Finite Group Databasebeta

← C29×#19339 #20314239

Subgroups — C29×#19339 #20314239

Order 7424.

658 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3254C211yesmaximal, characteristic, complemented
2C29×#3253C211yesmaximal, characteristic
3C29×#3167C211yesmaximal, characteristic, complemented
4C29×#2931C211yesmaximal, characteristic, complemented
5C29×#1691C212yesmaximal, complemented
6C29×#1685C212yesmaximal, complemented
7C29×#1683C212yesmaximal, complemented
8C29×#1681C212yesmaximal, complemented
9C29×#1567C211yesmaximal, characteristic, complemented
10C29×#1561C211yesmaximal, characteristic, complemented
11C29×#1560C211yesmaximal, characteristic, complemented
12C2×C29×#131—21no—
13C29×#533C2211yescharacteristic
14C29×#532C2211yescharacteristic
15C29×#532C2211yescharacteristic
16C29×#498C2211yescharacteristic
17C29×#492C2211yescharacteristic
18C29×#487C2211yescharacteristic
19C29×#486C2211yescharacteristic
20C29×#477—21no—
21C29×#476—21no—
22C29×#476C2212yes—
23C29×#474C2212yes—
24C29×#469—22no—
25C29×#468—22no—
26C29×#465—21no—
27C29×#465—21no—
28C29×#461C2212yes—
29C29×#460—21no—
30C29×#459—21no—
31C29×#459C2212yes—
32C4×SD16×C29—21no—
33C4×SD16×C29—21no—
34C29×#436—21no—
35C29×#436C2212yes—
36C8×D4×C29—21no—
37C8×D4×C29C2212yes—
38C29×#423C2211yescharacteristic
39C29×#423C2211yescharacteristic
40C29×#423C2211yescharacteristic
41C29×#408—21no—
42C2×C4×C8×C29C2211yescharacteristic
43C29×#335C2212yes—
44C29×#335C2212yes—
45C29×#333C2212yes—
46C29×#332C2212yes—
47C29×#332C2212yes—
48C29×#331C2212yes—
49C2×#41×C29—21no—
50C2×#41×C29—21no—
51C2×SD16×C29—22no—
52C2×SD16×C29—21no—
53C2×SD16×C29—21no—
54C2×D8×C29—22no—
55C29×#131—44no—
56C2×M16×C29—21no—
57C2×M16×C29—21no—
58C2×M16×C29—21no—
59C2×M16×C29—22no—
60C22×C8×C29—22no—
61C22×C8×C29D411yescharacteristic
62C22×C8×C29D411yescharacteristic
63C29×C4⋊Q8D411yescharacteristic
64C29×C4⋊Q8C2311yescharacteristic
65C29×C4⋊Q8C2311yescharacteristic
66C29×C4⋊Q8C2311yescharacteristic
67C29×#127D411yescharacteristic
68C29×#127C2311yescharacteristic
69C29×#125—21no—
70C29×#124—21no—
71C29×#124—21no—
72C29×C22⋊Q8—21no—
73C29×C22⋊Q8—21no—
74C29×#121—21no—
75C29×#121—21no—
76C29×#121—21no—
77C29×#121D412yes—
78C4×Q8×C29—21no—
79C4×Q8×C29—21no—
80C4×D4×C29—21no—
81C4×D4×C29—21no—
82C4×D4×C29—21no—
83C4×D4×C29C2312yes—
84C29×#117—21no—
85C2×C42×C29C2311yescharacteristic
86C29×#107—22no—
87C29×#106—21no—
88C29×#106—21no—
89C29×#106—22no—
90C29×C4⋊C8—21no—
91C29×C4⋊C8—21no—
92C29×C4⋊C8—21no—
93C29×C4⋊C8C2312yes—
94C29×C4⋊C8C2312yes—
95C29×C4⋊C8C2312yes—
96C29×#103—21no—
97C29×#103—21no—
98C29×#103—22no—
99C29×#102—22no—
100C29×#102—22no—
101C29×#102—21no—
102C29×#102—21no—
103C29×#102—22no—
104C29×C22⋊C8—22no—
105C29×C22⋊C8—22no—
106C4×C8×C29D411yescharacteristic
107C4×C8×C29D411yescharacteristic
