Finite Group Databasebeta

← C29×#18971 #20313871

Subgroups — C29×#18971 #20313871

Order 7424.

874 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3554C211yesmaximal, characteristic
2C29×#3229C211yesmaximal, characteristic, complemented
3C29×#3227C211yesmaximal, characteristic, complemented
4C29×#3218C211yesmaximal, characteristic, complemented
5C29×#1653C212yesmaximal, complemented
6C29×#1651C212yesmaximal, complemented
7C29×#1642C212yesmaximal, complemented
8C29×#1640C212yesmaximal, complemented
9C29×#1553C211yesmaximal, characteristic, complemented
10C29×#1497C211yesmaximal, characteristic, complemented
11C29×#1482C211yesmaximal, characteristic, complemented
12C29×#562—22no—
13C29×#559—21no—
14C29×#559C2211yescharacteristic
15C29×#557C2211yescharacteristic
16C29×#554—21no—
17C29×#550C2211yescharacteristic
18D4×Q8×C29C2211yescharacteristic
19C29×#548—21no—
20C29×#547—21no—
21C29×#542—21no—
22C29×#542—21no—
23C29×#540—21no—
24C29×#539—22no—
25C29×#536—21no—
26C29×#533C2211yescharacteristic
27C29×#532C2211yescharacteristic
28C2×C29×C4⋊Q8C2211yescharacteristic
29C29×#529C2211yescharacteristic
30C29×#498—21no—
31C29×#498C2212yes—
32C29×#497—21no—
33C29×#491—21no—
34C29×#487—21no—
35C29×#486C2212yes—
36C29×#483—21no—
37C29×#483—21no—
38C29×#481—22no—
39C29×#476—22no—
40C29×#475C2212yes—
41C29×#475C2212yes—
42C29×#462C2212yes—
43C29×#461C2212yes—
44C29×#451—21no—
45C29×#448—21no—
46C29×#432C2211yescharacteristic
47C29×#431C2211yescharacteristic
48C29×#431C2211yescharacteristic
49C29×#332C2212yes—
50C29×#331C2212yes—
51C29×Q8⋊C8C2212yes—
52C29×Q8⋊C8C2212yes—
53C29×Q8⋊C8C2212yes—
54C29×D4⋊C8C2212yes—
55C2×#41×C29—21no—
56C2×#41×C29—21no—
57C22×Q8×C29—21no—
58C22×Q8×C29—21no—
59C2×Q16×C29—22no—
60C2×SD16×C29—22no—
61C29×C4⋊Q8—21no—
62C29×C4⋊Q8—21no—
63C29×C4⋊Q8—21no—
64C29×C4⋊Q8—21no—
65C29×C4⋊Q8—21no—
66C29×C4⋊Q8D411yescharacteristic
67C29×C4⋊Q8D411yescharacteristic
68C29×C4⋊Q8C2312yes—
69C29×C4⋊Q8C2311yescharacteristic
70C29×#127—21no—
71C29×#127C2311yescharacteristic
72C29×#126—22no—
73C29×#126—21no—
74C29×#125—22no—
75C29×#125—21no—
76C29×#125—21no—
77C29×#125D411yescharacteristic
78C29×#124—22no—
79C29×#124—22no—
80C29×#124—21no—
81C29×#124—21no—
82C29×#124—21no—
83C29×#124D411yescharacteristic
84C29×#123—22no—
85C29×#123—22no—
86C29×#123—22no—
87C29×#123—22no—
88C29×#123—22no—
89C29×#123—22no—
90C29×#123—21no—
91C29×C22⋊Q8—22no—
92C29×C22⋊Q8—22no—
93C29×C22⋊Q8—22no—
94C29×C22⋊Q8—22no—
95C29×C22⋊Q8—21no—
96C29×C22⋊Q8—22no—
97C29×C22⋊Q8—21no—
98C29×C22⋊Q8D411yescharacteristic
99C29×C22⋊Q8D411yescharacteristic
100C29×C22⋊Q8D411yescharacteristic
101C29×#121—22no—
102C29×#121—22no—
103C29×#121—22no—
104C29×#121—21no—
105C29×#121—21no—
106C29×#121D411yescharacteristic
107C29×#121D412yes—
108C4×Q8×C29—21no—
109C4×Q8×C29—21no—
110C4×Q8×C29—21no—
111C4×Q8×C29C2311yescharacteristic
112C4×Q8×C29C2311yescharacteristic
113C4×Q8×C29C2311yescharacteristic
114C4×D4×C29—22no—
115C4×D4×C29—21no—
116C4×D4×C29—21no—
117C4×D4×C29—21no—
118C4×D4×C29—21no—
119C4×D4×C29—21no—
120C4×D4×C29—21no—
121C4×D4×C29D412yes—
122C4×D4×C29C2311yescharacteristic
123C29×#117—21no—
124C29×#117—21no—
125C2×C4⋊C4×C29—22no—
126C2×C4⋊C4×C29—21no—
127C2×C4⋊C4×C29—21no—
128C2×C42×C29C2311yescharacteristic
129C29×#106—22no—
