Finite Group Databasebeta

← C29×#19836 #20314736

Subgroups — C29×#19836 #20314736

Order 7424.

670 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×#3366C211yesmaximal, characteristic, complemented
2C29×#3358C211yesmaximal, characteristic, complemented
3C29×#3299C211yesmaximal, characteristic, complemented
4C29×#3287C211yesmaximal, characteristic, complemented
5C29×#1717C211yesmaximal, characteristic, complemented
6C29×#1702C211yesmaximal, characteristic, complemented
7C29×#1683C211yesmaximal, characteristic, complemented
8C29×#1678C211yesmaximal, characteristic, complemented
9C29×#1667C211yesmaximal, characteristic, complemented
10C29×#1641C211yesmaximal, characteristic, complemented
11C29×#1631C211yesmaximal, characteristic, complemented
12C29×#1627C211yesmaximal, characteristic, complemented
13C29×#1622C211yesmaximal, characteristic, complemented
14C29×#1584C211yesmaximal, characteristic, complemented
15C29×#1580C211yesmaximal, characteristic, complemented
16C2×C29×#135—21no—
17C29×#554C2211yescharacteristic
18C29×#550C2211yescharacteristic
19C29×#550C2211yescharacteristic
20D4×Q8×C29C2211yescharacteristic
21C29×#493C2211yescharacteristic
22C29×#492C2211yescharacteristic
23C29×#490—21no—
24C29×#487C2211yescharacteristic
25C29×#486—21no—
26C29×#486C2211yescharacteristic
27C29×#486C2211yescharacteristic
28C29×#486C2211yescharacteristic
29C29×#484—21no—
30C29×#478—21no—
31C29×#477C2211yescharacteristic
32C29×#476C2211yescharacteristic
33C29×#474—21no—
34C29×#474C2211yescharacteristic
35C29×#467—21no—
36C29×#466—21no—
37C29×#462C2211yescharacteristic
38C29×#460C2211yescharacteristic
39C29×#460C2211yescharacteristic
40C29×#459—21no—
41C29×#459—21no—
42C29×#459C2211yescharacteristic
43C29×#459C2211yescharacteristic
44C29×#451—21no—
45C29×#449—21no—
46C29×#449—21no—
47C29×#446C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C29×#442—21no—
50C4×Q16×C29C2211yescharacteristic
51C4×D8×C29—21no—
52C4×D8×C29C2211yescharacteristic
53C8×D4×C29C2211yescharacteristic
54C8×D4×C29C2211yescharacteristic
55C2×C29×#103—21no—
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#331C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C29×#322C2211yescharacteristic
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C22×Q8×C29—21no—
70C29×#135—44no—
71C2×Q16×C29—21no—
72C2×Q16×C29D411yescharacteristic
73C2×SD16×C29—21no—
74C2×SD16×C29—21no—
75C2×SD16×C29—41no—
76C2×D8×C29—21no—
77C2×D8×C29—21no—
78C2×D8×C29—21no—
79C2×D8×C29—21no—
80C2×D8×C29D411yescharacteristic
81C22×C8×C29—21no—
82C22×C8×C29—21no—
83C29×C4⋊Q8—21no—
84C29×C4⋊Q8C2311yescharacteristic
85C29×C4⋊Q8C2311yescharacteristic
86C29×#127—21no—
87C29×#127—21no—
88C29×#127C2311yescharacteristic
89C29×#127C2311yescharacteristic
90C29×#125—21no—
91C29×C22⋊Q8—21no—
92C29×C22⋊Q8—21no—
93C29×C22⋊Q8—41no—
94C29×C22⋊Q8—41no—
95C29×#121—21no—
96C29×#121—21no—
97C29×#121—41no—
98C29×#121—41no—
99C4×Q8×C29C2311yescharacteristic
100C4×Q8×C29C2311yescharacteristic
101C4×D4×C29—21no—
102C4×D4×C29—21no—
103C4×D4×C29—21no—
104C4×D4×C29—21no—
105C4×D4×C29C2311yescharacteristic
106C4×D4×C29C2311yescharacteristic
107C2×C4⋊C4×C29—21no—
108C29×#107—21no—
109C29×#107—21no—
110C29×#107D411yescharacteristic
111C29×#107D411yescharacteristic
112C29×#106—21no—
113C29×C4⋊C8—21no—
114C29×C4⋊C8—21no—
115C29×C4⋊C8C2311yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×#103—21no—
120C29×#103—21no—
121C29×#103—21no—
122C29×#103—21no—
