Finite Group Databasebeta

← C29×#24056 #20318956

Subgroups — C29×#24056 #20318956

Order 7424.

1820 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3484C211yesmaximal, characteristic
2C29×#2849C212yesmaximal, complemented
3C2×C29×#386C211yesmaximal, characteristic, complemented
4C29×#2044C214yesmaximal, complemented
5C29×#1898C212yesmaximal, complemented
6C29×#1867C212yesmaximal, complemented
7C29×#1790C212yesmaximal, complemented
8C29×#1781C211yesmaximal, characteristic, complemented
9C2×C29×H(5,𝔽2)C2211yescharacteristic
10C23×D4×C29C2211yescharacteristic
11C24×C4×C29C2211yescharacteristic, complemented
12C29×#546—22no—
13C29×#546—22no—
14D42×C29—22no—
15D42×C29—22no—
16C29×#535—21no—
17C29×#534—21no—
18C29×#534C2212yes—
19C29×#525—21no—
20C2×C29×#123—22no—
21C2×C29×#120—21no—
22C2×C29×#120C2212yes—
23C29×#518C2211yescharacteristic
24C22×C22⋊C4×C29—21no—
25C22×C22⋊C4×C29C2211yescharacteristic, complemented
26C2×C29×#99C2212yes—
27C2×C29×#99C2212yescomplemented
28C2×C29×#99C2214yescomplemented
29C29×#386—21no—
30C29×#386—21no—
31C29×#386—22no—
32C29×#386C2212yes—
33C29×#386C2212yescomplemented
34C29×#386C2214yescomplemented
35C29×#385—22no—
36C29×#385C2214yescomplemented
37C29×#381—22no—
38C29×#379C2212yescomplemented
39C2×C29×#95—21no—
40C29×#342C2214yescomplemented
41C25×C29D411yescharacteristic
42C25×C29C2311yescharacteristic
43C29×H(5,𝔽2)—24no—
44C29×H(5,𝔽2)—42no—
45C2×#41×C29—21no—
46C2×#41×C29—22no—
47C22×D4×C29—21no—
48C22×D4×C29—22no—
49C22×D4×C29—22no—
50C22×D4×C29—22no—
51C22×D4×C29—21no—
52C22×D4×C29—21no—
53C22×D4×C29—24no—
54C22×D4×C29—42no—
55C22×D4×C29D411yescharacteristic
56C22×D4×C29D411yescharacteristic
57C22×D4×C29D412yes—
58C22×D4×C29D412yes—
59C22×D4×C29C2312yes—
60C22×D4×C29C2311yescharacteristic
61C22×D4×C29C2311yescharacteristic
62C23×C4×C29—21no—
63C23×C4×C29—22no—
64C23×C4×C29—21no—
65C23×C4×C29—22no—
66C23×C4×C29—21no—
67C23×C4×C29—44no—
68C23×C4×C29D411yescharacteristic
69C23×C4×C29C2312yes—
70C29×#127—22no—
71C29×#124—22no—
72C29×#123—22no—
73C29×#123—22no—
74C29×#123—22no—
75C29×#123—48no—
76C29×C22⋊Q8—21no—
77C29×C22⋊Q8—21no—
78C29×#121—21no—
79C29×#121—21no—
80C29×#121—22no—
81C29×#121—22no—
82C29×#121—22no—
83C29×#121—22no—
84C29×#121—22no—
85C29×#121—22no—
86C29×#120—22no—
87C29×#120—22no—
88C29×#120—22no—
89C29×#120—22no—
90C29×#120—22no—
91C29×#120—22no—
92C29×#120—22no—
93C29×#120—22no—
94C29×#120—22no—
95C4×D4×C29—22no—
96C4×D4×C29—22no—
97C4×D4×C29—22no—
98C4×D4×C29—22no—
99C29×#117—21no—
100C2×C4⋊C4×C29—24no—
101C2×C22⋊C4×C29—21no—
102C2×C22⋊C4×C29—21no—
103C2×C22⋊C4×C29—21no—
104C2×C22⋊C4×C29—22no—
105C2×C22⋊C4×C29—22no—
106C2×C22⋊C4×C29—21no—
107C2×C22⋊C4×C29—22no—
108C2×C22⋊C4×C29—24no—
109C2×C22⋊C4×C29—22no—
110C2×C22⋊C4×C29—42no—
111C2×C22⋊C4×C29—44no—
112C2×C22⋊C4×C29D412yes—
113C2×C22⋊C4×C29D412yes—
114C2×C22⋊C4×C29C2312yes—
115C2×C22⋊C4×C29C2314yes—
116C2×C22⋊C4×C29C2312yes—
117C29×#99—24no—
118C29×#99—44no—
119C29×#99—42no—
120C29×#95—22no—
121C29×#95—22no—
122C29×#95—24no—
