Finite Group Databasebeta

← C29×#19370 #20314270

Subgroups — C29×#19370 #20314270

Order 7424.

678 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3253C211yesmaximal, characteristic, complemented
2C29×#3214C211yesmaximal, characteristic, complemented
3C29×#3184C211yesmaximal, characteristic, complemented
4C29×#2935C211yesmaximal, characteristic, complemented
5C29×#1701C211yesmaximal, characteristic, complemented
6C29×#1697C211yesmaximal, characteristic, complemented
7C29×#1691C211yesmaximal, characteristic, complemented
8C29×#1687C211yesmaximal, characteristic, complemented
9C29×#1681C211yesmaximal, characteristic, complemented
10C29×#1677C211yesmaximal, characteristic, complemented
11C29×#1671C211yesmaximal, characteristic, complemented
12C29×#1667C211yesmaximal, characteristic, complemented
13C29×#1569C211yesmaximal, characteristic, complemented
14C29×#1551C211yesmaximal, characteristic, complemented
15C29×#1547C211yesmaximal, characteristic, complemented
16C2×C29×#131—21no—
17C29×#532C2211yescharacteristic
18C29×#532C2211yescharacteristic
19C29×#532C2211yescharacteristic
20C29×#498C2211yescharacteristic
21C29×#496—21no—
22C29×#493C2211yescharacteristic
23C29×#489—21no—
24C29×#486C2211yescharacteristic
25C29×#486C2211yescharacteristic
26C29×#476—21no—
27C29×#476C2211yescharacteristic
28C29×#476C2211yescharacteristic
29C29×#469—21no—
30C29×#469—21no—
31C29×#469—21no—
32C29×#469—21no—
33C29×#461C2211yescharacteristic
34C29×#461C2211yescharacteristic
35C29×#459—21no—
36C29×#459C2211yescharacteristic
37C29×#459C2211yescharacteristic
38C29×#459C2211yescharacteristic
39C29×#459C2211yescharacteristic
40C29×#449—21no—
41C29×#449—21no—
42C29×#442—21no—
43C29×#442—21no—
44C29×#436C2211yescharacteristic
45C29×#436C2211yescharacteristic
46C29×#435—21no—
47C29×#435—21no—
48C8×D4×C29C2211yescharacteristic
49C8×D4×C29C2211yescharacteristic
50C29×#432C2211yescharacteristic
51C29×#423C2211yescharacteristic
52C2×C29×C4⋊C8C2211yescharacteristic
53C29×#408—21no—
54C4×M16×C29C2211yescharacteristic
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×#332C2211yescharacteristic
63C29×#331C2211yescharacteristic
64C29×#331C2211yescharacteristic
65C29×#331C2211yescharacteristic
66C29×#331C2211yescharacteristic
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C2×#41×C29—21no—
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C2×D8×C29—21no—
73C2×D8×C29—21no—
74C2×D8×C29—21no—
75C2×D8×C29—21no—
76C2×D8×C29—21no—
77C2×D8×C29—21no—
78C29×#131—44no—
79C2×M16×C29—21no—
80C2×M16×C29—21no—
81C2×M16×C29—21no—
82C2×M16×C29D411yescharacteristic
83C2×M16×C29D411yescharacteristic
84C22×C8×C29—21no—
85C22×C8×C29—21no—
86C22×C8×C29—21no—
87C29×C4⋊Q8D411yescharacteristic
88C29×C4⋊Q8C2311yescharacteristic
89C29×C4⋊Q8C2311yescharacteristic
90C29×#127D411yescharacteristic
91C29×#127C2311yescharacteristic
92C29×#127C2311yescharacteristic
93C29×#124—21no—
94C29×#124—21no—
