Finite Group Databasebeta

← C29×#24140 #20319040

Subgroups — C29×#24140 #20319040

Order 7424.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3505C211yesmaximal, characteristic, complemented
2C29×#2848C211yesmaximal, characteristic, complemented
3C29×#2847C211yesmaximal, characteristic, complemented
4C4×C29×#120C211yesmaximal, characteristic, complemented
5C29×#2044C212yesmaximal, complemented
6C29×#2021C212yesmaximal, complemented
7C29×#1996C211yesmaximal, characteristic, complemented
8C29×#1964C211yesmaximal, characteristic, complemented
9C29×#1889C212yesmaximal, complemented
10C29×#1867C212yesmaximal, complemented
11C29×#1799C211yesmaximal, characteristic, complemented
12C24×C4×C29C2211yescharacteristic
13C29×#553—21no—
14C29×#553—22no—
15C29×#552—21no—
16C29×#551—22no—
17C29×#548—21no—
18C29×#546—21no—
19C29×#539—21no—
20C29×#538—21no—
21C29×#534C2212yes—
22C29×#529—21no—
23C29×#525—21no—
24C2×C29×C22⋊Q8—21no—
25C2×C29×C22⋊Q8C2211yescharacteristic
26C2×C29×#121—21no—
27C2×C29×#121C2211yescharacteristic
28C2×C29×#120C2211yescharacteristic
29C2×C29×#120C2212yes—
30C29×#518C2212yes—
31C2×C4×D4×C29—21no—
32C2×C4×D4×C29C2211yescharacteristic
33C2×C29×#99C2212yes—
34C2×C29×#99C2212yes—
35C2×C29×#99C2212yes—
36C29×#386—21no—
37C29×#386—22no—
38C29×#386C2211yescharacteristic
39C29×#386C2212yes—
40C29×#385—21no—
41C29×#385—22no—
42C29×#385C2211yescharacteristic
43C29×#385C2212yes—
44C29×#380—21no—
45C29×#380—21no—
46C29×#380C2211yescharacteristic
47C29×#380C2211yescharacteristic
48C29×#379C2212yes—
49C29×#379C2211yescharacteristic
50C4×C22⋊C4×C29—21no—
51C4×C22⋊C4×C29C2211yescharacteristic
52C29×#342C2212yes—
53C29×#342C2212yes—
54C29×#342C2212yes—
55C25×C29C2311yescharacteristic
56C2×#41×C29—21no—
57C22×Q8×C29D411yescharacteristic, complemented
58C22×D4×C29—21no—
59C22×D4×C29—22no—
60C22×D4×C29D411yescharacteristic, complemented
61C22×D4×C29C2311yescharacteristic
62C22×D4×C29C2312yes—
63C23×C4×C29—21no—
64C23×C4×C29—21no—
65C23×C4×C29—21no—
66C23×C4×C29—21no—
67C23×C4×C29—21no—
68C23×C4×C29—21no—
69C23×C4×C29—44no—
70C23×C4×C29D411yescharacteristic, complemented
71C23×C4×C29C2311yescharacteristic
72C23×C4×C29C2311yescharacteristic
73C29×#126—22no—
74C29×#126—22no—
75C29×#126—22no—
76C29×#125—21no—
77C29×#125—22no—
78C29×#124—21no—
79C29×#124—22no—
80C29×#123—22no—
81C29×#123—22no—
82C29×#123—22no—
83C29×#123—22no—
84C29×#123—22no—
85C29×C22⋊Q8—21no—
86C29×C22⋊Q8—22no—
87C29×C22⋊Q8—21no—
88C29×C22⋊Q8—21no—
89C29×C22⋊Q8—21no—
90C29×C22⋊Q8—21no—
91C29×C22⋊Q8—44no—
92C29×#121—21no—
93C29×#121—22no—
94C29×#121—21no—
95C29×#121—21no—
96C29×#121—21no—
97C29×#121—21no—
98C29×#121—22no—
99C29×#121—22no—
100C29×#121—44no—
101C29×#120—22no—
102C29×#120—22no—
103C29×#120—22no—
104C29×#120—22no—
105C29×#120—24no—
106C29×#120—42no—
107C4×Q8×C29—21no—
108C4×D4×C29—22no—
109C4×D4×C29—21no—
110C4×D4×C29—21no—
111C4×D4×C29—21no—
112C4×D4×C29—21no—
113C4×D4×C29—21no—
114C4×D4×C29—22no—
115C4×D4×C29—22no—
116C4×D4×C29—22no—
117C4×D4×C29—22no—
118C4×D4×C29—44no—
119C29×#117—21no—
120C29×#117—22no—
