Finite Group Databasebeta

← C29×#19180 #20314080

Subgroups — C29×#19180 #20314080

Order 7424.

670 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×#3184C211yesmaximal, characteristic, complemented
2C29×#3106C211yesmaximal, characteristic, complemented
3C29×#3035C211yesmaximal, characteristic, complemented
4C29×#2970C211yesmaximal, characteristic, complemented
5C29×#1702C211yesmaximal, characteristic, complemented
6C29×#1698C211yesmaximal, characteristic, complemented
7C29×#1692C211yesmaximal, characteristic, complemented
8C29×#1688C211yesmaximal, characteristic, complemented
9C29×#1681C211yesmaximal, characteristic, complemented
10C29×#1677C211yesmaximal, characteristic, complemented
11C29×#1671C211yesmaximal, characteristic, complemented
12C29×#1667C211yesmaximal, characteristic, complemented
13C29×#1565C211yesmaximal, characteristic, complemented
14C29×#1553C211yesmaximal, characteristic, complemented
15C29×#1551C211yesmaximal, characteristic, complemented
16C2×C29×#135—21no—
17C29×#532C2211yescharacteristic
18C29×#532C2211yescharacteristic
19C4×#41×C29C2211yescharacteristic
20C29×#498C2211yescharacteristic
21C29×#493C2211yescharacteristic
22C29×#486C2211yescharacteristic
23C29×#486C2211yescharacteristic
24C29×#482—21no—
25C29×#477C2211yescharacteristic
26C29×#476C2211yescharacteristic
27C29×#469—21no—
28C29×#469—21no—
29C29×#464—21no—
30C29×#463—21no—
31C29×#462C2211yescharacteristic
32C29×#461C2211yescharacteristic
33C29×#460C2211yescharacteristic
34C29×#460C2211yescharacteristic
35C29×#459C2211yescharacteristic
36C29×#459C2211yescharacteristic
37C29×#449—21no—
38C29×#446C2211yescharacteristic
39C29×#446C2211yescharacteristic
40C29×#442—21no—
41C29×#442—21no—
42C4×SD16×C29—21no—
43C4×D8×C29—21no—
44C29×#435—21no—
45C29×#435—21no—
46C8×D4×C29C2211yescharacteristic
47C8×D4×C29C2211yescharacteristic
48C29×#432—21no—
49C29×#432C2211yescharacteristic
50C29×#431C2211yescharacteristic
51C2×C29×C4⋊C8C2211yescharacteristic
52C29×#416—21no—
53C4×M16×C29C2211yescharacteristic
54C2×C29×#97—21no—
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×C29D411yescharacteristic
70C29×#135—44no—
71C2×Q16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×SD16×C29—21no—
75C2×D8×C29—21no—
76C2×D8×C29—21no—
77C2×D8×C29—21no—
78C2×D8×C29—21no—
79C2×M16×C29D411yescharacteristic
80C2×M16×C29D411yescharacteristic
81C22×C8×C29—21no—
82C22×C8×C29—21no—
83C22×C8×C29—21no—
84C29×C4⋊Q8C2311yescharacteristic
85C29×C4⋊Q8C2311yescharacteristic
86C29×#127C2311yescharacteristic
87C29×#127C2311yescharacteristic
88C29×#124—21no—
89C29×#124—21no—
90C29×#121—21no—
91C29×#121—21no—
92C29×#121—21no—
93C29×#121—21no—
94C4×Q8×C29D411yescharacteristic
95C4×Q8×C29C2311yescharacteristic
96C4×D4×C29—21no—
97C4×D4×C29—21no—
98C4×D4×C29—21no—
99C4×D4×C29—21no—
100C4×D4×C29—21no—
101C4×D4×C29—21no—
102C4×D4×C29D411yescharacteristic
103C4×D4×C29C2311yescharacteristic
104C29×#117—21no—
105C29×#117D411yescharacteristic
106C2×C42×C29—21no—
107C2×C42×C29C2311yescharacteristic
108C29×#107—21no—
109C29×#106—21no—
110C29×#106—21no—
111C29×#106—21no—
112C29×C4⋊C8—21no—
113C29×C4⋊C8—21no—
114C29×C4⋊C8—21no—
115C29×C4⋊C8C2311yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×#103—21no—
122C29×#103—21no—
123C29×#103—21no—
124C29×#102—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×C22⋊C8—21no—
134C29×C22⋊C8—21no—
135C29×C22⋊C8—21no—
136C29×C22⋊C8—21no—
137C29×#97—21no—
138C29×#97—21no—
139C29×#97—21no—
140C29×#97D411yescharacteristic
141C29×#97D411yescharacteristic
142C4×C8×C29—21no—
143C4×C8×C29C2311yescharacteristic
