Finite Group Databasebeta

← C29×#19587 #20314487

Subgroups — C29×#19587 #20314487

Order 7424.

550 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×#3252C211yesmaximal, characteristic
2C29×#3233C211yesmaximal, characteristic
3C29×#3231C211yesmaximal, characteristic, complemented
4C29×#2994C211yesmaximal, characteristic
5C29×#1703C211yesmaximal, characteristic, complemented
6C29×#1700C211yesmaximal, characteristic, complemented
7C29×#1696C211yesmaximal, characteristic, complemented
8C29×#1691C211yesmaximal, characteristic, complemented
9C29×#1684C211yesmaximal, characteristic, complemented
10C29×#1679C211yesmaximal, characteristic, complemented
11C29×#1675C211yesmaximal, characteristic, complemented
12C29×#1672C211yesmaximal, characteristic, complemented
13C29×#1574C211yesmaximal, characteristic, complemented
14C29×#1550C211yesmaximal, characteristic, complemented
15C29×#1542C211yesmaximal, characteristic, complemented
16C29×#533C2211yescharacteristic
17C29×#533C2211yescharacteristic
18C29×#529C2211yescharacteristic
19C29×#500C2211yescharacteristic
20C29×#499—21no—
21C29×#498C2211yescharacteristic
22C29×#488—21no—
23C29×#487C2211yescharacteristic
24C29×#487C2211yescharacteristic
25C29×#485—21no—
26C29×#485—21no—
27C29×#485—21no—
28C29×#482—21no—
29C29×#479—21no—
30C29×#479—21no—
31C29×#479—21no—
32C29×#477C2211yescharacteristic
33C29×#477C2211yescharacteristic
34C29×#476C2211yescharacteristic
35C29×#476C2211yescharacteristic
36C29×#475C2211yescharacteristic
37C29×#474C2211yescharacteristic
38C29×#470—21no—
39C29×#468—21no—
40C29×#464—21no—
41C29×#462C2211yescharacteristic
42C29×#461C2211yescharacteristic
43C29×#446C2211yescharacteristic
44C8×Q8×C29C2211yescharacteristic
45C29×#436C2211yescharacteristic
46C29×#435—21no—
47C8×D4×C29—21no—
48C8×D4×C29C2211yescharacteristic
49C29×#433—21no—
50C29×#431C2211yescharacteristic
51C29×#431C2211yescharacteristic
52C29×#424—21no—
53C29×#423C2211yescharacteristic
54C2×C29×C4⋊C8C2211yescharacteristic
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×Q16×C29—21no—
68C2×SD16×C29—21no—
69C2×M16×C29—21no—
70C2×M16×C29—21no—
71C22×C8×C29—21no—
72C22×C8×C29—21no—
73C29×C4⋊Q8C2311yescharacteristic
74C29×C4⋊Q8C2311yescharacteristic
75C29×C4⋊Q8C2311yescharacteristic
76C29×C4⋊Q8C2311yescharacteristic
77C29×#126—21no—
78C29×#125—21no—
79C29×#125—21no—
80C29×#125D411yescharacteristic
81C29×#124D411yescharacteristic
82C29×#123—21no—
83C29×C22⋊Q8—21no—
84C29×C22⋊Q8—21no—
85C29×C22⋊Q8—21no—
86C29×C22⋊Q8—21no—
87C29×C22⋊Q8D411yescharacteristic
88C29×#121D411yescharacteristic
89C4×Q8×C29—21no—
90C4×Q8×C29—21no—
91C4×Q8×C29—21no—
92C4×Q8×C29—21no—
93C4×Q8×C29C2311yescharacteristic
94C4×D4×C29—21no—
95C4×D4×C29C2311yescharacteristic
96C29×#117—21no—
97C29×#117—21no—
98C29×#117—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—
140C4×C8×C29—21no—
141C4×C8×C29—21no—
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×D4×C29—21no—
150C2×D4×C29C2×D411yescharacteristic
151C22×C4×C29—21no—
