Finite Group Databasebeta

← C29×#19864 #20314764

Subgroups — C29×#19864 #20314764

Order 7424.

578 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3360C211yesmaximal, characteristic, complemented
2C29×#3357C211yesmaximal, characteristic, complemented
3C29×#3341C211yesmaximal, characteristic
4C29×#3340C211yesmaximal, characteristic, complemented
5C29×#1723C211yesmaximal, characteristic, complemented
6C29×#1691C211yesmaximal, characteristic, complemented
7C29×#1683C211yesmaximal, characteristic, complemented
8C29×#1676C211yesmaximal, characteristic, complemented
9C29×#1675C211yesmaximal, characteristic, complemented
10C29×#1646C211yesmaximal, characteristic, complemented
11C29×#1638C211yesmaximal, characteristic, complemented
12C29×#1634C211yesmaximal, characteristic, complemented
13C29×#1632C211yesmaximal, characteristic, complemented
14C29×#1581C211yesmaximal, characteristic, complemented
15C29×SD16⋊C8C211yesmaximal, characteristic, complemented
16C29×#556C2211yescharacteristic
17C29×#555C2211yescharacteristic
18C29×#555C2211yescharacteristic
19C29×#554C2211yescharacteristic
20C29×#500C2211yescharacteristic
21C29×#500C2211yescharacteristic
22C29×#498C2211yescharacteristic
23C29×#494C2211yescharacteristic
24C29×#488—21no—
25C29×#487C2211yescharacteristic
26C29×#487C2211yescharacteristic
27C29×#485—21no—
28C29×#485—21no—
29C29×#482—21no—
30C29×#482—21no—
31C29×#482—21no—
32C29×#480—21no—
33C29×#479—21no—
34C29×#477C2211yescharacteristic
35C29×#477C2211yescharacteristic
36C29×#476C2211yescharacteristic
37C29×#476C2211yescharacteristic
38C29×#476C2211yescharacteristic
39C29×#476C2211yescharacteristic
40C29×#474C2211yescharacteristic
41C29×#468—21no—
42C29×#466—21no—
43C29×#465—21no—
44C29×#463—21no—
45C29×#461C2211yescharacteristic
46C8×Q8×C29C2211yescharacteristic
47C4×SD16×C29—21no—
48C4×SD16×C29C2211yescharacteristic
49C4×D8×C29C2211yescharacteristic
50C29×#436C2211yescharacteristic
51C8×D4×C29C2211yescharacteristic
52C8×D4×C29C2211yescharacteristic
53C29×#428—21no—
54C29×#427—21no—
55C29×#427—21no—
56C29×#335C2211yescharacteristic
57C29×#335C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×D4⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C29×#322C2211yescharacteristic
67C2×Q16×C29—41no—
68C2×SD16×C29—21no—
69C2×SD16×C29D411yescharacteristic
70C2×D8×C29D411yescharacteristic
71C2×M16×C29—21no—
72C22×C8×C29—21no—
73C22×C8×C29—21no—
74C29×C4⋊Q8C2311yescharacteristic
75C29×C4⋊Q8C2311yescharacteristic
76C29×C4⋊Q8C2311yescharacteristic
77C29×C4⋊Q8C2311yescharacteristic
78C29×#126—41no—
79C29×#125—21no—
80C29×#124—21no—
81C29×#124—41no—
82C29×#124—41no—
83C29×C22⋊Q8—21no—
84C29×C22⋊Q8—21no—
85C29×C22⋊Q8—41no—
86C29×#121—21no—
87C29×#121—21no—
88C29×#121—21no—
89C29×#121—21no—
90C4×Q8×C29—21no—
91C4×Q8×C29C2311yescharacteristic
92C4×D4×C29—21no—
93C4×D4×C29C2311yescharacteristic
94C4×D4×C29C2311yescharacteristic
95C4×D4×C29C2311yescharacteristic
96C29×#117—21no—
97C29×#117—21no—
98C29×#117—21no—
99C29×#117—21no—
100C29×#117—21no—
101C2×C4⋊C4×C29—21no—
102C29×#107—21no—
103C29×#107—21no—
104C29×#107—21no—
105C29×#107—21no—
106C29×#107—21no—
107C29×#107—21no—
108C29×#107—21no—
109C29×#107D411yescharacteristic
110C29×#106—21no—
111C29×#106—21no—
112C29×#106—21no—
113C29×#106—21no—
114C29×#106—21no—
115C29×#106—21no—
116C29×#106D411yescharacteristic
117C29×C4⋊C8—21no—
