Finite Group Databasebeta

← C29×#62105 #20357005

Subgroups — C29×#62105 #20357005

Order 7424.

1728 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3518C211yesmaximal, characteristic, complemented
2C29×#3482C211yesmaximal, characteristic, complemented
3Q8×SD16×C29C211yesmaximal, characteristic, complemented
4Q8×D8×C29C211yesmaximal, characteristic, complemented
5C29×#3363C211yesmaximal, characteristic, complemented
6C29×#3359C211yesmaximal, characteristic, complemented
7C29×#3342C213yesmaximal, complemented
8C29×#3340C213yesmaximal, complemented
9C29×#3303C213yesmaximal, complemented
10C29×#3302C213yesmaximal, complemented
11C29×#3248C213yesmaximal, complemented
12C29×#3231C213yesmaximal, complemented
13C29×#3102C213yesmaximal, complemented
14C29×#3076C213yesmaximal, complemented
15C29×#2988C211yesmaximal, characteristic, complemented
16Q82×C29C2211yescharacteristic
17C29×#557C2211yescharacteristic
18C29×#556—23no—
19C29×#556C2213yes—
20C29×#556C2213yes—
21C29×#555C2213yes—
22C29×#552—23no—
23D4×Q8×C29C2211yescharacteristic
24D4×Q8×C29C2211yescharacteristic
25C29×#548—21no—
26C29×#548—21no—
27C29×#547C2213yes—
28C29×#542—23no—
29C29×#533C2213yes—
30C29×#533C2213yes—
31C29×#529—23no—
32C29×#529C2213yes—
33C29×#519—21no—
34C4×#41×C29C2213yes—
35C4×#41×C29C2211yescharacteristic
36C2×C4×Q8×C29—21no—
37C29×#500C2213yes—
38C29×#498C2213yes—
39C29×#487C2213yes—
40C29×#487C2213yes—
41C29×#485C2216yes—
42C29×#485C2216yes—
43C29×#485C2213yes—
44C29×#482C2213yes—
45C29×#479C2213yes—
46C29×#479C2216yes—
47C29×#478C2213yes—
48C29×#477C2213yes—
49C29×#476C2213yes—
50C29×#475C2213yes—
51C29×#475C2213yes—
52C29×#474C2213yes—
53C29×#474C2213yes—
54C29×#467C2216yes—
55C29×#465C2216yes—
56C29×#464C2213yes—
57C29×#463C2211yescharacteristic
58C29×#462C2213yes—
59C29×#461C2213yes—
60C29×#452C2213yes—
61C29×#449C2213yes—
62C8×Q8×C29C2211yescharacteristic
63C8×Q8×C29C2211yescharacteristic
64C4×Q16×C29C2213yes—
65C4×SD16×C29C2213yes—
66C4×SD16×C29C2213yes—
67C4×D8×C29C2213yes—
68C8×D4×C29C2213yes—
69C8×D4×C29C2213yes—
70C29×#431C2213yes—
71C29×#427C2216yes—
72C2×C29×C4⋊C8C2213yes—
73C29×#416C2216yes—
74C2×#41×C29D411yescharacteristic
75C2×#41×C29C2313yes—
76C22×Q8×C29—21no—
77C22×Q8×C29—21no—
78C2×Q16×C29C2313yes—
79C2×SD16×C29C2311yescharacteristic
80C2×SD16×C29C2313yes—
81C2×D8×C29C2311yescharacteristic
82C22×C8×C29C2316yes—
83C29×C4⋊Q8—23no—
84C29×C4⋊Q8C2313yes—
85C29×C4⋊Q8C2313yes—
86C29×C4⋊Q8C2313yes—
87C29×C4⋊Q8C2313yes—
88C29×#126—26no—
89C29×#126—26no—
90C29×#126—23no—
91C29×#125—23no—
92C29×#125—23no—
93C29×#125C2313yes—
94C29×#124—23no—
95C29×#124—23no—
96C29×#124—26no—
97C29×#124C2311yescharacteristic
98C29×#123—23no—
99C29×#123—26no—
100C29×C22⋊Q8—23no—
101C29×C22⋊Q8—23no—
102C29×C22⋊Q8—23no—
103C29×C22⋊Q8—23no—
104C29×C22⋊Q8—23no—
105C29×C22⋊Q8C2313yes—
106C29×C22⋊Q8C2316yes—
107C29×#121—23no—
108C29×#121—23no—
109C29×#121C2313yes—
