Finite Group Databasebeta

← C29×#19860 #20314760

Subgroups — C29×#19860 #20314760

Order 7424.

632 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3360C211yesmaximal, characteristic, complemented
2C29×#3353C211yesmaximal, characteristic, complemented
3C29×#3335C211yesmaximal, characteristic, complemented
4C29×#3283C211yesmaximal, characteristic
5C29×#1723C211yesmaximal, characteristic, complemented
6C29×#1691C211yesmaximal, characteristic, complemented
7C29×#1683C211yesmaximal, characteristic, complemented
8C29×#1673C211yesmaximal, characteristic, complemented
9C29×#1670C211yesmaximal, characteristic, complemented
10C29×#1650C211yesmaximal, characteristic, complemented
11C29×#1647C211yesmaximal, characteristic, complemented
12C29×#1643C211yesmaximal, characteristic, complemented
13C29×#1635C211yesmaximal, characteristic, complemented
14C29×#1581C211yesmaximal, characteristic, complemented
15C29×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×C29×#135—21no—
17C29×#556C2211yescharacteristic
18C29×#554C2211yescharacteristic
19C29×#547C2211yescharacteristic
20C29×#547C2211yescharacteristic
21C29×#500C2211yescharacteristic
22C29×#500C2211yescharacteristic
23C29×#498C2211yescharacteristic
24C29×#494C2211yescharacteristic
25C29×#488—21no—
26C29×#487C2211yescharacteristic
27C29×#487C2211yescharacteristic
28C29×#484—21no—
29C29×#483—21no—
30C29×#482—21no—
31C29×#481—21no—
32C29×#479—21no—
33C29×#476C2211yescharacteristic
34C29×#476C2211yescharacteristic
35C29×#475C2211yescharacteristic
36C29×#475C2211yescharacteristic
37C29×#474C2211yescharacteristic
38C29×#468—21no—
39C29×#467—21no—
40C29×#465—21no—
41C29×#463—21no—
42C29×#461C2211yescharacteristic
43C29×#461C2211yescharacteristic
44C29×#461C2211yescharacteristic
45C29×#452—21no—
46C29×#452—21no—
47C8×Q8×C29C2211yescharacteristic
48C4×SD16×C29—21no—
49C4×SD16×C29C2211yescharacteristic
50C4×D8×C29C2211yescharacteristic
51C29×#436C2211yescharacteristic
52C8×D4×C29C2211yescharacteristic
53C8×D4×C29C2211yescharacteristic
54C29×#428—21no—
55C2×C29×#106—21no—
56C29×#335C2211yescharacteristic
57C29×#335C2211yescharacteristic
58C29×#333C2211yescharacteristic
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—
69C29×#135—44no—
70C2×Q16×C29—21no—
71C2×Q16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×SD16×C29—21no—
75C2×SD16×C29D411yescharacteristic
76C2×D8×C29D411yescharacteristic
77C2×M16×C29—21no—
78C22×C8×C29—21no—
79C22×C8×C29—21no—
80C29×C4⋊Q8C2311yescharacteristic
81C29×C4⋊Q8C2311yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×C4⋊Q8C2311yescharacteristic
84C29×#126—41no—
85C29×#125—21no—
86C29×#124—21no—
87C29×#123—41no—
88C29×#123—41no—
89C29×C22⋊Q8—21no—
90C29×C22⋊Q8—21no—
91C29×C22⋊Q8—21no—
92C29×C22⋊Q8—21no—
93C29×C22⋊Q8—41no—
94C29×#121—21no—
95C29×#121—21no—
96C4×Q8×C29—21no—
97C4×Q8×C29C2311yescharacteristic
98C4×D4×C29—21no—
99C4×D4×C29C2311yescharacteristic
100C4×D4×C29C2311yescharacteristic
101C4×D4×C29C2311yescharacteristic
102C29×#117—21no—
103C2×C4⋊C4×C29—21no—
104C2×C4⋊C4×C29—21no—
105C2×C4⋊C4×C29—21no—
106C29×#107—21no—
107C29×#107—21no—
108C29×#107—21no—
109C29×#107—41no—
110C29×#107D411yescharacteristic
111C29×#106—21no—
112C29×#106—21no—
113C29×#106—21no—
114C29×#106—21no—
115C29×#106—21no—
116C29×#106—21no—
117C29×#106D411yescharacteristic
118C29×C4⋊C8—21no—
