Finite Group Databasebeta

← C29×#24625 #20319525

Subgroups — C29×#24625 #20319525

Order 7424.

696 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3094C211yesmaximal, characteristic
2C2×C29×#482C211yesmaximal, characteristic
3C29×#2924C211yesmaximal, characteristic, complemented
4C29×#2911C211yesmaximal, characteristic, complemented
5C29×#2090C211yesmaximal, characteristic, complemented
6C29×#2089C211yesmaximal, characteristic, complemented
7C29×#2063C211yesmaximal, characteristic, complemented
8C29×#2063C211yesmaximal, characteristic, complemented
9C29×#1952C211yesmaximal, characteristic, complemented
10C29×#1951C211yesmaximal, characteristic, complemented
11C29×#1931C211yesmaximal, characteristic, complemented
12C29×#1931C211yesmaximal, characteristic, complemented
13C29×#1900C211yesmaximal, characteristic
14C29×#1855C211yesmaximal, characteristic, complemented
15C29×#1822C211yesmaximal, characteristic, complemented
16C22×M16×C29C2211yescharacteristic
17C2×C29×#121C2211yescharacteristic
18C2×C29×#117C2211yescharacteristic
19C2×C29×#117C2211yescharacteristic
20C29×#482—21no—
21C29×#482—21no—
22C29×#482—21no—
23C29×#482—21no—
24C29×#482—21no—
25C29×#482—21no—
26C29×#481—21no—
27C29×#480—21no—
28C29×#433—21no—
29C29×#433—21no—
30C29×#432—21no—
31C29×#431—21no—
32C2×C29×#108C2211yescharacteristic
33C2×C29×#108C2211yescharacteristic
34C29×#428—21no—
35C29×#428—21no—
36C29×#428C2211yescharacteristic
37C29×#428C2211yescharacteristic
38C29×#428C2211yescharacteristic
39C29×#428C2211yescharacteristic
40C29×#428C2211yescharacteristic
41C29×#428C2211yescharacteristic
42C29×#427—21no—
43C29×#427—21no—
44C2×C29×#107C2211yescharacteristic
45C2×C29×#106C2211yescharacteristic
46C29×#424C2211yescharacteristic
47C29×#424C2211yescharacteristic
48C29×#418C2211yescharacteristic
49C29×#418C2211yescharacteristic
50C2×C29×#102C2211yescharacteristic
51C2×C29×#102C2211yescharacteristic
52C2×C29×#100C2211yescharacteristic
53C2×C29×#100C2211yescharacteristic
54C29×#407C2211yescharacteristic
55C29×#407C2211yescharacteristic
56C2×C29×C22⋊C8C2211yescharacteristic
57C29×#405C2211yescharacteristic
58C29×#405C2211yescharacteristic
59C29×#343C2211yescharacteristic
60C29×#343C2211yescharacteristic
61C29×#343C2211yescharacteristic
62C29×#343C2211yescharacteristic
63C29×#343C2211yescharacteristic
64C29×#343C2211yescharacteristic
65C29×#341C2211yescharacteristic
66C29×#341C2211yescharacteristic
67C22×D4×C29—21no—
68C22×D4×C29C2311yescharacteristic
69C23×C4×C29C2311yescharacteristic
70C2×M16×C29—21no—
71C2×M16×C29—22no—
72C2×M16×C29—22no—
73C2×M16×C29C2311yescharacteristic
74C2×M16×C29C2311yescharacteristic
75C2×M16×C29C2311yescharacteristic
76C2×M16×C29C2311yescharacteristic
77C2×M16×C29C2311yescharacteristic
78C2×M16×C29C2311yescharacteristic
79C22×C8×C29—21no—
80C22×C8×C29C2311yescharacteristic
81C22×C8×C29C2311yescharacteristic
82C29×#121—21no—
83C29×#121—21no—
84C29×#121—21no—
85C29×#121—21no—
86C29×#117—21no—
87C29×#117—21no—
88C29×#117—21no—
89C29×#117—21no—
90C29×#117—21no—
