Finite Group Databasebeta

← C29×#19380 #20314280

Subgroups — C29×#19380 #20314280

Order 7424.

636 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3252C211yesmaximal, characteristic, complemented
2C29×#3217C211yesmaximal, characteristic
3C29×#3138C211yesmaximal, characteristic, complemented
4C29×#2969C211yesmaximal, characteristic, complemented
5C29×#1702C211yesmaximal, characteristic, complemented
6C29×#1701C211yesmaximal, characteristic, complemented
7C29×#1698C211yesmaximal, characteristic, complemented
8C29×#1697C211yesmaximal, characteristic, complemented
9C29×#1682C211yesmaximal, characteristic, complemented
10C29×#1681C211yesmaximal, characteristic, complemented
11C29×#1678C211yesmaximal, characteristic, complemented
12C29×#1677C211yesmaximal, characteristic, complemented
13C29×#1569C211yesmaximal, characteristic, complemented
14C29×#1554C211yesmaximal, characteristic, complemented
15C29×#1545C211yesmaximal, characteristic, complemented
16C29×#533C2211yescharacteristic
17C2×C29×#127C2211yescharacteristic
18C29×#529C2211yescharacteristic
19C29×#496—21no—
20C29×#490—21no—
21C29×#490—21no—
22C29×#490—21no—
23C29×#486C2211yescharacteristic
24C29×#486C2211yescharacteristic
25C29×#486C2211yescharacteristic
26C29×#486C2211yescharacteristic
27C29×#479—21no—
28C29×#477C2211yescharacteristic, complemented
29C29×#476C2211yescharacteristic, complemented
30C29×#470—21no—
31C29×#468—21no—
32C29×#464—21no—
33C29×#462C2211yescharacteristic, complemented
34C29×#461C2211yescharacteristic, complemented
35C29×#460C2211yescharacteristic
36C29×#460C2211yescharacteristic
37C29×#459C2211yescharacteristic
38C29×#459C2211yescharacteristic
39C29×#450—21no—
40C29×#447—21no—
41C29×#446C2211yescharacteristic, complemented
42C8×Q8×C29C2211yescharacteristic, complemented
43C29×#436—21no—
44C29×#436C2211yescharacteristic, complemented
45C29×#435—21no—
46C8×D4×C29C2211yescharacteristic, complemented
47C29×#433—21no—
48C29×#432C2211yescharacteristic
49C29×#431C2211yescharacteristic
50C29×#423C2211yescharacteristic
51C29×#418—21no—
52C29×#418—21no—
53C29×#405—21no—
54C4×M16×C29C2211yescharacteristic
55C29×#335C2211yescharacteristic, complemented
56C29×#335C2211yescharacteristic, complemented
57C29×#334C2211yescharacteristic, complemented
58C29×#334C2211yescharacteristic, complemented
59C29×#333C2211yescharacteristic, complemented
60C29×#333C2211yescharacteristic, complemented
61C29×#332C2211yescharacteristic, complemented
62C29×#332C2211yescharacteristic, complemented
63C29×#331C2211yescharacteristic
64C29×#331C2211yescharacteristic
65C29×#331C2211yescharacteristic
66C29×#331C2211yescharacteristic
67C22×D4×C29—21no—
68C22×D4×C29—21no—
69C22×D4×C29—21no—
70C2×Q16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×D8×C29—21no—
75C2×D8×C29—21no—
76C2×M16×C29—21no—
77C2×M16×C29—21no—
78C2×M16×C29D411yescharacteristic
79C2×M16×C29D411yescharacteristic
80C22×C8×C29—21no—
81C29×C4⋊Q8C2311yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×#127—21no—
84C29×#127—21no—
85C29×#127—21no—
