Finite Group Databasebeta

← C29×#19790 #20314690

Subgroups — C29×#19790 #20314690

Order 7424.

626 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3381C211yesmaximal, characteristic, complemented
2C29×#3372C211yesmaximal, characteristic, complemented
3C29×#3295C211yesmaximal, characteristic
4C29×#3295C211yesmaximal, characteristic
5C29×#1720C211yesmaximal, characteristic, complemented
6C29×#1698C211yesmaximal, characteristic, complemented
7C29×#1683C211yesmaximal, characteristic, complemented
8C29×#1678C211yesmaximal, characteristic, complemented
9C29×#1671C211yesmaximal, characteristic, complemented
10C29×#1639C211yesmaximal, characteristic
11C29×#1632C211yesmaximal, characteristic, complemented
12C29×#1632C211yesmaximal, characteristic, complemented
13C29×#1626C211yesmaximal, characteristic, complemented
14C29×#1582C211yesmaximal, characteristic, complemented
15C29×SD16⋊C8C211yesmaximal, characteristic, complemented
16C29×#557C2211yescharacteristic, complemented
17C29×#554C2211yescharacteristic
18C29×#554C2211yescharacteristic
19D42×C29C2211yescharacteristic
20C29×#499—21no—
21C29×#498C2211yescharacteristic, complemented
22C29×#494C2211yescharacteristic, complemented
23C29×#491—21no—
24C29×#487C2211yescharacteristic, complemented
25C29×#486C2211yescharacteristic
26C29×#486C2211yescharacteristic
27C29×#486C2211yescharacteristic
28C29×#481—21no—
29C29×#481—21no—
30C29×#479—21no—
31C29×#479—21no—
32C29×#478—21no—
33C29×#477C2211yescharacteristic, complemented
34C29×#477C2211yescharacteristic, complemented
35C29×#476C2211yescharacteristic
36C29×#476C2211yescharacteristic
37C29×#474C2211yescharacteristic
38C29×#465—21no—
39C29×#465—21no—
40C29×#461—21no—
41C29×#461C2211yescharacteristic
42C29×#460C2211yescharacteristic
43C29×#460C2211yescharacteristic
44C29×#450—21no—
45C29×#450—21no—
46C29×#446C2211yescharacteristic, complemented
47C8×Q8×C29C2211yescharacteristic, complemented
48C29×#440—21no—
49C4×SD16×C29—21no—
50C4×SD16×C29C2211yescharacteristic
51C4×SD16×C29C2211yescharacteristic
52C8×D4×C29C2211yescharacteristic
53C8×D4×C29C2211yescharacteristic
54C2×C29×#102—21no—
55C2×C29×#102—21no—
56C29×#335C2211yescharacteristic, complemented
57C29×#334C2211yescharacteristic, complemented
58C29×#333C2211yescharacteristic, complemented
59C29×#333C2211yescharacteristic, complemented
60C29×#332C2211yescharacteristic, complemented
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic, complemented
63C29×Q8⋊C8C2211yescharacteristic, complemented
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C29×#322C2211yescharacteristic, complemented
67C22×D4×C29—21no—
68C22×D4×C29—21no—
69C2×Q16×C29—41no—
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29D411yescharacteristic
74C2×SD16×C29D411yescharacteristic
75C22×C8×C29—21no—
76C22×C8×C29—21no—
77C29×C4⋊Q8—21no—
78C29×C4⋊Q8C2311yescharacteristic
79C29×C4⋊Q8C2311yescharacteristic
80C29×C4⋊Q8C2311yescharacteristic
81C29×#127C2311yescharacteristic
82C29×#125—21no—
83C29×#125—21no—
84C29×#125—21no—
85C29×#125—41no—
86C29×C22⋊Q8—21no—
87C29×C22⋊Q8—21no—
88C29×C22⋊Q8—41no—
89C29×C22⋊Q8—41no—
90C29×#121—21no—
91C29×#121—21no—
92C29×#120—41no—
93C4×Q8×C29—21no—
94C4×Q8×C29—21no—
95C4×Q8×C29C2311yescharacteristic
96C4×Q8×C29C2311yescharacteristic
97C4×D4×C29—21no—
98C4×D4×C29—21no—
99C4×D4×C29C2311yescharacteristic
100C4×D4×C29C2311yescharacteristic
101C2×C4⋊C4×C29—21no—
102C2×C4⋊C4×C29—21no—
103C29×#107—21no—
104C29×#107—21no—
105C29×#107—21no—
106C29×#106—21no—
107C29×#106—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×#106D411yescharacteristic
111C29×#106D411yescharacteristic
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×#103D411yescharacteristic
124C29×#103D411yescharacteristic
