Finite Group Databasebeta

← C29×#19474 #20314374

Subgroups — C29×#19474 #20314374

Order 7424.

630 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3227C211yesmaximal, characteristic
2C29×#3112C211yesmaximal, characteristic
3C2×C29×#462C211yesmaximal, characteristic, complemented
4C29×#2984C211yesmaximal, characteristic, complemented
5C29×#1702C212yesmaximal, complemented
6C29×#1692C212yesmaximal, complemented
7C29×#1682C212yesmaximal, complemented
8C29×#1672C212yesmaximal, complemented
9C29×#1573C211yesmaximal, characteristic, complemented
10C29×#1556C211yesmaximal, characteristic, complemented
11C29×#1551C211yesmaximal, characteristic
12C22×Q16×C29—21no—
13C29×#532C2211yescharacteristic
14C2×C29×C4⋊Q8C2211yescharacteristic
15C2×C4×Q8×C29C2211yescharacteristic
16C29×#498C2212yes—
17C29×#486C2212yes—
18C29×#481—21no—
19C29×#481—21no—
20C29×#480—21no—
21C29×#477C2211yescharacteristic
22C29×#477C2211yescharacteristic
23C29×#476—22no—
24C29×#462—21no—
25C29×#462—21no—
26C29×#462C2212yes—
27C29×#462C2212yes—
28C29×#460C2211yescharacteristic
29C29×#460C2211yescharacteristic
30C29×#448—21no—
31C29×#446—22no—
32C29×#446C2212yes—
33C8×Q8×C29C2212yes—
34C29×#440—21no—
35C29×#440—21no—
36C29×#432—21no—
37C29×#432C2211yescharacteristic
38C29×#432C2211yescharacteristic
39C29×#431—21no—
40C29×#431C2211yescharacteristic
41C2×C29×C4⋊C8C2211yescharacteristic
42C2×C29×#103—21no—
43C29×#335C2212yes—
44C29×#334C2212yes—
45C29×#333C2212yes—
46C29×#332C2212yes—
47C29×#332C2212yes—
48C29×#331C2212yes—
49C2×#41×C29—21no—
50C22×Q8×C29—21no—
51C22×Q8×C29D411yescharacteristic
52C2×Q16×C29—22no—
53C2×Q16×C29—22no—
54C2×Q16×C29—44no—
55C2×SD16×C29—21no—
56C2×SD16×C29—21no—
57C22×C8×C29—21no—
58C29×C4⋊Q8—21no—
59C29×C4⋊Q8—21no—
60C29×C4⋊Q8—21no—
61C29×C4⋊Q8C2312yes—
62C29×C4⋊Q8C2311yescharacteristic
63C29×#127C2311yescharacteristic
64C29×#124—21no—
65C29×#121—21no—
66C29×#121—21no—
67C4×Q8×C29—21no—
68C4×Q8×C29—21no—
69C4×Q8×C29D411yescharacteristic
70C4×Q8×C29D411yescharacteristic
71C4×Q8×C29C2311yescharacteristic
72C4×Q8×C29C2311yescharacteristic
73C4×D4×C29—21no—
74C4×D4×C29—21no—
75C2×C4⋊C4×C29—21no—
76C2×C4⋊C4×C29—21no—
77C2×C4⋊C4×C29—21no—
78C2×C4⋊C4×C29D411yescharacteristic
79C2×C42×C29—21no—
80C2×C42×C29C2311yescharacteristic
81C29×#107—21no—
82C29×#107—21no—
83C29×#106—22no—
84C29×#106—22no—
85C29×C4⋊C8—22no—
86C29×C4⋊C8—22no—
87C29×C4⋊C8—21no—
88C29×C4⋊C8D412yes—
89C29×C4⋊C8C2312yes—
90C29×C4⋊C8C2311yescharacteristic
91C29×C4⋊C8C2311yescharacteristic
92C29×C4⋊C8C2312yes—
93C29×#103—21no—
94C29×#103—21no—
95C29×#103—22no—
96C29×#103—22no—
97C29×#102—22no—
98C29×#102—22no—
99C29×#102—21no—
100C29×#102—21no—
101C29×C22⋊C8—21no—
102C29×C22⋊C8—21no—
103C29×C22⋊C8D411yescharacteristic
104C29×C22⋊C8D411yescharacteristic
105C29×#97—22no—
106C29×#97—21no—
107C29×#97—21no—
108C4×C8×C29—22no—
109C4×C8×C29C2312yes—
110#41×C29—82no—
111C2×Q8×C29—21no—
112C2×Q8×C29—22no—
113C2×Q8×C29—22no—
114C2×Q8×C29—21no—
115C2×Q8×C29—41no—
116C2×Q8×C29—42no—
117C2×Q8×C29—42no—
118C2×Q8×C29—41no—
119C2×Q8×C29C2×D411yescharacteristic
120C2×Q8×C29C2×D411yescharacteristic
121C2×D4×C29—21no—
122C2×D4×C29—21no—
123C2×D4×C29—21no—
124C2×D4×C29—41no—
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—42no—
135SD16×C29—42no—
136C2×C8×C29—22no—
137C2×C8×C29—21no—
138C2×C8×C29—21no—
139C2×C8×C29—22no—
140C2×C8×C29—42no—
141C2×C8×C29C2×D412yes—
142C2×C8×C29C2×D412yes—
143C4⋊C4×C29—21no—
144C4⋊C4×C29—21no—
145C4⋊C4×C29—21no—
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—41no—
