Finite Group Databasebeta

← C29×#18695 #20313595

Subgroups — C29×#18695 #20313595

Order 7424.

866 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3552C211yesmaximal, characteristic
2C29×#3238C211yesmaximal, characteristic, complemented
3C29×#3238C211yesmaximal, characteristic, complemented
4C2×C29×#487C211yesmaximal, characteristic, complemented
5C29×#1638C212yesmaximal, complemented
6C29×#1637C212yesmaximal, complemented
7C29×#1636C212yesmaximal, complemented
8C29×#1635C212yesmaximal, complemented
9C29×#1556C211yesmaximal, characteristic, complemented
10C29×#1494C211yesmaximal, characteristic, complemented
11C29×#1494C211yesmaximal, characteristic, complemented
12C29×#563—22no—
13C29×#557C2211yescharacteristic
14C29×#556C2211yescharacteristic
15C29×#554—21no—
16C29×#553—21no—
17D4×Q8×C29—21no—
18D4×Q8×C29C2211yescharacteristic
19C29×#548—21no—
20C29×#547C2211yescharacteristic
21C29×#544—21no—
22C29×#542—21no—
23C29×#541—21no—
24C29×#539—22no—
25C29×#536—21no—
26C2×C29×C4⋊Q8C2211yescharacteristic
27C2×C29×C4⋊Q8C2211yescharacteristic
28C29×#529C2211yescharacteristic
29C29×#529C2211yescharacteristic
30C29×#501—21no—
31C29×#501—21no—
32C29×#489—21no—
33C29×#489—21no—
34C29×#487—22no—
35C29×#487C2212yes—
36C29×#487C2212yes—
37C29×#483—21no—
38C29×#483—21no—
39C29×#480—21no—
40C29×#480—21no—
41C29×#477C2212yes—
42C29×#477C2212yes—
43C29×#476C2212yes—
44C29×#476C2212yes—
45C29×#432C2211yescharacteristic
46C29×#432C2211yescharacteristic
47C2×C29×#103—22no—
48C2×C4×C8×C29C2211yescharacteristic
49C29×#332C2212yes—
50C29×#332C2212yes—
51C29×Q8⋊C8C2212yes—
52C29×Q8⋊C8C2212yes—
53C29×D4⋊C8C2212yes—
54C29×D4⋊C8C2212yes—
55C2×#41×C29—21no—
56C22×Q8×C29—21no—
57C22×Q8×C29—21no—
58C22×Q8×C29—21no—
59C22×C8×C29—21no—
60C29×C4⋊Q8—22no—
61C29×C4⋊Q8—21no—
62C29×C4⋊Q8—21no—
63C29×C4⋊Q8—21no—
64C29×C4⋊Q8—21no—
65C29×C4⋊Q8—21no—
66C29×C4⋊Q8—21no—
67C29×C4⋊Q8—21no—
68C29×C4⋊Q8D412yes—
69C29×C4⋊Q8C2312yes—
70C29×C4⋊Q8C2311yescharacteristic
71C29×C4⋊Q8C2311yescharacteristic
72C29×#126—22no—
73C29×#126—22no—
74C29×#126—22no—
75C29×#126—21no—
76C29×#126—21no—
77C29×#125—22no—
78C29×#125—22no—
79C29×#125—22no—
80C29×#125—21no—
81C29×#125D411yescharacteristic
82C29×#125D411yescharacteristic
83C29×#124—22no—
84C29×#124—21no—
85C29×#124D411yescharacteristic
86C29×#124D411yescharacteristic
87C29×#123—22no—
88C29×#123—22no—
89C29×#123—21no—
90C29×#123—21no—
91C29×#123—22no—
92C29×C22⋊Q8—22no—
93C29×C22⋊Q8—22no—
94C29×C22⋊Q8—22no—
95C29×C22⋊Q8—22no—
96C29×C22⋊Q8—22no—
97C29×C22⋊Q8—21no—
98C29×C22⋊Q8—22no—
99C29×C22⋊Q8—21no—
100C29×C22⋊Q8—21no—
101C29×C22⋊Q8D411yescharacteristic
102C29×C22⋊Q8D411yescharacteristic
103C29×#121—22no—
104C29×#121—21no—
105C29×#121D411yescharacteristic
106C29×#121D411yescharacteristic
107C4×Q8×C29—21no—
108C4×Q8×C29—21no—
109C4×Q8×C29—21no—
110C4×Q8×C29C2311yescharacteristic
111C4×Q8×C29C2311yescharacteristic
112C4×D4×C29—22no—
113C4×D4×C29—22no—
114C4×D4×C29—21no—
115C4×D4×C29—21no—
116C4×D4×C29—21no—
117C4×D4×C29C2311yescharacteristic
118C4×D4×C29C2311yescharacteristic
119C29×#117—21no—
120C29×#117—21no—
121C29×#117—21no—
122C2×C4⋊C4×C29—21no—
123C2×C4⋊C4×C29—21no—
124C2×C4⋊C4×C29—21no—
125C2×C4⋊C4×C29—21no—
126C2×C4⋊C4×C29D412yes—
