Finite Group Databasebeta

← C29×#19248 #20314148

Subgroups — C29×#19248 #20314148

Order 7424.

624 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×#3247C211yesmaximal, characteristic, complemented
2C29×#3212C211yesmaximal, characteristic, complemented
3C29×#3184C211yesmaximal, characteristic, complemented
4C29×#2969C211yesmaximal, characteristic, complemented
5C29×#1701C211yesmaximal, characteristic, complemented
6C29×#1697C211yesmaximal, characteristic, complemented
7C29×#1692C211yesmaximal, characteristic, complemented
8C29×#1688C211yesmaximal, characteristic, complemented
9C29×#1682C211yesmaximal, characteristic, complemented
10C29×#1678C211yesmaximal, characteristic, complemented
11C29×#1671C211yesmaximal, characteristic, complemented
12C29×#1667C211yesmaximal, characteristic, complemented
13C29×#1565C211yesmaximal, characteristic, complemented
14C29×#1543C211yesmaximal, characteristic, complemented
15C29×#1540C211yesmaximal, characteristic, complemented
16C29×#532C2211yescharacteristic
17C29×#532C2211yescharacteristic
18C29×#529C2211yescharacteristic
19C29×#498C2211yescharacteristic
20C29×#495—21no—
21C29×#493C2211yescharacteristic
22C29×#488—21no—
23C29×#486C2211yescharacteristic
24C29×#486C2211yescharacteristic
25C29×#478—21no—
26C29×#477C2211yescharacteristic
27C29×#476C2211yescharacteristic
28C29×#469—21no—
29C29×#469—21no—
30C29×#466—21no—
31C29×#465—21no—
32C29×#463—21no—
33C29×#462C2211yescharacteristic
34C29×#461C2211yescharacteristic
35C29×#460C2211yescharacteristic
36C29×#460C2211yescharacteristic
37C29×#459C2211yescharacteristic
38C29×#459C2211yescharacteristic
39C29×#452—21no—
40C29×#449—21no—
41C29×#446C2211yescharacteristic
42C8×Q8×C29C2211yescharacteristic
43C29×#442—21no—
44C29×#442—21no—
45C29×#436—21no—
46C29×#436C2211yescharacteristic
47C29×#435—21no—
48C8×D4×C29C2211yescharacteristic
49C29×#433—21no—
50C29×#431C2211yescharacteristic
51C29×#431C2211yescharacteristic
52C2×C29×C4⋊C8C2211yescharacteristic
53C29×#405—21no—
54C4×M16×C29C2211yescharacteristic
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×Q16×C29—21no—
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×D8×C29—21no—
74C2×D8×C29—21no—
75C2×D8×C29—21no—
76C2×D8×C29—21no—
77C2×M16×C29—21no—
78C2×M16×C29D411yescharacteristic
79C2×M16×C29D411yescharacteristic
80C22×C8×C29—21no—
81C22×C8×C29—21no—
82C29×C4⋊Q8C2311yescharacteristic
83C29×C4⋊Q8C2311yescharacteristic
84C29×#127C2311yescharacteristic
85C29×#127C2311yescharacteristic
86C29×#126—21no—
87C29×#125D411yescharacteristic
88C29×#124—21no—
89C29×#124—21no—
90C29×#124D411yescharacteristic
91C29×#123—21no—
92C29×C22⋊Q8D411yescharacteristic
93C29×#121—21no—
94C29×#121—21no—
95C29×#121—21no—
96C29×#121—21no—
97C29×#121D411yescharacteristic
98C4×Q8×C29C2311yescharacteristic
99C4×D4×C29—21no—
100C4×D4×C29—21no—
101C4×D4×C29—21no—
102C4×D4×C29—21no—
103C4×D4×C29—21no—
104C4×D4×C29C2311yescharacteristic
105C29×#117—21no—
106C2×C42×C29C2311yescharacteristic
107C29×#107—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×#106—21no—
111C29×C4⋊C8—21no—
112C29×C4⋊C8—21no—
113C29×C4⋊C8—21no—
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×#102—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×#97—21no—
