Finite Group Databasebeta

← C29×#61957 #20356857

Subgroups — C29×#61957 #20356857

Order 7424.

1868 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3517C211yesmaximal, characteristic, complemented
2C29×#3482C211yesmaximal, characteristic, complemented
3C29×#3395C211yesmaximal, characteristic, complemented
4C29×#3392C211yesmaximal, characteristic, complemented
5C29×#3359C211yesmaximal, characteristic, complemented
6C29×#3358C211yesmaximal, characteristic, complemented
7C29×#3304C213yesmaximal, complemented
8C29×#3302C213yesmaximal, complemented
9C29×#3284C213yesmaximal, complemented
10C29×#3283C213yesmaximal, complemented
11C29×#3248C213yesmaximal, complemented
12C29×#3210C213yesmaximal, complemented
13C29×#3102C213yesmaximal, complemented
14C29×#3035C213yesmaximal, complemented
15C29×#2988C211yesmaximal, characteristic, complemented
16C2×C29×#135C2216yes—
17C29×#557C2211yescharacteristic
18C29×#557C2211yescharacteristic
19C29×#556C2213yes—
20C29×#553—23no—
21C29×#552—23no—
22C29×#550—21no—
23C29×#550C2213yes—
24C29×#550C2211yescharacteristic
25D4×Q8×C29C2211yescharacteristic
26C29×#548—21no—
27C29×#547C2213yes—
28C29×#547C2213yes—
29C29×#540—23no—
30C29×#533C2213yes—
31C29×#532C2213yes—
32C29×#529—23no—
33C29×#529C2213yes—
34C29×#520—21no—
35C4×#41×C29C2213yes—
36C4×#41×C29C2211yescharacteristic
37C2×C4×Q8×C29—21no—
38C29×#494C2213yes—
39C29×#492C2213yes—
40C29×#487C2213yes—
41C29×#486C2213yes—
42C29×#485C2213yes—
43C29×#482C2213yes—
44C29×#479C2213yes—
45C29×#478C2211yescharacteristic
46C29×#475C2213yes—
47C29×#474C2213yes—
48C29×#467C2216yes—
49C29×#465C2216yes—
50C29×#464C2213yes—
51C29×#464C2216yes—
52C29×#463C2213yes—
53C29×#462C2213yes—
54C29×#462C2213yes—
55C29×#461C2213yes—
56C29×#461C2213yes—
57C29×#460C2213yes—
58C29×#459C2213yes—
59C29×#452C2216yes—
60C29×#452C2216yes—
61C29×#452C2213yes—
62C29×#449C2213yes—
63C8×Q8×C29C2211yescharacteristic
64C8×Q8×C29C2211yescharacteristic
65C4×Q16×C29C2213yes—
66C4×SD16×C29C2213yes—
67C4×SD16×C29C2213yes—
68C4×D8×C29C2213yes—
69C8×D4×C29C2213yes—
70C8×D4×C29C2213yes—
71C29×#431C2213yes—
72C2×C29×C4⋊C8C2213yes—
73C29×#416C2216yes—
74C2×#41×C29—21no—
75C2×#41×C29D411yescharacteristic
76C2×#41×C29C2313yes—
77C2×#41×C29C2316yes—
78C22×Q8×C29—21no—
79C29×#135—412no—
80C2×Q16×C29C2313yes—
81C2×Q16×C29C2316yes—
82C2×SD16×C29C2313yes—
83C2×SD16×C29C2313yes—
84C2×SD16×C29C2316yes—
85C2×D8×C29C2313yes—
86C22×C8×C29C2316yes—
87C29×C4⋊Q8C2313yes—
88C29×C4⋊Q8C2313yes—
89C29×C4⋊Q8C2313yes—