91C29×#117—21no—
92C29×#117D411yescharacteristic
93C29×#117D411yescharacteristic
94C29×#117C2311yescharacteristic
95C29×#117C2311yescharacteristic
96C2×C4⋊C4×C29D411yescharacteristic
97C2×C4⋊C4×C29D411yescharacteristic
98C2×C4⋊C4×C29C2311yescharacteristic
99C2×C4⋊C4×C29C2311yescharacteristic
100C2×C4⋊C4×C29C2311yescharacteristic
101C2×C22⋊C4×C29—21no—
102C2×C22⋊C4×C29—21no—
103C2×C22⋊C4×C29—21no—
104C2×C42×C29—21no—
105C2×C42×C29—21no—
106C29×#108—22no—
107C29×#108—22no—
108C29×#107—21no—
109C29×#107—21no—
110C29×#107—21no—
111C29×#107—21no—
112C29×#107—21no—
113C29×#107—21no—
114C29×#107—21no—
115C29×#107—21no—
116C29×#106—21no—
117C29×#106—21no—
118C29×#106—21no—
119C29×#106—21no—
120C29×#106—21no—
121C29×#106—21no—
122C29×#106—21no—
123C29×#106—21no—
124C29×C4⋊C8—21no—
125C29×C4⋊C8—21no—
126C29×C4⋊C8—21no—
127C29×C4⋊C8—21no—
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×#102—21no—
136C29×#100—22no—
137C29×#100—22no—
138C29×C22⋊C8—21no—
139C29×C22⋊C8—21no—
140C29×C22⋊C8—21no—
141C29×C22⋊C8—21no—
142C29×C22⋊C8D411yescharacteristic
143C29×C22⋊C8D411yescharacteristic
144C29×C22⋊C8D411yescharacteristic
145C29×C22⋊C8D411yescharacteristic
146C29×#97—21no—
147C29×#97—21no—
148C4×C8×C29—21no—
149C4×C8×C29—21no—
150C24×C29—21no—
151C24×C29#4111yescharacteristic
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29—21no—
158C2×D4×C29—41no—
159C2×D4×C29—41no—
160C2×D4×C29—82no—
161C22×C4×C29—21no—
162C22×C4×C29—21no—
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×C29C2×D411yescharacteristic
171C22×C4×C29C2×D411yescharacteristic
172C22×C4×C29C2×D411yescharacteristic
173C22×C4×C29C2×D411yescharacteristic
174C22×C4×C29#4111yescharacteristic
175C22×C4×C29C2411yescharacteristic
176M16×C29—24no—
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—21no—
187M16×C29#4112yes—
188M16×C29#4112yes—
189C2×C8×C29—24no—
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×C29—21no—
198C2×C8×C29—21no—
199C2×C8×C29—21no—
200C2×C8×C29C2×D411yescharacteristic
201C2×C8×C29C2×D411yescharacteristic
202C2×C8×C29C2×D411yescharacteristic
203C2×C8×C29C2×D411yescharacteristic
204C4⋊C4×C29—21no—
205C4⋊C4×C29—21no—
206C4⋊C4×C29—21no—
207C4⋊C4×C29—21no—
208C4⋊C4×C29—21no—
209C4⋊C4×C29—21no—
210C4⋊C4×C29—21no—
211C4⋊C4×C29—21no—
212C4⋊C4×C29C2×D411yescharacteristic
213C4⋊C4×C29C2×D411yescharacteristic
214C4⋊C4×C29C2×D411yescharacteristic
215C4⋊C4×C29C2×D411yescharacteristic
216C22⋊C4×C29—21no—
217C22⋊C4×C29—21no—
218C22⋊C4×C29—21no—
219C22⋊C4×C29—21no—
220C22⋊C4×C29—41no—
221C22⋊C4×C29—41no—
222C22⋊C4×C29—41no—
223C22⋊C4×C29—41no—
224C42×C29—21no—
225C42×C29—21no—
226C42×C29—21no—
227C42×C29—21no—
228C42×C29—41no—
229C42×C29—41no—
230#24625C2911yesmaximal, characteristic, direct product factor, Sylow
231C23×C29—21no—
232C23×C29—21no—
233C23×C29—41no—
234C23×C29—41no—
235C23×C29—41no—
236C23×C29—41no—
237C23×C29—41no—
238C23×C29—81no—
239C23×C29—81no—
240C23×C29#12111yescharacteristic
241C23×C29#12111yescharacteristic
242C23×C29C2×#4111yescharacteristic
243D4×C29—41no—
244D4×C29—41no—