108C4×C8×C29C2311yescharacteristic
109C4×C8×C29C2311yescharacteristic
110#41×C29—42no—
111#41×C29—42no—
112#41×C29—82no—
113C2×Q8×C29—21no—
114C2×Q8×C29—21no—
115C2×Q8×C29—21no—
116C2×Q8×C29—21no—
117C2×D4×C29—22no—
118C2×D4×C29—21no—
119C2×D4×C29—21no—
120C2×D4×C29—21no—
121C2×D4×C29—21no—
122C2×D4×C29—21no—
123C2×D4×C29—41no—
124C2×D4×C29C2×D412yes—
125C22×C4×C29—22no—
126C22×C4×C29—41no—
127C22×C4×C29C2×D411yescharacteristic
128C22×C4×C29C2×D411yescharacteristic
129C22×C4×C29#4111yescharacteristic
130SD16×C29—42no—
131SD16×C29—42no—
132SD16×C29—82no—
133D8×C29—82no—
134M16×C29—42no—
135M16×C29—44no—
136M16×C29—81no—
137M16×C29—81no—
138C2×C8×C29—22no—
139C2×C8×C29—22no—
140C2×C8×C29—22no—
141C2×C8×C29—22no—
142C2×C8×C29—41no—
143C2×C8×C29—44no—
144C2×C8×C29C2×D411yescharacteristic
145C2×C8×C29C2×D411yescharacteristic
146C2×C8×C29C2×D411yescharacteristic
147C2×C8×C29C2×D411yescharacteristic
148C4⋊C4×C29—21no—
149C4⋊C4×C29—21no—
150C4⋊C4×C29—21no—
151C4⋊C4×C29—21no—
152C4⋊C4×C29—21no—
153C4⋊C4×C29—21no—
154C4⋊C4×C29—21no—
155C4⋊C4×C29—41no—
156C4⋊C4×C29—41no—
157C4⋊C4×C29C2×D412yes—
158C22⋊C4×C29—22no—
159C22⋊C4×C29—22no—
160C22⋊C4×C29—41no—
161C22⋊C4×C29—41no—
162C22⋊C4×C29—41no—
163C42×C29—41no—
164C42×C29C2×D411yescharacteristic
165C42×C29C2×D411yescharacteristic
166C42×C29#4111yescharacteristic
167C42×C29C2411yescharacteristic
168#19339C2911yesmaximal, characteristic, direct product factor, Sylow
169C23×C29—22no—
170C23×C29—41no—
171C23×C29#12111yescharacteristic
172Q8×C29—42no—
173Q8×C29—41no—
174Q8×C29—41no—
175Q8×C29—41no—
176Q8×C29—41no—
177Q8×C29—81no—
178D4×C29—22no—
179D4×C29—22no—
180D4×C29—42no—
181D4×C29—44no—
182D4×C29—41no—
183D4×C29—41no—
184D4×C29—41no—
185D4×C29—41no—
186D4×C29—42no—
187D4×C29—81no—
188D4×C29—82no—
189C2×C4×C29—21no—
190C2×C4×C29—21no—
191C2×C4×C29—21no—
192C2×C4×C29—21no—
193C2×C4×C29—22no—
194C2×C4×C29—22no—
195C2×C4×C29—42no—
196C2×C4×C29—42no—
197C2×C4×C29—41no—
198C2×C4×C29—41no—
199C2×C4×C29—41no—
200C2×C4×C29—82no—
201C2×C4×C29#12111yescharacteristic
202C2×C4×C29#12111yescharacteristic
203C2×C4×C29#12111yescharacteristic
204C2×C4×C29C22×D411yescharacteristic
205C2×C4×C29C22×D411yescharacteristic
206C2×C4×C29C2×#4111yescharacteristic
207C8×C29—21no—
208C8×C29—21no—
209C8×C29—21no—
210C8×C29—42no—
211C8×C29—42no—
212C8×C29—42no—
213C8×C29AGL(1,ℤ/8)12yes—
214#3254C2×C2911yescharacteristic, complemented
215#3253C2×C2911yescharacteristic
216#3167C2×C2911yescharacteristic, complemented
217#2931C2×C2911yescharacteristic, complemented
218#1691C2×C2912yescomplemented
219#1685C2×C2912yescomplemented
220#1683C2×C2912yescomplemented
221#1681C2×C2912yescomplemented
222#1567C2×C2911yescharacteristic, complemented
223#1561C2×C2911yescharacteristic, complemented
224#1560C2×C2911yescharacteristic, complemented
225C22×C29—21no—
226C22×C29—21no—
