Finite Group Databasebeta

← C29×#25586 #20320486

Subgroups — C29×#25586 #20320486

Order 7424.

1196 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3505C211yesmaximal, characteristic
2C29×#2503C211yesmaximal, characteristic, complemented
3C29×#2501C211yesmaximal, characteristic, complemented
4C29×#2486C211yesmaximal, characteristic, complemented
5C29×#2022C214yesmaximal, complemented
6C29×#1996C211yesmaximal, characteristic, complemented
7C29×#1964C211yesmaximal, characteristic, complemented
8C29×#1890C214yesmaximal, complemented
9C4×C29×#99C211yesmaximal, characteristic, complemented
10C29×#553—21no—
11C29×#553—22no—
12C29×#552—21no—
13C29×#551—22no—
14C29×#548—21no—
15C29×#546—21no—
16C29×#539—21no—
17C29×#538—21no—
18C29×#534C2212yes—
19C29×#529—21no—
20C29×#525—21no—
21C2×C29×#123C2214yes—
22C2×C29×#123C2212yes—
23C2×C29×C22⋊Q8C2211yescharacteristic
24C2×C29×#121C2211yescharacteristic
25C29×#518C2212yes—
26C2×C4×D4×C29C2211yescharacteristic
27C22×C4⋊C4×C29C2211yescharacteristic
28C2×C29×#99C2212yes—
29C2×C29×#99C2214yes—
30C29×#400—22no—
31C29×#399—22no—
32C29×#398—21no—
33C29×#397—21no—
34C29×#391—21no—
35C29×#390—21no—
36C29×#389—21no—
37C29×#384—21no—
38C29×#382—21no—
39C29×#381C2212yes—
40C29×#381C2214yes—
41C29×#380—21no—
42C29×#380C2211yescharacteristic
43C4×C22⋊C4×C29C2211yescharacteristic
44C4×C22⋊C4×C29C2211yescharacteristic
45C29×#342C2214yes—
46C29×#342C2212yes—
47C2×#41×C29—21no—
48C22×Q8×C29D411yescharacteristic
49C22×D4×C29D411yescharacteristic
50C22×D4×C29C2311yescharacteristic
51C22×D4×C29C2312yes—
52C23×C4×C29D411yescharacteristic
53C23×C4×C29C2312yes—
54C23×C4×C29C2311yescharacteristic
55C29×#126—22no—
56C29×#126—22no—
57C29×#126—22no—
58C29×#125—21no—
59C29×#125—22no—
60C29×#124—21no—
61C29×#124—22no—
62C29×#123—22no—
63C29×#123—22no—
64C29×#123—22no—
65C29×#123—22no—
66C29×#123—22no—
67C29×#123—28no—
68C29×#123—44no—
69C29×#123—44no—
70C29×C22⋊Q8—21no—
71C29×C22⋊Q8—22no—
72C29×C22⋊Q8—21no—
73C29×C22⋊Q8—21no—
74C29×C22⋊Q8—21no—
75C29×C22⋊Q8—21no—
76C29×#121—21no—
77C29×#121—22no—
78C29×#121—21no—
79C29×#121—21no—
80C29×#121—21no—
81C29×#121—21no—
82C29×#121—22no—
83C29×#121—22no—
84C29×#120—22no—
85C29×#120—22no—
86C4×Q8×C29—21no—
87C4×D4×C29—22no—
88C4×D4×C29—21no—
89C4×D4×C29—21no—
90C4×D4×C29—21no—
91C4×D4×C29—21no—
92C4×D4×C29—21no—
93C4×D4×C29—22no—
94C4×D4×C29—22no—
95C4×D4×C29—22no—
96C4×D4×C29—22no—
97C29×#117—21no—
98C29×#117—22no—
99C29×#117—22no—
100C2×C4⋊C4×C29—21no—
101C2×C4⋊C4×C29—21no—
102C2×C4⋊C4×C29—21no—
103C2×C4⋊C4×C29—21no—
104C2×C4⋊C4×C29—21no—
105C2×C4⋊C4×C29—21no—
106C2×C4⋊C4×C29—24no—
107C2×C4⋊C4×C29—22no—
108C2×C4⋊C4×C29—21no—
109C2×C4⋊C4×C29D411yescharacteristic
110C2×C4⋊C4×C29D411yescharacteristic
111C2×C4⋊C4×C29D411yescharacteristic
