Finite Group Databasebeta

← C29×#19313 #20314213

Subgroups — C29×#19313 #20314213

Order 7424.

684 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3152C211yesmaximal, characteristic, complemented
2C29×#3115C211yesmaximal, characteristic
3C29×#3079C211yesmaximal, characteristic, complemented
4C29×#2970C211yesmaximal, characteristic, complemented
5C29×#1690C212yesmaximal, complemented
6C29×#1686C212yesmaximal, complemented
7C29×#1669C212yesmaximal, complemented
8C29×#1665C212yesmaximal, complemented
9C29×#1569C211yesmaximal, characteristic, complemented
10C29×#1557C211yesmaximal, characteristic, complemented
11C29×#1556C211yesmaximal, characteristic, complemented
12C2×C29×#137—22no—
13C29×#532C2211yescharacteristic
14C2×C29×C4⋊Q8C2211yescharacteristic
15C4×#41×C29C2211yescharacteristic
16C29×#497—21no—
17C29×#497—21no—
18C29×#494C2212yes—
19C29×#492C2212yes—
20C29×#482—21no—
21C29×#477—21no—
22C29×#476—21no—
23C29×#475C2212yes—
24C29×#475C2211yescharacteristic
25C29×#474C2212yes—
26C29×#474C2211yescharacteristic
27C29×#460C2211yescharacteristic
28C29×#459C2211yescharacteristic
29C29×#449—21no—
30C29×#446C2212yes—
31C29×#442—21no—
32C29×#440—21no—
33C29×#435—22no—
34C8×D4×C29C2212yes—
35C29×#432—21no—
36C29×#432C2211yescharacteristic
37C29×#432C2211yescharacteristic
38C29×#428—21no—
39C29×#423C2211yescharacteristic
40C29×#417—21no—
41C4×M16×C29C2211yescharacteristic
42C2×C29×#97—21no—
43C29×#335C2212yes—
44C29×#334C2212yes—
45C29×#332C2212yes—
46C29×#332C2212yes—
47C29×#332C2212yes—
48C29×#331C2212yes—
49C2×#41×C29—21no—
50C2×#41×C29D411yescharacteristic
51C22×Q8×C29—21no—
52C29×#137—48no—
53C2×Q16×C29—22no—
54C2×Q16×C29—22no—
55C2×SD16×C29—21no—
56C2×SD16×C29—22no—
57C2×SD16×C29—22no—
58C2×D8×C29—21no—
59C2×M16×C29—21no—
60C2×M16×C29D412yes—
61C22×C8×C29—22no—
62C29×C4⋊Q8—21no—
63C29×C4⋊Q8—21no—
64C29×C4⋊Q8—21no—
65C29×C4⋊Q8C2312yes—
66C29×C4⋊Q8C2311yescharacteristic
67C29×#127C2311yescharacteristic
68C29×#124—21no—
69C29×#121—21no—
70C29×#121—21no—
71C4×Q8×C29D411yescharacteristic
72C4×Q8×C29C2311yescharacteristic
73C4×D4×C29—21no—
74C4×D4×C29—21no—
75C4×D4×C29—21no—
76C4×D4×C29—21no—
77C4×D4×C29D411yescharacteristic
78C4×D4×C29C2311yescharacteristic
79C29×#117—21no—
80C29×#117D411yescharacteristic
81C2×C4⋊C4×C29—21no—
82C2×C4⋊C4×C29—21no—
83C2×C42×C29—21no—
84C2×C42×C29C2311yescharacteristic
85C29×#107—22no—
86C29×#107—21no—
87C29×#106—22no—
88C29×#106—21no—
89C29×C4⋊C8—22no—
90C29×C4⋊C8—21no—
91C29×C4⋊C8C2312yes—
92C29×C4⋊C8C2311yescharacteristic
93C29×C4⋊C8C2311yescharacteristic
94C29×C4⋊C8C2312yes—
95C29×#103—21no—
96C29×#103—22no—
97C29×#102—21no—
98C29×#102—22no—
99C29×#102—21no—
100C29×#102—21no—
101C29×C22⋊C8—21no—
102C29×C22⋊C8—21no—
103C29×C22⋊C8—22no—
104C29×#97—22no—
105C29×#97—21no—
106C29×#97—21no—
