Finite Group Databasebeta

← C29×#24725 #20319625

Subgroups — C29×#24725 #20319625

Order 7424.

658 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3080C211yesmaximal, characteristic
2C2×C29×#479C211yesmaximal, characteristic, complemented
3C4×C29×#137C211yesmaximal, characteristic
4C29×#2925C211yesmaximal, characteristic
5C29×#2079C211yesmaximal, characteristic
6C29×#2078C211yesmaximal, characteristic
7C29×#2052C211yesmaximal, characteristic
8C29×#2052C211yesmaximal, characteristic
9C29×#1998C211yesmaximal, characteristic, complemented
10C29×#1952C211yesmaximal, characteristic, complemented
11C29×#1951C211yesmaximal, characteristic, complemented
12C29×#1950C211yesmaximal, characteristic, complemented
13C29×#1930C211yesmaximal, characteristic, complemented
14C29×#1930C211yesmaximal, characteristic, complemented
15C29×#1801C211yesmaximal, characteristic, complemented
16C2×C29×#137C2211yescharacteristic
17C2×C29×#125C2211yescharacteristic
18C4×#41×C29C2211yescharacteristic
19C2×C4×Q8×C29C2211yescharacteristic
20C29×#479—21no—
21C29×#479—21no—
22C29×#479—21no—
23C29×#479—21no—
24C29×#479—21no—
25C29×#479—21no—
26C29×#478—21no—
27C29×#478—21no—
28C29×#441—21no—
29C29×#440—21no—
30C4×Q16×C29—21no—
31C4×SD16×C29—21no—
32C29×#433—21no—
33C29×#433—21no—
34C29×#432—21no—
35C29×#431—21no—
36C2×C29×#108C2211yescharacteristic
37C2×C29×#108C2211yescharacteristic
38C29×#428C2211yescharacteristic
39C29×#428C2211yescharacteristic
40C29×#428C2211yescharacteristic
41C2×C29×#107C2211yescharacteristic
42C2×C29×#106C2211yescharacteristic
43C29×#423C2211yescharacteristic
44C29×#423C2211yescharacteristic
45C2×C29×C4⋊C8C2211yescharacteristic
46C29×#419C2211yescharacteristic
47C29×#417C2211yescharacteristic
48C29×#417C2211yescharacteristic
49C29×#417C2211yescharacteristic
50C2×C29×#103C2211yescharacteristic
51C2×C29×#103C2211yescharacteristic
52C2×C29×#101C2211yescharacteristic
53C2×C29×#101C2211yescharacteristic
54C29×#408C2211yescharacteristic
55C29×#408C2211yescharacteristic
56C29×#405C2211yescharacteristic
57C29×#405C2211yescharacteristic
58C4×M16×C29C2211yescharacteristic
59C29×#343C2211yescharacteristic
60C29×#343C2211yescharacteristic
61C29×#343C2211yescharacteristic
62C29×#343C2211yescharacteristic
63C29×#343C2211yescharacteristic
64C29×#343C2211yescharacteristic
65C29×#341C2211yescharacteristic
66C29×#341C2211yescharacteristic
67C2×#41×C29C2311yescharacteristic
68C22×Q8×C29C2311yescharacteristic
69C29×#137—22no—
70C29×#137—22no—
71C2×Q16×C29—21no—
72C2×SD16×C29—21no—
73C2×M16×C29C2311yescharacteristic
74C2×M16×C29C2311yescharacteristic
75C2×M16×C29C2311yescharacteristic
76C2×M16×C29C2311yescharacteristic
77C2×M16×C29C2311yescharacteristic
78C2×M16×C29C2311yescharacteristic
79C22×C8×C29C2311yescharacteristic
80C22×C8×C29C2311yescharacteristic
81C29×#125—21no—
82C29×#125—21no—
83C29×#125—21no—
84C29×#125—21no—
85C4×Q8×C29—21no—
86C4×Q8×C29—21no—
87C4×Q8×C29—21no—
88C4×Q8×C29—21no—
