Finite Group Databasebeta

← C29×#24110 #20319010

Subgroups — C29×#24110 #20319010

Order 7424.

1088 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#552C211yesmaximal, characteristic
2C2×C29×#484C211yesmaximal, characteristic, complemented
3C2×C29×#428C211yesmaximal, characteristic, complemented
4C29×#2486C211yesmaximal, characteristic
5C29×#2059C212yesmaximal, complemented
6C29×#2035C212yesmaximal, complemented
7C29×#1894C211yesmaximal, characteristic, complemented
8C29×#1870C211yesmaximal, characteristic
9C29×#1863C212yesmaximal, complemented
10C29×#1852C212yesmaximal, complemented
11C29×#1825C211yesmaximal, characteristic, complemented
12C22×M16×C29C2211yescharacteristic
13C29×#552—24no—
14C29×#552—24no—
15C2×C29×#126—21no—
16C2×C29×#125—21no—
17C2×C29×#125C2211yescharacteristic
18C2×C29×#123—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
27C22×C4⋊C4×C29C2211yescharacteristic
28C29×#484—24no—
29C29×#428—24no—
30C2×C29×#107C2212yes—
31C2×C29×#107C2212yes—
32C2×C29×#106C2212yes—
33C2×C29×#103C2212yes—
34C2×C29×#103C2212yes—
35C2×C29×C22⋊C8C2212yes—
36C2×C29×C22⋊C8C2211yescharacteristic
37C29×#398—21no—
38C29×#397—21no—
39C29×#389C2212yes—
40C29×#381—21no—
41C29×#380C2212yes—
42C29×#380C2211yescharacteristic
43C29×#340C2212yes—
44C29×#340C2212yes—
45C29×#340C2212yes—
46C29×#336C2212yes—
47C22×Q8×C29C2311yescharacteristic
48C22×D4×C29D411yescharacteristic
49C23×C4×C29—21no—
50C23×C4×C29—21no—
51C23×C4×C29C2311yescharacteristic
52C23×C4×C29C2311yescharacteristic
53C2×M16×C29—22no—
54C2×M16×C29—24no—
55C22×C8×C29C2312yes—
56C22×C8×C29C2312yes—
57C29×#126—28no—
58C29×#125—28no—
59C29×#125—22no—
60C29×#125—22no—
61C29×#123—28no—
62C29×#123—44no—
63C29×C22⋊Q8—22no—
64C29×C22⋊Q8—22no—
65C29×C22⋊Q8—22no—
66C29×C22⋊Q8D414yes—
67C4×Q8×C29—22no—
68C4×Q8×C29—22no—
69C4×D4×C29—22no—
70C4×D4×C29—22no—
71C29×#117—28no—
72C29×#117—22no—
73C29×#117D414yes—
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—22no—
83C2×C4⋊C4×C29—22no—
84C2×C4⋊C4×C29—21no—
85C2×C4⋊C4×C29—22no—
86C2×C4⋊C4×C29D411yescharacteristic
87C2×C4⋊C4×C29C2312yes—
88C2×C4⋊C4×C29C2312yes—
89C2×C4⋊C4×C29C2311yescharacteristic
90C2×C4⋊C4×C29C2311yescharacteristic
91C2×C4⋊C4×C29C2311yescharacteristic
92C2×C22⋊C4×C29—21no—
93C2×C22⋊C4×C29—21no—
94C2×C22⋊C4×C29—21no—
95C2×C22⋊C4×C29—21no—
96C2×C22⋊C4×C29—22no—
97C2×C22⋊C4×C29D411yescharacteristic
98C2×C22⋊C4×C29D411yescharacteristic
99C2×C42×C29—21no—
100C2×C42×C29—21no—
101C2×C42×C29C2311yescharacteristic
102C29×#107—24no—
103C29×#107—24no—
104C29×#106—24no—
105C29×#103—24no—
106C29×#103—24no—
107C29×C22⋊C8—22no—
108C29×C22⋊C8—24no—
109C29×#95—22no—
110C29×#95—21no—
111C29×#95—22no—
112C24×C29C2×D411yescharacteristic
113C24×C29C2×D411yescharacteristic
114C2×Q8×C29—21no—
115C2×Q8×C29—22no—
116C2×Q8×C29—22no—
