Finite Group Databasebeta

← C29×#19522 #20314422

Subgroups — C29×#19522 #20314422

Order 7424.

646 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3216C211yesmaximal, characteristic, complemented
2C29×#3208C211yesmaximal, characteristic, complemented
3C29×#3205C211yesmaximal, characteristic
4C29×#2985C211yesmaximal, characteristic, complemented
5C29×#1702C212yesmaximal, complemented
6C29×#1688C212yesmaximal, complemented
7C29×#1682C212yesmaximal, complemented
8C29×#1668C212yesmaximal, complemented
9C29×#1572C211yesmaximal, characteristic, complemented
10C29×#1555C211yesmaximal, characteristic, complemented
11C29×#1553C211yesmaximal, characteristic, complemented
12C29×#533C2211yescharacteristic
13C29×#532C2211yescharacteristic
14C2×C29×#127C2211yescharacteristic
15C29×#497—21no—
16C29×#493C2211yescharacteristic
17C29×#493C2211yescharacteristic
18C29×#492—21no—
19C29×#489—21no—
20C29×#486—21no—
21C29×#486C2211yescharacteristic
22C29×#486C2211yescharacteristic
23C29×#462C2212yescomplemented
24C29×#460C2212yes—
25C29×#460C2212yes—
26C29×#460C2212yescomplemented
27C29×#459—22no—
28C29×#452—22no—
29C29×#450—22no—
30C29×#447—22no—
31C29×#446—22no—
32C29×#446C2212yescomplemented
33C8×Q8×C29C2212yescomplemented
34C29×#433—22no—
35C29×#432C2211yescharacteristic
36C29×#432C2211yescharacteristic
37C29×#431C2211yescharacteristic
38C29×#431C2211yescharacteristic
39C29×#335C2212yescomplemented
40C29×#334C2212yescomplemented
41C29×#332C2212yescomplemented
42C29×#331C2212yes—
43C29×#331C2212yes—
44C29×#331C2212yescomplemented
45C2×#41×C29—21no—
46C22×D4×C29—21no—
47C22×D4×C29—21no—
48C22×D4×C29—21no—
49C2×Q16×C29—22no—
50C2×SD16×C29—22no—
51C2×SD16×C29—22no—
52C2×SD16×C29—22no—
53C2×D8×C29—22no—
54C2×D8×C29—22no—
55C29×C4⋊Q8D411yescharacteristic
56C29×C4⋊Q8D411yescharacteristic
57C29×C4⋊Q8C2311yescharacteristic
58C29×#127—21no—
59C29×#127—21no—
60C29×#127—21no—
61C29×#127C2311yescharacteristic
62C29×#127C2311yescharacteristic
63C29×#127C2311yescharacteristic
64C29×#125—21no—
65C29×#124—21no—
66C29×C22⋊Q8—21no—
67C29×C22⋊Q8D412yes—
68C29×#121—21no—
69C29×#121—21no—
70C4×Q8×C29—21no—
71C4×Q8×C29C2312yes—
72C4×D4×C29—21no—
73C4×D4×C29—21no—
74C29×#117—21no—
75C2×C42×C29C2311yescharacteristic
76C29×C4⋊C8—22no—
77C29×C4⋊C8—22no—
78C29×C4⋊C8D412yes—
79C29×C4⋊C8C2312yes—
80C29×C4⋊C8C2312yes—
81C29×C4⋊C8C2312yes—
82C29×#103—22no—
83C29×#102—22no—
84C29×#102—22no—
85C29×#102—22no—
86C29×#102—22no—
87C29×#102—22no—
88C29×C22⋊C8—21no—
89C29×C22⋊C8—21no—
90C29×C22⋊C8—21no—
91C29×C22⋊C8D412yes—
92C29×#97—22no—
93C29×#97—21no—
94C29×#97—21no—
95C4×C8×C29—22no—
96C4×C8×C29—21no—
97C4×C8×C29C2311yescharacteristic
98C4×C8×C29C2311yescharacteristic
99C24×C29—41no—
