Finite Group Databasebeta

← C29×#8437 #20303337

Subgroups — C29×#8437 #20303337

Order 7424.

782 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3480C211yesmaximal, characteristic
2C29×#1806C211yesmaximal, characteristic, complemented
3C4×C29×#103C211yesmaximal, characteristic, complemented
4C29×#1502C211yesmaximal, characteristic, complemented
5C29×#1492C211yesmaximal, characteristic, complemented
6C29×#1487C211yesmaximal, characteristic, complemented
7C29×#1476C211yesmaximal, characteristic, complemented
8C29×#559—21no—
9C29×#559C411yescharacteristic, complemented
10C29×#557C411yescharacteristic, complemented
11C29×#556—21no—
12C29×#556C411yescharacteristic, complemented
13C29×#553—22no—
14C29×#553—21no—
15C29×#550C411yescharacteristic, complemented
16C29×#548—21no—
17C29×#532—21no—
18C29×#532C2211yescharacteristic
19C29×#529—21no—
20C29×#529—22no—
21C4×#41×C29—21no—
22C4×#41×C29—21no—
23C4×#41×C29C2211yescharacteristic
24C2×C4×Q8×C29C2211yescharacteristic
25C29×#431C2211yescharacteristic
26C29×#423C2211yescharacteristic
27C2×C29×#104—21no—
28C2×C29×#103—21no—
29C2×C4×C8×C29C2211yescharacteristic
30C4×C4⋊C4×C29C2211yescharacteristic
31C29×#340—21no—
32C29×#339—21no—
33C29×#327—22no—
34C29×Q8⋊C8—21no—
35C29×Q8⋊C8—21no—
36C29×Q8⋊C8—21no—
37C29×D4⋊C8—21no—
38C29×D4⋊C8—22no—
39C2×#41×C29—21no—
40C2×#41×C29—21no—
41C2×#41×C29D411yescharacteristic
42C22×Q8×C29D411yescharacteristic
43C2×M16×C29—21no—
44C22×C8×C29—21no—
45C29×C4⋊Q8—21no—
46C29×C4⋊Q8C2×C411yescharacteristic
47C29×#127—21no—
48C29×#127C2×C411yescharacteristic
49C29×#126—22no—
50C29×#126—22no—
51C29×#126—22no—
52C29×#125—22no—
53C29×#125—21no—
54C29×#124—22no—
55C29×#124—21no—
56C29×#124—21no—
57C29×#124—21no—
58C29×#124—21no—
59C29×#123—22no—
60C29×#123—22no—
61C29×#123—22no—
62C29×C22⋊Q8—22no—
63C29×C22⋊Q8—21no—
64C29×#121—22no—
65C29×#121—22no—
66C29×#121—22no—
67C29×#121—21no—
68C29×#121—21no—
69C29×#121D412yes—
70C4×Q8×C29—21no—
71C4×Q8×C29—21no—
72C4×Q8×C29—21no—
73C4×Q8×C29—21no—
74C4×Q8×C29—21no—
75C4×Q8×C29C2×C411yescharacteristic
76C4×Q8×C29C2×C411yescharacteristic
77C4×Q8×C29C2×C411yescharacteristic
78C4×Q8×C29D411yescharacteristic
79C4×Q8×C29D411yescharacteristic
80C4×Q8×C29D411yescharacteristic
81C4×D4×C29—22no—
82C4×D4×C29—22no—
83C4×D4×C29—22no—
84C4×D4×C29—22no—
85C4×D4×C29—22no—
86C4×D4×C29—21no—
87C4×D4×C29—21no—
88C4×D4×C29—21no—
89C4×D4×C29—21no—
90C4×D4×C29—21no—
91C4×D4×C29—21no—
92C4×D4×C29C2×C411yescharacteristic
93C4×D4×C29D411yescharacteristic
94C4×D4×C29D412yes—
95C29×#117—22no—
96C29×#117—22no—
97C29×#117—21no—
98C29×#117—21no—
99C29×#117D411yescharacteristic
100C2×C4⋊C4×C29—21no—
101C2×C4⋊C4×C29—21no—
102C2×C4⋊C4×C29D411yescharacteristic
