Finite Group Databasebeta

← C29×#19030 #20313930

Subgroups — C29×#19030 #20313930

Order 7424.

902 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3559C211yesmaximal, characteristic, complemented
2C29×#3214C211yesmaximal, characteristic, complemented
3C29×#3171C211yesmaximal, characteristic, complemented
4C29×#3142C211yesmaximal, characteristic, complemented
5C29×#1664C212yesmaximal, complemented
6C29×#1662C212yesmaximal, complemented
7C29×#1657C212yesmaximal, complemented
8C29×#1656C212yesmaximal, complemented
9C29×#1529C211yesmaximal, characteristic, complemented
10C29×#1528C211yesmaximal, characteristic, complemented
11C29×#1525C211yesmaximal, characteristic, complemented
12C29×#563C2212yes—
13C29×#562C2212yes—
14C29×#554—21no—
15C29×#553—21no—
16C29×#553—21no—
17C29×#547—22no—
18C29×#547—21no—
19C29×#544—21no—
20C29×#540—21no—
21C29×#539—22no—
22C29×#539—21no—
23C29×#537—21no—
24C29×#532C2211yescharacteristic
25C29×#532C2211yescharacteristic
26C29×#529C2211yescharacteristic
27C2×C29×#125C2211yescharacteristic
28C29×#501C2211yescharacteristic
29C29×#496C2211yescharacteristic
30C29×#496C2212yes—
31C29×#491C2212yes—
32C29×#490C2212yes—
33C29×#490C2211yescharacteristic
34C29×#489C2211yescharacteristic
35C29×#489C2212yes—
36C29×#488—22no—
37C29×#469—21no—
38C29×#468—21no—
39C29×#461—21no—
40C29×#459—21no—
41C29×#449—22no—
42C4×SD16×C29—21no—
43C4×D8×C29—21no—
44C29×#432C2211yescharacteristic
45C29×#417—21no—
46C29×#417—21no—
47C4×M16×C29C2211yescharacteristic
48C4×M16×C29C2211yescharacteristic
49C29×#330C2212yes—
50C29×#330C2212yes—
51C29×#330C2212yes—
52C29×#329C2212yes—
53C29×#329C2212yes—
54C29×#329C2212yes—
55C2×#41×C29—22no—
56C2×#41×C29—21no—
57C2×#41×C29D412yes—
58C2×SD16×C29—21no—
59C2×SD16×C29—22no—
60C2×D8×C29—21no—
61C2×D8×C29—22no—
62C2×M16×C29—21no—
63C2×M16×C29—21no—
64C29×C4⋊Q8—21no—
65C29×C4⋊Q8—22no—
66C29×C4⋊Q8D411yescharacteristic
67C29×C4⋊Q8C2311yescharacteristic
68C29×#127D411yescharacteristic
69C29×#127C2311yescharacteristic
70C29×#126—22no—
71C29×#126—22no—
72C29×#126—21no—
73C29×#125—22no—
74C29×#125—21no—
75C29×#125—21no—
76C29×#125—21no—
77C29×#125D412yes—
78C29×#125C2312yes—
79C29×#125C2311yescharacteristic
80C29×#124—21no—
81C29×#124C2311yescharacteristic
82C29×#124C2312yes—
83C29×#123—22no—
84C29×#123—22no—
85C29×#123—22no—
86C29×#123—22no—
87C29×#123—21no—
88C29×#123—22no—
89C29×#123—22no—
90C29×C22⋊Q8—22no—
91C29×C22⋊Q8—22no—
92C29×C22⋊Q8—22no—
93C29×C22⋊Q8—22no—
94C29×C22⋊Q8—22no—
95C29×C22⋊Q8—22no—
96C29×C22⋊Q8D411yescharacteristic
97C29×#121—22no—
98C29×#121—22no—
99C29×#121—21no—
100C29×#121—21no—
101C29×#121—22no—
102C29×#121—22no—
103C29×#121—21no—
104C29×#121—21no—
