Finite Group Databasebeta

← C29×#19981 #20314881

Subgroups — C29×#19981 #20314881

Order 7424.

658 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×SD16×C29C211yesmaximal, characteristic, complemented
2C29×#3362C211yesmaximal, characteristic, complemented
3C29×#3298C211yesmaximal, characteristic, complemented
4C29×#3284C211yesmaximal, characteristic
5C29×#1708C211yesmaximal, characteristic, complemented
6C29×#1680C211yesmaximal, characteristic, complemented
7C29×#1677C211yesmaximal, characteristic, complemented
8C29×#1671C211yesmaximal, characteristic, complemented
9C29×#1666C211yesmaximal, characteristic, complemented
10C29×#1645C211yesmaximal, characteristic, complemented
11C29×#1642C211yesmaximal, characteristic, complemented
12C29×#1635C211yesmaximal, characteristic, complemented
13C29×#1627C211yesmaximal, characteristic, complemented
14C8×SD16×C29C211yesmaximal, characteristic, complemented
15C8×SD16×C29C211yesmaximal, characteristic, complemented
16C2×C29×#135—21no—
17Q82×C29C2211yescharacteristic
18C29×#550C2211yescharacteristic
19D4×Q8×C29C2211yescharacteristic
20C29×#547C2211yescharacteristic
21C29×#498—21no—
22C29×#498C2211yescharacteristic
23C29×#492C2211yescharacteristic
24C29×#487C2211yescharacteristic
25C29×#487C2211yescharacteristic
26C29×#486—21no—
27C29×#486C2211yescharacteristic
28C29×#486C2211yescharacteristic
29C29×#483—21no—
30C29×#476—21no—
31C29×#476—21no—
32C29×#476C2211yescharacteristic
33C29×#476C2211yescharacteristic
34C29×#475—21no—
35C29×#475C2211yescharacteristic
36C29×#475C2211yescharacteristic
37C29×#465—21no—
38C29×#465—21no—
39C29×#462C2211yescharacteristic
40C29×#461C2211yescharacteristic
41C29×#460—21no—
42C29×#460C2211yescharacteristic
43C29×#459C2211yescharacteristic
44C29×#452—21no—
45C29×#449—21no—
46C29×#448—21no—
47C8×Q8×C29C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C4×SD16×C29—21no—
50C4×SD16×C29—21no—
51C4×SD16×C29C2211yescharacteristic
52C4×SD16×C29C2211yescharacteristic
53C8×D4×C29C2211yescharacteristic
54C8×D4×C29C2211yescharacteristic
55C2×C29×#103—21no—
56C29×#334C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C82×C29C2211yescharacteristic
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C22×Q8×C29—21no—
70C29×#135—44no—
71C2×Q16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×SD16×C29—21no—
75C2×SD16×C29—21no—
76C2×SD16×C29D411yescharacteristic
77C2×SD16×C29D411yescharacteristic
78C2×D8×C29—21no—
79C22×C8×C29—21no—
80C22×C8×C29—21no—
81C29×C4⋊Q8—21no—
82C29×C4⋊Q8—21no—
83C29×C4⋊Q8—21no—
84C29×C4⋊Q8—41no—
85C29×C4⋊Q8C2311yescharacteristic
86C29×C4⋊Q8C2311yescharacteristic
87C29×C4⋊Q8C2311yescharacteristic
88C29×#127—21no—
89C29×#127C2311yescharacteristic
90C29×#123—41no—
91C29×C22⋊Q8—21no—
92C29×C22⋊Q8—21no—
93C29×C22⋊Q8—41no—
94C29×#121—21no—
95C29×#121—21no—
96C29×#121—41no—
97C4×Q8×C29—21no—
98C4×Q8×C29—21no—
99C4×Q8×C29C2311yescharacteristic
100C4×Q8×C29C2311yescharacteristic
101C4×D4×C29—21no—
102C4×D4×C29—21no—
103C4×D4×C29C2311yescharacteristic
104C4×D4×C29C2311yescharacteristic
105C2×C4⋊C4×C29—21no—
106C29×#106—21no—
107C29×#106—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×#106—21no—
111C29×#106—21no—
112C29×#106D411yescharacteristic
113C29×#106D411yescharacteristic
114C29×C4⋊C8—21no—
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—21no—
126C29×#103—41no—
127C29×#103D411yescharacteristic
