Finite Group Databasebeta

← C29×#18445 #20313345

Subgroups — C29×#18445 #20313345

Order 7424.

848 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3564C211yesmaximal, characteristic
2C29×#3236C211yesmaximal, characteristic, complemented
3C29×#3232C211yesmaximal, characteristic, complemented
4C29×#2664C211yesmaximal, characteristic, complemented
5C29×#1618C211yesmaximal, characteristic
6C29×#1617C211yesmaximal, characteristic, complemented
7C29×#1615C211yesmaximal, characteristic, complemented
8C29×#1614C211yesmaximal, characteristic, complemented
9C29×#1612C211yesmaximal, characteristic
10C29×#1611C211yesmaximal, characteristic, complemented
11C29×#1609C211yesmaximal, characteristic, complemented
12C29×#1608C211yesmaximal, characteristic, complemented
13C29×#1509C211yesmaximal, characteristic, complemented
14C29×#1503C211yesmaximal, 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×C29×#125C2211yescharacteristic
36C29×#501—21no—
37C29×#499—21no—
38C29×#491—21no—
39C29×#488—21no—
40C29×#484C2211yescharacteristic
41C29×#484C2211yescharacteristic
42C29×#484C2211yescharacteristic
43C29×#483C2211yescharacteristic
44C29×#483C2211yescharacteristic
45C29×#483C2211yescharacteristic
46C29×#481C2211yescharacteristic
47C29×#480C2211yescharacteristic
48C29×#479—21no—
49C29×#479—21no—
50C29×#479—21no—
51C29×#478—21no—
52C29×#432C2211yescharacteristic
53C29×#431C2211yescharacteristic
54C29×#400C2211yescharacteristic
55C29×#399C2211yescharacteristic
56C29×#398—21no—
57C29×#398C2211yescharacteristic
58C29×#397C2211yescharacteristic
59C29×#396—21no—
60C29×#389—21no—
61C29×#388—21no—
62C4×C4⋊C4×C29C2211yescharacteristic
63C29×#328C2211yescharacteristic
64C29×#328C2211yescharacteristic
65C29×#328C2211yescharacteristic
66C29×#328C2211yescharacteristic
67C29×#328C2211yescharacteristic
68C29×#328C2211yescharacteristic
69C29×#327C2211yescharacteristic
70C29×#327C2211yescharacteristic
71C29×#324C2211yescharacteristic
72C29×#324C2211yescharacteristic
73C29×#323C2211yescharacteristic
74C29×#323C2211yescharacteristic
75C29×C4⋊Q8—21no—
76C29×C4⋊Q8—21no—
77C29×C4⋊Q8—21no—
78C29×C4⋊Q8D411yescharacteristic
79C29×C4⋊Q8D411yescharacteristic
80C29×#126—21no—
81C29×#126—21no—
82C29×#126—21no—
83C29×#126—21no—
84C29×#126—21no—
85C29×#126—21no—
86C29×#126—21no—
87C29×#126—21no—
88C29×#126—21no—
89C29×#126—21no—
90C29×#126—21no—
91C29×#126—21no—
92C29×#126—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×#125—21no—
102C29×#125—21no—
103C29×#125—21no—
104C29×#125—21no—
105C29×#125—21no—
106C29×#125D411yescharacteristic
107C29×#124—21no—
108C29×#124—21no—
109C29×#124—21no—
110C29×#124D411yescharacteristic
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×C22⋊Q8—21no—
120C29×C22⋊Q8—21no—
121C29×C22⋊Q8—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⋊Q8C2311yescharacteristic
134C29×C22⋊Q8C2311yescharacteristic
135C29×C22⋊Q8C2311yescharacteristic
136C29×#121—21no—
137C29×#121C2311yescharacteristic
138C29×#120—21no—
139C4×Q8×C29—21no—
140C4×Q8×C29—21no—
141C4×Q8×C29—21no—
142C4×Q8×C29D411yescharacteristic
143C4×Q8×C29D411yescharacteristic
144C4×Q8×C29D411yescharacteristic
145C4×D4×C29—21no—
146C4×D4×C29—21no—
147C4×D4×C29—21no—
148C4×D4×C29—21no—
