Finite Group Databasebeta

← C29×#19413 #20314313

Subgroups — C29×#19413 #20314313

Order 7424.

628 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3210C211yesmaximal, characteristic, complemented
2C29×#3115C211yesmaximal, characteristic
3C29×#3107C211yesmaximal, characteristic, complemented
4C29×#2988C211yesmaximal, characteristic, complemented
5C29×#1682C211yesmaximal, characteristic, complemented
6C29×#1681C211yesmaximal, characteristic, complemented
7C29×#1680C211yesmaximal, characteristic, complemented
8C29×#1679C211yesmaximal, characteristic, complemented
9C29×#1670C211yesmaximal, characteristic, complemented
10C29×#1669C211yesmaximal, characteristic, complemented
11C29×#1666C211yesmaximal, characteristic, complemented
12C29×#1665C211yesmaximal, characteristic, complemented
13C29×#1572C211yesmaximal, characteristic, complemented
14C29×#1552C211yesmaximal, characteristic, complemented
15C29×#1540C211yesmaximal, characteristic, complemented
16C29×#533C2211yescharacteristic
17C29×#532C2211yescharacteristic
18C4×#41×C29C2211yescharacteristic
19C29×#494C2211yescharacteristic
20C29×#492C2211yescharacteristic
21C29×#487C2211yescharacteristic
22C29×#486C2211yescharacteristic
23C29×#485—21no—
24C29×#482—21no—
25C29×#475C2211yescharacteristic
26C29×#475C2211yescharacteristic
27C29×#474C2211yescharacteristic
28C29×#474C2211yescharacteristic
29C29×#464—21no—
30C29×#464—21no—
31C29×#462C2211yescharacteristic
32C29×#461C2211yescharacteristic
33C29×#460C2211yescharacteristic
34C29×#459C2211yescharacteristic
35C29×#452—21no—
36C29×#452—21no—
37C29×#452—21no—
38C29×#449—21no—
39C8×Q8×C29C2211yescharacteristic
40C8×Q8×C29C2211yescharacteristic
41C29×#442—21no—
42C29×#440—21no—
43C4×Q16×C29—21no—
44C4×SD16×C29—21no—
45C8×D4×C29—21no—
46C8×D4×C29—21no—
47C8×D4×C29C2211yescharacteristic
48C8×D4×C29C2211yescharacteristic
49C29×#432C2211yescharacteristic
50C29×#431—21no—
51C29×#431C2211yescharacteristic
52C29×#431C2211yescharacteristic
53C2×C29×C4⋊C8—21no—
54C2×C29×C4⋊C8C2211yescharacteristic
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×#332C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#331C2211yescharacteristic
66C29×#331C2211yescharacteristic
67C2×#41×C29—21no—
68C2×#41×C29D411yescharacteristic
69C2×Q16×C29—21no—
70C2×Q16×C29—21no—
71C2×Q16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×SD16×C29—21no—
75C2×SD16×C29—21no—
76C2×D8×C29—21no—
77C22×C8×C29—21no—
78C22×C8×C29—21no—
79C22×C8×C29—21no—
80C29×C4⋊Q8C2311yescharacteristic
81C29×C4⋊Q8C2311yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×#127C2311yescharacteristic
84C29×#125—21no—
85C29×#124—21no—
86C29×C22⋊Q8—21no—
87C29×C22⋊Q8—21no—
88C29×#121—21no—
89C29×#121—21no—
90C4×Q8×C29—21no—
91C4×Q8×C29—21no—
92C4×Q8×C29D411yescharacteristic
93C4×Q8×C29C2311yescharacteristic
94C4×D4×C29—21no—
95C4×D4×C29—21no—
96C4×D4×C29—21no—
97C4×D4×C29—21no—
98C4×D4×C29D411yescharacteristic
99C4×D4×C29C2311yescharacteristic
100C29×#117—21no—
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×#103—21no—
125C29×#103—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—
139C4×C8×C29—21no—
140C4×C8×C29—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144#41×C29—22no—
