Finite Group Databasebeta

← C29×#19068 #20313968

Subgroups — C29×#19068 #20313968

Order 7424.

920 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3545C211yesmaximal, characteristic, complemented
2C29×#3219C211yesmaximal, characteristic, complemented
3C29×#3213C211yesmaximal, characteristic, complemented
4C29×#3171C211yesmaximal, characteristic, complemented
5C29×#1664C211yesmaximal, characteristic, complemented
6C29×#1662C211yesmaximal, characteristic, complemented
7C29×#1661C211yesmaximal, characteristic, complemented
8C29×#1659C211yesmaximal, characteristic, complemented
9C29×#1657C211yesmaximal, characteristic, complemented
10C29×#1656C211yesmaximal, characteristic, complemented
11C29×#1656C211yesmaximal, characteristic, complemented
12C29×#1655C211yesmaximal, characteristic, complemented
13C29×#1535C211yesmaximal, characteristic, complemented
14C29×#1529C211yesmaximal, characteristic, complemented
15C29×#1527C211yesmaximal, characteristic, complemented
16C29×#563C2211yescharacteristic
17C29×#562C2211yescharacteristic
18C29×#562C2211yescharacteristic
19C29×H(3,𝔽4)C2211yescharacteristic
20C29×#555—21no—
21C29×#551—21no—
22C29×#551—21no—
23C29×#551—21no—
24C29×#546—21no—
25C29×#546—21no—
26C29×#542—21no—
27C29×#542—21no—
28C29×#538—21no—
29C29×#538—21no—
30C29×#536—21no—
31C29×#534—21no—
32C29×#532C2211yescharacteristic, complemented
33C29×#529C2211yescharacteristic
34C29×#529C2211yescharacteristic
35C2×C29×#124C2211yescharacteristic
36C29×#501C2211yescharacteristic, complemented
37C29×#497C2211yescharacteristic, complemented
38C29×#496C2211yescharacteristic
39C29×#496C2211yescharacteristic, complemented
40C29×#496C2211yescharacteristic, complemented
41C29×#496C2211yescharacteristic, complemented
42C29×#491C2211yescharacteristic, complemented
43C29×#490C2211yescharacteristic, complemented
44C29×#490C2211yescharacteristic, complemented
45C29×#489C2211yescharacteristic
46C29×#489C2211yescharacteristic, complemented
47C29×#489C2211yescharacteristic, complemented
48C29×#469—21no—
49C29×#468—21no—
50C29×#464—21no—
51C29×#463—21no—
52C29×#463—21no—
53C29×#463—21no—
54C29×#452—21no—
55C29×#449—21no—
56C29×#448—21no—
57C29×#447—21no—
58C4×SD16×C29—21no—
59C4×D8×C29—21no—
60C29×#432C2211yescharacteristic, complemented
61C29×#432C2211yescharacteristic, complemented
62C4×M16×C29C2211yescharacteristic, complemented
63C29×#330C2211yescharacteristic, complemented
64C29×#330C2211yescharacteristic, complemented
65C29×#330C2211yescharacteristic, complemented
66C29×#330C2211yescharacteristic, complemented
67C29×#329C2211yescharacteristic
68C29×#329C2211yescharacteristic
69C29×#329C2211yescharacteristic, complemented
70C29×#329C2211yescharacteristic, complemented
71C29×#329C2211yescharacteristic, complemented
72C29×#329C2211yescharacteristic, complemented
73C29×#329C2211yescharacteristic, complemented
74C29×#329C2211yescharacteristic, complemented
75C2×#41×C29—21no—
76C2×#41×C29—21no—
77C22×Q8×C29D411yescharacteristic
78C22×D4×C29—21no—
79C22×D4×C29D411yescharacteristic
80C2×Q16×C29—21no—
81C2×SD16×C29—21no—
82C2×SD16×C29—21no—
83C2×SD16×C29—21no—
84C2×SD16×C29—21no—
85C2×SD16×C29—21no—
86C2×D8×C29—21no—
87C2×D8×C29—21no—
88C2×D8×C29—21no—
