Finite Group Databasebeta

← C29×#25664 #20320564

Subgroups — C29×#25664 #20320564

Order 7424.

1136 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3505C211yesmaximal, characteristic
2C29×#2504C211yesmaximal, characteristic, complemented
3C29×#2502C211yesmaximal, characteristic, complemented
4C29×#2487C211yesmaximal, characteristic, complemented
5C29×#2044C214yesmaximal, complemented
6C29×#1996C211yesmaximal, characteristic, complemented
7C29×#1964C211yesmaximal, characteristic, complemented
8C29×#1867C214yesmaximal, 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×C22⋊Q8C2211yescharacteristic
22C2×C29×#121C2211yescharacteristic
23C29×#518C2212yes—
24C2×C4×D4×C29C2211yescharacteristic
25C22×C4⋊C4×C29C2211yescharacteristic
26C2×C29×#99C2214yes—
27C2×C29×#99C2212yes—
28C29×#400—21no—
29C29×#399—21no—
30C29×#398—22no—
31C29×#397—22no—
32C29×#391—21no—
33C29×#390—21no—
34C29×#389—21no—
35C29×#386C2212yes—
36C29×#386C2214yes—
37C29×#385C2212yes—
38C29×#385C2214yes—
39C29×#384—21no—
40C29×#382—21no—
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×C22⋊Q8—21no—
68C29×C22⋊Q8—22no—
69C29×C22⋊Q8—21no—
70C29×C22⋊Q8—21no—
71C29×C22⋊Q8—21no—
72C29×C22⋊Q8—21no—
73C29×#121—21no—
74C29×#121—22no—
75C29×#121—21no—
76C29×#121—21no—
77C29×#121—21no—
78C29×#121—21no—
79C29×#121—22no—
80C29×#121—22no—
81C29×#120—22no—
82C29×#120—22no—
83C4×Q8×C29—21no—
84C4×D4×C29—22no—
85C4×D4×C29—21no—
86C4×D4×C29—21no—
87C4×D4×C29—21no—
88C4×D4×C29—21no—
89C4×D4×C29—21no—
90C4×D4×C29—22no—
91C4×D4×C29—22no—
92C4×D4×C29—22no—
93C4×D4×C29—22no—
94C29×#117—21no—
95C29×#117—22no—
96C29×#117—22no—
97C2×C4⋊C4×C29—21no—
98C2×C4⋊C4×C29—21no—
99C2×C4⋊C4×C29—21no—
100C2×C4⋊C4×C29—21no—
101C2×C4⋊C4×C29—21no—
102C2×C4⋊C4×C29—21no—
103C2×C4⋊C4×C29—21no—
104C2×C4⋊C4×C29—24no—
105C2×C4⋊C4×C29—22no—
106C2×C4⋊C4×C29D411yescharacteristic
107C2×C4⋊C4×C29D411yescharacteristic
108C2×C4⋊C4×C29D411yescharacteristic
109C2×C4⋊C4×C29D412yes—
110C2×C22⋊C4×C29—22no—
111C2×C22⋊C4×C29—22no—
112C2×C22⋊C4×C29—24no—
113C2×C22⋊C4×C29D411yescharacteristic
114C2×C22⋊C4×C29D412yes—
115C2×C22⋊C4×C29C2312yes—
116C2×C22⋊C4×C29C2312yes—
117C2×C22⋊C4×C29C2311yescharacteristic
118C2×C22⋊C4×C29C2312yes—
119C2×C22⋊C4×C29C2312yes—
120C2×C42×C29—21no—
121C2×C42×C29—21no—
122C2×C42×C29D411yescharacteristic
123C29×#99—28no—
124C29×#99—24no—
125C29×#95—21no—
126C29×#95—21no—
127C29×#95—22no—
128C29×#95—21no—
129C29×#95—24no—
130C29×#95—24no—
131C29×#95—22no—
132C24×C29C2×D412yes—
133C24×C29C2×D411yescharacteristic
134C24×C29C2411yescharacteristic
135#41×C29—82no—
136C2×Q8×C29—21no—
137C2×Q8×C29—21no—
138C2×Q8×C29—42no—
139C2×D4×C29—21no—
140C2×D4×C29—22no—
141C2×D4×C29—21no—
142C2×D4×C29—22no—
143C2×D4×C29—22no—
144C2×D4×C29—24no—
145C2×D4×C29—22no—
146C2×D4×C29—24no—
147C2×D4×C29—22no—
148C2×D4×C29—22no—
149C2×D4×C29—21no—
150C2×D4×C29—21no—
151C2×D4×C29—42no—
152C22×C4×C29—22no—
153C22×C4×C29—22no—
154C22×C4×C29—22no—
155C22×C4×C29—21no—
156C22×C4×C29—21no—
157C22×C4×C29—22no—
158C22×C4×C29—22no—
159C22×C4×C29—22no—
160C22×C4×C29—22no—
161C22×C4×C29—22no—
162C22×C4×C29—42no—
163C22×C4×C29—42no—
164C22×C4×C29—82no—
165C22×C4×C29C2×D411yescharacteristic
166C22×C4×C29C2×D412yes—
167C22×C4×C29C2×D411yescharacteristic
