Finite Group Databasebeta

← C29×#19487 #20314387

Subgroups — C29×#19487 #20314387

Order 7424.

576 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3231C211yesmaximal, characteristic, complemented
2C29×#3116C211yesmaximal, characteristic
3C29×#3076C211yesmaximal, characteristic
4C29×#2990C211yesmaximal, characteristic
5C29×#1704C211yesmaximal, characteristic, complemented
6C29×#1700C211yesmaximal, characteristic, complemented
7C29×#1696C211yesmaximal, characteristic, complemented
8C29×#1692C211yesmaximal, characteristic, complemented
9C29×#1683C211yesmaximal, characteristic, complemented
10C29×#1679C211yesmaximal, characteristic, complemented
11C29×#1675C211yesmaximal, characteristic, complemented
12C29×#1671C211yesmaximal, characteristic, complemented
13C29×#1573C211yesmaximal, characteristic, complemented
14C29×#1559C211yesmaximal, characteristic, complemented
15C29×#1550C211yesmaximal, characteristic, complemented
16C29×#533C2211yescharacteristic
17C29×#533C2211yescharacteristic
18C4×#41×C29C2211yescharacteristic
19C29×#500C2211yescharacteristic
20C29×#498C2211yescharacteristic
21C29×#487C2211yescharacteristic
22C29×#487C2211yescharacteristic
23C29×#485—21no—
24C29×#485—21no—
25C29×#485—21no—
26C29×#479—21no—
27C29×#479—21no—
28C29×#479—21no—
29C29×#478—21no—
30C29×#477C2211yescharacteristic
31C29×#477C2211yescharacteristic
32C29×#476C2211yescharacteristic
33C29×#476C2211yescharacteristic
34C29×#475C2211yescharacteristic
35C29×#474C2211yescharacteristic
36C29×#462C2211yescharacteristic
37C29×#461C2211yescharacteristic
38C29×#452—21no—
39C29×#446C2211yescharacteristic
40C29×#446C2211yescharacteristic
41C29×#441—21no—
42C29×#440—21no—
43C29×#435—21no—
44C29×#435—21no—
45C8×D4×C29C2211yescharacteristic
46C8×D4×C29C2211yescharacteristic
47C29×#432—21no—
48C29×#432C2211yescharacteristic
49C29×#431C2211yescharacteristic
50C29×#427—21no—
51C29×#423C2211yescharacteristic
52C2×C29×C4⋊C8—21no—
53C2×C29×C4⋊C8C2211yescharacteristic
54C29×#416—21no—
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#333C2211yescharacteristic
62C29×#333C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#332C2211yescharacteristic
66C29×#332C2211yescharacteristic
67C2×#41×C29D411yescharacteristic
68C2×Q16×C29—21no—
69C2×SD16×C29—21no—
70C2×M16×C29—21no—
71C22×C8×C29—21no—
72C22×C8×C29—21no—
73C22×C8×C29—21no—
74C29×C4⋊Q8C2311yescharacteristic
75C29×C4⋊Q8C2311yescharacteristic
76C29×C4⋊Q8C2311yescharacteristic
77C29×C4⋊Q8C2311yescharacteristic
78C29×#125—21no—
79C29×#125—21no—
80C29×C22⋊Q8—21no—
81C29×C22⋊Q8—21no—
82C29×C22⋊Q8—21no—
83C29×C22⋊Q8—21no—
84C4×Q8×C29—21no—
85C4×Q8×C29—21no—
86C4×Q8×C29—21no—
87C4×Q8×C29—21no—
88C4×Q8×C29D411yescharacteristic
89C4×Q8×C29C2311yescharacteristic
90C4×D4×C29—21no—
91C4×D4×C29—21no—
92C4×D4×C29D411yescharacteristic
93C4×D4×C29C2311yescharacteristic
94C29×#117—21no—
95C29×#117—21no—
96C29×#117—21no—
97C29×#117D411yescharacteristic
98C2×C42×C29—21no—
99C2×C42×C29C2311yescharacteristic
100C29×#107—21no—
101C29×#107—21no—
102C29×#107—21no—
103C29×#107—21no—
104C29×#107—21no—
105C29×#106—21no—
106C29×#106—21no—
107C29×#106—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×C4⋊C8—21no—
111C29×C4⋊C8—21no—
112C29×C4⋊C8—21no—
