Finite Group Databasebeta

← C29×#19473 #20314373

Subgroups — C29×#19473 #20314373

Order 7424.

646 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3207C211yesmaximal, characteristic
2C29×#3103C211yesmaximal, characteristic, complemented
3C29×#3037C211yesmaximal, characteristic, complemented
4C29×#2984C211yesmaximal, characteristic, complemented
5C29×#1702C211yesmaximal, characteristic, complemented
6C29×#1700C211yesmaximal, characteristic, complemented
7C29×#1688C211yesmaximal, characteristic, complemented
8C29×#1686C211yesmaximal, characteristic, complemented
9C29×#1682C211yesmaximal, characteristic, complemented
10C29×#1680C211yesmaximal, characteristic, complemented
11C29×#1668C211yesmaximal, characteristic, complemented
12C29×#1666C211yesmaximal, characteristic, complemented
13C29×#1574C211yesmaximal, characteristic, complemented
14C29×#1557C211yesmaximal, characteristic, complemented
15C29×#1553C211yesmaximal, characteristic, complemented
16C2×C29×#137—21no—
17C29×#532C2211yescharacteristic
18C29×#532C2211yescharacteristic
19C2×C4×Q8×C29C2211yescharacteristic
20C29×#493C2211yescharacteristic
21C29×#492C2211yescharacteristic
22C29×#487C2211yescharacteristic
23C29×#486C2211yescharacteristic
24C29×#481—21no—
25C29×#475C2211yescharacteristic
26C29×#475C2211yescharacteristic
27C29×#464—21no—
28C29×#464—21no—
29C29×#463—21no—
30C29×#463—21no—
31C29×#462C2211yescharacteristic
32C29×#462C2211yescharacteristic
33C29×#460C2211yescharacteristic
34C29×#460C2211yescharacteristic
35C29×#460C2211yescharacteristic
36C29×#460C2211yescharacteristic
37C29×#449—21no—
38C29×#449—21no—
39C29×#448—21no—
40C29×#446—21no—
41C29×#446—21no—
42C29×#446C2211yescharacteristic
43C29×#446C2211yescharacteristic
44C8×Q8×C29C2211yescharacteristic
45C8×Q8×C29C2211yescharacteristic
46C4×SD16×C29—21no—
47C4×SD16×C29—21no—
48C29×#432—21no—
49C29×#432C2211yescharacteristic
50C29×#431—21no—
51C29×#431C2211yescharacteristic
52C29×#431C2211yescharacteristic
53C29×#423C2211yescharacteristic
54C29×#417—21no—
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×#332C2211yescharacteristic
63C29×#331C2211yescharacteristic
64C29×#331C2211yescharacteristic
65C29×#331C2211yescharacteristic
66C29×#331C2211yescharacteristic
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C22×Q8×C29D411yescharacteristic
70C29×#137—44no—
71C2×Q16×C29—21no—
72C2×Q16×C29—21no—
73C2×SD16×C29—21no—
74C2×SD16×C29—21no—
75C2×SD16×C29—21no—
76C2×SD16×C29—21no—
77C2×SD16×C29—21no—
78C2×SD16×C29—21no—
79C2×D8×C29—21no—
80C2×D8×C29—21no—
81C2×M16×C29—21no—
82C29×C4⋊Q8C2311yescharacteristic
83C29×C4⋊Q8C2311yescharacteristic
84C29×#127C2311yescharacteristic
85C29×#127C2311yescharacteristic
86C29×#124—21no—
87C29×#124—21no—
88C29×#121—21no—
89C29×#121—21no—
90C29×#121—21no—
91C29×#121—21no—
92C4×Q8×C29—21no—
93C4×Q8×C29—21no—
94C4×Q8×C29D411yescharacteristic
95C4×Q8×C29D411yescharacteristic
96C4×Q8×C29C2311yescharacteristic
97C4×Q8×C29C2311yescharacteristic
98C4×D4×C29—21no—
99C4×D4×C29—21no—
100C4×D4×C29—21no—
101C4×D4×C29—21no—
102C2×C4⋊C4×C29—21no—
103C2×C4⋊C4×C29D411yescharacteristic
104C2×C42×C29—21no—
105C2×C42×C29C2311yescharacteristic
106C29×#106—21no—
107C29×#106—21no—
108C29×C4⋊C8—21no—
109C29×C4⋊C8—21no—
110C29×C4⋊C8—21no—
111C29×C4⋊C8—21no—
112C29×C4⋊C8—21no—
113C29×C4⋊C8D411yescharacteristic
114C29×C4⋊C8D411yescharacteristic
115C29×C4⋊C8C2311yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×#103—21no—
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—21no—