89C4×Q8×C29D411yescharacteristic
90C4×Q8×C29D411yescharacteristic
91C4×D4×C29—21no—
92C4×D4×C29—21no—
93C4×D4×C29D411yescharacteristic
94C4×D4×C29D411yescharacteristic
95C29×#117—21no—
96C29×#117C2311yescharacteristic
97C2×C4⋊C4×C29—21no—
98C2×C4⋊C4×C29—21no—
99C2×C4⋊C4×C29—21no—
100C2×C4⋊C4×C29C2311yescharacteristic
101C2×C4⋊C4×C29C2311yescharacteristic
102C2×C4⋊C4×C29C2311yescharacteristic
103C2×C42×C29—21no—
104C2×C42×C29—21no—
105C2×C42×C29C2311yescharacteristic
106C29×#108—22no—
107C29×#108—22no—
108C29×#107—21no—
109C29×#107—21no—
110C29×#107—21no—
111C29×#107—21no—
112C29×#107—21no—
113C29×#106—21no—
114C29×#106—21no—
115C29×#106—21no—
116C29×#106—21no—
117C29×#106—21no—
118C29×C4⋊C8—21no—
119C29×C4⋊C8—21no—
120C29×C4⋊C8—21no—
121C29×C4⋊C8—21no—
122C29×C4⋊C8D411yescharacteristic
123C29×C4⋊C8D411yescharacteristic
124C29×C4⋊C8D411yescharacteristic
125C29×C4⋊C8D411yescharacteristic
126C29×#103—21no—
127C29×#103—21no—
128C29×#103—21no—
129C29×#103—21no—
130C29×#103—21no—
131C29×#103—21no—
132C29×#103—21no—
133C29×#103—21no—
134C29×#103—21no—
135C29×#102—21no—
136C29×#102—21no—
137C29×#102—21no—
138C29×#101—22no—
139C29×#101—22no—
140C29×C22⋊C8—21no—
141C29×C22⋊C8—21no—
142C29×C22⋊C8—21no—
143C29×C22⋊C8—21no—
144C29×#97—21no—
145C29×#97—21no—
146C29×#97—21no—
147C4×C8×C29—21no—
148C4×C8×C29—21no—
149C4×C8×C29—21no—
150#41×C29—21no—
151#41×C29—21no—
152#41×C29—21no—
153#41×C29—21no—
154C2×Q8×C29—21no—
155C2×Q8×C29—21no—
156C2×Q8×C29—21no—
157C2×Q8×C29—21no—
158C2×Q8×C29—21no—
159C2×Q8×C29C2×D411yescharacteristic
160C2×Q8×C29#4112yes—
161C2×D4×C29—21no—
162C2×D4×C29C2×D411yescharacteristic
163C22×C4×C29—21no—
164C22×C4×C29—21no—
165C22×C4×C29—21no—
166C22×C4×C29—21no—
167C22×C4×C29—21no—
168C22×C4×C29—21no—
169C22×C4×C29—21no—
170C22×C4×C29#4111yescharacteristic
171C22×C4×C29#4111yescharacteristic
172C22×C4×C29C2411yescharacteristic
173Q16×C29—24no—
174SD16×C29—24no—
175M16×C29—21no—
176M16×C29—21no—
177M16×C29—21no—
178M16×C29—21no—
179M16×C29—21no—
180M16×C29—21no—
181M16×C29—21no—
182M16×C29—21no—
183M16×C29—21no—
184M16×C29—21no—
185M16×C29—21no—
186M16×C29#4112yes—
187C2×C8×C29—21no—
188C2×C8×C29—21no—
189C2×C8×C29—21no—
190C2×C8×C29—21no—
191C2×C8×C29—21no—
192C2×C8×C29—21no—
193C2×C8×C29—21no—
194C2×C8×C29—21no—
195C2×C8×C29—21no—
196C2×C8×C29—21no—
197C2×C8×C29C2×D411yescharacteristic
198C2×C8×C29C2×D411yescharacteristic
199C2×C8×C29C2×D411yescharacteristic
200C2×C8×C29C2×D411yescharacteristic
201C4⋊C4×C29—21no—
202C4⋊C4×C29—21no—
203C4⋊C4×C29—21no—
204C4⋊C4×C29—21no—
205C4⋊C4×C29—21no—
206C4⋊C4×C29—21no—
207C4⋊C4×C29—21no—
208C4⋊C4×C29—21no—
209C4⋊C4×C29—41no—
210C4⋊C4×C29—41no—
211C4⋊C4×C29—41no—
212C4⋊C4×C29—41no—
213C4⋊C4×C29—41no—
214C4⋊C4×C29—41no—
215C4⋊C4×C29C2×D411yescharacteristic
216C4⋊C4×C29C2×D411yescharacteristic
217C22⋊C4×C29—21no—
218C22⋊C4×C29—21no—
219C22⋊C4×C29—21no—
220C42×C29—21no—
221C42×C29—21no—
222C42×C29—21no—
223C42×C29—41no—
224C42×C29—41no—
