Finite Group Databasebeta

← C29×#19249 #20314149

Subgroups — C29×#19249 #20314149

Order 7424.

568 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×#3248C211yesmaximal, characteristic
2C29×#3233C211yesmaximal, characteristic
3C29×#3185C211yesmaximal, characteristic, complemented
4C29×#2969C211yesmaximal, characteristic
5C29×#1703C211yesmaximal, characteristic, complemented
6C29×#1699C211yesmaximal, characteristic, complemented
7C29×#1692C211yesmaximal, characteristic, complemented
8C29×#1690C211yesmaximal, characteristic, complemented
9C29×#1684C211yesmaximal, characteristic, complemented
10C29×#1680C211yesmaximal, characteristic, complemented
11C29×#1671C211yesmaximal, characteristic, complemented
12C29×#1669C211yesmaximal, characteristic, complemented
13C29×#1565C211yesmaximal, characteristic, complemented
14C29×#1544C211yesmaximal, characteristic, complemented
15C29×#1542C211yesmaximal, characteristic, complemented
16C29×#533C2211yescharacteristic
17C29×#533C2211yescharacteristic
18C29×#529C2211yescharacteristic
19C29×#499—21no—
20C29×#498C2211yescharacteristic
21C29×#494C2211yescharacteristic
22C29×#488—21no—
23C29×#487C2211yescharacteristic
24C29×#487C2211yescharacteristic
25C29×#485—21no—
26C29×#482—21no—
27C29×#479—21no—
28C29×#477C2211yescharacteristic
29C29×#476C2211yescharacteristic
30C29×#475C2211yescharacteristic
31C29×#475C2211yescharacteristic
32C29×#474C2211yescharacteristic
33C29×#474C2211yescharacteristic
34C29×#470—21no—
35C29×#470—21no—
36C29×#467—21no—
37C29×#465—21no—
38C29×#464—21no—
39C29×#462C2211yescharacteristic
40C29×#461C2211yescharacteristic
41C29×#446C2211yescharacteristic
42C8×Q8×C29C2211yescharacteristic
43C29×#441—21no—
44C29×#441—21no—
45C29×#436—21no—
46C29×#436C2211yescharacteristic
47C29×#435—21no—
48C8×D4×C29C2211yescharacteristic
49C29×#433—21no—
50C29×#431C2211yescharacteristic
51C29×#431C2211yescharacteristic
52C2×C29×C4⋊C8C2211yescharacteristic
53C29×#405—21no—
54C4×M16×C29C2211yescharacteristic
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×#332C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#332C2211yescharacteristic
66C29×#332C2211yescharacteristic
67C2×Q16×C29—21no—
68C2×Q16×C29—21no—
69C2×Q16×C29—21no—
70C2×SD16×C29—21no—
71C2×M16×C29—21no—
72C2×M16×C29D411yescharacteristic
73C2×M16×C29D411yescharacteristic
74C22×C8×C29—21no—
75C22×C8×C29—21no—
76C29×C4⋊Q8C2311yescharacteristic
77C29×C4⋊Q8C2311yescharacteristic
78C29×C4⋊Q8C2311yescharacteristic
79C29×C4⋊Q8C2311yescharacteristic
80C29×#126—21no—
81C29×#125—21no—
82C29×#125—21no—
83C29×#125D411yescharacteristic
84C29×#124D411yescharacteristic
85C29×#123—21no—
86C29×C22⋊Q8—21no—
87C29×C22⋊Q8—21no—
88C29×C22⋊Q8—21no—
89C29×C22⋊Q8—21no—
90C29×C22⋊Q8D411yescharacteristic
91C29×#121D411yescharacteristic
92C4×Q8×C29—21no—
93C4×Q8×C29—21no—
94C4×Q8×C29—21no—
95C4×Q8×C29—21no—
96C4×Q8×C29C2311yescharacteristic
97C4×D4×C29—21no—
98C4×D4×C29C2311yescharacteristic
99C29×#117—21no—
100C29×#117—21no—
101C29×#117—21no—
102C2×C42×C29C2311yescharacteristic
103C29×#107—21no—
104C29×#107—21no—
105C29×#107—21no—
106C29×#106—21no—
107C29×#106—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×#106—21no—
111C29×C4⋊C8—21no—
112C29×C4⋊C8—21no—
113C29×C4⋊C8—21no—
114C29×C4⋊C8C2311yescharacteristic
115C29×C4⋊C8C2311yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×#103—21no—
121C29×#103—21no—
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—21no—
126C29×#103—21no—
127C29×#103—21no—
128C29×#103—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×C22⋊C8—21no—
133C29×C22⋊C8—21no—
134C29×C22⋊C8—21no—
135C29×C22⋊C8—21no—
136C29×#97—21no—
137C29×#97D411yescharacteristic
138C29×#97D411yescharacteristic
139C4×C8×C29—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—42no—
156Q16×C29—42no—
157Q16×C29—81no—
158SD16×C29—81no—
159M16×C29—22no—
160M16×C29—41no—
