Finite Group Databasebeta

← C29×#25665 #20320565

Subgroups — C29×#25665 #20320565

Order 7424.

1136 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3505C211yesmaximal, characteristic
2C29×#2591C211yesmaximal, characteristic, complemented
3C29×#2583C211yesmaximal, characteristic, complemented
4C29×#2579C211yesmaximal, characteristic, complemented
5C29×#2044C212yesmaximal, complemented
6C29×#2044C212yesmaximal, complemented
7C29×#1996C211yesmaximal, characteristic, complemented
8C29×#1964C211yesmaximal, characteristic, complemented
9C29×#1867C212yesmaximal, complemented
10C29×#1867C212yesmaximal, complemented
11C4×C29×#99C211yesmaximal, characteristic, complemented
12C29×#553—22no—
13C29×#553—21no—
14C29×#552—21no—
15C29×#551—22no—
16C29×#548—21no—
17C29×#546—21no—
18C29×#539—21no—
19C29×#538—21no—
20C29×#534C2212yes—
21C29×#529—21no—
22C29×#525—21no—
23C2×C29×C22⋊Q8C2211yescharacteristic
24C2×C29×#121C2211yescharacteristic
25C29×#518C2212yes—
26C2×C4×D4×C29C2211yescharacteristic
27C22×C4⋊C4×C29C2211yescharacteristic
28C2×C29×#99C2212yes—
29C2×C29×#99C2212yes—
30C2×C29×#99C2212yes—
31C29×#400—21no—
32C29×#398—21no—
33C29×#398—21no—
34C29×#396—21no—
35C29×#395—21no—
36C29×#394—21no—
37C29×#389—22no—
38C29×#388—22no—
39C29×#387—21no—
40C29×#386C2211yescharacteristic
41C29×#386C2211yescharacteristic
42C29×#386C2212yes—
43C29×#386C2212yes—
44C29×#385—21no—
45C29×#385C2212yes—
46C29×#385C2212yes—
47C29×#385C2211yescharacteristic
48C29×#385C2211yescharacteristic
49C29×#380C2211yescharacteristic
50C4×C22⋊C4×C29C2211yescharacteristic
51C4×C22⋊C4×C29C2211yescharacteristic
52C29×#342C2212yes—
53C29×#342C2212yes—
54C29×#342C2212yes—
55C2×#41×C29—21no—
56C22×Q8×C29D411yescharacteristic
57C22×D4×C29D411yescharacteristic
58C22×D4×C29C2311yescharacteristic
59C22×D4×C29C2312yes—
60C23×C4×C29D411yescharacteristic
61C23×C4×C29C2311yescharacteristic
62C23×C4×C29C2311yescharacteristic
63C23×C4×C29C2311yescharacteristic
64C29×#126—22no—
65C29×#126—22no—
66C29×#126—22no—
67C29×#125—21no—
68C29×#125—22no—
69C29×#124—21no—
70C29×#124—22no—
71C29×#123—22no—
72C29×#123—22no—
73C29×#123—22no—
74C29×#123—22no—
75C29×#123—22no—
76C29×C22⋊Q8—21no—
77C29×C22⋊Q8—22no—
78C29×C22⋊Q8—21no—
79C29×C22⋊Q8—21no—
80C29×C22⋊Q8—21no—
81C29×C22⋊Q8—21no—
82C29×#121—21no—
83C29×#121—22no—
84C29×#121—21no—
85C29×#121—21no—
86C29×#121—21no—
87C29×#121—21no—
88C29×#121—22no—
89C29×#121—22no—
90C29×#120—22no—
91C29×#120—22no—
92C4×Q8×C29—21no—
93C4×D4×C29—22no—
94C4×D4×C29—21no—
95C4×D4×C29—21no—
96C4×D4×C29—21no—
97C4×D4×C29—21no—
98C4×D4×C29—21no—
99C4×D4×C29—22no—
100C4×D4×C29—22no—
101C4×D4×C29—22no—
102C4×D4×C29—22no—
103C29×#117—21no—
104C29×#117—22no—
105C29×#117—22no—
106C2×C4⋊C4×C29—21no—
107C2×C4⋊C4×C29—21no—
108C2×C4⋊C4×C29—21no—
109C2×C4⋊C4×C29—21no—
110C2×C4⋊C4×C29—21no—
111C2×C4⋊C4×C29—21no—
112C2×C4⋊C4×C29—21no—
113C2×C4⋊C4×C29—22no—
114C2×C4⋊C4×C29—21no—
115C2×C4⋊C4×C29—21no—
116C2×C4⋊C4×C29—22no—
117C2×C4⋊C4×C29D411yescharacteristic
118C2×C4⋊C4×C29D411yescharacteristic
119C2×C4⋊C4×C29D412yes—
