Finite Group Databasebeta

← C29×#18961 #20313861

Subgroups — C29×#18961 #20313861

Order 7424.

818 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3555C211yesmaximal, characteristic
2C29×#3238C211yesmaximal, characteristic
3C29×#3230C211yesmaximal, characteristic, complemented
4C29×#3209C211yesmaximal, characteristic, complemented
5C29×#1638C212yesmaximal, complemented
6C29×#1636C212yesmaximal, complemented
7C29×#1633C212yesmaximal, complemented
8C29×#1632C212yesmaximal, complemented
9C29×#1554C211yesmaximal, characteristic, complemented
10C29×#1497C211yesmaximal, characteristic, complemented
11C29×#1482C211yesmaximal, characteristic
12C29×#563—22no—
13Q82×C29C2211yescharacteristic
14C29×#557—21no—
15C29×#557C2211yescharacteristic
16C29×#556—21no—
17C29×#556—21no—
18C29×#556C2211yescharacteristic
19C29×#554C2211yescharacteristic
20C29×#552—21no—
21C29×#544—21no—
22C29×#542—21no—
23C29×#541—21no—
24C29×#541—21no—
25C29×#541—22no—
26C29×#533C2211yescharacteristic
27C29×#533C2211yescharacteristic
28C2×C29×C4⋊Q8C2211yescharacteristic
29C29×#529C2211yescharacteristic
30C29×#501—21no—
31C29×#500—21no—
32C29×#494C2212yes—
33C29×#489—21no—
34C29×#487—21no—
35C29×#487C2212yes—
36C29×#484—21no—
37C29×#484—21no—
38C29×#483—21no—
39C29×#480—21no—
40C29×#477C2212yes—
41C29×#477C2212yes—
42C29×#477C2212yes—
43C29×#476C2212yes—
44C29×#462—22no—
45C29×#451—22no—
46C29×#432C2211yescharacteristic
47C29×#431C2211yescharacteristic
48C29×#431C2211yescharacteristic
49C29×#333C2212yes—
50C29×#332C2212yes—
51C29×Q8⋊C8C2212yes—
52C29×Q8⋊C8C2212yes—
53C29×Q8⋊C8C2212yes—
54C29×D4⋊C8C2212yes—
55C22×Q8×C29—21no—
56C2×Q16×C29—24no—
57C29×C4⋊Q8—22no—
58C29×C4⋊Q8—21no—
59C29×C4⋊Q8—22no—
60C29×C4⋊Q8—21no—
61C29×C4⋊Q8—21no—
62C29×C4⋊Q8—21no—
63C29×C4⋊Q8—21no—
64C29×C4⋊Q8—21no—
65C29×C4⋊Q8D411yescharacteristic
66C29×C4⋊Q8D411yescharacteristic
67C29×C4⋊Q8C2312yes—
68C29×C4⋊Q8C2311yescharacteristic
69C29×C4⋊Q8C2311yescharacteristic
70C29×#126—22no—
71C29×#126—22no—
72C29×#126—22no—
73C29×#126—22no—
74C29×#126—22no—
75C29×#126—22no—
76C29×#126—21no—
77C29×#125—22no—
78C29×#125—22no—
79C29×#125—22no—
80C29×#125—22no—
81C29×#125—21no—
82C29×#125—22no—
83C29×#125—21no—
84C29×#125—21no—
85C29×#125—21no—
86C29×#125D411yescharacteristic
87C29×#124—22no—
88C29×#124—21no—
89C29×#124D411yescharacteristic
90C29×#123—22no—
91C29×#123—21no—
92C29×C22⋊Q8—22no—
93C29×C22⋊Q8—22no—
94C29×C22⋊Q8—21no—
95C29×C22⋊Q8—21no—
96C29×C22⋊Q8—22no—
97C29×C22⋊Q8—21no—
98C29×C22⋊Q8—21no—
99C29×C22⋊Q8D412yes—
100C29×C22⋊Q8D411yescharacteristic
101C29×C22⋊Q8D411yescharacteristic
102C29×C22⋊Q8D411yescharacteristic
103C29×#121D411yescharacteristic
104C4×Q8×C29—22no—
105C4×Q8×C29—21no—
106C4×Q8×C29—21no—
107C4×Q8×C29—21no—
108C4×Q8×C29—21no—
109C4×Q8×C29—21no—
110C4×Q8×C29—21no—
111C4×Q8×C29—21no—
112C4×Q8×C29D412yes—
113C4×Q8×C29C2311yescharacteristic
114C4×Q8×C29C2311yescharacteristic
115C4×Q8×C29C2311yescharacteristic
116C4×D4×C29—21no—
117C4×D4×C29—21no—
118C4×D4×C29C2311yescharacteristic
119C29×#117—22no—
120C29×#117—21no—
121C29×#117—21no—
122C29×#117—21no—
123C29×#117—21no—
124C2×C4⋊C4×C29—21no—
125C2×C4⋊C4×C29—21no—
126C2×C4⋊C4×C29—21no—
127C2×C42×C29C2311yescharacteristic
