Finite Group Databasebeta

← C29×#18282 #20313182

Subgroups — C29×#18282 #20313182

Order 7424.

942 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3564C211yesmaximal, characteristic, complemented
2C29×#3114C211yesmaximal, characteristic, complemented
3C29×#3101C211yesmaximal, characteristic, complemented
4C29×#2603C211yesmaximal, characteristic, complemented
5C29×#1612C211yesmaximal, characteristic, complemented
6C29×#1611C211yesmaximal, characteristic, complemented
7C29×#1609C211yesmaximal, characteristic, complemented
8C29×#1608C211yesmaximal, characteristic, complemented
9C29×#1600C211yesmaximal, characteristic
10C29×#1599C211yesmaximal, characteristic, complemented
11C29×#1597C211yesmaximal, characteristic, complemented
12C29×#1596C211yesmaximal, characteristic, complemented
13C29×#1506C211yesmaximal, characteristic, complemented
14C29×#1500C211yesmaximal, characteristic, complemented
15C29×#1473C211yesmaximal, characteristic, complemented
16C29×#563—21no—
17C29×#563—21no—
18C29×#556—21no—
19C29×#554—21no—
20C29×#552—21no—
21C29×#552—21no—
22C29×#551—21no—
23C29×#551—21no—
24C29×#544C2211yescharacteristic
25C29×#543C2211yescharacteristic
26C29×#542—21no—
27C29×#541—21no—
28C29×#541—21no—
29C29×#539—21no—
30C29×#539C2211yescharacteristic
31C29×#538C2211yescharacteristic
32C29×#533C2211yescharacteristic
33C29×#529C2211yescharacteristic
34C2×C29×#126C2211yescharacteristic
35C2×C4×D4×C29C2211yescharacteristic
36C29×#483C2211yescharacteristic
37C29×#483C2211yescharacteristic
38C29×#483C2211yescharacteristic
39C29×#480C2211yescharacteristic
40C29×#478—21no—
41C29×#476—21no—
42C29×#463—21no—
43C29×#461—21no—
44C29×#450C2211yescharacteristic
45C29×#450C2211yescharacteristic
46C29×#450C2211yescharacteristic
47C29×#447C2211yescharacteristic
48C29×#442—21no—
49C29×#440—21no—
50C4×SD16×C29—21no—
51C4×SD16×C29—21no—
52C29×#432C2211yescharacteristic
53C29×#431C2211yescharacteristic
54C29×#398C2211yescharacteristic
55C29×#397C2211yescharacteristic
56C29×#394C2211yescharacteristic
57C29×#392C2211yescharacteristic
58C29×#390—21no—
59C29×#388—21no—
60C29×#386—21no—
61C29×#385—21no—
62C29×#376C2211yescharacteristic
63C29×#328C2211yescharacteristic
64C29×#328C2211yescharacteristic
65C29×#328C2211yescharacteristic
66C29×#328C2211yescharacteristic
67C29×#328C2211yescharacteristic
68C29×#328C2211yescharacteristic
69C29×#327C2211yescharacteristic
70C29×#327C2211yescharacteristic
71C29×#324C2211yescharacteristic
72C29×#324C2211yescharacteristic
73C29×#323C2211yescharacteristic
74C29×#323C2211yescharacteristic
75C22×D4×C29—21no—
76C22×D4×C29C2311yescharacteristic
77C23×C4×C29—21no—
78C2×SD16×C29—21no—
79C2×SD16×C29—21no—
80C2×SD16×C29—21no—
81C2×D8×C29—21no—
82C29×C4⋊Q8—21no—
83C29×C4⋊Q8—21no—
84C29×C4⋊Q8—21no—
85C29×C4⋊Q8D411yescharacteristic, complemented
86C29×C4⋊Q8D411yescharacteristic, complemented
87C29×#126—21no—
88C29×#126—21no—
89C29×#126—21no—
90C29×#126—21no—
91C29×#126—21no—
92C29×#126—21no—
93C29×#126—21no—
94C29×#126—21no—
95C29×#126—21no—
