Finite Group Databasebeta

← C29×#13103 #20308003

Subgroups — C29×#13103 #20308003

Order 7424.

646 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3010C211yesmaximal, characteristic
2C29×#2884C211yesmaximal, characteristic, complemented
3C29×#2128C211yesmaximal, characteristic, complemented
4C29×#2122C211yesmaximal, characteristic, complemented
5C29×#1796C211yesmaximal, characteristic, complemented
6C29×#1395C211yesmaximal, characteristic, complemented
7C29×#1391C211yesmaximal, characteristic, complemented
8C2×C29×2−1+4C2211yescharacteristic
9C2×C29×AGL(1,ℤ/8)C411yescharacteristic, complemented
10C22×SD16×C29C411yescharacteristic, complemented
11C29×#535C2211yescharacteristic
12C29×#519—21no—
13C29×#449—21no—
14C29×#449—21no—
15C29×#448—21no—
16C29×#448—21no—
17C29×#421—21no—
18C29×#419—21no—
19C29×#419C411yescharacteristic, complemented
20C29×#416C411yescharacteristic, complemented
21C29×#413C2211yescharacteristic
22C29×#410—22no—
23C29×#410—22no—
24C29×#410—21no—
25C29×#410C2211yescharacteristic
26C29×#410C2211yescharacteristic
27C29×#410C2211yescharacteristic
28C29×#408C2211yescharacteristic
29C29×#353—22no—
30C29×AΣL(1,𝔽16)—22no—
31C29×2−1+4—42no—
32C29×2−1+4—42no—
33C2×#41×C29—21no—
34C2×#41×C29—21no—
35C2×#41×C29—21no—
36C2×#41×C29C2×C411yescharacteristic
37C2×#41×C29D411yescharacteristic
38C2×#41×C29D411yescharacteristic
39C2×#41×C29C2311yescharacteristic
40C22×Q8×C29—21no—
41C22×Q8×C29C2×C411yescharacteristic
42C22×Q8×C29D411yescharacteristic
43C22×Q8×C29D411yescharacteristic
44C22×D4×C29C2×C411yescharacteristic
45C29×AGL(1,ℤ/8)—42no—
46C2×SD16×C29—21no—
47C2×SD16×C29—21no—
48C2×SD16×C29—21no—
49C2×SD16×C29—42no—
50C2×D8×C29—21no—
51C2×M16×C29—21no—
52C2×M16×C29C2×C411yescharacteristic
53C22×C8×C29C2×C411yescharacteristic
54C29×#127—21no—
55C29×#124—21no—
56C29×#121—21no—
57C29×#121—21no—
58C29×#120—21no—
59C29×#120—21no—
60C4×Q8×C29—42no—
61C4×Q8×C29—42no—
62C29×#117—24no—
63C29×#117—21no—
64C29×#117—21no—
65C29×#117—21no—
66C29×#117C2×C411yescharacteristic
67C29×#104—42no—
68C29×#103—21no—
69C29×#103—21no—
70C29×#103—21no—
71C29×#103—42no—
72C29×#102—21no—
73C29×#101—21no—
74C29×#100—21no—
75C29×#99—24no—
76C29×#99—21no—
77C29×#99—21no—
78C29×#99—21no—
79C29×#99—21no—
80C29×#99D412yes—
81C29×#99D412yes—
82C29×C22⋊C8—21no—
83C29×C22⋊C8—21no—
84C24×C29—21no—
85#41×C29—22no—
86#41×C29—22no—
87#41×C29—41no—
88#41×C29—41no—
89#41×C29—41no—
90#41×C29—41no—
91#41×C29—41no—
92#41×C29—41no—
93#41×C29—44no—
94#41×C29—44no—
95#41×C29—44no—
96C2×Q8×C29—22no—
97C2×Q8×C29—22no—
98C2×Q8×C29—21no—
99C2×Q8×C29—21no—
100C2×Q8×C29—21no—
101C2×Q8×C29—22no—
102C2×Q8×C29—22no—
103C2×Q8×C29—41no—
104C2×Q8×C29—41no—
105C2×Q8×C29—44no—
106C2×Q8×C29C22⋊C411yescharacteristic