145#41×C29—22no—
146#41×C29—81no—
147#41×C29—81no—
148C2×Q8×C29—21no—
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—41no—
157C2×D4×C29C2×D411yescharacteristic
158C22×C4×C29—21no—
159C22×C4×C29—21no—
160C22×C4×C29—21no—
161C22×C4×C29—41no—
162C22×C4×C29C2×D411yescharacteristic
163C22×C4×C29C2×D411yescharacteristic
164C22×C4×C29#4111yescharacteristic
165Q16×C29—42no—
166Q16×C29—81no—
167Q16×C29—81no—
168SD16×C29—42no—
169SD16×C29—42no—
170SD16×C29—81no—
171SD16×C29—81no—
172D8×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—21no—
179C2×C8×C29—81no—
180C2×C8×C29—81no—
181C2×C8×C29—81no—
182C2×C8×C29C2×D411yescharacteristic
183C2×C8×C29C2×D411yescharacteristic
184C2×C8×C29C2×D411yescharacteristic
185C2×C8×C29C2×D411yescharacteristic
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—21no—
194C4⋊C4×C29—41no—
195C4⋊C4×C29—41no—
196C4⋊C4×C29C2×D411yescharacteristic
197C4⋊C4×C29C2×D411yescharacteristic
198C22⋊C4×C29—21no—
199C22⋊C4×C29—21no—
200C22⋊C4×C29—21no—
201C22⋊C4×C29—41no—
202C22⋊C4×C29—41no—
203C22⋊C4×C29—41no—
204C42×C29—21no—
205C42×C29—21no—
206C42×C29—21no—
207C42×C29—41no—
208C42×C29C2×D411yescharacteristic
209C42×C29C2×D411yescharacteristic
210C42×C29#4111yescharacteristic
211C42×C29C2411yescharacteristic
212#19413C2911yesmaximal, characteristic, direct product factor, Sylow
213C23×C29—21no—
214C23×C29—41no—
215C23×C29#12111yescharacteristic
216Q8×C29—21no—
217Q8×C29—41no—
218Q8×C29—41no—
219Q8×C29—41no—
220Q8×C29—41no—
221Q8×C29—41no—
222Q8×C29—41no—
223Q8×C29#13512yes—
224D4×C29—24no—
225D4×C29—21no—
226D4×C29—41no—
227D4×C29—41no—
228D4×C29—41no—
229D4×C29—41no—
230D4×C29—81no—
231D4×C29—82no—
232D4×C29#13512yes—
233C2×C4×C29—24no—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—21no—
239C2×C4×C29—21no—
240C2×C4×C29—21no—
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—81no—
248C2×C4×C29—82no—
249C2×C4×C29#12111yescharacteristic
250C2×C4×C29#12111yescharacteristic
251C2×C4×C29#12111yescharacteristic
252C2×C4×C29C22×D411yescharacteristic
253C2×C4×C29C22×D411yescharacteristic
254C2×C4×C29C2×#4111yescharacteristic
255C8×C29—21no—
256C8×C29—21no—
257C8×C29—21no—
258C8×C29—21no—
259C8×C29—41no—
260C8×C29—41no—
261C8×C29—41no—
262C8×C29—41no—
263C8×C29—41no—
264C8×C29—41no—
265#3210C2×C2911yescharacteristic, complemented
266#3115C2×C2911yescharacteristic
267#3107C2×C2911yescharacteristic, complemented
268#2988C2×C2911yescharacteristic, complemented
269#1682C2×C2911yescharacteristic, complemented
270#1681C2×C2911yescharacteristic, complemented
271#1680C2×C2911yescharacteristic, complemented
272#1679C2×C2911yescharacteristic, complemented
273#1670C2×C2911yescharacteristic, complemented
274#1669C2×C2911yescharacteristic, complemented
275#1666C2×C2911yescharacteristic, complemented
276#1665C2×C2911yescharacteristic, complemented
277#1572C2×C2911yescharacteristic, complemented
278#1552C2×C2911yescharacteristic, complemented
279#1540C2×C2911yescharacteristic, complemented
280C22×C29—21no—
281C22×C29—21no—
282C22×C29—22no—
283C22×C29—21no—
284C22×C29—41no—
285C22×C29—41no—
286C22×C29—81no—
287C22×C29—81no—
288C22×C29—81no—
289C22×C29C2×#12111yescharacteristic
290C4×C29—21no—
291C4×C29—21no—
292C4×C29—22no—
293C4×C29—21no—
