Finite Group Databasebeta

← C29×#25715 #20320615

Subgroups — C29×#25715 #20320615

Order 7424.

1038 conjugacy classes of subgroups.

The subgroup lattice has 540 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×#475C211yesmaximal, characteristic, complemented
4C29×#2563C211yesmaximal, characteristic
5C29×#2036C212yesmaximal, complemented
6C29×#2035C212yesmaximal, complemented
7C29×#1989C211yesmaximal, characteristic, complemented
8C29×#1955C211yesmaximal, characteristic
9C29×#1854C212yesmaximal, complemented
10C29×#1853C212yesmaximal, 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×#123—21no—
19C2×C29×C22⋊Q8C2211yescharacteristic
20C2×C29×C22⋊Q8C2211yescharacteristic
21C2×C4×Q8×C29C2211yescharacteristic
22C2×C4×D4×C29C2211yescharacteristic
23C2×C29×#117—21no—
24C2×C29×#117C2211yescharacteristic
25C22×C4⋊C4×C29C2211yescharacteristic
26C29×#501—24no—
27C29×#475—24no—
28C2×C29×#107C2212yes—
29C2×C29×#106C2212yes—
30C2×C29×#106C2212yes—
31C2×C29×C4⋊C8C2211yescharacteristic
32C2×C29×#103C2212yes—
33C2×C29×#103C2212yes—
34C2×C29×C22⋊C8C2212yes—
35C2×C29×C22⋊C8C2212yes—
36C2×C29×#97C2211yescharacteristic
37C29×#393—21no—
38C29×#393—21no—
39C29×#390—21no—
40C29×#382—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×#123—28no—
62C29×C22⋊Q8—22no—
63C29×C22⋊Q8—22no—
64C29×C22⋊Q8—22no—
65C29×C22⋊Q8—22no—
66C4×Q8×C29—22no—
67C4×Q8×C29D414yes—
68C4×D4×C29—22no—
69C4×D4×C29—22no—
70C29×#117—28no—
71C29×#117—22no—
72C29×#117—22no—
73C2×C4⋊C4×C29—21no—
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—22no—
80C2×C4⋊C4×C29—22no—
81C2×C4⋊C4×C29—21no—
82C2×C4⋊C4×C29D411yescharacteristic
83C2×C4⋊C4×C29C2312yes—
84C2×C4⋊C4×C29C2312yes—
85C2×C4⋊C4×C29C2311yescharacteristic
86C2×C4⋊C4×C29C2311yescharacteristic
87C2×C4⋊C4×C29C2311yescharacteristic
88C2×C22⋊C4×C29—21no—
89C2×C22⋊C4×C29—21no—
90C2×C22⋊C4×C29—21no—
91C2×C22⋊C4×C29—22no—
92C2×C22⋊C4×C29—22no—
93C2×C22⋊C4×C29D411yescharacteristic
94C2×C22⋊C4×C29D411yescharacteristic
95C2×C42×C29—21no—
96C2×C42×C29—21no—
97C2×C42×C29—21no—
98C2×C42×C29C2311yescharacteristic
99C29×#107—24no—
100C29×#106—24no—
101C29×#106—24no—
102C29×C4⋊C8—22no—
103C29×#103—24no—
104C29×#103—24no—
105C29×C22⋊C8—24no—
106C29×C22⋊C8—24no—
107C29×#97—22no—
108C29×#95—21no—
109C29×#95—22no—
110C29×#95—22no—
111C24×C29C2×D411yescharacteristic
112C24×C29C2×D411yescharacteristic
113C2×Q8×C29—21no—
114C2×Q8×C29—22no—
115C2×Q8×C29—22no—
116C2×Q8×C29—42no—
117C2×Q8×C29—82no—
118C2×Q8×C29C2×D412yes—
119C2×D4×C29—22no—
120C2×D4×C29—22no—
121C2×D4×C29—41no—
122C22×C4×C29—24no—
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×C29—21no—
130C22×C4×C29—21no—
131C22×C4×C29—22no—
132C22×C4×C29—22no—
133C22×C4×C29—22no—
134C22×C4×C29—22no—
135C22×C4×C29—22no—
136C22×C4×C29—22no—
137C22×C4×C29—42no—
138C22×C4×C29—42no—
139C22×C4×C29C2×D411yescharacteristic
140C22×C4×C29C2×D411yescharacteristic
141C22×C4×C29C2×D411yescharacteristic
142C22×C4×C29C2×D411yescharacteristic
143C22×C4×C29C2411yescharacteristic
144C2×C8×C29—22no—
145C2×C8×C29—22no—
146C2×C8×C29—22no—
147C2×C8×C29—22no—
148C2×C8×C29—22no—
149C2×C8×C29#4114yes—
150C4⋊C4×C29—24no—
151C4⋊C4×C29—24no—
152C4⋊C4×C29—24no—
153C4⋊C4×C29—24no—
154C4⋊C4×C29—24no—
155C4⋊C4×C29—24no—
156C4⋊C4×C29—22no—
157C4⋊C4×C29—21no—
158C4⋊C4×C29—21no—
159C4⋊C4×C29—21no—
160C4⋊C4×C29—22no—
161C4⋊C4×C29—22no—
162C4⋊C4×C29—22no—
163C4⋊C4×C29—22no—
164C4⋊C4×C29—42no—
165C4⋊C4×C29C2×D412yes—
166C4⋊C4×C29C2×D412yes—
167C4⋊C4×C29C2×D412yes—
168C22⋊C4×C29—24no—
169C22⋊C4×C29—24no—
170C22⋊C4×C29—24no—
171C22⋊C4×C29—22no—
172C22⋊C4×C29—22no—
173C22⋊C4×C29—82no—
