Finite Group Databasebeta

← C29×#18384 #20313284

Subgroups — C29×#18384 #20313284

Order 7424.

1082 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3505C211yesmaximal, characteristic, complemented
2C29×#3187C211yesmaximal, characteristic, complemented
3C29×#3186C211yesmaximal, characteristic, complemented
4C29×#2543C211yesmaximal, characteristic, complemented
5C29×#1612C212yesmaximal, complemented
6C29×#1609C212yesmaximal, complemented
7C29×#1600C212yesmaximal, complemented
8C29×#1597C212yesmaximal, complemented
9C2×C29×#328C211yesmaximal, characteristic, complemented
10C2×C29×#327C211yesmaximal, characteristic, complemented
11C29×#1459C211yesmaximal, characteristic, complemented
12C29×#553—22no—
13C29×#553—21no—
14C29×#552—21no—
15C29×#551—22no—
16C29×#548—21no—
17C29×#546—21no—
18C29×#539C2212yes—
19C29×#538C2212yes—
20C29×#534—21no—
21C29×#529—21no—
22C29×#525—21no—
23C2×C29×C22⋊Q8C2211yescharacteristic
24C2×C29×#121—21no—
25C2×C29×#121C2211yescharacteristic
26C2×C29×#121C2211yescharacteristic
27C29×#518—21no—
28C2×C4×D4×C29C2211yescharacteristic
29C29×#483C2212yescomplemented
30C29×#481—21no—
31C29×#480—21no—
32C29×#480C2212yes—
33C29×#466—22no—
34C29×#465—22no—
35C29×#450C2212yescomplemented
36C29×#448—21no—
37C29×#447—21no—
38C29×#447C2212yes—
39C2×C29×C22⋊C8C2211yescharacteristic
40C2×C29×C22⋊C8C2211yescharacteristic
41C29×#398C2211yescharacteristic, complemented
42C29×#397C2211yescharacteristic, complemented
43C29×#394C2211yescharacteristic, complemented
44C29×#392C2211yescharacteristic, complemented
45C29×#388—21no—
46C29×#386—21no—
47C29×#386—21no—
48C2×C29×#95C2211yescharacteristic
49C29×#328C2212yescomplemented
50C29×#328C2212yescomplemented
51C29×#327C2212yes—
52C29×#327C2212yes—
53C29×#324C2212yescomplemented
54C29×#323C2212yescomplemented
55C2×#41×C29—21no—
56C22×Q8×C29D411yescharacteristic, complemented
57C22×D4×C29—21no—
58C22×D4×C29—21no—
59C22×D4×C29—21no—
60C22×D4×C29D411yescharacteristic
61C22×D4×C29D411yescharacteristic, complemented
62C22×D4×C29C2311yescharacteristic
63C23×C4×C29—21no—
64C23×C4×C29D411yescharacteristic
65C23×C4×C29C2311yescharacteristic
66C2×SD16×C29—22no—
67C2×D8×C29—22no—
68C22×C8×C29—21no—
69C22×C8×C29—21no—
70C29×#126—22no—
71C29×#126—22no—
72C29×#126—22no—
73C29×#125—21no—
74C29×#125—22no—
75C29×#124—21no—
76C29×#124—22no—
77C29×#123—22no—
78C29×#123—22no—
79C29×#123—22no—
80C29×#123—22no—
81C29×#123—22no—
82C29×C22⋊Q8—21no—
83C29×C22⋊Q8—22no—
84C29×C22⋊Q8—21no—
85C29×C22⋊Q8—21no—
86C29×C22⋊Q8D412yescomplemented
87C29×C22⋊Q8C2312yes—
88C29×#121—21no—
89C29×#121—22no—
90C29×#121—22no—
91C29×#121—22no—
92C29×#121—21no—
93C29×#121—21no—
94C29×#121—21no—
95C29×#121—21no—
96C29×#121—21no—
97C29×#121—21no—
