Finite Group Databasebeta

← C29×#18435 #20313335

Subgroups — C29×#18435 #20313335

Order 7424.

922 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3564C211yesmaximal, characteristic, complemented
2C29×#3215C211yesmaximal, characteristic, complemented
3C29×#3211C211yesmaximal, characteristic, complemented
4C29×#2662C211yesmaximal, characteristic, complemented
5C29×#1606C211yesmaximal, characteristic, complemented
6C29×#1605C211yesmaximal, characteristic, complemented
7C29×#1603C211yesmaximal, characteristic, complemented
8C29×#1602C211yesmaximal, characteristic, complemented
9C29×#1600C211yesmaximal, characteristic
10C29×#1599C211yesmaximal, characteristic, complemented
11C29×#1597C211yesmaximal, characteristic, complemented
12C29×#1596C211yesmaximal, 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×#124C2211yescharacteristic
36C29×#497—21no—
37C29×#495—21no—
38C29×#489—21no—
39C29×#488—21no—
40C29×#464—21no—
41C29×#464—21no—
42C29×#464—21no—
43C29×#463—21no—
44C29×#451C2211yescharacteristic
45C29×#451C2211yescharacteristic
46C29×#451C2211yescharacteristic
47C29×#450C2211yescharacteristic
48C29×#450C2211yescharacteristic
49C29×#450C2211yescharacteristic
50C29×#448C2211yescharacteristic
51C29×#447C2211yescharacteristic
52C29×#432C2211yescharacteristic
53C29×#431C2211yescharacteristic
54C29×#396—21no—
55C29×#395C2211yescharacteristic
56C29×#394—21no—
57C29×#394C2211yescharacteristic
58C29×#393C2211yescharacteristic
59C29×#392C2211yescharacteristic
60C29×#390—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
75C22×Q8×C29C2311yescharacteristic
76C22×D4×C29—21no—
77C22×D4×C29C2311yescharacteristic
78C2×Q16×C29—21no—
79C2×Q16×C29—21no—
80C2×Q16×C29—21no—
81C2×SD16×C29—21no—
82C2×SD16×C29—21no—
83C2×SD16×C29—21no—
84C2×SD16×C29—21no—
85C2×D8×C29—21no—
86C29×C4⋊Q8—21no—
87C29×C4⋊Q8—21no—
88C29×C4⋊Q8—21no—
89C29×C4⋊Q8D411yescharacteristic, complemented
90C29×C4⋊Q8D411yescharacteristic, complemented
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×#126—21no—
101C29×#126—21no—
102C29×#126—21no—
103C29×#126—21no—
104C29×#125—21no—
105C29×#125—21no—
106C29×#125—21no—
107C29×#125—21no—
108C29×#125—21no—
109C29×#125—21no—
110C29×#125—21no—
111C29×#125—21no—
112C29×#125—21no—
113C29×#125D411yescharacteristic, complemented
114C29×#124—21no—
115C29×#124—21no—
116C29×#124—21no—
117C29×#124—21no—
118C29×#124—21no—
119C29×#124—21no—
120C29×#124—21no—
121C29×#124D411yescharacteristic, complemented
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⋊Q8—21no—
139C29×C22⋊Q8—21no—
140C29×C22⋊Q8—21no—
141C29×C22⋊Q8—21no—
142C29×C22⋊Q8—21no—
143C29×C22⋊Q8—21no—
144C29×C22⋊Q8C2311yescharacteristic
145C29×C22⋊Q8C2311yescharacteristic
146C29×C22⋊Q8C2311yescharacteristic
147C29×#121—21no—
148C29×#121C2311yescharacteristic
149C29×#120—21no—
150C4×Q8×C29—21no—
151C4×Q8×C29—21no—
152C4×Q8×C29—21no—
153C4×Q8×C29D411yescharacteristic, complemented
154C4×Q8×C29D411yescharacteristic, complemented
155C4×Q8×C29D411yescharacteristic, complemented
156C4×D4×C29—21no—
157C4×D4×C29—21no—
158C4×D4×C29—21no—
159C4×D4×C29—21no—
160C4×D4×C29—21no—
161C4×D4×C29D411yescharacteristic, complemented
162C29×#117—21no—
163C29×#117—21no—
164C29×#117—21no—
165C29×#117—21no—
166C29×#117—21no—
167C29×#117—21no—
168C2×C4⋊C4×C29—21no—
169C2×C4⋊C4×C29—21no—
170C2×C4⋊C4×C29—21no—
