Finite Group Databasebeta

← C29×#18439 #20313339

Subgroups — C29×#18439 #20313339

Order 7424.

964 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3561C211yesmaximal, characteristic
2C29×#3239C211yesmaximal, characteristic, complemented
3C29×#3230C211yesmaximal, characteristic, complemented
4C29×#2658C211yesmaximal, characteristic, complemented
5C29×#1618C214yesmaximal, complemented
6C29×#1614C214yesmaximal, complemented
7C29×#1506C211yesmaximal, characteristic, complemented
8C29×#1500C211yesmaximal, characteristic, complemented
9C29×#1469C211yesmaximal, characteristic, complemented
10C29×#563—21no—
11C29×#562—21no—
12C29×#556—21no—
13C29×#551—22no—
14D4×Q8×C29—21no—
15C29×#548—21no—
16C29×#546—21no—
17C29×#543C2212yes—
18C29×#542—21no—
19C29×#542—22no—
20C29×#538C2212yes—
21C29×#536—21no—
22C29×#533C2211yescharacteristic
23C2×C29×C4⋊Q8—21no—
24C2×C29×C4⋊Q8C2211yescharacteristic
25C29×#529C2211yescharacteristic
26C2×C29×#124—21no—
27C2×C29×#124C2211yescharacteristic
28C29×#501—21no—
29C29×#500—21no—
30C29×#489—21no—
31C29×#487—21no—
32C29×#484C2214yes—
33C29×#484C2212yes—
34C29×#481C2212yes—
35C29×#477—22no—
36C29×#475—21no—
37C29×#474—21no—
38C29×#432C2211yescharacteristic
39C29×#431C2211yescharacteristic
40C29×#399—22no—
41C29×#399C2214yes—
42C29×#376C2211yescharacteristic
43C29×#328C2212yes—
44C29×#328C2214yes—
45C29×#327C2212yes—
46C29×#323C2214yes—
47C2×#41×C29—21no—
48C22×Q8×C29—21no—
49C22×Q8×C29—21no—
50C22×Q8×C29D411yescharacteristic
51C22×D4×C29D411yescharacteristic
52C29×C4⋊Q8—21no—
53C29×C4⋊Q8—22no—
54C29×C4⋊Q8—21no—
55C29×C4⋊Q8—21no—
56C29×C4⋊Q8—21no—
57C29×C4⋊Q8—21no—
58C29×C4⋊Q8—44no—
59C29×C4⋊Q8D411yescharacteristic
60C29×C4⋊Q8D411yescharacteristic
61C29×#126—22no—
62C29×#126—22no—
63C29×#126—22no—
64C29×#126—21no—
65C29×#125—21no—
66C29×#125D411yescharacteristic
67C29×#124—21no—
68C29×#124—22no—
69C29×#124—22no—
70C29×#124—21no—
71C29×#124—21no—
72C29×#124—21no—
73C29×#124—21no—
74C29×#124—44no—
75C29×#124D411yescharacteristic
76C29×#123—22no—
77C29×#123—22no—
78C29×#123—22no—
79C29×#123—21no—
80C29×#123—22no—
81C29×C22⋊Q8—22no—
82C29×C22⋊Q8—21no—
83C29×C22⋊Q8—22no—
84C29×C22⋊Q8—22no—
85C29×C22⋊Q8—22no—
86C29×C22⋊Q8—21no—
87C29×C22⋊Q8—22no—
88C29×C22⋊Q8—22no—
89C29×C22⋊Q8—22no—
90C29×C22⋊Q8C2311yescharacteristic
91C29×C22⋊Q8C2312yes—
92C29×#121—21no—
93C29×#121—22no—
94C29×#121—22no—
95C29×#121C2311yescharacteristic
96C29×#120—22no—
97C4×Q8×C29—21no—
98C4×Q8×C29—21no—
99C4×Q8×C29D411yescharacteristic
100C4×Q8×C29D412yes—
101C4×D4×C29—21no—
102C4×D4×C29—22no—
103C4×D4×C29—21no—
104C4×D4×C29—22no—
105C4×D4×C29D411yescharacteristic
106C29×#117—22no—
107C29×#117—21no—
108C29×#117—21no—
109C2×C4⋊C4×C29—24no—
110C2×C4⋊C4×C29—21no—
111C2×C4⋊C4×C29C2312yes—
112C2×C22⋊C4×C29—22no—
113C2×C22⋊C4×C29—24no—
114C2×C22⋊C4×C29D412yes—
115C2×C22⋊C4×C29C2312yes—
116C2×C42×C29—21no—
117C2×C42×C29C2311yescharacteristic
118C29×#107—22no—
119C29×#107—24no—
120C29×#106—22no—
121C29×C4⋊C8—21no—
122C29×C4⋊C8—21no—
123C29×#103—22no—
124C29×#103—24no—
125C29×#102—22no—