107C29×#97D411yescharacteristic
108C29×#97D411yescharacteristic
109C4×C8×C29C2312yes—
110#41×C29—22no—
111#41×C29—41no—
112#41×C29—44no—
113C2×Q8×C29—21no—
114C2×Q8×C29—22no—
115C2×Q8×C29—44no—
116C2×Q8×C29—41no—
117C2×Q8×C29C2×D411yescharacteristic
118C2×D4×C29—21no—
119C2×D4×C29—21no—
120C2×D4×C29—21no—
121C2×D4×C29—21no—
122C2×D4×C29—41no—
123C2×D4×C29C2×D411yescharacteristic
124C22×C4×C29—21no—
125C22×C4×C29—21no—
126C22×C4×C29—21no—
127C22×C4×C29—41no—
128C22×C4×C29—41no—
129C22×C4×C29C2×D411yescharacteristic
130C22×C4×C29C2×D411yescharacteristic
131C22×C4×C29#4111yescharacteristic
132Q16×C29—44no—
133Q16×C29—44no—
134SD16×C29—44no—
135SD16×C29—42no—
136SD16×C29—44no—
137D8×C29—42no—
138M16×C29—24no—
139M16×C29—42no—
140C2×C8×C29—22no—
141C2×C8×C29—22no—
142C2×C8×C29—21no—
143C2×C8×C29—21no—
144C2×C8×C29—44no—
145C2×C8×C29C2×D412yes—
146C2×C8×C29C2×D412yes—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—21no—
149C4⋊C4×C29—22no—
150C4⋊C4×C29—21no—
151C4⋊C4×C29—22no—
152C4⋊C4×C29—21no—
153C4⋊C4×C29—41no—
154C4⋊C4×C29—41no—
155C4⋊C4×C29C2×D411yescharacteristic
156C4⋊C4×C29C2×D411yescharacteristic
157C22⋊C4×C29—21no—
158C22⋊C4×C29—21no—
159C22⋊C4×C29—21no—
160C22⋊C4×C29—41no—
161C22⋊C4×C29—41no—
162C42×C29—21no—
163C42×C29—21no—
164C42×C29—21no—
165C42×C29C2×D411yescharacteristic
166C42×C29C2×D411yescharacteristic
167C42×C29#4111yescharacteristic
168C42×C29C2411yescharacteristic
169#19313C2911yesmaximal, characteristic, direct product factor, Sylow
170C23×C29—21no—
171C23×C29—41no—
172C23×C29#12111yescharacteristic
173Q8×C29—21no—
174Q8×C29—21no—
175Q8×C29—42no—
176Q8×C29—42no—
177Q8×C29—42no—
178Q8×C29—82no—
179D4×C29—21no—
180D4×C29—42no—
181D4×C29—42no—
182D4×C29—41no—
183D4×C29—41no—
184D4×C29—81no—
185D4×C29—82no—
186D4×C29#13712yescomplemented
187C2×C4×C29—22no—
188C2×C4×C29—21no—
189C2×C4×C29—21no—
190C2×C4×C29—21no—
191C2×C4×C29—21no—
192C2×C4×C29—21no—
193C2×C4×C29—41no—
194C2×C4×C29—42no—
195C2×C4×C29—42no—
196C2×C4×C29—41no—
197C2×C4×C29—42no—
198C2×C4×C29—81no—
199C2×C4×C29—82no—
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—42no—
209C8×C29—41no—
210C8×C29—42no—
211C8×C29—41no—
212C8×C29AGL(1,ℤ/8)14yes—
213#3152C2×C2911yescharacteristic, complemented
214#3115C2×C2911yescharacteristic
215#3079C2×C2911yescharacteristic, complemented
216#2970C2×C2911yescharacteristic, complemented
217#1690C2×C2912yescomplemented
218#1686C2×C2912yescomplemented
219#1669C2×C2912yescomplemented
220#1665C2×C2912yescomplemented
221#1569C2×C2911yescharacteristic, complemented
222#1557C2×C2911yescharacteristic, complemented
223#1556C2×C2911yescharacteristic, complemented
224C22×C29—21no—
225C22×C29—21no—
226C22×C29—22no—
227C22×C29—21no—
228C22×C29—41no—
229C22×C29—41no—
230C22×C29—81no—
231C22×C29—81no—
232C22×C29—81no—