227C22×C29—21no—
228C22×C29—42no—
229C22×C29—42no—
230C22×C29—42no—
231C22×C29—81no—
232C22×C29—81no—
233C22×C29—81no—
234C22×C29C2×#12111yescharacteristic
235C4×C29—21no—
236C4×C29—21no—
237C4×C29—21no—
238C4×C29—42no—
239C4×C29—81no—
240C4×C29—81no—
241C4×C29—81no—
242C4×C29#47112yes—
243C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
244C4×C29#57511yescharacteristic
245C4×C29#57611yescharacteristic
246C4×C29#57811yescharacteristic
247C2×#131—21no—
248#533C22×C2911yescharacteristic
249#532C22×C2911yescharacteristic
250#532C22×C2911yescharacteristic
251#498C22×C2911yescharacteristic
252#492C22×C2911yescharacteristic
253#487C22×C2911yescharacteristic
254#486C22×C2911yescharacteristic
255#477—21no—
256#476—21no—
257#476C22×C2912yes—
258#474C22×C2912yes—
259#469—22no—
260#468—22no—
261#465—21no—
262#465—21no—
263#461C22×C2912yes—
264#460—21no—
265#459—21no—
266#459C22×C2912yes—
267C4×SD16—21no—
268C4×SD16—21no—
269#436—21no—
270#436C22×C2912yes—
271C8×D4—21no—
272C8×D4C22×C2912yes—
273#423C22×C2911yescharacteristic
274#423C22×C2911yescharacteristic
275#423C22×C2911yescharacteristic
276#408—21no—
277C2×C4×C8C22×C2911yescharacteristic
278#335C22×C2912yes—
279#335C22×C2912yes—
280#333C22×C2912yes—
281#332C22×C2912yes—
282#332C22×C2912yes—
283#331C22×C2912yes—
284C2×C29—41no—
285C2×C29—82no—
286C2×C29—161no—
287C2×C29#303611yescharacteristic
288C2×C29#306111yescharacteristic
289C2×C29C2×#47111yescharacteristic
290C2×#41—21no—
291C2×#41—21no—
292C2×SD16—22no—
293C2×SD16—21no—
294C2×SD16—21no—
295C2×D8—22no—
296#131—44no—
297C2×M16—21no—
298C2×M16—21no—
299C2×M16—21no—
300C2×M16—22no—
301C22×C8—22no—
302C22×C8D4×C2911yescharacteristic
303C22×C8D4×C2911yescharacteristic
304C4⋊Q8D4×C2911yescharacteristic
305C4⋊Q8C23×C2911yescharacteristic
306C4⋊Q8C23×C2911yescharacteristic
307C4⋊Q8C23×C2911yescharacteristic
308#127D4×C2911yescharacteristic
309#127C23×C2911yescharacteristic
310#125—21no—
311#124—21no—
312#124—21no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315#121—21no—
316#121—21no—
317#121—21no—
318#121D4×C2912yes—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4C23×C2912yes—
325#117—21no—
326C2×C42C23×C2911yescharacteristic
327#107—22no—
328#106—21no—
329#106—21no—
330#106—22no—
331C4⋊C8—21no—
332C4⋊C8—21no—
333C4⋊C8—21no—
334C4⋊C8C23×C2912yes—
335C4⋊C8C23×C2912yes—
336C4⋊C8C23×C2912yes—
337#103—21no—
338#103—21no—
339#103—22no—
340#102—22no—
341#102—22no—
342#102—21no—
343#102—21no—
344#102—22no—
345C22⋊C8—22no—
346C22⋊C8—22no—
347C4×C8D4×C2911yescharacteristic
348C4×C8D4×C2911yescharacteristic
349C4×C8C23×C2911yescharacteristic
350C4×C8C23×C2911yescharacteristic
351C29#1933911yescharacteristic, direct product factor, Sylow
352#41—42no—
353#41—42no—
354#41—82no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×D4—22no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—41no—