103C2×C42×C29—22no—
104C2×C42×C29—21no—
105C2×C42×C29—21no—
106C2×C42×C29—21no—
107C2×C42×C29C2311yescharacteristic
108C29×C4⋊C8—21no—
109C29×C4⋊C8—21no—
110C29×C4⋊C8—21no—
111C29×#104—42no—
112C29×#103—24no—
113C29×C22⋊C8—21no—
114C4×C8×C29—21no—
115C4×C8×C29—21no—
116C4×C8×C29—21no—
117C29×#95—21no—
118#41×C29—21no—
119#41×C29—21no—
120#41×C29—21no—
121#41×C29—21no—
122#41×C29—42no—
123#41×C29—42no—
124#41×C29—41no—
125#41×C29—41no—
126#41×C29—41no—
127#41×C29—41no—
128C2×Q8×C29—21no—
129C2×Q8×C29—21no—
130C2×Q8×C29—22no—
131C2×Q8×C29—41no—
132C2×Q8×C29C22⋊C411yescharacteristic
133C2×Q8×C29C22⋊C411yescharacteristic
134C2×Q8×C29C22⋊C411yescharacteristic
135C2×D4×C29—22no—
136C2×D4×C29—21no—
137C2×D4×C29—22no—
138C2×D4×C29—22no—
139C2×D4×C29—21no—
140C2×D4×C29—21no—
141C2×D4×C29C22⋊C411yescharacteristic
142C2×D4×C29C22⋊C412yes—
143C22×C4×C29—22no—
144C22×C4×C29—21no—
145C22×C4×C29—22no—
146C22×C4×C29—21no—
147C22×C4×C29—21no—
148C22×C4×C29—21no—
149C22×C4×C29—22no—
150C22×C4×C29—21no—
151C22×C4×C29—41no—
152C22×C4×C29C2×D411yescharacteristic
153C22×C4×C29C2×D411yescharacteristic
154C22×C4×C29C2×D411yescharacteristic
155M16×C29—41no—
156M16×C29—41no—
157C2×C8×C29—22no—
158C2×C8×C29—41no—
159C2×C8×C29—41no—
160C2×C8×C29—41no—
161C2×C8×C29—41no—
162C4⋊C4×C29—22no—
163C4⋊C4×C29—22no—
164C4⋊C4×C29—22no—
165C4⋊C4×C29—22no—
166C4⋊C4×C29—21no—
167C4⋊C4×C29—21no—
168C4⋊C4×C29—21no—
169C4⋊C4×C29—21no—
170C4⋊C4×C29—21no—
171C4⋊C4×C29—21no—
172C4⋊C4×C29—21no—
173C4⋊C4×C29—21no—
174C4⋊C4×C29—22no—
175C4⋊C4×C29—41no—
176C4⋊C4×C29C22⋊C411yescharacteristic
177C4⋊C4×C29C22⋊C411yescharacteristic
178C4⋊C4×C29C22⋊C411yescharacteristic
179C4⋊C4×C29C22⋊C411yescharacteristic
180C4⋊C4×C29C22⋊C412yes—
181C22⋊C4×C29—22no—
182C22⋊C4×C29—22no—
183C22⋊C4×C29—22no—
184C22⋊C4×C29—22no—
185C22⋊C4×C29—22no—
186C22⋊C4×C29—22no—
187C22⋊C4×C29—21no—
188C22⋊C4×C29—21no—
189C22⋊C4×C29—22no—
190C22⋊C4×C29—21no—
191C22⋊C4×C29—22no—
192C42×C29—22no—
193C42×C29—22no—
194C42×C29—21no—
195C42×C29—21no—
196C42×C29—21no—
197C42×C29—21no—
198C42×C29—21no—
199C42×C29—21no—
200C42×C29—21no—
201C42×C29—41no—
202C42×C29—41no—
203C42×C29C22×C411yescharacteristic
204C42×C29C2×D411yescharacteristic
205C42×C29C2×D411yescharacteristic
206C42×C29C2×D411yescharacteristic
207#8437C2911yesmaximal, characteristic, direct product factor, Sylow
208C23×C29—22no—
209C23×C29—21no—
210C23×C29#12011yescharacteristic
211Q8×C29—21no—
212Q8×C29—21no—
213Q8×C29—21no—
214Q8×C29—21no—
215Q8×C29—21no—
216Q8×C29—42no—
217Q8×C29—41no—
218Q8×C29—41no—
219Q8×C29#10412yescomplemented
220D4×C29—21no—
221D4×C29—21no—
222D4×C29—42no—
223D4×C29—44no—
224D4×C29—41no—
225D4×C29—42no—
226D4×C29—41no—
227D4×C29—42no—
228D4×C29—41no—