100#41×C29—82no—
101C2×Q8×C29—21no—
102C2×Q8×C29—21no—
103C2×Q8×C29C2×D412yes—
104C2×D4×C29—21no—
105C2×D4×C29—21no—
106C2×D4×C29—21no—
107C2×D4×C29—21no—
108C2×D4×C29—21no—
109C2×D4×C29—21no—
110C2×D4×C29—21no—
111C2×D4×C29—21no—
112C2×D4×C29—21no—
113C2×D4×C29—41no—
114C2×D4×C29—41no—
115C2×D4×C29—41no—
116C2×D4×C29—41no—
117C2×D4×C29—82no—
118C2×D4×C29—82no—
119C2×D4×C29—82no—
120C22×C4×C29—41no—
121C22×C4×C29C2×D411yescharacteristic
122C22×C4×C29C2×D411yescharacteristic
123C22×C4×C29#4111yescharacteristic
124Q16×C29—82no—
125SD16×C29—82no—
126SD16×C29—82no—
127SD16×C29—82no—
128D8×C29—82no—
129D8×C29—82no—
130C2×C8×C29—22no—
131C2×C8×C29—22no—
132C2×C8×C29—22no—
133C2×C8×C29C2×D412yes—
134C2×C8×C29C2×D412yes—
135C4⋊C4×C29—21no—
136C4⋊C4×C29—21no—
137C4⋊C4×C29—21no—
138C4⋊C4×C29—22no—
139C4⋊C4×C29—22no—
140C4⋊C4×C29—21no—
141C4⋊C4×C29—21no—
142C4⋊C4×C29C2×D412yes—
143C22⋊C4×C29—22no—
144C22⋊C4×C29—41no—
145C22⋊C4×C29—41no—
146C42×C29—22no—
147C42×C29C2×D411yescharacteristic
148C42×C29C2×D411yescharacteristic
149C42×C29#4111yescharacteristic
150C42×C29C2411yescharacteristic
151#19522C2911yesmaximal, characteristic, direct product factor, Sylow
152C23×C29—41no—
153C23×C29—41no—
154C23×C29—41no—
155C23×C29—82no—
156C23×C29—82no—
157C23×C29—82no—
158C23×C29#12111yescharacteristic
159Q8×C29—22no—
160Q8×C29—22no—
161Q8×C29—42no—
162Q8×C29—81no—
163D4×C29—42no—
164D4×C29—42no—
165D4×C29—42no—
166D4×C29—42no—
167D4×C29—42no—
168D4×C29—42no—
169D4×C29—81no—
170D4×C29—81no—
171D4×C29—81no—
172D4×C29—82no—
173D4×C29—82no—
174D4×C29—82no—
175D4×C29—82no—
176C2×C4×C29—22no—
177C2×C4×C29—22no—
178C2×C4×C29—22no—
179C2×C4×C29—22no—
180C2×C4×C29—41no—
181C2×C4×C29—41no—
182C2×C4×C29—82no—
183C2×C4×C29#12111yescharacteristic
184C2×C4×C29#12111yescharacteristic
185C2×C4×C29#12111yescharacteristic
186C2×C4×C29C22×D411yescharacteristic
187C2×C4×C29C22×D411yescharacteristic
188C2×C4×C29C2×#4111yescharacteristic
189C8×C29—22no—
190C8×C29—22no—
191C8×C29—42no—
192C8×C29—42no—
193C8×C29—42no—
194#3216C2×C2911yescharacteristic, complemented
195#3208C2×C2911yescharacteristic, complemented
196#3205C2×C2911yescharacteristic
197#2985C2×C2911yescharacteristic, complemented
198#1702C2×C2912yescomplemented
199#1688C2×C2912yescomplemented
200#1682C2×C2912yescomplemented
201#1668C2×C2912yescomplemented
202#1572C2×C2911yescharacteristic, complemented
203#1555C2×C2911yescharacteristic, complemented
204#1553C2×C2911yescharacteristic, complemented
205C22×C29—21no—
206C22×C29—21no—
207C22×C29—21no—
208C22×C29—81no—
209C22×C29—81no—
210C22×C29—81no—
211C22×C29—81no—
212C22×C29—81no—
213C22×C29—81no—
214C22×C29—81no—
215C22×C29—81no—
216C22×C29—81no—
217C22×C29—164no—