171C2×C4⋊C4×C29D411yescharacteristic
172C2×C4⋊C4×C29D411yescharacteristic
173C2×C4⋊C4×C29C2311yescharacteristic
174C2×C22⋊C4×C29—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×C22⋊C4×C29—21no—
181C2×C22⋊C4×C29D411yescharacteristic
182C2×C22⋊C4×C29D411yescharacteristic
183C2×C22⋊C4×C29C2311yescharacteristic
184C2×C42×C29—21no—
185C2×C42×C29C2311yescharacteristic
186C29×C4⋊C8—21no—
187C29×C4⋊C8—21no—
188C29×#103—21no—
189C29×#103—21no—
190C29×#103—21no—
191C29×#103—21no—
192C29×#102—21no—
193C29×#102—21no—
194C29×#102—21no—
195C29×#102—21no—
196C29×C22⋊C8C2311yescharacteristic
197C29×C22⋊C8C2311yescharacteristic
198C29×C22⋊C8C2311yescharacteristic
199C29×C22⋊C8C2311yescharacteristic
200C29×#97—21no—
201C4×C8×C29—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×C29—21no—
212C2×Q8×C29—21no—
213C2×Q8×C29—81no—
214C2×Q8×C29C2×D411yescharacteristic
215C2×Q8×C29C2×D411yescharacteristic
216C2×Q8×C29C2×D411yescharacteristic
217C2×D4×C29—21no—
218C2×D4×C29—21no—
219C2×D4×C29—21no—
220C2×D4×C29—21no—
221C2×D4×C29—21no—
222C2×D4×C29—42no—
223C2×D4×C29—81no—
224C2×D4×C29—81no—
225C2×D4×C29—81no—
226C2×D4×C29C2×D411yescharacteristic
227C22×C4×C29—21no—
228C22×C4×C29—21no—
229C22×C4×C29—21no—
230C22×C4×C29—21no—
231C22×C4×C29—21no—
232C22×C4×C29—21no—
233C22×C4×C29—21no—
234C22×C4×C29—21no—
235C22×C4×C29C2×D411yescharacteristic
236C22×C4×C29C2×D411yescharacteristic
237C22×C4×C29C2×D411yescharacteristic
238C22×C4×C29C2×D411yescharacteristic
239C22×C4×C29C2×D411yescharacteristic
240C22×C4×C29C2411yescharacteristic
241Q16×C29—81no—
242Q16×C29—81no—
243Q16×C29—81no—
244SD16×C29—81no—
245SD16×C29—81no—
246SD16×C29—81no—
247SD16×C29—81no—
248D8×C29—81no—
249C2×C8×C29—21no—
250C2×C8×C29—21no—
251C2×C8×C29—21no—
252C2×C8×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—21no—
282C4⋊C4×C29—42no—
283C4⋊C4×C29—81no—
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—42no—
310C22⋊C4×C29—41no—
311C22⋊C4×C29—41no—
312C22⋊C4×C29—41no—
313C22⋊C4×C29—41no—
314C22⋊C4×C29—81no—
315C22⋊C4×C29—81no—
316C22⋊C4×C29—81no—
317C42×C29—21no—
318C42×C29—21no—
319C42×C29—21no—
320C42×C29—21no—
321C42×C29—21no—
322C42×C29—21no—
323C42×C29—21no—
324C42×C29—81no—
325C42×C29C2×D411yescharacteristic
326C42×C29C2×D411yescharacteristic
327C42×C29C2×D411yescharacteristic
328C42×C29C2×D411yescharacteristic
329#18435C2911yesmaximal, characteristic, direct product factor, Sylow
330C23×C29—21no—
331C23×C29—21no—
332C23×C29—21no—
333C23×C29—21no—
334C23×C29—41no—
335C23×C29—41no—
336C23×C29—41no—
337C23×C29—41no—
338C23×C29—41no—
339C23×C29—41no—
340C23×C29—41no—
341C23×C29—41no—
342C23×C29—41no—
343C23×C29C22×D411yescharacteristic
344Q8×C29—41no—
345Q8×C29—41no—
346Q8×C29—41no—
347Q8×C29—41no—
348Q8×C29—41no—
349Q8×C29—41no—
350Q8×C29—41no—
351Q8×C29—81no—
352Q8×C29—81no—
353Q8×C29—81no—
354D4×C29—41no—
355D4×C29—41no—
356D4×C29—41no—
357D4×C29—41no—
358D4×C29—41no—
359D4×C29—41no—
360D4×C29—41no—
361D4×C29—81no—
362D4×C29—81no—
363D4×C29—84no—
364C2×C4×C29—21no—
365C2×C4×C29—21no—
366C2×C4×C29—22no—
367C2×C4×C29—21no—
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—21no—
377C2×C4×C29—21no—
378C2×C4×C29—21no—
379C2×C4×C29—41no—
380C2×C4×C29—41no—
381C2×C4×C29—41no—
382C2×C4×C29—41no—
383C2×C4×C29—41no—
384C2×C4×C29—41no—
385C2×C4×C29—41no—
386C2×C4×C29—41no—
387C2×C4×C29—41no—
388C2×C4×C29—41no—