168C22×C4×C29C2×D411yescharacteristic
169C22×C4×C29C2×D411yescharacteristic
170C22×C4×C29C2×D411yescharacteristic
171C22×C4×C29C2×D412yes—
172C22×C4×C29C2×D411yescharacteristic
173C22×C4×C29C2×D412yes—
174C22×C4×C29C2×D411yescharacteristic
175C22×C4×C29C2×D411yescharacteristic
176C22×C4×C29C2×D411yescharacteristic
177C4⋊C4×C29—22no—
178C4⋊C4×C29—22no—
179C4⋊C4×C29—22no—
180C4⋊C4×C29—22no—
181C4⋊C4×C29—21no—
182C4⋊C4×C29—22no—
183C4⋊C4×C29—21no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—22no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—42no—
190C4⋊C4×C29—41no—
191C4⋊C4×C29—41no—
192C4⋊C4×C29—41no—
193C4⋊C4×C29—41no—
194C4⋊C4×C29—84no—
195C4⋊C4×C29—82no—
196C22⋊C4×C29—22no—
197C22⋊C4×C29—22no—
198C22⋊C4×C29—22no—
199C22⋊C4×C29—22no—
200C22⋊C4×C29—22no—
201C22⋊C4×C29—22no—
202C22⋊C4×C29—21no—
203C22⋊C4×C29—22no—
204C22⋊C4×C29—21no—
205C22⋊C4×C29—22no—
206C22⋊C4×C29—22no—
207C22⋊C4×C29—22no—
208C22⋊C4×C29—21no—
209C22⋊C4×C29—21no—
210C22⋊C4×C29—22no—
211C22⋊C4×C29—24no—
212C22⋊C4×C29—22no—
213C22⋊C4×C29—22no—
214C22⋊C4×C29—84no—
215C22⋊C4×C29—82no—
216C22⋊C4×C29#4114yescomplemented
217C42×C29—22no—
218C42×C29—22no—
219C42×C29—21no—
220C42×C29—21no—
221C42×C29—42no—
222C42×C29—42no—
223#25664C2911yesmaximal, characteristic, direct product factor, Sylow
224C23×C29—21no—
225C23×C29—22no—
226C23×C29—21no—
227C23×C29—21no—
228C23×C29—24no—
229C23×C29—41no—
230C23×C29—41no—
231C23×C29—41no—
232C23×C29—41no—
233C23×C29—42no—
234C23×C29—42no—
235C23×C29C22×D411yescharacteristic
236C23×C29C22×D411yescharacteristic
237C23×C29C22×D411yescharacteristic
238C23×C29C2×#4112yes—
239C23×C292−1+412yes—
240Q8×C29—42no—
241Q8×C29—81no—
242D4×C29—42no—
243D4×C29—42no—
244D4×C29—42no—
245D4×C29—42no—
246D4×C29—44no—
247D4×C29—42no—
248D4×C29—81no—
249D4×C29—82no—
250D4×C29—82no—
251C2×C4×C29—22no—
252C2×C4×C29—22no—
253C2×C4×C29—22no—
254C2×C4×C29—21no—
255C2×C4×C29—22no—
256C2×C4×C29—21no—
257C2×C4×C29—21no—
258C2×C4×C29—22no—
259C2×C4×C29—22no—
260C2×C4×C29—21no—
261C2×C4×C29—21no—
262C2×C4×C29—24no—
263C2×C4×C29—24no—
264C2×C4×C29—41no—
265C2×C4×C29—41no—
266C2×C4×C29—41no—
267C2×C4×C29—42no—
268C2×C4×C29—42no—
269C2×C4×C29—42no—
270C2×C4×C29—41no—
271C2×C4×C29—42no—
272C2×C4×C29—41no—
273C2×C4×C29—42no—
274C2×C4×C29—42no—
275C2×C4×C29—42no—
276C2×C4×C29—42no—
277C2×C4×C29—42no—
278C2×C4×C29—44no—
279C2×C4×C29—42no—
280C2×C4×C29—44no—
281C2×C4×C29—42no—
282C2×C4×C29—42no—
283C2×C4×C29—42no—
284C2×C4×C29—42no—
285C2×C4×C29—81no—
286C2×C4×C29—82no—
287C2×C4×C29—82no—
288C2×C4×C29#12011yescharacteristic
289C2×C4×C29#12011yescharacteristic
290C2×C4×C29#12011yescharacteristic
291C2×C4×C29#12011yescharacteristic
292#3505C2×C2911yescharacteristic
293#2504C2×C2911yescharacteristic, complemented
294#2502C2×C2911yescharacteristic, complemented
295#2487C2×C2911yescharacteristic, complemented
296#2044C2×C2914yescomplemented
297#1996C2×C2911yescharacteristic, complemented
298#1964C2×C2911yescharacteristic, complemented
299#1867C2×C2914yescomplemented
300C4×#99C2×C2911yescharacteristic, complemented
301C22×C29—21no—
302C22×C29—21no—
303C22×C29—21no—
304C22×C29—21no—
305C22×C29—21no—
306C22×C29—21no—
307C22×C29—42no—
308C22×C29—42no—
309C22×C29—42no—