96C29×#126—21no—
97C29×#126—21no—
98C29×#126—21no—
99C29×#126—21no—
100C29×#125—21no—
101C29×#125—21no—
102C29×#125—21no—
103C29×#125—21no—
104C29×#125—21no—
105C29×#125—21no—
106C29×#125—21no—
107C29×#125—21no—
108C29×#125—21no—
109C29×#125D411yescharacteristic, complemented
110C29×#124—21no—
111C29×#124—21no—
112C29×#124—21no—
113C29×#124D411yescharacteristic, complemented
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⋊Q8—21no—
131C29×C22⋊Q8—21no—
132C29×C22⋊Q8—21no—
133C29×C22⋊Q8—21no—
134C29×C22⋊Q8—21no—
135C29×C22⋊Q8—21no—
136C29×C22⋊Q8C2311yescharacteristic
137C29×C22⋊Q8C2311yescharacteristic
138C29×C22⋊Q8C2311yescharacteristic
139C29×#121—21no—
140C29×#121C2311yescharacteristic
141C29×#120—21no—
142C4×Q8×C29—21no—
143C4×Q8×C29—21no—
144C4×Q8×C29—21no—
145C4×Q8×C29D411yescharacteristic, complemented
146C4×Q8×C29D411yescharacteristic, complemented
147C4×Q8×C29D411yescharacteristic, complemented
148C4×D4×C29—21no—
149C4×D4×C29—21no—
150C4×D4×C29—21no—
151C4×D4×C29—21no—
152C4×D4×C29—21no—
153C4×D4×C29—21no—
154C4×D4×C29—21no—
155C4×D4×C29—21no—
156C4×D4×C29—21no—
157C4×D4×C29D411yescharacteristic, complemented
158C29×#117—21no—
159C29×#117—21no—
160C29×#117—21no—
161C29×#117—21no—
162C29×#117—21no—
163C29×#117—21no—
164C2×C4⋊C4×C29—21no—
165C2×C4⋊C4×C29—21no—
166C2×C4⋊C4×C29D411yescharacteristic
167C2×C4⋊C4×C29D411yescharacteristic
168C2×C4⋊C4×C29C2311yescharacteristic
169C2×C4⋊C4×C29C2311yescharacteristic
170C2×C22⋊C4×C29—21no—
171C2×C22⋊C4×C29—21no—
172C2×C22⋊C4×C29—21no—
173C2×C22⋊C4×C29—21no—
174C2×C22⋊C4×C29—21no—
175C2×C22⋊C4×C29—21no—
176C2×C22⋊C4×C29D411yescharacteristic
177C2×C22⋊C4×C29D411yescharacteristic
178C2×C22⋊C4×C29C2311yescharacteristic
179C2×C42×C29—21no—
180C2×C42×C29C2311yescharacteristic
181C29×#107—21no—
182C29×#106—21no—
183C29×#106—21no—
184C29×#106—21no—
185C29×C4⋊C8—21no—
186C29×C4⋊C8—21no—
187C29×#103—21no—
188C29×#103—21no—
189C29×#103—21no—
190C29×#102—21no—
191C29×#102—21no—
192C29×#102—21no—
193C29×#102—21no—
194C29×#102—21no—
195C29×C22⋊C8C2311yescharacteristic
196C29×C22⋊C8C2311yescharacteristic
197C29×C22⋊C8C2311yescharacteristic
198C29×C22⋊C8C2311yescharacteristic
199C29×#97—21no—
200C4×C8×C29—21no—
201C29×#95—21no—
202C29×#95—21no—
203C29×#95—21no—
204C29×#95C2311yescharacteristic
205C29×#95C2311yescharacteristic
206C24×C29—21no—
207C24×C29C2×D411yescharacteristic
208C2×Q8×C29—21no—
209C2×Q8×C29—21no—
210C2×Q8×C29—21no—
211C2×Q8×C29C2×D411yescharacteristic
212C2×Q8×C29C2×D411yescharacteristic
213C2×Q8×C29C2×D411yescharacteristic
214C2×D4×C29—21no—
215C2×D4×C29—21no—
216C2×D4×C29—21no—
217C2×D4×C29—21no—
218C2×D4×C29—21no—
219C2×D4×C29—42no—
220C2×D4×C29—42no—
221C2×D4×C29—42no—
222C2×D4×C29—81no—
223C2×D4×C29C2×D411yescharacteristic
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×C29—41no—
233C22×C4×C29—41no—
234C22×C4×C29—81no—
235C22×C4×C29—81no—
236C22×C4×C29C2×D411yescharacteristic
237C22×C4×C29C2×D411yescharacteristic
238C22×C4×C29C2×D411yescharacteristic
