Finite Group Databasebeta

← C29×#25521 #20320421

Subgroups — C29×#25521 #20320421

Order 7424.

1118 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3492C211yesmaximal, characteristic, complemented
2C29×#3055C212yesmaximal, complemented
3C29×#2504C211yesmaximal, characteristic, complemented
4C29×#2061C211yesmaximal, characteristic, complemented
5C29×#2040C211yesmaximal, characteristic, complemented
6C29×#2027C211yesmaximal, characteristic, complemented
7C29×#2006C211yesmaximal, characteristic, complemented
8C29×#1883C212yesmaximal, complemented
9C29×#1871C212yesmaximal, complemented
10C29×#1860C212yesmaximal, complemented
11C2×C29×#343C211yesmaximal, characteristic, complemented
12C2×C29×AGL(1,ℤ/8)C2212yes—
13C22×M16×C29C2212yes—
14C29×#554—22no—
15C29×#553—22no—
16C29×#552—22no—
17C29×#547—22no—
18C29×#544C2211yescharacteristic
19C29×#539—22no—
20C29×#537C2211yescharacteristic
21C29×#525—22no—
22C29×#525C2212yes—
23C2×C29×#121C2211yescharacteristic
24C29×#520C2212yes—
25C22×C4⋊C4×C29C2211yescharacteristic
26C29×#469—22no—
27C29×#468—22no—
28C29×#466—22no—
29C29×#465—22no—
30C29×#428C2212yes—
31C2×C29×#104C2212yes—
32C2×C29×#104C2212yes—
33C29×#418C2212yes—
34C29×#417C2212yes—
35C29×#397—22no—
36C29×#390C2211yescharacteristic
37C29×#390C2211yescharacteristic
38C29×#386—22no—
39C29×#382C2211yescharacteristic
40C29×#382C2211yescharacteristic
41C4×C22⋊C4×C29C2211yescharacteristic
42C29×#343C2211yescharacteristic
43C29×#343C2211yescharacteristic
44C29×#343C2212yes—
45C29×#339C2212yes—
46C29×#339C2212yes—
47C2×#41×C29—22no—
48C2×#41×C29C2312yes—
49C22×D4×C29—21no—
50C22×D4×C29C2311yescharacteristic
51C23×C4×C29D412yes—
52C23×C4×C29C2311yescharacteristic
53C29×AGL(1,ℤ/8)—24no—
54C29×AGL(1,ℤ/8)—42no—
55C2×SD16×C29—22no—
56C2×D8×C29—22no—
57C2×M16×C29—22no—
58C2×M16×C29—24no—
59C2×M16×C29—42no—
60C2×M16×C29C2312yes—
61C2×M16×C29C2312yes—
62C22×C8×C29—22no—
63C29×C4⋊Q8—22no—
64C29×#126—24no—
65C29×#125—24no—
66C29×#125—22no—
67C29×#123—24no—
68C29×#123—24no—
69C29×#123—22no—
70C29×C22⋊Q8—22no—
71C29×C22⋊Q8—24no—
72C29×C22⋊Q8—22no—
73C29×C22⋊Q8—22no—
74C29×C22⋊Q8D412yes—
75C29×C22⋊Q8D412yes—
76C29×#121—22no—
77C29×#121—22no—
78C29×#121—22no—
79C29×#121—22no—
80C29×#121—22no—
81C29×#121D412yes—
82C29×#121D412yes—
83C29×#120—22no—
84C4×Q8×C29—22no—
85C4×D4×C29—24no—
86C4×D4×C29—22no—
87C4×D4×C29—24no—
88C4×D4×C29—22no—
89C4×D4×C29—22no—
90C29×#117—22no—
91C29×#117—22no—
92C29×#117C2312yes—
93C2×C4⋊C4×C29—22no—
94C2×C4⋊C4×C29—22no—
95C2×C4⋊C4×C29—22no—
96C2×C4⋊C4×C29D412yes—
97C2×C4⋊C4×C29C2311yescharacteristic
98C2×C4⋊C4×C29C2311yescharacteristic
99C2×C4⋊C4×C29C2311yescharacteristic
100C2×C22⋊C4×C29—21no—
101C2×C22⋊C4×C29—21no—
102C2×C22⋊C4×C29—22no—
103C2×C22⋊C4×C29—22no—
104C2×C42×C29C2311yescharacteristic
105C2×C42×C29C2311yescharacteristic
106C29×#107—22no—
107C29×#106—22no—
108C29×#104—24no—
109C29×#104—42no—
110C29×#103—22no—
111C29×#102—22no—
112C29×#102—22no—
113C29×#102—22no—
114C29×#95—21no—
115C29×#95—22no—
116C29×#95—22no—
117C24×C29—21no—
118C24×C29C2×D411yescharacteristic
119#41×C29—22no—
120#41×C29—22no—
