Finite Group Databasebeta

← C29×#19025 #20313925

Subgroups — C29×#19025 #20313925

Order 7424.

872 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3561C211yesmaximal, characteristic
2C29×#3237C211yesmaximal, characteristic, complemented
3C29×#3172C211yesmaximal, characteristic, complemented
4C29×#3140C211yesmaximal, characteristic, complemented
5C29×#1664C212yesmaximal, complemented
6C29×#1664C212yesmaximal, complemented
7C29×#1662C212yesmaximal, complemented
8C29×#1661C212yesmaximal, complemented
9C29×#1529C211yesmaximal, characteristic, complemented
10C29×#1527C211yesmaximal, characteristic, complemented
11C29×#1526C211yesmaximal, characteristic, complemented
12C29×#563C2212yes—
13C29×#562C2212yes—
14C29×#556—21no—
15C29×#551—22no—
16D4×Q8×C29—21no—
17C29×#548—21no—
18C29×#546—21no—
19C29×#543—21no—
20C29×#542—21no—
21C29×#542—22no—
22C29×#538—21no—
23C29×#536—21no—
24C29×#533C2211yescharacteristic
25C29×#533C2211yescharacteristic
26C29×#529C2211yescharacteristic
27C2×C29×#124C2211yescharacteristic
28C29×#501C2212yescomplemented
29C29×#501C2211yescharacteristic, complemented
30C29×#497C2211yescharacteristic, complemented
31C29×#491C2212yescomplemented
32C29×#491C2211yescharacteristic, complemented
33C29×#489C2212yes—
34C29×#489C2212yes—
35C29×#489C2211yescharacteristic, complemented
36C29×#488—22no—
37C29×#485—22no—
38C29×#477—21no—
39C29×#475—21no—
40C29×#470—21no—
41C29×#468—21no—
42C4×Q16×C29—21no—
43C4×SD16×C29—21no—
44C29×#432C2211yescharacteristic
45C29×#419—21no—
46C29×#418—21no—
47C4×M16×C29C2211yescharacteristic
48C4×M16×C29C2211yescharacteristic
49C29×#330C2212yescomplemented
50C29×#330C2212yescomplemented
51C29×#330C2212yescomplemented
52C29×#329C2212yes—
53C29×#329C2212yes—
54C29×#329C2212yescomplemented
55C2×#41×C29—21no—
56C22×Q8×C29—21no—
57C22×Q8×C29D411yescharacteristic
58C22×D4×C29D411yescharacteristic
59C2×Q16×C29—21no—
60C2×SD16×C29—21no—
61C2×M16×C29—21no—
62C2×M16×C29—21no—
63C29×C4⋊Q8—21no—
64C29×C4⋊Q8—22no—
65C29×C4⋊Q8D411yescharacteristic
66C29×C4⋊Q8D411yescharacteristic
67C29×C4⋊Q8C2311yescharacteristic
68C29×C4⋊Q8C2311yescharacteristic
69C29×#126—22no—
70C29×#126—22no—
71C29×#126—22no—
72C29×#126—21no—
73C29×#125—21no—
74C29×#125C2311yescharacteristic
75C29×#125C2312yes—
76C29×#124—21no—
77C29×#124—22no—
78C29×#124—22no—
79C29×#124—21no—
80C29×#124—21no—
81C29×#124D412yes—
82C29×#124C2312yes—
83C29×#124C2311yescharacteristic
84C29×#123—22no—
85C29×#123—22no—
86C29×#123—21no—
87C29×#123—22no—
88C29×#123—22no—
89C29×C22⋊Q8—22no—
90C29×C22⋊Q8—22no—
91C29×C22⋊Q8—21no—
92C29×C22⋊Q8—22no—
93C29×C22⋊Q8—22no—
94C29×C22⋊Q8—22no—
95C29×C22⋊Q8—21no—
96C29×C22⋊Q8—21no—
97C29×C22⋊Q8—22no—
98C29×C22⋊Q8—22no—
99C29×C22⋊Q8—21no—
100C29×C22⋊Q8—21no—
101C29×C22⋊Q8D411yescharacteristic
102C29×#121—21no—
103C29×#121—22no—
104C29×#121—22no—
105C29×#121D411yescharacteristic
106C29×#120—22no—
107C4×Q8×C29—21no—
108C4×Q8×C29—21no—
109C4×Q8×C29—21no—
110C4×Q8×C29—21no—
111C4×Q8×C29—21no—
112C4×Q8×C29D411yescharacteristic
113C4×D4×C29—22no—
114C4×D4×C29—21no—
115C4×D4×C29—22no—
116C4×D4×C29—21no—
117C4×D4×C29D411yescharacteristic
118C29×#117—22no—
119C29×#117—21no—
120C29×#117—21no—
121C29×#117D412yes—
122C2×C22⋊C4×C29—22no—
123C2×C22⋊C4×C29—21no—
124C2×C22⋊C4×C29—21no—
125C2×C42×C29C2311yescharacteristic
126C29×#107—21no—
127C29×#107—22no—
128C29×#106—21no—
129C29×#106—22no—
130C29×C4⋊C8—21no—
131C29×#103—21no—
132C29×#103—22no—
