Finite Group Databasebeta

← C29×#20029 #20314929

Subgroups — C29×#20029 #20314929

Order 7424.

644 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3367C211yesmaximal, characteristic, complemented
2C29×#3334C211yesmaximal, characteristic
3C29×#3302C211yesmaximal, characteristic, complemented
4C29×#3276C211yesmaximal, characteristic, complemented
5C29×#1723C211yesmaximal, characteristic, complemented
6C29×#1699C211yesmaximal, characteristic, complemented
7C29×#1694C211yesmaximal, characteristic, complemented
8C29×#1679C211yesmaximal, characteristic, complemented
9C29×#1669C211yesmaximal, characteristic, complemented
10C29×#1654C211yesmaximal, characteristic, complemented
11C29×#1652C211yesmaximal, characteristic, complemented
12C29×#1649C211yesmaximal, characteristic, complemented
13C29×#1647C211yesmaximal, characteristic, complemented
14C29×#1586C211yesmaximal, characteristic, complemented
15C29×#1585C211yesmaximal, characteristic, complemented
16C2×C29×#137—21no—
17C29×#556C2211yescharacteristic
18D4×Q8×C29C2211yescharacteristic
19C29×#547C2211yescharacteristic
20C29×#547C2211yescharacteristic
21C29×#500C2211yescharacteristic
22C29×#500C2211yescharacteristic
23C29×#498C2211yescharacteristic
24C29×#494C2211yescharacteristic
25C29×#489—21no—
26C29×#487C2211yescharacteristic
27C29×#487C2211yescharacteristic
28C29×#485—21no—
29C29×#480—21no—
30C29×#480—21no—
31C29×#477—21no—
32C29×#474C2211yescharacteristic
33C29×#474C2211yescharacteristic
34C29×#474C2211yescharacteristic
35C29×#474C2211yescharacteristic
36C29×#470—21no—
37C29×#467—21no—
38C29×#466—21no—
39C29×#463—21no—
40C29×#462C2211yescharacteristic
41C29×#462C2211yescharacteristic
42C29×#461C2211yescharacteristic
43C29×#461C2211yescharacteristic
44C29×#452—21no—
45C29×#452—21no—
46C29×#451—21no—
47C29×#446C2211yescharacteristic
48C29×#440—21no—
49C4×SD16×C29C2211yescharacteristic
50C4×D8×C29C2211yescharacteristic
51C29×#436C2211yescharacteristic
52C8×D4×C29C2211yescharacteristic
53C8×D4×C29C2211yescharacteristic
54C2×C29×#107—21no—
55C29×#416—21no—
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#332C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×D4⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C29×#322C2211yescharacteristic
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C22×Q8×C29—21no—
70C29×#137—44no—
71C2×Q16×C29—21no—
72C2×Q16×C29—21no—
73C2×Q16×C29—21no—
74C2×Q16×C29—21no—
75C2×SD16×C29—21no—
76C2×SD16×C29—21no—
77C2×SD16×C29D411yescharacteristic
78C2×D8×C29D411yescharacteristic
79C2×M16×C29—21no—
80C22×C8×C29—21no—
81C22×C8×C29—21no—
82C29×C4⋊Q8—21no—
83C29×C4⋊Q8C2311yescharacteristic
84C29×C4⋊Q8C2311yescharacteristic
85C29×C4⋊Q8C2311yescharacteristic
86C29×C4⋊Q8C2311yescharacteristic
87C29×#126—41no—
88C29×#124—21no—
89C29×#123—41no—
90C29×#123—41no—
91C29×C22⋊Q8—21no—
92C29×C22⋊Q8—21no—
93C29×C22⋊Q8—21no—
94C29×C22⋊Q8—21no—
95C29×C22⋊Q8—41no—
96C29×#121—21no—
97C29×#121—21no—
98C4×Q8×C29—21no—
99C4×Q8×C29C2311yescharacteristic
100C4×D4×C29—21no—
101C4×D4×C29C2311yescharacteristic
102C4×D4×C29C2311yescharacteristic
103C4×D4×C29C2311yescharacteristic
104C29×#117—21no—
105C2×C4⋊C4×C29—21no—
106C2×C4⋊C4×C29—21no—
107C29×#107—21no—
108C29×#107—21no—
109C29×#107—21no—
110C29×#107—21no—
111C29×#107—21no—
112C29×#107—21no—
113C29×#107—41no—
114C29×#107D411yescharacteristic