137C29×#97D411yescharacteristic
138C29×#97D411yescharacteristic
139C4×C8×C29—21no—
140C4×C8×C29—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144#41×C29—81no—
145#41×C29—81no—
146#41×C29—82no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29C2×D411yescharacteristic
150C2×D4×C29—21no—
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29—41no—
158C2×D4×C29—41no—
159C2×D4×C29C2×D411yescharacteristic
160C22×C4×C29—21no—
161C22×C4×C29—41no—
162C22×C4×C29—41no—
163C22×C4×C29C2×D411yescharacteristic
164C22×C4×C29C2×D411yescharacteristic
165C22×C4×C29#4111yescharacteristic
166Q16×C29—81no—
167SD16×C29—81no—
168SD16×C29—81no—
169SD16×C29—81no—
170D8×C29—42no—
171D8×C29—42no—
172D8×C29—81no—
173D8×C29—81no—
174M16×C29—22no—
175M16×C29—41no—
176M16×C29—42no—
177C2×C8×C29—21no—
178C2×C8×C29—21no—
179C2×C8×C29—21no—
180C2×C8×C29—21no—
181C2×C8×C29—21no—
182C2×C8×C29—21no—
183C2×C8×C29—42no—
184C2×C8×C29—81no—
185C2×C8×C29C2×D411yescharacteristic
186C2×C8×C29C2×D411yescharacteristic
187C2×C8×C29C2×D411yescharacteristic
188C2×C8×C29C2×D411yescharacteristic
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
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—21no—
203C22⋊C4×C29—21no—
204C22⋊C4×C29—41no—
205C22⋊C4×C29—41no—
206C22⋊C4×C29—41no—
207C22⋊C4×C29—41no—
208C42×C29—21no—
209C42×C29C2×D411yescharacteristic
210C42×C29C2×D411yescharacteristic
211C42×C29#4111yescharacteristic
212C42×C29C2411yescharacteristic
213#19248C2911yesmaximal, 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—41no—
226D4×C29—41no—
227D4×C29—41no—
228D4×C29—41no—
229D4×C29—41no—
230D4×C29—41no—
231D4×C29—41no—
232D4×C29—41no—
233D4×C29—81no—
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—41no—
247C2×C4×C29—41no—
248C2×C4×C29—41no—
249C2×C4×C29—41no—
250C2×C4×C29—82no—
251C2×C4×C29—82no—
252C2×C4×C29#12111yescharacteristic
253C2×C4×C29#12111yescharacteristic
254C2×C4×C29#12111yescharacteristic
255C2×C4×C29C22×D411yescharacteristic
256C2×C4×C29C22×D411yescharacteristic
257C2×C4×C29C2×#4111yescharacteristic
258C8×C29—21no—
259C8×C29—21no—
260C8×C29—21no—
261C8×C29—41no—
262C8×C29—41no—
263C8×C29—41no—
264C8×C29—41no—
265C8×C29—41no—
266C8×C29—41no—
267C8×C29#13512yes—
268#3247C2×C2911yescharacteristic, complemented
269#3212C2×C2911yescharacteristic, complemented
270#3184C2×C2911yescharacteristic, complemented
271#2969C2×C2911yescharacteristic, complemented
272#1701C2×C2911yescharacteristic, complemented
273#1697C2×C2911yescharacteristic, complemented
274#1692C2×C2911yescharacteristic, complemented
275#1688C2×C2911yescharacteristic, complemented
276#1682C2×C2911yescharacteristic, complemented
277#1678C2×C2911yescharacteristic, complemented
278#1671C2×C2911yescharacteristic, complemented
279#1667C2×C2911yescharacteristic, complemented
280#1565C2×C2911yescharacteristic, complemented
281#1543C2×C2911yescharacteristic, complemented
282#1540C2×C2911yescharacteristic, complemented
283C22×C29—21no—
284C22×C29—21no—
285C22×C29—21no—
286C22×C29—41no—
287C22×C29—41no—
288C22×C29—41no—
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—21no—
299C4×C29—21no—
300C4×C29—41no—
301C4×C29—41no—
302C4×C29—41no—
303C4×C29—81no—