121C29×#117—22no—
122C2×C4⋊C4×C29—21no—
123C2×C4⋊C4×C29—21no—
124C2×C4⋊C4×C29—21no—
125C2×C4⋊C4×C29—22no—
126C2×C4⋊C4×C29D411yescharacteristic, complemented
127C2×C4⋊C4×C29D411yescharacteristic, complemented
128C2×C4⋊C4×C29D411yescharacteristic, complemented
129C2×C4⋊C4×C29D412yescomplemented
130C2×C22⋊C4×C29—22no—
131C2×C22⋊C4×C29—21no—
132C2×C22⋊C4×C29—21no—
133C2×C22⋊C4×C29—22no—
134C2×C22⋊C4×C29—21no—
135C2×C22⋊C4×C29—22no—
136C2×C22⋊C4×C29—22no—
137C2×C22⋊C4×C29—21no—
138C2×C22⋊C4×C29—22no—
139C2×C22⋊C4×C29D411yescharacteristic, complemented
140C2×C22⋊C4×C29D412yescomplemented
141C2×C22⋊C4×C29C2312yes—
142C2×C22⋊C4×C29C2311yescharacteristic
143C2×C22⋊C4×C29C2312yes—
144C2×C22⋊C4×C29C2311yescharacteristic
145C2×C22⋊C4×C29C2312yes—
146C2×C22⋊C4×C29C2311yescharacteristic
147C2×C42×C29—21no—
148C2×C42×C29D411yescharacteristic, complemented
149C29×#99—24no—
150C29×#99—42no—
151C29×#99—42no—
152C29×#95—21no—
153C29×#95—21no—
154C29×#95—21no—
155C29×#95—22no—
156C29×#95—22no—
157C29×#95—21no—
158C29×#95—21no—
159C24×C29—21no—
160C24×C29—21no—
161C24×C29—21no—
162C24×C29—21no—
163C24×C29—21no—
164C24×C29—21no—
165C24×C29—42no—
166C24×C29—42no—
167C24×C29C2×D412yes—
168C24×C29C2×D411yescharacteristic
169C24×C29#4112yescomplemented
170C24×C29C2411yescharacteristic
171#41×C29—82no—
172C2×Q8×C29—21no—
173C2×Q8×C29—21no—
174C2×Q8×C29—42no—
175C2×D4×C29—24no—
176C2×D4×C29—21no—
177C2×D4×C29—22no—
178C2×D4×C29—21no—
179C2×D4×C29—22no—
180C2×D4×C29—21no—
181C2×D4×C29—21no—
182C2×D4×C29—22no—
183C2×D4×C29—22no—
184C2×D4×C29—22no—
185C2×D4×C29—21no—
186C2×D4×C29—21no—
187C2×D4×C29—22no—
188C2×D4×C29—22no—
189C2×D4×C29—22no—
190C2×D4×C29—21no—
191C2×D4×C29—21no—
192C2×D4×C29—42no—
193C2×D4×C29—42no—
194C2×D4×C29—42no—
195C2×D4×C29—44no—
196C2×D4×C29—44no—
197C2×D4×C29—44no—
198C22×C4×C29—24no—
199C22×C4×C29—24no—
200C22×C4×C29—24no—
201C22×C4×C29—21no—
202C22×C4×C29—21no—
203C22×C4×C29—21no—
204C22×C4×C29—21no—
205C22×C4×C29—22no—
206C22×C4×C29—22no—
207C22×C4×C29—21no—
208C22×C4×C29—21no—
209C22×C4×C29—21no—
210C22×C4×C29—22no—
211C22×C4×C29—22no—
212C22×C4×C29—42no—
213C22×C4×C29—42no—
214C22×C4×C29—42no—
215C22×C4×C29—42no—
216C22×C4×C29—42no—
217C22×C4×C29—42no—
218C22×C4×C29—42no—
219C22×C4×C29—42no—
220C22×C4×C29—42no—
221C22×C4×C29—42no—
222C22×C4×C29—42no—
223C22×C4×C29—42no—
224C22×C4×C29—41no—
225C22×C4×C29—41no—
226C22×C4×C29—41no—
227C22×C4×C29—41no—
228C22×C4×C29C2×D411yescharacteristic
229C22×C4×C29C2×D412yes—
230C22×C4×C29C2×D411yescharacteristic
231C22×C4×C29C2×D411yescharacteristic
232C22×C4×C29C2×D411yescharacteristic
233C22×C4×C29C2×D411yescharacteristic
234C22×C4×C29C2×D411yescharacteristic
235C22×C4×C29C2×D412yes—
236C22×C4×C29C2×D412yes—
237C22×C4×C29C2×D411yescharacteristic
238C22×C4×C29C2×D411yescharacteristic
239C22×C4×C29C2×D411yescharacteristic
240C4⋊C4×C29—22no—
241C4⋊C4×C29—22no—
242C4⋊C4×C29—22no—
243C4⋊C4×C29—22no—
244C4⋊C4×C29—21no—
245C4⋊C4×C29—22no—
246C4⋊C4×C29—21no—
247C4⋊C4×C29—21no—
248C4⋊C4×C29—21no—
249C4⋊C4×C29—21no—
250C4⋊C4×C29—22no—
251C4⋊C4×C29—21no—