133C29×#103—22no—
134C29×#103—21no—
135C29×#103—21no—
136C29×#103—22no—
137C29×#103—22no—
138C29×#102—21no—
139C29×#102—22no—
140C29×#102—22no—
141C29×C22⋊C8—21no—
142C29×#97C2312yes—
143C29×#97C2312yes—
144C29×#97C2311yescharacteristic
145C29×#97C2311yescharacteristic
146C4×C8×C29—21no—
147C4×C8×C29—21no—
148C24×C29—21no—
149#41×C29—82no—
150C2×Q8×C29—22no—
151C2×Q8×C29—21no—
152C2×Q8×C29—21no—
153C2×Q8×C29—21no—
154C2×Q8×C29—21no—
155C2×Q8×C29—21no—
156C2×Q8×C29—42no—
157C2×Q8×C29—82no—
158C2×Q8×C29C2×D411yescharacteristic
159C2×Q8×C29C2×D412yes—
160C2×D4×C29—21no—
161C2×D4×C29—22no—
162C2×D4×C29—22no—
163C2×D4×C29—21no—
164C2×D4×C29—42no—
165C2×D4×C29C2×D411yescharacteristic
166C2×D4×C29C2×D412yes—
167C22×C4×C29—22no—
168C22×C4×C29—22no—
169C22×C4×C29—22no—
170C22×C4×C29—21no—
171C22×C4×C29—21no—
172C22×C4×C29C2×D411yescharacteristic
173C22×C4×C29C2×D411yescharacteristic
174C22×C4×C29C2×D411yescharacteristic
175Q16×C29—42no—
176SD16×C29—42no—
177M16×C29—42no—
178M16×C29—42no—
179C2×C8×C29—21no—
180C2×C8×C29—22no—
181C2×C8×C29—21no—
182C2×C8×C29—22no—
183C4⋊C4×C29—22no—
184C4⋊C4×C29—22no—
185C4⋊C4×C29—22no—
186C4⋊C4×C29—22no—
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—22no—
194C4⋊C4×C29—22no—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—21no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29—21no—
199C4⋊C4×C29—41no—
200C4⋊C4×C29—41no—
201C4⋊C4×C29C2×D412yes—
202C4⋊C4×C29C2×D412yes—
203C4⋊C4×C29C2×D411yescharacteristic
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—22no—
212C22⋊C4×C29—22no—
213C22⋊C4×C29—22no—
214C22⋊C4×C29—21no—
215C22⋊C4×C29—21no—
216C22⋊C4×C29—22no—
217C22⋊C4×C29—22no—
218C22⋊C4×C29—21no—
219C22⋊C4×C29—21no—
220C22⋊C4×C29—41no—
221C42×C29—22no—
222C42×C29—22no—
223C42×C29—21no—
224C42×C29—41no—
225C42×C29C2×D411yescharacteristic
226C42×C29C2×D411yescharacteristic
227C42×C29C2×D411yescharacteristic
228C42×C29C2411yescharacteristic
229#19025C2911yesmaximal, characteristic, direct product factor, Sylow
230C23×C29—22no—
231C23×C29—21no—
232C23×C29—42no—
233C23×C29—81no—
234C23×C29—81no—
235C23×C29#12011yescharacteristic
236Q8×C29—41no—
237Q8×C29—42no—
238Q8×C29—41no—
239Q8×C29—41no—
240Q8×C29—42no—
241Q8×C29—42no—
242Q8×C29—42no—
243Q8×C29—81no—
244Q8×C29—82no—
245D4×C29—41no—
246D4×C29—42no—
247D4×C29—42no—
248D4×C29—42no—
249D4×C29—82no—
250D4×C29—82no—
251C2×C4×C29—22no—
252C2×C4×C29—21no—
253C2×C4×C29—22no—
254C2×C4×C29—21no—
255C2×C4×C29—22no—
256C2×C4×C29—22no—
257C2×C4×C29—21no—
258C2×C4×C29—41no—
259C2×C4×C29—41no—
260C2×C4×C29—42no—
261C2×C4×C29—41no—
262C2×C4×C29—41no—
263C2×C4×C29—81no—
264C2×C4×C29—82no—
265C2×C4×C29—82no—
266C2×C4×C29—82no—
267C2×C4×C29#12011yescharacteristic
268C2×C4×C29#12011yescharacteristic
269C2×C4×C29#12011yescharacteristic
270C2×C4×C29C22×D411yescharacteristic
271C2×C4×C29C22×D411yescharacteristic
272C2×C4×C29C22×D411yescharacteristic
273C8×C29—22no—
274C8×C29—42no—
275C8×C29—42no—
276C8×C29—41no—
277#3561C2×C2911yescharacteristic
278#3237C2×C2911yescharacteristic, complemented
279#3172C2×C2911yescharacteristic, complemented
280#3140C2×C2911yescharacteristic, complemented
281#1664C2×C2912yescomplemented
282#1664C2×C2912yescomplemented
283#1662C2×C2912yescomplemented
284#1661C2×C2912yescomplemented
285#1529C2×C2911yescharacteristic, complemented
286#1527C2×C2911yescharacteristic, complemented
287#1526C2×C2911yescharacteristic, complemented
288C22×C29—21no—
