Finite Group Databasebeta

← C29×#18793 #20313693

Subgroups — C29×#18793 #20313693

Order 7424.

948 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3475C211yesmaximal, characteristic
2C29×#3209C211yesmaximal, characteristic, complemented
3C29×#3079C211yesmaximal, characteristic, complemented
4C2×C29×#476C211yesmaximal, characteristic, complemented
5C29×#1638C212yesmaximal, complemented
6C29×#1635C212yesmaximal, complemented
7C29×#1634C212yesmaximal, complemented
8C29×#1632C212yesmaximal, complemented
9C29×#1550C211yesmaximal, characteristic, complemented
10C29×#1486C211yesmaximal, characteristic, complemented
11C29×#1477C211yesmaximal, characteristic, complemented
12C29×#556C2211yescharacteristic
13C29×#555C2211yescharacteristic
14C29×#554C2211yescharacteristic
15C29×#553—21no—
16C29×#552—21no—
17C29×#552—21no—
18C29×#551—22no—
19C29×#547C2211yescharacteristic
20C29×#546—21no—
21C29×#533C2211yescharacteristic
22C2×C29×C4⋊Q8C2211yescharacteristic
23C29×#529—22no—
24C29×#529—21no—
25C29×#525—21no—
26C4×#41×C29—21no—
27C4×#41×C29C2211yescharacteristic
28C2×C4×D4×C29C2211yescharacteristic
29C2×C29×#117—21no—
30C29×#494C2212yescomplemented
31C29×#487C2212yescomplemented
32C29×#477C2212yescomplemented
33C29×#476—21no—
34C29×#476—21no—
35C29×#476C2212yes—
36C29×#476C2212yes—
37C29×#476C2212yescomplemented
38C29×#475—21no—
39C29×#474—21no—
40C29×#462—22no—
41C29×#451—22no—
42C29×#431C2211yescharacteristic
43C29×#428—21no—
44C2×C29×#106—21no—
45C29×#423C2211yescharacteristic
46C2×C29×C4⋊C8C2211yescharacteristic
47C29×#417—21no—
48C2×C29×#102—21no—
49C29×#333C2212yescomplemented
50C29×#332C2212yescomplemented
51C29×Q8⋊C8C2212yescomplemented
52C29×D4⋊C8C2212yes—
53C29×D4⋊C8C2212yes—
54C29×D4⋊C8C2212yescomplemented
55C2×#41×C29—21no—
56C2×#41×C29D411yescharacteristic
57C22×Q8×C29—21no—
58C22×D4×C29D411yescharacteristic
59C23×C4×C29—21no—
60C2×Q16×C29—24no—
61C2×M16×C29—21no—
62C22×C8×C29—21no—
63C29×C4⋊Q8—21no—
64C29×C4⋊Q8—21no—
65C29×C4⋊Q8—21no—
66C29×C4⋊Q8C2312yes—
67C29×C4⋊Q8C2311yescharacteristic
68C29×C4⋊Q8C2311yescharacteristic
69C29×#126—22no—
70C29×#126—22no—
71C29×#126—22no—
72C29×#125—22no—
73C29×#125—21no—
74C29×#125—21no—
75C29×#124—22no—
76C29×#124—21no—
77C29×#123—22no—
78C29×#123—22no—
79C29×#123—22no—
80C29×#123—22no—
81C29×C22⋊Q8—21no—
82C29×C22⋊Q8—21no—
83C29×C22⋊Q8—22no—
84C29×C22⋊Q8—21no—
85C29×C22⋊Q8—21no—
86C29×C22⋊Q8D412yes—
87C29×#121—22no—
88C29×#121—21no—
89C29×#121—21no—
90C29×#121—21no—
91C29×#120—22no—
92C4×Q8×C29—21no—
93C4×Q8×C29—21no—
94C4×Q8×C29D412yes—
95C4×Q8×C29D411yescharacteristic
96C4×Q8×C29C2311yescharacteristic
97C4×D4×C29—22no—
98C4×D4×C29—22no—
99C4×D4×C29—22no—
100C4×D4×C29—21no—
101C4×D4×C29—21no—
102C4×D4×C29—21no—
103C4×D4×C29—21no—
104C4×D4×C29—21no—
105C4×D4×C29D411yescharacteristic
106C4×D4×C29D411yescharacteristic
107C4×D4×C29D411yescharacteristic
108C4×D4×C29C2311yescharacteristic
109C4×D4×C29C2311yescharacteristic
110C4×D4×C29C2311yescharacteristic
111C29×#117—22no—
