Finite Group Databasebeta

← C29×#18444 #20313344

Subgroups — C29×#18444 #20313344

Order 7424.

908 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3560C211yesmaximal, characteristic
2C29×#3234C211yesmaximal, characteristic, complemented
3C29×#3232C211yesmaximal, characteristic, complemented
4C29×#2664C211yesmaximal, characteristic, complemented
5C29×#1618C211yesmaximal, characteristic, complemented
6C29×#1616C211yesmaximal, characteristic, complemented
7C29×#1615C211yesmaximal, characteristic, complemented
8C29×#1613C211yesmaximal, characteristic, complemented
9C29×#1612C211yesmaximal, characteristic, complemented
10C29×#1610C211yesmaximal, characteristic, complemented
11C29×#1609C211yesmaximal, characteristic, complemented
12C29×#1607C211yesmaximal, characteristic, complemented
13C29×#1509C211yesmaximal, characteristic, complemented
14C29×#1502C211yesmaximal, characteristic, complemented
15C29×#1473C211yesmaximal, characteristic, complemented
16C29×#563—21no—
17C29×#560—21no—
18C29×#553—21no—
19C29×#553—21no—
20C29×#551—21no—
21C29×#547—21no—
22C29×#546—21no—
23C29×#546—21no—
24C29×#542—21no—
25C29×#539—21no—
26C29×#539C2211yescharacteristic
27C29×#538—21no—
28C29×#538—21no—
29C29×#538C2211yescharacteristic
30C29×#537C2211yescharacteristic
31C29×#534C2211yescharacteristic
32C29×#532C2211yescharacteristic
33C29×#529C2211yescharacteristic
34C2×C29×#126C2211yescharacteristic
35C2×C29×#125C2211yescharacteristic, complemented
36C29×#501—21no—
37C29×#499—21no—
38C29×#490—21no—
39C29×#488—21no—
40C29×#484C2211yescharacteristic, complemented
41C29×#483C2211yescharacteristic, complemented
42C29×#481C2211yescharacteristic
43C29×#481C2211yescharacteristic
44C29×#481C2211yescharacteristic, complemented
45C29×#480C2211yescharacteristic
46C29×#480C2211yescharacteristic
47C29×#480C2211yescharacteristic, complemented
48C29×#479—21no—
49C29×#478—21no—
50C29×#478—21no—
51C29×#478—21no—
52C29×#432C2211yescharacteristic, complemented
53C29×#431C2211yescharacteristic, complemented
54C29×#400C2211yescharacteristic, complemented
55C29×#399C2211yescharacteristic
56C29×#398—21no—
57C29×#398C2211yescharacteristic, complemented
58C29×#397C2211yescharacteristic
59C29×#396—21no—
60C29×#389—21no—
61C29×#388—21no—
62C4×C4⋊C4×C29C2211yescharacteristic, complemented
63C29×#328C2211yescharacteristic, complemented
64C29×#328C2211yescharacteristic, complemented
65C29×#327C2211yescharacteristic
66C29×#327C2211yescharacteristic
67C29×#327C2211yescharacteristic
68C29×#327C2211yescharacteristic
69C29×#327C2211yescharacteristic, complemented
70C29×#327C2211yescharacteristic, complemented
71C29×#324C2211yescharacteristic, complemented
72C29×#324C2211yescharacteristic, complemented
73C29×#323C2211yescharacteristic
74C29×#323C2211yescharacteristic
75C2×#41×C29—21no—
76C2×#41×C29—21no—
77C22×D4×C29—21no—
78C29×C4⋊Q8—21no—
79C29×C4⋊Q8D411yescharacteristic
80C29×#127D411yescharacteristic
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×#125—21no—
91C29×#125—21no—
92C29×#125—21no—
93C29×#125—21no—
94C29×#125—21no—
95C29×#125—21no—
96C29×#125D411yescharacteristic
97C29×#124—21no—
98C29×#124—21no—
99C29×#124—21no—
100C29×#124—21no—
101C29×#124D411yescharacteristic
102C29×#123—21no—
103C29×#123—21no—
104C29×#123—21no—
105C29×#123—21no—
106C29×#123—21no—
107C29×#123—21no—
108C29×#123—21no—
109C29×#123—21no—
110C29×#123—21no—
111C29×#123—21no—
112C29×#123—21no—
113C29×#123—21no—
114C29×C22⋊Q8—21no—