95C29×#124—21no—
96C29×#121—21no—
97C29×#121—21no—
98C29×#121—21no—
99C29×#121—21no—
100C29×#121—21no—
101C29×#121D411yescharacteristic
102C29×#121D411yescharacteristic
103C4×D4×C29—21no—
104C4×D4×C29—21no—
105C4×D4×C29—21no—
106C4×D4×C29—21no—
107C4×D4×C29—21no—
108C4×D4×C29C2311yescharacteristic
109C4×D4×C29C2311yescharacteristic
110C2×C42×C29C2311yescharacteristic
111C29×#106—21no—
112C29×#106—21no—
113C29×#106—21no—
114C29×#106—21no—
115C29×C4⋊C8—21no—
116C29×C4⋊C8—21no—
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×C4⋊C8C2311yescharacteristic
122C29×C4⋊C8C2311yescharacteristic
123C29×#103—21no—
124C29×#103—21no—
125C29×#102—21no—
126C29×#102—21no—
127C29×#102—21no—
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×C22⋊C8—21no—
136C29×C22⋊C8—21no—
137C29×C22⋊C8—21no—
138C29×C22⋊C8—21no—
139C29×C22⋊C8—21no—
140C29×#97—21no—
141C29×#97D411yescharacteristic
142C29×#97D411yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C4×C8×C29C2311yescharacteristic
145#41×C29—42no—
146#41×C29—42no—
147#41×C29—81no—
148#41×C29—81no—
149#41×C29—82no—
150C2×Q8×C29—21no—
151C2×Q8×C29—21no—
152C2×Q8×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29—21no—
158C2×D4×C29—21no—
159C2×D4×C29—21no—
160C2×D4×C29—21no—
161C2×D4×C29—21no—
162C2×D4×C29—21no—
163C2×D4×C29—41no—
164C2×D4×C29—41no—
165C2×D4×C29C2×D411yescharacteristic
166C2×D4×C29C2×D411yescharacteristic
167C22×C4×C29—21no—
168C22×C4×C29—21no—
169C22×C4×C29—41no—
170C22×C4×C29—41no—
171C22×C4×C29C2×D411yescharacteristic
172C22×C4×C29C2×D411yescharacteristic
173C22×C4×C29#4111yescharacteristic
174SD16×C29—81no—
175SD16×C29—81no—
176D8×C29—42no—
177D8×C29—42no—
178D8×C29—81no—
179D8×C29—81no—
180D8×C29—81no—
181D8×C29—81no—
182M16×C29—22no—
183M16×C29—41no—
184M16×C29—42no—
185M16×C29—42no—
186M16×C29—81no—
187C2×C8×C29—21no—
188C2×C8×C29—21no—
189C2×C8×C29—21no—
190C2×C8×C29—21no—
191C2×C8×C29—21no—
192C2×C8×C29—21no—
193C2×C8×C29—42no—
194C2×C8×C29—42no—
195C2×C8×C29—42no—
196C2×C8×C29C2×D411yescharacteristic
197C2×C8×C29C2×D411yescharacteristic
198C2×C8×C29C2×D411yescharacteristic
199C2×C8×C29C2×D411yescharacteristic
200C4⋊C4×C29—21no—
201C4⋊C4×C29—21no—
202C4⋊C4×C29—21no—
203C4⋊C4×C29—21no—
204C4⋊C4×C29—21no—
205C4⋊C4×C29C2×D411yescharacteristic
206C4⋊C4×C29C2×D411yescharacteristic
207C22⋊C4×C29—21no—
208C22⋊C4×C29—21no—
209C22⋊C4×C29—21no—
210C22⋊C4×C29—21no—
211C22⋊C4×C29—41no—
212C22⋊C4×C29—41no—
213C22⋊C4×C29—41no—
214C22⋊C4×C29—41no—
215C42×C29C2×D411yescharacteristic
216C42×C29C2×D411yescharacteristic
217C42×C29#4111yescharacteristic
218C42×C29C2411yescharacteristic
219#19370C2911yesmaximal, characteristic, direct product factor, Sylow
220C23×C29—21no—
221C23×C29—21no—
222C23×C29—41no—
223C23×C29—41no—
224C23×C29#12111yescharacteristic
225Q8×C29—42no—
226Q8×C29—41no—
227Q8×C29—41no—
228Q8×C29—81no—
229D4×C29—21no—
230D4×C29—21no—
231D4×C29—21no—
232D4×C29—21no—
233D4×C29—42no—
234D4×C29—42no—
