Finite Group Databasebeta

← C29×#19837 #20314737

Subgroups — C29×#19837 #20314737

Order 7424.

628 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3373C211yesmaximal, characteristic
2C29×#3365C211yesmaximal, characteristic, complemented
3C29×#3359C211yesmaximal, characteristic, complemented
4D4×Q16×C29C211yesmaximal, characteristic, complemented
5C29×#1720C211yesmaximal, characteristic, complemented
6C29×#1700C211yesmaximal, characteristic, complemented
7C29×#1682C211yesmaximal, characteristic, complemented
8C29×#1681C211yesmaximal, characteristic
9C29×#1670C211yesmaximal, characteristic, complemented
10C29×#1653C211yesmaximal, characteristic, complemented
11C29×#1651C211yesmaximal, characteristic, complemented
12C29×#1640C211yesmaximal, characteristic, complemented
13C29×#1627C211yesmaximal, characteristic
14C29×#1584C211yesmaximal, characteristic, complemented
15C29×SD16⋊C8C211yesmaximal, characteristic, complemented
16C22×Q16×C29—21no—
17C29×#559C2211yescharacteristic
18C29×#557C2211yescharacteristic
19D4×Q8×C29C2211yescharacteristic
20D4×Q8×C29C2211yescharacteristic
21C29×#498C2211yescharacteristic
22C29×#494C2211yescharacteristic
23C29×#489—21no—
24C29×#488—21no—
25C29×#487—21no—
26C29×#487C2211yescharacteristic
27C29×#486C2211yescharacteristic
28C29×#486C2211yescharacteristic
29C29×#486C2211yescharacteristic
30C29×#478—21no—
31C29×#476—21no—
32C29×#475—21no—
33C29×#475C2211yescharacteristic
34C29×#475C2211yescharacteristic
35C29×#475C2211yescharacteristic
36C29×#467—21no—
37C29×#464—21no—
38C29×#463—21no—
39C29×#462C2211yescharacteristic
40C29×#462C2211yescharacteristic
41C29×#461—21no—
42C29×#461C2211yescharacteristic
43C29×#460C2211yescharacteristic
44C29×#459C2211yescharacteristic
45C29×#451—21no—
46C29×#451—21no—
47C29×#446C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C8×Q8×C29C2211yescharacteristic
50C29×#442—21no—
51C4×Q16×C29C2211yescharacteristic
52C4×SD16×C29—21no—
53C4×SD16×C29—21no—
54C4×SD16×C29C2211yescharacteristic
55C8×D4×C29C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#335C2211yescharacteristic
58C29×#332C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×Q8⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C29×#322C2211yescharacteristic
67C22×Q8×C29—21no—
68C22×Q8×C29—21no—
69C2×Q16×C29—21no—
70C2×Q16×C29—21no—
71C2×Q16×C29—21no—
72C2×Q16×C29—21no—
73C2×Q16×C29—44no—
74C2×Q16×C29D411yescharacteristic
75C2×SD16×C29—21no—
76C2×SD16×C29—21no—
77C2×SD16×C29D411yescharacteristic
78C2×D8×C29—21no—
79C22×C8×C29—21no—
80C29×C4⋊Q8—21no—
81C29×C4⋊Q8—21no—
82C29×C4⋊Q8—21no—
83C29×C4⋊Q8C2311yescharacteristic
84C29×C4⋊Q8C2311yescharacteristic
85C29×C4⋊Q8C2311yescharacteristic
86C29×#127C2311yescharacteristic
87C29×#125—21no—
88C29×#125—41no—
89C29×#124—21no—
90C29×#124—21no—
91C29×#123—41no—
92C29×C22⋊Q8—21no—
93C29×C22⋊Q8—21no—
94C29×C22⋊Q8—41no—
95C29×C22⋊Q8—41no—
96C4×Q8×C29—21no—
97C4×Q8×C29—21no—
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—
105C4×D4×C29C2311yescharacteristic
106C29×#107D411yescharacteristic
107C29×#106—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×#106—41no—
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—21no—
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×#102D411yescharacteristic