239C22×C4×C29C2×D411yescharacteristic
240C22×C4×C29C2×D411yescharacteristic
241C22×C4×C29C2411yescharacteristic
242SD16×C29—42no—
243SD16×C29—42no—
244SD16×C29—42no—
245D8×C29—42no—
246C2×C8×C29—21no—
247C2×C8×C29—21no—
248C2×C8×C29—21no—
249C2×C8×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—21no—
276C4⋊C4×C29—21no—
277C4⋊C4×C29—21no—
278C4⋊C4×C29—21no—
279C4⋊C4×C29—21no—
280C4⋊C4×C29—21no—
281C4⋊C4×C29—81no—
282C4⋊C4×C29C2×D411yescharacteristic
283C4⋊C4×C29C2×D411yescharacteristic
284C4⋊C4×C29C2×D411yescharacteristic
285C4⋊C4×C29C2×D411yescharacteristic
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—21no—
305C22⋊C4×C29—21no—
306C22⋊C4×C29—21no—
307C22⋊C4×C29—42no—
308C22⋊C4×C29—42no—
309C22⋊C4×C29—41no—
310C22⋊C4×C29—41no—
311C22⋊C4×C29—81no—
312C22⋊C4×C29—81no—
313C42×C29—21no—
314C42×C29—21no—
315C42×C29—21no—
316C42×C29—21no—
317C42×C29—21no—
318C42×C29—21no—
319C42×C29—21no—
320C42×C29—42no—
321C42×C29C2×D411yescharacteristic
322C42×C29C2×D411yescharacteristic
323C42×C29C2×D411yescharacteristic
324C42×C29C2×D411yescharacteristic
325#18282C2911yesmaximal, characteristic, direct product factor, Sylow
326C23×C29—22no—
327C23×C29—21no—
328C23×C29—21no—
329C23×C29—21no—
330C23×C29—21no—
331C23×C29—41no—
332C23×C29—41no—
333C23×C29—41no—
334C23×C29—41no—
335C23×C29—41no—
336C23×C29—41no—
337C23×C29—41no—
338C23×C29—41no—
339C23×C29C22×D411yescharacteristic
340Q8×C29—41no—
341Q8×C29—41no—
342Q8×C29—41no—
343Q8×C29—81no—
344Q8×C29—81no—
345Q8×C29—81no—
346D4×C29—22no—
347D4×C29—22no—
348D4×C29—41no—
349D4×C29—41no—
350D4×C29—41no—
351D4×C29—41no—
352D4×C29—41no—
353D4×C29—81no—
354D4×C29—81no—
355D4×C29—84no—
356C2×C4×C29—21no—
357C2×C4×C29—21no—
358C2×C4×C29—22no—
359C2×C4×C29—21no—
360C2×C4×C29—21no—
361C2×C4×C29—21no—
362C2×C4×C29—21no—
363C2×C4×C29—21no—
364C2×C4×C29—21no—
365C2×C4×C29—21no—
366C2×C4×C29—21no—
367C2×C4×C29—21no—
368C2×C4×C29—21no—
369C2×C4×C29—21no—
370C2×C4×C29—21no—
371C2×C4×C29—41no—
372C2×C4×C29—41no—
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—41no—
380C2×C4×C29—41no—
381C2×C4×C29—41no—
382C2×C4×C29—41no—
383C2×C4×C29—81no—
384C2×C4×C29—82no—
385C2×C4×C29—82no—
386C2×C4×C29—81no—
387C2×C4×C29—81no—
388C2×C4×C29—81no—
389C2×C4×C29—81no—
390C2×C4×C29#12011yescharacteristic
391C2×C4×C29#12011yescharacteristic
392C2×C4×C29#12011yescharacteristic
393C2×C4×C29#12011yescharacteristic
394C2×C4×C29C22×D411yescharacteristic
395C2×C4×C29C22×D411yescharacteristic
396C8×C29—41no—
397C8×C29—41no—
398C8×C29—41no—
399C8×C29—41no—
400#3564C2×C2911yescharacteristic, complemented
401#3114C2×C2911yescharacteristic, complemented
402#3101C2×C2911yescharacteristic, complemented
403#2603C2×C2911yescharacteristic, complemented
404#1612C2×C2911yescharacteristic, complemented
405#1611C2×C2911yescharacteristic, complemented
406#1609C2×C2911yescharacteristic, complemented
407#1608C2×C2911yescharacteristic, complemented
408#1600C2×C2911yescharacteristic
409#1599C2×C2911yescharacteristic, complemented
410#1597C2×C2911yescharacteristic, complemented