174C22⋊C4×C29—82no—
175C42×C29—24no—
176C42×C29—24no—
177C42×C29—42no—
178C42×C29C2×D412yes—
179C42×C29C2×D412yes—
180#25715C2911yesmaximal, characteristic, direct product factor, Sylow
181C23×C29—21no—
182C23×C29—22no—
183C23×C29—21no—
184C23×C29—22no—
185C23×C29—21no—
186C23×C29—22no—
187C23×C29—21no—
188C23×C29—21no—
189C23×C29—22no—
190C23×C29#13712yes—
191C23×C29C22×D411yescharacteristic
192Q8×C29—22no—
193Q8×C29—22no—
194Q8×C29—42no—
195Q8×C29—84no—
196D4×C29—44no—
197C2×C4×C29—21no—
198C2×C4×C29—21no—
199C2×C4×C29—22no—
200C2×C4×C29—21no—
201C2×C4×C29—22no—
202C2×C4×C29—22no—
203C2×C4×C29—22no—
204C2×C4×C29—21no—
205C2×C4×C29—22no—
206C2×C4×C29—22no—
207C2×C4×C29—22no—
208C2×C4×C29—48no—
209C2×C4×C29—42no—
210C2×C4×C29—41no—
211C2×C4×C29—41no—
212C2×C4×C29—41no—
213C2×C4×C29—41no—
214C2×C4×C29—42no—
215C2×C4×C29—41no—
216C2×C4×C29—41no—
217C2×C4×C29—41no—
218C2×C4×C29—41no—
219C2×C4×C29—42no—
220C2×C4×C29—42no—
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#12012yes—
228C2×C4×C29#12012yes—
229C2×C4×C29C22×D411yescharacteristic
230C2×C4×C29C22×D411yescharacteristic
231C2×C4×C29C2×#4112yes—
232C2×C4×C292−1+412yes—
233C8×C29—24no—
234C8×C29—42no—
235C2×#552C2×C2911yescharacteristic
236C2×#501C2×C2911yescharacteristic, complemented
237C2×#475C2×C2911yescharacteristic, complemented
238#2563C2×C2911yescharacteristic
239#2036C2×C2912yescomplemented
240#2035C2×C2912yescomplemented
241#1989C2×C2911yescharacteristic, complemented
242#1955C2×C2911yescharacteristic
243#1854C2×C2912yescomplemented
244#1853C2×C2912yescomplemented
245#1763C2×C2911yescharacteristic, complemented
246C22×C29—24no—
247C22×C29—22no—
248C22×C29—42no—
249C22×C29—41no—
250C22×C29—41no—
251C22×C29—42no—
252C22×C29—42no—
253C22×C29—41no—
254C22×C29—41no—
255C22×C29—41no—
256C22×C29C2×#12011yescharacteristic
257C22×C29#54712yes—
258C22×C29C2×#13711yescharacteristic
259C22×C29#57511yescharacteristic
260C22×C29#57712yes—
261C4×C29—22no—
262C4×C29—22no—
263C4×C29—41no—
264C4×C29—41no—
265C4×C29—42no—
266C4×C29—42no—
267C4×C29—42no—
268C4×C29—42no—
269C4×C29—82no—
270C4×C29—82no—
271C4×C29#53211yescharacteristic
272C4×C29#53611yescharacteristic
273C4×C29#54812yes—
274#552—24no—
275#552—24no—
276C2×C4⋊Q8C22×C2911yescharacteristic
277C2×#126—21no—
278C2×#125—21no—
279C2×#125C22×C2911yescharacteristic
280C2×#123—21no—
281C2×C22⋊Q8C22×C2911yescharacteristic
282C2×C22⋊Q8C22×C2911yescharacteristic
283C2×C4×Q8C22×C2911yescharacteristic
284C2×C4×D4C22×C2911yescharacteristic
285C2×#117—21no—
286C2×#117C22×C2911yescharacteristic
287C22×C4⋊C4C22×C2911yescharacteristic
288#501—24no—
289#475—24no—
290C2×#107C22×C2912yes—
291C2×#106C22×C2912yes—
292C2×#106C22×C2912yes—
293C2×C4⋊C8C22×C2911yescharacteristic
294C2×#103C22×C2912yes—
295C2×#103C22×C2912yes—
296C2×C22⋊C8C22×C2912yes—
297C2×C22⋊C8C22×C2912yes—
298C2×#97C22×C2911yescharacteristic
299#393—21no—
300#393—21no—
301#390—21no—
302#382—21no—
303#380C22×C2912yes—
304#380C22×C2912yes—
305C4×C4⋊C4C22×C2911yescharacteristic
306#340C22×C2912yes—
307#340C22×C2912yes—
308#340C22×C2912yes—
309C2×C29—42no—
310C2×C29—81no—
311C2×C29#243211yescharacteristic
312C2×C29#300711yescharacteristic
313C2×C29#301011yescharacteristic
314C2×C29#334412yes—
315C2×C29#334812yes—
316C22×Q8—21no—
317C22×Q8C23×C2911yescharacteristic
318C22×D4D4×C2911yescharacteristic
319C23×C4—21no—
320C23×C4C23×C2911yescharacteristic
321C23×C4C23×C2911yescharacteristic
322C22×C8C23×C2912yes—
323C22×C8C23×C2912yes—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326#126—28no—
327#125—28no—
328#125—22no—
329#125D4×C2914yes—
