Finite Group Databasebeta

← C29×#19375 #20314275

Subgroups — C29×#19375 #20314275

Order 7424.

554 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3255C211yesmaximal, characteristic
2C29×#3237C211yesmaximal, characteristic
3C29×#3185C211yesmaximal, characteristic
4C29×#2962C211yesmaximal, 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×#1552C211yesmaximal, characteristic
15C29×#1550C211yesmaximal, characteristic
16C29×#533C2211yescharacteristic
17C29×#533C2211yescharacteristic
18C29×#533C2211yescharacteristic
19C29×#501—21no—
20C29×#498C2211yescharacteristic
21C29×#494C2211yescharacteristic
22C29×#491—21no—
23C29×#487C2211yescharacteristic
24C29×#487C2211yescharacteristic
25C29×#485—21no—
26C29×#485—21no—
27C29×#477C2211yescharacteristic
28C29×#477C2211yescharacteristic
29C29×#475—21no—
30C29×#475C2211yescharacteristic
31C29×#475C2211yescharacteristic
32C29×#475C2211yescharacteristic
33C29×#475C2211yescharacteristic
34C29×#470—21no—
35C29×#470—21no—
36C29×#470—21no—
37C29×#470—21no—
38C29×#462—21no—
39C29×#462C2211yescharacteristic
40C29×#462C2211yescharacteristic
41C29×#446—21no—
42C29×#446—21no—
43C29×#446C2211yescharacteristic
44C29×#446C2211yescharacteristic
45C8×Q8×C29C2211yescharacteristic
46C8×Q8×C29C2211yescharacteristic
47C29×#441—21no—
48C29×#441—21no—
49C29×#432C2211yescharacteristic
50C29×#424—21no—
51C29×#423C2211yescharacteristic
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×Q16×C29—21no—
71C2×M16×C29—21no—
72C2×M16×C29D411yescharacteristic
73C2×M16×C29D411yescharacteristic
74C22×C8×C29—21no—
75C29×C4⋊Q8D411yescharacteristic
76C29×C4⋊Q8D411yescharacteristic
77C29×C4⋊Q8C2311yescharacteristic
78C29×C4⋊Q8C2311yescharacteristic
79C29×C4⋊Q8C2311yescharacteristic
80C29×C4⋊Q8C2311yescharacteristic
81C29×#125—21no—
82C29×#125—21no—
83C29×#125—21no—
84C29×C22⋊Q8—21no—
85C29×C22⋊Q8—21no—
86C29×C22⋊Q8—21no—
87C29×C22⋊Q8—21no—
88C29×C22⋊Q8—21no—
89C29×C22⋊Q8D411yescharacteristic
90C29×C22⋊Q8D411yescharacteristic
91C4×Q8×C29—21no—
92C4×Q8×C29—21no—
93C4×Q8×C29—21no—
94C4×Q8×C29—21no—
95C4×Q8×C29—21no—
96C4×Q8×C29C2311yescharacteristic
97C4×Q8×C29C2311yescharacteristic
98C29×#117—21no—
99C29×#117—21no—
100C29×#117—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—21no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29C2×D411yescharacteristic
150C2×Q8×C29C2×D411yescharacteristic
151C22×C4×C29C2×D411yescharacteristic
152C22×C4×C29C2×D411yescharacteristic
153C22×C4×C29#4111yescharacteristic
154Q16×C29—42no—
155Q16×C29—42no—
156Q16×C29—81no—
157Q16×C29—81no—
158M16×C29—22no—
159M16×C29—41no—
160M16×C29—81no—
161C2×C8×C29—21no—
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—21no—
183C4⋊C4×C29—21no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—41no—
188C4⋊C4×C29—41no—
189C4⋊C4×C29—41no—
190C4⋊C4×C29—41no—
191C4⋊C4×C29C2×D411yescharacteristic
192C4⋊C4×C29C2×D411yescharacteristic
193C22⋊C4×C29—21no—
194C22⋊C4×C29—21no—
195C22⋊C4×C29—41no—
196C22⋊C4×C29—41no—
197C42×C29—21no—
198C42×C29—21no—
199C42×C29—41no—
200C42×C29—41no—
201C42×C29C2×D411yescharacteristic
202C42×C29C2×D411yescharacteristic
203C42×C29#4111yescharacteristic
204C42×C29C2411yescharacteristic
205#19375C2911yesmaximal, characteristic, direct product factor, Sylow
206C23×C29#12111yescharacteristic
207Q8×C29—21no—
208Q8×C29—21no—
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—
218Q8×C29—81no—
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—21no—
