Finite Group Databasebeta

← C29×#19849 #20314749

Subgroups — C29×#19849 #20314749

Order 7424.

566 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3395C211yesmaximal, characteristic, complemented
2C29×#3374C211yesmaximal, characteristic, complemented
3C29×#3365C211yesmaximal, characteristic
4C29×#3365C211yesmaximal, characteristic
5C29×#1720C211yesmaximal, characteristic
6C29×#1702C211yesmaximal, characteristic
7C29×#1682C211yesmaximal, characteristic
8C29×#1680C211yesmaximal, characteristic, complemented
9C29×#1670C211yesmaximal, characteristic, complemented
10C29×#1653C211yesmaximal, characteristic, complemented
11C29×#1653C211yesmaximal, characteristic, complemented
12C29×#1640C211yesmaximal, characteristic
13C29×#1626C211yesmaximal, characteristic
14C29×#1584C211yesmaximal, characteristic, complemented
15C29×#1579C211yesmaximal, characteristic, complemented
16C29×#559C2211yescharacteristic
17C29×#557C2211yescharacteristic
18C29×#557C2211yescharacteristic
19C29×#557C2211yescharacteristic
20C29×#498C2211yescharacteristic
21C29×#494—21no—
22C29×#494C2211yescharacteristic
23C29×#491—21no—
24C29×#488—21no—
25C29×#488—21no—
26C29×#487C2211yescharacteristic
27C29×#486C2211yescharacteristic
28C29×#486C2211yescharacteristic
29C29×#486C2211yescharacteristic
30C29×#479—21no—
31C29×#478—21no—
32C29×#478—21no—
33C29×#475C2211yescharacteristic
34C29×#475C2211yescharacteristic
35C29×#475C2211yescharacteristic
36C29×#464—21no—
37C29×#464—21no—
38C29×#462—21no—
39C29×#462—21no—
40C29×#462—21no—
41C29×#462C2211yescharacteristic
42C29×#462C2211yescharacteristic
43C29×#462C2211yescharacteristic
44C29×#460C2211yescharacteristic
45C29×#460C2211yescharacteristic
46C29×#446C2211yescharacteristic
47C8×Q8×C29C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C8×Q8×C29C2211yescharacteristic
50C29×#441—21no—
51C4×Q16×C29—21no—
52C4×Q16×C29C2211yescharacteristic
53C4×Q16×C29C2211yescharacteristic
54C4×SD16×C29—21no—
55C4×SD16×C29—21no—
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#332C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×Q8⋊C8C2211yescharacteristic
65C29×Q8⋊C8C2211yescharacteristic
66C29×#322C2211yescharacteristic
67C2×Q16×C29—21no—
68C2×Q16×C29—21no—
69C2×Q16×C29—21no—
70C2×Q16×C29—21no—
71C2×Q16×C29—21no—
72C2×Q16×C29D411yescharacteristic
73C2×Q16×C29D411yescharacteristic
74C2×SD16×C29—21no—
75C2×SD16×C29—21no—
76C29×C4⋊Q8—21no—
77C29×C4⋊Q8—21no—
78C29×C4⋊Q8—21no—
79C29×C4⋊Q8C2311yescharacteristic
80C29×C4⋊Q8C2311yescharacteristic
81C29×C4⋊Q8C2311yescharacteristic
82C29×#127C2311yescharacteristic
83C29×#125—21no—
84C29×#125—21no—
85C29×#125—21no—
86C29×#125—41no—
87C29×#125—41no—
88C29×#125—41no—
89C29×#124—21no—
90C29×#124—21no—
91C29×#123—41no—
92C4×Q8×C29—21no—
93C4×Q8×C29—21no—
94C4×Q8×C29—21no—
95C4×Q8×C29—21no—
96C4×Q8×C29—21no—
97C4×Q8×C29—21no—
98C4×Q8×C29C2311yescharacteristic
99C4×Q8×C29C2311yescharacteristic
100C4×Q8×C29C2311yescharacteristic
101C4×Q8×C29C2311yescharacteristic
102C4×D4×C29—21no—
103C4×D4×C29—21no—
104C29×#107D411yescharacteristic
105C29×#107D411yescharacteristic
106C29×#106—21no—
107C29×#106—21no—
108C29×#106—21no—
109C29×#106—41no—
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×#103—21no—
125C29×#103—21no—
126C29×#103D411yescharacteristic
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×#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—21no—
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—
154C22×C4×C29—41no—
155Q16×C29—22no—
156Q16×C29—41no—
157Q16×C29—42no—
158Q16×C29—42no—
159Q16×C29—81no—
160Q16×C29—81no—
161Q16×C29—81no—
162SD16×C29—42no—
163SD16×C29—42no—
164C2×C8×C29—21no—
165C2×C8×C29—21no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29C2×D411yescharacteristic
170C2×C8×C29C2×D411yescharacteristic