130C29×#106—22no—
131C29×#106—24no—
132C29×C4⋊C8—21no—
133C29×C4⋊C8C2312yes—
134C29×C4⋊C8C2312yes—
135C29×#103—22no—
136C29×#103—22no—
137C29×#103—22no—
138C29×#103—22no—
139C29×#102—24no—
140C29×C22⋊C8—21no—
141C29×C22⋊C8—21no—
142C29×C22⋊C8—21no—
143C29×#97—21no—
144C4×C8×C29—21no—
145C4×C8×C29C2312yes—
146#41×C29—82no—
147#41×C29—82no—
148C2×Q8×C29—22no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×Q8×C29—22no—
152C2×Q8×C29—41no—
153C2×Q8×C29—82no—
154C2×Q8×C29—82no—
155C2×Q8×C29C2×D411yescharacteristic
156C2×Q8×C29C2×D411yescharacteristic
157C2×Q8×C29C2×D411yescharacteristic
158C2×D4×C29—22no—
159C2×D4×C29—22no—
160C2×D4×C29—21no—
161C2×D4×C29—22no—
162C2×D4×C29—21no—
163C2×D4×C29—21no—
164C2×D4×C29C2×D411yescharacteristic
165C2×D4×C29C2×D412yes—
166C22×C4×C29—22no—
167C22×C4×C29—22no—
168C22×C4×C29—22no—
169C22×C4×C29—21no—
170C22×C4×C29—22no—
171C22×C4×C29—41no—
172C22×C4×C29C2×D411yescharacteristic
173C22×C4×C29C2×D411yescharacteristic
174C22×C4×C29C2×D411yescharacteristic
175Q16×C29—82no—
176SD16×C29—82no—
177C2×C8×C29—22no—
178C2×C8×C29—22no—
179C2×C8×C29—22no—
180C4⋊C4×C29—22no—
181C4⋊C4×C29—22no—
182C4⋊C4×C29—22no—
183C4⋊C4×C29—22no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—21no—
194C4⋊C4×C29—21no—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—22no—
197C4⋊C4×C29—22no—
198C4⋊C4×C29—41no—
199C4⋊C4×C29—41no—
200C4⋊C4×C29C2×D411yescharacteristic
201C4⋊C4×C29C2×D411yescharacteristic
202C4⋊C4×C29C2×D411yescharacteristic
203C4⋊C4×C29C2×D412yes—
204C4⋊C4×C29C2×D411yescharacteristic
205C22⋊C4×C29—22no—
206C22⋊C4×C29—22no—
207C22⋊C4×C29—22no—
208C22⋊C4×C29—22no—
209C22⋊C4×C29—22no—
210C22⋊C4×C29—21no—
211C22⋊C4×C29—21no—
212C22⋊C4×C29—21no—
213C22⋊C4×C29—21no—
214C22⋊C4×C29—21no—
215C22⋊C4×C29—21no—
216C22⋊C4×C29—22no—
217C22⋊C4×C29—22no—
218C22⋊C4×C29—21no—
219C42×C29—22no—
220C42×C29—21no—
221C42×C29—21no—
222C42×C29—21no—
223C42×C29C2×D411yescharacteristic
224C42×C29C2×D411yescharacteristic
225C42×C29C2×D411yescharacteristic
226C42×C29C2411yescharacteristic
227#18971C2911yesmaximal, characteristic, direct product factor, Sylow
228C23×C29—21no—
229C23×C29—22no—
230C23×C29#12011yescharacteristic
231Q8×C29—22no—
232Q8×C29—22no—
233Q8×C29—22no—
234Q8×C29—42no—
235Q8×C29—42no—
236Q8×C29—42no—
237Q8×C29—81no—
238Q8×C29—82no—
239Q8×C29—82no—
240D4×C29—22no—
241D4×C29—42no—
242D4×C29—42no—
243D4×C29—42no—
244D4×C29—81no—
245D4×C29—82no—
246D4×C29—82no—
247D4×C29—82no—
248C2×C4×C29—22no—
249C2×C4×C29—22no—
250C2×C4×C29—21no—
251C2×C4×C29—21no—
252C2×C4×C29—21no—
253C2×C4×C29—21no—
254C2×C4×C29—21no—
255C2×C4×C29—22no—
256C2×C4×C29—21no—
257C2×C4×C29—21no—
258C2×C4×C29—41no—
259C2×C4×C29—42no—
260C2×C4×C29—42no—
261C2×C4×C29—82no—
262C2×C4×C29—82no—
263C2×C4×C29—82no—
264C2×C4×C29—82no—
265C2×C4×C29—82no—
266C2×C4×C29#12011yescharacteristic
267C2×C4×C29#12011yescharacteristic
268C2×C4×C29#12011yescharacteristic
269C2×C4×C29C22×D411yescharacteristic
270C2×C4×C29C22×D411yescharacteristic
271C2×C4×C29C22×D411yescharacteristic
272C8×C29—42no—
273C8×C29—42no—
274C8×C29—42no—
275#3554C2×C2911yescharacteristic
276#3229C2×C2911yescharacteristic, complemented
277#3227C2×C2911yescharacteristic, complemented
278#3218C2×C2911yescharacteristic, complemented
279#1653C2×C2912yescomplemented
