Finite Group Databasebeta

← C29×#24405 #20319305

Subgroups — C29×#24405 #20319305

Order 7424.

1698 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3484C211yesmaximal, characteristic
2C2×C29×#458C211yesmaximal, characteristic, complemented
3C22×C29×#99C211yesmaximal, characteristic, complemented
4C29×#2412C212yesmaximal, complemented
5C29×#2405C211yesmaximal, characteristic, complemented
6C29×#2044C212yesmaximal, complemented
7C29×#2022C212yesmaximal, complemented
8C29×#1898C212yesmaximal, complemented
9C29×#1890C211yesmaximal, characteristic, complemented
10C29×#1867C211yesmaximal, characteristic, complemented
11C29×#1790C211yesmaximal, characteristic, complemented
12C2×C29×H(5,𝔽2)C2211yescharacteristic
13C23×D4×C29C2211yescharacteristic
14C29×#546—22no—
15C29×#546—22no—
16D42×C29—22no—
17D42×C29—22no—
18C29×#535—21no—
19C29×#534—21no—
20C29×#534C2212yes—
21C29×#525—21no—
22C2×C29×#123C2211yescharacteristic
23C2×C29×#123C2212yescomplemented
24C2×C29×#123C2211yescharacteristic, complemented
25C2×C29×#120—21no—
26C2×C29×#120C2212yes—
27C29×#518C2211yescharacteristic
28C22×C22⋊C4×C29C2211yescharacteristic, complemented
29C22×C22⋊C4×C29C2212yescomplemented
30C29×#458—24no—
31C2×C29×#99—24no—
32C2×C29×#99C2211yescharacteristic
33C2×C29×#99C2211yescharacteristic
34C2×C29×#99C2212yescomplemented
35C2×C29×#99C2212yescomplemented
36C2×C29×#99C2212yescomplemented
37C29×#397—22no—
38C29×#394—21no—
39C29×#394—21no—
40C29×#394—22no—
41C29×#386—22no—
42C29×#386C2211yescharacteristic
43C29×#386C2211yescharacteristic, complemented
44C29×#386C2212yescomplemented
45C29×#385—21no—
46C29×#385C2212yescomplemented
47C29×#381C2212yescomplemented
48C29×#380—22no—
49C29×#379—21no—
50C29×#379C2211yescharacteristic, complemented
51C29×#342C2212yescomplemented
52C29×#342C2212yescomplemented
53C25×C29D411yescharacteristic
54C25×C29C2311yescharacteristic
55C29×H(5,𝔽2)—22no—
56C29×H(5,𝔽2)—22no—
57C29×H(5,𝔽2)—42no—
58C2×#41×C29—21no—
59C2×#41×C29—22no—
60C22×D4×C29—21no—
61C22×D4×C29—22no—
62C22×D4×C29—22no—
63C22×D4×C29—22no—
64C22×D4×C29—21no—
65C22×D4×C29—21no—
66C22×D4×C29—22no—
67C22×D4×C29—22no—
68C22×D4×C29—42no—
69C22×D4×C29D411yescharacteristic
70C22×D4×C29D411yescharacteristic
71C22×D4×C29D412yes—
72C22×D4×C29D412yes—
73C22×D4×C29C2312yes—
74C22×D4×C29C2311yescharacteristic
75C22×D4×C29C2311yescharacteristic
76C23×C4×C29—22no—
77C23×C4×C29D411yescharacteristic
78C23×C4×C29C2311yescharacteristic
79C23×C4×C29C2311yescharacteristic
80C29×#127—22no—
81C29×#124—22no—
82C29×#123—22no—
83C29×#123—22no—
84C29×#123—22no—
85C29×#123—22no—
86C29×#123—22no—
87C29×#123—24no—
88C29×#123—42no—
89C29×#123—42no—
90C29×C22⋊Q8—21no—
91C29×C22⋊Q8—21no—
92C29×#121—21no—
93C29×#121—21no—
94C29×#121—22no—
95C29×#121—22no—
96C29×#121—22no—
97C29×#121—22no—
98C29×#121—22no—
99C29×#121—22no—
100C29×#120—22no—
101C29×#120—22no—
102C29×#120—22no—
103C29×#120—22no—
104C29×#120—22no—
105C29×#120—22no—
106C29×#120—22no—
107C29×#120—22no—
108C29×#120—22no—
109C4×D4×C29—22no—
110C4×D4×C29—22no—
