Finite Group Databasebeta

← C29×#19941 #20314841

Subgroups — C29×#19941 #20314841

Order 7424.

560 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3375C211yesmaximal, characteristic
2C29×#3374C211yesmaximal, characteristic, complemented
3C29×#3365C211yesmaximal, characteristic
4C29×#3363C211yesmaximal, characteristic, complemented
5C29×#1711C211yesmaximal, characteristic
6C29×#1700C211yesmaximal, characteristic, complemented
7C29×#1698C211yesmaximal, characteristic
8C29×#1684C211yesmaximal, characteristic, complemented
9C29×#1682C211yesmaximal, characteristic
10C29×#1645C211yesmaximal, characteristic, complemented
11C29×#1640C211yesmaximal, characteristic
12C29×#1636C211yesmaximal, characteristic, complemented
13C29×#1626C211yesmaximal, characteristic
14C29×#1591C211yesmaximal, characteristic, complemented
15C8×Q16×C29C211yesmaximal, characteristic, complemented
16C29×#559C2211yescharacteristic
17Q82×C29C2211yescharacteristic
18C29×#557C2211yescharacteristic
19C29×#557C2211yescharacteristic
20C29×#491—21no—
21C29×#489—21no—
22C29×#488—21no—
23C29×#487—21no—
24C29×#487C2211yescharacteristic
25C29×#487C2211yescharacteristic
26C29×#487C2211yescharacteristic
27C29×#486C2211yescharacteristic
28C29×#486C2211yescharacteristic
29C29×#486C2211yescharacteristic
30C29×#479—21no—
31C29×#478—21no—
32C29×#477—21no—
33C29×#477C2211yescharacteristic
34C29×#477C2211yescharacteristic
35C29×#475C2211yescharacteristic
36C29×#475C2211yescharacteristic
37C29×#474—21no—
38C29×#464—21no—
39C29×#464—21no—
40C29×#462—21no—
41C29×#462—21no—
42C29×#462C2211yescharacteristic
43C29×#462C2211yescharacteristic
44C29×#460C2211yescharacteristic
45C29×#460C2211yescharacteristic
46C29×#446C2211yescharacteristic
47C29×#446C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C8×Q8×C29C2211yescharacteristic
50C29×#441—21no—
51C29×#440—21no—
52C4×Q16×C29—21no—
53C4×Q16×C29C2211yescharacteristic
54C4×Q16×C29C2211yescharacteristic
55C4×SD16×C29—21no—
56C29×#335C2211yescharacteristic
57C29×#335C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×Q8⋊C8C2211yescharacteristic
65C29×Q8⋊C8C2211yescharacteristic
66C82×C29C2211yescharacteristic
67C2×Q16×C29—21no—
68C2×Q16×C29—21no—
69C2×Q16×C29D411yescharacteristic
70C2×Q16×C29D411yescharacteristic
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C29×C4⋊Q8—21no—
74C29×C4⋊Q8—21no—
75C29×C4⋊Q8—21no—
76C29×C4⋊Q8—21no—
77C29×C4⋊Q8—41no—
78C29×C4⋊Q8C2311yescharacteristic
79C29×C4⋊Q8C2311yescharacteristic
80C29×C4⋊Q8C2311yescharacteristic
81C29×#127C2311yescharacteristic
82C29×#125—21no—
83C29×#125—21no—
84C29×#125—41no—
85C29×#125—41no—
86C29×#124—21no—
87C29×#124—21no—
88C29×#123—41no—
89C4×Q8×C29—21no—
90C4×Q8×C29—21no—
91C4×Q8×C29—21no—
92C4×Q8×C29—21no—
93C4×Q8×C29—21no—
94C4×Q8×C29—21no—
95C4×Q8×C29C2311yescharacteristic
96C4×Q8×C29C2311yescharacteristic
97C4×Q8×C29C2311yescharacteristic
98C4×Q8×C29C2311yescharacteristic
99C4×D4×C29—21no—
100C4×D4×C29—21no—
101C29×#107—21no—
102C29×#107—21no—
103C29×#107D411yescharacteristic
104C29×#107D411yescharacteristic
