Finite Group Databasebeta

← C29×#19368 #20314268

Subgroups — C29×#19368 #20314268

Order 7424.

656 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3254C211yesmaximal, characteristic, complemented
2C29×#3214C211yesmaximal, characteristic
3C29×#3182C211yesmaximal, characteristic, complemented
4C29×#2935C211yesmaximal, characteristic, complemented
5C29×#1701C211yesmaximal, characteristic, complemented
6C29×#1699C211yesmaximal, characteristic, complemented
7C29×#1693C211yesmaximal, characteristic, complemented
8C29×#1685C211yesmaximal, characteristic, complemented
9C29×#1681C211yesmaximal, characteristic, complemented
10C29×#1679C211yesmaximal, characteristic, complemented
11C29×#1673C211yesmaximal, characteristic, complemented
12C29×#1665C211yesmaximal, characteristic, complemented
13C29×#1569C211yesmaximal, characteristic, complemented
14C29×#1552C211yesmaximal, characteristic, complemented
15C29×#1547C211yesmaximal, characteristic, complemented
16C2×C29×#131—21no—
17C29×#533C2211yescharacteristic
18C29×#532C2211yescharacteristic
19C29×#532C2211yescharacteristic
20C29×#500C2211yescharacteristic
21C29×#496—21no—
22C29×#492C2211yescharacteristic
23C29×#489—21no—
24C29×#487C2211yescharacteristic
25C29×#486C2211yescharacteristic
26C29×#477—21no—
27C29×#474C2211yescharacteristic
28C29×#474C2211yescharacteristic
29C29×#468—21no—
30C29×#468—21no—
31C29×#468—21no—
32C29×#468—21no—
33C29×#461C2211yescharacteristic
34C29×#461C2211yescharacteristic
35C29×#461C2211yescharacteristic
36C29×#461C2211yescharacteristic
37C29×#460—21no—
38C29×#459C2211yescharacteristic
39C29×#459C2211yescharacteristic
40C29×#449—21no—
41C29×#449—21no—
42C29×#440—21no—
43C29×#440—21no—
44C29×#436C2211yescharacteristic
45C29×#436C2211yescharacteristic
46C29×#435—21no—
47C29×#435—21no—
48C8×D4×C29C2211yescharacteristic
49C8×D4×C29C2211yescharacteristic
50C29×#432C2211yescharacteristic
51C29×#423C2211yescharacteristic
52C2×C29×C4⋊C8C2211yescharacteristic
53C29×#408—21no—
54C4×M16×C29C2211yescharacteristic
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×#332C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#331C2211yescharacteristic
66C29×#331C2211yescharacteristic
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C2×SD16×C29—21no—
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×SD16×C29—21no—
75C2×D8×C29—21no—
76C2×D8×C29—21no—
77C29×#131—44no—
78C2×M16×C29—21no—
79C2×M16×C29—21no—
80C2×M16×C29—21no—
81C2×M16×C29D411yescharacteristic
82C2×M16×C29D411yescharacteristic
83C22×C8×C29—21no—
84C22×C8×C29—21no—
85C22×C8×C29—21no—
86C29×C4⋊Q8D411yescharacteristic
87C29×C4⋊Q8C2311yescharacteristic
88C29×C4⋊Q8C2311yescharacteristic
89C29×C4⋊Q8C2311yescharacteristic
90C29×#127D411yescharacteristic
91C29×#127C2311yescharacteristic
92C29×#125—21no—
93C29×#124—21no—
94C29×#124—21no—
95C29×C22⋊Q8—21no—
96C29×C22⋊Q8—21no—
97C29×#121—21no—
98C29×#121—21no—
99C29×#121—21no—
100C29×#121D411yescharacteristic
101C29×#121D411yescharacteristic
102C4×Q8×C29—21no—
103C4×Q8×C29—21no—
104C4×D4×C29—21no—
105C4×D4×C29—21no—
106C4×D4×C29—21no—
107C4×D4×C29C2311yescharacteristic
108C4×D4×C29C2311yescharacteristic
109C29×#117—21no—
110C2×C42×C29C2311yescharacteristic
111C29×#107—21no—
112C29×#107—21no—
113C29×#107—21no—
114C29×#107—21no—
115C29×C4⋊C8—21no—
116C29×C4⋊C8—21no—
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×C4⋊C8C2311yescharacteristic
122C29×C4⋊C8C2311yescharacteristic
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—21no—
126C29×#103—21no—
127C29×#103—21no—