233C22×C29C2×#12111yescharacteristic
234C4×C29—21no—
235C4×C29—21no—
236C4×C29—21no—
237C4×C29—21no—
238C4×C29—41no—
239C4×C29—41no—
240C4×C29—41no—
241C4×C29—81no—
242C4×C29—82no—
243C4×C29C2×AGL(1,ℤ/8)12yes—
244C4×C29C2×#13711yescharacteristic
245C4×C29#57511yescharacteristic
246C2×#137—22no—
247#532C22×C2911yescharacteristic
248C2×C4⋊Q8C22×C2911yescharacteristic
249C4×#41C22×C2911yescharacteristic
250#497—21no—
251#497—21no—
252#494C22×C2912yes—
253#492C22×C2912yes—
254#482—21no—
255#477—21no—
256#476—21no—
257#475C22×C2912yes—
258#475C22×C2911yescharacteristic
259#474C22×C2912yes—
260#474C22×C2911yescharacteristic
261#460C22×C2911yescharacteristic
262#459C22×C2911yescharacteristic
263#449—21no—
264#446C22×C2912yes—
265#442—21no—
266#440—21no—
267#435—22no—
268C8×D4C22×C2912yes—
269#432—21no—
270#432C22×C2911yescharacteristic
271#432C22×C2911yescharacteristic
272#428—21no—
273#423C22×C2911yescharacteristic
274#417—21no—
275C4×M16C22×C2911yescharacteristic
276C2×#97—21no—
277#335C22×C2912yes—
278#334C22×C2912yes—
279#332C22×C2912yes—
280#332C22×C2912yes—
281#332C22×C2912yes—
282#331C22×C2912yes—
283C2×C29—41no—
284C2×C29—42no—
285C2×C29—161no—
286C2×C29#303811yescharacteristic
287C2×C29#305611yescharacteristic
288C2×C29#306911yescharacteristic
289C2×#41—21no—
290C2×#41D4×C2911yescharacteristic
291C22×Q8—21no—
292#137—48no—
293C2×Q16—22no—
294C2×Q16—22no—
295C2×SD16—21no—
296C2×SD16—22no—
297C2×SD16—22no—
298C2×D8—21no—
299C2×M16—21no—
300C2×M16D4×C2912yes—
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×Q8D4×C2911yescharacteristic
312C4×Q8C23×C2911yescharacteristic
313C4×D4—21no—
314C4×D4—21no—
315C4×D4—21no—
316C4×D4—21no—
317C4×D4D4×C2911yescharacteristic
318C4×D4C23×C2911yescharacteristic
319#117—21no—
320#117D4×C2911yescharacteristic
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C42—21no—
324C2×C42C23×C2911yescharacteristic
325#107—22no—
326#107—21no—
327#106—22no—
328#106—21no—
329C4⋊C8—22no—
330C4⋊C8—21no—
331C4⋊C8C23×C2912yes—
332C4⋊C8C23×C2912yes—
333C4⋊C8C23×C2911yescharacteristic
334C4⋊C8C23×C2911yescharacteristic
335#103—22no—
336#103—21no—
337#102—22no—
338#102—21no—
339#102—21no—
340#102—21no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C22⋊C8—22no—
344#97—22no—
345#97—21no—
346#97—21no—
347#97D4×C2911yescharacteristic
348#97D4×C2911yescharacteristic
349C4×C8C23×C2912yes—
350C29#1931311yescharacteristic, direct product factor, Sylow
351#41—22no—
352#41—41no—
353#41—44no—
354C2×Q8—21no—
355C2×Q8—22no—
356C2×Q8—44no—
357C2×Q8—41no—
358C2×Q8C2×D4×C2911yescharacteristic
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—41no—
364C2×D4C2×D4×C2911yescharacteristic
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4C2×D4×C2911yescharacteristic
371C22×C4C2×D4×C2911yescharacteristic