225C42×C29C2×D411yescharacteristic
226C42×C29C2×D411yescharacteristic
227C42×C29C2×D411yescharacteristic
228C42×C29C2×D411yescharacteristic
229#24725C2911yesmaximal, characteristic, direct product factor, Sylow
230C23×C29—21no—
231C23×C29C2×#4111yescharacteristic
232Q8×C29—22no—
233Q8×C29—21no—
234Q8×C29—21no—
235Q8×C29—22no—
236Q8×C29—41no—
237Q8×C29—41no—
238D4×C29—21no—
239D4×C29—21no—
240D4×C29—41no—
241D4×C29—41no—
242C2×C4×C29—21no—
243C2×C4×C29—21no—
244C2×C4×C29—21no—
245C2×C4×C29—22no—
246C2×C4×C29—41no—
247C2×C4×C29—41no—
248C2×C4×C29—42no—
249C2×C4×C29—41no—
250C2×C4×C29—41no—
251C2×C4×C29—41no—
252C2×C4×C29—41no—
253C2×C4×C29—41no—
254C2×C4×C29—41no—
255C2×C4×C29—41no—
256C2×C4×C29—81no—
257C2×C4×C29—81no—
258C2×C4×C29—81no—
259C2×C4×C29—81no—
260C2×C4×C29#12111yescharacteristic
261C2×C4×C29#12111yescharacteristic
262C2×C4×C29#12111yescharacteristic
263C2×C4×C29#12111yescharacteristic
264C2×C4×C29C22×D411yescharacteristic
265C2×C4×C29C22×D411yescharacteristic
266C2×C4×C29C2×#4111yescharacteristic
267C2×C4×C29C2×#4111yescharacteristic
268C2×C4×C292−1+411yescharacteristic
269C2×C4×C292−1+411yescharacteristic
270C8×C29—22no—
271C8×C29—21no—
272C8×C29—21no—
273C8×C29—21no—
274C8×C29—21no—
275C8×C29—41no—
276C8×C29—41no—
277C8×C29—41no—
278C8×C29—41no—
279C8×C29—41no—
280#3080C2×C2911yescharacteristic
281C2×#479C2×C2911yescharacteristic, complemented
282C4×#137C2×C2911yescharacteristic
283#2925C2×C2911yescharacteristic
284#2079C2×C2911yescharacteristic
285#2078C2×C2911yescharacteristic
286#2052C2×C2911yescharacteristic
287#2052C2×C2911yescharacteristic
288#1998C2×C2911yescharacteristic, complemented
289#1952C2×C2911yescharacteristic, complemented
290#1951C2×C2911yescharacteristic, complemented
291#1950C2×C2911yescharacteristic, complemented
292#1930C2×C2911yescharacteristic, complemented
293#1930C2×C2911yescharacteristic, complemented
294#1801C2×C2911yescharacteristic, complemented
295C22×C29—21no—
296C22×C29—21no—
297C22×C29—41no—
298C22×C29—41no—
299C22×C29—41no—
300C22×C29C2×#12111yescharacteristic
301C22×C29#55211yescharacteristic
302C22×C29#55611yescharacteristic
303C4×C29—21no—
304C4×C29—21no—
305C4×C29—21no—
306C4×C29—21no—
307C4×C29—41no—
308C4×C29—42no—
309C4×C29—41no—
310C4×C29—41no—
311C4×C29—81no—
312C4×C29—81no—
313C4×C29—81no—
314C4×C29#52511yescharacteristic
315C4×C29#53611yescharacteristic
316C4×C29#54711yescharacteristic
317C4×C29#54811yescharacteristic
318C2×#137C22×C2911yescharacteristic
319C2×#125C22×C2911yescharacteristic
320C4×#41C22×C2911yescharacteristic
321C2×C4×Q8C22×C2911yescharacteristic
322#479—21no—
323#479—21no—
324#479—21no—
325#479—21no—
326#479—21no—
327#479—21no—
328#478—21no—
329#478—21no—
330#441—21no—
331#440—21no—
332C4×Q16—21no—
333C4×SD16—21no—
334#433—21no—
335#433—21no—
336#432—21no—
337#431—21no—
338C2×#108C22×C2911yescharacteristic
339C2×#108C22×C2911yescharacteristic
340#428C22×C2911yescharacteristic
341#428C22×C2911yescharacteristic
