Finite Group Databasebeta

← C29×#18257 #20313157

Subgroups — C29×#18257 #20313157

Order 7424.

1192 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×#3536C211yesmaximal, characteristic
2C29×#3004C211yesmaximal, characteristic, complemented
3C2×C29×#451C211yesmaximal, characteristic, complemented
4C29×#2436C211yesmaximal, characteristic, complemented
5C29×#1606C214yesmaximal, complemented
6C29×#1602C214yesmaximal, complemented
7C29×#1508C211yesmaximal, characteristic, complemented
8C29×#1501C211yesmaximal, characteristic, complemented
9C29×#1471C211yesmaximal, characteristic, complemented
10C23×Q8×C29C2211yescharacteristic
11C2×C29×#137—21no—
12C22×Q16×C29—21no—
13C29×#562—22no—
14C29×#554—21no—
15C29×#548—21no—
16C29×#547—21no—
17C29×#546—22no—
18C29×#546—21no—
19C29×#543C2212yes—
20C29×#542—21no—
21C29×#539—21no—
22C29×#538C2212yes—
23C29×#537—21no—
24C29×#537—21no—
25C2×C29×#124—21no—
26C29×#525C2211yescharacteristic
27C2×C29×C22⋊Q8C2211yescharacteristic
28C2×C29×#121C2211yescharacteristic
29C29×#451—22no—
30C29×#451—21no—
31C29×#451C2214yes—
32C29×#451C2212yes—
33C29×#448—21no—
34C29×#448C2212yes—
35C29×#419—21no—
36C2×C29×#103—21no—
37C29×#407C2211yescharacteristic
38C2×C29×C22⋊C8C2211yescharacteristic
39C29×#393C2214yes—
40C29×#391—21no—
41C29×#386—22no—
42C4×C22⋊C4×C29C2211yescharacteristic
43C29×#328C2212yes—
44C29×#328C2214yes—
45C29×#327C2212yes—
46C29×#323C2214yes—
47C2×#41×C29—22no—
48C2×#41×C29—21no—
49C2×#41×C29D411yescharacteristic
50C22×Q8×C29—21no—
51C22×Q8×C29—21no—
52C22×Q8×C29—21no—
53C22×Q8×C29—21no—
54C22×Q8×C29—21no—
55C22×Q8×C29—44no—
56C22×Q8×C29D411yescharacteristic
57C22×Q8×C29C2312yes—
58C22×D4×C29D411yescharacteristic
59C22×D4×C29D412yes—
60C23×C4×C29—21no—
61C23×C4×C29C2311yescharacteristic
62C29×#137—44no—
63C2×Q16×C29—24no—
64C2×Q16×C29—22no—
65C2×Q16×C29—44no—
66C2×SD16×C29—22no—
67C2×M16×C29—21no—
68C22×C8×C29—21no—
69C29×C4⋊Q8—21no—
70C29×#126—22no—
71C29×#125—22no—
72C29×#124—21no—
73C29×#124—22no—
74C29×#124—22no—
75C29×#124—44no—
76C29×#123—22no—
77C29×#123—22no—
78C29×#123—22no—
79C29×#123—21no—
80C29×#123—22no—
81C29×C22⋊Q8—21no—
82C29×C22⋊Q8—22no—
83C29×C22⋊Q8—22no—
84C29×C22⋊Q8—22no—
85C29×C22⋊Q8—21no—
86C29×C22⋊Q8—21no—
87C29×C22⋊Q8—22no—
88C29×C22⋊Q8—22no—
89C29×C22⋊Q8—22no—
90C29×C22⋊Q8D412yes—
91C29×C22⋊Q8D411yescharacteristic
92C29×C22⋊Q8C2312yes—
93C29×C22⋊Q8C2311yescharacteristic
94C29×#121—21no—
95C29×#121—22no—
96C29×#121—22no—
97C29×#121—22no—
98C29×#121—22no—
99C29×#121—22no—
100C29×#121—21no—
101C29×#121—21no—
102C29×#121—21no—
103C29×#121—21no—
104C29×#121D411yescharacteristic
105C29×#121C2311yescharacteristic
106C29×#120—21no—
107C29×#120—22no—
108C4×Q8×C29—21no—
109C4×D4×C29—22no—