120C2×C4⋊C4×C29D411yescharacteristic
121C2×C22⋊C4×C29—22no—
122C2×C22⋊C4×C29—21no—
123C2×C22⋊C4×C29—22no—
124C2×C22⋊C4×C29—21no—
125C2×C22⋊C4×C29—22no—
126C2×C22⋊C4×C29D411yescharacteristic
127C2×C22⋊C4×C29D412yes—
128C2×C22⋊C4×C29C2312yes—
129C2×C22⋊C4×C29C2311yescharacteristic
130C2×C22⋊C4×C29C2311yescharacteristic
131C2×C22⋊C4×C29C2311yescharacteristic
132C2×C22⋊C4×C29C2312yes—
133C2×C22⋊C4×C29C2312yes—
134C2×C42×C29—21no—
135C2×C42×C29—21no—
136C2×C42×C29D411yescharacteristic
137C29×#99—24no—
138C29×#99—24no—
139C29×#99—24no—
140C29×#95—21no—
141C29×#95—21no—
142C29×#95—21no—
143C29×#95—21no—
144C29×#95—21no—
145C29×#95—22no—
146C29×#95—22no—
147C29×#95—21no—
148C29×#95—21no—
149C29×#95—22no—
150C29×#95—22no—
151C24×C29C2×D412yes—
152C24×C29C2×D411yescharacteristic
153C24×C29C2411yescharacteristic
154#41×C29—82no—
155C2×Q8×C29—21no—
156C2×Q8×C29—21no—
157C2×Q8×C29—81no—
158C2×D4×C29—21no—
159C2×D4×C29—22no—
160C2×D4×C29—21no—
161C2×D4×C29—22no—
162C2×D4×C29—22no—
163C2×D4×C29—22no—
164C2×D4×C29—22no—
165C2×D4×C29—22no—
166C2×D4×C29—22no—
167C2×D4×C29—22no—
168C2×D4×C29—22no—
169C2×D4×C29—22no—
170C2×D4×C29—21no—
171C2×D4×C29—21no—
172C2×D4×C29—81no—
173C22×C4×C29—22no—
174C22×C4×C29—21no—
175C22×C4×C29—21no—
176C22×C4×C29—21no—
177C22×C4×C29—22no—
178C22×C4×C29—22no—
179C22×C4×C29—21no—
180C22×C4×C29—21no—
181C22×C4×C29—22no—
182C22×C4×C29—21no—
183C22×C4×C29—21no—
184C22×C4×C29—21no—
185C22×C4×C29—21no—
186C22×C4×C29—21no—
187C22×C4×C29—42no—
188C22×C4×C29—81no—
189C22×C4×C29—81no—
190C22×C4×C29—81no—
191C22×C4×C29C2×D411yescharacteristic
192C22×C4×C29C2×D412yes—
193C22×C4×C29C2×D411yescharacteristic
194C22×C4×C29C2×D412yes—
195C22×C4×C29C2×D411yescharacteristic
196C22×C4×C29C2×D412yes—
197C22×C4×C29C2×D411yescharacteristic
198C22×C4×C29C2×D411yescharacteristic
199C22×C4×C29C2×D411yescharacteristic
200C22×C4×C29C2×D411yescharacteristic
201C22×C4×C29C2×D411yescharacteristic
202C22×C4×C29C2×D411yescharacteristic
203C4⋊C4×C29—22no—
204C4⋊C4×C29—22no—
205C4⋊C4×C29—22no—
206C4⋊C4×C29—22no—
207C4⋊C4×C29—21no—
208C4⋊C4×C29—22no—
209C4⋊C4×C29—21no—
210C4⋊C4×C29—21no—
211C4⋊C4×C29—21no—
212C4⋊C4×C29—21no—
213C4⋊C4×C29—22no—
214C4⋊C4×C29—21no—
215C4⋊C4×C29—42no—
216C4⋊C4×C29—44no—
217C4⋊C4×C29—41no—
218C4⋊C4×C29—41no—
219C4⋊C4×C29—41no—
220C4⋊C4×C29—41no—
221C4⋊C4×C29—81no—
222C4⋊C4×C29—82no—
223C4⋊C4×C29—81no—
224C22⋊C4×C29—22no—
225C22⋊C4×C29—22no—
226C22⋊C4×C29—22no—
227C22⋊C4×C29—22no—
228C22⋊C4×C29—22no—
229C22⋊C4×C29—22no—
230C22⋊C4×C29—21no—
231C22⋊C4×C29—22no—
232C22⋊C4×C29—21no—
233C22⋊C4×C29—22no—
234C22⋊C4×C29—22no—
235C22⋊C4×C29—22no—
236C22⋊C4×C29—21no—
237C22⋊C4×C29—21no—
238C22⋊C4×C29—22no—
239C22⋊C4×C29—22no—
240C22⋊C4×C29—22no—
241C22⋊C4×C29—22no—
242C22⋊C4×C29—22no—
243C22⋊C4×C29—44no—
244C22⋊C4×C29—42no—
245C22⋊C4×C29—82no—
246C22⋊C4×C29—81no—
247C22⋊C4×C29#4114yescomplemented
248C42×C29—22no—
249C42×C29—22no—
250C42×C29—21no—
251C42×C29—21no—
252C42×C29—81no—
253C42×C29—81no—
254#25665C2911yesmaximal, characteristic, direct product factor, Sylow
255C23×C29—22no—