125C29×#102—21no—
126C29×#102—21no—
127C29×#102—21no—
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—41no—
135C29×#102D411yescharacteristic
136C29×#102D411yescharacteristic
137C29×C22⋊C8—21no—
138C29×C22⋊C8—21no—
139C29×#97—21no—
140C4×C8×C29—21no—
141C4×C8×C29C2311yescharacteristic
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C24×C29—41no—
145C2×Q8×C29—21no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29C2×D411yescharacteristic
149C2×Q8×C29C2×D411yescharacteristic
150C2×D4×C29—21no—
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—41no—
154C2×D4×C29—41no—
155C2×D4×C29—42no—
156C2×D4×C29—42no—
157C2×D4×C29—81no—
158C2×D4×C29—81no—
159C2×D4×C29C2×D411yescharacteristic
160C2×D4×C29C2×D411yescharacteristic
161C22×C4×C29—21no—
162C22×C4×C29—21no—
163C22×C4×C29—41no—
164C22×C4×C29—41no—
165Q16×C29—82no—
166SD16×C29—22no—
167SD16×C29—22no—
168SD16×C29—42no—
169SD16×C29—81no—
170SD16×C29—81no—
171C2×C8×C29—21no—
172C2×C8×C29—21no—
173C2×C8×C29—21no—
174C2×C8×C29—21no—
175C2×C8×C29—21no—
176C2×C8×C29—81no—
177C2×C8×C29—81no—
178C2×C8×C29C2×D411yescharacteristic
179C2×C8×C29C2×D411yescharacteristic
180C2×C8×C29C2×D411yescharacteristic
181C2×C8×C29C2×D411yescharacteristic
182C4⋊C4×C29—21no—
183C4⋊C4×C29—21no—
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—41no—
191C4⋊C4×C29—41no—
192C4⋊C4×C29—41no—
193C4⋊C4×C29—41no—
194C4⋊C4×C29—41no—
195C4⋊C4×C29—41no—
196C4⋊C4×C29—41no—
197C4⋊C4×C29C2×D411yescharacteristic
198C4⋊C4×C29C2×D411yescharacteristic
199C4⋊C4×C29C2×D411yescharacteristic
200C4⋊C4×C29C2×D411yescharacteristic
201C22⋊C4×C29—21no—
202C22⋊C4×C29—21no—
203C22⋊C4×C29—41no—
204C22⋊C4×C29—41no—
205C22⋊C4×C29—41no—
206C42×C29—21no—
207C42×C29—21no—
208C42×C29—41no—
209C42×C29C2411yescharacteristic
210#19790C2911yesmaximal, characteristic, direct product factor, Sylow
211C23×C29—21no—
212C23×C29—21no—
213C23×C29—41no—
214C23×C29—82no—
215C23×C29—82no—
216C23×C29—161no—
217Q8×C29—21no—
218Q8×C29—21no—
219Q8×C29—21no—
220Q8×C29—21no—
221Q8×C29—41no—
222Q8×C29—41no—
223Q8×C29—81no—
224Q8×C29—81no—
225D4×C29—21no—
226D4×C29—21no—
227D4×C29—41no—
228D4×C29—41no—
229D4×C29—41no—
230D4×C29—41no—
231D4×C29—81no—
232D4×C29—82no—
233D4×C29—82no—
234D4×C29#13512yes—
235D4×C29#13712yes—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—21no—
239C2×C4×C29—21no—
240C2×C4×C29—21no—
241C2×C4×C29—21no—
242C2×C4×C29—41no—
243C2×C4×C29—41no—
244C2×C4×C29—41no—
245C2×C4×C29—41no—
246C2×C4×C29—41no—
247C2×C4×C29—41no—
248C2×C4×C29—41no—
249C2×C4×C29—161no—
250C2×C4×C29—161no—
251C2×C4×C29C22×D411yescharacteristic
252C2×C4×C29C22×D411yescharacteristic
253C2×C4×C29H(5,𝔽2)11yescharacteristic
254C8×C29—21no—
255C8×C29—21no—
256C8×C29—21no—
257C8×C29—21no—
258C8×C29—41no—
259C8×C29—41no—
260C8×C29—41no—
261C8×C29—41no—
262C8×C29—41no—
263#3381C2×C2911yescharacteristic, complemented
264#3372C2×C2911yescharacteristic, complemented
265#3295C2×C2911yescharacteristic
266#3295C2×C2911yescharacteristic
267#1720C2×C2911yescharacteristic, complemented
268#1698C2×C2911yescharacteristic, complemented
269#1683C2×C2911yescharacteristic, complemented
270#1678C2×C2911yescharacteristic, complemented
271#1671C2×C2911yescharacteristic, complemented
272#1639C2×C2911yescharacteristic
273#1632C2×C2911yescharacteristic, complemented
274#1632C2×C2911yescharacteristic, complemented
275#1626C2×C2911yescharacteristic, complemented
276#1582C2×C2911yescharacteristic, complemented
277SD16⋊C8C2×C2911yescharacteristic, complemented
278C22×C29—22no—
279C22×C29—22no—
280C22×C29—41no—
281C22×C29—41no—
282C22×C29—41no—
283C22×C29—41no—
284C22×C29—81no—
285C22×C29—81no—
286C22×C29—81no—
287C22×C29—164no—
288C22×C29D4211yescharacteristic
289C4×C29—21no—
290C4×C29—41no—