111C4×D4×C29—22no—
112C4×D4×C29—22no—
113C29×#117—21no—
114C2×C4⋊C4×C29—21no—
115C2×C4⋊C4×C29—22no—
116C2×C4⋊C4×C29—21no—
117C2×C4⋊C4×C29—22no—
118C2×C22⋊C4×C29—21no—
119C2×C22⋊C4×C29—21no—
120C2×C22⋊C4×C29—21no—
121C2×C22⋊C4×C29—24no—
122C2×C22⋊C4×C29—21no—
123C2×C22⋊C4×C29—22no—
124C2×C22⋊C4×C29—21no—
125C2×C22⋊C4×C29—22no—
126C2×C22⋊C4×C29—22no—
127C2×C22⋊C4×C29—21no—
128C2×C22⋊C4×C29—21no—
129C2×C22⋊C4×C29—22no—
130C2×C22⋊C4×C29—21no—
131C2×C22⋊C4×C29—21no—
132C2×C22⋊C4×C29—21no—
133C2×C22⋊C4×C29—21no—
134C2×C22⋊C4×C29—22no—
135C2×C22⋊C4×C29—42no—
136C2×C22⋊C4×C29D412yes—
137C2×C22⋊C4×C29D412yes—
138C2×C22⋊C4×C29C2312yes—
139C2×C22⋊C4×C29C2311yescharacteristic
140C2×C22⋊C4×C29C2311yescharacteristic
141C2×C22⋊C4×C29C2312yes—
142C2×C22⋊C4×C29C2312yes—
143C29×#99—22no—
144C29×#99—24no—
145C29×#99—24no—
146C29×#99—42no—
147C29×#99D414yescomplemented
148C29×#95—22no—
149C29×#95—22no—
150C29×#95—22no—
151C29×#95—21no—
152C29×#95—21no—
153C29×#95—22no—
154C24×C29—21no—
155C24×C29—21no—
156C24×C29—22no—
157C24×C29—21no—
158C24×C29—21no—
159C24×C29—21no—
160C24×C29—22no—
161C24×C29—41no—
162C24×C29—42no—
163C24×C29—42no—
164C24×C29—81no—
165C24×C29—81no—
166C24×C29C2×D411yescharacteristic
167C24×C29C2×D412yes—
168C24×C29C2×D411yescharacteristic
169C24×C29C2×D412yes—
170C24×C29C2×D412yes—
171C24×C29C2×D411yescharacteristic
172C24×C29C2×D411yescharacteristic
173C24×C29C2411yescharacteristic
174#41×C29—44no—
175#41×C29—44no—
176#41×C29—42no—
177#41×C29—42no—
178C2×Q8×C29—21no—
179C2×D4×C29—22no—
180C2×D4×C29—22no—
181C2×D4×C29—22no—
182C2×D4×C29—21no—
183C2×D4×C29—22no—
184C2×D4×C29—22no—
185C2×D4×C29—22no—
186C2×D4×C29—22no—
187C2×D4×C29—22no—
188C2×D4×C29—22no—
189C2×D4×C29—22no—
190C2×D4×C29—22no—
191C2×D4×C29—22no—
192C2×D4×C29—21no—
193C2×D4×C29—21no—
194C2×D4×C29—22no—
195C2×D4×C29—22no—
196C2×D4×C29—22no—
197C2×D4×C29—22no—
198C2×D4×C29—22no—
199C2×D4×C29—22no—
200C2×D4×C29—22no—
201C2×D4×C29—22no—
202C2×D4×C29—22no—
203C2×D4×C29—41no—
204C2×D4×C29—41no—
205C2×D4×C29—44no—
206C2×D4×C29—44no—
207C2×D4×C29—44no—
208C2×D4×C29—44no—
209C2×D4×C29—44no—
210C2×D4×C29—44no—
211C2×D4×C29—42no—
212C2×D4×C29—42no—
213C2×D4×C29—44no—
214C2×D4×C29—82no—
215C2×D4×C29—82no—
216C2×D4×C29—82no—
217C2×D4×C29C2×D412yes—
218C2×D4×C29#4112yes—
219C22×C4×C29—21no—
220C22×C4×C29—22no—
221C22×C4×C29—21no—
222C22×C4×C29—21no—
223C22×C4×C29—22no—
224C22×C4×C29—21no—
225C22×C4×C29—21no—
226C22×C4×C29—22no—
227C22×C4×C29—21no—
228C22×C4×C29—21no—
229C22×C4×C29—21no—
230C22×C4×C29—21no—
231C22×C4×C29—22no—
232C22×C4×C29—22no—
233C22×C4×C29—22no—
234C22×C4×C29—21no—
235C22×C4×C29—21no—
236C22×C4×C29—22no—
237C22×C4×C29—41no—
238C22×C4×C29—44no—
239C22×C4×C29—44no—
240C22×C4×C29—81no—
241C22×C4×C29—82no—
242C22×C4×C29C2×D412yes—
243C22×C4×C29C2×D411yescharacteristic
244C22×C4×C29C2×D411yescharacteristic
245C22×C4×C29C2×D412yes—
246C22×C4×C29C2×D412yes—
247C4⋊C4×C29—21no—
248C4⋊C4×C29—21no—
249C4⋊C4×C29—22no—
250C4⋊C4×C29—22no—
251C4⋊C4×C29—44no—
252C4⋊C4×C29—42no—
