Finite Group Databasebeta

← C29×#19945 #20314845

Subgroups — C29×#19945 #20314845

Order 7424.

654 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3397C211yesmaximal, characteristic, complemented
2C29×#3354C211yesmaximal, characteristic, complemented
3C29×#3340C211yesmaximal, characteristic, complemented
4C29×#3284C211yesmaximal, characteristic, complemented
5C29×#1705C211yesmaximal, characteristic, complemented
6C29×#1692C211yesmaximal, characteristic, complemented
7C29×#1685C211yesmaximal, characteristic, complemented
8C29×#1671C211yesmaximal, characteristic, complemented
9C29×#1665C211yesmaximal, characteristic, complemented
10C29×#1654C211yesmaximal, characteristic, complemented
11C29×#1652C211yesmaximal, characteristic, complemented
12C29×#1631C211yesmaximal, characteristic, complemented
13C29×#1624C211yesmaximal, characteristic, complemented
14C29×#1590C211yesmaximal, characteristic, complemented
15C8×D8×C29C211yesmaximal, characteristic, complemented
16C2×C29×#135—21no—
17C29×#556C2211yescharacteristic
18C29×#555C2211yescharacteristic
19C29×#550C2211yescharacteristic
20C29×#547C2211yescharacteristic
21C29×#498C2211yescharacteristic
22C29×#498C2211yescharacteristic
23C29×#498C2211yescharacteristic
24C29×#496—21no—
25C29×#492C2211yescharacteristic
26C29×#492C2211yescharacteristic
27C29×#492C2211yescharacteristic
28C29×#485—21no—
29C29×#482—21no—
30C29×#482—21no—
31C29×#481—21no—
32C29×#477C2211yescharacteristic
33C29×#476C2211yescharacteristic
34C29×#474C2211yescharacteristic
35C29×#474C2211yescharacteristic
36C29×#469—21no—
37C29×#465—21no—
38C29×#465—21no—
39C29×#463—21no—
40C29×#462C2211yescharacteristic
41C29×#461C2211yescharacteristic
42C29×#460—21no—
43C29×#459C2211yescharacteristic
44C29×#459C2211yescharacteristic
45C29×#452—21no—
46C29×#449—21no—
47C29×#446C2211yescharacteristic
48C29×#440—21no—
49C4×SD16×C29C2211yescharacteristic
50C4×D8×C29C2211yescharacteristic
51C29×#436C2211yescharacteristic
52C8×D4×C29C2211yescharacteristic
53C8×D4×C29C2211yescharacteristic
54C29×#428—21no—
55C29×#427—21no—
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×D4⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C82×C29C2211yescharacteristic
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C29×#135—44no—
70C2×Q16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×SD16×C29—21no—
75C2×SD16×C29—21no—
76C2×SD16×C29—41no—
77C2×SD16×C29D411yescharacteristic
78C2×D8×C29—21no—
79C2×D8×C29—21no—
80C2×D8×C29D411yescharacteristic
81C2×M16×C29—21no—
82C22×C8×C29—21no—
83C22×C8×C29—21no—
84C29×C4⋊Q8C2311yescharacteristic
85C29×C4⋊Q8C2311yescharacteristic
86C29×C4⋊Q8C2311yescharacteristic
87C29×#127—21no—
88C29×#127C2311yescharacteristic
89C29×#126—41no—
90C29×#124—21no—
91C29×#124—41no—
92C29×#123—41no—
93C29×C22⋊Q8—21no—
94C29×C22⋊Q8—21no—
95C29×#121—21no—
96C29×#121—21no—
97C29×#121—21no—
98C29×#121—21no—
99C29×#121—41no—
100C4×Q8×C29—21no—
101C4×Q8×C29C2311yescharacteristic
102C4×D4×C29—21no—
103C4×D4×C29C2311yescharacteristic
104C4×D4×C29C2311yescharacteristic
105C4×D4×C29C2311yescharacteristic
106C29×#117—21no—
107C29×#117—21no—
108C29×#117—21no—
109C2×C4⋊C4×C29—21no—
110C29×#107—21no—
111C29×#107—21no—
112C29×#107—21no—
113C29×#107D411yescharacteristic
114C29×#106—21no—
115C29×#106—21no—
116C29×#106—21no—
117C29×#106—21no—
118C29×#106—21no—
119C29×#106—41no—
120C29×#106D411yescharacteristic
121C29×C4⋊C8—21no—
122C29×C4⋊C8C2311yescharacteristic
123C29×C4⋊C8C2311yescharacteristic
124C29×C4⋊C8C2311yescharacteristic
125C29×C4⋊C8C2311yescharacteristic
126C29×#103—21no—
127C29×#103—21no—
128C29×#103—21no—
129C29×#103D411yescharacteristic
