Finite Group Databasebeta

← C29×#19364 #20314264

Subgroups — C29×#19364 #20314264

Order 7424.

660 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3218C211yesmaximal, characteristic, complemented
2C29×#3217C211yesmaximal, characteristic
3C2×C29×#486C211yesmaximal, characteristic, complemented
4C29×#2966C211yesmaximal, characteristic, complemented
5C29×#1702C212yesmaximal, complemented
6C29×#1701C212yesmaximal, complemented
7C29×#1682C212yesmaximal, complemented
8C29×#1681C212yesmaximal, complemented
9C29×#1568C211yesmaximal, characteristic, complemented
10C29×#1556C211yesmaximal, characteristic, complemented
11C29×#1555C211yesmaximal, characteristic, complemented
12C2×C29×C4⋊Q8C2211yescharacteristic
13C2×C29×#127C2211yescharacteristic
14C29×#529C2211yescharacteristic
15C29×#497—21no—
16C29×#496—21no—
17C29×#491—21no—
18C29×#490—21no—
19C29×#486—21no—
20C29×#486—21no—
21C29×#486C2212yes—
22C29×#486C2212yes—
23C29×#462C2212yescomplemented
24C29×#461C2212yescomplemented
25C29×#460C2212yes—
26C29×#459C2212yes—
27C29×#451—21no—
28C29×#450—21no—
29C29×#448—21no—
30C29×#447—21no—
31C29×#446C2211yescharacteristic, complemented
32C8×Q8×C29C2211yescharacteristic, complemented
33C29×#436C2211yescharacteristic, complemented
34C29×#435—21no—
35C8×D4×C29—21no—
36C8×D4×C29C2211yescharacteristic, complemented
37C29×#433—21no—
38C29×#432C2211yescharacteristic
39C29×#432C2211yescharacteristic
40C29×#432C2211yescharacteristic
41C2×C29×#102—21no—
42C2×C29×#102—21no—
43C29×#405—21no—
44C2×C4×C8×C29C2211yescharacteristic
45C29×#335C2212yescomplemented
46C29×#334C2212yescomplemented
47C29×#332C2212yescomplemented
48C29×#332C2212yescomplemented
49C29×#331C2212yes—
50C29×#331C2212yes—
51C22×Q8×C29—21no—
52C22×D4×C29—21no—
53C22×D4×C29—21no—
54C22×D4×C29—21no—
55C2×Q16×C29—22no—
56C2×SD16×C29—22no—
57C2×SD16×C29—22no—
58C2×D8×C29—22no—
59C2×M16×C29—21no—
60C22×C8×C29—21no—
61C22×C8×C29D411yescharacteristic
62C22×C8×C29D411yescharacteristic
63C29×C4⋊Q8—21no—
64C29×C4⋊Q8—21no—
65C29×C4⋊Q8—21no—
66C29×C4⋊Q8C2312yes—
67C29×#127—21no—
68C29×#127—21no—
69C29×#127—21no—
70C29×#127C2312yes—
71C29×#126—21no—
72C29×#125D411yescharacteristic
73C29×#124D411yescharacteristic
74C29×#123—21no—
75C29×C22⋊Q8D411yescharacteristic
76C29×#121D411yescharacteristic
77C4×Q8×C29C2311yescharacteristic
78C4×D4×C29—21no—
79C4×D4×C29C2311yescharacteristic
80C29×#117—21no—
81C2×C4⋊C4×C29—21no—
82C2×C4⋊C4×C29—21no—
83C2×C42×C29C2311yescharacteristic
84C29×C4⋊C8—21no—
85C29×C4⋊C8—21no—
86C29×C4⋊C8C2311yescharacteristic
87C29×C4⋊C8C2311yescharacteristic
88C29×C4⋊C8C2312yes—
89C29×C4⋊C8C2312yes—
90C29×#103—22no—
91C29×#103—22no—
92C29×#102—22no—
93C29×#102—22no—
94C29×#102—22no—
95C29×#102—22no—
96C29×#102—22no—
97C29×#102—22no—
98C29×C22⋊C8—21no—
99C29×C22⋊C8—21no—
100C29×C22⋊C8—21no—
101C29×C22⋊C8—21no—
102C29×C22⋊C8—21no—
103C29×#97—21no—
104C29×#97—21no—
105C29×#97—21no—
106C29×#97—21no—
107C4×C8×C29—21no—
108C4×C8×C29D411yescharacteristic
109C4×C8×C29D411yescharacteristic
110C4×C8×C29C2311yescharacteristic
111C4×C8×C29C2311yescharacteristic
112C24×C29—41no—
