Finite Group Databasebeta

← C29×#19041 #20313941

Subgroups — C29×#19041 #20313941

Order 7424.

838 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3567C211yesmaximal, characteristic
2C29×#3240C211yesmaximal, characteristic, complemented
3C29×#3181C211yesmaximal, characteristic, complemented
4C29×#3172C211yesmaximal, characteristic, complemented
5C29×#1663C211yesmaximal, characteristic, complemented
6C29×#1663C211yesmaximal, characteristic, complemented
7C29×#1662C211yesmaximal, characteristic, complemented
8C29×#1662C211yesmaximal, characteristic, complemented
9C29×#1661C211yesmaximal, characteristic, complemented
10C29×#1661C211yesmaximal, characteristic, complemented
11C29×#1661C211yesmaximal, characteristic, complemented
12C29×#1661C211yesmaximal, characteristic, complemented
13C29×#1532C211yesmaximal, characteristic, complemented
14C29×#1529C211yesmaximal, characteristic, complemented
15C29×#1524C211yesmaximal, characteristic, complemented
16C29×#564C2211yescharacteristic
17C29×#562C2211yescharacteristic
18C29×#562C2211yescharacteristic
19C29×#562C2211yescharacteristic
20C29×#553—21no—
21C29×#553—21no—
22C29×#553—21no—
23C29×#552—21no—
24C29×#552—21no—
25C29×#552—21no—
26C29×#540—21no—
27C29×#540—21no—
28C29×#540—21no—
29C29×#539—21no—
30C29×#539—21no—
31C29×#539—21no—
32C29×#533C2211yescharacteristic
33C29×#529C2211yescharacteristic
34C29×#529C2211yescharacteristic
35C29×#529C2211yescharacteristic
36C29×#501C2211yescharacteristic
37C29×#501C2211yescharacteristic
38C29×#501C2211yescharacteristic
39C29×#501C2211yescharacteristic
40C29×#497C2211yescharacteristic
41C29×#497C2211yescharacteristic
42C29×#491C2211yescharacteristic
43C29×#491C2211yescharacteristic
44C29×#489C2211yescharacteristic
45C29×#489C2211yescharacteristic
46C29×#489C2211yescharacteristic
47C29×#489C2211yescharacteristic
48C29×#485—21no—
49C29×#482—21no—
50C29×#479—21no—
51C29×#478—21no—
52C29×#470—21no—
53C29×#468—21no—
54C29×#467—21no—
55C29×#465—21no—
56C29×#441—21no—
57C29×#440—21no—
58C4×Q16×C29—21no—
59C4×SD16×C29—21no—
60C29×#432C2211yescharacteristic
61C4×M16×C29C2211yescharacteristic
62C2×C29×#97C2211yescharacteristic
63C29×#330C2211yescharacteristic
64C29×#330C2211yescharacteristic
65C29×#330C2211yescharacteristic
66C29×#330C2211yescharacteristic
67C29×#330C2211yescharacteristic
68C29×#330C2211yescharacteristic
69C29×#329C2211yescharacteristic
70C29×#329C2211yescharacteristic
71C29×#329C2211yescharacteristic
72C29×#329C2211yescharacteristic
73C29×#329C2211yescharacteristic
74C29×#329C2211yescharacteristic
75C2×Q16×C29—21no—
76C2×Q16×C29—21no—
77C2×SD16×C29—21no—
78C2×SD16×C29—21no—
79C2×M16×C29—21no—
80C22×C8×C29—21no—
81C29×C4⋊Q8C2311yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×#127—21no—
84C29×#126—21no—
85C29×#126—21no—
86C29×#126—21no—
87C29×#126—21no—
88C29×#126—21no—
89C29×#126—21no—
90C29×#126—21no—
91C29×#125—21no—
92C29×#125—21no—
93C29×#125—21no—