245D4×C29—41no—
246D4×C29—41no—
247D4×C29—82no—
248D4×C29—82no—
249C2×C4×C29—21no—
250C2×C4×C29—21no—
251C2×C4×C29—21no—
252C2×C4×C29—21no—
253C2×C4×C29—21no—
254C2×C4×C29—21no—
255C2×C4×C29—21no—
256C2×C4×C29—21no—
257C2×C4×C29—21no—
258C2×C4×C29—21no—
259C2×C4×C29—21no—
260C2×C4×C29—21no—
261C2×C4×C29—21no—
262C2×C4×C29—21no—
263C2×C4×C29—42no—
264C2×C4×C29—41no—
265C2×C4×C29—41no—
266C2×C4×C29—41no—
267C2×C4×C29—81no—
268C2×C4×C29—81no—
269C2×C4×C29—81no—
270C2×C4×C29—81no—
271C2×C4×C29#12111yescharacteristic
272C2×C4×C29#12111yescharacteristic
273C2×C4×C29C22×D411yescharacteristic
274C2×C4×C29C22×D411yescharacteristic
275C2×C4×C29C2×#4111yescharacteristic
276C2×C4×C29C2×#4111yescharacteristic
277C2×C4×C292−1+411yescharacteristic
278C2×C4×C292−1+411yescharacteristic
279C8×C29—22no—
280C8×C29—22no—
281C8×C29—21no—
282C8×C29—21no—
283C8×C29—21no—
284C8×C29—21no—
285C8×C29—41no—
286C8×C29—41no—
287C8×C29—41no—
288C8×C29—41no—
289#3094C2×C2911yescharacteristic
290C2×#482C2×C2911yescharacteristic
291#2924C2×C2911yescharacteristic, complemented
292#2911C2×C2911yescharacteristic, complemented
293#2090C2×C2911yescharacteristic, complemented
294#2089C2×C2911yescharacteristic, complemented
295#2063C2×C2911yescharacteristic, complemented
296#2063C2×C2911yescharacteristic, complemented
297#1952C2×C2911yescharacteristic, complemented
298#1951C2×C2911yescharacteristic, complemented
299#1931C2×C2911yescharacteristic, complemented
300#1931C2×C2911yescharacteristic, complemented
301#1900C2×C2911yescharacteristic
302#1855C2×C2911yescharacteristic, complemented
303#1822C2×C2911yescharacteristic, complemented
304C22×C29—21no—
305C22×C29—21no—
306C22×C29—21no—
307C22×C29—21no—
308C22×C29—21no—
309C22×C29—21no—
310C22×C29—21no—
311C22×C29—21no—
312C22×C29—81no—
313C22×C29—81no—
314C22×C29—81no—
315C22×C29—81no—
316C22×C29—81no—
317C22×C29—161no—
318C22×C29—161no—
319C22×C29C2×#12111yescharacteristic
320C22×C29#55211yescharacteristic
321C22×C29#55211yescharacteristic
322C4×C29—21no—
323C4×C29—21no—
324C4×C29—41no—
325C4×C29—41no—
326C4×C29—41no—
327C4×C29—41no—
328C4×C29—81no—
329C4×C29—81no—
330C4×C29—81no—
331C4×C29#52511yescharacteristic
332C4×C29#53611yescharacteristic
333C4×C29#54711yescharacteristic
334C4×C29#54711yescharacteristic
335C22×M16C22×C2911yescharacteristic
336C2×#121C22×C2911yescharacteristic
337C2×#117C22×C2911yescharacteristic
338C2×#117C22×C2911yescharacteristic
339#482—21no—
340#482—21no—
341#482—21no—
342#482—21no—
343#482—21no—
344#482—21no—
345#481—21no—
346#480—21no—
347#433—21no—
348#433—21no—
349#432—21no—
350#431—21no—
351C2×#108C22×C2911yescharacteristic
352C2×#108C22×C2911yescharacteristic
353#428—21no—
354#428—21no—
355#428C22×C2911yescharacteristic
356#428C22×C2911yescharacteristic
357#428C22×C2911yescharacteristic
358#428C22×C2911yescharacteristic
359#428C22×C2911yescharacteristic
360#428C22×C2911yescharacteristic
361#427—21no—
362#427—21no—
363C2×#107C22×C2911yescharacteristic
364C2×#106C22×C2911yescharacteristic
365#424C22×C2911yescharacteristic
