Finite Group Databasebeta

← C29×#9042 #20303942

Subgroups — C29×#9042 #20303942

Order 7424.

966 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#450C211yesmaximal, characteristic
2C29×#2329C211yesmaximal, characteristic, complemented
3C29×#1786C211yesmaximal, characteristic
4C2×C29×#328C211yesmaximal, characteristic, complemented
5C29×#1438C211yesmaximal, characteristic
6C29×#1294C211yesmaximal, characteristic, complemented
7C29×#1280C211yesmaximal, characteristic, complemented
8C23×D4×C29C2211yescharacteristic
9C22×SD16×C29—21no—
10C2×C29×C22⋊Q8C2211yescharacteristic
11C22×C22⋊C4×C29—21no—
12C22×C22⋊C4×C29—21no—
13C29×#450—22no—
14C29×#450C414yescomplemented
15C2×C29×#102—21no—
16C2×C29×#102—21no—
17C2×C29×#102—21no—
18C2×C29×C22⋊C8C2211yescharacteristic
19C2×C29×C22⋊C8C2211yescharacteristic
20C29×#391—21no—
21C29×#389—21no—
22C29×#387—21no—
23C29×#387—21no—
24C29×#385—21no—
25C29×#380C2211yescharacteristic
26C4×C22⋊C4×C29—21no—
27C2×C29×#95C2211yescharacteristic
28C2×C29×#95C2211yescharacteristic
29C29×#328—22no—
30C25×C29—21no—
31C22×Q8×C29D411yescharacteristic
32C22×D4×C29—21no—
33C22×D4×C29—21no—
34C22×D4×C29—21no—
35C22×D4×C29—21no—
36C22×D4×C29—21no—
37C22×D4×C29—42no—
38C22×D4×C29—42no—
39C22×D4×C29C2×C412yes—
40C23×C4×C29—21no—
41C23×C4×C29D411yescharacteristic
42C23×C4×C29D411yescharacteristic
43C23×C4×C29C2311yescharacteristic
44C2×SD16×C29—24no—
45C2×SD16×C29—42no—
46C2×SD16×C29—42no—
47C22×C8×C29—21no—
48C22×C8×C29—21no—
49C29×C22⋊Q8—21no—
50C29×C22⋊Q8—21no—
51C29×C22⋊Q8C2×C412yes—
52C29×C22⋊Q8D412yes—
53C2×C4⋊C4×C29—21no—
54C2×C4⋊C4×C29—21no—
55C2×C4⋊C4×C29—21no—
56C2×C4⋊C4×C29D411yescharacteristic
57C2×C4⋊C4×C29D411yescharacteristic
58C2×C4⋊C4×C29D411yescharacteristic
59C2×C22⋊C4×C29—21no—
60C2×C22⋊C4×C29—21no—
61C2×C22⋊C4×C29—42no—
62C2×C22⋊C4×C29—42no—
63C2×C22⋊C4×C29—42no—
64C2×C22⋊C4×C29—42no—
65C2×C22⋊C4×C29—42no—
66C2×C22⋊C4×C29—42no—
67C2×C42×C29—21no—
68C2×C42×C29—21no—
69C29×#102—24no—
70C29×#102—42no—
71C29×#102—42no—
72C29×C22⋊C8—21no—
73C29×C22⋊C8—21no—
74C29×C22⋊C8—21no—
75C29×C22⋊C8C2×C412yes—
76C29×#95—21no—
77C29×#95—21no—
78C29×#95—21no—
79C29×#95—21no—
80C29×#95—21no—
81C29×#95—21no—
82C29×#95—21no—
83C29×#95—21no—
84C29×#95—21no—
85C24×C29—22no—
86C24×C29—22no—
87C24×C29—22no—
88C24×C29—41no—
89C24×C29—41no—
90C24×C29—41no—
91C24×C29—41no—
92C24×C29—41no—
93C24×C29—41no—
94C24×C29—41no—
95C24×C29—41no—
96C24×C29—41no—
97C24×C29—41no—
98C24×C29—41no—
99C24×C29—41no—
100C24×C29C2×D411yescharacteristic
101C2×Q8×C29—21no—
102C2×Q8×C29—41no—
103C2×Q8×C29—41no—
104C2×Q8×C29C22⋊C412yescomplemented
105C2×D4×C29—22no—
106C2×D4×C29—22no—
107C2×D4×C29—22no—
108C2×D4×C29—22no—
109C2×D4×C29—22no—
110C2×D4×C29—22no—
111C2×D4×C29—41no—
112C2×D4×C29—41no—
113C2×D4×C29—41no—
114C2×D4×C29—41no—
115C2×D4×C29—44no—
116C2×D4×C29—44no—
117C2×D4×C29—44no—
118C2×D4×C29—44no—
119C2×D4×C29—41no—
120C2×D4×C29—41no—
121C22×C4×C29—21no—
122C22×C4×C29—21no—
123C22×C4×C29—21no—
124C22×C4×C29—21no—
125C22×C4×C29—22no—
126C22×C4×C29—21no—
127C22×C4×C29—21no—
128C22×C4×C29—21no—
129C22×C4×C29—21no—
130C22×C4×C29—21no—
131C22×C4×C29—41no—
132C22×C4×C29—41no—
133C22×C4×C29—41no—
134C22×C4×C29—41no—
135C22×C4×C29—41no—
136C22×C4×C29—41no—
