Finite Group Databasebeta

← C29×#19489 #20314389

Subgroups — C29×#19489 #20314389

Order 7424.

646 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3227C211yesmaximal, characteristic, complemented
2C29×#3106C211yesmaximal, characteristic
3C29×#3039C211yesmaximal, characteristic, complemented
4C29×#2990C211yesmaximal, characteristic, complemented
5C29×#1702C212yesmaximal, complemented
6C29×#1692C212yesmaximal, complemented
7C29×#1681C212yesmaximal, complemented
8C29×#1671C212yesmaximal, complemented
9C29×#1574C211yesmaximal, characteristic, complemented
10C29×#1560C211yesmaximal, characteristic, complemented
11C29×#1549C211yesmaximal, characteristic, complemented
12C2×C29×#137—21no—
13C29×#532C2211yescharacteristic
14C2×C29×C4⋊Q8C2211yescharacteristic
15C4×#41×C29C2211yescharacteristic
16C29×#498C2212yes—
17C29×#486C2212yes—
18C29×#482—21no—
19C29×#481—22no—
20C29×#477C2211yescharacteristic
21C29×#476—21no—
22C29×#476—21no—
23C29×#476C2211yescharacteristic
24C29×#462—21no—
25C29×#462C2212yes—
26C29×#461—21no—
27C29×#461C2212yes—
28C29×#460C2211yescharacteristic
29C29×#459C2211yescharacteristic
30C29×#449—21no—
31C29×#446C2212yes—
32C4×SD16×C29—21no—
33C4×D8×C29—21no—
34C29×#435—22no—
35C8×D4×C29C2212yes—
36C29×#432—21no—
37C29×#431C2211yescharacteristic
38C29×#431C2211yescharacteristic
39C29×#423C2211yescharacteristic
40C29×#423C2211yescharacteristic
41C2×C29×C4⋊C8—21no—
42C29×#419—21no—
43C29×#335C2212yes—
44C29×#334C2212yes—
45C29×#333C2212yes—
46C29×#332C2212yes—
47C29×#332C2212yes—
48C29×#331C2212yes—
49C2×#41×C29—21no—
50C2×#41×C29D411yescharacteristic
51C22×Q8×C29—21no—
52C29×#137—44no—
53C2×Q16×C29—22no—
54C2×SD16×C29—21no—
55C2×SD16×C29—22no—
56C2×D8×C29—21no—
57C2×M16×C29—21no—
58C2×M16×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×#127C2311yescharacteristic
66C29×#124—21no—
67C29×#121—21no—
68C29×#121—21no—
69C4×Q8×C29D411yescharacteristic
70C4×Q8×C29C2311yescharacteristic
71C4×D4×C29—21no—
72C4×D4×C29—21no—
73C4×D4×C29—21no—
74C4×D4×C29—21no—
75C4×D4×C29D411yescharacteristic
76C4×D4×C29C2311yescharacteristic
77C29×#117—21no—
78C29×#117D411yescharacteristic
79C2×C4⋊C4×C29—21no—
80C2×C4⋊C4×C29—21no—
81C2×C42×C29—21no—
82C2×C42×C29C2311yescharacteristic
83C29×#107—21no—
84C29×#106—22no—
85C29×#106—22no—
86C29×#106—21no—
87C29×C4⋊C8—22no—
88C29×C4⋊C8—21no—
89C29×C4⋊C8—21no—
90C29×C4⋊C8D411yescharacteristic
91C29×C4⋊C8D411yescharacteristic
92C29×C4⋊C8C2311yescharacteristic
93C29×C4⋊C8C2311yescharacteristic
94C29×C4⋊C8C2312yes—
95C29×C4⋊C8C2312yes—
96C29×#103—21no—
97C29×#103—22no—
98C29×#103—22no—
99C29×#102—21no—
100C29×#102—22no—
101C29×#102—22no—
102C29×#102—21no—
103C29×#102—21no—
104C29×C22⋊C8—21no—
105C29×C22⋊C8—22no—
106C29×C22⋊C8D412yes—
107C29×#97—22no—
108C4×C8×C29—21no—
109C4×C8×C29C2312yes—
