Finite Group Databasebeta

← C29×#19813 #20314713

Subgroups — C29×#19813 #20314713

Order 7424.

580 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3385C211yesmaximal, characteristic
2Q8×Q16×C29C211yesmaximal, characteristic, complemented
3Q8×SD16×C29C211yesmaximal, characteristic
4C29×#3299C211yesmaximal, characteristic
5C29×#1723C211yesmaximal, characteristic, complemented
6C29×#1692C211yesmaximal, characteristic, complemented
7C29×#1684C211yesmaximal, characteristic, complemented
8C29×#1676C211yesmaximal, characteristic, complemented
9C29×#1675C211yesmaximal, characteristic
10C29×#1645C211yesmaximal, characteristic, complemented
11C29×#1637C211yesmaximal, characteristic
12C29×#1633C211yesmaximal, characteristic, complemented
13C29×#1632C211yesmaximal, characteristic
14C29×#1584C211yesmaximal, characteristic, complemented
15C29×SD16⋊C8C211yesmaximal, characteristic
16Q82×C29C2211yescharacteristic
17Q82×C29C2211yescharacteristic
18C29×#554C2211yescharacteristic
19D4×Q8×C29C2211yescharacteristic
20C29×#501—21no—
21C29×#500—21no—
22C29×#500C2211yescharacteristic
23C29×#500C2211yescharacteristic
24C29×#498—21no—
25C29×#498C2211yescharacteristic
26C29×#494C2211yescharacteristic
27C29×#487C2211yescharacteristic
28C29×#487C2211yescharacteristic
29C29×#484—21no—
30C29×#479—21no—
31C29×#477—21no—
32C29×#477—21no—
33C29×#477C2211yescharacteristic
34C29×#477C2211yescharacteristic
35C29×#477C2211yescharacteristic
36C29×#477C2211yescharacteristic
37C29×#476—21no—
38C29×#476C2211yescharacteristic
39C29×#476C2211yescharacteristic
40C29×#475—21no—
41C29×#475C2211yescharacteristic
42C29×#474—21no—
43C29×#467—21no—
44C29×#462C2211yescharacteristic
45C29×#451—21no—
46C29×#446C2211yescharacteristic
47C8×Q8×C29C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C29×#440—21no—
50C4×Q16×C29—21no—
51C4×Q16×C29C2211yescharacteristic
52C4×SD16×C29—21no—
53C4×SD16×C29C2211yescharacteristic
54C8×D4×C29C2211yescharacteristic
55C2×C29×#103—21no—
56C29×#335C2211yescharacteristic
57C29×#335C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×Q8⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C29×#322C2211yescharacteristic
67C22×Q8×C29—21no—
68C2×Q16×C29—21no—
69C2×Q16×C29—41no—
70C2×Q16×C29D411yescharacteristic
71C2×SD16×C29D411yescharacteristic
72C22×C8×C29—21no—
73C29×C4⋊Q8—21no—
74C29×C4⋊Q8—21no—
75C29×C4⋊Q8—21no—
76C29×C4⋊Q8—21no—
77C29×C4⋊Q8—21no—
78C29×C4⋊Q8—41no—
79C29×C4⋊Q8—41no—
80C29×C4⋊Q8C2311yescharacteristic
81C29×C4⋊Q8C2311yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×C4⋊Q8C2311yescharacteristic
84C29×#125—21no—
85C29×C22⋊Q8—21no—
86C29×C22⋊Q8—21no—
87C29×C22⋊Q8—41no—
88C29×C22⋊Q8—41no—
89C4×Q8×C29—21no—
90C4×Q8×C29—21no—
91C4×Q8×C29—21no—
92C4×Q8×C29—21no—
93C4×Q8×C29C2311yescharacteristic
94C4×Q8×C29C2311yescharacteristic
95C4×Q8×C29C2311yescharacteristic
96C4×D4×C29—21no—
97C4×D4×C29—21no—
98C4×D4×C29C2311yescharacteristic
99C2×C4⋊C4×C29—21no—
100C29×#107—21no—
101C29×#107—21no—
102C29×#107—21no—
103C29×#107—21no—
104C29×#107—21no—
105C29×#107—21no—
106C29×#107—21no—
107C29×#107—21no—
108C29×#107D411yescharacteristic
109C29×#106—21no—
110C29×#106—21no—
111C29×#106—21no—
112C29×#106—21no—
113C29×#106—21no—
114C29×#106D411yescharacteristic