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—21no—
168C2×C8×C29—42no—
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—21no—
186C4⋊C4×C29—41no—
187C4⋊C4×C29—41no—
188C4⋊C4×C29—41no—
189C4⋊C4×C29—41no—
190C4⋊C4×C29C2×D411yescharacteristic
191C4⋊C4×C29C2×D411yescharacteristic
192C22⋊C4×C29—21no—
193C22⋊C4×C29—21no—
194C22⋊C4×C29—21no—
195C22⋊C4×C29—21no—
196C22⋊C4×C29—21no—
197C22⋊C4×C29—41no—
198C22⋊C4×C29—41no—
199C42×C29—21no—
200C42×C29—41no—
201C42×C29—41no—
202C42×C29C2×D411yescharacteristic
203C42×C29C2×D411yescharacteristic
204C42×C29#4111yescharacteristic
205C42×C29C2411yescharacteristic
206#19249C2911yesmaximal, characteristic, direct product factor, Sylow
207C23×C29—21no—
208C23×C29#12111yescharacteristic
209Q8×C29—21no—
210Q8×C29—21no—
211Q8×C29—41no—
212Q8×C29—41no—
213Q8×C29—41no—
214Q8×C29—41no—
215Q8×C29—41no—
216Q8×C29—41no—
217Q8×C29—81no—
218D4×C29—21no—
219D4×C29—21no—
220D4×C29—81no—
221C2×C4×C29—21no—
222C2×C4×C29—21no—
223C2×C4×C29—21no—
224C2×C4×C29—21no—
225C2×C4×C29—21no—
226C2×C4×C29—21no—
227C2×C4×C29—21no—
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—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—41no—
245C8×C29—41no—
246C8×C29—41no—
247C8×C29—41no—
248C8×C29—41no—
249C8×C29—41no—
250C8×C29#13512yes—
251#3248C2×C2911yescharacteristic
252#3233C2×C2911yescharacteristic
253#3185C2×C2911yescharacteristic, complemented
254#2969C2×C2911yescharacteristic
255#1703C2×C2911yescharacteristic, complemented
256#1699C2×C2911yescharacteristic, complemented
257#1692C2×C2911yescharacteristic, complemented
258#1690C2×C2911yescharacteristic, complemented
259#1684C2×C2911yescharacteristic, complemented
260#1680C2×C2911yescharacteristic, complemented
261#1671C2×C2911yescharacteristic, complemented
262#1669C2×C2911yescharacteristic, complemented
263#1565C2×C2911yescharacteristic, complemented
264#1544C2×C2911yescharacteristic, complemented
265#1542C2×C2911yescharacteristic, complemented
266C22×C29—21no—
267C22×C29—21no—
268C22×C29—21no—
269C22×C29—41no—
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×#13511yescharacteristic
285C4×C29#57511yescharacteristic
286C4×C29#57711yescharacteristic
287C4×C29#57811yescharacteristic
288#533C22×C2911yescharacteristic
289#533C22×C2911yescharacteristic
290#529C22×C2911yescharacteristic
291#499—21no—
292#498C22×C2911yescharacteristic
293#494C22×C2911yescharacteristic
294#488—21no—
295#487C22×C2911yescharacteristic
296#487C22×C2911yescharacteristic
297#485—21no—
298#482—21no—
299#479—21no—
300#477C22×C2911yescharacteristic
301#476C22×C2911yescharacteristic
302#475C22×C2911yescharacteristic
303#475C22×C2911yescharacteristic
304#474C22×C2911yescharacteristic
305#474C22×C2911yescharacteristic
306#470—21no—
307#470—21no—
308#467—21no—
309#465—21no—
310#464—21no—
311#462C22×C2911yescharacteristic
312#461C22×C2911yescharacteristic
313#446C22×C2911yescharacteristic
314C8×Q8C22×C2911yescharacteristic
315#441—21no—
316#441—21no—
317#436—21no—
318#436C22×C2911yescharacteristic
319#435—21no—
320C8×D4C22×C2911yescharacteristic
321#433—21no—
322#431C22×C2911yescharacteristic
323#431C22×C2911yescharacteristic
324C2×C4⋊C8C22×C2911yescharacteristic
325#405—21no—
326C4×M16C22×C2911yescharacteristic
327#335C22×C2911yescharacteristic
328#335C22×C2911yescharacteristic
329#334C22×C2911yescharacteristic
330#334C22×C2911yescharacteristic
331#333C22×C2911yescharacteristic
332#333C22×C2911yescharacteristic
333#332C22×C2911yescharacteristic
334#332C22×C2911yescharacteristic
335#332C22×C2911yescharacteristic
336#332C22×C2911yescharacteristic
337#332C22×C2911yescharacteristic
338#332C22×C2911yescharacteristic
339C2×C29—41no—
340C2×C29—81no—
341C2×C29#303511yescharacteristic
342C2×C29#306311yescharacteristic
343C2×C29#306911yescharacteristic
344C2×Q16—21no—
345C2×Q16—21no—
346C2×Q16—21no—
347C2×SD16—21no—
348C2×M16—21no—
349C2×M16D4×C2911yescharacteristic
