Finite Group Databasebeta

← C29×#25564 #20320464

Subgroups — C29×#25564 #20320464

Order 7424.

1250 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3491C211yesmaximal, characteristic, complemented
2C29×#2482C211yesmaximal, characteristic, complemented
3C29×#2411C212yesmaximal, complemented
4C29×#2062C211yesmaximal, characteristic, complemented
5C29×#2044C211yesmaximal, characteristic, complemented
6C29×#2029C211yesmaximal, characteristic, complemented
7C29×#2021C211yesmaximal, characteristic
8C29×#1899C212yesmaximal, complemented
9C29×#1889C212yesmaximal, complemented
10C29×#1867C212yesmaximal, complemented
11C29×#1740C211yesmaximal, characteristic, complemented
12C29×#552—22no—
13C29×#552—22no—
14C29×#551—22no—
15C29×#551—22no—
16C29×#543C2211yescharacteristic
17C29×#539—21no—
18C29×#539—21no—
19C29×#534C2211yescharacteristic
20C29×#529—21no—
21C29×#529—21no—
22C2×C29×#123C2212yes—
23C2×C29×#120C2212yes—
24C29×#518C2212yes—
25C2×C29×#117C2212yes—
26C2×C29×#117C2211yescharacteristic
27C22×C22⋊C4×C29C2211yescharacteristic
28C2×C29×#99C2212yes—
29C2×C29×#99C2212yes—
30C29×#399—21no—
31C29×#397—21no—
32C29×#396—22no—
33C29×#394—22no—
34C29×#390—22no—
35C29×#388—22no—
36C29×#388—21no—
37C29×#388—21no—
38C29×#386C2212yes—
39C29×#385C2211yescharacteristic
40C29×#385C2211yescharacteristic
41C29×#385C2212yes—
42C29×#381C2211yescharacteristic
43C29×#379C2211yescharacteristic
44C29×#379C2211yescharacteristic
45C29×#379C2212yes—
46C29×#342C2211yescharacteristic
47C29×#342C2211yescharacteristic
48C29×#342C2212yes—
49C29×#342C2212yes—
50C29×#342C2212yes—
51C25×C29C2311yescharacteristic
52C22×D4×C29—22no—
53C22×D4×C29C2312yes—
54C23×C4×C29C2311yescharacteristic
55C23×C4×C29C2311yescharacteristic
56C29×#126—22no—
57C29×#126—22no—
58C29×#126—22no—
59C29×#126—22no—
60C29×#125—21no—
61C29×#125—21no—
62C29×#125—22no—
63C29×#125—22no—
64C29×#124—21no—
65C29×#124—21no—
66C29×#123—22no—
67C29×#123—22no—
68C29×#123—22no—
69C29×#123—22no—
70C29×#123—22no—
71C29×#123—22no—
72C29×#123—22no—
73C29×C22⋊Q8—22no—
74C29×C22⋊Q8—22no—
75C29×C22⋊Q8—21no—
76C29×C22⋊Q8—21no—
77C29×C22⋊Q8—22no—
78C29×C22⋊Q8—22no—
79C29×#121—21no—
80C29×#121—21no—
81C29×#120—22no—
82C29×#120—24no—
83C29×#120—42no—
84C4×Q8×C29—21no—
85C4×Q8×C29—21no—
86C4×D4×C29—21no—
87C4×D4×C29—21no—
88C4×D4×C29—22no—
89C4×D4×C29—22no—
90C4×D4×C29—22no—
91C4×D4×C29—22no—
92C29×#117—22no—
93C29×#117—22no—
94C29×#117—22no—
95C29×#117—22no—
96C29×#117—22no—
97C29×#117—24no—
98C29×#117—42no—
99C2×C4⋊C4×C29—22no—
100C2×C4⋊C4×C29—21no—
101C2×C4⋊C4×C29—21no—
102C2×C4⋊C4×C29—22no—
103C2×C4⋊C4×C29D411yescharacteristic, complemented
104C2×C4⋊C4×C29D411yescharacteristic, complemented
105C2×C4⋊C4×C29D412yescomplemented
106C2×C4⋊C4×C29D412yescomplemented
107C2×C22⋊C4×C29—22no—
108C2×C22⋊C4×C29—21no—
109C2×C22⋊C4×C29—22no—
110C2×C22⋊C4×C29—22no—
111C2×C22⋊C4×C29—21no—
112C2×C22⋊C4×C29—22no—
113C2×C22⋊C4×C29—22no—
114C2×C22⋊C4×C29—21no—
115C2×C22⋊C4×C29—21no—
116C2×C22⋊C4×C29—22no—
117C2×C22⋊C4×C29—21no—
118C2×C22⋊C4×C29—21no—