149C4×D4×C29—21no—
150C4×D4×C29D411yescharacteristic
151C29×#117—21no—
152C29×#117—21no—
153C29×#117—21no—
154C29×#117—21no—
155C29×#117—21no—
156C29×#117—21no—
157C2×C4⋊C4×C29—21no—
158C2×C4⋊C4×C29—21no—
159C2×C4⋊C4×C29—21no—
160C2×C4⋊C4×C29—21no—
161C2×C4⋊C4×C29—21no—
162C2×C4⋊C4×C29—21no—
163C2×C4⋊C4×C29D411yescharacteristic
164C2×C4⋊C4×C29D411yescharacteristic
165C2×C4⋊C4×C29C2311yescharacteristic
166C2×C4⋊C4×C29C2311yescharacteristic
167C2×C4⋊C4×C29C2311yescharacteristic
168C2×C22⋊C4×C29—21no—
169C2×C22⋊C4×C29—21no—
170C2×C22⋊C4×C29—21no—
171C2×C22⋊C4×C29D411yescharacteristic
172C2×C22⋊C4×C29D411yescharacteristic
173C2×C22⋊C4×C29C2311yescharacteristic
174C2×C42×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×C4⋊C8—21no—
186C29×#103—21no—
187C29×#103—21no—
188C29×#103—21no—
189C29×#103—21no—
190C29×#103—21no—
191C29×#103—21no—
192C29×#102—21no—
193C29×#102—21no—
194C29×C22⋊C8C2311yescharacteristic
195C29×C22⋊C8C2311yescharacteristic
196C29×C22⋊C8C2311yescharacteristic
197C29×C22⋊C8C2311yescharacteristic
198C29×#97—21no—
199C4×C8×C29—21no—
200C29×#95—21no—
201C29×#95—21no—
202C29×#95—21no—
203C29×#95—21no—
204C29×#95C2311yescharacteristic
205C29×#95C2311yescharacteristic
206C24×C29C2×D411yescharacteristic
207C2×Q8×C29—21no—
208C2×Q8×C29—21no—
209C2×Q8×C29—21no—
210C2×Q8×C29C2×D411yescharacteristic
211C2×Q8×C29C2×D411yescharacteristic
212C2×Q8×C29C2×D411yescharacteristic
213C2×D4×C29—21no—
214C2×D4×C29—21no—
215C2×D4×C29—21no—
216C2×D4×C29C2×D411yescharacteristic
217C22×C4×C29—21no—
218C22×C4×C29—21no—
219C22×C4×C29—21no—
220C22×C4×C29—21no—
221C22×C4×C29—21no—
222C22×C4×C29—21no—
223C22×C4×C29—21no—
224C22×C4×C29—21no—
225C22×C4×C29—21no—
226C22×C4×C29C2×D411yescharacteristic
227C22×C4×C29C2×D411yescharacteristic
228C22×C4×C29C2×D411yescharacteristic
229C22×C4×C29C2×D411yescharacteristic
230C22×C4×C29C2×D411yescharacteristic
231C22×C4×C29C2411yescharacteristic
232C2×C8×C29—21no—
233C2×C8×C29—21no—
234C2×C8×C29—21no—
235C2×C8×C29—21no—
236C4⋊C4×C29—21no—
237C4⋊C4×C29—21no—
238C4⋊C4×C29—21no—
239C4⋊C4×C29—21no—
240C4⋊C4×C29—21no—
241C4⋊C4×C29—21no—
242C4⋊C4×C29—21no—
243C4⋊C4×C29—21no—
244C4⋊C4×C29—21no—
245C4⋊C4×C29—21no—
246C4⋊C4×C29—21no—
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—42no—
270C4⋊C4×C29—42no—
271C4⋊C4×C29—41no—
272C4⋊C4×C29—41no—
273C4⋊C4×C29—41no—
274C4⋊C4×C29—41no—
275C4⋊C4×C29—81no—
276C4⋊C4×C29C2×D411yescharacteristic
277C4⋊C4×C29C2×D411yescharacteristic
278C4⋊C4×C29C2×D411yescharacteristic
279C4⋊C4×C29C2×D411yescharacteristic
280C22⋊C4×C29—21no—
281C22⋊C4×C29—21no—
282C22⋊C4×C29—21no—
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—42no—
302C22⋊C4×C29—81no—
303C42×C29—21no—
304C42×C29—21no—
305C42×C29—21no—
306C42×C29—21no—
307C42×C29—21no—
308C42×C29—21no—
309C42×C29—21no—
310C42×C29—81no—
311C42×C29C2×D411yescharacteristic
312C42×C29C2×D411yescharacteristic
313C42×C29C2×D411yescharacteristic
314C42×C29C2×D411yescharacteristic
315#18445C2911yesmaximal, characteristic, direct product factor, Sylow
316C23×C29—21no—
317C23×C29—21no—
318C23×C29—21no—
319C23×C29—21no—
320C23×C29—41no—
321C23×C29—41no—
322C23×C29C22×D411yescharacteristic
323Q8×C29—41no—
324Q8×C29—41no—
325Q8×C29—41no—