110C4×Q8×C29—21no—
111C4×Q8×C29—21no—
112C4×Q8×C29—23no—
113C4×Q8×C29—23no—
114C4×Q8×C29—23no—
115C4×Q8×C29—23no—
116C4×Q8×C29—23no—
117C4×Q8×C29D411yescharacteristic
118C4×Q8×C29C2313yes—
119C4×Q8×C29C2313yes—
120C4×Q8×C29C2313yes—
121C4×Q8×C29C2311yescharacteristic
122C4×D4×C29—23no—
123C4×D4×C29—23no—
124C4×D4×C29—23no—
125C4×D4×C29D413yes—
126C4×D4×C29C2313yes—
127C4×D4×C29C2313yes—
128C4×D4×C29C2311yescharacteristic
129C4×D4×C29C2313yes—
130C29×#117—23no—
131C29×#117—23no—
132C29×#117—23no—
133C29×#117—23no—
134C29×#117D413yes—
135C29×#117C2313yes—
136C29×#117C2316yes—
137C2×C4⋊C4×C29—23no—
138C2×C42×C29—23no—
139C2×C42×C29C2313yes—
140C29×#107C2313yes—
141C29×#107C2316yes—
142C29×#107C2313yes—
143C29×#106C2313yes—
144C29×#106C2316yes—
145C29×#106C2313yes—
146C29×C4⋊C8C2311yescharacteristic
147C29×C4⋊C8C2313yes—
148C29×C4⋊C8C2313yes—
149C29×C4⋊C8C2313yes—
150C29×#103C2313yes—
151C29×#103C2313yes—
152C29×#103C2311yescharacteristic
153C29×#103C2313yes—
154C29×#103C2316yes—
155C29×#103C2316yes—
156C29×#102C2313yes—
157C29×#102C2313yes—
158C29×#102C2311yescharacteristic
159C29×#102C2313yes—
160C29×C22⋊C8C2313yes—
161C29×C22⋊C8C2313yes—
162C4×C8×C29C2313yes—
163C4×C8×C29C2313yes—
164#41×C29—24no—
165#41×C29—26no—
166#41×C29—43no—
167C2×Q8×C29—23no—
168C2×Q8×C29—23no—
169C2×Q8×C29—23no—
170C2×Q8×C29—44no—
171C2×Q8×C29—44no—
172C2×Q8×C29C2×D411yescharacteristic
173C2×Q8×C29C2411yescharacteristic
174C2×Q8×C29C2413yes—
175C2×D4×C29—23no—
176C2×D4×C29—23no—
177C2×D4×C29C2×D413yes—
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×C29C2413yes—
187Q16×C29—43no—
188SD16×C29—22no—
189SD16×C29—43no—
190D8×C29—22no—
191C2×C8×C29—46no—
192C2×C8×C29C2413yes—
193C2×C8×C29C2413yes—
194C2×C8×C29C2411yescharacteristic
195C2×C8×C29C2411yescharacteristic
196C4⋊C4×C29—23no—
197C4⋊C4×C29—26no—
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—23no—
207C4⋊C4×C29—23no—
208C4⋊C4×C29C2×D413yes—
209C4⋊C4×C29C2×D413yes—
210C4⋊C4×C29C2411yescharacteristic
211C4⋊C4×C29C2413yes—
212C4⋊C4×C29C2413yes—
213C4⋊C4×C29C2413yes—
214C22⋊C4×C29—26no—
215C22⋊C4×C29—23no—
216C22⋊C4×C29—26no—
217C22⋊C4×C29—23no—
218C22⋊C4×C29—21no—
219C22⋊C4×C29—23no—
220C22⋊C4×C29—21no—
221C22⋊C4×C29—23no—
222C22⋊C4×C29—21no—
223C22⋊C4×C29—23no—
224C22⋊C4×C29C2×D416yes—
225C42×C29—23no—
226C42×C29—23no—
227C42×C29—23no—
228C42×C29—26no—
229C42×C29—23no—
230C42×C29C2×D413yes—
231C42×C29C2×D413yes—
232C42×C29C2411yescharacteristic
233C42×C29C2413yes—
234#62105C2911yesmaximal, characteristic, direct product factor, Sylow
235C23×C29—21no—
236C23×C29—21no—
237C23×C29C22×D413yes—
238Q8×C29—21no—
239Q8×C29—23no—
240Q8×C29—23no—
241Q8×C29—21no—
242Q8×C29—46no—
243Q8×C29—46no—
244Q8×C29—83no—
245Q8×C29#13514yes—
246D4×C29—26no—
247D4×C29—21no—
248D4×C29—21no—
249D4×C29—21no—
250D4×C29—46no—
251D4×C29—83no—
252D4×C292−1+412yes—
253C2×C4×C29—26no—
254C2×C4×C29—23no—
255C2×C4×C29—23no—
