Finite Group Databasebeta

← C29×#19450 #20314350

Subgroups — C29×#19450 #20314350

Order 7424.

640 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×#3227C211yesmaximal, characteristic, complemented
2C29×#3079C211yesmaximal, characteristic, complemented
3C29×#3035C211yesmaximal, characteristic
4C29×#2989C211yesmaximal, characteristic, complemented
5C29×#1698C212yesmaximal, complemented
6C29×#1697C212yesmaximal, complemented
7C29×#1692C212yesmaximal, complemented
8C29×#1691C212yesmaximal, complemented
9C29×#1571C211yesmaximal, characteristic, complemented
10C29×#1547C211yesmaximal, characteristic, complemented
11C2×C29×#333C211yesmaximal, characteristic, complemented
12C2×C29×#135—21no—
13C29×#532C2211yescharacteristic
14C2×C29×C4⋊Q8C2211yescharacteristic
15C4×#41×C29C2211yescharacteristic
16C29×#498C2212yes—
17C29×#486C2212yes—
18C29×#481—22no—
19C29×#477C2212yes—
20C29×#476—21no—
21C29×#476—21no—
22C29×#476C2212yes—
23C29×#475—21no—
24C29×#474—21no—
25C29×#464—21no—
26C29×#463—21no—
27C29×#462C2211yescharacteristic
28C29×#461C2211yescharacteristic
29C29×#460C2211yescharacteristic
30C29×#459C2211yescharacteristic
31C29×#446C2212yes—
32C29×#436C2212yes—
33C29×#435—22no—
34C29×#432—21no—
35C29×#431C2211yescharacteristic
36C29×#428—21no—
37C29×#423—21no—
38C29×#423C2211yescharacteristic
39C2×C29×C4⋊C8C2211yescharacteristic
40C2×C29×C4⋊C8C2211yescharacteristic
41C29×#417—21no—
42C29×#416—21no—
43C29×#335C2212yes—
44C29×#335C2212yes—
45C29×#333C2212yes—
46C29×#333C2212yes—
47C29×#332C2212yes—
48C29×#331C2212yes—
49C2×#41×C29—21no—
50C2×#41×C29D411yescharacteristic
51C22×Q8×C29—21no—
52C29×#135—44no—
53C2×Q16×C29—21no—
54C2×SD16×C29—21no—
55C2×SD16×C29—21no—
56C2×D8×C29—21no—
57C2×M16×C29—21no—
58C2×M16×C29—22no—
59C22×C8×C29—21no—
60C22×C8×C29—21no—
61C29×C4⋊Q8—21no—
62C29×C4⋊Q8—21no—
63C29×C4⋊Q8—21no—
64C29×C4⋊Q8C2311yescharacteristic
65C29×C4⋊Q8C2312yes—
66C29×#127C2311yescharacteristic
67C29×#124—21no—
68C29×#121—21no—
69C29×#121—21no—
70C4×Q8×C29D411yescharacteristic
71C4×Q8×C29C2311yescharacteristic
72C4×D4×C29—21no—
73C4×D4×C29—21no—
74C4×D4×C29—21no—
75C4×D4×C29—21no—
76C4×D4×C29D411yescharacteristic
77C4×D4×C29C2311yescharacteristic
78C29×#117—21no—
79C29×#117D411yescharacteristic
80C2×C4⋊C4×C29—21no—
81C2×C4⋊C4×C29—21no—
82C2×C42×C29—21no—
83C2×C42×C29C2311yescharacteristic
84C29×#107—22no—
85C29×#106—22no—
86C29×#106—22no—
87C29×#106—22no—
88C29×C4⋊C8—22no—
89C29×C4⋊C8—21no—
90C29×C4⋊C8—21no—
91C29×C4⋊C8—21no—
92C29×C4⋊C8D411yescharacteristic
93C29×C4⋊C8D411yescharacteristic
94C29×C4⋊C8C2312yes—
95C29×C4⋊C8C2311yescharacteristic
96C29×C4⋊C8C2311yescharacteristic
97C29×C4⋊C8C2312yes—
98C29×#103—22no—
99C29×#103—21no—
100C29×#103—21no—
101C29×#102—22no—
102C29×#102—22no—
103C29×#102—22no—
104C29×#102—21no—
105C29×#102—21no—
106C29×C22⋊C8—22no—
107C29×C22⋊C8D412yes—
108C29×#97—22no—
109C4×C8×C29C2312yes—
110#41×C29—22no—
111#41×C29—22no—
112#41×C29—42no—
113#41×C29—42no—
114C2×Q8×C29—21no—
115C2×Q8×C29—22no—
116C2×Q8×C29—41no—
117C2×Q8×C29—82no—
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—42no—
134SD16×C29—42no—
135SD16×C29—42no—
136D8×C29—42no—
137M16×C29—42no—
138M16×C29—82no—
139C2×C8×C29—22no—
140C2×C8×C29—21no—
141C2×C8×C29—21no—
142C2×C8×C29—22no—
143C2×C8×C29—42no—
144C2×C8×C29—81no—
145C2×C8×C29C2×D412yes—
146C2×C8×C29C2×D412yes—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—21no—
149C4⋊C4×C29—22no—
150C4⋊C4×C29—22no—
151C4⋊C4×C29—21no—
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#19450C2911yesmaximal, characteristic, direct product factor, Sylow