86C29×#127C2311yescharacteristic
87C29×#127C2311yescharacteristic
88C29×#126—21no—
89C29×#125—21no—
90C29×#125D411yescharacteristic
91C29×#124D411yescharacteristic
92C29×#123—21no—
93C29×C22⋊Q8—21no—
94C29×C22⋊Q8—21no—
95C29×C22⋊Q8D411yescharacteristic
96C29×#121D411yescharacteristic
97C4×Q8×C29—21no—
98C4×Q8×C29—21no—
99C4×Q8×C29C2311yescharacteristic
100C4×D4×C29—21no—
101C4×D4×C29C2311yescharacteristic
102C29×#117—21no—
103C29×#117—21no—
104C2×C42×C29C2311yescharacteristic
105C29×#107—21no—
106C29×#106—21no—
107C29×C4⋊C8—21no—
108C29×C4⋊C8—21no—
109C29×C4⋊C8—21no—
110C29×C4⋊C8C2311yescharacteristic
111C29×C4⋊C8C2311yescharacteristic
112C29×C4⋊C8C2311yescharacteristic
113C29×C4⋊C8C2311yescharacteristic
114C29×C4⋊C8C2311yescharacteristic
115C29×C4⋊C8C2311yescharacteristic
116C29×#103—21no—
117C29×#103—21no—
118C29×#103—21no—
119C29×#102—21no—
120C29×#102—21no—
121C29×#102—21no—
122C29×#102—21no—
123C29×#102—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×C22⋊C8—21no—
133C29×C22⋊C8—21no—
134C29×C22⋊C8—21no—
135C29×C22⋊C8—21no—
136C29×#97—21no—
137C29×#97—21no—
138C29×#97D411yescharacteristic
139C29×#97D411yescharacteristic
140C4×C8×C29—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C24×C29—41no—
145C2×Q8×C29—21no—
146C2×Q8×C29—21no—
147C2×Q8×C29C2×D411yescharacteristic
148C2×D4×C29—21no—
149C2×D4×C29—21no—
150C2×D4×C29—21no—
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—42no—
156C2×D4×C29—42no—
157C2×D4×C29—41no—
158C2×D4×C29—41no—
159C2×D4×C29—41no—
160C2×D4×C29—81no—
161C2×D4×C29—81no—
162C2×D4×C29—82no—
163C2×D4×C29C2×D411yescharacteristic
164C22×C4×C29—21no—
165C22×C4×C29C2×D411yescharacteristic
166C22×C4×C29C2×D411yescharacteristic
167C22×C4×C29#4111yescharacteristic
168Q16×C29—81no—
169SD16×C29—81no—
170SD16×C29—81no—
171SD16×C29—81no—
172D8×C29—81no—
173D8×C29—81no—
174M16×C29—41no—
175M16×C29—41no—
176M16×C29—42no—
177M16×C29—81no—
178C2×C8×C29—21no—
179C2×C8×C29—21no—
180C2×C8×C29—21no—
181C2×C8×C29—21no—
182C2×C8×C29—21no—
183C2×C8×C29—21no—
184C2×C8×C29—42no—
185C2×C8×C29C2×D411yescharacteristic
186C2×C8×C29C2×D411yescharacteristic
187C2×C8×C29C2×D411yescharacteristic
188C2×C8×C29C2×D411yescharacteristic
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—21no—
197C4⋊C4×C29—41no—
198C4⋊C4×C29—41no—
199C4⋊C4×C29C2×D411yescharacteristic
200C4⋊C4×C29C2×D411yescharacteristic
201C22⋊C4×C29—21no—
202C22⋊C4×C29—21no—
203C22⋊C4×C29—21no—
204C22⋊C4×C29—21no—
205C22⋊C4×C29—21no—
206C22⋊C4×C29—41no—
207C42×C29—21no—
208C42×C29—41no—
209C42×C29C2×D411yescharacteristic
210C42×C29C2×D411yescharacteristic
211C42×C29#4111yescharacteristic
212C42×C29C2411yescharacteristic
213#19380C2911yesmaximal, characteristic, direct product factor, Sylow
214C23×C29—21no—
215C23×C29—41no—
216C23×C29—41no—
217C23×C29—82no—
218C23×C29—82no—
219C23×C29—82no—
220C23×C29#12111yescharacteristic
221Q8×C29—21no—
222Q8×C29—21no—
223Q8×C29—41no—
224Q8×C29—41no—
225Q8×C29—81no—
226D4×C29—21no—
227D4×C29—21no—
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×C29—82no—
