Finite Group Databasebeta

← C29×#19919 #20314819

Subgroups — C29×#19919 #20314819

Order 7424.

586 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×SD16×C29C211yesmaximal, characteristic, complemented
2C29×#3369C211yesmaximal, characteristic, complemented
3C29×#3340C211yesmaximal, characteristic
4C29×#3329C211yesmaximal, characteristic
5C29×#1707C211yesmaximal, characteristic, complemented
6C29×#1704C211yesmaximal, characteristic, complemented
7C29×#1703C211yesmaximal, characteristic, complemented
8C29×#1672C211yesmaximal, characteristic, complemented
9C29×#1671C211yesmaximal, characteristic, complemented
10C29×#1650C211yesmaximal, characteristic, complemented
11C29×#1649C211yesmaximal, characteristic, complemented
12C29×#1634C211yesmaximal, characteristic
13C29×#1633C211yesmaximal, characteristic, complemented
14C29×#1590C211yesmaximal, characteristic, complemented
15C8×SD16×C29C211yesmaximal, characteristic, complemented
16Q82×C29C2211yescharacteristic
17C29×#556C2211yescharacteristic
18C29×#555C2211yescharacteristic
19D4×Q8×C29C2211yescharacteristic
20C29×#500C2211yescharacteristic
21C29×#498—21no—
22C29×#498C2211yescharacteristic
23C29×#498C2211yescharacteristic
24C29×#494C2211yescharacteristic
25C29×#489—21no—
26C29×#487C2211yescharacteristic
27C29×#487C2211yescharacteristic
28C29×#485—21no—
29C29×#485—21no—
30C29×#482—21no—
31C29×#477C2211yescharacteristic
32C29×#477C2211yescharacteristic
33C29×#476—21no—
34C29×#476C2211yescharacteristic
35C29×#476C2211yescharacteristic
36C29×#475—21no—
37C29×#475—21no—
38C29×#475C2211yescharacteristic
39C29×#474C2211yescharacteristic
40C29×#468—21no—
41C29×#465—21no—
42C29×#464—21no—
43C29×#462C2211yescharacteristic
44C29×#461C2211yescharacteristic
45C29×#448—21no—
46C29×#446C2211yescharacteristic
47C8×Q8×C29C2211yescharacteristic
48C29×#441—21no—
49C4×SD16×C29—21no—
50C4×SD16×C29C2211yescharacteristic
51C4×SD16×C29C2211yescharacteristic
52C29×#436C2211yescharacteristic
53C8×D4×C29C2211yescharacteristic
54C29×#427—21no—
55C29×#419—21no—
56C29×#334C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C82×C29C2211yescharacteristic
67C22×Q8×C29—21no—
68C2×Q16×C29—21no—
69C2×Q16×C29—41no—
70C2×SD16×C29—21no—
71C2×SD16×C29D411yescharacteristic
72C2×SD16×C29D411yescharacteristic
73C2×M16×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×C4⋊Q8C2311yescharacteristic
83C29×#126—41no—
84C29×#124—21no—
85C29×#124—41no—
86C29×C22⋊Q8—21no—
87C29×C22⋊Q8—21no—
88C29×C22⋊Q8—41no—
89C29×#121—21no—
90C29×#121—21no—
91C4×Q8×C29—21no—
92C4×Q8×C29—21no—
93C4×Q8×C29—21no—
94C4×Q8×C29C2311yescharacteristic
95C4×Q8×C29C2311yescharacteristic
96C4×D4×C29—21no—
97C4×D4×C29C2311yescharacteristic
98C4×D4×C29C2311yescharacteristic
99C29×#117—21no—
100C29×#117—21no—
101C29×#117—21no—
102C29×#107—21no—
103C29×#107—21no—
104C29×#107—21no—
105C29×#107—41no—
106C29×#106—21no—
107C29×#106—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×#106—21no—
111C29×#106—21no—
112C29×#106—21no—
113C29×#106D411yescharacteristic
114C29×#106D411yescharacteristic
115C29×C4⋊C8—21no—
116C29×C4⋊C8—21no—
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×#103—21no—