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×#102D411yescharacteristic
136C29×#102D411yescharacteristic
137C29×#102D411yescharacteristic
138C29×C22⋊C8—21no—
139C29×C22⋊C8—21no—
140C29×C22⋊C8—21no—
141C29×#97—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C4×C8×C29C2311yescharacteristic
145#41×C29—42no—
146#41×C29—42no—
147#41×C29—81no—
148#41×C29—81no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×Q8×C29—21no—
152C2×Q8×C29C2×D411yescharacteristic
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—41no—
157C2×D4×C29—41no—
158C2×D4×C29—41no—
159C2×D4×C29—41no—
160C2×D4×C29C2×D411yescharacteristic
161C2×D4×C29C2×D411yescharacteristic
162C2×D4×C29C2×D411yescharacteristic
163C22×C4×C29—21no—
164C22×C4×C29—21no—
165C22×C4×C29—21no—
166C22×C4×C29—41no—
167C22×C4×C29—41no—
168Q16×C29—42no—
169SD16×C29—22no—
170SD16×C29—42no—
171SD16×C29—42no—
172SD16×C29—81no—
173SD16×C29—81no—
174SD16×C29—82no—
175SD16×C29—81no—
176D8×C29—22no—
177D8×C29—42no—
178D8×C29—81no—
179M16×C29—42no—
180C2×C8×C29—21no—
181C2×C8×C29—21no—
182C2×C8×C29—21no—
183C2×C8×C29—21no—
184C2×C8×C29—21no—
185C2×C8×C29—42no—
186C2×C8×C29—42no—
187C2×C8×C29C2×D411yescharacteristic
188C2×C8×C29C2×D411yescharacteristic
189C2×C8×C29C2×D411yescharacteristic
190C2×C8×C29C2×D411yescharacteristic
191C4⋊C4×C29—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—21no—
194C4⋊C4×C29—21no—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—21no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29—41no—
199C4⋊C4×C29—41no—
200C4⋊C4×C29C2×D411yescharacteristic
201C4⋊C4×C29C2×D411yescharacteristic
202C4⋊C4×C29C2×D411yescharacteristic
203C4⋊C4×C29C2×D411yescharacteristic
204C22⋊C4×C29—21no—
205C22⋊C4×C29—21no—
206C22⋊C4×C29—21no—
207C22⋊C4×C29—41no—
208C22⋊C4×C29—41no—
209C22⋊C4×C29—41no—
210C22⋊C4×C29—41no—
211C22⋊C4×C29—41no—
212C22⋊C4×C29—41no—
213C42×C29—21no—
214C42×C29—41no—
215C42×C29—41no—
216C42×C29C2411yescharacteristic
217#19945C2911yesmaximal, characteristic, direct product factor, Sylow
218C23×C29—21no—
219C23×C29—21no—
220C23×C29—21no—
221C23×C29—41no—
222Q8×C29—21no—
223Q8×C29—21no—
224Q8×C29—41no—
225Q8×C29—41no—
226Q8×C29—41no—
227Q8×C29—41no—
228Q8×C29—81no—
229D4×C29—21no—
230D4×C29—21no—
231D4×C29—21no—
232D4×C29—21no—
233D4×C29—21no—
234D4×C29—21no—
235D4×C29—41no—
236D4×C29—41no—
237D4×C29—41no—
238D4×C29—41no—
239D4×C29—81no—
240D4×C29—82no—
241D4×C29—82no—
242D4×C29—161no—
243D4×C29—161no—
244C2×C4×C29—21no—
245C2×C4×C29—21no—
246C2×C4×C29—21no—
247C2×C4×C29—21no—
248C2×C4×C29—21no—
249C2×C4×C29—41no—
250C2×C4×C29—41no—
251C2×C4×C29—41no—
252C2×C4×C29—41no—
253C2×C4×C29—41no—
254C2×C4×C29—41no—
255C2×C4×C29—41no—
256C2×C4×C29—41no—
257C2×C4×C29—41no—
258C2×C4×C29—82no—
259C2×C4×C29—82no—
260C2×C4×C29C22×D411yescharacteristic
261C2×C4×C29C22×D411yescharacteristic
262C2×C4×C29H(5,𝔽2)11yescharacteristic
263C8×C29—22no—
264C8×C29—21no—
265C8×C29—21no—
266C8×C29—41no—
267C8×C29—41no—
268C8×C29—41no—
269C8×C29—41no—
270C8×C29#13512yescomplemented
271C8×C29AGL(1,ℤ/8)12yes—
272#3397C2×C2911yescharacteristic, complemented
273#3354C2×C2911yescharacteristic, complemented
274#3340C2×C2911yescharacteristic, complemented
275#3284C2×C2911yescharacteristic, complemented
276#1705C2×C2911yescharacteristic, complemented
277#1692C2×C2911yescharacteristic, complemented
278#1685C2×C2911yescharacteristic, complemented
279#1671C2×C2911yescharacteristic, complemented
280#1665C2×C2911yescharacteristic, complemented
281#1654C2×C2911yescharacteristic, complemented
282#1652C2×C2911yescharacteristic, complemented
283#1631C2×C2911yescharacteristic, complemented
