Finite Group Databasebeta

← C29×#19464 #20314364

Subgroups — C29×#19464 #20314364

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×#3230C211yesmaximal, characteristic, complemented
2C29×#3110C211yesmaximal, characteristic
3C2×C29×#461C211yesmaximal, characteristic
4C29×#2974C211yesmaximal, characteristic
5C29×#1699C212yesmaximal, complemented
6C29×#1693C212yesmaximal, complemented
7C29×#1679C212yesmaximal, complemented
8C29×#1673C212yesmaximal, complemented
9C29×#1573C211yesmaximal, characteristic, complemented
10C29×#1556C211yesmaximal, characteristic, complemented
11C29×#1552C211yesmaximal, characteristic, complemented
12C22×SD16×C29—21no—
13C29×#533C2211yescharacteristic
14C2×C29×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C29C2211yescharacteristic
16C29×#500C2212yescomplemented
17C29×#487C2212yescomplemented
18C29×#484—21no—
19C29×#484—21no—
20C29×#484—21no—
21C29×#477—22no—
22C29×#474C2211yescharacteristic
23C29×#474C2211yescharacteristic
24C29×#461—21no—
25C29×#461—21no—
26C29×#461C2211yescharacteristic
27C29×#461C2212yes—
28C29×#461C2211yescharacteristic
29C29×#461C2212yes—
30C29×#450—21no—
31C29×#440—21no—
32C29×#440—21no—
33C29×#436C2212yes—
34C29×#435—22no—
35C8×D4×C29C2212yes—
36C29×#432C2211yescharacteristic
37C29×#432C2211yescharacteristic
38C29×#431C2211yescharacteristic
39C2×C29×C4⋊C8C2211yescharacteristic
40C2×C29×#103—21no—
41C29×#407—21no—
42C2×C29×C22⋊C8—21no—
43C29×#335C2212yescomplemented
44C29×#334C2212yescomplemented
45C29×#332C2212yescomplemented
46C29×#332C2212yescomplemented
47C29×#332C2212yescomplemented
48C29×#332C2212yescomplemented
49C22×Q8×C29—21no—
50C22×D4×C29D411yescharacteristic
51C23×C4×C29—21no—
52C2×SD16×C29—21no—
53C2×SD16×C29—21no—
54C2×SD16×C29—22no—
55C2×SD16×C29—22no—
56C2×SD16×C29—44no—
57C2×M16×C29—22no—
58C22×C8×C29—21no—
59C22×C8×C29—22no—
60C29×C4⋊Q8—21no—
61C29×C4⋊Q8—21no—
62C29×C4⋊Q8—21no—
63C29×C4⋊Q8C2312yes—
64C29×C4⋊Q8C2311yescharacteristic
65C29×C4⋊Q8C2311yescharacteristic
66C29×#125—21no—
67C29×C22⋊Q8—21no—
68C29×C22⋊Q8—21no—
69C4×Q8×C29—21no—
70C4×Q8×C29—21no—
71C4×D4×C29—21no—
72C4×D4×C29—21no—
73C4×D4×C29D411yescharacteristic
74C4×D4×C29D411yescharacteristic
75C4×D4×C29C2311yescharacteristic
76C4×D4×C29C2311yescharacteristic
77C29×#117—21no—
78C2×C4⋊C4×C29—21no—
79C2×C4⋊C4×C29—21no—
80C2×C4⋊C4×C29D411yescharacteristic
81C2×C22⋊C4×C29—21no—
82C2×C42×C29C2311yescharacteristic
83C29×#107—22no—
84C29×#107—22no—
85C29×#107—21no—
86C29×#107—21no—
87C29×C4⋊C8—21no—
88C29×C4⋊C8D412yes—
89C29×C4⋊C8C2312yes—
90C29×C4⋊C8C2311yescharacteristic
91C29×C4⋊C8C2311yescharacteristic
92C29×C4⋊C8C2312yes—
93C29×#103—22no—
94C29×#103—22no—
95C29×#103—21no—
96C29×#103—21no—
97C29×#103—22no—
98C29×#103—22no—
99C29×#102—21no—
100C29×#102—21no—
101C29×C22⋊C8—21no—
102C29×C22⋊C8—21no—
103C29×C22⋊C8—22no—
104C29×C22⋊C8—22no—
105C29×C22⋊C8D411yescharacteristic
106C29×C22⋊C8D411yescharacteristic
107C29×#97—21no—
108C29×#97—21no—
109C4×C8×C29C2312yes—
110C24×C29—21no—
111C2×Q8×C29—21no—
112C2×Q8×C29—21no—
113C2×Q8×C29—22no—
114C2×Q8×C29—42no—
115C2×Q8×C29—42no—
116C2×Q8×C29—41no—
117C2×D4×C29—22no—
118C2×D4×C29—21no—
119C2×D4×C29—41no—
120C2×D4×C29C2×D411yescharacteristic
121C2×D4×C29C2×D411yescharacteristic
122C22×C4×C29—21no—
123C22×C4×C29—21no—
124C22×C4×C29—21no—
125C22×C4×C29—21no—
126C22×C4×C29—21no—
127C22×C4×C29—41no—
128C22×C4×C29—82no—
129C22×C4×C29C2×D411yescharacteristic
130C22×C4×C29C2×D411yescharacteristic
131C22×C4×C29#4111yescharacteristic
132SD16×C29—42no—
133SD16×C29—44no—
134SD16×C29—42no—
135SD16×C29—44no—
136M16×C29—82no—
137C2×C8×C29—22no—
138C2×C8×C29—22no—
139C2×C8×C29—21no—
140C2×C8×C29—21no—
141C2×C8×C29—42no—