294C4×C29—21no—
295C4×C29—41no—
296C4×C29—41no—
297C4×C29—81no—
298C4×C29—81no—
299C4×C29—81no—
300C4×C29C2×#13511yescharacteristic
301C4×C29C2×#13511yescharacteristic
302C4×C29#57611yescharacteristic
303C4×C29#57711yescharacteristic
304#533C22×C2911yescharacteristic
305#532C22×C2911yescharacteristic
306C4×#41C22×C2911yescharacteristic
307#494C22×C2911yescharacteristic
308#492C22×C2911yescharacteristic
309#487C22×C2911yescharacteristic
310#486C22×C2911yescharacteristic
311#485—21no—
312#482—21no—
313#475C22×C2911yescharacteristic
314#475C22×C2911yescharacteristic
315#474C22×C2911yescharacteristic
316#474C22×C2911yescharacteristic
317#464—21no—
318#464—21no—
319#462C22×C2911yescharacteristic
320#461C22×C2911yescharacteristic
321#460C22×C2911yescharacteristic
322#459C22×C2911yescharacteristic
323#452—21no—
324#452—21no—
325#452—21no—
326#449—21no—
327C8×Q8C22×C2911yescharacteristic
328C8×Q8C22×C2911yescharacteristic
329#442—21no—
330#440—21no—
331C4×Q16—21no—
332C4×SD16—21no—
333C8×D4—21no—
334C8×D4—21no—
335C8×D4C22×C2911yescharacteristic
336C8×D4C22×C2911yescharacteristic
337#432C22×C2911yescharacteristic
338#431—21no—
339#431C22×C2911yescharacteristic
340#431C22×C2911yescharacteristic
341C2×C4⋊C8—21no—
342C2×C4⋊C8C22×C2911yescharacteristic
343#335C22×C2911yescharacteristic
344#335C22×C2911yescharacteristic
345#334C22×C2911yescharacteristic
346#334C22×C2911yescharacteristic
347#332C22×C2911yescharacteristic
348#332C22×C2911yescharacteristic
349#332C22×C2911yescharacteristic
350#332C22×C2911yescharacteristic
351#332C22×C2911yescharacteristic
352#332C22×C2911yescharacteristic
353#331C22×C2911yescharacteristic
354#331C22×C2911yescharacteristic
355C2×C29—41no—
356C2×C29—42no—
357C2×C29—161no—
358C2×C29#304511yescharacteristic
359C2×C29#305011yescharacteristic
360C2×C29#306911yescharacteristic
361C2×#41—21no—
362C2×#41D4×C2911yescharacteristic
363C2×Q16—21no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×D8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C4⋊Q8C23×C2911yescharacteristic
375C4⋊Q8C23×C2911yescharacteristic
376C4⋊Q8C23×C2911yescharacteristic
377#127C23×C2911yescharacteristic
378#125—21no—
379#124—21no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382#121—21no—
383#121—21no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8D4×C2911yescharacteristic
387C4×Q8C23×C2911yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4D4×C2911yescharacteristic
393C4×D4C23×C2911yescharacteristic
394#117—21no—
395#117—21no—
396#117D4×C2911yescharacteristic
397C2×C42—21no—
398C2×C42C23×C2911yescharacteristic
399#107—21no—
400#107—21no—
401#106—21no—
402#106—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8D4×C2911yescharacteristic
407C4⋊C8D4×C2911yescharacteristic
408C4⋊C8C23×C2911yescharacteristic
409C4⋊C8C23×C2911yescharacteristic
410C4⋊C8C23×C2911yescharacteristic
411C4⋊C8C23×C2911yescharacteristic
412C4⋊C8C23×C2911yescharacteristic
413C4⋊C8C23×C2911yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8D4×C2911yescharacteristic
431C22⋊C8D4×C2911yescharacteristic
432#97—21no—
433C4×C8—21no—
434C4×C8—21no—
435C4×C8—21no—
436C4×C8C23×C2911yescharacteristic
437C4×C8C23×C2911yescharacteristic