127C2×C42×C29C2311yescharacteristic
128C29×#107—22no—
129C29×#107—22no—
130C29×#106—22no—
131C29×#106—22no—
132C29×C4⋊C8C2312yes—
133C29×C4⋊C8C2312yes—
134C29×#103—22no—
135C29×#103—22no—
136C29×#103—24no—
137C29×#103—24no—
138C29×#102—22no—
139C29×#102—22no—
140C29×C22⋊C8—21no—
141C29×C22⋊C8—21no—
142C29×#97—21no—
143C29×#97—21no—
144C4×C8×C29—21no—
145C4×C8×C29C2312yes—
146#41×C29—82no—
147C2×Q8×C29—22no—
148C2×Q8×C29—22no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×Q8×C29—22no—
152C2×Q8×C29—44no—
153C2×Q8×C29—41no—
154C2×Q8×C29—82no—
155C2×Q8×C29—82no—
156C2×Q8×C29C2×D411yescharacteristic
157C2×Q8×C29C2×D411yescharacteristic
158C2×D4×C29—21no—
159C2×D4×C29—21no—
160C2×D4×C29—22no—
161C2×D4×C29C2×D411yescharacteristic
162C2×D4×C29C2×D411yescharacteristic
163C22×C4×C29—22no—
164C22×C4×C29—22no—
165C22×C4×C29—22no—
166C22×C4×C29—21no—
167C22×C4×C29—21no—
168C22×C4×C29—41no—
169C22×C4×C29C2×D411yescharacteristic
170C22×C4×C29C2×D411yescharacteristic
171C22×C4×C29C2×D411yescharacteristic
172C2×C8×C29—22no—
173C2×C8×C29—22no—
174C2×C8×C29—22no—
175C2×C8×C29—42no—
176C4⋊C4×C29—22no—
177C4⋊C4×C29—22no—
178C4⋊C4×C29—22no—
179C4⋊C4×C29—22no—
180C4⋊C4×C29—22no—
181C4⋊C4×C29—22no—
182C4⋊C4×C29—22no—
183C4⋊C4×C29—22no—
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—21no—
194C4⋊C4×C29—22no—
195C4⋊C4×C29—22no—
196C4⋊C4×C29—41no—
197C4⋊C4×C29—41no—
198C4⋊C4×C29C2×D411yescharacteristic
199C4⋊C4×C29C2×D412yes—
200C4⋊C4×C29C2×D412yes—
201C4⋊C4×C29C2×D411yescharacteristic
202C4⋊C4×C29C2×D411yescharacteristic
203C4⋊C4×C29C2×D411yescharacteristic
204C22⋊C4×C29—22no—
205C22⋊C4×C29—22no—
206C22⋊C4×C29—22no—
207C22⋊C4×C29—22no—
208C22⋊C4×C29—21no—
209C22⋊C4×C29—21no—
210C22⋊C4×C29—21no—
211C22⋊C4×C29—21no—
212C22⋊C4×C29—21no—
213C22⋊C4×C29—21no—
214C22⋊C4×C29—21no—
215C22⋊C4×C29—21no—
216C22⋊C4×C29—21no—
217C22⋊C4×C29—21no—
218C42×C29—22no—
219C42×C29—22no—
220C42×C29—21no—
221C42×C29—21no—
222C42×C29C2×D411yescharacteristic
223C42×C29C2×D411yescharacteristic
224C42×C29C2×D411yescharacteristic
225C42×C29C2411yescharacteristic
226#18695C2911yesmaximal, characteristic, direct product factor, Sylow
227C23×C29—21no—
228C23×C29—21no—
229C23×C29#12011yescharacteristic
230Q8×C29—22no—
231Q8×C29—22no—
232Q8×C29—44no—
233Q8×C29—42no—
234Q8×C29—42no—
235Q8×C29—82no—
236Q8×C29—82no—
237Q8×C29—82no—
238D4×C29—22no—
239D4×C29—22no—
240D4×C29—42no—
241D4×C29—42no—
242D4×C29—82no—
243C2×C4×C29—22no—
244C2×C4×C29—22no—
245C2×C4×C29—22no—
246C2×C4×C29—21no—
247C2×C4×C29—21no—
248C2×C4×C29—21no—
249C2×C4×C29—21no—
250C2×C4×C29—21no—
251C2×C4×C29—22no—
252C2×C4×C29—22no—
253C2×C4×C29—21no—
254C2×C4×C29—42no—
255C2×C4×C29—42no—
256C2×C4×C29—42no—
257C2×C4×C29—82no—
258C2×C4×C29—82no—
259C2×C4×C29—82no—
260C2×C4×C29—82no—
261C2×C4×C29#12011yescharacteristic
262C2×C4×C29#12011yescharacteristic
263C2×C4×C29#12011yescharacteristic
264C2×C4×C29C22×D411yescharacteristic
265C2×C4×C29C22×D411yescharacteristic
266C2×C4×C29C22×D411yescharacteristic
267C8×C29—42no—
268C8×C29—42no—
269C8×C29—42no—
270#3552C2×C2911yescharacteristic
271#3238C2×C2911yescharacteristic, complemented
272#3238C2×C2911yescharacteristic, complemented
273C2×#487C2×C2911yescharacteristic, complemented