112C2×C4⋊C4×C29D412yes—
113C2×C22⋊C4×C29—22no—
114C2×C22⋊C4×C29—22no—
115C2×C22⋊C4×C29—24no—
116C2×C22⋊C4×C29D411yescharacteristic
117C2×C22⋊C4×C29D412yes—
118C2×C22⋊C4×C29C2312yes—
119C2×C22⋊C4×C29C2312yes—
120C2×C22⋊C4×C29C2311yescharacteristic
121C2×C22⋊C4×C29C2312yes—
122C2×C22⋊C4×C29C2312yes—
123C2×C42×C29—21no—
124C2×C42×C29—21no—
125C2×C42×C29D411yescharacteristic
126C29×#99—24no—
127C29×#99—44no—
128C29×#95—21no—
129C29×#95—21no—
130C29×#95—22no—
131C29×#95—21no—
132C29×#95—24no—
133C29×#95—22no—
134C29×#95—24no—
135C24×C29C2×D412yes—
136C24×C29C2×D411yescharacteristic
137C24×C29C2411yescharacteristic
138#41×C29—82no—
139C2×Q8×C29—21no—
140C2×Q8×C29—21no—
141C2×Q8×C29—42no—
142C2×D4×C29—21no—
143C2×D4×C29—22no—
144C2×D4×C29—21no—
145C2×D4×C29—22no—
146C2×D4×C29—24no—
147C2×D4×C29—22no—
148C2×D4×C29—22no—
149C2×D4×C29—24no—
150C2×D4×C29—22no—
151C2×D4×C29—22no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—42no—
155C22×C4×C29—22no—
156C22×C4×C29—22no—
157C22×C4×C29—22no—
158C22×C4×C29—21no—
159C22×C4×C29—21no—
160C22×C4×C29—22no—
161C22×C4×C29—22no—
162C22×C4×C29—22no—
163C22×C4×C29—22no—
164C22×C4×C29—22no—
165C22×C4×C29—24no—
166C22×C4×C29—24no—
167C22×C4×C29—42no—
168C22×C4×C29—42no—
169C22×C4×C29C2×D411yescharacteristic
170C22×C4×C29C2×D412yes—
171C22×C4×C29C2×D411yescharacteristic
172C22×C4×C29C2×D411yescharacteristic
173C22×C4×C29C2×D411yescharacteristic
174C22×C4×C29C2×D411yescharacteristic
175C22×C4×C29C2×D412yes—
176C22×C4×C29C2×D411yescharacteristic
177C22×C4×C29C2×D412yes—
178C22×C4×C29C2×D411yescharacteristic
179C22×C4×C29C2×D411yescharacteristic
180C22×C4×C29C2×D411yescharacteristic
181C4⋊C4×C29—22no—
182C4⋊C4×C29—22no—
183C4⋊C4×C29—22no—
184C4⋊C4×C29—22no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—22no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—22no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—48no—
194C4⋊C4×C29—42no—
195C4⋊C4×C29—44no—
196C4⋊C4×C29—41no—
197C4⋊C4×C29—41no—
198C4⋊C4×C29—41no—
199C4⋊C4×C29—41no—
200C22⋊C4×C29—22no—
201C22⋊C4×C29—22no—
202C22⋊C4×C29—22no—
203C22⋊C4×C29—22no—
204C22⋊C4×C29—22no—
205C22⋊C4×C29—22no—
206C22⋊C4×C29—21no—
207C22⋊C4×C29—22no—
208C22⋊C4×C29—21no—
209C22⋊C4×C29—22no—
210C22⋊C4×C29—22no—
211C22⋊C4×C29—22no—
212C22⋊C4×C29—21no—
213C22⋊C4×C29—21no—
214C22⋊C4×C29—22no—
215C22⋊C4×C29—22no—
216C22⋊C4×C29—24no—
217C22⋊C4×C29—22no—
218C22⋊C4×C29—48no—
219C22⋊C4×C29—44no—
220C22⋊C4×C29#4114yescomplemented
221C42×C29—22no—
222C42×C29—22no—
223C42×C29—21no—
224C42×C29—21no—
225C42×C29—42no—
226C42×C29—42no—
227#25586C2911yesmaximal, characteristic, direct product factor, Sylow
228C23×C29—21no—
229C23×C29—22no—
230C23×C29—21no—
231C23×C29—21no—
232C23×C29—24no—
233C23×C29—41no—
234C23×C29—41no—
235C23×C29—41no—
236C23×C29—41no—