113C2×Q8×C29—22no—
114C2×Q8×C29—41no—
115C2×Q8×C29—82no—
116C2×Q8×C29C2×D411yescharacteristic
117C2×D4×C29—21no—
118C2×D4×C29—22no—
119C2×D4×C29—22no—
120C2×D4×C29—22no—
121C2×D4×C29—42no—
122C2×D4×C29—42no—
123C2×D4×C29—41no—
124C2×D4×C29—41no—
125C2×D4×C29—41no—
126C2×D4×C29—82no—
127C2×D4×C29—82no—
128C2×D4×C29C2×D411yescharacteristic
129C22×C4×C29—21no—
130C22×C4×C29—41no—
131C22×C4×C29C2×D411yescharacteristic
132C22×C4×C29C2×D411yescharacteristic
133C22×C4×C29#4111yescharacteristic
134Q16×C29—82no—
135SD16×C29—82no—
136SD16×C29—82no—
137D8×C29—82no—
138M16×C29—42no—
139C2×C8×C29—21no—
140C2×C8×C29—21no—
141C2×C8×C29—22no—
142C2×C8×C29—22no—
143C2×C8×C29—41no—
144C2×C8×C29—41no—
145C2×C8×C29—42no—
146C2×C8×C29C2×D411yescharacteristic
147C2×C8×C29C2×D411yescharacteristic
148C2×C8×C29C2×D411yescharacteristic
149C2×C8×C29C2×D411yescharacteristic
150C4⋊C4×C29—21no—
151C4⋊C4×C29—21no—
152C4⋊C4×C29—21no—
153C4⋊C4×C29—21no—
154C4⋊C4×C29—22no—
155C4⋊C4×C29—22no—
156C4⋊C4×C29—41no—
157C4⋊C4×C29—41no—
158C4⋊C4×C29C2×D411yescharacteristic
159C4⋊C4×C29C2×D411yescharacteristic
160C22⋊C4×C29—21no—
161C22⋊C4×C29—21no—
162C22⋊C4×C29—21no—
163C22⋊C4×C29—21no—
164C22⋊C4×C29—21no—
165C42×C29—21no—
166C42×C29C2×D411yescharacteristic
167C42×C29C2×D411yescharacteristic
168C42×C29#4111yescharacteristic
169C42×C29C2411yescharacteristic
170#19364C2911yesmaximal, characteristic, direct product factor, Sylow
171C23×C29—21no—
172C23×C29—42no—
173C23×C29—82no—
174C23×C29—82no—
175C23×C29—82no—
176C23×C29#12111yescharacteristic
177Q8×C29—22no—
178Q8×C29—42no—
179Q8×C29—42no—
180Q8×C29—82no—
181D4×C29—22no—
182D4×C29—42no—
183D4×C29—42no—
184D4×C29—42no—
185D4×C29—42no—
186D4×C29—42no—
187D4×C29—82no—
188D4×C29—82no—
189D4×C29—82no—
190D4×C29—82no—
191C2×C4×C29—22no—
192C2×C4×C29—21no—
193C2×C4×C29—21no—
194C2×C4×C29—22no—
195C2×C4×C29—21no—
196C2×C4×C29—21no—
197C2×C4×C29—21no—
198C2×C4×C29—41no—
199C2×C4×C29—41no—
200C2×C4×C29—42no—
201C2×C4×C29—82no—
202C2×C4×C29#12111yescharacteristic
203C2×C4×C29#12111yescharacteristic
204C2×C4×C29#12111yescharacteristic
205C2×C4×C29C22×D411yescharacteristic
206C2×C4×C29C22×D411yescharacteristic
207C2×C4×C29C2×#4111yescharacteristic
208C8×C29—21no—
209C8×C29—21no—
210C8×C29—21no—
211C8×C29—21no—
212C8×C29—41no—
213C8×C29—41no—
214C8×C29—42no—
215C8×C29—42no—
216#3218C2×C2911yescharacteristic, complemented
217#3217C2×C2911yescharacteristic
218C2×#486C2×C2911yescharacteristic, complemented
219#2966C2×C2911yescharacteristic, complemented
220#1702C2×C2912yescomplemented
221#1701C2×C2912yescomplemented
222#1682C2×C2912yescomplemented
223#1681C2×C2912yescomplemented
224#1568C2×C2911yescharacteristic, complemented
225#1556C2×C2911yescharacteristic, complemented
226#1555C2×C2911yescharacteristic, complemented
227C22×C29—21no—
228C22×C29—21no—
229C22×C29—41no—
230C22×C29—41no—
231C22×C29—41no—
232C22×C29—82no—
233C22×C29—82no—
234C22×C29—82no—
235C22×C29—164no—
236C22×C29#47112yes—
237C22×C29C2×#12111yescharacteristic
238C4×C29—21no—
239C4×C29—21no—
240C4×C29—21no—
241C4×C29—21no—
242C4×C29—41no—
