Finite Group Databasebeta

← C29×#19463 #20314363

Subgroups — C29×#19463 #20314363

Order 7424.

626 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3229C211yesmaximal, characteristic, complemented
2C29×#3110C211yesmaximal, characteristic
3C2×C29×#476C211yesmaximal, characteristic
4C29×#2974C211yesmaximal, characteristic
5C29×#1703C212yesmaximal, complemented
6C29×#1691C212yesmaximal, complemented
7C29×#1683C212yesmaximal, complemented
8C29×#1671C212yesmaximal, complemented
9C29×#1573C211yesmaximal, characteristic, complemented
10C29×#1558C211yesmaximal, characteristic, complemented
11C29×#1552C211yesmaximal, characteristic, complemented
12C29×#533C2211yescharacteristic
13C2×C29×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C29C2211yescharacteristic
15C29×#498C2212yescomplemented
16C29×#487C2212yescomplemented
17C29×#484—21no—
18C29×#483—21no—
19C29×#483—21no—
20C29×#476—21no—
21C29×#476—21no—
22C29×#476C2212yes—
23C29×#476C2212yes—
24C29×#475—22no—
25C29×#474C2211yescharacteristic
26C29×#474C2211yescharacteristic
27C29×#461C2211yescharacteristic
28C29×#461C2211yescharacteristic
29C29×#450—21no—
30C29×#440—21no—
31C29×#440—21no—
32C29×#436C2212yes—
33C29×#435—22no—
34C8×D4×C29C2212yes—
35C29×#432C2211yescharacteristic
36C29×#432C2211yescharacteristic
37C29×#431C2211yescharacteristic
38C2×C29×#106—21no—
39C2×C29×C4⋊C8C2211yescharacteristic
40C2×C29×#102—21no—
41C29×#407—21no—
42C2×C29×C22⋊C8—21no—
43C29×#335C2212yescomplemented
44C29×#334C2212yescomplemented
45C29×#333C2212yescomplemented
46C29×#333C2212yescomplemented
47C29×#332C2212yescomplemented
48C29×#332C2212yescomplemented
49C22×Q8×C29—21no—
50C22×D4×C29D411yescharacteristic
51C23×C4×C29—21no—
52C2×SD16×C29—21no—
53C2×SD16×C29—21no—
54C2×M16×C29—22no—
55C22×C8×C29—21no—
56C22×C8×C29—22no—
57C29×C4⋊Q8—21no—
58C29×C4⋊Q8—21no—
59C29×C4⋊Q8—21no—
60C29×C4⋊Q8C2311yescharacteristic
61C29×C4⋊Q8C2311yescharacteristic
62C29×C4⋊Q8C2312yes—
63C29×#125—21no—
64C29×C22⋊Q8—21no—
65C29×C22⋊Q8—21no—
66C4×Q8×C29—21no—
67C4×Q8×C29—21no—
68C4×D4×C29—21no—
69C4×D4×C29—21no—
70C4×D4×C29D411yescharacteristic
71C4×D4×C29D411yescharacteristic
72C4×D4×C29C2311yescharacteristic
73C4×D4×C29C2311yescharacteristic
74C29×#117—21no—
75C2×C4⋊C4×C29—21no—
76C2×C4⋊C4×C29—21no—
77C2×C4⋊C4×C29D411yescharacteristic
78C2×C22⋊C4×C29—21no—
79C2×C42×C29C2311yescharacteristic
80C29×#107—21no—
81C29×#107—21no—
82C29×#106—22no—
83C29×#106—22no—
84C29×#106—22no—
85C29×#106—22no—
86C29×C4⋊C8—21no—
87C29×C4⋊C8D412yes—
88C29×C4⋊C8C2312yes—
89C29×C4⋊C8C2311yescharacteristic
90C29×C4⋊C8C2311yescharacteristic
91C29×C4⋊C8C2312yes—
92C29×#103—22no—
93C29×#103—22no—
94C29×#103—21no—
95C29×#103—21no—
96C29×#102—21no—
97C29×#102—21no—
98C29×#102—22no—
99C29×#102—22no—
100C29×C22⋊C8—21no—
101C29×C22⋊C8—21no—
102C29×C22⋊C8—22no—
103C29×C22⋊C8—22no—
104C29×C22⋊C8D411yescharacteristic
105C29×C22⋊C8D411yescharacteristic