128C29×#107—22no—
129C29×#107—22no—
130C29×#107—22no—
131C29×#106—22no—
132C29×C4⋊C8—21no—
133C29×C4⋊C8C2312yes—
134C29×C4⋊C8C2312yes—
135C29×#103—22no—
136C29×#103—22no—
137C29×#103—22no—
138C29×#103—24no—
139C29×#102—22no—
140C29×C22⋊C8—21no—
141C29×C22⋊C8—21no—
142C29×C22⋊C8—21no—
143C29×#97—21no—
144C4×C8×C29—21no—
145C4×C8×C29C2312yes—
146C2×Q8×C29—22no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—22no—
150C2×Q8×C29—41no—
151C2×Q8×C29—82no—
152C2×Q8×C29C2×D411yescharacteristic
153C2×Q8×C29C2×D411yescharacteristic
154C2×Q8×C29C2×D411yescharacteristic
155C2×Q8×C29C2×D412yes—
156C2×D4×C29—21no—
157C2×D4×C29C2×D411yescharacteristic
158C22×C4×C29—22no—
159C22×C4×C29—21no—
160C22×C4×C29—41no—
161C22×C4×C29C2×D411yescharacteristic
162C22×C4×C29C2×D411yescharacteristic
163C22×C4×C29C2×D411yescharacteristic
164Q16×C29—84no—
165C2×C8×C29—22no—
166C2×C8×C29—22no—
167C2×C8×C29—22no—
168C4⋊C4×C29—22no—
169C4⋊C4×C29—22no—
170C4⋊C4×C29—22no—
171C4⋊C4×C29—22no—
172C4⋊C4×C29—22no—
173C4⋊C4×C29—22no—
174C4⋊C4×C29—22no—
175C4⋊C4×C29—22no—
176C4⋊C4×C29—21no—
177C4⋊C4×C29—21no—
178C4⋊C4×C29—21no—
179C4⋊C4×C29—21no—
180C4⋊C4×C29—21no—
181C4⋊C4×C29—21no—
182C4⋊C4×C29—21no—
183C4⋊C4×C29—22no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—22no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—22no—
193C4⋊C4×C29—22no—
194C4⋊C4×C29—41no—
195C4⋊C4×C29—41no—
196C4⋊C4×C29C2×D411yescharacteristic
197C4⋊C4×C29C2×D411yescharacteristic
198C4⋊C4×C29C2×D411yescharacteristic
199C4⋊C4×C29C2×D411yescharacteristic
200C4⋊C4×C29C2×D412yes—
201C22⋊C4×C29—22no—
202C22⋊C4×C29—22no—
203C22⋊C4×C29—22no—
204C22⋊C4×C29—21no—
205C22⋊C4×C29—22no—
206C22⋊C4×C29—21no—
207C22⋊C4×C29—21no—
208C22⋊C4×C29—21no—
209C22⋊C4×C29—21no—
210C22⋊C4×C29—21no—
211C22⋊C4×C29—21no—
212C42×C29—22no—
213C42×C29—22no—
214C42×C29—22no—
215C42×C29—22no—
216C42×C29—21no—
217C42×C29—21no—
218C42×C29—21no—
219C42×C29C2×D411yescharacteristic
220C42×C29C2×D411yescharacteristic
221C42×C29C2×D411yescharacteristic
222C42×C29C2411yescharacteristic
223#18961C2911yesmaximal, characteristic, direct product factor, Sylow
224C23×C29—21no—
225C23×C29#12011yescharacteristic
226Q8×C29—22no—
227Q8×C29—22no—
228Q8×C29—22no—
229Q8×C29—42no—
230Q8×C29—44no—
231Q8×C29—42no—
232Q8×C29—81no—
233Q8×C29—82no—
234Q8×C29—82no—
235D4×C29—22no—
236D4×C29—81no—
237C2×C4×C29—22no—
238C2×C4×C29—22no—
239C2×C4×C29—21no—
240C2×C4×C29—21no—
241C2×C4×C29—21no—
242C2×C4×C29—22no—
243C2×C4×C29—21no—
244C2×C4×C29—21no—
245C2×C4×C29—21no—
246C2×C4×C29—22no—
247C2×C4×C29—21no—
248C2×C4×C29—41no—
249C2×C4×C29—42no—
250C2×C4×C29—42no—
251C2×C4×C29—82no—
252C2×C4×C29—82no—
253C2×C4×C29#12011yescharacteristic
254C2×C4×C29#12011yescharacteristic
255C2×C4×C29#12011yescharacteristic
256C2×C4×C29C22×D411yescharacteristic
257C2×C4×C29C22×D411yescharacteristic
258C2×C4×C29C22×D411yescharacteristic
259C8×C29—42no—
260C8×C29—42no—
261C8×C29—42no—
262#3555C2×C2911yescharacteristic
263#3238C2×C2911yescharacteristic
264#3230C2×C2911yescharacteristic, complemented
265#3209C2×C2911yescharacteristic, complemented
266#1638C2×C2912yescomplemented
267#1636C2×C2912yescomplemented
268#1633C2×C2912yescomplemented
269#1632C2×C2912yescomplemented