330#123—28no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C4×Q8—22no—
336C4×Q8D4×C2914yes—
337C4×D4—22no—
338C4×D4—22no—
339#117—28no—
340#117—22no—
341#117—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4D4×C2911yescharacteristic
352C2×C4⋊C4C23×C2912yes—
353C2×C4⋊C4C23×C2912yes—
354C2×C4⋊C4C23×C2911yescharacteristic
355C2×C4⋊C4C23×C2911yescharacteristic
356C2×C4⋊C4C23×C2911yescharacteristic
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4D4×C2911yescharacteristic
363C2×C22⋊C4D4×C2911yescharacteristic
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42C23×C2911yescharacteristic
368#107—24no—
369#106—24no—
370#106—24no—
371C4⋊C8—22no—
372#103—24no—
373#103—24no—
374C22⋊C8—24no—
375C22⋊C8—24no—
376#97—22no—
377#95—21no—
378#95—22no—
379#95—22no—
380C29#2571511yescharacteristic, direct product factor, Sylow
381C24C2×D4×C2911yescharacteristic
382C24C2×D4×C2911yescharacteristic
383C2×Q8—21no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—42no—
387C2×Q8—82no—
388C2×Q8C2×D4×C2912yes—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—41no—
392C22×C4—24no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4C2×D4×C2911yescharacteristic
410C22×C4C2×D4×C2911yescharacteristic
411C22×C4C2×D4×C2911yescharacteristic
412C22×C4C2×D4×C2911yescharacteristic
413C22×C4C24×C2911yescharacteristic
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8#41×C2914yes—
420C4⋊C4—24no—
421C4⋊C4—24no—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—42no—
435C4⋊C4C2×D4×C2912yes—
436C4⋊C4C2×D4×C2912yes—
437C4⋊C4C2×D4×C2912yes—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—82no—
444C22⋊C4—82no—
445C42—24no—
446C42—24no—
447C42—42no—
448C42C2×D4×C2912yes—
449C42C2×D4×C2912yes—
450C23—21no—
451C23—22no—
452C23—21no—
453C23—22no—
454C23—21no—
455C23—22no—
456C23—21no—
457C23—21no—
458C23—22no—
459C23C29×#13712yes—
460C23C22×D4×C2911yescharacteristic
461Q8—22no—
462Q8—22no—
463Q8—42no—
464Q8—84no—
465D4—44no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—48no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4C29×#12012yes—
497C2×C4C29×#12012yes—
498C2×C4C22×D4×C2911yescharacteristic
499C2×C4C22×D4×C2911yescharacteristic
500C2×C4C2×#41×C2912yes—
501C2×C4C29×2−1+412yes—
502C8—24no—
503C8—42no—
504C22—22no—
505C22—24no—
506C22—41no—
507C22—41no—
508C22—42no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—42no—
513C22—42no—
514C22C2×C29×#12011yescharacteristic
515C22C29×#54712yes—
516C22C2×C29×#13711yescharacteristic
517C22C29×#57511yescharacteristic
518C22C29×#57712yes—
519C4—22no—
520C4—22no—
521C4—41no—
522C4—41no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—82no—
528C4—82no—
529C4C29×#53211yescharacteristic
530C4C29×#53611yescharacteristic
531C4C29×#54812yes—
532C2—42no—
533C2—81no—
534C2C29×#243211yescharacteristic
535C2C29×#300711yescharacteristic
536C2C29×#301011yescharacteristic
537C2C29×#334412yes—
538C2C29×#334812yes—
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×#475C2semidirect
5. C29×#2036C2semidirect
6. C29×#2035C2semidirect
7. C29×#1989C2semidirect
9. C29×#1854C2semidirect
10. C29×#1853C2semidirect
11. C29×#1763C2semidirect
180. #25715C29direct (N × H)
236. C2×#501C2×C29semidirect
237. C2×#475C2×C29semidirect
239. #2036C2×C29semidirect
240. #2035C2×C29semidirect
241. #1989C2×C29semidirect
243. #1854C2×C29semidirect
244. #1853C2×C29semidirect
245. #1763C2×C29semidirect
380. C29#25715direct (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×#4752
C29×#25632
C29×#20362
C29×#20352
C29×#19892
C29×#19552
C29×#18542
C29×#18532
C29×#17632
#2571529