256C2×C4×C29—21no—
257C2×C4×C29—21no—
258C2×C4×C29—23no—
259C2×C4×C29—23no—
260C2×C4×C29—23no—
261C2×C4×C29—23no—
262C2×C4×C29—43no—
263C2×C4×C29—46no—
264C2×C4×C29—42no—
265C2×C4×C29—46no—
266C2×C4×C29—46no—
267C2×C4×C29C22×D411yescharacteristic
268C2×C4×C29C22×D413yes—
269C2×C4×C29C22×D411yescharacteristic
270C2×C4×C29C22×D413yes—
271C2×C4×C29C22×D413yes—
272C2×C4×C29C2511yescharacteristic
273C8×C29—21no—
274C8×C29—21no—
275C8×C29—23no—
276C8×C29—23no—
277#3518C2×C2911yescharacteristic, complemented
278#3482C2×C2911yescharacteristic, complemented
279Q8×SD16C2×C2911yescharacteristic, complemented
280Q8×D8C2×C2911yescharacteristic, complemented
281#3363C2×C2911yescharacteristic, complemented
282#3359C2×C2911yescharacteristic, complemented
283#3342C2×C2913yescomplemented
284#3340C2×C2913yescomplemented
285#3303C2×C2913yescomplemented
286#3302C2×C2913yescomplemented
287#3248C2×C2913yescomplemented
288#3231C2×C2913yescomplemented
289#3102C2×C2913yescomplemented
290#3076C2×C2913yescomplemented
291#2988C2×C2911yescharacteristic, complemented
292C22×C29—23no—
293C22×C29—23no—
294C22×C29—22no—
295C22×C29—23no—
296C22×C29—41no—
297C22×C29—41no—
298C22×C29—41no—
299C22×C29—41no—
300C22×C29—41no—
301C22×C29C23×D411yescharacteristic
302C4×C29—21no—
303C4×C29—23no—
304C4×C29—23no—
305C4×C29—21no—
306C4×C29—41no—
307C4×C29—43no—
308C4×C29—43no—
309C4×C29—41no—
310C4×C29—43no—
311C4×C29—43no—
312C4×C29C2×#13516yes—
313C4×C29C2×2−1+411yescharacteristic
314C4×C29#58511yescharacteristic
315Q82C22×C2911yescharacteristic
316#557C22×C2911yescharacteristic
317#556—23no—
318#556C22×C2913yes—
319#556C22×C2913yes—
320#555C22×C2913yes—
321#552—23no—
322D4×Q8C22×C2911yescharacteristic
323D4×Q8C22×C2911yescharacteristic
324#548—21no—
325#548—21no—
326#547C22×C2913yes—
327#542—23no—
328#533C22×C2913yes—
329#533C22×C2913yes—
330#529—23no—
331#529C22×C2913yes—
332#519—21no—
333C4×#41C22×C2913yes—
334C4×#41C22×C2911yescharacteristic
335C2×C4×Q8—21no—
336#500C22×C2913yes—
337#498C22×C2913yes—
338#487C22×C2913yes—
339#487C22×C2913yes—
340#485C22×C2916yes—
341#485C22×C2913yes—
342#485C22×C2916yes—
343#482C22×C2913yes—
344#479C22×C2916yes—
345#479C22×C2913yes—
346#478C22×C2913yes—
347#477C22×C2913yes—
348#476C22×C2913yes—
349#475C22×C2913yes—
350#475C22×C2913yes—
351#474C22×C2913yes—
352#474C22×C2913yes—
353#467C22×C2916yes—
354#465C22×C2916yes—
355#464C22×C2913yes—
356#463C22×C2911yescharacteristic
357#462C22×C2913yes—
358#461C22×C2913yes—
359#452C22×C2913yes—
360#449C22×C2913yes—
361C8×Q8C22×C2911yescharacteristic
362C8×Q8C22×C2911yescharacteristic
363C4×Q16C22×C2913yes—
364C4×SD16C22×C2913yes—
365C4×SD16C22×C2913yes—
366C4×D8C22×C2913yes—
367C8×D4C22×C2913yes—
368C8×D4C22×C2913yes—
369#431C22×C2913yes—
370#427C22×C2916yes—
371C2×C4⋊C8C22×C2913yes—
372#416C22×C2916yes—
373C2×C29—43no—
374C2×C29—42no—
375C2×C29—81no—
376C2×C29#348911yescharacteristic