157C22⋊C4×C29—41no—
158C42×C29—21no—
159C42×C29—21no—
160C42×C29—21no—
161C42×C29—21no—
162C42×C29C2×D411yescharacteristic
163C42×C29C2×D411yescharacteristic
164C42×C29#4111yescharacteristic
165C42×C29C2411yescharacteristic
166#19474C2911yesmaximal, characteristic, direct product factor, Sylow
167C23×C29—41no—
168C23×C29#12111yescharacteristic
169Q8×C29—21no—
170Q8×C29—21no—
171Q8×C29—21no—
172Q8×C29—42no—
173Q8×C29—42no—
174Q8×C29—42no—
175Q8×C29—81no—
176Q8×C29—82no—
177Q8×C29AGL(1,ℤ/8)12yes—
178D4×C29—41no—
179D4×C29—41no—
180D4×C29—42no—
181D4×C29—81no—
182D4×C29—82no—
183C2×C4×C29—21no—
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—21no—
191C2×C4×C29—42no—
192C2×C4×C29—42no—
193C2×C4×C29—41no—
194C2×C4×C29—42no—
195C2×C4×C29—82no—
196C2×C4×C29—82no—
197C2×C4×C29#12111yescharacteristic
198C2×C4×C29#12111yescharacteristic
199C2×C4×C29#12111yescharacteristic
200C2×C4×C29C22×D411yescharacteristic
201C2×C4×C29C22×D411yescharacteristic
202C2×C4×C29C2×#4111yescharacteristic
203C8×C29—22no—
204C8×C29—22no—
205C8×C29—42no—
206C8×C29—41no—
207C8×C29—41no—
208C8×C29—42no—
209#3227C2×C2911yescharacteristic
210#3112C2×C2911yescharacteristic
211C2×#462C2×C2911yescharacteristic, complemented
212#2984C2×C2911yescharacteristic, complemented
213#1702C2×C2912yescomplemented
214#1692C2×C2912yescomplemented
215#1682C2×C2912yescomplemented
216#1672C2×C2912yescomplemented
217#1573C2×C2911yescharacteristic, complemented
218#1556C2×C2911yescharacteristic, complemented
219#1551C2×C2911yescharacteristic
220C22×C29—21no—
221C22×C29—21no—
222C22×C29—81no—
223C22×C29—81no—
224C22×C29—81no—
225C22×C29#47112yes—
226C22×C29C2×#12111yescharacteristic
227C4×C29—21no—
228C4×C29—21no—
229C4×C29—22no—
230C4×C29—21no—
231C4×C29—21no—
232C4×C29—41no—
233C4×C29—41no—
234C4×C29—41no—
235C4×C29—82no—
236C4×C29—81no—
237C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
238C4×C29#57511yescharacteristic
239C4×C29#57812yes—
240C22×Q16—21no—
241#532C22×C2911yescharacteristic
242C2×C4⋊Q8C22×C2911yescharacteristic
243C2×C4×Q8C22×C2911yescharacteristic
244#498C22×C2912yes—
245#486C22×C2912yes—
246#481—21no—
247#481—21no—
248#480—21no—
249#477C22×C2911yescharacteristic
250#477C22×C2911yescharacteristic
251#476—22no—
252#462—21no—
253#462—21no—
254#462C22×C2912yes—
255#462C22×C2912yes—
256#460C22×C2911yescharacteristic
257#460C22×C2911yescharacteristic
258#448—21no—
259#446—22no—
260#446C22×C2912yes—
261C8×Q8C22×C2912yes—
262#440—21no—
263#440—21no—
264#432—21no—
265#432C22×C2911yescharacteristic
266#432C22×C2911yescharacteristic
267#431—21no—
268#431C22×C2911yescharacteristic
269C2×C4⋊C8C22×C2911yescharacteristic
270C2×#103—21no—
271#335C22×C2912yes—
272#334C22×C2912yes—
273#333C22×C2912yes—
274#332C22×C2912yes—
275#332C22×C2912yes—
276#331C22×C2912yes—
277C2×C29—22no—
278C2×C29—161no—
279C2×C29#304411yescharacteristic
280C2×C29#305511yescharacteristic
281C2×C29C2×#47111yescharacteristic
282C2×#41—21no—
283C22×Q8—21no—
284C22×Q8D4×C2911yescharacteristic
285C2×Q16—22no—
286C2×Q16—22no—
287C2×Q16—44no—
288C2×SD16—21no—
289C2×SD16—21no—
290C22×C8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8C23×C2912yes—
295C4⋊Q8C23×C2911yescharacteristic
296#127C23×C2911yescharacteristic
297#124—21no—
298#121—21no—
299#121—21no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8D4×C2911yescharacteristic
303C4×Q8D4×C2911yescharacteristic
304C4×Q8C23×C2911yescharacteristic
305C4×Q8C23×C2911yescharacteristic
306C4×D4—21no—
