Finite Group Databasebeta

← C29×#19951 #20314851

Subgroups — C29×#19951 #20314851

Order 7424.

574 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3400C211yesmaximal, characteristic, complemented
2C29×#3364C211yesmaximal, characteristic, complemented
3C29×#3361C211yesmaximal, characteristic
4C29×#3356C211yesmaximal, characteristic, complemented
5C29×#1708C211yesmaximal, characteristic, complemented
6C29×#1692C211yesmaximal, characteristic, complemented
7C29×#1685C211yesmaximal, characteristic
8C29×#1680C211yesmaximal, characteristic, complemented
9C29×#1678C211yesmaximal, characteristic, complemented
10C29×#1644C211yesmaximal, characteristic, complemented
11C29×#1640C211yesmaximal, characteristic, complemented
12C29×#1636C211yesmaximal, characteristic, complemented
13C29×#1628C211yesmaximal, characteristic
14C29×#1590C211yesmaximal, characteristic, complemented
15C8×Q16×C29C211yesmaximal, characteristic, complemented
16C29×#559C2211yescharacteristic
17C29×#557C2211yescharacteristic
18C29×#556C2211yescharacteristic
19C29×#554C2211yescharacteristic
20C29×#498C2211yescharacteristic
21C29×#497—21no—
22C29×#492C2211yescharacteristic
23C29×#488—21no—
24C29×#488—21no—
25C29×#487C2211yescharacteristic
26C29×#487C2211yescharacteristic
27C29×#486C2211yescharacteristic
28C29×#486C2211yescharacteristic
29C29×#485—21no—
30C29×#483—21no—
31C29×#479—21no—
32C29×#478—21no—
33C29×#477C2211yescharacteristic
34C29×#477C2211yescharacteristic
35C29×#475C2211yescharacteristic
36C29×#474C2211yescharacteristic
37C29×#470—21no—
38C29×#464—21no—
39C29×#464—21no—
40C29×#463—21no—
41C29×#462C2211yescharacteristic
42C29×#462C2211yescharacteristic
43C29×#461—21no—
44C29×#460C2211yescharacteristic
45C29×#459C2211yescharacteristic
46C29×#446C2211yescharacteristic
47C8×Q8×C29C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C29×#440—21no—
50C4×Q16×C29—21no—
51C4×Q16×C29C2211yescharacteristic
52C4×SD16×C29C2211yescharacteristic
53C4×D8×C29—21no—
54C29×#436C2211yescharacteristic
55C29×#428—21no—
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×Q8⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C82×C29C2211yescharacteristic
67C2×Q16×C29—21no—
68C2×Q16×C29—21no—
69C2×Q16×C29D411yescharacteristic
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29D411yescharacteristic
74C2×D8×C29—21no—
75C2×M16×C29—21no—
76C29×C4⋊Q8—21no—
77C29×C4⋊Q8C2311yescharacteristic
78C29×C4⋊Q8C2311yescharacteristic
79C29×C4⋊Q8C2311yescharacteristic
80C29×#127C2311yescharacteristic
81C29×#126—41no—
82C29×#125—21no—
83C29×#125—21no—
84C29×#125—41no—
85C29×#124—21no—
86C29×#124—21no—
87C29×#124—21no—
88C29×#123—41no—
89C29×C22⋊Q8—21no—
90C29×C22⋊Q8—21no—
91C29×C22⋊Q8—41no—
92C4×Q8×C29—21no—
93C4×Q8×C29—21no—
94C4×Q8×C29—21no—
95C4×Q8×C29C2311yescharacteristic
96C4×Q8×C29C2311yescharacteristic
97C4×Q8×C29C2311yescharacteristic
98C4×D4×C29—21no—
99C4×D4×C29—21no—
100C4×D4×C29—21no—
101C4×D4×C29C2311yescharacteristic
102C29×#117—21no—
103C2×C4⋊C4×C29—21no—
104C29×#107—21no—
105C29×#107—21no—
106C29×#107—21no—
107C29×#107D411yescharacteristic
108C29×#106—21no—
109C29×#106—21no—
110C29×#106—21no—
111C29×#106D411yescharacteristic
112C29×C4⋊C8—21no—
113C29×C4⋊C8—21no—
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—41no—
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
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—
157Q16×C29—22no—
158Q16×C29—42no—
159Q16×C29—81no—
160SD16×C29—41no—
161SD16×C29—42no—
162SD16×C29—81no—
163SD16×C29—81no—
164D8×C29—42no—
165M16×C29—42no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29C2×D411yescharacteristic
172C2×C8×C29C2×D411yescharacteristic
173C2×C8×C29C2×D411yescharacteristic
174C2×C8×C29C2×D411yescharacteristic
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—21no—
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—
200C22⋊C4×C29—41no—
201C42×C29—21no—
202C42×C29—21no—
203C42×C29—21no—