119C2×C22⋊C4×C29—22no—
120C2×C22⋊C4×C29D412yescomplemented
121C2×C22⋊C4×C29D412yescomplemented
122C2×C22⋊C4×C29C2312yes—
123C2×C22⋊C4×C29C2311yescharacteristic
124C2×C22⋊C4×C29C2311yescharacteristic
125C2×C22⋊C4×C29C2311yescharacteristic
126C2×C22⋊C4×C29C2311yescharacteristic
127C2×C22⋊C4×C29C2312yes—
128C2×C22⋊C4×C29C2312yes—
129C2×C42×C29—22no—
130C2×C42×C29D411yescharacteristic, complemented
131C2×C42×C29D411yescharacteristic, complemented
132C29×#99—24no—
133C29×#99—42no—
134C29×#95—21no—
135C29×#95—21no—
136C29×#95—22no—
137C29×#95—21no—
138C29×#95—21no—
139C29×#95—22no—
140C24×C29—21no—
141C24×C29—22no—
142C24×C29—22no—
143C24×C29—21no—
144C24×C29—21no—
145C24×C29—42no—
146C24×C29—81no—
147C24×C29C2×D412yes—
148C24×C29C2411yescharacteristic
149C2×Q8×C29—21no—
150C2×Q8×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—21no—
158C2×D4×C29—21no—
159C2×D4×C29—44no—
160C2×D4×C29—44no—
161C2×D4×C29—82no—
162C22×C4×C29—22no—
163C22×C4×C29—21no—
164C22×C4×C29—21no—
165C22×C4×C29—22no—
166C22×C4×C29—22no—
167C22×C4×C29—22no—
168C22×C4×C29—22no—
169C22×C4×C29—22no—
170C22×C4×C29—21no—
171C22×C4×C29—21no—
172C22×C4×C29—21no—
173C22×C4×C29—81no—
174C22×C4×C29C2×D412yes—
175C22×C4×C29C2×D412yes—
176C22×C4×C29C2×D411yescharacteristic
177C22×C4×C29C2×D412yes—
178C22×C4×C29C2×D411yescharacteristic
179C22×C4×C29C2×D411yescharacteristic
180C22×C4×C29C2×D411yescharacteristic
181C22×C4×C29C2×D411yescharacteristic
182C22×C4×C29C2×D411yescharacteristic
183C22×C4×C29C2×D412yes—
184C22×C4×C29C2×D412yes—
185C4⋊C4×C29—22no—
186C4⋊C4×C29—22no—
187C4⋊C4×C29—22no—
188C4⋊C4×C29—22no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—22no—
194C4⋊C4×C29—22no—
195C4⋊C4×C29—22no—
196C4⋊C4×C29—22no—
197C4⋊C4×C29—22no—
198C4⋊C4×C29—22no—
199C4⋊C4×C29—44no—
200C4⋊C4×C29—82no—
201C4⋊C4×C29—81no—
202C4⋊C4×C29—81no—
203C22⋊C4×C29—22no—
204C22⋊C4×C29—22no—
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—22no—
212C22⋊C4×C29—22no—
213C22⋊C4×C29—22no—
214C22⋊C4×C29—22no—
215C22⋊C4×C29—22no—
216C22⋊C4×C29—22no—
217C22⋊C4×C29—22no—
218C22⋊C4×C29—22no—
219C22⋊C4×C29—21no—
220C22⋊C4×C29—21no—
221C22⋊C4×C29—44no—
222C22⋊C4×C29—42no—
223C22⋊C4×C29—42no—
224C22⋊C4×C29—44no—
225C22⋊C4×C29—41no—
226C22⋊C4×C29—41no—
227C22⋊C4×C29—42no—
228C22⋊C4×C29—82no—
229C22⋊C4×C29—81no—
230C22⋊C4×C29—81no—
231C22⋊C4×C29—82no—
232C22⋊C4×C29#4114yes—
233C42×C29—22no—
234C42×C29—22no—
235C42×C29—21no—
236C42×C29—21no—
237C42×C29—21no—
238C42×C29—21no—
239C42×C29—44no—
240#25564C2911yesmaximal, characteristic, direct product factor, Sylow
241C23×C29—22no—
242C23×C29—24no—
243C23×C29—22no—
244C23×C29—22no—
245C23×C29—22no—
246C23×C29—41no—
247C23×C29—41no—
248C23×C29—41no—
249C23×C29—41no—
250C23×C29—42no—
251C23×C29—42no—
252C23×C29—41no—
253C23×C29—42no—
254C23×C29—42no—
255C23×C29—42no—
256C23×C29—41no—
257C23×C29—41no—
258C23×C29—41no—
259C23×C29—42no—
260C23×C29—42no—
261C23×C29—84no—
262C23×C29—82no—
263C23×C29—82no—
264C23×C29C22×D411yescharacteristic
265C23×C29C22×D412yes—