115C29×C4⋊C8—21no—
116C29×C4⋊C8—21no—
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×#103—41no—
131C29×#103D411yescharacteristic
132C29×#103D411yescharacteristic
133C29×#103D411yescharacteristic
134C29×#102—21no—
135C29×#102—21no—
136C29×#102D411yescharacteristic
137C29×C22⋊C8—21no—
138C29×#97—21no—
139C4×C8×C29—21no—
140C4×C8×C29—21no—
141C4×C8×C29C2311yescharacteristic
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C2×Q8×C29—21no—
145C2×Q8×C29—21no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—41no—
149C2×Q8×C29—41no—
150C2×Q8×C29—41no—
151C2×Q8×C29—42no—
152C2×Q8×C29—81no—
153C2×Q8×C29C2×D411yescharacteristic
154C2×Q8×C29C2×D411yescharacteristic
155C2×Q8×C29C2×D411yescharacteristic
156C2×D4×C29C2×D411yescharacteristic
157C22×C4×C29—21no—
158C22×C4×C29—41no—
159C22×C4×C29—41no—
160Q16×C29—22no—
161Q16×C29—81no—
162Q16×C29—82no—
163SD16×C29Q1614yescomplemented
164C2×C8×C29—21no—
165C2×C8×C29—21no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—81no—
170C2×C8×C29C2×D411yescharacteristic
171C2×C8×C29C2×D411yescharacteristic
172C2×C8×C29C2×D411yescharacteristic
173C2×C8×C29C2×D411yescharacteristic
174C4⋊C4×C29—21no—
175C4⋊C4×C29—21no—
176C4⋊C4×C29—21no—
177C4⋊C4×C29—21no—
178C4⋊C4×C29—21no—
179C4⋊C4×C29—21no—
180C4⋊C4×C29—21no—
181C4⋊C4×C29—21no—
182C4⋊C4×C29—21no—
183C4⋊C4×C29—21no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—41no—
186C4⋊C4×C29—41no—
187C4⋊C4×C29—41no—
188C4⋊C4×C29—41no—
189C4⋊C4×C29—41no—
190C4⋊C4×C29—41no—
191C4⋊C4×C29—41no—
192C4⋊C4×C29C2×D411yescharacteristic
193C4⋊C4×C29C2×D411yescharacteristic
194C4⋊C4×C29C2×D411yescharacteristic
195C4⋊C4×C29C2×D411yescharacteristic
196C22⋊C4×C29—21no—
197C22⋊C4×C29—41no—
198C22⋊C4×C29—41no—
199C42×C29—21no—
200C42×C29—21no—
201C42×C29—21no—
202C42×C29—41no—
203C42×C29—41no—
204C42×C29C2411yescharacteristic
205#19813C2911yesmaximal, characteristic, direct product factor, Sylow
206C23×C29—21no—
207Q8×C29—21no—
208Q8×C29—21no—
209Q8×C29—21no—
210Q8×C29—21no—
211Q8×C29—41no—
212Q8×C29—41no—
213Q8×C29—82no—
214Q8×C29—81no—
215Q8×C29—81no—
216Q8×C29—81no—
217Q8×C29—161no—
218Q8×C29—161no—
219Q8×C29C2×Q1612yes—
220Q8×C29#13712yes—
221D4×C29—21no—
222D4×C29C2×Q1612yes—
223C2×C4×C29—21no—
224C2×C4×C29—21no—
225C2×C4×C29—21no—
226C2×C4×C29—21no—
227C2×C4×C29—21no—
228C2×C4×C29—21no—
229C2×C4×C29—21no—
230C2×C4×C29—41no—
231C2×C4×C29—41no—
232C2×C4×C29—41no—
233C2×C4×C29—41no—
234C2×C4×C29—41no—
235C2×C4×C29—41no—
236C2×C4×C29—82no—
237C2×C4×C29—161no—
238C2×C4×C29C22×D411yescharacteristic
239C2×C4×C29C22×D411yescharacteristic
240C2×C4×C29H(5,𝔽2)11yescharacteristic
241C8×C29—21no—
242C8×C29—21no—
243C8×C29—21no—
244C8×C29—41no—
245C8×C29—41no—
246C8×C29—41no—
247C8×C29—41no—
248C8×C29—41no—
249C8×C29C2×Q1612yes—
250#3385C2×C2911yescharacteristic
251Q8×Q16C2×C2911yescharacteristic, complemented
252Q8×SD16C2×C2911yescharacteristic
253#3299C2×C2911yescharacteristic
254#1723C2×C2911yescharacteristic, complemented
255#1692C2×C2911yescharacteristic, complemented
256#1684C2×C2911yescharacteristic, complemented
257#1676C2×C2911yescharacteristic, complemented
258#1675C2×C2911yescharacteristic
259#1645C2×C2911yescharacteristic, complemented
260#1637C2×C2911yescharacteristic