310C22×C29—41no—
311C22×C29—42no—
312C22×C29—41no—
313C22×C29—42no—
314C22×C29—42no—
315C22×C29—41no—
316C22×C29—81no—
317C22×C29—84no—
318C22×C29C2×#12011yescharacteristic
319C22×C29#53211yescharacteristic
320C22×C29#53611yescharacteristic
321C22×C29#54712yes—
322C22×C29#54812yes—
323C4×C29—21no—
324C4×C29—21no—
325C4×C29—21no—
326C4×C29—44no—
327C4×C29—41no—
328C4×C29—42no—
329C4×C29—41no—
330C4×C29—42no—
331C4×C29—41no—
332C4×C29—42no—
333C4×C29—82no—
334C4×C29—82no—
335C4×C29—82no—
336C4×C29#45812yes—
337#553—21no—
338#553—22no—
339#552—21no—
340#551—22no—
341#548—21no—
342#546—21no—
343#539—21no—
344#538—21no—
345#534C22×C2912yes—
346#529—21no—
347#525—21no—
348C2×C22⋊Q8C22×C2911yescharacteristic
349C2×#121C22×C2911yescharacteristic
350#518C22×C2912yes—
351C2×C4×D4C22×C2911yescharacteristic
352C22×C4⋊C4C22×C2911yescharacteristic
353C2×#99C22×C2914yes—
354C2×#99C22×C2912yes—
355#400—21no—
356#399—21no—
357#398—22no—
358#397—22no—
359#391—21no—
360#390—21no—
361#389—21no—
362#386C22×C2914yes—
363#386C22×C2912yes—
364#385C22×C2912yes—
365#385C22×C2914yes—
366#384—21no—
367#382—21no—
368#380—21no—
369#380C22×C2911yescharacteristic
370C4×C22⋊C4C22×C2911yescharacteristic
371C4×C22⋊C4C22×C2911yescharacteristic
372#342C22×C2912yes—
373#342C22×C2914yes—
374C2×C29—22no—
375C2×C29—21no—
376C2×C29—22no—
377C2×C29—21no—
378C2×C29—81no—
379C2×C29—82no—
380C2×C29#243211yescharacteristic
381C2×C29C2×#45811yescharacteristic
382C2×C29#302711yescharacteristic
383C2×#41—21no—
384C22×Q8D4×C2911yescharacteristic
385C22×D4D4×C2911yescharacteristic
386C22×D4C23×C2911yescharacteristic
387C22×D4C23×C2912yes—
388C23×C4D4×C2911yescharacteristic
389C23×C4C23×C2912yes—
390C23×C4C23×C2911yescharacteristic
391#126—22no—
392#126—22no—
393#126—22no—
394#125—21no—
395#125—22no—
396#124—21no—
397#124—22no—
398#123—22no—
399#123—22no—
400#123—22no—
401#123—22no—
402#123—22no—
403C22⋊Q8—21no—
404C22⋊Q8—22no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409#121—21no—
410#121—22no—
411#121—21no—
412#121—21no—
413#121—21no—
414#121—21no—
415#121—22no—
416#121—22no—
417#120—22no—
418#120—22no—
419C4×Q8—21no—
420C4×D4—22no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4—22no—
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430#117—21no—
431#117—22no—
432#117—22no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4D4×C2911yescharacteristic
443C2×C4⋊C4D4×C2911yescharacteristic
444C2×C4⋊C4D4×C2911yescharacteristic
445C2×C4⋊C4D4×C2912yes—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4D4×C2911yescharacteristic
450C2×C22⋊C4D4×C2912yes—
451C2×C22⋊C4C23×C2912yes—
452C2×C22⋊C4C23×C2912yes—
453C2×C22⋊C4C23×C2911yescharacteristic
454C2×C22⋊C4C23×C2912yes—
455C2×C22⋊C4C23×C2912yes—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42D4×C2911yescharacteristic
459#99—28no—
460#99—24no—
461#95—21no—
462#95—21no—
463#95—22no—
464#95—21no—
465#95—24no—
466#95—24no—
467#95—22no—
468C29#2566411yescharacteristic, direct product factor, Sylow
469C24C2×D4×C2912yes—
470C24C2×D4×C2911yescharacteristic
471C24C24×C2911yescharacteristic
472#41—82no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—42no—
476C2×D4—21no—
477C2×D4—22no—
478C2×D4—21no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—24no—
