Finite Group Databasebeta

← C29×#19798 #20314698

Subgroups — C29×#19798 #20314698

Order 7424.

592 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×SD16×C29C211yesmaximal, characteristic, complemented
2C29×#3375C211yesmaximal, characteristic, complemented
3C29×#3361C211yesmaximal, characteristic
4C29×#3299C211yesmaximal, characteristic, complemented
5C29×#1720C211yesmaximal, characteristic, complemented
6C29×#1704C211yesmaximal, characteristic, complemented
7C29×#1678C211yesmaximal, characteristic, complemented
8C29×#1677C211yesmaximal, characteristic
9C29×#1672C211yesmaximal, characteristic, complemented
10C29×#1640C211yesmaximal, characteristic, complemented
11C29×#1633C211yesmaximal, characteristic, complemented
12C29×#1632C211yesmaximal, characteristic, complemented
13C29×#1627C211yesmaximal, characteristic
14C29×#1582C211yesmaximal, characteristic, complemented
15C29×#1579C211yesmaximal, characteristic, complemented
16C29×#559C2211yescharacteristic
17Q82×C29C2211yescharacteristic
18C29×#554C2211yescharacteristic
19D4×Q8×C29C2211yescharacteristic
20C29×#498—21no—
21C29×#498C2211yescharacteristic
22C29×#494C2211yescharacteristic
23C29×#489—21no—
24C29×#488—21no—
25C29×#487C2211yescharacteristic
26C29×#486C2211yescharacteristic
27C29×#486C2211yescharacteristic
28C29×#486C2211yescharacteristic
29C29×#484—21no—
30C29×#478—21no—
31C29×#477C2211yescharacteristic
32C29×#477C2211yescharacteristic
33C29×#477C2211yescharacteristic
34C29×#476—21no—
35C29×#476C2211yescharacteristic
36C29×#475—21no—
37C29×#475C2211yescharacteristic
38C29×#474—21no—
39C29×#467—21no—
40C29×#464—21no—
41C29×#463—21no—
42C29×#462C2211yescharacteristic
43C29×#460C2211yescharacteristic
44C29×#459C2211yescharacteristic
45C29×#451—21no—
46C29×#446C2211yescharacteristic
47C8×Q8×C29C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C29×#440—21no—
50C4×Q16×C29C2211yescharacteristic
51C4×SD16×C29—21no—
52C4×SD16×C29C2211yescharacteristic
53C4×D8×C29—21no—
54C8×D4×C29C2211yescharacteristic
55C2×C29×#103—21no—
56C29×#334C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×Q8⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C29×#322C2211yescharacteristic
67C22×Q8×C29—21no—
68C2×Q16×C29—21no—
69C2×Q16×C29—41no—
70C2×Q16×C29D411yescharacteristic
71C2×SD16×C29—21no—
72C2×SD16×C29D411yescharacteristic
73C2×D8×C29—21no—
74C22×C8×C29—21no—
75C29×C4⋊Q8—21no—
76C29×C4⋊Q8—21no—
77C29×C4⋊Q8—21no—
78C29×C4⋊Q8—41no—
79C29×C4⋊Q8C2311yescharacteristic
80C29×C4⋊Q8C2311yescharacteristic
81C29×C4⋊Q8C2311yescharacteristic
82C29×#127C2311yescharacteristic
83C29×#125—21no—
84C29×#124—21no—
85C29×#124—21no—
86C29×#123—41no—
87C29×C22⋊Q8—21no—
88C29×C22⋊Q8—21no—
89C29×C22⋊Q8—41no—
90C29×C22⋊Q8—41no—
91C4×Q8×C29—21no—
92C4×Q8×C29—21no—
93C4×Q8×C29C2311yescharacteristic
94C4×Q8×C29C2311yescharacteristic
95C4×Q8×C29C2311yescharacteristic
96C4×D4×C29—21no—
97C4×D4×C29—21no—
98C4×D4×C29—21no—
99C4×D4×C29—21no—
100C4×D4×C29C2311yescharacteristic
101C2×C4⋊C4×C29—21no—
102C29×#107—21no—
103C29×#107—21no—
104C29×#107—21no—
105C29×#107D411yescharacteristic
106C29×#106—21no—
107C29×#106—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×#106D411yescharacteristic
111C29×C4⋊C8—21no—
