Finite Group Databasebeta

← C29×#18208 #20313108

Subgroups — C29×#18208 #20313108

Order 7424.

994 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3491C211yesmaximal, characteristic, complemented
2C29×#3105C212yesmaximal, complemented
3C29×#2598C211yesmaximal, characteristic, complemented
4C29×#1615C212yesmaximal, complemented
5C29×#1614C211yesmaximal, characteristic, complemented
6C29×#1613C211yesmaximal, characteristic, complemented
7C29×#1597C212yesmaximal, complemented
8C29×#1596C211yesmaximal, characteristic, complemented
9C29×#1595C211yesmaximal, characteristic
10C29×#1521C212yesmaximal, complemented
11C29×#1458C211yesmaximal, characteristic, complemented
12C29×#552—22no—
13C29×#552—22no—
14C29×#551—22no—
15C29×#551—22no—
16C29×#543C2211yescharacteristic
17C29×#539—21no—
18C29×#539C2212yes—
19C29×#534C2211yescharacteristic
20C29×#529—21no—
21C29×#529C2212yes—
22C2×C29×#123—21no—
23C29×#518—21no—
24C2×C4×D4×C29C2211yescharacteristic, complemented
25C2×C29×#117C2211yescharacteristic
26C29×#484C2212yescomplemented
27C29×#481C2212yes—
28C29×#478—22no—
29C29×#463—22no—
30C29×#450C2212yescomplemented
31C29×#447C2212yes—
32C4×SD16×C29—22no—
33C4×D8×C29—22no—
34C29×#431C2212yescomplemented
35C29×#400C2211yescharacteristic, complemented
36C29×#399C2211yescharacteristic
37C29×#394C2211yescharacteristic, complemented
38C29×#392C2211yescharacteristic
39C29×#388—21no—
40C29×#386—21no—
41C29×#386—21no—
42C29×#385—21no—
43C29×#383C2211yescharacteristic, complemented
44C29×#328C2212yescomplemented
45C29×#328C2212yescomplemented
46C29×#327C2212yes—
47C29×#327C2212yes—
48C29×#324C2212yescomplemented
49C29×#323C2211yescharacteristic
50C29×#323C2211yescharacteristic
51C22×D4×C29—21no—
52C22×D4×C29—21no—
53C22×D4×C29C2311yescharacteristic
54C23×C4×C29—21no—
55C23×C4×C29D411yescharacteristic
56C2×SD16×C29—22no—
57C2×D8×C29—22no—
58C29×#126—22no—
59C29×#126—22no—
60C29×#126—22no—
61C29×#126—22no—
62C29×#125—21no—
63C29×#125—22no—
64C29×#125—22no—
65C29×#125D412yescomplemented
66C29×#124—21no—
67C29×#124D412yescomplemented
68C29×#123—22no—
69C29×#123—22no—
70C29×#123—22no—
71C29×#123—22no—
72C29×#123—22no—
73C29×#123—22no—
74C29×#123—22no—
75C29×C22⋊Q8—22no—
76C29×C22⋊Q8—22no—
77C29×C22⋊Q8—22no—
78C29×C22⋊Q8—21no—
79C29×C22⋊Q8—22no—
80C29×C22⋊Q8C2312yes—
81C29×#121—21no—
82C29×#121C2312yes—
83C29×#120—22no—
84C4×Q8×C29—21no—
85C4×Q8×C29D412yescomplemented
86C4×D4×C29—22no—
87C4×D4×C29—22no—
88C4×D4×C29—21no—
89C4×D4×C29—22no—
90C4×D4×C29—22no—
91C4×D4×C29—22no—
92C4×D4×C29—22no—
93C4×D4×C29D412yescomplemented
94C29×#117—22no—
95C29×#117—22no—
96C29×#117—22no—
97C29×#117—22no—
98C29×#117—22no—
99C2×C4⋊C4×C29—21no—
100C2×C4⋊C4×C29—21no—
101C2×C4⋊C4×C29—21no—
102C2×C4⋊C4×C29D411yescharacteristic
103C2×C4⋊C4×C29C2311yescharacteristic
104C2×C4⋊C4×C29C2311yescharacteristic