128C29×#103D411yescharacteristic
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—
140C4×C8×C29—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—21no—
152C2×Q8×C29—41no—
153C2×Q8×C29—41no—
154C2×Q8×C29—42no—
155C2×Q8×C29—81no—
156C2×Q8×C29C2×D411yescharacteristic
157C2×Q8×C29C2×D411yescharacteristic
158C2×D4×C29—21no—
159C2×D4×C29—21no—
160C2×D4×C29—21no—
161C2×D4×C29—41no—
162C2×D4×C29—41no—
163C2×D4×C29—41no—
164C2×D4×C29C2×D411yescharacteristic
165C2×D4×C29C2×D411yescharacteristic
166C22×C4×C29—21no—
167C22×C4×C29—21no—
168C22×C4×C29—41no—
169C22×C4×C29—41no—
170C22×C4×C29—41no—
171Q16×C29—42no—
172SD16×C29—22no—
173SD16×C29—42no—
174SD16×C29—42no—
175SD16×C29—81no—
176SD16×C29—81no—
177SD16×C29SD1614yescomplemented
178D8×C29—42no—
179C2×C8×C29—21no—
180C2×C8×C29—21no—
181C2×C8×C29—21no—
182C2×C8×C29—21no—
183C2×C8×C29—21no—
184C2×C8×C29—42no—
185C2×C8×C29—81no—
186C2×C8×C29C2×D411yescharacteristic
187C2×C8×C29C2×D411yescharacteristic
188C2×C8×C29C2×D411yescharacteristic
189C2×C8×C29C2×D411yescharacteristic
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×C29—21no—
198C4⋊C4×C29—41no—
199C4⋊C4×C29—41no—
200C4⋊C4×C29—41no—
201C4⋊C4×C29—41no—
202C4⋊C4×C29C2×D411yescharacteristic
203C4⋊C4×C29C2×D411yescharacteristic
204C4⋊C4×C29C2×D411yescharacteristic
205C4⋊C4×C29C2×D411yescharacteristic
206C22⋊C4×C29—21no—
207C22⋊C4×C29—21no—
208C22⋊C4×C29—41no—
209C22⋊C4×C29—41no—
210C22⋊C4×C29—41no—
211C42×C29—21no—
212C42×C29—21no—
213C42×C29—41no—
214C42×C29C2411yescharacteristic
215#19981C2911yesmaximal, characteristic, direct product factor, Sylow
216C23×C29—21no—
217C23×C29—21no—
218C23×C29—41no—
219Q8×C29—21no—
220Q8×C29—21no—
221Q8×C29—41no—
222Q8×C29—41no—
223Q8×C29—41no—
224Q8×C29—41no—
225Q8×C29—82no—
226Q8×C29—81no—
227Q8×C29—161no—
228Q8×C29C2×SD1612yes—
229Q8×C29#13512yescomplemented
230D4×C29—21no—
231D4×C29—21no—
232D4×C29—21no—
233D4×C29—41no—
234D4×C29—41no—
235D4×C29—41no—
236D4×C29—41no—
237D4×C29—82no—
238D4×C29—81no—
239D4×C29—82no—
240D4×C29—161no—
241D4×C29C2×SD1612yes—
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—41no—
250C2×C4×C29—41no—
251C2×C4×C29—41no—
252C2×C4×C29—41no—
253C2×C4×C29—41no—
254C2×C4×C29—41no—
255C2×C4×C29—82no—
256C2×C4×C29—82no—
257C2×C4×C29—82no—
258C2×C4×C29C22×D411yescharacteristic
259C2×C4×C29C22×D411yescharacteristic
260C2×C4×C29H(5,𝔽2)11yescharacteristic
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×C29C2×SD1612yes—
270Q8×SD16C2×C2911yescharacteristic, complemented
271#3362C2×C2911yescharacteristic, complemented
272#3298C2×C2911yescharacteristic, complemented
273#3284C2×C2911yescharacteristic
274#1708C2×C2911yescharacteristic, complemented
275#1680C2×C2911yescharacteristic, complemented
276#1677C2×C2911yescharacteristic, complemented
277#1671C2×C2911yescharacteristic, complemented
278#1666C2×C2911yescharacteristic, complemented
279#1645C2×C2911yescharacteristic, complemented
280#1642C2×C2911yescharacteristic, complemented
281#1635C2×C2911yescharacteristic, complemented
282#1627C2×C2911yescharacteristic, complemented
283C8×SD16C2×C2911yescharacteristic, complemented
284C8×SD16C2×C2911yescharacteristic, complemented
285C22×C29—22no—
286C22×C29—41no—
287C22×C29—41no—
288C22×C29—41no—
289C22×C29—41no—
290C22×C29—41no—
291C22×C29—81no—
292C22×C29—81no—
293C22×C29—81no—
294C22×C29D4211yescharacteristic
295C4×C29—22no—