289C22×C29—21no—
290C22×C29—21no—
291C22×C29—41no—
292C22×C29—42no—
293C22×C29—42no—
294C22×C29—41no—
295C22×C29—41no—
296C22×C29—42no—
297C22×C29—162no—
298C22×C29C2×#12011yescharacteristic
299C4×C29—21no—
300C4×C29—21no—
301C4×C29—21no—
302C4×C29—21no—
303C4×C29—21no—
304C4×C29—41no—
305C4×C29—42no—
306C4×C29—42no—
307C4×C29—41no—
308C4×C29—42no—
309C4×C29—41no—
310C4×C29—81no—
311C4×C29—81no—
312C4×C29#45512yes—
313#563C22×C2912yes—
314#562C22×C2912yes—
315#556—21no—
316#551—22no—
317D4×Q8—21no—
318#548—21no—
319#546—21no—
320#543—21no—
321#542—21no—
322#542—22no—
323#538—21no—
324#536—21no—
325#533C22×C2911yescharacteristic
326#533C22×C2911yescharacteristic
327#529C22×C2911yescharacteristic
328C2×#124C22×C2911yescharacteristic
329#501C22×C2911yescharacteristic, complemented
330#501C22×C2912yescomplemented
331#497C22×C2911yescharacteristic, complemented
332#491C22×C2911yescharacteristic, complemented
333#491C22×C2912yescomplemented
334#489C22×C2912yes—
335#489C22×C2912yes—
336#489C22×C2911yescharacteristic, complemented
337#488—22no—
338#485—22no—
339#477—21no—
340#475—21no—
341#470—21no—
342#468—21no—
343C4×Q16—21no—
344C4×SD16—21no—
345#432C22×C2911yescharacteristic
346#419—21no—
347#418—21no—
348C4×M16C22×C2911yescharacteristic
349C4×M16C22×C2911yescharacteristic
350#330C22×C2912yescomplemented
351#330C22×C2912yescomplemented
352#330C22×C2912yescomplemented
353#329C22×C2912yes—
354#329C22×C2912yes—
355#329C22×C2912yescomplemented
356C2×C29—41no—
357C2×C29—81no—
358C2×C29—82no—
359C2×C29C2×#45511yescharacteristic
360C2×C29#301811yescharacteristic
361C2×C29#302011yescharacteristic
362C2×#41—21no—
363C22×Q8—21no—
364C22×Q8D4×C2911yescharacteristic
365C22×D4D4×C2911yescharacteristic
366C2×Q16—21no—
367C2×SD16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C4⋊Q8—21no—
371C4⋊Q8—22no—
372C4⋊Q8D4×C2911yescharacteristic
373C4⋊Q8D4×C2911yescharacteristic
374C4⋊Q8C23×C2911yescharacteristic
375C4⋊Q8C23×C2911yescharacteristic
376#126—22no—
377#126—22no—
378#126—22no—
379#126—21no—
380#125—21no—
381#125C23×C2911yescharacteristic
382#125C23×C2912yes—
383#124—21no—
384#124—22no—
385#124—22no—
386#124—21no—
387#124—21no—
388#124D4×C2912yes—
389#124C23×C2912yes—
390#124C23×C2911yescharacteristic
391#123—22no—
392#123—22no—
393#123—21no—
394#123—22no—
395#123—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—21no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C22⋊Q8D4×C2911yescharacteristic
409#121—21no—
410#121—22no—
411#121—22no—
412#121D4×C2911yescharacteristic
413#120—22no—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8—21no—
419C4×Q8D4×C2911yescharacteristic
420C4×D4—22no—
421C4×D4—21no—
422C4×D4—22no—
423C4×D4—21no—
424C4×D4D4×C2911yescharacteristic
425#117—22no—
426#117—21no—
427#117—21no—
428#117D4×C2912yes—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C42C23×C2911yescharacteristic
433#107—21no—
434#107—22no—
435#106—21no—
436#106—22no—
437C4⋊C8—21no—
438#103—22no—
439#103—22no—
440#103—21no—
441#103—21no—
442#103—21no—
443#103—22no—
444#103—22no—
445#102—22no—
446#102—22no—
447#102—21no—
448C22⋊C8—21no—
449#97C23×C2912yes—
450#97C23×C2911yescharacteristic
451#97C23×C2911yescharacteristic
452#97C23×C2912yes—
453C4×C8—21no—
454C4×C8—21no—
455C29#1902511yescharacteristic, direct product factor, Sylow
456C24—21no—
457#41—82no—
458C2×Q8—22no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—42no—
465C2×Q8—82no—