253C4⋊C4×C29—42no—
254C4⋊C4×C29—82no—
255C22⋊C4×C29—22no—
256C22⋊C4×C29—22no—
257C22⋊C4×C29—22no—
258C22⋊C4×C29—22no—
259C22⋊C4×C29—22no—
260C22⋊C4×C29—22no—
261C22⋊C4×C29—22no—
262C22⋊C4×C29—22no—
263C22⋊C4×C29—22no—
264C22⋊C4×C29—22no—
265C22⋊C4×C29—22no—
266C22⋊C4×C29—22no—
267C22⋊C4×C29—22no—
268C22⋊C4×C29—21no—
269C22⋊C4×C29—21no—
270C22⋊C4×C29—22no—
271C22⋊C4×C29—22no—
272C22⋊C4×C29—44no—
273C22⋊C4×C29—44no—
274C22⋊C4×C29—42no—
275C22⋊C4×C29—42no—
276C22⋊C4×C29—41no—
277C22⋊C4×C29—42no—
278C22⋊C4×C29—41no—
279C22⋊C4×C29—42no—
280C22⋊C4×C29—81no—
281C22⋊C4×C29—81no—
282C22⋊C4×C29—81no—
283C22⋊C4×C29—82no—
284C22⋊C4×C29C2×D414yescomplemented
285C42×C29—22no—
286#24405C2911yesmaximal, characteristic, direct product factor, Sylow
287C23×C29—21no—
288C23×C29—21no—
289C23×C29—21no—
290C23×C29—22no—
291C23×C29—22no—
292C23×C29—22no—
293C23×C29—24no—
294C23×C29—21no—
295C23×C29—21no—
296C23×C29—21no—
297C23×C29—22no—
298C23×C29—22no—
299C23×C29—21no—
300C23×C29—22no—
301C23×C29—21no—
302C23×C29—21no—
303C23×C29—22no—
304C23×C29—22no—
305C23×C29—42no—
306C23×C29—41no—
307C23×C29—41no—
308C23×C29—41no—
309C23×C29—41no—
310C23×C29—42no—
311C23×C29—42no—
312C23×C29—41no—
313C23×C29—42no—
314C23×C29—42no—
315C23×C29—41no—
316C23×C29—41no—
317C23×C29—41no—
318C23×C29—41no—
319C23×C29—42no—
320C23×C29—42no—
321C23×C29—42no—
322C23×C29—42no—
323C23×C29—42no—
324C23×C29—81no—
325C23×C29—81no—
326C23×C29—82no—
327C23×C29—82no—
328C23×C29—84no—
329C23×C29—81no—
330C23×C29—81no—
331C23×C29—84no—
332C23×C29—84no—
333C23×C29#12011yescharacteristic
334C23×C29#12012yes—
335C23×C29#12011yescharacteristic
336C23×C29#12112yes—
337C23×C29C22×D411yescharacteristic
338C23×C29C22×D412yes—
339C23×C29C22×D411yescharacteristic
340C23×C29C2×#4111yescharacteristic
341C23×C29H(5,𝔽2)12yes—
342Q8×C29—42no—
343D4×C29—24no—
344D4×C29—24no—
345D4×C29—44no—
346D4×C29—42no—
347D4×C29—44no—
348D4×C29—44no—
349D4×C29—44no—
350D4×C29—42no—
351D4×C29—42no—
352D4×C29—42no—
353D4×C29—42no—
354D4×C29—42no—
355D4×C29—42no—
356D4×C29—44no—
357D4×C29—82no—
358D4×C29—82no—
359D4×C29—82no—
360D4×C29—82no—
361C2×C4×C29—21no—
362C2×C4×C29—21no—
363C2×C4×C29—22no—
364C2×C4×C29—22no—
365C2×C4×C29—22no—
366C2×C4×C29—21no—
367C2×C4×C29—21no—
368C2×C4×C29—21no—
369C2×C4×C29—24no—
370C2×C4×C29—22no—
371C2×C4×C29—22no—
372C2×C4×C29—42no—
373C2×C4×C29—42no—
374C2×C4×C29—44no—
375C2×C4×C29—42no—
376C2×C4×C29—42no—
377C2×C4×C29—42no—
378C2×C4×C29—42no—
379C2×C4×C29—42no—
380C2×C4×C29—41no—
381C2×C4×C29—41no—
382C2×C4×C29—41no—
383C2×C4×C29—41no—
384C2×C4×C29—42no—
385C2×C4×C29—42no—
386C2×C4×C29—41no—
387C2×C4×C29—41no—
388C2×C4×C29—42no—
389C2×C4×C29—42no—
390C2×C4×C29—41no—
391C2×C4×C29—41no—
392C2×C4×C29—41no—
393C2×C4×C29—41no—
394C2×C4×C29—41no—
395C2×C4×C29—41no—
396C2×C4×C29—42no—
397C2×C4×C29—42no—
398C2×C4×C29—42no—
399C2×C4×C29—81no—
400C2×C4×C29—81no—
401C2×C4×C29—88no—
402C2×C4×C29#12112yes—
403#3484C2×C2911yescharacteristic
404C2×#458C2×C2911yescharacteristic, complemented