112C29×#117—22no—
113C29×#117—22no—
114C29×#117—21no—
115C29×#117—21no—
116C29×#117—21no—
117C29×#117—21no—
118C29×#117—21no—
119C29×#117D411yescharacteristic
120C2×C4⋊C4×C29—21no—
121C2×C4⋊C4×C29—21no—
122C2×C4⋊C4×C29—21no—
123C2×C4⋊C4×C29—21no—
124C2×C4⋊C4×C29D411yescharacteristic
125C2×C22⋊C4×C29—22no—
126C2×C22⋊C4×C29—21no—
127C2×C42×C29—22no—
128C2×C42×C29—21no—
129C2×C42×C29C2311yescharacteristic
130C29×#107—22no—
131C29×#106—22no—
132C29×#106—22no—
133C29×#106—22no—
134C29×C4⋊C8—21no—
135C29×C4⋊C8—21no—
136C29×C4⋊C8—21no—
137C29×C4⋊C8C2312yes—
138C29×C4⋊C8C2312yes—
139C29×#103—22no—
140C29×#103—24no—
141C29×#102—22no—
142C29×#102—22no—
143C29×#102—22no—
144C29×C22⋊C8—21no—
145C4×C8×C29C2312yes—
146C24×C29—21no—
147#41×C29—22no—
148#41×C29—22no—
149#41×C29—42no—
150#41×C29—42no—
151C2×Q8×C29—21no—
152C2×Q8×C29—22no—
153C2×Q8×C29—41no—
154C2×Q8×C29—82no—
155C2×Q8×C29C2×D411yescharacteristic
156C2×Q8×C29C2×D412yes—
157C2×D4×C29—22no—
158C2×D4×C29—22no—
159C2×D4×C29—21no—
160C2×D4×C29—22no—
161C2×D4×C29—21no—
162C2×D4×C29—41no—
163C2×D4×C29C2×D411yescharacteristic
164C2×D4×C29C2×D411yescharacteristic
165C2×D4×C29C2×D411yescharacteristic
166C22×C4×C29—22no—
167C22×C4×C29—21no—
168C22×C4×C29—22no—
169C22×C4×C29—21no—
170C22×C4×C29—21no—
171C22×C4×C29—21no—
172C22×C4×C29—21no—
173C22×C4×C29—21no—
174C22×C4×C29—21no—
175C22×C4×C29—21no—
176C22×C4×C29—42no—
177C22×C4×C29—42no—
178C22×C4×C29—41no—
179C22×C4×C29C2×D411yescharacteristic
180C22×C4×C29C2×D411yescharacteristic
181C22×C4×C29C2×D411yescharacteristic
182Q16×C29—84no—
183M16×C29—42no—
184C2×C8×C29—22no—
185C2×C8×C29—22no—
186C2×C8×C29—22no—
187C2×C8×C29—42no—
188C4⋊C4×C29—22no—
189C4⋊C4×C29—22no—
190C4⋊C4×C29—22no—
191C4⋊C4×C29—22no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—22no—
194C4⋊C4×C29—21no—
195C4⋊C4×C29—22no—
196C4⋊C4×C29—21no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29—21no—
199C4⋊C4×C29—21no—
200C4⋊C4×C29—22no—
201C4⋊C4×C29—22no—
202C4⋊C4×C29—41no—
203C4⋊C4×C29—41no—
204C4⋊C4×C29C2×D411yescharacteristic
205C4⋊C4×C29C2×D411yescharacteristic
206C4⋊C4×C29C2×D411yescharacteristic
207C4⋊C4×C29C2×D411yescharacteristic
208C4⋊C4×C29C2×D412yes—
209C22⋊C4×C29—22no—
210C22⋊C4×C29—22no—
211C22⋊C4×C29—22no—
212C22⋊C4×C29—22no—
213C22⋊C4×C29—22no—
214C22⋊C4×C29—22no—
215C22⋊C4×C29—21no—
216C22⋊C4×C29—22no—
217C22⋊C4×C29—21no—
218C22⋊C4×C29—21no—
219C22⋊C4×C29—21no—
220C22⋊C4×C29—21no—
221C22⋊C4×C29—21no—
222C22⋊C4×C29—21no—
223C42×C29—22no—
224C42×C29—22no—
225C42×C29—21no—
226C42×C29—22no—
227C42×C29—21no—
228C42×C29—21no—
229C42×C29C2×D411yescharacteristic
230C42×C29C2×D411yescharacteristic
231C42×C29C2×D411yescharacteristic
232C42×C29C2411yescharacteristic
233#18793C2911yesmaximal, characteristic, direct product factor, Sylow
234C23×C29—21no—
235C23×C29—21no—
236C23×C29—21no—
237C23×C29—42no—
238C23×C29—42no—
239C23×C29—81no—
240C23×C29#12011yescharacteristic
241Q8×C29—21no—
242Q8×C29—21no—
243Q8×C29—42no—
244Q8×C29—44no—
245Q8×C29—41no—