229D4×C29—41no—
230D4×C29—41no—
231D4×C29—41no—
232D4×C29—82no—
233C2×C4×C29—21no—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—21no—
239C2×C4×C29—21no—
240C2×C4×C29—21no—
241C2×C4×C29—22no—
242C2×C4×C29—21no—
243C2×C4×C29—41no—
244C2×C4×C29—42no—
245C2×C4×C29—44no—
246C2×C4×C29—41no—
247C2×C4×C29—41no—
248C2×C4×C29—41no—
249C2×C4×C29—42no—
250C2×C4×C29—41no—
251C2×C4×C29—42no—
252C2×C4×C29—42no—
253C2×C4×C29—81no—
254C2×C4×C29—81no—
255C2×C4×C29—82no—
256C2×C4×C29—81no—
257C2×C4×C29—81no—
258C2×C4×C29C2×C22⋊C411yescharacteristic
259C2×C4×C29C2×C22⋊C411yescharacteristic
260C2×C4×C29C2×C22⋊C411yescharacteristic
261C2×C4×C29#12011yescharacteristic
262C2×C4×C29#12011yescharacteristic
263C2×C4×C29#12011yescharacteristic
264C2×C4×C29#13511yescharacteristic
265C2×C4×C29#13511yescharacteristic
266C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
267C2×C4×C29#13711yescharacteristic
268C8×C29—42no—
269C8×C29—81no—
270C8×C29—81no—
271#3480C2×C2911yescharacteristic
272#1806C2×C2911yescharacteristic, complemented
273C4×#103C2×C2911yescharacteristic, complemented
274#1502C2×C2911yescharacteristic, complemented
275#1492C2×C2911yescharacteristic, complemented
276#1487C2×C2911yescharacteristic, complemented
277#1476C2×C2911yescharacteristic, complemented
278C22×C29—21no—
279C22×C29—21no—
280C22×C29—42no—
281C22×C29—41no—
282C22×C29—41no—
283C22×C29—42no—
284C22×C29—42no—
285C22×C29—41no—
286C22×C29#37911yescharacteristic
287C22×C29#44911yescharacteristic
288C22×C29#45211yescharacteristic
289C4×C29—21no—
290C4×C29—21no—
291C4×C29—21no—
292C4×C29—22no—
293C4×C29—41no—
294C4×C29—41no—
295C4×C29—41no—
296C4×C29—41no—
297C4×C29—42no—
298C4×C29—41no—
299C4×C29—41no—
300C4×C29—82no—
301C4×C29#41611yescharacteristic
302C4×C29#41711yescharacteristic
303C4×C29C2×#10411yescharacteristic
304C4×C29#42111yescharacteristic
305C4×C29#44911yescharacteristic
306C4×C29#45211yescharacteristic
307#559—21no—
308#559C4×C2911yescharacteristic, complemented
309#557C4×C2911yescharacteristic, complemented
310#556—21no—
311#556C4×C2911yescharacteristic, complemented
312#553—22no—
313#553—21no—
314#550C4×C2911yescharacteristic, complemented
315#548—21no—
316#532—21no—
317#532C22×C2911yescharacteristic
318#529—21no—
319#529—22no—
320C4×#41—21no—
321C4×#41—21no—
322C4×#41C22×C2911yescharacteristic
323C2×C4×Q8C22×C2911yescharacteristic
324#431C22×C2911yescharacteristic
325#423C22×C2911yescharacteristic
326C2×#104—21no—
327C2×#103—21no—
328C2×C4×C8C22×C2911yescharacteristic
329C4×C4⋊C4C22×C2911yescharacteristic
330#340—21no—
331#339—21no—
332#327—22no—
333Q8⋊C8—21no—
334Q8⋊C8—21no—
335Q8⋊C8—21no—
336D4⋊C8—21no—
337D4⋊C8—22no—
338C2×C29—21no—
339C2×C29—21no—
340C2×C29—82no—