274#1638C2×C2912yescomplemented
275#1637C2×C2912yescomplemented
276#1636C2×C2912yescomplemented
277#1635C2×C2912yescomplemented
278#1556C2×C2911yescharacteristic, complemented
279#1494C2×C2911yescharacteristic, complemented
280#1494C2×C2911yescharacteristic, complemented
281C22×C29—21no—
282C22×C29—21no—
283C22×C29—41no—
284C22×C29—41no—
285C22×C29—41no—
286C22×C29—41no—
287C22×C29—41no—
288C22×C29—41no—
289C22×C29#45412yes—
290C22×C29C2×#12011yescharacteristic
291C4×C29—21no—
292C4×C29—21no—
293C4×C29—21no—
294C4×C29—21no—
295C4×C29—41no—
296C4×C29—42no—
297C4×C29—41no—
298C4×C29—42no—
299C4×C29—41no—
300C4×C29—41no—
301C4×C29—41no—
302C4×C29—41no—
303C4×C29—82no—
304C4×C29#57712yes—
305C4×C29#57812yes—
306#563—22no—
307#557C22×C2911yescharacteristic
308#556C22×C2911yescharacteristic
309#554—21no—
310#553—21no—
311D4×Q8—21no—
312D4×Q8C22×C2911yescharacteristic
313#548—21no—
314#547C22×C2911yescharacteristic
315#544—21no—
316#542—21no—
317#541—21no—
318#539—22no—
319#536—21no—
320C2×C4⋊Q8C22×C2911yescharacteristic
321C2×C4⋊Q8C22×C2911yescharacteristic
322#529C22×C2911yescharacteristic
323#529C22×C2911yescharacteristic
324#501—21no—
325#501—21no—
326#489—21no—
327#489—21no—
328#487—22no—
329#487C22×C2912yes—
330#487C22×C2912yes—
331#483—21no—
332#483—21no—
333#480—21no—
334#480—21no—
335#477C22×C2912yes—
336#477C22×C2912yes—
337#476C22×C2912yes—
338#476C22×C2912yes—
339#432C22×C2911yescharacteristic
340#432C22×C2911yescharacteristic
341C2×#103—22no—
342C2×C4×C8C22×C2911yescharacteristic
343#332C22×C2912yes—
344#332C22×C2912yes—
345Q8⋊C8C22×C2912yes—
346Q8⋊C8C22×C2912yes—
347D4⋊C8C22×C2912yes—
348D4⋊C8C22×C2912yes—
349C2×C29—22no—
350C2×C29—81no—
351C2×C29—81no—
352C2×C29#300911yescharacteristic
353C2×C29#301111yescharacteristic
354C2×C29C2×#45411yescharacteristic
355C2×#41—21no—
356C22×Q8—21no—
357C22×Q8—21no—
358C22×Q8—21no—
359C22×C8—21no—
360C4⋊Q8—22no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8—21no—
368C4⋊Q8D4×C2912yes—
369C4⋊Q8C23×C2912yes—
370C4⋊Q8C23×C2911yescharacteristic
371C4⋊Q8C23×C2911yescharacteristic
372#126—22no—
373#126—22no—
374#126—22no—
375#126—21no—
376#126—21no—
377#125—22no—
378#125—22no—
379#125—22no—
380#125—21no—
381#125D4×C2911yescharacteristic
382#125D4×C2911yescharacteristic
383#124—22no—
384#124—21no—
385#124D4×C2911yescharacteristic
386#124D4×C2911yescharacteristic
387#123—22no—
388#123—22no—
389#123—21no—
390#123—21no—
391#123—22no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—21no—
398C22⋊Q8—22no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8D4×C2911yescharacteristic
402C22⋊Q8D4×C2911yescharacteristic
403#121—22no—
404#121—21no—
405#121D4×C2911yescharacteristic
406#121D4×C2911yescharacteristic
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8C23×C2911yescharacteristic
411C4×Q8C23×C2911yescharacteristic
412C4×D4—22no—
413C4×D4—22no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4C23×C2911yescharacteristic
418C4×D4C23×C2911yescharacteristic
419#117—21no—
420#117—21no—
421#117—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4D4×C2912yes—
427C2×C42C23×C2911yescharacteristic
428#107—22no—
429#107—22no—
430#106—22no—
431#106—22no—
432C4⋊C8C23×C2912yes—