246Q8×C29—41no—
247Q8×C29—82no—
248D4×C29—21no—
249D4×C29—21no—
250D4×C29—21no—
251D4×C29—21no—
252D4×C29—21no—
253D4×C29—42no—
254D4×C29—44no—
255D4×C29—42no—
256D4×C29—82no—
257D4×C29#13712yes—
258C2×C4×C29—21no—
259C2×C4×C29—21no—
260C2×C4×C29—21no—
261C2×C4×C29—21no—
262C2×C4×C29—21no—
263C2×C4×C29—21no—
264C2×C4×C29—22no—
265C2×C4×C29—22no—
266C2×C4×C29—21no—
267C2×C4×C29—41no—
268C2×C4×C29—44no—
269C2×C4×C29—42no—
270C2×C4×C29—41no—
271C2×C4×C29—41no—
272C2×C4×C29—41no—
273C2×C4×C29—41no—
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—81no—
281C2×C4×C29—82no—
282C2×C4×C29—82no—
283C2×C4×C29#12011yescharacteristic
284C2×C4×C29#12011yescharacteristic
285C2×C4×C29#12011yescharacteristic
286C2×C4×C29#13512yes—
287C2×C4×C29#13712yes—
288C2×C4×C29C22×D411yescharacteristic
289C2×C4×C29C22×D411yescharacteristic
290C2×C4×C29C22×D411yescharacteristic
291C8×C29—42no—
292C8×C29—42no—
293C8×C29—42no—
294#3475C2×C2911yescharacteristic
295#3209C2×C2911yescharacteristic, complemented
296#3079C2×C2911yescharacteristic, complemented
297C2×#476C2×C2911yescharacteristic, complemented
298#1638C2×C2912yescomplemented
299#1635C2×C2912yescomplemented
300#1634C2×C2912yescomplemented
301#1632C2×C2912yescomplemented
302#1550C2×C2911yescharacteristic, complemented
303#1486C2×C2911yescharacteristic, complemented
304#1477C2×C2911yescharacteristic, complemented
305C22×C29—21no—
306C22×C29—21no—
307C22×C29—22no—
308C22×C29—41no—
309C22×C29—41no—
310C22×C29—41no—
311C22×C29—41no—
312C22×C29—41no—
313C22×C29—41no—
314C22×C29—41no—
315C22×C29—41no—
316C22×C29—84no—
317C22×C29#45212yes—
318C22×C29C2×#12011yescharacteristic
319C4×C29—21no—
320C4×C29—21no—
321C4×C29—21no—
322C4×C29—41no—
323C4×C29—41no—
324C4×C29—41no—
325C4×C29—41no—
326C4×C29—42no—
327C4×C29—41no—
328C4×C29—42no—
329C4×C29—82no—
330C4×C29#45212yes—
331C4×C29C2×#13511yescharacteristic
332C4×C29C2×#13711yescharacteristic
333C4×C29C2×#13711yescharacteristic
334C4×C29#57511yescharacteristic
335#556C22×C2911yescharacteristic
336#555C22×C2911yescharacteristic
337#554C22×C2911yescharacteristic
338#553—21no—
339#552—21no—
340#552—21no—
341#551—22no—
342#547C22×C2911yescharacteristic
343#546—21no—
344#533C22×C2911yescharacteristic
345C2×C4⋊Q8C22×C2911yescharacteristic
346#529—22no—
347#529—21no—
348#525—21no—
349C4×#41—21no—
350C4×#41C22×C2911yescharacteristic
351C2×C4×D4C22×C2911yescharacteristic
352C2×#117—21no—
353#494C22×C2912yescomplemented
354#487C22×C2912yescomplemented
355#477C22×C2912yescomplemented
356#476—21no—
357#476—21no—
358#476C22×C2912yes—
359#476C22×C2912yes—
360#476C22×C2912yescomplemented
361#475—21no—
362#474—21no—
363#462—22no—
364#451—22no—
365#431C22×C2911yescharacteristic
366#428—21no—
367C2×#106—21no—
368#423C22×C2911yescharacteristic
369C2×C4⋊C8C22×C2911yescharacteristic
370#417—21no—
371C2×#102—21no—
372#333C22×C2912yescomplemented
373#332C22×C2912yescomplemented
374Q8⋊C8C22×C2912yescomplemented
375D4⋊C8C22×C2912yes—
376D4⋊C8C22×C2912yes—
