Finite Group Databasebeta

← C29×#19915 #20314815

Subgroups — C29×#19915 #20314815

Order 7424.

660 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×#3366C211yesmaximal, characteristic, complemented
2C29×#3335C211yesmaximal, characteristic, complemented
3C29×#3330C211yesmaximal, characteristic, complemented
4C29×#3284C211yesmaximal, characteristic, complemented
5C29×#1708C211yesmaximal, characteristic, complemented
6C29×#1700C211yesmaximal, characteristic, complemented
7C29×#1697C211yesmaximal, characteristic, complemented
8C29×#1671C211yesmaximal, characteristic, complemented
9C29×#1665C211yesmaximal, characteristic, complemented
10C29×#1644C211yesmaximal, characteristic, complemented
11C29×#1642C211yesmaximal, characteristic, complemented
12C29×#1635C211yesmaximal, characteristic, complemented
13C29×#1625C211yesmaximal, characteristic, complemented
14C29×#1590C211yesmaximal, characteristic, complemented
15C8×D8×C29C211yesmaximal, characteristic, complemented
16C2×C29×#135—21no—
17C29×#554C2211yescharacteristic
18C29×#550C2211yescharacteristic
19C29×#547C2211yescharacteristic
20C29×#547C2211yescharacteristic
21C29×#498C2211yescharacteristic
22C29×#492C2211yescharacteristic
23C29×#490—21no—
24C29×#487C2211yescharacteristic
25C29×#487C2211yescharacteristic
26C29×#486C2211yescharacteristic
27C29×#486C2211yescharacteristic
28C29×#484—21no—
29C29×#483—21no—
30C29×#481—21no—
31C29×#478—21no—
32C29×#476C2211yescharacteristic
33C29×#476C2211yescharacteristic
34C29×#475C2211yescharacteristic
35C29×#474C2211yescharacteristic
36C29×#468—21no—
37C29×#465—21no—
38C29×#465—21no—
39C29×#462C2211yescharacteristic
40C29×#461C2211yescharacteristic
41C29×#459—21no—
42C29×#459C2211yescharacteristic
43C29×#459C2211yescharacteristic
44C29×#452—21no—
45C29×#449—21no—
46C29×#449—21no—
47C29×#446C2211yescharacteristic
48C29×#442—21no—
49C4×SD16×C29C2211yescharacteristic
50C4×D8×C29C2211yescharacteristic
51C29×#436C2211yescharacteristic
52C8×D4×C29C2211yescharacteristic
53C8×D4×C29C2211yescharacteristic
54C2×C29×#106—21no—
55C29×#417—21no—
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×D4⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C82×C29C2211yescharacteristic
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C2×#41×C29—21no—
70C29×#135—44no—
71C2×Q16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×SD16×C29—21no—
75C2×SD16×C29D411yescharacteristic
76C2×D8×C29—21no—
77C2×D8×C29—21no—
78C2×D8×C29D411yescharacteristic
79C2×M16×C29—21no—
80C22×C8×C29—21no—
81C22×C8×C29—21no—
82C29×C4⋊Q8C2311yescharacteristic
83C29×C4⋊Q8C2311yescharacteristic
84C29×C4⋊Q8C2311yescharacteristic
85C29×#127—21no—
86C29×#127C2311yescharacteristic
87C29×#125—21no—
88C29×#123—41no—
89C29×#123—41no—
90C29×C22⋊Q8—21no—
91C29×C22⋊Q8—21no—
92C29×C22⋊Q8—21no—
93C29×C22⋊Q8—41no—
94C29×#121—21no—
95C29×#121—21no—
96C29×#121—21no—
97C29×#121—41no—
98C4×Q8×C29C2311yescharacteristic
99C4×D4×C29—21no—
100C4×D4×C29—21no—
101C4×D4×C29C2311yescharacteristic
102C4×D4×C29C2311yescharacteristic
103C4×D4×C29C2311yescharacteristic
104C2×C4⋊C4×C29—21no—
105C2×C4⋊C4×C29—21no—
106C2×C4⋊C4×C29—21no—
107C29×#107—21no—
108C29×#107D411yescharacteristic
109C29×#106—21no—
110C29×#106—21no—
111C29×#106—21no—
112C29×#106—21no—
113C29×#106—21no—
114C29×#106D411yescharacteristic
115C29×C4⋊C8—21no—
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×#103—21no—
