Finite Group Databasebeta

← C29×#19481 #20314381

Subgroups — C29×#19481 #20314381

Order 7424.

610 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3210C211yesmaximal, characteristic, complemented
2C29×#3115C211yesmaximal, characteristic
3C29×#3076C211yesmaximal, characteristic, complemented
4C29×#2990C211yesmaximal, characteristic, complemented
5C29×#1704C211yesmaximal, characteristic, complemented
6C29×#1698C211yesmaximal, characteristic, complemented
7C29×#1690C211yesmaximal, characteristic, complemented
8C29×#1686C211yesmaximal, characteristic, complemented
9C29×#1683C211yesmaximal, characteristic, complemented
10C29×#1677C211yesmaximal, characteristic, complemented
11C29×#1669C211yesmaximal, characteristic, complemented
12C29×#1665C211yesmaximal, characteristic, complemented
13C29×#1573C211yesmaximal, characteristic, complemented
14C29×#1559C211yesmaximal, characteristic, complemented
15C29×#1547C211yesmaximal, characteristic, complemented
16C29×#533C2211yescharacteristic
17C29×#532C2211yescharacteristic
18C4×#41×C29C2211yescharacteristic
19C29×#494C2211yescharacteristic
20C29×#492C2211yescharacteristic
21C29×#487C2211yescharacteristic
22C29×#486C2211yescharacteristic
23C29×#482—21no—
24C29×#479—21no—
25C29×#478—21no—
26C29×#477C2211yescharacteristic
27C29×#476C2211yescharacteristic
28C29×#475C2211yescharacteristic
29C29×#475C2211yescharacteristic
30C29×#474C2211yescharacteristic
31C29×#474C2211yescharacteristic
32C29×#464—21no—
33C29×#464—21no—
34C29×#460C2211yescharacteristic
35C29×#459C2211yescharacteristic
36C29×#452—21no—
37C29×#452—21no—
38C29×#449—21no—
39C29×#446C2211yescharacteristic
40C29×#446C2211yescharacteristic
41C29×#442—21no—
42C29×#440—21no—
43C29×#435—21no—
44C29×#435—21no—
45C8×D4×C29C2211yescharacteristic
46C8×D4×C29C2211yescharacteristic
47C29×#432—21no—
48C29×#432C2211yescharacteristic
49C29×#431C2211yescharacteristic
50C29×#427—21no—
51C29×#423C2211yescharacteristic
52C2×C29×C4⋊C8—21no—
53C2×C29×C4⋊C8C2211yescharacteristic
54C29×#416—21no—
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×#332C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#331C2211yescharacteristic
66C29×#331C2211yescharacteristic
67C2×#41×C29—21no—
68C2×#41×C29D411yescharacteristic
69C2×Q16×C29—21no—
70C2×Q16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×D8×C29—21no—
75C2×M16×C29—21no—
76C22×C8×C29—21no—
77C22×C8×C29—21no—
78C22×C8×C29—21no—
79C29×C4⋊Q8C2311yescharacteristic
80C29×C4⋊Q8C2311yescharacteristic
81C29×C4⋊Q8C2311yescharacteristic
82C29×#127C2311yescharacteristic
83C29×#125—21no—
84C29×#124—21no—
85C29×C22⋊Q8—21no—
86C29×C22⋊Q8—21no—
87C29×#121—21no—
88C29×#121—21no—
89C4×Q8×C29—21no—
90C4×Q8×C29—21no—
91C4×Q8×C29D411yescharacteristic
92C4×Q8×C29C2311yescharacteristic
93C4×D4×C29—21no—
94C4×D4×C29—21no—
95C4×D4×C29—21no—
96C4×D4×C29—21no—
97C4×D4×C29D411yescharacteristic
98C4×D4×C29C2311yescharacteristic
99C29×#117—21no—
100C29×#117—21no—
101C29×#117D411yescharacteristic
102C2×C42×C29—21no—
103C2×C42×C29C2311yescharacteristic
104C29×#107—21no—
105C29×#107—21no—
106C29×#107—21no—
107C29×#106—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×C4⋊C8—21no—
111C29×C4⋊C8—21no—
112C29×C4⋊C8—21no—
113C29×C4⋊C8—21no—
114C29×C4⋊C8D411yescharacteristic
115C29×C4⋊C8D411yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×C4⋊C8C2311yescharacteristic
