Finite Group Databasebeta

← C29×#18860 #20313760

Subgroups — C29×#18860 #20313760

Order 7424.

894 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3518C211yesmaximal, characteristic
2C29×#3239C211yesmaximal, characteristic, complemented
3C29×#3230C211yesmaximal, characteristic, complemented
4C29×#3039C211yesmaximal, characteristic, complemented
5C29×#1650C212yesmaximal, complemented
6C29×#1649C212yesmaximal, complemented
7C29×#1646C212yesmaximal, complemented
8C29×#1645C212yesmaximal, complemented
9C29×#1559C211yesmaximal, characteristic, complemented
10C29×#1495C211yesmaximal, characteristic, complemented
11C29×#1488C211yesmaximal, characteristic, complemented
12C2×C29×#137—21no—
13Q82×C29C2211yescharacteristic
14C29×#556—21no—
15C29×#556—22no—
16C29×#556—21no—
17C29×#556C2211yescharacteristic
18C29×#555—21no—
19C29×#555C2211yescharacteristic
20D4×Q8×C29C2211yescharacteristic
21C29×#548—21no—
22C29×#542—22no—
23C29×#542—21no—
24C29×#533—21no—
25C29×#533C2211yescharacteristic
26C2×C29×C4⋊Q8C2211yescharacteristic
27C29×#529—21no—
28C29×#529C2211yescharacteristic
29C29×#519—21no—
30C4×#41×C29C2211yescharacteristic
31C29×#501—21no—
32C29×#500C2212yes—
33C29×#489—21no—
34C29×#487C2212yes—
35C29×#484—22no—
36C29×#484—21no—
37C29×#481—21no—
38C29×#477—22no—
39C29×#475C2212yes—
40C29×#474C2212yes—
41C29×#462—21no—
42C29×#462C2212yes—
43C29×#461—21no—
44C29×#461C2212yes—
45C29×#432C2211yescharacteristic
46C29×#431C2211yescharacteristic
47C29×#423C2211yescharacteristic
48C29×#419—21no—
49C29×#333C2212yes—
50C29×#332C2212yes—
51C29×Q8⋊C8C2212yes—
52C29×Q8⋊C8C2212yes—
53C29×D4⋊C8C2212yes—
54C29×D4⋊C8C2212yes—
55C2×#41×C29D411yescharacteristic
56C22×Q8×C29—21no—
57C22×Q8×C29—21no—
58C29×#137—44no—
59C2×Q16×C29—22no—
60C2×SD16×C29—22no—
61C2×M16×C29—21no—
62C29×C4⋊Q8—22no—
63C29×C4⋊Q8—21no—
64C29×C4⋊Q8—21no—
65C29×C4⋊Q8—21no—
66C29×C4⋊Q8—21no—
67C29×C4⋊Q8—21no—
68C29×C4⋊Q8—21no—
69C29×C4⋊Q8C2312yes—
70C29×C4⋊Q8C2311yescharacteristic
71C29×C4⋊Q8C2311yescharacteristic
72C29×#126—22no—
73C29×#126—22no—
74C29×#126—22no—
75C29×#126—22no—
76C29×#126—21no—
77C29×#125—21no—
78C29×#125D411yescharacteristic
79C29×#124—22no—
80C29×#124—22no—
81C29×#124—22no—
82C29×#124—22no—
83C29×#124—21no—
84C29×#124D411yescharacteristic
85C29×#123—22no—
86C29×#123—21no—
87C29×C22⋊Q8—22no—
88C29×C22⋊Q8—22no—
89C29×C22⋊Q8—21no—
90C29×C22⋊Q8—21no—
91C29×C22⋊Q8—21no—
92C29×C22⋊Q8—22no—
93C29×C22⋊Q8D411yescharacteristic
94C29×C22⋊Q8D412yes—
95C29×#121—22no—
96C29×#121—21no—
97C29×#121—21no—
98C29×#121D411yescharacteristic
99C4×Q8×C29—22no—
100C4×Q8×C29—22no—
101C4×Q8×C29—22no—
102C4×Q8×C29—21no—
103C4×Q8×C29—21no—
104C4×Q8×C29—21no—
105C4×Q8×C29—21no—
106C4×Q8×C29D411yescharacteristic
107C4×Q8×C29D412yes—
108C4×Q8×C29C2311yescharacteristic
109C4×Q8×C29C2311yescharacteristic
110C4×D4×C29—22no—
111C4×D4×C29—21no—
112C4×D4×C29—21no—
113C4×D4×C29—21no—
114C4×D4×C29—21no—
115C4×D4×C29D411yescharacteristic
116C4×D4×C29C2311yescharacteristic
117C4×D4×C29C2311yescharacteristic
118C29×#117—22no—
119C29×#117—22no—
120C29×#117—21no—
121C29×#117—21no—
122C29×#117—21no—
123C29×#117—21no—
124C29×#117—21no—
125C29×#117—21no—
126C29×#117D411yescharacteristic
127C2×C4⋊C4×C29—21no—
128C2×C4⋊C4×C29—21no—
129C2×C42×C29—21no—
130C2×C42×C29C2311yescharacteristic
131C29×#107—22no—
132C29×#107—24no—
133C29×#106—22no—