235D4×C29—42no—
236D4×C29—41no—
237D4×C29—41no—
238D4×C29—41no—
239D4×C29—41no—
240D4×C29—41no—
241D4×C29—41no—
242D4×C29—41no—
243D4×C29—41no—
244D4×C29—81no—
245D4×C29—81no—
246D4×C29—81no—
247D4×C29—82no—
248D4×C29—82no—
249C2×C4×C29—21no—
250C2×C4×C29—21no—
251C2×C4×C29—21no—
252C2×C4×C29—21no—
253C2×C4×C29—21no—
254C2×C4×C29—21no—
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—41no—
262C2×C4×C29—82no—
263C2×C4×C29—82no—
264C2×C4×C29#12111yescharacteristic
265C2×C4×C29#12111yescharacteristic
266C2×C4×C29#12111yescharacteristic
267C2×C4×C29C22×D411yescharacteristic
268C2×C4×C29C22×D411yescharacteristic
269C2×C4×C29C2×#4111yescharacteristic
270C8×C29—21no—
271C8×C29—21no—
272C8×C29—21no—
273C8×C29—41no—
274C8×C29—41no—
275C8×C29—41no—
276C8×C29—41no—
277C8×C29—41no—
278C8×C29—41no—
279C8×C29AGL(1,ℤ/8)12yes—
280#3253C2×C2911yescharacteristic, complemented
281#3214C2×C2911yescharacteristic, complemented
282#3184C2×C2911yescharacteristic, complemented
283#2935C2×C2911yescharacteristic, complemented
284#1701C2×C2911yescharacteristic, complemented
285#1697C2×C2911yescharacteristic, complemented
286#1691C2×C2911yescharacteristic, complemented
287#1687C2×C2911yescharacteristic, complemented
288#1681C2×C2911yescharacteristic, complemented
289#1677C2×C2911yescharacteristic, complemented
290#1671C2×C2911yescharacteristic, complemented
291#1667C2×C2911yescharacteristic, complemented
292#1569C2×C2911yescharacteristic, complemented
293#1551C2×C2911yescharacteristic, complemented
294#1547C2×C2911yescharacteristic, complemented
295C22×C29—21no—
296C22×C29—21no—
297C22×C29—21no—
298C22×C29—41no—
299C22×C29—41no—
300C22×C29—41no—
301C22×C29—41no—
302C22×C29—41no—
303C22×C29—41no—
304C22×C29—81no—
305C22×C29—81no—
306C22×C29—81no—
307C22×C29—81no—
308C22×C29—81no—
309C22×C29—81no—
310C22×C29C2×#12111yescharacteristic
311C4×C29—21no—
312C4×C29—21no—
313C4×C29—21no—
314C4×C29—21no—
315C4×C29—41no—
316C4×C29—41no—
317C4×C29—81no—
318C4×C29—81no—
319C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
320C4×C29#57511yescharacteristic
321C4×C29#57611yescharacteristic
322C4×C29#57711yescharacteristic
323C2×#131—21no—
324#532C22×C2911yescharacteristic
325#532C22×C2911yescharacteristic
326#532C22×C2911yescharacteristic
327#498C22×C2911yescharacteristic
328#496—21no—
329#493C22×C2911yescharacteristic
330#489—21no—
331#486C22×C2911yescharacteristic
332#486C22×C2911yescharacteristic
333#476—21no—
334#476C22×C2911yescharacteristic
335#476C22×C2911yescharacteristic
336#469—21no—
337#469—21no—
338#469—21no—
339#469—21no—
340#461C22×C2911yescharacteristic
341#461C22×C2911yescharacteristic
342#459—21no—
343#459C22×C2911yescharacteristic
344#459C22×C2911yescharacteristic
345#459C22×C2911yescharacteristic
346#459C22×C2911yescharacteristic
347#449—21no—
348#449—21no—
349#442—21no—
350#442—21no—
351#436C22×C2911yescharacteristic
352#436C22×C2911yescharacteristic
353#435—21no—