105C29×#121—21no—
106C29×#121—21no—
107C29×#121D411yescharacteristic
108C4×Q8×C29D411yescharacteristic
109C4×D4×C29—22no—
110C4×D4×C29—22no—
111C4×D4×C29—21no—
112C4×D4×C29—21no—
113C4×D4×C29—21no—
114C4×D4×C29—21no—
115C4×D4×C29—21no—
116C4×D4×C29—21no—
117C4×D4×C29—21no—
118C4×D4×C29D411yescharacteristic
119C29×#117—21no—
120C29×#117—21no—
121C2×C4⋊C4×C29—22no—
122C2×C4⋊C4×C29—21no—
123C2×C4⋊C4×C29—21no—
124C2×C4⋊C4×C29—21no—
125C2×C4⋊C4×C29D411yescharacteristic
126C2×C4⋊C4×C29D411yescharacteristic
127C2×C42×C29C2311yescharacteristic
128C29×#107—21no—
129C29×#106—21no—
130C29×C4⋊C8—21no—
131C29×#103—21no—
132C29×#103—22no—
133C29×#103—22no—
134C29×#103—22no—
135C29×#102—21no—
136C29×#102—22no—
137C29×#102—21no—
138C29×#102—21no—
139C29×#102—22no—
140C29×#102—22no—
141C29×C22⋊C8—21no—
142C29×#97C2312yes—
143C29×#97C2311yescharacteristic
144C29×#97C2312yes—
145C29×#97C2311yescharacteristic
146C4×C8×C29—21no—
147C4×C8×C29—21no—
148#41×C29—44no—
149#41×C29—84no—
150#41×C29—82no—
151C2×Q8×C29—22no—
152C2×Q8×C29—21no—
153C2×Q8×C29C2×D411yescharacteristic
154C2×Q8×C29C2×D412yes—
155C2×D4×C29—22no—
156C2×D4×C29—21no—
157C2×D4×C29—22no—
158C2×D4×C29—22no—
159C2×D4×C29—21no—
160C2×D4×C29—21no—
161C2×D4×C29—21no—
162C2×D4×C29—21no—
163C2×D4×C29—21no—
164C2×D4×C29—41no—
165C2×D4×C29C2×D411yescharacteristic
166C2×D4×C29C2×D412yes—
167C22×C4×C29—21no—
168C22×C4×C29—22no—
169C22×C4×C29—22no—
170C22×C4×C29—22no—
171C22×C4×C29—21no—
172C22×C4×C29—21no—
173C22×C4×C29—22no—
174C22×C4×C29—41no—
175C22×C4×C29C2×D411yescharacteristic
176C22×C4×C29C2×D411yescharacteristic
177C22×C4×C29C2×D411yescharacteristic
178SD16×C29—42no—
179SD16×C29—82no—
180D8×C29—42no—
181D8×C29—82no—
182M16×C29—42no—
183M16×C29—42no—
184C2×C8×C29—21no—
185C2×C8×C29—21no—
186C2×C8×C29—22no—
187C2×C8×C29—22no—
188C4⋊C4×C29—22no—
189C4⋊C4×C29—22no—
190C4⋊C4×C29—22no—
191C4⋊C4×C29—22no—
192C4⋊C4×C29—22no—
193C4⋊C4×C29—21no—
194C4⋊C4×C29—21no—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—22no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29—21no—
199C4⋊C4×C29—21no—
200C4⋊C4×C29—22no—
201C4⋊C4×C29—22no—
202C4⋊C4×C29—21no—
203C4⋊C4×C29—21no—
204C4⋊C4×C29—21no—
205C4⋊C4×C29—21no—
206C4⋊C4×C29C2×D412yes—
207C4⋊C4×C29C2×D412yes—
208C4⋊C4×C29C2×D411yescharacteristic
209C4⋊C4×C29C2×D411yescharacteristic
210C22⋊C4×C29—22no—
211C22⋊C4×C29—22no—
212C22⋊C4×C29—22no—
213C22⋊C4×C29—22no—
214C22⋊C4×C29—22no—
215C22⋊C4×C29—21no—
216C22⋊C4×C29—21no—
217C22⋊C4×C29—21no—
218C22⋊C4×C29—21no—
219C22⋊C4×C29—22no—
220C22⋊C4×C29—22no—
221C22⋊C4×C29—21no—
222C22⋊C4×C29—41no—
223C22⋊C4×C29—41no—
224C42×C29—22no—
225C42×C29—21no—
226C42×C29C2×D411yescharacteristic