98C29×#121—44no—
99C29×#121D412yescomplemented
100C29×#121C2312yes—
101C29×#120—22no—
102C29×#120—22no—
103C4×Q8×C29—21no—
104C4×D4×C29—22no—
105C4×D4×C29—22no—
106C4×D4×C29—22no—
107C4×D4×C29—21no—
108C4×D4×C29—21no—
109C4×D4×C29—21no—
110C4×D4×C29—21no—
111C4×D4×C29—21no—
112C4×D4×C29—22no—
113C4×D4×C29—22no—
114C29×#117—22no—
115C29×#117—21no—
116C29×#117—22no—
117C2×C4⋊C4×C29—21no—
118C2×C4⋊C4×C29—21no—
119C2×C4⋊C4×C29D411yescharacteristic, complemented
120C2×C4⋊C4×C29D411yescharacteristic, complemented
121C2×C4⋊C4×C29C2311yescharacteristic
122C2×C4⋊C4×C29C2311yescharacteristic
123C2×C22⋊C4×C29—22no—
124C2×C22⋊C4×C29—21no—
125C2×C22⋊C4×C29—21no—
126C2×C22⋊C4×C29—21no—
127C2×C22⋊C4×C29—21no—
128C2×C22⋊C4×C29—21no—
129C2×C22⋊C4×C29—21no—
130C2×C22⋊C4×C29—21no—
131C2×C22⋊C4×C29D411yescharacteristic
132C2×C22⋊C4×C29C2311yescharacteristic
133C2×C42×C29D411yescharacteristic
134C29×#107—22no—
135C29×#106—22no—
136C29×#103—22no—
137C29×#102—22no—
138C29×#102—22no—
139C29×#102—22no—
140C29×C22⋊C8—21no—
141C29×C22⋊C8—21no—
142C29×C22⋊C8C2312yes—
143C29×C22⋊C8C2312yes—
144C29×#95—21no—
145C29×#95—21no—
146C29×#95—21no—
147C29×#95C2311yescharacteristic
148C29×#95C2311yescharacteristic
149C24×C29—21no—
150C24×C29—21no—
151C24×C29C2×D411yescharacteristic
152C24×C29C2×D411yescharacteristic
153#41×C29—82no—
154C2×Q8×C29—21no—
155C2×Q8×C29—81no—
156C2×Q8×C29C2×D412yes—
157C2×D4×C29—21no—
158C2×D4×C29—21no—
159C2×D4×C29—22no—
160C2×D4×C29—22no—
161C2×D4×C29—22no—
162C2×D4×C29—22no—
163C2×D4×C29—22no—
164C2×D4×C29—22no—
165C2×D4×C29—21no—
166C2×D4×C29—21no—
167C2×D4×C29—21no—
168C2×D4×C29—42no—
169C2×D4×C29—42no—
170C2×D4×C29—42no—
171C2×D4×C29—42no—
172C2×D4×C29—41no—
173C2×D4×C29—41no—
174C2×D4×C29—42no—
175C2×D4×C29—42no—
176C2×D4×C29—81no—
177C2×D4×C29—81no—
178C2×D4×C29—81no—
179C2×D4×C29C2×D412yes—
180C22×C4×C29—21no—
181C22×C4×C29—21no—
182C22×C4×C29—22no—
183C22×C4×C29—22no—
184C22×C4×C29—21no—
185C22×C4×C29—21no—
186C22×C4×C29—21no—
187C22×C4×C29—21no—
188C22×C4×C29—21no—
189C22×C4×C29—21no—
190C22×C4×C29—42no—
191C22×C4×C29—42no—
192C22×C4×C29—81no—
193C22×C4×C29—81no—
194C22×C4×C29—81no—
195C22×C4×C29C2×D411yescharacteristic
196C22×C4×C29C2×D411yescharacteristic
197C22×C4×C29C2×D411yescharacteristic
198C22×C4×C29C2×D411yescharacteristic
199C22×C4×C29C2×D411yescharacteristic
200C22×C4×C29C2×D411yescharacteristic
201C22×C4×C29C2×D411yescharacteristic
202C22×C4×C29C2×D411yescharacteristic
203C22×C4×C29C2411yescharacteristic
204SD16×C29—82no—
205D8×C29—82no—
206C2×C8×C29—22no—
207C2×C8×C29—22no—
208C2×C8×C29—81no—
209C2×C8×C29—81no—
210C4⋊C4×C29—22no—
211C4⋊C4×C29—22no—
212C4⋊C4×C29—22no—
213C4⋊C4×C29—22no—
214C4⋊C4×C29—22no—
215C4⋊C4×C29—21no—