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×C4⋊C8C2311yescharacteristic
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—21no—
126C29×#103—21no—
127C29×#103—41no—
128C29×#103D411yescharacteristic
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102D411yescharacteristic
135C29×#102D411yescharacteristic
136C29×#102D411yescharacteristic
137C29×C22⋊C8—21no—
138C29×C22⋊C8—21no—
139C29×C22⋊C8—21no—
140C4×C8×C29—21no—
141C4×C8×C29C2311yescharacteristic
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C2×Q8×C29—21no—
145C2×Q8×C29—21no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29C2×D411yescharacteristic
149C2×D4×C29—41no—
150C2×D4×C29—41no—
151C2×D4×C29C2×D411yescharacteristic
152C2×D4×C29C2×D411yescharacteristic
153C2×D4×C29C2×D411yescharacteristic
154C22×C4×C29—21no—
155C22×C4×C29—21no—
156C22×C4×C29—21no—
157C22×C4×C29—41no—
158Q16×C29—82no—
159SD16×C29—22no—
160SD16×C29—42no—
161D8×C29—41no—
162M16×C29—42no—
163C2×C8×C29—21no—
164C2×C8×C29—21no—
165C2×C8×C29—21no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—42no—
169C2×C8×C29—42no—
170C2×C8×C29C2×D411yescharacteristic
171C2×C8×C29C2×D411yescharacteristic
172C2×C8×C29C2×D411yescharacteristic
173C2×C8×C29C2×D411yescharacteristic
174C4⋊C4×C29—21no—
175C4⋊C4×C29—21no—
176C4⋊C4×C29—21no—
177C4⋊C4×C29—21no—
178C4⋊C4×C29—21no—
179C4⋊C4×C29—21no—
180C4⋊C4×C29—21no—
181C4⋊C4×C29—21no—
182C4⋊C4×C29—21no—
183C4⋊C4×C29—41no—
184C4⋊C4×C29—41no—
185C4⋊C4×C29—41no—
186C4⋊C4×C29C2×D411yescharacteristic
187C4⋊C4×C29C2×D411yescharacteristic
188C4⋊C4×C29C2×D411yescharacteristic
189C4⋊C4×C29C2×D411yescharacteristic
190C22⋊C4×C29—21no—
191C22⋊C4×C29—21no—
192C22⋊C4×C29—21no—
193C22⋊C4×C29—41no—
194C22⋊C4×C29—41no—
195C22⋊C4×C29—41no—
196C22⋊C4×C29—41no—
197C22⋊C4×C29—41no—
198C22⋊C4×C29—41no—
199C22⋊C4×C29—41no—
200C42×C29—21no—
201C42×C29—41no—
202C42×C29—41no—
203C42×C29—41no—
204C42×C29C2411yescharacteristic
205#19864C2911yesmaximal, characteristic, direct product factor, Sylow
206C23×C29—21no—
207C23×C29—21no—
208C23×C29—21no—
209Q8×C29—21no—
210Q8×C29—21no—
211Q8×C29—41no—
212Q8×C29—41no—
213Q8×C29—81no—
214Q8×C29—81no—
215Q8×C29—81no—
216D4×C29—21no—
217D4×C29—21no—
218D4×C29—21no—
219D4×C29—21no—
220D4×C29—21no—
221D4×C29—21no—
222D4×C29—161no—
223D4×C29—161no—
224C2×C4×C29—21no—
225C2×C4×C29—21no—
226C2×C4×C29—21no—
227C2×C4×C29—21no—
228C2×C4×C29—21no—
229C2×C4×C29—41no—
230C2×C4×C29—41no—
231C2×C4×C29—41no—
232C2×C4×C29—41no—
233C2×C4×C29—41no—
234C2×C4×C29—41no—
235C2×C4×C29—41no—
236C2×C4×C29—41no—
237C2×C4×C29—41no—
238C2×C4×C29—41no—
239C2×C4×C29—161no—
240C2×C4×C29C22×D411yescharacteristic
241C2×C4×C29C22×D411yescharacteristic
242C2×C4×C29H(5,𝔽2)11yescharacteristic
243C8×C29—21no—
244C8×C29—21no—
245C8×C29—21no—
246C8×C29—41no—
247C8×C29—41no—
248C8×C29—41no—
249C8×C29—41no—
250C8×C29—41no—
251C8×C29#13512yes—
252#3360C2×C2911yescharacteristic, complemented
253#3357C2×C2911yescharacteristic, complemented
254#3341C2×C2911yescharacteristic
255#3340C2×C2911yescharacteristic, complemented
256#1723C2×C2911yescharacteristic, complemented
257#1691C2×C2911yescharacteristic, complemented
258#1683C2×C2911yescharacteristic, complemented
259#1676C2×C2911yescharacteristic, complemented
260#1675C2×C2911yescharacteristic, complemented
261#1646C2×C2911yescharacteristic, complemented
262#1638C2×C2911yescharacteristic, complemented