291C4×C29—41no—
292C4×C29—41no—
293C4×C29—41no—
294C4×C29—41no—
295C4×C29—41no—
296C4×C29—81no—
297C4×C29—81no—
298C4×C29—81no—
299C4×C29C2×#13511yescharacteristic
300C4×C29C2×#13711yescharacteristic
301C4×C29#57711yescharacteristic
302C4×C29#57711yescharacteristic
303#557C22×C2911yescharacteristic, complemented
304#554C22×C2911yescharacteristic
305#554C22×C2911yescharacteristic
306D42C22×C2911yescharacteristic
307#499—21no—
308#498C22×C2911yescharacteristic, complemented
309#494C22×C2911yescharacteristic, complemented
310#491—21no—
311#487C22×C2911yescharacteristic, complemented
312#486C22×C2911yescharacteristic
313#486C22×C2911yescharacteristic
314#486C22×C2911yescharacteristic
315#481—21no—
316#481—21no—
317#479—21no—
318#479—21no—
319#478—21no—
320#477C22×C2911yescharacteristic, complemented
321#477C22×C2911yescharacteristic, complemented
322#476C22×C2911yescharacteristic
323#476C22×C2911yescharacteristic
324#474C22×C2911yescharacteristic
325#465—21no—
326#465—21no—
327#461—21no—
328#461C22×C2911yescharacteristic
329#460C22×C2911yescharacteristic
330#460C22×C2911yescharacteristic
331#450—21no—
332#450—21no—
333#446C22×C2911yescharacteristic, complemented
334C8×Q8C22×C2911yescharacteristic, complemented
335#440—21no—
336C4×SD16—21no—
337C4×SD16C22×C2911yescharacteristic
338C4×SD16C22×C2911yescharacteristic
339C8×D4C22×C2911yescharacteristic
340C8×D4C22×C2911yescharacteristic
341C2×#102—21no—
342C2×#102—21no—
343#335C22×C2911yescharacteristic, complemented
344#334C22×C2911yescharacteristic, complemented
345#333C22×C2911yescharacteristic, complemented
346#333C22×C2911yescharacteristic, complemented
347#332C22×C2911yescharacteristic, complemented
348#331C22×C2911yescharacteristic
349Q8⋊C8C22×C2911yescharacteristic, complemented
350Q8⋊C8C22×C2911yescharacteristic, complemented
351D4⋊C8C22×C2911yescharacteristic
352D4⋊C8C22×C2911yescharacteristic
353#322C22×C2911yescharacteristic, complemented
354C2×C29—42no—
355C2×C29—42no—
356C2×C29—161no—
357C2×C29#326611yescharacteristic
358C2×C29#328211yescharacteristic
359C2×C29#328811yescharacteristic
360C22×D4—21no—
361C22×D4—21no—
362C2×Q16—41no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16D4×C2911yescharacteristic
367C2×SD16D4×C2911yescharacteristic
368C22×C8—21no—
369C22×C8—21no—
370C4⋊Q8—21no—
371C4⋊Q8C23×C2911yescharacteristic
372C4⋊Q8C23×C2911yescharacteristic
373C4⋊Q8C23×C2911yescharacteristic
374#127C23×C2911yescharacteristic
375#125—21no—
376#125—21no—
377#125—21no—
378#125—41no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—41no—
382C22⋊Q8—41no—
383#121—21no—
384#121—21no—
385#120—41no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8C23×C2911yescharacteristic
389C4×Q8C23×C2911yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4C23×C2911yescharacteristic
393C4×D4C23×C2911yescharacteristic
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396#107—21no—
397#107—21no—
398#107—21no—
399#106—21no—
400#106—21no—
401#106—21no—
402#106—21no—
403#106D4×C2911yescharacteristic
404#106D4×C2911yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8C23×C2911yescharacteristic
408C4⋊C8C23×C2911yescharacteristic
409C4⋊C8C23×C2911yescharacteristic
410C4⋊C8C23×C2911yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103D4×C2911yescharacteristic
417#103D4×C2911yescharacteristic
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—41no—
428#102D4×C2911yescharacteristic
429#102D4×C2911yescharacteristic
430C22⋊C8—21no—
431C22⋊C8—21no—
432#97—21no—
433C4×C8—21no—
434C4×C8C23×C2911yescharacteristic
435C4×C8C23×C2911yescharacteristic
436C4×C8C23×C2911yescharacteristic
437C29#1979011yescharacteristic, direct product factor, Sylow