216C4⋊C4×C29—21no—
217C4⋊C4×C29—22no—
218C4⋊C4×C29—21no—
219C4⋊C4×C29—21no—
220C4⋊C4×C29—21no—
221C4⋊C4×C29—21no—
222C4⋊C4×C29—42no—
223C4⋊C4×C29C2×D412yes—
224C4⋊C4×C29C2×D412yes—
225C22⋊C4×C29—22no—
226C22⋊C4×C29—22no—
227C22⋊C4×C29—22no—
228C22⋊C4×C29—22no—
229C22⋊C4×C29—22no—
230C22⋊C4×C29—22no—
231C22⋊C4×C29—21no—
232C22⋊C4×C29—22no—
233C22⋊C4×C29—21no—
234C22⋊C4×C29—22no—
235C22⋊C4×C29—22no—
236C22⋊C4×C29—22no—
237C22⋊C4×C29—21no—
238C22⋊C4×C29—21no—
239C22⋊C4×C29—42no—
240C22⋊C4×C29—42no—
241C22⋊C4×C29—42no—
242C22⋊C4×C29—41no—
243C22⋊C4×C29—41no—
244C22⋊C4×C29—81no—
245C42×C29—22no—
246C42×C29—22no—
247C42×C29—21no—
248C42×C29—21no—
249#18384C2911yesmaximal, characteristic, direct product factor, Sylow
250C23×C29—21no—
251C23×C29—22no—
252C23×C29—21no—
253C23×C29—21no—
254C23×C29—41no—
255C23×C29—41no—
256C23×C29—41no—
257C23×C29—41no—
258C23×C29—41no—
259C23×C29—41no—
260C23×C29—41no—
261C23×C29—41no—
262C23×C29—42no—
263C23×C29—41no—
264C23×C29—41no—
265C23×C29—41no—
266C23×C29—81no—
267C23×C29—81no—
268C23×C29#12011yescharacteristic
269C23×C29#12011yescharacteristic
270C23×C29#13512yes—
271C23×C29AGL(1,ℤ/8)12yes—
272C23×C29C22×D411yescharacteristic
273Q8×C29—42no—
274Q8×C29—42no—
275D4×C29—42no—
276D4×C29—42no—
277D4×C29—42no—
278D4×C29—42no—
279D4×C29—42no—
280D4×C29—42no—
281D4×C29—42no—
282D4×C29—42no—
283D4×C29—44no—
284D4×C29—82no—
285D4×C29—82no—
286D4×C29—84no—
287D4×C29—82no—
288D4×C29—82no—
289C2×C4×C29—22no—
290C2×C4×C29—21no—
291C2×C4×C29—21no—
292C2×C4×C29—22no—
293C2×C4×C29—21no—
294C2×C4×C29—22no—
295C2×C4×C29—22no—
296C2×C4×C29—21no—
297C2×C4×C29—21no—
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—41no—
306C2×C4×C29—41no—
307C2×C4×C29—42no—
308C2×C4×C29—41no—
309C2×C4×C29—41no—
310C2×C4×C29—41no—
311C2×C4×C29—41no—
312C2×C4×C29—41no—
313C2×C4×C29—41no—
314C2×C4×C29—41no—
315C2×C4×C29—41no—
316C2×C4×C29—81no—
317C2×C4×C29—81no—
318C2×C4×C29—81no—
319C2×C4×C29—82no—
320C2×C4×C29—82no—
321C2×C4×C29—84no—
322C2×C4×C29#12011yescharacteristic
323C2×C4×C29#12011yescharacteristic
324C2×C4×C29C22×D411yescharacteristic
325C2×C4×C29C22×D411yescharacteristic
326C8×C29—42no—
327C8×C29—42no—
328#3505C2×C2911yescharacteristic, complemented
329#3187C2×C2911yescharacteristic, complemented
330#3186C2×C2911yescharacteristic, complemented
331#2543C2×C2911yescharacteristic, complemented
332#1612C2×C2912yescomplemented
333#1609C2×C2912yescomplemented
334#1600C2×C2912yescomplemented
335#1597C2×C2912yescomplemented
336C2×#328C2×C2911yescharacteristic, complemented
337C2×#327C2×C2911yescharacteristic, complemented
338#1459C2×C2911yescharacteristic, complemented
339C22×C29—21no—
340C22×C29—21no—
341C22×C29—21no—
342C22×C29—21no—
343C22×C29—21no—
