Finite Group Databasebeta

← C29×#19316 #20314216

Subgroups — C29×#19316 #20314216

Order 7424.

682 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×#3138C211yesmaximal, characteristic, complemented
2C29×#3116C211yesmaximal, characteristic, complemented
3C29×#3038C211yesmaximal, characteristic
4C29×#2970C211yesmaximal, characteristic, complemented
5C29×#1702C212yesmaximal, complemented
6C29×#1698C212yesmaximal, complemented
7C29×#1681C212yesmaximal, complemented
8C29×#1677C212yesmaximal, complemented
9C29×#1569C211yesmaximal, characteristic, complemented
10C29×#1559C211yesmaximal, characteristic, complemented
11C29×#1555C211yesmaximal, characteristic, complemented
12C2×C29×AGL(1,ℤ/8)—21no—
13C29×#533C2211yescharacteristic
14C2×C29×#127C2211yescharacteristic
15C4×#41×C29C2211yescharacteristic
16C29×#490—21no—
17C29×#490—21no—
18C29×#486C2212yes—
19C29×#486C2212yes—
20C29×#485—21no—
21C29×#477C2211yescharacteristic, complemented
22C29×#476C2211yescharacteristic, complemented
23C29×#462C2211yescharacteristic, complemented
24C29×#461C2211yescharacteristic, complemented
25C29×#460—21no—
26C29×#460C2212yes—
27C29×#459—21no—
28C29×#459C2212yes—
29C29×#452—21no—
30C29×#446C2212yescomplemented
31C29×#441—21no—
32C29×#440—21no—
33C29×#435—22no—
34C8×D4×C29C2212yescomplemented
35C29×#432—21no—
36C29×#432C2211yescharacteristic
37C29×#432C2211yescharacteristic
38C29×#423C2211yescharacteristic
39C29×#418—22no—
40C29×#418—21no—
41C4×M16×C29C2211yescharacteristic
42C2×C29×#97—21no—
43C29×#335C2212yescomplemented
44C29×#334C2212yescomplemented
45C29×#333C2212yescomplemented
46C29×#332C2212yescomplemented
47C29×#331C2212yes—
48C29×#331C2212yes—
49C2×#41×C29D411yescharacteristic
50C22×D4×C29—21no—
51C22×D4×C29—21no—
52C22×D4×C29—21no—
53C29×AGL(1,ℤ/8)—44no—
54C2×Q16×C29—21no—
55C2×SD16×C29—22no—
56C2×SD16×C29—21no—
57C2×D8×C29—22no—
58C2×M16×C29—21no—
59C2×M16×C29D412yes—
60C22×C8×C29—22no—
61C29×C4⋊Q8C2311yescharacteristic
62C29×C4⋊Q8C2311yescharacteristic
63C29×#127—21no—
64C29×#127—21no—
65C29×#127—21no—
66C29×#127C2312yes—
67C29×#125—21no—
68C29×C22⋊Q8—21no—
69C29×C22⋊Q8—21no—
70C4×Q8×C29—21no—
71C4×Q8×C29—21no—
72C4×Q8×C29D411yescharacteristic
73C4×Q8×C29C2311yescharacteristic
74C4×D4×C29—21no—
75C4×D4×C29—21no—
76C4×D4×C29D411yescharacteristic
77C4×D4×C29C2311yescharacteristic
78C29×#117—21no—
79C29×#117—21no—
80C29×#117D411yescharacteristic
81C2×C42×C29—21no—
82C2×C42×C29C2311yescharacteristic
83C29×#107—21no—
84C29×#106—21no—
85C29×C4⋊C8—22no—
86C29×C4⋊C8—21no—
87C29×C4⋊C8C2312yes—
88C29×C4⋊C8C2311yescharacteristic
89C29×C4⋊C8C2311yescharacteristic
90C29×C4⋊C8C2312yes—
91C29×#103—21no—
92C29×#103—21no—
93C29×#103—21no—
94C29×#102—21no—
95C29×#102—22no—
96C29×#102—22no—
97C29×#102—22no—
98C29×#102—22no—
99C29×#102—22no—
100C29×#102—22no—
101C29×C22⋊C8—21no—
102C29×C22⋊C8—21no—
103C29×C22⋊C8—22no—
104C29×#97—22no—
105C29×#97—21no—
106C29×#97—21no—
107C29×#97D411yescharacteristic
108C29×#97D411yescharacteristic
109C4×C8×C29C2312yes—
110C24×C29—41no—
111#41×C29—22no—
112#41×C29—41no—
113C2×Q8×C29—21no—