307C4×D4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4D4×C2911yescharacteristic
312C2×C42—21no—
313C2×C42C23×C2911yescharacteristic
314#107—21no—
315#107—21no—
316#106—22no—
317#106—22no—
318C4⋊C8—22no—
319C4⋊C8—22no—
320C4⋊C8—21no—
321C4⋊C8D4×C2912yes—
322C4⋊C8C23×C2912yes—
323C4⋊C8C23×C2912yes—
324C4⋊C8C23×C2911yescharacteristic
325C4⋊C8C23×C2911yescharacteristic
326#103—21no—
327#103—21no—
328#103—22no—
329#103—22no—
330#102—22no—
331#102—22no—
332#102—21no—
333#102—21no—
334C22⋊C8—21no—
335C22⋊C8—21no—
336C22⋊C8D4×C2911yescharacteristic
337C22⋊C8D4×C2911yescharacteristic
338#97—22no—
339#97—21no—
340#97—21no—
341C4×C8—22no—
342C4×C8C23×C2912yes—
343C29#1947411yescharacteristic, direct product factor, Sylow
344#41—82no—
345C2×Q8—21no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—21no—
349C2×Q8—41no—
350C2×Q8—42no—
351C2×Q8—42no—
352C2×Q8—41no—
353C2×Q8C2×D4×C2911yescharacteristic
354C2×Q8C2×D4×C2911yescharacteristic
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—41no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4C2×D4×C2911yescharacteristic
364C22×C4C2×D4×C2911yescharacteristic
365C22×C4#41×C2911yescharacteristic
366Q16—44no—
367Q16—44no—
368SD16—42no—
369SD16—42no—
370C2×C8—22no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—22no—
374C2×C8—42no—
375C2×C8C2×D4×C2912yes—
376C2×C8C2×D4×C2912yes—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4C2×D4×C2911yescharacteristic
389C4⋊C4C2×D4×C2911yescharacteristic
390C22⋊C4—41no—
391C22⋊C4—41no—
392C42—21no—
393C42—21no—
394C42—21no—
395C42—21no—
396C42C2×D4×C2911yescharacteristic
397C42C2×D4×C2911yescharacteristic
398C42#41×C2911yescharacteristic
399C42C24×C2911yescharacteristic
400C23—41no—
401C23C29×#12111yescharacteristic
402Q8—21no—
403Q8—21no—
404Q8—21no—
405Q8—42no—
406Q8—42no—
407Q8—42no—
408Q8—81no—
409Q8—82no—
410Q8C29×AGL(1,ℤ/8)12yes—
411D4—41no—
412D4—41no—
413D4—42no—
414D4—81no—
415D4—82no—
416C2×C4—22no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—82no—
429C2×C4—82no—
430C2×C4C29×#12111yescharacteristic
431C2×C4C29×#12111yescharacteristic
432C2×C4C29×#12111yescharacteristic
433C2×C4C22×D4×C2911yescharacteristic
434C2×C4C22×D4×C2911yescharacteristic
435C2×C4C2×#41×C2911yescharacteristic
436C8—22no—
437C8—22no—
438C8—42no—
439C8—41no—
440C8—41no—
441C8—42no—
442C22—21no—
443C22—21no—
444C22—81no—
445C22—81no—
446C22—81no—
447C22C29×#47112yes—
448C22C2×C29×#12111yescharacteristic
449C4—21no—
450C4—21no—
451C4—22no—
452C4—21no—
453C4—21no—
454C4—41no—
455C4—41no—
456C4—41no—
457C4—82no—
458C4—81no—
459C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
460C4C29×#57511yescharacteristic
461C4C29×#57812yes—
462C2—22no—
463C2—161no—
464C2C29×#304411yescharacteristic
465C2C29×#305511yescharacteristic
466C2C2×C29×#47111yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#532C22
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
3. C2×C29×#462C2semidirect
4. C29×#2984C2semidirect
5. C29×#1702C2semidirect
6. C29×#1692C2semidirect
7. C29×#1682C2semidirect
8. C29×#1672C2semidirect
9. C29×#1573C2semidirect
10. C29×#1556C2semidirect
166. #19474C29direct (N × H)
211. C2×#462C2×C29semidirect
212. #2984C2×C29semidirect
213. #1702C2×C29semidirect
214. #1692C2×C29semidirect
215. #1682C2×C29semidirect
216. #1672C2×C29semidirect
217. #1573C2×C29semidirect
218. #1556C2×C29semidirect
343. C29#19474direct (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×#31122
C2×C29×#4622
C29×#29842
C29×#17022
C29×#16922
C29×#16822
C29×#16722
C29×#15732
C29×#15562
C29×#15512
#1947429