344C22×C29—21no—
345C22×C29—42no—
346C22×C29—42no—
347C22×C29—42no—
348C22×C29—41no—
349C22×C29—42no—
350C22×C29—42no—
351C22×C29—41no—
352C22×C29—41no—
353C22×C29—42no—
354C22×C29—81no—
355C22×C29—81no—
356C22×C29—81no—
357C22×C29—81no—
358C22×C29—81no—
359C22×C29—81no—
360C22×C29—81no—
361C22×C29—81no—
362C22×C29—162no—
363C22×C29#44912yes—
364C22×C29#44912yes—
365C22×C29C2×#12011yescharacteristic
366C22×C29C2×#13511yescharacteristic
367C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
368C4×C29—21no—
369C4×C29—21no—
370C4×C29—21no—
371C4×C29—21no—
372C4×C29—42no—
373C4×C29—41no—
374C4×C29—42no—
375C4×C29—41no—
376C4×C29—42no—
377C4×C29—41no—
378C4×C29—42no—
379C4×C29—81no—
380C4×C29—81no—
381#553—22no—
382#553—21no—
383#552—21no—
384#551—22no—
385#548—21no—
386#546—21no—
387#539C22×C2912yes—
388#538C22×C2912yes—
389#534—21no—
390#529—21no—
391#525—21no—
392C2×C22⋊Q8C22×C2911yescharacteristic
393C2×#121—21no—
394C2×#121C22×C2911yescharacteristic
395C2×#121C22×C2911yescharacteristic
396#518—21no—
397C2×C4×D4C22×C2911yescharacteristic
398#483C22×C2912yescomplemented
399#481—21no—
400#480—21no—
401#480C22×C2912yes—
402#466—22no—
403#465—22no—
404#450C22×C2912yescomplemented
405#448—21no—
406#447—21no—
407#447C22×C2912yes—
408C2×C22⋊C8C22×C2911yescharacteristic
409C2×C22⋊C8C22×C2911yescharacteristic
410#398C22×C2911yescharacteristic, complemented
411#397C22×C2911yescharacteristic, complemented
412#394C22×C2911yescharacteristic, complemented
413#392C22×C2911yescharacteristic, complemented
414#388—21no—
415#386—21no—
416#386—21no—
417C2×#95C22×C2911yescharacteristic
418#328C22×C2912yescomplemented
419#328C22×C2912yescomplemented
420#327C22×C2912yes—
421#327C22×C2912yes—
422#324C22×C2912yescomplemented
423#323C22×C2912yescomplemented
424C2×C29—21no—
425C2×C29—21no—
426C2×C29—22no—
427C2×C29—22no—
428C2×C29—81no—
429C2×C29—82no—
430C2×C29—161no—
431C2×C29C2×#44911yescharacteristic
432C2×C29#301811yescharacteristic
433C2×C29#302611yescharacteristic
434C2×#41—21no—
435C22×Q8D4×C2911yescharacteristic, complemented
436C22×D4—21no—
437C22×D4—21no—
438C22×D4—21no—
439C22×D4D4×C2911yescharacteristic
440C22×D4D4×C2911yescharacteristic, complemented
441C22×D4C23×C2911yescharacteristic
442C23×C4—21no—
443C23×C4D4×C2911yescharacteristic
444C23×C4C23×C2911yescharacteristic
445C2×SD16—22no—
446C2×D8—22no—
447C22×C8—21no—
448C22×C8—21no—
449#126—22no—
450#126—22no—
451#126—22no—
452#125—21no—
453#125—22no—
454#124—21no—
455#124—22no—
456#123—22no—
457#123—22no—
458#123—22no—
459#123—22no—
460#123—22no—
461C22⋊Q8—21no—
462C22⋊Q8—22no—
463C22⋊Q8—21no—
464C22⋊Q8—21no—
465C22⋊Q8D4×C2912yescomplemented
466C22⋊Q8C23×C2912yes—
467#121—21no—
468#121—22no—
469#121—22no—
