Finite Group Databasebeta

← C29×#19865 #20314765

Subgroups — C29×#19865 #20314765

Order 7424.

572 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3380C211yesmaximal, characteristic
2C29×#3360C211yesmaximal, characteristic
3C29×#3356C211yesmaximal, characteristic, complemented
4C29×#3338C211yesmaximal, characteristic, complemented
5C29×#1723C211yesmaximal, characteristic, complemented
6C29×#1695C211yesmaximal, characteristic, complemented
7C29×#1684C211yesmaximal, characteristic, complemented
8C29×#1676C211yesmaximal, characteristic, complemented
9C29×#1671C211yesmaximal, characteristic, complemented
10C29×#1643C211yesmaximal, characteristic, complemented
11C29×#1638C211yesmaximal, characteristic, complemented
12C29×#1632C211yesmaximal, characteristic, complemented
13C29×#1632C211yesmaximal, characteristic, complemented
14C29×#1581C211yesmaximal, characteristic
15C29×#1579C211yesmaximal, characteristic, complemented
16C29×#556C2211yescharacteristic
17C29×#554C2211yescharacteristic
18C29×#554C2211yescharacteristic
19C29×#554C2211yescharacteristic
20C29×#500C2211yescharacteristic
21C29×#500C2211yescharacteristic
22C29×#499—21no—
23C29×#498C2211yescharacteristic
24C29×#494C2211yescharacteristic
25C29×#488—21no—
26C29×#487C2211yescharacteristic
27C29×#487C2211yescharacteristic
28C29×#485—21no—
29C29×#484—21no—
30C29×#484—21no—
31C29×#483—21no—
32C29×#479—21no—
33C29×#478—21no—
34C29×#478—21no—
35C29×#477C2211yescharacteristic
36C29×#477C2211yescharacteristic
37C29×#477C2211yescharacteristic
38C29×#476C2211yescharacteristic
39C29×#476C2211yescharacteristic
40C29×#476C2211yescharacteristic
41C29×#475C2211yescharacteristic
42C29×#470—21no—
43C29×#467—21no—
44C29×#463—21no—
45C29×#461C2211yescharacteristic
46C8×Q8×C29C2211yescharacteristic
47C8×Q8×C29C2211yescharacteristic
48C4×Q16×C29C2211yescharacteristic
49C4×SD16×C29—21no—
50C4×D8×C29—21no—
51C4×D8×C29C2211yescharacteristic
52C29×#436C2211yescharacteristic
53C8×D4×C29C2211yescharacteristic
54C29×#428—21no—
55C2×C29×#107—21no—
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C29×#322C2211yescharacteristic
67C2×Q16×C29—41no—
68C2×Q16×C29D411yescharacteristic
69C2×SD16×C29—21no—
70C2×D8×C29D411yescharacteristic
71C2×M16×C29—21no—
72C22×C8×C29—21no—
73C29×C4⋊Q8C2311yescharacteristic
74C29×C4⋊Q8C2311yescharacteristic
75C29×C4⋊Q8C2311yescharacteristic
76C29×C4⋊Q8C2311yescharacteristic
77C29×#126—41no—
78C29×#125—21no—
79C29×#125—21no—
80C29×#125—21no—
81C29×#124—21no—
82C29×C22⋊Q8—21no—
83C29×C22⋊Q8—21no—
84C29×C22⋊Q8—21no—
85C29×C22⋊Q8—21no—
86C29×C22⋊Q8—41no—
87C29×C22⋊Q8—41no—
88C29×C22⋊Q8—41no—
89C4×Q8×C29—21no—
90C4×Q8×C29C2311yescharacteristic
91C4×Q8×C29C2311yescharacteristic
92C4×D4×C29—21no—
93C4×D4×C29—21no—
94C4×D4×C29—21no—
95C4×D4×C29C2311yescharacteristic
96C4×D4×C29C2311yescharacteristic
97C29×#117—21no—
98C2×C4⋊C4×C29—21no—
99C2×C4⋊C4×C29—21no—
100C2×C4⋊C4×C29—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×#107D411yescharacteristic
110C29×#106—21no—
111C29×#106—21no—
112C29×#106—21no—
113C29×#106—21no—
114C29×#106—21no—
115C29×#106—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—41no—
