Finite Group Databasebeta

← C29×#19459 #20314359

Subgroups — C29×#19459 #20314359

Order 7424.

638 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3209C211yesmaximal, characteristic, complemented
2C29×#3110C211yesmaximal, characteristic
3C2×C29×#474C211yesmaximal, characteristic
4C29×#2974C211yesmaximal, characteristic
5C29×#1699C212yesmaximal, complemented
6C29×#1689C212yesmaximal, complemented
7C29×#1679C212yesmaximal, complemented
8C29×#1669C212yesmaximal, complemented
9C29×#1573C211yesmaximal, characteristic, complemented
10C29×#1556C211yesmaximal, characteristic, complemented
11C29×#1552C211yesmaximal, characteristic, complemented
12C29×#533C2211yescharacteristic
13C2×C29×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C29C2211yescharacteristic
15C29×#494C2212yescomplemented
16C29×#487C2212yescomplemented
17C29×#484—21no—
18C29×#474—21no—
19C29×#474—21no—
20C29×#474C2211yescharacteristic
21C29×#474C2212yes—
22C29×#474C2211yescharacteristic
23C29×#474C2212yes—
24C29×#462—22no—
25C29×#461C2211yescharacteristic
26C29×#461C2211yescharacteristic
27C29×#451—21no—
28C29×#451—21no—
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×#107—21no—
39C2×C29×C4⋊C8C2211yescharacteristic
40C2×C29×#102—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×Q16×C29—22no—
53C2×Q16×C29—22no—
54C2×SD16×C29—21no—
55C2×SD16×C29—21no—
56C2×M16×C29—22no—
57C22×C8×C29—21no—
58C22×C8×C29—22no—
59C29×C4⋊Q8—21no—
60C29×C4⋊Q8—21no—
61C29×C4⋊Q8—21no—
62C29×C4⋊Q8C2311yescharacteristic
63C29×C4⋊Q8C2312yes—
64C29×C4⋊Q8C2311yescharacteristic
65C29×#125—21no—
66C29×C22⋊Q8—21no—
67C29×C22⋊Q8—21no—
68C4×Q8×C29—21no—
69C4×Q8×C29—21no—
70C4×D4×C29—21no—
71C4×D4×C29—21no—
72C4×D4×C29D411yescharacteristic
73C4×D4×C29D411yescharacteristic
74C4×D4×C29C2311yescharacteristic
75C4×D4×C29C2311yescharacteristic
76C29×#117—21no—
77C2×C4⋊C4×C29—21no—
78C2×C4⋊C4×C29—21no—
79C2×C4⋊C4×C29D411yescharacteristic
80C2×C22⋊C4×C29—21no—
81C2×C42×C29C2311yescharacteristic
82C29×#107—22no—
83C29×#107—22no—
84C29×#107—21no—
85C29×#107—21no—
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
130Q16×C29—82no—
131Q16×C29—82no—
132SD16×C29—42no—
133SD16×C29—42no—
134M16×C29—82no—
135C2×C8×C29—22no—
136C2×C8×C29—22no—
137C2×C8×C29—21no—
138C2×C8×C29—21no—
139C2×C8×C29—42no—
140C2×C8×C29—82no—
141C2×C8×C29C2×D412yes—
142C2×C8×C29C2×D412yes—
143C4⋊C4×C29—21no—
144C4⋊C4×C29—22no—
145C4⋊C4×C29—21no—
146C4⋊C4×C29—21no—
147C4⋊C4×C29—22no—
148C4⋊C4×C29—21no—
149C4⋊C4×C29—21no—
150C4⋊C4×C29—41no—
151C4⋊C4×C29—41no—
152C4⋊C4×C29—41no—
153C4⋊C4×C29—41no—
154C4⋊C4×C29C2×D411yescharacteristic
155C4⋊C4×C29C2×D411yescharacteristic
156C22⋊C4×C29—21no—
157C22⋊C4×C29—21no—
158C22⋊C4×C29—21no—
159C22⋊C4×C29—21no—
160C22⋊C4×C29—41no—
161C42×C29—41no—
162C42×C29C2×D411yescharacteristic
163C42×C29C2×D411yescharacteristic
164C42×C29#4111yescharacteristic
165C42×C29C2411yescharacteristic
166#19459C2911yesmaximal, characteristic, direct product factor, Sylow
167C23×C29—21no—
168C23×C29—21no—
169C23×C29—42no—
170C23×C29—42no—
171C23×C29—81no—
172C23×C29#12111yescharacteristic
173Q8×C29—41no—
174Q8×C29—41no—
175Q8×C29—42no—
176Q8×C29—42no—
177Q8×C29—42no—
178Q8×C29—82no—
179D4×C29—21no—
180D4×C29—21no—
181D4×C29—21no—
182D4×C29—42no—
183D4×C29#13712yes—
184C2×C4×C29—22no—
185C2×C4×C29—21no—
186C2×C4×C29—21no—
187C2×C4×C29—22no—
188C2×C4×C29—21no—
189C2×C4×C29—21no—
190C2×C4×C29—42no—
191C2×C4×C29—42no—
192C2×C4×C29—41no—
193C2×C4×C29—41no—