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—21no—
126C29×#103—21no—
127C29×#102—21no—
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×C22⋊C8—21no—
135C29×C22⋊C8—21no—
136C29×C22⋊C8—21no—
137C29×C22⋊C8D411yescharacteristic
138C29×C22⋊C8D411yescharacteristic
139C29×#97—21no—
140C29×#97—21no—
141C29×#97—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144#41×C29—22no—
145#41×C29—41no—
146#41×C29—81no—
147#41×C29—81no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×Q8×C29C2×D411yescharacteristic
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—41no—
157C2×D4×C29C2×D411yescharacteristic
158C22×C4×C29—21no—
159C22×C4×C29—21no—
160C22×C4×C29—21no—
161C22×C4×C29—41no—
162C22×C4×C29C2×D411yescharacteristic
163C22×C4×C29C2×D411yescharacteristic
164C22×C4×C29#4111yescharacteristic
165Q16×C29—81no—
166Q16×C29—81no—
167SD16×C29—42no—
168SD16×C29—81no—
169SD16×C29—81no—
170D8×C29—42no—
171M16×C29—81no—
172C2×C8×C29—21no—
173C2×C8×C29—21no—
174C2×C8×C29—21no—
175C2×C8×C29—21no—
176C2×C8×C29—21no—
177C2×C8×C29—21no—
178C2×C8×C29—42no—
179C2×C8×C29—81no—
180C2×C8×C29—81no—
181C2×C8×C29C2×D411yescharacteristic
182C2×C8×C29C2×D411yescharacteristic
183C2×C8×C29C2×D411yescharacteristic
184C2×C8×C29C2×D411yescharacteristic
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×C29C2×D411yescharacteristic
196C4⋊C4×C29C2×D411yescharacteristic
197C22⋊C4×C29—21no—
198C22⋊C4×C29—21no—
199C22⋊C4×C29—21no—
200C22⋊C4×C29—41no—
201C22⋊C4×C29—41no—
202C22⋊C4×C29—41no—
203C42×C29—21no—
204C42×C29—21no—
205C42×C29—21no—
206C42×C29—41no—
207C42×C29C2×D411yescharacteristic
208C42×C29C2×D411yescharacteristic
209C42×C29#4111yescharacteristic
210C42×C29C2411yescharacteristic
211#19481C2911yesmaximal, characteristic, direct product factor, Sylow
212C23×C29—21no—
213C23×C29—41no—
214C23×C29#12111yescharacteristic
215Q8×C29—21no—
216Q8×C29—21no—
217Q8×C29—41no—
218Q8×C29—41no—
219Q8×C29—41no—
220Q8×C29—41no—
221Q8×C29—81no—
222D4×C29—21no—
223D4×C29—42no—
224D4×C29—41no—
225D4×C29—41no—
226D4×C29—41no—
227D4×C29—41no—
228D4×C29—81no—
229D4×C29—82no—
230D4×C29#13712yes—
231C2×C4×C29—21no—
232C2×C4×C29—21no—
233C2×C4×C29—21no—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—41no—
239C2×C4×C29—42no—
240C2×C4×C29—42no—
241C2×C4×C29—41no—
242C2×C4×C29—41no—
243C2×C4×C29—41no—
244C2×C4×C29—41no—
245C2×C4×C29—41no—
246C2×C4×C29—82no—
247C2×C4×C29#12111yescharacteristic
248C2×C4×C29#12111yescharacteristic
249C2×C4×C29#12111yescharacteristic
250C2×C4×C29C22×D411yescharacteristic
251C2×C4×C29C22×D411yescharacteristic
252C2×C4×C29C2×#4111yescharacteristic
253C8×C29—21no—
254C8×C29—21no—
255C8×C29—21no—
256C8×C29—21no—
257C8×C29—41no—
258C8×C29—41no—
259C8×C29—41no—
260C8×C29—41no—
261C8×C29—41no—
262C8×C29—41no—
263#3210C2×C2911yescharacteristic, complemented
264#3115C2×C2911yescharacteristic
265#3076C2×C2911yescharacteristic, complemented
266#2990C2×C2911yescharacteristic, complemented
267#1704C2×C2911yescharacteristic, complemented
268#1698C2×C2911yescharacteristic, complemented
269#1690C2×C2911yescharacteristic, complemented
270#1686C2×C2911yescharacteristic, complemented
271#1683C2×C2911yescharacteristic, complemented
272#1677C2×C2911yescharacteristic, complemented
273#1669C2×C2911yescharacteristic, complemented
274#1665C2×C2911yescharacteristic, complemented
275#1573C2×C2911yescharacteristic, complemented
276#1559C2×C2911yescharacteristic, complemented