90C29×#127—23no—
91C29×#127C2313yes—
92C29×#126—26no—
93C29×#126—23no—
94C29×#125—23no—
95C29×#125—23no—
96C29×#125—23no—
97C29×#125C2311yescharacteristic
98C29×#124—23no—
99C29×#124C2313yes—
100C29×#123—23no—
101C29×#123—26no—
102C29×#123—26no—
103C29×C22⋊Q8—23no—
104C29×C22⋊Q8—23no—
105C29×C22⋊Q8C2316yes—
106C29×C22⋊Q8C2313yes—
107C29×#121—23no—
108C29×#121—23no—
109C29×#121—23no—
110C29×#121—23no—
111C29×#121—23no—
112C29×#121—26no—
113C29×#121C2313yes—
114C4×Q8×C29—21no—
115C4×Q8×C29—21no—
116C4×Q8×C29—23no—
117C4×Q8×C29—23no—
118C4×Q8×C29D411yescharacteristic
119C4×Q8×C29C2313yes—
120C4×Q8×C29C2313yes—
121C4×Q8×C29C2313yes—
122C4×Q8×C29C2311yescharacteristic
123C4×D4×C29—23no—
124C4×D4×C29—23no—
125C4×D4×C29—23no—
126C4×D4×C29—23no—
127C4×D4×C29—23no—
128C4×D4×C29—23no—
129C4×D4×C29D413yes—
130C4×D4×C29C2313yes—
131C4×D4×C29C2313yes—
132C4×D4×C29C2311yescharacteristic
133C4×D4×C29C2313yes—
134C29×#117—23no—
135C29×#117—23no—
136C29×#117—23no—
137C29×#117D413yes—
138C29×#117C2313yes—
139C2×C4⋊C4×C29—23no—
140C2×C4⋊C4×C29—23no—
141C2×C42×C29—23no—
142C2×C42×C29C2313yes—
143C29×#107C2313yes—
144C29×#107C2311yescharacteristic
145C29×#106C2311yescharacteristic
146C29×#106C2313yes—
147C29×C4⋊C8C2311yescharacteristic
148C29×C4⋊C8C2313yes—
149C29×C4⋊C8C2313yes—
150C29×C4⋊C8C2313yes—
151C29×#103C2313yes—
152C29×#103C2313yes—
153C29×#103C2313yes—
154C29×#103C2313yes—
155C29×#103C2316yes—
156C29×#102C2311yescharacteristic
157C29×#102C2313yes—
158C29×#102C2311yescharacteristic
159C29×#102C2313yes—
160C29×#102C2316yes—
161C29×C22⋊C8C2313yes—
162C29×C22⋊C8C2313yes—
163C4×C8×C29C2313yes—
164C4×C8×C29C2313yes—
165#41×C29—24no—
166#41×C29—26no—
167#41×C29—43no—
168#41×C29—46no—
169#41×C29—46no—
170#41×C29—44no—
171C2×Q8×C29—23no—
172C2×Q8×C29—44no—
173C2×Q8×C29C2×D411yescharacteristic
174C2×Q8×C29C2413yes—
175C2×Q8×C29C2413yes—
176C2×D4×C29—23no—
177C2×D4×C29—23no—
178C2×D4×C29—26no—
179C2×D4×C29—23no—
180C2×D4×C29—23no—
181C2×D4×C29C2×D413yes—
182C2×D4×C29C2413yes—
183C2×D4×C29C2411yescharacteristic
184C22×C4×C29—21no—
185C22×C4×C29—23no—
186C22×C4×C29—23no—
187C22×C4×C29—23no—
188C22×C4×C29—26no—
189C22×C4×C29C2×D413yes—
190C22×C4×C29C2×D413yes—
191C22×C4×C29C2413yes—
192Q16×C29—43no—
193Q16×C29—46no—
194SD16×C29—26no—
195SD16×C29—43no—
196SD16×C29—46no—
197D8×C29—26no—
198C2×C8×C29—46no—
199C2×C8×C29C2413yes—
200C2×C8×C29C2413yes—
201C2×C8×C29C2411yescharacteristic
202C2×C8×C29C2411yescharacteristic
203C4⋊C4×C29—23no—
204C4⋊C4×C29—23no—