411#1596C2×C2911yescharacteristic, complemented
412#1506C2×C2911yescharacteristic, complemented
413#1500C2×C2911yescharacteristic, complemented
414#1473C2×C2911yescharacteristic, complemented
415C22×C29—21no—
416C22×C29—21no—
417C22×C29—42no—
418C22×C29—42no—
419C22×C29—41no—
420C22×C29—41no—
421C22×C29—41no—
422C22×C29—41no—
423C22×C29—41no—
424C22×C29—41no—
425C22×C29—42no—
426C22×C29—81no—
427C22×C29—81no—
428C22×C29—81no—
429C22×C29—81no—
430C22×C29—81no—
431C22×C29—81no—
432C22×C29C2×#12011yescharacteristic
433C22×C29#57711yescharacteristic
434C22×C29#57711yescharacteristic
435C4×C29—21no—
436C4×C29—21no—
437C4×C29—21no—
438C4×C29—21no—
439C4×C29—21no—
440C4×C29—21no—
441C4×C29—42no—
442C4×C29—41no—
443C4×C29—41no—
444C4×C29—41no—
445C4×C29—41no—
446C4×C29—41no—
447C4×C29—41no—
448C4×C29—41no—
449C4×C29—41no—
450C4×C29—41no—
451C4×C29—41no—
452C4×C29—81no—
453C4×C29—81no—
454#563—21no—
455#563—21no—
456#556—21no—
457#554—21no—
458#552—21no—
459#552—21no—
460#551—21no—
461#551—21no—
462#544C22×C2911yescharacteristic
463#543C22×C2911yescharacteristic
464#542—21no—
465#541—21no—
466#541—21no—
467#539—21no—
468#539C22×C2911yescharacteristic
469#538C22×C2911yescharacteristic
470#533C22×C2911yescharacteristic
471#529C22×C2911yescharacteristic
472C2×#126C22×C2911yescharacteristic
473C2×C4×D4C22×C2911yescharacteristic
474#483C22×C2911yescharacteristic
475#483C22×C2911yescharacteristic
476#483C22×C2911yescharacteristic
477#480C22×C2911yescharacteristic
478#478—21no—
479#476—21no—
480#463—21no—
481#461—21no—
482#450C22×C2911yescharacteristic
483#450C22×C2911yescharacteristic
484#450C22×C2911yescharacteristic
485#447C22×C2911yescharacteristic
486#442—21no—
487#440—21no—
488C4×SD16—21no—
489C4×SD16—21no—
490#432C22×C2911yescharacteristic
491#431C22×C2911yescharacteristic
492#398C22×C2911yescharacteristic
493#397C22×C2911yescharacteristic
494#394C22×C2911yescharacteristic
495#392C22×C2911yescharacteristic
496#390—21no—
497#388—21no—
498#386—21no—
499#385—21no—
500#376C22×C2911yescharacteristic
501#328C22×C2911yescharacteristic
502#328C22×C2911yescharacteristic
503#328C22×C2911yescharacteristic
504#328C22×C2911yescharacteristic
505#328C22×C2911yescharacteristic
506#328C22×C2911yescharacteristic
507#327C22×C2911yescharacteristic
508#327C22×C2911yescharacteristic
509#324C22×C2911yescharacteristic
510#324C22×C2911yescharacteristic
511#323C22×C2911yescharacteristic
512#323C22×C2911yescharacteristic
513C2×C29—21no—
514C2×C29—21no—
515C2×C29—81no—
516C2×C29—81no—
517C2×C29—82no—
518C2×C29#301011yescharacteristic
519C2×C29#301811yescharacteristic
520C2×C29#302511yescharacteristic
521C22×D4—21no—
522C22×D4C23×C2911yescharacteristic
523C23×C4—21no—
524C2×SD16—21no—
525C2×SD16—21no—
526C2×SD16—21no—
527C2×D8—21no—
528C4⋊Q8—21no—
529C4⋊Q8—21no—
530C4⋊Q8—21no—
531C4⋊Q8D4×C2911yescharacteristic, complemented
532C4⋊Q8D4×C2911yescharacteristic, complemented
533#126—21no—
534#126—21no—
535#126—21no—
536#126—21no—
537#126—21no—
538#126—21no—