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—21no—
126C29×#103—21no—
127C29×#103—21no—
128C29×#103—21no—
129C29×#103—21no—
130C29×#103D411yescharacteristic
131C29×#103D411yescharacteristic
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×#102D411yescharacteristic
136C29×#102D411yescharacteristic
137C29×C22⋊C8—21no—
138C29×C22⋊C8—21no—
139C29×#97—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×C29—41no—
149C2×Q8×C29—41no—
150C2×Q8×C29—42no—
151C2×Q8×C29—81no—
152C2×Q8×C29C2×D411yescharacteristic
153C2×Q8×C29C2×D411yescharacteristic
154C2×D4×C29—41no—
155C2×D4×C29C2×D411yescharacteristic
156C2×D4×C29C2×D411yescharacteristic
157C22×C4×C29—21no—
158C22×C4×C29—21no—
159C22×C4×C29—41no—
160Q16×C29—42no—
161Q16×C29—82no—
162SD16×C29—22no—
163SD16×C29—22no—
164SD16×C29—81no—
165M16×C29—81no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—42no—
172C2×C8×C29C2×D411yescharacteristic
173C2×C8×C29C2×D411yescharacteristic
174C2×C8×C29C2×D411yescharacteristic
175C2×C8×C29C2×D411yescharacteristic
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—21no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—41no—
187C4⋊C4×C29—41no—
188C4⋊C4×C29—41no—
189C4⋊C4×C29—41no—
190C4⋊C4×C29C2×D411yescharacteristic
191C4⋊C4×C29C2×D411yescharacteristic
192C4⋊C4×C29C2×D411yescharacteristic
193C4⋊C4×C29C2×D411yescharacteristic
194C22⋊C4×C29—21no—
195C22⋊C4×C29—21no—
196C22⋊C4×C29—41no—
197C22⋊C4×C29—41no—
198C22⋊C4×C29—41no—
199C22⋊C4×C29—41no—
200C22⋊C4×C29—41no—
201C42×C29—21no—
202C42×C29—21no—
203C42×C29—41no—
204C42×C29—41no—
205C42×C29—41no—
206C42×C29C2411yescharacteristic
207#19919C2911yesmaximal, characteristic, direct product factor, Sylow
208C23×C29—21no—
209C23×C29—21no—
210Q8×C29—21no—
211Q8×C29—21no—
212Q8×C29—21no—
213Q8×C29—41no—
214Q8×C29—41no—
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—21no—
224D4×C29—21no—
225D4×C29—21no—
226D4×C29—161no—
227C2×C4×C29—21no—
228C2×C4×C29—21no—
229C2×C4×C29—21no—
230C2×C4×C29—21no—
231C2×C4×C29—21no—
232C2×C4×C29—21no—
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—41no—
240C2×C4×C29—41no—
241C2×C4×C29—82no—
242C2×C4×C29C22×D411yescharacteristic
243C2×C4×C29C22×D411yescharacteristic
244C2×C4×C29H(5,𝔽2)11yescharacteristic
245C8×C29—22no—
246C8×C29—21no—
247C8×C29—21no—
248C8×C29—21no—
249C8×C29—41no—
250C8×C29—41no—
251C8×C29—41no—
252C8×C29—41no—
253C8×C29#13712yes—
254Q8×SD16C2×C2911yescharacteristic, complemented
255#3369C2×C2911yescharacteristic, complemented
256#3340C2×C2911yescharacteristic
257#3329C2×C2911yescharacteristic
258#1707C2×C2911yescharacteristic, complemented
259#1704C2×C2911yescharacteristic, complemented
260#1703C2×C2911yescharacteristic, complemented
261#1672C2×C2911yescharacteristic, complemented
262#1671C2×C2911yescharacteristic, complemented
263#1650C2×C2911yescharacteristic, complemented
264#1649C2×C2911yescharacteristic, complemented
265#1634C2×C2911yescharacteristic
266#1633C2×C2911yescharacteristic, complemented
267#1590C2×C2911yescharacteristic, complemented
268C8×SD16C2×C2911yescharacteristic, complemented
269C22×C29—41no—
270C22×C29—41no—
