Finite Group Databasebeta

← C29×#25716 #20320616

Subgroups — C29×#25716 #20320616

Order 7424.

1058 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#552C211yesmaximal, characteristic
2C2×C29×#501C211yesmaximal, characteristic, complemented
3C2×C29×#477C211yesmaximal, characteristic, complemented
4C29×#2547C211yesmaximal, characteristic
5C29×#2036C212yesmaximal, complemented
6C29×#2035C212yesmaximal, complemented
7C29×#1989C211yesmaximal, characteristic, complemented
8C29×#1955C211yesmaximal, characteristic
9C29×#1854C212yesmaximal, complemented
10C29×#1852C212yesmaximal, complemented
11C29×#1763C211yesmaximal, characteristic, complemented
12C29×#552—24no—
13C29×#552—24no—
14C2×C29×C4⋊Q8C2211yescharacteristic
15C2×C29×#126—21no—
16C2×C29×#125—21no—
17C2×C29×#125C2211yescharacteristic
18C2×C29×#124—21no—
19C2×C29×#123—21no—
20C2×C29×C22⋊Q8C2211yescharacteristic
21C2×C29×C22⋊Q8C2211yescharacteristic
22C2×C4×Q8×C29C2211yescharacteristic
23C2×C4×D4×C29C2211yescharacteristic
24C2×C29×#117—21no—
25C2×C29×#117C2211yescharacteristic
26C22×C4⋊C4×C29C2211yescharacteristic
27C29×#501—24no—
28C29×#477—24no—
29C2×C29×#107C2212yes—
30C2×C29×#107C2212yes—
31C2×C29×#106C2212yes—
32C2×C29×C4⋊C8C2211yescharacteristic
33C2×C29×#103C2212yes—
34C2×C29×#103C2212yes—
35C2×C29×C22⋊C8C2212yes—
36C2×C29×C22⋊C8C2212yes—
37C2×C29×#97C2211yescharacteristic
38C29×#397—21no—
39C29×#397—21no—
40C29×#391—21no—
41C29×#380C2212yes—
42C29×#380C2212yes—
43C4×C4⋊C4×C29C2211yescharacteristic
44C29×#340C2212yes—
45C29×#340C2212yes—
46C29×#340C2212yes—
47C22×Q8×C29—21no—
48C22×Q8×C29C2311yescharacteristic
49C22×D4×C29D411yescharacteristic
50C23×C4×C29—21no—
51C23×C4×C29C2311yescharacteristic
52C23×C4×C29C2311yescharacteristic
53C22×C8×C29C2312yes—
54C22×C8×C29C2312yes—
55C29×C4⋊Q8—22no—
56C29×C4⋊Q8—22no—
57C29×#126—28no—
58C29×#125—28no—
59C29×#125—22no—
60C29×#125D414yes—
61C29×#124—44no—
62C29×#123—28no—
63C29×C22⋊Q8—22no—
64C29×C22⋊Q8—22no—
65C29×C22⋊Q8—22no—
66C29×C22⋊Q8—22no—
67C4×Q8×C29—22no—
68C4×Q8×C29D414yes—
69C4×D4×C29—22no—
70C4×D4×C29—22no—
71C29×#117—28no—
72C29×#117—22no—
73C29×#117—22no—
74C2×C4⋊C4×C29—21no—
75C2×C4⋊C4×C29—21no—
76C2×C4⋊C4×C29—21no—
77C2×C4⋊C4×C29—21no—
78C2×C4⋊C4×C29—21no—
79C2×C4⋊C4×C29—21no—
80C2×C4⋊C4×C29—22no—
81C2×C4⋊C4×C29—22no—
82C2×C4⋊C4×C29—21no—
83C2×C4⋊C4×C29D411yescharacteristic
84C2×C4⋊C4×C29C2312yes—
85C2×C4⋊C4×C29C2312yes—
86C2×C4⋊C4×C29C2311yescharacteristic
87C2×C4⋊C4×C29C2311yescharacteristic
88C2×C4⋊C4×C29C2311yescharacteristic
89C2×C22⋊C4×C29—21no—
90C2×C22⋊C4×C29—21no—
91C2×C22⋊C4×C29—21no—
92C2×C22⋊C4×C29—22no—
93C2×C22⋊C4×C29—22no—
94C2×C22⋊C4×C29D411yescharacteristic
95C2×C22⋊C4×C29D411yescharacteristic
96C2×C42×C29—21no—
97C2×C42×C29—21no—
98C2×C42×C29—21no—
99C2×C42×C29C2311yescharacteristic
100C29×#107—24no—
101C29×#107—24no—
102C29×#106—24no—
103C29×C4⋊C8—22no—
104C29×#103—24no—
105C29×#103—24no—
106C29×C22⋊C8—24no—
107C29×C22⋊C8—24no—
108C29×#97—22no—