366#424C22×C2911yescharacteristic
367#418C22×C2911yescharacteristic
368#418C22×C2911yescharacteristic
369C2×#102C22×C2911yescharacteristic
370C2×#102C22×C2911yescharacteristic
371C2×#100C22×C2911yescharacteristic
372C2×#100C22×C2911yescharacteristic
373#407C22×C2911yescharacteristic
374#407C22×C2911yescharacteristic
375C2×C22⋊C8C22×C2911yescharacteristic
376#405C22×C2911yescharacteristic
377#405C22×C2911yescharacteristic
378#343C22×C2911yescharacteristic
379#343C22×C2911yescharacteristic
380#343C22×C2911yescharacteristic
381#343C22×C2911yescharacteristic
382#343C22×C2911yescharacteristic
383#343C22×C2911yescharacteristic
384#341C22×C2911yescharacteristic
385#341C22×C2911yescharacteristic
386C2×C29—21no—
387C2×C29—21no—
388C2×C29—41no—
389C2×C29—41no—
390C2×C29—161no—
391C2×C29#241311yescharacteristic
392C2×C29#306711yescharacteristic
393C2×C29#306811yescharacteristic
394C22×D4—21no—
395C22×D4C23×C2911yescharacteristic
396C23×C4C23×C2911yescharacteristic
397C2×M16—21no—
398C2×M16—22no—
399C2×M16—22no—
400C2×M16C23×C2911yescharacteristic
401C2×M16C23×C2911yescharacteristic
402C2×M16C23×C2911yescharacteristic
403C2×M16C23×C2911yescharacteristic
404C2×M16C23×C2911yescharacteristic
405C2×M16C23×C2911yescharacteristic
406C22×C8—21no—
407C22×C8C23×C2911yescharacteristic
408C22×C8C23×C2911yescharacteristic
409#121—21no—
410#121—21no—
411#121—21no—
412#121—21no—
413#117—21no—
414#117—21no—
415#117—21no—
416#117—21no—
417#117—21no—
418#117—21no—
419#117D4×C2911yescharacteristic
420#117D4×C2911yescharacteristic
421#117C23×C2911yescharacteristic
422#117C23×C2911yescharacteristic
423C2×C4⋊C4D4×C2911yescharacteristic
424C2×C4⋊C4D4×C2911yescharacteristic
425C2×C4⋊C4C23×C2911yescharacteristic
426C2×C4⋊C4C23×C2911yescharacteristic
427C2×C4⋊C4C23×C2911yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C42—21no—
432C2×C42—21no—
433#108—22no—
434#108—22no—
435#107—21no—
436#107—21no—
437#107—21no—
438#107—21no—
439#107—21no—
440#107—21no—
441#107—21no—
442#107—21no—
443#106—21no—
444#106—21no—
445#106—21no—
446#106—21no—
447#106—21no—
448#106—21no—
449#106—21no—
450#106—21no—
451C4⋊C8—21no—
452C4⋊C8—21no—
453C4⋊C8—21no—
454C4⋊C8—21no—
455#102—21no—
456#102—21no—
457#102—21no—
458#102—21no—
459#102—21no—
460#102—21no—
461#102—21no—
462#102—21no—
463#100—22no—
464#100—22no—
465C22⋊C8—21no—
466C22⋊C8—21no—
467C22⋊C8—21no—
468C22⋊C8—21no—
469C22⋊C8D4×C2911yescharacteristic
470C22⋊C8D4×C2911yescharacteristic
471C22⋊C8D4×C2911yescharacteristic
472C22⋊C8D4×C2911yescharacteristic
473#97—21no—
474#97—21no—
475C4×C8—21no—
476C4×C8—21no—
477C29#2462511yescharacteristic, direct product factor, Sylow
478C24—21no—
479C24#41×C2911yescharacteristic
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—82no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4C2×D4×C2911yescharacteristic
499C22×C4C2×D4×C2911yescharacteristic
500C22×C4C2×D4×C2911yescharacteristic
501C22×C4C2×D4×C2911yescharacteristic
502C22×C4#41×C2911yescharacteristic
503C22×C4C24×C2911yescharacteristic