142C2×C8×C29—82no—
143C2×C8×C29C2×D412yes—
144C2×C8×C29C2×D412yes—
145C4⋊C4×C29—21no—
146C4⋊C4×C29—22no—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—21no—
149C4⋊C4×C29—22no—
150C4⋊C4×C29—21no—
151C4⋊C4×C29—21no—
152C4⋊C4×C29—41no—
153C4⋊C4×C29—41no—
154C4⋊C4×C29—41no—
155C4⋊C4×C29—41no—
156C4⋊C4×C29C2×D411yescharacteristic
157C4⋊C4×C29C2×D411yescharacteristic
158C22⋊C4×C29—21no—
159C22⋊C4×C29—21no—
160C22⋊C4×C29—21no—
161C22⋊C4×C29—21no—
162C22⋊C4×C29—41no—
163C42×C29—41no—
164C42×C29C2×D411yescharacteristic
165C42×C29C2×D411yescharacteristic
166C42×C29#4111yescharacteristic
167C42×C29C2411yescharacteristic
168#19464C2911yesmaximal, characteristic, direct product factor, Sylow
169C23×C29—21no—
170C23×C29—21no—
171C23×C29—42no—
172C23×C29—42no—
173C23×C29—81no—
174C23×C29#12111yescharacteristic
175Q8×C29—42no—
176Q8×C29—41no—
177Q8×C29—41no—
178Q8×C29—42no—
179Q8×C29—42no—
180Q8×C29—82no—
181D4×C29—21no—
182D4×C29—21no—
183D4×C29—21no—
184D4×C29—42no—
185D4×C29AGL(1,ℤ/8)12yes—
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—41no—
196C2×C4×C29—42no—
197C2×C4×C29—81no—
198C2×C4×C29—81no—
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—42no—
210C8×C29—41no—
211C8×C29—41no—
212C8×C29—42no—
213#3230C2×C2911yescharacteristic, complemented
214#3110C2×C2911yescharacteristic
215C2×#461C2×C2911yescharacteristic
216#2974C2×C2911yescharacteristic
217#1699C2×C2912yescomplemented
218#1693C2×C2912yescomplemented
219#1679C2×C2912yescomplemented
220#1673C2×C2912yescomplemented
221#1573C2×C2911yescharacteristic, complemented
222#1556C2×C2911yescharacteristic, complemented
223#1552C2×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#47312yes—
234C22×C29C2×#12111yescharacteristic
235C4×C29—21no—
236C4×C29—21no—
237C4×C29—21no—
238C4×C29—21no—
239C4×C29—41no—
240C4×C29—41no—
241C4×C29—81no—
242C4×C29—82no—
243C4×C29—81no—
244C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
245C4×C29#57511yescharacteristic
246C4×C29#57712yes—
247C22×SD16—21no—
248#533C22×C2911yescharacteristic
249C2×C4⋊Q8C22×C2911yescharacteristic
250C2×C4×D4C22×C2911yescharacteristic
251#500C22×C2912yescomplemented
252#487C22×C2912yescomplemented
253#484—21no—
254#484—21no—
255#484—21no—
256#477—22no—
257#474C22×C2911yescharacteristic
258#474C22×C2911yescharacteristic
259#461—21no—
260#461—21no—
261#461C22×C2911yescharacteristic
262#461C22×C2911yescharacteristic
263#461C22×C2912yes—
264#461C22×C2912yes—
265#450—21no—
266#440—21no—
267#440—21no—
268#436C22×C2912yes—
269#435—22no—
270C8×D4C22×C2912yes—
271#432C22×C2911yescharacteristic
272#432C22×C2911yescharacteristic
273#431C22×C2911yescharacteristic
274C2×C4⋊C8C22×C2911yescharacteristic
275C2×#103—21no—
276#407—21no—
277C2×C22⋊C8—21no—
278#335C22×C2912yescomplemented
279#334C22×C2912yescomplemented
280#332C22×C2912yescomplemented
281#332C22×C2912yescomplemented
282#332C22×C2912yescomplemented
283#332C22×C2912yescomplemented
284C2×C29—22no—
285C2×C29—42no—
286C2×C29—81no—
287C2×C29#304211yescharacteristic
288C2×C29#305511yescharacteristic
289C2×C29C2×#47311yescharacteristic
290C22×Q8—21no—
291C22×D4D4×C2911yescharacteristic
292C23×C4—21no—
293C2×SD16—22no—
294C2×SD16—22no—
295C2×SD16—21no—
296C2×SD16—21no—
297C2×SD16—44no—
298C2×M16—22no—
299C22×C8—21no—
300C22×C8—22no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8C23×C2912yes—
305C4⋊Q8C23×C2911yescharacteristic
306C4⋊Q8C23×C2911yescharacteristic
307#125—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4D4×C2911yescharacteristic
315C4×D4D4×C2911yescharacteristic
316C4×D4C23×C2911yescharacteristic
317C4×D4C23×C2911yescharacteristic
318#117—21no—
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#107—21no—