342#428C22×C2911yescharacteristic
343C2×#107C22×C2911yescharacteristic
344C2×#106C22×C2911yescharacteristic
345#423C22×C2911yescharacteristic
346#423C22×C2911yescharacteristic
347C2×C4⋊C8C22×C2911yescharacteristic
348#419C22×C2911yescharacteristic
349#417C22×C2911yescharacteristic
350#417C22×C2911yescharacteristic
351#417C22×C2911yescharacteristic
352C2×#103C22×C2911yescharacteristic
353C2×#103C22×C2911yescharacteristic
354C2×#101C22×C2911yescharacteristic
355C2×#101C22×C2911yescharacteristic
356#408C22×C2911yescharacteristic
357#408C22×C2911yescharacteristic
358#405C22×C2911yescharacteristic
359#405C22×C2911yescharacteristic
360C4×M16C22×C2911yescharacteristic
361#343C22×C2911yescharacteristic
362#343C22×C2911yescharacteristic
363#343C22×C2911yescharacteristic
364#343C22×C2911yescharacteristic
365#343C22×C2911yescharacteristic
366#343C22×C2911yescharacteristic
367#341C22×C2911yescharacteristic
368#341C22×C2911yescharacteristic
369C2×C29—21no—
370C2×C29—21no—
371C2×C29—81no—
372C2×C29#241511yescharacteristic
373C2×C29#306711yescharacteristic
374C2×C29#306911yescharacteristic
375C2×#41C23×C2911yescharacteristic
376C22×Q8C23×C2911yescharacteristic
377#137—22no—
378#137—22no—
379C2×Q16—21no—
380C2×SD16—21no—
381C2×M16C23×C2911yescharacteristic
382C2×M16C23×C2911yescharacteristic
383C2×M16C23×C2911yescharacteristic
384C2×M16C23×C2911yescharacteristic
385C2×M16C23×C2911yescharacteristic
386C2×M16C23×C2911yescharacteristic
387C22×C8C23×C2911yescharacteristic
388C22×C8C23×C2911yescharacteristic
389#125—21no—
390#125—21no—
391#125—21no—
392#125—21no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8D4×C2911yescharacteristic
398C4×Q8D4×C2911yescharacteristic
399C4×D4—21no—
400C4×D4—21no—
401C4×D4D4×C2911yescharacteristic
402C4×D4D4×C2911yescharacteristic
403#117—21no—
404#117C23×C2911yescharacteristic
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4C23×C2911yescharacteristic
409C2×C4⋊C4C23×C2911yescharacteristic
410C2×C4⋊C4C23×C2911yescharacteristic
411C2×C42—21no—
412C2×C42—21no—
413C2×C42C23×C2911yescharacteristic
414#108—22no—
415#108—22no—
416#107—21no—
417#107—21no—
418#107—21no—
419#107—21no—
420#107—21no—
421#106—21no—
422#106—21no—
423#106—21no—
424#106—21no—
425#106—21no—
426C4⋊C8—21no—
427C4⋊C8—21no—
428C4⋊C8—21no—
429C4⋊C8—21no—
430C4⋊C8D4×C2911yescharacteristic
431C4⋊C8D4×C2911yescharacteristic
432C4⋊C8D4×C2911yescharacteristic
433C4⋊C8D4×C2911yescharacteristic
434#103—21no—
435#103—21no—
436#103—21no—
437#103—21no—
438#103—21no—
439#103—21no—
440#103—21no—
441#103—21no—
442#103—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#101—22no—
447#101—22no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452#97—21no—
453#97—21no—
454#97—21no—
455C4×C8—21no—
456C4×C8—21no—
457C4×C8—21no—
458C29#2472511yescharacteristic, direct product factor, Sylow
459#41—21no—
460#41—21no—
461#41—21no—
462#41—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8C2×D4×C2911yescharacteristic
