Finite Group Databasebeta

← C29×#61824 #20356724

Subgroups — C29×#61824 #20356724

Order 7424.

1694 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3523C211yesmaximal, characteristic, complemented
2Q8×#41×C29C211yesmaximal, characteristic, complemented
3C29×#3383C213yesmaximal, complemented
4C29×#3381C213yesmaximal, complemented
5Q8×SD16×C29C211yesmaximal, characteristic, complemented
6Q8×D8×C29C211yesmaximal, characteristic, complemented
7C29×#3364C213yesmaximal, complemented
8C29×#3363C211yesmaximal, characteristic, complemented
9C29×#3360C213yesmaximal, complemented
10C29×#3359C211yesmaximal, characteristic, complemented
11C29×#3233C213yesmaximal, complemented
12C29×#3231C213yesmaximal, complemented
13C29×#3107C213yesmaximal, complemented
14C29×#3102C213yesmaximal
15C29×#2982C211yesmaximal, characteristic, complemented
16Q82×C29C2211yescharacteristic
17C29×#557C2211yescharacteristic
18C29×#557C2213yes—
19C29×#557C2213yes—
20C29×#556C2213yes—
21C29×#554—23no—
22C29×#554C2213yes—
23C29×#552—23no—
24D4×Q8×C29—21no—
25D4×Q8×C29—21no—
26D4×Q8×C29C2211yescharacteristic
27D4×Q8×C29C2211yescharacteristic
28C29×#541—23no—
29C29×#533—23no—
30C29×#533C2213yes—
31C29×#533C2213yes—
32C29×#529C2213yes—
33C29×#519—21no—
34C4×#41×C29C2213yes—
35C2×C4×Q8×C29—21no—
36C2×C4×Q8×C29C2211yescharacteristic
37C29×#500C2213yes—
38C29×#499C2216yes—
39C29×#498C2213yes—
40C29×#488C2216yes—
41C29×#487C2213yes—
42C29×#487C2213yes—
43C29×#485C2213yes—
44C29×#485C2216yes—
45C29×#482C2213yes—
46C29×#479C2216yes—
47C29×#479C2216yes—
48C29×#479C2213yes—
49C29×#478C2213yes—
50C29×#477C2213yes—
51C29×#476C2213yes—
52C29×#475C2213yes—
53C29×#475C2213yes—
54C29×#474C2213yes—
55C29×#474C2213yes—
56C29×#464C2213yes—
57C29×#463C2213yes—
58C29×#462C2213yes—
59C29×#461C2213yes—
60C29×#452C2213yes—
61C29×#449C2211yescharacteristic
62C8×Q8×C29C2211yescharacteristic
63C8×Q8×C29C2213yes—
64C8×Q8×C29C2211yescharacteristic
65C8×Q8×C29C2213yes—
66C4×Q16×C29C2213yes—
67C4×Q16×C29C2216yes—
68C4×SD16×C29C2213yes—
69C4×SD16×C29C2213yes—
70C4×SD16×C29C2216yes—
71C4×D8×C29C2213yes—
72C29×#431C2213yes—
73C29×#431C2213yes—
74C2×#41×C29C2311yescharacteristic
75C22×Q8×C29—21no—
76C22×Q8×C29—21no—
77C22×Q8×C29D411yescharacteristic
78C2×Q16×C29C2313yes—
79C2×SD16×C29C2311yescharacteristic
80C2×SD16×C29C2313yes—
81C2×D8×C29C2311yescharacteristic
82C29×C4⋊Q8—23no—
83C29×C4⋊Q8—23no—
84C29×C4⋊Q8—23no—
85C29×C4⋊Q8C2313yes—
86C29×C4⋊Q8C2313yes—