105C29×#106—21no—
106C29×#106—21no—
107C29×C4⋊C8—21no—
108C29×C4⋊C8—21no—
109C29×C4⋊C8—21no—
110C29×C4⋊C8—21no—
111C29×C4⋊C8C2311yescharacteristic
112C29×C4⋊C8C2311yescharacteristic
113C29×C4⋊C8C2311yescharacteristic
114C29×C4⋊C8C2311yescharacteristic
115C29×#103—21no—
116C29×#103—21no—
117C29×#103—21no—
118C29×#103—21no—
119C29×#103—21no—
120C29×#103—21no—
121C29×#103—21no—
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—41no—
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—
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×C29—41no—
148C2×Q8×C29C2×D411yescharacteristic
149C2×Q8×C29C2×D411yescharacteristic
150C2×Q8×C29C2×D411yescharacteristic
151C2×Q8×C29C2×D411yescharacteristic
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C22×C4×C29—41no—
156Q16×C29—22no—
157Q16×C29—41no—
158Q16×C29—42no—
159Q16×C29—42no—
160SD16×C29—42no—
161SD16×C29—42no—
162C2×C8×C29—21no—
163C2×C8×C29—21no—
164C2×C8×C29—21no—
165C2×C8×C29—21no—
166C2×C8×C29—21no—
167C2×C8×C29C2×D411yescharacteristic
168C2×C8×C29C2×D411yescharacteristic
169C2×C8×C29C2×D411yescharacteristic
170C2×C8×C29C2×D411yescharacteristic
171C4⋊C4×C29—21no—
172C4⋊C4×C29—21no—
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—41no—
182C4⋊C4×C29—41no—
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×C29C2×D411yescharacteristic
190C4⋊C4×C29C2×D411yescharacteristic
191C4⋊C4×C29C2×D411yescharacteristic
192C4⋊C4×C29C2×D411yescharacteristic
193C22⋊C4×C29—41no—
194C22⋊C4×C29—41no—
195C22⋊C4×C29—41no—
196C42×C29—21no—
197C42×C29—21no—
198C42×C29—21no—
199C42×C29—21no—
200C42×C29—41no—
201C42×C29—41no—
202C42×C29—41no—
203C42×C29C2411yescharacteristic
204#19941C2911yesmaximal, characteristic, direct product factor, Sylow
205C23×C29—41no—
206Q8×C29—21no—
207Q8×C29—21no—
208Q8×C29—21no—
209Q8×C29—21no—
210Q8×C29—21no—
211Q8×C29—21no—
212Q8×C29—21no—
213Q8×C29—41no—
214Q8×C29—41no—
215Q8×C29—41no—
216Q8×C29—41no—
217Q8×C29—81no—
218Q8×C29—161no—
219Q8×C29#13512yes—
220D4×C29—41no—
221D4×C29—41no—
222D4×C29—41no—
223D4×C29—41no—
224D4×C29—81no—
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—21no—
233C2×C4×C29—41no—
234C2×C4×C29—41no—
235C2×C4×C29—41no—
236C2×C4×C29—161no—
237C2×C4×C29C22×D411yescharacteristic
238C2×C4×C29C22×D411yescharacteristic
239C2×C4×C29H(5,𝔽2)11yescharacteristic
240C8×C29—21no—
241C8×C29—21no—
242C8×C29—21no—
243C8×C29—21no—
244C8×C29—41no—
245C8×C29—41no—
246C8×C29—41no—
247C8×C29—41no—
248C8×C29—41no—
249#3375C2×C2911yescharacteristic
250#3374C2×C2911yescharacteristic, complemented
251#3365C2×C2911yescharacteristic
252#3363C2×C2911yescharacteristic, complemented
253#1711C2×C2911yescharacteristic
254#1700C2×C2911yescharacteristic, complemented
255#1698C2×C2911yescharacteristic
256#1684C2×C2911yescharacteristic, complemented
257#1682C2×C2911yescharacteristic
258#1645C2×C2911yescharacteristic, complemented
259#1640C2×C2911yescharacteristic
260#1636C2×C2911yescharacteristic, complemented
261#1626C2×C2911yescharacteristic
262#1591C2×C2911yescharacteristic, complemented
263C8×Q16C2×C2911yescharacteristic, complemented