469C2×Q8#41×C2912yes—
470C2×D4—21no—
471C2×D4C2×D4×C2911yescharacteristic
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4#41×C2911yescharacteristic
480C22×C4#41×C2911yescharacteristic
481C22×C4C24×C2911yescharacteristic
482Q16—24no—
483SD16—24no—
484M16—21no—
485M16—21no—
486M16—21no—
487M16—21no—
488M16—21no—
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16#41×C2912yes—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8C2×D4×C2911yescharacteristic
507C2×C8C2×D4×C2911yescharacteristic
508C2×C8C2×D4×C2911yescharacteristic
509C2×C8C2×D4×C2911yescharacteristic
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4C2×D4×C2911yescharacteristic
525C4⋊C4C2×D4×C2911yescharacteristic
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—41no—
533C42—41no—
534C42C2×D4×C2911yescharacteristic
535C42C2×D4×C2911yescharacteristic
536C42C2×D4×C2911yescharacteristic
537C42C2×D4×C2911yescharacteristic
538C23—21no—
539C23C2×#41×C2911yescharacteristic
540Q8—22no—
541Q8—21no—
542Q8—21no—
543Q8—22no—
544Q8—41no—
545Q8—41no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4—81no—
567C2×C4—81no—
568C2×C4C29×#12111yescharacteristic
569C2×C4C29×#12111yescharacteristic
570C2×C4C29×#12111yescharacteristic
571C2×C4C29×#12111yescharacteristic
572C2×C4C22×D4×C2911yescharacteristic
573C2×C4C22×D4×C2911yescharacteristic
574C2×C4C2×#41×C2911yescharacteristic
575C2×C4C2×#41×C2911yescharacteristic
576C2×C4C29×2−1+411yescharacteristic
577C2×C4C29×2−1+411yescharacteristic
578C8—22no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—21no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C22—21no—
589C22—21no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22C2×C29×#12111yescharacteristic
594C22C29×#55211yescharacteristic
595C22C29×#55611yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—41no—
601C4—42no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4C29×#52511yescharacteristic
608C4C29×#53611yescharacteristic
609C4C29×#54711yescharacteristic
610C4C29×#54811yescharacteristic
611C2—21no—
612C2—21no—
613C2—81no—
614C2C29×#241511yescharacteristic
615C2C29×#306711yescharacteristic
616C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×#41×C29C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#479C2semidirect
9. C29×#1998C2semidirect
10. C29×#1952C2semidirect
11. C29×#1951C2semidirect
12. C29×#1950C2semidirect
13. C29×#1930C2semidirect
14. C29×#1930C2semidirect
15. C29×#1801C2semidirect
229. #24725C29direct (N × H)
281. C2×#479C2×C29semidirect
288. #1998C2×C29semidirect
289. #1952C2×C29semidirect
290. #1951C2×C29semidirect
291. #1950C2×C29semidirect
292. #1930C2×C29semidirect
293. #1930C2×C29semidirect
294. #1801C2×C29semidirect
458. C29#24725direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30802
C2×C29×#4792
C4×C29×#1372
C29×#29252
C29×#20792
C29×#20782
C29×#20522
C29×#19982
C29×#19522
C29×#19512
C29×#19502
C29×#19302
C29×#18012
#2472529