112C29×C4⋊C8—21no—
113C29×C4⋊C8—21no—
114C29×C4⋊C8C2311yescharacteristic
115C29×C4⋊C8C2311yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×#103—21no—
119C29×#103—21no—
120C29×#103—21no—
121C29×#103—21no—
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103D411yescharacteristic
126C29×#103D411yescharacteristic
127C29×#103D411yescharacteristic
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×#102—41no—
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×C29—41no—
148C2×Q8×C29—41no—
149C2×Q8×C29—42no—
150C2×Q8×C29—81no—
151C2×Q8×C29C2×D411yescharacteristic
152C2×Q8×C29C2×D411yescharacteristic
153C2×Q8×C29C2×D411yescharacteristic
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29C2×D411yescharacteristic
158C22×C4×C29—21no—
159C22×C4×C29—41no—
160C22×C4×C29—41no—
161C22×C4×C29—41no—
162Q16×C29—22no—
163Q16×C29—81no—
164Q16×C29—82no—
165SD16×C29—22no—
166SD16×C29—42no—
167D8×C29—42no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C2×C8×C29—21no—
173C2×C8×C29—81no—
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×C29C2×D411yescharacteristic
193C4⋊C4×C29C2×D411yescharacteristic
194C4⋊C4×C29C2×D411yescharacteristic
195C4⋊C4×C29C2×D411yescharacteristic
196C22⋊C4×C29—21no—
197C22⋊C4×C29—41no—
198C22⋊C4×C29—41no—
199C22⋊C4×C29—41no—
200C22⋊C4×C29—41no—
201C22⋊C4×C29—41no—
202C42×C29—21no—
203C42×C29—21no—
204C42×C29—21no—
205C42×C29—41no—
206C42×C29C2411yescharacteristic
207#19798C2911yesmaximal, characteristic, direct product factor, Sylow
208C23×C29—21no—
209C23×C29—41no—
210Q8×C29—21no—
211Q8×C29—21no—
212Q8×C29—21no—
213Q8×C29—21no—
214Q8×C29—21no—
215Q8×C29—41no—
216Q8×C29—41no—
217Q8×C29—82no—
218Q8×C29—81no—
219Q8×C29—81no—
220Q8×C29—161no—
221Q8×C29#13512yes—
222D4×C29—21no—
223D4×C29—41no—
224D4×C29—41no—
225D4×C29—41no—
226D4×C29—41no—
227D4×C29—81no—
228D4×C29#13712yes—
229C2×C4×C29—21no—
230C2×C4×C29—21no—
231C2×C4×C29—21no—
232C2×C4×C29—21no—
233C2×C4×C29—21no—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—41no—
237C2×C4×C29—41no—
238C2×C4×C29—41no—
239C2×C4×C29—41no—
240C2×C4×C29—41no—
241C2×C4×C29—82no—
242C2×C4×C29—161no—
243C2×C4×C29—161no—
244C2×C4×C29C22×D411yescharacteristic
245C2×C4×C29C22×D411yescharacteristic
246C2×C4×C29H(5,𝔽2)11yescharacteristic
247C8×C29—21no—
248C8×C29—21no—
249C8×C29—21no—
250C8×C29—21no—
251C8×C29—41no—
252C8×C29—41no—
253C8×C29—41no—
254C8×C29—41no—
255C8×C29—41no—
256Q8×SD16C2×C2911yescharacteristic, complemented
257#3375C2×C2911yescharacteristic, complemented
258#3361C2×C2911yescharacteristic
259#3299C2×C2911yescharacteristic, complemented
260#1720C2×C2911yescharacteristic, complemented
261#1704C2×C2911yescharacteristic, complemented
262#1678C2×C2911yescharacteristic, complemented
263#1677C2×C2911yescharacteristic
264#1672C2×C2911yescharacteristic, complemented
265#1640C2×C2911yescharacteristic, complemented
266#1633C2×C2911yescharacteristic, complemented
267#1632C2×C2911yescharacteristic, complemented
268#1627C2×C2911yescharacteristic
269#1582C2×C2911yescharacteristic, complemented
270#1579C2×C2911yescharacteristic, complemented
271C22×C29—22no—
272C22×C29—41no—
273C22×C29—41no—
274C22×C29—81no—
275C22×C29—81no—
276C22×C29—81no—
277C22×C29D4211yescharacteristic