277#1547C2×C2911yescharacteristic, complemented
278C22×C29—21no—
279C22×C29—21no—
280C22×C29—22no—
281C22×C29—21no—
282C22×C29—41no—
283C22×C29—41no—
284C22×C29—81no—
285C22×C29—81no—
286C22×C29—81no—
287C22×C29C2×#12111yescharacteristic
288C4×C29—21no—
289C4×C29—21no—
290C4×C29—21no—
291C4×C29—21no—
292C4×C29—41no—
293C4×C29—41no—
294C4×C29—41no—
295C4×C29—81no—
296C4×C29—81no—
297C4×C29—81no—
298C4×C29C2×#13711yescharacteristic
299C4×C29#57511yescharacteristic
300C4×C29#57611yescharacteristic
301C4×C29#57711yescharacteristic
302#533C22×C2911yescharacteristic
303#532C22×C2911yescharacteristic
304C4×#41C22×C2911yescharacteristic
305#494C22×C2911yescharacteristic
306#492C22×C2911yescharacteristic
307#487C22×C2911yescharacteristic
308#486C22×C2911yescharacteristic
309#482—21no—
310#479—21no—
311#478—21no—
312#477C22×C2911yescharacteristic
313#476C22×C2911yescharacteristic
314#475C22×C2911yescharacteristic
315#475C22×C2911yescharacteristic
316#474C22×C2911yescharacteristic
317#474C22×C2911yescharacteristic
318#464—21no—
319#464—21no—
320#460C22×C2911yescharacteristic
321#459C22×C2911yescharacteristic
322#452—21no—
323#452—21no—
324#449—21no—
325#446C22×C2911yescharacteristic
326#446C22×C2911yescharacteristic
327#442—21no—
328#440—21no—
329#435—21no—
330#435—21no—
331C8×D4C22×C2911yescharacteristic
332C8×D4C22×C2911yescharacteristic
333#432—21no—
334#432C22×C2911yescharacteristic
335#431C22×C2911yescharacteristic
336#427—21no—
337#423C22×C2911yescharacteristic
338C2×C4⋊C8—21no—
339C2×C4⋊C8C22×C2911yescharacteristic
340#416—21no—
341#335C22×C2911yescharacteristic
342#335C22×C2911yescharacteristic
343#334C22×C2911yescharacteristic
344#334C22×C2911yescharacteristic
345#333C22×C2911yescharacteristic
346#333C22×C2911yescharacteristic
347#332C22×C2911yescharacteristic
348#332C22×C2911yescharacteristic
349#332C22×C2911yescharacteristic
350#332C22×C2911yescharacteristic
351#331C22×C2911yescharacteristic
352#331C22×C2911yescharacteristic
353C2×C29—41no—
354C2×C29—42no—
355C2×C29—161no—
356C2×C29#304511yescharacteristic
357C2×C29#305611yescharacteristic
358C2×C29#306711yescharacteristic
359C2×#41—21no—
360C2×#41D4×C2911yescharacteristic
361C2×Q16—21no—
362C2×Q16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×D8—21no—
367C2×M16—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C4⋊Q8C23×C2911yescharacteristic
372C4⋊Q8C23×C2911yescharacteristic
373C4⋊Q8C23×C2911yescharacteristic
374#127C23×C2911yescharacteristic
375#125—21no—
376#124—21no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379#121—21no—
380#121—21no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8D4×C2911yescharacteristic
384C4×Q8C23×C2911yescharacteristic
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4D4×C2911yescharacteristic
390C4×D4C23×C2911yescharacteristic
391#117—21no—
392#117—21no—
393#117D4×C2911yescharacteristic
394C2×C42—21no—
395C2×C42C23×C2911yescharacteristic
396#107—21no—
397#107—21no—
398#107—21no—
399#106—21no—
400#106—21no—
401#106—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8D4×C2911yescharacteristic
407C4⋊C8D4×C2911yescharacteristic
408C4⋊C8C23×C2911yescharacteristic
409C4⋊C8C23×C2911yescharacteristic
410C4⋊C8C23×C2911yescharacteristic
411C4⋊C8C23×C2911yescharacteristic
412C4⋊C8C23×C2911yescharacteristic
413C4⋊C8C23×C2911yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8D4×C2911yescharacteristic