110#41×C29—22no—
111#41×C29—41no—
112#41×C29—82no—
113C2×Q8×C29—22no—
114C2×Q8×C29—21no—
115C2×Q8×C29—42no—
116C2×Q8×C29—42no—
117C2×Q8×C29—41no—
118C2×Q8×C29C2×D411yescharacteristic
119C2×D4×C29—21no—
120C2×D4×C29—21no—
121C2×D4×C29—21no—
122C2×D4×C29—21no—
123C2×D4×C29—41no—
124C2×D4×C29C2×D411yescharacteristic
125C22×C4×C29—21no—
126C22×C4×C29—21no—
127C22×C4×C29—21no—
128C22×C4×C29—41no—
129C22×C4×C29—41no—
130C22×C4×C29C2×D411yescharacteristic
131C22×C4×C29C2×D411yescharacteristic
132C22×C4×C29#4111yescharacteristic
133Q16×C29—44no—
134SD16×C29—42no—
135SD16×C29—44no—
136D8×C29—42no—
137M16×C29—42no—
138M16×C29—81no—
139C2×C8×C29—22no—
140C2×C8×C29—22no—
141C2×C8×C29—21no—
142C2×C8×C29—21no—
143C2×C8×C29—82no—
144C2×C8×C29C2×D412yes—
145C2×C8×C29C2×D412yes—
146C4⋊C4×C29—21no—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—22no—
149C4⋊C4×C29—21no—
150C4⋊C4×C29—21no—
151C4⋊C4×C29—22no—
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—41no—
160C22⋊C4×C29—41no—
161C42×C29—21no—
162C42×C29—21no—
163C42×C29—21no—
164C42×C29C2×D411yescharacteristic
165C42×C29C2×D411yescharacteristic
166C42×C29#4111yescharacteristic
167C42×C29C2411yescharacteristic
168#19489C2911yesmaximal, characteristic, direct product factor, Sylow
169C23×C29—21no—
170C23×C29—41no—
171C23×C29#12111yescharacteristic
172Q8×C29—21no—
173Q8×C29—21no—
174Q8×C29—42no—
175Q8×C29—42no—
176Q8×C29—81no—
177Q8×C29—82no—
178D4×C29—21no—
179D4×C29—42no—
180D4×C29—41no—
181D4×C29—41no—
182D4×C29—41no—
183D4×C29—41no—
184D4×C29—81no—
185D4×C29—82no—
186D4×C29AGL(1,ℤ/8)12yes—
187C2×C4×C29—21no—
188C2×C4×C29—21no—
189C2×C4×C29—21no—
190C2×C4×C29—21no—
191C2×C4×C29—22no—
192C2×C4×C29—21no—
193C2×C4×C29—21no—
194C2×C4×C29—21no—
195C2×C4×C29—42no—
196C2×C4×C29—41no—
197C2×C4×C29—41no—
198C2×C4×C29—42no—
199C2×C4×C29—41no—
200C2×C4×C29—42no—
201C2×C4×C29—82no—
202C2×C4×C29—82no—
203C2×C4×C29#12111yescharacteristic
204C2×C4×C29#12111yescharacteristic
205C2×C4×C29#12111yescharacteristic
206C2×C4×C29C22×D411yescharacteristic
207C2×C4×C29C22×D411yescharacteristic
208C2×C4×C29C2×#4111yescharacteristic
209C8×C29—22no—
210C8×C29—22no—
211C8×C29—42no—
212C8×C29—41no—
213C8×C29—41no—
214C8×C29—42no—
215#3227C2×C2911yescharacteristic, complemented
216#3106C2×C2911yescharacteristic
217#3039C2×C2911yescharacteristic, complemented
218#2990C2×C2911yescharacteristic, complemented
219#1702C2×C2912yescomplemented
220#1692C2×C2912yescomplemented
221#1681C2×C2912yescomplemented
222#1671C2×C2912yescomplemented
223#1574C2×C2911yescharacteristic, complemented
224#1560C2×C2911yescharacteristic, complemented
225#1549C2×C2911yescharacteristic, complemented
226C22×C29—21no—
227C22×C29—21no—
228C22×C29—22no—
229C22×C29—21no—
230C22×C29—41no—
231C22×C29—41no—
232C22×C29—81no—
233C22×C29—81no—
234C22×C29—81no—