115C29×C22⋊Q8—21no—
116C29×C22⋊Q8—21no—
117C29×C22⋊Q8—21no—
118C29×C22⋊Q8—21no—
119C29×C22⋊Q8—21no—
120C29×C22⋊Q8—21no—
121C29×C22⋊Q8C2311yescharacteristic
122C29×#121—21no—
123C29×#121—21no—
124C29×#121—21no—
125C29×#121—21no—
126C29×#121—21no—
127C29×#121—21no—
128C29×#121—21no—
129C29×#121—21no—
130C29×#121—21no—
131C29×#121—21no—
132C29×#121—21no—
133C29×#121—21no—
134C29×#121C2311yescharacteristic
135C29×#121C2311yescharacteristic
136C29×#121C2311yescharacteristic
137C29×#120—21no—
138C29×#120—21no—
139C29×#120—21no—
140C29×#120—21no—
141C29×#120—21no—
142C4×Q8×C29D411yescharacteristic
143C4×D4×C29—21no—
144C4×D4×C29—21no—
145C4×D4×C29—21no—
146C4×D4×C29—21no—
147C4×D4×C29—21no—
148C4×D4×C29—21no—
149C4×D4×C29—21no—
150C4×D4×C29—21no—
151C4×D4×C29D411yescharacteristic
152C4×D4×C29D411yescharacteristic
153C4×D4×C29D411yescharacteristic
154C29×#117—21no—
155C29×#117—21no—
156C2×C4⋊C4×C29—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×C29D411yescharacteristic
163C2×C4⋊C4×C29D411yescharacteristic
164C2×C4⋊C4×C29C2311yescharacteristic
165C2×C4⋊C4×C29C2311yescharacteristic
166C2×C4⋊C4×C29C2311yescharacteristic
167C2×C22⋊C4×C29—21no—
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×#102—21no—
189C29×#102—21no—
190C29×#102—21no—
191C29×#102—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×C29—21no—
207C24×C29C2×D411yescharacteristic
208#41×C29—81no—
209#41×C29—81no—
210#41×C29—81no—
211#41×C29—81no—
212C2×Q8×C29—21no—
213C2×Q8×C29—21no—
214C2×Q8×C29C2×D411yescharacteristic
215C2×D4×C29—21no—
216C2×D4×C29—21no—
217C2×D4×C29—21no—
218C2×D4×C29—21no—
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—81no—
228C2×D4×C29—81no—
229C2×D4×C29C2×D411yescharacteristic
230C2×D4×C29C2×D411yescharacteristic
231C2×D4×C29C2×D411yescharacteristic
232C22×C4×C29—21no—
233C22×C4×C29—21no—
234C22×C4×C29—21no—
235C22×C4×C29—21no—
236C22×C4×C29—21no—
237C22×C4×C29—21no—
238C22×C4×C29—21no—
239C22×C4×C29—21no—
240C22×C4×C29—21no—
241C22×C4×C29—21no—
242C22×C4×C29—21no—
243C22×C4×C29—21no—
244C22×C4×C29C2×D411yescharacteristic
245C22×C4×C29C2×D411yescharacteristic
246C22×C4×C29C2×D411yescharacteristic
247C22×C4×C29C2×D411yescharacteristic
248C22×C4×C29C2×D411yescharacteristic
249C22×C4×C29C2411yescharacteristic
250C2×C8×C29—21no—
251C2×C8×C29—21no—
252C2×C8×C29—21no—
253C2×C8×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—42no—
276C4⋊C4×C29—42no—
277C4⋊C4×C29—41no—
278C4⋊C4×C29—41no—
279C4⋊C4×C29—41no—
280C4⋊C4×C29—41no—
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—21no—
308C22⋊C4×C29—21no—
309C22⋊C4×C29—21no—
310C22⋊C4×C29—21no—
311C22⋊C4×C29—42no—
312C22⋊C4×C29—81no—
313C42×C29—21no—
314C42×C29—21no—
315C42×C29—21no—
316C42×C29—81no—
317C42×C29C2×D411yescharacteristic
318C42×C29C2×D411yescharacteristic
319C42×C29C2×D411yescharacteristic
320C42×C29C2×D411yescharacteristic
321#18444C2911yesmaximal, characteristic, direct product factor, Sylow
322C23×C29—21no—
323C23×C29—21no—
324C23×C29—21no—
325C23×C29—21no—
326C23×C29—21no—
327C23×C29—21no—
328C23×C29—41no—
329C23×C29—41no—
330C23×C29—81no—
331C23×C29—81no—
332C23×C29—81no—
333C23×C29C22×D411yescharacteristic
334Q8×C29—41no—
335Q8×C29—81no—
336Q8×C29—81no—
337D4×C29—41no—
338D4×C29—41no—
339D4×C29—41no—
340D4×C29—41no—
341D4×C29—41no—
342D4×C29—41no—
343D4×C29—41no—
344D4×C29—41no—
345D4×C29—41no—
346D4×C29—81no—
347D4×C29—81no—
348D4×C29—81no—
349D4×C29—81no—
350D4×C29—81no—