107C2×Q8×C29C22⋊C411yescharacteristic
108C2×Q8×C29C22⋊C411yescharacteristic
109C2×Q8×C29#4111yescharacteristic
110C2×D4×C29—21no—
111C2×D4×C29—21no—
112C2×D4×C29—21no—
113C2×D4×C29—21no—
114C2×D4×C29—21no—
115C2×D4×C29—41no—
116C2×D4×C29—41no—
117C2×D4×C29—41no—
118C2×D4×C29—41no—
119C2×D4×C29C22⋊C411yescharacteristic
120C2×D4×C29C2×D411yescharacteristic
121C2×D4×C29C2×D411yescharacteristic
122C2×D4×C29#4111yescharacteristic
123C22×C4×C29—21no—
124C22×C4×C29—21no—
125C22×C4×C29—21no—
126C22×C4×C29—21no—
127C22×C4×C29—21no—
128C22×C4×C29—21no—
129C22×C4×C29C22×C411yescharacteristic
130C22×C4×C29C2×D411yescharacteristic
131C22×C4×C29C2×D411yescharacteristic
132SD16×C29—42no—
133SD16×C29—42no—
134SD16×C29—42no—
135D8×C29—42no—
136M16×C29—41no—
137M16×C29—41no—
138M16×C29—41no—
139C2×C8×C29—21no—
140C2×C8×C29—21no—
141C2×C8×C29—41no—
142C2×C8×C29—41no—
143C4⋊C4×C29—21no—
144C4⋊C4×C29—44no—
145C4⋊C4×C29—41no—
146C4⋊C4×C29—41no—
147C4⋊C4×C29—41no—
148C22⋊C4×C29—21no—
149C22⋊C4×C29—22no—
150C22⋊C4×C29—22no—
151C22⋊C4×C29—41no—
152C22⋊C4×C29—41no—
153C22⋊C4×C29—41no—
154C42×C29—21no—
155C42×C29—44no—
156C42×C29—41no—
157C42×C29—41no—
158C42×C29—41no—
159#13103C2911yesmaximal, characteristic, direct product factor, Sylow
160C23×C29—21no—
161C23×C29—41no—
162C23×C29—81no—
163C23×C29—161no—
164C23×C29C4×D411yescharacteristic
165C23×C29#12011yescharacteristic
166C23×C29#12111yescharacteristic
167Q8×C29—24no—
168Q8×C29—21no—
169Q8×C29—21no—
170Q8×C29—21no—
171Q8×C29—21no—
172Q8×C29—41no—
173Q8×C29—42no—
174Q8×C29—42no—
175Q8×C29#9912yes—
176Q8×C29#9912yes—
177D4×C29—21no—
178D4×C29—21no—
179D4×C29—41no—
180D4×C29—41no—
181D4×C29—41no—
182D4×C29—42no—
183D4×C29—42no—
184D4×C29—42no—
185D4×C29—41no—
186D4×C29—41no—
187D4×C29—81no—
188D4×C29—161no—
189D4×C29—161no—
190C2×C4×C29—24no—
191C2×C4×C29—21no—
192C2×C4×C29—21no—
193C2×C4×C29—21no—
194C2×C4×C29—21no—
195C2×C4×C29—21no—
196C2×C4×C29—21no—
197C2×C4×C29—21no—
198C2×C4×C29—21no—
199C2×C4×C29—21no—
200C2×C4×C29—42no—
201C2×C4×C29—42no—
202C2×C4×C29—42no—
203C2×C4×C29—42no—
204C2×C4×C29—42no—
205C2×C4×C29—42no—
206C2×C4×C29—42no—
207C2×C4×C29—41no—
208C2×C4×C29—81no—
209C2×C4×C29C2×C22⋊C411yescharacteristic
210C2×C4×C29C4×D411yescharacteristic
211C2×C4×C29#12111yescharacteristic
212C2×C4×C29#12311yescharacteristic
213C8×C29—41no—
214C8×C29—41no—
215C8×C29—81no—
216#3010C2×C2911yescharacteristic
217#2884C2×C2911yescharacteristic, complemented
218#2128C2×C2911yescharacteristic, complemented
219#2122C2×C2911yescharacteristic, complemented
220#1796C2×C2911yescharacteristic, complemented
221#1395C2×C2911yescharacteristic, complemented
222#1391C2×C2911yescharacteristic, complemented
223C22×C29—21no—
224C22×C29—21no—
225C22×C29—21no—