389C2×C4×C29—41no—
390C2×C4×C29—41no—
391C2×C4×C29—81no—
392C2×C4×C29—81no—
393C2×C4×C29—81no—
394C2×C4×C29—81no—
395C2×C4×C29—81no—
396C2×C4×C29#12011yescharacteristic
397C2×C4×C29#12011yescharacteristic
398C2×C4×C29#12011yescharacteristic
399C2×C4×C29#12011yescharacteristic
400C2×C4×C29C22×D411yescharacteristic
401C2×C4×C29C22×D411yescharacteristic
402C8×C29—41no—
403C8×C29—41no—
404C8×C29—41no—
405C8×C29—41no—
406#3564C2×C2911yescharacteristic, complemented
407#3215C2×C2911yescharacteristic, complemented
408#3211C2×C2911yescharacteristic, complemented
409#2662C2×C2911yescharacteristic, complemented
410#1606C2×C2911yescharacteristic, complemented
411#1605C2×C2911yescharacteristic, complemented
412#1603C2×C2911yescharacteristic, complemented
413#1602C2×C2911yescharacteristic, complemented
414#1600C2×C2911yescharacteristic
415#1599C2×C2911yescharacteristic, complemented
416#1597C2×C2911yescharacteristic, complemented
417#1596C2×C2911yescharacteristic, complemented
418#1509C2×C2911yescharacteristic, complemented
419#1503C2×C2911yescharacteristic, complemented
420#1473C2×C2911yescharacteristic, complemented
421C22×C29—21no—
422C22×C29—21no—
423C22×C29—41no—
424C22×C29—41no—
425C22×C29—41no—
426C22×C29—41no—
427C22×C29—41no—
428C22×C29—41no—
429C22×C29—81no—
430C22×C29—81no—
431C22×C29—81no—
432C22×C29—81no—
433C22×C29—81no—
434C22×C29—81no—
435C22×C29—81no—
436C22×C29—81no—
437C22×C29—81no—
438C22×C29C2×#12011yescharacteristic
439C22×C29#57711yescharacteristic
440C22×C29#57811yescharacteristic
441C4×C29—21no—
442C4×C29—21no—
443C4×C29—21no—
444C4×C29—21no—
445C4×C29—21no—
446C4×C29—21no—
447C4×C29—42no—
448C4×C29—41no—
449C4×C29—41no—
450C4×C29—41no—
451C4×C29—41no—
452C4×C29—41no—
453C4×C29—41no—
454C4×C29—41no—
455C4×C29—41no—
456C4×C29—41no—
457C4×C29—41no—
458C4×C29—81no—
459C4×C29—81no—
460#563—21no—
461#563—21no—
462#556—21no—
463#554—21no—
464#552—21no—
465#552—21no—
466#551—21no—
467#551—21no—
468#544C22×C2911yescharacteristic
469#543C22×C2911yescharacteristic
470#542—21no—
471#541—21no—
472#541—21no—
473#539—21no—
474#539C22×C2911yescharacteristic
475#538C22×C2911yescharacteristic
476#533C22×C2911yescharacteristic
477#529C22×C2911yescharacteristic
478C2×#126C22×C2911yescharacteristic
479C2×#124C22×C2911yescharacteristic
480#497—21no—
481#495—21no—
482#489—21no—
483#488—21no—
484#464—21no—
485#464—21no—
486#464—21no—
487#463—21no—
488#451C22×C2911yescharacteristic
489#451C22×C2911yescharacteristic
490#451C22×C2911yescharacteristic
491#450C22×C2911yescharacteristic
492#450C22×C2911yescharacteristic
493#450C22×C2911yescharacteristic
494#448C22×C2911yescharacteristic
495#447C22×C2911yescharacteristic
496#432C22×C2911yescharacteristic
497#431C22×C2911yescharacteristic
498#396—21no—
499#395C22×C2911yescharacteristic
500#394—21no—
501#394C22×C2911yescharacteristic
502#393C22×C2911yescharacteristic
503#392C22×C2911yescharacteristic
504#390—21no—
505#388—21no—
506C4×C4⋊C4C22×C2911yescharacteristic
507#328C22×C2911yescharacteristic
508#328C22×C2911yescharacteristic
509#328C22×C2911yescharacteristic
510#328C22×C2911yescharacteristic
511#328C22×C2911yescharacteristic
512#328C22×C2911yescharacteristic
513#327C22×C2911yescharacteristic
514#327C22×C2911yescharacteristic
515#324C22×C2911yescharacteristic
516#324C22×C2911yescharacteristic