110C4×D4×C29—21no—
111C4×D4×C29—21no—
112C4×D4×C29—21no—
113C4×D4×C29—22no—
114C29×#117D411yescharacteristic
115C2×C4⋊C4×C29—21no—
116C2×C4⋊C4×C29—21no—
117C2×C4⋊C4×C29D411yescharacteristic
118C2×C4⋊C4×C29D411yescharacteristic
119C2×C22⋊C4×C29—21no—
120C2×C22⋊C4×C29—22no—
121C2×C22⋊C4×C29—24no—
122C2×C22⋊C4×C29—21no—
123C2×C22⋊C4×C29C2312yes—
124C2×C42×C29—21no—
125C29×#103—22no—
126C29×#103—22no—
127C29×#103—24no—
128C29×C22⋊C8—21no—
129C29×C22⋊C8—21no—
130C29×C22⋊C8C2312yes—
131C29×C22⋊C8C2312yes—
132C29×#95—24no—
133C29×#95C2312yes—
134C24×C29C2×D411yescharacteristic
135C24×C29C2×D412yes—
136#41×C29—42no—
137#41×C29—84no—
138#41×C29—82no—
139C2×Q8×C29—24no—
140C2×Q8×C29—22no—
141C2×Q8×C29—21no—
142C2×Q8×C29—24no—
143C2×Q8×C29—24no—
144C2×Q8×C29—22no—
145C2×Q8×C29—22no—
146C2×Q8×C29—44no—
147C2×Q8×C29—42no—
148C2×Q8×C29—42no—
149C2×Q8×C29—42no—
150C2×Q8×C29—42no—
151C2×Q8×C29—44no—
152C2×Q8×C29—44no—
153C2×Q8×C29—41no—
154C2×Q8×C29—41no—
155C2×Q8×C29C2×D411yescharacteristic
156C2×Q8×C29C2×D412yes—
157C2×D4×C29—21no—
158C2×D4×C29—22no—
159C2×D4×C29—21no—
160C2×D4×C29—22no—
161C2×D4×C29—22no—
162C2×D4×C29—21no—
163C2×D4×C29—22no—
164C2×D4×C29—21no—
165C2×D4×C29—21no—
166C2×D4×C29—42no—
167C2×D4×C29—44no—
168C2×D4×C29C2×D411yescharacteristic
169C22×C4×C29—21no—
170C22×C4×C29—22no—
171C22×C4×C29—22no—
172C22×C4×C29—22no—
173C22×C4×C29—22no—
174C22×C4×C29—21no—
175C22×C4×C29—21no—
176C22×C4×C29—22no—
177C22×C4×C29—42no—
178C22×C4×C29—44no—
179C22×C4×C29—41no—
180C22×C4×C29—41no—
181C22×C4×C29C2×D411yescharacteristic
182C22×C4×C29C2×D411yescharacteristic
183C22×C4×C29C2×D411yescharacteristic
184C22×C4×C29C2×D412yes—
185C22×C4×C29C2×D411yescharacteristic
186C22×C4×C29C2×D411yescharacteristic
187C22×C4×C29C2411yescharacteristic
188Q16×C29—48no—
189Q16×C29—44no—
190SD16×C29—44no—
191M16×C29—42no—
192C2×C8×C29—22no—
193C2×C8×C29—22no—
194C2×C8×C29—42no—
195C4⋊C4×C29—22no—
196C4⋊C4×C29—22no—
197C4⋊C4×C29—22no—
198C4⋊C4×C29—22no—
199C4⋊C4×C29—21no—
200C4⋊C4×C29—21no—
201C4⋊C4×C29—22no—
202C4⋊C4×C29—21no—
203C4⋊C4×C29—21no—
204C4⋊C4×C29—22no—
205C4⋊C4×C29—21no—
206C4⋊C4×C29C2×D412yes—
207C4⋊C4×C29C2×D411yescharacteristic
208C4⋊C4×C29C2×D411yescharacteristic
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—21no—
217C22⋊C4×C29—22no—
218C22⋊C4×C29—21no—
219C22⋊C4×C29—21no—
220C22⋊C4×C29—22no—
221C22⋊C4×C29—22no—
222C22⋊C4×C29—21no—
223C22⋊C4×C29—48no—
224C22⋊C4×C29—42no—
225C42×C29—22no—
226C42×C29—21no—
227C42×C29—42no—
228#18257C2911yesmaximal, characteristic, direct product factor, Sylow
229C23×C29—22no—
230C23×C29—22no—
231C23×C29—22no—
232C23×C29—21no—
233C23×C29—24no—
234C23×C29—41no—
235C23×C29—42no—
236C23×C29—42no—
237C23×C29#12011yescharacteristic