252C4⋊C4×C29—42no—
253C4⋊C4×C29—42no—
254C4⋊C4×C29—42no—
255C4⋊C4×C29—44no—
256C22⋊C4×C29—22no—
257C22⋊C4×C29—22no—
258C22⋊C4×C29—24no—
259C22⋊C4×C29—22no—
260C22⋊C4×C29—22no—
261C22⋊C4×C29—22no—
262C22⋊C4×C29—22no—
263C22⋊C4×C29—21no—
264C22⋊C4×C29—22no—
265C22⋊C4×C29—21no—
266C22⋊C4×C29—22no—
267C22⋊C4×C29—21no—
268C22⋊C4×C29—22no—
269C22⋊C4×C29—21no—
270C22⋊C4×C29—21no—
271C22⋊C4×C29—22no—
272C22⋊C4×C29—22no—
273C22⋊C4×C29—22no—
274C22⋊C4×C29—22no—
275C22⋊C4×C29—21no—
276C22⋊C4×C29—22no—
277C22⋊C4×C29—21no—
278C22⋊C4×C29—44no—
279C22⋊C4×C29—42no—
280C22⋊C4×C29—44no—
281C22⋊C4×C29—44no—
282C22⋊C4×C29—42no—
283C22⋊C4×C29—42no—
284C22⋊C4×C29—44no—
285C22⋊C4×C29#4112yescomplemented
286C42×C29—22no—
287C42×C29—22no—
288C42×C29—21no—
289C42×C29—21no—
290C42×C29—42no—
291#24140C2911yesmaximal, characteristic, direct product factor, Sylow
292C23×C29—22no—
293C23×C29—22no—
294C23×C29—22no—
295C23×C29—22no—
296C23×C29—22no—
297C23×C29—22no—
298C23×C29—22no—
299C23×C29—22no—
300C23×C29—22no—
301C23×C29—21no—
302C23×C29—22no—
303C23×C29—21no—
304C23×C29—21no—
305C23×C29—22no—
306C23×C29—22no—
307C23×C29—41no—
308C23×C29—44no—
309C23×C29—41no—
310C23×C29—41no—
311C23×C29—41no—
312C23×C29—41no—
313C23×C29—41no—
314C23×C29—41no—
315C23×C29—41no—
316C23×C29—44no—
317C23×C29—44no—
318C23×C29—44no—
319C23×C29—41no—
320C23×C29—41no—
321C23×C29—42no—
322C23×C29—42no—
323C23×C29—41no—
324C23×C29—41no—
325C23×C29—41no—
326C23×C29—41no—
327C23×C29C22×D411yescharacteristic
328C23×C29C22×D411yescharacteristic
329C23×C29C22×D411yescharacteristic
330C23×C29C2×#4111yescharacteristic
331C23×C29C2×#4111yescharacteristic
332C23×C29H(5,𝔽2)11yescharacteristic
333C23×C292−1+411yescharacteristic
334Q8×C29—42no—
335Q8×C29—81no—
336D4×C29—48no—
337D4×C29—42no—
338D4×C29—42no—
339D4×C29—41no—
340D4×C29—41no—
341D4×C29—41no—
342D4×C29—42no—
343D4×C29—41no—
344D4×C29—42no—
345D4×C29—42no—
346D4×C29—81no—
347D4×C29—82no—
348D4×C29—82no—
349D4×C29—88no—
350C2×C4×C29—22no—
351C2×C4×C29—22no—
352C2×C4×C29—22no—
353C2×C4×C29—22no—
354C2×C4×C29—22no—
355C2×C4×C29—22no—
356C2×C4×C29—21no—
357C2×C4×C29—22no—
358C2×C4×C29—21no—
359C2×C4×C29—21no—
360C2×C4×C29—22no—
361C2×C4×C29—22no—
362C2×C4×C29—21no—
363C2×C4×C29—22no—
364C2×C4×C29—21no—
365C2×C4×C29—22no—
366C2×C4×C29—22no—
367C2×C4×C29—41no—
368C2×C4×C29—41no—
369C2×C4×C29—41no—
370C2×C4×C29—44no—
371C2×C4×C29—44no—
372C2×C4×C29—44no—
373C2×C4×C29—41no—
374C2×C4×C29—41no—
375C2×C4×C29—41no—
376C2×C4×C29—41no—
377C2×C4×C29—41no—
378C2×C4×C29—41no—
379C2×C4×C29—44no—
380C2×C4×C29—42no—
381C2×C4×C29—41no—
382C2×C4×C29—42no—
383C2×C4×C29—41no—
384C2×C4×C29—42no—
385C2×C4×C29—41no—
386C2×C4×C29—42no—
387C2×C4×C29—42no—
388C2×C4×C29—42no—
389C2×C4×C29—41no—
390C2×C4×C29—42no—
391C2×C4×C29—41no—
392C2×C4×C29—42no—
393C2×C4×C29—42no—
394C2×C4×C29—81no—
395C2×C4×C29—82no—
396C2×C4×C29—82no—
397C2×C4×C29#12011yescharacteristic
398C2×C4×C29#12011yescharacteristic
399C2×C4×C29#12011yescharacteristic
400C2×C4×C29#12011yescharacteristic
401#3505C2×C2911yescharacteristic, complemented