405C22×#99C2×C2911yescharacteristic, complemented
406#2412C2×C2912yescomplemented
407#2405C2×C2911yescharacteristic, complemented
408#2044C2×C2912yescomplemented
409#2022C2×C2912yescomplemented
410#1898C2×C2912yescomplemented
411#1890C2×C2911yescharacteristic, complemented
412#1867C2×C2911yescharacteristic, complemented
413#1790C2×C2911yescharacteristic, complemented
414C22×C29—21no—
415C22×C29—22no—
416C22×C29—21no—
417C22×C29—22no—
418C22×C29—21no—
419C22×C29—21no—
420C22×C29—21no—
421C22×C29—22no—
422C22×C29—22no—
423C22×C29—22no—
424C22×C29—21no—
425C22×C29—21no—
426C22×C29—22no—
427C22×C29—41no—
428C22×C29—41no—
429C22×C29—42no—
430C22×C29—44no—
431C22×C29—44no—
432C22×C29—42no—
433C22×C29—42no—
434C22×C29—42no—
435C22×C29—42no—
436C22×C29—41no—
437C22×C29—41no—
438C22×C29—42no—
439C22×C29—41no—
440C22×C29—42no—
441C22×C29—41no—
442C22×C29—42no—
443C22×C29—41no—
444C22×C29—82no—
445C22×C29—81no—
446C22×C29—81no—
447C22×C29—81no—
448C22×C29—82no—
449C22×C29—84no—
450C22×C29—82no—
451C22×C29—82no—
452C22×C29—81no—
453C22×C29—84no—
454C22×C29—162no—
455C22×C29#45812yescomplemented
456C22×C29C2×#12011yescharacteristic
457C22×C29C2×#12111yescharacteristic
458C22×C29#53411yescharacteristic
459C22×C29D4212yes—
460C22×C29#54612yes—
461C4×C29—22no—
462C4×C29—44no—
463C4×C29—41no—
464C4×C29—42no—
465C4×C29—42no—
466C4×C29—42no—
467C4×C29—81no—
468C4×C29—81no—
469C4×C29—82no—
470C4×C29—81no—
471C4×C29—81no—
472C2×H(5,𝔽2)C22×C2911yescharacteristic
473C23×D4C22×C2911yescharacteristic
474#546—22no—
475#546—22no—
476D42—22no—
477D42—22no—
478#535—21no—
479#534—21no—
480#534C22×C2912yes—
481#525—21no—
482C2×#123C22×C2911yescharacteristic
483C2×#123C22×C2912yescomplemented
484C2×#123C22×C2911yescharacteristic, complemented
485C2×#120—21no—
486C2×#120C22×C2912yes—
487#518C22×C2911yescharacteristic
488C22×C22⋊C4C22×C2911yescharacteristic, complemented
489C22×C22⋊C4C22×C2912yescomplemented
490#458—24no—
491C2×#99—24no—
492C2×#99C22×C2911yescharacteristic
493C2×#99C22×C2911yescharacteristic
494C2×#99C22×C2912yescomplemented
495C2×#99C22×C2912yescomplemented
496C2×#99C22×C2912yescomplemented
497#397—22no—
498#394—21no—
499#394—21no—
500#394—22no—
501#386—22no—
502#386C22×C2911yescharacteristic
503#386C22×C2911yescharacteristic, complemented
504#386C22×C2912yescomplemented
505#385—21no—
506#385C22×C2912yescomplemented
507#381C22×C2912yescomplemented
508#380—22no—
509#379—21no—
510#379C22×C2911yescharacteristic, complemented
511#342C22×C2912yescomplemented
512#342C22×C2912yescomplemented
513C2×C29—22no—
514C2×C29—21no—
515C2×C29—21no—
516C2×C29—22no—
517C2×C29—22no—
518C2×C29—42no—
519C2×C29—41no—
520C2×C29—42no—
521C2×C29—81no—
522C2×C29—82no—
523C2×C29#241011yescharacteristic
524C2×C29C2×#45811yescharacteristic
525C2×C29#302611yescharacteristic
526C25D4×C2911yescharacteristic
527C25C23×C2911yescharacteristic
528H(5,𝔽2)—22no—
529H(5,𝔽2)—22no—
530H(5,𝔽2)—42no—
531C2×#41—21no—
532C2×#41—22no—
533C22×D4—21no—
534C22×D4—22no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—42no—