113C29×C4⋊C8—21no—
114C29×C4⋊C8D411yescharacteristic
115C29×C4⋊C8D411yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
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—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×C22⋊C8—21no—
135C29×C22⋊C8—21no—
136C29×C22⋊C8—21no—
137C29×C22⋊C8D411yescharacteristic
138C29×C22⋊C8D411yescharacteristic
139C29×#97—21no—
140C29×#97—21no—
141C29×#97—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144#41×C29—22no—
145#41×C29—41no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29C2×D411yescharacteristic
151C2×D4×C29—21no—
152C2×D4×C29C2×D411yescharacteristic
153C22×C4×C29—21no—
154C22×C4×C29—21no—
155C22×C4×C29—21no—
156C22×C4×C29C2×D411yescharacteristic
157C22×C4×C29C2×D411yescharacteristic
158C22×C4×C29#4111yescharacteristic
159Q16×C29—42no—
160SD16×C29—42no—
161M16×C29—81no—
162C2×C8×C29—21no—
163C2×C8×C29—21no—
164C2×C8×C29—21no—
165C2×C8×C29—21no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—42no—
169C2×C8×C29—81no—
170C2×C8×C29—81no—
171C2×C8×C29C2×D411yescharacteristic
172C2×C8×C29C2×D411yescharacteristic
173C2×C8×C29C2×D411yescharacteristic
174C2×C8×C29C2×D411yescharacteristic
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×C29C2×D411yescharacteristic
190C4⋊C4×C29C2×D411yescharacteristic
191C22⋊C4×C29—21no—
192C22⋊C4×C29—21no—
193C22⋊C4×C29—21no—
194C22⋊C4×C29—41no—
195C22⋊C4×C29—41no—
196C42×C29—21no—
197C42×C29—21no—
198C42×C29—21no—
199C42×C29—41no—
200C42×C29—41no—
201C42×C29C2×D411yescharacteristic
202C42×C29C2×D411yescharacteristic
203C42×C29#4111yescharacteristic
204C42×C29C2411yescharacteristic
205#19487C2911yesmaximal, characteristic, direct product factor, Sylow
206C23×C29—21no—
207C23×C29#12111yescharacteristic
208Q8×C29—21no—
209Q8×C29—21no—
210Q8×C29—41no—
211Q8×C29—41no—
212Q8×C29—41no—
213Q8×C29—41no—
214Q8×C29—81no—
215Q8×C29—81no—
216D4×C29—21no—
217D4×C29—42no—
218D4×C29#13712yes—
219C2×C4×C29—21no—
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—42no—
228C2×C4×C29—42no—
229C2×C4×C29—41no—
230C2×C4×C29—41no—
231C2×C4×C29—41no—
232C2×C4×C29—41no—
233C2×C4×C29—41no—
234C2×C4×C29—41no—
235C2×C4×C29#12111yescharacteristic
236C2×C4×C29#12111yescharacteristic
237C2×C4×C29#12111yescharacteristic
238C2×C4×C29C22×D411yescharacteristic
239C2×C4×C29C22×D411yescharacteristic
240C2×C4×C29C2×#4111yescharacteristic
241C8×C29—21no—
242C8×C29—21no—
243C8×C29—21no—
244C8×C29—21no—
245C8×C29—41no—
246C8×C29—41no—
247C8×C29—41no—
248C8×C29—41no—
249C8×C29—41no—
250C8×C29—41no—
251#3231C2×C2911yescharacteristic, complemented
252#3116C2×C2911yescharacteristic
253#3076C2×C2911yescharacteristic
254#2990C2×C2911yescharacteristic
255#1704C2×C2911yescharacteristic, complemented
256#1700C2×C2911yescharacteristic, complemented
257#1696C2×C2911yescharacteristic, complemented
258#1692C2×C2911yescharacteristic, complemented
259#1683C2×C2911yescharacteristic, complemented
260#1679C2×C2911yescharacteristic, complemented
261#1675C2×C2911yescharacteristic, complemented
262#1671C2×C2911yescharacteristic, complemented
263#1573C2×C2911yescharacteristic, complemented
264#1559C2×C2911yescharacteristic, complemented
265#1550C2×C2911yescharacteristic, complemented
266C22×C29—21no—
267C22×C29—21no—