266C23×C29C2×#4112yes—
267C23×C29H(5,𝔽2)11yescharacteristic
268C23×C292−1+411yescharacteristic
269Q8×C29—81no—
270Q8×C29—81no—
271D4×C29—42no—
272D4×C29—42no—
273D4×C29—42no—
274D4×C29—42no—
275D4×C29—81no—
276D4×C29—81no—
277D4×C29—88no—
278C2×C4×C29—21no—
279C2×C4×C29—21no—
280C2×C4×C29—21no—
281C2×C4×C29—21no—
282C2×C4×C29—22no—
283C2×C4×C29—22no—
284C2×C4×C29—22no—
285C2×C4×C29—22no—
286C2×C4×C29—21no—
287C2×C4×C29—21no—
288C2×C4×C29—21no—
289C2×C4×C29—21no—
290C2×C4×C29—22no—
291C2×C4×C29—22no—
292C2×C4×C29—22no—
293C2×C4×C29—24no—
294C2×C4×C29—22no—
295C2×C4×C29—22no—
296C2×C4×C29—42no—
297C2×C4×C29—42no—
298C2×C4×C29—41no—
299C2×C4×C29—42no—
300C2×C4×C29—41no—
301C2×C4×C29—41no—
302C2×C4×C29—42no—
303C2×C4×C29—41no—
304C2×C4×C29—41no—
305C2×C4×C29—41no—
306C2×C4×C29—42no—
307C2×C4×C29—42no—
308C2×C4×C29—41no—
309C2×C4×C29—41no—
310C2×C4×C29—42no—
311C2×C4×C29—41no—
312C2×C4×C29—41no—
313C2×C4×C29—42no—
314C2×C4×C29—41no—
315C2×C4×C29—41no—
316C2×C4×C29—41no—
317C2×C4×C29—42no—
318C2×C4×C29—82no—
319C2×C4×C29—82no—
320C2×C4×C29#12011yescharacteristic
321C2×C4×C29#12011yescharacteristic
322C2×C4×C29#12012yes—
323#3491C2×C2911yescharacteristic, complemented
324#2482C2×C2911yescharacteristic, complemented
325#2411C2×C2912yescomplemented
326#2062C2×C2911yescharacteristic, complemented
327#2044C2×C2911yescharacteristic, complemented
328#2029C2×C2911yescharacteristic, complemented
329#2021C2×C2911yescharacteristic
330#1899C2×C2912yescomplemented
331#1889C2×C2912yescomplemented
332#1867C2×C2912yescomplemented
333#1740C2×C2911yescharacteristic, complemented
334C22×C29—21no—
335C22×C29—22no—
336C22×C29—21no—
337C22×C29—22no—
338C22×C29—42no—
339C22×C29—41no—
340C22×C29—41no—
341C22×C29—44no—
342C22×C29—42no—
343C22×C29—42no—
344C22×C29—44no—
345C22×C29—42no—
346C22×C29—42no—
347C22×C29—42no—
348C22×C29—42no—
349C22×C29—82no—
350C22×C29—82no—
351C22×C29—82no—
352C22×C29—81no—
353C22×C29—81no—
354C22×C29—82no—
355C22×C29—81no—
356C22×C29—81no—
357C22×C29C2×#12011yescharacteristic
358C22×C29#53211yescharacteristic
359C22×C29#53711yescharacteristic
360C22×C29#54612yes—
361C22×C29#54712yes—
362C4×C29—21no—
363C4×C29—22no—
364C4×C29—21no—
365C4×C29—44no—
366C4×C29—42no—
367C4×C29—41no—
368C4×C29—42no—
369C4×C29—41no—
370C4×C29—41no—
371C4×C29—42no—
372C4×C29—41no—
373C4×C29—82no—
374C4×C29—81no—
375C4×C29—81no—
376C4×C29—81no—
377#552—22no—
378#552—22no—
379#551—22no—
380#551—22no—
381#543C22×C2911yescharacteristic
382#539—21no—
383#539—21no—
384#534C22×C2911yescharacteristic
385#529—21no—
386#529—21no—
387C2×#123C22×C2912yes—
388C2×#120C22×C2912yes—
389#518C22×C2912yes—
390C2×#117C22×C2912yes—
391C2×#117C22×C2911yescharacteristic
392C22×C22⋊C4C22×C2911yescharacteristic
393C2×#99C22×C2912yes—
394C2×#99C22×C2912yes—
395#399—21no—
396#397—21no—
397#396—22no—
398#394—22no—
399#390—22no—
400#388—22no—
401#388—21no—
402#388—21no—
403#386C22×C2912yes—
404#385C22×C2912yes—
405#385C22×C2911yescharacteristic
406#385C22×C2911yescharacteristic
407#381C22×C2911yescharacteristic