134C29×C4⋊C8—21no—
135C29×C4⋊C8—21no—
136C29×C4⋊C8C2312yes—
137C29×C4⋊C8C2312yes—
138C29×#103—22no—
139C29×#103—24no—
140C29×#103—22no—
141C29×#103—22no—
142C29×#102—22no—
143C29×C22⋊C8—21no—
144C29×C22⋊C8—21no—
145C29×#97—21no—
146C4×C8×C29C2312yes—
147#41×C29—22no—
148#41×C29—41no—
149C2×Q8×C29—22no—
150C2×Q8×C29—22no—
151C2×Q8×C29—21no—
152C2×Q8×C29—22no—
153C2×Q8×C29—42no—
154C2×Q8×C29—42no—
155C2×Q8×C29—42no—
156C2×Q8×C29—42no—
157C2×Q8×C29—41no—
158C2×Q8×C29C2×D411yescharacteristic
159C2×Q8×C29C2×D411yescharacteristic
160C2×Q8×C29C2×D412yes—
161C2×D4×C29—21no—
162C2×D4×C29—22no—
163C2×D4×C29—21no—
164C2×D4×C29C2×D411yescharacteristic
165C2×D4×C29C2×D411yescharacteristic
166C22×C4×C29—22no—
167C22×C4×C29—21no—
168C22×C4×C29—21no—
169C22×C4×C29—21no—
170C22×C4×C29—21no—
171C22×C4×C29—41no—
172C22×C4×C29C2×D411yescharacteristic
173C22×C4×C29C2×D411yescharacteristic
174C22×C4×C29C2×D411yescharacteristic
175Q16×C29—44no—
176SD16×C29—44no—
177M16×C29—42no—
178C2×C8×C29—22no—
179C2×C8×C29—22no—
180C2×C8×C29—22no—
181C4⋊C4×C29—22no—
182C4⋊C4×C29—22no—
183C4⋊C4×C29—22no—
184C4⋊C4×C29—22no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—22no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—22no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—21no—
194C4⋊C4×C29—21no—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—22no—
197C4⋊C4×C29—22no—
198C4⋊C4×C29—41no—
199C4⋊C4×C29—41no—
200C4⋊C4×C29C2×D411yescharacteristic
201C4⋊C4×C29C2×D411yescharacteristic
202C4⋊C4×C29C2×D411yescharacteristic
203C4⋊C4×C29C2×D411yescharacteristic
204C4⋊C4×C29C2×D412yes—
205C22⋊C4×C29—22no—
206C22⋊C4×C29—22no—
207C22⋊C4×C29—22no—
208C22⋊C4×C29—22no—
209C22⋊C4×C29—22no—
210C22⋊C4×C29—22no—
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—
218C22⋊C4×C29—21no—
219C42×C29—22no—
220C42×C29—22no—
221C42×C29—22no—
222C42×C29—21no—
223C42×C29—21no—
224C42×C29—22no—
225C42×C29—21no—
226C42×C29—21no—
227C42×C29C2×D411yescharacteristic
228C42×C29C2×D411yescharacteristic
229C42×C29C2×D411yescharacteristic
230C42×C29C2411yescharacteristic
231#18860C2911yesmaximal, characteristic, direct product factor, Sylow
232C23×C29—21no—
233C23×C29—21no—
234C23×C29#12011yescharacteristic
235Q8×C29—21no—
236Q8×C29—22no—
237Q8×C29—42no—
238Q8×C29—44no—
239Q8×C29—41no—
240Q8×C29—41no—
241Q8×C29—42no—
242Q8×C29—42no—
243Q8×C29—82no—
244Q8×C29—82no—
245Q8×C29AGL(1,ℤ/8)12yes—
246D4×C29—21no—
247D4×C29—21no—
248D4×C29—22no—
249D4×C29—42no—
250D4×C29—81no—
251D4×C29—82no—
252C2×C4×C29—21no—
253C2×C4×C29—21no—
254C2×C4×C29—21no—
255C2×C4×C29—22no—
256C2×C4×C29—21no—
257C2×C4×C29—21no—
258C2×C4×C29—22no—
259C2×C4×C29—21no—
260C2×C4×C29—21no—
261C2×C4×C29—22no—
262C2×C4×C29—21no—
263C2×C4×C29—41no—
264C2×C4×C29—42no—
265C2×C4×C29—44no—
266C2×C4×C29—41no—
267C2×C4×C29—41no—
268C2×C4×C29—42no—
269C2×C4×C29—42no—
270C2×C4×C29—81no—
271C2×C4×C29—82no—
272C2×C4×C29#12011yescharacteristic
273C2×C4×C29#12011yescharacteristic
274C2×C4×C29#12011yescharacteristic
275C2×C4×C29C22×D411yescharacteristic
276C2×C4×C29C22×D411yescharacteristic
277C2×C4×C29C22×D411yescharacteristic
278C8×C29—42no—
279C8×C29—42no—
280C8×C29—42no—
281#3518C2×C2911yescharacteristic
282#3239C2×C2911yescharacteristic, complemented
283#3230C2×C2911yescharacteristic, complemented
284#3039C2×C2911yescharacteristic, complemented