341C2×C29—81no—
342C2×C29#178811yescharacteristic
343C2×C29#178911yescharacteristic
344C2×C29#179411yescharacteristic
345C2×#41—21no—
346C2×#41—21no—
347C2×#41D4×C2911yescharacteristic
348C22×Q8D4×C2911yescharacteristic
349C2×M16—21no—
350C22×C8—21no—
351C4⋊Q8—21no—
352C4⋊Q8C2×C4×C2911yescharacteristic
353#127—21no—
354#127C2×C4×C2911yescharacteristic
355#126—22no—
356#126—22no—
357#126—22no—
358#125—22no—
359#125—21no—
360#124—22no—
361#124—21no—
362#124—21no—
363#124—21no—
364#124—21no—
365#123—22no—
366#123—22no—
367#123—22no—
368C22⋊Q8—22no—
369C22⋊Q8—21no—
370#121—22no—
371#121—22no—
372#121—22no—
373#121—21no—
374#121—21no—
375#121D4×C2912yes—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8C2×C4×C2911yescharacteristic
382C4×Q8C2×C4×C2911yescharacteristic
383C4×Q8C2×C4×C2911yescharacteristic
384C4×Q8D4×C2911yescharacteristic
385C4×Q8D4×C2911yescharacteristic
386C4×Q8D4×C2911yescharacteristic
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4C2×C4×C2911yescharacteristic
399C4×D4D4×C2911yescharacteristic
400C4×D4D4×C2912yes—
401#117—22no—
402#117—22no—
403#117—21no—
404#117—21no—
405#117D4×C2911yescharacteristic
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4D4×C2911yescharacteristic
409C2×C42—22no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42C23×C2911yescharacteristic
414C4⋊C8—21no—
415C4⋊C8—21no—
416C4⋊C8—21no—
417#104—42no—
418#103—24no—
419C22⋊C8—21no—
420C4×C8—21no—
421C4×C8—21no—
422C4×C8—21no—
423#95—21no—
424C29#843711yescharacteristic, direct product factor, Sylow
425#41—21no—
426#41—21no—
427#41—21no—
428#41—21no—
429#41—42no—
430#41—42no—
431#41—41no—
432#41—41no—
433#41—41no—
434#41—41no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—22no—
438C2×Q8—41no—
439C2×Q8C22⋊C4×C2911yescharacteristic
440C2×Q8C22⋊C4×C2911yescharacteristic
441C2×Q8C22⋊C4×C2911yescharacteristic
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4C22⋊C4×C2911yescharacteristic
449C2×D4C22⋊C4×C2912yes—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—41no—
459C22×C4C2×D4×C2911yescharacteristic
460C22×C4C2×D4×C2911yescharacteristic
461C22×C4C2×D4×C2911yescharacteristic
462M16—41no—
463M16—41no—
464C2×C8—22no—
465C2×C8—41no—
466C2×C8—41no—
467C2×C8—41no—
468C2×C8—41no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—22no—
482C4⋊C4—41no—
483C4⋊C4C22⋊C4×C2911yescharacteristic
484C4⋊C4C22⋊C4×C2911yescharacteristic
485C4⋊C4C22⋊C4×C2911yescharacteristic
486C4⋊C4C22⋊C4×C2911yescharacteristic
487C4⋊C4C22⋊C4×C2912yes—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—22no—
497C22⋊C4—21no—
498C22⋊C4—22no—
499C42—22no—
500C42—22no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—41no—
509C42—41no—
510C42C22×C4×C2911yescharacteristic
