Finite Group Databasebeta

← C29×#19465 #20314365

Subgroups — C29×#19465 #20314365

Order 7424.

648 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3226C211yesmaximal, characteristic, complemented
2C29×#3109C211yesmaximal, characteristic
3C2×C29×#476C211yesmaximal, characteristic, complemented
4C29×#2974C211yesmaximal, characteristic, complemented
5C29×#1697C212yesmaximal, complemented
6C29×#1695C212yesmaximal, complemented
7C29×#1677C212yesmaximal, complemented
8C29×#1675C212yesmaximal, complemented
9C29×#1573C211yesmaximal, characteristic, complemented
10C29×#1558C211yesmaximal, characteristic, complemented
11C29×#1551C211yesmaximal, characteristic, complemented
12C29×#532C2211yescharacteristic
13C2×C29×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C29C2211yescharacteristic
15C29×#500C2212yescomplemented
16C29×#486C2212yescomplemented
17C29×#481—21no—
18C29×#480—21no—
19C29×#480—21no—
20C29×#476—21no—
21C29×#476—21no—
22C29×#476C2211yescharacteristic
23C29×#476C2212yes—
24C29×#476C2211yescharacteristic
25C29×#476C2212yes—
26C29×#474—22no—
27C29×#459C2211yescharacteristic
28C29×#459C2211yescharacteristic
29C29×#447—21no—
30C29×#442—21no—
31C29×#442—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×#333C2212yescomplemented
48C29×#331C2212yescomplemented
49C2×#41×C29—21no—
50C22×Q8×C29—21no—
51C22×D4×C29D411yescharacteristic
52C23×C4×C29—21no—
53C2×D8×C29—21no—
54C2×D8×C29—21no—
55C2×M16×C29—22no—
56C22×C8×C29—21no—
57C22×C8×C29—22no—
58C29×C4⋊Q8—21no—
59C29×C4⋊Q8—21no—
60C29×C4⋊Q8—21no—
61C29×C4⋊Q8C2312yes—
62C29×C4⋊Q8C2311yescharacteristic
63C29×#127C2311yescharacteristic
64C29×#124—21no—
65C29×#121—21no—
66C29×#121—21no—
67C4×D4×C29—21no—
68C4×D4×C29—21no—
69C4×D4×C29—21no—
70C4×D4×C29—21no—
71C4×D4×C29D411yescharacteristic
72C4×D4×C29D411yescharacteristic
73C4×D4×C29C2311yescharacteristic
74C4×D4×C29C2311yescharacteristic
75C2×C4⋊C4×C29—21no—
76C2×C4⋊C4×C29—21no—
77C2×C4⋊C4×C29D411yescharacteristic
78C2×C22⋊C4×C29—21no—
79C2×C42×C29C2311yescharacteristic
80C29×#107—22no—
81C29×#107—22no—
82C29×#106—22no—
83C29×#106—22no—
84C29×#106—21no—
85C29×#106—21no—
86C29×C4⋊C8—21no—
87C29×C4⋊C8D412yes—
88C29×C4⋊C8C2312yes—
89C29×C4⋊C8C2311yescharacteristic
90C29×C4⋊C8C2311yescharacteristic
91C29×C4⋊C8C2312yes—
92C29×#102—21no—
93C29×#102—21no—
94C29×#102—22no—
95C29×#102—22no—
96C29×#102—22no—
97C29×#102—22no—
98C29×#102—21no—
99C29×#102—21no—
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—
110#41×C29—82no—
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—21no—
118C2×D4×C29—21no—
119C2×D4×C29—21no—
120C2×D4×C29—41no—
121C2×D4×C29—41no—
122C2×D4×C29C2×D411yescharacteristic
123C2×D4×C29C2×D411yescharacteristic
124C22×C4×C29—21no—
125C22×C4×C29—21no—
126C22×C4×C29—21no—
127C22×C4×C29—21no—
128C22×C4×C29—21no—
129C22×C4×C29—41no—
130C22×C4×C29—41no—
131C22×C4×C29—82no—
132C22×C4×C29C2×D411yescharacteristic
133C22×C4×C29C2×D411yescharacteristic
134C22×C4×C29#4111yescharacteristic
135D8×C29—42no—
136D8×C29—42no—
137M16×C29—82no—
138C2×C8×C29—22no—
139C2×C8×C29—22no—
140C2×C8×C29—21no—
141C2×C8×C29—21no—
142C2×C8×C29—42no—
143C2×C8×C29—82no—
144C2×C8×C29C2×D412yes—
145C2×C8×C29C2×D412yes—
146C4⋊C4×C29—21no—
147C4⋊C4×C29—22no—
148C4⋊C4×C29—22no—
149C4⋊C4×C29—21no—
150C4⋊C4×C29—21no—
151C4⋊C4×C29—41no—
152C4⋊C4×C29—41no—
153C4⋊C4×C29C2×D411yescharacteristic
154C4⋊C4×C29C2×D411yescharacteristic
155C22⋊C4×C29—21no—
156C22⋊C4×C29—21no—
157C22⋊C4×C29—21no—
158C22⋊C4×C29—21no—
159C22⋊C4×C29—41no—
160C22⋊C4×C29—41no—
161C42×C29C2×D411yescharacteristic
162C42×C29C2×D411yescharacteristic
163C42×C29#4111yescharacteristic
164C42×C29C2411yescharacteristic