94C29×#125—21no—
95C29×#125—21no—
96C29×#125—21no—
97C29×#125—21no—
98C29×#125—21no—
99C29×#125—21no—
100C29×#125—21no—
101C29×#125C2311yescharacteristic
102C29×#125C2311yescharacteristic
103C29×#125C2311yescharacteristic
104C29×#124C2311yescharacteristic
105C29×#124C2311yescharacteristic
106C29×#124C2311yescharacteristic
107C29×#123—21no—
108C29×#123—21no—
109C29×#123—21no—
110C29×#123—21no—
111C29×#123—21no—
112C29×#123—21no—
113C29×#123—21no—
114C29×#123—21no—
115C29×#123—21no—
116C29×#123—21no—
117C29×#123—21no—
118C29×#123—21no—
119C29×#123—21no—
120C29×#123—21no—
121C29×#123—21no—
122C29×C22⋊Q8—21no—
123C29×C22⋊Q8—21no—
124C29×C22⋊Q8—21no—
125C29×C22⋊Q8—21no—
126C29×C22⋊Q8—21no—
127C29×C22⋊Q8—21no—
128C29×C22⋊Q8—21no—
129C29×C22⋊Q8—21no—
130C29×C22⋊Q8D411yescharacteristic
131C29×C22⋊Q8D411yescharacteristic
132C29×C22⋊Q8D411yescharacteristic
133C29×#121—21no—
134C29×#121—21no—
135C29×#121—21no—
136C29×#121—21no—
137C29×#121—21no—
138C29×#121—21no—
139C29×#121—21no—
140C29×#121—21no—
141C29×#121—21no—
142C29×#121—21no—
143C29×#121—21no—
144C29×#121—21no—
145C29×#121D411yescharacteristic
146C29×#121D411yescharacteristic
147C29×#121D411yescharacteristic
148C4×Q8×C29—21no—
149C4×Q8×C29—21no—
150C4×Q8×C29D411yescharacteristic
151C4×Q8×C29D411yescharacteristic
152C4×Q8×C29D411yescharacteristic
153C4×D4×C29—21no—
154C4×D4×C29—21no—
155C4×D4×C29—21no—
156C4×D4×C29—21no—
157C4×D4×C29—21no—
158C4×D4×C29—21no—
159C4×D4×C29—21no—
160C4×D4×C29—21no—
161C4×D4×C29—21no—
162C4×D4×C29D411yescharacteristic
163C4×D4×C29D411yescharacteristic
164C4×D4×C29D411yescharacteristic
165C29×#117—21no—
166C29×#117—21no—
167C29×#117—21no—
168C29×#117—21no—
169C29×#117—21no—
170C29×#117—21no—
171C29×#117—21no—
172C2×C4⋊C4×C29—21no—
173C2×C4⋊C4×C29—21no—
174C2×C4⋊C4×C29—21no—
175C2×C42×C29C2311yescharacteristic
176C29×#107—21no—
177C29×#107—21no—
178C29×#107—21no—
179C29×#107—21no—
180C29×#106—21no—
181C29×#106—21no—
182C29×#106—21no—
183C29×#106—21no—
184C29×C4⋊C8—21no—
185C29×#103—21no—
186C29×#103—21no—
187C29×#103—21no—
188C29×#103—21no—
189C29×#103—21no—
190C29×#103—21no—
191C29×#103—21no—
192C29×#103—21no—
193C29×#102—21no—
194C29×#102—21no—
195C29×#102—21no—
196C29×#102—21no—
197C29×C22⋊C8—21no—
198C29×#97—21no—
199C29×#97C2311yescharacteristic
200C29×#97C2311yescharacteristic
201C29×#97C2311yescharacteristic
202C29×#97C2311yescharacteristic
203C29×#97C2311yescharacteristic
204C29×#97C2311yescharacteristic
205C4×C8×C29—21no—
206C2×Q8×C29—21no—
207C2×Q8×C29—21no—
208C2×Q8×C29C2×D411yescharacteristic
209C2×Q8×C29C2×D411yescharacteristic
210C2×Q8×C29C2×D411yescharacteristic
211C2×D4×C29—21no—
212C2×D4×C29—21no—
213C2×D4×C29—21no—
214C2×D4×C29—21no—
215C2×D4×C29—21no—
216C2×D4×C29—21no—
217C2×D4×C29—21no—
218C2×D4×C29—21no—
219C2×D4×C29—21no—
220C2×D4×C29C2×D411yescharacteristic
221C2×D4×C29C2×D411yescharacteristic
222C2×D4×C29C2×D411yescharacteristic
223C22×C4×C29—21no—