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×C4⋊C8C2311yescharacteristic
122C29×C4⋊C8C2311yescharacteristic
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—21no—
126C29×#103—21no—
127C29×#103—21no—
128C29×#103—21no—
129C29×#103—21no—
130C29×#103—41no—
131C29×#103D411yescharacteristic
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—
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—21no—
153C2×Q8×C29C2×D411yescharacteristic
154C2×D4×C29—41no—
155C2×D4×C29—41no—
156C2×D4×C29C2×D411yescharacteristic
157C2×D4×C29C2×D411yescharacteristic
158C2×D4×C29C2×D411yescharacteristic
159C22×C4×C29—21no—
160C22×C4×C29—21no—
161C22×C4×C29—21no—
162C22×C4×C29—41no—
163C22×C4×C29—41no—
164C22×C4×C29—41no—
165Q16×C29—42no—
166Q16×C29—81no—
167SD16×C29—22no—
168SD16×C29—42no—
169SD16×C29—42no—
170SD16×C29—42no—
171D8×C29—22no—
172M16×C29—42no—
173C2×C8×C29—21no—
174C2×C8×C29—21no—
175C2×C8×C29—21no—
176C2×C8×C29—21no—
177C2×C8×C29—21no—
178C2×C8×C29—42no—
179C2×C8×C29—42no—
180C2×C8×C29C2×D411yescharacteristic
181C2×C8×C29C2×D411yescharacteristic
182C2×C8×C29C2×D411yescharacteristic
183C2×C8×C29C2×D411yescharacteristic
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—41no—
194C4⋊C4×C29—41no—
195C4⋊C4×C29—41no—
196C4⋊C4×C29—41no—
197C4⋊C4×C29—41no—
198C4⋊C4×C29C2×D411yescharacteristic
199C4⋊C4×C29C2×D411yescharacteristic
200C4⋊C4×C29C2×D411yescharacteristic
201C4⋊C4×C29C2×D411yescharacteristic
202C22⋊C4×C29—21no—
203C22⋊C4×C29—21no—
204C22⋊C4×C29—21no—
205C22⋊C4×C29—41no—
206C22⋊C4×C29—41no—
207C22⋊C4×C29—41no—
208C22⋊C4×C29—41no—
209C22⋊C4×C29—41no—
210C42×C29—21no—
211C42×C29—41no—
212C42×C29C2411yescharacteristic
213#19860C2911yesmaximal, characteristic, direct product factor, Sylow
214C23×C29—21no—
215C23×C29—21no—
216C23×C29—21no—
217Q8×C29—21no—
218Q8×C29—21no—
219Q8×C29—41no—
220Q8×C29—41no—
221Q8×C29—41no—
222Q8×C29—41no—
223Q8×C29—41no—
224Q8×C29—41no—
225Q8×C29—81no—
226D4×C29—21no—
227D4×C29—21no—
228D4×C29—21no—
229D4×C29—21no—
230D4×C29—21no—
231D4×C29—82no—
232D4×C29—82no—
233D4×C29AGL(1,ℤ/8)12yes—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—21no—
239C2×C4×C29—41no—
240C2×C4×C29—41no—
241C2×C4×C29—41no—
242C2×C4×C29—41no—
243C2×C4×C29—41no—
244C2×C4×C29—41no—
245C2×C4×C29—41no—
246C2×C4×C29—41no—
247C2×C4×C29—41no—
248C2×C4×C29—41no—
249C2×C4×C29—82no—
250C2×C4×C29—82no—
251C2×C4×C29—161no—
252C2×C4×C29C22×D411yescharacteristic
253C2×C4×C29C22×D411yescharacteristic
254C2×C4×C29H(5,𝔽2)11yescharacteristic
255C8×C29—21no—
256C8×C29—21no—
257C8×C29—21no—
258C8×C29—41no—
259C8×C29—41no—
260C8×C29—41no—
261C8×C29—41no—
262C8×C29—41no—
263C8×C29#13512yescomplemented
264#3360C2×C2911yescharacteristic, complemented
265#3353C2×C2911yescharacteristic, complemented
266#3335C2×C2911yescharacteristic, complemented
267#3283C2×C2911yescharacteristic
268#1723C2×C2911yescharacteristic, complemented
269#1691C2×C2911yescharacteristic, complemented
270#1683C2×C2911yescharacteristic, complemented
271#1673C2×C2911yescharacteristic, complemented
272#1670C2×C2911yescharacteristic, complemented
273#1650C2×C2911yescharacteristic, complemented
274#1647C2×C2911yescharacteristic, complemented
275#1643C2×C2911yescharacteristic, complemented
276#1635C2×C2911yescharacteristic, complemented
277#1581C2×C2911yescharacteristic, complemented
278SD16⋊C8C2×C2911yescharacteristic, complemented
279C22×C29—22no—
280C22×C29—41no—