271C22×C29—41no—
272C22×C29—41no—
273C22×C29—41no—
274C22×C29—41no—
275C22×C29D4211yescharacteristic
276C4×C29—22no—
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×C29C2×#13711yescharacteristic
289C4×C29#57711yescharacteristic
290C4×C29#57811yescharacteristic
291Q82C22×C2911yescharacteristic
292#556C22×C2911yescharacteristic
293#555C22×C2911yescharacteristic
294D4×Q8C22×C2911yescharacteristic
295#500C22×C2911yescharacteristic
296#498—21no—
297#498C22×C2911yescharacteristic
298#498C22×C2911yescharacteristic
299#494C22×C2911yescharacteristic
300#489—21no—
301#487C22×C2911yescharacteristic
302#487C22×C2911yescharacteristic
303#485—21no—
304#485—21no—
305#482—21no—
306#477C22×C2911yescharacteristic
307#477C22×C2911yescharacteristic
308#476—21no—
309#476C22×C2911yescharacteristic
310#476C22×C2911yescharacteristic
311#475—21no—
312#475—21no—
313#475C22×C2911yescharacteristic
314#474C22×C2911yescharacteristic
315#468—21no—
316#465—21no—
317#464—21no—
318#462C22×C2911yescharacteristic
319#461C22×C2911yescharacteristic
320#448—21no—
321#446C22×C2911yescharacteristic
322C8×Q8C22×C2911yescharacteristic
323#441—21no—
324C4×SD16—21no—
325C4×SD16C22×C2911yescharacteristic
326C4×SD16C22×C2911yescharacteristic
327#436C22×C2911yescharacteristic
328C8×D4C22×C2911yescharacteristic
329#427—21no—
330#419—21no—
331#334C22×C2911yescharacteristic
332#334C22×C2911yescharacteristic
333#333C22×C2911yescharacteristic
334#333C22×C2911yescharacteristic
335#332C22×C2911yescharacteristic
336#332C22×C2911yescharacteristic
337Q8⋊C8C22×C2911yescharacteristic
338Q8⋊C8C22×C2911yescharacteristic
339D4⋊C8C22×C2911yescharacteristic
340D4⋊C8C22×C2911yescharacteristic
341C82C22×C2911yescharacteristic
342C2×C29—81no—
343C2×C29—81no—
344C2×C29#327611yescharacteristic
345C2×C29#328211yescharacteristic
346C2×C29#329111yescharacteristic
347C22×Q8—21no—
348C2×Q16—21no—
349C2×Q16—41no—
350C2×SD16—21no—
351C2×SD16D4×C2911yescharacteristic
352C2×SD16D4×C2911yescharacteristic
353C2×M16—21no—
354C22×C8—21no—
355C4⋊Q8—21no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8—41no—
359C4⋊Q8C23×C2911yescharacteristic
360C4⋊Q8C23×C2911yescharacteristic
361C4⋊Q8C23×C2911yescharacteristic
362C4⋊Q8C23×C2911yescharacteristic
363#126—41no—
364#124—21no—
365#124—41no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—41no—
369#121—21no—
370#121—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8C23×C2911yescharacteristic
375C4×Q8C23×C2911yescharacteristic
376C4×D4—21no—
377C4×D4C23×C2911yescharacteristic
378C4×D4C23×C2911yescharacteristic
379#117—21no—
380#117—21no—
381#117—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#107—41no—
386#106—21no—
387#106—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106—21no—
392#106—21no—
393#106D4×C2911yescharacteristic
394#106D4×C2911yescharacteristic
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8C23×C2911yescharacteristic
398C4⋊C8C23×C2911yescharacteristic
399C4⋊C8C23×C2911yescharacteristic
400C4⋊C8C23×C2911yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103D4×C2911yescharacteristic
411#103D4×C2911yescharacteristic
412#102—21no—