123C29×#103D411yescharacteristic
124C29×#103D411yescharacteristic
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×#102—41no—
136C29×#102D411yescharacteristic
137C29×#102D411yescharacteristic
138C29×C22⋊C8—21no—
139C29×C22⋊C8—21no—
140C29×#97—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
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—21no—
151C2×Q8×C29—41no—
152C2×Q8×C29—42no—
153C2×Q8×C29—81no—
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—
164C2×D4×C29—41no—
165C2×D4×C29—41no—
166C2×D4×C29C2×D411yescharacteristic
167C2×D4×C29C2×D411yescharacteristic
168C22×C4×C29—21no—
169C22×C4×C29—21no—
170C22×C4×C29—41no—
171C22×C4×C29—41no—
172C22×C4×C29—41no—
173C22×C4×C29—41no—
174Q16×C29—22no—
175Q16×C29—81no—
176SD16×C29—42no—
177SD16×C29—42no—
178SD16×C29—82no—
179D8×C29—22no—
180D8×C29—42no—
181D8×C29—42no—
182D8×C29—42no—
183D8×C29—81no—
184C2×C8×C29—21no—
185C2×C8×C29—21no—
186C2×C8×C29—21no—
187C2×C8×C29—21no—
188C2×C8×C29—21no—
189C2×C8×C29—42no—
190C2×C8×C29—81no—
191C2×C8×C29C2×D411yescharacteristic
192C2×C8×C29C2×D411yescharacteristic
193C2×C8×C29C2×D411yescharacteristic
194C2×C8×C29C2×D411yescharacteristic
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×C29—41no—
202C4⋊C4×C29—41no—
203C4⋊C4×C29—41no—
204C4⋊C4×C29C2×D411yescharacteristic
205C4⋊C4×C29C2×D411yescharacteristic
206C4⋊C4×C29C2×D411yescharacteristic
207C4⋊C4×C29C2×D411yescharacteristic
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×C29—21no—
216C42×C29C2411yescharacteristic
217#19836C2911yesmaximal, characteristic, direct product factor, Sylow
218C23×C29—21no—
219C23×C29—21no—
220C23×C29—41no—
221C23×C29—41no—
222Q8×C29—21no—
223Q8×C29—21no—
224Q8×C29—21no—
225Q8×C29—41no—
226Q8×C29—41no—
227Q8×C29—82no—
228Q8×C29—81no—
229Q8×C29AGL(1,ℤ/8)12yes—
230D4×C29—21no—
231D4×C29—21no—
232D4×C29—21no—
233D4×C29—41no—
234D4×C29—41no—
235D4×C29—41no—
236D4×C29—41no—
237D4×C29—41no—
238D4×C29—41no—
239D4×C29—41no—
240D4×C29—41no—
241D4×C29—82no—
242D4×C29—81no—
243D4×C29—81no—
244D4×C29—82no—
245D4×C29—161no—
246D4×C29—161no—
247D4×C29#13512yescomplemented
248C2×C4×C29—21no—
249C2×C4×C29—21no—
250C2×C4×C29—21no—
251C2×C4×C29—21no—
252C2×C4×C29—21no—
253C2×C4×C29—21no—
254C2×C4×C29—41no—
255C2×C4×C29—41no—
256C2×C4×C29—41no—
257C2×C4×C29—41no—
258C2×C4×C29—41no—
259C2×C4×C29—41no—
260C2×C4×C29—82no—
261C2×C4×C29—82no—
262C2×C4×C29—82no—
263C2×C4×C29—161no—
264C2×C4×C29C22×D411yescharacteristic
265C2×C4×C29C22×D411yescharacteristic
266C2×C4×C29H(5,𝔽2)11yescharacteristic
267C8×C29—21no—
268C8×C29—21no—
269C8×C29—21no—
270C8×C29—21no—
271C8×C29—41no—
272C8×C29—41no—
273C8×C29—41no—
274C8×C29—41no—
275C8×C29—41no—
276#3366C2×C2911yescharacteristic, complemented
277#3358C2×C2911yescharacteristic, complemented
278#3299C2×C2911yescharacteristic, complemented
279#3287C2×C2911yescharacteristic, complemented
280#1717C2×C2911yescharacteristic, complemented
281#1702C2×C2911yescharacteristic, complemented
282#1683C2×C2911yescharacteristic, complemented
283#1678C2×C2911yescharacteristic, complemented
284#1667C2×C2911yescharacteristic, complemented
285#1641C2×C2911yescharacteristic, complemented
286#1631C2×C2911yescharacteristic, complemented
287#1627C2×C2911yescharacteristic, complemented
288#1622C2×C2911yescharacteristic, complemented
289#1584C2×C2911yescharacteristic, complemented
290#1580C2×C2911yescharacteristic, complemented
291C22×C29—22no—
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×C29—81no—