89C2×D8×C29—21no—
90C2×M16×C29—21no—
91C29×C4⋊Q8—21no—
92C29×C4⋊Q8—21no—
93C29×C4⋊Q8C2311yescharacteristic
94C29×#127C2311yescharacteristic
95C29×#126—21no—
96C29×#126—21no—
97C29×#126—21no—
98C29×#126—21no—
99C29×#126—21no—
100C29×#126—21no—
101C29×#125C2311yescharacteristic
102C29×#125C2311yescharacteristic
103C29×#124—21no—
104C29×#124—21no—
105C29×#124—21no—
106C29×#124—21no—
107C29×#124—21no—
108C29×#124—21no—
109C29×#124—21no—
110C29×#124—21no—
111C29×#124—21no—
112C29×#124D411yescharacteristic
113C29×#124D411yescharacteristic
114C29×#124C2311yescharacteristic
115C29×#124C2311yescharacteristic
116C29×#124C2311yescharacteristic
117C29×#124C2311yescharacteristic
118C29×#123—21no—
119C29×#123—21no—
120C29×#123—21no—
121C29×#123—21no—
122C29×#123—21no—
123C29×#123—21no—
124C29×#123—21no—
125C29×#123—21no—
126C29×#123—21no—
127C29×#123—21no—
128C29×#123—21no—
129C29×#123—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⋊Q8—21no—
137C29×C22⋊Q8—21no—
138C29×C22⋊Q8D411yescharacteristic
139C29×C22⋊Q8D411yescharacteristic
140C29×#121—21no—
141C29×#121—21no—
142C29×#121—21no—
143C29×#121—21no—
144C29×#121—21no—
145C29×#121—21no—
146C29×#121—21no—
147C29×#121—21no—
148C29×#121—21no—
149C29×#121—21no—
150C29×#121D411yescharacteristic
151C29×#121D411yescharacteristic
152C29×#120—21no—
153C29×#120—21no—
154C29×#120—21no—
155C29×#120—21no—
156C29×#120—21no—
157C29×#120—21no—
158C4×Q8×C29D411yescharacteristic
159C4×Q8×C29D411yescharacteristic
160C4×D4×C29—21no—
161C4×D4×C29—21no—
162C4×D4×C29—21no—
163C4×D4×C29—21no—
164C4×D4×C29—21no—
165C4×D4×C29—21no—
166C4×D4×C29—21no—
167C4×D4×C29—21no—
168C4×D4×C29D411yescharacteristic
169C4×D4×C29D411yescharacteristic
170C29×#117—21no—
171C29×#117—21no—
172C29×#117—21no—
173C29×#117—21no—
174C29×#117—21no—
175C2×C22⋊C4×C29—21no—
176C2×C22⋊C4×C29—21no—
177C2×C22⋊C4×C29—21no—
178C2×C22⋊C4×C29—21no—
179C2×C22⋊C4×C29—21no—
180C2×C42×C29C2311yescharacteristic
181C29×#107—21no—
182C29×#106—21no—
183C29×C4⋊C8—21no—
184C29×C4⋊C8—21no—
185C29×#103—21no—
186C29×#103—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×#102—21no—
196C29×#102—21no—
197C29×C22⋊C8—21no—
198C29×C22⋊C8—21no—
199C29×#97C2311yescharacteristic
200C29×#97C2311yescharacteristic
201C29×#97C2311yescharacteristic
202C29×#97C2311yescharacteristic
203C29×#97C2311yescharacteristic
204C29×#97C2311yescharacteristic
205C4×C8×C29—21no—
206C24×C29—21no—
207C24×C29—21no—
208#41×C29—82no—
209#41×C29—81no—
210#41×C29—81no—
211C2×Q8×C29—21no—
212C2×Q8×C29—21no—
213C2×Q8×C29—21no—
214C2×Q8×C29—81no—
215C2×Q8×C29C2×D411yescharacteristic
216C2×Q8×C29C2×D411yescharacteristic
217C2×Q8×C29C2×D411yescharacteristic
218C2×Q8×C29C2×D411yescharacteristic
219C2×D4×C29—21no—
220C2×D4×C29—21no—
221C2×D4×C29—21no—
222C2×D4×C29—21no—
223C2×D4×C29—21no—
224C2×D4×C29—21no—
225C2×D4×C29—21no—
226C2×D4×C29—21no—
227C2×D4×C29—21no—
228C2×D4×C29—21no—
229C2×D4×C29—21no—
230C2×D4×C29—21no—
231C2×D4×C29—21no—
232C2×D4×C29—41no—
233C2×D4×C29—81no—
234C2×D4×C29—82no—
235C2×D4×C29C2×D411yescharacteristic
236C2×D4×C29C2×D411yescharacteristic
237C2×D4×C29C2×D411yescharacteristic
238C2×D4×C29C2×D411yescharacteristic
239C22×C4×C29—21no—
240C22×C4×C29—21no—
241C22×C4×C29—21no—
242C22×C4×C29—21no—