304C4×C29—81no—
305C4×C29C2×#13511yescharacteristic
306C4×C29#57511yescharacteristic
307C4×C29#57611yescharacteristic
308C4×C29#57711yescharacteristic
309#532C22×C2911yescharacteristic
310#532C22×C2911yescharacteristic
311#529C22×C2911yescharacteristic
312#498C22×C2911yescharacteristic
313#495—21no—
314#493C22×C2911yescharacteristic
315#488—21no—
316#486C22×C2911yescharacteristic
317#486C22×C2911yescharacteristic
318#478—21no—
319#477C22×C2911yescharacteristic
320#476C22×C2911yescharacteristic
321#469—21no—
322#469—21no—
323#466—21no—
324#465—21no—
325#463—21no—
326#462C22×C2911yescharacteristic
327#461C22×C2911yescharacteristic
328#460C22×C2911yescharacteristic
329#460C22×C2911yescharacteristic
330#459C22×C2911yescharacteristic
331#459C22×C2911yescharacteristic
332#452—21no—
333#449—21no—
334#446C22×C2911yescharacteristic
335C8×Q8C22×C2911yescharacteristic
336#442—21no—
337#442—21no—
338#436—21no—
339#436C22×C2911yescharacteristic
340#435—21no—
341C8×D4C22×C2911yescharacteristic
342#433—21no—
343#431C22×C2911yescharacteristic
344#431C22×C2911yescharacteristic
345C2×C4⋊C8C22×C2911yescharacteristic
346#405—21no—
347C4×M16C22×C2911yescharacteristic
348#335C22×C2911yescharacteristic
349#335C22×C2911yescharacteristic
350#334C22×C2911yescharacteristic
351#334C22×C2911yescharacteristic
352#333C22×C2911yescharacteristic
353#333C22×C2911yescharacteristic
354#332C22×C2911yescharacteristic
355#332C22×C2911yescharacteristic
356#331C22×C2911yescharacteristic
357#331C22×C2911yescharacteristic
358#331C22×C2911yescharacteristic
359#331C22×C2911yescharacteristic
360C2×C29—41no—
361C2×C29—81no—
362C2×C29—161no—
363C2×C29—161no—
364C2×C29#303511yescharacteristic
365C2×C29#306211yescharacteristic
366C2×C29#306811yescharacteristic
367C2×#41—21no—
368C2×#41—21no—
369C2×Q16—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×D8—21no—
374C2×D8—21no—
375C2×D8—21no—
376C2×D8—21no—
377C2×M16—21no—
378C2×M16D4×C2911yescharacteristic
379C2×M16D4×C2911yescharacteristic
380C22×C8—21no—
381C22×C8—21no—
382C4⋊Q8C23×C2911yescharacteristic
383C4⋊Q8C23×C2911yescharacteristic
384#127C23×C2911yescharacteristic
385#127C23×C2911yescharacteristic
386#126—21no—
387#125D4×C2911yescharacteristic
388#124—21no—
389#124—21no—
390#124D4×C2911yescharacteristic
391#123—21no—
392C22⋊Q8D4×C2911yescharacteristic
393#121—21no—
394#121—21no—
395#121—21no—
396#121—21no—
397#121D4×C2911yescharacteristic
398C4×Q8C23×C2911yescharacteristic
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4C23×C2911yescharacteristic
405#117—21no—
406C2×C42C23×C2911yescharacteristic
407#107—21no—
408#106—21no—
409#106—21no—
410#106—21no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8C23×C2911yescharacteristic
415C4⋊C8C23×C2911yescharacteristic
416C4⋊C8C23×C2911yescharacteristic
417C4⋊C8C23×C2911yescharacteristic
418C4⋊C8C23×C2911yescharacteristic
419C4⋊C8C23×C2911yescharacteristic
420#103—21no—
421#103—21no—
422#103—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432C22⋊C8—21no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435C22⋊C8—21no—
436#97—21no—
437#97D4×C2911yescharacteristic
438#97D4×C2911yescharacteristic
439C4×C8—21no—
440C4×C8—21no—
441C4×C8—21no—