268C22×C29—22no—
269C22×C29—21no—
270C22×C29—41no—
271C22×C29—41no—
272C22×C29C2×#12111yescharacteristic
273C4×C29—21no—
274C4×C29—21no—
275C4×C29—21no—
276C4×C29—21no—
277C4×C29—41no—
278C4×C29—41no—
279C4×C29—41no—
280C4×C29—81no—
281C4×C29—81no—
282C4×C29—81no—
283C4×C29—81no—
284C4×C29C2×#13711yescharacteristic
285C4×C29#57511yescharacteristic
286C4×C29#57711yescharacteristic
287C4×C29#57811yescharacteristic
288#533C22×C2911yescharacteristic
289#533C22×C2911yescharacteristic
290C4×#41C22×C2911yescharacteristic
291#500C22×C2911yescharacteristic
292#498C22×C2911yescharacteristic
293#487C22×C2911yescharacteristic
294#487C22×C2911yescharacteristic
295#485—21no—
296#485—21no—
297#485—21no—
298#479—21no—
299#479—21no—
300#479—21no—
301#478—21no—
302#477C22×C2911yescharacteristic
303#477C22×C2911yescharacteristic
304#476C22×C2911yescharacteristic
305#476C22×C2911yescharacteristic
306#475C22×C2911yescharacteristic
307#474C22×C2911yescharacteristic
308#462C22×C2911yescharacteristic
309#461C22×C2911yescharacteristic
310#452—21no—
311#446C22×C2911yescharacteristic
312#446C22×C2911yescharacteristic
313#441—21no—
314#440—21no—
315#435—21no—
316#435—21no—
317C8×D4C22×C2911yescharacteristic
318C8×D4C22×C2911yescharacteristic
319#432—21no—
320#432C22×C2911yescharacteristic
321#431C22×C2911yescharacteristic
322#427—21no—
323#423C22×C2911yescharacteristic
324C2×C4⋊C8—21no—
325C2×C4⋊C8C22×C2911yescharacteristic
326#416—21no—
327#335C22×C2911yescharacteristic
328#335C22×C2911yescharacteristic
329#334C22×C2911yescharacteristic
330#334C22×C2911yescharacteristic
331#333C22×C2911yescharacteristic
332#333C22×C2911yescharacteristic
333#333C22×C2911yescharacteristic
334#333C22×C2911yescharacteristic
335#332C22×C2911yescharacteristic
336#332C22×C2911yescharacteristic
337#332C22×C2911yescharacteristic
338#332C22×C2911yescharacteristic
339C2×C29—41no—
340C2×C29—42no—
341C2×C29#304611yescharacteristic
342C2×C29#305611yescharacteristic
343C2×C29#306711yescharacteristic
344C2×#41D4×C2911yescharacteristic
345C2×Q16—21no—
346C2×SD16—21no—
347C2×M16—21no—
348C22×C8—21no—
349C22×C8—21no—
350C22×C8—21no—
351C4⋊Q8C23×C2911yescharacteristic
352C4⋊Q8C23×C2911yescharacteristic
353C4⋊Q8C23×C2911yescharacteristic
354C4⋊Q8C23×C2911yescharacteristic
355#125—21no—
356#125—21no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8D4×C2911yescharacteristic
366C4×Q8C23×C2911yescharacteristic
367C4×D4—21no—
368C4×D4—21no—
369C4×D4D4×C2911yescharacteristic
370C4×D4C23×C2911yescharacteristic
371#117—21no—
372#117—21no—
373#117—21no—
374#117D4×C2911yescharacteristic
375C2×C42—21no—
376C2×C42C23×C2911yescharacteristic
377#107—21no—
378#107—21no—
379#107—21no—
380#107—21no—
381#107—21no—
382#106—21no—
383#106—21no—
384#106—21no—
385#106—21no—
386#106—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8D4×C2911yescharacteristic
392C4⋊C8D4×C2911yescharacteristic
393C4⋊C8C23×C2911yescharacteristic
394C4⋊C8C23×C2911yescharacteristic
395C4⋊C8C23×C2911yescharacteristic
396C4⋊C8C23×C2911yescharacteristic
397C4⋊C8C23×C2911yescharacteristic
398C4⋊C8C23×C2911yescharacteristic
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#102—21no—
409#102—21no—
410#102—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8D4×C2911yescharacteristic