377C2×C29C22×#13511yescharacteristic
378C2×C29#358611yescharacteristic
379C2×#41D4×C2911yescharacteristic
380C2×#41C23×C2913yes—
381C22×Q8—21no—
382C22×Q8—21no—
383C2×Q16C23×C2913yes—
384C2×SD16C23×C2911yescharacteristic
385C2×SD16C23×C2913yes—
386C2×D8C23×C2911yescharacteristic
387C22×C8C23×C2916yes—
388C4⋊Q8—23no—
389C4⋊Q8C23×C2913yes—
390C4⋊Q8C23×C2913yes—
391C4⋊Q8C23×C2913yes—
392C4⋊Q8C23×C2913yes—
393#126—26no—
394#126—26no—
395#126—23no—
396#125—23no—
397#125—23no—
398#125C23×C2913yes—
399#124—23no—
400#124—23no—
401#124—26no—
402#124C23×C2911yescharacteristic
403#123—23no—
404#123—26no—
405C22⋊Q8—23no—
406C22⋊Q8—23no—
407C22⋊Q8—23no—
408C22⋊Q8—23no—
409C22⋊Q8—23no—
410C22⋊Q8C23×C2913yes—
411C22⋊Q8C23×C2916yes—
412#121—23no—
413#121—23no—
414#121C23×C2913yes—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8—23no—
418C4×Q8—23no—
419C4×Q8—23no—
420C4×Q8—23no—
421C4×Q8—23no—
422C4×Q8D4×C2911yescharacteristic
423C4×Q8C23×C2913yes—
424C4×Q8C23×C2913yes—
425C4×Q8C23×C2913yes—
426C4×Q8C23×C2911yescharacteristic
427C4×D4—23no—
428C4×D4—23no—
429C4×D4—23no—
430C4×D4D4×C2913yes—
431C4×D4C23×C2911yescharacteristic
432C4×D4C23×C2913yes—
433C4×D4C23×C2913yes—
434C4×D4C23×C2913yes—
435#117—23no—
436#117—23no—
437#117—23no—
438#117—23no—
439#117D4×C2913yes—
440#117C23×C2913yes—
441#117C23×C2916yes—
442C2×C4⋊C4—23no—
443C2×C42—23no—
444C2×C42C23×C2913yes—
445#107C23×C2913yes—
446#107C23×C2916yes—
447#107C23×C2913yes—
448#106C23×C2913yes—
449#106C23×C2916yes—
450#106C23×C2913yes—
451C4⋊C8C23×C2913yes—
452C4⋊C8C23×C2913yes—
453C4⋊C8C23×C2913yes—
454C4⋊C8C23×C2911yescharacteristic
455#103C23×C2916yes—
456#103C23×C2916yes—
457#103C23×C2913yes—
458#103C23×C2913yes—
459#103C23×C2911yescharacteristic
460#103C23×C2913yes—
461#102C23×C2913yes—
462#102C23×C2913yes—
463#102C23×C2913yes—
464#102C23×C2911yescharacteristic
465C22⋊C8C23×C2913yes—
466C22⋊C8C23×C2913yes—
467C4×C8C23×C2913yes—
468C4×C8C23×C2913yes—
469C29#6210511yescharacteristic, direct product factor, Sylow
470#41—24no—
471#41—26no—
472#41—43no—
473C2×Q8—23no—
474C2×Q8—23no—
475C2×Q8—23no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8C2×D4×C2911yescharacteristic
479C2×Q8C24×C2913yes—
480C2×Q8C24×C2911yescharacteristic
481C2×D4—23no—
482C2×D4—23no—
483C2×D4C2×D4×C2913yes—
484C2×D4C24×C2911yescharacteristic
485C2×D4C24×C2911yescharacteristic
486C22×C4—21no—
487C22×C4—23no—
488C22×C4—23no—
489C22×C4—23no—
490C22×C4C2×D4×C2913yes—
491C22×C4C2×D4×C2913yes—
492C22×C4C24×C2913yes—
493Q16—43no—
494SD16—22no—
495SD16—43no—
496D8—22no—
497C2×C8—46no—
498C2×C8C24×C2911yescharacteristic
499C2×C8C24×C2911yescharacteristic
500C2×C8C24×C2913yes—
501C2×C8C24×C2913yes—
502C4⋊C4—23no—
503C4⋊C4—26no—
504C4⋊C4—23no—
505C4⋊C4—23no—
506C4⋊C4—23no—
507C4⋊C4—23no—
508C4⋊C4—23no—
509C4⋊C4—23no—
510C4⋊C4—23no—
511C4⋊C4—23no—
512C4⋊C4—23no—
513C4⋊C4—23no—
514C4⋊C4C2×D4×C2913yes—
515C4⋊C4C2×D4×C2913yes—