123C29×#95—24no—
124C24×C29—22no—
125C24×C29—22no—
126C24×C29—21no—
127C24×C29—22no—
128C24×C29—21no—
129C24×C29—21no—
130C24×C29—42no—
131C24×C29—42no—
132C24×C29—41no—
133C24×C29—42no—
134C24×C29—42no—
135C24×C29C2×D411yescharacteristic
136C24×C29C2×D412yes—
137C24×C29C2×D412yes—
138C24×C29C2×D411yescharacteristic
139C24×C29C2×D412yes—
140C24×C29C2×D411yescharacteristic
141C24×C29C2×D411yescharacteristic
142C24×C29C2411yescharacteristic
143#41×C29—48no—
144#41×C29—42no—
145#41×C29—42no—
146C2×Q8×C29—21no—
147C2×D4×C29—22no—
148C2×D4×C29—22no—
149C2×D4×C29—22no—
150C2×D4×C29—21no—
151C2×D4×C29—22no—
152C2×D4×C29—22no—
153C2×D4×C29—22no—
154C2×D4×C29—22no—
155C2×D4×C29—22no—
156C2×D4×C29—22no—
157C2×D4×C29—22no—
158C2×D4×C29—22no—
159C2×D4×C29—22no—
160C2×D4×C29—24no—
161C2×D4×C29—22no—
162C2×D4×C29—24no—
163C2×D4×C29—22no—
164C2×D4×C29—22no—
165C2×D4×C29—22no—
166C2×D4×C29—22no—
167C2×D4×C29—22no—
168C2×D4×C29—41no—
169C2×D4×C29—41no—
170C2×D4×C29—48no—
171C2×D4×C29—48no—
172C2×D4×C29—48no—
173C2×D4×C29—42no—
174C2×D4×C29—42no—
175C2×D4×C29—44no—
176C2×D4×C29—44no—
177C2×D4×C29—82no—
178C2×D4×C29—82no—
179C2×D4×C29#4114yes—
180C22×C4×C29—21no—
181C22×C4×C29—24no—
182C22×C4×C29—22no—
183C22×C4×C29—28no—
184C22×C4×C29—21no—
185C22×C4×C29—21no—
186C22×C4×C29—22no—
187C22×C4×C29—24no—
188C22×C4×C29—21no—
189C22×C4×C29—21no—
190C22×C4×C29—22no—
191C22×C4×C29—24no—
192C22×C4×C29—22no—
193C22×C4×C29—44no—
194C22×C4×C29—41no—
195C22×C4×C29—44no—
196C22×C4×C29—48no—
197C22×C4×C29—42no—
198C22×C4×C29—44no—
199C22×C4×C29—42no—
200C22×C4×C29—41no—
201C22×C4×C29—41no—
202C22×C4×C29—42no—
203C22×C4×C29—42no—
204C22×C4×C29—42no—
205C22×C4×C29C2×D412yes—
206C22×C4×C29C2×D411yescharacteristic
207C22×C4×C29C2×D411yescharacteristic
208C22×C4×C29C2×D412yes—
209C22×C4×C29C2×D412yes—
210C4⋊C4×C29—21no—
211C4⋊C4×C29—21no—
212C4⋊C4×C29—22no—
213C4⋊C4×C29—22no—
214C4⋊C4×C29—48no—
215C22⋊C4×C29—22no—
216C22⋊C4×C29—22no—
217C22⋊C4×C29—22no—
218C22⋊C4×C29—22no—
219C22⋊C4×C29—22no—
220C22⋊C4×C29—22no—
221C22⋊C4×C29—22no—
222C22⋊C4×C29—22no—
223C22⋊C4×C29—22no—
224C22⋊C4×C29—22no—
225C22⋊C4×C29—22no—
226C22⋊C4×C29—24no—
227C22⋊C4×C29—24no—
228C22⋊C4×C29—24no—
229C22⋊C4×C29—44no—
230C22⋊C4×C29—44no—
231C22⋊C4×C29—48no—
232C22⋊C4×C29—44no—
233C22⋊C4×C29—42no—
234C22⋊C4×C29—44no—
235C42×C29—22no—
236#24056C2911yesmaximal, characteristic, direct product factor, Sylow
237C23×C29—21no—
238C23×C29—21no—
239C23×C29—22no—
240C23×C29—22no—
241C23×C29—21no—
242C23×C29—21no—
243C23×C29—21no—
244C23×C29—24no—
245C23×C29—24no—
246C23×C29—24no—
247C23×C29—24no—
248C23×C29—21no—
249C23×C29—21no—
250C23×C29—22no—
251C23×C29—21no—
252C23×C29—21no—
253C23×C29—24no—
254C23×C29—42no—
255C23×C29—41no—
256C23×C29—41no—
257C23×C29—42no—
258C23×C29—41no—
259C23×C29—41no—
260C23×C29—42no—
261C23×C29—42no—
262C23×C29—48no—
263C23×C29—48no—
264C23×C29—41no—
265C23×C29—41no—
266C23×C29—41no—
267C23×C29—41no—
268C23×C29—48no—
269C23×C29—42no—
270C23×C29—42no—
271C23×C29—42no—