408#379C22×C2911yescharacteristic
409#379C22×C2912yes—
410#379C22×C2911yescharacteristic
411#342C22×C2912yes—
412#342C22×C2911yescharacteristic
413#342C22×C2912yes—
414#342C22×C2912yes—
415#342C22×C2911yescharacteristic
416C2×C29—22no—
417C2×C29—21no—
418C2×C29—21no—
419C2×C29—22no—
420C2×C29—82no—
421C2×C29—82no—
422C2×C29#243011yescharacteristic
423C2×C29#302511yescharacteristic
424C2×C29#302711yescharacteristic
425C25C23×C2911yescharacteristic
426C22×D4—22no—
427C22×D4C23×C2912yes—
428C23×C4C23×C2911yescharacteristic
429C23×C4C23×C2911yescharacteristic
430#126—22no—
431#126—22no—
432#126—22no—
433#126—22no—
434#125—21no—
435#125—21no—
436#125—22no—
437#125—22no—
438#124—21no—
439#124—21no—
440#123—22no—
441#123—22no—
442#123—22no—
443#123—22no—
444#123—22no—
445#123—22no—
446#123—22no—
447C22⋊Q8—22no—
448C22⋊Q8—22no—
449C22⋊Q8—21no—
450C22⋊Q8—21no—
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453#121—21no—
454#121—21no—
455#120—22no—
456#120—24no—
457#120—42no—
458C4×Q8—21no—
459C4×Q8—21no—
460C4×D4—21no—
461C4×D4—21no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—22no—
465C4×D4—22no—
466#117—22no—
467#117—22no—
468#117—22no—
469#117—22no—
470#117—22no—
471#117—24no—
472#117—42no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4D4×C2911yescharacteristic, complemented
478C2×C4⋊C4D4×C2911yescharacteristic, complemented
479C2×C4⋊C4D4×C2912yescomplemented
480C2×C4⋊C4D4×C2912yescomplemented
481C2×C22⋊C4—22no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4D4×C2912yescomplemented
495C2×C22⋊C4D4×C2912yescomplemented
496C2×C22⋊C4C23×C2912yes—
497C2×C22⋊C4C23×C2911yescharacteristic
498C2×C22⋊C4C23×C2911yescharacteristic
499C2×C22⋊C4C23×C2911yescharacteristic
500C2×C22⋊C4C23×C2911yescharacteristic
501C2×C22⋊C4C23×C2912yes—
502C2×C22⋊C4C23×C2912yes—
503C2×C42—22no—
504C2×C42D4×C2911yescharacteristic, complemented
505C2×C42D4×C2911yescharacteristic, complemented
506#99—24no—
507#99—42no—
508#95—21no—
509#95—21no—
510#95—22no—
511#95—21no—
512#95—21no—
513#95—22no—
514C29#2556411yescharacteristic, direct product factor, Sylow
515C24—21no—
516C24—22no—
517C24—22no—
518C24—21no—
519C24—21no—
520C24—42no—
521C24—81no—
522C24C2×D4×C2912yes—
523C24C24×C2911yescharacteristic
524C2×Q8—21no—
525C2×Q8—21no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—82no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—81no—
549C22×C4C2×D4×C2912yes—
550C22×C4C2×D4×C2911yescharacteristic
551C22×C4C2×D4×C2911yescharacteristic
552C22×C4C2×D4×C2912yes—
553C22×C4C2×D4×C2912yes—
554C22×C4C2×D4×C2911yescharacteristic
555C22×C4C2×D4×C2911yescharacteristic
556C22×C4C2×D4×C2912yes—
557C22×C4C2×D4×C2911yescharacteristic
558C22×C4C2×D4×C2911yescharacteristic
559C22×C4C2×D4×C2912yes—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—44no—
575C4⋊C4—82no—
576C4⋊C4—81no—
577C4⋊C4—81no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—22no—
593C22⋊C4—21no—
594C22⋊C4—22no—
595C22⋊C4—21no—
596C22⋊C4—44no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—44no—