126C29×C22⋊C8C2312yes—
127C29×C22⋊C8C2312yes—
128C29×#97—21no—
129C4×C8×C29—21no—
130C29×#95—21no—
131C29×#95C2312yes—
132C24×C29C2×D412yes—
133#41×C29—82no—
134C2×Q8×C29—22no—
135C2×Q8×C29—21no—
136C2×Q8×C29—21no—
137C2×Q8×C29—21no—
138C2×Q8×C29—42no—
139C2×Q8×C29—42no—
140C2×Q8×C29—42no—
141C2×Q8×C29—41no—
142C2×Q8×C29—41no—
143C2×Q8×C29—82no—
144C2×Q8×C29C2×D411yescharacteristic
145C2×Q8×C29C2×D412yes—
146C2×D4×C29—21no—
147C2×D4×C29—22no—
148C2×D4×C29—22no—
149C2×D4×C29—21no—
150C2×D4×C29—21no—
151C2×D4×C29—42no—
152C2×D4×C29C2×D411yescharacteristic
153C22×C4×C29—22no—
154C22×C4×C29—22no—
155C22×C4×C29—22no—
156C22×C4×C29—22no—
157C22×C4×C29—21no—
158C22×C4×C29—22no—
159C22×C4×C29C2×D411yescharacteristic
160C22×C4×C29C2×D411yescharacteristic
161C22×C4×C29C2×D412yes—
162C22×C4×C29C2411yescharacteristic
163C2×C8×C29—22no—
164C2×C8×C29—22no—
165C4⋊C4×C29—22no—
166C4⋊C4×C29—22no—
167C4⋊C4×C29—22no—
168C4⋊C4×C29—22no—
169C4⋊C4×C29—21no—
170C4⋊C4×C29—21no—
171C4⋊C4×C29—21no—
172C4⋊C4×C29—21no—
173C4⋊C4×C29—21no—
174C4⋊C4×C29—21no—
175C4⋊C4×C29—22no—
176C4⋊C4×C29—21no—
177C4⋊C4×C29—22no—
178C4⋊C4×C29—22no—
179C4⋊C4×C29—22no—
180C4⋊C4×C29—48no—
181C4⋊C4×C29—41no—
182C4⋊C4×C29—41no—
183C4⋊C4×C29C2×D411yescharacteristic
184C4⋊C4×C29C2×D411yescharacteristic
185C4⋊C4×C29C2×D412yes—
186C22⋊C4×C29—22no—
187C22⋊C4×C29—22no—
188C22⋊C4×C29—22no—
189C22⋊C4×C29—22no—
190C22⋊C4×C29—22no—
191C22⋊C4×C29—21no—
192C22⋊C4×C29—22no—
193C22⋊C4×C29—22no—
194C22⋊C4×C29—22no—
195C22⋊C4×C29—21no—
196C22⋊C4×C29—21no—
197C22⋊C4×C29—21no—
198C22⋊C4×C29—22no—
199C22⋊C4×C29—22no—
200C22⋊C4×C29—21no—
201C22⋊C4×C29—48no—
202C42×C29—24no—
203C42×C29—22no—
204C42×C29—22no—
205C42×C29—21no—
206C42×C29C2×D411yescharacteristic
207C42×C29C2×D411yescharacteristic
208C42×C29C2×D411yescharacteristic
209C42×C29C2×D411yescharacteristic
210#18439C2911yesmaximal, characteristic, direct product factor, Sylow
211C23×C29—22no—
212C23×C29—21no—
213C23×C29—24no—
214C23×C29—42no—
215C23×C29—42no—
216C23×C29C22×D411yescharacteristic
217Q8×C29—41no—
218Q8×C29—42no—
219Q8×C29—42no—
220Q8×C29—42no—
221Q8×C29—81no—
222Q8×C29—82no—
223Q8×C29—82no—
224Q8×C29—82no—
225D4×C29—41no—
226D4×C29—42no—
227D4×C29—42no—
228D4×C29—81no—
229D4×C29—82no—
230D4×C29—82no—
231C2×C4×C29—22no—
232C2×C4×C29—22no—
233C2×C4×C29—24no—
234C2×C4×C29—21no—
235C2×C4×C29—22no—
236C2×C4×C29—21no—
237C2×C4×C29—22no—
238C2×C4×C29—22no—
239C2×C4×C29—21no—
240C2×C4×C29—41no—
241C2×C4×C29—42no—
242C2×C4×C29—42no—
243C2×C4×C29—42no—
244C2×C4×C29—42no—
245C2×C4×C29—42no—
246C2×C4×C29—42no—
247C2×C4×C29—42no—
248C2×C4×C29—82no—
249C2×C4×C29—82no—
250C2×C4×C29—82no—
251C2×C4×C29#12011yescharacteristic
252C2×C4×C29#12011yescharacteristic
253C2×C4×C29#12011yescharacteristic
254C2×C4×C29#12011yescharacteristic
255C2×C4×C29C22×D411yescharacteristic
256C2×C4×C29C22×D411yescharacteristic
257C8×C29—42no—
258C8×C29—42no—
259#3561C2×C2911yescharacteristic
260#3239C2×C2911yescharacteristic, complemented
261#3230C2×C2911yescharacteristic, complemented