227C42×C29C2×D411yescharacteristic
228C42×C29C2×D411yescharacteristic
229C42×C29C2411yescharacteristic
230#19030C2911yesmaximal, characteristic, direct product factor, Sylow
231C23×C29—21no—
232C23×C29—22no—
233C23×C29—41no—
234C23×C29#12011yescharacteristic
235Q8×C29—41no—
236Q8×C29—42no—
237Q8×C29—42no—
238Q8×C29—82no—
239D4×C29—41no—
240D4×C29—42no—
241D4×C29—41no—
242D4×C29—41no—
243D4×C29—41no—
244D4×C29—41no—
245D4×C29—42no—
246D4×C29—44no—
247D4×C29—42no—
248D4×C29—42no—
249D4×C29—81no—
250D4×C29—82no—
251D4×C29—82no—
252D4×C29—82no—
253C2×C4×C29—22no—
254C2×C4×C29—21no—
255C2×C4×C29—21no—
256C2×C4×C29—22no—
257C2×C4×C29—22no—
258C2×C4×C29—21no—
259C2×C4×C29—22no—
260C2×C4×C29—41no—
261C2×C4×C29—41no—
262C2×C4×C29—42no—
263C2×C4×C29—42no—
264C2×C4×C29—41no—
265C2×C4×C29—82no—
266C2×C4×C29—81no—
267C2×C4×C29—82no—
268C2×C4×C29—82no—
269C2×C4×C29—82no—
270C2×C4×C29—82no—
271C2×C4×C29#12011yescharacteristic
272C2×C4×C29#12011yescharacteristic
273C2×C4×C29#12011yescharacteristic
274C2×C4×C29C22×D411yescharacteristic
275C2×C4×C29C22×D411yescharacteristic
276C2×C4×C29C22×D411yescharacteristic
277C8×C29—22no—
278C8×C29—42no—
279C8×C29—41no—
280C8×C29—42no—
281#3559C2×C2911yescharacteristic, complemented
282#3214C2×C2911yescharacteristic, complemented
283#3171C2×C2911yescharacteristic, complemented
284#3142C2×C2911yescharacteristic, complemented
285#1664C2×C2912yescomplemented
286#1662C2×C2912yescomplemented
287#1657C2×C2912yescomplemented
288#1656C2×C2912yescomplemented
289#1529C2×C2911yescharacteristic, complemented
290#1528C2×C2911yescharacteristic, complemented
291#1525C2×C2911yescharacteristic, complemented
292C22×C29—21no—
293C22×C29—21no—
294C22×C29—21no—
295C22×C29—41no—
296C22×C29—42no—
297C22×C29—42no—
298C22×C29—41no—
299C22×C29—42no—
300C22×C29—41no—
301C22×C29—81no—
302C22×C29—81no—
303C22×C29—81no—
304C22×C29C2×#12011yescharacteristic
305C4×C29—21no—
306C4×C29—21no—
307C4×C29—21no—
308C4×C29—21no—
309C4×C29—21no—
310C4×C29—41no—
311C4×C29—42no—
312C4×C29—41no—
313C4×C29—42no—
314C4×C29—42no—
315C4×C29—41no—
316C4×C29—81no—
317C4×C29#45412yes—
318#563C22×C2912yes—
319#562C22×C2912yes—
320#554—21no—
321#553—21no—
322#553—21no—
323#547—22no—
324#547—21no—
325#544—21no—
326#540—21no—
327#539—22no—
328#539—21no—
329#537—21no—
330#532C22×C2911yescharacteristic
331#532C22×C2911yescharacteristic
332#529C22×C2911yescharacteristic
333C2×#125C22×C2911yescharacteristic
334#501C22×C2911yescharacteristic
335#496C22×C2911yescharacteristic
336#496C22×C2912yes—
337#491C22×C2912yes—
338#490C22×C2912yes—
339#490C22×C2911yescharacteristic
340#489C22×C2911yescharacteristic
341#489C22×C2912yes—
342#488—22no—
343#469—21no—