87C29×C4⋊Q8C2313yes—
88C29×C4⋊Q8C2313yes—
89C29×#126—26no—
90C29×#126—23no—
91C29×#125—26no—
92C29×#125—26no—
93C29×#125—23no—
94C29×#125—23no—
95C29×#125C2313yes—
96C29×#125C2316yes—
97C29×#124C2313yes—
98C29×#123—23no—
99C29×C22⋊Q8—23no—
100C29×C22⋊Q8—23no—
101C29×C22⋊Q8—23no—
102C29×C22⋊Q8—23no—
103C29×C22⋊Q8—23no—
104C29×C22⋊Q8—23no—
105C29×C22⋊Q8—26no—
106C29×C22⋊Q8—23no—
107C29×C22⋊Q8C2313yes—
108C29×#121C2311yescharacteristic
109C4×Q8×C29—21no—
110C4×Q8×C29—21no—
111C4×Q8×C29—23no—
112C4×Q8×C29—23no—
113C4×Q8×C29—23no—
114C4×Q8×C29—23no—
115C4×Q8×C29—23no—
116C4×Q8×C29D411yescharacteristic
117C4×Q8×C29D413yes—
118C4×Q8×C29C2313yes—
119C4×Q8×C29C2313yes—
120C4×Q8×C29C2316yes—
121C4×Q8×C29C2313yes—
122C4×Q8×C29C2311yescharacteristic
123C4×Q8×C29C2313yes—
124C4×D4×C29—23no—
125C4×D4×C29—23no—
126C4×D4×C29—23no—
127C4×D4×C29C2313yes—
128C4×D4×C29C2313yes—
129C4×D4×C29C2313yes—
130C29×#117—23no—
131C29×#117—23no—
132C29×#117—23no—
133C29×#117—23no—
134C29×#117C2313yes—
135C2×C4⋊C4×C29—23no—
136C2×C4⋊C4×C29D413yes—
137C2×C42×C29—23no—
138C2×C42×C29C2313yes—
139C29×#107C2313yes—
140C29×#107C2316yes—
141C29×#107C2313yes—
142C29×#106C2313yes—
143C29×#106C2316yes—
144C29×#106C2313yes—
145C29×C4⋊C8C2313yes—
146C29×C4⋊C8C2313yes—
147C29×C4⋊C8C2313yes—
148C29×C4⋊C8C2313yes—
149C29×#103C2313yes—
150C29×#103C2316yes—
151C29×#103C2313yes—
152C29×#103C2311yescharacteristic
153C29×#103C2316yes—
154C29×#103C2313yes—
155C29×#102C2313yes—
156C29×#102C2313yes—
157C29×#102C2311yescharacteristic
158C29×#102C2313yes—
159C29×C22⋊C8C2311yescharacteristic
160C29×C22⋊C8C2313yes—
161C4×C8×C29C2313yes—
162C4×C8×C29C2313yes—
163C4×C8×C29C2316yes—
164#41×C29—22no—
165#41×C29—22no—
166C2×Q8×C29—24no—
167C2×Q8×C29—23no—
168C2×Q8×C29—23no—
169C2×Q8×C29—23no—
170C2×Q8×C29—44no—
171C2×Q8×C29—44no—
172C2×Q8×C29C2×D413yes—
173C2×Q8×C29C2×D411yescharacteristic
174C2×Q8×C29C2413yes—
175C2×Q8×C29C2411yescharacteristic
176C2×D4×C29—21no—
177C2×D4×C29—21no—
178C2×D4×C29C2411yescharacteristic
179C2×D4×C29C2411yescharacteristic
180C22×C4×C29—21no—
181C22×C4×C29—23no—
182C22×C4×C29—23no—
183C22×C4×C29—23no—
184C22×C4×C29C2×D413yes—
185C22×C4×C29C2×D413yes—
186C22×C4×C29C2411yescharacteristic
187Q16×C29—26no—
188SD16×C29—22no—
189SD16×C29—26no—
190D8×C29—22no—
191C2×C8×C29C2411yescharacteristic
192C2×C8×C29C2411yescharacteristic
193C2×C8×C29C2413yes—
194C2×C8×C29C2413yes—
195C4⋊C4×C29—26no—
196C4⋊C4×C29—23no—
197C4⋊C4×C29—23no—