106C29×#97—21no—
107C29×#97—21no—
108C4×C8×C29C2312yes—
109C24×C29—21no—
110C2×Q8×C29—21no—
111C2×Q8×C29—21no—
112C2×Q8×C29—22no—
113C2×Q8×C29—41no—
114C2×Q8×C29—82no—
115C2×D4×C29—22no—
116C2×D4×C29—21no—
117C2×D4×C29—41no—
118C2×D4×C29C2×D411yescharacteristic
119C2×D4×C29C2×D411yescharacteristic
120C22×C4×C29—21no—
121C22×C4×C29—21no—
122C22×C4×C29—21no—
123C22×C4×C29—21no—
124C22×C4×C29—21no—
125C22×C4×C29—41no—
126C22×C4×C29—82no—
127C22×C4×C29C2×D411yescharacteristic
128C22×C4×C29C2×D411yescharacteristic
129C22×C4×C29#4111yescharacteristic
130SD16×C29—42no—
131SD16×C29—42no—
132M16×C29—82no—
133C2×C8×C29—22no—
134C2×C8×C29—22no—
135C2×C8×C29—21no—
136C2×C8×C29—21no—
137C2×C8×C29—42no—
138C2×C8×C29—82no—
139C2×C8×C29C2×D412yes—
140C2×C8×C29C2×D412yes—
141C4⋊C4×C29—21no—
142C4⋊C4×C29—22no—
143C4⋊C4×C29—22no—
144C4⋊C4×C29—21no—
145C4⋊C4×C29—21no—
146C4⋊C4×C29—21no—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—41no—
149C4⋊C4×C29—41no—
150C4⋊C4×C29—41no—
151C4⋊C4×C29—41no—
152C4⋊C4×C29C2×D411yescharacteristic
153C4⋊C4×C29C2×D411yescharacteristic
154C22⋊C4×C29—21no—
155C22⋊C4×C29—21no—
156C22⋊C4×C29—21no—
157C22⋊C4×C29—21no—
158C22⋊C4×C29—41no—
159C42×C29—41no—
160C42×C29C2×D411yescharacteristic
161C42×C29C2×D411yescharacteristic
162C42×C29#4111yescharacteristic
163C42×C29C2411yescharacteristic
164#19463C2911yesmaximal, characteristic, direct product factor, Sylow
165C23×C29—21no—
166C23×C29—21no—
167C23×C29—42no—
168C23×C29—42no—
169C23×C29—81no—
170C23×C29#12111yescharacteristic
171Q8×C29—41no—
172Q8×C29—41no—
173Q8×C29—42no—
174Q8×C29—82no—
175Q8×C29—82no—
176D4×C29—21no—
177D4×C29—21no—
178D4×C29—21no—
179D4×C29—42no—
180D4×C29#13712yes—
181C2×C4×C29—22no—
182C2×C4×C29—21no—
183C2×C4×C29—21no—
184C2×C4×C29—22no—
185C2×C4×C29—21no—
186C2×C4×C29—21no—
187C2×C4×C29—42no—
188C2×C4×C29—42no—
189C2×C4×C29—41no—
190C2×C4×C29—41no—
191C2×C4×C29—42no—
192C2×C4×C29—81no—
193C2×C4×C29—81no—
194C2×C4×C29—81no—
195C2×C4×C29—82no—
196C2×C4×C29#12111yescharacteristic
197C2×C4×C29#12111yescharacteristic
198C2×C4×C29#12111yescharacteristic
199C2×C4×C29C22×D411yescharacteristic
200C2×C4×C29C22×D411yescharacteristic
201C2×C4×C29C2×#4111yescharacteristic
202C8×C29—22no—
203C8×C29—22no—
204C8×C29—41no—
205C8×C29—42no—
206C8×C29—41no—
207C8×C29—42no—
208#3229C2×C2911yescharacteristic, complemented
209#3110C2×C2911yescharacteristic
210C2×#476C2×C2911yescharacteristic
211#2974C2×C2911yescharacteristic
212#1703C2×C2912yescomplemented
213#1691C2×C2912yescomplemented
214#1683C2×C2912yescomplemented
215#1671C2×C2912yescomplemented
216#1573C2×C2911yescharacteristic, complemented
217#1558C2×C2911yescharacteristic, complemented
218#1552C2×C2911yescharacteristic, complemented
219C22×C29—21no—
220C22×C29—21no—
221C22×C29—22no—
222C22×C29—41no—
223C22×C29—41no—
224C22×C29—41no—
225C22×C29—41no—
226C22×C29—41no—
227C22×C29—84no—
228C22×C29#47112yes—