165#19465C2911yesmaximal, characteristic, direct product factor, Sylow
166C23×C29—21no—
167C23×C29—21no—
168C23×C29—42no—
169C23×C29—42no—
170C23×C29—41no—
171C23×C29—81no—
172C23×C29#12111yescharacteristic
173Q8×C29—82no—
174Q8×C29—81no—
175Q8×C29—82no—
176D4×C29—21no—
177D4×C29—21no—
178D4×C29—21no—
179D4×C29—42no—
180D4×C29—41no—
181D4×C29—41no—
182D4×C29—42no—
183D4×C29—81no—
184D4×C29—82no—
185D4×C29#13712yes—
186C2×C4×C29—22no—
187C2×C4×C29—21no—
188C2×C4×C29—21no—
189C2×C4×C29—22no—
190C2×C4×C29—21no—
191C2×C4×C29—21no—
192C2×C4×C29—42no—
193C2×C4×C29—42no—
194C2×C4×C29—41no—
195C2×C4×C29—42no—
196C2×C4×C29—81no—
197C2×C4×C29—81no—
198C2×C4×C29—82no—
199C2×C4×C29—81no—
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—22no—
208C8×C29—22no—
209C8×C29—41no—
210C8×C29—42no—
211C8×C29—41no—
212C8×C29—42no—
213#3226C2×C2911yescharacteristic, complemented
214#3109C2×C2911yescharacteristic
215C2×#476C2×C2911yescharacteristic, complemented
216#2974C2×C2911yescharacteristic, complemented
217#1697C2×C2912yescomplemented
218#1695C2×C2912yescomplemented
219#1677C2×C2912yescomplemented
220#1675C2×C2912yescomplemented
221#1573C2×C2911yescharacteristic, complemented
222#1558C2×C2911yescharacteristic, complemented
223#1551C2×C2911yescharacteristic, complemented
224C22×C29—21no—
225C22×C29—21no—
226C22×C29—22no—
227C22×C29—41no—
228C22×C29—41no—
229C22×C29—41no—
230C22×C29—41no—
231C22×C29—41no—
232C22×C29—84no—
233C22×C29—81no—
234C22×C29—81no—
235C22×C29—81no—
236C22×C29#47212yes—
237C22×C29C2×#12111yescharacteristic
238C4×C29—21no—
239C4×C29—21no—
240C4×C29—21no—
241C4×C29—21no—
242C4×C29—41no—
243C4×C29—41no—
244C4×C29—81no—
245C4×C29—82no—
246C4×C29C2×#13711yescharacteristic
247C4×C29#57511yescharacteristic
248C4×C29#57712yes—
249#532C22×C2911yescharacteristic
250C2×C4⋊Q8C22×C2911yescharacteristic
251C2×C4×D4C22×C2911yescharacteristic
252#500C22×C2912yescomplemented
253#486C22×C2912yescomplemented
254#481—21no—
255#480—21no—
256#480—21no—
257#476—21no—
258#476—21no—
259#476C22×C2911yescharacteristic
260#476C22×C2911yescharacteristic
261#476C22×C2912yes—
262#476C22×C2912yes—
263#474—22no—
264#459C22×C2911yescharacteristic
265#459C22×C2911yescharacteristic
266#447—21no—
267#442—21no—
268#442—21no—
269#436C22×C2912yes—
270#435—22no—
271C8×D4C22×C2912yes—
272#432C22×C2911yescharacteristic
273#432C22×C2911yescharacteristic
274#431C22×C2911yescharacteristic
275C2×#106—21no—
276C2×C4⋊C8C22×C2911yescharacteristic
277C2×#102—21no—
278#407—21no—
279C2×C22⋊C8—21no—
280#335C22×C2912yescomplemented
281#334C22×C2912yescomplemented
282#333C22×C2912yescomplemented
283#333C22×C2912yescomplemented
284#333C22×C2912yescomplemented
285#331C22×C2912yescomplemented
286C2×C29—22no—
287C2×C29—42no—
288C2×C29—81no—
289C2×C29—161no—
290C2×C29#304211yescharacteristic
291C2×C29#305611yescharacteristic
292C2×C29C2×#47211yescharacteristic
293C2×#41—21no—
294C22×Q8—21no—
295C22×D4D4×C2911yescharacteristic
296C23×C4—21no—
297C2×D8—21no—
298C2×D8—21no—
299C2×M16—22no—
300C22×C8—21no—
301C22×C8—22no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8C23×C2912yes—
306C4⋊Q8C23×C2911yescharacteristic
307#127C23×C2911yescharacteristic
308#124—21no—
309#121—21no—
310#121—21no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4D4×C2911yescharacteristic
316C4×D4D4×C2911yescharacteristic
317C4×D4C23×C2911yescharacteristic
318C4×D4C23×C2911yescharacteristic
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4D4×C2911yescharacteristic
322C2×C22⋊C4—21no—
323C2×C42C23×C2911yescharacteristic
324#107—22no—
325#107—22no—
326#106—22no—
327#106—22no—
328#106—21no—
329#106—21no—
330C4⋊C8—21no—
331C4⋊C8D4×C2912yes—
332C4⋊C8C23×C2912yes—
333C4⋊C8C23×C2912yes—