137C22×C4×C29—41no—
138C22×C4×C29—41no—
139C22×C4×C29—41no—
140C22×C4×C29—41no—
141C22×C4×C29—41no—
142C22×C4×C29—41no—
143C22×C4×C29SD1612yescomplemented
144C22×C4×C29C22×C411yescharacteristic
145C22×C4×C29C2×D411yescharacteristic
146C22×C4×C29C2×D411yescharacteristic
147C22×C4×C29C2×D411yescharacteristic
148C22×C4×C29#4111yescharacteristic
149C22×C4×C29#4111yescharacteristic
150SD16×C29—48no—
151C2×C8×C29—22no—
152C2×C8×C29—41no—
153C2×C8×C29—41no—
154C2×C8×C29—41no—
155C2×C8×C29—41no—
156C2×C8×C29—41no—
157C4⋊C4×C29—22no—
158C4⋊C4×C29—22no—
159C4⋊C4×C29—21no—
160C4⋊C4×C29—41no—
161C4⋊C4×C29—41no—
162C4⋊C4×C29—81no—
163C4⋊C4×C29—81no—
164C4⋊C4×C29C22⋊C412yescomplemented
165C22⋊C4×C29—22no—
166C22⋊C4×C29—22no—
167C22⋊C4×C29—48no—
168C22⋊C4×C29—48no—
169C22⋊C4×C29—41no—
170C22⋊C4×C29—41no—
171C42×C29—81no—
172C42×C29—81no—
173#9042C2911yesmaximal, characteristic, direct product factor, Sylow
174C23×C29—21no—
175C23×C29—21no—
176C23×C29—21no—
177C23×C29—21no—
178C23×C29—24no—
179C23×C29—42no—
180C23×C29—42no—
181C23×C29—42no—
182C23×C29—42no—
183C23×C29—42no—
184C23×C29—42no—
185C23×C29—42no—
186C23×C29—42no—
187C23×C29—42no—
188C23×C29—42no—
189C23×C29—42no—
190C23×C29—42no—
191C23×C29—42no—
192C23×C29—42no—
193C23×C29—42no—
194C23×C29—42no—
195C23×C29—42no—
196C23×C29—42no—
197C23×C29—81no—
198C23×C29—81no—
199C23×C29—81no—
200C23×C29—81no—
201C23×C29—81no—
202C23×C29—81no—
203C23×C29—81no—
204C23×C29—81no—
205C23×C29—81no—
206C23×C29—81no—
207C23×C29—81no—
208C23×C29—81no—
209C23×C29—81no—
210C23×C29—81no—
211C23×C29—81no—
212C23×C29—81no—
213C23×C29C4×D411yescharacteristic
214C23×C29#12011yescharacteristic
215C23×C29#12111yescharacteristic
216C23×C29C2×SD1611yescharacteristic
217C23×C29#13511yescharacteristic
218C23×C29AGL(1,ℤ/8)11yescharacteristic
219C23×C29#13711yescharacteristic
220Q8×C29—42no—
221Q8×C29—81no—
222D4×C29—24no—
223D4×C29—24no—
224D4×C29—42no—
225D4×C29—42no—
226D4×C29—42no—
227D4×C29—42no—
228D4×C29—42no—
229D4×C29—42no—
230C2×C4×C29—21no—
231C2×C4×C29—21no—
232C2×C4×C29—21no—
233C2×C4×C29—21no—
234C2×C4×C29—22no—
235C2×C4×C29—22no—
236C2×C4×C29—22no—
237C2×C4×C29—41no—
238C2×C4×C29—41no—
239C2×C4×C29—41no—
240C2×C4×C29—41no—
241C2×C4×C29—41no—
242C2×C4×C29—41no—
243C2×C4×C29—41no—
244C2×C4×C29—41no—
245C2×C4×C29—41no—
246C2×C4×C29—41no—
247C2×C4×C29—42no—
248C2×C4×C29—42no—
249C2×C4×C29—42no—
250C2×C4×C29—42no—
251C2×C4×C29—42no—
252C2×C4×C29—41no—
253C2×C4×C29—41no—
254C2×C4×C29—41no—
255C2×C4×C29—41no—
256C2×C4×C29—41no—
257C2×C4×C29—41no—
258C2×C4×C29—41no—
259C2×C4×C29—41no—
260C2×C4×C29—41no—
261C2×C4×C29—81no—
262C2×C4×C29—81no—
263C2×C4×C29—81no—
264C2×C4×C29—81no—
265C2×C4×C29—81no—
266C2×C4×C29—81no—
267C2×C4×C29C2×C22⋊C411yescharacteristic
268C2×C4×C29C4×D411yescharacteristic
269C2×C4×C29#12111yescharacteristic
270C2×C4×C29#12311yescharacteristic
271C8×C29—42no—
272C8×C29—81no—
273C2×#450C2×C2911yescharacteristic
274#2329C2×C2911yescharacteristic, complemented
275#1786C2×C2911yescharacteristic
276C2×#328C2×C2911yescharacteristic, complemented
277#1438C2×C2911yescharacteristic
278#1294C2×C2911yescharacteristic, complemented
279#1280C2×C2911yescharacteristic, complemented
280C22×C29—21no—
281C22×C29—21no—
