Finite Group Databasebeta

← C29×#19448 #20314348

Subgroups — C29×#19448 #20314348

Order 7424.

628 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3207C211yesmaximal, characteristic, complemented
2C29×#3115C211yesmaximal, characteristic, complemented
3C29×#3106C211yesmaximal, characteristic, complemented
4C29×#2989C211yesmaximal, characteristic, complemented
5C29×#1704C211yesmaximal, characteristic, complemented
6C29×#1703C211yesmaximal, characteristic, complemented
7C29×#1698C211yesmaximal, characteristic, complemented
8C29×#1697C211yesmaximal, characteristic, complemented
9C29×#1688C211yesmaximal, characteristic, complemented
10C29×#1687C211yesmaximal, characteristic, complemented
11C29×#1686C211yesmaximal, characteristic, complemented
12C29×#1685C211yesmaximal, characteristic, complemented
13C29×#1572C211yesmaximal, characteristic, complemented
14C29×#1551C211yesmaximal, characteristic, complemented
15C29×#1540C211yesmaximal, characteristic, complemented
16C29×#532C2211yescharacteristic
17C29×#532C2211yescharacteristic
18C4×#41×C29C2211yescharacteristic
19C29×#493C2211yescharacteristic
20C29×#492C2211yescharacteristic
21C29×#487C2211yescharacteristic
22C29×#486C2211yescharacteristic
23C29×#482—21no—
24C29×#482—21no—
25C29×#477C2211yescharacteristic
26C29×#476C2211yescharacteristic
27C29×#475C2211yescharacteristic
28C29×#474C2211yescharacteristic
29C29×#463—21no—
30C29×#463—21no—
31C29×#460C2211yescharacteristic
32C29×#460C2211yescharacteristic
33C29×#459C2211yescharacteristic
34C29×#459C2211yescharacteristic
35C29×#449—21no—
36C29×#449—21no—
37C29×#449—21no—
38C29×#449—21no—
39C29×#446C2211yescharacteristic
40C29×#446C2211yescharacteristic
41C29×#442—21no—
42C29×#440—21no—
43C4×SD16×C29—21no—
44C4×D8×C29—21no—
45C29×#436C2211yescharacteristic
46C29×#436C2211yescharacteristic
47C29×#435—21no—
48C29×#435—21no—
49C29×#432—21no—
50C29×#432C2211yescharacteristic
51C29×#431C2211yescharacteristic
52C29×#431C2211yescharacteristic
53C29×#423—21no—
54C2×C29×C4⋊C8C2211yescharacteristic
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×#332C2211yescharacteristic
63C29×#331C2211yescharacteristic
64C29×#331C2211yescharacteristic
65C29×#331C2211yescharacteristic
66C29×#331C2211yescharacteristic
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C2×#41×C29D411yescharacteristic
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×D8×C29—21no—
75C2×D8×C29—21no—
76C2×D8×C29—21no—
77C2×D8×C29—21no—
78C2×M16×C29—21no—
79C2×M16×C29—21no—
80C22×C8×C29—21no—
81C29×C4⋊Q8C2311yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×#127C2311yescharacteristic
84C29×#127C2311yescharacteristic
85C29×#124—21no—
86C29×#124—21no—
87C29×#121—21no—
88C29×#121—21no—
89C29×#121—21no—
90C29×#121—21no—
91C4×Q8×C29D411yescharacteristic
92C4×Q8×C29C2311yescharacteristic
93C4×D4×C29—21no—
94C4×D4×C29—21no—
95C4×D4×C29—21no—
96C4×D4×C29—21no—
97C4×D4×C29—21no—
98C4×D4×C29—21no—
99C4×D4×C29D411yescharacteristic
100C4×D4×C29C2311yescharacteristic
101C29×#117—21no—
102C29×#117D411yescharacteristic
103C2×C42×C29—21no—
104C2×C42×C29C2311yescharacteristic
105C29×#107—21no—
106C29×#107—21no—
107C29×#106—21no—
108C29×#106—21no—
109C29×C4⋊C8—21no—
110C29×C4⋊C8—21no—
111C29×C4⋊C8—21no—
112C29×C4⋊C8D411yescharacteristic
113C29×C4⋊C8D411yescharacteristic
114C29×C4⋊C8C2311yescharacteristic
115C29×C4⋊C8C2311yescharacteristic
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×#102—21no—