377D4⋊C8C22×C2912yescomplemented
378C2×C29—22no—
379C2×C29—42no—
380C2×C29—81no—
381C2×C29—81no—
382C2×C29C2×#45211yescharacteristic
383C2×C29#300711yescharacteristic
384C2×C29#302111yescharacteristic
385C2×#41—21no—
386C2×#41D4×C2911yescharacteristic
387C22×Q8—21no—
388C22×D4D4×C2911yescharacteristic
389C23×C4—21no—
390C2×Q16—24no—
391C2×M16—21no—
392C22×C8—21no—
393C4⋊Q8—21no—
394C4⋊Q8—21no—
395C4⋊Q8—21no—
396C4⋊Q8C23×C2912yes—
397C4⋊Q8C23×C2911yescharacteristic
398C4⋊Q8C23×C2911yescharacteristic
399#126—22no—
400#126—22no—
401#126—22no—
402#125—22no—
403#125—21no—
404#125—21no—
405#124—22no—
406#124—21no—
407#123—22no—
408#123—22no—
409#123—22no—
410#123—22no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8—22no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8D4×C2912yes—
417#121—22no—
418#121—21no—
419#121—21no—
420#121—21no—
421#120—22no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8D4×C2911yescharacteristic
425C4×Q8D4×C2912yes—
426C4×Q8C23×C2911yescharacteristic
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4D4×C2911yescharacteristic
436C4×D4D4×C2911yescharacteristic
437C4×D4D4×C2911yescharacteristic
438C4×D4C23×C2911yescharacteristic
439C4×D4C23×C2911yescharacteristic
440C4×D4C23×C2911yescharacteristic
441#117—22no—
442#117—22no—
443#117—22no—
444#117—21no—
445#117—21no—
446#117—21no—
447#117—21no—
448#117—21no—
449#117D4×C2911yescharacteristic
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4D4×C2911yescharacteristic
455C2×C22⋊C4—22no—
456C2×C22⋊C4—21no—
457C2×C42—22no—
458C2×C42—21no—
459C2×C42C23×C2911yescharacteristic
460#107—22no—
461#106—22no—
462#106—22no—
463#106—22no—
464C4⋊C8—21no—
465C4⋊C8—21no—
466C4⋊C8—21no—
467C4⋊C8C23×C2912yes—
468C4⋊C8C23×C2912yes—
469#103—22no—
470#103—24no—
471#102—22no—
472#102—22no—
473#102—22no—
474C22⋊C8—21no—
475C4×C8C23×C2912yes—
476C29#1879311yescharacteristic, direct product factor, Sylow
477C24—21no—
478#41—22no—
479#41—22no—
480#41—42no—
481#41—42no—
482C2×Q8—21no—
483C2×Q8—22no—
484C2×Q8—41no—
485C2×Q8—82no—
486C2×Q8C2×D4×C2911yescharacteristic
487C2×Q8C2×D4×C2912yes—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—21no—
491C2×D4—22no—
492C2×D4—21no—
493C2×D4—41no—
494C2×D4C2×D4×C2911yescharacteristic
495C2×D4C2×D4×C2911yescharacteristic
496C2×D4C2×D4×C2911yescharacteristic
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—41no—
510C22×C4C2×D4×C2911yescharacteristic
511C22×C4C2×D4×C2911yescharacteristic
512C22×C4C2×D4×C2911yescharacteristic
513Q16—84no—
514M16—42no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—42no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—22no—
525C4⋊C4—21no—
526C4⋊C4—22no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4C2×D4×C2912yes—
536C4⋊C4C2×D4×C2911yescharacteristic
537C4⋊C4C2×D4×C2911yescharacteristic
538C4⋊C4C2×D4×C2911yescharacteristic
539C4⋊C4C2×D4×C2911yescharacteristic
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—21no—
547C22⋊C4—22no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C22⋊C4—21no—