326Q8×C29—81no—
327Q8×C29—81no—
328Q8×C29—81no—
329D4×C29—41no—
330D4×C29—41no—
331D4×C29—41no—
332D4×C29—81no—
333D4×C29—81no—
334C2×C4×C29—21no—
335C2×C4×C29—21no—
336C2×C4×C29—22no—
337C2×C4×C29—21no—
338C2×C4×C29—21no—
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—21no—
349C2×C4×C29—41no—
350C2×C4×C29—41no—
351C2×C4×C29—41no—
352C2×C4×C29—41no—
353C2×C4×C29—41no—
354C2×C4×C29—41no—
355C2×C4×C29—41no—
356C2×C4×C29—41no—
357C2×C4×C29—41no—
358C2×C4×C29—41no—
359C2×C4×C29—41no—
360C2×C4×C29—41no—
361C2×C4×C29—41no—
362C2×C4×C29—41no—
363C2×C4×C29—41no—
364C2×C4×C29—81no—
365C2×C4×C29—81no—
366C2×C4×C29—81no—
367C2×C4×C29—81no—
368C2×C4×C29—81no—
369C2×C4×C29#12011yescharacteristic
370C2×C4×C29#12011yescharacteristic
371C2×C4×C29#12011yescharacteristic
372C2×C4×C29#12011yescharacteristic
373C2×C4×C29C22×D411yescharacteristic
374C2×C4×C29C22×D411yescharacteristic
375C8×C29—41no—
376C8×C29—41no—
377C8×C29—41no—
378C8×C29—41no—
379#3564C2×C2911yescharacteristic
380#3236C2×C2911yescharacteristic, complemented
381#3232C2×C2911yescharacteristic, complemented
382#2664C2×C2911yescharacteristic, complemented
383#1618C2×C2911yescharacteristic
384#1617C2×C2911yescharacteristic, complemented
385#1615C2×C2911yescharacteristic, complemented
386#1614C2×C2911yescharacteristic, complemented
387#1612C2×C2911yescharacteristic
388#1611C2×C2911yescharacteristic, complemented
389#1609C2×C2911yescharacteristic, complemented
390#1608C2×C2911yescharacteristic, complemented
391#1509C2×C2911yescharacteristic, complemented
392#1503C2×C2911yescharacteristic, complemented
393#1473C2×C2911yescharacteristic, complemented
394C22×C29—21no—
395C22×C29—21no—
396C22×C29—41no—
397C22×C29—41no—
398C22×C29—41no—
399C22×C29—41no—
400C22×C29—41no—
401C22×C29—41no—
402C22×C29—81no—
403C22×C29—81no—
404C22×C29C2×#12011yescharacteristic
405C22×C29#57711yescharacteristic
406C22×C29#57811yescharacteristic
407C4×C29—21no—
408C4×C29—21no—
409C4×C29—21no—
410C4×C29—21no—
411C4×C29—21no—
412C4×C29—21no—
413C4×C29—42no—
414C4×C29—41no—
415C4×C29—41no—
416C4×C29—41no—
417C4×C29—41no—
418C4×C29—41no—
419C4×C29—41no—
420C4×C29—41no—
421C4×C29—41no—
422C4×C29—41no—
423C4×C29—41no—
424C4×C29—81no—
425C4×C29—81no—
426C4×C29—81no—
427#563—21no—
428#563—21no—
429#556—21no—
430#554—21no—
431#552—21no—
432#552—21no—
433#551—21no—
434#551—21no—
435#544C22×C2911yescharacteristic
436#543C22×C2911yescharacteristic
437#542—21no—
438#541—21no—
439#541—21no—
440#539—21no—
441#539C22×C2911yescharacteristic
442#538C22×C2911yescharacteristic
443#533C22×C2911yescharacteristic
444#529C22×C2911yescharacteristic
445C2×#126C22×C2911yescharacteristic
446C2×#125C22×C2911yescharacteristic
447#501—21no—
448#499—21no—
449#491—21no—
450#488—21no—
451#484C22×C2911yescharacteristic
452#484C22×C2911yescharacteristic
453#484C22×C2911yescharacteristic
454#483C22×C2911yescharacteristic
455#483C22×C2911yescharacteristic
456#483C22×C2911yescharacteristic
457#481C22×C2911yescharacteristic
458#480C22×C2911yescharacteristic
459#479—21no—
460#479—21no—
461#479—21no—
462#478—21no—
463#432C22×C2911yescharacteristic
464#431C22×C2911yescharacteristic
465#400C22×C2911yescharacteristic
466#399C22×C2911yescharacteristic