114C2×Q8×C29—21no—
115C2×Q8×C29C2×D411yescharacteristic
116C2×D4×C29—21no—
117C2×D4×C29—22no—
118C2×D4×C29—22no—
119C2×D4×C29—22no—
120C2×D4×C29—42no—
121C2×D4×C29—44no—
122C2×D4×C29—42no—
123C2×D4×C29—41no—
124C2×D4×C29—41no—
125C2×D4×C29—41no—
126C2×D4×C29—82no—
127C2×D4×C29C2×D411yescharacteristic
128C22×C4×C29—21no—
129C22×C4×C29—21no—
130C22×C4×C29—21no—
131C22×C4×C29C2×D411yescharacteristic
132C22×C4×C29C2×D411yescharacteristic
133C22×C4×C29#4111yescharacteristic
134Q16×C29—42no—
135SD16×C29—44no—
136SD16×C29—42no—
137D8×C29—44no—
138M16×C29—42no—
139M16×C29—42no—
140C2×C8×C29—22no—
141C2×C8×C29—22no—
142C2×C8×C29—21no—
143C2×C8×C29—21no—
144C2×C8×C29—44no—
145C2×C8×C29C2×D412yes—
146C2×C8×C29C2×D412yes—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—21no—
149C4⋊C4×C29—21no—
150C4⋊C4×C29—21no—
151C4⋊C4×C29—21no—
152C4⋊C4×C29—21no—
153C4⋊C4×C29—41no—
154C4⋊C4×C29—41no—
155C4⋊C4×C29C2×D411yescharacteristic
156C4⋊C4×C29C2×D411yescharacteristic
157C22⋊C4×C29—21no—
158C22⋊C4×C29—21no—
159C22⋊C4×C29—21no—
160C22⋊C4×C29—41no—
161C42×C29—21no—
162C42×C29—21no—
163C42×C29—21no—
164C42×C29—41no—
165C42×C29C2×D411yescharacteristic
166C42×C29C2×D411yescharacteristic
167C42×C29#4111yescharacteristic
168C42×C29C2411yescharacteristic
169#19316C2911yesmaximal, characteristic, direct product factor, Sylow
170C23×C29—21no—
171C23×C29—42no—
172C23×C29—82no—
173C23×C29—82no—
174C23×C29—82no—
175C23×C29#12111yescharacteristic
176Q8×C29—21no—
177Q8×C29—21no—
178Q8×C29—41no—
179Q8×C29—41no—
180Q8×C29—81no—
181D4×C29—21no—
182D4×C29—42no—
183D4×C29—42no—
184D4×C29—44no—
185D4×C29—42no—
186D4×C29—82no—
187D4×C29—82no—
188D4×C29—82no—
189D4×C29—82no—
190D4×C29AGL(1,ℤ/8)12yes—
191C2×C4×C29—21no—
192C2×C4×C29—22no—
193C2×C4×C29—21no—
194C2×C4×C29—21no—
195C2×C4×C29—21no—
196C2×C4×C29—21no—
197C2×C4×C29—41no—
198C2×C4×C29—42no—
199C2×C4×C29—42no—
200C2×C4×C29—41no—
201C2×C4×C29—41no—
202C2×C4×C29—81no—
203C2×C4×C29#12111yescharacteristic
204C2×C4×C29#12111yescharacteristic
205C2×C4×C29#12111yescharacteristic
206C2×C4×C29C22×D411yescharacteristic
207C2×C4×C29C22×D411yescharacteristic
208C2×C4×C29C2×#4111yescharacteristic
209C8×C29—22no—
210C8×C29—22no—
211C8×C29—42no—
212C8×C29—41no—
213C8×C29—42no—
214C8×C29—41no—
215#3138C2×C2911yescharacteristic, complemented
216#3116C2×C2911yescharacteristic, complemented
217#3038C2×C2911yescharacteristic
218#2970C2×C2911yescharacteristic, complemented
219#1702C2×C2912yescomplemented
220#1698C2×C2912yescomplemented
221#1681C2×C2912yescomplemented
222#1677C2×C2912yescomplemented
223#1569C2×C2911yescharacteristic, complemented
224#1559C2×C2911yescharacteristic, complemented
225#1555C2×C2911yescharacteristic, complemented
226C22×C29—21no—
227C22×C29—21no—
228C22×C29—22no—
229C22×C29—21no—
230C22×C29—41no—
231C22×C29—41no—
232C22×C29—82no—
233C22×C29—82no—
234C22×C29—82no—
235C22×C29—164no—
236C22×C29C2×#12111yescharacteristic
237C4×C29—21no—
238C4×C29—21no—
239C4×C29—21no—
240C4×C29—21no—
241C4×C29—41no—
242C4×C29—41no—
243C4×C29—41no—
244C4×C29—81no—
245C4×C29—81no—