237C23×C29—42no—
238C23×C29—42no—
239C23×C29C22×D411yescharacteristic
240C23×C29C22×D411yescharacteristic
241C23×C29C22×D411yescharacteristic
242C23×C29C2×#4112yes—
243C23×C29H(5,𝔽2)12yes—
244Q8×C29—42no—
245Q8×C29—81no—
246D4×C29—42no—
247D4×C29—42no—
248D4×C29—42no—
249D4×C29—44no—
250D4×C29—42no—
251D4×C29—42no—
252D4×C29—81no—
253D4×C29—82no—
254D4×C29—82no—
255C2×C4×C29—22no—
256C2×C4×C29—22no—
257C2×C4×C29—22no—
258C2×C4×C29—21no—
259C2×C4×C29—22no—
260C2×C4×C29—21no—
261C2×C4×C29—21no—
262C2×C4×C29—22no—
263C2×C4×C29—22no—
264C2×C4×C29—21no—
265C2×C4×C29—21no—
266C2×C4×C29—24no—
267C2×C4×C29—24no—
268C2×C4×C29—41no—
269C2×C4×C29—41no—
270C2×C4×C29—41no—
271C2×C4×C29—42no—
272C2×C4×C29—42no—
273C2×C4×C29—42no—
274C2×C4×C29—41no—
275C2×C4×C29—41no—
276C2×C4×C29—42no—
277C2×C4×C29—42no—
278C2×C4×C29—42no—
279C2×C4×C29—42no—
280C2×C4×C29—42no—
281C2×C4×C29—42no—
282C2×C4×C29—42no—
283C2×C4×C29—42no—
284C2×C4×C29—42no—
285C2×C4×C29—42no—
286C2×C4×C29—44no—
287C2×C4×C29—42no—
288C2×C4×C29—44no—
289C2×C4×C29—81no—
290C2×C4×C29—82no—
291C2×C4×C29—82no—
292C2×C4×C29#12011yescharacteristic
293C2×C4×C29#12011yescharacteristic
294C2×C4×C29#12011yescharacteristic
295C2×C4×C29#12011yescharacteristic
296#3505C2×C2911yescharacteristic
297#2503C2×C2911yescharacteristic, complemented
298#2501C2×C2911yescharacteristic, complemented
299#2486C2×C2911yescharacteristic, complemented
300#2022C2×C2914yescomplemented
301#1996C2×C2911yescharacteristic, complemented
302#1964C2×C2911yescharacteristic, complemented
303#1890C2×C2914yescomplemented
304C4×#99C2×C2911yescharacteristic, complemented
305C22×C29—21no—
306C22×C29—21no—
307C22×C29—21no—
308C22×C29—21no—
309C22×C29—21no—
310C22×C29—21no—
311C22×C29—42no—
312C22×C29—42no—
313C22×C29—42no—
314C22×C29—41no—
315C22×C29—42no—
316C22×C29—41no—
317C22×C29—42no—
318C22×C29—42no—
319C22×C29—41no—
320C22×C29—84no—
321C22×C29—81no—
322C22×C29C2×#12011yescharacteristic
323C22×C29#53211yescharacteristic
324C22×C29#53511yescharacteristic
325C22×C29#54612yes—
326C22×C29#55012yes—
327C4×C29—21no—
328C4×C29—21no—
329C4×C29—21no—
330C4×C29—44no—
331C4×C29—41no—
332C4×C29—42no—
333C4×C29—41no—
334C4×C29—42no—
335C4×C29—41no—
336C4×C29—42no—
337C4×C29—82no—
338C4×C29—82no—
339C4×C29—82no—
340C4×C29#45812yes—
341#553—21no—
342#553—22no—
343#552—21no—
344#551—22no—
345#548—21no—
346#546—21no—
347#539—21no—
348#538—21no—
349#534C22×C2912yes—
350#529—21no—
351#525—21no—
352C2×#123C22×C2914yes—
353C2×#123C22×C2912yes—
354C2×C22⋊Q8C22×C2911yescharacteristic
355C2×#121C22×C2911yescharacteristic
356#518C22×C2912yes—
357C2×C4×D4C22×C2911yescharacteristic
358C22×C4⋊C4C22×C2911yescharacteristic
359C2×#99C22×C2912yes—
360C2×#99C22×C2914yes—
361#400—22no—
362#399—22no—
363#398—21no—
364#397—21no—