138C29×C22⋊C8—21no—
139C29×#97—21no—
140C4×C8×C29—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C4×C8×C29C2311yescharacteristic
145C2×Q8×C29—21no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—41no—
149C2×Q8×C29—41no—
150C2×Q8×C29—42no—
151C2×Q8×C29—42no—
152C2×Q8×C29—81no—
153C2×Q8×C29—81no—
154C2×Q8×C29C2×D411yescharacteristic
155C2×Q8×C29C2×D411yescharacteristic
156C2×Q8×C29C2×D411yescharacteristic
157C2×D4×C29—21no—
158C2×D4×C29—21no—
159C2×D4×C29—21no—
160C2×D4×C29C2×D411yescharacteristic
161C22×C4×C29—21no—
162C22×C4×C29—41no—
163C22×C4×C29—41no—
164C22×C4×C29—41no—
165Q16×C29—22no—
166Q16×C29—42no—
167Q16×C29—42no—
168Q16×C29—42no—
169Q16×C29—81no—
170SD16×C29—22no—
171SD16×C29—42no—
172SD16×C29—42no—
173D8×C29—42no—
174C2×C8×C29—21no—
175C2×C8×C29—21no—
176C2×C8×C29—21no—
177C2×C8×C29—21no—
178C2×C8×C29—21no—
179C2×C8×C29—42no—
180C2×C8×C29C2×D411yescharacteristic
181C2×C8×C29C2×D411yescharacteristic
182C2×C8×C29C2×D411yescharacteristic
183C2×C8×C29C2×D411yescharacteristic
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—41no—
194C4⋊C4×C29—41no—
195C4⋊C4×C29—41no—
196C4⋊C4×C29—41no—
197C4⋊C4×C29—41no—
198C4⋊C4×C29C2×D411yescharacteristic
199C4⋊C4×C29C2×D411yescharacteristic
200C4⋊C4×C29C2×D411yescharacteristic
201C4⋊C4×C29C2×D411yescharacteristic
202C22⋊C4×C29—21no—
203C22⋊C4×C29—41no—
204C22⋊C4×C29—41no—
205C22⋊C4×C29—41no—
206C22⋊C4×C29—41no—
207C22⋊C4×C29—41no—
208C42×C29—21no—
209C42×C29—21no—
210C42×C29—21no—
211C42×C29—41no—
212C42×C29C2411yescharacteristic
213#19837C2911yesmaximal, characteristic, direct product factor, Sylow
214C23×C29—21no—
215C23×C29—41no—
216Q8×C29—21no—
217Q8×C29—21no—
218Q8×C29—21no—
219Q8×C29—21no—
220Q8×C29—21no—
221Q8×C29—41no—
222Q8×C29—41no—
223Q8×C29—41no—
224Q8×C29—41no—
225Q8×C29—41no—
226Q8×C29—41no—
227Q8×C29—82no—
228Q8×C29—82no—
229Q8×C29AGL(1,ℤ/8)12yes—
230D4×C29—21no—
231D4×C29—41no—
232D4×C29—41no—
233D4×C29—41no—
234D4×C29—41no—
235D4×C29—81no—
236D4×C29#13512yes—
237C2×C4×C29—21no—
238C2×C4×C29—21no—
239C2×C4×C29—21no—
240C2×C4×C29—21no—
241C2×C4×C29—21no—
242C2×C4×C29—21no—
243C2×C4×C29—21no—
244C2×C4×C29—41no—
245C2×C4×C29—41no—
246C2×C4×C29—41no—
247C2×C4×C29—41no—
248C2×C4×C29—41no—
249C2×C4×C29—82no—
250C2×C4×C29—82no—
251C2×C4×C29—161no—
252C2×C4×C29C22×D411yescharacteristic
253C2×C4×C29C22×D411yescharacteristic
254C2×C4×C29H(5,𝔽2)11yescharacteristic
255C8×C29—21no—
256C8×C29—21no—
257C8×C29—21no—
258C8×C29—21no—
259C8×C29—41no—
260C8×C29—41no—
261C8×C29—41no—
262C8×C29—41no—
263C8×C29—41no—
264#3373C2×C2911yescharacteristic
265#3365C2×C2911yescharacteristic, complemented
266#3359C2×C2911yescharacteristic, complemented
267D4×Q16C2×C2911yescharacteristic, complemented
268#1720C2×C2911yescharacteristic, complemented
269#1700C2×C2911yescharacteristic, complemented
270#1682C2×C2911yescharacteristic, complemented
271#1681C2×C2911yescharacteristic
272#1670C2×C2911yescharacteristic, complemented
273#1653C2×C2911yescharacteristic, complemented
274#1651C2×C2911yescharacteristic, complemented
275#1640C2×C2911yescharacteristic, complemented
276#1627C2×C2911yescharacteristic
277#1584C2×C2911yescharacteristic, complemented
278SD16⋊C8C2×C2911yescharacteristic, complemented
279C22×C29—22no—
280C22×C29—41no—