517#323C22×C2911yescharacteristic
518#323C22×C2911yescharacteristic
519C2×C29—21no—
520C2×C29—21no—
521C2×C29—81no—
522C2×C29—81no—
523C2×C29—161no—
524C2×C29#301311yescharacteristic
525C2×C29#301811yescharacteristic
526C2×C29#302711yescharacteristic
527C22×Q8C23×C2911yescharacteristic
528C22×D4—21no—
529C22×D4C23×C2911yescharacteristic
530C2×Q16—21no—
531C2×Q16—21no—
532C2×Q16—21no—
533C2×SD16—21no—
534C2×SD16—21no—
535C2×SD16—21no—
536C2×SD16—21no—
537C2×D8—21no—
538C4⋊Q8—21no—
539C4⋊Q8—21no—
540C4⋊Q8—21no—
541C4⋊Q8D4×C2911yescharacteristic, complemented
542C4⋊Q8D4×C2911yescharacteristic, complemented
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#126—21no—
548#126—21no—
549#126—21no—
550#126—21no—
551#126—21no—
552#126—21no—
553#126—21no—
554#126—21no—
555#126—21no—
556#125—21no—
557#125—21no—
558#125—21no—
559#125—21no—
560#125—21no—
561#125—21no—
562#125—21no—
563#125—21no—
564#125—21no—
565#125D4×C2911yescharacteristic, complemented
566#124—21no—
567#124—21no—
568#124—21no—
569#124—21no—
570#124—21no—
571#124—21no—
572#124—21no—
573#124D4×C2911yescharacteristic, complemented
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8—21no—
585C22⋊Q8—21no—
586C22⋊Q8—21no—
587C22⋊Q8—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8—21no—
594C22⋊Q8—21no—
595C22⋊Q8—21no—
596C22⋊Q8C23×C2911yescharacteristic
597C22⋊Q8C23×C2911yescharacteristic
598C22⋊Q8C23×C2911yescharacteristic
599#121—21no—
600#121C23×C2911yescharacteristic
601#120—21no—
602C4×Q8—21no—
603C4×Q8—21no—
604C4×Q8—21no—
605C4×Q8D4×C2911yescharacteristic, complemented
606C4×Q8D4×C2911yescharacteristic, complemented
607C4×Q8D4×C2911yescharacteristic, complemented
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4D4×C2911yescharacteristic, complemented
614#117—21no—
615#117—21no—
616#117—21no—
617#117—21no—
618#117—21no—
619#117—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4D4×C2911yescharacteristic
624C2×C4⋊C4D4×C2911yescharacteristic
625C2×C4⋊C4C23×C2911yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4D4×C2911yescharacteristic
634C2×C22⋊C4D4×C2911yescharacteristic
635C2×C22⋊C4C23×C2911yescharacteristic
636C2×C42—21no—
637C2×C42C23×C2911yescharacteristic
638C4⋊C8—21no—
639C4⋊C8—21no—
640#103—21no—
641#103—21no—
642#103—21no—
643#103—21no—
644#102—21no—
645#102—21no—
646#102—21no—
647#102—21no—
648C22⋊C8C23×C2911yescharacteristic
649C22⋊C8C23×C2911yescharacteristic
650C22⋊C8C23×C2911yescharacteristic
651C22⋊C8C23×C2911yescharacteristic
652#97—21no—
653C4×C8—21no—
654#95—21no—
655#95—21no—
656#95C23×C2911yescharacteristic
657#95C23×C2911yescharacteristic
658C29#1843511yescharacteristic, direct product factor, Sylow
659C24—21no—
660C24C2×D4×C2911yescharacteristic
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—81no—
667C2×Q8C2×D4×C2911yescharacteristic
668C2×Q8C2×D4×C2911yescharacteristic
669C2×Q8C2×D4×C2911yescharacteristic
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—42no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4—81no—
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×C4C2×D4×C2911yescharacteristic
689C22×C4C2×D4×C2911yescharacteristic
690C22×C4C2×D4×C2911yescharacteristic
691C22×C4C2×D4×C2911yescharacteristic
692C22×C4C2×D4×C2911yescharacteristic
693C22×C4C24×C2911yescharacteristic
694Q16—81no—
695Q16—81no—
696Q16—81no—
697SD16—81no—
698SD16—81no—