171C2×C8×C29C2×D411yescharacteristic
172C2×C8×C29C2×D411yescharacteristic
173C4⋊C4×C29—21no—
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×C29—41no—
191C4⋊C4×C29—41no—
192C4⋊C4×C29C2×D411yescharacteristic
193C4⋊C4×C29C2×D411yescharacteristic
194C4⋊C4×C29C2×D411yescharacteristic
195C4⋊C4×C29C2×D411yescharacteristic
196C22⋊C4×C29—41no—
197C22⋊C4×C29—41no—
198C22⋊C4×C29—41no—
199C42×C29—21no—
200C42×C29—21no—
201C42×C29—21no—
202C42×C29—21no—
203C42×C29—41no—
204C42×C29—41no—
205C42×C29—41no—
206C42×C29C2411yescharacteristic
207#19849C2911yesmaximal, characteristic, direct product factor, Sylow
208C23×C29—41no—
209Q8×C29—21no—
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—41no—
221Q8×C29—41no—
222Q8×C29#13512yes—
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—21no—
236C2×C4×C29—41no—
237C2×C4×C29—41no—
238C2×C4×C29—41no—
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#3395C2×C2911yescharacteristic, complemented
253#3374C2×C2911yescharacteristic, complemented
254#3365C2×C2911yescharacteristic
255#3365C2×C2911yescharacteristic
256#1720C2×C2911yescharacteristic
257#1702C2×C2911yescharacteristic
258#1682C2×C2911yescharacteristic
259#1680C2×C2911yescharacteristic, complemented
260#1670C2×C2911yescharacteristic, complemented
261#1653C2×C2911yescharacteristic, complemented
262#1653C2×C2911yescharacteristic, complemented
263#1640C2×C2911yescharacteristic
264#1626C2×C2911yescharacteristic
265#1584C2×C2911yescharacteristic, complemented
266#1579C2×C2911yescharacteristic, complemented
267C22×C29—81no—
268C22×C29—81no—
269C22×C29—81no—
270C22×C29D4211yescharacteristic
271C4×C29—22no—
272C4×C29—21no—
273C4×C29—41no—
274C4×C29—41no—
275C4×C29—41no—
276C4×C29—41no—
277C4×C29—41no—
278C4×C29—41no—
279C4×C29—41no—
280C4×C29—81no—
281C4×C29—81no—
282C4×C29—81no—
283C4×C29C2×#13511yescharacteristic
284C4×C29#57511yescharacteristic
285C4×C29#57711yescharacteristic
286C4×C29#57811yescharacteristic
287#559C22×C2911yescharacteristic
288#557C22×C2911yescharacteristic
289#557C22×C2911yescharacteristic
290#557C22×C2911yescharacteristic
291#498C22×C2911yescharacteristic
292#494—21no—
293#494C22×C2911yescharacteristic
294#491—21no—
295#488—21no—
296#488—21no—
297#487C22×C2911yescharacteristic
298#486C22×C2911yescharacteristic
299#486C22×C2911yescharacteristic
300#486C22×C2911yescharacteristic
301#479—21no—
302#478—21no—
303#478—21no—
304#475C22×C2911yescharacteristic
305#475C22×C2911yescharacteristic
306#475C22×C2911yescharacteristic
307#464—21no—
308#464—21no—
309#462—21no—
310#462—21no—
311#462—21no—
312#462C22×C2911yescharacteristic
313#462C22×C2911yescharacteristic
314#462C22×C2911yescharacteristic
315#460C22×C2911yescharacteristic
316#460C22×C2911yescharacteristic
317#446C22×C2911yescharacteristic
318C8×Q8C22×C2911yescharacteristic
319C8×Q8C22×C2911yescharacteristic
320C8×Q8C22×C2911yescharacteristic
321#441—21no—
322C4×Q16—21no—
323C4×Q16C22×C2911yescharacteristic
324C4×Q16C22×C2911yescharacteristic
325C4×SD16—21no—
326C4×SD16—21no—
327#335C22×C2911yescharacteristic
328#334C22×C2911yescharacteristic
329#332C22×C2911yescharacteristic
330#332C22×C2911yescharacteristic
331#332C22×C2911yescharacteristic
332#331C22×C2911yescharacteristic
333Q8⋊C8C22×C2911yescharacteristic
334Q8⋊C8C22×C2911yescharacteristic
335Q8⋊C8C22×C2911yescharacteristic
336Q8⋊C8C22×C2911yescharacteristic
337#322C22×C2911yescharacteristic
338C2×C29—161no—
339C2×C29#327111yescharacteristic
340C2×C29#328511yescharacteristic
341C2×C29#328911yescharacteristic
342C2×Q16—21no—
343C2×Q16—21no—
344C2×Q16—21no—
345C2×Q16—21no—
346C2×Q16—21no—
347C2×Q16D4×C2911yescharacteristic
348C2×Q16D4×C2911yescharacteristic
349C2×SD16—21no—
350C2×SD16—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8C23×C2911yescharacteristic
355C4⋊Q8C23×C2911yescharacteristic
