Finite Group Databasebeta

← C29×#19850 #20314750

Subgroups — C29×#19850 #20314750

Order 7424.

584 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3396C211yesmaximal, characteristic
2C29×#3375C211yesmaximal, characteristic, complemented
3C29×#3365C211yesmaximal, characteristic, complemented
4C29×#3363C211yesmaximal, characteristic, complemented
5C29×#1717C211yesmaximal, characteristic
6C29×#1702C211yesmaximal, characteristic, complemented
7C29×#1684C211yesmaximal, characteristic, complemented
8C29×#1678C211yesmaximal, characteristic, complemented
9C29×#1668C211yesmaximal, characteristic
10C29×#1640C211yesmaximal, characteristic, complemented
11C29×#1630C211yesmaximal, characteristic, complemented
12C29×#1626C211yesmaximal, characteristic, complemented
13C29×#1623C211yesmaximal, characteristic, complemented
14C29×#1584C211yesmaximal, characteristic, complemented
15C29×#1579C211yesmaximal, characteristic, complemented
16C29×#559C2211yescharacteristic
17C29×#559C2211yescharacteristic
18Q82×C29C2211yescharacteristic
19C29×#557C2211yescharacteristic
20C29×#495—21no—
21C29×#493C2211yescharacteristic
22C29×#492C2211yescharacteristic
23C29×#489—21no—
24C29×#488—21no—
25C29×#487—21no—
26C29×#487C2211yescharacteristic
27C29×#486C2211yescharacteristic
28C29×#486C2211yescharacteristic
29C29×#486C2211yescharacteristic
30C29×#478—21no—
31C29×#477—21no—
32C29×#477C2211yescharacteristic
33C29×#477C2211yescharacteristic
34C29×#475C2211yescharacteristic
35C29×#474—21no—
36C29×#464—21no—
37C29×#464—21no—
38C29×#463—21no—
39C29×#463—21no—
40C29×#462—21no—
41C29×#462C2211yescharacteristic
42C29×#460C2211yescharacteristic
43C29×#460C2211yescharacteristic
44C29×#460C2211yescharacteristic
45C29×#460C2211yescharacteristic
46C29×#446C2211yescharacteristic
47C8×Q8×C29C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C8×Q8×C29C2211yescharacteristic
50C29×#440—21no—
51C4×Q16×C29—21no—
52C4×Q16×C29C2211yescharacteristic
53C4×Q16×C29C2211yescharacteristic
54C4×SD16×C29—21no—
55C4×D8×C29—21no—
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#331C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×Q8⋊C8C2211yescharacteristic
65C29×Q8⋊C8C2211yescharacteristic
66C29×#322C2211yescharacteristic
67C2×Q16×C29—21no—
68C2×Q16×C29D411yescharacteristic
69C2×Q16×C29D411yescharacteristic
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×SD16×C29—41no—
75C2×D8×C29—21no—
76C2×D8×C29—21no—
77C29×C4⋊Q8—21no—
78C29×C4⋊Q8—21no—
79C29×C4⋊Q8—21no—
80C29×C4⋊Q8—41no—
81C29×C4⋊Q8C2311yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×#127C2311yescharacteristic
84C29×#127C2311yescharacteristic
85C29×#125—21no—
86C29×#125—41no—
87C29×#124—21no—
88C29×#124—21no—
89C29×#124—21no—
90C29×#124—21no—
91C29×#123—41no—
92C29×#123—41no—
93C4×Q8×C29—21no—
94C4×Q8×C29—21no—
95C4×Q8×C29—21no—
96C4×Q8×C29—21no—
97C4×Q8×C29C2311yescharacteristic
98C4×Q8×C29C2311yescharacteristic
99C4×Q8×C29C2311yescharacteristic
100C4×Q8×C29C2311yescharacteristic
101C4×D4×C29—21no—
102C4×D4×C29—21no—
103C4×D4×C29—21no—
104C4×D4×C29—21no—
105C29×#107—21no—
106C29×#107—21no—
107C29×#107D411yescharacteristic