121C29×#103—21no—
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—41no—
126C29×#103D411yescharacteristic
127C29×#102—21no—
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—41no—
135C29×#102D411yescharacteristic
136C29×#102D411yescharacteristic
137C29×#102D411yescharacteristic
138C29×C22⋊C8—21no—
139C29×C22⋊C8—21no—
140C29×C22⋊C8—21no—
141C29×#97—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C4×C8×C29C2311yescharacteristic
145#41×C29—42no—
146#41×C29—42no—
147#41×C29—42no—
148#41×C29—81no—
149#41×C29—81no—
150#41×C29—81no—
151C2×Q8×C29—21no—
152C2×Q8×C29—21no—
153C2×Q8×C29—21no—
154C2×Q8×C29C2×D411yescharacteristic
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29—21no—
158C2×D4×C29—41no—
159C2×D4×C29—41no—
160C2×D4×C29—41no—
161C2×D4×C29—41no—
162C2×D4×C29C2×D411yescharacteristic
163C2×D4×C29C2×D411yescharacteristic
164C2×D4×C29C2×D411yescharacteristic
165C22×C4×C29—21no—
166C22×C4×C29—21no—
167C22×C4×C29—21no—
168C22×C4×C29—41no—
169C22×C4×C29—41no—
170C22×C4×C29—41no—
171C22×C4×C29—41no—
172Q16×C29—42no—
173SD16×C29—22no—
174SD16×C29—42no—
175SD16×C29—81no—
176SD16×C29—81no—
177D8×C29—22no—
178D8×C29—42no—
179D8×C29—42no—
180M16×C29—81no—
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×C29—41no—
202C4⋊C4×C29—41no—
203C4⋊C4×C29C2×D411yescharacteristic
204C4⋊C4×C29C2×D411yescharacteristic
205C4⋊C4×C29C2×D411yescharacteristic
206C4⋊C4×C29C2×D411yescharacteristic
207C22⋊C4×C29—21no—
208C22⋊C4×C29—21no—
209C22⋊C4×C29—21no—
210C22⋊C4×C29—41no—
211C22⋊C4×C29—41no—
212C22⋊C4×C29—41no—
213C22⋊C4×C29—41no—
214C42×C29—21no—
215C42×C29C2411yescharacteristic
216#19915C2911yesmaximal, characteristic, direct product factor, Sylow
217C23×C29—21no—
218C23×C29—21no—
219C23×C29—21no—
220C23×C29—41no—
221Q8×C29—21no—
222Q8×C29—21no—
223Q8×C29—41no—
224Q8×C29—41no—
225Q8×C29—41no—
226Q8×C29—41no—
227Q8×C29—81no—
228D4×C29—21no—
229D4×C29—21no—
230D4×C29—21no—
231D4×C29—21no—
232D4×C29—21no—
233D4×C29—41no—
234D4×C29—41no—
235D4×C29—41no—
236D4×C29—41no—
237D4×C29—81no—
238D4×C29—82no—
239D4×C29—82no—
240D4×C29—82no—
241D4×C29—161no—
242D4×C29#13512yescomplemented
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—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—41no—
257C2×C4×C29—82no—
258C2×C4×C29—82no—
259C2×C4×C29—82no—
260C2×C4×C29—161no—
261C2×C4×C29C22×D411yescharacteristic
262C2×C4×C29C22×D411yescharacteristic
263C2×C4×C29H(5,𝔽2)11yescharacteristic
264C8×C29—21no—
265C8×C29—21no—
266C8×C29—21no—
267C8×C29—41no—
268C8×C29—41no—
269C8×C29—41no—
270C8×C29—41no—
271C8×C29—41no—
272C8×C29AGL(1,ℤ/8)12yes—
273#3366C2×C2911yescharacteristic, complemented
274#3335C2×C2911yescharacteristic, complemented
275#3330C2×C2911yescharacteristic, complemented
276#3284C2×C2911yescharacteristic, complemented
277#1708C2×C2911yescharacteristic, complemented
278#1700C2×C2911yescharacteristic, complemented
279#1697C2×C2911yescharacteristic, complemented
280#1671C2×C2911yescharacteristic, complemented
281#1665C2×C2911yescharacteristic, complemented
282#1644C2×C2911yescharacteristic, complemented
283#1642C2×C2911yescharacteristic, complemented
284#1635C2×C2911yescharacteristic, complemented
285#1625C2×C2911yescharacteristic, complemented
286#1590C2×C2911yescharacteristic, complemented
287C8×D8C2×C2911yescharacteristic, complemented
288C22×C29—22no—
289C22×C29—41no—
290C22×C29—41no—
291C22×C29—41no—
292C22×C29—41no—