109C29×#95—21no—
110C29×#95—22no—
111C29×#95—22no—
112C24×C29C2×D411yescharacteristic
113C24×C29C2×D411yescharacteristic
114C2×Q8×C29—21no—
115C2×Q8×C29—22no—
116C2×Q8×C29—22no—
117C2×Q8×C29—42no—
118C2×Q8×C29—42no—
119C2×Q8×C29—42no—
120C2×Q8×C29C2×D412yes—
121C2×D4×C29—22no—
122C2×D4×C29—22no—
123C2×D4×C29—41no—
124C22×C4×C29—24no—
125C22×C4×C29—21no—
126C22×C4×C29—21no—
127C22×C4×C29—21no—
128C22×C4×C29—21no—
129C22×C4×C29—21no—
130C22×C4×C29—21no—
131C22×C4×C29—21no—
132C22×C4×C29—21no—
133C22×C4×C29—22no—
134C22×C4×C29—22no—
135C22×C4×C29—22no—
136C22×C4×C29—22no—
137C22×C4×C29—22no—
138C22×C4×C29—22no—
139C22×C4×C29—42no—
140C22×C4×C29—42no—
141C22×C4×C29C2×D411yescharacteristic
142C22×C4×C29C2×D411yescharacteristic
143C22×C4×C29C2×D411yescharacteristic
144C22×C4×C29C2×D411yescharacteristic
145C22×C4×C29C2411yescharacteristic
146C2×C8×C29—22no—
147C2×C8×C29—22no—
148C2×C8×C29—22no—
149C2×C8×C29—22no—
150C2×C8×C29—22no—
151C2×C8×C29#4114yes—
152C4⋊C4×C29—24no—
153C4⋊C4×C29—24no—
154C4⋊C4×C29—24no—
155C4⋊C4×C29—24no—
156C4⋊C4×C29—24no—
157C4⋊C4×C29—24no—
158C4⋊C4×C29—22no—
159C4⋊C4×C29—21no—
160C4⋊C4×C29—21no—
161C4⋊C4×C29—21no—
162C4⋊C4×C29—22no—
163C4⋊C4×C29—22no—
164C4⋊C4×C29—22no—
165C4⋊C4×C29—22no—
166C4⋊C4×C29—42no—
167C4⋊C4×C29C2×D412yes—
168C4⋊C4×C29C2×D412yes—
169C4⋊C4×C29C2×D412yes—
170C22⋊C4×C29—24no—
171C22⋊C4×C29—24no—
172C22⋊C4×C29—24no—
173C22⋊C4×C29—22no—
174C22⋊C4×C29—22no—
175C22⋊C4×C29—44no—
176C22⋊C4×C29—44no—
177C42×C29—24no—
178C42×C29—24no—
179C42×C29—42no—
180C42×C29C2×D412yes—
181C42×C29C2×D412yes—
182#25716C2911yesmaximal, characteristic, direct product factor, Sylow
183C23×C29—21no—
184C23×C29—22no—
185C23×C29—21no—
186C23×C29—22no—
187C23×C29—21no—
188C23×C29—22no—
189C23×C29—21no—
190C23×C29—21no—
191C23×C29—22no—
192C23×C29AGL(1,ℤ/8)12yes—
193C23×C29C22×D411yescharacteristic
194Q8×C29—22no—
195Q8×C29—22no—
196Q8×C29—42no—
197Q8×C29—84no—
198D4×C29—44no—
199C2×C4×C29—21no—
200C2×C4×C29—21no—
201C2×C4×C29—22no—
202C2×C4×C29—21no—
203C2×C4×C29—22no—
204C2×C4×C29—22no—
205C2×C4×C29—22no—
206C2×C4×C29—21no—
207C2×C4×C29—22no—
208C2×C4×C29—22no—
209C2×C4×C29—22no—
210C2×C4×C29—48no—
211C2×C4×C29—42no—
212C2×C4×C29—41no—
213C2×C4×C29—41no—
214C2×C4×C29—41no—
215C2×C4×C29—41no—
216C2×C4×C29—42no—
217C2×C4×C29—41no—
218C2×C4×C29—41no—
219C2×C4×C29—41no—
220C2×C4×C29—41no—
221C2×C4×C29—42no—
222C2×C4×C29—42no—
223C2×C4×C29—42no—
224C2×C4×C29—42no—
225C2×C4×C29—42no—
226C2×C4×C29—42no—
227C2×C4×C29—42no—
228C2×C4×C29—42no—
229C2×C4×C29#12012yes—
230C2×C4×C29#12012yes—
231C2×C4×C29C22×D411yescharacteristic
232C2×C4×C29C22×D411yescharacteristic
233C2×C4×C29C2×#4112yes—
234C2×C4×C292−1+412yes—
235C8×C29—24no—
236C8×C29—42no—
237C2×#552C2×C2911yescharacteristic
238C2×#501C2×C2911yescharacteristic, complemented
239C2×#477C2×C2911yescharacteristic, complemented
240#2547C2×C2911yescharacteristic
241#2036C2×C2912yescomplemented
242#2035C2×C2912yescomplemented