130C29×#103D411yescharacteristic
131C29×#103D411yescharacteristic
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×#102D411yescharacteristic
136C29×#102D411yescharacteristic
137C29×C22⋊C8—21no—
138C29×C22⋊C8—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×C29C2×D411yescharacteristic
149C2×Q8×C29C2×D411yescharacteristic
150C2×D4×C29C2×D411yescharacteristic
151C2×D4×C29C2×D411yescharacteristic
152C22×C4×C29—21no—
153C22×C4×C29—21no—
154C22×C4×C29—41no—
155C22×C4×C29—41no—
156C22×C4×C29—41no—
157Q16×C29—22no—
158Q16×C29—82no—
159SD16×C29—42no—
160D8×C29—22no—
161M16×C29—42no—
162C2×C8×C29—21no—
163C2×C8×C29—21no—
164C2×C8×C29—21no—
165C2×C8×C29—21no—
166C2×C8×C29—21no—
167C2×C8×C29—42no—
168C2×C8×C29C2×D411yescharacteristic
169C2×C8×C29C2×D411yescharacteristic
170C2×C8×C29C2×D411yescharacteristic
171C2×C8×C29C2×D411yescharacteristic
172C4⋊C4×C29—21no—
173C4⋊C4×C29—21no—
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—41no—
183C4⋊C4×C29—41no—
184C4⋊C4×C29—41no—
185C4⋊C4×C29—41no—
186C4⋊C4×C29—41no—
187C4⋊C4×C29—41no—
188C4⋊C4×C29—41no—
189C4⋊C4×C29C2×D411yescharacteristic
190C4⋊C4×C29C2×D411yescharacteristic
191C4⋊C4×C29C2×D411yescharacteristic
192C4⋊C4×C29C2×D411yescharacteristic
193C22⋊C4×C29—21no—
194C22⋊C4×C29—21no—
195C22⋊C4×C29—41no—
196C22⋊C4×C29—41no—
197C22⋊C4×C29—41no—
198C22⋊C4×C29—41no—
199C22⋊C4×C29—41no—
200C42×C29—21no—
201C42×C29—21no—
202C42×C29—41no—
203C42×C29C2411yescharacteristic
204#19865C2911yesmaximal, characteristic, direct product factor, Sylow
205C23×C29—21no—
206C23×C29—21no—
207Q8×C29—21no—
208Q8×C29—21no—
209Q8×C29—21no—
210Q8×C29—21no—
211Q8×C29—41no—
212Q8×C29—41no—
213Q8×C29—81no—
214Q8×C29—81no—
215Q8×C29—81no—
216D4×C29—21no—
217D4×C29—21no—
218D4×C29—21no—
219D4×C29#13712yes—
220C2×C4×C29—21no—
221C2×C4×C29—21no—
222C2×C4×C29—21no—
223C2×C4×C29—21no—
224C2×C4×C29—21no—
225C2×C4×C29—21no—
226C2×C4×C29—41no—
227C2×C4×C29—41no—
228C2×C4×C29—41no—
229C2×C4×C29—41no—
230C2×C4×C29—41no—
231C2×C4×C29—41no—
232C2×C4×C29—41no—
233C2×C4×C29—41no—
234C2×C4×C29—161no—
235C2×C4×C29—161no—
236C2×C4×C29—161no—
237C2×C4×C29C22×D411yescharacteristic
238C2×C4×C29C22×D411yescharacteristic
239C2×C4×C29H(5,𝔽2)11yescharacteristic
240C8×C29—21no—
241C8×C29—21no—
242C8×C29—21no—
243C8×C29—41no—
244C8×C29—41no—
245C8×C29—41no—
246C8×C29—41no—
247C8×C29—41no—
248C8×C29#13512yes—
249#3380C2×C2911yescharacteristic
250#3360C2×C2911yescharacteristic
251#3356C2×C2911yescharacteristic, complemented
252#3338C2×C2911yescharacteristic, complemented
253#1723C2×C2911yescharacteristic, complemented
254#1695C2×C2911yescharacteristic, complemented
255#1684C2×C2911yescharacteristic, complemented
256#1676C2×C2911yescharacteristic, complemented
257#1671C2×C2911yescharacteristic, complemented
258#1643C2×C2911yescharacteristic, complemented
259#1638C2×C2911yescharacteristic, complemented
260#1632C2×C2911yescharacteristic, complemented
261#1632C2×C2911yescharacteristic, complemented
262#1581C2×C2911yescharacteristic
263#1579C2×C2911yescharacteristic, complemented
264C22×C29—22no—
265C22×C29—41no—
266C22×C29—41no—