293C22×C29—41no—
294C22×C29—41no—
295C22×C29—41no—
296C22×C29—41no—
297C22×C29—81no—
298C22×C29—81no—
299C22×C29—81no—
300C22×C29D4211yescharacteristic
301C4×C29—21no—
302C4×C29—41no—
303C4×C29—41no—
304C4×C29—41no—
305C4×C29—41no—
306C4×C29—41no—
307C4×C29—81no—
308C4×C29—81no—
309C4×C29—81no—
310C4×C29C2×#13511yescharacteristic
311C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
312C4×C29#57711yescharacteristic
313C4×C29#57711yescharacteristic
314C2×#135—21no—
315#554C22×C2911yescharacteristic
316#550C22×C2911yescharacteristic
317#547C22×C2911yescharacteristic
318#547C22×C2911yescharacteristic
319#498C22×C2911yescharacteristic
320#492C22×C2911yescharacteristic
321#490—21no—
322#487C22×C2911yescharacteristic
323#487C22×C2911yescharacteristic
324#486C22×C2911yescharacteristic
325#486C22×C2911yescharacteristic
326#484—21no—
327#483—21no—
328#481—21no—
329#478—21no—
330#476C22×C2911yescharacteristic
331#476C22×C2911yescharacteristic
332#475C22×C2911yescharacteristic
333#474C22×C2911yescharacteristic
334#468—21no—
335#465—21no—
336#465—21no—
337#462C22×C2911yescharacteristic
338#461C22×C2911yescharacteristic
339#459—21no—
340#459C22×C2911yescharacteristic
341#459C22×C2911yescharacteristic
342#452—21no—
343#449—21no—
344#449—21no—
345#446C22×C2911yescharacteristic
346#442—21no—
347C4×SD16C22×C2911yescharacteristic
348C4×D8C22×C2911yescharacteristic
349#436C22×C2911yescharacteristic
350C8×D4C22×C2911yescharacteristic
351C8×D4C22×C2911yescharacteristic
352C2×#106—21no—
353#417—21no—
354#335C22×C2911yescharacteristic
355#334C22×C2911yescharacteristic
356#333C22×C2911yescharacteristic
357#332C22×C2911yescharacteristic
358#332C22×C2911yescharacteristic
359#331C22×C2911yescharacteristic
360Q8⋊C8C22×C2911yescharacteristic
361D4⋊C8C22×C2911yescharacteristic
362D4⋊C8C22×C2911yescharacteristic
363D4⋊C8C22×C2911yescharacteristic
364C82C22×C2911yescharacteristic
365C2×C29—42no—
366C2×C29—81no—
367C2×C29—81no—
368C2×C29—161no—
369C2×C29#327211yescharacteristic
370C2×C29#328211yescharacteristic
371C2×C29#329011yescharacteristic
372C2×#41—21no—
373C2×#41—21no—
374C2×#41—21no—
375#135—44no—
376C2×Q16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16D4×C2911yescharacteristic
381C2×D8—21no—
382C2×D8—21no—
383C2×D8D4×C2911yescharacteristic
384C2×M16—21no—
385C22×C8—21no—
386C22×C8—21no—
387C4⋊Q8C23×C2911yescharacteristic
388C4⋊Q8C23×C2911yescharacteristic
389C4⋊Q8C23×C2911yescharacteristic
390#127—21no—
391#127C23×C2911yescharacteristic
392#125—21no—
393#123—41no—
394#123—41no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—41no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121—41no—
403C4×Q8C23×C2911yescharacteristic
404C4×D4—21no—
405C4×D4—21no—
406C4×D4C23×C2911yescharacteristic
407C4×D4C23×C2911yescharacteristic
408C4×D4C23×C2911yescharacteristic
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412#107—21no—
413#107D4×C2911yescharacteristic
414#106—21no—
415#106—21no—
416#106—21no—
417#106—21no—
418#106—21no—
419#106D4×C2911yescharacteristic
420C4⋊C8—21no—
421C4⋊C8C23×C2911yescharacteristic
422C4⋊C8C23×C2911yescharacteristic
423C4⋊C8C23×C2911yescharacteristic
424C4⋊C8C23×C2911yescharacteristic
425#103—21no—
426#103—21no—
427#103—21no—
428#103—21no—
429#103—21no—
430#103—41no—
431#103D4×C2911yescharacteristic
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—41no—
440#102D4×C2911yescharacteristic
