Finite Group Databasebeta

← C29×#19305 #20314205

Subgroups — C29×#19305 #20314205

Order 7424.

678 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3182C211yesmaximal, characteristic, complemented
2C29×#3109C211yesmaximal, characteristic
3C29×#3077C211yesmaximal, characteristic, complemented
4D4×M16×C29C211yesmaximal, characteristic, complemented
5C29×#1703C211yesmaximal, characteristic, complemented
6C29×#1697C211yesmaximal, characteristic, complemented
7C29×#1695C211yesmaximal, characteristic, complemented
8C29×#1685C211yesmaximal, characteristic, complemented
9C29×#1683C211yesmaximal, characteristic, complemented
10C29×#1677C211yesmaximal, characteristic, complemented
11C29×#1675C211yesmaximal, characteristic, complemented
12C29×#1665C211yesmaximal, characteristic, complemented
13C29×#1569C211yesmaximal, characteristic, complemented
14C29×#1560C211yesmaximal, characteristic, complemented
15C29×#1559C211yesmaximal, characteristic, complemented
16C22×M16×C29—21no—
17C29×#533C2211yescharacteristic
18C29×#532C2211yescharacteristic
19C2×C4×D4×C29C2211yescharacteristic
20C29×#500C2211yescharacteristic, complemented
21C29×#492C2211yescharacteristic, complemented
22C29×#487C2211yescharacteristic, complemented
23C29×#486C2211yescharacteristic, complemented
24C29×#481—21no—
25C29×#478—21no—
26C29×#478—21no—
27C29×#476C2211yescharacteristic
28C29×#476C2211yescharacteristic
29C29×#476C2211yescharacteristic
30C29×#476C2211yescharacteristic
31C29×#474C2211yescharacteristic
32C29×#474C2211yescharacteristic
33C29×#468—21no—
34C29×#468—21no—
35C29×#459C2211yescharacteristic
36C29×#459C2211yescharacteristic
37C29×#447—21no—
38C29×#442—21no—
39C29×#442—21no—
40C29×#440—21no—
41C29×#440—21no—
42C29×#436C2211yescharacteristic
43C29×#436C2211yescharacteristic
44C29×#435—21no—
45C29×#435—21no—
46C8×D4×C29C2211yescharacteristic
47C8×D4×C29C2211yescharacteristic
48C29×#432C2211yescharacteristic
49C29×#428—21no—
50C29×#423C2211yescharacteristic
51C29×#423C2211yescharacteristic
52C29×#418—21no—
53C29×#407—21no—
54C4×M16×C29C2211yescharacteristic
55C29×#335C2211yescharacteristic, complemented
56C29×#335C2211yescharacteristic, complemented
57C29×#334C2211yescharacteristic, complemented
58C29×#334C2211yescharacteristic, complemented
59C29×#333C2211yescharacteristic, complemented
60C29×#333C2211yescharacteristic, complemented
61C29×#333C2211yescharacteristic, complemented
62C29×#333C2211yescharacteristic, complemented
63C29×#332C2211yescharacteristic, complemented
64C29×#332C2211yescharacteristic, complemented
65C29×#331C2211yescharacteristic, complemented
66C29×#331C2211yescharacteristic, complemented
67C2×#41×C29—21no—
68C22×D4×C29D411yescharacteristic
69C23×C4×C29—21no—
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C2×D8×C29—21no—
73C2×D8×C29—21no—
74C2×M16×C29—21no—
75C2×M16×C29—21no—
76C2×M16×C29—21no—
77C2×M16×C29—21no—
78C2×M16×C29—44no—
79C2×M16×C29D411yescharacteristic
80C2×M16×C29D411yescharacteristic
81C22×C8×C29—21no—
82C22×C8×C29—21no—
83C29×C4⋊Q8C2311yescharacteristic
84C29×C4⋊Q8C2311yescharacteristic
85C29×C4⋊Q8C2311yescharacteristic
86C29×#127C2311yescharacteristic
87C29×#125—21no—
88C29×#124—21no—