126C29×#103—21no—
127C29×#102—21no—
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×C22⋊C8—21no—
134C29×C22⋊C8—21no—
135C29×C22⋊C8D411yescharacteristic
136C29×C22⋊C8D411yescharacteristic
137C29×#97—21no—
138C29×#97—21no—
139C29×#97—21no—
140C4×C8×C29—21no—
141C4×C8×C29—21no—
142C4×C8×C29—21no—
143C4×C8×C29C2311yescharacteristic
144C4×C8×C29C2311yescharacteristic
145#41×C29—42no—
146#41×C29—42no—
147#41×C29—81no—
148#41×C29—81no—
149C2×Q8×C29—21no—
150C2×Q8×C29—22no—
151C2×Q8×C29—21no—
152C2×Q8×C29—21no—
153C2×Q8×C29—41no—
154C2×Q8×C29C2×D411yescharacteristic
155C2×Q8×C29C2×D411yescharacteristic
156C2×D4×C29—21no—
157C2×D4×C29—21no—
158C2×D4×C29—21no—
159C2×D4×C29—21no—
160C2×D4×C29—21no—
161C2×D4×C29—21no—
162C2×D4×C29—41no—
163C2×D4×C29—41no—
164C22×C4×C29—21no—
165C22×C4×C29—21no—
166C22×C4×C29—41no—
167C22×C4×C29—41no—
168C22×C4×C29C2×D411yescharacteristic
169C22×C4×C29C2×D411yescharacteristic
170C22×C4×C29#4111yescharacteristic
171Q16×C29—42no—
172Q16×C29—42no—
173SD16×C29—42no—
174SD16×C29—42no—
175SD16×C29—42no—
176SD16×C29—42no—
177SD16×C29—81no—
178SD16×C29—81no—
179D8×C29—81no—
180D8×C29—81no—
181M16×C29—42no—
182C2×C8×C29—21no—
183C2×C8×C29—21no—
184C2×C8×C29—21no—
185C2×C8×C29—21no—
186C2×C8×C29—21no—
187C2×C8×C29—21no—
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—21no—
200C4⋊C4×C29—21no—
201C4⋊C4×C29C2×D411yescharacteristic
202C4⋊C4×C29C2×D411yescharacteristic
203C22⋊C4×C29—41no—
204C22⋊C4×C29—41no—
205C22⋊C4×C29—41no—
206C22⋊C4×C29—41no—
207C42×C29—21no—
208C42×C29—21no—
209C42×C29—21no—
210C42×C29—21no—
211C42×C29C2×D411yescharacteristic
212C42×C29C2×D411yescharacteristic
213C42×C29#4111yescharacteristic
214C42×C29C2411yescharacteristic
215#19473C2911yesmaximal, characteristic, direct product factor, Sylow
216C23×C29—41no—
217C23×C29—41no—
218C23×C29#12111yescharacteristic
219Q8×C29—21no—
220Q8×C29—21no—
221Q8×C29—21no—
222Q8×C29—42no—
223Q8×C29—41no—
224Q8×C29—41no—
225Q8×C29—41no—
226Q8×C29—41no—
227Q8×C29AGL(1,ℤ/8)12yes—
228D4×C29—41no—
229D4×C29—41no—
230D4×C29—41no—
231D4×C29—41no—
232D4×C29—41no—
233D4×C29—41no—
234D4×C29—41no—
235D4×C29—41no—
236D4×C29—81no—
237D4×C29—81no—
238D4×C29—82no—
239D4×C29—82no—
240C2×C4×C29—21no—
241C2×C4×C29—21no—
242C2×C4×C29—21no—
243C2×C4×C29—21no—
244C2×C4×C29—21no—
245C2×C4×C29—21no—
246C2×C4×C29—21no—
247C2×C4×C29—21no—
248C2×C4×C29—41no—
249C2×C4×C29—42no—
250C2×C4×C29—42no—
251C2×C4×C29—41no—
252C2×C4×C29—41no—
253C2×C4×C29—82no—
254C2×C4×C29—82no—
255C2×C4×C29#12111yescharacteristic
256C2×C4×C29#12111yescharacteristic
257C2×C4×C29#12111yescharacteristic
258C2×C4×C29C22×D411yescharacteristic
259C2×C4×C29C22×D411yescharacteristic
260C2×C4×C29C2×#4111yescharacteristic
261C8×C29—21no—
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—
271#3207C2×C2911yescharacteristic
272#3103C2×C2911yescharacteristic, complemented
273#3037C2×C2911yescharacteristic, complemented
274#2984C2×C2911yescharacteristic, complemented
275#1702C2×C2911yescharacteristic, complemented
276#1700C2×C2911yescharacteristic, complemented
277#1688C2×C2911yescharacteristic, complemented
278#1686C2×C2911yescharacteristic, complemented
279#1682C2×C2911yescharacteristic, complemented
280#1680C2×C2911yescharacteristic, complemented
281#1668C2×C2911yescharacteristic, complemented
282#1666C2×C2911yescharacteristic, complemented
283#1574C2×C2911yescharacteristic, complemented
284#1557C2×C2911yescharacteristic, complemented
285#1553C2×C2911yescharacteristic, complemented