470#121—22no—
471#121—21no—
472#121—21no—
473#121—21no—
474#121—21no—
475#121—21no—
476#121—21no—
477#121—44no—
478#121D4×C2912yescomplemented
479#121C23×C2912yes—
480#120—22no—
481#120—22no—
482C4×Q8—21no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4—21no—
491C4×D4—22no—
492C4×D4—22no—
493#117—22no—
494#117—21no—
495#117—22no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4D4×C2911yescharacteristic, complemented
499C2×C4⋊C4D4×C2911yescharacteristic, complemented
500C2×C4⋊C4C23×C2911yescharacteristic
501C2×C4⋊C4C23×C2911yescharacteristic
502C2×C22⋊C4—22no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4D4×C2911yescharacteristic
511C2×C22⋊C4C23×C2911yescharacteristic
512C2×C42D4×C2911yescharacteristic
513#107—22no—
514#106—22no—
515#103—22no—
516#102—22no—
517#102—22no—
518#102—22no—
519C22⋊C8—21no—
520C22⋊C8—21no—
521C22⋊C8C23×C2912yes—
522C22⋊C8C23×C2912yes—
523#95—21no—
524#95—21no—
525#95—21no—
526#95C23×C2911yescharacteristic
527#95C23×C2911yescharacteristic
528C29#1838411yescharacteristic, direct product factor, Sylow
529C24—21no—
530C24—21no—
531C24C2×D4×C2911yescharacteristic
532C24C2×D4×C2911yescharacteristic
533#41—82no—
534C2×Q8—21no—
535C2×Q8—81no—
536C2×Q8C2×D4×C2912yes—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4—81no—
559C2×D4C2×D4×C2912yes—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—81no—
573C22×C4—81no—
574C22×C4—81no—
575C22×C4C2×D4×C2911yescharacteristic
576C22×C4C2×D4×C2911yescharacteristic
577C22×C4C2×D4×C2911yescharacteristic
578C22×C4C2×D4×C2911yescharacteristic
579C22×C4C2×D4×C2911yescharacteristic
580C22×C4C2×D4×C2911yescharacteristic
581C22×C4C2×D4×C2911yescharacteristic
582C22×C4C2×D4×C2911yescharacteristic
583C22×C4C24×C2911yescharacteristic
584SD16—82no—
585D8—82no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—81no—
589C2×C8—81no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4C2×D4×C2912yes—
604C4⋊C4C2×D4×C2912yes—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—21no—
612C22⋊C4—22no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—41no—
623C22⋊C4—41no—
624C22⋊C4—81no—
625C42—22no—
626C42—22no—
627C42—21no—
628C42—21no—
629C23—21no—
630C23—22no—
631C23—21no—
632C23—21no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—42no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—81no—
646C23—81no—
647C23C29×#12011yescharacteristic
648C23C29×#12011yescharacteristic
649C23C29×#13512yes—
650C23C29×AGL(1,ℤ/8)12yes—
651C23C22×D4×C2911yescharacteristic
652Q8—42no—
653Q8—42no—
654D4—42no—
655D4—42no—
656D4—42no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—44no—
661D4—42no—
662D4—42no—
663D4—82no—
664D4—82no—
665D4—84no—
666D4—82no—