144C4×C8×C29C2311yescharacteristic
145#41×C29—22no—
146#41×C29—41no—
147#41×C29—42no—
148#41×C29—42no—
149#41×C29—82no—
150C2×Q8×C29—21no—
151C2×Q8×C29—21no—
152C2×Q8×C29C2×D411yescharacteristic
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—41no—
161C2×D4×C29—41no—
162C2×D4×C29C2×D411yescharacteristic
163C22×C4×C29—21no—
164C22×C4×C29—21no—
165C22×C4×C29—21no—
166C22×C4×C29—41no—
167C22×C4×C29—41no—
168C22×C4×C29C2×D411yescharacteristic
169C22×C4×C29C2×D411yescharacteristic
170C22×C4×C29#4111yescharacteristic
171Q16×C29—42no—
172SD16×C29—42no—
173SD16×C29—42no—
174SD16×C29—42no—
175D8×C29—42no—
176D8×C29—42no—
177D8×C29—42no—
178D8×C29—42no—
179M16×C29—22no—
180M16×C29—41no—
181C2×C8×C29—21no—
182C2×C8×C29—21no—
183C2×C8×C29—21no—
184C2×C8×C29—21no—
185C2×C8×C29—21no—
186C2×C8×C29—21no—
187C2×C8×C29—42no—
188C2×C8×C29—42no—
189C2×C8×C29—42no—
190C2×C8×C29C2×D411yescharacteristic
191C2×C8×C29C2×D411yescharacteristic
192C2×C8×C29C2×D411yescharacteristic
193C2×C8×C29C2×D411yescharacteristic
194C4⋊C4×C29—21no—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—21no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29—21no—
199C4⋊C4×C29—21no—
200C4⋊C4×C29C2×D411yescharacteristic
201C4⋊C4×C29C2×D411yescharacteristic
202C22⋊C4×C29—21no—
203C22⋊C4×C29—21no—
204C22⋊C4×C29—21no—
205C22⋊C4×C29—41no—
206C22⋊C4×C29—41no—
207C22⋊C4×C29—41no—
208C22⋊C4×C29—41no—
209C42×C29—21no—
210C42×C29—21no—
211C42×C29—21no—
212C42×C29C2×D411yescharacteristic
213C42×C29C2×D411yescharacteristic
214C42×C29#4111yescharacteristic
215C42×C29C2411yescharacteristic
216#19180C2911yesmaximal, characteristic, direct product factor, Sylow
217C23×C29—21no—
218C23×C29—41no—
219C23×C29—41no—
220C23×C29#12111yescharacteristic
221Q8×C29—21no—
222Q8×C29—21no—
223Q8×C29—41no—
224Q8×C29—41no—
225Q8×C29—81no—
226D4×C29—21no—
227D4×C29—42no—
228D4×C29—41no—
229D4×C29—41no—
230D4×C29—41no—
231D4×C29—41no—
232D4×C29—41no—
233D4×C29—41no—
234D4×C29—41no—
235D4×C29—41no—
236D4×C29—81no—
237D4×C29—81no—
238D4×C29—82no—
239D4×C29—82no—
240D4×C29AGL(1,ℤ/8)12yes—
241C2×C4×C29—21no—
242C2×C4×C29—21no—
243C2×C4×C29—21no—
244C2×C4×C29—21no—
245C2×C4×C29—21no—
246C2×C4×C29—21no—
247C2×C4×C29—21no—
248C2×C4×C29—41no—
249C2×C4×C29—42no—
250C2×C4×C29—41no—
251C2×C4×C29—41no—
252C2×C4×C29—41no—
253C2×C4×C29—41no—
254C2×C4×C29—81no—
255C2×C4×C29—82no—
256C2×C4×C29—82no—
257C2×C4×C29#12111yescharacteristic
258C2×C4×C29#12111yescharacteristic
259C2×C4×C29#12111yescharacteristic
260C2×C4×C29C22×D411yescharacteristic
261C2×C4×C29C22×D411yescharacteristic
262C2×C4×C29C2×#4111yescharacteristic
263C8×C29—21no—
264C8×C29—21no—
265C8×C29—21no—
266C8×C29—41no—
267C8×C29—41no—
268C8×C29—41no—
269C8×C29—41no—
270C8×C29—41no—
271C8×C29—41no—
272C8×C29#13512yescomplemented
273#3184C2×C2911yescharacteristic, complemented
274#3106C2×C2911yescharacteristic, complemented
275#3035C2×C2911yescharacteristic, complemented
276#2970C2×C2911yescharacteristic, complemented
277#1702C2×C2911yescharacteristic, complemented
278#1698C2×C2911yescharacteristic, complemented
279#1692C2×C2911yescharacteristic, complemented
280#1688C2×C2911yescharacteristic, complemented
281#1681C2×C2911yescharacteristic, complemented
282#1677C2×C2911yescharacteristic, complemented
283#1671C2×C2911yescharacteristic, complemented
284#1667C2×C2911yescharacteristic, complemented
285#1565C2×C2911yescharacteristic, complemented
286#1553C2×C2911yescharacteristic, complemented
287#1551C2×C2911yescharacteristic, complemented
288C22×C29—21no—
289C22×C29—21no—
290C22×C29—22no—