241D4×C29—81no—
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—21no—
249C2×C4×C29—41no—
250C2×C4×C29—41no—
251C2×C4×C29—41no—
252C2×C4×C29—41no—
253C2×C4×C29—41no—
254C2×C4×C29#12111yescharacteristic
255C2×C4×C29#12111yescharacteristic
256C2×C4×C29#12111yescharacteristic
257C2×C4×C29C22×D411yescharacteristic
258C2×C4×C29C22×D411yescharacteristic
259C2×C4×C29C2×#4111yescharacteristic
260C8×C29—21no—
261C8×C29—21no—
262C8×C29—21no—
263C8×C29—21no—
264C8×C29—41no—
265C8×C29—41no—
266C8×C29—41no—
267C8×C29—41no—
268C8×C29—41no—
269C8×C29—41no—
270#3252C2×C2911yescharacteristic, complemented
271#3217C2×C2911yescharacteristic
272#3138C2×C2911yescharacteristic, complemented
273#2969C2×C2911yescharacteristic, complemented
274#1702C2×C2911yescharacteristic, complemented
275#1701C2×C2911yescharacteristic, complemented
276#1698C2×C2911yescharacteristic, complemented
277#1697C2×C2911yescharacteristic, complemented
278#1682C2×C2911yescharacteristic, complemented
279#1681C2×C2911yescharacteristic, complemented
280#1678C2×C2911yescharacteristic, complemented
281#1677C2×C2911yescharacteristic, complemented
282#1569C2×C2911yescharacteristic, complemented
283#1554C2×C2911yescharacteristic, complemented
284#1545C2×C2911yescharacteristic, complemented
285C22×C29—21no—
286C22×C29—21no—
287C22×C29—21no—
288C22×C29—41no—
289C22×C29—41no—
290C22×C29—41no—
291C22×C29—81no—
292C22×C29—81no—
293C22×C29—81no—
294C22×C29—81no—
295C22×C29—81no—
296C22×C29—81no—
297C22×C29—164no—
298C22×C29C2×#12111yescharacteristic
299C4×C29—21no—
300C4×C29—21no—
301C4×C29—21no—
302C4×C29—21no—
303C4×C29—41no—
304C4×C29—41no—
305C4×C29—41no—
306C4×C29—81no—
307C4×C29—81no—
308C4×C29#57511yescharacteristic
309C4×C29#57511yescharacteristic
310C4×C29#57611yescharacteristic
311C4×C29#57711yescharacteristic
312#533C22×C2911yescharacteristic
313C2×#127C22×C2911yescharacteristic
314#529C22×C2911yescharacteristic
315#496—21no—
316#490—21no—
317#490—21no—
318#490—21no—
319#486C22×C2911yescharacteristic
320#486C22×C2911yescharacteristic
321#486C22×C2911yescharacteristic
322#486C22×C2911yescharacteristic
323#479—21no—
324#477C22×C2911yescharacteristic, complemented
325#476C22×C2911yescharacteristic, complemented
326#470—21no—
327#468—21no—
328#464—21no—
329#462C22×C2911yescharacteristic, complemented
330#461C22×C2911yescharacteristic, complemented
331#460C22×C2911yescharacteristic
332#460C22×C2911yescharacteristic
333#459C22×C2911yescharacteristic
334#459C22×C2911yescharacteristic
335#450—21no—
336#447—21no—
337#446C22×C2911yescharacteristic, complemented
338C8×Q8C22×C2911yescharacteristic, complemented
339#436—21no—
340#436C22×C2911yescharacteristic, complemented
341#435—21no—
342C8×D4C22×C2911yescharacteristic, complemented
343#433—21no—
344#432C22×C2911yescharacteristic
345#431C22×C2911yescharacteristic
346#423C22×C2911yescharacteristic
347#418—21no—
348#418—21no—
349#405—21no—
350C4×M16C22×C2911yescharacteristic
351#335C22×C2911yescharacteristic, complemented
352#335C22×C2911yescharacteristic, complemented