402#2848C2×C2911yescharacteristic, complemented
403#2847C2×C2911yescharacteristic, complemented
404C4×#120C2×C2911yescharacteristic, complemented
405#2044C2×C2912yescomplemented
406#2021C2×C2912yescomplemented
407#1996C2×C2911yescharacteristic, complemented
408#1964C2×C2911yescharacteristic, complemented
409#1889C2×C2912yescomplemented
410#1867C2×C2912yescomplemented
411#1799C2×C2911yescharacteristic, complemented
412C22×C29—21no—
413C22×C29—21no—
414C22×C29—21no—
415C22×C29—21no—
416C22×C29—21no—
417C22×C29—21no—
418C22×C29—24no—
419C22×C29—24no—
420C22×C29—24no—
421C22×C29—41no—
422C22×C29—41no—
423C22×C29—41no—
424C22×C29—41no—
425C22×C29—42no—
426C22×C29—42no—
427C22×C29—42no—
428C22×C29—42no—
429C22×C29—42no—
430C22×C29—42no—
431C22×C29—42no—
432C22×C29—42no—
433C22×C29—42no—
434C22×C29—42no—
435C22×C29—42no—
436C22×C29—42no—
437C22×C29—42no—
438C22×C29—41no—
439C22×C29—42no—
440C22×C29—41no—
441C22×C29—42no—
442C22×C29—42no—
443C22×C29—41no—
444C22×C29—82no—
445C22×C29—81no—
446C22×C29—82no—
447C22×C29C2×#12011yescharacteristic
448C22×C29#52511yescharacteristic
449C22×C29#53711yescharacteristic
450C22×C29#54611yescharacteristic
451C22×C29#54711yescharacteristic
452C22×C29#54811yescharacteristic
453C22×C29#55011yescharacteristic
454C4×C29—21no—
455C4×C29—21no—
456C4×C29—21no—
457C4×C29—42no—
458C4×C29—41no—
459C4×C29—42no—
460C4×C29—42no—
461C4×C29—41no—
462C4×C29—42no—
463C4×C29—41no—
464C4×C29—42no—
465C4×C29—82no—
466C4×C29—81no—
467C4×C29—82no—
468C4×C29B(4,𝔽2)12yes—
469C24×C4C22×C2911yescharacteristic
470#553—21no—
471#553—22no—
472#552—21no—
473#551—22no—
474#548—21no—
475#546—21no—
476#539—21no—
477#538—21no—
478#534C22×C2912yes—
479#529—21no—
480#525—21no—
481C2×C22⋊Q8—21no—
482C2×C22⋊Q8C22×C2911yescharacteristic
483C2×#121—21no—
484C2×#121C22×C2911yescharacteristic
485C2×#120C22×C2911yescharacteristic
486C2×#120C22×C2912yes—
487#518C22×C2912yes—
488C2×C4×D4—21no—
489C2×C4×D4C22×C2911yescharacteristic
490C2×#99C22×C2912yes—
491C2×#99C22×C2912yes—
492C2×#99C22×C2912yes—
493#386—22no—
494#386—21no—
495#386C22×C2912yes—
496#386C22×C2911yescharacteristic
497#385—22no—
498#385—21no—
499#385C22×C2912yes—
500#385C22×C2911yescharacteristic
501#380—21no—
502#380—21no—
503#380C22×C2911yescharacteristic
504#380C22×C2911yescharacteristic
505#379C22×C2912yes—
506#379C22×C2911yescharacteristic
507C4×C22⋊C4—21no—
508C4×C22⋊C4C22×C2911yescharacteristic
509#342C22×C2912yes—
510#342C22×C2912yes—
511#342C22×C2912yes—
512C2×C29—21no—
513C2×C29—21no—
514C2×C29—21no—
515C2×C29—21no—
516C2×C29—21no—
517C2×C29—21no—
518C2×C29—44no—
519C2×C29—81no—
520C2×C29—82no—
521C2×C29#240711yescharacteristic
522C2×C29C2×B(4,𝔽2)11yescharacteristic
523C2×C29#302511yescharacteristic
524C25C23×C2911yescharacteristic
525C2×#41—21no—
526C22×Q8D4×C2911yescharacteristic, complemented
527C22×D4—21no—
528C22×D4—22no—
529C22×D4D4×C2911yescharacteristic, complemented
530C22×D4C23×C2911yescharacteristic
531C22×D4C23×C2912yes—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—44no—
539C23×C4D4×C2911yescharacteristic, complemented