291C22×C29—21no—
292C22×C29—41no—
293C22×C29—41no—
294C22×C29—81no—
295C22×C29—81no—
296C22×C29—81no—
297C22×C29—81no—
298C22×C29—81no—
299C22×C29—81no—
300C22×C29C2×#12111yescharacteristic
301C4×C29—21no—
302C4×C29—21no—
303C4×C29—21no—
304C4×C29—21no—
305C4×C29—41no—
306C4×C29—41no—
307C4×C29—41no—
308C4×C29—81no—
309C4×C29—81no—
310C4×C29C2×#13511yescharacteristic
311C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
312C4×C29#57511yescharacteristic
313C4×C29#57511yescharacteristic
314C2×#135—21no—
315#532C22×C2911yescharacteristic
316#532C22×C2911yescharacteristic
317C4×#41C22×C2911yescharacteristic
318#498C22×C2911yescharacteristic
319#493C22×C2911yescharacteristic
320#486C22×C2911yescharacteristic
321#486C22×C2911yescharacteristic
322#482—21no—
323#477C22×C2911yescharacteristic
324#476C22×C2911yescharacteristic
325#469—21no—
326#469—21no—
327#464—21no—
328#463—21no—
329#462C22×C2911yescharacteristic
330#461C22×C2911yescharacteristic
331#460C22×C2911yescharacteristic
332#460C22×C2911yescharacteristic
333#459C22×C2911yescharacteristic
334#459C22×C2911yescharacteristic
335#449—21no—
336#446C22×C2911yescharacteristic
337#446C22×C2911yescharacteristic
338#442—21no—
339#442—21no—
340C4×SD16—21no—
341C4×D8—21no—
342#435—21no—
343#435—21no—
344C8×D4C22×C2911yescharacteristic
345C8×D4C22×C2911yescharacteristic
346#432—21no—
347#432C22×C2911yescharacteristic
348#431C22×C2911yescharacteristic
349C2×C4⋊C8C22×C2911yescharacteristic
350#416—21no—
351C4×M16C22×C2911yescharacteristic
352C2×#97—21no—
353#335C22×C2911yescharacteristic
354#335C22×C2911yescharacteristic
355#334C22×C2911yescharacteristic
356#334C22×C2911yescharacteristic
357#333C22×C2911yescharacteristic
358#333C22×C2911yescharacteristic
359#332C22×C2911yescharacteristic
360#332C22×C2911yescharacteristic
361#331C22×C2911yescharacteristic
362#331C22×C2911yescharacteristic
363#331C22×C2911yescharacteristic
364#331C22×C2911yescharacteristic
365C2×C29—41no—
366C2×C29—42no—
367C2×C29—161no—
368C2×C29—161no—
369C2×C29#303511yescharacteristic
370C2×C29#305511yescharacteristic
371C2×C29#306811yescharacteristic
372C2×#41—21no—
373C2×#41—21no—
374C2×#41D4×C2911yescharacteristic
375#135—44no—
376C2×Q16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×D8—21no—
381C2×D8—21no—
382C2×D8—21no—
383C2×D8—21no—
384C2×M16D4×C2911yescharacteristic
385C2×M16D4×C2911yescharacteristic
386C22×C8—21no—
387C22×C8—21no—
388C22×C8—21no—
389C4⋊Q8C23×C2911yescharacteristic
390C4⋊Q8C23×C2911yescharacteristic
391#127C23×C2911yescharacteristic
392#127C23×C2911yescharacteristic
393#124—21no—
394#124—21no—
395#121—21no—
396#121—21no—
397#121—21no—
398#121—21no—
399C4×Q8D4×C2911yescharacteristic
400C4×Q8C23×C2911yescharacteristic
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4D4×C2911yescharacteristic
408C4×D4C23×C2911yescharacteristic
409#117—21no—
410#117D4×C2911yescharacteristic
411C2×C42—21no—
412C2×C42C23×C2911yescharacteristic
413#107—21no—
414#106—21no—
415#106—21no—
416#106—21no—
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8—21no—
420C4⋊C8C23×C2911yescharacteristic
421C4⋊C8C23×C2911yescharacteristic
422C4⋊C8C23×C2911yescharacteristic
423C4⋊C8C23×C2911yescharacteristic
424C4⋊C8C23×C2911yescharacteristic
425C4⋊C8C23×C2911yescharacteristic
426#103—21no—
427#103—21no—
428#103—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438C22⋊C8—21no—
439C22⋊C8—21no—
440C22⋊C8—21no—
441C22⋊C8—21no—
442#97—21no—
443#97—21no—
444#97—21no—
445#97D4×C2911yescharacteristic
446#97D4×C2911yescharacteristic
447C4×C8—21no—
448C4×C8C23×C2911yescharacteristic