372C22×C4#41×C2911yescharacteristic
373Q16—44no—
374Q16—44no—
375SD16—44no—
376SD16—42no—
377SD16—44no—
378D8—42no—
379M16—24no—
380M16—42no—
381C2×C8—22no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—22no—
385C2×C8—44no—
386C2×C8C2×D4×C2912yes—
387C2×C8C2×D4×C2912yes—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4C2×D4×C2911yescharacteristic
397C4⋊C4C2×D4×C2911yescharacteristic
398C22⋊C4—21no—
399C22⋊C4—21no—
400C22⋊C4—21no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C42—21no—
404C42—21no—
405C42—21no—
406C42C2×D4×C2911yescharacteristic
407C42C2×D4×C2911yescharacteristic
408C42#41×C2911yescharacteristic
409C42C24×C2911yescharacteristic
410C23—21no—
411C23—41no—
412C23C29×#12111yescharacteristic
413Q8—21no—
414Q8—21no—
415Q8—42no—
416Q8—42no—
417Q8—42no—
418Q8—82no—
419D4—21no—
420D4—42no—
421D4—42no—
422D4—41no—
423D4—41no—
424D4—81no—
425D4—82no—
426D4C29×#13712yescomplemented
427C2×C4—22no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—81no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4C29×#12111yescharacteristic
442C2×C4C29×#12111yescharacteristic
443C2×C4C29×#12111yescharacteristic
444C2×C4C22×D4×C2911yescharacteristic
445C2×C4C22×D4×C2911yescharacteristic
446C2×C4C2×#41×C2911yescharacteristic
447C8—22no—
448C8—42no—
449C8—41no—
450C8—42no—
451C8—41no—
452C8C29×AGL(1,ℤ/8)14yes—
453C22—21no—
454C22—21no—
455C22—22no—
456C22—21no—
457C22—41no—
458C22—41no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22C2×C29×#12111yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—21no—
467C4—41no—
468C4—41no—
469C4—41no—
470C4—81no—
471C4—82no—
472C4C2×C29×AGL(1,ℤ/8)12yes—
473C4C2×C29×#13711yescharacteristic
474C4C29×#57511yescharacteristic
475C2—41no—
476C2—42no—
477C2—161no—
478C2C29×#303811yescharacteristic
479C2C29×#305611yescharacteristic
480C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3115C2
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×#3152C2semidirect
3. C29×#3079C2semidirect
4. C29×#2970C2semidirect
5. C29×#1690C2semidirect
6. C29×#1686C2semidirect
7. C29×#1669C2semidirect
8. C29×#1665C2semidirect
9. C29×#1569C2semidirect
10. C29×#1557C2semidirect
11. C29×#1556C2semidirect
169. #19313C29direct (N × H)
186. D4×C29#137semidirect
213. #3152C2×C29semidirect
215. #3079C2×C29semidirect
216. #2970C2×C29semidirect
217. #1690C2×C29semidirect
218. #1686C2×C29semidirect
219. #1669C2×C29semidirect
220. #1665C2×C29semidirect
221. #1569C2×C29semidirect
222. #1557C2×C29semidirect
223. #1556C2×C29semidirect
350. C29#19313direct (N × H)
426. D4C29×#137semidirect

Maximal subgroups

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

subgroupindex
C29×#31522
C29×#31152
C29×#30792
C29×#29702
C29×#16902
C29×#16862
C29×#16692
C29×#16652
C29×#15692
C29×#15572
C29×#15562
#1931329