243C22×C4×C29—21no—
244C22×C4×C29—21no—
245C22×C4×C29—21no—
246C22×C4×C29—21no—
247C22×C4×C29—41no—
248C22×C4×C29C2×D411yescharacteristic
249C22×C4×C29C2×D411yescharacteristic
250C22×C4×C29C2×D411yescharacteristic
251Q16×C29—81no—
252SD16×C29—42no—
253SD16×C29—81no—
254SD16×C29—81no—
255SD16×C29—81no—
256SD16×C29—81no—
257D8×C29—42no—
258D8×C29—81no—
259D8×C29—81no—
260D8×C29—81no—
261M16×C29—42no—
262C2×C8×C29—21no—
263C2×C8×C29—21no—
264C2×C8×C29—21no—
265C2×C8×C29—21no—
266C2×C8×C29—21no—
267C2×C8×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—21no—
282C4⋊C4×C29—21no—
283C4⋊C4×C29—21no—
284C4⋊C4×C29C2×D411yescharacteristic
285C4⋊C4×C29C2×D411yescharacteristic
286C4⋊C4×C29C2×D411yescharacteristic
287C4⋊C4×C29C2×D411yescharacteristic
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—21no—
308C22⋊C4×C29—21no—
309C22⋊C4×C29—21no—
310C22⋊C4×C29—21no—
311C22⋊C4×C29—21no—
312C22⋊C4×C29—21no—
313C22⋊C4×C29—21no—
314C22⋊C4×C29—21no—
315C22⋊C4×C29—21no—
316C22⋊C4×C29—41no—
317C22⋊C4×C29—41no—
318C42×C29—21no—
319C42×C29—21no—
320C42×C29—21no—
321C42×C29—21no—
322C42×C29C2×D411yescharacteristic
323C42×C29C2×D411yescharacteristic
324C42×C29C2×D411yescharacteristic
325C42×C29C2411yescharacteristic
326#19068C2911yesmaximal, characteristic, direct product factor, Sylow
327C23×C29—21no—
328C23×C29—21no—
329C23×C29—21no—
330C23×C29—21no—
331C23×C29—42no—
332C23×C29—41no—
333C23×C29—81no—
334C23×C29—81no—
335C23×C29—81no—
336C23×C29—81no—
337C23×C29—81no—
338C23×C29#12011yescharacteristic
339Q8×C29—41no—
340Q8×C29—41no—
341Q8×C29—41no—
342Q8×C29—41no—
343Q8×C29—41no—
344Q8×C29—41no—
345Q8×C29—81no—
346Q8×C29—81no—
347D4×C29—41no—
348D4×C29—41no—
349D4×C29—41no—
350D4×C29—41no—
351D4×C29—41no—
352D4×C29—41no—
353D4×C29—41no—
354D4×C29—41no—
355D4×C29—41no—
356D4×C29—41no—
357D4×C29—42no—
358D4×C29—42no—
359D4×C29—81no—
360D4×C29—81no—
361D4×C29—81no—
362D4×C29—81no—
363D4×C29—81no—
364D4×C29—81no—
365D4×C29—81no—
366D4×C29—81no—
367D4×C29—82no—
368C2×C4×C29—21no—
369C2×C4×C29—21no—
370C2×C4×C29—21no—
371C2×C4×C29—21no—
372C2×C4×C29—21no—
373C2×C4×C29—21no—
374C2×C4×C29—21no—
375C2×C4×C29—21no—
376C2×C4×C29—41no—
377C2×C4×C29—41no—
378C2×C4×C29—41no—
379C2×C4×C29—42no—
380C2×C4×C29—41no—
381C2×C4×C29—81no—
382C2×C4×C29—81no—
383C2×C4×C29—82no—
384C2×C4×C29—81no—
385C2×C4×C29—81no—
386C2×C4×C29—81no—
387C2×C4×C29—81no—
388C2×C4×C29—81no—
389C2×C4×C29#12011yescharacteristic
390C2×C4×C29#12011yescharacteristic
391C2×C4×C29#12011yescharacteristic
392C2×C4×C29C22×D411yescharacteristic
393C2×C4×C29C22×D411yescharacteristic
394C2×C4×C29C22×D411yescharacteristic
395C8×C29—22no—
396C8×C29—41no—
397C8×C29—41no—
398C8×C29—41no—
399C8×C29—41no—
400C8×C29—41no—
401#3545C2×C2911yescharacteristic, complemented
402#3219C2×C2911yescharacteristic, complemented
403#3213C2×C2911yescharacteristic, complemented
404#3171C2×C2911yescharacteristic, complemented
405#1664C2×C2911yescharacteristic, complemented
406#1662C2×C2911yescharacteristic, complemented
407#1661C2×C2911yescharacteristic, complemented
408#1659C2×C2911yescharacteristic, complemented
409#1657C2×C2911yescharacteristic, complemented
410#1656C2×C2911yescharacteristic, complemented