286C22×C29—21no—
287C22×C29—21no—
288C22×C29—21no—
289C22×C29—81no—
290C22×C29—81no—
291C22×C29—81no—
292C22×C29—81no—
293C22×C29—81no—
294C22×C29—81no—
295C22×C29C2×#12111yescharacteristic
296C4×C29—21no—
297C4×C29—21no—
298C4×C29—22no—
299C4×C29—21no—
300C4×C29—21no—
301C4×C29—41no—
302C4×C29—41no—
303C4×C29—41no—
304C4×C29—81no—
305C4×C29—81no—
306C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
307C4×C29#57511yescharacteristic
308C4×C29#57711yescharacteristic
309C4×C29#57711yescharacteristic
310C2×#137—21no—
311#532C22×C2911yescharacteristic
312#532C22×C2911yescharacteristic
313C2×C4×Q8C22×C2911yescharacteristic
314#493C22×C2911yescharacteristic
315#492C22×C2911yescharacteristic
316#487C22×C2911yescharacteristic
317#486C22×C2911yescharacteristic
318#481—21no—
319#475C22×C2911yescharacteristic
320#475C22×C2911yescharacteristic
321#464—21no—
322#464—21no—
323#463—21no—
324#463—21no—
325#462C22×C2911yescharacteristic
326#462C22×C2911yescharacteristic
327#460C22×C2911yescharacteristic
328#460C22×C2911yescharacteristic
329#460C22×C2911yescharacteristic
330#460C22×C2911yescharacteristic
331#449—21no—
332#449—21no—
333#448—21no—
334#446—21no—
335#446—21no—
336#446C22×C2911yescharacteristic
337#446C22×C2911yescharacteristic
338C8×Q8C22×C2911yescharacteristic
339C8×Q8C22×C2911yescharacteristic
340C4×SD16—21no—
341C4×SD16—21no—
342#432—21no—
343#432C22×C2911yescharacteristic
344#431—21no—
345#431C22×C2911yescharacteristic
346#431C22×C2911yescharacteristic
347#423C22×C2911yescharacteristic
348#417—21no—
349#335C22×C2911yescharacteristic
350#335C22×C2911yescharacteristic
351#334C22×C2911yescharacteristic
352#334C22×C2911yescharacteristic
353#332C22×C2911yescharacteristic
354#332C22×C2911yescharacteristic
355#332C22×C2911yescharacteristic
356#332C22×C2911yescharacteristic
357#331C22×C2911yescharacteristic
358#331C22×C2911yescharacteristic
359#331C22×C2911yescharacteristic
360#331C22×C2911yescharacteristic
361C2×C29—41no—
362C2×C29—161no—
363C2×C29—161no—
364C2×C29#304311yescharacteristic
365C2×C29#305511yescharacteristic
366C2×C29#306711yescharacteristic
367C2×#41—21no—
368C2×#41—21no—
369C22×Q8D4×C2911yescharacteristic
370#137—44no—
371C2×Q16—21no—
372C2×Q16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×D8—21no—
380C2×D8—21no—
381C2×M16—21no—
382C4⋊Q8C23×C2911yescharacteristic
383C4⋊Q8C23×C2911yescharacteristic
384#127C23×C2911yescharacteristic
385#127C23×C2911yescharacteristic
386#124—21no—
387#124—21no—
388#121—21no—
389#121—21no—
390#121—21no—
391#121—21no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8D4×C2911yescharacteristic
395C4×Q8D4×C2911yescharacteristic
396C4×Q8C23×C2911yescharacteristic
397C4×Q8C23×C2911yescharacteristic
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4D4×C2911yescharacteristic
404C2×C42—21no—
405C2×C42C23×C2911yescharacteristic
406#106—21no—
407#106—21no—
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8—21no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8D4×C2911yescharacteristic
414C4⋊C8D4×C2911yescharacteristic
415C4⋊C8C23×C2911yescharacteristic
416C4⋊C8C23×C2911yescharacteristic
417C4⋊C8C23×C2911yescharacteristic
418C4⋊C8C23×C2911yescharacteristic
419C4⋊C8C23×C2911yescharacteristic
420C4⋊C8C23×C2911yescharacteristic
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435C22⋊C8D4×C2911yescharacteristic
436C22⋊C8D4×C2911yescharacteristic
437#97—21no—
438#97—21no—
439#97—21no—
440C4×C8—21no—
441C4×C8—21no—
442C4×C8—21no—
443C4×C8C23×C2911yescharacteristic