198C4⋊C4×C29—23no—
199C4⋊C4×C29—23no—
200C4⋊C4×C29—23no—
201C4⋊C4×C29—23no—
202C4⋊C4×C29—23no—
203C4⋊C4×C29—23no—
204C4⋊C4×C29—23no—
205C4⋊C4×C29—23no—
206C4⋊C4×C29—26no—
207C4⋊C4×C29—26no—
208C4⋊C4×C29—23no—
209C4⋊C4×C29C2×D413yes—
210C4⋊C4×C29C2×D413yes—
211C4⋊C4×C29C2×D416yes—
212C4⋊C4×C29C2413yes—
213C4⋊C4×C29C2413yes—
214C4⋊C4×C29C2413yes—
215C4⋊C4×C29C2411yescharacteristic
216C22⋊C4×C29—23no—
217C22⋊C4×C29—23no—
218C22⋊C4×C29—21no—
219C22⋊C4×C29—23no—
220C22⋊C4×C29—23no—
221C22⋊C4×C29—23no—
222C22⋊C4×C29—23no—
223C22⋊C4×C29—23no—
224C42×C29—23no—
225C42×C29—23no—
226C42×C29—23no—
227C42×C29—26no—
228C42×C29—23no—
229C42×C29C2×D413yes—
230C42×C29C2×D413yes—
231C42×C29C2413yes—
232C42×C29C2413yes—
233#61824C2911yesmaximal, characteristic, direct product factor, Sylow
234C23×C29—21no—
235C23×C29—21no—
236C23×C29C22×D411yescharacteristic
237Q8×C29—26no—
238Q8×C29—21no—
239Q8×C29—23no—
240Q8×C29—23no—
241Q8×C29—46no—
242Q8×C29—46no—
243Q8×C29—83no—
244Q8×C29#13514yes—
245Q8×C292−1+412yes—
246D4×C29—24no—
247D4×C29—21no—
248D4×C29—21no—
249D4×C29—21no—
250D4×C29—42no—
251D4×C292−1+412yes—
252C2×C4×C29—24no—
253C2×C4×C29—21no—
254C2×C4×C29—26no—
255C2×C4×C29—21no—
256C2×C4×C29—21no—
257C2×C4×C29—23no—
258C2×C4×C29—21no—
259C2×C4×C29—23no—
260C2×C4×C29—23no—
261C2×C4×C29—23no—
262C2×C4×C29—43no—
263C2×C4×C29—46no—
264C2×C4×C29—46no—
265C2×C4×C29—83no—
266C2×C4×C29C22×D411yescharacteristic
267C2×C4×C29C22×D413yes—
268C2×C4×C29C22×D413yes—
269C2×C4×C29C22×D413yes—
270C2×C4×C29C22×D413yes—
271C2×C4×C29C2511yescharacteristic
272C8×C29—21no—
273C8×C29—21no—
274C8×C29—23no—
275C8×C29—23no—
276#3523C2×C2911yescharacteristic, complemented
277Q8×#41C2×C2911yescharacteristic, complemented
278#3383C2×C2913yescomplemented
279#3381C2×C2913yescomplemented
280Q8×SD16C2×C2911yescharacteristic, complemented
281Q8×D8C2×C2911yescharacteristic, complemented
282#3364C2×C2913yescomplemented
283#3363C2×C2911yescharacteristic, complemented
284#3360C2×C2913yescomplemented
285#3359C2×C2911yescharacteristic, complemented
286#3233C2×C2913yescomplemented
287#3231C2×C2913yescomplemented
288#3107C2×C2913yescomplemented
289#3102C2×C2913yes—
290#2982C2×C2911yescharacteristic, complemented
291C22×C29—21no—
292C22×C29—21no—
293C22×C29—22no—
294C22×C29—21no—
295C22×C29—41no—
296C22×C29—41no—
297C22×C29—41no—
298C22×C29—41no—
299C22×C29—41no—
300C22×C29C23×D411yescharacteristic
301C4×C29—23no—
302C4×C29—23no—
303C4×C29—21no—
304C4×C29—22no—