105C2×C22⋊C4×C29—22no—
106C2×C22⋊C4×C29—21no—
107C2×C22⋊C4×C29—21no—
108C2×C22⋊C4×C29—21no—
109C2×C22⋊C4×C29—21no—
110C2×C22⋊C4×C29—21no—
111C2×C22⋊C4×C29—21no—
112C2×C22⋊C4×C29—21no—
113C2×C22⋊C4×C29—21no—
114C2×C22⋊C4×C29D411yescharacteristic
115C2×C22⋊C4×C29C2311yescharacteristic
116C2×C42×C29D411yescharacteristic
117C2×C42×C29C2311yescharacteristic
118C29×#107—22no—
119C29×#106—22no—
120C29×C4⋊C8—22no—
121C29×#103—22no—
122C29×#102—22no—
123C29×#102—22no—
124C29×#102—22no—
125C29×C22⋊C8C2312yes—
126C29×C22⋊C8C2312yes—
127C4×C8×C29—22no—
128C29×#95—21no—
129C29×#95—21no—
130C29×#95—21no—
131C29×#95—21no—
132C29×#95C2311yescharacteristic
133C29×#95C2311yescharacteristic
134C24×C29—21no—
135C24×C29—21no—
136C24×C29C2×D411yescharacteristic
137C2×Q8×C29—21no—
138C2×Q8×C29C2×D412yes—
139C2×D4×C29—22no—
140C2×D4×C29—22no—
141C2×D4×C29—21no—
142C2×D4×C29—22no—
143C2×D4×C29—42no—
144C2×D4×C29—42no—
145C2×D4×C29—42no—
146C2×D4×C29—42no—
147C2×D4×C29—42no—
148C2×D4×C29—81no—
149C2×D4×C29C2×D412yes—
150C22×C4×C29—21no—
151C22×C4×C29—22no—
152C22×C4×C29—21no—
153C22×C4×C29—21no—
154C22×C4×C29—22no—
155C22×C4×C29—21no—
156C22×C4×C29—21no—
157C22×C4×C29—22no—
158C22×C4×C29—21no—
159C22×C4×C29—21no—
160C22×C4×C29—21no—
161C22×C4×C29—41no—
162C22×C4×C29—42no—
163C22×C4×C29—81no—
164C22×C4×C29—81no—
165C22×C4×C29C2×D411yescharacteristic
166C22×C4×C29C2×D411yescharacteristic
167C22×C4×C29C2×D411yescharacteristic
168C22×C4×C29C2×D411yescharacteristic
169C22×C4×C29C2×D411yescharacteristic
170C22×C4×C29C2411yescharacteristic
171SD16×C29—44no—
172D8×C29—44no—
173C2×C8×C29—22no—
174C2×C8×C29—22no—
175C4⋊C4×C29—22no—
176C4⋊C4×C29—22no—
177C4⋊C4×C29—22no—
178C4⋊C4×C29—22no—
179C4⋊C4×C29—21no—
180C4⋊C4×C29—21no—
181C4⋊C4×C29—22no—
182C4⋊C4×C29—22no—
183C4⋊C4×C29—22no—
184C4⋊C4×C29—22no—
185C4⋊C4×C29—22no—
186C4⋊C4×C29—22no—
187C4⋊C4×C29—22no—
188C4⋊C4×C29—81no—
189C4⋊C4×C29C2×D412yes—
190C4⋊C4×C29C2×D412yes—
191C22⋊C4×C29—22no—
192C22⋊C4×C29—22no—
193C22⋊C4×C29—22no—
194C22⋊C4×C29—22no—
195C22⋊C4×C29—22no—
196C22⋊C4×C29—22no—
197C22⋊C4×C29—22no—
198C22⋊C4×C29—22no—
199C22⋊C4×C29—22no—
200C22⋊C4×C29—22no—
201C22⋊C4×C29—22no—
202C22⋊C4×C29—22no—
203C22⋊C4×C29—42no—
204C22⋊C4×C29—42no—
205C22⋊C4×C29—41no—
206C22⋊C4×C29—41no—
207C22⋊C4×C29—81no—
208C22⋊C4×C29—81no—
209C42×C29—22no—
210C42×C29—21no—
211C42×C29—21no—
212C42×C29—22no—
213C42×C29C2×D412yes—
214C42×C29C2×D412yes—
215#18208C2911yesmaximal, characteristic, direct product factor, Sylow
216C23×C29—21no—
217C23×C29—21no—
218C23×C29—22no—
219C23×C29—22no—
220C23×C29—41no—
221C23×C29—41no—
222C23×C29—41no—
223C23×C29—41no—
224C23×C29—41no—
225C23×C29—42no—
226C23×C29—41no—
227C23×C29—41no—
228C23×C29—41no—
229C23×C29—81no—
230C23×C29—81no—
231C23×C29#13512yes—
232C23×C29C22×D411yescharacteristic
233Q8×C29—42no—