327#107—21no—
328C4⋊C8—21no—
329C4⋊C8D4×C2912yes—
330C4⋊C8C23×C2912yes—
331C4⋊C8C23×C2911yescharacteristic
332C4⋊C8C23×C2912yes—
333C4⋊C8C23×C2911yescharacteristic
334#103—22no—
335#103—22no—
336#103—22no—
337#103—22no—
338#103—21no—
339#103—21no—
340#102—21no—
341#102—21no—
342C22⋊C8—21no—
343C22⋊C8—21no—
344C22⋊C8—22no—
345C22⋊C8—22no—
346C22⋊C8D4×C2911yescharacteristic
347C22⋊C8D4×C2911yescharacteristic
348#97—21no—
349#97—21no—
350C4×C8C23×C2912yes—
351C29#1946411yescharacteristic, direct product factor, Sylow
352C24—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—22no—
356C2×Q8—42no—
357C2×Q8—42no—
358C2×Q8—41no—
359C2×D4—22no—
360C2×D4—21no—
361C2×D4—41no—
362C2×D4C2×D4×C2911yescharacteristic
363C2×D4C2×D4×C2911yescharacteristic
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—41no—
370C22×C4—82no—
371C22×C4C2×D4×C2911yescharacteristic
372C22×C4C2×D4×C2911yescharacteristic
373C22×C4#41×C2911yescharacteristic
374SD16—44no—
375SD16—42no—
376SD16—44no—
377SD16—42no—
378M16—82no—
379C2×C8—22no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—22no—
383C2×C8—42no—
384C2×C8—82no—
385C2×C8C2×D4×C2912yes—
386C2×C8C2×D4×C2912yes—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—22no—
390C4⋊C4—21no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—41no—
395C4⋊C4—41no—
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—
405C42—41no—
406C42C2×D4×C2911yescharacteristic
407C42C2×D4×C2911yescharacteristic
408C42#41×C2911yescharacteristic
409C42C24×C2911yescharacteristic
410C23—21no—
411C23—21no—
412C23—42no—
413C23—42no—
414C23—81no—
415C23C29×#12111yescharacteristic
416Q8—42no—
417Q8—41no—
418Q8—41no—
419Q8—42no—
420Q8—42no—
421Q8—82no—
422D4—21no—
423D4—21no—
424D4—21no—
425D4—42no—
426D4C29×AGL(1,ℤ/8)12yes—
427C2×C4—22no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—81no—
439C2×C4—81no—
440C2×C4—81no—
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—22no—
449C8—22no—
450C8—42no—
451C8—41no—
452C8—41no—
453C8—42no—
454C22—21no—
455C22—21no—
456C22—22no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—84no—
463C22C29×#47312yes—
464C22C2×C29×#12111yescharacteristic
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—41no—
470C4—41no—
471C4—81no—
472C4—82no—
473C4—81no—
474C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
475C4C29×#57511yescharacteristic
476C4C29×#57712yes—
477C2—22no—
478C2—42no—
479C2—81no—
480C2C29×#304211yescharacteristic
481C2C29×#305511yescharacteristic
482C2C2×C29×#47311yescharacteristic
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×#3230C2semidirect
5. C29×#1699C2semidirect
6. C29×#1693C2semidirect
7. C29×#1679C2semidirect
8. C29×#1673C2semidirect
9. C29×#1573C2semidirect
10. C29×#1556C2semidirect
11. C29×#1552C2semidirect
16. C29×#500C22semidirect
17. C29×#487C22semidirect
43. C29×#335C22semidirect
44. C29×#334C22semidirect
45. C29×#332C22semidirect
46. C29×#332C22semidirect
47. C29×#332C22semidirect
48. C29×#332C22semidirect
168. #19464C29direct (N × H)
213. #3230C2×C29semidirect
217. #1699C2×C29semidirect
218. #1693C2×C29semidirect
219. #1679C2×C29semidirect
220. #1673C2×C29semidirect
221. #1573C2×C29semidirect
222. #1556C2×C29semidirect
223. #1552C2×C29semidirect
251. #500C22×C29semidirect
252. #487C22×C29semidirect
278. #335C22×C29semidirect
279. #334C22×C29semidirect
280. #332C22×C29semidirect
281. #332C22×C29semidirect
282. #332C22×C29semidirect
283. #332C22×C29semidirect
351. C29#19464direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32302
C29×#31102
C2×C29×#4612
C29×#29742
C29×#16992
C29×#16932
C29×#16792
C29×#16732
C29×#15732
C29×#15562
C29×#15522
#1946429