224C22×C4×C29—21no—
225C22×C4×C29—21no—
226C22×C4×C29—21no—
227C22×C4×C29—21no—
228C22×C4×C29—21no—
229C22×C4×C29—21no—
230C22×C4×C29—21no—
231C22×C4×C29—21no—
232C22×C4×C29C2×D411yescharacteristic
233C22×C4×C29C2×D411yescharacteristic
234C22×C4×C29C2×D411yescharacteristic
235Q16×C29—42no—
236Q16×C29—42no—
237SD16×C29—42no—
238SD16×C29—42no—
239M16×C29—42no—
240C2×C8×C29—21no—
241C2×C8×C29—21no—
242C2×C8×C29—21no—
243C2×C8×C29—21no—
244C2×C8×C29—21no—
245C2×C8×C29—21no—
246C2×C8×C29—42no—
247C4⋊C4×C29—21no—
248C4⋊C4×C29—21no—
249C4⋊C4×C29—21no—
250C4⋊C4×C29—21no—
251C4⋊C4×C29—21no—
252C4⋊C4×C29—21no—
253C4⋊C4×C29—21no—
254C4⋊C4×C29—21no—
255C4⋊C4×C29—21no—
256C4⋊C4×C29—21no—
257C4⋊C4×C29—21no—
258C4⋊C4×C29—21no—
259C4⋊C4×C29—21no—
260C4⋊C4×C29—21no—
261C4⋊C4×C29—21no—
262C4⋊C4×C29—21no—
263C4⋊C4×C29—21no—
264C4⋊C4×C29—21no—
265C4⋊C4×C29—21no—
266C4⋊C4×C29—21no—
267C4⋊C4×C29—21no—
268C4⋊C4×C29—21no—
269C4⋊C4×C29—21no—
270C4⋊C4×C29—21no—
271C4⋊C4×C29—21no—
272C4⋊C4×C29—21no—
273C4⋊C4×C29—21no—
274C4⋊C4×C29—21no—
275C4⋊C4×C29—41no—
276C4⋊C4×C29—41no—
277C4⋊C4×C29C2×D411yescharacteristic
278C4⋊C4×C29C2×D411yescharacteristic
279C4⋊C4×C29C2×D411yescharacteristic
280C4⋊C4×C29C2×D411yescharacteristic
281C4⋊C4×C29C2×D411yescharacteristic
282C4⋊C4×C29C2×D411yescharacteristic
283C22⋊C4×C29—21no—
284C22⋊C4×C29—21no—
285C22⋊C4×C29—21no—
286C22⋊C4×C29—21no—
287C22⋊C4×C29—21no—
288C22⋊C4×C29—21no—
289C22⋊C4×C29—21no—
290C22⋊C4×C29—21no—
291C22⋊C4×C29—21no—
292C22⋊C4×C29—21no—
293C22⋊C4×C29—21no—
294C22⋊C4×C29—21no—
295C22⋊C4×C29—21no—
296C22⋊C4×C29—21no—
297C22⋊C4×C29—21no—
298C22⋊C4×C29—21no—
299C22⋊C4×C29—21no—
300C22⋊C4×C29—21no—
301C22⋊C4×C29—21no—
302C22⋊C4×C29—21no—
303C22⋊C4×C29—21no—
304C22⋊C4×C29—41no—
305C42×C29—21no—
306C42×C29—21no—
307C42×C29—21no—
308C42×C29—21no—
309C42×C29—21no—
310C42×C29—41no—
311C42×C29C2×D411yescharacteristic
312C42×C29C2×D411yescharacteristic
313C42×C29C2×D411yescharacteristic
314C42×C29C2411yescharacteristic
315#19041C2911yesmaximal, characteristic, direct product factor, Sylow
316C23×C29—21no—
317C23×C29—21no—
318C23×C29—21no—
319C23×C29#12011yescharacteristic
320Q8×C29—41no—
321Q8×C29—41no—
322Q8×C29—41no—
323Q8×C29—41no—
324Q8×C29—41no—
325Q8×C29—41no—
326Q8×C29—41no—
327D4×C29—41no—
328D4×C29—41no—
329D4×C29—41no—
330D4×C29—81no—
331D4×C29—81no—
332D4×C29—81no—
333D4×C29—81no—
334D4×C29—81no—
335D4×C29—81no—
336D4×C29—81no—
337D4×C29—81no—
338D4×C29—81no—
339C2×C4×C29—21no—
340C2×C4×C29—21no—
341C2×C4×C29—21no—
342C2×C4×C29—21no—
343C2×C4×C29—21no—
344C2×C4×C29—21no—
345C2×C4×C29—21no—
346C2×C4×C29—21no—
347C2×C4×C29—21no—
348C2×C4×C29—41no—
349C2×C4×C29—41no—
350C2×C4×C29—41no—
351C2×C4×C29—41no—
352C2×C4×C29—41no—
353C2×C4×C29—81no—
354C2×C4×C29—81no—
355C2×C4×C29—81no—
356C2×C4×C29—81no—
357C2×C4×C29—81no—
358C2×C4×C29—81no—
359C2×C4×C29—81no—
360C2×C4×C29—81no—
361C2×C4×C29—81no—
362C2×C4×C29#12011yescharacteristic