482C2×D4—22no—
483C2×D4—24no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—42no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—82no—
502C22×C4C2×D4×C2911yescharacteristic
503C22×C4C2×D4×C2912yes—
504C22×C4C2×D4×C2911yescharacteristic
505C22×C4C2×D4×C2911yescharacteristic
506C22×C4C2×D4×C2911yescharacteristic
507C22×C4C2×D4×C2911yescharacteristic
508C22×C4C2×D4×C2912yes—
509C22×C4C2×D4×C2911yescharacteristic
510C22×C4C2×D4×C2912yes—
511C22×C4C2×D4×C2911yescharacteristic
512C22×C4C2×D4×C2911yescharacteristic
513C22×C4C2×D4×C2911yescharacteristic
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—22no—
525C4⋊C4—21no—
526C4⋊C4—42no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—84no—
532C4⋊C4—82no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—21no—
540C22⋊C4—22no—
541C22⋊C4—21no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—22no—
548C22⋊C4—24no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—84no—
552C22⋊C4—82no—
553C22⋊C4#41×C2914yescomplemented
554C42—22no—
555C42—22no—
556C42—21no—
557C42—21no—
558C42—42no—
559C42—42no—
560C23—21no—
561C23—22no—
562C23—21no—
563C23—21no—
564C23—24no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—42no—
570C23—42no—
571C23C22×D4×C2911yescharacteristic
572C23C22×D4×C2911yescharacteristic
573C23C22×D4×C2911yescharacteristic
574C23C2×#41×C2912yes—
575C23C29×2−1+412yes—
576Q8—42no—
577Q8—81no—
578D4—42no—
579D4—42no—
580D4—42no—
581D4—42no—
582D4—44no—
583D4—42no—
584D4—81no—
585D4—82no—
586D4—82no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—44no—
615C2×C4—42no—
616C2×C4—44no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—81no—
622C2×C4—82no—
623C2×C4—82no—
624C2×C4C29×#12011yescharacteristic
625C2×C4C29×#12011yescharacteristic
626C2×C4C29×#12011yescharacteristic
627C2×C4C29×#12011yescharacteristic
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—41no—
638C22—42no—
639C22—41no—
640C22—42no—
641C22—42no—
642C22—41no—
643C22—81no—
644C22—84no—
645C22C2×C29×#12011yescharacteristic
646C22C29×#53211yescharacteristic
647C22C29×#53611yescharacteristic
648C22C29×#54712yes—
649C22C29×#54812yes—
650C4—21no—
651C4—21no—
652C4—21no—
653C4—44no—
654C4—41no—
655C4—42no—
656C4—41no—
657C4—42no—
658C4—41no—
659C4—42no—
660C4—82no—
661C4—82no—
662C4—82no—
663C4C29×#45812yes—
664C2—22no—
665C2—21no—
666C2—22no—
667C2—21no—
668C2—81no—
669C2—82no—
670C2C29×#243211yescharacteristic
671C2C2×C29×#45811yescharacteristic
672C2C29×#302711yescharacteristic
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×#2504C2semidirect
3. C29×#2502C2semidirect
4. C29×#2487C2semidirect
5. C29×#2044C2semidirect
6. C29×#1996C2semidirect
7. C29×#1964C2semidirect
8. C29×#1867C2semidirect
9. C4×C29×#99C2semidirect
216. C22⋊C4×C29#41semidirect
223. #25664C29direct (N × H)
293. #2504C2×C29semidirect
294. #2502C2×C29semidirect
295. #2487C2×C29semidirect
296. #2044C2×C29semidirect
297. #1996C2×C29semidirect
298. #1964C2×C29semidirect
299. #1867C2×C29semidirect
300. C4×#99C2×C29semidirect
468. C29#25664direct (N × H)
553. 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×#25042
C29×#25022
C29×#24872
C29×#20442
C29×#19962
C29×#19642
C29×#18672
C4×C29×#992
#2566429