305C4×C29—23no—
306C4×C29—43no—
307C4×C29—41no—
308C4×C29—43no—
309C4×C29—43no—
310C4×C29—43no—
311C4×C29C2×#13516yes—
312C4×C29C2×2−1+411yescharacteristic
313C4×C29C2×2−1+411yescharacteristic
314Q82C22×C2911yescharacteristic
315#557C22×C2911yescharacteristic
316#557C22×C2913yes—
317#557C22×C2913yes—
318#556C22×C2913yes—
319#554—23no—
320#554C22×C2913yes—
321#552—23no—
322D4×Q8—21no—
323D4×Q8—21no—
324D4×Q8C22×C2911yescharacteristic
325D4×Q8C22×C2911yescharacteristic
326#541—23no—
327#533—23no—
328#533C22×C2913yes—
329#533C22×C2913yes—
330#529C22×C2913yes—
331#519—21no—
332C4×#41C22×C2913yes—
333C2×C4×Q8—21no—
334C2×C4×Q8C22×C2911yescharacteristic
335#500C22×C2913yes—
336#499C22×C2916yes—
337#498C22×C2913yes—
338#488C22×C2916yes—
339#487C22×C2913yes—
340#487C22×C2913yes—
341#485C22×C2913yes—
342#485C22×C2916yes—
343#482C22×C2913yes—
344#479C22×C2913yes—
345#479C22×C2916yes—
346#479C22×C2916yes—
347#478C22×C2913yes—
348#477C22×C2913yes—
349#476C22×C2913yes—
350#475C22×C2913yes—
351#475C22×C2913yes—
352#474C22×C2913yes—
353#474C22×C2913yes—
354#464C22×C2913yes—
355#463C22×C2913yes—
356#462C22×C2913yes—
357#461C22×C2913yes—
358#452C22×C2913yes—
359#449C22×C2911yescharacteristic
360C8×Q8C22×C2911yescharacteristic
361C8×Q8C22×C2913yes—
362C8×Q8C22×C2911yescharacteristic
363C8×Q8C22×C2913yes—
364C4×Q16C22×C2913yes—
365C4×Q16C22×C2916yes—
366C4×SD16C22×C2913yes—
367C4×SD16C22×C2913yes—
368C4×SD16C22×C2916yes—
369C4×D8C22×C2913yes—
370#431C22×C2913yes—
371#431C22×C2913yes—
372C2×C29—41no—
373C2×C29—42no—
374C2×C29—81no—
375C2×C29#348611yescharacteristic
376C2×C29C22×#13511yescharacteristic
377C2×C29#358611yescharacteristic
378C2×#41C23×C2911yescharacteristic
379C22×Q8—21no—
380C22×Q8—21no—
381C22×Q8D4×C2911yescharacteristic
382C2×Q16C23×C2913yes—
383C2×SD16C23×C2911yescharacteristic
384C2×SD16C23×C2913yes—
385C2×D8C23×C2911yescharacteristic
386C4⋊Q8—23no—
387C4⋊Q8—23no—
388C4⋊Q8—23no—
389C4⋊Q8C23×C2913yes—
390C4⋊Q8C23×C2913yes—
391C4⋊Q8C23×C2913yes—
392C4⋊Q8C23×C2913yes—
393#126—26no—
394#126—23no—
395#125—26no—
396#125—26no—
397#125—23no—
398#125—23no—
399#125C23×C2913yes—
400#125C23×C2916yes—
401#124C23×C2913yes—
402#123—23no—
403C22⋊Q8—23no—
404C22⋊Q8—23no—
405C22⋊Q8—23no—
406C22⋊Q8—23no—
407C22⋊Q8—23no—
408C22⋊Q8—23no—
409C22⋊Q8—26no—
410C22⋊Q8—23no—
411C22⋊Q8C23×C2913yes—
412#121C23×C2911yescharacteristic
413C4×Q8—21no—
414C4×Q8—21no—
415C4×Q8—23no—
416C4×Q8—23no—
417C4×Q8—23no—
418C4×Q8—23no—