430C22⋊C8D4×C2911yescharacteristic
431#97—21no—
432#97—21no—
433#97—21no—
434C4×C8C23×C2911yescharacteristic
435C4×C8C23×C2911yescharacteristic
436C29#1948111yescharacteristic, direct product factor, Sylow
437#41—22no—
438#41—41no—
439#41—81no—
440#41—81no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8C2×D4×C2911yescharacteristic
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—41no—
450C2×D4C2×D4×C2911yescharacteristic
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—41no—
455C22×C4C2×D4×C2911yescharacteristic
456C22×C4C2×D4×C2911yescharacteristic
457C22×C4#41×C2911yescharacteristic
458Q16—81no—
459Q16—81no—
460SD16—42no—
461SD16—81no—
462SD16—81no—
463D8—42no—
464M16—81no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—42no—
472C2×C8—81no—
473C2×C8—81no—
474C2×C8C2×D4×C2911yescharacteristic
475C2×C8C2×D4×C2911yescharacteristic
476C2×C8C2×D4×C2911yescharacteristic
477C2×C8C2×D4×C2911yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4C2×D4×C2911yescharacteristic
489C4⋊C4C2×D4×C2911yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—41no—
500C42C2×D4×C2911yescharacteristic
501C42C2×D4×C2911yescharacteristic
502C42#41×C2911yescharacteristic
503C42C24×C2911yescharacteristic
504C23—21no—
505C23—41no—
506C23C29×#12111yescharacteristic
507Q8—21no—
508Q8—21no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—81no—
514D4—21no—
515D4—42no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—81no—
521D4—82no—
522D4C29×#13712yes—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4C29×#12111yescharacteristic
540C2×C4C29×#12111yescharacteristic
541C2×C4C29×#12111yescharacteristic
542C2×C4C22×D4×C2911yescharacteristic
543C2×C4C22×D4×C2911yescharacteristic
544C2×C4C2×#41×C2911yescharacteristic
545C8—21no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C22—21no—
556C22—21no—
557C22—22no—
558C22—21no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22C2×C29×#12111yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C2×C29×#13711yescharacteristic
576C4C29×#57511yescharacteristic
577C4C29×#57611yescharacteristic
578C4C29×#57711yescharacteristic
579C2—41no—
580C2—42no—
581C2—161no—
582C2C29×#304511yescharacteristic
583C2C29×#305611yescharacteristic
584C2C29×#306711yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3115C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C29×#3210C2semidirect
3. C29×#3076C2semidirect
4. C29×#2990C2semidirect
5. C29×#1704C2semidirect
6. C29×#1698C2semidirect
7. C29×#1690C2semidirect
8. C29×#1686C2semidirect
9. C29×#1683C2semidirect
10. C29×#1677C2semidirect
11. C29×#1669C2semidirect
12. C29×#1665C2semidirect
13. C29×#1573C2semidirect
14. C29×#1559C2semidirect
15. C29×#1547C2semidirect
211. #19481C29direct (N × H)
263. #3210C2×C29semidirect
265. #3076C2×C29semidirect
266. #2990C2×C29semidirect
267. #1704C2×C29semidirect
268. #1698C2×C29semidirect
269. #1690C2×C29semidirect
270. #1686C2×C29semidirect
271. #1683C2×C29semidirect
272. #1677C2×C29semidirect
273. #1669C2×C29semidirect
274. #1665C2×C29semidirect
275. #1573C2×C29semidirect
276. #1559C2×C29semidirect
277. #1547C2×C29semidirect
436. C29#19481direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32102
C29×#31152
C29×#30762
C29×#29902
C29×#17042
C29×#16982
C29×#16902
C29×#16862
C29×#16832
C29×#16772
C29×#16692
C29×#16652
C29×#15732
C29×#15592
C29×#15472
#1948129