Finite Group Databasebeta

← C29×#19952 #20314852

Subgroups — C29×#19952 #20314852

Order 7424.

586 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3400C211yesmaximal, characteristic, complemented
2C29×#3394C211yesmaximal, characteristic
3C29×#3381C211yesmaximal, characteristic, complemented
4C29×#3356C211yesmaximal, characteristic, complemented
5C29×#1705C211yesmaximal, characteristic, complemented
6C29×#1692C211yesmaximal, characteristic, complemented
7C29×#1685C211yesmaximal, characteristic
8C29×#1672C211yesmaximal, characteristic, complemented
9C29×#1666C211yesmaximal, characteristic, complemented
10C29×#1653C211yesmaximal, characteristic, complemented
11C29×#1652C211yesmaximal, characteristic, complemented
12C29×#1630C211yesmaximal, characteristic, complemented
13C29×#1622C211yesmaximal, characteristic
14C29×#1590C211yesmaximal, characteristic, complemented
15C8×Q16×C29C211yesmaximal, characteristic, complemented
16C29×#559C2211yescharacteristic
17C29×#557C2211yescharacteristic
18C29×#556C2211yescharacteristic
19C29×#554C2211yescharacteristic
20C29×#499—21no—
21C29×#498C2211yescharacteristic
22C29×#498C2211yescharacteristic
23C29×#498C2211yescharacteristic
24C29×#497—21no—
25C29×#495—21no—
26C29×#492C2211yescharacteristic
27C29×#492C2211yescharacteristic
28C29×#492C2211yescharacteristic
29C29×#485—21no—
30C29×#483—21no—
31C29×#479—21no—
32C29×#478—21no—
33C29×#477C2211yescharacteristic
34C29×#477C2211yescharacteristic
35C29×#475C2211yescharacteristic
36C29×#474C2211yescharacteristic
37C29×#470—21no—
38C29×#464—21no—
39C29×#464—21no—
40C29×#463—21no—
41C29×#462C2211yescharacteristic
42C29×#462C2211yescharacteristic
43C29×#461—21no—
44C29×#460C2211yescharacteristic
45C29×#459C2211yescharacteristic
46C29×#446C2211yescharacteristic
47C8×Q8×C29C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C29×#440—21no—
50C4×Q16×C29C2211yescharacteristic
51C4×SD16×C29—21no—
52C4×SD16×C29—21no—
53C4×SD16×C29C2211yescharacteristic
54C29×#436C2211yescharacteristic
55C29×#428—21no—
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×Q8⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C82×C29C2211yescharacteristic
67C2×Q16×C29—21no—
68C2×Q16×C29—21no—
69C2×Q16×C29D411yescharacteristic
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×SD16×C29—21no—
75C2×SD16×C29—41no—
76C2×SD16×C29D411yescharacteristic
77C2×D8×C29—21no—
78C2×M16×C29—21no—
79C29×C4⋊Q8—21no—
80C29×C4⋊Q8C2311yescharacteristic
81C29×C4⋊Q8C2311yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×#127C2311yescharacteristic
84C29×#126—41no—
85C29×#125—21no—
86C29×#125—21no—
87C29×#125—41no—
88C29×#124—21no—
89C29×#124—21no—
90C29×#124—21no—
91C29×#123—41no—
92C29×C22⋊Q8—21no—
93C29×C22⋊Q8—21no—
94C29×C22⋊Q8—41no—
95C4×Q8×C29—21no—
96C4×Q8×C29—21no—
97C4×Q8×C29—21no—
98C4×Q8×C29C2311yescharacteristic
99C4×Q8×C29C2311yescharacteristic
100C4×Q8×C29C2311yescharacteristic
101C4×D4×C29—21no—
102C4×D4×C29—21no—
103C4×D4×C29—21no—
104C4×D4×C29C2311yescharacteristic
105C29×#117—21no—
106C2×C4⋊C4×C29—21no—
107C29×#107—21no—
108C29×#107—21no—
109C29×#107—21no—
110C29×#107D411yescharacteristic
111C29×#106—21no—
112C29×#106—21no—
113C29×#106—21no—
114C29×#106—21no—
115C29×#106—21no—
116C29×#106—41no—
117C29×#106D411yescharacteristic
118C29×C4⋊C8—21no—
119C29×C4⋊C8—21no—
120C29×C4⋊C8—21no—