226C22×C29—41no—
227C22×C29—41no—
228C22×C29—41no—
229C22×C29—41no—
230C22×C29—81no—
231C22×C29—81no—
232C22×C29—81no—
233C22×C29—81no—
234C22×C29—162no—
235C22×C29#38611yescharacteristic
236C4×C29—21no—
237C4×C29—22no—
238C4×C29—22no—
239C4×C29—21no—
240C4×C29—21no—
241C4×C29—41no—
242C4×C29—81no—
243C4×C29—82no—
244C4×C29—82no—
245C4×C29—161no—
246C4×C29C2×#9911yescharacteristic
247C4×C29C2×#9911yescharacteristic
248C2×2−1+4C22×C2911yescharacteristic
249C2×AGL(1,ℤ/8)C4×C2911yescharacteristic, complemented
250C22×SD16C4×C2911yescharacteristic, complemented
251#535C22×C2911yescharacteristic
252#519—21no—
253#449—21no—
254#449—21no—
255#448—21no—
256#448—21no—
257#421—21no—
258#419—21no—
259#419C4×C2911yescharacteristic, complemented
260#416C4×C2911yescharacteristic, complemented
261#413C22×C2911yescharacteristic
262#410—21no—
263#410—22no—
264#410—22no—
265#410C22×C2911yescharacteristic
266#410C22×C2911yescharacteristic
267#410C22×C2911yescharacteristic
268#408C22×C2911yescharacteristic
269#353—22no—
270AΣL(1,𝔽16)—22no—
271C2×C29—21no—
272C2×C29—41no—
273C2×C29—41no—
274C2×C29—41no—
275C2×C29—81no—
276C2×C29—161no—
277C2×C29#189811yescharacteristic
2782−1+4—42no—
2792−1+4—42no—
280C2×#41—21no—
281C2×#41—21no—
282C2×#41—21no—
283C2×#41C2×C4×C2911yescharacteristic
284C2×#41D4×C2911yescharacteristic
285C2×#41D4×C2911yescharacteristic
286C2×#41C23×C2911yescharacteristic
287C22×Q8—21no—
288C22×Q8C2×C4×C2911yescharacteristic
289C22×Q8D4×C2911yescharacteristic
290C22×Q8D4×C2911yescharacteristic
291C22×D4C2×C4×C2911yescharacteristic
292AGL(1,ℤ/8)—42no—
293C2×SD16—21no—
294C2×SD16—21no—
295C2×SD16—21no—
296C2×SD16—42no—
297C2×D8—21no—
298C2×M16—21no—
299C2×M16C2×C4×C2911yescharacteristic
300C22×C8C2×C4×C2911yescharacteristic
301#127—21no—
302#124—21no—
303#121—21no—
304#121—21no—
305#120—21no—
306#120—21no—
307C4×Q8—42no—
308C4×Q8—42no—
309#117—24no—
310#117—21no—
311#117—21no—
312#117—21no—
313#117C2×C4×C2911yescharacteristic
314#104—42no—
315#103—21no—
316#103—21no—
317#103—21no—
318#103—42no—
319#102—21no—
320#101—21no—
321#100—21no—
322#99—24no—
323#99—21no—
324#99—21no—
325#99—21no—
326#99—21no—
327#99D4×C2912yes—
328#99D4×C2912yes—
329C22⋊C8—21no—
330C22⋊C8—21no—
331C29#1310311yescharacteristic, direct product factor, Sylow
332C24—21no—
333#41—22no—
334#41—22no—
335#41—41no—
336#41—41no—
337#41—41no—
338#41—41no—
339#41—41no—
340#41—41no—
341#41—44no—
342#41—44no—
343#41—44no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—41no—
352C2×Q8—41no—
353C2×Q8—44no—
354C2×Q8C22⋊C4×C2911yescharacteristic
355C2×Q8C22⋊C4×C2911yescharacteristic
356C2×Q8C22⋊C4×C2911yescharacteristic
357C2×Q8#41×C2911yescharacteristic
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4C22⋊C4×C2911yescharacteristic