301C22×C29—81no—
302C22×C29—81no—
303C22×C29D4211yescharacteristic
304C4×C29—22no—
305C4×C29—21no—
306C4×C29—41no—
307C4×C29—41no—
308C4×C29—41no—
309C4×C29—41no—
310C4×C29—41no—
311C4×C29—81no—
312C4×C29—81no—
313C4×C29C2×#13511yescharacteristic
314C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
315C4×C29#57611yescharacteristic
316C4×C29#57811yescharacteristic
317C2×#135—21no—
318#554C22×C2911yescharacteristic
319#550C22×C2911yescharacteristic
320#550C22×C2911yescharacteristic
321D4×Q8C22×C2911yescharacteristic
322#493C22×C2911yescharacteristic
323#492C22×C2911yescharacteristic
324#490—21no—
325#487C22×C2911yescharacteristic
326#486—21no—
327#486C22×C2911yescharacteristic
328#486C22×C2911yescharacteristic
329#486C22×C2911yescharacteristic
330#484—21no—
331#478—21no—
332#477C22×C2911yescharacteristic
333#476C22×C2911yescharacteristic
334#474—21no—
335#474C22×C2911yescharacteristic
336#467—21no—
337#466—21no—
338#462C22×C2911yescharacteristic
339#460C22×C2911yescharacteristic
340#460C22×C2911yescharacteristic
341#459—21no—
342#459—21no—
343#459C22×C2911yescharacteristic
344#459C22×C2911yescharacteristic
345#451—21no—
346#449—21no—
347#449—21no—
348#446C22×C2911yescharacteristic
349C8×Q8C22×C2911yescharacteristic
350#442—21no—
351C4×Q16C22×C2911yescharacteristic
352C4×D8—21no—
353C4×D8C22×C2911yescharacteristic
354C8×D4C22×C2911yescharacteristic
355C8×D4C22×C2911yescharacteristic
356C2×#103—21no—
357#335C22×C2911yescharacteristic
358#334C22×C2911yescharacteristic
359#333C22×C2911yescharacteristic
360#332C22×C2911yescharacteristic
361#331C22×C2911yescharacteristic
362#331C22×C2911yescharacteristic
363Q8⋊C8C22×C2911yescharacteristic
364Q8⋊C8C22×C2911yescharacteristic
365D4⋊C8C22×C2911yescharacteristic
366D4⋊C8C22×C2911yescharacteristic
367#322C22×C2911yescharacteristic
368C2×C29—42no—
369C2×C29—81no—
370C2×C29—161no—
371C2×C29—161no—
372C2×C29#326411yescharacteristic
373C2×C29#328511yescharacteristic
374C2×C29#328811yescharacteristic
375C2×#41—21no—
376C2×#41—21no—
377C22×Q8—21no—
378#135—44no—
379C2×Q16—21no—
380C2×Q16D4×C2911yescharacteristic
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—41no—
384C2×D8—21no—
385C2×D8—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×D8D4×C2911yescharacteristic
389C22×C8—21no—
390C22×C8—21no—
391C4⋊Q8—21no—
392C4⋊Q8C23×C2911yescharacteristic
393C4⋊Q8C23×C2911yescharacteristic
394#127—21no—
395#127—21no—
396#127C23×C2911yescharacteristic
397#127C23×C2911yescharacteristic
398#125—21no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—41no—
402C22⋊Q8—41no—
403#121—21no—
404#121—21no—
405#121—41no—
406#121—41no—
407C4×Q8C23×C2911yescharacteristic
408C4×Q8C23×C2911yescharacteristic
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4C23×C2911yescharacteristic
414C4×D4C23×C2911yescharacteristic
415C2×C4⋊C4—21no—
416#107—21no—
417#107—21no—
418#107D4×C2911yescharacteristic
419#107D4×C2911yescharacteristic
420#106—21no—
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8C23×C2911yescharacteristic
424C4⋊C8C23×C2911yescharacteristic
425C4⋊C8C23×C2911yescharacteristic
426C4⋊C8C23×C2911yescharacteristic
427#103—21no—
428#103—21no—
429#103—21no—
430#103—21no—
431#103D4×C2911yescharacteristic
432#103D4×C2911yescharacteristic
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—41no—
444#102D4×C2911yescharacteristic
445#102D4×C2911yescharacteristic
446C22⋊C8—21no—
447C22⋊C8—21no—
448#97—21no—