121C29×C4⋊C8C2311yescharacteristic
122C29×C4⋊C8C2311yescharacteristic
123C29×C4⋊C8C2311yescharacteristic
124C29×C4⋊C8C2311yescharacteristic
125C29×#103—21no—
126C29×#103—21no—
127C29×#103—21no—
128C29×#103—21no—
129C29×#103—21no—
130C29×#103D411yescharacteristic
131C29×#103D411yescharacteristic
132C29×#103D411yescharacteristic
133C29×#102—21no—
134C29×#102—21no—
135C29×#102—21no—
136C29×#102D411yescharacteristic
137C29×C22⋊C8—21no—
138C29×#97—21no—
139C4×C8×C29—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×C29C2×D411yescharacteristic
148C2×Q8×C29C2×D411yescharacteristic
149C2×Q8×C29C2×D411yescharacteristic
150C2×D4×C29—21no—
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29C2×D411yescharacteristic
154C22×C4×C29—21no—
155C22×C4×C29—41no—
156C22×C4×C29—41no—
157Q16×C29—22no—
158Q16×C29—81no—
159Q16×C29—81no—
160SD16×C29—22no—
161SD16×C29—42no—
162SD16×C29—42no—
163SD16×C29—81no—
164SD16×C29—81no—
165SD16×C29—82no—
166SD16×C29—81no—
167D8×C29—81no—
168M16×C29—42no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C2×C8×C29—21no—
173C2×C8×C29—21no—
174C2×C8×C29C2×D411yescharacteristic
175C2×C8×C29C2×D411yescharacteristic
176C2×C8×C29C2×D411yescharacteristic
177C2×C8×C29C2×D411yescharacteristic
178C4⋊C4×C29—21no—
179C4⋊C4×C29—21no—
180C4⋊C4×C29—21no—
181C4⋊C4×C29—21no—
182C4⋊C4×C29—21no—
183C4⋊C4×C29—21no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—41no—
188C4⋊C4×C29—41no—
189C4⋊C4×C29—41no—
190C4⋊C4×C29—41no—
191C4⋊C4×C29—41no—
192C4⋊C4×C29—41no—
193C4⋊C4×C29C2×D411yescharacteristic
194C4⋊C4×C29C2×D411yescharacteristic
195C4⋊C4×C29C2×D411yescharacteristic
196C4⋊C4×C29C2×D411yescharacteristic
197C22⋊C4×C29—21no—
198C22⋊C4×C29—41no—
199C22⋊C4×C29—41no—
200C22⋊C4×C29—41no—
201C22⋊C4×C29—41no—
202C22⋊C4×C29—41no—
203C22⋊C4×C29—41no—
204C42×C29—21no—
205C42×C29—21no—
206C42×C29—21no—
207C42×C29—41no—
208C42×C29—41no—
209C42×C29C2411yescharacteristic
210#19952C2911yesmaximal, characteristic, direct product factor, Sylow
211C23×C29—21no—
212C23×C29—41no—
213Q8×C29—21no—
214Q8×C29—21no—
215Q8×C29—21no—
216Q8×C29—21no—
217Q8×C29—21no—
218Q8×C29—21no—
219Q8×C29—41no—
220Q8×C29—41no—
221Q8×C29—41no—
222Q8×C29—41no—
223Q8×C29—81no—
224D4×C29—21no—
225D4×C29—21no—
226D4×C29—41no—
227D4×C29—41no—
228D4×C29—41no—
229D4×C29—41no—
230D4×C29—81no—
231C2×C4×C29—21no—
232C2×C4×C29—21no—
233C2×C4×C29—21no—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—41no—
239C2×C4×C29—41no—
240C2×C4×C29—41no—
241C2×C4×C29—41no—
242C2×C4×C29—41no—
243C2×C4×C29—161no—
244C2×C4×C29—161no—
245C2×C4×C29C22×D411yescharacteristic
246C2×C4×C29C22×D411yescharacteristic
247C2×C4×C29H(5,𝔽2)11yescharacteristic
248C8×C29—22no—
249C8×C29—21no—
250C8×C29—21no—
251C8×C29—41no—
252C8×C29—41no—
253C8×C29—41no—
254C8×C29—41no—
255C8×C29#13512yes—
256C8×C29#13712yes—
257#3400C2×C2911yescharacteristic, complemented
258#3394C2×C2911yescharacteristic
259#3381C2×C2911yescharacteristic, complemented
260#3356C2×C2911yescharacteristic, complemented
261#1705C2×C2911yescharacteristic, complemented
262#1692C2×C2911yescharacteristic, complemented
263#1685C2×C2911yescharacteristic
264#1672C2×C2911yescharacteristic, complemented
265#1666C2×C2911yescharacteristic, complemented
266#1653C2×C2911yescharacteristic, complemented
267#1652C2×C2911yescharacteristic, complemented
268#1630C2×C2911yescharacteristic, complemented