170C23×C29—21no—
171C23×C29—41no—
172C23×C29#12111yescharacteristic
173Q8×C29—21no—
174Q8×C29—21no—
175Q8×C29—41no—
176Q8×C29—41no—
177Q8×C29—82no—
178Q8×C29—82no—
179D4×C29—21no—
180D4×C29—21no—
181D4×C29—42no—
182D4×C29—41no—
183D4×C29—41no—
184D4×C29—41no—
185D4×C29—41no—
186D4×C29—81no—
187D4×C29—82no—
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—41no—
195C2×C4×C29—41no—
196C2×C4×C29—42no—
197C2×C4×C29—41no—
198C2×C4×C29—42no—
199C2×C4×C29—81no—
200C2×C4×C29—82no—
201C2×C4×C29—82no—
202C2×C4×C29#12111yescharacteristic
203C2×C4×C29#12111yescharacteristic
204C2×C4×C29#12111yescharacteristic
205C2×C4×C29AGL(1,ℤ/8)12yes—
206C2×C4×C29#13712yes—
207C2×C4×C29C22×D411yescharacteristic
208C2×C4×C29C22×D411yescharacteristic
209C2×C4×C29C2×#4111yescharacteristic
210C8×C29—22no—
211C8×C29—22no—
212C8×C29—41no—
213C8×C29—41no—
214C8×C29—42no—
215C8×C29—42no—
216#3227C2×C2911yescharacteristic, complemented
217#3079C2×C2911yescharacteristic, complemented
218#3035C2×C2911yescharacteristic
219#2989C2×C2911yescharacteristic, complemented
220#1698C2×C2912yescomplemented
221#1697C2×C2912yescomplemented
222#1692C2×C2912yescomplemented
223#1691C2×C2912yescomplemented
224#1571C2×C2911yescharacteristic, complemented
225#1547C2×C2911yescharacteristic, complemented
226C2×#333C2×C2911yescharacteristic, complemented
227C22×C29—21no—
228C22×C29—21no—
229C22×C29—41no—
230C22×C29—41no—
231C22×C29—41no—
232C22×C29—81no—
233C22×C29—81no—
234C22×C29—81no—
235C22×C29#46812yes—
236C22×C29C2×#12111yescharacteristic
237C4×C29—21no—
238C4×C29—21no—
239C4×C29—21no—
240C4×C29—41no—
241C4×C29—41no—
242C4×C29—41no—
243C4×C29—81no—
244C4×C29—82no—
245C4×C29#46812yes—
246C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
247C4×C29C2×#13711yescharacteristic
248C4×C29#57711yescharacteristic
249C4×C29#57811yescharacteristic
250C2×#135—21no—
251#532C22×C2911yescharacteristic
252C2×C4⋊Q8C22×C2911yescharacteristic
253C4×#41C22×C2911yescharacteristic
254#498C22×C2912yes—
255#486C22×C2912yes—
256#481—22no—
257#477C22×C2912yes—
258#476—21no—
259#476—21no—
260#476C22×C2912yes—
261#475—21no—
262#474—21no—
263#464—21no—
264#463—21no—
265#462C22×C2911yescharacteristic
266#461C22×C2911yescharacteristic
267#460C22×C2911yescharacteristic
268#459C22×C2911yescharacteristic
269#446C22×C2912yes—
270#436C22×C2912yes—
271#435—22no—
272#432—21no—
273#431C22×C2911yescharacteristic
274#428—21no—
275#423—21no—
276#423C22×C2911yescharacteristic
277C2×C4⋊C8C22×C2911yescharacteristic
278C2×C4⋊C8C22×C2911yescharacteristic
279#417—21no—
280#416—21no—
281#335C22×C2912yes—
282#335C22×C2912yes—
283#333C22×C2912yes—
284#333C22×C2912yes—
285#332C22×C2912yes—
286#331C22×C2912yes—
287C2×C29—22no—
288C2×C29—81no—
289C2×C29—161no—
290C2×C29#304611yescharacteristic
291C2×C29C2×#46811yescharacteristic
292C2×C29#306811yescharacteristic
293C2×#41—21no—
294C2×#41D4×C2911yescharacteristic
295C22×Q8—21no—
296#135—44no—
297C2×Q16—21no—
298C2×SD16—21no—
299C2×SD16—21no—
300C2×D8—21no—
301C2×M16—21no—
302C2×M16—22no—
303C22×C8—21no—
304C22×C8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8C23×C2912yes—
309C4⋊Q8C23×C2911yescharacteristic
310#127C23×C2911yescharacteristic
311#124—21no—
312#121—21no—
313#121—21no—
314C4×Q8D4×C2911yescharacteristic
315C4×Q8C23×C2911yescharacteristic
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4D4×C2911yescharacteristic
321C4×D4C23×C2911yescharacteristic
322#117—21no—
323#117D4×C2911yescharacteristic
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C42—21no—
327C2×C42C23×C2911yescharacteristic
328#107—22no—