667D4—82no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—82no—
699C2×C4—82no—
700C2×C4—84no—
701C2×C4C29×#12011yescharacteristic
702C2×C4C29×#12011yescharacteristic
703C2×C4C22×D4×C2911yescharacteristic
704C2×C4C22×D4×C2911yescharacteristic
705C8—42no—
706C8—42no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—41no—
717C22—42no—
718C22—42no—
719C22—41no—
720C22—41no—
721C22—42no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—162no—
731C22C29×#44912yes—
732C22C29×#44912yes—
733C22C2×C29×#12011yescharacteristic
734C22C2×C29×#13511yescharacteristic
735C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
736C4—21no—
737C4—21no—
738C4—21no—
739C4—21no—
740C4—42no—
741C4—41no—
742C4—42no—
743C4—41no—
744C4—42no—
745C4—41no—
746C4—42no—
747C4—81no—
748C4—81no—
749C2—21no—
750C2—21no—
751C2—22no—
752C2—22no—
753C2—81no—
754C2—82no—
755C2—161no—
756C2C2×C29×#44911yescharacteristic
757C2C29×#301811yescharacteristic
758C2C29×#302611yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
LCSG ▷ C22×C4 ▷ C22 ▷ 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×#3187C2semidirect
3. C29×#3186C2semidirect
4. C29×#2543C2semidirect
5. C29×#1612C2semidirect
6. C29×#1609C2semidirect
7. C29×#1600C2semidirect
8. C29×#1597C2semidirect
9. C2×C29×#328C2semidirect
10. C2×C29×#327C2semidirect
11. C29×#1459C2semidirect
29. C29×#483C22semidirect
35. C29×#450C22semidirect
41. C29×#398C22semidirect
42. C29×#397C22semidirect
43. C29×#394C22semidirect
44. C29×#392C22semidirect
49. C29×#328C22semidirect
50. C29×#328C22semidirect
53. C29×#324C22semidirect
54. C29×#323C22semidirect
56. C22×Q8×C29D4semidirect
61. C22×D4×C29D4semidirect
86. C29×C22⋊Q8D4semidirect
99. C29×#121D4semidirect
119. C2×C4⋊C4×C29D4semidirect
120. C2×C4⋊C4×C29D4semidirect
249. #18384C29direct (N × H)
328. #3505C2×C29semidirect
329. #3187C2×C29semidirect
330. #3186C2×C29semidirect
331. #2543C2×C29semidirect
332. #1612C2×C29semidirect
333. #1609C2×C29semidirect
334. #1600C2×C29semidirect
335. #1597C2×C29semidirect
336. C2×#328C2×C29semidirect
337. C2×#327C2×C29semidirect
338. #1459C2×C29semidirect
398. #483C22×C29semidirect
404. #450C22×C29semidirect
410. #398C22×C29semidirect
411. #397C22×C29semidirect
412. #394C22×C29semidirect
413. #392C22×C29semidirect
418. #328C22×C29semidirect
419. #328C22×C29semidirect
422. #324C22×C29semidirect
423. #323C22×C29semidirect
435. C22×Q8D4×C29semidirect
440. C22×D4D4×C29semidirect
465. C22⋊Q8D4×C29semidirect
478. #121D4×C29semidirect
498. C2×C4⋊C4D4×C29semidirect
499. C2×C4⋊C4D4×C29semidirect
528. C29#18384direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35052
C29×#31872
C29×#31862
C29×#25432
C29×#16122
C29×#16092
C29×#16002
C29×#15972
C2×C29×#3282
C2×C29×#3272
C29×#14592
#1838429