334C4⋊C8C23×C2911yescharacteristic
335C4⋊C8C23×C2911yescharacteristic
336#102—22no—
337#102—22no—
338#102—21no—
339#102—21no—
340#102—22no—
341#102—22no—
342#102—21no—
343#102—21no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C22⋊C8—22no—
347C22⋊C8—22no—
348C22⋊C8D4×C2911yescharacteristic
349C22⋊C8D4×C2911yescharacteristic
350#97—21no—
351#97—21no—
352C4×C8C23×C2912yes—
353C29#1946511yescharacteristic, direct product factor, Sylow
354C24—21no—
355#41—82no—
356C2×Q8—21no—
357C2×Q8—22no—
358C2×Q8—41no—
359C2×Q8—82no—
360C2×D4—22no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4C2×D4×C2911yescharacteristic
368C2×D4C2×D4×C2911yescharacteristic
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—82no—
377C22×C4C2×D4×C2911yescharacteristic
378C22×C4C2×D4×C2911yescharacteristic
379C22×C4#41×C2911yescharacteristic
380D8—42no—
381D8—42no—
382M16—82no—
383C2×C8—22no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—22no—
387C2×C8—42no—
388C2×C8—82no—
389C2×C8C2×D4×C2912yes—
390C2×C8C2×D4×C2912yes—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4C2×D4×C2911yescharacteristic
399C4⋊C4C2×D4×C2911yescharacteristic
400C22⋊C4—21no—
401C22⋊C4—21no—
402C22⋊C4—21no—
403C22⋊C4—21no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C42C2×D4×C2911yescharacteristic
407C42C2×D4×C2911yescharacteristic
408C42#41×C2911yescharacteristic
409C42C24×C2911yescharacteristic
410C23—21no—
411C23—21no—
412C23—42no—
413C23—42no—
414C23—41no—
415C23—81no—
416C23C29×#12111yescharacteristic
417Q8—82no—
418Q8—81no—
419Q8—82no—
420D4—21no—
421D4—21no—
422D4—21no—
423D4—42no—
424D4—41no—
425D4—41no—
426D4—42no—
427D4—81no—
428D4—82no—
429D4C29×#13712yes—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—82no—
443C2×C4—81no—
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—22no—
452C8—22no—
453C8—41no—
454C8—42no—
455C8—41no—
456C8—42no—
457C22—21no—
458C22—21no—
459C22—22no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—84no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22C29×#47212yes—
470C22C2×C29×#12111yescharacteristic
471C4—21no—
472C4—21no—
473C4—21no—
474C4—21no—
475C4—41no—
476C4—41no—
477C4—81no—
478C4—82no—
479C4C2×C29×#13711yescharacteristic
480C4C29×#57511yescharacteristic
481C4C29×#57712yes—
482C2—22no—
483C2—42no—
484C2—81no—
485C2—161no—
486C2C29×#304211yescharacteristic
487C2C29×#305611yescharacteristic
488C2C2×C29×#47211yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3109C2
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×#3226C2semidirect
3. C2×C29×#476C2semidirect
4. C29×#2974C2semidirect
5. C29×#1697C2semidirect
6. C29×#1695C2semidirect
7. C29×#1677C2semidirect
8. C29×#1675C2semidirect
9. C29×#1573C2semidirect
10. C29×#1558C2semidirect
11. C29×#1551C2semidirect
15. C29×#500C22semidirect
16. C29×#486C22semidirect
43. C29×#335C22semidirect
44. C29×#334C22semidirect
45. C29×#333C22semidirect
46. C29×#333C22semidirect
47. C29×#333C22semidirect
48. C29×#331C22semidirect
165. #19465C29direct (N × H)
213. #3226C2×C29semidirect
215. C2×#476C2×C29semidirect
216. #2974C2×C29semidirect
217. #1697C2×C29semidirect
218. #1695C2×C29semidirect
219. #1677C2×C29semidirect
220. #1675C2×C29semidirect
221. #1573C2×C29semidirect
222. #1558C2×C29semidirect
223. #1551C2×C29semidirect
252. #500C22×C29semidirect
253. #486C22×C29semidirect
280. #335C22×C29semidirect
281. #334C22×C29semidirect
282. #333C22×C29semidirect
283. #333C22×C29semidirect
284. #333C22×C29semidirect
285. #331C22×C29semidirect
353. C29#19465direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32262
C29×#31092
C2×C29×#4762
C29×#29742
C29×#16972
C29×#16952
C29×#16772
C29×#16752
C29×#15732
C29×#15582
C29×#15512
#1946529