204C42×C29—41no—
205C42×C29—41no—
206C42×C29C2411yescharacteristic
207#19951C2911yesmaximal, characteristic, direct product factor, Sylow
208C23×C29—21no—
209C23×C29—41no—
210Q8×C29—21no—
211Q8×C29—21no—
212Q8×C29—21no—
213Q8×C29—21no—
214Q8×C29—21no—
215Q8×C29—21no—
216Q8×C29—41no—
217Q8×C29—41no—
218Q8×C29—41no—
219Q8×C29—41no—
220Q8×C29—81no—
221D4×C29—21no—
222D4×C29—21no—
223D4×C29—41no—
224D4×C29—41no—
225D4×C29—41no—
226D4×C29—41no—
227D4×C29—81no—
228C2×C4×C29—21no—
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—41no—
236C2×C4×C29—41no—
237C2×C4×C29—41no—
238C2×C4×C29—41no—
239C2×C4×C29—41no—
240C2×C4×C29—161no—
241C2×C4×C29—161no—
242C2×C4×C29C22×D411yescharacteristic
243C2×C4×C29C22×D411yescharacteristic
244C2×C4×C29H(5,𝔽2)11yescharacteristic
245C8×C29—21no—
246C8×C29—21no—
247C8×C29—21no—
248C8×C29—41no—
249C8×C29—41no—
250C8×C29—41no—
251C8×C29—41no—
252C8×C29—41no—
253C8×C29#13512yes—
254#3400C2×C2911yescharacteristic, complemented
255#3364C2×C2911yescharacteristic, complemented
256#3361C2×C2911yescharacteristic
257#3356C2×C2911yescharacteristic, complemented
258#1708C2×C2911yescharacteristic, complemented
259#1692C2×C2911yescharacteristic, complemented
260#1685C2×C2911yescharacteristic
261#1680C2×C2911yescharacteristic, complemented
262#1678C2×C2911yescharacteristic, complemented
263#1644C2×C2911yescharacteristic, complemented
264#1640C2×C2911yescharacteristic, complemented
265#1636C2×C2911yescharacteristic, complemented
266#1628C2×C2911yescharacteristic
267#1590C2×C2911yescharacteristic, complemented
268C8×Q16C2×C2911yescharacteristic, complemented
269C22×C29—41no—
270C22×C29—41no—
271C22×C29—41no—
272C22×C29—81no—
273C22×C29—81no—
274C22×C29—81no—
275C22×C29D4211yescharacteristic
276C4×C29—21no—
277C4×C29—41no—
278C4×C29—41no—
279C4×C29—41no—
280C4×C29—41no—
281C4×C29—41no—
282C4×C29—41no—
283C4×C29—41no—
284C4×C29—81no—
285C4×C29—81no—
286C4×C29—81no—
287C4×C29C2×#13511yescharacteristic
288C4×C29#57511yescharacteristic
289C4×C29#57711yescharacteristic
290C4×C29#57811yescharacteristic
291#559C22×C2911yescharacteristic
292#557C22×C2911yescharacteristic
293#556C22×C2911yescharacteristic
294#554C22×C2911yescharacteristic
295#498C22×C2911yescharacteristic
296#497—21no—
297#492C22×C2911yescharacteristic
298#488—21no—
299#488—21no—
300#487C22×C2911yescharacteristic
301#487C22×C2911yescharacteristic
302#486C22×C2911yescharacteristic
303#486C22×C2911yescharacteristic
304#485—21no—
305#483—21no—
306#479—21no—
307#478—21no—
308#477C22×C2911yescharacteristic
309#477C22×C2911yescharacteristic
310#475C22×C2911yescharacteristic
311#474C22×C2911yescharacteristic
312#470—21no—
313#464—21no—
314#464—21no—
315#463—21no—
316#462C22×C2911yescharacteristic
317#462C22×C2911yescharacteristic
318#461—21no—
319#460C22×C2911yescharacteristic
320#459C22×C2911yescharacteristic
321#446C22×C2911yescharacteristic
322C8×Q8C22×C2911yescharacteristic
323C8×Q8C22×C2911yescharacteristic
324#440—21no—
325C4×Q16—21no—
326C4×Q16C22×C2911yescharacteristic
327C4×SD16C22×C2911yescharacteristic
328C4×D8—21no—
329#436C22×C2911yescharacteristic
330#428—21no—
331#335C22×C2911yescharacteristic
332#334C22×C2911yescharacteristic
333#333C22×C2911yescharacteristic
334#332C22×C2911yescharacteristic
335#332C22×C2911yescharacteristic
336#331C22×C2911yescharacteristic
337Q8⋊C8C22×C2911yescharacteristic
338Q8⋊C8C22×C2911yescharacteristic
339Q8⋊C8C22×C2911yescharacteristic
340D4⋊C8C22×C2911yescharacteristic
341C82C22×C2911yescharacteristic
342C2×C29—81no—
343C2×C29—161no—
344C2×C29#327711yescharacteristic
345C2×C29#328411yescharacteristic
346C2×C29#329011yescharacteristic
347C2×Q16—21no—
348C2×Q16—21no—
349C2×Q16D4×C2911yescharacteristic
350C2×SD16—21no—
351C2×SD16—21no—
352C2×SD16—21no—
353C2×SD16D4×C2911yescharacteristic
354C2×D8—21no—
355C2×M16—21no—
356C4⋊Q8—21no—
357C4⋊Q8C23×C2911yescharacteristic
358C4⋊Q8C23×C2911yescharacteristic