272C23×C29—42no—
273C23×C29—42no—
274C23×C29—81no—
275C23×C29—81no—
276C23×C29—84no—
277C23×C29—81no—
278C23×C29—81no—
279C23×C29#12012yes—
280C23×C29#12011yescharacteristic
281C23×C29#12011yescharacteristic
282C23×C29#12312yescomplemented
283C23×C29C22×D411yescharacteristic
284C23×C29C22×D412yes—
285C23×C29C2×#4112yes—
286C23×C29H(5,𝔽2)12yes—
287Q8×C29—42no—
288D4×C29—28no—
289D4×C29—44no—
290D4×C29—42no—
291D4×C29—44no—
292D4×C29—44no—
293D4×C29—42no—
294D4×C29—42no—
295D4×C29—44no—
296D4×C29—44no—
297D4×C29—44no—
298D4×C29—44no—
299D4×C29—82no—
300D4×C29—82no—
301D4×C29—82no—
302D4×C29—82no—
303C2×C4×C29—21no—
304C2×C4×C29—21no—
305C2×C4×C29—24no—
306C2×C4×C29—28no—
307C2×C4×C29—22no—
308C2×C4×C29—22no—
309C2×C4×C29—22no—
310C2×C4×C29—21no—
311C2×C4×C29—21no—
312C2×C4×C29—21no—
313C2×C4×C29—24no—
314C2×C4×C29—42no—
315C2×C4×C29—42no—
316C2×C4×C29—44no—
317C2×C4×C29—44no—
318C2×C4×C29—42no—
319C2×C4×C29—44no—
320C2×C4×C29—48no—
321C2×C4×C29—42no—
322C2×C4×C29—42no—
323C2×C4×C29—44no—
324C2×C4×C29—42no—
325C2×C4×C29—42no—
326C2×C4×C29—44no—
327C2×C4×C29—42no—
328C2×C4×C29—44no—
329C2×C4×C29—42no—
330C2×C4×C29—42no—
331C2×C4×C29—44no—
332C2×C4×C29—81no—
333C2×C4×C29—81no—
334C2×C4×C29—84no—
335C2×C4×C29#12312yescomplemented
336#3484C2×C2911yescharacteristic
337#2849C2×C2912yescomplemented
338C2×#386C2×C2911yescharacteristic, complemented
339#2044C2×C2914yescomplemented
340#1898C2×C2912yescomplemented
341#1867C2×C2912yescomplemented
342#1790C2×C2912yescomplemented
343#1781C2×C2911yescharacteristic, complemented
344C22×C29—24no—
345C22×C29—24no—
346C22×C29—21no—
347C22×C29—21no—
348C22×C29—22no—
349C22×C29—21no—
350C22×C29—21no—
351C22×C29—22no—
352C22×C29—21no—
353C22×C29—21no—
354C22×C29—22no—
355C22×C29—22no—
356C22×C29—22no—
357C22×C29—22no—
358C22×C29—42no—
359C22×C29—42no—
360C22×C29—48no—
361C22×C29—48no—
362C22×C29—42no—
363C22×C29—42no—
364C22×C29—42no—
365C22×C29—42no—
366C22×C29—41no—
367C22×C29—41no—
368C22×C29—42no—
369C22×C29—41no—
370C22×C29—42no—
371C22×C29—41no—
372C22×C29—42no—
373C22×C29—41no—
374C22×C29—81no—
375C22×C29—84no—
376C22×C29—84no—
377C22×C29—84no—
378C22×C29—81no—
379C22×C29—162no—
380C22×C29B(4,𝔽2)12yes—
381C22×C29#45812yes—
382C22×C29C2×#12011yescharacteristic
383C22×C29C2×#12311yescharacteristic
384C22×C29#53411yescharacteristic
385C22×C29#54614yes—
386C4×C29—22no—
387C4×C29—41no—
388C4×C29—42no—
389C4×C29—44no—
390C4×C29—42no—
391C4×C29—42no—
392C4×C29—84no—
393C4×C29—82no—
394C2×H(5,𝔽2)C22×C2911yescharacteristic
395C23×D4C22×C2911yescharacteristic
396C24×C4C22×C2911yescharacteristic, complemented
397#546—22no—
398#546—22no—
399D42—22no—
400D42—22no—
401#535—21no—
402#534—21no—
403#534C22×C2912yes—
404#525—21no—
405C2×#123—22no—
406C2×#120—21no—
407C2×#120C22×C2912yes—
408#518C22×C2911yescharacteristic
409C22×C22⋊C4—21no—
410C22×C22⋊C4C22×C2911yescharacteristic, complemented
411C2×#99C22×C2912yes—
412C2×#99C22×C2914yescomplemented
413C2×#99C22×C2912yescomplemented
414#386—22no—
415#386—21no—