368C2×D4C2×D4×C2911yescharacteristic
369C2×D4C2×D4×C2911yescharacteristic
370C2×D4#41×C2911yescharacteristic
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4C22×C4×C2911yescharacteristic
378C22×C4C2×D4×C2911yescharacteristic
379C22×C4C2×D4×C2911yescharacteristic
380SD16—42no—
381SD16—42no—
382SD16—42no—
383D8—42no—
384M16—41no—
385M16—41no—
386M16—41no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—41no—
390C2×C8—41no—
391C4⋊C4—21no—
392C4⋊C4—44no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C22⋊C4—21no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C42—21no—
403C42—44no—
404C42—41no—
405C42—41no—
406C42—41no—
407C23—21no—
408C23—41no—
409C23—81no—
410C23—161no—
411C23C4×D4×C2911yescharacteristic
412C23C29×#12011yescharacteristic
413C23C29×#12111yescharacteristic
414Q8—24no—
415Q8—21no—
416Q8—21no—
417Q8—21no—
418Q8—21no—
419Q8—41no—
420Q8—42no—
421Q8—42no—
422Q8C29×#9912yes—
423Q8C29×#9912yes—
424D4—21no—
425D4—21no—
426D4—41no—
427D4—41no—
428D4—41no—
429D4—42no—
430D4—42no—
431D4—42no—
432D4—41no—
433D4—41no—
434D4—81no—
435D4—161no—
436D4—161no—
437C2×C4—24no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—81no—
456C2×C4C2×C22⋊C4×C2911yescharacteristic
457C2×C4C4×D4×C2911yescharacteristic
458C2×C4C29×#12111yescharacteristic
459C2×C4C29×#12311yescharacteristic
460C8—41no—
461C8—41no—
462C8—81no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—162no—
475C22C29×#38611yescharacteristic
476C4—21no—
477C4—22no—
478C4—22no—
479C4—21no—
480C4—21no—
481C4—41no—
482C4—81no—
483C4—82no—
484C4—82no—
485C4—161no—
486C4C2×C29×#9911yescharacteristic
487C4C2×C29×#9911yescharacteristic
488C2—21no—
489C2—41no—
490C2—41no—
491C2—41no—
492C2—81no—
493C2—161no—
494C2C29×#189811yescharacteristic
subgroupG/H
center, socleC2×C29#1898
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×#41C23×C29
prime radicalC29×#3010C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C2×C29×2−1+4 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C29×#2884C2semidirect
3. C29×#2128C2semidirect
4. C29×#2122C2semidirect
5. C29×#1796C2semidirect
6. C29×#1395C2semidirect
7. C29×#1391C2semidirect
9. C2×C29×AGL(1,ℤ/8)C4semidirect
10. C22×SD16×C29C4semidirect
19. C29×#419C4semidirect
20. C29×#416C4semidirect
159. #13103C29direct (N × H)
217. #2884C2×C29semidirect
218. #2128C2×C29semidirect
219. #2122C2×C29semidirect
220. #1796C2×C29semidirect
221. #1395C2×C29semidirect
222. #1391C2×C29semidirect
249. C2×AGL(1,ℤ/8)C4×C29semidirect
250. C22×SD16C4×C29semidirect
259. #419C4×C29semidirect
260. #416C4×C29semidirect
331. C29#13103direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30102
C29×#28842
C29×#21282
C29×#21222
C29×#17962
C29×#13952
C29×#13912
#1310329