89C29×C22⋊Q8—21no—
90C29×C22⋊Q8—21no—
91C29×#121—21no—
92C29×#121—21no—
93C4×Q8×C29—21no—
94C4×Q8×C29—21no—
95C4×D4×C29—21no—
96C4×D4×C29—21no—
97C4×D4×C29—21no—
98C4×D4×C29—21no—
99C4×D4×C29D411yescharacteristic
100C4×D4×C29D411yescharacteristic
101C4×D4×C29C2311yescharacteristic
102C4×D4×C29C2311yescharacteristic
103C29×#117—21no—
104C2×C4⋊C4×C29D411yescharacteristic
105C2×C22⋊C4×C29—21no—
106C2×C42×C29C2311yescharacteristic
107C29×#107—21no—
108C29×#107—21no—
109C29×#107—21no—
110C29×#107—21no—
111C29×#106—21no—
112C29×#106—21no—
113C29×#106—21no—
114C29×#106—21no—
115C29×C4⋊C8—21no—
116C29×C4⋊C8—21no—
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×C4⋊C8C2311yescharacteristic
122C29×C4⋊C8C2311yescharacteristic
123C29×#103—21no—
124C29×#103—21no—
125C29×#102—21no—
126C29×#102—21no—
127C29×#102—21no—
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×C22⋊C8—21no—
136C29×C22⋊C8—21no—
137C29×C22⋊C8—21no—
138C29×C22⋊C8—21no—
139C29×C22⋊C8—21no—
140C29×#97—21no—
141C29×#97D411yescharacteristic
142C29×#97D411yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C4×C8×C29C2311yescharacteristic
145C24×C29—21no—
146#41×C29—82no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×D4×C29—22no—
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—41no—
156C2×D4×C29—41no—
157C2×D4×C29C2×D411yescharacteristic
158C2×D4×C29C2×D411yescharacteristic
159C22×C4×C29—21no—
160C22×C4×C29—21no—
161C22×C4×C29—21no—
162C22×C4×C29—21no—
163C22×C4×C29—21no—
164C22×C4×C29—42no—
165C22×C4×C29—42no—
166C22×C4×C29—41no—
167C22×C4×C29C2×D411yescharacteristic
168C22×C4×C29C2×D411yescharacteristic
169C22×C4×C29#4111yescharacteristic
170SD16×C29—42no—
171SD16×C29—42no—
172D8×C29—42no—
173D8×C29—42no—
174M16×C29—22no—
175M16×C29—41no—
176M16×C29—42no—
177M16×C29—42no—
178M16×C29—42no—
179M16×C29—42no—
180C2×C8×C29—21no—
181C2×C8×C29—21no—
182C2×C8×C29—21no—
183C2×C8×C29—21no—
184C2×C8×C29—21no—
185C2×C8×C29—21no—
186C2×C8×C29—42no—
187C2×C8×C29—42no—
188C2×C8×C29C2×D411yescharacteristic
189C2×C8×C29C2×D411yescharacteristic
190C2×C8×C29C2×D411yescharacteristic
191C2×C8×C29C2×D411yescharacteristic
192C4⋊C4×C29—21no—
193C4⋊C4×C29—21no—
194C4⋊C4×C29—21no—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—21no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29—21no—
199C4⋊C4×C29—41no—
200C4⋊C4×C29—41no—
201C4⋊C4×C29C2×D411yescharacteristic
202C4⋊C4×C29C2×D411yescharacteristic
203C22⋊C4×C29—21no—
204C22⋊C4×C29—21no—
205C22⋊C4×C29—21no—
206C22⋊C4×C29—21no—
207C22⋊C4×C29—41no—
208C22⋊C4×C29—41no—
209C22⋊C4×C29—41no—
210C42×C29—41no—
211C42×C29C2×D411yescharacteristic
212C42×C29C2×D411yescharacteristic
213C42×C29#4111yescharacteristic
214C42×C29C2411yescharacteristic
215#19305C2911yesmaximal, characteristic, direct product factor, Sylow
216C23×C29—21no—
217C23×C29—21no—
218C23×C29—42no—
219C23×C29—42no—
220C23×C29—41no—
221C23×C29—81no—
222C23×C29#12111yescharacteristic
223Q8×C29—41no—
224Q8×C29—41no—
225Q8×C29—81no—
226Q8×C29—81no—
227D4×C29—21no—
228D4×C29—21no—
229D4×C29—21no—
230D4×C29—42no—
231D4×C29—41no—
232D4×C29—41no—
233D4×C29—41no—
234D4×C29—41no—
235D4×C29—81no—
236D4×C29—82no—
237D4×C29#13712yes—
238C2×C4×C29—21no—
239C2×C4×C29—21no—