117C2×Q8×C29C2×D412yes—
118C2×D4×C29—22no—
119C2×D4×C29—22no—
120C2×D4×C29—41no—
121C22×C4×C29—22no—
122C22×C4×C29—22no—
123C22×C4×C29—24no—
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—22no—
131C22×C4×C29—22no—
132C22×C4×C29—22no—
133C22×C4×C29—22no—
134C22×C4×C29—42no—
135C22×C4×C29—42no—
136C22×C4×C29—42no—
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×C29C2×D412yes—
144C22×C4×C29C2×D412yes—
145C22×C4×C29C2411yescharacteristic
146M16×C29—28no—
147C2×C8×C29—22no—
148C2×C8×C29—22no—
149C2×C8×C29—22no—
150C2×C8×C29—22no—
151C2×C8×C29—22no—
152C2×C8×C29#4114yes—
153C4⋊C4×C29—24no—
154C4⋊C4×C29—24no—
155C4⋊C4×C29—24no—
156C4⋊C4×C29—24no—
157C4⋊C4×C29—24no—
158C4⋊C4×C29—24no—
159C4⋊C4×C29—22no—
160C4⋊C4×C29—21no—
161C4⋊C4×C29—21no—
162C4⋊C4×C29—21no—
163C4⋊C4×C29—22no—
164C4⋊C4×C29—22no—
165C4⋊C4×C29—22no—
166C4⋊C4×C29—22no—
167C4⋊C4×C29—44no—
168C4⋊C4×C29—42no—
169C4⋊C4×C29C2×D412yes—
170C4⋊C4×C29C2×D412yes—
171C4⋊C4×C29C2×D412yes—
172C22⋊C4×C29—24no—
173C22⋊C4×C29—24no—
174C22⋊C4×C29—24no—
175C22⋊C4×C29—22no—
176C22⋊C4×C29—22no—
177C22⋊C4×C29—42no—
178C22⋊C4×C29—44no—
179C42×C29—24no—
180C42×C29—24no—
181C42×C29—21no—
182C42×C29—21no—
183#24110C2911yesmaximal, characteristic, direct product factor, Sylow
184C23×C29—21no—
185C23×C29—22no—
186C23×C29—22no—
187C23×C29—21no—
188C23×C29—21no—
189C23×C29—21no—
190C23×C29—22no—
191C23×C29—22no—
192C23×C29#12012yes—
193C23×C29AGL(1,ℤ/8)12yes—
194C23×C29C22×D411yescharacteristic
195Q8×C29—24no—
196Q8×C29—41no—
197Q8×C29—41no—
198D4×C29—44no—
199C2×C4×C29—22no—
200C2×C4×C29—22no—
201C2×C4×C29—22no—
202C2×C4×C29—24no—
203C2×C4×C29—21no—
204C2×C4×C29—22no—
205C2×C4×C29—22no—
206C2×C4×C29—22no—
207C2×C4×C29—21no—
208C2×C4×C29—21no—
209C2×C4×C29—22no—
210C2×C4×C29—22no—
211C2×C4×C29—21no—
212C2×C4×C29—21no—
213C2×C4×C29—22no—
214C2×C4×C29—48no—
215C2×C4×C29—42no—
216C2×C4×C29—41no—
217C2×C4×C29—41no—
218C2×C4×C29—41no—
219C2×C4×C29—41no—
220C2×C4×C29—42no—
221C2×C4×C29—41no—
222C2×C4×C29—41no—
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—42no—
230C2×C4×C29—84no—
231C2×C4×C29#12012yes—
232C2×C4×C29C22×D411yescharacteristic
233C2×C4×C29C22×D411yescharacteristic
234C2×C4×C29C2×#4112yes—
235C2×C4×C292−1+412yes—
236C8×C29—24no—
237C8×C29—42no—
238C2×#552C2×C2911yescharacteristic
239C2×#484C2×C2911yescharacteristic, complemented
240C2×#428C2×C2911yescharacteristic, complemented
241#2486C2×C2911yescharacteristic
242#2059C2×C2912yescomplemented
243#2035C2×C2912yescomplemented
244#1894C2×C2911yescharacteristic, complemented
245#1870C2×C2911yescharacteristic
246#1863C2×C2912yescomplemented
247#1852C2×C2912yescomplemented
248#1825C2×C2911yescharacteristic, complemented
249C22×C29—24no—
250C22×C29—22no—
251C22×C29—22no—
252C22×C29—22no—
253C22×C29—22no—
254C22×C29—42no—