269#1622C2×C2911yescharacteristic
270#1590C2×C2911yescharacteristic, complemented
271C8×Q16C2×C2911yescharacteristic, complemented
272C22×C29—41no—
273C22×C29—41no—
274C22×C29—41no—
275C22×C29—81no—
276C22×C29—81no—
277C22×C29—81no—
278C22×C29D4211yescharacteristic
279C4×C29—21no—
280C4×C29—41no—
281C4×C29—41no—
282C4×C29—41no—
283C4×C29—41no—
284C4×C29—41no—
285C4×C29—41no—
286C4×C29—41no—
287C4×C29—81no—
288C4×C29—81no—
289C4×C29—81no—
290C4×C29C2×#13511yescharacteristic
291C4×C29C2×#13711yescharacteristic
292C4×C29#57711yescharacteristic
293C4×C29#57711yescharacteristic
294#559C22×C2911yescharacteristic
295#557C22×C2911yescharacteristic
296#556C22×C2911yescharacteristic
297#554C22×C2911yescharacteristic
298#499—21no—
299#498C22×C2911yescharacteristic
300#498C22×C2911yescharacteristic
301#498C22×C2911yescharacteristic
302#497—21no—
303#495—21no—
304#492C22×C2911yescharacteristic
305#492C22×C2911yescharacteristic
306#492C22×C2911yescharacteristic
307#485—21no—
308#483—21no—
309#479—21no—
310#478—21no—
311#477C22×C2911yescharacteristic
312#477C22×C2911yescharacteristic
313#475C22×C2911yescharacteristic
314#474C22×C2911yescharacteristic
315#470—21no—
316#464—21no—
317#464—21no—
318#463—21no—
319#462C22×C2911yescharacteristic
320#462C22×C2911yescharacteristic
321#461—21no—
322#460C22×C2911yescharacteristic
323#459C22×C2911yescharacteristic
324#446C22×C2911yescharacteristic
325C8×Q8C22×C2911yescharacteristic
326C8×Q8C22×C2911yescharacteristic
327#440—21no—
328C4×Q16C22×C2911yescharacteristic
329C4×SD16—21no—
330C4×SD16—21no—
331C4×SD16C22×C2911yescharacteristic
332#436C22×C2911yescharacteristic
333#428—21no—
334#335C22×C2911yescharacteristic
335#334C22×C2911yescharacteristic
336#333C22×C2911yescharacteristic
337#332C22×C2911yescharacteristic
338#332C22×C2911yescharacteristic
339#331C22×C2911yescharacteristic
340Q8⋊C8C22×C2911yescharacteristic
341Q8⋊C8C22×C2911yescharacteristic
342Q8⋊C8C22×C2911yescharacteristic
343D4⋊C8C22×C2911yescharacteristic
344C82C22×C2911yescharacteristic
345C2×C29—81no—
346C2×C29—161no—
347C2×C29#327811yescharacteristic
348C2×C29#328411yescharacteristic
349C2×C29#329111yescharacteristic
350C2×Q16—21no—
351C2×Q16—21no—
352C2×Q16D4×C2911yescharacteristic
353C2×SD16—21no—
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16—21no—
357C2×SD16—21no—
358C2×SD16—41no—
359C2×SD16D4×C2911yescharacteristic
360C2×D8—21no—
361C2×M16—21no—
362C4⋊Q8—21no—
363C4⋊Q8C23×C2911yescharacteristic
364C4⋊Q8C23×C2911yescharacteristic
365C4⋊Q8C23×C2911yescharacteristic
366#127C23×C2911yescharacteristic
367#126—41no—
368#125—21no—
369#125—21no—
370#125—41no—
371#124—21no—
372#124—21no—
373#124—21no—
374#123—41no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—41no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8C23×C2911yescharacteristic
382C4×Q8C23×C2911yescharacteristic
383C4×Q8C23×C2911yescharacteristic
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4C23×C2911yescharacteristic
388#117—21no—
389C2×C4⋊C4—21no—
390#107—21no—
391#107—21no—
392#107—21no—
393#107D4×C2911yescharacteristic
394#106—21no—
395#106—21no—
396#106—21no—
397#106—21no—
398#106—21no—
399#106—41no—
400#106D4×C2911yescharacteristic
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8C23×C2911yescharacteristic
405C4⋊C8C23×C2911yescharacteristic
406C4⋊C8C23×C2911yescharacteristic