353#334C22×C2911yescharacteristic, complemented
354#334C22×C2911yescharacteristic, complemented
355#333C22×C2911yescharacteristic, complemented
356#333C22×C2911yescharacteristic, complemented
357#332C22×C2911yescharacteristic, complemented
358#332C22×C2911yescharacteristic, complemented
359#331C22×C2911yescharacteristic
360#331C22×C2911yescharacteristic
361#331C22×C2911yescharacteristic
362#331C22×C2911yescharacteristic
363C2×C29—41no—
364C2×C29—81no—
365C2×C29—161no—
366C2×C29—161no—
367C2×C29#304011yescharacteristic
368C2×C29#306211yescharacteristic
369C2×C29#306811yescharacteristic
370C22×D4—21no—
371C22×D4—21no—
372C22×D4—21no—
373C2×Q16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×D8—21no—
378C2×D8—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16D4×C2911yescharacteristic
382C2×M16D4×C2911yescharacteristic
383C22×C8—21no—
384C4⋊Q8C23×C2911yescharacteristic
385C4⋊Q8C23×C2911yescharacteristic
386#127—21no—
387#127—21no—
388#127—21no—
389#127C23×C2911yescharacteristic
390#127C23×C2911yescharacteristic
391#126—21no—
392#125—21no—
393#125D4×C2911yescharacteristic
394#124D4×C2911yescharacteristic
395#123—21no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8D4×C2911yescharacteristic
399#121D4×C2911yescharacteristic
400C4×Q8—21no—
401C4×Q8—21no—
402C4×Q8C23×C2911yescharacteristic
403C4×D4—21no—
404C4×D4C23×C2911yescharacteristic
405#117—21no—
406#117—21no—
407C2×C42C23×C2911yescharacteristic
408#107—21no—
409#106—21no—
410C4⋊C8—21no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8C23×C2911yescharacteristic
414C4⋊C8C23×C2911yescharacteristic
415C4⋊C8C23×C2911yescharacteristic
416C4⋊C8C23×C2911yescharacteristic
417C4⋊C8C23×C2911yescharacteristic
418C4⋊C8C23×C2911yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439#97—21no—
440#97—21no—
441#97D4×C2911yescharacteristic
442#97D4×C2911yescharacteristic
443C4×C8—21no—
444C4×C8—21no—
445C4×C8C23×C2911yescharacteristic
446C4×C8C23×C2911yescharacteristic
447C29#1938011yescharacteristic, direct product factor, Sylow
448C24—41no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8C2×D4×C2911yescharacteristic
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—42no—
460C2×D4—42no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4—82no—
467C2×D4C2×D4×C2911yescharacteristic
468C22×C4—21no—
469C22×C4C2×D4×C2911yescharacteristic
470C22×C4C2×D4×C2911yescharacteristic
471C22×C4#41×C2911yescharacteristic
472Q16—81no—
473SD16—81no—
474SD16—81no—
475SD16—81no—
476D8—81no—
477D8—81no—
478M16—41no—
479M16—41no—
480M16—42no—
481M16—81no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—42no—
489C2×C8C2×D4×C2911yescharacteristic
490C2×C8C2×D4×C2911yescharacteristic
491C2×C8C2×D4×C2911yescharacteristic
492C2×C8C2×D4×C2911yescharacteristic
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—41no—
502C4⋊C4—41no—
503C4⋊C4C2×D4×C2911yescharacteristic
504C4⋊C4C2×D4×C2911yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—41no—
511C42—21no—
512C42—41no—
513C42C2×D4×C2911yescharacteristic