256C23×C29—21no—
257C23×C29—21no—
258C23×C29—21no—
259C23×C29—22no—
260C23×C29—22no—
261C23×C29—41no—
262C23×C29—41no—
263C23×C29—41no—
264C23×C29—41no—
265C23×C29—42no—
266C23×C29—42no—
267C23×C29C22×D411yescharacteristic
268C23×C29C22×D411yescharacteristic
269C23×C29C22×D411yescharacteristic
270C23×C29C2×#4112yes—
271C23×C292−1+412yes—
272Q8×C29—42no—
273Q8×C29—81no—
274D4×C29—42no—
275D4×C29—42no—
276D4×C29—42no—
277D4×C29—42no—
278D4×C29—42no—
279D4×C29—42no—
280D4×C29—42no—
281D4×C29—81no—
282D4×C29—82no—
283D4×C29—82no—
284C2×C4×C29—22no—
285C2×C4×C29—22no—
286C2×C4×C29—22no—
287C2×C4×C29—21no—
288C2×C4×C29—22no—
289C2×C4×C29—21no—
290C2×C4×C29—21no—
291C2×C4×C29—22no—
292C2×C4×C29—22no—
293C2×C4×C29—21no—
294C2×C4×C29—21no—
295C2×C4×C29—22no—
296C2×C4×C29—22no—
297C2×C4×C29—24no—
298C2×C4×C29—41no—
299C2×C4×C29—41no—
300C2×C4×C29—41no—
301C2×C4×C29—41no—
302C2×C4×C29—41no—
303C2×C4×C29—41no—
304C2×C4×C29—42no—
305C2×C4×C29—42no—
306C2×C4×C29—42no—
307C2×C4×C29—41no—
308C2×C4×C29—41no—
309C2×C4×C29—41no—
310C2×C4×C29—41no—
311C2×C4×C29—41no—
312C2×C4×C29—42no—
313C2×C4×C29—41no—
314C2×C4×C29—42no—
315C2×C4×C29—42no—
316C2×C4×C29—41no—
317C2×C4×C29—42no—
318C2×C4×C29—41no—
319C2×C4×C29—41no—
320C2×C4×C29—42no—
321C2×C4×C29—41no—
322C2×C4×C29—41no—
323C2×C4×C29—42no—
324C2×C4×C29—41no—
325C2×C4×C29—41no—
326C2×C4×C29—41no—
327C2×C4×C29—41no—
328C2×C4×C29—42no—
329C2×C4×C29—81no—
330C2×C4×C29—82no—
331C2×C4×C29—82no—
332C2×C4×C29#12011yescharacteristic
333C2×C4×C29#12011yescharacteristic
334C2×C4×C29#12011yescharacteristic
335C2×C4×C29#12011yescharacteristic
336#3505C2×C2911yescharacteristic
337#2591C2×C2911yescharacteristic, complemented
338#2583C2×C2911yescharacteristic, complemented
339#2579C2×C2911yescharacteristic, complemented
340#2044C2×C2912yescomplemented
341#2044C2×C2912yescomplemented
342#1996C2×C2911yescharacteristic, complemented
343#1964C2×C2911yescharacteristic, complemented
344#1867C2×C2912yescomplemented
345#1867C2×C2912yescomplemented
346C4×#99C2×C2911yescharacteristic, complemented
347C22×C29—21no—
348C22×C29—21no—
349C22×C29—21no—
350C22×C29—21no—
351C22×C29—21no—
352C22×C29—21no—
353C22×C29—42no—
354C22×C29—42no—
355C22×C29—42no—
356C22×C29—41no—
357C22×C29—42no—
358C22×C29—42no—
359C22×C29—41no—
360C22×C29—41no—
361C22×C29—42no—
362C22×C29—81no—
363C22×C29—82no—
364C22×C29—82no—
365C22×C29C2×#12011yescharacteristic
366C22×C29#53211yescharacteristic
367C22×C29#53611yescharacteristic
368C22×C29#54712yes—
369C22×C29#54812yes—
370C4×C29—21no—
371C4×C29—21no—
372C4×C29—21no—
373C4×C29—21no—
374C4×C29—44no—
375C4×C29—41no—
376C4×C29—42no—
377C4×C29—42no—
378C4×C29—41no—
379C4×C29—42no—
380C4×C29—41no—
381C4×C29—42no—
382C4×C29—81no—
383C4×C29—81no—
384C4×C29—82no—
385C4×C29—81no—
386#553—22no—
387#553—21no—
388#552—21no—
389#551—22no—
390#548—21no—
391#546—21no—
392#539—21no—
393#538—21no—
394#534C22×C2912yes—
395#529—21no—
396#525—21no—
397C2×C22⋊Q8C22×C2911yescharacteristic
398C2×#121C22×C2911yescharacteristic
399#518C22×C2912yes—
400C2×C4×D4C22×C2911yescharacteristic