444C4×C8C23×C2911yescharacteristic
445C29#1947311yescharacteristic, direct product factor, Sylow
446#41—42no—
447#41—42no—
448#41—81no—
449#41—81no—
450C2×Q8—21no—
451C2×Q8—22no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—41no—
455C2×Q8C2×D4×C2911yescharacteristic
456C2×Q8C2×D4×C2911yescharacteristic
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—41no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4C2×D4×C2911yescharacteristic
470C22×C4C2×D4×C2911yescharacteristic
471C22×C4#41×C2911yescharacteristic
472Q16—42no—
473Q16—42no—
474SD16—42no—
475SD16—42no—
476SD16—42no—
477SD16—42no—
478SD16—81no—
479SD16—81no—
480D8—81no—
481D8—81no—
482M16—42no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8C2×D4×C2911yescharacteristic
490C2×C8C2×D4×C2911yescharacteristic
491C2×C8C2×D4×C2911yescharacteristic
492C2×C8C2×D4×C2911yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4C2×D4×C2911yescharacteristic
503C4⋊C4C2×D4×C2911yescharacteristic
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42C2×D4×C2911yescharacteristic
513C42C2×D4×C2911yescharacteristic
514C42#41×C2911yescharacteristic
515C42C24×C2911yescharacteristic
516C23—41no—
517C23—41no—
518C23C29×#12111yescharacteristic
519Q8—21no—
520Q8—21no—
521Q8—21no—
522Q8—42no—
523Q8—41no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8C29×AGL(1,ℤ/8)12yes—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—81no—
537D4—81no—
538D4—82no—
539D4—82no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—82no—
554C2×C4—82no—
555C2×C4C29×#12111yescharacteristic
556C2×C4C29×#12111yescharacteristic
557C2×C4C29×#12111yescharacteristic
558C2×C4C22×D4×C2911yescharacteristic
559C2×C4C22×D4×C2911yescharacteristic
560C2×C4C2×#41×C2911yescharacteristic
561C8—21no—
562C8—21no—
563C8—21no—
564C8—21no—
565C8—41no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—41no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22C2×C29×#12111yescharacteristic
581C4—21no—
582C4—21no—
583C4—22no—
584C4—21no—
585C4—21no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—81no—
590C4—81no—
591C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
592C4C29×#57511yescharacteristic
593C4C29×#57711yescharacteristic
594C4C29×#57711yescharacteristic
595C2—41no—
596C2—161no—
597C2—161no—
598C2C29×#304311yescharacteristic
599C2C29×#305511yescharacteristic
600C2C29×#306711yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3207C2
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
2. C29×#3103C2semidirect
3. C29×#3037C2semidirect
4. C29×#2984C2semidirect
5. C29×#1702C2semidirect
6. C29×#1700C2semidirect
7. C29×#1688C2semidirect
8. C29×#1686C2semidirect
9. C29×#1682C2semidirect
10. C29×#1680C2semidirect
11. C29×#1668C2semidirect
12. C29×#1666C2semidirect
13. C29×#1574C2semidirect
14. C29×#1557C2semidirect
15. C29×#1553C2semidirect
215. #19473C29direct (N × H)
272. #3103C2×C29semidirect
273. #3037C2×C29semidirect
274. #2984C2×C29semidirect
275. #1702C2×C29semidirect
276. #1700C2×C29semidirect
277. #1688C2×C29semidirect
278. #1686C2×C29semidirect
279. #1682C2×C29semidirect
280. #1680C2×C29semidirect
281. #1668C2×C29semidirect
282. #1666C2×C29semidirect
283. #1574C2×C29semidirect
284. #1557C2×C29semidirect
285. #1553C2×C29semidirect
445. C29#19473direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32072
C29×#31032
C29×#30372
C29×#29842
C29×#17022
C29×#17002
C29×#16882
C29×#16862
C29×#16822
C29×#16802
C29×#16682
C29×#16662
C29×#15742
C29×#15572
C29×#15532
#1947329