514C42C2×D4×C2911yescharacteristic
515C42#41×C2911yescharacteristic
516C42C24×C2911yescharacteristic
517C23—21no—
518C23—41no—
519C23—41no—
520C23—82no—
521C23—82no—
522C23—82no—
523C23C29×#12111yescharacteristic
524Q8—21no—
525Q8—21no—
526Q8—41no—
527Q8—41no—
528Q8—81no—
529D4—21no—
530D4—21no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—81no—
540D4—81no—
541D4—82no—
542D4—82no—
543D4—82no—
544D4—81no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4C29×#12111yescharacteristic
558C2×C4C29×#12111yescharacteristic
559C2×C4C29×#12111yescharacteristic
560C2×C4C22×D4×C2911yescharacteristic
561C2×C4C22×D4×C2911yescharacteristic
562C2×C4C2×#41×C2911yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—164no—
586C22C2×C29×#12111yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—81no—
596C4C29×#57511yescharacteristic
597C4C29×#57511yescharacteristic
598C4C29×#57611yescharacteristic
599C4C29×#57711yescharacteristic
600C2—41no—
601C2—81no—
602C2—161no—
603C2—161no—
604C2C29×#304011yescharacteristic
605C2C29×#306211yescharacteristic
606C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3217C2
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×#3252C2semidirect
3. C29×#3138C2semidirect
4. C29×#2969C2semidirect
5. C29×#1702C2semidirect
6. C29×#1701C2semidirect
7. C29×#1698C2semidirect
8. C29×#1697C2semidirect
9. C29×#1682C2semidirect
10. C29×#1681C2semidirect
11. C29×#1678C2semidirect
12. C29×#1677C2semidirect
13. C29×#1569C2semidirect
14. C29×#1554C2semidirect
15. C29×#1545C2semidirect
28. C29×#477C22semidirect
29. C29×#476C22semidirect
33. C29×#462C22semidirect
34. C29×#461C22semidirect
41. C29×#446C22semidirect
42. C8×Q8×C29C22semidirect
44. C29×#436C22semidirect
46. C8×D4×C29C22semidirect
55. C29×#335C22semidirect
56. C29×#335C22semidirect
57. C29×#334C22semidirect
58. C29×#334C22semidirect
59. C29×#333C22semidirect
60. C29×#333C22semidirect
61. C29×#332C22semidirect
62. C29×#332C22semidirect
213. #19380C29direct (N × H)
270. #3252C2×C29semidirect
272. #3138C2×C29semidirect
273. #2969C2×C29semidirect
274. #1702C2×C29semidirect
275. #1701C2×C29semidirect
276. #1698C2×C29semidirect
277. #1697C2×C29semidirect
278. #1682C2×C29semidirect
279. #1681C2×C29semidirect
280. #1678C2×C29semidirect
281. #1677C2×C29semidirect
282. #1569C2×C29semidirect
283. #1554C2×C29semidirect
284. #1545C2×C29semidirect
324. #477C22×C29semidirect
325. #476C22×C29semidirect
329. #462C22×C29semidirect
330. #461C22×C29semidirect
337. #446C22×C29semidirect
338. C8×Q8C22×C29semidirect
340. #436C22×C29semidirect
342. C8×D4C22×C29semidirect
351. #335C22×C29semidirect
352. #335C22×C29semidirect
353. #334C22×C29semidirect
354. #334C22×C29semidirect
355. #333C22×C29semidirect
356. #333C22×C29semidirect
357. #332C22×C29semidirect
358. #332C22×C29semidirect
447. C29#19380direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32522
C29×#32172
C29×#31382
C29×#29692
C29×#17022
C29×#17012
C29×#16982
C29×#16972
C29×#16822
C29×#16812
C29×#16782
C29×#16772
C29×#15692
C29×#15542
C29×#15452
#1938029