351D4×C29—81no—
352D4×C29—81no—
353D4×C29—81no—
354D4×C29—81no—
355C2×C4×C29—21no—
356C2×C4×C29—21no—
357C2×C4×C29—22no—
358C2×C4×C29—21no—
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—41no—
369C2×C4×C29—41no—
370C2×C4×C29—41no—
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—81no—
385C2×C4×C29—81no—
386C2×C4×C29—81no—
387C2×C4×C29—81no—
388C2×C4×C29—81no—
389C2×C4×C29—81no—
390C2×C4×C29—81no—
391C2×C4×C29#12011yescharacteristic
392C2×C4×C29#12011yescharacteristic
393C2×C4×C29#12011yescharacteristic
394C2×C4×C29#12011yescharacteristic
395C2×C4×C29C22×D411yescharacteristic
396C2×C4×C29C22×D411yescharacteristic
397C8×C29—41no—
398C8×C29—41no—
399C8×C29—41no—
400C8×C29—41no—
401#3560C2×C2911yescharacteristic
402#3234C2×C2911yescharacteristic, complemented
403#3232C2×C2911yescharacteristic, complemented
404#2664C2×C2911yescharacteristic, complemented
405#1618C2×C2911yescharacteristic, complemented
406#1616C2×C2911yescharacteristic, complemented
407#1615C2×C2911yescharacteristic, complemented
408#1613C2×C2911yescharacteristic, complemented
409#1612C2×C2911yescharacteristic, complemented
410#1610C2×C2911yescharacteristic, complemented
411#1609C2×C2911yescharacteristic, complemented
412#1607C2×C2911yescharacteristic, complemented
413#1509C2×C2911yescharacteristic, complemented
414#1502C2×C2911yescharacteristic, complemented
415#1473C2×C2911yescharacteristic, complemented
416C22×C29—21no—
417C22×C29—21no—
418C22×C29—41no—
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—81no—
431C22×C29—81no—
432C22×C29—162no—
433C22×C29C2×#12011yescharacteristic
434C22×C29#57611yescharacteristic
435C22×C29#57711yescharacteristic
436C4×C29—21no—
437C4×C29—21no—
438C4×C29—21no—
439C4×C29—21no—
440C4×C29—21no—
441C4×C29—21no—
442C4×C29—42no—
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—
452C4×C29—81no—
453C4×C29—81no—
454#563—21no—
455#560—21no—
456#553—21no—
457#553—21no—
458#551—21no—
459#547—21no—
460#546—21no—
461#546—21no—
462#542—21no—
463#539—21no—
464#539C22×C2911yescharacteristic
465#538—21no—
466#538—21no—
467#538C22×C2911yescharacteristic
468#537C22×C2911yescharacteristic
469#534C22×C2911yescharacteristic
470#532C22×C2911yescharacteristic
471#529C22×C2911yescharacteristic
472C2×#126C22×C2911yescharacteristic
473C2×#125C22×C2911yescharacteristic, complemented
474#501—21no—
475#499—21no—
476#490—21no—
477#488—21no—
478#484C22×C2911yescharacteristic, complemented
479#483C22×C2911yescharacteristic, complemented
480#481C22×C2911yescharacteristic
481#481C22×C2911yescharacteristic
482#481C22×C2911yescharacteristic, complemented
483#480C22×C2911yescharacteristic
484#480C22×C2911yescharacteristic
485#480C22×C2911yescharacteristic, complemented
486#479—21no—
487#478—21no—
488#478—21no—
489#478—21no—
490#432C22×C2911yescharacteristic, complemented
491#431C22×C2911yescharacteristic, complemented
492#400C22×C2911yescharacteristic, complemented
493#399C22×C2911yescharacteristic
494#398—21no—
495#398C22×C2911yescharacteristic, complemented
496#397C22×C2911yescharacteristic
497#396—21no—
498#389—21no—
499#388—21no—
500C4×C4⋊C4C22×C2911yescharacteristic, complemented
501#328C22×C2911yescharacteristic, complemented
502#328C22×C2911yescharacteristic, complemented
503#327C22×C2911yescharacteristic
504#327C22×C2911yescharacteristic
505#327C22×C2911yescharacteristic
506#327C22×C2911yescharacteristic
507#327C22×C2911yescharacteristic, complemented