128C29×#103—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×C22⋊C8—21no—
136C29×C22⋊C8—21no—
137C29×C22⋊C8—21no—
138C29×C22⋊C8—21no—
139C29×C22⋊C8—21no—
140C29×#97—21no—
141C29×#97D411yescharacteristic
142C29×#97D411yescharacteristic
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×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29—21no—
158C2×D4×C29—21no—
159C2×D4×C29—21no—
160C2×D4×C29—41no—
161C2×D4×C29C2×D411yescharacteristic
162C2×D4×C29C2×D411yescharacteristic
163C22×C4×C29—21no—
164C22×C4×C29—21no—
165C22×C4×C29—41no—
166C22×C4×C29C2×D411yescharacteristic
167C22×C4×C29C2×D411yescharacteristic
168C22×C4×C29#4111yescharacteristic
169SD16×C29—42no—
170SD16×C29—42no—
171SD16×C29—81no—
172SD16×C29—81no—
173SD16×C29—81no—
174SD16×C29—81no—
175D8×C29—81no—
176D8×C29—81no—
177M16×C29—22no—
178M16×C29—41no—
179M16×C29—42no—
180M16×C29—42no—
181M16×C29—81no—
182C2×C8×C29—21no—
183C2×C8×C29—21no—
184C2×C8×C29—21no—
185C2×C8×C29—21no—
186C2×C8×C29—21no—
187C2×C8×C29—21no—
188C2×C8×C29—42no—
189C2×C8×C29—42no—
190C2×C8×C29—42no—
191C2×C8×C29C2×D411yescharacteristic
192C2×C8×C29C2×D411yescharacteristic
193C2×C8×C29C2×D411yescharacteristic
194C2×C8×C29C2×D411yescharacteristic
195C4⋊C4×C29—21no—
196C4⋊C4×C29—21no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29—21no—
199C4⋊C4×C29—21no—
200C4⋊C4×C29—21no—
201C4⋊C4×C29—21no—
202C4⋊C4×C29—41no—
203C4⋊C4×C29—41no—
204C4⋊C4×C29C2×D411yescharacteristic
205C4⋊C4×C29C2×D411yescharacteristic
206C22⋊C4×C29—21no—
207C22⋊C4×C29—21no—
208C22⋊C4×C29—21no—
209C22⋊C4×C29—21no—
210C22⋊C4×C29—41no—
211C22⋊C4×C29—41no—
212C22⋊C4×C29—41no—
213C42×C29—41no—
214C42×C29C2×D411yescharacteristic
215C42×C29C2×D411yescharacteristic
216C42×C29#4111yescharacteristic
217C42×C29C2411yescharacteristic
218#19368C2911yesmaximal, characteristic, direct product factor, Sylow
219C23×C29—21no—
220C23×C29—21no—
221C23×C29—41no—
222C23×C29#12111yescharacteristic
223Q8×C29—42no—
224Q8×C29—41no—
225Q8×C29—41no—
226Q8×C29—41no—
227Q8×C29—41no—
228Q8×C29—41no—
229Q8×C29—41no—
230D4×C29—21no—
231D4×C29—21no—
232D4×C29—21no—
233D4×C29—21no—
234D4×C29—42no—
235D4×C29—42no—
236D4×C29—42no—
237D4×C29—41no—
238D4×C29—41no—
239D4×C29—41no—
240D4×C29—41no—
241D4×C29—81no—
242D4×C29—81no—
243D4×C29—82no—
244C2×C4×C29—21no—
245C2×C4×C29—21no—
246C2×C4×C29—21no—
247C2×C4×C29—21no—
248C2×C4×C29—21no—
249C2×C4×C29—21no—
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#12111yescharacteristic
260C2×C4×C29#12111yescharacteristic
261C2×C4×C29#12111yescharacteristic
262C2×C4×C29C22×D411yescharacteristic
263C2×C4×C29C22×D411yescharacteristic
264C2×C4×C29C2×#4111yescharacteristic
265C8×C29—21no—
266C8×C29—21no—
267C8×C29—21no—
268C8×C29—41no—
269C8×C29—41no—
270C8×C29—41no—
271C8×C29—41no—
272C8×C29—41no—
273C8×C29—41no—
274C8×C29AGL(1,ℤ/8)12yes—
275#3254C2×C2911yescharacteristic, complemented
276#3214C2×C2911yescharacteristic
277#3182C2×C2911yescharacteristic, complemented
278#2935C2×C2911yescharacteristic, complemented
279#1701C2×C2911yescharacteristic, complemented
280#1699C2×C2911yescharacteristic, complemented
281#1693C2×C2911yescharacteristic, complemented
282#1685C2×C2911yescharacteristic, complemented
283#1681C2×C2911yescharacteristic, complemented
284#1679C2×C2911yescharacteristic, complemented
285#1673C2×C2911yescharacteristic, complemented
286#1665C2×C2911yescharacteristic, complemented
287#1569C2×C2911yescharacteristic, complemented
288#1552C2×C2911yescharacteristic, complemented
289#1547C2×C2911yescharacteristic, complemented