280#1651C2×C2912yescomplemented
281#1642C2×C2912yescomplemented
282#1640C2×C2912yescomplemented
283#1553C2×C2911yescharacteristic, complemented
284#1497C2×C2911yescharacteristic, complemented
285#1482C2×C2911yescharacteristic, complemented
286C22×C29—21no—
287C22×C29—21no—
288C22×C29—21no—
289C22×C29—41no—
290C22×C29—42no—
291C22×C29—41no—
292C22×C29—42no—
293C22×C29—42no—
294C22×C29—41no—
295C22×C29C2×#12011yescharacteristic
296C4×C29—21no—
297C4×C29—21no—
298C4×C29—21no—
299C4×C29—21no—
300C4×C29—41no—
301C4×C29—41no—
302C4×C29—42no—
303C4×C29—41no—
304C4×C29—41no—
305C4×C29—41no—
306C4×C29—41no—
307C4×C29—41no—
308C4×C29—82no—
309C4×C29#57712yes—
310C4×C29#57712yes—
311#562—22no—
312#559—21no—
313#559C22×C2911yescharacteristic
314#557C22×C2911yescharacteristic
315#554—21no—
316#550C22×C2911yescharacteristic
317D4×Q8C22×C2911yescharacteristic
318#548—21no—
319#547—21no—
320#542—21no—
321#542—21no—
322#540—21no—
323#539—22no—
324#536—21no—
325#533C22×C2911yescharacteristic
326#532C22×C2911yescharacteristic
327C2×C4⋊Q8C22×C2911yescharacteristic
328#529C22×C2911yescharacteristic
329#498—21no—
330#498C22×C2912yes—
331#497—21no—
332#491—21no—
333#487—21no—
334#486C22×C2912yes—
335#483—21no—
336#483—21no—
337#481—22no—
338#476—22no—
339#475C22×C2912yes—
340#475C22×C2912yes—
341#462C22×C2912yes—
342#461C22×C2912yes—
343#451—21no—
344#448—21no—
345#432C22×C2911yescharacteristic
346#431C22×C2911yescharacteristic
347#431C22×C2911yescharacteristic
348#332C22×C2912yes—
349#331C22×C2912yes—
350Q8⋊C8C22×C2912yes—
351Q8⋊C8C22×C2912yes—
352Q8⋊C8C22×C2912yes—
353D4⋊C8C22×C2912yes—
354C2×C29—41no—
355C2×C29—81no—
356C2×C29—82no—
357C2×C29#300911yescharacteristic
358C2×C29#301011yescharacteristic
359C2×C29#302211yescharacteristic
360C2×#41—21no—
361C2×#41—21no—
362C22×Q8—21no—
363C22×Q8—21no—
364C2×Q16—22no—
365C2×SD16—22no—
366C4⋊Q8—21no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8D4×C2911yescharacteristic
372C4⋊Q8D4×C2911yescharacteristic
373C4⋊Q8C23×C2912yes—
374C4⋊Q8C23×C2911yescharacteristic
375#127—21no—
376#127C23×C2911yescharacteristic
377#126—22no—
378#126—21no—
379#125—22no—
380#125—21no—
381#125—21no—
382#125D4×C2911yescharacteristic
383#124—22no—
384#124—22no—
385#124—21no—
386#124—21no—
387#124—21no—
388#124D4×C2911yescharacteristic
389#123—22no—
390#123—22no—
391#123—22no—
392#123—22no—
393#123—22no—
394#123—22no—
395#123—21no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—21no—
401C22⋊Q8—22no—
402C22⋊Q8—21no—
403C22⋊Q8D4×C2911yescharacteristic
404C22⋊Q8D4×C2911yescharacteristic
405C22⋊Q8D4×C2911yescharacteristic
406#121—22no—
407#121—22no—
408#121—22no—
409#121—21no—
410#121—21no—
411#121D4×C2911yescharacteristic
412#121D4×C2912yes—
413C4×Q8—21no—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8C23×C2911yescharacteristic
417C4×Q8C23×C2911yescharacteristic
418C4×Q8C23×C2911yescharacteristic
419C4×D4—22no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4D4×C2912yes—
427C4×D4C23×C2911yescharacteristic
428#117—21no—
429#117—21no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C42C23×C2911yescharacteristic
434#106—22no—
435#106—22no—
436#106—24no—
437C4⋊C8—21no—
438C4⋊C8C23×C2912yes—
439C4⋊C8C23×C2912yes—
440#103—22no—
441#103—22no—
442#103—22no—
443#103—22no—