365#391—21no—
366#390—21no—
367#389—21no—
368#384—21no—
369#382—21no—
370#381C22×C2912yes—
371#381C22×C2914yes—
372#380—21no—
373#380C22×C2911yescharacteristic
374C4×C22⋊C4C22×C2911yescharacteristic
375C4×C22⋊C4C22×C2911yescharacteristic
376#342C22×C2912yes—
377#342C22×C2914yes—
378C2×C29—22no—
379C2×C29—21no—
380C2×C29—22no—
381C2×C29—21no—
382C2×C29—81no—
383C2×C29—82no—
384C2×C29#243111yescharacteristic
385C2×C29C2×#45811yescharacteristic
386C2×C29#302811yescharacteristic
387C2×#41—21no—
388C22×Q8D4×C2911yescharacteristic
389C22×D4D4×C2911yescharacteristic
390C22×D4C23×C2911yescharacteristic
391C22×D4C23×C2912yes—
392C23×C4D4×C2911yescharacteristic
393C23×C4C23×C2912yes—
394C23×C4C23×C2911yescharacteristic
395#126—22no—
396#126—22no—
397#126—22no—
398#125—21no—
399#125—22no—
400#124—21no—
401#124—22no—
402#123—22no—
403#123—22no—
404#123—22no—
405#123—22no—
406#123—22no—
407#123—28no—
408#123—44no—
409#123—44no—
410C22⋊Q8—21no—
411C22⋊Q8—22no—
412C22⋊Q8—21no—
413C22⋊Q8—21no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416#121—21no—
417#121—22no—
418#121—21no—
419#121—21no—
420#121—21no—
421#121—21no—
422#121—22no—
423#121—22no—
424#120—22no—
425#120—22no—
426C4×Q8—21no—
427C4×D4—22no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437#117—21no—
438#117—22no—
439#117—22no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4D4×C2911yescharacteristic
450C2×C4⋊C4D4×C2911yescharacteristic
451C2×C4⋊C4D4×C2911yescharacteristic
452C2×C4⋊C4D4×C2912yes—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4D4×C2911yescharacteristic
457C2×C22⋊C4D4×C2912yes—
458C2×C22⋊C4C23×C2912yes—
459C2×C22⋊C4C23×C2912yes—
460C2×C22⋊C4C23×C2911yescharacteristic
461C2×C22⋊C4C23×C2912yes—
462C2×C22⋊C4C23×C2912yes—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42D4×C2911yescharacteristic
466#99—24no—
467#99—44no—
468#95—21no—
469#95—21no—
470#95—22no—
471#95—21no—
472#95—24no—
473#95—22no—
474#95—24no—
475C29#2558611yescharacteristic, direct product factor, Sylow
476C24C2×D4×C2912yes—
477C24C2×D4×C2911yescharacteristic
478C24C24×C2911yescharacteristic
479#41—82no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—42no—
483C2×D4—21no—
484C2×D4—22no—
485C2×D4—21no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—24no—
489C2×D4—24no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4C2×D4×C2911yescharacteristic
511C22×C4C2×D4×C2912yes—
512C22×C4C2×D4×C2911yescharacteristic
513C22×C4C2×D4×C2911yescharacteristic
514C22×C4C2×D4×C2911yescharacteristic
515C22×C4C2×D4×C2911yescharacteristic
516C22×C4C2×D4×C2912yes—
517C22×C4C2×D4×C2911yescharacteristic
518C22×C4C2×D4×C2912yes—
519C22×C4C2×D4×C2911yescharacteristic
520C22×C4C2×D4×C2911yescharacteristic
521C22×C4C2×D4×C2911yescharacteristic