238C23×C29#12011yescharacteristic
239C23×C29C22×D411yescharacteristic
240Q8×C29—24no—
241Q8×C29—24no—
242Q8×C29—42no—
243Q8×C29—41no—
244Q8×C29—42no—
245Q8×C29—42no—
246Q8×C29—44no—
247Q8×C29—44no—
248Q8×C29—42no—
249Q8×C29—82no—
250D4×C29—41no—
251D4×C29—42no—
252D4×C29—44no—
253D4×C29—42no—
254D4×C29—42no—
255D4×C29—81no—
256D4×C29—82no—
257D4×C29—81no—
258D4×C29—82no—
259D4×C29—82no—
260C2×C4×C29—22no—
261C2×C4×C29—22no—
262C2×C4×C29—22no—
263C2×C4×C29—24no—
264C2×C4×C29—21no—
265C2×C4×C29—22no—
266C2×C4×C29—21no—
267C2×C4×C29—22no—
268C2×C4×C29—21no—
269C2×C4×C29—22no—
270C2×C4×C29—41no—
271C2×C4×C29—41no—
272C2×C4×C29—41no—
273C2×C4×C29—42no—
274C2×C4×C29—44no—
275C2×C4×C29—44no—
276C2×C4×C29—42no—
277C2×C4×C29—42no—
278C2×C4×C29—42no—
279C2×C4×C29—42no—
280C2×C4×C29—42no—
281C2×C4×C29—42no—
282C2×C4×C29—42no—
283C2×C4×C29—81no—
284C2×C4×C29—82no—
285C2×C4×C29—82no—
286C2×C4×C29—82no—
287C2×C4×C29#12011yescharacteristic
288C2×C4×C29#12011yescharacteristic
289C2×C4×C29C22×D411yescharacteristic
290C2×C4×C29C22×D411yescharacteristic
291C8×C29—42no—
292C8×C29—42no—
293#3536C2×C2911yescharacteristic
294#3004C2×C2911yescharacteristic, complemented
295C2×#451C2×C2911yescharacteristic, complemented
296#2436C2×C2911yescharacteristic, complemented
297#1606C2×C2914yescomplemented
298#1602C2×C2914yescomplemented
299#1508C2×C2911yescharacteristic, complemented
300#1501C2×C2911yescharacteristic, complemented
301#1471C2×C2911yescharacteristic, complemented
302C22×C29—21no—
303C22×C29—21no—
304C22×C29—21no—
305C22×C29—21no—
306C22×C29—21no—
307C22×C29—21no—
308C22×C29—21no—
309C22×C29—44no—
310C22×C29—41no—
311C22×C29—42no—
312C22×C29—41no—
313C22×C29—42no—
314C22×C29—41no—
315C22×C29—42no—
316C22×C29—84no—
317C22×C29#45512yes—
318C22×C29C2×#12011yescharacteristic
319C22×C29#57812yes—
320C4×C29—21no—
321C4×C29—21no—
322C4×C29—21no—
323C4×C29—41no—
324C4×C29—42no—
325C4×C29—42no—
326C4×C29—41no—
327C4×C29—44no—
328C4×C29—41no—
329C4×C29—42no—
330C4×C29—82no—
331C4×C29B(4,𝔽2)12yes—
332C23×Q8C22×C2911yescharacteristic
333C2×#137—21no—
334C22×Q16—21no—
335#562—22no—
336#554—21no—
337#548—21no—
338#547—21no—
339#546—22no—
340#546—21no—
341#543C22×C2912yes—
342#542—21no—
343#539—21no—
344#538C22×C2912yes—
345#537—21no—
346#537—21no—
347C2×#124—21no—
348#525C22×C2911yescharacteristic
349C2×C22⋊Q8C22×C2911yescharacteristic
350C2×#121C22×C2911yescharacteristic
351#451—22no—
352#451—21no—
353#451C22×C2912yes—
354#451C22×C2914yes—
355#448—21no—
356#448C22×C2912yes—
357#419—21no—
358C2×#103—21no—
359#407C22×C2911yescharacteristic
360C2×C22⋊C8C22×C2911yescharacteristic
361#393C22×C2914yes—
362#391—21no—
363#386—22no—
364C4×C22⋊C4C22×C2911yescharacteristic