290C22×C29—21no—
291C22×C29—21no—
292C22×C29—21no—
293C22×C29—41no—
294C22×C29—41no—
295C22×C29—41no—
296C22×C29—41no—
297C22×C29—41no—
298C22×C29—41no—
299C22×C29—81no—
300C22×C29—81no—
301C22×C29—81no—
302C22×C29C2×#12111yescharacteristic
303C4×C29—21no—
304C4×C29—21no—
305C4×C29—21no—
306C4×C29—21no—
307C4×C29—41no—
308C4×C29—41no—
309C4×C29—81no—
310C4×C29—81no—
311C4×C29—81no—
312C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
313C4×C29#57511yescharacteristic
314C4×C29#57611yescharacteristic
315C4×C29#57711yescharacteristic
316C2×#131—21no—
317#533C22×C2911yescharacteristic
318#532C22×C2911yescharacteristic
319#532C22×C2911yescharacteristic
320#500C22×C2911yescharacteristic
321#496—21no—
322#492C22×C2911yescharacteristic
323#489—21no—
324#487C22×C2911yescharacteristic
325#486C22×C2911yescharacteristic
326#477—21no—
327#474C22×C2911yescharacteristic
328#474C22×C2911yescharacteristic
329#468—21no—
330#468—21no—
331#468—21no—
332#468—21no—
333#461C22×C2911yescharacteristic
334#461C22×C2911yescharacteristic
335#461C22×C2911yescharacteristic
336#461C22×C2911yescharacteristic
337#460—21no—
338#459C22×C2911yescharacteristic
339#459C22×C2911yescharacteristic
340#449—21no—
341#449—21no—
342#440—21no—
343#440—21no—
344#436C22×C2911yescharacteristic
345#436C22×C2911yescharacteristic
346#435—21no—
347#435—21no—
348C8×D4C22×C2911yescharacteristic
349C8×D4C22×C2911yescharacteristic
350#432C22×C2911yescharacteristic
351#423C22×C2911yescharacteristic
352C2×C4⋊C8C22×C2911yescharacteristic
353#408—21no—
354C4×M16C22×C2911yescharacteristic
355#335C22×C2911yescharacteristic
356#335C22×C2911yescharacteristic
357#334C22×C2911yescharacteristic
358#334C22×C2911yescharacteristic
359#332C22×C2911yescharacteristic
360#332C22×C2911yescharacteristic
361#332C22×C2911yescharacteristic
362#332C22×C2911yescharacteristic
363#332C22×C2911yescharacteristic
364#332C22×C2911yescharacteristic
365#331C22×C2911yescharacteristic
366#331C22×C2911yescharacteristic
367C2×C29—41no—
368C2×C29—81no—
369C2×C29—81no—
370C2×C29—161no—
371C2×C29#303611yescharacteristic
372C2×C29#306211yescharacteristic
373C2×C29#306911yescharacteristic
374C2×#41—21no—
375C2×#41—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×D8—21no—
383C2×D8—21no—
384#131—44no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—21no—
388C2×M16D4×C2911yescharacteristic
389C2×M16D4×C2911yescharacteristic
390C22×C8—21no—
391C22×C8—21no—
392C22×C8—21no—
393C4⋊Q8D4×C2911yescharacteristic
394C4⋊Q8C23×C2911yescharacteristic
395C4⋊Q8C23×C2911yescharacteristic
396C4⋊Q8C23×C2911yescharacteristic
397#127D4×C2911yescharacteristic
398#127C23×C2911yescharacteristic
399#125—21no—
400#124—21no—
401#124—21no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121D4×C2911yescharacteristic
408#121D4×C2911yescharacteristic
409C4×Q8—21no—
410C4×Q8—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4C23×C2911yescharacteristic
415C4×D4C23×C2911yescharacteristic
416#117—21no—
417C2×C42C23×C2911yescharacteristic
418#107—21no—
419#107—21no—
420#107—21no—
421#107—21no—
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8C23×C2911yescharacteristic
425C4⋊C8C23×C2911yescharacteristic
426C4⋊C8C23×C2911yescharacteristic
427C4⋊C8C23×C2911yescharacteristic
428C4⋊C8C23×C2911yescharacteristic
429C4⋊C8C23×C2911yescharacteristic
430#103—21no—
431#103—21no—
432#103—21no—
433#103—21no—
434#103—21no—
435#103—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442C22⋊C8—21no—
443C22⋊C8—21no—
444C22⋊C8—21no—
445C22⋊C8—21no—