282C22×C29—21no—
283C22×C29—21no—
284C22×C29—21no—
285C22×C29—21no—
286C22×C29—21no—
287C22×C29—21no—
288C22×C29—21no—
289C22×C29—21no—
290C22×C29—21no—
291C22×C29—21no—
292C22×C29—44no—
293C22×C29—44no—
294C22×C29—44no—
295C22×C29—82no—
296C22×C29—82no—
297C22×C29—82no—
298C22×C29—82no—
299C22×C29—82no—
300C22×C29—82no—
301C22×C29—82no—
302C22×C29—82no—
303C22×C29—82no—
304C22×C29—82no—
305C22×C29—82no—
306C22×C29—82no—
307C22×C29#38611yescharacteristic
308C22×C29C4×SD1611yescharacteristic
309C22×C29#44011yescharacteristic
310C22×C29#44811yescharacteristic
311C22×C29#44911yescharacteristic
312C22×C29#45311yescharacteristic
313C22×C29#45411yescharacteristic
314C22×C29B(4,𝔽2)11yescharacteristic
315C22×C29B(4,𝔽2)11yescharacteristic
316C22×C29#46011yescharacteristic
317C22×C29#46411yescharacteristic
318C4×C29—21no—
319C4×C29—21no—
320C4×C29—21no—
321C4×C29—21no—
322C4×C29—42no—
323C4×C29—42no—
324C4×C29—42no—
325C4×C29—82no—
326C4×C29—81no—
327C4×C29—81no—
328C4×C29—81no—
329C23×D4C22×C2911yescharacteristic
330C22×SD16—21no—
331C2×C22⋊Q8C22×C2911yescharacteristic
332C22×C22⋊C4—21no—
333C22×C22⋊C4—21no—
334#450—22no—
335#450C4×C2914yescomplemented
336C2×#102—21no—
337C2×#102—21no—
338C2×#102—21no—
339C2×C22⋊C8C22×C2911yescharacteristic
340C2×C22⋊C8C22×C2911yescharacteristic
341#391—21no—
342#389—21no—
343#387—21no—
344#387—21no—
345#385—21no—
346#380C22×C2911yescharacteristic
347C4×C22⋊C4—21no—
348C2×#95C22×C2911yescharacteristic
349C2×#95C22×C2911yescharacteristic
350#328—22no—
351C2×C29—21no—
352C2×C29—21no—
353C2×C29—21no—
354C2×C29—21no—
355C2×C29—84no—
356C2×C29#159611yescharacteristic
357C2×C29#159711yescharacteristic
358C2×C29#159911yescharacteristic
359C2×C29#160011yescharacteristic
360C2×C29#188011yescharacteristic
361C2×C29#188311yescharacteristic
362C2×C29#188911yescharacteristic
363C25—21no—
364C22×Q8D4×C2911yescharacteristic
365C22×D4—21no—
366C22×D4—21no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4C2×C4×C2912yes—
373C23×C4—21no—
374C23×C4D4×C2911yescharacteristic
375C23×C4D4×C2911yescharacteristic
376C23×C4C23×C2911yescharacteristic
377C2×SD16—24no—
378C2×SD16—42no—
379C2×SD16—42no—
380C22×C8—21no—
381C22×C8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—21no—
384C22⋊Q8C2×C4×C2912yes—
385C22⋊Q8D4×C2912yes—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4D4×C2911yescharacteristic
390C2×C4⋊C4D4×C2911yescharacteristic
391C2×C4⋊C4D4×C2911yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C42—21no—
401C2×C42—21no—
402#102—24no—
403#102—42no—
404#102—42no—
405C22⋊C8—21no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8C2×C4×C2912yes—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418C29#904211yescharacteristic, direct product factor, Sylow
419C24—22no—
420C24—22no—
421C24—22no—
422C24—41no—
423C24—41no—
424C24—41no—
425C24—41no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24C2×D4×C2911yescharacteristic
435C2×Q8—21no—
436C2×Q8—41no—
437C2×Q8—41no—
438C2×Q8C22⋊C4×C2912yescomplemented
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—41no—
454C2×D4—41no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4SD16×C2912yescomplemented
478C22×C4C22×C4×C2911yescharacteristic
479C22×C4C2×D4×C2911yescharacteristic