218C22×C29C2×#12111yescharacteristic
219C4×C29—21no—
220C4×C29—21no—
221C4×C29—21no—
222C4×C29—21no—
223C4×C29—42no—
224C4×C29—42no—
225C4×C29—81no—
226C4×C29#57612yes—
227C4×C29#57712yes—
228#533C22×C2911yescharacteristic
229#532C22×C2911yescharacteristic
230C2×#127C22×C2911yescharacteristic
231#497—21no—
232#493C22×C2911yescharacteristic
233#493C22×C2911yescharacteristic
234#492—21no—
235#489—21no—
236#486—21no—
237#486C22×C2911yescharacteristic
238#486C22×C2911yescharacteristic
239#462C22×C2912yescomplemented
240#460C22×C2912yes—
241#460C22×C2912yes—
242#460C22×C2912yescomplemented
243#459—22no—
244#452—22no—
245#450—22no—
246#447—22no—
247#446—22no—
248#446C22×C2912yescomplemented
249C8×Q8C22×C2912yescomplemented
250#433—22no—
251#432C22×C2911yescharacteristic
252#432C22×C2911yescharacteristic
253#431C22×C2911yescharacteristic
254#431C22×C2911yescharacteristic
255#335C22×C2912yescomplemented
256#334C22×C2912yescomplemented
257#332C22×C2912yescomplemented
258#331C22×C2912yes—
259#331C22×C2912yes—
260#331C22×C2912yescomplemented
261C2×C29—41no—
262C2×C29—161no—
263C2×C29—161no—
264C2×C29—161no—
265C2×C29#304311yescharacteristic
266C2×C29#305811yescharacteristic
267C2×C29#306811yescharacteristic
268C2×#41—21no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—21no—
272C2×Q16—22no—
273C2×SD16—22no—
274C2×SD16—22no—
275C2×SD16—22no—
276C2×D8—22no—
277C2×D8—22no—
278C4⋊Q8D4×C2911yescharacteristic
279C4⋊Q8D4×C2911yescharacteristic
280C4⋊Q8C23×C2911yescharacteristic
281#127—21no—
282#127—21no—
283#127—21no—
284#127C23×C2911yescharacteristic
285#127C23×C2911yescharacteristic
286#127C23×C2911yescharacteristic
287#125—21no—
288#124—21no—
289C22⋊Q8—21no—
290C22⋊Q8D4×C2912yes—
291#121—21no—
292#121—21no—
293C4×Q8—21no—
294C4×Q8C23×C2912yes—
295C4×D4—21no—
296C4×D4—21no—
297#117—21no—
298C2×C42C23×C2911yescharacteristic
299C4⋊C8—22no—
300C4⋊C8—22no—
301C4⋊C8D4×C2912yes—
302C4⋊C8C23×C2912yes—
303C4⋊C8C23×C2912yes—
304C4⋊C8C23×C2912yes—
305#103—22no—
306#102—22no—
307#102—22no—
308#102—22no—
309#102—22no—
310#102—22no—
311C22⋊C8—21no—
312C22⋊C8—21no—
313C22⋊C8—21no—
314C22⋊C8D4×C2912yes—
315#97—22no—
316#97—21no—
317#97—21no—
318C4×C8—22no—
319C4×C8—21no—
320C4×C8C23×C2911yescharacteristic
321C4×C8C23×C2911yescharacteristic
322C29#1952211yescharacteristic, direct product factor, Sylow
323C24—41no—
324#41—82no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8C2×D4×C2912yes—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—82no—
342C2×D4—82no—
343C2×D4—82no—
344C22×C4—41no—
345C22×C4C2×D4×C2911yescharacteristic
346C22×C4C2×D4×C2911yescharacteristic
347C22×C4#41×C2911yescharacteristic
348Q16—82no—
349SD16—82no—
350SD16—82no—
351SD16—82no—