235C22×C29C2×#12111yescharacteristic
236C4×C29—21no—
237C4×C29—21no—
238C4×C29—21no—
239C4×C29—41no—
240C4×C29—41no—
241C4×C29—41no—
242C4×C29—82no—
243C4×C29—81no—
244C4×C29#47112yes—
245C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
246C4×C29#57511yescharacteristic
247C4×C29#57711yescharacteristic
248C4×C29#57811yescharacteristic
249C2×#137—21no—
250#532C22×C2911yescharacteristic
251C2×C4⋊Q8C22×C2911yescharacteristic
252C4×#41C22×C2911yescharacteristic
253#498C22×C2912yes—
254#486C22×C2912yes—
255#482—21no—
256#481—22no—
257#477C22×C2911yescharacteristic
258#476—21no—
259#476—21no—
260#476C22×C2911yescharacteristic
261#462—21no—
262#462C22×C2912yes—
263#461—21no—
264#461C22×C2912yes—
265#460C22×C2911yescharacteristic
266#459C22×C2911yescharacteristic
267#449—21no—
268#446C22×C2912yes—
269C4×SD16—21no—
270C4×D8—21no—
271#435—22no—
272C8×D4C22×C2912yes—
273#432—21no—
274#431C22×C2911yescharacteristic
275#431C22×C2911yescharacteristic
276#423C22×C2911yescharacteristic
277#423C22×C2911yescharacteristic
278C2×C4⋊C8—21no—
279#419—21no—
280#335C22×C2912yes—
281#334C22×C2912yes—
282#333C22×C2912yes—
283#332C22×C2912yes—
284#332C22×C2912yes—
285#331C22×C2912yes—
286C2×C29—41no—
287C2×C29—42no—
288C2×C29—161no—
289C2×C29#304611yescharacteristic
290C2×C29#305511yescharacteristic
291C2×C29C2×#47111yescharacteristic
292C2×#41—21no—
293C2×#41D4×C2911yescharacteristic
294C22×Q8—21no—
295#137—44no—
296C2×Q16—22no—
297C2×SD16—21no—
298C2×SD16—22no—
299C2×D8—21no—
300C2×M16—21no—
301C2×M16—21no—
302C22×C8—22no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8C23×C2912yes—
307C4⋊Q8C23×C2911yescharacteristic
308#127C23×C2911yescharacteristic
309#124—21no—
310#121—21no—
311#121—21no—
312C4×Q8D4×C2911yescharacteristic
313C4×Q8C23×C2911yescharacteristic
314C4×D4—21no—
315C4×D4—21no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4D4×C2911yescharacteristic
319C4×D4C23×C2911yescharacteristic
320#117—21no—
321#117D4×C2911yescharacteristic
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C42—21no—
325C2×C42C23×C2911yescharacteristic
326#107—21no—
327#106—22no—
328#106—22no—
329#106—21no—
330C4⋊C8—22no—
331C4⋊C8—21no—
332C4⋊C8—21no—
333C4⋊C8D4×C2911yescharacteristic
334C4⋊C8D4×C2911yescharacteristic
335C4⋊C8C23×C2912yes—
336C4⋊C8C23×C2912yes—
337C4⋊C8C23×C2911yescharacteristic
338C4⋊C8C23×C2911yescharacteristic
339#103—21no—
340#103—22no—
341#103—22no—
342#102—21no—
343#102—22no—
344#102—22no—
345#102—21no—
346#102—21no—
347C22⋊C8—21no—
348C22⋊C8—22no—
349C22⋊C8D4×C2912yes—
350#97—22no—
351C4×C8—21no—
352C4×C8C23×C2912yes—
353C29#1948911yescharacteristic, direct product factor, Sylow
354#41—22no—
355#41—41no—
356#41—82no—
357C2×Q8—22no—
358C2×Q8—21no—
359C2×Q8—42no—
360C2×Q8—42no—
361C2×Q8—41no—
362C2×Q8C2×D4×C2911yescharacteristic