152C22×C4×C29C2×D411yescharacteristic
153C22×C4×C29C2×D411yescharacteristic
154C22×C4×C29#4111yescharacteristic
155Q16×C29—81no—
156SD16×C29—81no—
157M16×C29—81no—
158M16×C29—81no—
159C2×C8×C29—21no—
160C2×C8×C29—21no—
161C2×C8×C29—21no—
162C2×C8×C29—21no—
163C2×C8×C29—21no—
164C2×C8×C29—21no—
165C2×C8×C29—81no—
166C2×C8×C29—81no—
167C2×C8×C29C2×D411yescharacteristic
168C2×C8×C29C2×D411yescharacteristic
169C2×C8×C29C2×D411yescharacteristic
170C2×C8×C29C2×D411yescharacteristic
171C4⋊C4×C29—21no—
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—21no—
183C4⋊C4×C29—41no—
184C4⋊C4×C29—41no—
185C4⋊C4×C29—41no—
186C4⋊C4×C29—41no—
187C4⋊C4×C29C2×D411yescharacteristic
188C4⋊C4×C29C2×D411yescharacteristic
189C22⋊C4×C29—21no—
190C22⋊C4×C29—21no—
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—41no—
198C42×C29—41no—
199C42×C29C2×D411yescharacteristic
200C42×C29C2×D411yescharacteristic
201C42×C29#4111yescharacteristic
202C42×C29C2411yescharacteristic
203#19587C2911yesmaximal, characteristic, direct product factor, Sylow
204C23×C29—21no—
205C23×C29#12111yescharacteristic
206Q8×C29—21no—
207Q8×C29—21no—
208Q8×C29—41no—
209Q8×C29—41no—
210Q8×C29—41no—
211Q8×C29—41no—
212Q8×C29—81no—
213Q8×C29—81no—
214D4×C29—21no—
215D4×C29—21no—
216D4×C29—42no—
217C2×C4×C29—21no—
218C2×C4×C29—21no—
219C2×C4×C29—21no—
220C2×C4×C29—21no—
221C2×C4×C29—21no—
222C2×C4×C29—21no—
223C2×C4×C29—21no—
224C2×C4×C29—41no—
225C2×C4×C29—41no—
226C2×C4×C29—41no—
227C2×C4×C29—41no—
228C2×C4×C29—41no—
229C2×C4×C29—41no—
230C2×C4×C29—41no—
231C2×C4×C29#12111yescharacteristic
232C2×C4×C29#12111yescharacteristic
233C2×C4×C29#12111yescharacteristic
234C2×C4×C29C22×D411yescharacteristic
235C2×C4×C29C22×D411yescharacteristic
236C2×C4×C29C2×#4111yescharacteristic
237C8×C29—21no—
238C8×C29—21no—
239C8×C29—21no—
240C8×C29—21no—
241C8×C29—41no—
242C8×C29—41no—
243C8×C29—41no—
244C8×C29—41no—
245C8×C29—41no—
246C8×C29—41no—
247#3252C2×C2911yescharacteristic
248#3233C2×C2911yescharacteristic
249#3231C2×C2911yescharacteristic, complemented
250#2994C2×C2911yescharacteristic
251#1703C2×C2911yescharacteristic, complemented
252#1700C2×C2911yescharacteristic, complemented
253#1696C2×C2911yescharacteristic, complemented
254#1691C2×C2911yescharacteristic, complemented
255#1684C2×C2911yescharacteristic, complemented
256#1679C2×C2911yescharacteristic, complemented
257#1675C2×C2911yescharacteristic, complemented
258#1672C2×C2911yescharacteristic, complemented
259#1574C2×C2911yescharacteristic, complemented
260#1550C2×C2911yescharacteristic, complemented
261#1542C2×C2911yescharacteristic, complemented
262C22×C29—21no—
263C22×C29—21no—
264C22×C29—21no—
265C22×C29—41no—
266C22×C29—41no—
267C22×C29—41no—
268C22×C29C2×#12111yescharacteristic
269C4×C29—21no—
270C4×C29—21no—
271C4×C29—21no—
272C4×C29—21no—
273C4×C29—41no—
274C4×C29—41no—
275C4×C29—41no—
276C4×C29—81no—
277C4×C29—81no—
278C4×C29—81no—
279C4×C29—81no—
280C4×C29#57711yescharacteristic
281C4×C29#57711yescharacteristic