194C2×C4×C29—42no—
195C2×C4×C29—81no—
196C2×C4×C29—81no—
197C2×C4×C29—81no—
198C2×C4×C29—82no—
199C2×C4×C29#12111yescharacteristic
200C2×C4×C29#12111yescharacteristic
201C2×C4×C29#12111yescharacteristic
202C2×C4×C29C22×D411yescharacteristic
203C2×C4×C29C22×D411yescharacteristic
204C2×C4×C29C2×#4111yescharacteristic
205C8×C29—22no—
206C8×C29—22no—
207C8×C29—41no—
208C8×C29—42no—
209C8×C29—41no—
210C8×C29—42no—
211#3209C2×C2911yescharacteristic, complemented
212#3110C2×C2911yescharacteristic
213C2×#474C2×C2911yescharacteristic
214#2974C2×C2911yescharacteristic
215#1699C2×C2912yescomplemented
216#1689C2×C2912yescomplemented
217#1679C2×C2912yescomplemented
218#1669C2×C2912yescomplemented
219#1573C2×C2911yescharacteristic, complemented
220#1556C2×C2911yescharacteristic, complemented
221#1552C2×C2911yescharacteristic, complemented
222C22×C29—21no—
223C22×C29—21no—
224C22×C29—22no—
225C22×C29—41no—
226C22×C29—41no—
227C22×C29—41no—
228C22×C29—41no—
229C22×C29—41no—
230C22×C29—84no—
231C22×C29#47312yes—
232C22×C29C2×#12111yescharacteristic
233C4×C29—21no—
234C4×C29—21no—
235C4×C29—21no—
236C4×C29—21no—
237C4×C29—41no—
238C4×C29—41no—
239C4×C29—82no—
240C4×C29—81no—
241C4×C29—81no—
242C4×C29C2×#13711yescharacteristic
243C4×C29#57511yescharacteristic
244C4×C29#57612yes—
245#533C22×C2911yescharacteristic
246C2×C4⋊Q8C22×C2911yescharacteristic
247C2×C4×D4C22×C2911yescharacteristic
248#494C22×C2912yescomplemented
249#487C22×C2912yescomplemented
250#484—21no—
251#474—21no—
252#474—21no—
253#474C22×C2911yescharacteristic
254#474C22×C2911yescharacteristic
255#474C22×C2912yes—
256#474C22×C2912yes—
257#462—22no—
258#461C22×C2911yescharacteristic
259#461C22×C2911yescharacteristic
260#451—21no—
261#451—21no—
262#450—21no—
263#440—21no—
264#440—21no—
265#436C22×C2912yes—
266#435—22no—
267C8×D4C22×C2912yes—
268#432C22×C2911yescharacteristic
269#432C22×C2911yescharacteristic
270#431C22×C2911yescharacteristic
271C2×#107—21no—
272C2×C4⋊C8C22×C2911yescharacteristic
273C2×#102—21no—
274#407—21no—
275C2×C22⋊C8—21no—
276#335C22×C2912yescomplemented
277#334C22×C2912yescomplemented
278#332C22×C2912yescomplemented
279#332C22×C2912yescomplemented
280#332C22×C2912yescomplemented
281#332C22×C2912yescomplemented
282C2×C29—22no—
283C2×C29—42no—
284C2×C29—81no—
285C2×C29#304111yescharacteristic
286C2×C29#305611yescharacteristic
287C2×C29C2×#47311yescharacteristic
288C22×Q8—21no—
289C22×D4D4×C2911yescharacteristic
290C23×C4—21no—
291C2×Q16—22no—
292C2×Q16—22no—
293C2×SD16—21no—
294C2×SD16—21no—
295C2×M16—22no—
296C22×C8—21no—
297C22×C8—22no—
298C4⋊Q8—21no—
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8C23×C2912yes—
302C4⋊Q8C23×C2911yescharacteristic
303C4⋊Q8C23×C2911yescharacteristic
304#125—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307C4×Q8—21no—
308C4×Q8—21no—
309C4×D4—21no—
310C4×D4—21no—
311C4×D4D4×C2911yescharacteristic
312C4×D4D4×C2911yescharacteristic
313C4×D4C23×C2911yescharacteristic
314C4×D4C23×C2911yescharacteristic
315#117—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4D4×C2911yescharacteristic
319C2×C22⋊C4—21no—
320C2×C42C23×C2911yescharacteristic
321#107—22no—
322#107—22no—
323#107—21no—
324#107—21no—
325C4⋊C8—21no—
326C4⋊C8D4×C2912yes—
327C4⋊C8C23×C2912yes—
328C4⋊C8C23×C2911yescharacteristic
329C4⋊C8C23×C2912yes—
330C4⋊C8C23×C2911yescharacteristic
331#103—22no—
332#103—22no—
333#103—21no—
334#103—21no—
335#102—22no—
336#102—22no—
337#102—21no—