262#2658C2×C2911yescharacteristic, complemented
263#1618C2×C2914yescomplemented
264#1614C2×C2914yescomplemented
265#1506C2×C2911yescharacteristic, complemented
266#1500C2×C2911yescharacteristic, complemented
267#1469C2×C2911yescharacteristic, complemented
268C22×C29—21no—
269C22×C29—21no—
270C22×C29—41no—
271C22×C29—42no—
272C22×C29—41no—
273C22×C29—42no—
274C22×C29—42no—
275C22×C29—41no—
276C22×C29—84no—
277C22×C29C2×#12011yescharacteristic
278C22×C29#57812yes—
279C4×C29—21no—
280C4×C29—21no—
281C4×C29—21no—
282C4×C29—21no—
283C4×C29—21no—
284C4×C29—44no—
285C4×C29—41no—
286C4×C29—41no—
287C4×C29—42no—
288C4×C29—42no—
289C4×C29—41no—
290C4×C29—42no—
291C4×C29—82no—
292C4×C29#45312yes—
293#563—21no—
294#562—21no—
295#556—21no—
296#551—22no—
297D4×Q8—21no—
298#548—21no—
299#546—21no—
300#543C22×C2912yes—
301#542—21no—
302#542—22no—
303#538C22×C2912yes—
304#536—21no—
305#533C22×C2911yescharacteristic
306C2×C4⋊Q8—21no—
307C2×C4⋊Q8C22×C2911yescharacteristic
308#529C22×C2911yescharacteristic
309C2×#124—21no—
310C2×#124C22×C2911yescharacteristic
311#501—21no—
312#500—21no—
313#489—21no—
314#487—21no—
315#484C22×C2912yes—
316#484C22×C2914yes—
317#481C22×C2912yes—
318#477—22no—
319#475—21no—
320#474—21no—
321#432C22×C2911yescharacteristic
322#431C22×C2911yescharacteristic
323#399—22no—
324#399C22×C2914yes—
325#376C22×C2911yescharacteristic
326#328C22×C2912yes—
327#328C22×C2914yes—
328#327C22×C2912yes—
329#323C22×C2914yes—
330C2×C29—22no—
331C2×C29—81no—
332C2×C29—82no—
333C2×C29#301111yescharacteristic
334C2×C29C2×#45311yescharacteristic
335C2×C29#302811yescharacteristic
336C2×#41—21no—
337C22×Q8—21no—
338C22×Q8—21no—
339C22×Q8D4×C2911yescharacteristic
340C22×D4D4×C2911yescharacteristic
341C4⋊Q8—21no—
342C4⋊Q8—22no—
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—21no—
347C4⋊Q8—44no—
348C4⋊Q8D4×C2911yescharacteristic
349C4⋊Q8D4×C2911yescharacteristic
350#126—22no—
351#126—22no—
352#126—22no—
353#126—21no—
354#125—21no—
355#125D4×C2911yescharacteristic
356#124—21no—
357#124—22no—
358#124—22no—
359#124—21no—
360#124—21no—
361#124—21no—
362#124—21no—
363#124—44no—
364#124D4×C2911yescharacteristic
365#123—22no—
366#123—22no—
367#123—22no—
368#123—21no—
369#123—22no—
370C22⋊Q8—22no—
371C22⋊Q8—21no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C22⋊Q8—21no—
376C22⋊Q8—22no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8C23×C2911yescharacteristic
380C22⋊Q8C23×C2912yes—
381#121—21no—
382#121—22no—
383#121—22no—
384#121C23×C2911yescharacteristic
385#120—22no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8D4×C2911yescharacteristic
389C4×Q8D4×C2912yes—
390C4×D4—21no—
391C4×D4—22no—
392C4×D4—21no—
393C4×D4—22no—
394C4×D4D4×C2911yescharacteristic
395#117—22no—
396#117—21no—
397#117—21no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4C23×C2912yes—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4D4×C2912yes—
404C2×C22⋊C4C23×C2912yes—
405C2×C42—21no—
406C2×C42C23×C2911yescharacteristic
407#107—22no—
408#107—24no—
409#106—22no—
410C4⋊C8—21no—
411C4⋊C8—21no—
412#103—22no—
413#103—24no—