255C22×C29—42no—
256C22×C29—42no—
257C22×C29—41no—
258C22×C29—41no—
259C22×C29C2×#12011yescharacteristic
260C22×C29#54712yes—
261C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
262C22×C29#57511yescharacteristic
263C22×C29#57812yes—
264C4×C29—22no—
265C4×C29—41no—
266C4×C29—42no—
267C4×C29—41no—
268C4×C29—42no—
269C4×C29—42no—
270C4×C29—41no—
271C4×C29—42no—
272C4×C29—82no—
273C4×C29—82no—
274C4×C29#52511yescharacteristic
275C4×C29#53611yescharacteristic
276C4×C29#54712yes—
277C22×M16C22×C2911yescharacteristic
278#552—24no—
279#552—24no—
280C2×#126—21no—
281C2×#125—21no—
282C2×#125C22×C2911yescharacteristic
283C2×#123—21no—
284C2×#123—21no—
285C2×C22⋊Q8C22×C2911yescharacteristic
286C2×C22⋊Q8C22×C2911yescharacteristic
287C2×C4×Q8C22×C2911yescharacteristic
288C2×C4×D4C22×C2911yescharacteristic
289C2×#117—21no—
290C2×#117C22×C2911yescharacteristic
291C22×C4⋊C4C22×C2911yescharacteristic
292C22×C4⋊C4C22×C2911yescharacteristic
293#484—24no—
294#428—24no—
295C2×#107C22×C2912yes—
296C2×#107C22×C2912yes—
297C2×#106C22×C2912yes—
298C2×#103C22×C2912yes—
299C2×#103C22×C2912yes—
300C2×C22⋊C8C22×C2911yescharacteristic
301C2×C22⋊C8C22×C2912yes—
302#398—21no—
303#397—21no—
304#389C22×C2912yes—
305#381—21no—
306#380C22×C2911yescharacteristic
307#380C22×C2912yes—
308#340C22×C2912yes—
309#340C22×C2912yes—
310#340C22×C2912yes—
311#336C22×C2912yes—
312C2×C29—42no—
313C2×C29—42no—
314C2×C29#240611yescharacteristic
315C2×C29#300611yescharacteristic
316C2×C29#301111yescharacteristic
317C2×C29#334312yes—
318C2×C29#335212yes—
319C22×Q8C23×C2911yescharacteristic
320C22×D4D4×C2911yescharacteristic
321C23×C4—21no—
322C23×C4—21no—
323C23×C4C23×C2911yescharacteristic
324C23×C4C23×C2911yescharacteristic
325C2×M16—22no—
326C2×M16—24no—
327C22×C8C23×C2912yes—
328C22×C8C23×C2912yes—
329#126—28no—
330#125—28no—
331#125—22no—
332#125—22no—
333#123—28no—
334#123—44no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8D4×C2914yes—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×D4—22no—
342C4×D4—22no—
343#117—28no—
344#117—22no—
345#117D4×C2914yes—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4D4×C2911yescharacteristic
359C2×C4⋊C4C23×C2912yes—
360C2×C4⋊C4C23×C2912yes—
361C2×C4⋊C4C23×C2911yescharacteristic
362C2×C4⋊C4C23×C2911yescharacteristic
363C2×C4⋊C4C23×C2911yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4D4×C2911yescharacteristic
370C2×C22⋊C4D4×C2911yescharacteristic
371C2×C42—21no—
372C2×C42—21no—
373C2×C42C23×C2911yescharacteristic
374#107—24no—
375#107—24no—
376#106—24no—
377#103—24no—
378#103—24no—
379C22⋊C8—22no—
380C22⋊C8—24no—
381#95—22no—
382#95—21no—
383#95—22no—
384C29#2411011yescharacteristic, direct product factor, Sylow
385C24C2×D4×C2911yescharacteristic
386C24C2×D4×C2911yescharacteristic