278C4×C29—22no—
279C4×C29—21no—
280C4×C29—41no—
281C4×C29—41no—
282C4×C29—41no—
283C4×C29—41no—
284C4×C29—41no—
285C4×C29—41no—
286C4×C29—81no—
287C4×C29—81no—
288C4×C29—81no—
289C4×C29C2×#13511yescharacteristic
290C4×C29C2×#13711yescharacteristic
291C4×C29#57711yescharacteristic
292C4×C29#57811yescharacteristic
293#559C22×C2911yescharacteristic
294Q82C22×C2911yescharacteristic
295#554C22×C2911yescharacteristic
296D4×Q8C22×C2911yescharacteristic
297#498—21no—
298#498C22×C2911yescharacteristic
299#494C22×C2911yescharacteristic
300#489—21no—
301#488—21no—
302#487C22×C2911yescharacteristic
303#486C22×C2911yescharacteristic
304#486C22×C2911yescharacteristic
305#486C22×C2911yescharacteristic
306#484—21no—
307#478—21no—
308#477C22×C2911yescharacteristic
309#477C22×C2911yescharacteristic
310#477C22×C2911yescharacteristic
311#476—21no—
312#476C22×C2911yescharacteristic
313#475—21no—
314#475C22×C2911yescharacteristic
315#474—21no—
316#467—21no—
317#464—21no—
318#463—21no—
319#462C22×C2911yescharacteristic
320#460C22×C2911yescharacteristic
321#459C22×C2911yescharacteristic
322#451—21no—
323#446C22×C2911yescharacteristic
324C8×Q8C22×C2911yescharacteristic
325C8×Q8C22×C2911yescharacteristic
326#440—21no—
327C4×Q16C22×C2911yescharacteristic
328C4×SD16—21no—
329C4×SD16C22×C2911yescharacteristic
330C4×D8—21no—
331C8×D4C22×C2911yescharacteristic
332C2×#103—21no—
333#334C22×C2911yescharacteristic
334#334C22×C2911yescharacteristic
335#333C22×C2911yescharacteristic
336#333C22×C2911yescharacteristic
337#332C22×C2911yescharacteristic
338#331C22×C2911yescharacteristic
339Q8⋊C8C22×C2911yescharacteristic
340Q8⋊C8C22×C2911yescharacteristic
341Q8⋊C8C22×C2911yescharacteristic
342D4⋊C8C22×C2911yescharacteristic
343#322C22×C2911yescharacteristic
344C2×C29—42no—
345C2×C29—161no—
346C2×C29#327011yescharacteristic
347C2×C29#328211yescharacteristic
348C2×C29#328811yescharacteristic
349C22×Q8—21no—
350C2×Q16—21no—
351C2×Q16—41no—
352C2×Q16D4×C2911yescharacteristic
353C2×SD16—21no—
354C2×SD16D4×C2911yescharacteristic
355C2×D8—21no—
356C22×C8—21no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8—41no—
361C4⋊Q8C23×C2911yescharacteristic
362C4⋊Q8C23×C2911yescharacteristic
363C4⋊Q8C23×C2911yescharacteristic
364#127C23×C2911yescharacteristic
365#125—21no—
366#124—21no—
367#124—21no—
368#123—41no—
369C22⋊Q8—21no—
370C22⋊Q8—21no—
371C22⋊Q8—41no—
372C22⋊Q8—41no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8C23×C2911yescharacteristic
376C4×Q8C23×C2911yescharacteristic
377C4×Q8C23×C2911yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4C23×C2911yescharacteristic
383C2×C4⋊C4—21no—
384#107—21no—
385#107—21no—
386#107—21no—
387#107D4×C2911yescharacteristic
388#106—21no—
389#106—21no—
390#106—21no—
391#106—21no—
392#106D4×C2911yescharacteristic
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8C23×C2911yescharacteristic
397C4⋊C8C23×C2911yescharacteristic
398C4⋊C8C23×C2911yescharacteristic
399C4⋊C8C23×C2911yescharacteristic
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103D4×C2911yescharacteristic
408#103D4×C2911yescharacteristic
409#103D4×C2911yescharacteristic
410#102—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—41no—