438C29#1941311yescharacteristic, direct product factor, Sylow
439#41—22no—
440#41—22no—
441#41—81no—
442#41—81no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8C2×D4×C2911yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4C2×D4×C2911yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4C2×D4×C2911yescharacteristic
458C22×C4C2×D4×C2911yescharacteristic
459C22×C4#41×C2911yescharacteristic
460Q16—42no—
461Q16—81no—
462Q16—81no—
463SD16—42no—
464SD16—42no—
465SD16—81no—
466SD16—81no—
467D8—42no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—81no—
475C2×C8—81no—
476C2×C8—81no—
477C2×C8C2×D4×C2911yescharacteristic
478C2×C8C2×D4×C2911yescharacteristic
479C2×C8C2×D4×C2911yescharacteristic
480C2×C8C2×D4×C2911yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4C2×D4×C2911yescharacteristic
492C4⋊C4C2×D4×C2911yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—41no—
503C42C2×D4×C2911yescharacteristic
504C42C2×D4×C2911yescharacteristic
505C42#41×C2911yescharacteristic
506C42C24×C2911yescharacteristic
507C23—21no—
508C23—41no—
509C23C29×#12111yescharacteristic
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8C29×#13512yes—
518D4—24no—
519D4—21no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526D4C29×#13512yes—
527C2×C4—24no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—81no—
542C2×C4—82no—
543C2×C4C29×#12111yescharacteristic
544C2×C4C29×#12111yescharacteristic
545C2×C4C29×#12111yescharacteristic
546C2×C4C22×D4×C2911yescharacteristic
547C2×C4C22×D4×C2911yescharacteristic
548C2×C4C2×#41×C2911yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C22—21no—
560C22—21no—
561C22—22no—
562C22—21no—
563C22—41no—
564C22—41no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22C2×C29×#12111yescharacteristic
569C4—21no—
570C4—21no—
571C4—22no—
572C4—21no—
573C4—21no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4C2×C29×#13511yescharacteristic
580C4C2×C29×#13511yescharacteristic
581C4C29×#57611yescharacteristic
582C4C29×#57711yescharacteristic
583C2—41no—
584C2—42no—
585C2—161no—
586C2C29×#304511yescharacteristic
587C2C29×#305011yescharacteristic
588C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3115C2
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×#3210C2semidirect
3. C29×#3107C2semidirect
4. C29×#2988C2semidirect
5. C29×#1682C2semidirect
6. C29×#1681C2semidirect
7. C29×#1680C2semidirect
8. C29×#1679C2semidirect
9. C29×#1670C2semidirect
10. C29×#1669C2semidirect
11. C29×#1666C2semidirect
12. C29×#1665C2semidirect
13. C29×#1572C2semidirect
14. C29×#1552C2semidirect
15. C29×#1540C2semidirect
212. #19413C29direct (N × H)
265. #3210C2×C29semidirect
267. #3107C2×C29semidirect
268. #2988C2×C29semidirect
269. #1682C2×C29semidirect
270. #1681C2×C29semidirect
271. #1680C2×C29semidirect
272. #1679C2×C29semidirect
273. #1670C2×C29semidirect
274. #1669C2×C29semidirect
275. #1666C2×C29semidirect
276. #1665C2×C29semidirect
277. #1572C2×C29semidirect
278. #1552C2×C29semidirect
279. #1540C2×C29semidirect
438. C29#19413direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32102
C29×#31152
C29×#31072
C29×#29882
C29×#16822
C29×#16812
C29×#16802
C29×#16792
C29×#16702
C29×#16692
C29×#16662
C29×#16652
C29×#15722
C29×#15522
C29×#15402
#1941329