419C4×Q8—23no—
420C4×Q8D4×C2911yescharacteristic
421C4×Q8D4×C2913yes—
422C4×Q8C23×C2913yes—
423C4×Q8C23×C2913yes—
424C4×Q8C23×C2913yes—
425C4×Q8C23×C2916yes—
426C4×Q8C23×C2911yescharacteristic
427C4×Q8C23×C2913yes—
428C4×D4—23no—
429C4×D4—23no—
430C4×D4—23no—
431C4×D4C23×C2913yes—
432C4×D4C23×C2913yes—
433C4×D4C23×C2913yes—
434#117—23no—
435#117—23no—
436#117—23no—
437#117—23no—
438#117C23×C2913yes—
439C2×C4⋊C4—23no—
440C2×C4⋊C4D4×C2913yes—
441C2×C42—23no—
442C2×C42C23×C2913yes—
443#107C23×C2913yes—
444#107C23×C2916yes—
445#107C23×C2913yes—
446#106C23×C2913yes—
447#106C23×C2916yes—
448#106C23×C2913yes—
449C4⋊C8C23×C2913yes—
450C4⋊C8C23×C2913yes—
451C4⋊C8C23×C2913yes—
452C4⋊C8C23×C2913yes—
453#103C23×C2913yes—
454#103C23×C2916yes—
455#103C23×C2913yes—
456#103C23×C2911yescharacteristic
457#103C23×C2916yes—
458#103C23×C2913yes—
459#102C23×C2913yes—
460#102C23×C2913yes—
461#102C23×C2911yescharacteristic
462#102C23×C2913yes—
463C22⋊C8C23×C2911yescharacteristic
464C22⋊C8C23×C2913yes—
465C4×C8C23×C2913yes—
466C4×C8C23×C2913yes—
467C4×C8C23×C2916yes—
468C29#6182411yescharacteristic, direct product factor, Sylow
469#41—22no—
470#41—22no—
471C2×Q8—24no—
472C2×Q8—23no—
473C2×Q8—23no—
474C2×Q8—23no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8C2×D4×C2913yes—
478C2×Q8C2×D4×C2911yescharacteristic
479C2×Q8C24×C2913yes—
480C2×Q8C24×C2911yescharacteristic
481C2×D4—21no—
482C2×D4—21no—
483C2×D4C24×C2911yescharacteristic
484C2×D4C24×C2911yescharacteristic
485C22×C4—21no—
486C22×C4—23no—
487C22×C4—23no—
488C22×C4—23no—
489C22×C4C2×D4×C2913yes—
490C22×C4C2×D4×C2913yes—
491C22×C4C24×C2911yescharacteristic
492Q16—26no—
493SD16—22no—
494SD16—26no—
495D8—22no—
496C2×C8C24×C2913yes—
497C2×C8C24×C2911yescharacteristic
498C2×C8C24×C2913yes—
499C2×C8C24×C2911yescharacteristic
500C4⋊C4—26no—
501C4⋊C4—23no—
502C4⋊C4—23no—
503C4⋊C4—23no—
504C4⋊C4—23no—
505C4⋊C4—23no—
506C4⋊C4—23no—
507C4⋊C4—23no—
508C4⋊C4—23no—
509C4⋊C4—23no—
510C4⋊C4—23no—
511C4⋊C4—26no—
512C4⋊C4—26no—
513C4⋊C4—23no—
514C4⋊C4C2×D4×C2913yes—
515C4⋊C4C2×D4×C2913yes—
516C4⋊C4C2×D4×C2916yes—
517C4⋊C4C24×C2913yes—
518C4⋊C4C24×C2913yes—
519C4⋊C4C24×C2913yes—
520C4⋊C4C24×C2911yescharacteristic
521C22⋊C4—23no—
522C22⋊C4—23no—
523C22⋊C4—21no—
524C22⋊C4—23no—
525C22⋊C4—23no—
526C22⋊C4—23no—
527C22⋊C4—23no—
528C22⋊C4—23no—
529C42—23no—
530C42—23no—
531C42—23no—
532C42—26no—
533C42—23no—
534C42C2×D4×C2913yes—
535C42C2×D4×C2913yes—
536C42C24×C2913yes—