108C29×#107D411yescharacteristic
109C29×#106—21no—
110C29×C4⋊C8—21no—
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×#103D411yescharacteristic
125C29×#103D411yescharacteristic
126C29×#103D411yescharacteristic
127C29×#103D411yescharacteristic
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×#102—21no—
136C29×#102—41no—
137C29×#97—21no—
138C4×C8×C29—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—41no—
147C2×Q8×C29C2×D411yescharacteristic
148C2×Q8×C29C2×D411yescharacteristic
149C2×Q8×C29C2×D411yescharacteristic
150C2×Q8×C29C2×D411yescharacteristic
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C22×C4×C29—41no—
158C22×C4×C29—41no—
159Q16×C29—22no—
160Q16×C29—41no—
161Q16×C29—42no—
162SD16×C29—42no—
163SD16×C29—42no—
164SD16×C29—81no—
165SD16×C29—81no—
166SD16×C29—82no—
167D8×C29—42no—
168D8×C29—81no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C2×C8×C29—21no—
173C2×C8×C29—21no—
174C2×C8×C29C2×D411yescharacteristic
175C2×C8×C29C2×D411yescharacteristic
176C2×C8×C29C2×D411yescharacteristic
177C2×C8×C29C2×D411yescharacteristic
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×C29—41no—
191C4⋊C4×C29C2×D411yescharacteristic
192C4⋊C4×C29C2×D411yescharacteristic
193C4⋊C4×C29C2×D411yescharacteristic
194C4⋊C4×C29C2×D411yescharacteristic
195C22⋊C4×C29—41no—
196C22⋊C4×C29—41no—
197C22⋊C4×C29—41no—
198C22⋊C4×C29—41no—
199C22⋊C4×C29—41no—
200C22⋊C4×C29—41no—
201C42×C29—21no—
202C42×C29—21no—
203C42×C29—21no—
204C42×C29—21no—
205C42×C29—41no—
206C42×C29—41no—
207C42×C29C2411yescharacteristic
208#19850C2911yesmaximal, characteristic, direct product factor, Sylow
209C23×C29—41no—
210C23×C29—41no—
211Q8×C29—21no—
212Q8×C29—21no—
213Q8×C29—21no—
214Q8×C29—21no—
215Q8×C29—21no—
216Q8×C29—21no—
217Q8×C29—21no—
218Q8×C29—41no—
219Q8×C29—41no—
220Q8×C29—81no—
221Q8×C29—161no—
222Q8×C29#13512yes—
223D4×C29—41no—
224D4×C29—41no—
225D4×C29—41no—
226D4×C29—41no—
227D4×C29—41no—
228D4×C29—41no—
229D4×C29—41no—
230D4×C29—41no—
231D4×C29—81no—
232D4×C29—81no—
233C2×C4×C29—21no—
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—161no—
244C2×C4×C29—161no—
245C2×C4×C29C22×D411yescharacteristic
246C2×C4×C29C22×D411yescharacteristic
247C2×C4×C29H(5,𝔽2)11yescharacteristic
248C8×C29—21no—
249C8×C29—21no—
250C8×C29—21no—
251C8×C29—21no—
252C8×C29—41no—
253C8×C29—41no—
254C8×C29—41no—
255C8×C29—41no—
256C8×C29—41no—
257#3396C2×C2911yescharacteristic
258#3375C2×C2911yescharacteristic, complemented
259#3365C2×C2911yescharacteristic, complemented
260#3363C2×C2911yescharacteristic, complemented
261#1717C2×C2911yescharacteristic
262#1702C2×C2911yescharacteristic, complemented
263#1684C2×C2911yescharacteristic, complemented
264#1678C2×C2911yescharacteristic, complemented
265#1668C2×C2911yescharacteristic
266#1640C2×C2911yescharacteristic, complemented
267#1630C2×C2911yescharacteristic, complemented
268#1626C2×C2911yescharacteristic, complemented
269#1623C2×C2911yescharacteristic, complemented
270#1584C2×C2911yescharacteristic, complemented
271#1579C2×C2911yescharacteristic, complemented
272C22×C29—81no—
273C22×C29—81no—
274C22×C29—81no—