261#1633C2×C2911yescharacteristic, complemented
262#1632C2×C2911yescharacteristic
263#1584C2×C2911yescharacteristic, complemented
264SD16⋊C8C2×C2911yescharacteristic
265C22×C29—22no—
266C22×C29—41no—
267C22×C29—41no—
268C22×C29D4211yescharacteristic
269C4×C29—22no—
270C4×C29—22no—
271C4×C29—21no—
272C4×C29—41no—
273C4×C29—41no—
274C4×C29—41no—
275C4×C29—41no—
276C4×C29—41no—
277C4×C29—81no—
278C4×C29—81no—
279C4×C29—81no—
280C4×C29—81no—
281C4×C29C22×Q1611yescharacteristic
282C4×C29C2×#13711yescharacteristic
283C4×C29#57711yescharacteristic
284C4×C29#57811yescharacteristic
285Q82C22×C2911yescharacteristic
286Q82C22×C2911yescharacteristic
287#554C22×C2911yescharacteristic
288D4×Q8C22×C2911yescharacteristic
289#501—21no—
290#500—21no—
291#500C22×C2911yescharacteristic
292#500C22×C2911yescharacteristic
293#498—21no—
294#498C22×C2911yescharacteristic
295#494C22×C2911yescharacteristic
296#487C22×C2911yescharacteristic
297#487C22×C2911yescharacteristic
298#484—21no—
299#479—21no—
300#477—21no—
301#477—21no—
302#477C22×C2911yescharacteristic
303#477C22×C2911yescharacteristic
304#477C22×C2911yescharacteristic
305#477C22×C2911yescharacteristic
306#476—21no—
307#476C22×C2911yescharacteristic
308#476C22×C2911yescharacteristic
309#475—21no—
310#475C22×C2911yescharacteristic
311#474—21no—
312#467—21no—
313#462C22×C2911yescharacteristic
314#451—21no—
315#446C22×C2911yescharacteristic
316C8×Q8C22×C2911yescharacteristic
317C8×Q8C22×C2911yescharacteristic
318#440—21no—
319C4×Q16—21no—
320C4×Q16C22×C2911yescharacteristic
321C4×SD16—21no—
322C4×SD16C22×C2911yescharacteristic
323C8×D4C22×C2911yescharacteristic
324C2×#103—21no—
325#335C22×C2911yescharacteristic
326#335C22×C2911yescharacteristic
327#333C22×C2911yescharacteristic
328#333C22×C2911yescharacteristic
329#333C22×C2911yescharacteristic
330#332C22×C2911yescharacteristic
331Q8⋊C8C22×C2911yescharacteristic
332Q8⋊C8C22×C2911yescharacteristic
333Q8⋊C8C22×C2911yescharacteristic
334D4⋊C8C22×C2911yescharacteristic
335#322C22×C2911yescharacteristic
336C2×C29—42no—
337C2×C29#326611yescharacteristic
338C2×C29D4×Q1611yescharacteristic
339C2×C29#328811yescharacteristic
340C22×Q8—21no—
341C2×Q16—21no—
342C2×Q16—41no—
343C2×Q16D4×C2911yescharacteristic
344C2×SD16D4×C2911yescharacteristic
345C22×C8—21no—
346C4⋊Q8—21no—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—41no—
352C4⋊Q8—41no—
353C4⋊Q8C23×C2911yescharacteristic
354C4⋊Q8C23×C2911yescharacteristic
355C4⋊Q8C23×C2911yescharacteristic
356C4⋊Q8C23×C2911yescharacteristic
357#125—21no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—41no—
361C22⋊Q8—41no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8C23×C2911yescharacteristic
367C4×Q8C23×C2911yescharacteristic
368C4×Q8C23×C2911yescharacteristic
369C4×D4—21no—
370C4×D4—21no—
371C4×D4C23×C2911yescharacteristic
372C2×C4⋊C4—21no—
373#107—21no—
374#107—21no—
375#107—21no—
376#107—21no—
377#107—21no—
378#107—21no—
379#107—21no—
380#107—21no—
381#107D4×C2911yescharacteristic
382#106—21no—
383#106—21no—
384#106—21no—
385#106—21no—
386#106—21no—
387#106D4×C2911yescharacteristic
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8C23×C2911yescharacteristic
392C4⋊C8C23×C2911yescharacteristic
393C4⋊C8C23×C2911yescharacteristic