433C4⋊C8C23×C2912yes—
434#103—22no—
435#103—22no—
436#103—24no—
437#103—24no—
438#102—22no—
439#102—22no—
440C22⋊C8—21no—
441C22⋊C8—21no—
442#97—21no—
443#97—21no—
444C4×C8—21no—
445C4×C8C23×C2912yes—
446C29#1869511yescharacteristic, direct product factor, Sylow
447#41—82no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—22no—
453C2×Q8—44no—
454C2×Q8—41no—
455C2×Q8—82no—
456C2×Q8—82no—
457C2×Q8C2×D4×C2911yescharacteristic
458C2×Q8C2×D4×C2911yescharacteristic
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—22no—
462C2×D4C2×D4×C2911yescharacteristic
463C2×D4C2×D4×C2911yescharacteristic
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—41no—
470C22×C4C2×D4×C2911yescharacteristic
471C22×C4C2×D4×C2911yescharacteristic
472C22×C4C2×D4×C2911yescharacteristic
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—42no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4C2×D4×C2912yes—
500C4⋊C4C2×D4×C2912yes—
501C4⋊C4C2×D4×C2911yescharacteristic
502C4⋊C4C2×D4×C2911yescharacteristic
503C4⋊C4C2×D4×C2911yescharacteristic
504C4⋊C4C2×D4×C2911yescharacteristic
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C42—22no—
520C42—22no—
521C42—21no—
522C42—21no—
523C42C2×D4×C2911yescharacteristic
524C42C2×D4×C2911yescharacteristic
525C42C2×D4×C2911yescharacteristic
526C42C24×C2911yescharacteristic
527C23—21no—
528C23—21no—
529C23C29×#12011yescharacteristic
530Q8—22no—
531Q8—22no—
532Q8—44no—
533Q8—42no—
534Q8—42no—
535Q8—82no—
536Q8—82no—
537Q8—82no—
538D4—22no—
539D4—22no—
540D4—42no—
541D4—42no—
542D4—82no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—82no—
558C2×C4—82no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4C29×#12011yescharacteristic
562C2×C4C29×#12011yescharacteristic
563C2×C4C29×#12011yescharacteristic
564C2×C4C22×D4×C2911yescharacteristic
565C2×C4C22×D4×C2911yescharacteristic
566C2×C4C22×D4×C2911yescharacteristic
567C8—42no—
568C8—42no—
569C8—42no—
570C22—21no—
571C22—21no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22C29×#45412yes—
579C22C2×C29×#12011yescharacteristic
580C4—21no—
581C4—21no—
582C4—21no—
583C4—21no—
584C4—41no—
585C4—42no—
586C4—41no—
587C4—42no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—82no—
593C4C29×#57712yes—
594C4C29×#57812yes—
595C2—22no—
596C2—81no—
597C2—81no—
598C2C29×#300911yescharacteristic
599C2C29×#301111yescharacteristic
600C2C2×C29×#45411yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3552C2
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
2. C29×#3238C2semidirect
3. C29×#3238C2semidirect
4. C2×C29×#487C2semidirect
5. C29×#1638C2semidirect
6. C29×#1637C2semidirect
7. C29×#1636C2semidirect
8. C29×#1635C2semidirect
9. C29×#1556C2semidirect
10. C29×#1494C2semidirect
11. C29×#1494C2semidirect
226. #18695C29direct (N × H)
271. #3238C2×C29semidirect
272. #3238C2×C29semidirect
273. C2×#487C2×C29semidirect
274. #1638C2×C29semidirect
275. #1637C2×C29semidirect
276. #1636C2×C29semidirect
277. #1635C2×C29semidirect
278. #1556C2×C29semidirect
279. #1494C2×C29semidirect
280. #1494C2×C29semidirect
446. C29#18695direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35522
C29×#32382
C2×C29×#4872
C29×#16382
C29×#16372
C29×#16362
C29×#16352
C29×#15562
C29×#14942
#1869529