121#41×C29—22no—
122#41×C29—22no—
123#41×C29—84no—
124C2×Q8×C29—22no—
125C2×Q8×C29C2×D412yes—
126C2×D4×C29—22no—
127C2×D4×C29—22no—
128C2×D4×C29—22no—
129C2×D4×C29—22no—
130C2×D4×C29—22no—
131C2×D4×C29—22no—
132C2×D4×C29—21no—
133C2×D4×C29—21no—
134C2×D4×C29—44no—
135C2×D4×C29—41no—
136C2×D4×C29—41no—
137C2×D4×C29C2×D412yes—
138C22×C4×C29—22no—
139C22×C4×C29—21no—
140C22×C4×C29—21no—
141C22×C4×C29—22no—
142C22×C4×C29—24no—
143C22×C4×C29—22no—
144C22×C4×C29—22no—
145C22×C4×C29—21no—
146C22×C4×C29—21no—
147C22×C4×C29—21no—
148C22×C4×C29—82no—
149C22×C4×C29C2×D411yescharacteristic
150C22×C4×C29C2×D412yes—
151C22×C4×C29C2×D412yes—
152C22×C4×C29C2×D412yes—
153C22×C4×C29C2×D412yes—
154C22×C4×C29C2411yescharacteristic
155SD16×C29—44no—
156D8×C29—44no—
157M16×C29—22no—
158M16×C29—22no—
159M16×C29—22no—
160M16×C29—44no—
161M16×C29#4114yescomplemented
162C2×C8×C29—22no—
163C2×C8×C29—22no—
164C2×C8×C29—44no—
165C4⋊C4×C29—24no—
166C4⋊C4×C29—22no—
167C4⋊C4×C29—22no—
168C4⋊C4×C29—24no—
169C4⋊C4×C29—24no—
170C4⋊C4×C29—22no—
171C4⋊C4×C29—22no—
172C4⋊C4×C29—22no—
173C4⋊C4×C29—22no—
174C4⋊C4×C29—22no—
175C4⋊C4×C29C2×D412yes—
176C4⋊C4×C29C2×D412yes—
177C22⋊C4×C29—24no—
178C22⋊C4×C29—24no—
179C22⋊C4×C29—22no—
180C22⋊C4×C29—22no—
181C22⋊C4×C29—22no—
182C22⋊C4×C29—22no—
183C22⋊C4×C29—22no—
184C22⋊C4×C29—42no—
185C22⋊C4×C29—42no—
186C22⋊C4×C29—82no—
187C22⋊C4×C29—82no—
188C42×C29—24no—
189C42×C29—22no—
190C42×C29—22no—
191C42×C29—21no—
192C42×C29—21no—
193#25521C2911yesmaximal, characteristic, direct product factor, Sylow
194C23×C29—21no—
195C23×C29—21no—
196C23×C29—22no—
197C23×C29—22no—
198C23×C29—41no—
199C23×C29—42no—
200C23×C29—42no—
201C23×C29—41no—
202C23×C29—41no—
203C23×C29—41no—
204C23×C29#12011yescharacteristic
205C23×C29#12011yescharacteristic
206C23×C29C22×D411yescharacteristic
207Q8×C29—22no—
208Q8×C29—22no—
209Q8×C29—82no—
210D4×C29—22no—
211D4×C29—22no—
212D4×C29—44no—
213D4×C29—42no—
214D4×C29—42no—
215D4×C29—44no—
216D4×C29—42no—
217D4×C29—42no—
218D4×C29—82no—
219D4×C29—82no—
220D4×C29—82no—
221C2×C4×C29—21no—
222C2×C4×C29—21no—
223C2×C4×C29—22no—
224C2×C4×C29—22no—
225C2×C4×C29—22no—
226C2×C4×C29—22no—
227C2×C4×C29—22no—
228C2×C4×C29—22no—
229C2×C4×C29—22no—
230C2×C4×C29—22no—
231C2×C4×C29—22no—
232C2×C4×C29—44no—
233C2×C4×C29—42no—
234C2×C4×C29—42no—
235C2×C4×C29—42no—
236C2×C4×C29—42no—
237C2×C4×C29—41no—
238C2×C4×C29—41no—
239C2×C4×C29—41no—
240C2×C4×C29—41no—
241C2×C4×C29—42no—
242C2×C4×C29—41no—
243C2×C4×C29—41no—
244C2×C4×C29—41no—
245C2×C4×C29—82no—
246C2×C4×C29—84no—
247C2×C4×C29#12012yes—
248C2×C4×C29C22×D412yes—
249C2×C4×C29C2×#4112yes—
250C2×C4×C29H(5,𝔽2)11yescharacteristic
251C2×C4×C292−1+411yescharacteristic
252C8×C29—24no—
253C8×C29—42no—
254#3492C2×C2911yescharacteristic, complemented
255#3055C2×C2912yescomplemented
256#2504C2×C2911yescharacteristic, complemented
257#2061C2×C2911yescharacteristic, complemented
258#2040C2×C2911yescharacteristic, complemented
259#2027C2×C2911yescharacteristic, complemented
260#2006C2×C2911yescharacteristic, complemented
261#1883C2×C2912yescomplemented
262#1871C2×C2912yescomplemented
