8×C29—21no—
145C2×Q8×C29—21no—
146C2×Q8×C29—21no—
147C2×Q8×C29C2×D411yescharacteristic
148C2×Q8×C29C2×D411yescharacteristic
149C2×Q8×C29C2×D411yescharacteristic
150C2×D4×C29—21no—
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29C2×D411yescharacteristic
154C22×C4×C29—21no—
155C22×C4×C29—41no—
156C22×C4×C29—41no—
157C22×C4×C29—41no—
158Q16×C29—41no—
159SD16×C29—22no—
160SD16×C29—42no—
161SD16×C29—42no—
162SD16×C29—82no—
163D8×C29—42no—
164C2×C8×C29—21no—
165C2×C8×C29—21no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—42no—
170C2×C8×C29C2×D411yescharacteristic
171C2×C8×C29C2×D411yescharacteristic
172C2×C8×C29C2×D411yescharacteristic
173C2×C8×C29C2×D411yescharacteristic
174C4⋊C4×C29—21no—
175C4⋊C4×C29—21no—
176C4⋊C4×C29—21no—
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—41no—
184C4⋊C4×C29—41no—
185C4⋊C4×C29—41no—
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—41no—
196C22⋊C4×C29—41no—
197C22⋊C4×C29—41no—
198C22⋊C4×C29—41no—
199C22⋊C4×C29—41no—
200C42×C29—21no—
201C42×C29—21no—
202C42×C29—21no—
203C42×C29—41no—
204C42×C29C2411yescharacteristic
205#19842C2911yesmaximal, characteristic, direct product factor, Sylow
206C23×C29—21no—
207C23×C29—41no—
208Q8×C29—21no—
209Q8×C29—21no—
210Q8×C29—21no—
211Q8×C29—21no—
212Q8×C29—21no—
213Q8×C29—21no—
214Q8×C29—41no—
215Q8×C29—41no—
216Q8×C29—81no—
217Q8×C29—81no—
218D4×C29—21no—
219D4×C29—41no—
220D4×C29—41no—
221D4×C29—41no—
222D4×C29—41no—
223D4×C29—81no—
224D4×C29#13512yes—
225C2×C4×C29—21no—
226C2×C4×C29—21no—
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—161no—
238C2×C4×C29—161no—
239C2×C4×C29—161no—
240C2×C4×C29C22×D411yescharacteristic
241C2×C4×C29C22×D411yescharacteristic
242C2×C4×C29H(5,𝔽2)11yescharacteristic
243C8×C29—21no—
244C8×C29—21no—
245C8×C29—21no—
246C8×C29—21no—
247C8×C29—41no—
248C8×C29—41no—
249C8×C29—41no—
250C8×C29—41no—
251C8×C29—41no—
252#3372C2×C2911yescharacteristic, complemented
253#3365C2×C2911yescharacteristic, complemented
254#3361C2×C2911yescharacteristic
255#3338C2×C2911yescharacteristic, complemented
256#1719C2×C2911yescharacteristic, complemented
257#1698C2×C2911yescharacteristic, complemented
258#1684C2×C2911yescharacteristic, complemented
259#1681C2×C2911yescharacteristic
260#1676C2×C2911yescharacteristic, complemented
261#1643C2×C2911yescharacteristic, complemented
262#1636C2×C2911yescharacteristic, complemented
263#1630C2×C2911yescharacteristic, complemented
264#1622C2×C2911yescharacteristic
265#1584C2×C2911yescharacteristic, complemented
266SD16⋊C8C2×C2911yescharacteristic, complemented
267C22×C29—22no—
268C22×C29—41no—
269C22×C29—41no—
270C22×C29—81no—
271C22×C29—81no—
272C22×C29—81no—
273C22×C29D4211yescharacteristic
274C4×C29—21no—
275C4×C29—41no—
276C4×C29—41no—
277C4×C29—41no—
278C4×C29—41no—
279C4×C29—41no—
280C4×C29—41no—
281C4×C29—41no—
282C4×C29—81no—
283C4×C29—81no—
284C4×C29—81no—
285C4×C29C2×#13511yescharacteristic
286C4×C29#57511yescharacteristic
287C4×C29#57811yescharacteristic
288C4×C29#57811yescharacteristic
289#559C22×C2911yescharacteristic
290#557C22×C2911yescharacteristic
291#554C22×C2911yescharacteristic
292#554C22×C2911yescharacteristic
293#500C22×C2911yescharacteristic
294#492C22×C2911yescharacteristic
295#491—21no—
296#488—21no—
297#488—21no—
298#487C22×C2911yescharacteristic
299#487C22×C2911yescharacteristic
300#486C22×C2911yescharacteristic
301#486C22×C2911yescharacteristic
302#484—21no—
303#484—21no—
304#479—21no—
305#478—21no—
306#478—21no—
307#477C22×C2911yescharacteristic
308#477C22×C2911yescharacteristic
309#477C22×C2911yescharacteristic
310#477C22×C2911yescharacteristic
311#475C22×C2911yescharacteristic
312#467—21no—
313#464—21no—
314#463—21no—
315#461—21no—
316#461C22×C2911yescharacteristic
317#460C22×C2911yescharacteristic
318#459C22×C2911yescharacteristic
319#446C22×C2911yescharacteristic
320C8×Q8C22×C2911yescharacteristic
321C8×Q8C22×C2911yescharacteristic
322#440—21no—
323C4×Q16C22×C2911yescharacteristic
324C4×SD16—21no—
325C4×SD16C22×C2911yescharacteristic
326C4×D8—21no—
327C8×D4C22×C2911yescharacteristic
328C2×#107—21no—
329#335C22×C2911yescharacteristic
330#335C22×C2911yescharacteristic
331#333C22×C2911yescharacteristic
332#333C22×C2911yescharacteristic
333#332C22×C2911yescharacteristic
334#331C22×C2911yescharacteristic
335Q8⋊C8C22×C2911yescharacteristic
336Q8⋊C8C22×C2911yescharacteristic
337Q8⋊C8C22×C2911yescharacteristic
338D4⋊C8C22×C2911yescharacteristic
339#322C22×C2911yescharacteristic
340C2×C29—42no—
341C2×C29—161no—