264C22×C29—81no—
265C22×C29—81no—
266C22×C29—81no—
267C22×C29D4211yescharacteristic
268C4×C29—22no—
269C4×C29—21no—
270C4×C29—41no—
271C4×C29—41no—
272C4×C29—41no—
273C4×C29—41no—
274C4×C29—41no—
275C4×C29—41no—
276C4×C29—41no—
277C4×C29—81no—
278C4×C29—81no—
279C4×C29—81no—
280C4×C29C2×#13511yescharacteristic
281C4×C29#57511yescharacteristic
282C4×C29#57811yescharacteristic
283C4×C29#57811yescharacteristic
284#559C22×C2911yescharacteristic
285Q82C22×C2911yescharacteristic
286#557C22×C2911yescharacteristic
287#557C22×C2911yescharacteristic
288#491—21no—
289#489—21no—
290#488—21no—
291#487—21no—
292#487C22×C2911yescharacteristic
293#487C22×C2911yescharacteristic
294#487C22×C2911yescharacteristic
295#486C22×C2911yescharacteristic
296#486C22×C2911yescharacteristic
297#486C22×C2911yescharacteristic
298#479—21no—
299#478—21no—
300#477—21no—
301#477C22×C2911yescharacteristic
302#477C22×C2911yescharacteristic
303#475C22×C2911yescharacteristic
304#475C22×C2911yescharacteristic
305#474—21no—
306#464—21no—
307#464—21no—
308#462—21no—
309#462—21no—
310#462C22×C2911yescharacteristic
311#462C22×C2911yescharacteristic
312#460C22×C2911yescharacteristic
313#460C22×C2911yescharacteristic
314#446C22×C2911yescharacteristic
315#446C22×C2911yescharacteristic
316C8×Q8C22×C2911yescharacteristic
317C8×Q8C22×C2911yescharacteristic
318#441—21no—
319#440—21no—
320C4×Q16—21no—
321C4×Q16C22×C2911yescharacteristic
322C4×Q16C22×C2911yescharacteristic
323C4×SD16—21no—
324#335C22×C2911yescharacteristic
325#335C22×C2911yescharacteristic
326#333C22×C2911yescharacteristic
327#332C22×C2911yescharacteristic
328#332C22×C2911yescharacteristic
329#331C22×C2911yescharacteristic
330Q8⋊C8C22×C2911yescharacteristic
331Q8⋊C8C22×C2911yescharacteristic
332Q8⋊C8C22×C2911yescharacteristic
333Q8⋊C8C22×C2911yescharacteristic
334C82C22×C2911yescharacteristic
335C2×C29—161no—
336C2×C29#327711yescharacteristic
337C2×C29#328511yescharacteristic
338C2×C29#329011yescharacteristic
339C2×Q16—21no—
340C2×Q16—21no—
341C2×Q16D4×C2911yescharacteristic
342C2×Q16D4×C2911yescharacteristic
343C2×SD16—21no—
344C2×SD16—21no—
345C4⋊Q8—21no—
346C4⋊Q8—21no—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8—41no—
350C4⋊Q8C23×C2911yescharacteristic
351C4⋊Q8C23×C2911yescharacteristic
352C4⋊Q8C23×C2911yescharacteristic
353#127C23×C2911yescharacteristic
354#125—21no—
355#125—21no—
356#125—41no—
357#125—41no—
358#124—21no—
359#124—21no—
360#123—41no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8C23×C2911yescharacteristic
368C4×Q8C23×C2911yescharacteristic
369C4×Q8C23×C2911yescharacteristic
370C4×Q8C23×C2911yescharacteristic
371C4×D4—21no—
372C4×D4—21no—
373#107—21no—
374#107—21no—
375#107D4×C2911yescharacteristic
376#107D4×C2911yescharacteristic
377#106—21no—
378#106—21no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8C23×C2911yescharacteristic
384C4⋊C8C23×C2911yescharacteristic
385C4⋊C8C23×C2911yescharacteristic
386C4⋊C8C23×C2911yescharacteristic
387#103—21no—
388#103—21no—
389#103—21no—
390#103—21no—
391#103—21no—