344#468—21no—
345#461—21no—
346#459—21no—
347#449—22no—
348C4×SD16—21no—
349C4×D8—21no—
350#432C22×C2911yescharacteristic
351#417—21no—
352#417—21no—
353C4×M16C22×C2911yescharacteristic
354C4×M16C22×C2911yescharacteristic
355#330C22×C2912yes—
356#330C22×C2912yes—
357#330C22×C2912yes—
358#329C22×C2912yes—
359#329C22×C2912yes—
360#329C22×C2912yes—
361C2×C29—41no—
362C2×C29—81no—
363C2×C29—82no—
364C2×C29—161no—
365C2×C29C2×#45411yescharacteristic
366C2×C29#301811yescharacteristic
367C2×C29#301911yescharacteristic
368C2×#41—22no—
369C2×#41—21no—
370C2×#41D4×C2912yes—
371C2×SD16—21no—
372C2×SD16—22no—
373C2×D8—21no—
374C2×D8—22no—
375C2×M16—21no—
376C2×M16—21no—
377C4⋊Q8—21no—
378C4⋊Q8—22no—
379C4⋊Q8D4×C2911yescharacteristic
380C4⋊Q8C23×C2911yescharacteristic
381#127D4×C2911yescharacteristic
382#127C23×C2911yescharacteristic
383#126—22no—
384#126—22no—
385#126—21no—
386#125—22no—
387#125—21no—
388#125—21no—
389#125—21no—
390#125D4×C2912yes—
391#125C23×C2912yes—
392#125C23×C2911yescharacteristic
393#124—21no—
394#124C23×C2911yescharacteristic
395#124C23×C2912yes—
396#123—22no—
397#123—22no—
398#123—22no—
399#123—22no—
400#123—21no—
401#123—22no—
402#123—22no—
403C22⋊Q8—22no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8D4×C2911yescharacteristic
410#121—22no—
411#121—22no—
412#121—21no—
413#121—21no—
414#121—22no—
415#121—22no—
416#121—21no—
417#121—21no—
418#121—21no—
419#121—21no—
420#121D4×C2911yescharacteristic
421C4×Q8D4×C2911yescharacteristic
422C4×D4—22no—
423C4×D4—22no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4—21no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4D4×C2911yescharacteristic
432#117—21no—
433#117—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4D4×C2911yescharacteristic
439C2×C4⋊C4D4×C2911yescharacteristic
440C2×C42C23×C2911yescharacteristic
441#107—21no—
442#106—21no—
443C4⋊C8—21no—
444#103—21no—
445#103—22no—
446#103—22no—
447#103—22no—
448#102—21no—
449#102—22no—
450#102—22no—
451#102—22no—
452#102—21no—
453#102—21no—
454C22⋊C8—21no—
455#97C23×C2912yes—
456#97C23×C2911yescharacteristic
457#97C23×C2911yescharacteristic
458#97C23×C2912yes—
459C4×C8—21no—
460C4×C8—21no—
461C29#1903011yescharacteristic, direct product factor, Sylow
462#41—44no—
463#41—84no—
464#41—82no—
465C2×Q8—22no—
466C2×Q8—21no—
467C2×Q8C2×D4×C2911yescharacteristic
468C2×Q8C2×D4×C2912yes—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—41no—
479C2×D4C2×D4×C2911yescharacteristic
480C2×D4C2×D4×C2912yes—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—41no—
489C22×C4C2×D4×C2911yescharacteristic
490C22×C4C2×D4×C2911yescharacteristic
491C22×C4C2×D4×C2911yescharacteristic
492SD16—42no—