438C24—41no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×D4×C2911yescharacteristic
443C2×Q8C2×D4×C2911yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—81no—
452C2×D4—81no—
453C2×D4C2×D4×C2911yescharacteristic
454C2×D4C2×D4×C2911yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—41no—
459Q16—82no—
460SD16—22no—
461SD16—22no—
462SD16—42no—
463SD16—81no—
464SD16—81no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—81no—
471C2×C8—81no—
472C2×C8C2×D4×C2911yescharacteristic
473C2×C8C2×D4×C2911yescharacteristic
474C2×C8C2×D4×C2911yescharacteristic
475C2×C8C2×D4×C2911yescharacteristic
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⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4C2×D4×C2911yescharacteristic
492C4⋊C4C2×D4×C2911yescharacteristic
493C4⋊C4C2×D4×C2911yescharacteristic
494C4⋊C4C2×D4×C2911yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C42—21no—
501C42—21no—
502C42—41no—
503C42C24×C2911yescharacteristic
504C23—21no—
505C23—21no—
506C23—41no—
507C23—82no—
508C23—82no—
509C23—161no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—81no—
517Q8—81no—
518D4—21no—
519D4—21no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526D4—82no—
527D4C29×#13512yes—
528D4C29×#13712yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—161no—
543C2×C4—161no—
544C2×C4C22×D4×C2911yescharacteristic
545C2×C4C22×D4×C2911yescharacteristic
546C2×C4C29×H(5,𝔽2)11yescharacteristic
547C8—21no—
548C8—21no—
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C22—22no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—164no—
566C22D42×C2911yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4C2×C29×#13511yescharacteristic
578C4C2×C29×#13711yescharacteristic
579C4C29×#57711yescharacteristic
580C4C29×#57711yescharacteristic
581C2—42no—
582C2—42no—
583C2—161no—
584C2C29×#326611yescharacteristic
585C2C29×#328211yescharacteristic
586C2C29×#328811yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalD42×C29C22
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×#3381C2semidirect
2. C29×#3372C2semidirect
5. C29×#1720C2semidirect
6. C29×#1698C2semidirect
7. C29×#1683C2semidirect
8. C29×#1678C2semidirect
9. C29×#1671C2semidirect
11. C29×#1632C2semidirect
12. C29×#1632C2semidirect
13. C29×#1626C2semidirect
14. C29×#1582C2semidirect
15. C29×SD16⋊C8C2semidirect
16. C29×#557C22semidirect
21. C29×#498C22semidirect
22. C29×#494C22semidirect
24. C29×#487C22semidirect
33. C29×#477C22semidirect
34. C29×#477C22semidirect
46. C29×#446C22semidirect
47. C8×Q8×C29C22semidirect
56. C29×#335C22semidirect
57. C29×#334C22semidirect
58. C29×#333C22semidirect
59. C29×#333C22semidirect
60. C29×#332C22semidirect
62. C29×Q8⋊C8C22semidirect
63. C29×Q8⋊C8C22semidirect
66. C29×#322C22semidirect
210. #19790C29direct (N × H)
263. #3381C2×C29semidirect
264. #3372C2×C29semidirect
267. #1720C2×C29semidirect
268. #1698C2×C29semidirect
269. #1683C2×C29semidirect
270. #1678C2×C29semidirect
271. #1671C2×C29semidirect
273. #1632C2×C29semidirect
274. #1632C2×C29semidirect
275. #1626C2×C29semidirect
276. #1582C2×C29semidirect
277. SD16⋊C8C2×C29semidirect
303. #557C22×C29semidirect
308. #498C22×C29semidirect
309. #494C22×C29semidirect
311. #487C22×C29semidirect
320. #477C22×C29semidirect
321. #477C22×C29semidirect
333. #446C22×C29semidirect
334. C8×Q8C22×C29semidirect
343. #335C22×C29semidirect
344. #334C22×C29semidirect
345. #333C22×C29semidirect
346. #333C22×C29semidirect
347. #332C22×C29semidirect
349. Q8⋊C8C22×C29semidirect
350. Q8⋊C8C22×C29semidirect
353. #322C22×C29semidirect
437. C29#19790direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33812
C29×#33722
C29×#32952
C29×#17202
C29×#16982
C29×#16832
C29×#16782
C29×#16712
C29×#16392
C29×#16322
C29×#16262
C29×#15822
C29×SD16⋊C82
#1979029