363C2×C4×C29#12011yescharacteristic
364C2×C4×C29#12011yescharacteristic
365C2×C4×C29C22×D411yescharacteristic
366C2×C4×C29C22×D411yescharacteristic
367C2×C4×C29C22×D411yescharacteristic
368C8×C29—22no—
369C8×C29—22no—
370C8×C29—41no—
371C8×C29—41no—
372C8×C29—41no—
373C8×C29—41no—
374#3567C2×C2911yescharacteristic
375#3240C2×C2911yescharacteristic, complemented
376#3181C2×C2911yescharacteristic, complemented
377#3172C2×C2911yescharacteristic, complemented
378#1663C2×C2911yescharacteristic, complemented
379#1663C2×C2911yescharacteristic, complemented
380#1662C2×C2911yescharacteristic, complemented
381#1662C2×C2911yescharacteristic, complemented
382#1661C2×C2911yescharacteristic, complemented
383#1661C2×C2911yescharacteristic, complemented
384#1661C2×C2911yescharacteristic, complemented
385#1661C2×C2911yescharacteristic, complemented
386#1532C2×C2911yescharacteristic, complemented
387#1529C2×C2911yescharacteristic, complemented
388#1524C2×C2911yescharacteristic, complemented
389C22×C29—21no—
390C22×C29—21no—
391C22×C29—21no—
392C22×C29—41no—
393C22×C29—41no—
394C22×C29—41no—
395C22×C29—41no—
396C22×C29—41no—
397C22×C29—41no—
398C22×C29—41no—
399C22×C29—41no—
400C22×C29—41no—
401C22×C29C2×#12011yescharacteristic
402C4×C29—21no—
403C4×C29—21no—
404C4×C29—21no—
405C4×C29—21no—
406C4×C29—21no—
407C4×C29—21no—
408C4×C29—41no—
409C4×C29—41no—
410C4×C29—41no—
411C4×C29—41no—
412C4×C29—41no—
413C4×C29—41no—
414C4×C29—41no—
415C4×C29—41no—
416C4×C29—41no—
417C4×C29—81no—
418C4×C29—81no—
419#564C22×C2911yescharacteristic
420#562C22×C2911yescharacteristic
421#562C22×C2911yescharacteristic
422#562C22×C2911yescharacteristic
423#553—21no—
424#553—21no—
425#553—21no—
426#552—21no—
427#552—21no—
428#552—21no—
429#540—21no—
430#540—21no—
431#540—21no—
432#539—21no—
433#539—21no—
434#539—21no—
435#533C22×C2911yescharacteristic
436#529C22×C2911yescharacteristic
437#529C22×C2911yescharacteristic
438#529C22×C2911yescharacteristic
439#501C22×C2911yescharacteristic
440#501C22×C2911yescharacteristic
441#501C22×C2911yescharacteristic
442#501C22×C2911yescharacteristic
443#497C22×C2911yescharacteristic
444#497C22×C2911yescharacteristic
445#491C22×C2911yescharacteristic
446#491C22×C2911yescharacteristic
447#489C22×C2911yescharacteristic
448#489C22×C2911yescharacteristic
449#489C22×C2911yescharacteristic
450#489C22×C2911yescharacteristic
451#485—21no—
452#482—21no—
453#479—21no—
454#478—21no—
455#470—21no—
456#468—21no—
457#467—21no—
458#465—21no—
459#441—21no—
460#440—21no—
461C4×Q16—21no—
462C4×SD16—21no—
463#432C22×C2911yescharacteristic
464C4×M16C22×C2911yescharacteristic
465C2×#97C22×C2911yescharacteristic
466#330C22×C2911yescharacteristic
467#330C22×C2911yescharacteristic
468#330C22×C2911yescharacteristic
469#330C22×C2911yescharacteristic
470#330C22×C2911yescharacteristic
471#330C22×C2911yescharacteristic
472#329C22×C2911yescharacteristic
473#329C22×C2911yescharacteristic