263#1860C2×C2912yescomplemented
264C2×#343C2×C2911yescharacteristic, complemented
265C22×C29—21no—
266C22×C29—21no—
267C22×C29—21no—
268C22×C29—21no—
269C22×C29—21no—
270C22×C29—21no—
271C22×C29—21no—
272C22×C29—42no—
273C22×C29—42no—
274C22×C29—42no—
275C22×C29—42no—
276C22×C29—42no—
277C22×C29—82no—
278C22×C29—82no—
279C22×C29—81no—
280C22×C29—81no—
281C22×C29—81no—
282C22×C29#45412yes—
283C22×C29C2×#12011yescharacteristic
284C22×C29#53211yescharacteristic
285C22×C29#53711yescharacteristic
286C4×C29—22no—
287C4×C29—42no—
288C4×C29—42no—
289C4×C29—42no—
290C4×C29—42no—
291C4×C29—42no—
292C4×C29—81no—
293C4×C29—81no—
294C4×C29—81no—
295C4×C29#54612yes—
296C4×C29#54712yes—
297C2×AGL(1,ℤ/8)C22×C2912yes—
298C22×M16C22×C2912yes—
299#554—22no—
300#553—22no—
301#552—22no—
302#547—22no—
303#544C22×C2911yescharacteristic
304#539—22no—
305#537C22×C2911yescharacteristic
306#525—22no—
307#525C22×C2912yes—
308C2×#121C22×C2911yescharacteristic
309#520C22×C2912yes—
310C22×C4⋊C4C22×C2911yescharacteristic
311#469—22no—
312#468—22no—
313#466—22no—
314#465—22no—
315#428C22×C2912yes—
316C2×#104C22×C2912yes—
317C2×#104C22×C2912yes—
318#418C22×C2912yes—
319#417C22×C2912yes—
320#397—22no—
321#390C22×C2911yescharacteristic
322#390C22×C2911yescharacteristic
323#386—22no—
324#382C22×C2911yescharacteristic
325#382C22×C2911yescharacteristic
326C4×C22⋊C4C22×C2911yescharacteristic
327#343C22×C2911yescharacteristic
328#343C22×C2912yes—
329#343C22×C2911yescharacteristic
330#339C22×C2912yes—
331#339C22×C2912yes—
332C2×C29—21no—
333C2×C29—21no—
334C2×C29—22no—
335C2×C29—41no—
336C2×C29—82no—
337C2×C29—161no—
338C2×C29#243011yescharacteristic
339C2×C29C2×#45411yescharacteristic
340C2×C29#301911yescharacteristic
341C2×#41—22no—
342C2×#41C23×C2912yes—
343C22×D4—21no—
344C22×D4C23×C2911yescharacteristic
345C23×C4D4×C2912yes—
346C23×C4C23×C2911yescharacteristic
347AGL(1,ℤ/8)—24no—
348AGL(1,ℤ/8)—42no—
349C2×SD16—22no—
350C2×D8—22no—
351C2×M16—22no—
352C2×M16—24no—
353C2×M16—42no—
354C2×M16C23×C2912yes—
355C2×M16C23×C2912yes—
356C22×C8—22no—
357C4⋊Q8—22no—
358#126—24no—
359#125—24no—
360#125—22no—
361#123—24no—
362#123—24no—
363#123—22no—
364C22⋊Q8—22no—
365C22⋊Q8—24no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8D4×C2912yes—
369C22⋊Q8D4×C2912yes—
370#121—22no—
371#121—22no—
372#121—22no—
373#121—22no—
374#121—22no—
375#121D4×C2912yes—
376#121D4×C2912yes—
377#120—22no—
378C4×Q8—22no—
379C4×D4—24no—
380C4×D4—22no—
381C4×D4—24no—
382C4×D4—22no—
383C4×D4—22no—
384#117—22no—
385#117—22no—
386#117C23×C2912yes—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4D4×C2912yes—
391C2×C4⋊C4C23×C2911yescharacteristic
392C2×C4⋊C4C23×C2911yescharacteristic
393C2×C4⋊C4C23×C2911yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C42C23×C2911yescharacteristic
399C2×C42C23×C2911yescharacteristic
400#107—22no—
401#106—22no—
402#104—24no—
403#104—42no—
404#103—22no—
405#102—22no—
406#102—22no—
407#102—22no—
408#95—21no—
409#95—22no—
410#95—22no—
411C29#2552111yescharacteristic, direct product factor, Sylow
412C24—21no—
413C24C2×D4×C2911yescharacteristic
414#41—22no—