234Q8×C29—81no—
235D4×C29—24no—
236D4×C29—42no—
237D4×C29—42no—
238D4×C29—44no—
239D4×C29—42no—
240D4×C29—42no—
241D4×C29—81no—
242D4×C29—84no—
243C2×C4×C29—21no—
244C2×C4×C29—21no—
245C2×C4×C29—21no—
246C2×C4×C29—21no—
247C2×C4×C29—22no—
248C2×C4×C29—22no—
249C2×C4×C29—22no—
250C2×C4×C29—21no—
251C2×C4×C29—21no—
252C2×C4×C29—21no—
253C2×C4×C29—41no—
254C2×C4×C29—41no—
255C2×C4×C29—42no—
256C2×C4×C29—42no—
257C2×C4×C29—42no—
258C2×C4×C29—41no—
259C2×C4×C29—41no—
260C2×C4×C29—41no—
261C2×C4×C29—41no—
262C2×C4×C29—41no—
263C2×C4×C29—41no—
264C2×C4×C29—41no—
265C2×C4×C29—41no—
266C2×C4×C29—41no—
267C2×C4×C29—41no—
268C2×C4×C29—41no—
269C2×C4×C29—82no—
270C2×C4×C29—84no—
271C2×C4×C29—81no—
272C2×C4×C29—82no—
273C2×C4×C29—81no—
274C2×C4×C29#12011yescharacteristic
275C2×C4×C29#12011yescharacteristic
276C2×C4×C29#12012yes—
277C2×C4×C29C22×D412yes—
278C8×C29—42no—
279C8×C29—42no—
280#3491C2×C2911yescharacteristic, complemented
281#3105C2×C2912yescomplemented
282#2598C2×C2911yescharacteristic, complemented
283#1615C2×C2912yescomplemented
284#1614C2×C2911yescharacteristic, complemented
285#1613C2×C2911yescharacteristic, complemented
286#1597C2×C2912yescomplemented
287#1596C2×C2911yescharacteristic, complemented
288#1595C2×C2911yescharacteristic
289#1521C2×C2912yescomplemented
290#1458C2×C2911yescharacteristic, complemented
291C22×C29—21no—
292C22×C29—21no—
293C22×C29—22no—
294C22×C29—42no—
295C22×C29—42no—
296C22×C29—42no—
297C22×C29—41no—
298C22×C29—41no—
299C22×C29—42no—
300C22×C29—42no—
301C22×C29—42no—
302C22×C29—42no—
303C22×C29—81no—
304C22×C29—81no—
305C22×C29—81no—
306C22×C29—81no—
307C22×C29—81no—
308C22×C29—162no—
309C22×C29C2×#12011yescharacteristic
310C22×C29C2×#13511yescharacteristic
311C22×C29#57511yescharacteristic
312C4×C29—21no—
313C4×C29—21no—
314C4×C29—22no—
315C4×C29—22no—
316C4×C29—41no—
317C4×C29—42no—
318C4×C29—41no—
319C4×C29—42no—
320C4×C29—41no—
321C4×C29—42no—
322C4×C29—81no—
323C4×C29—81no—
324C4×C29—81no—
325#552—22no—
326#552—22no—
327#551—22no—
328#551—22no—
329#543C22×C2911yescharacteristic
330#539—21no—
331#539C22×C2912yes—
332#534C22×C2911yescharacteristic
333#529—21no—
334#529C22×C2912yes—
335C2×#123—21no—
336#518—21no—
337C2×C4×D4C22×C2911yescharacteristic, complemented
338C2×#117C22×C2911yescharacteristic
339#484C22×C2912yescomplemented
340#481C22×C2912yes—
341#478—22no—
342#463—22no—
343#450C22×C2912yescomplemented
344#447C22×C2912yes—
345C4×SD16—22no—
346C4×D8—22no—
347#431C22×C2912yescomplemented
348#400C22×C2911yescharacteristic, complemented
349#399C22×C2911yescharacteristic
350#394C22×C2911yescharacteristic, complemented
351#392C22×C2911yescharacteristic
352#388—21no—
353#386—21no—
354#386—21no—
355#385—21no—
356#383C22×C2911yescharacteristic, complemented
357#328C22×C2912yescomplemented
358#328C22×C2912yescomplemented