229C22×C29C2×#12111yescharacteristic
230C4×C29—21no—
231C4×C29—21no—
232C4×C29—21no—
233C4×C29—21no—
234C4×C29—41no—
235C4×C29—41no—
236C4×C29—81no—
237C4×C29—81no—
238C4×C29—82no—
239C4×C29C2×#13711yescharacteristic
240C4×C29#57511yescharacteristic
241C4×C29#57712yes—
242#533C22×C2911yescharacteristic
243C2×C4⋊Q8C22×C2911yescharacteristic
244C2×C4×D4C22×C2911yescharacteristic
245#498C22×C2912yescomplemented
246#487C22×C2912yescomplemented
247#484—21no—
248#483—21no—
249#483—21no—
250#476—21no—
251#476—21no—
252#476C22×C2912yes—
253#476C22×C2912yes—
254#475—22no—
255#474C22×C2911yescharacteristic
256#474C22×C2911yescharacteristic
257#461C22×C2911yescharacteristic
258#461C22×C2911yescharacteristic
259#450—21no—
260#440—21no—
261#440—21no—
262#436C22×C2912yes—
263#435—22no—
264C8×D4C22×C2912yes—
265#432C22×C2911yescharacteristic
266#432C22×C2911yescharacteristic
267#431C22×C2911yescharacteristic
268C2×#106—21no—
269C2×C4⋊C8C22×C2911yescharacteristic
270C2×#102—21no—
271#407—21no—
272C2×C22⋊C8—21no—
273#335C22×C2912yescomplemented
274#334C22×C2912yescomplemented
275#333C22×C2912yescomplemented
276#333C22×C2912yescomplemented
277#332C22×C2912yescomplemented
278#332C22×C2912yescomplemented
279C2×C29—22no—
280C2×C29—42no—
281C2×C29—81no—
282C2×C29#304211yescharacteristic
283C2×C29#305611yescharacteristic
284C2×C29C2×#47111yescharacteristic
285C22×Q8—21no—
286C22×D4D4×C2911yescharacteristic
287C23×C4—21no—
288C2×SD16—21no—
289C2×SD16—21no—
290C2×M16—22no—
291C22×C8—21no—
292C22×C8—22no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8C23×C2912yes—
297C4⋊Q8C23×C2911yescharacteristic
298C4⋊Q8C23×C2911yescharacteristic
299#125—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4D4×C2911yescharacteristic
307C4×D4D4×C2911yescharacteristic
308C4×D4C23×C2911yescharacteristic
309C4×D4C23×C2911yescharacteristic
310#117—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4D4×C2911yescharacteristic
314C2×C22⋊C4—21no—
315C2×C42C23×C2911yescharacteristic
316#107—21no—
317#107—21no—
318#106—22no—
319#106—22no—
320#106—22no—
321#106—22no—
322C4⋊C8—21no—
323C4⋊C8D4×C2912yes—
324C4⋊C8C23×C2912yes—
325C4⋊C8C23×C2912yes—
326C4⋊C8C23×C2911yescharacteristic
327C4⋊C8C23×C2911yescharacteristic
328#103—22no—
329#103—22no—
330#103—21no—
331#103—21no—
332#102—22no—
333#102—22no—
334#102—21no—
335#102—21no—
336C22⋊C8—21no—
337C22⋊C8—21no—
338C22⋊C8—22no—
339C22⋊C8—22no—
340C22⋊C8D4×C2911yescharacteristic
341C22⋊C8D4×C2911yescharacteristic
342#97—21no—
343#97—21no—
344C4×C8C23×C2912yes—
345C29#1946311yescharacteristic, direct product factor, Sylow
346C24—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—22no—
350C2×Q8—41no—
351C2×Q8—82no—
352C2×D4—22no—
353C2×D4—21no—
354C2×D4—41no—
355C2×D4C2×D4×C2911yescharacteristic
356C2×D4C2×D4×C2911yescharacteristic
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—41no—
363C22×C4—82no—
364C22×C4C2×D4×C2911yescharacteristic