352D8—82no—
353D8—82no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8C2×D4×C2912yes—
358C2×C8C2×D4×C2912yes—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4C2×D4×C2912yes—
367C22⋊C4—22no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C42—22no—
371C42C2×D4×C2911yescharacteristic
372C42C2×D4×C2911yescharacteristic
373C42#41×C2911yescharacteristic
374C42C24×C2911yescharacteristic
375C23—41no—
376C23—41no—
377C23—41no—
378C23—82no—
379C23—82no—
380C23—82no—
381C23C29×#12111yescharacteristic
382Q8—22no—
383Q8—22no—
384Q8—42no—
385Q8—81no—
386D4—42no—
387D4—42no—
388D4—42no—
389D4—42no—
390D4—42no—
391D4—42no—
392D4—81no—
393D4—81no—
394D4—81no—
395D4—82no—
396D4—82no—
397D4—82no—
398D4—82no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—82no—
406C2×C4C29×#12111yescharacteristic
407C2×C4C29×#12111yescharacteristic
408C2×C4C29×#12111yescharacteristic
409C2×C4C22×D4×C2911yescharacteristic
410C2×C4C22×D4×C2911yescharacteristic
411C2×C4C2×#41×C2911yescharacteristic
412C8—22no—
413C8—22no—
414C8—42no—
415C8—42no—
416C8—42no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—164no—
430C22C2×C29×#12111yescharacteristic
431C4—21no—
432C4—21no—
433C4—21no—
434C4—21no—
435C4—42no—
436C4—42no—
437C4—81no—
438C4C29×#57612yes—
439C4C29×#57712yes—
440C2—41no—
441C2—161no—
442C2—161no—
443C2—161no—
444C2C29×#304311yescharacteristic
445C2C29×#305811yescharacteristic
446C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3205C2
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×#3216C2semidirect
2. C29×#3208C2semidirect
4. C29×#2985C2semidirect
5. C29×#1702C2semidirect
6. C29×#1688C2semidirect
7. C29×#1682C2semidirect
8. C29×#1668C2semidirect
9. C29×#1572C2semidirect
10. C29×#1555C2semidirect
11. C29×#1553C2semidirect
23. C29×#462C22semidirect
26. C29×#460C22semidirect
32. C29×#446C22semidirect
33. C8×Q8×C29C22semidirect
39. C29×#335C22semidirect
40. C29×#334C22semidirect
41. C29×#332C22semidirect
44. C29×#331C22semidirect
151. #19522C29direct (N × H)
194. #3216C2×C29semidirect
195. #3208C2×C29semidirect
197. #2985C2×C29semidirect
198. #1702C2×C29semidirect
199. #1688C2×C29semidirect
200. #1682C2×C29semidirect
201. #1668C2×C29semidirect
202. #1572C2×C29semidirect
203. #1555C2×C29semidirect
204. #1553C2×C29semidirect
239. #462C22×C29semidirect
242. #460C22×C29semidirect
248. #446C22×C29semidirect
249. C8×Q8C22×C29semidirect
255. #335C22×C29semidirect
256. #334C22×C29semidirect
257. #332C22×C29semidirect
260. #331C22×C29semidirect
322. C29#19522direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32162
C29×#32082
C29×#32052
C29×#29852
C29×#17022
C29×#16882
C29×#16822
C29×#16682
C29×#15722
C29×#15552
C29×#15532
#1952229