115C29×#106—41no—
116C29×#106D411yescharacteristic
117C29×C4⋊C8—21no—
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×C4⋊C8C2311yescharacteristic
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—21no—
126C29×#103—21no—
127C29×#103—21no—
128C29×#103—21no—
129C29×#103—21no—
130C29×#103D411yescharacteristic
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
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—81no—
148#41×C29—81no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×Q8×C29—21no—
152C2×Q8×C29—21no—
153C2×Q8×C29—41no—
154C2×Q8×C29—42no—
155C2×Q8×C29—81no—
156C2×Q8×C29C2×D411yescharacteristic
157C2×D4×C29—41no—
158C2×D4×C29—41no—
159C2×D4×C29C2×D411yescharacteristic
160C2×D4×C29C2×D411yescharacteristic
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×C29—41no—
168Q16×C29—42no—
169Q16×C29—42no—
170Q16×C29—81no—
171Q16×C29—81no—
172SD16×C29—22no—
173SD16×C29—42no—
174SD16×C29—42no—
175D8×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—42no—
183C2×C8×C29—81no—
184C2×C8×C29C2×D411yescharacteristic
185C2×C8×C29C2×D411yescharacteristic
186C2×C8×C29C2×D411yescharacteristic
187C2×C8×C29C2×D411yescharacteristic
188C4⋊C4×C29—21no—
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×C29—41no—
198C4⋊C4×C29—41no—
199C4⋊C4×C29—41no—
200C4⋊C4×C29—41no—
201C4⋊C4×C29C2×D411yescharacteristic
202C4⋊C4×C29C2×D411yescharacteristic
203C4⋊C4×C29C2×D411yescharacteristic
204C4⋊C4×C29C2×D411yescharacteristic
205C22⋊C4×C29—21no—
206C22⋊C4×C29—21no—
207C22⋊C4×C29—21no—
208C22⋊C4×C29—41no—
209C22⋊C4×C29—41no—
210C22⋊C4×C29—41no—
211C22⋊C4×C29—41no—
212C22⋊C4×C29—41no—
213C42×C29—21no—
214C42×C29—41no—
215C42×C29C2411yescharacteristic
216#20029C2911yesmaximal, characteristic, direct product factor, Sylow
217C23×C29—21no—
218C23×C29—21no—
219C23×C29—21no—
220Q8×C29—21no—
221Q8×C29—21no—
222Q8×C29—41no—
223Q8×C29—41no—
224Q8×C29—41no—
225Q8×C29—41no—
226Q8×C29—41no—
227Q8×C29—41no—
228Q8×C29—41no—
229Q8×C29—41no—
230Q8×C29—82no—
231D4×C29—21no—
232D4×C29—21no—
233D4×C29—21no—
234D4×C29—21no—
235D4×C29—21no—
236D4×C29—82no—
237D4×C29—82no—
238D4×C29AGL(1,ℤ/8)12yes—
239C2×C4×C29—21no—
240C2×C4×C29—21no—
241C2×C4×C29—21no—
242C2×C4×C29—21no—
243C2×C4×C29—21no—
244C2×C4×C29—41no—
245C2×C4×C29—41no—
246C2×C4×C29—41no—
247C2×C4×C29—41no—
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—82no—
255C2×C4×C29—82no—
256C2×C4×C29—82no—
257C2×C4×C29C22×D411yescharacteristic
258C2×C4×C29C22×D411yescharacteristic
259C2×C4×C29H(5,𝔽2)11yescharacteristic
260C8×C29—22no—
261C8×C29—21no—
262C8×C29—21no—
263C8×C29—21no—
264C8×C29—21no—
265C8×C29—41no—
266C8×C29—41no—
267C8×C29—41no—
268C8×C29—41no—
269#3367C2×C2911yescharacteristic, complemented
270#3334C2×C2911yescharacteristic
271#3302C2×C2911yescharacteristic, complemented
272#3276C2×C2911yescharacteristic, complemented
273#1723C2×C2911yescharacteristic, complemented
274#1699C2×C2911yescharacteristic, complemented
275#1694C2×C2911yescharacteristic, complemented
276#1679C2×C2911yescharacteristic, complemented
277#1669C2×C2911yescharacteristic, complemented
278#1654C2×C2911yescharacteristic, complemented
279#1652C2×C2911yescharacteristic, complemented
280#1649C2×C2911yescharacteristic, complemented
281#1647C2×C2911yescharacteristic, complemented
282#1586C2×C2911yescharacteristic, complemented
283#1585C2×C2911yescharacteristic, complemented