365C22×C4C2×D4×C2911yescharacteristic
366C22×C4#41×C2911yescharacteristic
367SD16—42no—
368SD16—42no—
369M16—82no—
370C2×C8—22no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—22no—
374C2×C8—42no—
375C2×C8—82no—
376C2×C8C2×D4×C2912yes—
377C2×C8C2×D4×C2912yes—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4C2×D4×C2911yescharacteristic
390C4⋊C4C2×D4×C2911yescharacteristic
391C22⋊C4—21no—
392C22⋊C4—21no—
393C22⋊C4—21no—
394C22⋊C4—21no—
395C22⋊C4—41no—
396C42—41no—
397C42C2×D4×C2911yescharacteristic
398C42C2×D4×C2911yescharacteristic
399C42#41×C2911yescharacteristic
400C42C24×C2911yescharacteristic
401C23—21no—
402C23—21no—
403C23—42no—
404C23—42no—
405C23—81no—
406C23C29×#12111yescharacteristic
407Q8—41no—
408Q8—41no—
409Q8—42no—
410Q8—82no—
411Q8—82no—
412D4—21no—
413D4—21no—
414D4—21no—
415D4—42no—
416D4C29×#13712yes—
417C2×C4—22no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4—82no—
432C2×C4C29×#12111yescharacteristic
433C2×C4C29×#12111yescharacteristic
434C2×C4C29×#12111yescharacteristic
435C2×C4C22×D4×C2911yescharacteristic
436C2×C4C22×D4×C2911yescharacteristic
437C2×C4C2×#41×C2911yescharacteristic
438C8—22no—
439C8—22no—
440C8—41no—
441C8—42no—
442C8—41no—
443C8—42no—
444C22—21no—
445C22—21no—
446C22—22no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—84no—
453C22C29×#47112yes—
454C22C2×C29×#12111yescharacteristic
455C4—21no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—41no—
460C4—41no—
461C4—81no—
462C4—81no—
463C4—82no—
464C4C2×C29×#13711yescharacteristic
465C4C29×#57511yescharacteristic
466C4C29×#57712yes—
467C2—22no—
468C2—42no—
469C2—81no—
470C2C29×#304211yescharacteristic
471C2C29×#305611yescharacteristic
472C2C2×C29×#47111yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC22×D4×C29D4
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×#3229C2semidirect
5. C29×#1703C2semidirect
6. C29×#1691C2semidirect
7. C29×#1683C2semidirect
8. C29×#1671C2semidirect
9. C29×#1573C2semidirect
10. C29×#1558C2semidirect
11. C29×#1552C2semidirect
15. C29×#498C22semidirect
16. C29×#487C22semidirect
43. C29×#335C22semidirect
44. C29×#334C22semidirect
45. C29×#333C22semidirect
46. C29×#333C22semidirect
47. C29×#332C22semidirect
48. C29×#332C22semidirect
164. #19463C29direct (N × H)
208. #3229C2×C29semidirect
212. #1703C2×C29semidirect
213. #1691C2×C29semidirect
214. #1683C2×C29semidirect
215. #1671C2×C29semidirect
216. #1573C2×C29semidirect
217. #1558C2×C29semidirect
218. #1552C2×C29semidirect
245. #498C22×C29semidirect
246. #487C22×C29semidirect
273. #335C22×C29semidirect
274. #334C22×C29semidirect
275. #333C22×C29semidirect
276. #333C22×C29semidirect
277. #332C22×C29semidirect
278. #332C22×C29semidirect
345. C29#19463direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32292
C29×#31102
C2×C29×#4762
C29×#29742
C29×#17032
C29×#16912
C29×#16832
C29×#16712
C29×#15732
C29×#15582
C29×#15522
#1946329