285#1650C2×C2912yescomplemented
286#1649C2×C2912yescomplemented
287#1646C2×C2912yescomplemented
288#1645C2×C2912yescomplemented
289#1559C2×C2911yescharacteristic, complemented
290#1495C2×C2911yescharacteristic, complemented
291#1488C2×C2911yescharacteristic, complemented
292C22×C29—21no—
293C22×C29—21no—
294C22×C29—21no—
295C22×C29—41no—
296C22×C29—41no—
297C22×C29—41no—
298C22×C29—41no—
299C22×C29—41no—
300C22×C29—41no—
301C22×C29C2×#12011yescharacteristic
302C4×C29—21no—
303C4×C29—22no—
304C4×C29—21no—
305C4×C29—21no—
306C4×C29—21no—
307C4×C29—42no—
308C4×C29—41no—
309C4×C29—41no—
310C4×C29—41no—
311C4×C29—41no—
312C4×C29—42no—
313C4×C29—41no—
314C4×C29—82no—
315C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
316C4×C29#57511yescharacteristic
317C4×C29#57812yes—
318C2×#137—21no—
319Q82C22×C2911yescharacteristic
320#556—21no—
321#556—22no—
322#556—21no—
323#556C22×C2911yescharacteristic
324#555—21no—
325#555C22×C2911yescharacteristic
326D4×Q8C22×C2911yescharacteristic
327#548—21no—
328#542—22no—
329#542—21no—
330#533—21no—
331#533C22×C2911yescharacteristic
332C2×C4⋊Q8C22×C2911yescharacteristic
333#529—21no—
334#529C22×C2911yescharacteristic
335#519—21no—
336C4×#41C22×C2911yescharacteristic
337#501—21no—
338#500C22×C2912yes—
339#489—21no—
340#487C22×C2912yes—
341#484—22no—
342#484—21no—
343#481—21no—
344#477—22no—
345#475C22×C2912yes—
346#474C22×C2912yes—
347#462—21no—
348#462C22×C2912yes—
349#461—21no—
350#461C22×C2912yes—
351#432C22×C2911yescharacteristic
352#431C22×C2911yescharacteristic
353#423C22×C2911yescharacteristic
354#419—21no—
355#333C22×C2912yes—
356#332C22×C2912yes—
357Q8⋊C8C22×C2912yes—
358Q8⋊C8C22×C2912yes—
359D4⋊C8C22×C2912yes—
360D4⋊C8C22×C2912yes—
361C2×C29—41no—
362C2×C29—81no—
363C2×C29—81no—
364C2×C29#300611yescharacteristic
365C2×C29#301111yescharacteristic
366C2×C29#302211yescharacteristic
367C2×#41D4×C2911yescharacteristic
368C22×Q8—21no—
369C22×Q8—21no—
370#137—44no—
371C2×Q16—22no—
372C2×SD16—22no—
373C2×M16—21no—
374C4⋊Q8—22no—
375C4⋊Q8—21no—
376C4⋊Q8—21no—
377C4⋊Q8—21no—
378C4⋊Q8—21no—
379C4⋊Q8—21no—
380C4⋊Q8—21no—
381C4⋊Q8C23×C2912yes—
382C4⋊Q8C23×C2911yescharacteristic
383C4⋊Q8C23×C2911yescharacteristic
384#126—22no—
385#126—22no—
386#126—22no—
387#126—22no—
388#126—21no—
389#125—21no—
390#125D4×C2911yescharacteristic
391#124—22no—
392#124—22no—
393#124—22no—
394#124—22no—
395#124—21no—
396#124D4×C2911yescharacteristic
397#123—22no—
398#123—21no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8—22no—
405C22⋊Q8D4×C2911yescharacteristic
406C22⋊Q8D4×C2912yes—
407#121—22no—
408#121—21no—
409#121—21no—
410#121D4×C2911yescharacteristic
411C4×Q8—22no—
412C4×Q8—22no—
413C4×Q8—22no—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8D4×C2911yescharacteristic
419C4×Q8D4×C2912yes—
420C4×Q8C23×C2911yescharacteristic
421C4×Q8C23×C2911yescharacteristic
422C4×D4—22no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4D4×C2911yescharacteristic
428C4×D4C23×C2911yescharacteristic
429C4×D4C23×C2911yescharacteristic
430#117—22no—
431#117—22no—
432#117—21no—
433#117—21no—
434#117—21no—
435#117—21no—
436#117—21no—
437#117—21no—
438#117D4×C2911yescharacteristic
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C42—21no—
442C2×C42C23×C2911yescharacteristic
443#107—22no—
444#107—24no—
445#106—22no—
446C4⋊C8—21no—
447C4⋊C8—21no—
448C4⋊C8C23×C2912yes—