508#327C22×C2911yescharacteristic, complemented
509#324C22×C2911yescharacteristic, complemented
510#324C22×C2911yescharacteristic, complemented
511#323C22×C2911yescharacteristic
512#323C22×C2911yescharacteristic
513C2×C29—21no—
514C2×C29—21no—
515C2×C29—81no—
516C2×C29—81no—
517C2×C29—81no—
518C2×C29—81no—
519C2×C29#301211yescharacteristic
520C2×C29#301811yescharacteristic
521C2×C29#302811yescharacteristic
522C2×#41—21no—
523C2×#41—21no—
524C22×D4—21no—
525C4⋊Q8—21no—
526C4⋊Q8D4×C2911yescharacteristic
527#127D4×C2911yescharacteristic
528#126—21no—
529#126—21no—
530#126—21no—
531#126—21no—
532#126—21no—
533#126—21no—
534#126—21no—
535#126—21no—
536#126—21no—
537#125—21no—
538#125—21no—
539#125—21no—
540#125—21no—
541#125—21no—
542#125—21no—
543#125D4×C2911yescharacteristic
544#124—21no—
545#124—21no—
546#124—21no—
547#124—21no—
548#124D4×C2911yescharacteristic
549#123—21no—
550#123—21no—
551#123—21no—
552#123—21no—
553#123—21no—
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561C22⋊Q8—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8—21no—
568C22⋊Q8C23×C2911yescharacteristic
569#121—21no—
570#121—21no—
571#121—21no—
572#121—21no—
573#121—21no—
574#121—21no—
575#121—21no—
576#121—21no—
577#121—21no—
578#121—21no—
579#121—21no—
580#121—21no—
581#121C23×C2911yescharacteristic
582#121C23×C2911yescharacteristic
583#121C23×C2911yescharacteristic
584#120—21no—
585#120—21no—
586#120—21no—
587#120—21no—
588#120—21no—
589C4×Q8D4×C2911yescharacteristic
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4D4×C2911yescharacteristic
599C4×D4D4×C2911yescharacteristic
600C4×D4D4×C2911yescharacteristic
601#117—21no—
602#117—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4D4×C2911yescharacteristic
610C2×C4⋊C4D4×C2911yescharacteristic
611C2×C4⋊C4C23×C2911yescharacteristic
612C2×C4⋊C4C23×C2911yescharacteristic
613C2×C4⋊C4C23×C2911yescharacteristic
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4D4×C2911yescharacteristic
619C2×C22⋊C4D4×C2911yescharacteristic
620C2×C22⋊C4C23×C2911yescharacteristic
621C2×C42—21no—
622C2×C42C23×C2911yescharacteristic
623#107—21no—
624#107—21no—
625#107—21no—
626#107—21no—
627#106—21no—
628#106—21no—
629#106—21no—
630#106—21no—
631C4⋊C8—21no—
632C4⋊C8—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—
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#95—21no—
651#95C23×C2911yescharacteristic
652#95C23×C2911yescharacteristic
653C29#1844411yescharacteristic, direct product factor, Sylow
654C24—21no—
655C24C2×D4×C2911yescharacteristic
656#41—81no—
657#41—81no—
658#41—81no—
659#41—81no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8C2×D4×C2911yescharacteristic
663C2×D4—21no—
664C2×D4—21no—
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—81no—
676C2×D4—81no—
677C2×D4C2×D4×C2911yescharacteristic
678C2×D4C2×D4×C2911yescharacteristic
679C2×D4C2×D4×C2911yescharacteristic
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4C2×D4×C2911yescharacteristic
693C22×C4C2×D4×C2911yescharacteristic
694C22×C4C2×D4×C2911yescharacteristic
695C22×C4C2×D4×C2911yescharacteristic
696C22×C4C2×D4×C2911yescharacteristic
697C22×C4C24×C2911yescharacteristic
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—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—42no—
724C4⋊C4—42no—
725C4⋊C4—41no—
726C4⋊C4—41no—
727C4⋊C4—41no—
728C4⋊C4—41no—
729C4⋊C4—81no—
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—42no—
760C22⋊C4—81no—
761C42—21no—