125C29×#102—21no—
126C29×#102—21no—
127C29×#102—21no—
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×C22⋊C8—21no—
133C29×C22⋊C8—21no—
134C29×C22⋊C8—21no—
135C29×C22⋊C8—21no—
136C29×C22⋊C8D411yescharacteristic
137C29×C22⋊C8D411yescharacteristic
138C29×#97—21no—
139C29×#97—21no—
140C29×#97—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144#41×C29—41no—
145#41×C29—41no—
146#41×C29—81no—
147#41×C29—81no—
148#41×C29—82no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×Q8×C29C2×D411yescharacteristic
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—21no—
159C2×D4×C29—41no—
160C2×D4×C29—41no—
161C2×D4×C29C2×D411yescharacteristic
162C22×C4×C29—21no—
163C22×C4×C29—21no—
164C22×C4×C29—21no—
165C22×C4×C29—41no—
166C22×C4×C29—41no—
167C22×C4×C29C2×D411yescharacteristic
168C22×C4×C29C2×D411yescharacteristic
169C22×C4×C29#4111yescharacteristic
170SD16×C29—42no—
171SD16×C29—42no—
172SD16×C29—81no—
173SD16×C29—81no—
174D8×C29—42no—
175D8×C29—42no—
176D8×C29—81no—
177D8×C29—81no—
178M16×C29—81no—
179M16×C29—81no—
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—81no—
187C2×C8×C29C2×D411yescharacteristic
188C2×C8×C29C2×D411yescharacteristic
189C2×C8×C29C2×D411yescharacteristic
190C2×C8×C29C2×D411yescharacteristic
191C4⋊C4×C29—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—21no—
194C4⋊C4×C29—21no—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—21no—
197C4⋊C4×C29C2×D411yescharacteristic
198C4⋊C4×C29C2×D411yescharacteristic
199C22⋊C4×C29—21no—
200C22⋊C4×C29—21no—
201C22⋊C4×C29—21no—
202C22⋊C4×C29—41no—
203C22⋊C4×C29—41no—
204C22⋊C4×C29—41no—
205C22⋊C4×C29—41no—
206C42×C29—21no—
207C42×C29—21no—
208C42×C29—21no—
209C42×C29C2×D411yescharacteristic
210C42×C29C2×D411yescharacteristic
211C42×C29#4111yescharacteristic
212C42×C29C2411yescharacteristic
213#19448C2911yesmaximal, characteristic, direct product factor, Sylow
214C23×C29—21no—
215C23×C29—41no—
216C23×C29—41no—
217C23×C29#12111yescharacteristic
218Q8×C29—21no—
219Q8×C29—21no—
220Q8×C29—41no—
221Q8×C29—41no—
222Q8×C29—81no—
223D4×C29—21no—
224D4×C29—21no—
225D4×C29—42no—
226D4×C29—41no—
227D4×C29—41no—
228D4×C29—41no—
229D4×C29—41no—
230D4×C29—41no—
231D4×C29—41no—
232D4×C29—41no—
233D4×C29—41no—
234D4×C29—81no—
235D4×C29—81no—
236D4×C29—82no—
237D4×C29—82no—
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—21no—
245C2×C4×C29—41no—
246C2×C4×C29—42no—
247C2×C4×C29—41no—
248C2×C4×C29—41no—
249C2×C4×C29—41no—
250C2×C4×C29—41no—
251C2×C4×C29—81no—
252C2×C4×C29—82no—
253C2×C4×C29—82no—
254C2×C4×C29#12111yescharacteristic
255C2×C4×C29#12111yescharacteristic
256C2×C4×C29#12111yescharacteristic
257C2×C4×C29C22×D411yescharacteristic
258C2×C4×C29C22×D411yescharacteristic
259C2×C4×C29C2×#4111yescharacteristic
260C8×C29—21no—
261C8×C29—21no—
262C8×C29—21no—
263C8×C29—21no—
264C8×C29—41no—
265C8×C29—41no—
266C8×C29—41no—
267C8×C29—41no—
268C8×C29—41no—
269C8×C29—41no—
270#3207C2×C2911yescharacteristic, complemented
271#3115C2×C2911yescharacteristic, complemented
272#3106C2×C2911yescharacteristic, complemented
273#2989C2×C2911yescharacteristic, complemented
274#1704C2×C2911yescharacteristic, complemented
275#1703C2×C2911yescharacteristic, complemented
276#1698C2×C2911yescharacteristic, complemented
277#1697C2×C2911yescharacteristic, complemented
278#1688C2×C2911yescharacteristic, complemented
279#1687C2×C2911yescharacteristic, complemented
280#1686C2×C2911yescharacteristic, complemented