243C4×C29—41no—
244C4×C29—41no—
245C4×C29—82no—
246C4×C29#57511yescharacteristic
247C4×C29#57511yescharacteristic
248C4×C29#57612yes—
249C2×C4⋊Q8C22×C2911yescharacteristic
250C2×#127C22×C2911yescharacteristic
251#529C22×C2911yescharacteristic
252#497—21no—
253#496—21no—
254#491—21no—
255#490—21no—
256#486—21no—
257#486—21no—
258#486C22×C2912yes—
259#486C22×C2912yes—
260#462C22×C2912yescomplemented
261#461C22×C2912yescomplemented
262#460C22×C2912yes—
263#459C22×C2912yes—
264#451—21no—
265#450—21no—
266#448—21no—
267#447—21no—
268#446C22×C2911yescharacteristic, complemented
269C8×Q8C22×C2911yescharacteristic, complemented
270#436C22×C2911yescharacteristic, complemented
271#435—21no—
272C8×D4—21no—
273C8×D4C22×C2911yescharacteristic, complemented
274#433—21no—
275#432C22×C2911yescharacteristic
276#432C22×C2911yescharacteristic
277#432C22×C2911yescharacteristic
278C2×#102—21no—
279C2×#102—21no—
280#405—21no—
281C2×C4×C8C22×C2911yescharacteristic
282#335C22×C2912yescomplemented
283#334C22×C2912yescomplemented
284#332C22×C2912yescomplemented
285#332C22×C2912yescomplemented
286#331C22×C2912yes—
287#331C22×C2912yes—
288C2×C29—22no—
289C2×C29—81no—
290C2×C29—162no—
291C2×C29#304011yescharacteristic
292C2×C29#305811yescharacteristic
293C2×C29C2×#47111yescharacteristic
294C22×Q8—21no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4—21no—
298C2×Q16—22no—
299C2×SD16—22no—
300C2×SD16—22no—
301C2×D8—22no—
302C2×M16—21no—
303C22×C8—21no—
304C22×C8D4×C2911yescharacteristic
305C22×C8D4×C2911yescharacteristic
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8C23×C2912yes—
310#127—21no—
311#127—21no—
312#127—21no—
313#127C23×C2912yes—
314#126—21no—
315#125D4×C2911yescharacteristic
316#124D4×C2911yescharacteristic
317#123—21no—
318C22⋊Q8D4×C2911yescharacteristic
319#121D4×C2911yescharacteristic
320C4×Q8C23×C2911yescharacteristic
321C4×D4—21no—
322C4×D4C23×C2911yescharacteristic
323#117—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C42C23×C2911yescharacteristic
327C4⋊C8—21no—
328C4⋊C8—21no—
329C4⋊C8C23×C2911yescharacteristic
330C4⋊C8C23×C2911yescharacteristic
331C4⋊C8C23×C2912yes—
332C4⋊C8C23×C2912yes—
333#103—22no—
334#103—22no—
335#102—22no—
336#102—22no—
337#102—22no—
338#102—22no—
339#102—22no—
340#102—22no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346#97—21no—
347#97—21no—
348#97—21no—
349#97—21no—
350C4×C8—21no—
351C4×C8D4×C2911yescharacteristic
352C4×C8D4×C2911yescharacteristic
353C4×C8C23×C2911yescharacteristic
354C4×C8C23×C2911yescharacteristic
355C29#1936411yescharacteristic, direct product factor, Sylow
356C24—41no—
357C2×Q8—22no—
358C2×Q8—41no—
359C2×Q8—82no—
360C2×Q8C2×D4×C2911yescharacteristic
361C2×D4—21no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—82no—
371C2×D4—82no—
372C2×D4C2×D4×C2911yescharacteristic
373C22×C4—21no—
374C22×C4—41no—
375C22×C4C2×D4×C2911yescharacteristic
376C22×C4C2×D4×C2911yescharacteristic
377C22×C4#41×C2911yescharacteristic
378Q16—82no—
379SD16—82no—
380SD16—82no—
381D8—82no—
382M16—42no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—41no—
388C2×C8—41no—