296C4×C29—22no—
297C4×C29—21no—
298C4×C29—41no—
299C4×C29—41no—
300C4×C29—41no—
301C4×C29—41no—
302C4×C29—81no—
303C4×C29—81no—
304C4×C29—81no—
305C4×C29C22×SD1611yescharacteristic
306C4×C29C2×#13511yescharacteristic
307C4×C29#57711yescharacteristic
308C4×C29#57711yescharacteristic
309C2×#135—21no—
310Q82C22×C2911yescharacteristic
311#550C22×C2911yescharacteristic
312D4×Q8C22×C2911yescharacteristic
313#547C22×C2911yescharacteristic
314#498—21no—
315#498C22×C2911yescharacteristic
316#492C22×C2911yescharacteristic
317#487C22×C2911yescharacteristic
318#487C22×C2911yescharacteristic
319#486—21no—
320#486C22×C2911yescharacteristic
321#486C22×C2911yescharacteristic
322#483—21no—
323#476—21no—
324#476—21no—
325#476C22×C2911yescharacteristic
326#476C22×C2911yescharacteristic
327#475—21no—
328#475C22×C2911yescharacteristic
329#475C22×C2911yescharacteristic
330#465—21no—
331#465—21no—
332#462C22×C2911yescharacteristic
333#461C22×C2911yescharacteristic
334#460—21no—
335#460C22×C2911yescharacteristic
336#459C22×C2911yescharacteristic
337#452—21no—
338#449—21no—
339#448—21no—
340C8×Q8C22×C2911yescharacteristic
341C8×Q8C22×C2911yescharacteristic
342C4×SD16—21no—
343C4×SD16—21no—
344C4×SD16C22×C2911yescharacteristic
345C4×SD16C22×C2911yescharacteristic
346C8×D4C22×C2911yescharacteristic
347C8×D4C22×C2911yescharacteristic
348C2×#103—21no—
349#334C22×C2911yescharacteristic
350#334C22×C2911yescharacteristic
351#333C22×C2911yescharacteristic
352#332C22×C2911yescharacteristic
353#332C22×C2911yescharacteristic
354#331C22×C2911yescharacteristic
355Q8⋊C8C22×C2911yescharacteristic
356Q8⋊C8C22×C2911yescharacteristic
357D4⋊C8C22×C2911yescharacteristic
358D4⋊C8C22×C2911yescharacteristic
359C82C22×C2911yescharacteristic
360C2×C29—42no—
361C2×C29—81no—
362C2×C29—161no—
363C2×C29D4×SD1611yescharacteristic
364C2×C29#328211yescharacteristic
365C2×C29#329011yescharacteristic
366C2×#41—21no—
367C2×#41—21no—
368C22×Q8—21no—
369#135—44no—
370C2×Q16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16D4×C2911yescharacteristic
376C2×SD16D4×C2911yescharacteristic
377C2×D8—21no—
378C22×C8—21no—
379C22×C8—21no—
380C4⋊Q8—21no—
381C4⋊Q8—21no—
382C4⋊Q8—21no—
383C4⋊Q8—41no—
384C4⋊Q8C23×C2911yescharacteristic
385C4⋊Q8C23×C2911yescharacteristic
386C4⋊Q8C23×C2911yescharacteristic
387#127—21no—
388#127C23×C2911yescharacteristic
389#123—41no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392C22⋊Q8—41no—
393#121—21no—
394#121—21no—
395#121—41no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8C23×C2911yescharacteristic
399C4×Q8C23×C2911yescharacteristic
400C4×D4—21no—
401C4×D4—21no—
402C4×D4C23×C2911yescharacteristic
403C4×D4C23×C2911yescharacteristic
404C2×C4⋊C4—21no—
405#106—21no—
406#106—21no—
407#106—21no—
408#106—21no—
409#106—21no—
410#106—21no—
411#106D4×C2911yescharacteristic
412#106D4×C2911yescharacteristic
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8C23×C2911yescharacteristic
416C4⋊C8C23×C2911yescharacteristic
417C4⋊C8C23×C2911yescharacteristic
418C4⋊C8C23×C2911yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—41no—
426#103D4×C2911yescharacteristic
427#103D4×C2911yescharacteristic
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—41no—
435#102D4×C2911yescharacteristic
436#102D4×C2911yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—21no—
439C4×C8—21no—
440C4×C8—21no—
441C4×C8C23×C2911yescharacteristic