282C4×C29#57811yescharacteristic
283C4×C29#57811yescharacteristic
284#533C22×C2911yescharacteristic
285#533C22×C2911yescharacteristic
286#529C22×C2911yescharacteristic
287#500C22×C2911yescharacteristic
288#499—21no—
289#498C22×C2911yescharacteristic
290#488—21no—
291#487C22×C2911yescharacteristic
292#487C22×C2911yescharacteristic
293#485—21no—
294#485—21no—
295#485—21no—
296#482—21no—
297#479—21no—
298#479—21no—
299#479—21no—
300#477C22×C2911yescharacteristic
301#477C22×C2911yescharacteristic
302#476C22×C2911yescharacteristic
303#476C22×C2911yescharacteristic
304#475C22×C2911yescharacteristic
305#474C22×C2911yescharacteristic
306#470—21no—
307#468—21no—
308#464—21no—
309#462C22×C2911yescharacteristic
310#461C22×C2911yescharacteristic
311#446C22×C2911yescharacteristic
312C8×Q8C22×C2911yescharacteristic
313#436C22×C2911yescharacteristic
314#435—21no—
315C8×D4—21no—
316C8×D4C22×C2911yescharacteristic
317#433—21no—
318#431C22×C2911yescharacteristic
319#431C22×C2911yescharacteristic
320#424—21no—
321#423C22×C2911yescharacteristic
322C2×C4⋊C8C22×C2911yescharacteristic
323#335C22×C2911yescharacteristic
324#335C22×C2911yescharacteristic
325#334C22×C2911yescharacteristic
326#334C22×C2911yescharacteristic
327#333C22×C2911yescharacteristic
328#333C22×C2911yescharacteristic
329#333C22×C2911yescharacteristic
330#333C22×C2911yescharacteristic
331#332C22×C2911yescharacteristic
332#332C22×C2911yescharacteristic
333#332C22×C2911yescharacteristic
334#332C22×C2911yescharacteristic
335C2×C29—41no—
336C2×C29—81no—
337C2×C29#304611yescharacteristic
338C2×C29#306311yescharacteristic
339C2×C29#306711yescharacteristic
340C2×Q16—21no—
341C2×SD16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C22×C8—21no—
345C22×C8—21no—
346C4⋊Q8C23×C2911yescharacteristic
347C4⋊Q8C23×C2911yescharacteristic
348C4⋊Q8C23×C2911yescharacteristic
349C4⋊Q8C23×C2911yescharacteristic
350#126—21no—
351#125—21no—
352#125—21no—
353#125D4×C2911yescharacteristic
354#124D4×C2911yescharacteristic
355#123—21no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8D4×C2911yescharacteristic
361#121D4×C2911yescharacteristic
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8C23×C2911yescharacteristic
367C4×D4—21no—
368C4×D4C23×C2911yescharacteristic
369#117—21no—
370#117—21no—
371#117—21no—
372C2×C42C23×C2911yescharacteristic
373#107—21no—
374#107—21no—
375#107—21no—
376#107—21no—
377#107—21no—
378#106—21no—
379#106—21no—
380#106—21no—
381#106—21no—
382#106—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8D4×C2911yescharacteristic
388C4⋊C8D4×C2911yescharacteristic
389C4⋊C8C23×C2911yescharacteristic
390C4⋊C8C23×C2911yescharacteristic
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—21no—
404#102—21no—
405#102—21no—
406#102—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8D4×C2911yescharacteristic
411C22⋊C8D4×C2911yescharacteristic
412#97—21no—
413C4×C8—21no—
414C4×C8—21no—
415C4×C8C23×C2911yescharacteristic
416C4×C8C23×C2911yescharacteristic
417C29#1958711yescharacteristic, direct product factor, Sylow