365#328C22×C2912yes—
366#328C22×C2914yes—
367#327C22×C2912yes—
368#323C22×C2914yes—
369C2×C29—22no—
370C2×C29—22no—
371C2×C29—41no—
372C2×C29—81no—
373C2×C29—82no—
374C2×C29#301111yescharacteristic
375C2×C29C2×#45511yescharacteristic
376C2×C29C2×B(4,𝔽2)11yescharacteristic
377C2×#41—22no—
378C2×#41—21no—
379C2×#41D4×C2911yescharacteristic
380C22×Q8—21no—
381C22×Q8—21no—
382C22×Q8—21no—
383C22×Q8—21no—
384C22×Q8—21no—
385C22×Q8—44no—
386C22×Q8D4×C2911yescharacteristic
387C22×Q8C23×C2912yes—
388C22×D4D4×C2911yescharacteristic
389C22×D4D4×C2912yes—
390C23×C4—21no—
391C23×C4C23×C2911yescharacteristic
392#137—44no—
393C2×Q16—24no—
394C2×Q16—22no—
395C2×Q16—44no—
396C2×SD16—22no—
397C2×M16—21no—
398C22×C8—21no—
399C4⋊Q8—21no—
400#126—22no—
401#125—22no—
402#124—21no—
403#124—22no—
404#124—22no—
405#124—44no—
406#123—22no—
407#123—22no—
408#123—22no—
409#123—21no—
410#123—22no—
411C22⋊Q8—21no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—22no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8D4×C2912yes—
421C22⋊Q8D4×C2911yescharacteristic
422C22⋊Q8C23×C2912yes—
423C22⋊Q8C23×C2911yescharacteristic
424#121—21no—
425#121—22no—
426#121—22no—
427#121—22no—
428#121—22no—
429#121—22no—
430#121—21no—
431#121—21no—
432#121—21no—
433#121—21no—
434#121D4×C2911yescharacteristic
435#121C23×C2911yescharacteristic
436#120—21no—
437#120—22no—
438C4×Q8—21no—
439C4×D4—22no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4—21no—
443C4×D4—22no—
444#117D4×C2911yescharacteristic
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4D4×C2911yescharacteristic
448C2×C4⋊C4D4×C2911yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4C23×C2912yes—
454C2×C42—21no—
455#103—24no—
456#103—22no—
457#103—22no—
458C22⋊C8—21no—
459C22⋊C8—21no—
460C22⋊C8C23×C2912yes—
461C22⋊C8C23×C2912yes—
462#95—24no—
463#95C23×C2912yes—
464C29#1825711yescharacteristic, direct product factor, Sylow
465C24C2×D4×C2911yescharacteristic
466C24C2×D4×C2912yes—
467#41—42no—
468#41—84no—
469#41—82no—
470C2×Q8—24no—
471C2×Q8—22no—
472C2×Q8—21no—
473C2×Q8—24no—
474C2×Q8—24no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—44no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—41no—
485C2×Q8—41no—
486C2×Q8C2×D4×C2911yescharacteristic
487C2×Q8C2×D4×C2912yes—
488C2×D4—21no—
489C2×D4—22no—
490C2×D4—21no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—22no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—42no—
498C2×D4—44no—
499C2×D4C2×D4×C2911yescharacteristic
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—42no—
509C22×C4—44no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4C2×D4×C2911yescharacteristic
513C22×C4C2×D4×C2911yescharacteristic
514C22×C4C2×D4×C2911yescharacteristic