240C2×C4×C29—21no—
241C2×C4×C29—21no—
242C2×C4×C29—21no—
243C2×C4×C29—21no—
244C2×C4×C29—41no—
245C2×C4×C29—42no—
246C2×C4×C29—42no—
247C2×C4×C29—42no—
248C2×C4×C29—41no—
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—82no—
256C2×C4×C29#12111yescharacteristic
257C2×C4×C29#12111yescharacteristic
258C2×C4×C29#12111yescharacteristic
259C2×C4×C29C22×D411yescharacteristic
260C2×C4×C29C22×D411yescharacteristic
261C2×C4×C29C2×#4111yescharacteristic
262C8×C29—21no—
263C8×C29—21no—
264C8×C29—21no—
265C8×C29—41no—
266C8×C29—41no—
267C8×C29—41no—
268C8×C29—41no—
269C8×C29—41no—
270C8×C29—41no—
271C8×C29AGL(1,ℤ/8)12yes—
272#3182C2×C2911yescharacteristic, complemented
273#3109C2×C2911yescharacteristic
274#3077C2×C2911yescharacteristic, complemented
275D4×M16C2×C2911yescharacteristic, complemented
276#1703C2×C2911yescharacteristic, complemented
277#1697C2×C2911yescharacteristic, complemented
278#1695C2×C2911yescharacteristic, complemented
279#1685C2×C2911yescharacteristic, complemented
280#1683C2×C2911yescharacteristic, complemented
281#1677C2×C2911yescharacteristic, complemented
282#1675C2×C2911yescharacteristic, complemented
283#1665C2×C2911yescharacteristic, complemented
284#1569C2×C2911yescharacteristic, complemented
285#1560C2×C2911yescharacteristic, complemented
286#1559C2×C2911yescharacteristic, complemented
287C22×C29—21no—
288C22×C29—21no—
289C22×C29—22no—
290C22×C29—21no—
291C22×C29—41no—
292C22×C29—41no—
293C22×C29—41no—
294C22×C29—41no—
295C22×C29—41no—
296C22×C29—84no—
297C22×C29—81no—
298C22×C29—81no—
299C22×C29—81no—
300C22×C29C2×#12111yescharacteristic
301C4×C29—21no—
302C4×C29—21no—
303C4×C29—21no—
304C4×C29—21no—
305C4×C29—41no—
306C4×C29—41no—
307C4×C29—81no—
308C4×C29—81no—
309C4×C29—81no—
310C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
311C4×C29C2×#13711yescharacteristic
312C4×C29#57511yescharacteristic
313C4×C29#57511yescharacteristic
314C22×M16—21no—
315#533C22×C2911yescharacteristic
316#532C22×C2911yescharacteristic
317C2×C4×D4C22×C2911yescharacteristic
318#500C22×C2911yescharacteristic, complemented
319#492C22×C2911yescharacteristic, complemented
320#487C22×C2911yescharacteristic, complemented
321#486C22×C2911yescharacteristic, complemented
322#481—21no—
323#478—21no—
324#478—21no—
325#476C22×C2911yescharacteristic
326#476C22×C2911yescharacteristic
327#476C22×C2911yescharacteristic
328#476C22×C2911yescharacteristic
329#474C22×C2911yescharacteristic
330#474C22×C2911yescharacteristic
331#468—21no—
332#468—21no—
333#459C22×C2911yescharacteristic
334#459C22×C2911yescharacteristic
335#447—21no—
336#442—21no—
337#442—21no—
338#440—21no—
339#440—21no—
340#436C22×C2911yescharacteristic
341#436C22×C2911yescharacteristic
342#435—21no—
343#435—21no—
344C8×D4C22×C2911yescharacteristic
345C8×D4C22×C2911yescharacteristic
346#432C22×C2911yescharacteristic
347#428—21no—
348#423C22×C2911yescharacteristic
349#423C22×C2911yescharacteristic
350#418—21no—
351#407—21no—
352C4×M16C22×C2911yescharacteristic
353#335C22×C2911yescharacteristic, complemented
354#335C22×C2911yescharacteristic, complemented
355#334C22×C2911yescharacteristic, complemented
356#334C22×C2911yescharacteristic, complemented