284#1624C2×C2911yescharacteristic, complemented
285#1590C2×C2911yescharacteristic, complemented
286C8×D8C2×C2911yescharacteristic, complemented
287C22×C29—41no—
288C22×C29—41no—
289C22×C29—41no—
290C22×C29—41no—
291C22×C29—41no—
292C22×C29—41no—
293C22×C29—41no—
294C22×C29—41no—
295C22×C29—41no—
296C22×C29—81no—
297C22×C29—81no—
298C22×C29—81no—
299C22×C29D4211yescharacteristic
300C4×C29—21no—
301C4×C29—41no—
302C4×C29—41no—
303C4×C29—41no—
304C4×C29—41no—
305C4×C29—41no—
306C4×C29—81no—
307C4×C29—81no—
308C4×C29—81no—
309C4×C29C2×#13511yescharacteristic
310C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
311C4×C29#57711yescharacteristic
312C4×C29#57711yescharacteristic
313C2×#135—21no—
314#556C22×C2911yescharacteristic
315#555C22×C2911yescharacteristic
316#550C22×C2911yescharacteristic
317#547C22×C2911yescharacteristic
318#498C22×C2911yescharacteristic
319#498C22×C2911yescharacteristic
320#498C22×C2911yescharacteristic
321#496—21no—
322#492C22×C2911yescharacteristic
323#492C22×C2911yescharacteristic
324#492C22×C2911yescharacteristic
325#485—21no—
326#482—21no—
327#482—21no—
328#481—21no—
329#477C22×C2911yescharacteristic
330#476C22×C2911yescharacteristic
331#474C22×C2911yescharacteristic
332#474C22×C2911yescharacteristic
333#469—21no—
334#465—21no—
335#465—21no—
336#463—21no—
337#462C22×C2911yescharacteristic
338#461C22×C2911yescharacteristic
339#460—21no—
340#459C22×C2911yescharacteristic
341#459C22×C2911yescharacteristic
342#452—21no—
343#449—21no—
344#446C22×C2911yescharacteristic
345#440—21no—
346C4×SD16C22×C2911yescharacteristic
347C4×D8C22×C2911yescharacteristic
348#436C22×C2911yescharacteristic
349C8×D4C22×C2911yescharacteristic
350C8×D4C22×C2911yescharacteristic
351#428—21no—
352#427—21no—
353#335C22×C2911yescharacteristic
354#334C22×C2911yescharacteristic
355#333C22×C2911yescharacteristic
356#332C22×C2911yescharacteristic
357#332C22×C2911yescharacteristic
358#331C22×C2911yescharacteristic
359Q8⋊C8C22×C2911yescharacteristic
360D4⋊C8C22×C2911yescharacteristic
361D4⋊C8C22×C2911yescharacteristic
362D4⋊C8C22×C2911yescharacteristic
363C82C22×C2911yescharacteristic
364C2×C29—81no—
365C2×C29—81no—
366C2×C29—81no—
367C2×C29—161no—
368C2×C29#327211yescharacteristic
369C2×C29#328411yescharacteristic
370C2×C29#329111yescharacteristic
371C2×#41—21no—
372C2×#41—21no—
373#135—44no—
374C2×Q16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—41no—
381C2×SD16D4×C2911yescharacteristic
382C2×D8—21no—
383C2×D8—21no—
384C2×D8D4×C2911yescharacteristic
385C2×M16—21no—
386C22×C8—21no—
387C22×C8—21no—
388C4⋊Q8C23×C2911yescharacteristic
389C4⋊Q8C23×C2911yescharacteristic
390C4⋊Q8C23×C2911yescharacteristic
391#127—21no—
392#127C23×C2911yescharacteristic
393#126—41no—
394#124—21no—
395#124—41no—
396#123—41no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121—21no—
403#121—41no—
404C4×Q8—21no—
405C4×Q8C23×C2911yescharacteristic
406C4×D4—21no—
407C4×D4C23×C2911yescharacteristic
408C4×D4C23×C2911yescharacteristic
409C4×D4C23×C2911yescharacteristic
410#117—21no—
411#117—21no—
412#117—21no—
413C2×C4⋊C4—21no—
414#107—21no—
415#107—21no—
416#107—21no—
417#107D4×C2911yescharacteristic
418#106—21no—
419#106—21no—
420#106—21no—
421#106—21no—
422#106—21no—
423#106—41no—
424#106D4×C2911yescharacteristic
425C4⋊C8—21no—
426C4⋊C8C23×C2911yescharacteristic
427C4⋊C8C23×C2911yescharacteristic
428C4⋊C8C23×C2911yescharacteristic
429C4⋊C8C23×C2911yescharacteristic
430#103—21no—
431#103—21no—
432#103—21no—
433#103D4×C2911yescharacteristic
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102D4×C2911yescharacteristic
440#102D4×C2911yescharacteristic
