Finite Group Databasebeta

← C29×#19182 #20314082

Subgroups — C29×#19182 #20314082

Order 7424.

646 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3182C211yesmaximal, characteristic, complemented
2C29×#3107C211yesmaximal, characteristic, complemented
3C29×#3035C211yesmaximal, characteristic
4C29×#2971C211yesmaximal, characteristic, complemented
5C29×#1701C211yesmaximal, characteristic, complemented
6C29×#1699C211yesmaximal, characteristic, complemented
7C29×#1693C211yesmaximal, characteristic, complemented
8C29×#1685C211yesmaximal, characteristic, complemented
9C29×#1682C211yesmaximal, characteristic, complemented
10C29×#1680C211yesmaximal, characteristic, complemented
11C29×#1674C211yesmaximal, characteristic, complemented
12C29×#1666C211yesmaximal, characteristic, complemented
13C29×#1565C211yesmaximal, characteristic, complemented
14C29×#1553C211yesmaximal, characteristic, complemented
15C29×#1552C211yesmaximal, characteristic, complemented
16C2×C29×#135—21no—
17C29×#533C2211yescharacteristic
18C29×#532C2211yescharacteristic
19C4×#41×C29C2211yescharacteristic
20C29×#500C2211yescharacteristic
21C29×#492C2211yescharacteristic
22C29×#487C2211yescharacteristic
23C29×#486C2211yescharacteristic
24C29×#485—21no—
25C29×#475C2211yescharacteristic
26C29×#474C2211yescharacteristic
27C29×#468—21no—
28C29×#468—21no—
29C29×#464—21no—
30C29×#463—21no—
31C29×#462C2211yescharacteristic
32C29×#462C2211yescharacteristic
33C29×#461C2211yescharacteristic
34C29×#461C2211yescharacteristic
35C29×#460C2211yescharacteristic
36C29×#459C2211yescharacteristic
37C29×#452—21no—
38C8×Q8×C29C2211yescharacteristic
39C8×Q8×C29C2211yescharacteristic
40C29×#440—21no—
41C29×#440—21no—
42C4×Q16×C29—21no—
43C4×SD16×C29—21no—
44C29×#436—21no—
45C29×#436—21no—
46C29×#436C2211yescharacteristic
47C29×#436C2211yescharacteristic
48C29×#432—21no—
49C29×#432C2211yescharacteristic
50C29×#431C2211yescharacteristic
51C2×C29×C4⋊C8C2211yescharacteristic
52C29×#416—21no—
53C4×M16×C29—21no—
54C4×M16×C29C2211yescharacteristic
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
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×C29—21no—
76C2×SD16×C29—21no—
77C2×D8×C29—21no—
78C2×M16×C29—21no—
79C2×M16×C29—21no—
80C2×M16×C29D411yescharacteristic
81C2×M16×C29D411yescharacteristic
82C22×C8×C29—21no—
83C29×C4⋊Q8C2311yescharacteristic
84C29×C4⋊Q8C2311yescharacteristic
85C29×C4⋊Q8C2311yescharacteristic
86C29×#127C2311yescharacteristic
87C29×#125—21no—
88C29×#124—21no—
89C29×C22⋊Q8—21no—
90C29×C22⋊Q8—21no—
91C29×#121—21no—
92C29×#121—21no—
93C4×Q8×C29—21no—
94C4×Q8×C29—21no—
95C4×Q8×C29D411yescharacteristic
96C4×Q8×C29C2311yescharacteristic
97C4×D4×C29—21no—
98C4×D4×C29—21no—
99C4×D4×C29—21no—
100C4×D4×C29—21no—
101C4×D4×C29D411yescharacteristic
102C4×D4×C29C2311yescharacteristic
103C29×#117—21no—
104C29×#117—21no—
105C29×#117D411yescharacteristic
106C2×C42×C29—21no—
107C2×C42×C29C2311yescharacteristic
108C29×#107—21no—
109C29×#107—21no—
110C29×#107—21no—
111C29×#106—21no—
112C29×C4⋊C8—21no—
113C29×C4⋊C8—21no—
114C29×C4⋊C8—21no—
115C29×C4⋊C8C2311yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×#103—21no—
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—21no—
126C29×#103—21no—
127C29×#103—21no—