275C22×C29—81no—
276C22×C29—81no—
277C22×C29—81no—
278C22×C29D4211yescharacteristic
279C4×C29—22no—
280C4×C29—21no—
281C4×C29—41no—
282C4×C29—41no—
283C4×C29—41no—
284C4×C29—41no—
285C4×C29—41no—
286C4×C29—41no—
287C4×C29—41no—
288C4×C29—81no—
289C4×C29—81no—
290C4×C29C2×#13511yescharacteristic
291C4×C29#57511yescharacteristic
292C4×C29#57711yescharacteristic
293C4×C29#57811yescharacteristic
294#559C22×C2911yescharacteristic
295#559C22×C2911yescharacteristic
296Q82C22×C2911yescharacteristic
297#557C22×C2911yescharacteristic
298#495—21no—
299#493C22×C2911yescharacteristic
300#492C22×C2911yescharacteristic
301#489—21no—
302#488—21no—
303#487—21no—
304#487C22×C2911yescharacteristic
305#486C22×C2911yescharacteristic
306#486C22×C2911yescharacteristic
307#486C22×C2911yescharacteristic
308#478—21no—
309#477—21no—
310#477C22×C2911yescharacteristic
311#477C22×C2911yescharacteristic
312#475C22×C2911yescharacteristic
313#474—21no—
314#464—21no—
315#464—21no—
316#463—21no—
317#463—21no—
318#462—21no—
319#462C22×C2911yescharacteristic
320#460C22×C2911yescharacteristic
321#460C22×C2911yescharacteristic
322#460C22×C2911yescharacteristic
323#460C22×C2911yescharacteristic
324#446C22×C2911yescharacteristic
325C8×Q8C22×C2911yescharacteristic
326C8×Q8C22×C2911yescharacteristic
327C8×Q8C22×C2911yescharacteristic
328#440—21no—
329C4×Q16—21no—
330C4×Q16C22×C2911yescharacteristic
331C4×Q16C22×C2911yescharacteristic
332C4×SD16—21no—
333C4×D8—21no—
334#335C22×C2911yescharacteristic
335#334C22×C2911yescharacteristic
336#333C22×C2911yescharacteristic
337#332C22×C2911yescharacteristic
338#331C22×C2911yescharacteristic
339#331C22×C2911yescharacteristic
340Q8⋊C8C22×C2911yescharacteristic
341Q8⋊C8C22×C2911yescharacteristic
342Q8⋊C8C22×C2911yescharacteristic
343Q8⋊C8C22×C2911yescharacteristic
344#322C22×C2911yescharacteristic
345C2×C29—161no—
346C2×C29—161no—
347C2×C29#327111yescharacteristic
348C2×C29#328511yescharacteristic
349C2×C29#328811yescharacteristic
350C2×Q16—21no—
351C2×Q16D4×C2911yescharacteristic
352C2×Q16D4×C2911yescharacteristic
353C2×SD16—21no—
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16—21no—
357C2×SD16—41no—
358C2×D8—21no—
359C2×D8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—41no—
364C4⋊Q8C23×C2911yescharacteristic
365C4⋊Q8C23×C2911yescharacteristic
366#127C23×C2911yescharacteristic
367#127C23×C2911yescharacteristic
368#125—21no—
369#125—41no—
370#124—21no—
371#124—21no—
372#124—21no—
373#124—21no—
374#123—41no—
375#123—41no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8C23×C2911yescharacteristic
381C4×Q8C23×C2911yescharacteristic
382C4×Q8C23×C2911yescharacteristic
383C4×Q8C23×C2911yescharacteristic
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388#107—21no—
389#107—21no—
390#107D4×C2911yescharacteristic
391#107D4×C2911yescharacteristic
392#106—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8C23×C2911yescharacteristic
398C4⋊C8C23×C2911yescharacteristic
399C4⋊C8C23×C2911yescharacteristic
400C4⋊C8C23×C2911yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103D4×C2911yescharacteristic
408#103D4×C2911yescharacteristic