537C42C24×C2913yes—
538C23—21no—
539C23—21no—
540C23C22×D4×C2911yescharacteristic
541Q8—26no—
542Q8—21no—
543Q8—23no—
544Q8—23no—
545Q8—46no—
546Q8—46no—
547Q8—83no—
548Q8C29×#13514yes—
549Q8C29×2−1+412yes—
550D4—24no—
551D4—21no—
552D4—21no—
553D4—21no—
554D4—42no—
555D4C29×2−1+412yes—
556C2×C4—24no—
557C2×C4—21no—
558C2×C4—26no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—23no—
562C2×C4—21no—
563C2×C4—23no—
564C2×C4—23no—
565C2×C4—23no—
566C2×C4—43no—
567C2×C4—46no—
568C2×C4—46no—
569C2×C4—83no—
570C2×C4C22×D4×C2911yescharacteristic
571C2×C4C22×D4×C2913yes—
572C2×C4C22×D4×C2913yes—
573C2×C4C22×D4×C2913yes—
574C2×C4C22×D4×C2913yes—
575C2×C4C25×C2911yescharacteristic
576C8—21no—
577C8—21no—
578C8—23no—
579C8—23no—
580C22—21no—
581C22—22no—
582C22—21no—
583C22—21no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22C23×D4×C2911yescharacteristic
590C4—21no—
591C4—22no—
592C4—23no—
593C4—23no—
594C4—23no—
595C4—43no—
596C4—43no—
597C4—43no—
598C4—43no—
599C4—41no—
600C4C2×C29×#13516yes—
601C4C2×C29×2−1+411yescharacteristic
602C4C2×C29×2−1+411yescharacteristic
603C2—41no—
604C2—42no—
605C2—81no—
606C2C29×#348611yescharacteristic
607C2C22×C29×#13511yescharacteristic
608C2C29×#358611yescharacteristic
subgroupG/H
center, socleC22×C29C23×D4
commutator, Frattini, cosocleC2×C4C25×C29
prime radicalC29×#449C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C4×Q8×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3523C2semidirect
2. Q8×#41×C29C2semidirect
3. C29×#3383C2semidirect
4. C29×#3381C2semidirect
5. Q8×SD16×C29C2semidirect
6. Q8×D8×C29C2semidirect
7. C29×#3364C2semidirect
8. C29×#3363C2semidirect
9. C29×#3360C2semidirect
10. C29×#3359C2semidirect
11. C29×#3233C2semidirect
12. C29×#3231C2semidirect
13. C29×#3107C2semidirect
15. C29×#2982C2semidirect
233. #61824C29direct (N × H)
276. #3523C2×C29semidirect
277. Q8×#41C2×C29semidirect
278. #3383C2×C29semidirect
279. #3381C2×C29semidirect
280. Q8×SD16C2×C29semidirect
281. Q8×D8C2×C29semidirect
282. #3364C2×C29semidirect
283. #3363C2×C29semidirect
284. #3360C2×C29semidirect
285. #3359C2×C29semidirect
286. #3233C2×C29semidirect
287. #3231C2×C29semidirect
288. #3107C2×C29semidirect
290. #2982C2×C29semidirect
468. C29#61824direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35232
Q8×#41×C292
C29×#33832
C29×#33812
Q8×SD16×C292
Q8×D8×C292
C29×#33642
C29×#33632
C29×#33602
C29×#33592
C29×#32332
C29×#32312
C29×#31072
C29×#31022
C29×#29822
#6182429