392#103—21no—
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—41no—
398#103D4×C2911yescharacteristic
399#103D4×C2911yescharacteristic
400#103D4×C2911yescharacteristic
401#103D4×C2911yescharacteristic
402#102—21no—
403#102—21no—
404#102—21no—
405#102—21no—
406#102—21no—
407#102—21no—
408#102—41no—
409#97—21no—
410#97—21no—
411C4×C8—21no—
412C4×C8—21no—
413C4×C8C23×C2911yescharacteristic
414C4×C8C23×C2911yescharacteristic
415C4×C8C23×C2911yescharacteristic
416C29#1994111yescharacteristic, direct product factor, Sylow
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—41no—
421C2×Q8C2×D4×C2911yescharacteristic
422C2×Q8C2×D4×C2911yescharacteristic
423C2×Q8C2×D4×C2911yescharacteristic
424C2×Q8C2×D4×C2911yescharacteristic
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C22×C4—41no—
429Q16—22no—
430Q16—41no—
431Q16—42no—
432Q16—42no—
433SD16—42no—
434SD16—42no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8C2×D4×C2911yescharacteristic
441C2×C8C2×D4×C2911yescharacteristic
442C2×C8C2×D4×C2911yescharacteristic
443C2×C8C2×D4×C2911yescharacteristic
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4C2×D4×C2911yescharacteristic
463C4⋊C4C2×D4×C2911yescharacteristic
464C4⋊C4C2×D4×C2911yescharacteristic
465C4⋊C4C2×D4×C2911yescharacteristic
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—41no—
474C42—41no—
475C42—41no—
476C42C24×C2911yescharacteristic
477C23—41no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—41no—
486Q8—41no—
487Q8—41no—
488Q8—41no—
489Q8—81no—
490Q8—161no—
491Q8C29×#13512yes—
492D4—41no—
493D4—41no—
494D4—41no—
495D4—41no—
496D4—81no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—161no—
509C2×C4C22×D4×C2911yescharacteristic
510C2×C4C22×D4×C2911yescharacteristic
511C2×C4C29×H(5,𝔽2)11yescharacteristic
512C8—21no—
513C8—21no—
514C8—21no—
515C8—21no—
516C8—41no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8—41no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22D42×C2911yescharacteristic
525C4—22no—
526C4—21no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4C2×C29×#13511yescharacteristic
538C4C29×#57511yescharacteristic
539C4C29×#57811yescharacteristic
540C4C29×#57811yescharacteristic
541C2—161no—
542C2C29×#327711yescharacteristic
543C2C29×#328511yescharacteristic
544C2C29×#329011yescharacteristic
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
2. C29×#3374C2semidirect
4. C29×#3363C2semidirect
6. C29×#1700C2semidirect
8. C29×#1684C2semidirect
10. C29×#1645C2semidirect
12. C29×#1636C2semidirect
14. C29×#1591C2semidirect
15. C8×Q16×C29C2semidirect
204. #19941C29direct (N × H)
250. #3374C2×C29semidirect
252. #3363C2×C29semidirect
254. #1700C2×C29semidirect
256. #1684C2×C29semidirect
258. #1645C2×C29semidirect
260. #1636C2×C29semidirect
262. #1591C2×C29semidirect
263. C8×Q16C2×C29semidirect
416. C29#19941direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33752
C29×#33742
C29×#33652
C29×#33632
C29×#17112
C29×#17002
C29×#16982
C29×#16842
C29×#16822
C29×#16452
C29×#16402
C29×#16362
C29×#16262
C29×#15912
C8×Q16×C292
#1994129