281C22×C29—41no—
282C22×C29—41no—
283C22×C29—41no—
284C22×C29—41no—
285C22×C29—41no—
286C22×C29—41no—
287C22×C29—41no—
288C22×C29D4211yescharacteristic
289C4×C29—21no—
290C4×C29—41no—
291C4×C29—41no—
292C4×C29—41no—
293C4×C29—41no—
294C4×C29—41no—
295C4×C29—81no—
296C4×C29—81no—
297C4×C29—81no—
298C4×C29—81no—
299C4×C29C2×#13511yescharacteristic
300C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
301C4×C29#57711yescharacteristic
302C4×C29#57811yescharacteristic
303C2×#135—21no—
304#556C22×C2911yescharacteristic
305#554C22×C2911yescharacteristic
306#547C22×C2911yescharacteristic
307#547C22×C2911yescharacteristic
308#500C22×C2911yescharacteristic
309#500C22×C2911yescharacteristic
310#498C22×C2911yescharacteristic
311#494C22×C2911yescharacteristic
312#488—21no—
313#487C22×C2911yescharacteristic
314#487C22×C2911yescharacteristic
315#484—21no—
316#483—21no—
317#482—21no—
318#481—21no—
319#479—21no—
320#476C22×C2911yescharacteristic
321#476C22×C2911yescharacteristic
322#475C22×C2911yescharacteristic
323#475C22×C2911yescharacteristic
324#474C22×C2911yescharacteristic
325#468—21no—
326#467—21no—
327#465—21no—
328#463—21no—
329#461C22×C2911yescharacteristic
330#461C22×C2911yescharacteristic
331#461C22×C2911yescharacteristic
332#452—21no—
333#452—21no—
334C8×Q8C22×C2911yescharacteristic
335C4×SD16—21no—
336C4×SD16C22×C2911yescharacteristic
337C4×D8C22×C2911yescharacteristic
338#436C22×C2911yescharacteristic
339C8×D4C22×C2911yescharacteristic
340C8×D4C22×C2911yescharacteristic
341#428—21no—
342C2×#106—21no—
343#335C22×C2911yescharacteristic
344#335C22×C2911yescharacteristic
345#333C22×C2911yescharacteristic
346#332C22×C2911yescharacteristic
347#332C22×C2911yescharacteristic
348#332C22×C2911yescharacteristic
349Q8⋊C8C22×C2911yescharacteristic
350D4⋊C8C22×C2911yescharacteristic
351D4⋊C8C22×C2911yescharacteristic
352D4⋊C8C22×C2911yescharacteristic
353#322C22×C2911yescharacteristic
354C2×C29—42no—
355C2×C29—81no—
356C2×C29—81no—
357C2×C29#326511yescharacteristic
358C2×C29#328311yescharacteristic
359C2×C29#328911yescharacteristic
360C2×#41—21no—
361C2×#41—21no—
362#135—44no—
363C2×Q16—21no—
364C2×Q16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16D4×C2911yescharacteristic
369C2×D8D4×C2911yescharacteristic
370C2×M16—21no—
371C22×C8—21no—
372C22×C8—21no—
373C4⋊Q8C23×C2911yescharacteristic
374C4⋊Q8C23×C2911yescharacteristic
375C4⋊Q8C23×C2911yescharacteristic
376C4⋊Q8C23×C2911yescharacteristic
377#126—41no—
378#125—21no—
379#124—21no—
380#123—41no—
381#123—41no—
382C22⋊Q8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—41no—
387#121—21no—
388#121—21no—
389C4×Q8—21no—
390C4×Q8C23×C2911yescharacteristic
391C4×D4—21no—
392C4×D4C23×C2911yescharacteristic
393C4×D4C23×C2911yescharacteristic
394C4×D4C23×C2911yescharacteristic
395#117—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399#107—21no—
400#107—21no—
401#107—21no—
402#107—41no—
403#107D4×C2911yescharacteristic
404#106—21no—
405#106—21no—
406#106—21no—
407#106—21no—
408#106—21no—
409#106—21no—
410#106D4×C2911yescharacteristic
411C4⋊C8—21no—
412C4⋊C8C23×C2911yescharacteristic
413C4⋊C8C23×C2911yescharacteristic
414C4⋊C8C23×C2911yescharacteristic
415C4⋊C8C23×C2911yescharacteristic
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—41no—
424#103D4×C2911yescharacteristic
425#102—21no—
426#102—21no—
427#102—21no—