418#102D4×C2911yescharacteristic
419C22⋊C8—21no—
420#97—21no—
421C4×C8—21no—
422C4×C8—21no—
423C4×C8C23×C2911yescharacteristic
424C4×C8C23×C2911yescharacteristic
425C4×C8C23×C2911yescharacteristic
426C29#1979811yescharacteristic, direct product factor, Sylow
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—41no—
431C2×Q8—41no—
432C2×Q8—42no—
433C2×Q8—81no—
434C2×Q8C2×D4×C2911yescharacteristic
435C2×Q8C2×D4×C2911yescharacteristic
436C2×Q8C2×D4×C2911yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C2×D4×C2911yescharacteristic
441C22×C4—21no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445Q16—22no—
446Q16—81no—
447Q16—82no—
448SD16—22no—
449SD16—42no—
450D8—42no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—81no—
457C2×C8C2×D4×C2911yescharacteristic
458C2×C8C2×D4×C2911yescharacteristic
459C2×C8C2×D4×C2911yescharacteristic
460C2×C8C2×D4×C2911yescharacteristic
461C4⋊C4—21no—
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—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4C2×D4×C2911yescharacteristic
476C4⋊C4C2×D4×C2911yescharacteristic
477C4⋊C4C2×D4×C2911yescharacteristic
478C4⋊C4C2×D4×C2911yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—41no—
489C42C24×C2911yescharacteristic
490C23—21no—
491C23—41no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—41no—
498Q8—41no—
499Q8—82no—
500Q8—81no—
501Q8—81no—
502Q8—161no—
503Q8C29×#13512yes—
504D4—21no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—81no—
510D4C29×#13712yes—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—82no—
524C2×C4—161no—
525C2×C4—161no—
526C2×C4C22×D4×C2911yescharacteristic
527C2×C4C22×D4×C2911yescharacteristic
528C2×C4C29×H(5,𝔽2)11yescharacteristic
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C22—22no—
539C22—41no—
540C22—41no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22D42×C2911yescharacteristic
545C4—22no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4C2×C29×#13511yescharacteristic
557C4C2×C29×#13711yescharacteristic
558C4C29×#57711yescharacteristic
559C4C29×#57811yescharacteristic
560C2—42no—
561C2—161no—
562C2C29×#327011yescharacteristic
563C2C29×#328211yescharacteristic
564C2C29×#328811yescharacteristic
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. Q8×SD16×C29C2semidirect
2. C29×#3375C2semidirect
4. C29×#3299C2semidirect
5. C29×#1720C2semidirect
6. C29×#1704C2semidirect
7. C29×#1678C2semidirect
9. C29×#1672C2semidirect
10. C29×#1640C2semidirect
11. C29×#1633C2semidirect
12. C29×#1632C2semidirect
14. C29×#1582C2semidirect
15. C29×#1579C2semidirect
207. #19798C29direct (N × H)
256. Q8×SD16C2×C29semidirect
257. #3375C2×C29semidirect
259. #3299C2×C29semidirect
260. #1720C2×C29semidirect
261. #1704C2×C29semidirect
262. #1678C2×C29semidirect
264. #1672C2×C29semidirect
265. #1640C2×C29semidirect
266. #1633C2×C29semidirect
267. #1632C2×C29semidirect
269. #1582C2×C29semidirect
270. #1579C2×C29semidirect
426. C29#19798direct (N × H)

Maximal subgroups

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

subgroupindex
Q8×SD16×C292
C29×#33752
C29×#33612
C29×#32992
C29×#17202
C29×#17042
C29×#16782
C29×#16772
C29×#16722
C29×#16402
C29×#16332
C29×#16322
C29×#16272
C29×#15822
C29×#15792
#1979829