442C4×C8C23×C2911yescharacteristic
443C4×C8C23×C2911yescharacteristic
444C29#1998111yescharacteristic, direct product factor, Sylow
445#41—42no—
446#41—42no—
447#41—81no—
448#41—81no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—41no—
453C2×Q8—41no—
454C2×Q8—42no—
455C2×Q8—81no—
456C2×Q8C2×D4×C2911yescharacteristic
457C2×Q8C2×D4×C2911yescharacteristic
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4C2×D4×C2911yescharacteristic
465C2×D4C2×D4×C2911yescharacteristic
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471Q16—42no—
472SD16—22no—
473SD16—42no—
474SD16—42no—
475SD16—81no—
476SD16—81no—
477SD16SD16×C2914yescomplemented
478D8—42no—
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⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4C2×D4×C2911yescharacteristic
503C4⋊C4C2×D4×C2911yescharacteristic
504C4⋊C4C2×D4×C2911yescharacteristic
505C4⋊C4C2×D4×C2911yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C42—21no—
512C42—21no—
513C42—41no—
514C42C24×C2911yescharacteristic
515C23—21no—
516C23—21no—
517C23—41no—
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—82no—
525Q8—81no—
526Q8—161no—
527Q8C2×SD16×C2912yes—
528Q8C29×#13512yescomplemented
529D4—21no—
530D4—21no—
531D4—21no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—82no—
537D4—81no—
538D4—82no—
539D4—161no—
540D4C2×SD16×C2912yes—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—82no—
555C2×C4—82no—
556C2×C4—82no—
557C2×C4C22×D4×C2911yescharacteristic
558C2×C4C22×D4×C2911yescharacteristic
559C2×C4C29×H(5,𝔽2)11yescharacteristic
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—41no—
568C8C2×SD16×C2912yes—
569C22—22no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22D42×C2911yescharacteristic
579C4—22no—
580C4—22no—
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4C22×SD16×C2911yescharacteristic
590C4C2×C29×#13511yescharacteristic
591C4C29×#57711yescharacteristic
592C4C29×#57711yescharacteristic
593C2—42no—
594C2—81no—
595C2—161no—
596C2D4×SD16×C2911yescharacteristic
597C2C29×#328211yescharacteristic
598C2C29×#329011yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3284C2
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. Q8×SD16×C29C2semidirect
2. C29×#3362C2semidirect
3. C29×#3298C2semidirect
5. C29×#1708C2semidirect
6. C29×#1680C2semidirect
7. C29×#1677C2semidirect
8. C29×#1671C2semidirect
9. C29×#1666C2semidirect
10. C29×#1645C2semidirect
11. C29×#1642C2semidirect
12. C29×#1635C2semidirect
13. C29×#1627C2semidirect
14. C8×SD16×C29C2semidirect
15. C8×SD16×C29C2semidirect
177. SD16×C29SD16semidirect
215. #19981C29direct (N × H)
229. Q8×C29#135semidirect
270. Q8×SD16C2×C29semidirect
271. #3362C2×C29semidirect
272. #3298C2×C29semidirect
274. #1708C2×C29semidirect
275. #1680C2×C29semidirect
276. #1677C2×C29semidirect
277. #1671C2×C29semidirect
278. #1666C2×C29semidirect
279. #1645C2×C29semidirect
280. #1642C2×C29semidirect
281. #1635C2×C29semidirect
282. #1627C2×C29semidirect
283. C8×SD16C2×C29semidirect
284. C8×SD16C2×C29semidirect
444. C29#19981direct (N × H)
477. SD16SD16×C29semidirect
528. Q8C29×#135semidirect

Maximal subgroups

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

subgroupindex
Q8×SD16×C292
C29×#33622
C29×#32982
C29×#32842
C29×#17082
C29×#16802
C29×#16772
C29×#16712
C29×#16662
C29×#16452
C29×#16422
C29×#16352
C29×#16272
C8×SD16×C292
#1998129