416#386—21no—
417#386C22×C2912yes—
418#386C22×C2914yescomplemented
419#386C22×C2912yescomplemented
420#385—22no—
421#385C22×C2914yescomplemented
422#381—22no—
423#379C22×C2912yescomplemented
424C2×#95—21no—
425#342C22×C2914yescomplemented
426C2×C29—21no—
427C2×C29—24no—
428C2×C29—21no—
429C2×C29—22no—
430C2×C29—22no—
431C2×C29—42no—
432C2×C29—42no—
433C2×C29—81no—
434C2×C29—82no—
435C2×C29#240511yescharacteristic
436C2×C29C2×B(4,𝔽2)11yescharacteristic
437C2×C29C2×#45811yescharacteristic
438C25D4×C2911yescharacteristic
439C25C23×C2911yescharacteristic
440H(5,𝔽2)—24no—
441H(5,𝔽2)—42no—
442C2×#41—21no—
443C2×#41—22no—
444C22×D4—21no—
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—24no—
451C22×D4—42no—
452C22×D4D4×C2911yescharacteristic
453C22×D4D4×C2911yescharacteristic
454C22×D4D4×C2912yes—
455C22×D4D4×C2912yes—
456C22×D4C23×C2912yes—
457C22×D4C23×C2911yescharacteristic
458C22×D4C23×C2911yescharacteristic
459C23×C4—21no—
460C23×C4—22no—
461C23×C4—21no—
462C23×C4—22no—
463C23×C4—21no—
464C23×C4—44no—
465C23×C4D4×C2911yescharacteristic
466C23×C4C23×C2912yes—
467#127—22no—
468#124—22no—
469#123—22no—
470#123—22no—
471#123—22no—
472#123—48no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475#121—21no—
476#121—21no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—22no—
482#121—22no—
483#120—22no—
484#120—22no—
485#120—22no—
486#120—22no—
487#120—22no—
488#120—22no—
489#120—22no—
490#120—22no—
491#120—22no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496#117—21no—
497C2×C4⋊C4—24no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—44no—
509C2×C22⋊C4D4×C2912yes—
510C2×C22⋊C4D4×C2912yes—
511C2×C22⋊C4C23×C2912yes—
512C2×C22⋊C4C23×C2914yes—
513C2×C22⋊C4C23×C2912yes—
514#99—24no—
515#99—42no—
516#99—44no—
517#95—22no—
518#95—22no—
519#95—24no—
520#95—24no—
521C29#2405611yescharacteristic, direct product factor, Sylow
522C24—22no—
523C24—22no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—42no—
529C24—42no—
530C24—41no—
531C24—42no—
532C24—42no—
533C24C2×D4×C2911yescharacteristic
534C24C2×D4×C2912yes—
535C24C2×D4×C2912yes—
536C24C2×D4×C2911yescharacteristic
537C24C2×D4×C2912yes—
538C24C2×D4×C2911yescharacteristic
539C24C2×D4×C2911yescharacteristic
540C24C24×C2911yescharacteristic
541#41—48no—
542#41—42no—
543#41—42no—
544C2×Q8—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4#41×C2914yes—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—41no—
593C22×C4—44no—
594C22×C4—48no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C2912yes—
604C22×C4C2×D4×C2911yescharacteristic
605C22×C4C2×D4×C2911yescharacteristic
606C22×C4C2×D4×C2912yes—
607C22×C4C2×D4×C2912yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—48no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—48no—
630C22⋊C4—42no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C42—22no—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—21no—
638C23—24no—
639C23—24no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—24no—