446C22⋊C8—21no—
447#97—21no—
448#97D4×C2911yescharacteristic
449#97D4×C2911yescharacteristic
450C4×C8C23×C2911yescharacteristic
451C4×C8C23×C2911yescharacteristic
452C29#1936811yescharacteristic, direct product factor, Sylow
453#41—42no—
454#41—42no—
455#41—81no—
456#41—81no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—41no—
469C2×D4C2×D4×C2911yescharacteristic
470C2×D4C2×D4×C2911yescharacteristic
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—41no—
474C22×C4C2×D4×C2911yescharacteristic
475C22×C4C2×D4×C2911yescharacteristic
476C22×C4#41×C2911yescharacteristic
477SD16—42no—
478SD16—42no—
479SD16—81no—
480SD16—81no—
481SD16—81no—
482SD16—81no—
483D8—81no—
484D8—81no—
485M16—22no—
486M16—41no—
487M16—42no—
488M16—42no—
489M16—81no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—42no—
497C2×C8—42no—
498C2×C8—42no—
499C2×C8C2×D4×C2911yescharacteristic
500C2×C8C2×D4×C2911yescharacteristic
501C2×C8C2×D4×C2911yescharacteristic
502C2×C8C2×D4×C2911yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4C2×D4×C2911yescharacteristic
513C4⋊C4C2×D4×C2911yescharacteristic
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C42—41no—
522C42C2×D4×C2911yescharacteristic
523C42C2×D4×C2911yescharacteristic
524C42#41×C2911yescharacteristic
525C42C24×C2911yescharacteristic
526C23—21no—
527C23—21no—
528C23—41no—
529C23C29×#12111yescharacteristic
530Q8—42no—
531Q8—41no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—42no—
542D4—42no—
543D4—42no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—81no—
549D4—81no—
550D4—82no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—82no—
566C2×C4C29×#12111yescharacteristic
567C2×C4C29×#12111yescharacteristic
568C2×C4C29×#12111yescharacteristic
569C2×C4C22×D4×C2911yescharacteristic
570C2×C4C22×D4×C2911yescharacteristic
571C2×C4C2×#41×C2911yescharacteristic
572C8—21no—
573C8—21no—
574C8—21no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8C29×AGL(1,ℤ/8)12yes—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22C2×C29×#12111yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—41no—
600C4—41no—
601C4—81no—
602C4—81no—
603C4—81no—
604C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
605C4C29×#57511yescharacteristic
606C4C29×#57611yescharacteristic
607C4C29×#57711yescharacteristic
608C2—41no—
609C2—81no—
610C2—81no—
611C2—161no—
612C2C29×#303611yescharacteristic
613C2C29×#306211yescharacteristic
614C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3214C2
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×#3254C2semidirect
3. C29×#3182C2semidirect
4. C29×#2935C2semidirect
5. C29×#1701C2semidirect
6. C29×#1699C2semidirect
7. C29×#1693C2semidirect
8. C29×#1685C2semidirect
9. C29×#1681C2semidirect
10. C29×#1679C2semidirect
11. C29×#1673C2semidirect
12. C29×#1665C2semidirect
13. C29×#1569C2semidirect
14. C29×#1552C2semidirect
15. C29×#1547C2semidirect
218. #19368C29direct (N × H)
275. #3254C2×C29semidirect
277. #3182C2×C29semidirect
278. #2935C2×C29semidirect
279. #1701C2×C29semidirect
280. #1699C2×C29semidirect
281. #1693C2×C29semidirect
282. #1685C2×C29semidirect
283. #1681C2×C29semidirect
284. #1679C2×C29semidirect
285. #1673C2×C29semidirect
286. #1665C2×C29semidirect
287. #1569C2×C29semidirect
288. #1552C2×C29semidirect
289. #1547C2×C29semidirect
452. C29#19368direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32542
C29×#32142
C29×#31822
C29×#29352
C29×#17012
C29×#16992
C29×#16932
C29×#16852
C29×#16812
C29×#16792
C29×#16732
C29×#16652
C29×#15692
C29×#15522
C29×#15472
#1936829