441#102D4×C2911yescharacteristic
442#102D4×C2911yescharacteristic
443C22⋊C8—21no—
444C22⋊C8—21no—
445C22⋊C8—21no—
446#97—21no—
447C4×C8C23×C2911yescharacteristic
448C4×C8C23×C2911yescharacteristic
449C4×C8C23×C2911yescharacteristic
450C29#1991511yescharacteristic, direct product factor, Sylow
451#41—42no—
452#41—42no—
453#41—42no—
454#41—81no—
455#41—81no—
456#41—81no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8C2×D4×C2911yescharacteristic
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4C2×D4×C2911yescharacteristic
469C2×D4C2×D4×C2911yescharacteristic
470C2×D4C2×D4×C2911yescharacteristic
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478Q16—42no—
479SD16—22no—
480SD16—42no—
481SD16—81no—
482SD16—81no—
483D8—22no—
484D8—42no—
485D8—42no—
486M16—81no—
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⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4C2×D4×C2911yescharacteristic
510C4⋊C4C2×D4×C2911yescharacteristic
511C4⋊C4C2×D4×C2911yescharacteristic
512C4⋊C4C2×D4×C2911yescharacteristic
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C42—21no—
521C42C24×C2911yescharacteristic
522C23—21no—
523C23—21no—
524C23—21no—
525C23—41no—
526Q8—21no—
527Q8—21no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—41no—
532Q8—81no—
533D4—21no—
534D4—21no—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—81no—
543D4—82no—
544D4—82no—
545D4—82no—
546D4—161no—
547D4C29×#13512yescomplemented
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4—161no—
566C2×C4C22×D4×C2911yescharacteristic
567C2×C4C22×D4×C2911yescharacteristic
568C2×C4C29×H(5,𝔽2)11yescharacteristic
569C8—21no—
570C8—21no—
571C8—21no—
572C8—41no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8C29×AGL(1,ℤ/8)12yes—
578C22—22no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22D42×C2911yescharacteristic
591C4—21no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4C2×C29×#13511yescharacteristic
601C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
602C4C29×#57711yescharacteristic
603C4C29×#57711yescharacteristic
604C2—42no—
605C2—81no—
606C2—81no—
607C2—161no—
608C2C29×#327211yescharacteristic
609C2C29×#328211yescharacteristic
610C2C29×#329011yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3366C2semidirect
2. C29×#3335C2semidirect
3. C29×#3330C2semidirect
4. C29×#3284C2semidirect
5. C29×#1708C2semidirect
6. C29×#1700C2semidirect
7. C29×#1697C2semidirect
8. C29×#1671C2semidirect
9. C29×#1665C2semidirect
10. C29×#1644C2semidirect
11. C29×#1642C2semidirect
12. C29×#1635C2semidirect
13. C29×#1625C2semidirect
14. C29×#1590C2semidirect
15. C8×D8×C29C2semidirect
216. #19915C29direct (N × H)
242. D4×C29#135semidirect
273. #3366C2×C29semidirect
274. #3335C2×C29semidirect
275. #3330C2×C29semidirect
276. #3284C2×C29semidirect
277. #1708C2×C29semidirect
278. #1700C2×C29semidirect
279. #1697C2×C29semidirect
280. #1671C2×C29semidirect
281. #1665C2×C29semidirect
282. #1644C2×C29semidirect
283. #1642C2×C29semidirect
284. #1635C2×C29semidirect
285. #1625C2×C29semidirect
286. #1590C2×C29semidirect
287. C8×D8C2×C29semidirect
450. C29#19915direct (N × H)
547. D4C29×#135semidirect

Maximal subgroups

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

subgroupindex
C29×#33662
C29×#33352
C29×#33302
C29×#32842
C29×#17082
C29×#17002
C29×#16972
C29×#16712
C29×#16652
C29×#16442
C29×#16422
C29×#16352
C29×#16252
C29×#15902
C8×D8×C292
#1991529