267C22×C29—41no—
268C22×C29—41no—
269C22×C29—41no—
270C22×C29D4211yescharacteristic
271C4×C29—21no—
272C4×C29—41no—
273C4×C29—41no—
274C4×C29—41no—
275C4×C29—41no—
276C4×C29—41no—
277C4×C29—41no—
278C4×C29—81no—
279C4×C29—81no—
280C4×C29—81no—
281C4×C29—81no—
282C4×C29C2×#13511yescharacteristic
283C4×C29C2×#13711yescharacteristic
284C4×C29#57811yescharacteristic
285C4×C29#57811yescharacteristic
286#556C22×C2911yescharacteristic
287#554C22×C2911yescharacteristic
288#554C22×C2911yescharacteristic
289#554C22×C2911yescharacteristic
290#500C22×C2911yescharacteristic
291#500C22×C2911yescharacteristic
292#499—21no—
293#498C22×C2911yescharacteristic
294#494C22×C2911yescharacteristic
295#488—21no—
296#487C22×C2911yescharacteristic
297#487C22×C2911yescharacteristic
298#485—21no—
299#484—21no—
300#484—21no—
301#483—21no—
302#479—21no—
303#478—21no—
304#478—21no—
305#477C22×C2911yescharacteristic
306#477C22×C2911yescharacteristic
307#477C22×C2911yescharacteristic
308#476C22×C2911yescharacteristic
309#476C22×C2911yescharacteristic
310#476C22×C2911yescharacteristic
311#475C22×C2911yescharacteristic
312#470—21no—
313#467—21no—
314#463—21no—
315#461C22×C2911yescharacteristic
316C8×Q8C22×C2911yescharacteristic
317C8×Q8C22×C2911yescharacteristic
318C4×Q16C22×C2911yescharacteristic
319C4×SD16—21no—
320C4×D8—21no—
321C4×D8C22×C2911yescharacteristic
322#436C22×C2911yescharacteristic
323C8×D4C22×C2911yescharacteristic
324#428—21no—
325C2×#107—21no—
326#335C22×C2911yescharacteristic
327#334C22×C2911yescharacteristic
328#333C22×C2911yescharacteristic
329#333C22×C2911yescharacteristic
330#333C22×C2911yescharacteristic
331#332C22×C2911yescharacteristic
332Q8⋊C8C22×C2911yescharacteristic
333Q8⋊C8C22×C2911yescharacteristic
334D4⋊C8C22×C2911yescharacteristic
335D4⋊C8C22×C2911yescharacteristic
336#322C22×C2911yescharacteristic
337C2×C29—42no—
338C2×C29—81no—
339C2×C29#327011yescharacteristic
340C2×C29#328311yescharacteristic
341C2×C29#328811yescharacteristic
342C2×Q16—41no—
343C2×Q16D4×C2911yescharacteristic
344C2×SD16—21no—
345C2×D8D4×C2911yescharacteristic
346C2×M16—21no—
347C22×C8—21no—
348C4⋊Q8C23×C2911yescharacteristic
349C4⋊Q8C23×C2911yescharacteristic
350C4⋊Q8C23×C2911yescharacteristic
351C4⋊Q8C23×C2911yescharacteristic
352#126—41no—
353#125—21no—
354#125—21no—
355#125—21no—
356#124—21no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—41no—
362C22⋊Q8—41no—
363C22⋊Q8—41no—
364C4×Q8—21no—
365C4×Q8C23×C2911yescharacteristic
366C4×Q8C23×C2911yescharacteristic
367C4×D4—21no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4C23×C2911yescharacteristic
371C4×D4C23×C2911yescharacteristic
372#117—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376#107—21no—
377#107—21no—
378#107—21no—
379#107—21no—
380#107—21no—
381#107—21no—
382#107—21no—
383#107D4×C2911yescharacteristic
384#107D4×C2911yescharacteristic
385#106—21no—
386#106—21no—
387#106—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8C23×C2911yescharacteristic
394C4⋊C8C23×C2911yescharacteristic
395C4⋊C8C23×C2911yescharacteristic
396C4⋊C8C23×C2911yescharacteristic