354#435—21no—
355C8×D4C22×C2911yescharacteristic
356C8×D4C22×C2911yescharacteristic
357#432C22×C2911yescharacteristic
358#423C22×C2911yescharacteristic
359C2×C4⋊C8C22×C2911yescharacteristic
360#408—21no—
361C4×M16C22×C2911yescharacteristic
362#335C22×C2911yescharacteristic
363#335C22×C2911yescharacteristic
364#334C22×C2911yescharacteristic
365#334C22×C2911yescharacteristic
366#333C22×C2911yescharacteristic
367#333C22×C2911yescharacteristic
368#332C22×C2911yescharacteristic
369#332C22×C2911yescharacteristic
370#331C22×C2911yescharacteristic
371#331C22×C2911yescharacteristic
372#331C22×C2911yescharacteristic
373#331C22×C2911yescharacteristic
374C2×C29—41no—
375C2×C29—81no—
376C2×C29—81no—
377C2×C29—161no—
378C2×C29—161no—
379C2×C29#303611yescharacteristic
380C2×C29#306211yescharacteristic
381C2×C29#306811yescharacteristic
382C2×#41—21no—
383C2×#41—21no—
384C2×#41—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—21no—
391C2×D8—21no—
392C2×D8—21no—
393#131—44no—
394C2×M16—21no—
395C2×M16—21no—
396C2×M16—21no—
397C2×M16D4×C2911yescharacteristic
398C2×M16D4×C2911yescharacteristic
399C22×C8—21no—
400C22×C8—21no—
401C22×C8—21no—
402C4⋊Q8D4×C2911yescharacteristic
403C4⋊Q8C23×C2911yescharacteristic
404C4⋊Q8C23×C2911yescharacteristic
405#127D4×C2911yescharacteristic
406#127C23×C2911yescharacteristic
407#127C23×C2911yescharacteristic
408#124—21no—
409#124—21no—
410#124—21no—
411#121—21no—
412#121—21no—
413#121—21no—
414#121—21no—
415#121—21no—
416#121D4×C2911yescharacteristic
417#121D4×C2911yescharacteristic
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4C23×C2911yescharacteristic
424C4×D4C23×C2911yescharacteristic
425C2×C42C23×C2911yescharacteristic
426#106—21no—
427#106—21no—
428#106—21no—
429#106—21no—
430C4⋊C8—21no—
431C4⋊C8—21no—
432C4⋊C8C23×C2911yescharacteristic
433C4⋊C8C23×C2911yescharacteristic
434C4⋊C8C23×C2911yescharacteristic
435C4⋊C8C23×C2911yescharacteristic
436C4⋊C8C23×C2911yescharacteristic
437C4⋊C8C23×C2911yescharacteristic
438#103—21no—
439#103—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#102—21no—
448#102—21no—
449#102—21no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455#97—21no—
456#97D4×C2911yescharacteristic
457#97D4×C2911yescharacteristic
458C4×C8C23×C2911yescharacteristic
459C4×C8C23×C2911yescharacteristic
460C29#1937011yescharacteristic, direct product factor, Sylow
461#41—42no—
462#41—42no—
463#41—81no—
464#41—81no—
465#41—82no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4C2×D4×C2911yescharacteristic
482C2×D4C2×D4×C2911yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4C2×D4×C2911yescharacteristic
488C22×C4C2×D4×C2911yescharacteristic
489C22×C4#41×C2911yescharacteristic
490SD16—81no—
491SD16—81no—
492D8—42no—
493D8—42no—
494D8—81no—
495D8—81no—
496D8—81no—
497D8—81no—
498M16—22no—
499M16—41no—
500M16—42no—
501M16—42no—
502M16—81no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—42no—