449C4×C8—21no—
450C4×C8C23×C2911yescharacteristic
451C4×C8C23×C2911yescharacteristic
452C4×C8C23×C2911yescharacteristic
453C29#1983611yescharacteristic, direct product factor, Sylow
454#41—42no—
455#41—42no—
456#41—81no—
457#41—81no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—41no—
461C2×Q8—42no—
462C2×Q8—81no—
463C2×Q8C2×D4×C2911yescharacteristic
464C2×Q8C2×D4×C2911yescharacteristic
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4C2×D4×C2911yescharacteristic
476C2×D4C2×D4×C2911yescharacteristic
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483Q16—22no—
484Q16—81no—
485SD16—42no—
486SD16—42no—
487SD16—82no—
488D8—22no—
489D8—42no—
490D8—42no—
491D8—42no—
492D8—81no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—42no—
499C2×C8—81no—
500C2×C8C2×D4×C2911yescharacteristic
501C2×C8C2×D4×C2911yescharacteristic
502C2×C8C2×D4×C2911yescharacteristic
503C2×C8C2×D4×C2911yescharacteristic
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4C2×D4×C2911yescharacteristic
514C4⋊C4C2×D4×C2911yescharacteristic
515C4⋊C4C2×D4×C2911yescharacteristic
516C4⋊C4C2×D4×C2911yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C42—21no—
524C42—21no—
525C42C24×C2911yescharacteristic
526C23—21no—
527C23—21no—
528C23—41no—
529C23—41no—
530Q8—21no—
531Q8—21no—
532Q8—21no—
533Q8—41no—
534Q8—41no—
535Q8—82no—
536Q8—81no—
537Q8C29×AGL(1,ℤ/8)12yes—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—82no—
550D4—81no—
551D4—81no—
552D4—82no—
553D4—161no—
554D4—161no—
555D4C29×#13512yescomplemented
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—82no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4—161no—
572C2×C4C22×D4×C2911yescharacteristic
573C2×C4C22×D4×C2911yescharacteristic
574C2×C4C29×H(5,𝔽2)11yescharacteristic
575C8—21no—
576C8—21no—
577C8—21no—
578C8—21no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—41no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22D42×C2911yescharacteristic
597C4—22no—
598C4—21no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4C2×C29×#13511yescharacteristic
607C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
608C4C29×#57611yescharacteristic
609C4C29×#57811yescharacteristic
610C2—42no—
611C2—81no—
612C2—161no—
613C2—161no—
614C2C29×#326411yescharacteristic
615C2C29×#328511yescharacteristic
616C2C29×#328811yescharacteristic
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×#3358C2semidirect
3. C29×#3299C2semidirect
4. C29×#3287C2semidirect
5. C29×#1717C2semidirect
6. C29×#1702C2semidirect
7. C29×#1683C2semidirect
8. C29×#1678C2semidirect
9. C29×#1667C2semidirect
10. C29×#1641C2semidirect
11. C29×#1631C2semidirect
12. C29×#1627C2semidirect
13. C29×#1622C2semidirect
14. C29×#1584C2semidirect
15. C29×#1580C2semidirect
217. #19836C29direct (N × H)
247. D4×C29#135semidirect
276. #3366C2×C29semidirect
277. #3358C2×C29semidirect
278. #3299C2×C29semidirect
279. #3287C2×C29semidirect
280. #1717C2×C29semidirect
281. #1702C2×C29semidirect
282. #1683C2×C29semidirect
283. #1678C2×C29semidirect
284. #1667C2×C29semidirect
285. #1641C2×C29semidirect
286. #1631C2×C29semidirect
287. #1627C2×C29semidirect
288. #1622C2×C29semidirect
289. #1584C2×C29semidirect
290. #1580C2×C29semidirect
453. C29#19836direct (N × H)
555. 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×#33582
C29×#32992
C29×#32872
C29×#17172
C29×#17022
C29×#16832
C29×#16782
C29×#16672
C29×#16412
C29×#16312
C29×#16272
C29×#16222
C29×#15842
C29×#15802
#1983629