246C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
247C4×C29#57512yes—
248C4×C29#57511yescharacteristic
249C2×AGL(1,ℤ/8)—21no—
250#533C22×C2911yescharacteristic
251C2×#127C22×C2911yescharacteristic
252C4×#41C22×C2911yescharacteristic
253#490—21no—
254#490—21no—
255#486C22×C2912yes—
256#486C22×C2912yes—
257#485—21no—
258#477C22×C2911yescharacteristic, complemented
259#476C22×C2911yescharacteristic, complemented
260#462C22×C2911yescharacteristic, complemented
261#461C22×C2911yescharacteristic, complemented
262#460—21no—
263#460C22×C2912yes—
264#459—21no—
265#459C22×C2912yes—
266#452—21no—
267#446C22×C2912yescomplemented
268#441—21no—
269#440—21no—
270#435—22no—
271C8×D4C22×C2912yescomplemented
272#432—21no—
273#432C22×C2911yescharacteristic
274#432C22×C2911yescharacteristic
275#423C22×C2911yescharacteristic
276#418—22no—
277#418—21no—
278C4×M16C22×C2911yescharacteristic
279C2×#97—21no—
280#335C22×C2912yescomplemented
281#334C22×C2912yescomplemented
282#333C22×C2912yescomplemented
283#332C22×C2912yescomplemented
284#331C22×C2912yes—
285#331C22×C2912yes—
286C2×C29—41no—
287C2×C29—42no—
288C2×C29—162no—
289C2×C29#304011yescharacteristic
290C2×C29#305511yescharacteristic
291C2×C29#306811yescharacteristic
292C2×#41D4×C2911yescharacteristic
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—21no—
296AGL(1,ℤ/8)—44no—
297C2×Q16—21no—
298C2×SD16—22no—
299C2×SD16—21no—
300C2×D8—22no—
301C2×M16—21no—
302C2×M16D4×C2912yes—
303C22×C8—22no—
304C4⋊Q8C23×C2911yescharacteristic
305C4⋊Q8C23×C2911yescharacteristic
306#127—21no—
307#127—21no—
308#127—21no—
309#127C23×C2912yes—
310#125—21no—
311C22⋊Q8—21no—
312C22⋊Q8—21no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8D4×C2911yescharacteristic
316C4×Q8C23×C2911yescharacteristic
317C4×D4—21no—
318C4×D4—21no—
319C4×D4D4×C2911yescharacteristic
320C4×D4C23×C2911yescharacteristic
321#117—21no—
322#117—21no—
323#117D4×C2911yescharacteristic
324C2×C42—21no—
325C2×C42C23×C2911yescharacteristic
326#107—21no—
327#106—21no—
328C4⋊C8—22no—
329C4⋊C8—21no—
330C4⋊C8C23×C2912yes—
331C4⋊C8C23×C2911yescharacteristic
332C4⋊C8C23×C2911yescharacteristic
333C4⋊C8C23×C2912yes—
334#103—21no—
335#103—21no—
336#103—21no—
337#102—21no—
338#102—22no—
339#102—22no—
340#102—22no—
341#102—22no—
342#102—22no—
343#102—22no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C22⋊C8—22no—
347#97—22no—
348#97—21no—
349#97—21no—
350#97D4×C2911yescharacteristic
351#97D4×C2911yescharacteristic
352C4×C8C23×C2912yes—
353C29#1931611yescharacteristic, direct product factor, Sylow
354C24—41no—
355#41—22no—
356#41—41no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8C2×D4×C2911yescharacteristic
360C2×D4—21no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—42no—
365C2×D4—44no—
366C2×D4—42no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—82no—
371C2×D4C2×D4×C2911yescharacteristic
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4C2×D4×C2911yescharacteristic
376C22×C4C2×D4×C2911yescharacteristic
377C22×C4#41×C2911yescharacteristic
378Q16—42no—
379SD16—44no—
380SD16—42no—
381D8—44no—
382M16—42no—