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×C22⋊C8—21no—
134C29×C22⋊C8—21no—
135C29×C22⋊C8—21no—
136C29×C22⋊C8—21no—
137C29×#97—21no—
138C29×#97D411yescharacteristic
139C29×#97D411yescharacteristic
140C4×C8×C29—21no—
141C4×C8×C29—21no—
142C4×C8×C29—21no—
143C4×C8×C29C2311yescharacteristic
144C4×C8×C29C2311yescharacteristic
145#41×C29—22no—
146#41×C29—41no—
147#41×C29—42no—
148#41×C29—42no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×Q8×C29—21no—
152C2×Q8×C29C2×D411yescharacteristic
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29—41no—
158C2×D4×C29C2×D411yescharacteristic
159C22×C4×C29—21no—
160C22×C4×C29—21no—
161C22×C4×C29—21no—
162C22×C4×C29—41no—
163C22×C4×C29C2×D411yescharacteristic
164C22×C4×C29C2×D411yescharacteristic
165C22×C4×C29#4111yescharacteristic
166Q16×C29—42no—
167Q16×C29—42no—
168SD16×C29—42no—
169SD16×C29—42no—
170SD16×C29—42no—
171SD16×C29—42no—
172SD16×C29—42no—
173D8×C29—42no—
174M16×C29—22no—
175M16×C29—41no—
176M16×C29—42no—
177M16×C29—42no—
178C2×C8×C29—21no—
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×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×C29—41no—
198C4⋊C4×C29—41no—
199C4⋊C4×C29C2×D411yescharacteristic
200C4⋊C4×C29C2×D411yescharacteristic
201C22⋊C4×C29—21no—
202C22⋊C4×C29—21no—
203C22⋊C4×C29—21no—
204C22⋊C4×C29—41no—
205C22⋊C4×C29—41no—
206C22⋊C4×C29—41no—
207C42×C29—21no—
208C42×C29—21no—
209C42×C29—21no—
210C42×C29—41no—
211C42×C29C2×D411yescharacteristic
212C42×C29C2×D411yescharacteristic
213C42×C29#4111yescharacteristic
214C42×C29C2411yescharacteristic
215#19182C2911yesmaximal, characteristic, direct product factor, Sylow
216C23×C29—21no—
217C23×C29—41no—
218C23×C29#12111yescharacteristic
219Q8×C29—21no—
220Q8×C29—41no—
221Q8×C29—41no—
222Q8×C29—41no—
223Q8×C29—41no—
224Q8×C29—41no—
225Q8×C29—41no—
226Q8×C29AGL(1,ℤ/8)12yes—
227D4×C29—21no—
228D4×C29—21no—
229D4×C29—42no—
230D4×C29—41no—
231D4×C29—41no—
232D4×C29—41no—
233D4×C29—41no—
234D4×C29—81no—
235D4×C29—82no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—21no—
239C2×C4×C29—21no—
240C2×C4×C29—21no—
241C2×C4×C29—21no—
242C2×C4×C29—21no—
243C2×C4×C29—41no—
244C2×C4×C29—42no—
245C2×C4×C29—41no—
246C2×C4×C29—41no—
247C2×C4×C29—41no—
248C2×C4×C29—41no—
249C2×C4×C29—41no—
250C2×C4×C29—81no—
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#13512yescomplemented
268#3182C2×C2911yescharacteristic, complemented
269#3107C2×C2911yescharacteristic, complemented
270#3035C2×C2911yescharacteristic
271#2971C2×C2911yescharacteristic, complemented
272#1701C2×C2911yescharacteristic, complemented
273#1699C2×C2911yescharacteristic, complemented
274#1693C2×C2911yescharacteristic, complemented
275#1685C2×C2911yescharacteristic, complemented
276#1682C2×C2911yescharacteristic, complemented
277#1680C2×C2911yescharacteristic, complemented
278#1674C2×C2911yescharacteristic, complemented
279#1666C2×C2911yescharacteristic, complemented
280#1565C2×C2911yescharacteristic, complemented
281#1553C2×C2911yescharacteristic, complemented
282#1552C2×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×C29C2×#12111yescharacteristic
293C4×C29—21no—
294C4×C29—21no—
295C4×C29—22no—
296C4×C29—21no—
297C4×C29—21no—
298C4×C29—41no—
299C4×C29—41no—
300C4×C29—81no—
301C4×C29—81no—
302C4×C29—81no—
303C4×C29C2×#13511yescharacteristic