474#329C22×C2911yescharacteristic
475#329C22×C2911yescharacteristic
476#329C22×C2911yescharacteristic
477#329C22×C2911yescharacteristic
478C2×C29—41no—
479C2×C29—81no—
480C2×C29—81no—
481C2×C29—81no—
482C2×C29#301811yescharacteristic
483C2×C29#301811yescharacteristic
484C2×C29#302211yescharacteristic
485C2×Q16—21no—
486C2×Q16—21no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×M16—21no—
490C22×C8—21no—
491C4⋊Q8C23×C2911yescharacteristic
492C4⋊Q8C23×C2911yescharacteristic
493#127—21no—
494#126—21no—
495#126—21no—
496#126—21no—
497#126—21no—
498#126—21no—
499#126—21no—
500#126—21no—
501#125—21no—
502#125—21no—
503#125—21no—
504#125—21no—
505#125—21no—
506#125—21no—
507#125—21no—
508#125—21no—
509#125—21no—
510#125—21no—
511#125C23×C2911yescharacteristic
512#125C23×C2911yescharacteristic
513#125C23×C2911yescharacteristic
514#124C23×C2911yescharacteristic
515#124C23×C2911yescharacteristic
516#124C23×C2911yescharacteristic
517#123—21no—
518#123—21no—
519#123—21no—
520#123—21no—
521#123—21no—
522#123—21no—
523#123—21no—
524#123—21no—
525#123—21no—
526#123—21no—
527#123—21no—
528#123—21no—
529#123—21no—
530#123—21no—
531#123—21no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540C22⋊Q8D4×C2911yescharacteristic
541C22⋊Q8D4×C2911yescharacteristic
542C22⋊Q8D4×C2911yescharacteristic
543#121—21no—
544#121—21no—
545#121—21no—
546#121—21no—
547#121—21no—
548#121—21no—
549#121—21no—
550#121—21no—
551#121—21no—
552#121—21no—
553#121—21no—
554#121—21no—
555#121D4×C2911yescharacteristic
556#121D4×C2911yescharacteristic
557#121D4×C2911yescharacteristic
558C4×Q8—21no—
559C4×Q8—21no—
560C4×Q8D4×C2911yescharacteristic
561C4×Q8D4×C2911yescharacteristic
562C4×Q8D4×C2911yescharacteristic
563C4×D4—21no—
564C4×D4—21no—
565C4×D4—21no—
566C4×D4—21no—
567C4×D4—21no—
568C4×D4—21no—
569C4×D4—21no—
570C4×D4—21no—
571C4×D4—21no—
572C4×D4D4×C2911yescharacteristic
573C4×D4D4×C2911yescharacteristic
574C4×D4D4×C2911yescharacteristic
575#117—21no—
576#117—21no—
577#117—21no—
578#117—21no—
579#117—21no—
580#117—21no—
581#117—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C42C23×C2911yescharacteristic
586#107—21no—
587#107—21no—
588#107—21no—
589#107—21no—
590#106—21no—
591#106—21no—
592#106—21no—
593#106—21no—
594C4⋊C8—21no—
595#103—21no—
596#103—21no—
597#103—21no—
598#103—21no—
599#103—21no—
600#103—21no—
601#103—21no—
602#103—21no—
603#102—21no—
604#102—21no—
605#102—21no—
606#102—21no—
607C22⋊C8—21no—
608#97—21no—
609#97C23×C2911yescharacteristic
610#97C23×C2911yescharacteristic
611#97C23×C2911yescharacteristic
612#97C23×C2911yescharacteristic
613#97C23×C2911yescharacteristic
614#97C23×C2911yescharacteristic
615C4×C8—21no—
616C29#1904111yescharacteristic, direct product factor, Sylow
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8C2×D4×C2911yescharacteristic
620C2×Q8C2×D4×C2911yescharacteristic
621C2×Q8C2×D4×C2911yescharacteristic