539#126—21no—
540#126—21no—
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#125—21no—
547#125—21no—
548#125—21no—
549#125—21no—
550#125—21no—
551#125—21no—
552#125—21no—
553#125—21no—
554#125—21no—
555#125D4×C2911yescharacteristic, complemented
556#124—21no—
557#124—21no—
558#124—21no—
559#124D4×C2911yescharacteristic, complemented
560#123—21no—
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568C22⋊Q8—21no—
569C22⋊Q8—21no—
570C22⋊Q8—21no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8C23×C2911yescharacteristic
583C22⋊Q8C23×C2911yescharacteristic
584C22⋊Q8C23×C2911yescharacteristic
585#121—21no—
586#121C23×C2911yescharacteristic
587#120—21no—
588C4×Q8—21no—
589C4×Q8—21no—
590C4×Q8—21no—
591C4×Q8D4×C2911yescharacteristic, complemented
592C4×Q8D4×C2911yescharacteristic, complemented
593C4×Q8D4×C2911yescharacteristic, complemented
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—21no—
599C4×D4—21no—
600C4×D4—21no—
601C4×D4—21no—
602C4×D4—21no—
603C4×D4D4×C2911yescharacteristic, complemented
604#117—21no—
605#117—21no—
606#117—21no—
607#117—21no—
608#117—21no—
609#117—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4D4×C2911yescharacteristic
613C2×C4⋊C4D4×C2911yescharacteristic
614C2×C4⋊C4C23×C2911yescharacteristic
615C2×C4⋊C4C23×C2911yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4D4×C2911yescharacteristic
623C2×C22⋊C4D4×C2911yescharacteristic
624C2×C22⋊C4C23×C2911yescharacteristic
625C2×C42—21no—
626C2×C42C23×C2911yescharacteristic
627#107—21no—
628#106—21no—
629#106—21no—
630#106—21no—
631C4⋊C8—21no—
632C4⋊C8—21no—
633#103—21no—
634#103—21no—
635#103—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641C22⋊C8C23×C2911yescharacteristic
642C22⋊C8C23×C2911yescharacteristic
643C22⋊C8C23×C2911yescharacteristic
644C22⋊C8C23×C2911yescharacteristic
645#97—21no—
646C4×C8—21no—
647#95—21no—
648#95—21no—
649#95—21no—
650#95C23×C2911yescharacteristic
651#95C23×C2911yescharacteristic
652C29#1828211yescharacteristic, direct product factor, Sylow
653C24—21no—
654C24C2×D4×C2911yescharacteristic
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8C2×D4×C2911yescharacteristic
659C2×Q8C2×D4×C2911yescharacteristic
660C2×Q8C2×D4×C2911yescharacteristic
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—81no—
670C2×D4C2×D4×C2911yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—41no—
680C22×C4—41no—
681C22×C4—81no—
682C22×C4—81no—
683C22×C4C2×D4×C2911yescharacteristic
684C22×C4C2×D4×C2911yescharacteristic
685C22×C4C2×D4×C2911yescharacteristic
686C22×C4C2×D4×C2911yescharacteristic
687C22×C4C2×D4×C2911yescharacteristic
688C22×C4C24×C2911yescharacteristic
689SD16—42no—
690SD16—42no—
691SD16—42no—
692D8—42no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—81no—
729C4⋊C4C2×D4×C2911yescharacteristic
730C4⋊C4C2×D4×C2911yescharacteristic
731C4⋊C4C2×D4×C2911yescharacteristic
732C4⋊C4C2×D4×C2911yescharacteristic
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—41no—
757C22⋊C4—41no—
758C22⋊C4—81no—