510C2×C8—42no—
511C2×C8—42no—
512C2×C8C2×D4×C2911yescharacteristic
513C2×C8C2×D4×C2911yescharacteristic
514C2×C8C2×D4×C2911yescharacteristic
515C2×C8C2×D4×C2911yescharacteristic
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4C2×D4×C2911yescharacteristic
522C4⋊C4C2×D4×C2911yescharacteristic
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C22⋊C4—41no—
530C22⋊C4—41no—
531C42C2×D4×C2911yescharacteristic
532C42C2×D4×C2911yescharacteristic
533C42#41×C2911yescharacteristic
534C42C24×C2911yescharacteristic
535C23—21no—
536C23—21no—
537C23—41no—
538C23—41no—
539C23C29×#12111yescharacteristic
540Q8—42no—
541Q8—41no—
542Q8—41no—
543Q8—81no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—42no—
549D4—42no—
550D4—42no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—41no—
559D4—81no—
560D4—81no—
561D4—81no—
562D4—82no—
563D4—82no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—82no—
578C2×C4—82no—
579C2×C4C29×#12111yescharacteristic
580C2×C4C29×#12111yescharacteristic
581C2×C4C29×#12111yescharacteristic
582C2×C4C22×D4×C2911yescharacteristic
583C2×C4C22×D4×C2911yescharacteristic
584C2×C4C2×#41×C2911yescharacteristic
585C8—21no—
586C8—21no—
587C8—21no—
588C8—41no—
589C8—41no—
590C8—41no—
591C8—41no—
592C8—41no—
593C8—41no—
594C8C29×AGL(1,ℤ/8)12yes—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22C2×C29×#12111yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—21no—
615C4—41no—
616C4—41no—
617C4—81no—
618C4—81no—
619C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
620C4C29×#57511yescharacteristic
621C4C29×#57611yescharacteristic
622C4C29×#57711yescharacteristic
623C2—41no—
624C2—81no—
625C2—81no—
626C2—161no—
627C2—161no—
628C2C29×#303611yescharacteristic
629C2C29×#306211yescharacteristic
630C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
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
1. C29×#3253C2semidirect
2. C29×#3214C2semidirect
3. C29×#3184C2semidirect
4. C29×#2935C2semidirect
5. C29×#1701C2semidirect
6. C29×#1697C2semidirect
7. C29×#1691C2semidirect
8. C29×#1687C2semidirect
9. C29×#1681C2semidirect
10. C29×#1677C2semidirect
11. C29×#1671C2semidirect
12. C29×#1667C2semidirect
13. C29×#1569C2semidirect
14. C29×#1551C2semidirect
15. C29×#1547C2semidirect
219. #19370C29direct (N × H)
280. #3253C2×C29semidirect
281. #3214C2×C29semidirect
282. #3184C2×C29semidirect
283. #2935C2×C29semidirect
284. #1701C2×C29semidirect
285. #1697C2×C29semidirect
286. #1691C2×C29semidirect
287. #1687C2×C29semidirect
288. #1681C2×C29semidirect
289. #1677C2×C29semidirect
290. #1671C2×C29semidirect
291. #1667C2×C29semidirect
292. #1569C2×C29semidirect
293. #1551C2×C29semidirect
294. #1547C2×C29semidirect
460. C29#19370direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32532
C29×#32142
C29×#31842
C29×#29352
C29×#17012
C29×#16972
C29×#16912
C29×#16872
C29×#16812
C29×#16772
C29×#16712
C29×#16672
C29×#15692
C29×#15512
C29×#15472
#1937029