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—41no—
405#103D4×C2911yescharacteristic
406#103D4×C2911yescharacteristic
407#102—21no—
408#102—21no—
409#102—21no—
410#102D4×C2911yescharacteristic
411#102D4×C2911yescharacteristic
412C22⋊C8—21no—
413C22⋊C8—21no—
414C4×C8—21no—
415C4×C8—21no—
416C4×C8C23×C2911yescharacteristic
417C4×C8C23×C2911yescharacteristic
418C4×C8C23×C2911yescharacteristic
419C29#1986511yescharacteristic, direct product factor, Sylow
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8C2×D4×C2911yescharacteristic
425C2×Q8C2×D4×C2911yescharacteristic
426C2×D4C2×D4×C2911yescharacteristic
427C2×D4C2×D4×C2911yescharacteristic
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433Q16—22no—
434Q16—82no—
435SD16—42no—
436D8—22no—
437M16—42no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—42no—
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—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4C2×D4×C2911yescharacteristic
466C4⋊C4C2×D4×C2911yescharacteristic
467C4⋊C4C2×D4×C2911yescharacteristic
468C4⋊C4C2×D4×C2911yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C42—21no—
477C42—21no—
478C42—41no—
479C42C24×C2911yescharacteristic
480C23—21no—
481C23—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—41no—
487Q8—41no—
488Q8—81no—
489Q8—81no—
490Q8—81no—
491D4—21no—
492D4—21no—
493D4—21no—
494D4C29×#13712yes—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—161no—
510C2×C4—161no—
511C2×C4—161no—
512C2×C4C22×D4×C2911yescharacteristic
513C2×C4C22×D4×C2911yescharacteristic
514C2×C4C29×H(5,𝔽2)11yescharacteristic
515C8—21no—
516C8—21no—
517C8—21no—
518C8—41no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8C29×#13512yes—
524C22—22no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22D42×C2911yescharacteristic
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—81no—
539C4—81no—
540C4—81no—
541C4—81no—
542C4C2×C29×#13511yescharacteristic
543C4C2×C29×#13711yescharacteristic
544C4C29×#57811yescharacteristic
545C4C29×#57811yescharacteristic
546C2—42no—
547C2—81no—
548C2C29×#327011yescharacteristic
549C2C29×#328311yescharacteristic
550C2C29×#328811yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC2×D8×C29D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#3356C2semidirect
4. C29×#3338C2semidirect
5. C29×#1723C2semidirect
6. C29×#1695C2semidirect
7. C29×#1684C2semidirect
8. C29×#1676C2semidirect
9. C29×#1671C2semidirect
10. C29×#1643C2semidirect
11. C29×#1638C2semidirect
12. C29×#1632C2semidirect
13. C29×#1632C2semidirect
15. C29×#1579C2semidirect
204. #19865C29direct (N × H)
251. #3356C2×C29semidirect
252. #3338C2×C29semidirect
253. #1723C2×C29semidirect
254. #1695C2×C29semidirect
255. #1684C2×C29semidirect
256. #1676C2×C29semidirect
257. #1671C2×C29semidirect
258. #1643C2×C29semidirect
259. #1638C2×C29semidirect
260. #1632C2×C29semidirect
261. #1632C2×C29semidirect
263. #1579C2×C29semidirect
419. C29#19865direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33802
C29×#33602
C29×#33562
C29×#33382
C29×#17232
C29×#16952
C29×#16842
C29×#16762
C29×#16712
C29×#16432
C29×#16382
C29×#16322
C29×#15812
C29×#15792
#1986529