551C22⋊C4—21no—
552C22⋊C4—21no—
553C22⋊C4—21no—
554C42—22no—
555C42—22no—
556C42—21no—
557C42—22no—
558C42—21no—
559C42—21no—
560C42C2×D4×C2911yescharacteristic
561C42C2×D4×C2911yescharacteristic
562C42C2×D4×C2911yescharacteristic
563C42C24×C2911yescharacteristic
564C23—21no—
565C23—21no—
566C23—21no—
567C23—42no—
568C23—42no—
569C23—81no—
570C23C29×#12011yescharacteristic
571Q8—21no—
572Q8—21no—
573Q8—42no—
574Q8—44no—
575Q8—41no—
576Q8—41no—
577Q8—82no—
578D4—21no—
579D4—21no—
580D4—21no—
581D4—21no—
582D4—21no—
583D4—42no—
584D4—44no—
585D4—42no—
586D4—82no—
587D4C29×#13712yes—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—41no—
598C2×C4—44no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—81no—
611C2×C4—82no—
612C2×C4—82no—
613C2×C4C29×#12011yescharacteristic
614C2×C4C29×#12011yescharacteristic
615C2×C4C29×#12011yescharacteristic
616C2×C4C29×#13512yes—
617C2×C4C29×#13712yes—
618C2×C4C22×D4×C2911yescharacteristic
619C2×C4C22×D4×C2911yescharacteristic
620C2×C4C22×D4×C2911yescharacteristic
621C8—42no—
622C8—42no—
623C8—42no—
624C22—21no—
625C22—21no—
626C22—22no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—84no—
636C22C29×#45212yes—
637C22C2×C29×#12011yescharacteristic
638C4—21no—
639C4—21no—
640C4—21no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4—41no—
645C4—42no—
646C4—41no—
647C4—42no—
648C4—82no—
649C4C29×#45212yes—
650C4C2×C29×#13511yescharacteristic
651C4C2×C29×#13711yescharacteristic
652C4C2×C29×#13711yescharacteristic
653C4C29×#57511yescharacteristic
654C2—22no—
655C2—42no—
656C2—81no—
657C2—81no—
658C2C2×C29×#45211yescharacteristic
659C2C29×#300711yescharacteristic
660C2C29×#302111yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3475C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3209C2semidirect
3. C29×#3079C2semidirect
4. C2×C29×#476C2semidirect
5. C29×#1638C2semidirect
6. C29×#1635C2semidirect
7. C29×#1634C2semidirect
8. C29×#1632C2semidirect
9. C29×#1550C2semidirect
10. C29×#1486C2semidirect
11. C29×#1477C2semidirect
30. C29×#494C22semidirect
31. C29×#487C22semidirect
32. C29×#477C22semidirect
37. C29×#476C22semidirect
49. C29×#333C22semidirect
50. C29×#332C22semidirect
51. C29×Q8⋊C8C22semidirect
54. C29×D4⋊C8C22semidirect
233. #18793C29direct (N × H)
295. #3209C2×C29semidirect
296. #3079C2×C29semidirect
297. C2×#476C2×C29semidirect
298. #1638C2×C29semidirect
299. #1635C2×C29semidirect
300. #1634C2×C29semidirect
301. #1632C2×C29semidirect
302. #1550C2×C29semidirect
303. #1486C2×C29semidirect
304. #1477C2×C29semidirect
353. #494C22×C29semidirect
354. #487C22×C29semidirect
355. #477C22×C29semidirect
360. #476C22×C29semidirect
372. #333C22×C29semidirect
373. #332C22×C29semidirect
374. Q8⋊C8C22×C29semidirect
377. D4⋊C8C22×C29semidirect
476. C29#18793direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34752
C29×#32092
C29×#30792
C2×C29×#4762
C29×#16382
C29×#16352
C29×#16342
C29×#16322
C29×#15502
C29×#14862
C29×#14772
#1879329