205C4⋊C4×C29—23no—
206C4⋊C4×C29—26no—
207C4⋊C4×C29—21no—
208C4⋊C4×C29—23no—
209C4⋊C4×C29—23no—
210C4⋊C4×C29—23no—
211C4⋊C4×C29—23no—
212C4⋊C4×C29—21no—
213C4⋊C4×C29—23no—
214C4⋊C4×C29—23no—
215C4⋊C4×C29C2×D413yes—
216C4⋊C4×C29C2×D413yes—
217C4⋊C4×C29C2411yescharacteristic
218C4⋊C4×C29C2413yes—
219C4⋊C4×C29C2411yescharacteristic
220C4⋊C4×C29C2411yescharacteristic
221C22⋊C4×C29—26no—
222C22⋊C4×C29—23no—
223C22⋊C4×C29—23no—
224C22⋊C4×C29—21no—
225C22⋊C4×C29—23no—
226C22⋊C4×C29—23no—
227C22⋊C4×C29—23no—
228C22⋊C4×C29—23no—
229C22⋊C4×C29—23no—
230C22⋊C4×C29C2×D416yes—
231C42×C29—23no—
232C42×C29—23no—
233C42×C29—23no—
234C42×C29—23no—
235C42×C29C2×D413yes—
236C42×C29C2×D413yes—
237C42×C29C2411yescharacteristic
238C42×C29C2413yes—
239#61957C2911yesmaximal, characteristic, direct product factor, Sylow
240C23×C29—21no—
241C23×C29—23no—
242C23×C29C22×D413yes—
243Q8×C29—23no—
244Q8×C29—23no—
245Q8×C29—23no—
246Q8×C29—23no—
247Q8×C29—46no—
248Q8×C29#13514yescomplemented
249D4×C29—26no—
250D4×C29—23no—
251D4×C29—21no—
252D4×C29—23no—
253D4×C29—46no—
254D4×C29—46no—
255D4×C29—83no—
256D4×C29—83no—
257D4×C29—86no—
258D4×C29H(5,𝔽2)12yes—
259C2×C4×C29—26no—
260C2×C4×C29—23no—
261C2×C4×C29—23no—
262C2×C4×C29—21no—
263C2×C4×C29—21no—
264C2×C4×C29—23no—
265C2×C4×C29—23no—
266C2×C4×C29—23no—
267C2×C4×C29—21no—
268C2×C4×C29—43no—
269C2×C4×C29—46no—
270C2×C4×C29—42no—
271C2×C4×C29—46no—
272C2×C4×C29—46no—
273C2×C4×C29—86no—
274C2×C4×C29C22×D411yescharacteristic
275C2×C4×C29C22×D413yes—
276C2×C4×C29C22×D411yescharacteristic
277C2×C4×C29C22×D413yes—
278C2×C4×C29C22×D413yes—
279C2×C4×C29C2511yescharacteristic
280C8×C29—23no—
281C8×C29—23no—
282C8×C29—21no—
283C8×C29—21no—
284#3517C2×C2911yescharacteristic, complemented
285#3482C2×C2911yescharacteristic, complemented
286#3395C2×C2911yescharacteristic, complemented
287#3392C2×C2911yescharacteristic, complemented
288#3359C2×C2911yescharacteristic, complemented
289#3358C2×C2911yescharacteristic, complemented
290#3304C2×C2913yescomplemented
291#3302C2×C2913yescomplemented
292#3284C2×C2913yescomplemented
293#3283C2×C2913yescomplemented
294#3248C2×C2913yescomplemented
295#3210C2×C2913yescomplemented
296#3102C2×C2913yescomplemented
297#3035C2×C2913yescomplemented
298#2988C2×C2911yescharacteristic, complemented
299C22×C29—23no—
300C22×C29—23no—
301C22×C29—22no—
302C22×C29—23no—
303C22×C29—41no—
304C22×C29—41no—
305C22×C29—43no—
306C22×C29—43no—
307C22×C29—43no—
308C22×C29C23×D411yescharacteristic
309C4×C29—21no—