511C42C2×D4×C2911yescharacteristic
512C42C2×D4×C2911yescharacteristic
513C42C2×D4×C2911yescharacteristic
514C23—21no—
515C23—22no—
516C23C29×#12011yescharacteristic
517Q8—21no—
518Q8—21no—
519Q8—21no—
520Q8—21no—
521Q8—21no—
522Q8—42no—
523Q8—41no—
524Q8—41no—
525Q8C29×#10412yescomplemented
526D4—21no—
527D4—21no—
528D4—42no—
529D4—44no—
530D4—41no—
531D4—42no—
532D4—41no—
533D4—42no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—82no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—44no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4—82no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4C2×C22⋊C4×C2911yescharacteristic
565C2×C4C2×C22⋊C4×C2911yescharacteristic
566C2×C4C2×C22⋊C4×C2911yescharacteristic
567C2×C4C29×#12011yescharacteristic
568C2×C4C29×#12011yescharacteristic
569C2×C4C29×#12011yescharacteristic
570C2×C4C29×#13511yescharacteristic
571C2×C4C29×#13511yescharacteristic
572C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
573C2×C4C29×#13711yescharacteristic
574C8—42no—
575C8—81no—
576C8—81no—
577C22—21no—
578C22—21no—
579C22—41no—
580C22—42no—
581C22—42no—
582C22—41no—
583C22—42no—
584C22—41no—
585C22C29×#37911yescharacteristic
586C22C29×#44911yescharacteristic
587C22C29×#45211yescharacteristic
588C4—21no—
589C4—22no—
590C4—21no—
591C4—21no—
592C4—41no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—82no—
600C4C29×#41611yescharacteristic
601C4C29×#41711yescharacteristic
602C4C2×C29×#10411yescharacteristic
603C4C29×#42111yescharacteristic
604C4C29×#44911yescharacteristic
605C4C29×#45211yescharacteristic
606C2—21no—
607C2—21no—
608C2—81no—
609C2—82no—
610C2C29×#178811yescharacteristic
611C2C29×#178911yescharacteristic
612C2C29×#179411yescharacteristic
subgroupG/H
centerC2×C4×C29#120
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#379
prime radicalC29×#3480C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#1806C2semidirect
3. C4×C29×#103C2semidirect
4. C29×#1502C2semidirect
5. C29×#1492C2semidirect
6. C29×#1487C2semidirect
7. C29×#1476C2semidirect
9. C29×#559C4semidirect
10. C29×#557C4semidirect
12. C29×#556C4semidirect
15. C29×#550C4semidirect
207. #8437C29direct (N × H)
219. Q8×C29#104semidirect
272. #1806C2×C29semidirect
273. C4×#103C2×C29semidirect
274. #1502C2×C29semidirect
275. #1492C2×C29semidirect
276. #1487C2×C29semidirect
277. #1476C2×C29semidirect
308. #559C4×C29semidirect
309. #557C4×C29semidirect
311. #556C4×C29semidirect
314. #550C4×C29semidirect
424. C29#8437direct (N × H)
525. Q8C29×#104semidirect

Maximal subgroups

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

subgroupindex
C29×#34802
C29×#18062
C4×C29×#1032
C29×#15022
C29×#14922
C29×#14872
C29×#14762
#843729