342C2×C29#326911yescharacteristic
343C2×C29#328511yescharacteristic
344C2×C29#328811yescharacteristic
345C2×Q16D4×C2911yescharacteristic
346C2×SD16—21no—
347C2×SD16—21no—
348C2×SD16—41no—
349C2×SD16D4×C2911yescharacteristic
350C2×D8—21no—
351C22×C8—21no—
352C4⋊Q8—21no—
353C4⋊Q8C23×C2911yescharacteristic
354C4⋊Q8C23×C2911yescharacteristic
355C4⋊Q8C23×C2911yescharacteristic
356#127C23×C2911yescharacteristic
357#125—21no—
358#125—21no—
359#125—21no—
360#125—41no—
361#124—21no—
362#124—21no—
363#123—41no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—41no—
367C22⋊Q8—41no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8C23×C2911yescharacteristic
371C4×Q8C23×C2911yescharacteristic
372C4×Q8C23×C2911yescharacteristic
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4C23×C2911yescharacteristic
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380#107—21no—
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107D4×C2911yescharacteristic
387#106—21no—
388#106D4×C2911yescharacteristic
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8C23×C2911yescharacteristic
393C4⋊C8C23×C2911yescharacteristic
394C4⋊C8C23×C2911yescharacteristic
395C4⋊C8C23×C2911yescharacteristic
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—41no—
405#103D4×C2911yescharacteristic
406#103D4×C2911yescharacteristic
407#103D4×C2911yescharacteristic
408#102—21no—
409#102—21no—
410#102—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102D4×C2911yescharacteristic
415C22⋊C8—21no—
416#97—21no—
417C4×C8—21no—
418C4×C8—21no—
419C4×C8C23×C2911yescharacteristic
420C4×C8C23×C2911yescharacteristic
421C4×C8C23×C2911yescharacteristic
422C29#1984211yescharacteristic, direct product factor, Sylow
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8C2×D4×C2911yescharacteristic
427C2×Q8C2×D4×C2911yescharacteristic
428C2×Q8C2×D4×C2911yescharacteristic
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4C2×D4×C2911yescharacteristic
433C22×C4—21no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437Q16—41no—
438SD16—22no—
439SD16—42no—
440SD16—42no—
441SD16—82no—
442D8—42no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—42no—
449C2×C8C2×D4×C2911yescharacteristic
450C2×C8C2×D4×C2911yescharacteristic
451C2×C8C2×D4×C2911yescharacteristic
452C2×C8C2×D4×C2911yescharacteristic
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4C2×D4×C2911yescharacteristic
470C4⋊C4C2×D4×C2911yescharacteristic
471C4⋊C4C2×D4×C2911yescharacteristic
472C4⋊C4C2×D4×C2911yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42C24×C2911yescharacteristic
484C23—21no—
485C23—41no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8—81no—
496D4—21no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—41no—
501D4—81no—
502D4C29×#13512yes—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—161no—
516C2×C4—161no—
517C2×C4—161no—
518C2×C4C22×D4×C2911yescharacteristic
519C2×C4C22×D4×C2911yescharacteristic
520C2×C4C29×H(5,𝔽2)11yescharacteristic
521C8—21no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C22—22no—
531C22—41no—
532C22—41no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22D42×C2911yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—81no—
546C4—81no—
547C4—81no—
548C4C2×C29×#13511yescharacteristic
549C4C29×#57511yescharacteristic
550C4C29×#57811yescharacteristic
551C4C29×#57811yescharacteristic
552C2—42no—
553C2—161no—
554C2C29×#326911yescharacteristic
555C2C29×#328511yescharacteristic
556C2C29×#328811yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#459C22
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×#3372C2semidirect
2. C29×#3365C2semidirect
4. C29×#3338C2semidirect
5. C29×#1719C2semidirect
6. C29×#1698C2semidirect
7. C29×#1684C2semidirect
9. C29×#1676C2semidirect
10. C29×#1643C2semidirect
11. C29×#1636C2semidirect
12. C29×#1630C2semidirect
14. C29×#1584C2semidirect
15. C29×SD16⋊C8C2semidirect
205. #19842C29direct (N × H)
252. #3372C2×C29semidirect
253. #3365C2×C29semidirect
255. #3338C2×C29semidirect
256. #1719C2×C29semidirect
257. #1698C2×C29semidirect
258. #1684C2×C29semidirect
260. #1676C2×C29semidirect
261. #1643C2×C29semidirect
262. #1636C2×C29semidirect
263. #1630C2×C29semidirect
265. #1584C2×C29semidirect
266. SD16⋊C8C2×C29semidirect
422. C29#19842direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33722
C29×#33652
C29×#33612
C29×#33382
C29×#17192
C29×#16982
C29×#16842
C29×#16812
C29×#16762
C29×#16432
C29×#16362
C29×#16302
C29×#16222
C29×#15842
C29×SD16⋊C82
#1984229