413#102—21no—
414#102—21no—
415#102D4×C2911yescharacteristic
416#102D4×C2911yescharacteristic
417C22⋊C8—21no—
418C22⋊C8—21no—
419#97—21no—
420C4×C8—21no—
421C4×C8C23×C2911yescharacteristic
422C4×C8C23×C2911yescharacteristic
423C4×C8C23×C2911yescharacteristic
424C29#1991911yescharacteristic, direct product factor, Sylow
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—42no—
432C2×Q8—81no—
433C2×Q8C2×D4×C2911yescharacteristic
434C2×Q8C2×D4×C2911yescharacteristic
435C2×D4—41no—
436C2×D4C2×D4×C2911yescharacteristic
437C2×D4C2×D4×C2911yescharacteristic
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—41no—
441Q16—42no—
442Q16—82no—
443SD16—22no—
444SD16—22no—
445SD16—81no—
446M16—81no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—42no—
453C2×C8C2×D4×C2911yescharacteristic
454C2×C8C2×D4×C2911yescharacteristic
455C2×C8C2×D4×C2911yescharacteristic
456C2×C8C2×D4×C2911yescharacteristic
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—21no—
466C4⋊C4—21no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4C2×D4×C2911yescharacteristic
472C4⋊C4C2×D4×C2911yescharacteristic
473C4⋊C4C2×D4×C2911yescharacteristic
474C4⋊C4C2×D4×C2911yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C42—21no—
483C42—21no—
484C42—41no—
485C42—41no—
486C42—41no—
487C42C24×C2911yescharacteristic
488C23—21no—
489C23—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—82no—
498Q8—81no—
499Q8—81no—
500Q8—161no—
501Q8C29×#13512yes—
502D4—21no—
503D4—21no—
504D4—21no—
505D4—21no—
506D4—161no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4C22×D4×C2911yescharacteristic
523C2×C4C22×D4×C2911yescharacteristic
524C2×C4C29×H(5,𝔽2)11yescharacteristic
525C8—22no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8C29×#13712yes—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22D42×C2911yescharacteristic
541C4—22no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4C2×C29×#13511yescharacteristic
553C4C2×C29×#13711yescharacteristic
554C4C29×#57711yescharacteristic
555C4C29×#57811yescharacteristic
556C2—81no—
557C2—81no—
558C2C29×#327611yescharacteristic
559C2C29×#328211yescharacteristic
560C2C29×#329111yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#555C22
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×#3369C2semidirect
5. C29×#1707C2semidirect
6. C29×#1704C2semidirect
7. C29×#1703C2semidirect
8. C29×#1672C2semidirect
9. C29×#1671C2semidirect
10. C29×#1650C2semidirect
11. C29×#1649C2semidirect
13. C29×#1633C2semidirect
14. C29×#1590C2semidirect
15. C8×SD16×C29C2semidirect
207. #19919C29direct (N × H)
254. Q8×SD16C2×C29semidirect
255. #3369C2×C29semidirect
258. #1707C2×C29semidirect
259. #1704C2×C29semidirect
260. #1703C2×C29semidirect
261. #1672C2×C29semidirect
262. #1671C2×C29semidirect
263. #1650C2×C29semidirect
264. #1649C2×C29semidirect
266. #1633C2×C29semidirect
267. #1590C2×C29semidirect
268. C8×SD16C2×C29semidirect
424. C29#19919direct (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×#33692
C29×#33402
C29×#33292
C29×#17072
C29×#17042
C29×#17032
C29×#16722
C29×#16712
C29×#16502
C29×#16492
C29×#16342
C29×#16332
C29×#15902
C8×SD16×C292
#1991929