350C2×M16D4×C2911yescharacteristic
351C22×C8—21no—
352C22×C8—21no—
353C4⋊Q8C23×C2911yescharacteristic
354C4⋊Q8C23×C2911yescharacteristic
355C4⋊Q8C23×C2911yescharacteristic
356C4⋊Q8C23×C2911yescharacteristic
357#126—21no—
358#125—21no—
359#125—21no—
360#125D4×C2911yescharacteristic
361#124D4×C2911yescharacteristic
362#123—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8D4×C2911yescharacteristic
368#121D4×C2911yescharacteristic
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8C23×C2911yescharacteristic
374C4×D4—21no—
375C4×D4C23×C2911yescharacteristic
376#117—21no—
377#117—21no—
378#117—21no—
379C2×C42C23×C2911yescharacteristic
380#107—21no—
381#107—21no—
382#107—21no—
383#106—21no—
384#106—21no—
385#106—21no—
386#106—21no—
387#106—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8C23×C2911yescharacteristic
392C4⋊C8C23×C2911yescharacteristic
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—21no—
405#103—21no—
406#102—21no—
407#102—21no—
408#102—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413#97—21no—
414#97D4×C2911yescharacteristic
415#97D4×C2911yescharacteristic
416C4×C8—21no—
417C4×C8—21no—
418C4×C8—21no—
419C4×C8C23×C2911yescharacteristic
420C4×C8C23×C2911yescharacteristic
421C29#1924911yescharacteristic, direct product factor, Sylow
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8C2×D4×C2911yescharacteristic
427C2×D4—21no—
428C2×D4C2×D4×C2911yescharacteristic
429C22×C4—21no—
430C22×C4C2×D4×C2911yescharacteristic
431C22×C4C2×D4×C2911yescharacteristic
432C22×C4#41×C2911yescharacteristic
433Q16—42no—
434Q16—42no—
435Q16—81no—
436SD16—81no—
437M16—22no—
438M16—41no—
439M16—42no—
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×C8C2×D4×C2911yescharacteristic
449C2×C8C2×D4×C2911yescharacteristic
450C2×C8C2×D4×C2911yescharacteristic
451C2×C8C2×D4×C2911yescharacteristic
452C4⋊C4—21no—
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—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4C2×D4×C2911yescharacteristic
469C4⋊C4C2×D4×C2911yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C42—21no—
478C42—41no—
479C42—41no—
480C42C2×D4×C2911yescharacteristic
481C42C2×D4×C2911yescharacteristic
482C42#41×C2911yescharacteristic
483C42C24×C2911yescharacteristic
484C23—21no—
485C23C29×#12111yescharacteristic
486Q8—21no—
487Q8—21no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495D4—21no—
496D4—21no—
497D4—81no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
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—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8C29×#13512yes—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—41no—
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×#13511yescharacteristic
547C4C29×#57511yescharacteristic
548C4C29×#57711yescharacteristic
549C4C29×#57811yescharacteristic
550C2—41no—
551C2—81no—
552C2C29×#303511yescharacteristic
553C2C29×#306311yescharacteristic
554C2C29×#306911yescharacteristic
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×#3185C2semidirect
5. C29×#1703C2semidirect
6. C29×#1699C2semidirect
7. C29×#1692C2semidirect
8. C29×#1690C2semidirect
9. C29×#1684C2semidirect
10. C29×#1680C2semidirect
11. C29×#1671C2semidirect
12. C29×#1669C2semidirect
13. C29×#1565C2semidirect
14. C29×#1544C2semidirect
15. C29×#1542C2semidirect
206. #19249C29direct (N × H)
253. #3185C2×C29semidirect
255. #1703C2×C29semidirect
256. #1699C2×C29semidirect
257. #1692C2×C29semidirect
258. #1690C2×C29semidirect
259. #1684C2×C29semidirect
260. #1680C2×C29semidirect
261. #1671C2×C29semidirect
262. #1669C2×C29semidirect
263. #1565C2×C29semidirect
264. #1544C2×C29semidirect
265. #1542C2×C29semidirect
421. C29#19249direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32482
C29×#32332
C29×#31852
C29×#29692
C29×#17032
C29×#16992
C29×#16922
C29×#16902
C29×#16842
C29×#16802
C29×#16712
C29×#16692
C29×#15652
C29×#15442
C29×#15422
#1924929