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4C2×D4×C2911yescharacteristic
632C2×D4C2×D4×C2911yescharacteristic
633C2×D4C2×D4×C2911yescharacteristic
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4C2×D4×C2911yescharacteristic
644C22×C4C2×D4×C2911yescharacteristic
645C22×C4C2×D4×C2911yescharacteristic
646Q16—42no—
647Q16—42no—
648SD16—42no—
649SD16—42no—
650M16—42no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—42no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—41no—
687C4⋊C4—41no—
688C4⋊C4C2×D4×C2911yescharacteristic
689C4⋊C4C2×D4×C2911yescharacteristic
690C4⋊C4C2×D4×C2911yescharacteristic
691C4⋊C4C2×D4×C2911yescharacteristic
692C4⋊C4C2×D4×C2911yescharacteristic
693C4⋊C4C2×D4×C2911yescharacteristic
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—21no—
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—41no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—41no—
722C42C2×D4×C2911yescharacteristic
723C42C2×D4×C2911yescharacteristic
724C42C2×D4×C2911yescharacteristic
725C42C24×C2911yescharacteristic
726C23—21no—
727C23—21no—
728C23—21no—
729C23C29×#12011yescharacteristic
730Q8—41no—
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735Q8—41no—
736Q8—41no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—81no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4C29×#12011yescharacteristic
773C2×C4C29×#12011yescharacteristic
774C2×C4C29×#12011yescharacteristic
775C2×C4C22×D4×C2911yescharacteristic
776C2×C4C22×D4×C2911yescharacteristic
777C2×C4C22×D4×C2911yescharacteristic
778C8—22no—
779C8—22no—
780C8—41no—
781C8—41no—
782C8—41no—
783C8—41no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22C2×C29×#12011yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—81no—
813C4—81no—
814C2—41no—
815C2—81no—
816C2—81no—
817C2—81no—
818C2C29×#301811yescharacteristic
819C2C29×#301811yescharacteristic
820C2C29×#302211yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3567C2
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×#3240C2semidirect
3. C29×#3181C2semidirect
4. C29×#3172C2semidirect
5. C29×#1663C2semidirect
6. C29×#1663C2semidirect
7. C29×#1662C2semidirect
8. C29×#1662C2semidirect
9. C29×#1661C2semidirect
10. C29×#1661C2semidirect
11. C29×#1661C2semidirect
12. C29×#1661C2semidirect
13. C29×#1532C2semidirect
14. C29×#1529C2semidirect
15. C29×#1524C2semidirect
315. #19041C29direct (N × H)
375. #3240C2×C29semidirect
376. #3181C2×C29semidirect
377. #3172C2×C29semidirect
378. #1663C2×C29semidirect
379. #1663C2×C29semidirect
380. #1662C2×C29semidirect
381. #1662C2×C29semidirect
382. #1661C2×C29semidirect
383. #1661C2×C29semidirect
384. #1661C2×C29semidirect
385. #1661C2×C29semidirect
386. #1532C2×C29semidirect
387. #1529C2×C29semidirect
388. #1524C2×C29semidirect
616. C29#19041direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35672
C29×#32402
C29×#31812
C29×#31722
C29×#16632
C29×#16622
C29×#16612
C29×#15322
C29×#15292
C29×#15242
#1904129