409#103D4×C2911yescharacteristic
410#103D4×C2911yescharacteristic
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—41no—
420#97—21no—
421C4×C8—21no—
422C4×C8—21no—
423C4×C8—21no—
424C4×C8C23×C2911yescharacteristic
425C4×C8C23×C2911yescharacteristic
426C4×C8C23×C2911yescharacteristic
427C29#1985011yescharacteristic, direct product factor, Sylow
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—41no—
431C2×Q8C2×D4×C2911yescharacteristic
432C2×Q8C2×D4×C2911yescharacteristic
433C2×Q8C2×D4×C2911yescharacteristic
434C2×Q8C2×D4×C2911yescharacteristic
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C22×C4—41no—
442C22×C4—41no—
443Q16—22no—
444Q16—41no—
445Q16—42no—
446SD16—42no—
447SD16—42no—
448SD16—81no—
449SD16—81no—
450SD16—82no—
451D8—42no—
452D8—81no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8C2×D4×C2911yescharacteristic
459C2×C8C2×D4×C2911yescharacteristic
460C2×C8C2×D4×C2911yescharacteristic
461C2×C8C2×D4×C2911yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4C2×D4×C2911yescharacteristic
476C4⋊C4C2×D4×C2911yescharacteristic
477C4⋊C4C2×D4×C2911yescharacteristic
478C4⋊C4C2×D4×C2911yescharacteristic
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—41no—
490C42—41no—
491C42C24×C2911yescharacteristic
492C23—41no—
493C23—41no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—41no—
502Q8—41no—
503Q8—81no—
504Q8—161no—
505Q8C29×#13512yes—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—81no—
515D4—81no—
516C2×C4—21no—
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—161no—
527C2×C4—161no—
528C2×C4C22×D4×C2911yescharacteristic
529C2×C4C22×D4×C2911yescharacteristic
530C2×C4C29×H(5,𝔽2)11yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—41no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22D42×C2911yescharacteristic
547C4—22no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4C2×C29×#13511yescharacteristic
559C4C29×#57511yescharacteristic
560C4C29×#57711yescharacteristic
561C4C29×#57811yescharacteristic
562C2—161no—
563C2—161no—
564C2C29×#327111yescharacteristic
565C2C29×#328511yescharacteristic
566C2C29×#328811yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#493C22
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×#3375C2semidirect
3. C29×#3365C2semidirect
4. C29×#3363C2semidirect
6. C29×#1702C2semidirect
7. C29×#1684C2semidirect
8. C29×#1678C2semidirect
10. C29×#1640C2semidirect
11. C29×#1630C2semidirect
12. C29×#1626C2semidirect
13. C29×#1623C2semidirect
14. C29×#1584C2semidirect
15. C29×#1579C2semidirect
208. #19850C29direct (N × H)
258. #3375C2×C29semidirect
259. #3365C2×C29semidirect
260. #3363C2×C29semidirect
262. #1702C2×C29semidirect
263. #1684C2×C29semidirect
264. #1678C2×C29semidirect
266. #1640C2×C29semidirect
267. #1630C2×C29semidirect
268. #1626C2×C29semidirect
269. #1623C2×C29semidirect
270. #1584C2×C29semidirect
271. #1579C2×C29semidirect
427. C29#19850direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33962
C29×#33752
C29×#33652
C29×#33632
C29×#17172
C29×#17022
C29×#16842
C29×#16782
C29×#16682
C29×#16402
C29×#16302
C29×#16262
C29×#16232
C29×#15842
C29×#15792
#1985029