329#106—22no—
330#106—22no—
331#106—22no—
332C4⋊C8—22no—
333C4⋊C8—21no—
334C4⋊C8—21no—
335C4⋊C8—21no—
336C4⋊C8D4×C2911yescharacteristic
337C4⋊C8D4×C2911yescharacteristic
338C4⋊C8C23×C2912yes—
339C4⋊C8C23×C2912yes—
340C4⋊C8C23×C2911yescharacteristic
341C4⋊C8C23×C2911yescharacteristic
342#103—22no—
343#103—21no—
344#103—21no—
345#102—22no—
346#102—22no—
347#102—22no—
348#102—21no—
349#102—21no—
350C22⋊C8—22no—
351C22⋊C8D4×C2912yes—
352#97—22no—
353C4×C8C23×C2912yes—
354C29#1945011yescharacteristic, direct product factor, Sylow
355#41—22no—
356#41—22no—
357#41—42no—
358#41—42no—
359C2×Q8—21no—
360C2×Q8—22no—
361C2×Q8—41no—
362C2×Q8—82no—
363C2×Q8C2×D4×C2911yescharacteristic
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—41no—
369C2×D4C2×D4×C2911yescharacteristic
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4C2×D4×C2911yescharacteristic
376C22×C4C2×D4×C2911yescharacteristic
377C22×C4#41×C2911yescharacteristic
378Q16—42no—
379SD16—42no—
380SD16—42no—
381D8—42no—
382M16—42no—
383M16—82no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—42no—
389C2×C8—81no—
390C2×C8C2×D4×C2912yes—
391C2×C8C2×D4×C2912yes—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4C2×D4×C2911yescharacteristic
401C4⋊C4C2×D4×C2911yescharacteristic
402C22⋊C4—21no—
403C22⋊C4—21no—
404C22⋊C4—21no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C42—21no—
408C42—21no—
409C42—21no—
410C42C2×D4×C2911yescharacteristic
411C42C2×D4×C2911yescharacteristic
412C42#41×C2911yescharacteristic
413C42C24×C2911yescharacteristic
414C23—21no—
415C23—41no—
416C23C29×#12111yescharacteristic
417Q8—21no—
418Q8—21no—
419Q8—41no—
420Q8—41no—
421Q8—82no—
422Q8—82no—
423D4—21no—
424D4—21no—
425D4—42no—
426D4—41no—
427D4—41no—
428D4—41no—
429D4—41no—
430D4—81no—
431D4—82no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—81no—
444C2×C4—82no—
445C2×C4—82no—
446C2×C4C29×#12111yescharacteristic
447C2×C4C29×#12111yescharacteristic
448C2×C4C29×#12111yescharacteristic
449C2×C4C29×AGL(1,ℤ/8)12yes—
450C2×C4C29×#13712yes—
451C2×C4C22×D4×C2911yescharacteristic
452C2×C4C22×D4×C2911yescharacteristic
453C2×C4C2×#41×C2911yescharacteristic
454C8—22no—
455C8—22no—
456C8—41no—
457C8—41no—
458C8—42no—
459C8—42no—
460C22—21no—
461C22—21no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22C29×#46812yes—
469C22C2×C29×#12111yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—41no—
474C4—41no—
475C4—41no—
476C4—81no—
477C4—82no—
478C4C29×#46812yes—
479C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
480C4C2×C29×#13711yescharacteristic
481C4C29×#57711yescharacteristic
482C4C29×#57811yescharacteristic
483C2—22no—
484C2—81no—
485C2—161no—
486C2C29×#304611yescharacteristic
487C2C2×C29×#46811yescharacteristic
488C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3035C2
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
2. C29×#3079C2semidirect
4. C29×#2989C2semidirect
5. C29×#1698C2semidirect
6. C29×#1697C2semidirect
7. C29×#1692C2semidirect
8. C29×#1691C2semidirect
9. C29×#1571C2semidirect
10. C29×#1547C2semidirect
11. C2×C29×#333C2semidirect
169. #19450C29direct (N × H)
216. #3227C2×C29semidirect
217. #3079C2×C29semidirect
219. #2989C2×C29semidirect
220. #1698C2×C29semidirect
221. #1697C2×C29semidirect
222. #1692C2×C29semidirect
223. #1691C2×C29semidirect
224. #1571C2×C29semidirect
225. #1547C2×C29semidirect
226. C2×#333C2×C29semidirect
354. C29#19450direct (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×#30792
C29×#30352
C29×#29892
C29×#16982
C29×#16972
C29×#16922
C29×#16912
C29×#15712
C29×#15472
C2×C29×#3332
#1945029