699SD16—81no—
700SD16—81no—
701D8—81no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—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—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—42no—
736C4⋊C4—81no—
737C4⋊C4C2×D4×C2911yescharacteristic
738C4⋊C4C2×D4×C2911yescharacteristic
739C4⋊C4C2×D4×C2911yescharacteristic
740C4⋊C4C2×D4×C2911yescharacteristic
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—42no—
763C22⋊C4—41no—
764C22⋊C4—41no—
765C22⋊C4—41no—
766C22⋊C4—41no—
767C22⋊C4—81no—
768C22⋊C4—81no—
769C22⋊C4—81no—
770C42—21no—
771C42—21no—
772C42—21no—
773C42—21no—
774C42—21no—
775C42—21no—
776C42—21no—
777C42—81no—
778C42C2×D4×C2911yescharacteristic
779C42C2×D4×C2911yescharacteristic
780C42C2×D4×C2911yescharacteristic
781C42C2×D4×C2911yescharacteristic
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23C22×D4×C2911yescharacteristic
796Q8—41no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803Q8—81no—
804Q8—81no—
805Q8—81no—
806D4—41no—
807D4—41no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—81no—
814D4—81no—
815D4—84no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4C29×#12011yescharacteristic
849C2×C4C29×#12011yescharacteristic
850C2×C4C29×#12011yescharacteristic
851C2×C4C29×#12011yescharacteristic
852C2×C4C22×D4×C2911yescharacteristic
853C2×C4C22×D4×C2911yescharacteristic
854C8—41no—
855C8—41no—
856C8—41no—
857C8—41no—
858C22—21no—
859C22—21no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22C2×C29×#12011yescharacteristic
876C22C29×#57711yescharacteristic
877C22C29×#57811yescharacteristic
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—42no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—81no—
896C4—81no—
897C2—21no—
898C2—21no—
899C2—81no—
900C2—81no—
901C2—161no—
902C2C29×#301311yescharacteristic
903C2C29×#301811yescharacteristic
904C2C29×#302711yescharacteristic
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×#3215C2semidirect
3. C29×#3211C2semidirect
4. C29×#2662C2semidirect
5. C29×#1606C2semidirect
6. C29×#1605C2semidirect
7. C29×#1603C2semidirect
8. C29×#1602C2semidirect
10. C29×#1599C2semidirect
11. C29×#1597C2semidirect
12. C29×#1596C2semidirect
13. C29×#1509C2semidirect
14. C29×#1503C2semidirect
15. C29×#1473C2semidirect
89. C29×C4⋊Q8D4semidirect
90. C29×C4⋊Q8D4semidirect
113. C29×#125D4semidirect
121. C29×#124D4semidirect
153. C4×Q8×C29D4semidirect
154. C4×Q8×C29D4semidirect
155. C4×Q8×C29D4semidirect
161. C4×D4×C29D4semidirect
329. #18435C29direct (N × H)
406. #3564C2×C29semidirect
407. #3215C2×C29semidirect
408. #3211C2×C29semidirect
409. #2662C2×C29semidirect
410. #1606C2×C29semidirect
411. #1605C2×C29semidirect
412. #1603C2×C29semidirect
413. #1602C2×C29semidirect
415. #1599C2×C29semidirect
416. #1597C2×C29semidirect
417. #1596C2×C29semidirect
418. #1509C2×C29semidirect
419. #1503C2×C29semidirect
420. #1473C2×C29semidirect
541. C4⋊Q8D4×C29semidirect
542. C4⋊Q8D4×C29semidirect
565. #125D4×C29semidirect
573. #124D4×C29semidirect
605. C4×Q8D4×C29semidirect
606. C4×Q8D4×C29semidirect
607. C4×Q8D4×C29semidirect
613. C4×D4D4×C29semidirect
658. C29#18435direct (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×#32152
C29×#32112
C29×#26622
C29×#16062
C29×#16052
C29×#16032
C29×#16022
C29×#16002
C29×#15992
C29×#15972
C29×#15962
C29×#15092
C29×#15032
C29×#14732
#1843529