338#102—21no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—22no—
342C22⋊C8—22no—
343C22⋊C8D4×C2911yescharacteristic
344C22⋊C8D4×C2911yescharacteristic
345#97—21no—
346#97—21no—
347C4×C8C23×C2912yes—
348C29#1945911yescharacteristic, direct product factor, Sylow
349C24—21no—
350C2×Q8—21no—
351C2×Q8—22no—
352C2×Q8—21no—
353C2×Q8—41no—
354C2×Q8—82no—
355C2×D4—22no—
356C2×D4—21no—
357C2×D4—41no—
358C2×D4C2×D4×C2911yescharacteristic
359C2×D4C2×D4×C2911yescharacteristic
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—41no—
366C22×C4—82no—
367C22×C4C2×D4×C2911yescharacteristic
368C22×C4C2×D4×C2911yescharacteristic
369C22×C4#41×C2911yescharacteristic
370Q16—82no—
371Q16—82no—
372SD16—42no—
373SD16—42no—
374M16—82no—
375C2×C8—22no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—22no—
379C2×C8—42no—
380C2×C8—82no—
381C2×C8C2×D4×C2912yes—
382C2×C8C2×D4×C2912yes—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4C2×D4×C2911yescharacteristic
395C4⋊C4C2×D4×C2911yescharacteristic
396C22⋊C4—21no—
397C22⋊C4—21no—
398C22⋊C4—21no—
399C22⋊C4—21no—
400C22⋊C4—41no—
401C42—41no—
402C42C2×D4×C2911yescharacteristic
403C42C2×D4×C2911yescharacteristic
404C42#41×C2911yescharacteristic
405C42C24×C2911yescharacteristic
406C23—21no—
407C23—21no—
408C23—42no—
409C23—42no—
410C23—81no—
411C23C29×#12111yescharacteristic
412Q8—41no—
413Q8—41no—
414Q8—42no—
415Q8—42no—
416Q8—42no—
417Q8—82no—
418D4—21no—
419D4—21no—
420D4—21no—
421D4—42no—
422D4C29×#13712yes—
423C2×C4—22no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—81no—
437C2×C4—82no—
438C2×C4C29×#12111yescharacteristic
439C2×C4C29×#12111yescharacteristic
440C2×C4C29×#12111yescharacteristic
441C2×C4C22×D4×C2911yescharacteristic
442C2×C4C22×D4×C2911yescharacteristic
443C2×C4C2×#41×C2911yescharacteristic
444C8—22no—
445C8—22no—
446C8—41no—
447C8—42no—
448C8—41no—
449C8—42no—
450C22—21no—
451C22—21no—
452C22—22no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—84no—
459C22C29×#47312yes—
460C22C2×C29×#12111yescharacteristic
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—41no—
466C4—41no—
467C4—82no—
468C4—81no—
469C4—81no—
470C4C2×C29×#13711yescharacteristic
471C4C29×#57511yescharacteristic
472C4C29×#57612yes—
473C2—22no—
474C2—42no—
475C2—81no—
476C2C29×#304111yescharacteristic
477C2C29×#305611yescharacteristic
478C2C2×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×#3209C2semidirect
5. C29×#1699C2semidirect
6. C29×#1689C2semidirect
7. C29×#1679C2semidirect
8. C29×#1669C2semidirect
9. C29×#1573C2semidirect
10. C29×#1556C2semidirect
11. C29×#1552C2semidirect
15. C29×#494C22semidirect
16. C29×#487C22semidirect
43. C29×#335C22semidirect
44. C29×#334C22semidirect
45. C29×#332C22semidirect
46. C29×#332C22semidirect
47. C29×#332C22semidirect
48. C29×#332C22semidirect
166. #19459C29direct (N × H)
211. #3209C2×C29semidirect
215. #1699C2×C29semidirect
216. #1689C2×C29semidirect
217. #1679C2×C29semidirect
218. #1669C2×C29semidirect
219. #1573C2×C29semidirect
220. #1556C2×C29semidirect
221. #1552C2×C29semidirect
248. #494C22×C29semidirect
249. #487C22×C29semidirect
276. #335C22×C29semidirect
277. #334C22×C29semidirect
278. #332C22×C29semidirect
279. #332C22×C29semidirect
280. #332C22×C29semidirect
281. #332C22×C29semidirect
348. C29#19459direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32092
C29×#31102
C2×C29×#4742
C29×#29742
C29×#16992
C29×#16892
C29×#16792
C29×#16692
C29×#15732
C29×#15562
C29×#15522
#1945929