281C22×C29—41no—
282C22×C29—81no—
283C22×C29—81no—
284C22×C29—81no—
285C22×C29D4211yescharacteristic
286C4×C29—22no—
287C4×C29—21no—
288C4×C29—41no—
289C4×C29—41no—
290C4×C29—41no—
291C4×C29—41no—
292C4×C29—41no—
293C4×C29—41no—
294C4×C29—81no—
295C4×C29—81no—
296C4×C29—81no—
297C4×C29C2×#13511yescharacteristic
298C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C29#57711yescharacteristic
300C4×C29#57811yescharacteristic
301C22×Q16—21no—
302#559C22×C2911yescharacteristic
303#557C22×C2911yescharacteristic
304D4×Q8C22×C2911yescharacteristic
305D4×Q8C22×C2911yescharacteristic
306#498C22×C2911yescharacteristic
307#494C22×C2911yescharacteristic
308#489—21no—
309#488—21no—
310#487—21no—
311#487C22×C2911yescharacteristic
312#486C22×C2911yescharacteristic
313#486C22×C2911yescharacteristic
314#486C22×C2911yescharacteristic
315#478—21no—
316#476—21no—
317#475—21no—
318#475C22×C2911yescharacteristic
319#475C22×C2911yescharacteristic
320#475C22×C2911yescharacteristic
321#467—21no—
322#464—21no—
323#463—21no—
324#462C22×C2911yescharacteristic
325#462C22×C2911yescharacteristic
326#461—21no—
327#461C22×C2911yescharacteristic
328#460C22×C2911yescharacteristic
329#459C22×C2911yescharacteristic
330#451—21no—
331#451—21no—
332#446C22×C2911yescharacteristic
333C8×Q8C22×C2911yescharacteristic
334C8×Q8C22×C2911yescharacteristic
335#442—21no—
336C4×Q16C22×C2911yescharacteristic
337C4×SD16—21no—
338C4×SD16—21no—
339C4×SD16C22×C2911yescharacteristic
340C8×D4C22×C2911yescharacteristic
341#335C22×C2911yescharacteristic
342#335C22×C2911yescharacteristic
343#332C22×C2911yescharacteristic
344#332C22×C2911yescharacteristic
345#332C22×C2911yescharacteristic
346#331C22×C2911yescharacteristic
347Q8⋊C8C22×C2911yescharacteristic
348Q8⋊C8C22×C2911yescharacteristic
349Q8⋊C8C22×C2911yescharacteristic
350D4⋊C8C22×C2911yescharacteristic
351#322C22×C2911yescharacteristic
352C2×C29—42no—
353C2×C29—161no—
354C2×C29#326511yescharacteristic
355C2×C29#328511yescharacteristic
356C2×C29#328911yescharacteristic
357C22×Q8—21no—
358C22×Q8—21no—
359C2×Q16—21no—
360C2×Q16—21no—
361C2×Q16—21no—
362C2×Q16—21no—
363C2×Q16—44no—
364C2×Q16D4×C2911yescharacteristic
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16D4×C2911yescharacteristic
368C2×D8—21no—
369C22×C8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8C23×C2911yescharacteristic
374C4⋊Q8C23×C2911yescharacteristic
375C4⋊Q8C23×C2911yescharacteristic
376#127C23×C2911yescharacteristic
377#125—21no—
378#125—41no—
379#124—21no—
380#124—21no—
381#123—41no—
382C22⋊Q8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—41no—
385C22⋊Q8—41no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8C23×C2911yescharacteristic
389C4×Q8C23×C2911yescharacteristic
390C4×Q8C23×C2911yescharacteristic
391C4×D4—21no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4C23×C2911yescharacteristic
396#107D4×C2911yescharacteristic
397#106—21no—
398#106—21no—
399#106—21no—
400#106—41no—
401#106D4×C2911yescharacteristic
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8C23×C2911yescharacteristic
406C4⋊C8C23×C2911yescharacteristic
407C4⋊C8C23×C2911yescharacteristic
408C4⋊C8C23×C2911yescharacteristic
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103D4×C2911yescharacteristic