515C22×C4C2×D4×C2912yes—
516C22×C4C2×D4×C2911yescharacteristic
517C22×C4C2×D4×C2911yescharacteristic
518C22×C4C24×C2911yescharacteristic
519Q16—48no—
520Q16—44no—
521SD16—44no—
522M16—42no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—42no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—22no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—22no—
536C4⋊C4—21no—
537C4⋊C4C2×D4×C2912yes—
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—21no—
548C22⋊C4—22no—
549C22⋊C4—21no—
550C22⋊C4—21no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—21no—
554C22⋊C4—48no—
555C22⋊C4—42no—
556C42—22no—
557C42—21no—
558C42—42no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—21no—
563C23—24no—
564C23—41no—
565C23—42no—
566C23—42no—
567C23C29×#12011yescharacteristic
568C23C29×#12011yescharacteristic
569C23C22×D4×C2911yescharacteristic
570Q8—24no—
571Q8—24no—
572Q8—42no—
573Q8—41no—
574Q8—42no—
575Q8—42no—
576Q8—44no—
577Q8—44no—
578Q8—42no—
579Q8—82no—
580D4—41no—
581D4—44no—
582D4—42no—
583D4—42no—
584D4—42no—
585D4—81no—
586D4—82no—
587D4—81no—
588D4—82no—
589D4—82no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—44no—
605C2×C4—44no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—81no—
614C2×C4—82no—
615C2×C4—82no—
616C2×C4—82no—
617C2×C4C29×#12011yescharacteristic
618C2×C4C29×#12011yescharacteristic
619C2×C4C22×D4×C2911yescharacteristic
620C2×C4C22×D4×C2911yescharacteristic
621C8—42no—
622C8—42no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—44no—
631C22—41no—
632C22—42no—
633C22—41no—
634C22—42no—
635C22—41no—
636C22—42no—
637C22—84no—
638C22C29×#45512yes—
639C22C2×C29×#12011yescharacteristic
640C22C29×#57812yes—
641C4—21no—
642C4—21no—
643C4—21no—
644C4—41no—
645C4—42no—
646C4—42no—
647C4—41no—
648C4—44no—
649C4—41no—
650C4—42no—
651C4—82no—
652C4C29×B(4,𝔽2)12yes—
653C2—22no—
654C2—22no—
655C2—41no—
656C2—82no—
657C2—81no—
658C2C29×#301111yescharacteristic
659C2C2×C29×#45511yescharacteristic
660C2C2×C29×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#3536C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3004C2semidirect
3. C2×C29×#451C2semidirect
4. C29×#2436C2semidirect
5. C29×#1606C2semidirect
6. C29×#1602C2semidirect
7. C29×#1508C2semidirect
8. C29×#1501C2semidirect
9. C29×#1471C2semidirect
228. #18257C29direct (N × H)
294. #3004C2×C29semidirect
295. C2×#451C2×C29semidirect
296. #2436C2×C29semidirect
297. #1606C2×C29semidirect
298. #1602C2×C29semidirect
299. #1508C2×C29semidirect
300. #1501C2×C29semidirect
301. #1471C2×C29semidirect
464. C29#18257direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35362
C29×#30042
C2×C29×#4512
C29×#24362
C29×#16062
C29×#16022
C29×#15082
C29×#15012
C29×#14712
#1825729