394C4⋊C8C23×C2911yescharacteristic
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—41no—
404#103D4×C2911yescharacteristic
405#103D4×C2911yescharacteristic
406#103D4×C2911yescharacteristic
407#102—21no—
408#102—21no—
409#102D4×C2911yescharacteristic
410C22⋊C8—21no—
411#97—21no—
412C4×C8—21no—
413C4×C8—21no—
414C4×C8C23×C2911yescharacteristic
415C4×C8C23×C2911yescharacteristic
416C4×C8C23×C2911yescharacteristic
417C29#1981311yescharacteristic, direct product factor, Sylow
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—41no—
423C2×Q8—41no—
424C2×Q8—41no—
425C2×Q8—42no—
426C2×Q8—81no—
427C2×Q8C2×D4×C2911yescharacteristic
428C2×Q8C2×D4×C2911yescharacteristic
429C2×Q8C2×D4×C2911yescharacteristic
430C2×D4C2×D4×C2911yescharacteristic
431C22×C4—21no—
432C22×C4—41no—
433C22×C4—41no—
434Q16—22no—
435Q16—81no—
436Q16—82no—
437SD16Q16×C2914yescomplemented
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—81no—
444C2×C8C2×D4×C2911yescharacteristic
445C2×C8C2×D4×C2911yescharacteristic
446C2×C8C2×D4×C2911yescharacteristic
447C2×C8C2×D4×C2911yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4C2×D4×C2911yescharacteristic
467C4⋊C4C2×D4×C2911yescharacteristic
468C4⋊C4C2×D4×C2911yescharacteristic
469C4⋊C4C2×D4×C2911yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—41no—
477C42—41no—
478C42C24×C2911yescharacteristic
479C23—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—41no—
485Q8—41no—
486Q8—82no—
487Q8—81no—
488Q8—81no—
489Q8—81no—
490Q8—161no—
491Q8—161no—
492Q8C2×Q16×C2912yes—
493Q8C29×#13712yes—
494D4—21no—
495D4C2×Q16×C2912yes—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—82no—
510C2×C4—161no—
511C2×C4C22×D4×C2911yescharacteristic
512C2×C4C22×D4×C2911yescharacteristic
513C2×C4C29×H(5,𝔽2)11yescharacteristic
514C8—21no—
515C8—21no—
516C8—21no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8C2×Q16×C2912yes—
523C22—22no—
524C22—41no—
525C22—41no—
526C22D42×C2911yescharacteristic
527C4—22no—
528C4—22no—
529C4—21no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—81no—
536C4—81no—
537C4—81no—
538C4—81no—
539C4C22×Q16×C2911yescharacteristic
540C4C2×C29×#13711yescharacteristic
541C4C29×#57711yescharacteristic
542C4C29×#57811yescharacteristic
543C2—42no—
544C2C29×#326611yescharacteristic
545C2D4×Q16×C2911yescharacteristic
546C2C29×#328811yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC2×D4×C29C2×D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C42×C29 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. Q8×Q16×C29C2semidirect
5. C29×#1723C2semidirect
6. C29×#1692C2semidirect
7. C29×#1684C2semidirect
8. C29×#1676C2semidirect
10. C29×#1645C2semidirect
12. C29×#1633C2semidirect
14. C29×#1584C2semidirect
163. SD16×C29Q16semidirect
205. #19813C29direct (N × H)
251. Q8×Q16C2×C29semidirect
254. #1723C2×C29semidirect
255. #1692C2×C29semidirect
256. #1684C2×C29semidirect
257. #1676C2×C29semidirect
259. #1645C2×C29semidirect
261. #1633C2×C29semidirect
263. #1584C2×C29semidirect
417. C29#19813direct (N × H)
437. SD16Q16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#33852
Q8×Q16×C292
Q8×SD16×C292
C29×#32992
C29×#17232
C29×#16922
C29×#16842
C29×#16762
C29×#16752
C29×#16452
C29×#16372
C29×#16332
C29×#16322
C29×#15842
C29×SD16⋊C82
#1981329