540C23×C4C23×C2911yescharacteristic
541C23×C4C23×C2911yescharacteristic
542#126—22no—
543#126—22no—
544#126—22no—
545#125—21no—
546#125—22no—
547#124—21no—
548#124—22no—
549#123—22no—
550#123—22no—
551#123—22no—
552#123—22no—
553#123—22no—
554C22⋊Q8—21no—
555C22⋊Q8—22no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—44no—
561#121—21no—
562#121—22no—
563#121—21no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121—22no—
568#121—22no—
569#121—44no—
570#120—22no—
571#120—22no—
572#120—22no—
573#120—22no—
574#120—24no—
575#120—42no—
576C4×Q8—21no—
577C4×D4—22no—
578C4×D4—21no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—44no—
588#117—21no—
589#117—22no—
590#117—22no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4D4×C2911yescharacteristic, complemented
596C2×C4⋊C4D4×C2911yescharacteristic, complemented
597C2×C4⋊C4D4×C2911yescharacteristic, complemented
598C2×C4⋊C4D4×C2912yescomplemented
599C2×C22⋊C4—22no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4D4×C2911yescharacteristic, complemented
609C2×C22⋊C4D4×C2912yescomplemented
610C2×C22⋊C4C23×C2912yes—
611C2×C22⋊C4C23×C2911yescharacteristic
612C2×C22⋊C4C23×C2912yes—
613C2×C22⋊C4C23×C2911yescharacteristic
614C2×C22⋊C4C23×C2912yes—
615C2×C22⋊C4C23×C2911yescharacteristic
616C2×C42—21no—
617C2×C42D4×C2911yescharacteristic, complemented
618#99—24no—
619#99—42no—
620#99—42no—
621#95—21no—
622#95—21no—
623#95—21no—
624#95—22no—
625#95—22no—
626#95—21no—
627#95—21no—
628C29#2414011yescharacteristic, direct product factor, Sylow
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—42no—
636C24—42no—
637C24C2×D4×C2912yes—
638C24C2×D4×C2911yescharacteristic
639C24#41×C2912yescomplemented
640C24C24×C2911yescharacteristic
641#41—82no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—42no—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4C2×D4×C2911yescharacteristic
699C22×C4C2×D4×C2912yes—
700C22×C4C2×D4×C2911yescharacteristic
701C22×C4C2×D4×C2911yescharacteristic
702C22×C4C2×D4×C2911yescharacteristic
703C22×C4C2×D4×C2911yescharacteristic
704C22×C4C2×D4×C2912yes—
705C22×C4C2×D4×C2911yescharacteristic
706C22×C4C2×D4×C2912yes—
707C22×C4C2×D4×C2911yescharacteristic
708C22×C4C2×D4×C2911yescharacteristic
709C22×C4C2×D4×C2911yescharacteristic
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—22no—
721C4⋊C4—21no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—44no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—24no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—21no—
734C22⋊C4—22no—
735C22⋊C4—21no—
736C22⋊C4—22no—
737C22⋊C4—21no—
738C22⋊C4—22no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—21no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—21no—
748C22⋊C4—44no—
749C22⋊C4—42no—
750C22⋊C4—44no—
751C22⋊C4—42no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—42no—
755C22⋊C4#41×C2912yescomplemented
756C42—22no—
757C42—22no—
758C42—21no—
759C42—21no—
760C42—42no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—21no—