263#1634C2×C2911yescharacteristic, complemented
264#1632C2×C2911yescharacteristic, complemented
265#1581C2×C2911yescharacteristic, complemented
266SD16⋊C8C2×C2911yescharacteristic, complemented
267C22×C29—41no—
268C22×C29—41no—
269C22×C29—41no—
270C22×C29—41no—
271C22×C29—41no—
272C22×C29—41no—
273C22×C29—41no—
274C22×C29—41no—
275C22×C29—41no—
276C22×C29D4211yescharacteristic
277C4×C29—21no—
278C4×C29—41no—
279C4×C29—41no—
280C4×C29—41no—
281C4×C29—41no—
282C4×C29—41no—
283C4×C29—81no—
284C4×C29—81no—
285C4×C29—81no—
286C4×C29—81no—
287C4×C29C2×#13511yescharacteristic
288C4×C29#57511yescharacteristic
289C4×C29#57811yescharacteristic
290C4×C29#57811yescharacteristic
291#556C22×C2911yescharacteristic
292#555C22×C2911yescharacteristic
293#555C22×C2911yescharacteristic
294#554C22×C2911yescharacteristic
295#500C22×C2911yescharacteristic
296#500C22×C2911yescharacteristic
297#498C22×C2911yescharacteristic
298#494C22×C2911yescharacteristic
299#488—21no—
300#487C22×C2911yescharacteristic
301#487C22×C2911yescharacteristic
302#485—21no—
303#485—21no—
304#482—21no—
305#482—21no—
306#482—21no—
307#480—21no—
308#479—21no—
309#477C22×C2911yescharacteristic
310#477C22×C2911yescharacteristic
311#476C22×C2911yescharacteristic
312#476C22×C2911yescharacteristic
313#476C22×C2911yescharacteristic
314#476C22×C2911yescharacteristic
315#474C22×C2911yescharacteristic
316#468—21no—
317#466—21no—
318#465—21no—
319#463—21no—
320#461C22×C2911yescharacteristic
321C8×Q8C22×C2911yescharacteristic
322C4×SD16—21no—
323C4×SD16C22×C2911yescharacteristic
324C4×D8C22×C2911yescharacteristic
325#436C22×C2911yescharacteristic
326C8×D4C22×C2911yescharacteristic
327C8×D4C22×C2911yescharacteristic
328#428—21no—
329#427—21no—
330#427—21no—
331#335C22×C2911yescharacteristic
332#335C22×C2911yescharacteristic
333#333C22×C2911yescharacteristic
334#333C22×C2911yescharacteristic
335#333C22×C2911yescharacteristic
336#332C22×C2911yescharacteristic
337Q8⋊C8C22×C2911yescharacteristic
338D4⋊C8C22×C2911yescharacteristic
339D4⋊C8C22×C2911yescharacteristic
340D4⋊C8C22×C2911yescharacteristic
341#322C22×C2911yescharacteristic
342C2×C29—81no—
343C2×C29—81no—
344C2×C29—81no—
345C2×C29#326911yescharacteristic
346C2×C29#328311yescharacteristic
347C2×C29#328811yescharacteristic
348C2×Q16—41no—
349C2×SD16—21no—
350C2×SD16D4×C2911yescharacteristic
351C2×D8D4×C2911yescharacteristic
352C2×M16—21no—
353C22×C8—21no—
354C22×C8—21no—
355C4⋊Q8C23×C2911yescharacteristic
356C4⋊Q8C23×C2911yescharacteristic
357C4⋊Q8C23×C2911yescharacteristic
358C4⋊Q8C23×C2911yescharacteristic
359#126—41no—
360#125—21no—
361#124—21no—
362#124—41no—
363#124—41no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—41no—
367#121—21no—
368#121—21no—
369#121—21no—
370#121—21no—
371C4×Q8—21no—
372C4×Q8C23×C2911yescharacteristic
373C4×D4—21no—
374C4×D4C23×C2911yescharacteristic
375C4×D4C23×C2911yescharacteristic
376C4×D4C23×C2911yescharacteristic
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117—21no—
382C2×C4⋊C4—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#107—21no—
389#107—21no—
390#107D4×C2911yescharacteristic
391#106—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395#106—21no—
396#106—21no—
397#106D4×C2911yescharacteristic
398C4⋊C8—21no—
399C4⋊C8C23×C2911yescharacteristic
400C4⋊C8C23×C2911yescharacteristic
401C4⋊C8C23×C2911yescharacteristic