600C22⋊C4—41no—
601C22⋊C4—41no—
602C22⋊C4—42no—
603C22⋊C4—82no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—82no—
607C22⋊C4#41×C2914yes—
608C42—22no—
609C42—22no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—44no—
615C23—22no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—42no—
625C23—42no—
626C23—41no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—42no—
634C23—42no—
635C23—84no—
636C23—82no—
637C23—82no—
638C23C22×D4×C2911yescharacteristic
639C23C22×D4×C2912yes—
640C23C2×#41×C2912yes—
641C23C29×H(5,𝔽2)11yescharacteristic
642C23C29×2−1+411yescharacteristic
643Q8—81no—
644Q8—81no—
645D4—42no—
646D4—42no—
647D4—42no—
648D4—42no—
649D4—81no—
650D4—81no—
651D4—88no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—82no—
693C2×C4—82no—
694C2×C4C29×#12011yescharacteristic
695C2×C4C29×#12011yescharacteristic
696C2×C4C29×#12012yes—
697C22—21no—
698C22—22no—
699C22—21no—
700C22—22no—
701C22—42no—
702C22—41no—
703C22—41no—
704C22—44no—
705C22—42no—
706C22—42no—
707C22—44no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—82no—
713C22—82no—
714C22—82no—
715C22—81no—
716C22—81no—
717C22—82no—
718C22—81no—
719C22—81no—
720C22C2×C29×#12011yescharacteristic
721C22C29×#53211yescharacteristic
722C22C29×#53711yescharacteristic
723C22C29×#54612yes—
724C22C29×#54712yes—
725C4—21no—
726C4—22no—
727C4—21no—
728C4—44no—
729C4—42no—
730C4—41no—
731C4—42no—
732C4—41no—
733C4—41no—
734C4—42no—
735C4—41no—
736C4—82no—
737C4—81no—
738C4—81no—
739C4—81no—
740C2—22no—
741C2—21no—
742C2—21no—
743C2—22no—
744C2—82no—
745C2—82no—
746C2C29×#243011yescharacteristic
747C2C29×#302511yescharacteristic
748C2C29×#302711yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC24C24×C29
prime radicalC29×#2021C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3491C2semidirect
2. C29×#2482C2semidirect
3. C29×#2411C2semidirect
4. C29×#2062C2semidirect
5. C29×#2044C2semidirect
6. C29×#2029C2semidirect
8. C29×#1899C2semidirect
9. C29×#1889C2semidirect
10. C29×#1867C2semidirect
11. C29×#1740C2semidirect
103. C2×C4⋊C4×C29D4semidirect
104. C2×C4⋊C4×C29D4semidirect
105. C2×C4⋊C4×C29D4semidirect
106. C2×C4⋊C4×C29D4semidirect
120. C2×C22⋊C4×C29D4semidirect
121. C2×C22⋊C4×C29D4semidirect
130. C2×C42×C29D4semidirect
131. C2×C42×C29D4semidirect
240. #25564C29direct (N × H)
323. #3491C2×C29semidirect
324. #2482C2×C29semidirect
325. #2411C2×C29semidirect
326. #2062C2×C29semidirect
327. #2044C2×C29semidirect
328. #2029C2×C29semidirect
330. #1899C2×C29semidirect
331. #1889C2×C29semidirect
332. #1867C2×C29semidirect
333. #1740C2×C29semidirect
477. C2×C4⋊C4D4×C29semidirect
478. C2×C4⋊C4D4×C29semidirect
479. C2×C4⋊C4D4×C29semidirect
480. C2×C4⋊C4D4×C29semidirect
494. C2×C22⋊C4D4×C29semidirect
495. C2×C22⋊C4D4×C29semidirect
504. C2×C42D4×C29semidirect
505. C2×C42D4×C29semidirect
514. C29#25564direct (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×#24822
C29×#24112
C29×#20622
C29×#20442
C29×#20292
C29×#20212
C29×#18992
C29×#18892
C29×#18672
C29×#17402
#2556429