449C4×C8C23×C2911yescharacteristic
450C29#1918011yescharacteristic, direct product factor, Sylow
451#41—22no—
452#41—41no—
453#41—42no—
454#41—42no—
455#41—82no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8C2×D4×C2911yescharacteristic
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4C2×D4×C2911yescharacteristic
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4C2×D4×C2911yescharacteristic
475C22×C4C2×D4×C2911yescharacteristic
476C22×C4#41×C2911yescharacteristic
477Q16—42no—
478SD16—42no—
479SD16—42no—
480SD16—42no—
481D8—42no—
482D8—42no—
483D8—42no—
484D8—42no—
485M16—22no—
486M16—41no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—42no—
494C2×C8—42no—
495C2×C8—42no—
496C2×C8C2×D4×C2911yescharacteristic
497C2×C8C2×D4×C2911yescharacteristic
498C2×C8C2×D4×C2911yescharacteristic
499C2×C8C2×D4×C2911yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4C2×D4×C2911yescharacteristic
507C4⋊C4C2×D4×C2911yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42C2×D4×C2911yescharacteristic
519C42C2×D4×C2911yescharacteristic
520C42#41×C2911yescharacteristic
521C42C24×C2911yescharacteristic
522C23—21no—
523C23—41no—
524C23—41no—
525C23C29×#12111yescharacteristic
526Q8—21no—
527Q8—21no—
528Q8—41no—
529Q8—41no—
530Q8—81no—
531D4—21no—
532D4—42no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—81no—
542D4—81no—
543D4—82no—
544D4—82no—
545D4C29×AGL(1,ℤ/8)12yes—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—81no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4C29×#12111yescharacteristic
563C2×C4C29×#12111yescharacteristic
564C2×C4C29×#12111yescharacteristic
565C2×C4C22×D4×C2911yescharacteristic
566C2×C4C22×D4×C2911yescharacteristic
567C2×C4C2×#41×C2911yescharacteristic
568C8—21no—
569C8—21no—
570C8—21no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8C29×#13512yescomplemented
578C22—21no—
579C22—21no—
580C22—22no—
581C22—21no—
582C22—41no—
583C22—41no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22C2×C29×#12111yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4C2×C29×#13511yescharacteristic
601C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
602C4C29×#57511yescharacteristic
603C4C29×#57511yescharacteristic
604C2—41no—
605C2—42no—
606C2—161no—
607C2—161no—
608C2C29×#303511yescharacteristic
609C2C29×#305511yescharacteristic
610C2C29×#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×#3184C2semidirect
2. C29×#3106C2semidirect
3. C29×#3035C2semidirect
4. C29×#2970C2semidirect
5. C29×#1702C2semidirect
6. C29×#1698C2semidirect
7. C29×#1692C2semidirect
8. C29×#1688C2semidirect
9. C29×#1681C2semidirect
10. C29×#1677C2semidirect
11. C29×#1671C2semidirect
12. C29×#1667C2semidirect
13. C29×#1565C2semidirect
14. C29×#1553C2semidirect
15. C29×#1551C2semidirect
216. #19180C29direct (N × H)
272. C8×C29#135semidirect
273. #3184C2×C29semidirect
274. #3106C2×C29semidirect
275. #3035C2×C29semidirect
276. #2970C2×C29semidirect
277. #1702C2×C29semidirect
278. #1698C2×C29semidirect
279. #1692C2×C29semidirect
280. #1688C2×C29semidirect
281. #1681C2×C29semidirect
282. #1677C2×C29semidirect
283. #1671C2×C29semidirect
284. #1667C2×C29semidirect
285. #1565C2×C29semidirect
286. #1553C2×C29semidirect
287. #1551C2×C29semidirect
450. C29#19180direct (N × H)
577. C8C29×#135semidirect

Maximal subgroups

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

subgroupindex
C29×#31842
C29×#31062
C29×#30352
C29×#29702
C29×#17022
C29×#16982
C29×#16922
C29×#16882
C29×#16812
C29×#16772
C29×#16712
C29×#16672
C29×#15652
C29×#15532
C29×#15512
#1918029