449C4⋊C8C23×C2912yes—
450#103—22no—
451#103—24no—
452#103—22no—
453#103—22no—
454#102—22no—
455C22⋊C8—21no—
456C22⋊C8—21no—
457#97—21no—
458C4×C8C23×C2912yes—
459C29#1886011yescharacteristic, direct product factor, Sylow
460#41—22no—
461#41—41no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—21no—
465C2×Q8—22no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—41no—
471C2×Q8C2×D4×C2911yescharacteristic
472C2×Q8C2×D4×C2911yescharacteristic
473C2×Q8C2×D4×C2912yes—
474C2×D4—21no—
475C2×D4—22no—
476C2×D4—21no—
477C2×D4C2×D4×C2911yescharacteristic
478C2×D4C2×D4×C2911yescharacteristic
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485C22×C4C2×D4×C2911yescharacteristic
486C22×C4C2×D4×C2911yescharacteristic
487C22×C4C2×D4×C2911yescharacteristic
488Q16—44no—
489SD16—44no—
490M16—42no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4C2×D4×C2911yescharacteristic
514C4⋊C4C2×D4×C2911yescharacteristic
515C4⋊C4C2×D4×C2911yescharacteristic
516C4⋊C4C2×D4×C2911yescharacteristic
517C4⋊C4C2×D4×C2912yes—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C42—22no—
533C42—22no—
534C42—22no—
535C42—21no—
536C42—21no—
537C42—22no—
538C42—21no—
539C42—21no—
540C42C2×D4×C2911yescharacteristic
541C42C2×D4×C2911yescharacteristic
542C42C2×D4×C2911yescharacteristic
543C42C24×C2911yescharacteristic
544C23—21no—
545C23—21no—
546C23C29×#12011yescharacteristic
547Q8—21no—
548Q8—22no—
549Q8—42no—
550Q8—44no—
551Q8—41no—
552Q8—41no—
553Q8—42no—
554Q8—42no—
555Q8—82no—
556Q8—82no—
557Q8C29×AGL(1,ℤ/8)12yes—
558D4—21no—
559D4—21no—
560D4—22no—
561D4—42no—
562D4—81no—
563D4—82no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—44no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—81no—
583C2×C4—82no—
584C2×C4C29×#12011yescharacteristic
585C2×C4C29×#12011yescharacteristic
586C2×C4C29×#12011yescharacteristic
587C2×C4C22×D4×C2911yescharacteristic
588C2×C4C22×D4×C2911yescharacteristic
589C2×C4C22×D4×C2911yescharacteristic
590C8—42no—
591C8—42no—
592C8—42no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22C2×C29×#12011yescharacteristic
603C4—21no—
604C4—22no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—42no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—42no—
614C4—41no—
615C4—82no—
616C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
617C4C29×#57511yescharacteristic
618C4C29×#57812yes—
619C2—41no—
620C2—81no—
621C2—81no—
622C2C29×#300611yescharacteristic
623C2C29×#301111yescharacteristic
624C2C29×#302211yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3518C2
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×#3239C2semidirect
3. C29×#3230C2semidirect
4. C29×#3039C2semidirect
5. C29×#1650C2semidirect
6. C29×#1649C2semidirect
7. C29×#1646C2semidirect
8. C29×#1645C2semidirect
9. C29×#1559C2semidirect
10. C29×#1495C2semidirect
11. C29×#1488C2semidirect
231. #18860C29direct (N × H)
282. #3239C2×C29semidirect
283. #3230C2×C29semidirect
284. #3039C2×C29semidirect
285. #1650C2×C29semidirect
286. #1649C2×C29semidirect
287. #1646C2×C29semidirect
288. #1645C2×C29semidirect
289. #1559C2×C29semidirect
290. #1495C2×C29semidirect
291. #1488C2×C29semidirect
459. C29#18860direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35182
C29×#32392
C29×#32302
C29×#30392
C29×#16502
C29×#16492
C29×#16462
C29×#16452
C29×#15592
C29×#14952
C29×#14882
#1886029