759C22⋊C4—81no—
760C42—21no—
761C42—21no—
762C42—21no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—42no—
768C42C2×D4×C2911yescharacteristic
769C42C2×D4×C2911yescharacteristic
770C42C2×D4×C2911yescharacteristic
771C42C2×D4×C2911yescharacteristic
772C23—22no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23C22×D4×C2911yescharacteristic
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—81no—
790Q8—81no—
791Q8—81no—
792D4—22no—
793D4—22no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—81no—
800D4—81no—
801D4—84no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—81no—
830C2×C4—82no—
831C2×C4—82no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4C29×#12011yescharacteristic
837C2×C4C29×#12011yescharacteristic
838C2×C4C29×#12011yescharacteristic
839C2×C4C29×#12011yescharacteristic
840C2×C4C22×D4×C2911yescharacteristic
841C2×C4C22×D4×C2911yescharacteristic
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C22—21no—
847C22—21no—
848C22—42no—
849C22—42no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—42no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22C2×C29×#12011yescharacteristic
864C22C29×#57711yescharacteristic
865C22C29×#57711yescharacteristic
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—42no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C2—21no—
886C2—21no—
887C2—82no—
888C2—81no—
889C2—81no—
890C2C29×#301011yescharacteristic
891C2C29×#301811yescharacteristic
892C2C29×#302511yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#1600C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C29×#3564C2semidirect
2. C29×#3114C2semidirect
3. C29×#3101C2semidirect
4. C29×#2603C2semidirect
5. C29×#1612C2semidirect
6. C29×#1611C2semidirect
7. C29×#1609C2semidirect
8. C29×#1608C2semidirect
10. C29×#1599C2semidirect
11. C29×#1597C2semidirect
12. C29×#1596C2semidirect
13. C29×#1506C2semidirect
14. C29×#1500C2semidirect
15. C29×#1473C2semidirect
85. C29×C4⋊Q8D4semidirect
86. C29×C4⋊Q8D4semidirect
109. C29×#125D4semidirect
113. C29×#124D4semidirect
145. C4×Q8×C29D4semidirect
146. C4×Q8×C29D4semidirect
147. C4×Q8×C29D4semidirect
157. C4×D4×C29D4semidirect
325. #18282C29direct (N × H)
400. #3564C2×C29semidirect
401. #3114C2×C29semidirect
402. #3101C2×C29semidirect
403. #2603C2×C29semidirect
404. #1612C2×C29semidirect
405. #1611C2×C29semidirect
406. #1609C2×C29semidirect
407. #1608C2×C29semidirect
409. #1599C2×C29semidirect
410. #1597C2×C29semidirect
411. #1596C2×C29semidirect
412. #1506C2×C29semidirect
413. #1500C2×C29semidirect
414. #1473C2×C29semidirect
531. C4⋊Q8D4×C29semidirect
532. C4⋊Q8D4×C29semidirect
555. #125D4×C29semidirect
559. #124D4×C29semidirect
591. C4×Q8D4×C29semidirect
592. C4×Q8D4×C29semidirect
593. C4×Q8D4×C29semidirect
603. C4×D4D4×C29semidirect
652. C29#18282direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35642
C29×#31142
C29×#31012
C29×#26032
C29×#16122
C29×#16112
C29×#16092
C29×#16082
C29×#16002
C29×#15992
C29×#15972
C29×#15962
C29×#15062
C29×#15002
C29×#14732
#1828229