281#1685C2×C2911yescharacteristic, complemented
282#1572C2×C2911yescharacteristic, complemented
283#1551C2×C2911yescharacteristic, complemented
284#1540C2×C2911yescharacteristic, complemented
285C22×C29—21no—
286C22×C29—21no—
287C22×C29—21no—
288C22×C29—41no—
289C22×C29—41no—
290C22×C29—41no—
291C22×C29—81no—
292C22×C29—81no—
293C22×C29—81no—
294C22×C29—81no—
295C22×C29—81no—
296C22×C29—81no—
297C22×C29C2×#12111yescharacteristic
298C4×C29—21no—
299C4×C29—21no—
300C4×C29—21no—
301C4×C29—21no—
302C4×C29—41no—
303C4×C29—41no—
304C4×C29—41no—
305C4×C29—81no—
306C4×C29—81no—
307C4×C29#57511yescharacteristic
308C4×C29#57511yescharacteristic
309C4×C29#57611yescharacteristic
310C4×C29#57711yescharacteristic
311#532C22×C2911yescharacteristic
312#532C22×C2911yescharacteristic
313C4×#41C22×C2911yescharacteristic
314#493C22×C2911yescharacteristic
315#492C22×C2911yescharacteristic
316#487C22×C2911yescharacteristic
317#486C22×C2911yescharacteristic
318#482—21no—
319#482—21no—
320#477C22×C2911yescharacteristic
321#476C22×C2911yescharacteristic
322#475C22×C2911yescharacteristic
323#474C22×C2911yescharacteristic
324#463—21no—
325#463—21no—
326#460C22×C2911yescharacteristic
327#460C22×C2911yescharacteristic
328#459C22×C2911yescharacteristic
329#459C22×C2911yescharacteristic
330#449—21no—
331#449—21no—
332#449—21no—
333#449—21no—
334#446C22×C2911yescharacteristic
335#446C22×C2911yescharacteristic
336#442—21no—
337#440—21no—
338C4×SD16—21no—
339C4×D8—21no—
340#436C22×C2911yescharacteristic
341#436C22×C2911yescharacteristic
342#435—21no—
343#435—21no—
344#432—21no—
345#432C22×C2911yescharacteristic
346#431C22×C2911yescharacteristic
347#431C22×C2911yescharacteristic
348#423—21no—
349C2×C4⋊C8C22×C2911yescharacteristic
350#335C22×C2911yescharacteristic
351#335C22×C2911yescharacteristic
352#334C22×C2911yescharacteristic
353#334C22×C2911yescharacteristic
354#333C22×C2911yescharacteristic
355#333C22×C2911yescharacteristic
356#332C22×C2911yescharacteristic
357#332C22×C2911yescharacteristic
358#331C22×C2911yescharacteristic
359#331C22×C2911yescharacteristic
360#331C22×C2911yescharacteristic
361#331C22×C2911yescharacteristic
362C2×C29—41no—
363C2×C29—81no—
364C2×C29—161no—
365C2×C29—161no—
366C2×C29#304511yescharacteristic
367C2×C29#305411yescharacteristic
368C2×C29#306811yescharacteristic
369C2×#41—21no—
370C2×#41—21no—
371C2×#41D4×C2911yescharacteristic
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×D8—21no—
377C2×D8—21no—
378C2×D8—21no—
379C2×D8—21no—
380C2×M16—21no—
381C2×M16—21no—
382C22×C8—21no—
383C4⋊Q8C23×C2911yescharacteristic
384C4⋊Q8C23×C2911yescharacteristic
385#127C23×C2911yescharacteristic
386#127C23×C2911yescharacteristic
387#124—21no—
388#124—21no—
389#121—21no—
390#121—21no—
391#121—21no—
392#121—21no—
393C4×Q8D4×C2911yescharacteristic
394C4×Q8C23×C2911yescharacteristic
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4D4×C2911yescharacteristic
402C4×D4C23×C2911yescharacteristic
403#117—21no—
404#117D4×C2911yescharacteristic
405C2×C42—21no—
406C2×C42C23×C2911yescharacteristic
407#107—21no—
408#107—21no—
409#106—21no—
410#106—21no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8D4×C2911yescharacteristic
415C4⋊C8D4×C2911yescharacteristic
416C4⋊C8C23×C2911yescharacteristic
417C4⋊C8C23×C2911yescharacteristic
418C4⋊C8C23×C2911yescharacteristic
419C4⋊C8C23×C2911yescharacteristic
420C4⋊C8C23×C2911yescharacteristic
421C4⋊C8C23×C2911yescharacteristic