407C4⋊C8C23×C2911yescharacteristic
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103D4×C2911yescharacteristic
414#103D4×C2911yescharacteristic
415#103D4×C2911yescharacteristic
416#102—21no—
417#102—21no—
418#102—21no—
419#102D4×C2911yescharacteristic
420C22⋊C8—21no—
421#97—21no—
422C4×C8—21no—
423C4×C8—21no—
424C4×C8C23×C2911yescharacteristic
425C4×C8C23×C2911yescharacteristic
426C4×C8C23×C2911yescharacteristic
427C29#1995211yescharacteristic, direct product factor, Sylow
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8C2×D4×C2911yescharacteristic
432C2×Q8C2×D4×C2911yescharacteristic
433C2×Q8C2×D4×C2911yescharacteristic
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4C2×D4×C2911yescharacteristic
438C22×C4—21no—
439C22×C4—41no—
440C22×C4—41no—
441Q16—22no—
442Q16—81no—
443Q16—81no—
444SD16—22no—
445SD16—42no—
446SD16—42no—
447SD16—81no—
448SD16—81no—
449SD16—82no—
450SD16—81no—
451D8—81no—
452M16—42no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8C2×D4×C2911yescharacteristic
459C2×C8C2×D4×C2911yescharacteristic
460C2×C8C2×D4×C2911yescharacteristic
461C2×C8C2×D4×C2911yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4C2×D4×C2911yescharacteristic
478C4⋊C4C2×D4×C2911yescharacteristic
479C4⋊C4C2×D4×C2911yescharacteristic
480C4⋊C4C2×D4×C2911yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—41no—
492C42—41no—
493C42C24×C2911yescharacteristic
494C23—21no—
495C23—41no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—21no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—81no—
507D4—21no—
508D4—21no—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—81no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—161no—
527C2×C4—161no—
528C2×C4C22×D4×C2911yescharacteristic
529C2×C4C22×D4×C2911yescharacteristic
530C2×C4C29×H(5,𝔽2)11yescharacteristic
531C8—22no—
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8C29×#13512yes—
539C8C29×#13712yes—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22D42×C2911yescharacteristic
547C4—21no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4C2×C29×#13511yescharacteristic
559C4C2×C29×#13711yescharacteristic
560C4C29×#57711yescharacteristic
561C4C29×#57711yescharacteristic
562C2—81no—
563C2—161no—
564C2C29×#327811yescharacteristic
565C2C29×#328411yescharacteristic
566C2C29×#329111yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#459C22
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×#3400C2semidirect
3. C29×#3381C2semidirect
4. C29×#3356C2semidirect
5. C29×#1705C2semidirect
6. C29×#1692C2semidirect
8. C29×#1672C2semidirect
9. C29×#1666C2semidirect
10. C29×#1653C2semidirect
11. C29×#1652C2semidirect
12. C29×#1630C2semidirect
14. C29×#1590C2semidirect
15. C8×Q16×C29C2semidirect
210. #19952C29direct (N × H)
257. #3400C2×C29semidirect
259. #3381C2×C29semidirect
260. #3356C2×C29semidirect
261. #1705C2×C29semidirect
262. #1692C2×C29semidirect
264. #1672C2×C29semidirect
265. #1666C2×C29semidirect
266. #1653C2×C29semidirect
267. #1652C2×C29semidirect
268. #1630C2×C29semidirect
270. #1590C2×C29semidirect
271. C8×Q16C2×C29semidirect
427. C29#19952direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34002
C29×#33942
C29×#33812
C29×#33562
C29×#17052
C29×#16922
C29×#16852
C29×#16722
C29×#16662
C29×#16532
C29×#16522
C29×#16302
C29×#16222
C29×#15902
C8×Q16×C292
#1995229