415C22⋊C8D4×C2911yescharacteristic
416#97—21no—
417#97—21no—
418#97—21no—
419C4×C8C23×C2911yescharacteristic
420C4×C8C23×C2911yescharacteristic
421C29#1948711yescharacteristic, direct product factor, Sylow
422#41—22no—
423#41—41no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8C2×D4×C2911yescharacteristic
429C2×D4—21no—
430C2×D4C2×D4×C2911yescharacteristic
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4C2×D4×C2911yescharacteristic
435C22×C4C2×D4×C2911yescharacteristic
436C22×C4#41×C2911yescharacteristic
437Q16—42no—
438SD16—42no—
439M16—81no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—42no—
447C2×C8—81no—
448C2×C8—81no—
449C2×C8C2×D4×C2911yescharacteristic
450C2×C8C2×D4×C2911yescharacteristic
451C2×C8C2×D4×C2911yescharacteristic
452C2×C8C2×D4×C2911yescharacteristic
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4C2×D4×C2911yescharacteristic
468C4⋊C4C2×D4×C2911yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—41no—
478C42—41no—
479C42C2×D4×C2911yescharacteristic
480C42C2×D4×C2911yescharacteristic
481C42#41×C2911yescharacteristic
482C42C24×C2911yescharacteristic
483C23—21no—
484C23C29×#12111yescharacteristic
485Q8—21no—
486Q8—21no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—81no—
492Q8—81no—
493D4—21no—
494D4—42no—
495D4C29×#13712yes—
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—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4C29×#12111yescharacteristic
513C2×C4C29×#12111yescharacteristic
514C2×C4C29×#12111yescharacteristic
515C2×C4C22×D4×C2911yescharacteristic
516C2×C4C22×D4×C2911yescharacteristic
517C2×C4C2×#41×C2911yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—21no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C22—21no—
529C22—21no—
530C22—22no—
531C22—21no—
532C22—41no—
533C22—41no—
534C22C2×C29×#12111yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—81no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4C2×C29×#13711yescharacteristic
547C4C29×#57511yescharacteristic
548C4C29×#57711yescharacteristic
549C4C29×#57811yescharacteristic
550C2—41no—
551C2—42no—
552C2C29×#304611yescharacteristic
553C2C29×#305611yescharacteristic
554C2C29×#306711yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC2×#41×C29D4
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×#3231C2semidirect
5. C29×#1704C2semidirect
6. C29×#1700C2semidirect
7. C29×#1696C2semidirect
8. C29×#1692C2semidirect
9. C29×#1683C2semidirect
10. C29×#1679C2semidirect
11. C29×#1675C2semidirect
12. C29×#1671C2semidirect
13. C29×#1573C2semidirect
14. C29×#1559C2semidirect
15. C29×#1550C2semidirect
205. #19487C29direct (N × H)
251. #3231C2×C29semidirect
255. #1704C2×C29semidirect
256. #1700C2×C29semidirect
257. #1696C2×C29semidirect
258. #1692C2×C29semidirect
259. #1683C2×C29semidirect
260. #1679C2×C29semidirect
261. #1675C2×C29semidirect
262. #1671C2×C29semidirect
263. #1573C2×C29semidirect
264. #1559C2×C29semidirect
265. #1550C2×C29semidirect
421. C29#19487direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32312
C29×#31162
C29×#30762
C29×#29902
C29×#17042
C29×#17002
C29×#16962
C29×#16922
C29×#16832
C29×#16792
C29×#16752
C29×#16712
C29×#15732
C29×#15592
C29×#15502
#1948729