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4C2×D4×C2911yescharacteristic
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4C2×D4×C2911yescharacteristic
375C22×C4C2×D4×C2911yescharacteristic
376C22×C4#41×C2911yescharacteristic
377Q16—44no—
378SD16—42no—
379SD16—44no—
380D8—42no—
381M16—42no—
382M16—81no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—82no—
388C2×C8C2×D4×C2912yes—
389C2×C8C2×D4×C2912yes—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—22no—
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—41no—
404C22⋊C4—41no—
405C42—21no—
406C42—21no—
407C42—21no—
408C42C2×D4×C2911yescharacteristic
409C42C2×D4×C2911yescharacteristic
410C42#41×C2911yescharacteristic
411C42C24×C2911yescharacteristic
412C23—21no—
413C23—41no—
414C23C29×#12111yescharacteristic
415Q8—21no—
416Q8—21no—
417Q8—42no—
418Q8—42no—
419Q8—81no—
420Q8—82no—
421D4—21no—
422D4—42no—
423D4—41no—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—81no—
428D4—82no—
429D4C29×AGL(1,ℤ/8)12yes—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—82no—
445C2×C4—82no—
446C2×C4C29×#12111yescharacteristic
447C2×C4C29×#12111yescharacteristic
448C2×C4C29×#12111yescharacteristic
449C2×C4C22×D4×C2911yescharacteristic
450C2×C4C22×D4×C2911yescharacteristic
451C2×C4C2×#41×C2911yescharacteristic
452C8—22no—
453C8—22no—
454C8—42no—
455C8—41no—
456C8—41no—
457C8—42no—
458C22—21no—
459C22—21no—
460C22—22no—
461C22—21no—
462C22—41no—
463C22—41no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22C2×C29×#12111yescharacteristic
468C4—21no—
469C4—21no—
470C4—21no—
471C4—41no—
472C4—41no—
473C4—41no—
474C4—82no—
475C4—81no—
476C4C29×#47112yes—
477C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
478C4C29×#57511yescharacteristic
479C4C29×#57711yescharacteristic
480C4C29×#57811yescharacteristic
481C2—41no—
482C2—42no—
483C2—161no—
484C2C29×#304611yescharacteristic
485C2C29×#305511yescharacteristic
486C2C2×C29×#47111yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3106C2
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×#3227C2semidirect
3. C29×#3039C2semidirect
4. C29×#2990C2semidirect
5. C29×#1702C2semidirect
6. C29×#1692C2semidirect
7. C29×#1681C2semidirect
8. C29×#1671C2semidirect
9. C29×#1574C2semidirect
10. C29×#1560C2semidirect
11. C29×#1549C2semidirect
168. #19489C29direct (N × H)
215. #3227C2×C29semidirect
217. #3039C2×C29semidirect
218. #2990C2×C29semidirect
219. #1702C2×C29semidirect
220. #1692C2×C29semidirect
221. #1681C2×C29semidirect
222. #1671C2×C29semidirect
223. #1574C2×C29semidirect
224. #1560C2×C29semidirect
225. #1549C2×C29semidirect
353. C29#19489direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32272
C29×#31062
C29×#30392
C29×#29902
C29×#17022
C29×#16922
C29×#16812
C29×#16712
C29×#15742
C29×#15602
C29×#15492
#1948929