480C22×C4C2×D4×C2911yescharacteristic
481C22×C4C2×D4×C2911yescharacteristic
482C22×C4#41×C2911yescharacteristic
483C22×C4#41×C2911yescharacteristic
484SD16—48no—
485C2×C8—22no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—81no—
497C4⋊C4—81no—
498C4⋊C4C22⋊C4×C2912yescomplemented
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—48no—
502C22⋊C4—48no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C42—81no—
506C42—81no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—24no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—81no—
531C23—81no—
532C23—81no—
533C23—81no—
534C23—81no—
535C23—81no—
536C23—81no—
537C23—81no—
538C23—81no—
539C23—81no—
540C23—81no—
541C23—81no—
542C23—81no—
543C23—81no—
544C23—81no—
545C23—81no—
546C23C4×D4×C2911yescharacteristic
547C23C29×#12011yescharacteristic
548C23C29×#12111yescharacteristic
549C23C2×SD16×C2911yescharacteristic
550C23C29×#13511yescharacteristic
551C23C29×AGL(1,ℤ/8)11yescharacteristic
552C23C29×#13711yescharacteristic
553Q8—42no—
554Q8—81no—
555D4—24no—
556D4—24no—
557D4—42no—
558D4—42no—
559D4—42no—
560D4—42no—
561D4—42no—
562D4—42no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—81no—
599C2×C4—81no—
600C2×C4C2×C22⋊C4×C2911yescharacteristic
601C2×C4C4×D4×C2911yescharacteristic
602C2×C4C29×#12111yescharacteristic
603C2×C4C29×#12311yescharacteristic
604C8—42no—
605C8—81no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—82no—
622C22—82no—
623C22—82no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22—82no—
629C22—82no—
630C22—82no—
631C22—82no—
632C22—82no—
633C22C29×#38611yescharacteristic
634C22C4×SD16×C2911yescharacteristic
635C22C29×#44011yescharacteristic
636C22C29×#44811yescharacteristic
637C22C29×#44911yescharacteristic
638C22C29×#45311yescharacteristic
639C22C29×#45411yescharacteristic
640C22C29×B(4,𝔽2)11yescharacteristic
641C22C29×B(4,𝔽2)11yescharacteristic
642C22C29×#46011yescharacteristic
643C22C29×#46411yescharacteristic
644C4—21no—
645C4—21no—
646C4—21no—
647C4—21no—
648C4—42no—
649C4—42no—
650C4—42no—
651C4—82no—
652C4—81no—
653C4—81no—
654C4—81no—
655C2—21no—
656C2—21no—
657C2—21no—
658C2—21no—
659C2—84no—
660C2C29×#159611yescharacteristic
661C2C29×#159711yescharacteristic
662C2C29×#159911yescharacteristic
663C2C29×#160011yescharacteristic
664C2C29×#188011yescharacteristic
665C2C29×#188311yescharacteristic
666C2C29×#188911yescharacteristic
subgroupG/H
center, socleC23×C29#120
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC23×D4×C29C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2329C2semidirect
4. C2×C29×#328C2semidirect
6. C29×#1294C2semidirect
7. C29×#1280C2semidirect
14. C29×#450C4semidirect
104. C2×Q8×C29C22⋊C4semidirect
143. C22×C4×C29SD16semidirect
164. C4⋊C4×C29C22⋊C4semidirect
173. #9042C29direct (N × H)
274. #2329C2×C29semidirect
276. C2×#328C2×C29semidirect
278. #1294C2×C29semidirect
279. #1280C2×C29semidirect
335. #450C4×C29semidirect
418. C29#9042direct (N × H)
438. C2×Q8C22⋊C4×C29semidirect
477. C22×C4SD16×C29semidirect
498. C4⋊C4C22⋊C4×C29semidirect

Maximal subgroups

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

subgroupindex
C2×C29×#4502
C29×#23292
C29×#17862
C2×C29×#3282
C29×#14382
C29×#12942
C29×#12802
#904229