359C4⋊Q8C23×C2911yescharacteristic
360#127C23×C2911yescharacteristic
361#126—41no—
362#125—21no—
363#125—21no—
364#125—41no—
365#124—21no—
366#124—21no—
367#124—21no—
368#123—41no—
369C22⋊Q8—21no—
370C22⋊Q8—21no—
371C22⋊Q8—41no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8C23×C2911yescharacteristic
376C4×Q8C23×C2911yescharacteristic
377C4×Q8C23×C2911yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4C23×C2911yescharacteristic
382#117—21no—
383C2×C4⋊C4—21no—
384#107—21no—
385#107—21no—
386#107—21no—
387#107D4×C2911yescharacteristic
388#106—21no—
389#106—21no—
390#106—21no—
391#106D4×C2911yescharacteristic
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8C23×C2911yescharacteristic
396C4⋊C8C23×C2911yescharacteristic
397C4⋊C8C23×C2911yescharacteristic
398C4⋊C8C23×C2911yescharacteristic
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—41no—
407#103D4×C2911yescharacteristic
408#103D4×C2911yescharacteristic
409#103D4×C2911yescharacteristic
410#102—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—41no—
416#102D4×C2911yescharacteristic
417C22⋊C8—21no—
418#97—21no—
419C4×C8—21no—
420C4×C8—21no—
421C4×C8C23×C2911yescharacteristic
422C4×C8C23×C2911yescharacteristic
423C4×C8C23×C2911yescharacteristic
424C29#1995111yescharacteristic, direct product factor, Sylow
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8C2×D4×C2911yescharacteristic
429C2×Q8C2×D4×C2911yescharacteristic
430C2×Q8C2×D4×C2911yescharacteristic
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4C2×D4×C2911yescharacteristic
435C22×C4—21no—
436C22×C4—41no—
437C22×C4—41no—
438Q16—22no—
439Q16—42no—
440Q16—81no—
441SD16—41no—
442SD16—42no—
443SD16—81no—
444SD16—81no—
445D8—42no—
446M16—42no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8C2×D4×C2911yescharacteristic
453C2×C8C2×D4×C2911yescharacteristic
454C2×C8C2×D4×C2911yescharacteristic
455C2×C8C2×D4×C2911yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4C2×D4×C2911yescharacteristic
472C4⋊C4C2×D4×C2911yescharacteristic
473C4⋊C4C2×D4×C2911yescharacteristic
474C4⋊C4C2×D4×C2911yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—41no—
486C42—41no—
487C42C24×C2911yescharacteristic
488C23—21no—
489C23—41no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501D4—21no—
502D4—21no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—81no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—161no—
521C2×C4—161no—
522C2×C4C22×D4×C2911yescharacteristic
523C2×C4C22×D4×C2911yescharacteristic
524C2×C4C29×H(5,𝔽2)11yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8C29×#13512yes—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22D42×C2911yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4C2×C29×#13511yescharacteristic
553C4C29×#57511yescharacteristic
554C4C29×#57711yescharacteristic
555C4C29×#57811yescharacteristic
556C2—81no—
557C2—161no—
558C2C29×#327711yescharacteristic
559C2C29×#328411yescharacteristic
560C2C29×#329011yescharacteristic
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×#3400C2semidirect
2. C29×#3364C2semidirect
4. C29×#3356C2semidirect
5. C29×#1708C2semidirect
6. C29×#1692C2semidirect
8. C29×#1680C2semidirect
9. C29×#1678C2semidirect
10. C29×#1644C2semidirect
11. C29×#1640C2semidirect
12. C29×#1636C2semidirect
14. C29×#1590C2semidirect
15. C8×Q16×C29C2semidirect
207. #19951C29direct (N × H)
254. #3400C2×C29semidirect
255. #3364C2×C29semidirect
257. #3356C2×C29semidirect
258. #1708C2×C29semidirect
259. #1692C2×C29semidirect
261. #1680C2×C29semidirect
262. #1678C2×C29semidirect
263. #1644C2×C29semidirect
264. #1640C2×C29semidirect
265. #1636C2×C29semidirect
267. #1590C2×C29semidirect
268. C8×Q16C2×C29semidirect
424. C29#19951direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34002
C29×#33642
C29×#33612
C29×#33562
C29×#17082
C29×#16922
C29×#16852
C29×#16802
C29×#16782
C29×#16442
C29×#16402
C29×#16362
C29×#16282
C29×#15902
C8×Q16×C292
#1995129