359#327C22×C2912yes—
360#327C22×C2912yes—
361#324C22×C2912yescomplemented
362#323C22×C2911yescharacteristic
363#323C22×C2911yescharacteristic
364C2×C29—21no—
365C2×C29—21no—
366C2×C29—42no—
367C2×C29—82no—
368C2×C29—82no—
369C2×C29#300211yescharacteristic
370C2×C29#302111yescharacteristic
371C2×C29#302511yescharacteristic
372C22×D4—21no—
373C22×D4—21no—
374C22×D4C23×C2911yescharacteristic
375C23×C4—21no—
376C23×C4D4×C2911yescharacteristic
377C2×SD16—22no—
378C2×D8—22no—
379#126—22no—
380#126—22no—
381#126—22no—
382#126—22no—
383#125—21no—
384#125—22no—
385#125—22no—
386#125D4×C2912yescomplemented
387#124—21no—
388#124D4×C2912yescomplemented
389#123—22no—
390#123—22no—
391#123—22no—
392#123—22no—
393#123—22no—
394#123—22no—
395#123—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—21no—
400C22⋊Q8—22no—
401C22⋊Q8C23×C2912yes—
402#121—21no—
403#121C23×C2912yes—
404#120—22no—
405C4×Q8—21no—
406C4×Q8D4×C2912yescomplemented
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—21no—
410C4×D4—22no—
411C4×D4—22no—
412C4×D4—22no—
413C4×D4—22no—
414C4×D4D4×C2912yescomplemented
415#117—22no—
416#117—22no—
417#117—22no—
418#117—22no—
419#117—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4D4×C2911yescharacteristic
424C2×C4⋊C4C23×C2911yescharacteristic
425C2×C4⋊C4C23×C2911yescharacteristic
426C2×C22⋊C4—22no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4D4×C2911yescharacteristic
436C2×C22⋊C4C23×C2911yescharacteristic
437C2×C42D4×C2911yescharacteristic
438C2×C42C23×C2911yescharacteristic
439#107—22no—
440#106—22no—
441C4⋊C8—22no—
442#103—22no—
443#102—22no—
444#102—22no—
445#102—22no—
446C22⋊C8C23×C2912yes—
447C22⋊C8C23×C2912yes—
448C4×C8—22no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95C23×C2911yescharacteristic
454#95C23×C2911yescharacteristic
455C29#1820811yescharacteristic, direct product factor, Sylow
456C24—21no—
457C24—21no—
458C24C2×D4×C2911yescharacteristic
459C2×Q8—21no—
460C2×Q8C2×D4×C2912yes—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—81no—
471C2×D4C2×D4×C2912yes—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—41no—
484C22×C4—42no—
485C22×C4—81no—
486C22×C4—81no—
487C22×C4C2×D4×C2911yescharacteristic
488C22×C4C2×D4×C2911yescharacteristic
489C22×C4C2×D4×C2911yescharacteristic
490C22×C4C2×D4×C2911yescharacteristic
491C22×C4C2×D4×C2911yescharacteristic
492C22×C4C24×C2911yescharacteristic
493SD16—44no—
494D8—44no—
495C2×C8—22no—
496C2×C8—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—81no—
511C4⋊C4C2×D4×C2912yes—
512C4⋊C4C2×D4×C2912yes—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—42no—
526C22⋊C4—42no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C22⋊C4—81no—
530C22⋊C4—81no—
531C42—22no—
532C42—21no—
533C42—21no—
534C42—22no—
535C42C2×D4×C2912yes—
536C42C2×D4×C2912yes—
537C23—21no—