418#103D4×C2911yescharacteristic
419#103D4×C2911yescharacteristic
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—41no—
427#102D4×C2911yescharacteristic
428C22⋊C8—21no—
429#97—21no—
430C4×C8—21no—
431C4×C8—21no—
432C4×C8C23×C2911yescharacteristic
433C4×C8C23×C2911yescharacteristic
434C4×C8C23×C2911yescharacteristic
435C29#1983711yescharacteristic, direct product factor, Sylow
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—41no—
440C2×Q8—41no—
441C2×Q8—42no—
442C2×Q8—42no—
443C2×Q8—81no—
444C2×Q8—81no—
445C2×Q8C2×D4×C2911yescharacteristic
446C2×Q8C2×D4×C2911yescharacteristic
447C2×Q8C2×D4×C2911yescharacteristic
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4C2×D4×C2911yescharacteristic
452C22×C4—21no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456Q16—22no—
457Q16—42no—
458Q16—42no—
459Q16—42no—
460Q16—81no—
461SD16—22no—
462SD16—42no—
463SD16—42no—
464D8—42no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—42no—
471C2×C8C2×D4×C2911yescharacteristic
472C2×C8C2×D4×C2911yescharacteristic
473C2×C8C2×D4×C2911yescharacteristic
474C2×C8C2×D4×C2911yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4C2×D4×C2911yescharacteristic
490C4⋊C4C2×D4×C2911yescharacteristic
491C4⋊C4C2×D4×C2911yescharacteristic
492C4⋊C4C2×D4×C2911yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—41no—
503C42C24×C2911yescharacteristic
504C23—21no—
505C23—41no—
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—82no—
518Q8—82no—
519Q8C29×AGL(1,ℤ/8)12yes—
520D4—21no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—81no—
526D4C29×#13512yes—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4—161no—
542C2×C4C22×D4×C2911yescharacteristic
543C2×C4C22×D4×C2911yescharacteristic
544C2×C4C29×H(5,𝔽2)11yescharacteristic
545C8—21no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C22—22no—
555C22—41no—
556C22—41no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22D42×C2911yescharacteristic
561C4—22no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4C2×C29×#13511yescharacteristic
573C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
574C4C29×#57711yescharacteristic
575C4C29×#57811yescharacteristic
576C2—42no—
577C2—161no—
578C2C29×#326511yescharacteristic
579C2C29×#328511yescharacteristic
580C2C29×#328911yescharacteristic
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
2. C29×#3365C2semidirect
3. C29×#3359C2semidirect
4. D4×Q16×C29C2semidirect
5. C29×#1720C2semidirect
6. C29×#1700C2semidirect
7. C29×#1682C2semidirect
9. C29×#1670C2semidirect
10. C29×#1653C2semidirect
11. C29×#1651C2semidirect
12. C29×#1640C2semidirect
14. C29×#1584C2semidirect
15. C29×SD16⋊C8C2semidirect
213. #19837C29direct (N × H)
265. #3365C2×C29semidirect
266. #3359C2×C29semidirect
267. D4×Q16C2×C29semidirect
268. #1720C2×C29semidirect
269. #1700C2×C29semidirect
270. #1682C2×C29semidirect
272. #1670C2×C29semidirect
273. #1653C2×C29semidirect
274. #1651C2×C29semidirect
275. #1640C2×C29semidirect
277. #1584C2×C29semidirect
278. SD16⋊C8C2×C29semidirect
435. C29#19837direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33732
C29×#33652
C29×#33592
D4×Q16×C292
C29×#17202
C29×#17002
C29×#16822
C29×#16812
C29×#16702
C29×#16532
C29×#16512
C29×#16402
C29×#16272
C29×#15842
C29×SD16⋊C82
#1983729