442C4×C8C23×C2911yescharacteristic
443C4×C8C23×C2911yescharacteristic
444C29#1924811yescharacteristic, direct product factor, Sylow
445#41—81no—
446#41—81no—
447#41—82no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8C2×D4×C2911yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4C2×D4×C2911yescharacteristic
461C22×C4—21no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4C2×D4×C2911yescharacteristic
465C22×C4C2×D4×C2911yescharacteristic
466C22×C4#41×C2911yescharacteristic
467Q16—81no—
468SD16—81no—
469SD16—81no—
470SD16—81no—
471D8—42no—
472D8—42no—
473D8—81no—
474D8—81no—
475M16—22no—
476M16—41no—
477M16—42no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—42no—
485C2×C8—81no—
486C2×C8C2×D4×C2911yescharacteristic
487C2×C8C2×D4×C2911yescharacteristic
488C2×C8C2×D4×C2911yescharacteristic
489C2×C8C2×D4×C2911yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4C2×D4×C2911yescharacteristic
499C4⋊C4C2×D4×C2911yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C42—21no—
510C42C2×D4×C2911yescharacteristic
511C42C2×D4×C2911yescharacteristic
512C42#41×C2911yescharacteristic
513C42C24×C2911yescharacteristic
514C23—21no—
515C23—41no—
516C23—41no—
517C23C29×#12111yescharacteristic
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—81no—
523D4—21no—
524D4—21no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—81no—
534D4—81no—
535D4—81no—
536D4—82no—
537D4—82no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4C29×#12111yescharacteristic
553C2×C4C29×#12111yescharacteristic
554C2×C4C29×#12111yescharacteristic
555C2×C4C22×D4×C2911yescharacteristic
556C2×C4C22×D4×C2911yescharacteristic
557C2×C4C2×#41×C2911yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8C29×#13512yes—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22C2×C29×#12111yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4C2×C29×#13511yescharacteristic
591C4C29×#57511yescharacteristic
592C4C29×#57611yescharacteristic
593C4C29×#57711yescharacteristic
594C2—41no—
595C2—81no—
596C2—161no—
597C2—161no—
598C2C29×#303511yescharacteristic
599C2C29×#306211yescharacteristic
600C2C29×#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×#3247C2semidirect
2. C29×#3212C2semidirect
3. C29×#3184C2semidirect
4. C29×#2969C2semidirect
5. C29×#1701C2semidirect
6. C29×#1697C2semidirect
7. C29×#1692C2semidirect
8. C29×#1688C2semidirect
9. C29×#1682C2semidirect
10. C29×#1678C2semidirect
11. C29×#1671C2semidirect
12. C29×#1667C2semidirect
13. C29×#1565C2semidirect
14. C29×#1543C2semidirect
15. C29×#1540C2semidirect
213. #19248C29direct (N × H)
268. #3247C2×C29semidirect
269. #3212C2×C29semidirect
270. #3184C2×C29semidirect
271. #2969C2×C29semidirect
272. #1701C2×C29semidirect
273. #1697C2×C29semidirect
274. #1692C2×C29semidirect
275. #1688C2×C29semidirect
276. #1682C2×C29semidirect
277. #1678C2×C29semidirect
278. #1671C2×C29semidirect
279. #1667C2×C29semidirect
280. #1565C2×C29semidirect
281. #1543C2×C29semidirect
282. #1540C2×C29semidirect
444. C29#19248direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32472
C29×#32122
C29×#31842
C29×#29692
C29×#17012
C29×#16972
C29×#16922
C29×#16882
C29×#16822
C29×#16782
C29×#16712
C29×#16672
C29×#15652
C29×#15432
C29×#15402
#1924829