Finite Group Databasebeta

← C29×#19311 #20314211

Subgroups — C29×#19311 #20314211

Order 7424.

578 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×#3185C211yesmaximal, characteristic
2C29×#3113C211yesmaximal, characteristic
3C29×#3078C211yesmaximal, characteristic
4Q8×M16×C29C211yesmaximal, characteristic
5C29×#1704C211yesmaximal, characteristic, complemented
6C29×#1700C211yesmaximal, characteristic, complemented
7C29×#1692C211yesmaximal, characteristic, complemented
8C29×#1690C211yesmaximal, characteristic, complemented
9C29×#1684C211yesmaximal, characteristic, complemented
10C29×#1680C211yesmaximal, characteristic, complemented
11C29×#1672C211yesmaximal, characteristic, complemented
12C29×#1670C211yesmaximal, characteristic, complemented
13C29×#1569C211yesmaximal, characteristic
14C29×#1561C211yesmaximal, characteristic
15C29×#1559C211yesmaximal, characteristic
16C29×#533C2211yescharacteristic
17C29×#533C2211yescharacteristic
18C2×C4×Q8×C29C2211yescharacteristic
19C29×#498C2211yescharacteristic
20C29×#494C2211yescharacteristic
21C29×#487C2211yescharacteristic
22C29×#487C2211yescharacteristic
23C29×#483—21no—
24C29×#479—21no—
25C29×#479—21no—
26C29×#477C2211yescharacteristic
27C29×#477C2211yescharacteristic
28C29×#475C2211yescharacteristic
29C29×#475C2211yescharacteristic
30C29×#475C2211yescharacteristic
31C29×#475C2211yescharacteristic
32C29×#470—21no—
33C29×#470—21no—
34C29×#462C2211yescharacteristic
35C29×#462C2211yescharacteristic
36C29×#451—21no—
37C29×#446—21no—
38C29×#446—21no—
39C29×#446C2211yescharacteristic
40C29×#446C2211yescharacteristic
41C8×Q8×C29C2211yescharacteristic
42C8×Q8×C29C2211yescharacteristic
43C29×#441—21no—
44C29×#441—21no—
45C29×#441—21no—
46C29×#441—21no—
47C29×#432C2211yescharacteristic
48C29×#428—21no—
49C29×#423—21no—
50C29×#423C2211yescharacteristic
51C29×#423C2211yescharacteristic
52C29×#419—21no—
53C4×M16×C29—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
67C22×Q8×C29D411yescharacteristic
68C2×Q16×C29—21no—
69C2×Q16×C29—21no—
70C2×Q16×C29—21no—
71C2×Q16×C29—21no—
72C2×M16×C29—21no—
73C2×M16×C29—21no—
74C2×M16×C29D411yescharacteristic
75C2×M16×C29D411yescharacteristic
76C29×C4⋊Q8C2311yescharacteristic
77C29×C4⋊Q8C2311yescharacteristic
78C29×C4⋊Q8C2311yescharacteristic
79C29×C4⋊Q8C2311yescharacteristic
80C29×#125—21no—
81C29×#125—21no—
82C29×C22⋊Q8—21no—
83C29×C22⋊Q8—21no—
84C29×C22⋊Q8—21no—
85C29×C22⋊Q8—21no—
86C4×Q8×C29—21no—
87C4×Q8×C29—21no—
88C4×Q8×C29—21no—
89C4×Q8×C29—21no—
90C4×Q8×C29—21no—
91C4×Q8×C29—21no—
92C4×Q8×C29D411yescharacteristic
93C4×Q8×C29D411yescharacteristic
94C4×Q8×C29C2311yescharacteristic
95C4×Q8×C29C2311yescharacteristic
96C29×#117—21no—
97C29×#117—21no—
98C2×C4⋊C4×C29—21no—
99C2×C4⋊C4×C29D411yescharacteristic
100C2×C42×C29—21no—
101C2×C42×C29C2311yescharacteristic
102C29×#107—21no—
103C29×#107—21no—
104C29×#106—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⋊C8—21no—
115C29×C4⋊C8—21no—
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×#103—21no—
132C29×#103—21no—
133C29×#103—21no—
134C29×C22⋊C8—21no—
135C29×#97—21no—
136C29×#97—21no—
137C29×#97—21no—
138C29×#97D411yescharacteristic
139C29×#97D411yescharacteristic
140C4×C8×C29—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C2×Q8×C29—21no—
145C2×Q8×C29—22no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29—41no—
151C2×Q8×C29C2×D411yescharacteristic
152C2×Q8×C29C2×D411yescharacteristic
153C22×C4×C29—21no—
154C22×C4×C29—21no—
155C22×C4×C29C2×D411yescharacteristic
156C22×C4×C29C2×D411yescharacteristic
157C22×C4×C29#4111yescharacteristic
158Q16×C29—42no—
159Q16×C29—42no—
160Q16×C29—42no—
161Q16×C29—42no—
162M16×C29—22no—
163M16×C29—41no—
164M16×C29—42no—
165M16×C29—42no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C2×C8×C29C2×D411yescharacteristic
173C2×C8×C29C2×D411yescharacteristic
174C2×C8×C29C2×D411yescharacteristic