542C22×D4D4×C2911yescharacteristic
543C22×D4D4×C2911yescharacteristic
544C22×D4D4×C2912yes—
545C22×D4D4×C2912yes—
546C22×D4C23×C2912yes—
547C22×D4C23×C2911yescharacteristic
548C22×D4C23×C2911yescharacteristic
549C23×C4—22no—
550C23×C4D4×C2911yescharacteristic
551C23×C4C23×C2911yescharacteristic
552C23×C4C23×C2911yescharacteristic
553#127—22no—
554#124—22no—
555#123—22no—
556#123—22no—
557#123—22no—
558#123—22no—
559#123—22no—
560#123—24no—
561#123—42no—
562#123—42no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565#121—21no—
566#121—21no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#120—22no—
574#120—22no—
575#120—22no—
576#120—22no—
577#120—22no—
578#120—22no—
579#120—22no—
580#120—22no—
581#120—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586#117—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—22no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—24no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—42no—
609C2×C22⋊C4D4×C2912yes—
610C2×C22⋊C4D4×C2912yes—
611C2×C22⋊C4C23×C2912yes—
612C2×C22⋊C4C23×C2911yescharacteristic
613C2×C22⋊C4C23×C2911yescharacteristic
614C2×C22⋊C4C23×C2912yes—
615C2×C22⋊C4C23×C2912yes—
616#99—22no—
617#99—24no—
618#99—24no—
619#99—42no—
620#99D4×C2914yescomplemented
621#95—22no—
622#95—22no—
623#95—22no—
624#95—21no—
625#95—21no—
626#95—22no—
627C29#2440511yescharacteristic, direct product factor, Sylow
628C24—21no—
629C24—21no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—41no—
636C24—42no—
637C24—42no—
638C24—81no—
639C24—81no—
640C24C2×D4×C2911yescharacteristic
641C24C2×D4×C2912yes—
642C24C2×D4×C2911yescharacteristic
643C24C2×D4×C2912yes—
644C24C2×D4×C2912yes—
645C24C2×D4×C2911yescharacteristic
646C24C2×D4×C2911yescharacteristic
647C24C24×C2911yescharacteristic
648#41—44no—
649#41—44no—
650#41—42no—
651#41—42no—
652C2×Q8—21no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4C2×D4×C2912yes—
692C2×D4#41×C2912yes—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—41no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—81no—
715C22×C4—82no—
716C22×C4C2×D4×C2912yes—
717C22×C4C2×D4×C2911yescharacteristic
718C22×C4C2×D4×C2911yescharacteristic
719C22×C4C2×D4×C2912yes—
720C22×C4C2×D4×C2912yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—44no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—82no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—41no—
753C22⋊C4—42no—
754C22⋊C4—81no—
755C22⋊C4—81no—
756C22⋊C4—81no—
757C22⋊C4—82no—
758C22⋊C4C2×D4×C2914yescomplemented
759C42—22no—
760C23—22no—
761C23—24no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—22no—
777C23—22no—
778C23—42no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23—81no—
799C23—82no—
800C23—82no—
801C23—84no—
802C23—81no—
803C23—81no—
804C23—84no—
805C23—84no—
806C23C29×#12011yescharacteristic
807C23C29×#12012yes—
808C23C29×#12011yescharacteristic
809C23C29×#12112yes—
810C23C22×D4×C2911yescharacteristic
811C23C22×D4×C2912yes—
812C23C22×D4×C2911yescharacteristic
813C23C2×#41×C2911yescharacteristic