357#333C22×C2911yescharacteristic, complemented
358#333C22×C2911yescharacteristic, complemented
359#333C22×C2911yescharacteristic, complemented
360#333C22×C2911yescharacteristic, complemented
361#332C22×C2911yescharacteristic, complemented
362#332C22×C2911yescharacteristic, complemented
363#331C22×C2911yescharacteristic, complemented
364#331C22×C2911yescharacteristic, complemented
365C2×C29—41no—
366C2×C29—42no—
367C2×C29—81no—
368C2×C29—161no—
369C2×C29#303611yescharacteristic
370C2×C29#305611yescharacteristic
371C2×C29#306811yescharacteristic
372C2×#41—21no—
373C22×D4D4×C2911yescharacteristic
374C23×C4—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×D8—21no—
378C2×D8—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—44no—
384C2×M16D4×C2911yescharacteristic
385C2×M16D4×C2911yescharacteristic
386C22×C8—21no—
387C22×C8—21no—
388C4⋊Q8C23×C2911yescharacteristic
389C4⋊Q8C23×C2911yescharacteristic
390C4⋊Q8C23×C2911yescharacteristic
391#127C23×C2911yescharacteristic
392#125—21no—
393#124—21no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396#121—21no—
397#121—21no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4D4×C2911yescharacteristic
405C4×D4D4×C2911yescharacteristic
406C4×D4C23×C2911yescharacteristic
407C4×D4C23×C2911yescharacteristic
408#117—21no—
409C2×C4⋊C4D4×C2911yescharacteristic
410C2×C22⋊C4—21no—
411C2×C42C23×C2911yescharacteristic
412#107—21no—
413#107—21no—
414#107—21no—
415#107—21no—
416#106—21no—
417#106—21no—
418#106—21no—
419#106—21no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8C23×C2911yescharacteristic
423C4⋊C8C23×C2911yescharacteristic
424C4⋊C8C23×C2911yescharacteristic
425C4⋊C8C23×C2911yescharacteristic
426C4⋊C8C23×C2911yescharacteristic
427C4⋊C8C23×C2911yescharacteristic
428#103—21no—
429#103—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440C22⋊C8—21no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8—21no—
444C22⋊C8—21no—
445#97—21no—
446#97D4×C2911yescharacteristic
447#97D4×C2911yescharacteristic
448C4×C8C23×C2911yescharacteristic
449C4×C8C23×C2911yescharacteristic
450C29#1930511yescharacteristic, direct product factor, Sylow
451C24—21no—
452#41—82no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×D4—22no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4C2×D4×C2911yescharacteristic
464C2×D4C2×D4×C2911yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—41no—
473C22×C4C2×D4×C2911yescharacteristic
474C22×C4C2×D4×C2911yescharacteristic
475C22×C4#41×C2911yescharacteristic
476SD16—42no—
477SD16—42no—
478D8—42no—
479D8—42no—
480M16—22no—
481M16—41no—
482M16—42no—
483M16—42no—
484M16—42no—
485M16—42no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—42no—
493C2×C8—42no—
494C2×C8C2×D4×C2911yescharacteristic
495C2×C8C2×D4×C2911yescharacteristic
496C2×C8C2×D4×C2911yescharacteristic
497C2×C8C2×D4×C2911yescharacteristic
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4C2×D4×C2911yescharacteristic
508C4⋊C4C2×D4×C2911yescharacteristic
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C42—41no—
517C42C2×D4×C2911yescharacteristic
518C42C2×D4×C2911yescharacteristic
519C42#41×C2911yescharacteristic
520C42C24×C2911yescharacteristic
521C23—21no—