402C4⋊C8C23×C2911yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—41no—
409#103D4×C2911yescharacteristic
410#102—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102D4×C2911yescharacteristic
416#102D4×C2911yescharacteristic
417#102D4×C2911yescharacteristic
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C4×C8—21no—
422C4×C8C23×C2911yescharacteristic
423C4×C8C23×C2911yescharacteristic
424C4×C8C23×C2911yescharacteristic
425C29#1986411yescharacteristic, direct product factor, Sylow
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8C2×D4×C2911yescharacteristic
431C2×D4—41no—
432C2×D4—41no—
433C2×D4C2×D4×C2911yescharacteristic
434C2×D4C2×D4×C2911yescharacteristic
435C2×D4C2×D4×C2911yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—41no—
440Q16—82no—
441SD16—22no—
442SD16—42no—
443D8—41no—
444M16—42no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—42no—
451C2×C8—42no—
452C2×C8C2×D4×C2911yescharacteristic
453C2×C8C2×D4×C2911yescharacteristic
454C2×C8C2×D4×C2911yescharacteristic
455C2×C8C2×D4×C2911yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4C2×D4×C2911yescharacteristic
469C4⋊C4C2×D4×C2911yescharacteristic
470C4⋊C4C2×D4×C2911yescharacteristic
471C4⋊C4C2×D4×C2911yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C42—21no—
483C42—41no—
484C42—41no—
485C42—41no—
486C42C24×C2911yescharacteristic
487C23—21no—
488C23—21no—
489C23—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8—81no—
496Q8—81no—
497D4—21no—
498D4—21no—
499D4—21no—
500D4—21no—
501D4—21no—
502D4—21no—
503D4—161no—
504D4—161no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—161no—
521C2×C4C22×D4×C2911yescharacteristic
522C2×C4C22×D4×C2911yescharacteristic
523C2×C4C29×H(5,𝔽2)11yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8C29×#13512yes—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22D42×C2911yescharacteristic
543C4—21no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4—81no—
553C4C2×C29×#13511yescharacteristic
554C4C29×#57511yescharacteristic
555C4C29×#57811yescharacteristic
556C4C29×#57811yescharacteristic
557C2—81no—
558C2—81no—
559C2—81no—
560C2C29×#326911yescharacteristic
561C2C29×#328311yescharacteristic
562C2C29×#328811yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3341C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C42×C29 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C29×#3360C2semidirect
2. C29×#3357C2semidirect
4. C29×#3340C2semidirect
5. C29×#1723C2semidirect
6. C29×#1691C2semidirect
7. C29×#1683C2semidirect
8. C29×#1676C2semidirect
9. C29×#1675C2semidirect
10. C29×#1646C2semidirect
11. C29×#1638C2semidirect
12. C29×#1634C2semidirect
13. C29×#1632C2semidirect
14. C29×#1581C2semidirect
15. C29×SD16⋊C8C2semidirect
205. #19864C29direct (N × H)
252. #3360C2×C29semidirect
253. #3357C2×C29semidirect
255. #3340C2×C29semidirect
256. #1723C2×C29semidirect
257. #1691C2×C29semidirect
258. #1683C2×C29semidirect
259. #1676C2×C29semidirect
260. #1675C2×C29semidirect
261. #1646C2×C29semidirect
262. #1638C2×C29semidirect
263. #1634C2×C29semidirect
264. #1632C2×C29semidirect
265. #1581C2×C29semidirect
266. SD16⋊C8C2×C29semidirect
425. C29#19864direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33602
C29×#33572
C29×#33412
C29×#33402
C29×#17232
C29×#16912
C29×#16832
C29×#16762
C29×#16752
C29×#16462
C29×#16382
C29×#16342
C29×#16322
C29×#15812
C29×SD16⋊C82
#1986429