304C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
305C4×C29#57511yescharacteristic
306C4×C29#57511yescharacteristic
307C2×#135—21no—
308#533C22×C2911yescharacteristic
309#532C22×C2911yescharacteristic
310C4×#41C22×C2911yescharacteristic
311#500C22×C2911yescharacteristic
312#492C22×C2911yescharacteristic
313#487C22×C2911yescharacteristic
314#486C22×C2911yescharacteristic
315#485—21no—
316#475C22×C2911yescharacteristic
317#474C22×C2911yescharacteristic
318#468—21no—
319#468—21no—
320#464—21no—
321#463—21no—
322#462C22×C2911yescharacteristic
323#462C22×C2911yescharacteristic
324#461C22×C2911yescharacteristic
325#461C22×C2911yescharacteristic
326#460C22×C2911yescharacteristic
327#459C22×C2911yescharacteristic
328#452—21no—
329C8×Q8C22×C2911yescharacteristic
330C8×Q8C22×C2911yescharacteristic
331#440—21no—
332#440—21no—
333C4×Q16—21no—
334C4×SD16—21no—
335#436—21no—
336#436—21no—
337#436C22×C2911yescharacteristic
338#436C22×C2911yescharacteristic
339#432—21no—
340#432C22×C2911yescharacteristic
341#431C22×C2911yescharacteristic
342C2×C4⋊C8C22×C2911yescharacteristic
343#416—21no—
344C4×M16—21no—
345C4×M16C22×C2911yescharacteristic
346#335C22×C2911yescharacteristic
347#335C22×C2911yescharacteristic
348#334C22×C2911yescharacteristic
349#334C22×C2911yescharacteristic
350#332C22×C2911yescharacteristic
351#332C22×C2911yescharacteristic
352#332C22×C2911yescharacteristic
353#332C22×C2911yescharacteristic
354#332C22×C2911yescharacteristic
355#332C22×C2911yescharacteristic
356#331C22×C2911yescharacteristic
357#331C22×C2911yescharacteristic
358C2×C29—41no—
359C2×C29—81no—
360C2×C29—161no—
361C2×C29#303511yescharacteristic
362C2×C29#305511yescharacteristic
363C2×C29#306911yescharacteristic
364C2×#41—21no—
365C2×#41D4×C2911yescharacteristic
366#135—44no—
367C2×Q16—21no—
368C2×Q16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×D8—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16D4×C2911yescharacteristic
378C2×M16D4×C2911yescharacteristic
379C22×C8—21no—
380C4⋊Q8C23×C2911yescharacteristic
381C4⋊Q8C23×C2911yescharacteristic
382C4⋊Q8C23×C2911yescharacteristic
383#127C23×C2911yescharacteristic
384#125—21no—
385#124—21no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388#121—21no—
389#121—21no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8D4×C2911yescharacteristic
393C4×Q8C23×C2911yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4D4×C2911yescharacteristic
399C4×D4C23×C2911yescharacteristic
400#117—21no—
401#117—21no—
402#117D4×C2911yescharacteristic
403C2×C42—21no—
404C2×C42C23×C2911yescharacteristic
405#107—21no—
406#107—21no—
407#107—21no—
408#106—21no—
409C4⋊C8—21no—
410C4⋊C8—21no—
411C4⋊C8—21no—
412C4⋊C8C23×C2911yescharacteristic
413C4⋊C8C23×C2911yescharacteristic
414C4⋊C8C23×C2911yescharacteristic
415C4⋊C8C23×C2911yescharacteristic
416C4⋊C8C23×C2911yescharacteristic
417C4⋊C8C23×C2911yescharacteristic
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8—21no—
433C22⋊C8—21no—
434#97—21no—
435#97D4×C2911yescharacteristic
436#97D4×C2911yescharacteristic
437C4×C8—21no—
438C4×C8—21no—
439C4×C8—21no—
440C4×C8C23×C2911yescharacteristic
441C4×C8C23×C2911yescharacteristic
442C29#1918211yescharacteristic, direct product factor, Sylow
443#41—22no—
444#41—41no—
445#41—42no—