415#41—22no—
416#41—22no—
417#41—22no—
418#41—84no—
419C2×Q8—22no—
420C2×Q8C2×D4×C2912yes—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—44no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4C2×D4×C2912yes—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—82no—
444C22×C4C2×D4×C2911yescharacteristic
445C22×C4C2×D4×C2912yes—
446C22×C4C2×D4×C2912yes—
447C22×C4C2×D4×C2912yes—
448C22×C4C2×D4×C2912yes—
449C22×C4C24×C2911yescharacteristic
450SD16—44no—
451D8—44no—
452M16—22no—
453M16—22no—
454M16—22no—
455M16—44no—
456M16#41×C2914yescomplemented
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—44no—
460C4⋊C4—24no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4C2×D4×C2912yes—
471C4⋊C4C2×D4×C2912yes—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—42no—
480C22⋊C4—42no—
481C22⋊C4—82no—
482C22⋊C4—82no—
483C42—24no—
484C42—22no—
485C42—22no—
486C42—21no—
487C42—21no—
488C23—22no—
489C23—21no—
490C23—21no—
491C23—22no—
492C23—41no—
493C23—42no—
494C23—42no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23C29×#12011yescharacteristic
499C23C29×#12011yescharacteristic
500C23C22×D4×C2911yescharacteristic
501Q8—22no—
502Q8—22no—
503Q8—82no—
504D4—22no—
505D4—22no—
506D4—44no—
507D4—44no—
508D4—42no—
509D4—42no—
510D4—42no—
511D4—42no—
512D4—82no—
513D4—82no—
514D4—82no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—44no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—82no—
540C2×C4—84no—
541C2×C4C29×#12012yes—
542C2×C4C22×D4×C2912yes—
543C2×C4C2×#41×C2912yes—
544C2×C4C29×H(5,𝔽2)11yescharacteristic
545C2×C4C29×2−1+411yescharacteristic
546C8—24no—
547C8—42no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—82no—
561C22—82no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22C29×#45412yes—
566C22C2×C29×#12011yescharacteristic
567C22C29×#53211yescharacteristic
568C22C29×#53711yescharacteristic
569C4—22no—
570C4—42no—
571C4—42no—
572C4—42no—
573C4—42no—
574C4—42no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4C29×#54612yes—
579C4C29×#54712yes—
580C2—21no—
581C2—21no—
582C2—22no—
583C2—41no—
584C2—82no—
585C2—161no—
586C2C29×#243011yescharacteristic
587C2C2×C29×#45411yescharacteristic
588C2C29×#301911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3492C2semidirect
2. C29×#3055C2semidirect
3. C29×#2504C2semidirect
4. C29×#2061C2semidirect
5. C29×#2040C2semidirect
6. C29×#2027C2semidirect
7. C29×#2006C2semidirect
8. C29×#1883C2semidirect
9. C29×#1871C2semidirect
10. C29×#1860C2semidirect
11. C2×C29×#343C2semidirect
161. M16×C29#41semidirect
193. #25521C29direct (N × H)
254. #3492C2×C29semidirect
255. #3055C2×C29semidirect
256. #2504C2×C29semidirect
257. #2061C2×C29semidirect
258. #2040C2×C29semidirect
259. #2027C2×C29semidirect
260. #2006C2×C29semidirect
261. #1883C2×C29semidirect
262. #1871C2×C29semidirect
263. #1860C2×C29semidirect
264. C2×#343C2×C29semidirect
411. C29#25521direct (N × H)
456. M16#41×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#34922
C29×#30552
C29×#25042
C29×#20612
C29×#20402
C29×#20272
C29×#20062
C29×#18832
C29×#18712
C29×#18602
C2×C29×#3432
#2552129