762C42—21no—
763C42—21no—
764C42—81no—
765C42C2×D4×C2911yescharacteristic
766C42C2×D4×C2911yescharacteristic
767C42C2×D4×C2911yescharacteristic
768C42C2×D4×C2911yescharacteristic
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—41no—
777C23—81no—
778C23—81no—
779C23—81no—
780C23C22×D4×C2911yescharacteristic
781Q8—41no—
782Q8—81no—
783Q8—81no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—81no—
794D4—81no—
795D4—81no—
796D4—81no—
797D4—81no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
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—41no—
816C2×C4—41no—
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—41no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4C29×#12011yescharacteristic
839C2×C4C29×#12011yescharacteristic
840C2×C4C29×#12011yescharacteristic
841C2×C4C29×#12011yescharacteristic
842C2×C4C22×D4×C2911yescharacteristic
843C2×C4C22×D4×C2911yescharacteristic
844C8—41no—
845C8—41no—
846C8—41no—
847C8—41no—
848C22—21no—
849C22—21no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—81no—
863C22—81no—
864C22—162no—
865C22C2×C29×#12011yescharacteristic
866C22C29×#57611yescharacteristic
867C22C29×#57711yescharacteristic
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—42no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C4—81no—
886C2—21no—
887C2—21no—
888C2—81no—
889C2—81no—
890C2—81no—
891C2—81no—
892C2C29×#301211yescharacteristic
893C2C29×#301811yescharacteristic
894C2C29×#302811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#3560C2
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×#3234C2semidirect
3. C29×#3232C2semidirect
4. C29×#2664C2semidirect
5. C29×#1618C2semidirect
6. C29×#1616C2semidirect
7. C29×#1615C2semidirect
8. C29×#1613C2semidirect
9. C29×#1612C2semidirect
10. C29×#1610C2semidirect
11. C29×#1609C2semidirect
12. C29×#1607C2semidirect
13. C29×#1509C2semidirect
14. C29×#1502C2semidirect
15. C29×#1473C2semidirect
35. C2×C29×#125C22semidirect
40. C29×#484C22semidirect
41. C29×#483C22semidirect
44. C29×#481C22semidirect
47. C29×#480C22semidirect
52. C29×#432C22semidirect
53. C29×#431C22semidirect
54. C29×#400C22semidirect
57. C29×#398C22semidirect
62. C4×C4⋊C4×C29C22semidirect
63. C29×#328C22semidirect
64. C29×#328C22semidirect
69. C29×#327C22semidirect
70. C29×#327C22semidirect
71. C29×#324C22semidirect
72. C29×#324C22semidirect
321. #18444C29direct (N × H)
402. #3234C2×C29semidirect
403. #3232C2×C29semidirect
404. #2664C2×C29semidirect
405. #1618C2×C29semidirect
406. #1616C2×C29semidirect
407. #1615C2×C29semidirect
408. #1613C2×C29semidirect
409. #1612C2×C29semidirect
410. #1610C2×C29semidirect
411. #1609C2×C29semidirect
412. #1607C2×C29semidirect
413. #1509C2×C29semidirect
414. #1502C2×C29semidirect
415. #1473C2×C29semidirect
473. C2×#125C22×C29semidirect
478. #484C22×C29semidirect
479. #483C22×C29semidirect
482. #481C22×C29semidirect
485. #480C22×C29semidirect
490. #432C22×C29semidirect
491. #431C22×C29semidirect
492. #400C22×C29semidirect
495. #398C22×C29semidirect
500. C4×C4⋊C4C22×C29semidirect
501. #328C22×C29semidirect
502. #328C22×C29semidirect
507. #327C22×C29semidirect
508. #327C22×C29semidirect
509. #324C22×C29semidirect
510. #324C22×C29semidirect
653. C29#18444direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35602
C29×#32342
C29×#32322
C29×#26642
C29×#16182
C29×#16162
C29×#16152
C29×#16132
C29×#16122
C29×#16102
C29×#16092
C29×#16072
C29×#15092
C29×#15022
C29×#14732
#1844429