175C2×C8×C29C2×D411yescharacteristic
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—21no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—41no—
190C4⋊C4×C29—41no—
191C4⋊C4×C29—41no—
192C4⋊C4×C29—41no—
193C4⋊C4×C29C2×D411yescharacteristic
194C4⋊C4×C29C2×D411yescharacteristic
195C22⋊C4×C29—41no—
196C22⋊C4×C29—41no—
197C42×C29—21no—
198C42×C29—21no—
199C42×C29—21no—
200C42×C29—21no—
201C42×C29—41no—
202C42×C29—41no—
203C42×C29C2×D411yescharacteristic
204C42×C29C2×D411yescharacteristic
205C42×C29#4111yescharacteristic
206C42×C29C2411yescharacteristic
207#19311C2911yesmaximal, characteristic, direct product factor, Sylow
208C23×C29#12111yescharacteristic
209Q8×C29—21no—
210Q8×C29—21no—
211Q8×C29—21no—
212Q8×C29—42no—
213Q8×C29—41no—
214Q8×C29—41no—
215Q8×C29—41no—
216Q8×C29—41no—
217Q8×C29—41no—
218Q8×C29—41no—
219Q8×C29—81no—
220Q8×C29#13712yes—
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—21no—
229C2×C4×C29—41no—
230C2×C4×C29—42no—
231C2×C4×C29—41no—
232C2×C4×C29—41no—
233C2×C4×C29—41no—
234C2×C4×C29—41no—
235C2×C4×C29—81no—
236C2×C4×C29#12111yescharacteristic
237C2×C4×C29#12111yescharacteristic
238C2×C4×C29#12111yescharacteristic
239C2×C4×C29C22×D411yescharacteristic
240C2×C4×C29C22×D411yescharacteristic
241C2×C4×C29C2×#4111yescharacteristic
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—
251C8×C29#13712yes—
252#3185C2×C2911yescharacteristic
253#3113C2×C2911yescharacteristic
254#3078C2×C2911yescharacteristic
255Q8×M16C2×C2911yescharacteristic
256#1704C2×C2911yescharacteristic, complemented
257#1700C2×C2911yescharacteristic, complemented
258#1692C2×C2911yescharacteristic, complemented
259#1690C2×C2911yescharacteristic, complemented
260#1684C2×C2911yescharacteristic, complemented
261#1680C2×C2911yescharacteristic, complemented
262#1672C2×C2911yescharacteristic, complemented
263#1670C2×C2911yescharacteristic, complemented
264#1569C2×C2911yescharacteristic
265#1561C2×C2911yescharacteristic
266#1559C2×C2911yescharacteristic
267C22×C29—21no—
268C22×C29—21no—
269C22×C29—21no—
270C22×C29C2×#12111yescharacteristic
271C4×C29—21no—
272C4×C29—21no—
273C4×C29—22no—
274C4×C29—21no—
275C4×C29—21no—
276C4×C29—41no—
277C4×C29—41no—
278C4×C29—41no—
279C4×C29—81no—
280C4×C29—81no—
281C4×C29—81no—
282C4×C29—81no—
283C4×C29C2×#13711yescharacteristic
284C4×C29C2×#13711yescharacteristic
285C4×C29#57511yescharacteristic
286C4×C29#57511yescharacteristic
287#533C22×C2911yescharacteristic
288#533C22×C2911yescharacteristic
289C2×C4×Q8C22×C2911yescharacteristic
290#498C22×C2911yescharacteristic
291#494C22×C2911yescharacteristic
292#487C22×C2911yescharacteristic
293#487C22×C2911yescharacteristic
294#483—21no—
295#479—21no—
296#479—21no—
297#477C22×C2911yescharacteristic
298#477C22×C2911yescharacteristic
299#475C22×C2911yescharacteristic
300#475C22×C2911yescharacteristic
301#475C22×C2911yescharacteristic
302#475C22×C2911yescharacteristic
303#470—21no—
304#470—21no—
305#462C22×C2911yescharacteristic
306#462C22×C2911yescharacteristic
307#451—21no—
308#446—21no—
309#446—21no—
310#446C22×C2911yescharacteristic
311#446C22×C2911yescharacteristic
312C8×Q8C22×C2911yescharacteristic
313C8×Q8C22×C2911yescharacteristic
314#441—21no—
315#441—21no—
316#441—21no—
317#441—21no—
318#432C22×C2911yescharacteristic
319#428—21no—
320#423—21no—
321#423C22×C2911yescharacteristic
322#423C22×C2911yescharacteristic
323#419—21no—
324C4×M16—21no—
325C4×M16C22×C2911yescharacteristic
326#335C22×C2911yescharacteristic
327#335C22×C2911yescharacteristic
328#334C22×C2911yescharacteristic
329#334C22×C2911yescharacteristic
330#333C22×C2911yescharacteristic
331#333C22×C2911yescharacteristic
332#332C22×C2911yescharacteristic
333#332C22×C2911yescharacteristic
334#332C22×C2911yescharacteristic
335#332C22×C2911yescharacteristic
336#332C22×C2911yescharacteristic
337#332C22×C2911yescharacteristic
338C2×C29—41no—