389C2×C8—42no—
390C2×C8C2×D4×C2911yescharacteristic
391C2×C8C2×D4×C2911yescharacteristic
392C2×C8C2×D4×C2911yescharacteristic
393C2×C8C2×D4×C2911yescharacteristic
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4C2×D4×C2911yescharacteristic
403C4⋊C4C2×D4×C2911yescharacteristic
404C22⋊C4—21no—
405C22⋊C4—21no—
406C22⋊C4—21no—
407C22⋊C4—21no—
408C22⋊C4—21no—
409C42—21no—
410C42C2×D4×C2911yescharacteristic
411C42C2×D4×C2911yescharacteristic
412C42#41×C2911yescharacteristic
413C42C24×C2911yescharacteristic
414C23—21no—
415C23—42no—
416C23—82no—
417C23—82no—
418C23—82no—
419C23C29×#12111yescharacteristic
420Q8—22no—
421Q8—42no—
422Q8—42no—
423Q8—82no—
424D4—22no—
425D4—42no—
426D4—42no—
427D4—42no—
428D4—42no—
429D4—42no—
430D4—82no—
431D4—82no—
432D4—82no—
433D4—82no—
434C2×C4—22no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—82no—
445C2×C4C29×#12111yescharacteristic
446C2×C4C29×#12111yescharacteristic
447C2×C4C29×#12111yescharacteristic
448C2×C4C22×D4×C2911yescharacteristic
449C2×C4C22×D4×C2911yescharacteristic
450C2×C4C2×#41×C2911yescharacteristic
451C8—21no—
452C8—21no—
453C8—21no—
454C8—21no—
455C8—41no—
456C8—41no—
457C8—42no—
458C8—42no—
459C22—21no—
460C22—21no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—82no—
465C22—82no—
466C22—82no—
467C22—164no—
468C22C29×#47112yes—
469C22C2×C29×#12111yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—21no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—82no—
478C4C29×#57511yescharacteristic
479C4C29×#57511yescharacteristic
480C4C29×#57612yes—
481C2—22no—
482C2—81no—
483C2—162no—
484C2C29×#304011yescharacteristic
485C2C29×#305811yescharacteristic
486C2C2×C29×#47111yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3217C2
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×#3218C2semidirect
3. C2×C29×#486C2semidirect
4. C29×#2966C2semidirect
5. C29×#1702C2semidirect
6. C29×#1701C2semidirect
7. C29×#1682C2semidirect
8. C29×#1681C2semidirect
9. C29×#1568C2semidirect
10. C29×#1556C2semidirect
11. C29×#1555C2semidirect
23. C29×#462C22semidirect
24. C29×#461C22semidirect
31. C29×#446C22semidirect
32. C8×Q8×C29C22semidirect
33. C29×#436C22semidirect
36. C8×D4×C29C22semidirect
45. C29×#335C22semidirect
46. C29×#334C22semidirect
47. C29×#332C22semidirect
48. C29×#332C22semidirect
170. #19364C29direct (N × H)
216. #3218C2×C29semidirect
218. C2×#486C2×C29semidirect
219. #2966C2×C29semidirect
220. #1702C2×C29semidirect
221. #1701C2×C29semidirect
222. #1682C2×C29semidirect
223. #1681C2×C29semidirect
224. #1568C2×C29semidirect
225. #1556C2×C29semidirect
226. #1555C2×C29semidirect
260. #462C22×C29semidirect
261. #461C22×C29semidirect
268. #446C22×C29semidirect
269. C8×Q8C22×C29semidirect
270. #436C22×C29semidirect
273. C8×D4C22×C29semidirect
282. #335C22×C29semidirect
283. #334C22×C29semidirect
284. #332C22×C29semidirect
285. #332C22×C29semidirect
355. C29#19364direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32182
C29×#32172
C2×C29×#4862
C29×#29662
C29×#17022
C29×#17012
C29×#16822
C29×#16812
C29×#15682
C29×#15562
C29×#15552
#1936429