284C22×C29—22no—
285C22×C29—41no—
286C22×C29—41no—
287C22×C29—41no—
288C22×C29—41no—
289C22×C29—41no—
290C22×C29—41no—
291C22×C29—41no—
292C22×C29—41no—
293C22×C29D4211yescharacteristic
294C4×C29—21no—
295C4×C29—41no—
296C4×C29—41no—
297C4×C29—41no—
298C4×C29—41no—
299C4×C29—41no—
300C4×C29—81no—
301C4×C29—81no—
302C4×C29—81no—
303C4×C29—81no—
304C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
305C4×C29#57511yescharacteristic
306C4×C29#57611yescharacteristic
307C4×C29#57811yescharacteristic
308C2×#137—21no—
309#556C22×C2911yescharacteristic
310D4×Q8C22×C2911yescharacteristic
311#547C22×C2911yescharacteristic
312#547C22×C2911yescharacteristic
313#500C22×C2911yescharacteristic
314#500C22×C2911yescharacteristic
315#498C22×C2911yescharacteristic
316#494C22×C2911yescharacteristic
317#489—21no—
318#487C22×C2911yescharacteristic
319#487C22×C2911yescharacteristic
320#485—21no—
321#480—21no—
322#480—21no—
323#477—21no—
324#474C22×C2911yescharacteristic
325#474C22×C2911yescharacteristic
326#474C22×C2911yescharacteristic
327#474C22×C2911yescharacteristic
328#470—21no—
329#467—21no—
330#466—21no—
331#463—21no—
332#462C22×C2911yescharacteristic
333#462C22×C2911yescharacteristic
334#461C22×C2911yescharacteristic
335#461C22×C2911yescharacteristic
336#452—21no—
337#452—21no—
338#451—21no—
339#446C22×C2911yescharacteristic
340#440—21no—
341C4×SD16C22×C2911yescharacteristic
342C4×D8C22×C2911yescharacteristic
343#436C22×C2911yescharacteristic
344C8×D4C22×C2911yescharacteristic
345C8×D4C22×C2911yescharacteristic
346C2×#107—21no—
347#416—21no—
348#335C22×C2911yescharacteristic
349#334C22×C2911yescharacteristic
350#332C22×C2911yescharacteristic
351#332C22×C2911yescharacteristic
352#332C22×C2911yescharacteristic
353#332C22×C2911yescharacteristic
354Q8⋊C8C22×C2911yescharacteristic
355D4⋊C8C22×C2911yescharacteristic
356D4⋊C8C22×C2911yescharacteristic
357D4⋊C8C22×C2911yescharacteristic
358#322C22×C2911yescharacteristic
359C2×C29—42no—
360C2×C29—81no—
361C2×C29—81no—
362C2×C29#326411yescharacteristic
363C2×C29#326911yescharacteristic
364C2×C29#329311yescharacteristic
365C2×#41—21no—
366C2×#41—21no—
367C22×Q8—21no—
368#137—44no—
369C2×Q16—21no—
370C2×Q16—21no—
371C2×Q16—21no—
372C2×Q16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16D4×C2911yescharacteristic
376C2×D8D4×C2911yescharacteristic
377C2×M16—21no—
378C22×C8—21no—
379C22×C8—21no—
380C4⋊Q8—21no—
381C4⋊Q8C23×C2911yescharacteristic
382C4⋊Q8C23×C2911yescharacteristic
383C4⋊Q8C23×C2911yescharacteristic
384C4⋊Q8C23×C2911yescharacteristic
385#126—41no—
386#124—21no—
387#123—41no—
388#123—41no—
389C22⋊Q8—21no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—41no—
394#121—21no—
395#121—21no—
396C4×Q8—21no—
397C4×Q8C23×C2911yescharacteristic
398C4×D4—21no—
399C4×D4C23×C2911yescharacteristic
400C4×D4C23×C2911yescharacteristic
401C4×D4C23×C2911yescharacteristic
402#117—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405#107—21no—
406#107—21no—
407#107—21no—
408#107—21no—
409#107—21no—
410#107—21no—
411#107—41no—
412#107D4×C2911yescharacteristic
413#106—41no—
414#106D4×C2911yescharacteristic
415C4⋊C8—21no—
416C4⋊C8C23×C2911yescharacteristic
417C4⋊C8C23×C2911yescharacteristic
418C4⋊C8C23×C2911yescharacteristic
419C4⋊C8C23×C2911yescharacteristic
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#103—21no—