444#102—24no—
445C22⋊C8—21no—
446C22⋊C8—21no—
447C22⋊C8—21no—
448#97—21no—
449C4×C8—21no—
450C4×C8C23×C2912yes—
451C29#1897111yescharacteristic, direct product factor, Sylow
452#41—82no—
453#41—82no—
454C2×Q8—22no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—22no—
458C2×Q8—41no—
459C2×Q8—82no—
460C2×Q8—82no—
461C2×Q8C2×D4×C2911yescharacteristic
462C2×Q8C2×D4×C2911yescharacteristic
463C2×Q8C2×D4×C2911yescharacteristic
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—21no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4C2×D4×C2911yescharacteristic
471C2×D4C2×D4×C2912yes—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—41no—
478C22×C4C2×D4×C2911yescharacteristic
479C22×C4C2×D4×C2911yescharacteristic
480C22×C4C2×D4×C2911yescharacteristic
481Q16—82no—
482SD16—82no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4C2×D4×C2911yescharacteristic
507C4⋊C4C2×D4×C2911yescharacteristic
508C4⋊C4C2×D4×C2911yescharacteristic
509C4⋊C4C2×D4×C2912yes—
510C4⋊C4C2×D4×C2911yescharacteristic
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—21no—
525C42—22no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42C2×D4×C2911yescharacteristic
530C42C2×D4×C2911yescharacteristic
531C42C2×D4×C2911yescharacteristic
532C42C24×C2911yescharacteristic
533C23—21no—
534C23—22no—
535C23C29×#12011yescharacteristic
536Q8—22no—
537Q8—22no—
538Q8—22no—
539Q8—42no—
540Q8—42no—
541Q8—42no—
542Q8—81no—
543Q8—82no—
544Q8—82no—
545D4—22no—
546D4—42no—
547D4—42no—
548D4—42no—
549D4—82no—
550D4—81no—
551D4—82no—
552D4—82no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—82no—
567C2×C4—82no—
568C2×C4—82no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4C29×#12011yescharacteristic
572C2×C4C29×#12011yescharacteristic
573C2×C4C29×#12011yescharacteristic
574C2×C4C22×D4×C2911yescharacteristic
575C2×C4C22×D4×C2911yescharacteristic
576C2×C4C22×D4×C2911yescharacteristic
577C8—42no—
578C8—42no—
579C8—42no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—41no—
584C22—42no—
585C22—41no—
586C22—42no—
587C22—42no—
588C22—41no—
589C22C2×C29×#12011yescharacteristic
590C4—21no—
591C4—21no—
592C4—21no—
593C4—21no—
594C4—41no—
595C4—41no—
596C4—42no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—82no—
603C4C29×#57712yes—
604C4C29×#57712yes—
605C2—41no—
606C2—81no—
607C2—82no—
608C2C29×#300911yescharacteristic
609C2C29×#301011yescharacteristic
610C2C29×#302211yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3554C2
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×#3229C2semidirect
3. C29×#3227C2semidirect
4. C29×#3218C2semidirect
5. C29×#1653C2semidirect
6. C29×#1651C2semidirect
7. C29×#1642C2semidirect
8. C29×#1640C2semidirect
9. C29×#1553C2semidirect
10. C29×#1497C2semidirect
11. C29×#1482C2semidirect
227. #18971C29direct (N × H)
276. #3229C2×C29semidirect
277. #3227C2×C29semidirect
278. #3218C2×C29semidirect
279. #1653C2×C29semidirect
280. #1651C2×C29semidirect
281. #1642C2×C29semidirect
282. #1640C2×C29semidirect
283. #1553C2×C29semidirect
284. #1497C2×C29semidirect
285. #1482C2×C29semidirect
451. C29#18971direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35542
C29×#32292
C29×#32272
C29×#32182
C29×#16532
C29×#16512
C29×#16422
C29×#16402
C29×#15532
C29×#14972
C29×#14822
#1897129