428#102D4×C2911yescharacteristic
429#102D4×C2911yescharacteristic
430#102D4×C2911yescharacteristic
431C22⋊C8—21no—
432C22⋊C8—21no—
433C22⋊C8—21no—
434C4×C8—21no—
435C4×C8C23×C2911yescharacteristic
436C4×C8C23×C2911yescharacteristic
437C4×C8C23×C2911yescharacteristic
438C29#1986011yescharacteristic, direct product factor, Sylow
439#41—42no—
440#41—42no—
441#41—81no—
442#41—81no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8C2×D4×C2911yescharacteristic
448C2×D4—41no—
449C2×D4—41no—
450C2×D4C2×D4×C2911yescharacteristic
451C2×D4C2×D4×C2911yescharacteristic
452C2×D4C2×D4×C2911yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459Q16—42no—
460Q16—81no—
461SD16—22no—
462SD16—42no—
463SD16—42no—
464SD16—42no—
465D8—22no—
466M16—42no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—42no—
473C2×C8—42no—
474C2×C8C2×D4×C2911yescharacteristic
475C2×C8C2×D4×C2911yescharacteristic
476C2×C8C2×D4×C2911yescharacteristic
477C2×C8C2×D4×C2911yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4C2×D4×C2911yescharacteristic
493C4⋊C4C2×D4×C2911yescharacteristic
494C4⋊C4C2×D4×C2911yescharacteristic
495C4⋊C4C2×D4×C2911yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C42—21no—
505C42—41no—
506C42C24×C2911yescharacteristic
507C23—21no—
508C23—21no—
509C23—21no—
510Q8—21no—
511Q8—21no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—81no—
519D4—21no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—82no—
525D4—82no—
526D4C29×AGL(1,ℤ/8)12yes—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4—161no—
545C2×C4C22×D4×C2911yescharacteristic
546C2×C4C22×D4×C2911yescharacteristic
547C2×C4C29×H(5,𝔽2)11yescharacteristic
548C8—21no—
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8C29×#13512yescomplemented
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22D42×C2911yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4C2×C29×#13511yescharacteristic
578C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
579C4C29×#57711yescharacteristic
580C4C29×#57811yescharacteristic
581C2—42no—
582C2—81no—
583C2—81no—
584C2C29×#326511yescharacteristic
585C2C29×#328311yescharacteristic
586C2C29×#328911yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3283C2
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×#3360C2semidirect
2. C29×#3353C2semidirect
3. C29×#3335C2semidirect
5. C29×#1723C2semidirect
6. C29×#1691C2semidirect
7. C29×#1683C2semidirect
8. C29×#1673C2semidirect
9. C29×#1670C2semidirect
10. C29×#1650C2semidirect
11. C29×#1647C2semidirect
12. C29×#1643C2semidirect
13. C29×#1635C2semidirect
14. C29×#1581C2semidirect
15. C29×SD16⋊C8C2semidirect
213. #19860C29direct (N × H)
263. C8×C29#135semidirect
264. #3360C2×C29semidirect
265. #3353C2×C29semidirect
266. #3335C2×C29semidirect
268. #1723C2×C29semidirect
269. #1691C2×C29semidirect
270. #1683C2×C29semidirect
271. #1673C2×C29semidirect
272. #1670C2×C29semidirect
273. #1650C2×C29semidirect
274. #1647C2×C29semidirect
275. #1643C2×C29semidirect
276. #1635C2×C29semidirect
277. #1581C2×C29semidirect
278. SD16⋊C8C2×C29semidirect
438. C29#19860direct (N × H)
556. C8C29×#135semidirect

Maximal subgroups

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

subgroupindex
C29×#33602
C29×#33532
C29×#33352
C29×#32832
C29×#17232
C29×#16912
C29×#16832
C29×#16732
C29×#16702
C29×#16502
C29×#16472
C29×#16432
C29×#16352
C29×#15812
C29×SD16⋊C82
#1986029