356C4⋊Q8C23×C2911yescharacteristic
357#127C23×C2911yescharacteristic
358#125—21no—
359#125—21no—
360#125—21no—
361#125—41no—
362#125—41no—
363#125—41no—
364#124—21no—
365#124—21no—
366#123—41no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8C23×C2911yescharacteristic
374C4×Q8C23×C2911yescharacteristic
375C4×Q8C23×C2911yescharacteristic
376C4×Q8C23×C2911yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379#107D4×C2911yescharacteristic
380#107D4×C2911yescharacteristic
381#106—21no—
382#106—21no—
383#106—21no—
384#106—41no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8C23×C2911yescharacteristic
390C4⋊C8C23×C2911yescharacteristic
391C4⋊C8C23×C2911yescharacteristic
392C4⋊C8C23×C2911yescharacteristic
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103D4×C2911yescharacteristic
402#103D4×C2911yescharacteristic
403#103D4×C2911yescharacteristic
404#103D4×C2911yescharacteristic
405#102—21no—
406#102—21no—
407#102—21no—
408#102—21no—
409#102—21no—
410#102—21no—
411#102—41no—
412#97—21no—
413C4×C8—21no—
414C4×C8—21no—
415C4×C8—21no—
416C4×C8C23×C2911yescharacteristic
417C4×C8C23×C2911yescharacteristic
418C4×C8C23×C2911yescharacteristic
419C29#1984911yescharacteristic, direct product factor, Sylow
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8C2×D4×C2911yescharacteristic
424C2×Q8C2×D4×C2911yescharacteristic
425C2×Q8C2×D4×C2911yescharacteristic
426C2×Q8C2×D4×C2911yescharacteristic
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C22×C4—41no—
431Q16—22no—
432Q16—41no—
433Q16—42no—
434Q16—42no—
435Q16—81no—
436Q16—81no—
437Q16—81no—
438SD16—42no—
439SD16—42no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8C2×D4×C2911yescharacteristic
446C2×C8C2×D4×C2911yescharacteristic
447C2×C8C2×D4×C2911yescharacteristic
448C2×C8C2×D4×C2911yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4C2×D4×C2911yescharacteristic
469C4⋊C4C2×D4×C2911yescharacteristic
470C4⋊C4C2×D4×C2911yescharacteristic
471C4⋊C4C2×D4×C2911yescharacteristic
472C22⋊C4—41no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—41no—
480C42—41no—
481C42—41no—
482C42C24×C2911yescharacteristic
483C23—41no—
484Q8—21no—
485Q8—21no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8C29×#13512yes—
498D4—41no—
499D4—41no—
500D4—41no—
501D4—41no—
502D4—81no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—161no—
515C2×C4C22×D4×C2911yescharacteristic
516C2×C4C22×D4×C2911yescharacteristic
517C2×C4C29×H(5,𝔽2)11yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—21no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—41no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22D42×C2911yescharacteristic
531C4—22no—
532C4—21no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—81no—
541C4—81no—
542C4—81no—
543C4C2×C29×#13511yescharacteristic
544C4C29×#57511yescharacteristic
545C4C29×#57711yescharacteristic
546C4C29×#57811yescharacteristic
547C2—161no—
548C2C29×#327111yescharacteristic
549C2C29×#328511yescharacteristic
550C2C29×#328911yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#127C23
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×#3395C2semidirect
2. C29×#3374C2semidirect
8. C29×#1680C2semidirect
9. C29×#1670C2semidirect
10. C29×#1653C2semidirect
11. C29×#1653C2semidirect
14. C29×#1584C2semidirect
15. C29×#1579C2semidirect
207. #19849C29direct (N × H)
252. #3395C2×C29semidirect
253. #3374C2×C29semidirect
259. #1680C2×C29semidirect
260. #1670C2×C29semidirect
261. #1653C2×C29semidirect
262. #1653C2×C29semidirect
265. #1584C2×C29semidirect
266. #1579C2×C29semidirect
419. C29#19849direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33952
C29×#33742
C29×#33652
C29×#17202
C29×#17022
C29×#16822
C29×#16802
C29×#16702
C29×#16532
C29×#16402
C29×#16262
C29×#15842
C29×#15792
#1984929