310C4×C29—23no—
311C4×C29—23no—
312C4×C29—21no—
313C4×C29—41no—
314C4×C29—41no—
315C4×C29—43no—
316C4×C29—43no—
317C4×C29—41no—
318C4×C29—43no—
319C4×C29C2×#13516yes—
320C4×C29C2×H(5,𝔽2)11yescharacteristic
321C4×C29#58511yescharacteristic
322C2×#135C22×C2916yes—
323#557C22×C2911yescharacteristic
324#557C22×C2911yescharacteristic
325#556C22×C2913yes—
326#553—23no—
327#552—23no—
328#550—21no—
329#550C22×C2913yes—
330#550C22×C2911yescharacteristic
331D4×Q8C22×C2911yescharacteristic
332#548—21no—
333#547C22×C2913yes—
334#547C22×C2913yes—
335#540—23no—
336#533C22×C2913yes—
337#532C22×C2913yes—
338#529—23no—
339#529C22×C2913yes—
340#520—21no—
341C4×#41C22×C2913yes—
342C4×#41C22×C2911yescharacteristic
343C2×C4×Q8—21no—
344#494C22×C2913yes—
345#492C22×C2913yes—
346#487C22×C2913yes—
347#486C22×C2913yes—
348#485C22×C2913yes—
349#482C22×C2913yes—
350#479C22×C2913yes—
351#478C22×C2911yescharacteristic
352#475C22×C2913yes—
353#474C22×C2913yes—
354#467C22×C2916yes—
355#465C22×C2916yes—
356#464C22×C2913yes—
357#464C22×C2916yes—
358#463C22×C2913yes—
359#462C22×C2913yes—
360#462C22×C2913yes—
361#461C22×C2913yes—
362#461C22×C2913yes—
363#460C22×C2913yes—
364#459C22×C2913yes—
365#452C22×C2913yes—
366#452C22×C2916yes—
367#452C22×C2916yes—
368#449C22×C2913yes—
369C8×Q8C22×C2911yescharacteristic
370C8×Q8C22×C2911yescharacteristic
371C4×Q16C22×C2913yes—
372C4×SD16C22×C2913yes—
373C4×SD16C22×C2913yes—
374C4×D8C22×C2913yes—
375C8×D4C22×C2913yes—
376C8×D4C22×C2913yes—
377#431C22×C2913yes—
378C2×C4⋊C8C22×C2913yes—
379#416C22×C2916yes—
380C2×C29—43no—
381C2×C29—42no—
382C2×C29—83no—
383C2×C29#348811yescharacteristic
384C2×C29C22×#13511yescharacteristic
385C2×C29#358611yescharacteristic
386C2×#41—21no—
387C2×#41D4×C2911yescharacteristic
388C2×#41C23×C2913yes—
389C2×#41C23×C2916yes—
390C22×Q8—21no—
391#135—412no—
392C2×Q16C23×C2916yes—
393C2×Q16C23×C2913yes—
394C2×SD16C23×C2913yes—
395C2×SD16C23×C2916yes—
396C2×SD16C23×C2913yes—
397C2×D8C23×C2913yes—
398C22×C8C23×C2916yes—
399C4⋊Q8C23×C2913yes—
400C4⋊Q8C23×C2913yes—
401C4⋊Q8C23×C2913yes—
402#127—23no—
403#127C23×C2913yes—
404#126—26no—
405#126—23no—
406#125—23no—
407#125—23no—
408#125—23no—
409#125C23×C2911yescharacteristic
410#124—23no—
411#124C23×C2913yes—
412#123—23no—
413#123—26no—
414#123—26no—
415C22⋊Q8—23no—
416C22⋊Q8—23no—
417C22⋊Q8C23×C2913yes—
418C22⋊Q8C23×C2916yes—
419#121—23no—
420#121—23no—
421#121—23no—
422#121—23no—
423#121—23no—
424#121—26no—
425#121C23×C2913yes—
426C4×Q8—21no—
427C4×Q8—21no—