366C2×D4C2×D4×C2912yes—
367C22×C4—22no—
368C22×C4—41no—
369C22×C4C2×D4×C2911yescharacteristic
370C22×C4C2×D4×C2911yescharacteristic
371C22×C4#41×C2911yescharacteristic
372SD16—42no—
373SD16—42no—
374SD16—82no—
375D8—82no—
376M16—42no—
377M16—44no—
378M16—81no—
379M16—81no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—41no—
385C2×C8—44no—
386C2×C8C2×D4×C2911yescharacteristic
387C2×C8C2×D4×C2911yescharacteristic
388C2×C8C2×D4×C2911yescharacteristic
389C2×C8C2×D4×C2911yescharacteristic
390C4⋊C4—21no—
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×C2912yes—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C42—41no—
406C42C2×D4×C2911yescharacteristic
407C42C2×D4×C2911yescharacteristic
408C42#41×C2911yescharacteristic
409C42C24×C2911yescharacteristic
410C23—22no—
411C23—41no—
412C23C29×#12111yescharacteristic
413Q8—42no—
414Q8—41no—
415Q8—41no—
416Q8—41no—
417Q8—41no—
418Q8—81no—
419D4—22no—
420D4—22no—
421D4—42no—
422D4—44no—
423D4—42no—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—41no—
428D4—81no—
429D4—82no—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—82no—
442C2×C4C29×#12111yescharacteristic
443C2×C4C29×#12111yescharacteristic
444C2×C4C29×#12111yescharacteristic
445C2×C4C22×D4×C2911yescharacteristic
446C2×C4C22×D4×C2911yescharacteristic
447C2×C4C2×#41×C2911yescharacteristic
448C8—21no—
449C8—21no—
450C8—21no—
451C8—42no—
452C8—42no—
453C8—42no—
454C8C29×AGL(1,ℤ/8)12yes—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22C2×C29×#12111yescharacteristic
465C4—21no—
466C4—21no—
467C4—21no—
468C4—42no—
469C4—81no—
470C4—81no—
471C4—81no—
472C4C29×#47112yes—
473C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
474C4C29×#57511yescharacteristic
475C4C29×#57611yescharacteristic
476C4C29×#57811yescharacteristic
477C2—41no—
478C2—82no—
479C2—161no—
480C2C29×#303611yescharacteristic
481C2C29×#306111yescharacteristic
482C2C2×C29×#47111yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3253C2
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×#3254C2semidirect
3. C29×#3167C2semidirect
4. C29×#2931C2semidirect
5. C29×#1691C2semidirect
6. C29×#1685C2semidirect
7. C29×#1683C2semidirect
8. C29×#1681C2semidirect
9. C29×#1567C2semidirect
10. C29×#1561C2semidirect
11. C29×#1560C2semidirect
168. #19339C29direct (N × H)
214. #3254C2×C29semidirect
216. #3167C2×C29semidirect
217. #2931C2×C29semidirect
218. #1691C2×C29semidirect
219. #1685C2×C29semidirect
220. #1683C2×C29semidirect
221. #1681C2×C29semidirect
222. #1567C2×C29semidirect
223. #1561C2×C29semidirect
224. #1560C2×C29semidirect
351. C29#19339direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32542
C29×#32532
C29×#31672
C29×#29312
C29×#16912
C29×#16852
C29×#16832
C29×#16812
C29×#15672
C29×#15612
C29×#15602
#1933929