538C23—21no—
539C23—22no—
540C23—22no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—42no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—81no—
551C23—81no—
552C23C29×#13512yes—
553C23C22×D4×C2911yescharacteristic
554Q8—42no—
555Q8—81no—
556D4—24no—
557D4—42no—
558D4—42no—
559D4—44no—
560D4—42no—
561D4—42no—
562D4—81no—
563D4—84no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—82no—
591C2×C4—84no—
592C2×C4—81no—
593C2×C4—82no—
594C2×C4—81no—
595C2×C4C29×#12011yescharacteristic
596C2×C4C29×#12011yescharacteristic
597C2×C4C29×#12012yes—
598C2×C4C22×D4×C2912yes—
599C8—42no—
600C8—42no—
601C22—21no—
602C22—21no—
603C22—22no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—41no—
608C22—41no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—162no—
619C22C2×C29×#12011yescharacteristic
620C22C2×C29×#13511yescharacteristic
621C22C29×#57511yescharacteristic
622C4—21no—
623C4—21no—
624C4—22no—
625C4—22no—
626C4—41no—
627C4—42no—
628C4—41no—
629C4—42no—
630C4—41no—
631C4—42no—
632C4—81no—
633C4—81no—
634C4—81no—
635C2—21no—
636C2—21no—
637C2—42no—
638C2—82no—
639C2—82no—
640C2C29×#300211yescharacteristic
641C2C29×#302111yescharacteristic
642C2C29×#302511yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#1595C2
LCSG ▷ C22×C4 ▷ 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×#3491C2semidirect
2. C29×#3105C2semidirect
3. C29×#2598C2semidirect
4. C29×#1615C2semidirect
5. C29×#1614C2semidirect
6. C29×#1613C2semidirect
7. C29×#1597C2semidirect
8. C29×#1596C2semidirect
10. C29×#1521C2semidirect
11. C29×#1458C2semidirect
24. C2×C4×D4×C29C22semidirect
26. C29×#484C22semidirect
30. C29×#450C22semidirect
34. C29×#431C22semidirect
35. C29×#400C22semidirect
37. C29×#394C22semidirect
43. C29×#383C22semidirect
44. C29×#328C22semidirect
45. C29×#328C22semidirect
48. C29×#324C22semidirect
65. C29×#125D4semidirect
67. C29×#124D4semidirect
85. C4×Q8×C29D4semidirect
93. C4×D4×C29D4semidirect
215. #18208C29direct (N × H)
280. #3491C2×C29semidirect
281. #3105C2×C29semidirect
282. #2598C2×C29semidirect
283. #1615C2×C29semidirect
284. #1614C2×C29semidirect
285. #1613C2×C29semidirect
286. #1597C2×C29semidirect
287. #1596C2×C29semidirect
289. #1521C2×C29semidirect
290. #1458C2×C29semidirect
337. C2×C4×D4C22×C29semidirect
339. #484C22×C29semidirect
343. #450C22×C29semidirect
347. #431C22×C29semidirect
348. #400C22×C29semidirect
350. #394C22×C29semidirect
356. #383C22×C29semidirect
357. #328C22×C29semidirect
358. #328C22×C29semidirect
361. #324C22×C29semidirect
386. #125D4×C29semidirect
388. #124D4×C29semidirect
406. C4×Q8D4×C29semidirect
414. C4×D4D4×C29semidirect
455. C29#18208direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34912
C29×#31052
C29×#25982
C29×#16152
C29×#16142
C29×#16132
C29×#15972
C29×#15962
C29×#15952
C29×#15212
C29×#14582
#1820829