814C23C29×H(5,𝔽2)12yes—
815Q8—42no—
816D4—24no—
817D4—24no—
818D4—44no—
819D4—42no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—42no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—82no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—88no—
875C2×C4C29×#12112yes—
876C22—22no—
877C22—21no—
878C22—22no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—22no—
883C22—21no—
884C22—21no—
885C22—22no—
886C22—21no—
887C22—22no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—82no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—82no—
911C22—84no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—162no—
917C22C29×#45812yescomplemented
918C22C2×C29×#12011yescharacteristic
919C22C2×C29×#12111yescharacteristic
920C22C29×#53411yescharacteristic
921C22D42×C2912yes—
922C22C29×#54612yes—
923C4—22no—
924C4—44no—
925C4—42no—
926C4—42no—
927C4—41no—
928C4—42no—
929C4—82no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C2—22no—
935C2—21no—
936C2—21no—
937C2—22no—
938C2—22no—
939C2—41no—
940C2—42no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C29×#241011yescharacteristic
945C2C2×C29×#45811yescharacteristic
946C2C29×#302611yescharacteristic
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. C2×C29×#458C2semidirect
3. C22×C29×#99C2semidirect
4. C29×#2412C2semidirect
5. C29×#2405C2semidirect
6. C29×#2044C2semidirect
7. C29×#2022C2semidirect
8. C29×#1898C2semidirect
9. C29×#1890C2semidirect
10. C29×#1867C2semidirect
11. C29×#1790C2semidirect
23. C2×C29×#123C22semidirect
24. C2×C29×#123C22semidirect
28. C22×C22⋊C4×C29C22semidirect
29. C22×C22⋊C4×C29C22semidirect
34. C2×C29×#99C22semidirect
35. C2×C29×#99C22semidirect
36. C2×C29×#99C22semidirect
43. C29×#386C22semidirect
44. C29×#386C22semidirect
46. C29×#385C22semidirect
47. C29×#381C22semidirect
50. C29×#379C22semidirect
51. C29×#342C22semidirect
52. C29×#342C22semidirect
147. C29×#99D4semidirect
284. C22⋊C4×C29C2×D4semidirect
286. #24405C29direct (N × H)
404. C2×#458C2×C29semidirect
405. C22×#99C2×C29semidirect
406. #2412C2×C29semidirect
407. #2405C2×C29semidirect
408. #2044C2×C29semidirect
409. #2022C2×C29semidirect
410. #1898C2×C29semidirect
411. #1890C2×C29semidirect
412. #1867C2×C29semidirect
413. #1790C2×C29semidirect
455. C22×C29#458semidirect
483. C2×#123C22×C29semidirect
484. C2×#123C22×C29semidirect
488. C22×C22⋊C4C22×C29semidirect
489. C22×C22⋊C4C22×C29semidirect
494. C2×#99C22×C29semidirect
495. C2×#99C22×C29semidirect
496. C2×#99C22×C29semidirect
503. #386C22×C29semidirect
504. #386C22×C29semidirect
506. #385C22×C29semidirect
507. #381C22×C29semidirect
510. #379C22×C29semidirect
511. #342C22×C29semidirect
512. #342C22×C29semidirect
620. #99D4×C29semidirect
627. C29#24405direct (N × H)
758. C22⋊C4C2×D4×C29semidirect
917. C22C29×#458semidirect

Maximal subgroups

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

subgroupindex
C29×#34842
C2×C29×#4582
C22×C29×#992
C29×#24122
C29×#24052
C29×#20442
C29×#20222
C29×#18982
C29×#18902
C29×#18672
C29×#17902
#2440529