401C22×C4⋊C4C22×C2911yescharacteristic
402C2×#99C22×C2912yes—
403C2×#99C22×C2912yes—
404C2×#99C22×C2912yes—
405#400—21no—
406#398—21no—
407#398—21no—
408#396—21no—
409#395—21no—
410#394—21no—
411#389—22no—
412#388—22no—
413#387—21no—
414#386C22×C2911yescharacteristic
415#386C22×C2911yescharacteristic
416#386C22×C2912yes—
417#386C22×C2912yes—
418#385—21no—
419#385C22×C2911yescharacteristic
420#385C22×C2911yescharacteristic
421#385C22×C2912yes—
422#385C22×C2912yes—
423#380C22×C2911yescharacteristic
424C4×C22⋊C4C22×C2911yescharacteristic
425C4×C22⋊C4C22×C2911yescharacteristic
426#342C22×C2912yes—
427#342C22×C2912yes—
428#342C22×C2912yes—
429C2×C29—22no—
430C2×C29—21no—
431C2×C29—22no—
432C2×C29—21no—
433C2×C29—81no—
434C2×C29—82no—
435C2×C29#243211yescharacteristic
436C2×C29#302511yescharacteristic
437C2×C29#302611yescharacteristic
438C2×#41—21no—
439C22×Q8D4×C2911yescharacteristic
440C22×D4D4×C2911yescharacteristic
441C22×D4C23×C2911yescharacteristic
442C22×D4C23×C2912yes—
443C23×C4D4×C2911yescharacteristic
444C23×C4C23×C2911yescharacteristic
445C23×C4C23×C2911yescharacteristic
446C23×C4C23×C2911yescharacteristic
447#126—22no—
448#126—22no—
449#126—22no—
450#125—21no—
451#125—22no—
452#124—21no—
453#124—22no—
454#123—22no—
455#123—22no—
456#123—22no—
457#123—22no—
458#123—22no—
459C22⋊Q8—21no—
460C22⋊Q8—22no—
461C22⋊Q8—21no—
462C22⋊Q8—21no—
463C22⋊Q8—21no—
464C22⋊Q8—21no—
465#121—21no—
466#121—22no—
467#121—21no—
468#121—21no—
469#121—21no—
470#121—21no—
471#121—22no—
472#121—22no—
473#120—22no—
474#120—22no—
475C4×Q8—21no—
476C4×D4—22no—
477C4×D4—21no—
478C4×D4—21no—
479C4×D4—21no—
480C4×D4—21no—
481C4×D4—21no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486#117—21no—
487#117—22no—
488#117—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4D4×C2911yescharacteristic
501C2×C4⋊C4D4×C2911yescharacteristic
502C2×C4⋊C4D4×C2912yes—
503C2×C4⋊C4D4×C2911yescharacteristic
504C2×C22⋊C4—22no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4D4×C2911yescharacteristic
510C2×C22⋊C4D4×C2912yes—
511C2×C22⋊C4C23×C2912yes—
512C2×C22⋊C4C23×C2911yescharacteristic
513C2×C22⋊C4C23×C2911yescharacteristic
514C2×C22⋊C4C23×C2911yescharacteristic
515C2×C22⋊C4C23×C2912yes—
516C2×C22⋊C4C23×C2912yes—
517C2×C42—21no—
518C2×C42—21no—
519C2×C42D4×C2911yescharacteristic
520#99—24no—
521#99—24no—
522#99—24no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—22no—
529#95—22no—
530#95—21no—
531#95—21no—
532#95—22no—
533#95—22no—
534C29#2566511yescharacteristic, direct product factor, Sylow
535C24C2×D4×C2912yes—
536C24C2×D4×C2911yescharacteristic
537C24C24×C2911yescharacteristic
538#41—82no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—81no—
542C2×D4—21no—
543C2×D4—22no—
544C2×D4—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—81no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—42no—
572C22×C4—81no—
573C22×C4—81no—
574C22×C4—81no—
575C22×C4C2×D4×C2911yescharacteristic
576C22×C4C2×D4×C2912yes—
577C22×C4C2×D4×C2911yescharacteristic
578C22×C4C2×D4×C2912yes—