522C23—21no—
523C23—42no—
524C23—42no—
525C23—41no—
526C23—81no—
527C23C29×#12111yescharacteristic
528Q8—41no—
529Q8—41no—
530Q8—81no—
531Q8—81no—
532D4—21no—
533D4—21no—
534D4—21no—
535D4—42no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—81no—
541D4—82no—
542D4C29×#13712yes—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—82no—
561C2×C4C29×#12111yescharacteristic
562C2×C4C29×#12111yescharacteristic
563C2×C4C29×#12111yescharacteristic
564C2×C4C22×D4×C2911yescharacteristic
565C2×C4C22×D4×C2911yescharacteristic
566C2×C4C2×#41×C2911yescharacteristic
567C8—21no—
568C8—21no—
569C8—21no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8C29×AGL(1,ℤ/8)12yes—
577C22—21no—
578C22—21no—
579C22—22no—
580C22—21no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—84no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22C2×C29×#12111yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—41no—
596C4—41no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
601C4C2×C29×#13711yescharacteristic
602C4C29×#57511yescharacteristic
603C4C29×#57511yescharacteristic
604C2—41no—
605C2—42no—
606C2—81no—
607C2—161no—
608C2C29×#303611yescharacteristic
609C2C29×#305611yescharacteristic
610C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3109C2
LCSG ▷ C42 ▷ 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×#3182C2semidirect
3. C29×#3077C2semidirect
4. D4×M16×C29C2semidirect
5. C29×#1703C2semidirect
6. C29×#1697C2semidirect
7. C29×#1695C2semidirect
8. C29×#1685C2semidirect
9. C29×#1683C2semidirect
10. C29×#1677C2semidirect
11. C29×#1675C2semidirect
12. C29×#1665C2semidirect
13. C29×#1569C2semidirect
14. C29×#1560C2semidirect
15. C29×#1559C2semidirect
20. C29×#500C22semidirect
21. C29×#492C22semidirect
22. C29×#487C22semidirect
23. C29×#486C22semidirect
55. C29×#335C22semidirect
56. C29×#335C22semidirect
57. C29×#334C22semidirect
58. C29×#334C22semidirect
59. C29×#333C22semidirect
60. C29×#333C22semidirect
61. C29×#333C22semidirect
62. C29×#333C22semidirect
63. C29×#332C22semidirect
64. C29×#332C22semidirect
65. C29×#331C22semidirect
66. C29×#331C22semidirect
215. #19305C29direct (N × H)
272. #3182C2×C29semidirect
274. #3077C2×C29semidirect
275. D4×M16C2×C29semidirect
276. #1703C2×C29semidirect
277. #1697C2×C29semidirect
278. #1695C2×C29semidirect
279. #1685C2×C29semidirect
280. #1683C2×C29semidirect
281. #1677C2×C29semidirect
282. #1675C2×C29semidirect
283. #1665C2×C29semidirect
284. #1569C2×C29semidirect
285. #1560C2×C29semidirect
286. #1559C2×C29semidirect
318. #500C22×C29semidirect
319. #492C22×C29semidirect
320. #487C22×C29semidirect
321. #486C22×C29semidirect
353. #335C22×C29semidirect
354. #335C22×C29semidirect
355. #334C22×C29semidirect
356. #334C22×C29semidirect
357. #333C22×C29semidirect
358. #333C22×C29semidirect
359. #333C22×C29semidirect
360. #333C22×C29semidirect
361. #332C22×C29semidirect
362. #332C22×C29semidirect
363. #331C22×C29semidirect
364. #331C22×C29semidirect
450. C29#19305direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31822
C29×#31092
C29×#30772
D4×M16×C292
C29×#17032
C29×#16972
C29×#16952
C29×#16852
C29×#16832
C29×#16772
C29×#16752
C29×#16652
C29×#15692
C29×#15602
C29×#15592
#1930529