339C2×C29#303711yescharacteristic
340C2×C29#305611yescharacteristic
341C2×C29#306911yescharacteristic
342C22×Q8D4×C2911yescharacteristic
343C2×Q16—21no—
344C2×Q16—21no—
345C2×Q16—21no—
346C2×Q16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16D4×C2911yescharacteristic
350C2×M16D4×C2911yescharacteristic
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×Q8—21no—
366C4×Q8—21no—
367C4×Q8D4×C2911yescharacteristic
368C4×Q8D4×C2911yescharacteristic
369C4×Q8C23×C2911yescharacteristic
370C4×Q8C23×C2911yescharacteristic
371#117—21no—
372#117—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4D4×C2911yescharacteristic
375C2×C42—21no—
376C2×C42C23×C2911yescharacteristic
377#107—21no—
378#107—21no—
379#106—21no—
380#106—21no—
381#106—21no—
382#106—21no—
383#106—21no—
384#106—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—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#103—21no—
407#103—21no—
408#103—21no—
409C22⋊C8—21no—
410#97—21no—
411#97—21no—
412#97—21no—
413#97D4×C2911yescharacteristic
414#97D4×C2911yescharacteristic
415C4×C8—21no—
416C4×C8—21no—
417C4×C8C23×C2911yescharacteristic
418C4×C8C23×C2911yescharacteristic
419C29#1931111yescharacteristic, direct product factor, Sylow
420C2×Q8—21no—
421C2×Q8—22no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—41no—
427C2×Q8C2×D4×C2911yescharacteristic
428C2×Q8C2×D4×C2911yescharacteristic
429C22×C4—21no—
430C22×C4—21no—
431C22×C4C2×D4×C2911yescharacteristic
432C22×C4C2×D4×C2911yescharacteristic
433C22×C4#41×C2911yescharacteristic
434Q16—42no—
435Q16—42no—
436Q16—42no—
437Q16—42no—
438M16—22no—
439M16—41no—
440M16—42no—
441M16—42no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
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—21no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4C2×D4×C2911yescharacteristic
470C4⋊C4C2×D4×C2911yescharacteristic
471C22⋊C4—41no—
472C22⋊C4—41no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—41no—
478C42—41no—
479C42C2×D4×C2911yescharacteristic
480C42C2×D4×C2911yescharacteristic
481C42#41×C2911yescharacteristic
482C42C24×C2911yescharacteristic
483C23C29×#12111yescharacteristic
484Q8—21no—
485Q8—21no—
486Q8—21no—
487Q8—42no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8C29×#13712yes—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—81no—
511C2×C4C29×#12111yescharacteristic
512C2×C4C29×#12111yescharacteristic
513C2×C4C29×#12111yescharacteristic
514C2×C4C22×D4×C2911yescharacteristic
515C2×C4C22×D4×C2911yescharacteristic
516C2×C4C2×#41×C2911yescharacteristic
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8C29×#13712yes—
527C22—21no—
528C22—21no—
529C22—21no—
530C22C2×C29×#12111yescharacteristic
531C4—21no—
532C4—21no—
533C4—22no—
534C4—21no—
535C4—21no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—81no—
540C4—81no—
541C4—81no—
542C4—81no—
543C4C2×C29×#13711yescharacteristic
544C4C2×C29×#13711yescharacteristic
545C4C29×#57511yescharacteristic
546C4C29×#57511yescharacteristic
547C2—41no—
548C2C29×#303711yescharacteristic
549C2C29×#305611yescharacteristic
550C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC23×C29#121
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
5. C29×#1704C2semidirect
6. C29×#1700C2semidirect
7. C29×#1692C2semidirect
8. C29×#1690C2semidirect
9. C29×#1684C2semidirect
10. C29×#1680C2semidirect
11. C29×#1672C2semidirect
12. C29×#1670C2semidirect
207. #19311C29direct (N × H)
256. #1704C2×C29semidirect
257. #1700C2×C29semidirect
258. #1692C2×C29semidirect
259. #1690C2×C29semidirect
260. #1684C2×C29semidirect
261. #1680C2×C29semidirect
262. #1672C2×C29semidirect
263. #1670C2×C29semidirect
419. C29#19311direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31852
C29×#31132
C29×#30782
Q8×M16×C292
C29×#17042
C29×#17002
C29×#16922
C29×#16902
C29×#16842
C29×#16802
C29×#16722
C29×#16702
C29×#15692
C29×#15612
C29×#15592
#1931129