467#398—21no—
468#398C22×C2911yescharacteristic
469#397C22×C2911yescharacteristic
470#396—21no—
471#389—21no—
472#388—21no—
473C4×C4⋊C4C22×C2911yescharacteristic
474#328C22×C2911yescharacteristic
475#328C22×C2911yescharacteristic
476#328C22×C2911yescharacteristic
477#328C22×C2911yescharacteristic
478#328C22×C2911yescharacteristic
479#328C22×C2911yescharacteristic
480#327C22×C2911yescharacteristic
481#327C22×C2911yescharacteristic
482#324C22×C2911yescharacteristic
483#324C22×C2911yescharacteristic
484#323C22×C2911yescharacteristic
485#323C22×C2911yescharacteristic
486C2×C29—21no—
487C2×C29—21no—
488C2×C29—81no—
489C2×C29—81no—
490C2×C29#301311yescharacteristic
491C2×C29#301811yescharacteristic
492C2×C29#302811yescharacteristic
493C4⋊Q8—21no—
494C4⋊Q8—21no—
495C4⋊Q8—21no—
496C4⋊Q8D4×C2911yescharacteristic
497C4⋊Q8D4×C2911yescharacteristic
498#126—21no—
499#126—21no—
500#126—21no—
501#126—21no—
502#126—21no—
503#126—21no—
504#126—21no—
505#126—21no—
506#126—21no—
507#126—21no—
508#126—21no—
509#126—21no—
510#126—21no—
511#125—21no—
512#125—21no—
513#125—21no—
514#125—21no—
515#125—21no—
516#125—21no—
517#125—21no—
518#125—21no—
519#125—21no—
520#125—21no—
521#125—21no—
522#125—21no—
523#125—21no—
524#125D4×C2911yescharacteristic
525#124—21no—
526#124—21no—
527#124—21no—
528#124D4×C2911yescharacteristic
529#123—21no—
530#123—21no—
531#123—21no—
532#123—21no—
533#123—21no—
534#123—21no—
535#123—21no—
536#123—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540C22⋊Q8—21no—
541C22⋊Q8—21no—
542C22⋊Q8—21no—
543C22⋊Q8—21no—
544C22⋊Q8—21no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—21no—
550C22⋊Q8—21no—
551C22⋊Q8C23×C2911yescharacteristic
552C22⋊Q8C23×C2911yescharacteristic
553C22⋊Q8C23×C2911yescharacteristic
554#121—21no—
555#121C23×C2911yescharacteristic
556#120—21no—
557C4×Q8—21no—
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×D4D4×C2911yescharacteristic
569#117—21no—
570#117—21no—
571#117—21no—
572#117—21no—
573#117—21no—
574#117—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4D4×C2911yescharacteristic
582C2×C4⋊C4D4×C2911yescharacteristic
583C2×C4⋊C4C23×C2911yescharacteristic
584C2×C4⋊C4C23×C2911yescharacteristic
585C2×C4⋊C4C23×C2911yescharacteristic
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4D4×C2911yescharacteristic
590C2×C22⋊C4D4×C2911yescharacteristic
591C2×C22⋊C4C23×C2911yescharacteristic
592C2×C42—21no—
593C2×C42C23×C2911yescharacteristic
594#107—21no—
595#107—21no—
596#107—21no—
597#107—21no—
598#106—21no—
599#106—21no—
600#106—21no—
601#106—21no—
602C4⋊C8—21no—
603C4⋊C8—21no—
604#103—21no—
605#103—21no—
606#103—21no—
607#103—21no—
608#103—21no—
609#103—21no—
610#102—21no—
611#102—21no—
612C22⋊C8C23×C2911yescharacteristic
613C22⋊C8C23×C2911yescharacteristic
614C22⋊C8C23×C2911yescharacteristic
615C22⋊C8C23×C2911yescharacteristic
616#97—21no—
617C4×C8—21no—
618#95—21no—
619#95—21no—
620#95—21no—
621#95—21no—
622#95C23×C2911yescharacteristic
623#95C23×C2911yescharacteristic
624C29#1844511yescharacteristic, direct product factor, Sylow
625C24C2×D4×C2911yescharacteristic
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8C2×D4×C2911yescharacteristic
630C2×Q8C2×D4×C2911yescharacteristic