383M16—42no—
384C2×C8—22no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—22no—
388C2×C8—44no—
389C2×C8C2×D4×C2912yes—
390C2×C8C2×D4×C2912yes—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4C2×D4×C2911yescharacteristic
400C4⋊C4C2×D4×C2911yescharacteristic
401C22⋊C4—21no—
402C22⋊C4—21no—
403C22⋊C4—21no—
404C22⋊C4—41no—
405C42—21no—
406C42—21no—
407C42—21no—
408C42—41no—
409C42C2×D4×C2911yescharacteristic
410C42C2×D4×C2911yescharacteristic
411C42#41×C2911yescharacteristic
412C42C24×C2911yescharacteristic
413C23—21no—
414C23—42no—
415C23—82no—
416C23—82no—
417C23—82no—
418C23C29×#12111yescharacteristic
419Q8—21no—
420Q8—21no—
421Q8—41no—
422Q8—41no—
423Q8—81no—
424D4—21no—
425D4—42no—
426D4—42no—
427D4—44no—
428D4—42no—
429D4—82no—
430D4—82no—
431D4—82no—
432D4—82no—
433D4C29×AGL(1,ℤ/8)12yes—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—81no—
446C2×C4C29×#12111yescharacteristic
447C2×C4C29×#12111yescharacteristic
448C2×C4C29×#12111yescharacteristic
449C2×C4C22×D4×C2911yescharacteristic
450C2×C4C22×D4×C2911yescharacteristic
451C2×C4C2×#41×C2911yescharacteristic
452C8—22no—
453C8—22no—
454C8—42no—
455C8—41no—
456C8—42no—
457C8—41no—
458C22—21no—
459C22—21no—
460C22—22no—
461C22—21no—
462C22—41no—
463C22—41no—
464C22—82no—
465C22—82no—
466C22—82no—
467C22—164no—
468C22C2×C29×#12111yescharacteristic
469C4—21no—
470C4—21no—
471C4—21no—
472C4—21no—
473C4—41no—
474C4—41no—
475C4—41no—
476C4—81no—
477C4—81no—
478C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
479C4C29×#57512yes—
480C4C29×#57511yescharacteristic
481C2—41no—
482C2—42no—
483C2—162no—
484C2C29×#304011yescharacteristic
485C2C29×#305511yescharacteristic
486C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3038C2
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×#3138C2semidirect
2. C29×#3116C2semidirect
4. C29×#2970C2semidirect
5. C29×#1702C2semidirect
6. C29×#1698C2semidirect
7. C29×#1681C2semidirect
8. C29×#1677C2semidirect
9. C29×#1569C2semidirect
10. C29×#1559C2semidirect
11. C29×#1555C2semidirect
21. C29×#477C22semidirect
22. C29×#476C22semidirect
23. C29×#462C22semidirect
24. C29×#461C22semidirect
30. C29×#446C22semidirect
34. C8×D4×C29C22semidirect
43. C29×#335C22semidirect
44. C29×#334C22semidirect
45. C29×#333C22semidirect
46. C29×#332C22semidirect
169. #19316C29direct (N × H)
215. #3138C2×C29semidirect
216. #3116C2×C29semidirect
218. #2970C2×C29semidirect
219. #1702C2×C29semidirect
220. #1698C2×C29semidirect
221. #1681C2×C29semidirect
222. #1677C2×C29semidirect
223. #1569C2×C29semidirect
224. #1559C2×C29semidirect
225. #1555C2×C29semidirect
258. #477C22×C29semidirect
259. #476C22×C29semidirect
260. #462C22×C29semidirect
261. #461C22×C29semidirect
267. #446C22×C29semidirect
271. C8×D4C22×C29semidirect
280. #335C22×C29semidirect
281. #334C22×C29semidirect
282. #333C22×C29semidirect
283. #332C22×C29semidirect
353. C29#19316direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31382
C29×#31162
C29×#30382
C29×#29702
C29×#17022
C29×#16982
C29×#16812
C29×#16772
C29×#15692
C29×#15592
C29×#15552
#1931629