411#1656C2×C2911yescharacteristic, complemented
412#1655C2×C2911yescharacteristic, complemented
413#1535C2×C2911yescharacteristic, complemented
414#1529C2×C2911yescharacteristic, complemented
415#1527C2×C2911yescharacteristic, complemented
416C22×C29—21no—
417C22×C29—21no—
418C22×C29—21no—
419C22×C29—41no—
420C22×C29—41no—
421C22×C29—41no—
422C22×C29—41no—
423C22×C29—41no—
424C22×C29—41no—
425C22×C29—41no—
426C22×C29—41no—
427C22×C29—41no—
428C22×C29—41no—
429C22×C29—41no—
430C22×C29—41no—
431C22×C29—81no—
432C22×C29—81no—
433C22×C29—81no—
434C22×C29—162no—
435C22×C29—162no—
436C22×C29C2×#12011yescharacteristic
437C4×C29—21no—
438C4×C29—21no—
439C4×C29—21no—
440C4×C29—21no—
441C4×C29—21no—
442C4×C29—21no—
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—81no—
452#563C22×C2911yescharacteristic
453#562C22×C2911yescharacteristic
454#562C22×C2911yescharacteristic
455H(3,𝔽4)C22×C2911yescharacteristic
456#555—21no—
457#551—21no—
458#551—21no—
459#551—21no—
460#546—21no—
461#546—21no—
462#542—21no—
463#542—21no—
464#538—21no—
465#538—21no—
466#536—21no—
467#534—21no—
468#532C22×C2911yescharacteristic, complemented
469#529C22×C2911yescharacteristic
470#529C22×C2911yescharacteristic
471C2×#124C22×C2911yescharacteristic
472#501C22×C2911yescharacteristic, complemented
473#497C22×C2911yescharacteristic, complemented
474#496C22×C2911yescharacteristic
475#496C22×C2911yescharacteristic, complemented
476#496C22×C2911yescharacteristic, complemented
477#496C22×C2911yescharacteristic, complemented
478#491C22×C2911yescharacteristic, complemented
479#490C22×C2911yescharacteristic, complemented
480#490C22×C2911yescharacteristic, complemented
481#489C22×C2911yescharacteristic
482#489C22×C2911yescharacteristic, complemented
483#489C22×C2911yescharacteristic, complemented
484#469—21no—
485#468—21no—
486#464—21no—
487#463—21no—
488#463—21no—
489#463—21no—
490#452—21no—
491#449—21no—
492#448—21no—
493#447—21no—
494C4×SD16—21no—
495C4×D8—21no—
496#432C22×C2911yescharacteristic, complemented
497#432C22×C2911yescharacteristic, complemented
498C4×M16C22×C2911yescharacteristic, complemented
499#330C22×C2911yescharacteristic, complemented
500#330C22×C2911yescharacteristic, complemented
501#330C22×C2911yescharacteristic, complemented
502#330C22×C2911yescharacteristic, complemented
503#329C22×C2911yescharacteristic
504#329C22×C2911yescharacteristic
505#329C22×C2911yescharacteristic, complemented
506#329C22×C2911yescharacteristic, complemented
507#329C22×C2911yescharacteristic, complemented
508#329C22×C2911yescharacteristic, complemented
509#329C22×C2911yescharacteristic, complemented
510#329C22×C2911yescharacteristic, complemented
511C2×C29—41no—
512C2×C29—81no—
513C2×C29—81no—
514C2×C29—81no—
515C2×C29—81no—
516C2×C29—161no—
517C2×C29#301811yescharacteristic
518C2×C29#301911yescharacteristic
519C2×C29#302111yescharacteristic
520C2×#41—21no—
521C2×#41—21no—
522C22×Q8D4×C2911yescharacteristic
523C22×D4—21no—
524C22×D4D4×C2911yescharacteristic
525C2×Q16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×D8—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C2×M16—21no—
536C4⋊Q8—21no—
537C4⋊Q8—21no—
538C4⋊Q8C23×C2911yescharacteristic
539#127C23×C2911yescharacteristic
540#126—21no—