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8C2×D4×C2911yescharacteristic
423C2×D4—21no—
424C2×D4C2×D4×C2911yescharacteristic
425C22×C4—21no—
426C22×C4C2×D4×C2911yescharacteristic
427C22×C4C2×D4×C2911yescharacteristic
428C22×C4#41×C2911yescharacteristic
429Q16—81no—
430SD16—81no—
431M16—81no—
432M16—81no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—81no—
440C2×C8—81no—
441C2×C8C2×D4×C2911yescharacteristic
442C2×C8C2×D4×C2911yescharacteristic
443C2×C8C2×D4×C2911yescharacteristic
444C2×C8C2×D4×C2911yescharacteristic
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
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—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4C2×D4×C2911yescharacteristic
462C4⋊C4C2×D4×C2911yescharacteristic
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C42—21no—
471C42—41no—
472C42—41no—
473C42C2×D4×C2911yescharacteristic
474C42C2×D4×C2911yescharacteristic
475C42#41×C2911yescharacteristic
476C42C24×C2911yescharacteristic
477C23—21no—
478C23C29×#12111yescharacteristic
479Q8—21no—
480Q8—21no—
481Q8—41no—
482Q8—41no—
483Q8—41no—
484Q8—41no—
485Q8—81no—
486Q8—81no—
487D4—21no—
488D4—21no—
489D4—42no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4C29×#12111yescharacteristic
505C2×C4C29×#12111yescharacteristic
506C2×C4C29×#12111yescharacteristic
507C2×C4C22×D4×C2911yescharacteristic
508C2×C4C22×D4×C2911yescharacteristic
509C2×C4C2×#41×C2911yescharacteristic
510C8—21no—
511C8—21no—
512C8—21no—
513C8—21no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—41no—
518C8—41no—
519C8—41no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22C2×C29×#12111yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4—81no—
538C4C29×#57711yescharacteristic
539C4C29×#57711yescharacteristic
540C4C29×#57811yescharacteristic
541C4C29×#57811yescharacteristic
542C2—41no—
543C2—81no—
544C2C29×#304611yescharacteristic
545C2C29×#306311yescharacteristic
546C2C29×#306711yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#121D4
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
3. C29×#3231C2semidirect
5. C29×#1703C2semidirect
6. C29×#1700C2semidirect
7. C29×#1696C2semidirect
8. C29×#1691C2semidirect
9. C29×#1684C2semidirect
10. C29×#1679C2semidirect
11. C29×#1675C2semidirect
12. C29×#1672C2semidirect
13. C29×#1574C2semidirect
14. C29×#1550C2semidirect
15. C29×#1542C2semidirect
203. #19587C29direct (N × H)
249. #3231C2×C29semidirect
251. #1703C2×C29semidirect
252. #1700C2×C29semidirect
253. #1696C2×C29semidirect
254. #1691C2×C29semidirect
255. #1684C2×C29semidirect
256. #1679C2×C29semidirect
257. #1675C2×C29semidirect
258. #1672C2×C29semidirect
259. #1574C2×C29semidirect
260. #1550C2×C29semidirect
261. #1542C2×C29semidirect
417. C29#19587direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32522
C29×#32332
C29×#32312
C29×#29942
C29×#17032
C29×#17002
C29×#16962
C29×#16912
C29×#16842
C29×#16792
C29×#16752
C29×#16722
C29×#15742
C29×#15502
C29×#15422
#1958729