493SD16—82no—
494D8—42no—
495D8—82no—
496M16—42no—
497M16—42no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—22no—
501C2×C8—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4C2×D4×C2912yes—
521C4⋊C4C2×D4×C2912yes—
522C4⋊C4C2×D4×C2911yescharacteristic
523C4⋊C4C2×D4×C2911yescharacteristic
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—21no—
536C22⋊C4—41no—
537C22⋊C4—41no—
538C42—22no—
539C42—21no—
540C42C2×D4×C2911yescharacteristic
541C42C2×D4×C2911yescharacteristic
542C42C2×D4×C2911yescharacteristic
543C42C24×C2911yescharacteristic
544C23—21no—
545C23—22no—
546C23—41no—
547C23C29×#12011yescharacteristic
548Q8—41no—
549Q8—42no—
550Q8—42no—
551Q8—82no—
552D4—41no—
553D4—42no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—42no—
559D4—44no—
560D4—42no—
561D4—42no—
562D4—81no—
563D4—82no—
564D4—82no—
565D4—82no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—82no—
579C2×C4—81no—
580C2×C4—82no—
581C2×C4—82no—
582C2×C4—82no—
583C2×C4—82no—
584C2×C4C29×#12011yescharacteristic
585C2×C4C29×#12011yescharacteristic
586C2×C4C29×#12011yescharacteristic
587C2×C4C22×D4×C2911yescharacteristic
588C2×C4C22×D4×C2911yescharacteristic
589C2×C4C22×D4×C2911yescharacteristic
590C8—22no—
591C8—42no—
592C8—41no—
593C8—42no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—41no—
598C22—42no—
599C22—42no—
600C22—41no—
601C22—42no—
602C22—41no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22C2×C29×#12011yescharacteristic
607C4—21no—
608C4—21no—
609C4—21no—
610C4—21no—
611C4—21no—
612C4—41no—
613C4—42no—
614C4—41no—
615C4—42no—
616C4—42no—
617C4—41no—
618C4—81no—
619C4C29×#45412yes—
620C2—41no—
621C2—81no—
622C2—82no—
623C2—161no—
624C2C2×C29×#45411yescharacteristic
625C2C29×#301811yescharacteristic
626C2C29×#301911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
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×#3559C2semidirect
2. C29×#3214C2semidirect
3. C29×#3171C2semidirect
4. C29×#3142C2semidirect
5. C29×#1664C2semidirect
6. C29×#1662C2semidirect
7. C29×#1657C2semidirect
8. C29×#1656C2semidirect
9. C29×#1529C2semidirect
10. C29×#1528C2semidirect
11. C29×#1525C2semidirect
230. #19030C29direct (N × H)
281. #3559C2×C29semidirect
282. #3214C2×C29semidirect
283. #3171C2×C29semidirect
284. #3142C2×C29semidirect
285. #1664C2×C29semidirect
286. #1662C2×C29semidirect
287. #1657C2×C29semidirect
288. #1656C2×C29semidirect
289. #1529C2×C29semidirect
290. #1528C2×C29semidirect
291. #1525C2×C29semidirect
461. C29#19030direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35592
C29×#32142
C29×#31712
C29×#31422
C29×#16642
C29×#16622
C29×#16572
C29×#16562
C29×#15292
C29×#15282
C29×#15252
#1903029