428#103D4×C2911yescharacteristic
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102D4×C2911yescharacteristic
434#102D4×C2911yescharacteristic
435#102D4×C2911yescharacteristic
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439#97—21no—
440C4×C8C23×C2911yescharacteristic
441C4×C8C23×C2911yescharacteristic
442C4×C8C23×C2911yescharacteristic
443C29#2002911yescharacteristic, direct product factor, Sylow
444#41—42no—
445#41—42no—
446#41—81no—
447#41—81no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—41no—
453C2×Q8—42no—
454C2×Q8—81no—
455C2×Q8C2×D4×C2911yescharacteristic
456C2×D4—41no—
457C2×D4—41no—
458C2×D4C2×D4×C2911yescharacteristic
459C2×D4C2×D4×C2911yescharacteristic
460C2×D4C2×D4×C2911yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467Q16—42no—
468Q16—42no—
469Q16—81no—
470Q16—81no—
471SD16—22no—
472SD16—42no—
473SD16—42no—
474D8—41no—
475M16—42no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—42no—
482C2×C8—81no—
483C2×C8C2×D4×C2911yescharacteristic
484C2×C8C2×D4×C2911yescharacteristic
485C2×C8C2×D4×C2911yescharacteristic
486C2×C8C2×D4×C2911yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4C2×D4×C2911yescharacteristic
501C4⋊C4C2×D4×C2911yescharacteristic
502C4⋊C4C2×D4×C2911yescharacteristic
503C4⋊C4C2×D4×C2911yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C42—21no—
513C42—41no—
514C42C24×C2911yescharacteristic
515C23—21no—
516C23—21no—
517C23—21no—
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—82no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—21no—
534D4—82no—
535D4—82no—
536D4C29×AGL(1,ℤ/8)12yes—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—82no—
553C2×C4—82no—
554C2×C4—82no—
555C2×C4C22×D4×C2911yescharacteristic
556C2×C4C22×D4×C2911yescharacteristic
557C2×C4C29×H(5,𝔽2)11yescharacteristic
558C8—22no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C22—22no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22D42×C2911yescharacteristic
577C4—21no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
588C4C29×#57511yescharacteristic
589C4C29×#57611yescharacteristic
590C4C29×#57811yescharacteristic
591C2—42no—
592C2—81no—
593C2—81no—
594C2C29×#326411yescharacteristic
595C2C29×#326911yescharacteristic
596C2C29×#329311yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3334C2
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×#3367C2semidirect
3. C29×#3302C2semidirect
4. C29×#3276C2semidirect
5. C29×#1723C2semidirect
6. C29×#1699C2semidirect
7. C29×#1694C2semidirect
8. C29×#1679C2semidirect
9. C29×#1669C2semidirect
10. C29×#1654C2semidirect
11. C29×#1652C2semidirect
12. C29×#1649C2semidirect
13. C29×#1647C2semidirect
14. C29×#1586C2semidirect
15. C29×#1585C2semidirect
216. #20029C29direct (N × H)
269. #3367C2×C29semidirect
271. #3302C2×C29semidirect
272. #3276C2×C29semidirect
273. #1723C2×C29semidirect
274. #1699C2×C29semidirect
275. #1694C2×C29semidirect
276. #1679C2×C29semidirect
277. #1669C2×C29semidirect
278. #1654C2×C29semidirect
279. #1652C2×C29semidirect
280. #1649C2×C29semidirect
281. #1647C2×C29semidirect
282. #1586C2×C29semidirect
283. #1585C2×C29semidirect
443. C29#20029direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33672
C29×#33342
C29×#33022
C29×#32762
C29×#17232
C29×#16992
C29×#16942
C29×#16792
C29×#16692
C29×#16542
C29×#16522
C29×#16492
C29×#16472
C29×#15862
C29×#15852
#2002929