644C23—24no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—41no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—48no—
660C23—48no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—48no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23—81no—
673C23—84no—
674C23—81no—
675C23—81no—
676C23C29×#12012yes—
677C23C29×#12011yescharacteristic
678C23C29×#12011yescharacteristic
679C23C29×#12312yescomplemented
680C23C22×D4×C2911yescharacteristic
681C23C22×D4×C2912yes—
682C23C2×#41×C2912yes—
683C23C29×H(5,𝔽2)12yes—
684Q8—42no—
685D4—28no—
686D4—44no—
687D4—42no—
688D4—44no—
689D4—44no—
690D4—44no—
691D4—44no—
692D4—42no—
693D4—42no—
694D4—44no—
695D4—44no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—24no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—84no—
732C2×C4C29×#12312yescomplemented
733C22—24no—
734C22—24no—
735C22—22no—
736C22—21no—
737C22—21no—
738C22—22no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—42no—
748C22—42no—
749C22—48no—
750C22—48no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—81no—
764C22—84no—
765C22—84no—
766C22—81no—
767C22—84no—
768C22—162no—
769C22C29×B(4,𝔽2)12yes—
770C22C29×#45812yes—
771C22C2×C29×#12011yescharacteristic
772C22C2×C29×#12311yescharacteristic
773C22C29×#53411yescharacteristic
774C22C29×#54614yes—
775C4—22no—
776C4—44no—
777C4—42no—
778C4—42no—
779C4—41no—
780C4—42no—
781C4—82no—
782C4—84no—
783C2—21no—
784C2—24no—
785C2—21no—
786C2—22no—
787C2—22no—
788C2—42no—
789C2—42no—
790C2—81no—
791C2—82no—
792C2C29×#240511yescharacteristic
793C2C2×C29×B(4,𝔽2)11yescharacteristic
794C2C2×C29×#45811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC24C24×C29
prime radicalC29×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C25×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2849C2semidirect
3. C2×C29×#386C2semidirect
4. C29×#2044C2semidirect
5. C29×#1898C2semidirect
6. C29×#1867C2semidirect
7. C29×#1790C2semidirect
8. C29×#1781C2semidirect
11. C24×C4×C29C22semidirect
25. C22×C22⋊C4×C29C22semidirect
27. C2×C29×#99C22semidirect
28. C2×C29×#99C22semidirect
33. C29×#386C22semidirect
34. C29×#386C22semidirect
36. C29×#385C22semidirect
38. C29×#379C22semidirect
40. C29×#342C22semidirect
236. #24056C29direct (N × H)
282. C23×C29#123semidirect
335. C2×C4×C29#123semidirect
337. #2849C2×C29semidirect
338. C2×#386C2×C29semidirect
339. #2044C2×C29semidirect
340. #1898C2×C29semidirect
341. #1867C2×C29semidirect
342. #1790C2×C29semidirect
343. #1781C2×C29semidirect
396. C24×C4C22×C29semidirect
410. C22×C22⋊C4C22×C29semidirect
412. C2×#99C22×C29semidirect
413. C2×#99C22×C29semidirect
418. #386C22×C29semidirect
419. #386C22×C29semidirect
421. #385C22×C29semidirect
423. #379C22×C29semidirect
425. #342C22×C29semidirect
521. C29#24056direct (N × H)
679. C23C29×#123semidirect
732. C2×C4C29×#123semidirect

Maximal subgroups

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

subgroupindex
C29×#34842
C29×#28492
C2×C29×#3862
C29×#20442
C29×#18982
C29×#18672
C29×#17902
C29×#17812
#2405629