243#1989C2×C2911yescharacteristic, complemented
244#1955C2×C2911yescharacteristic
245#1854C2×C2912yescomplemented
246#1852C2×C2912yescomplemented
247#1763C2×C2911yescharacteristic, complemented
248C22×C29—24no—
249C22×C29—22no—
250C22×C29—42no—
251C22×C29—41no—
252C22×C29—41no—
253C22×C29—42no—
254C22×C29—42no—
255C22×C29—41no—
256C22×C29—41no—
257C22×C29—41no—
258C22×C29C2×#12011yescharacteristic
259C22×C29#54712yes—
260C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C29#57511yescharacteristic
262C22×C29#57812yes—
263C4×C29—22no—
264C4×C29—22no—
265C4×C29—41no—
266C4×C29—41no—
267C4×C29—42no—
268C4×C29—42no—
269C4×C29—42no—
270C4×C29—42no—
271C4×C29—82no—
272C4×C29—82no—
273C4×C29#53211yescharacteristic
274C4×C29#53611yescharacteristic
275C4×C29#54812yes—
276#552—24no—
277#552—24no—
278C2×C4⋊Q8C22×C2911yescharacteristic
279C2×#126—21no—
280C2×#125—21no—
281C2×#125C22×C2911yescharacteristic
282C2×#124—21no—
283C2×#123—21no—
284C2×C22⋊Q8C22×C2911yescharacteristic
285C2×C22⋊Q8C22×C2911yescharacteristic
286C2×C4×Q8C22×C2911yescharacteristic
287C2×C4×D4C22×C2911yescharacteristic
288C2×#117—21no—
289C2×#117C22×C2911yescharacteristic
290C22×C4⋊C4C22×C2911yescharacteristic
291#501—24no—
292#477—24no—
293C2×#107C22×C2912yes—
294C2×#107C22×C2912yes—
295C2×#106C22×C2912yes—
296C2×C4⋊C8C22×C2911yescharacteristic
297C2×#103C22×C2912yes—
298C2×#103C22×C2912yes—
299C2×C22⋊C8C22×C2912yes—
300C2×C22⋊C8C22×C2912yes—
301C2×#97C22×C2911yescharacteristic
302#397—21no—
303#397—21no—
304#391—21no—
305#380C22×C2912yes—
306#380C22×C2912yes—
307C4×C4⋊C4C22×C2911yescharacteristic
308#340C22×C2912yes—
309#340C22×C2912yes—
310#340C22×C2912yes—
311C2×C29—42no—
312C2×C29—81no—
313C2×C29#243211yescharacteristic
314C2×C29#300611yescharacteristic
315C2×C29#301111yescharacteristic
316C2×C29#334312yes—
317C2×C29#334912yes—
318C22×Q8—21no—
319C22×Q8C23×C2911yescharacteristic
320C22×D4D4×C2911yescharacteristic
321C23×C4—21no—
322C23×C4C23×C2911yescharacteristic
323C23×C4C23×C2911yescharacteristic
324C22×C8C23×C2912yes—
325C22×C8C23×C2912yes—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328#126—28no—
329#125—28no—
330#125—22no—
331#125D4×C2914yes—
332#124—44no—
333#123—28no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C4×Q8—22no—
339C4×Q8D4×C2914yes—
340C4×D4—22no—
341C4×D4—22no—
342#117—28no—
343#117—22no—
344#117—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4D4×C2911yescharacteristic
355C2×C4⋊C4C23×C2912yes—
356C2×C4⋊C4C23×C2912yes—
357C2×C4⋊C4C23×C2911yescharacteristic
358C2×C4⋊C4C23×C2911yescharacteristic
359C2×C4⋊C4C23×C2911yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4D4×C2911yescharacteristic
366C2×C22⋊C4D4×C2911yescharacteristic
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42C23×C2911yescharacteristic
371#107—24no—
372#107—24no—
373#106—24no—
374C4⋊C8—22no—
375#103—24no—
376#103—24no—
377C22⋊C8—24no—
378C22⋊C8—24no—
379#97—22no—
380#95—21no—
381#95—22no—
382#95—22no—