428C4×Q8—23no—
429C4×Q8—23no—
430C4×Q8D4×C2911yescharacteristic
431C4×Q8C23×C2913yes—
432C4×Q8C23×C2913yes—
433C4×Q8C23×C2913yes—
434C4×Q8C23×C2911yescharacteristic
435C4×D4—23no—
436C4×D4—23no—
437C4×D4—23no—
438C4×D4—23no—
439C4×D4—23no—
440C4×D4—23no—
441C4×D4D4×C2913yes—
442C4×D4C23×C2911yescharacteristic
443C4×D4C23×C2913yes—
444C4×D4C23×C2913yes—
445C4×D4C23×C2913yes—
446#117—23no—
447#117—23no—
448#117—23no—
449#117D4×C2913yes—
450#117C23×C2913yes—
451C2×C4⋊C4—23no—
452C2×C4⋊C4—23no—
453C2×C42—23no—
454C2×C42C23×C2913yes—
455#107C23×C2913yes—
456#107C23×C2911yescharacteristic
457#106C23×C2911yescharacteristic
458#106C23×C2913yes—
459C4⋊C8C23×C2913yes—
460C4⋊C8C23×C2913yes—
461C4⋊C8C23×C2913yes—
462C4⋊C8C23×C2911yescharacteristic
463#103C23×C2913yes—
464#103C23×C2916yes—
465#103C23×C2913yes—
466#103C23×C2913yes—
467#103C23×C2913yes—
468#102C23×C2913yes—
469#102C23×C2916yes—
470#102C23×C2911yescharacteristic
471#102C23×C2913yes—
472#102C23×C2911yescharacteristic
473C22⋊C8C23×C2913yes—
474C22⋊C8C23×C2913yes—
475C4×C8C23×C2913yes—
476C4×C8C23×C2913yes—
477C29#6195711yescharacteristic, direct product factor, Sylow
478#41—24no—
479#41—26no—
480#41—43no—
481#41—46no—
482#41—46no—
483#41—44no—
484C2×Q8—23no—
485C2×Q8—44no—
486C2×Q8C2×D4×C2911yescharacteristic
487C2×Q8C24×C2913yes—
488C2×Q8C24×C2913yes—
489C2×D4—23no—
490C2×D4—23no—
491C2×D4—26no—
492C2×D4—23no—
493C2×D4—23no—
494C2×D4C2×D4×C2913yes—
495C2×D4C24×C2913yes—
496C2×D4C24×C2911yescharacteristic
497C22×C4—21no—
498C22×C4—23no—
499C22×C4—23no—
500C22×C4—23no—
501C22×C4—26no—
502C22×C4C2×D4×C2913yes—
503C22×C4C2×D4×C2913yes—
504C22×C4C24×C2913yes—
505Q16—46no—
506Q16—43no—
507SD16—26no—
508SD16—46no—
509SD16—43no—
510D8—26no—
511C2×C8—46no—
512C2×C8C24×C2911yescharacteristic
513C2×C8C24×C2911yescharacteristic
514C2×C8C24×C2913yes—
515C2×C8C24×C2913yes—
516C4⋊C4—23no—
517C4⋊C4—23no—
518C4⋊C4—23no—
519C4⋊C4—26no—
520C4⋊C4—21no—
521C4⋊C4—23no—
522C4⋊C4—23no—
523C4⋊C4—23no—
524C4⋊C4—23no—
525C4⋊C4—21no—
526C4⋊C4—23no—
527C4⋊C4—23no—
528C4⋊C4C2×D4×C2913yes—
529C4⋊C4C2×D4×C2913yes—
530C4⋊C4C24×C2911yescharacteristic
531C4⋊C4C24×C2913yes—
532C4⋊C4C24×C2911yescharacteristic
533C4⋊C4C24×C2911yescharacteristic
534C22⋊C4—26no—
535C22⋊C4—23no—
536C22⋊C4—23no—
537C22⋊C4—21no—
538C22⋊C4—23no—
539C22⋊C4—23no—
540C22⋊C4—23no—
541C22⋊C4—23no—
542C22⋊C4—23no—
543C22⋊C4C2×D4×C2916yes—
544C42—23no—
545C42—23no—
546C42—23no—
547C42—23no—
548C42C2×D4×C2913yes—
549C42C2×D4×C2913yes—
550C42C24×C2913yes—