516C4⋊C4C24×C2913yes—
517C4⋊C4C24×C2913yes—
518C4⋊C4C24×C2911yescharacteristic
519C4⋊C4C24×C2913yes—
520C22⋊C4—26no—
521C22⋊C4—23no—
522C22⋊C4—26no—
523C22⋊C4—23no—
524C22⋊C4—21no—
525C22⋊C4—23no—
526C22⋊C4—21no—
527C22⋊C4—23no—
528C22⋊C4—21no—
529C22⋊C4—23no—
530C22⋊C4C2×D4×C2916yes—
531C42—23no—
532C42—23no—
533C42—23no—
534C42—26no—
535C42—23no—
536C42C2×D4×C2913yes—
537C42C2×D4×C2913yes—
538C42C24×C2913yes—
539C42C24×C2911yescharacteristic
540C23—21no—
541C23—21no—
542C23C22×D4×C2913yes—
543Q8—21no—
544Q8—23no—
545Q8—23no—
546Q8—21no—
547Q8—46no—
548Q8—46no—
549Q8—83no—
550Q8C29×#13514yes—
551D4—26no—
552D4—21no—
553D4—21no—
554D4—21no—
555D4—46no—
556D4—83no—
557D4C29×2−1+412yes—
558C2×C4—26no—
559C2×C4—23no—
560C2×C4—23no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—23no—
564C2×C4—23no—
565C2×C4—23no—
566C2×C4—23no—
567C2×C4—43no—
568C2×C4—46no—
569C2×C4—42no—
570C2×C4—46no—
571C2×C4—46no—
572C2×C4C22×D4×C2911yescharacteristic
573C2×C4C22×D4×C2913yes—
574C2×C4C22×D4×C2911yescharacteristic
575C2×C4C22×D4×C2913yes—
576C2×C4C22×D4×C2913yes—
577C2×C4C25×C2911yescharacteristic
578C8—21no—
579C8—21no—
580C8—23no—
581C8—23no—
582C22—23no—
583C22—22no—
584C22—23no—
585C22—23no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22C23×D4×C2911yescharacteristic
592C4—23no—
593C4—21no—
594C4—21no—
595C4—23no—
596C4—43no—
597C4—41no—
598C4—43no—
599C4—43no—
600C4—41no—
601C4—43no—
602C4C2×C29×#13516yes—
603C4C2×C29×2−1+411yescharacteristic
604C4C29×#58511yescharacteristic
605C2—43no—
606C2—42no—
607C2—81no—
608C2C29×#348911yescharacteristic
609C2C22×C29×#13511yescharacteristic
610C2C29×#358611yescharacteristic
subgroupG/H
center, socleC22×C29C23×D4
commutator, Frattini, cosocleC2×C4C25×C29
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C4×#41×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3518C2semidirect
2. C29×#3482C2semidirect
3. Q8×SD16×C29C2semidirect
4. Q8×D8×C29C2semidirect
5. C29×#3363C2semidirect
6. C29×#3359C2semidirect
7. C29×#3342C2semidirect
8. C29×#3340C2semidirect
9. C29×#3303C2semidirect
10. C29×#3302C2semidirect
11. C29×#3248C2semidirect
12. C29×#3231C2semidirect
13. C29×#3102C2semidirect
14. C29×#3076C2semidirect
15. C29×#2988C2semidirect
234. #62105C29direct (N × H)
277. #3518C2×C29semidirect
278. #3482C2×C29semidirect
279. Q8×SD16C2×C29semidirect
280. Q8×D8C2×C29semidirect
281. #3363C2×C29semidirect
282. #3359C2×C29semidirect
283. #3342C2×C29semidirect
284. #3340C2×C29semidirect
285. #3303C2×C29semidirect
286. #3302C2×C29semidirect
287. #3248C2×C29semidirect
288. #3231C2×C29semidirect
289. #3102C2×C29semidirect
290. #3076C2×C29semidirect
291. #2988C2×C29semidirect
469. C29#62105direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35182
C29×#34822
Q8×SD16×C292
Q8×D8×C292
C29×#33632
C29×#33592
C29×#33422
C29×#33402
C29×#33032
C29×#33022
C29×#32482
C29×#32312
C29×#31022
C29×#30762
C29×#29882
#6210529