383C29#2571611yescharacteristic, direct product factor, Sylow
384C24C2×D4×C2911yescharacteristic
385C24C2×D4×C2911yescharacteristic
386C2×Q8—21no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—42no—
390C2×Q8—42no—
391C2×Q8—42no—
392C2×Q8C2×D4×C2912yes—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—41no—
396C22×C4—24no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4C2×D4×C2911yescharacteristic
414C22×C4C2×D4×C2911yescharacteristic
415C22×C4C2×D4×C2911yescharacteristic
416C22×C4C2×D4×C2911yescharacteristic
417C22×C4C24×C2911yescharacteristic
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8#41×C2914yes—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—42no—
439C4⋊C4C2×D4×C2912yes—
440C4⋊C4C2×D4×C2912yes—
441C4⋊C4C2×D4×C2912yes—
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—44no—
448C22⋊C4—44no—
449C42—24no—
450C42—24no—
451C42—42no—
452C42C2×D4×C2912yes—
453C42C2×D4×C2912yes—
454C23—21no—
455C23—22no—
456C23—21no—
457C23—22no—
458C23—21no—
459C23—22no—
460C23—21no—
461C23—21no—
462C23—22no—
463C23C29×AGL(1,ℤ/8)12yes—
464C23C22×D4×C2911yescharacteristic
465Q8—22no—
466Q8—22no—
467Q8—42no—
468Q8—84no—
469D4—44no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—48no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4C29×#12012yes—
501C2×C4C29×#12012yes—
502C2×C4C22×D4×C2911yescharacteristic
503C2×C4C22×D4×C2911yescharacteristic
504C2×C4C2×#41×C2912yes—
505C2×C4C29×2−1+412yes—
506C8—24no—
507C8—42no—
508C22—22no—
509C22—24no—
510C22—41no—
511C22—41no—
512C22—42no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—42no—
517C22—42no—
518C22C2×C29×#12011yescharacteristic
519C22C29×#54712yes—
520C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
521C22C29×#57511yescharacteristic
522C22C29×#57812yes—
523C4—22no—
524C4—22no—
525C4—41no—
526C4—41no—
527C4—42no—
528C4—42no—
529C4—42no—
530C4—42no—
531C4—82no—
532C4—82no—
533C4C29×#53211yescharacteristic
534C4C29×#53611yescharacteristic
535C4C29×#54812yes—
536C2—42no—
537C2—81no—
538C2C29×#243211yescharacteristic
539C2C29×#300611yescharacteristic
540C2C29×#301111yescharacteristic
541C2C29×#334312yes—
542C2C29×#334912yes—
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC22×D4×C29D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C4×D4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#501C2semidirect
3. C2×C29×#477C2semidirect
5. C29×#2036C2semidirect
6. C29×#2035C2semidirect
7. C29×#1989C2semidirect
9. C29×#1854C2semidirect
10. C29×#1852C2semidirect
11. C29×#1763C2semidirect
182. #25716C29direct (N × H)
238. C2×#501C2×C29semidirect
239. C2×#477C2×C29semidirect
241. #2036C2×C29semidirect
242. #2035C2×C29semidirect
243. #1989C2×C29semidirect
245. #1854C2×C29semidirect
246. #1852C2×C29semidirect
247. #1763C2×C29semidirect
383. C29#25716direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5522
C2×C29×#5012
C2×C29×#4772
C29×#25472
C29×#20362
C29×#20352
C29×#19892
C29×#19552
C29×#18542
C29×#18522
C29×#17632
#2571629