631C2×Q8C2×D4×C2911yescharacteristic
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4C2×D4×C2911yescharacteristic
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4C2×D4×C2911yescharacteristic
646C22×C4C2×D4×C2911yescharacteristic
647C22×C4C2×D4×C2911yescharacteristic
648C22×C4C2×D4×C2911yescharacteristic
649C22×C4C2×D4×C2911yescharacteristic
650C22×C4C24×C2911yescharacteristic
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
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—21no—
687C4⋊C4—21no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—41no—
691C4⋊C4—41no—
692C4⋊C4—41no—
693C4⋊C4—41no—
694C4⋊C4—81no—
695C4⋊C4C2×D4×C2911yescharacteristic
696C4⋊C4C2×D4×C2911yescharacteristic
697C4⋊C4C2×D4×C2911yescharacteristic
698C4⋊C4C2×D4×C2911yescharacteristic
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—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—42no—
721C22⋊C4—81no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—21no—
729C42—81no—
730C42C2×D4×C2911yescharacteristic
731C42C2×D4×C2911yescharacteristic
732C42C2×D4×C2911yescharacteristic
733C42C2×D4×C2911yescharacteristic
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—41no—
739C23—41no—
740C23C22×D4×C2911yescharacteristic
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8—81no—
745Q8—81no—
746Q8—81no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—81no—
751D4—81no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4C29×#12011yescharacteristic
788C2×C4C29×#12011yescharacteristic
789C2×C4C29×#12011yescharacteristic
790C2×C4C29×#12011yescharacteristic
791C2×C4C22×D4×C2911yescharacteristic
792C2×C4C22×D4×C2911yescharacteristic
793C8—41no—
794C8—41no—
795C8—41no—
796C8—41no—
797C22—21no—
798C22—21no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—81no—
806C22—81no—
807C22C2×C29×#12011yescharacteristic
808C22C29×#57711yescharacteristic
809C22C29×#57811yescharacteristic
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—42no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—81no—
828C4—81no—
829C4—81no—
830C2—21no—
831C2—21no—
832C2—81no—
833C2—81no—
834C2C29×#301311yescharacteristic
835C2C29×#301811yescharacteristic
836C2C29×#302811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#538C22
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
2. C29×#3236C2semidirect
3. C29×#3232C2semidirect
4. C29×#2664C2semidirect
6. C29×#1617C2semidirect
7. C29×#1615C2semidirect
8. C29×#1614C2semidirect
10. C29×#1611C2semidirect
11. C29×#1609C2semidirect
12. C29×#1608C2semidirect
13. C29×#1509C2semidirect
14. C29×#1503C2semidirect
15. C29×#1473C2semidirect
315. #18445C29direct (N × H)
380. #3236C2×C29semidirect
381. #3232C2×C29semidirect
382. #2664C2×C29semidirect
384. #1617C2×C29semidirect
385. #1615C2×C29semidirect
386. #1614C2×C29semidirect
388. #1611C2×C29semidirect
389. #1609C2×C29semidirect
390. #1608C2×C29semidirect
391. #1509C2×C29semidirect
392. #1503C2×C29semidirect
393. #1473C2×C29semidirect
624. C29#18445direct (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×#32362
C29×#32322
C29×#26642
C29×#16182
C29×#16172
C29×#16152
C29×#16142
C29×#16122
C29×#16112
C29×#16092
C29×#16082
C29×#15092
C29×#15032
C29×#14732
#1844529