227C2×C4×C29—41no—
228C2×C4×C29—41no—
229C2×C4×C29—41no—
230C2×C4×C29—41no—
231C2×C4×C29—41no—
232C2×C4×C29#12111yescharacteristic
233C2×C4×C29#12111yescharacteristic
234C2×C4×C29#12111yescharacteristic
235C2×C4×C29C22×D411yescharacteristic
236C2×C4×C29C22×D411yescharacteristic
237C2×C4×C29C2×#4111yescharacteristic
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—
247C8×C29#13712yes—
248#3255C2×C2911yescharacteristic
249#3237C2×C2911yescharacteristic
250#3185C2×C2911yescharacteristic
251#2962C2×C2911yescharacteristic
252#1704C2×C2911yescharacteristic, complemented
253#1700C2×C2911yescharacteristic, complemented
254#1692C2×C2911yescharacteristic, complemented
255#1690C2×C2911yescharacteristic, complemented
256#1684C2×C2911yescharacteristic, complemented
257#1680C2×C2911yescharacteristic, complemented
258#1672C2×C2911yescharacteristic, complemented
259#1670C2×C2911yescharacteristic, complemented
260#1569C2×C2911yescharacteristic
261#1552C2×C2911yescharacteristic
262#1550C2×C2911yescharacteristic
263C22×C29—21no—
264C22×C29—21no—
265C22×C29—21no—
266C22×C29C2×#12111yescharacteristic
267C4×C29—21no—
268C4×C29—21no—
269C4×C29—21no—
270C4×C29—21no—
271C4×C29—41no—
272C4×C29—41no—
273C4×C29—41no—
274C4×C29—41no—
275C4×C29—81no—
276C4×C29—81no—
277C4×C29—81no—
278C4×C29—81no—
279C4×C29C2×#13711yescharacteristic
280C4×C29#57511yescharacteristic
281C4×C29#57711yescharacteristic
282C4×C29#57811yescharacteristic
283#533C22×C2911yescharacteristic
284#533C22×C2911yescharacteristic
285#533C22×C2911yescharacteristic
286#501—21no—
287#498C22×C2911yescharacteristic
288#494C22×C2911yescharacteristic
289#491—21no—
290#487C22×C2911yescharacteristic
291#487C22×C2911yescharacteristic
292#485—21no—
293#485—21no—
294#477C22×C2911yescharacteristic
295#477C22×C2911yescharacteristic
296#475—21no—
297#475C22×C2911yescharacteristic
298#475C22×C2911yescharacteristic
299#475C22×C2911yescharacteristic
300#475C22×C2911yescharacteristic
301#470—21no—
302#470—21no—
303#470—21no—
304#470—21no—
305#462—21no—
306#462C22×C2911yescharacteristic
307#462C22×C2911yescharacteristic
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#432C22×C2911yescharacteristic
317#424—21no—
318#423C22×C2911yescharacteristic
319C2×C4⋊C8C22×C2911yescharacteristic
320#405—21no—
321C4×M16C22×C2911yescharacteristic
322#335C22×C2911yescharacteristic
323#335C22×C2911yescharacteristic
324#334C22×C2911yescharacteristic
325#334C22×C2911yescharacteristic
326#333C22×C2911yescharacteristic
327#333C22×C2911yescharacteristic
328#332C22×C2911yescharacteristic
329#332C22×C2911yescharacteristic
330#332C22×C2911yescharacteristic
331#332C22×C2911yescharacteristic
332#332C22×C2911yescharacteristic
333#332C22×C2911yescharacteristic
334C2×C29—41no—
335C2×C29#303711yescharacteristic
336C2×C29#306311yescharacteristic
337C2×C29#306911yescharacteristic
338C2×Q16—21no—
339C2×Q16—21no—
340C2×Q16—21no—
341C2×Q16—21no—
342C2×M16—21no—
343C2×M16D4×C2911yescharacteristic
344C2×M16D4×C2911yescharacteristic
345C22×C8—21no—
346C4⋊Q8D4×C2911yescharacteristic
347C4⋊Q8D4×C2911yescharacteristic
348C4⋊Q8C23×C2911yescharacteristic
349C4⋊Q8C23×C2911yescharacteristic
350C4⋊Q8C23×C2911yescharacteristic
351C4⋊Q8C23×C2911yescharacteristic
352#125—21no—
353#125—21no—
354#125—21no—
355C22⋊Q8—21no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8D4×C2911yescharacteristic
361C22⋊Q8D4×C2911yescharacteristic