466C2×Q8C2×D4×C2912yes—
467C2×Q8C2×D4×C2911yescharacteristic
468C2×D4—21no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—42no—
473C2×D4C2×D4×C2912yes—
474C2×D4C2×D4×C2911yescharacteristic
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4C2×D4×C2911yescharacteristic
481C22×C4C2×D4×C2911yescharacteristic
482C22×C4C2×D4×C2911yescharacteristic
483Q16—42no—
484SD16—42no—
485M16—42no—
486M16—42no—
487C2×C8—21no—
488C2×C8—22no—
489C2×C8—21no—
490C2×C8—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4C2×D4×C2912yes—
510C4⋊C4C2×D4×C2911yescharacteristic
511C4⋊C4C2×D4×C2912yes—
512C4⋊C4C2×D4×C2911yescharacteristic
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—21no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—41no—
529C42—22no—
530C42—22no—
531C42—21no—
532C42—41no—
533C42C2×D4×C2911yescharacteristic
534C42C2×D4×C2911yescharacteristic
535C42C2×D4×C2911yescharacteristic
536C42C24×C2911yescharacteristic
537C23—22no—
538C23—21no—
539C23—42no—
540C23—81no—
541C23—81no—
542C23C29×#12011yescharacteristic
543Q8—41no—
544Q8—42no—
545Q8—41no—
546Q8—41no—
547Q8—42no—
548Q8—42no—
549Q8—42no—
550Q8—81no—
551Q8—82no—
552D4—41no—
553D4—42no—
554D4—42no—
555D4—42no—
556D4—82no—
557D4—82no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—81no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4C29×#12011yescharacteristic
575C2×C4C29×#12011yescharacteristic
576C2×C4C29×#12011yescharacteristic
577C2×C4C22×D4×C2911yescharacteristic
578C2×C4C22×D4×C2911yescharacteristic
579C2×C4C22×D4×C2911yescharacteristic
580C8—22no—
581C8—42no—
582C8—41no—
583C8—42no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—41no—
588C22—42no—
589C22—42no—
590C22—41no—
591C22—41no—
592C22—42no—
593C22—162no—
594C22C2×C29×#12011yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—41no—
601C4—42no—
602C4—42no—
603C4—41no—
604C4—42no—
605C4—41no—
606C4—81no—
607C4—81no—
608C4C29×#45512yes—
609C2—41no—
610C2—82no—
611C2—81no—
612C2C2×C29×#45511yescharacteristic
613C2C29×#301811yescharacteristic
614C2C29×#302011yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3561C2
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×#3237C2semidirect
3. C29×#3172C2semidirect
4. C29×#3140C2semidirect
5. C29×#1664C2semidirect
6. C29×#1664C2semidirect
7. C29×#1662C2semidirect
8. C29×#1661C2semidirect
9. C29×#1529C2semidirect
10. C29×#1527C2semidirect
11. C29×#1526C2semidirect
28. C29×#501C22semidirect
29. C29×#501C22semidirect
30. C29×#497C22semidirect
31. C29×#491C22semidirect
32. C29×#491C22semidirect
35. C29×#489C22semidirect
49. C29×#330C22semidirect
50. C29×#330C22semidirect
51. C29×#330C22semidirect
54. C29×#329C22semidirect
229. #19025C29direct (N × H)
278. #3237C2×C29semidirect
279. #3172C2×C29semidirect
280. #3140C2×C29semidirect
281. #1664C2×C29semidirect
282. #1664C2×C29semidirect
283. #1662C2×C29semidirect
284. #1661C2×C29semidirect
285. #1529C2×C29semidirect
286. #1527C2×C29semidirect
287. #1526C2×C29semidirect
329. #501C22×C29semidirect
330. #501C22×C29semidirect
331. #497C22×C29semidirect
332. #491C22×C29semidirect
333. #491C22×C29semidirect
336. #489C22×C29semidirect
350. #330C22×C29semidirect
351. #330C22×C29semidirect
352. #330C22×C29semidirect
355. #329C22×C29semidirect
455. C29#19025direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35612
C29×#32372
C29×#31722
C29×#31402
C29×#16642
C29×#16622
C29×#16612
C29×#15292
C29×#15272
C29×#15262
#1902529