771C23—22no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—44no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C22×D4×C2911yescharacteristic
797C23C22×D4×C2911yescharacteristic
798C23C22×D4×C2911yescharacteristic
799C23C2×#41×C2911yescharacteristic
800C23C2×#41×C2911yescharacteristic
801C23C29×H(5,𝔽2)11yescharacteristic
802C23C29×2−1+411yescharacteristic
803Q8—42no—
804Q8—81no—
805D4—48no—
806D4—42no—
807D4—42no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—42no—
812D4—42no—
813D4—41no—
814D4—42no—
815D4—81no—
816D4—82no—
817D4—82no—
818D4—88no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4C29×#12011yescharacteristic
867C2×C4C29×#12011yescharacteristic
868C2×C4C29×#12011yescharacteristic
869C2×C4C29×#12011yescharacteristic
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—42no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—82no—
903C22—81no—
904C22—82no—
905C22C2×C29×#12011yescharacteristic
906C22C29×#52511yescharacteristic
907C22C29×#53711yescharacteristic
908C22C29×#54611yescharacteristic
909C22C29×#54711yescharacteristic
910C22C29×#54811yescharacteristic
911C22C29×#55011yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—42no—
917C4—41no—
918C4—42no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—42no—
923C4—82no—
924C4—82no—
925C4—81no—
926C4C29×B(4,𝔽2)12yes—
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—44no—
934C2—81no—
935C2—82no—
936C2C29×#240711yescharacteristic
937C2C2×C29×B(4,𝔽2)11yescharacteristic
938C2C29×#302511yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC24C24×C29
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×#3505C2semidirect
2. C29×#2848C2semidirect
3. C29×#2847C2semidirect
4. C4×C29×#120C2semidirect
5. C29×#2044C2semidirect
6. C29×#2021C2semidirect
7. C29×#1996C2semidirect
8. C29×#1964C2semidirect
9. C29×#1889C2semidirect
10. C29×#1867C2semidirect
11. C29×#1799C2semidirect
57. C22×Q8×C29D4semidirect
60. C22×D4×C29D4semidirect
70. C23×C4×C29D4semidirect
126. C2×C4⋊C4×C29D4semidirect
127. C2×C4⋊C4×C29D4semidirect
128. C2×C4⋊C4×C29D4semidirect
129. C2×C4⋊C4×C29D4semidirect
139. C2×C22⋊C4×C29D4semidirect
140. C2×C22⋊C4×C29D4semidirect
148. C2×C42×C29D4semidirect
169. C24×C29#41semidirect
285. C22⋊C4×C29#41semidirect
291. #24140C29direct (N × H)
401. #3505C2×C29semidirect
402. #2848C2×C29semidirect
403. #2847C2×C29semidirect
404. C4×#120C2×C29semidirect
405. #2044C2×C29semidirect
406. #2021C2×C29semidirect
407. #1996C2×C29semidirect
408. #1964C2×C29semidirect
409. #1889C2×C29semidirect
410. #1867C2×C29semidirect
411. #1799C2×C29semidirect
526. C22×Q8D4×C29semidirect
529. C22×D4D4×C29semidirect
539. C23×C4D4×C29semidirect
595. C2×C4⋊C4D4×C29semidirect
596. C2×C4⋊C4D4×C29semidirect
597. C2×C4⋊C4D4×C29semidirect
598. C2×C4⋊C4D4×C29semidirect
608. C2×C22⋊C4D4×C29semidirect
609. C2×C22⋊C4D4×C29semidirect
617. C2×C42D4×C29semidirect
628. C29#24140direct (N × H)
639. C24#41×C29semidirect
755. C22⋊C4#41×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#35052
C29×#28482
C29×#28472
C4×C29×#1202
C29×#20442
C29×#20212
C29×#19962
C29×#19642
C29×#18892
C29×#18672
C29×#17992
#2414029