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—21no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—22no—
533C4⋊C4—21no—
534C4⋊C4—48no—
535C4⋊C4—44no—
536C4⋊C4—42no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—21no—
548C22⋊C4—22no—
549C22⋊C4—21no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—21no—
554C22⋊C4—21no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—24no—
559C22⋊C4—48no—
560C22⋊C4—44no—
561C22⋊C4#41×C2914yescomplemented
562C42—22no—
563C42—22no—
564C42—21no—
565C42—21no—
566C42—42no—
567C42—42no—
568C23—21no—
569C23—22no—
570C23—21no—
571C23—21no—
572C23—24no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—42no—
578C23—42no—
579C23C22×D4×C2911yescharacteristic
580C23C22×D4×C2911yescharacteristic
581C23C22×D4×C2911yescharacteristic
582C23C2×#41×C2912yes—
583C23C29×H(5,𝔽2)12yes—
584Q8—42no—
585Q8—81no—
586D4—42no—
587D4—42no—
588D4—42no—
589D4—42no—
590D4—44no—
591D4—42no—
592D4—81no—
593D4—82no—
594D4—82no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—44no—
627C2×C4—42no—
628C2×C4—44no—
629C2×C4—81no—
630C2×C4—82no—
631C2×C4—82no—
632C2×C4C29×#12011yescharacteristic
633C2×C4C29×#12011yescharacteristic
634C2×C4C29×#12011yescharacteristic
635C2×C4C29×#12011yescharacteristic
636C22—21no—
637C22—21no—
638C22—21no—
639C22—21no—
640C22—21no—
641C22—21no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—41no—
646C22—42no—
647C22—41no—
648C22—42no—
649C22—42no—
650C22—41no—
651C22—84no—
652C22—81no—
653C22C2×C29×#12011yescharacteristic
654C22C29×#53211yescharacteristic
655C22C29×#53511yescharacteristic
656C22C29×#54612yes—
657C22C29×#55012yes—
658C4—21no—
659C4—21no—
660C4—21no—
661C4—44no—
662C4—41no—
663C4—42no—
664C4—41no—
665C4—42no—
666C4—41no—
667C4—42no—
668C4—82no—
669C4—82no—
670C4—82no—
671C4C29×#45812yes—
672C2—22no—
673C2—21no—
674C2—22no—
675C2—21no—
676C2—81no—
677C2—82no—
678C2C29×#243111yescharacteristic
679C2C2×C29×#45811yescharacteristic
680C2C29×#302811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC24C24×C29
prime radicalC29×#3505C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2503C2semidirect
3. C29×#2501C2semidirect
4. C29×#2486C2semidirect
5. C29×#2022C2semidirect
6. C29×#1996C2semidirect
7. C29×#1964C2semidirect
8. C29×#1890C2semidirect
9. C4×C29×#99C2semidirect
220. C22⋊C4×C29#41semidirect
227. #25586C29direct (N × H)
297. #2503C2×C29semidirect
298. #2501C2×C29semidirect
299. #2486C2×C29semidirect
300. #2022C2×C29semidirect
301. #1996C2×C29semidirect
302. #1964C2×C29semidirect
303. #1890C2×C29semidirect
304. C4×#99C2×C29semidirect
475. C29#25586direct (N × H)
561. C22⋊C4#41×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#35052
C29×#25032
C29×#25012
C29×#24862
C29×#20222
C29×#19962
C29×#19642
C29×#18902
C4×C29×#992
#2558629