551C42C24×C2911yescharacteristic
552C23—21no—
553C23—23no—
554C23C22×D4×C2913yes—
555Q8—23no—
556Q8—23no—
557Q8—23no—
558Q8—23no—
559Q8—46no—
560Q8C29×#13514yescomplemented
561D4—26no—
562D4—23no—
563D4—21no—
564D4—23no—
565D4—46no—
566D4—46no—
567D4—83no—
568D4—86no—
569D4—83no—
570D4C29×H(5,𝔽2)12yes—
571C2×C4—26no—
572C2×C4—23no—
573C2×C4—23no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—23no—
577C2×C4—23no—
578C2×C4—23no—
579C2×C4—21no—
580C2×C4—43no—
581C2×C4—46no—
582C2×C4—42no—
583C2×C4—46no—
584C2×C4—46no—
585C2×C4—86no—
586C2×C4C22×D4×C2911yescharacteristic
587C2×C4C22×D4×C2913yes—
588C2×C4C22×D4×C2911yescharacteristic
589C2×C4C22×D4×C2913yes—
590C2×C4C22×D4×C2913yes—
591C2×C4C25×C2911yescharacteristic
592C8—23no—
593C8—23no—
594C8—21no—
595C8—21no—
596C22—23no—
597C22—22no—
598C22—23no—
599C22—23no—
600C22—41no—
601C22—41no—
602C22—43no—
603C22—43no—
604C22—43no—
605C22C23×D4×C2911yescharacteristic
606C4—23no—
607C4—21no—
608C4—21no—
609C4—23no—
610C4—43no—
611C4—43no—
612C4—41no—
613C4—43no—
614C4—41no—
615C4—41no—
616C4C2×C29×#13516yes—
617C4C2×C29×H(5,𝔽2)11yescharacteristic
618C4C29×#58511yescharacteristic
619C2—43no—
620C2—42no—
621C2—83no—
622C2C29×#348811yescharacteristic
623C2C22×C29×#13511yescharacteristic
624C2C29×#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×#3517C2semidirect
2. C29×#3482C2semidirect
3. C29×#3395C2semidirect
4. C29×#3392C2semidirect
5. C29×#3359C2semidirect
6. C29×#3358C2semidirect
7. C29×#3304C2semidirect
8. C29×#3302C2semidirect
9. C29×#3284C2semidirect
10. C29×#3283C2semidirect
11. C29×#3248C2semidirect
12. C29×#3210C2semidirect
13. C29×#3102C2semidirect
14. C29×#3035C2semidirect
15. C29×#2988C2semidirect
239. #61957C29direct (N × H)
248. Q8×C29#135semidirect
284. #3517C2×C29semidirect
285. #3482C2×C29semidirect
286. #3395C2×C29semidirect
287. #3392C2×C29semidirect
288. #3359C2×C29semidirect
289. #3358C2×C29semidirect
290. #3304C2×C29semidirect
291. #3302C2×C29semidirect
292. #3284C2×C29semidirect
293. #3283C2×C29semidirect
294. #3248C2×C29semidirect
295. #3210C2×C29semidirect
296. #3102C2×C29semidirect
297. #3035C2×C29semidirect
298. #2988C2×C29semidirect
477. C29#61957direct (N × H)
560. Q8C29×#135semidirect

Maximal subgroups

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

subgroupindex
C29×#35172
C29×#34822
C29×#33952
C29×#33922
C29×#33592
C29×#33582
C29×#33042
C29×#33022
C29×#32842
C29×#32832
C29×#32482
C29×#32102
C29×#31022
C29×#30352
C29×#29882
#6195729