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434C22⋊C8—21no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8D4×C2911yescharacteristic
439C22⋊C8D4×C2911yescharacteristic
440#97—21no—
441#97—21no—
442#97—21no—
443C4×C8—21no—
444C4×C8C23×C2911yescharacteristic
445C4×C8C23×C2911yescharacteristic
446C29#1944811yescharacteristic, direct product factor, Sylow
447#41—41no—
448#41—41no—
449#41—81no—
450#41—81no—
451#41—82no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8C2×D4×C2911yescharacteristic
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4C2×D4×C2911yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4C2×D4×C2911yescharacteristic
471C22×C4C2×D4×C2911yescharacteristic
472C22×C4#41×C2911yescharacteristic
473SD16—42no—
474SD16—42no—
475SD16—81no—
476SD16—81no—
477D8—42no—
478D8—42no—
479D8—81no—
480D8—81no—
481M16—81no—
482M16—81no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—81no—
490C2×C8C2×D4×C2911yescharacteristic
491C2×C8C2×D4×C2911yescharacteristic
492C2×C8C2×D4×C2911yescharacteristic
493C2×C8C2×D4×C2911yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4C2×D4×C2911yescharacteristic
501C4⋊C4C2×D4×C2911yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42C2×D4×C2911yescharacteristic
513C42C2×D4×C2911yescharacteristic
514C42#41×C2911yescharacteristic
515C42C24×C2911yescharacteristic
516C23—21no—
517C23—41no—
518C23—41no—
519C23C29×#12111yescharacteristic
520Q8—21no—
521Q8—21no—
522Q8—41no—
523Q8—41no—
524Q8—81no—
525D4—21no—
526D4—21no—
527D4—42no—
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—41no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—81no—
554C2×C4—82no—
555C2×C4—82no—
556C2×C4C29×#12111yescharacteristic
557C2×C4C29×#12111yescharacteristic
558C2×C4C29×#12111yescharacteristic
559C2×C4C22×D4×C2911yescharacteristic
560C2×C4C22×D4×C2911yescharacteristic
561C2×C4C2×#41×C2911yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22C2×C29×#12111yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—81no—
593C4—81no—
594C4C29×#57511yescharacteristic
595C4C29×#57511yescharacteristic
596C4C29×#57611yescharacteristic
597C4C29×#57711yescharacteristic
598C2—41no—
599C2—81no—
600C2—161no—
601C2—161no—
602C2C29×#304511yescharacteristic
603C2C29×#305411yescharacteristic
604C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
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×#3207C2semidirect
2. C29×#3115C2semidirect
3. C29×#3106C2semidirect
4. C29×#2989C2semidirect
5. C29×#1704C2semidirect
6. C29×#1703C2semidirect
7. C29×#1698C2semidirect
8. C29×#1697C2semidirect
9. C29×#1688C2semidirect
10. C29×#1687C2semidirect
11. C29×#1686C2semidirect
12. C29×#1685C2semidirect
13. C29×#1572C2semidirect
14. C29×#1551C2semidirect
15. C29×#1540C2semidirect
213. #19448C29direct (N × H)
270. #3207C2×C29semidirect
271. #3115C2×C29semidirect
272. #3106C2×C29semidirect
273. #2989C2×C29semidirect
274. #1704C2×C29semidirect
275. #1703C2×C29semidirect
276. #1698C2×C29semidirect
277. #1697C2×C29semidirect
278. #1688C2×C29semidirect
279. #1687C2×C29semidirect
280. #1686C2×C29semidirect
281. #1685C2×C29semidirect
282. #1572C2×C29semidirect
283. #1551C2×C29semidirect
284. #1540C2×C29semidirect
446. C29#19448direct (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×#31152
C29×#31062
C29×#29892
C29×#17042
C29×#17032
C29×#16982
C29×#16972
C29×#16882
C29×#16872
C29×#16862
C29×#16852
C29×#15722
C29×#15512
C29×#15402
#1944829