504M16—24no—
505M16—21no—
506M16—21no—
507M16—21no—
508M16—21no—
509M16—21no—
510M16—21no—
511M16—21no—
512M16—21no—
513M16—21no—
514M16—21no—
515M16#41×C2912yes—
516M16#41×C2912yes—
517C2×C8—24no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8C2×D4×C2911yescharacteristic
529C2×C8C2×D4×C2911yescharacteristic
530C2×C8C2×D4×C2911yescharacteristic
531C2×C8C2×D4×C2911yescharacteristic
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4C2×D4×C2911yescharacteristic
541C4⋊C4C2×D4×C2911yescharacteristic
542C4⋊C4C2×D4×C2911yescharacteristic
543C4⋊C4C2×D4×C2911yescharacteristic
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C22⋊C4—41no—
551C22⋊C4—41no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—41no—
557C42—41no—
558C23—21no—
559C23—21no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—81no—
566C23—81no—
567C23C29×#12111yescharacteristic
568C23C29×#12111yescharacteristic
569C23C2×#41×C2911yescharacteristic
570D4—41no—
571D4—41no—
572D4—41no—
573D4—41no—
574D4—82no—
575D4—82no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4C29×#12111yescharacteristic
599C2×C4C29×#12111yescharacteristic
600C2×C4C22×D4×C2911yescharacteristic
601C2×C4C22×D4×C2911yescharacteristic
602C2×C4C2×#41×C2911yescharacteristic
603C2×C4C2×#41×C2911yescharacteristic
604C2×C4C29×2−1+411yescharacteristic
605C2×C4C29×2−1+411yescharacteristic
606C8—22no—
607C8—22no—
608C8—21no—
609C8—21no—
610C8—21no—
611C8—21no—
612C8—41no—
613C8—41no—
614C8—41no—
615C8—41no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—21no—
623C22—21no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—161no—
630C22—161no—
631C22C2×C29×#12111yescharacteristic
632C22C29×#55211yescharacteristic
633C22C29×#55211yescharacteristic
634C4—21no—
635C4—21no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—81no—
641C4—81no—
642C4—81no—
643C4C29×#52511yescharacteristic
644C4C29×#53611yescharacteristic
645C4C29×#54711yescharacteristic
646C4C29×#54711yescharacteristic
647C2—21no—
648C2—21no—
649C2—41no—
650C2—41no—
651C2—161no—
652C2C29×#241311yescharacteristic
653C2C29×#306711yescharacteristic
654C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#2924C2semidirect
4. C29×#2911C2semidirect
5. C29×#2090C2semidirect
6. C29×#2089C2semidirect
7. C29×#2063C2semidirect
8. C29×#2063C2semidirect
9. C29×#1952C2semidirect
10. C29×#1951C2semidirect
11. C29×#1931C2semidirect
12. C29×#1931C2semidirect
14. C29×#1855C2semidirect
15. C29×#1822C2semidirect
230. #24625C29direct (N × H)
291. #2924C2×C29semidirect
292. #2911C2×C29semidirect
293. #2090C2×C29semidirect
294. #2089C2×C29semidirect
295. #2063C2×C29semidirect
296. #2063C2×C29semidirect
297. #1952C2×C29semidirect
298. #1951C2×C29semidirect
299. #1931C2×C29semidirect
300. #1931C2×C29semidirect
302. #1855C2×C29semidirect
303. #1822C2×C29semidirect
477. C29#24625direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30942
C2×C29×#4822
C29×#29242
C29×#29112
C29×#20902
C29×#20892
C29×#20632
C29×#19522
C29×#19512
C29×#19312
C29×#19002
C29×#18552
C29×#18222
#2462529