446#41—42no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8C2×D4×C2911yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—41no—
456C2×D4C2×D4×C2911yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—41no—
461C22×C4C2×D4×C2911yescharacteristic
462C22×C4C2×D4×C2911yescharacteristic
463C22×C4#41×C2911yescharacteristic
464Q16—42no—
465Q16—42no—
466SD16—42no—
467SD16—42no—
468SD16—42no—
469SD16—42no—
470SD16—42no—
471D8—42no—
472M16—22no—
473M16—41no—
474M16—42no—
475M16—42no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—42no—
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—41no—
496C4⋊C4—41no—
497C4⋊C4C2×D4×C2911yescharacteristic
498C4⋊C4C2×D4×C2911yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—41no—
509C42C2×D4×C2911yescharacteristic
510C42C2×D4×C2911yescharacteristic
511C42#41×C2911yescharacteristic
512C42C24×C2911yescharacteristic
513C23—21no—
514C23—41no—
515C23C29×#12111yescharacteristic
516Q8—21no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8C29×AGL(1,ℤ/8)12yes—
524D4—21no—
525D4—21no—
526D4—42no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—81no—
532D4—82no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—81no—
548C2×C4—82no—
549C2×C4C29×#12111yescharacteristic
550C2×C4C29×#12111yescharacteristic
551C2×C4C29×#12111yescharacteristic
552C2×C4C22×D4×C2911yescharacteristic
553C2×C4C22×D4×C2911yescharacteristic
554C2×C4C2×#41×C2911yescharacteristic
555C8—21no—
556C8—21no—
557C8—21no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8C29×#13512yescomplemented
565C22—21no—
566C22—21no—
567C22—21no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22C2×C29×#12111yescharacteristic
575C4—21no—
576C4—21no—
577C4—22no—
578C4—21no—
579C4—21no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4C2×C29×#13511yescharacteristic
586C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
587C4C29×#57511yescharacteristic
588C4C29×#57511yescharacteristic
589C2—41no—
590C2—81no—
591C2—161no—
592C2C29×#303511yescharacteristic
593C2C29×#305511yescharacteristic
594C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3035C2
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×#3182C2semidirect
2. C29×#3107C2semidirect
4. C29×#2971C2semidirect
5. C29×#1701C2semidirect
6. C29×#1699C2semidirect
7. C29×#1693C2semidirect
8. C29×#1685C2semidirect
9. C29×#1682C2semidirect
10. C29×#1680C2semidirect
11. C29×#1674C2semidirect
12. C29×#1666C2semidirect
13. C29×#1565C2semidirect
14. C29×#1553C2semidirect
15. C29×#1552C2semidirect
215. #19182C29direct (N × H)
267. C8×C29#135semidirect
268. #3182C2×C29semidirect
269. #3107C2×C29semidirect
271. #2971C2×C29semidirect
272. #1701C2×C29semidirect
273. #1699C2×C29semidirect
274. #1693C2×C29semidirect
275. #1685C2×C29semidirect
276. #1682C2×C29semidirect
277. #1680C2×C29semidirect
278. #1674C2×C29semidirect
279. #1666C2×C29semidirect
280. #1565C2×C29semidirect
281. #1553C2×C29semidirect
282. #1552C2×C29semidirect
442. C29#19182direct (N × H)
564. C8C29×#135semidirect

Maximal subgroups

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

subgroupindex
C29×#31822
C29×#31072
C29×#30352
C29×#29712
C29×#17012
C29×#16992
C29×#16932
C29×#16852
C29×#16822
C29×#16802
C29×#16742
C29×#16662
C29×#15652
C29×#15532
C29×#15522
#1918229