441#102D4×C2911yescharacteristic
442C22⋊C8—21no—
443C22⋊C8—21no—
444C22⋊C8—21no—
445#97—21no—
446C4×C8C23×C2911yescharacteristic
447C4×C8C23×C2911yescharacteristic
448C4×C8C23×C2911yescharacteristic
449C29#1994511yescharacteristic, direct product factor, Sylow
450#41—42no—
451#41—42no—
452#41—81no—
453#41—81no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8C2×D4×C2911yescharacteristic
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4C2×D4×C2911yescharacteristic
466C2×D4C2×D4×C2911yescharacteristic
467C2×D4C2×D4×C2911yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—41no—
472C22×C4—41no—
473Q16—42no—
474SD16—22no—
475SD16—42no—
476SD16—42no—
477SD16—81no—
478SD16—81no—
479SD16—82no—
480SD16—81no—
481D8—22no—
482D8—42no—
483D8—81no—
484M16—42no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—42no—
491C2×C8—42no—
492C2×C8C2×D4×C2911yescharacteristic
493C2×C8C2×D4×C2911yescharacteristic
494C2×C8C2×D4×C2911yescharacteristic
495C2×C8C2×D4×C2911yescharacteristic
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4C2×D4×C2911yescharacteristic
506C4⋊C4C2×D4×C2911yescharacteristic
507C4⋊C4C2×D4×C2911yescharacteristic
508C4⋊C4C2×D4×C2911yescharacteristic
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C42—21no—
519C42—41no—
520C42—41no—
521C42C24×C2911yescharacteristic
522C23—21no—
523C23—21no—
524C23—21no—
525C23—41no—
526Q8—21no—
527Q8—21no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—41no—
532Q8—81no—
533D4—21no—
534D4—21no—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—81no—
544D4—82no—
545D4—82no—
546D4—161no—
547D4—161no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4C22×D4×C2911yescharacteristic
565C2×C4C22×D4×C2911yescharacteristic
566C2×C4C29×H(5,𝔽2)11yescharacteristic
567C8—22no—
568C8—21no—
569C8—21no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8C29×#13512yescomplemented
575C8C29×AGL(1,ℤ/8)12yes—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22D42×C2911yescharacteristic
589C4—21no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—81no—
596C4—81no—
597C4—81no—
598C4C2×C29×#13511yescharacteristic
599C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
600C4C29×#57711yescharacteristic
601C4C29×#57711yescharacteristic
602C2—81no—
603C2—81no—
604C2—81no—
605C2—161no—
606C2C29×#327211yescharacteristic
607C2C29×#328411yescharacteristic
608C2C29×#329111yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
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×#3397C2semidirect
2. C29×#3354C2semidirect
3. C29×#3340C2semidirect
4. C29×#3284C2semidirect
5. C29×#1705C2semidirect
6. C29×#1692C2semidirect
7. C29×#1685C2semidirect
8. C29×#1671C2semidirect
9. C29×#1665C2semidirect
10. C29×#1654C2semidirect
11. C29×#1652C2semidirect
12. C29×#1631C2semidirect
13. C29×#1624C2semidirect
14. C29×#1590C2semidirect
15. C8×D8×C29C2semidirect
217. #19945C29direct (N × H)
270. C8×C29#135semidirect
272. #3397C2×C29semidirect
273. #3354C2×C29semidirect
274. #3340C2×C29semidirect
275. #3284C2×C29semidirect
276. #1705C2×C29semidirect
277. #1692C2×C29semidirect
278. #1685C2×C29semidirect
279. #1671C2×C29semidirect
280. #1665C2×C29semidirect
281. #1654C2×C29semidirect
282. #1652C2×C29semidirect
283. #1631C2×C29semidirect
284. #1624C2×C29semidirect
285. #1590C2×C29semidirect
286. C8×D8C2×C29semidirect
449. C29#19945direct (N × H)
574. C8C29×#135semidirect

Maximal subgroups

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

subgroupindex
C29×#33972
C29×#33542
C29×#33402
C29×#32842
C29×#17052
C29×#16922
C29×#16852
C29×#16712
C29×#16652
C29×#16542
C29×#16522
C29×#16312
C29×#16242
C29×#15902
C8×D8×C292
#1994529