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8C23×C2911yescharacteristic
368C4×Q8C23×C2911yescharacteristic
369#117—21no—
370#117—21no—
371#117—21no—
372C2×C42C23×C2911yescharacteristic
373#107—21no—
374#107—21no—
375#106—21no—
376#106—21no—
377#106—21no—
378#106—21no—
379#106—21no—
380#106—21no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8C23×C2911yescharacteristic
388C4⋊C8C23×C2911yescharacteristic
389C4⋊C8C23×C2911yescharacteristic
390C4⋊C8C23×C2911yescharacteristic
391C4⋊C8C23×C2911yescharacteristic
392C4⋊C8C23×C2911yescharacteristic
393#103—21no—
394#103—21no—
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#103—21no—
405C22⋊C8—21no—
406#97—21no—
407#97—21no—
408#97—21no—
409#97D4×C2911yescharacteristic
410#97D4×C2911yescharacteristic
411C4×C8—21no—
412C4×C8—21no—
413C4×C8C23×C2911yescharacteristic
414C4×C8C23×C2911yescharacteristic
415C29#1937511yescharacteristic, direct product factor, Sylow
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8C2×D4×C2911yescharacteristic
422C2×Q8C2×D4×C2911yescharacteristic
423C22×C4C2×D4×C2911yescharacteristic
424C22×C4C2×D4×C2911yescharacteristic
425C22×C4#41×C2911yescharacteristic
426Q16—42no—
427Q16—42no—
428Q16—81no—
429Q16—81no—
430M16—22no—
431M16—41no—
432M16—81no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—42no—
440C2×C8C2×D4×C2911yescharacteristic
441C2×C8C2×D4×C2911yescharacteristic
442C2×C8C2×D4×C2911yescharacteristic
443C2×C8C2×D4×C2911yescharacteristic
444C4⋊C4—21no—
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—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4C2×D4×C2911yescharacteristic
464C4⋊C4C2×D4×C2911yescharacteristic
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C42—21no—
470C42—21no—
471C42—41no—
472C42—41no—
473C42C2×D4×C2911yescharacteristic
474C42C2×D4×C2911yescharacteristic
475C42#41×C2911yescharacteristic
476C42C24×C2911yescharacteristic
477C23C29×#12111yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—41no—
483Q8—41no—
484Q8—41no—
485Q8—41no—
486Q8—41no—
487Q8—41no—
488Q8—81no—
489Q8—81no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4C29×#12111yescharacteristic
504C2×C4C29×#12111yescharacteristic
505C2×C4C29×#12111yescharacteristic
506C2×C4C22×D4×C2911yescharacteristic
507C2×C4C22×D4×C2911yescharacteristic
508C2×C4C2×#41×C2911yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—41no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—41no—
518C8C29×#13712yes—
519C22—21no—
520C22—21no—
521C22—21no—
522C22C2×C29×#12111yescharacteristic
523C4—21no—
524C4—21no—
525C4—21no—
526C4—21no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—81no—
532C4—81no—
533C4—81no—
534C4—81no—
535C4C2×C29×#13711yescharacteristic
536C4C29×#57511yescharacteristic
537C4C29×#57711yescharacteristic
538C4C29×#57811yescharacteristic
539C2—41no—
540C2C29×#303711yescharacteristic
541C2C29×#306311yescharacteristic
542C2C29×#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
205. #19375C29direct (N × H)
252. #1704C2×C29semidirect
253. #1700C2×C29semidirect
254. #1692C2×C29semidirect
255. #1690C2×C29semidirect
256. #1684C2×C29semidirect
257. #1680C2×C29semidirect
258. #1672C2×C29semidirect
259. #1670C2×C29semidirect
415. C29#19375direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32552
C29×#32372
C29×#31852
C29×#29622
C29×#17042
C29×#17002
C29×#16922
C29×#16902
C29×#16842
C29×#16802
C29×#16722
C29×#16702
C29×#15692
C29×#15522
C29×#15502
#1937529