414#102—22no—
415C22⋊C8C23×C2912yes—
416C22⋊C8C23×C2912yes—
417#97—21no—
418C4×C8—21no—
419#95—21no—
420#95C23×C2912yes—
421C29#1843911yescharacteristic, direct product factor, Sylow
422C24C2×D4×C2912yes—
423#41—82no—
424C2×Q8—22no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—42no—
429C2×Q8—42no—
430C2×Q8—42no—
431C2×Q8—41no—
432C2×Q8—41no—
433C2×Q8—82no—
434C2×Q8C2×D4×C2911yescharacteristic
435C2×Q8C2×D4×C2912yes—
436C2×D4—21no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—42no—
442C2×D4C2×D4×C2911yescharacteristic
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4C2×D4×C2911yescharacteristic
450C22×C4C2×D4×C2911yescharacteristic
451C22×C4C2×D4×C2912yes—
452C22×C4C24×C2911yescharacteristic
453C2×C8—22no—
454C2×C8—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—48no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4C2×D4×C2911yescharacteristic
474C4⋊C4C2×D4×C2911yescharacteristic
475C4⋊C4C2×D4×C2912yes—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—21no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—21no—
491C22⋊C4—48no—
492C42—24no—
493C42—22no—
494C42—22no—
495C42—21no—
496C42C2×D4×C2911yescharacteristic
497C42C2×D4×C2911yescharacteristic
498C42C2×D4×C2911yescharacteristic
499C42C2×D4×C2911yescharacteristic
500C23—22no—
501C23—21no—
502C23—24no—
503C23—42no—
504C23—42no—
505C23C22×D4×C2911yescharacteristic
506Q8—41no—
507Q8—42no—
508Q8—42no—
509Q8—42no—
510Q8—81no—
511Q8—82no—
512Q8—82no—
513Q8—82no—
514D4—41no—
515D4—42no—
516D4—42no—
517D4—81no—
518D4—82no—
519D4—82no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4C29×#12011yescharacteristic
541C2×C4C29×#12011yescharacteristic
542C2×C4C29×#12011yescharacteristic
543C2×C4C29×#12011yescharacteristic
544C2×C4C22×D4×C2911yescharacteristic
545C2×C4C22×D4×C2911yescharacteristic
546C8—42no—
547C8—42no—
548C22—21no—
549C22—21no—
550C22—41no—
551C22—42no—
552C22—41no—
553C22—42no—
554C22—42no—
555C22—41no—
556C22—84no—
557C22C2×C29×#12011yescharacteristic
558C22C29×#57812yes—
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—44no—
565C4—41no—
566C4—41no—
567C4—42no—
568C4—42no—
569C4—41no—
570C4—42no—
571C4—82no—
572C4C29×#45312yes—
573C2—22no—
574C2—82no—
575C2—81no—
576C2C29×#301111yescharacteristic
577C2C2×C29×#45311yescharacteristic
578C2C29×#302811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#3561C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C29×#3239C2semidirect
3. C29×#3230C2semidirect
4. C29×#2658C2semidirect
5. C29×#1618C2semidirect
6. C29×#1614C2semidirect
7. C29×#1506C2semidirect
8. C29×#1500C2semidirect
9. C29×#1469C2semidirect
210. #18439C29direct (N × H)
260. #3239C2×C29semidirect
261. #3230C2×C29semidirect
262. #2658C2×C29semidirect
263. #1618C2×C29semidirect
264. #1614C2×C29semidirect
265. #1506C2×C29semidirect
266. #1500C2×C29semidirect
267. #1469C2×C29semidirect
421. C29#18439direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35612
C29×#32392
C29×#32302
C29×#26582
C29×#16182
C29×#16142
C29×#15062
C29×#15002
C29×#14692
#1843929