387C2×Q8—21no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8C2×D4×C2912yes—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—41no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4C2×D4×C2911yescharacteristic
413C22×C4C2×D4×C2911yescharacteristic
414C22×C4C2×D4×C2911yescharacteristic
415C22×C4C2×D4×C2911yescharacteristic
416C22×C4C2×D4×C2912yes—
417C22×C4C2×D4×C2912yes—
418C22×C4C24×C2911yescharacteristic
419M16—28no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8#41×C2914yes—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—44no—
441C4⋊C4—42no—
442C4⋊C4C2×D4×C2912yes—
443C4⋊C4C2×D4×C2912yes—
444C4⋊C4C2×D4×C2912yes—
445C22⋊C4—24no—
446C22⋊C4—24no—
447C22⋊C4—24no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—42no—
451C22⋊C4—44no—
452C42—24no—
453C42—24no—
454C42—21no—
455C42—21no—
456C23—21no—
457C23—22no—
458C23—22no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—22no—
463C23—22no—
464C23C29×#12012yes—
465C23C29×AGL(1,ℤ/8)12yes—
466C23C22×D4×C2911yescharacteristic
467Q8—24no—
468Q8—41no—
469Q8—41no—
470D4—44no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—21no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—48no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—84no—
503C2×C4C29×#12012yes—
504C2×C4C22×D4×C2911yescharacteristic
505C2×C4C22×D4×C2911yescharacteristic
506C2×C4C2×#41×C2912yes—
507C2×C4C29×2−1+412yes—
508C8—24no—
509C8—42no—
510C22—22no—
511C22—22no—
512C22—22no—
513C22—24no—
514C22—22no—
515C22—41no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—41no—
520C22C2×C29×#12011yescharacteristic
521C22C29×#54712yes—
522C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
523C22C29×#57511yescharacteristic
524C22C29×#57812yes—
525C4—22no—
526C4—41no—
527C4—42no—
528C4—42no—
529C4—41no—
530C4—42no—
531C4—41no—
532C4—42no—
533C4—82no—
534C4—82no—
535C4C29×#52511yescharacteristic
536C4C29×#53611yescharacteristic
537C4C29×#54712yes—
538C2—42no—
539C2—42no—
540C2C29×#240611yescharacteristic
541C2C29×#300611yescharacteristic
542C2C29×#301111yescharacteristic
543C2C29×#334312yes—
544C2C29×#335212yes—
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×#484C2semidirect
3. C2×C29×#428C2semidirect
5. C29×#2059C2semidirect
6. C29×#2035C2semidirect
7. C29×#1894C2semidirect
9. C29×#1863C2semidirect
10. C29×#1852C2semidirect
11. C29×#1825C2semidirect
183. #24110C29direct (N × H)
239. C2×#484C2×C29semidirect
240. C2×#428C2×C29semidirect
242. #2059C2×C29semidirect
243. #2035C2×C29semidirect
244. #1894C2×C29semidirect
246. #1863C2×C29semidirect
247. #1852C2×C29semidirect
248. #1825C2×C29semidirect
384. C29#24110direct (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×#4842
C2×C29×#4282
C29×#24862
C29×#20592
C29×#20352
C29×#18942
C29×#18702
C29×#18632
C29×#18522
C29×#18252
#2411029