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#125C23×C2911yescharacteristic
547#125C23×C2911yescharacteristic
548#124—21no—
549#124—21no—
550#124—21no—
551#124—21no—
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124D4×C2911yescharacteristic
558#124D4×C2911yescharacteristic
559#124C23×C2911yescharacteristic
560#124C23×C2911yescharacteristic
561#124C23×C2911yescharacteristic
562#124C23×C2911yescharacteristic
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573#123—21no—
574#123—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8D4×C2911yescharacteristic
584C22⋊Q8D4×C2911yescharacteristic
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121—21no—
595#121D4×C2911yescharacteristic
596#121D4×C2911yescharacteristic
597#120—21no—
598#120—21no—
599#120—21no—
600#120—21no—
601#120—21no—
602#120—21no—
603C4×Q8D4×C2911yescharacteristic
604C4×Q8D4×C2911yescharacteristic
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4D4×C2911yescharacteristic
614C4×D4D4×C2911yescharacteristic
615#117—21no—
616#117—21no—
617#117—21no—
618#117—21no—
619#117—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C42C23×C2911yescharacteristic
626#107—21no—
627#106—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630#103—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644#97C23×C2911yescharacteristic
645#97C23×C2911yescharacteristic
646#97C23×C2911yescharacteristic
647#97C23×C2911yescharacteristic
648#97C23×C2911yescharacteristic
649#97C23×C2911yescharacteristic
650C4×C8—21no—
651C29#1906811yescharacteristic, direct product factor, Sylow
652C24—21no—
653C24—21no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—81no—
661C2×Q8C2×D4×C2911yescharacteristic
662C2×Q8C2×D4×C2911yescharacteristic
663C2×Q8C2×D4×C2911yescharacteristic
664C2×Q8C2×D4×C2911yescharacteristic
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—41no—
679C2×D4—81no—
680C2×D4—82no—
681C2×D4C2×D4×C2911yescharacteristic
682C2×D4C2×D4×C2911yescharacteristic
683C2×D4C2×D4×C2911yescharacteristic
684C2×D4C2×D4×C2911yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—41no—
694C22×C4C2×D4×C2911yescharacteristic
695C22×C4C2×D4×C2911yescharacteristic
696C22×C4C2×D4×C2911yescharacteristic
697Q16—81no—
698SD16—42no—
699SD16—81no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703D8—42no—
704D8—81no—
705D8—81no—
706D8—81no—
707M16—42no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—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—21no—
729C4⋊C4—21no—
730C4⋊C4C2×D4×C2911yescharacteristic
731C4⋊C4C2×D4×C2911yescharacteristic
732C4⋊C4C2×D4×C2911yescharacteristic
733C4⋊C4C2×D4×C2911yescharacteristic
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—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—41no—
763C22⋊C4—41no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42C2×D4×C2911yescharacteristic
769C42C2×D4×C2911yescharacteristic
770C42C2×D4×C2911yescharacteristic
771C42C24×C2911yescharacteristic
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—42no—
777C23—41no—
778C23—81no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23C29×#12011yescharacteristic
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—81no—