579C22×C4C2×D4×C2911yescharacteristic
580C22×C4C2×D4×C2912yes—
581C22×C4C2×D4×C2911yescharacteristic
582C22×C4C2×D4×C2911yescharacteristic
583C22×C4C2×D4×C2911yescharacteristic
584C22×C4C2×D4×C2911yescharacteristic
585C22×C4C2×D4×C2911yescharacteristic
586C22×C4C2×D4×C2911yescharacteristic
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—22no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—44no—
601C4⋊C4—41no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—41no—
605C4⋊C4—81no—
606C4⋊C4—82no—
607C4⋊C4—81no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—21no—
615C22⋊C4—22no—
616C22⋊C4—21no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—44no—
628C22⋊C4—42no—
629C22⋊C4—82no—
630C22⋊C4—81no—
631C22⋊C4#41×C2914yescomplemented
632C42—22no—
633C42—22no—
634C42—21no—
635C42—21no—
636C42—81no—
637C42—81no—
638C23—22no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—22no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—42no—
649C23—42no—
650C23C22×D4×C2911yescharacteristic
651C23C22×D4×C2911yescharacteristic
652C23C22×D4×C2911yescharacteristic
653C23C2×#41×C2912yes—
654C23C29×2−1+412yes—
655Q8—42no—
656Q8—81no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—42no—
664D4—81no—
665D4—82no—
666D4—82no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—81no—
713C2×C4—82no—
714C2×C4—82no—
715C2×C4C29×#12011yescharacteristic
716C2×C4C29×#12011yescharacteristic
717C2×C4C29×#12011yescharacteristic
718C2×C4C29×#12011yescharacteristic
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—41no—
729C22—42no—
730C22—42no—
731C22—41no—
732C22—41no—
733C22—42no—
734C22—81no—
735C22—82no—
736C22—82no—
737C22C2×C29×#12011yescharacteristic
738C22C29×#53211yescharacteristic
739C22C29×#53611yescharacteristic
740C22C29×#54712yes—
741C22C29×#54812yes—
742C4—21no—
743C4—21no—
744C4—21no—
745C4—21no—
746C4—44no—
747C4—41no—
748C4—42no—
749C4—42no—
750C4—41no—
751C4—42no—
752C4—41no—
753C4—42no—
754C4—81no—
755C4—81no—
756C4—82no—
757C4—81no—
758C2—22no—
759C2—21no—
760C2—22no—
761C2—21no—
762C2—81no—
763C2—82no—
764C2C29×#243211yescharacteristic
765C2C29×#302511yescharacteristic
766C2C29×#302611yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC24C24×C29
prime radicalC29×#3505C2
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
2. C29×#2591C2semidirect
3. C29×#2583C2semidirect
4. C29×#2579C2semidirect
5. C29×#2044C2semidirect
6. C29×#2044C2semidirect
7. C29×#1996C2semidirect
8. C29×#1964C2semidirect
9. C29×#1867C2semidirect
10. C29×#1867C2semidirect
11. C4×C29×#99C2semidirect
247. C22⋊C4×C29#41semidirect
254. #25665C29direct (N × H)
337. #2591C2×C29semidirect
338. #2583C2×C29semidirect
339. #2579C2×C29semidirect
340. #2044C2×C29semidirect
341. #2044C2×C29semidirect
342. #1996C2×C29semidirect
343. #1964C2×C29semidirect
344. #1867C2×C29semidirect
345. #1867C2×C29semidirect
346. C4×#99C2×C29semidirect
534. C29#25665direct (N × H)
631. 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×#25912
C29×#25832
C29×#25792
C29×#20442
C29×#19962
C29×#19642
C29×#18672
C4×C29×#992
#2566529