791Q8—81no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—42no—
803D4—42no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—82no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—82no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4C29×#12011yescharacteristic
835C2×C4C29×#12011yescharacteristic
836C2×C4C29×#12011yescharacteristic
837C2×C4C22×D4×C2911yescharacteristic
838C2×C4C22×D4×C2911yescharacteristic
839C2×C4C22×D4×C2911yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—162no—
865C22—162no—
866C22C2×C29×#12011yescharacteristic
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—81no—
882C2—41no—
883C2—81no—
884C2—81no—
885C2—81no—
886C2—81no—
887C2—161no—
888C2C29×#301811yescharacteristic
889C2C29×#301911yescharacteristic
890C2C29×#302111yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC42C24×C29
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
1. C29×#3545C2semidirect
2. C29×#3219C2semidirect
3. C29×#3213C2semidirect
4. C29×#3171C2semidirect
5. C29×#1664C2semidirect
6. C29×#1662C2semidirect
7. C29×#1661C2semidirect
8. C29×#1659C2semidirect
9. C29×#1657C2semidirect
10. C29×#1656C2semidirect
11. C29×#1656C2semidirect
12. C29×#1655C2semidirect
13. C29×#1535C2semidirect
14. C29×#1529C2semidirect
15. C29×#1527C2semidirect
32. C29×#532C22semidirect
36. C29×#501C22semidirect
37. C29×#497C22semidirect
39. C29×#496C22semidirect
40. C29×#496C22semidirect
41. C29×#496C22semidirect
42. C29×#491C22semidirect
43. C29×#490C22semidirect
44. C29×#490C22semidirect
46. C29×#489C22semidirect
47. C29×#489C22semidirect
60. C29×#432C22semidirect
61. C29×#432C22semidirect
62. C4×M16×C29C22semidirect
63. C29×#330C22semidirect
64. C29×#330C22semidirect
65. C29×#330C22semidirect
66. C29×#330C22semidirect
69. C29×#329C22semidirect
70. C29×#329C22semidirect
71. C29×#329C22semidirect
72. C29×#329C22semidirect
73. C29×#329C22semidirect
74. C29×#329C22semidirect
326. #19068C29direct (N × H)
401. #3545C2×C29semidirect
402. #3219C2×C29semidirect
403. #3213C2×C29semidirect
404. #3171C2×C29semidirect
405. #1664C2×C29semidirect
406. #1662C2×C29semidirect
407. #1661C2×C29semidirect
408. #1659C2×C29semidirect
409. #1657C2×C29semidirect
410. #1656C2×C29semidirect
411. #1656C2×C29semidirect
412. #1655C2×C29semidirect
413. #1535C2×C29semidirect
414. #1529C2×C29semidirect
415. #1527C2×C29semidirect
468. #532C22×C29semidirect
472. #501C22×C29semidirect
473. #497C22×C29semidirect
475. #496C22×C29semidirect
476. #496C22×C29semidirect
477. #496C22×C29semidirect
478. #491C22×C29semidirect
479. #490C22×C29semidirect
480. #490C22×C29semidirect
482. #489C22×C29semidirect
483. #489C22×C29semidirect
496. #432C22×C29semidirect
497. #432C22×C29semidirect
498. C4×M16C22×C29semidirect
499. #330C22×C29semidirect
500. #330C22×C29semidirect
501. #330C22×C29semidirect
502. #330C22×C29semidirect
505. #329C22×C29semidirect
506. #329C22×C29semidirect
507. #329C22×C29semidirect
508. #329C22×C29semidirect
509. #329C22×C29semidirect
510. #329C22×C29semidirect
651. C29#19068direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35452
C29×#32192
C29×#32132
C29×#31712
C29×#16642
C29×#16622
C29×#16612
C29×#16592
C29×#16572
C29×#16562
C29×#16552
C29×#15352
C29×#15292
C29×#15272
#1906829