270#1554C2×C2911yescharacteristic, complemented
271#1497C2×C2911yescharacteristic, complemented
272#1482C2×C2911yescharacteristic
273C22×C29—21no—
274C22×C29—21no—
275C22×C29—21no—
276C22×C29—41no—
277C22×C29—41no—
278C22×C29—41no—
279C22×C29C2×#12011yescharacteristic
280C4×C29—21no—
281C4×C29—21no—
282C4×C29—21no—
283C4×C29—21no—
284C4×C29—41no—
285C4×C29—41no—
286C4×C29—41no—
287C4×C29—41no—
288C4×C29—42no—
289C4×C29—41no—
290C4×C29—42no—
291C4×C29—41no—
292C4×C29—41no—
293C4×C29—82no—
294C4×C29#57812yes—
295C4×C29#57812yes—
296#563—22no—
297Q82C22×C2911yescharacteristic
298#557—21no—
299#557C22×C2911yescharacteristic
300#556—21no—
301#556—21no—
302#556C22×C2911yescharacteristic
303#554C22×C2911yescharacteristic
304#552—21no—
305#544—21no—
306#542—21no—
307#541—21no—
308#541—21no—
309#541—22no—
310#533C22×C2911yescharacteristic
311#533C22×C2911yescharacteristic
312C2×C4⋊Q8C22×C2911yescharacteristic
313#529C22×C2911yescharacteristic
314#501—21no—
315#500—21no—
316#494C22×C2912yes—
317#489—21no—
318#487—21no—
319#487C22×C2912yes—
320#484—21no—
321#484—21no—
322#483—21no—
323#480—21no—
324#477C22×C2912yes—
325#477C22×C2912yes—
326#477C22×C2912yes—
327#476C22×C2912yes—
328#462—22no—
329#451—22no—
330#432C22×C2911yescharacteristic
331#431C22×C2911yescharacteristic
332#431C22×C2911yescharacteristic
333#333C22×C2912yes—
334#332C22×C2912yes—
335Q8⋊C8C22×C2912yes—
336Q8⋊C8C22×C2912yes—
337Q8⋊C8C22×C2912yes—
338D4⋊C8C22×C2912yes—
339C2×C29—41no—
340C2×C29—81no—
341C2×C29#301111yescharacteristic
342C2×C29#301111yescharacteristic
343C2×C29#302111yescharacteristic
344C22×Q8—21no—
345C2×Q16—24no—
346C4⋊Q8—22no—
347C4⋊Q8—21no—
348C4⋊Q8—22no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8D4×C2911yescharacteristic
355C4⋊Q8D4×C2911yescharacteristic
356C4⋊Q8C23×C2912yes—
357C4⋊Q8C23×C2911yescharacteristic
358C4⋊Q8C23×C2911yescharacteristic
359#126—22no—
360#126—22no—
361#126—22no—
362#126—22no—
363#126—22no—
364#126—22no—
365#126—21no—
366#125—22no—
367#125—22no—
368#125—22no—
369#125—22no—
370#125—21no—
371#125—22no—
372#125—21no—
373#125—21no—
374#125—21no—
375#125D4×C2911yescharacteristic
376#124—22no—
377#124—21no—
378#124D4×C2911yescharacteristic
379#123—22no—
380#123—21no—
381C22⋊Q8—22no—
382C22⋊Q8—22no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—22no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8D4×C2911yescharacteristic
389C22⋊Q8D4×C2911yescharacteristic
390C22⋊Q8D4×C2911yescharacteristic
391C22⋊Q8D4×C2912yes—
392#121D4×C2911yescharacteristic
393C4×Q8—22no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×Q8—21no—
401C4×Q8D4×C2912yes—
402C4×Q8C23×C2911yescharacteristic
403C4×Q8C23×C2911yescharacteristic
404C4×Q8C23×C2911yescharacteristic
405C4×D4—21no—
406C4×D4—21no—
407C4×D4C23×C2911yescharacteristic
408#117—22no—
409#117—21no—
410#117—21no—
411#117—21no—
412#117—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C42C23×C2911yescharacteristic
417#107—22no—
418#107—22no—
419#107—22no—
420#106—22no—
421C4⋊C8—21no—
422C4⋊C8C23×C2912yes—
423C4⋊C8C23×C2912yes—
424#103—22no—
425#103—22no—
426#103—22no—
427#103—24no—
428#102—22no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432#97—21no—
433C4×C8—21no—
434C4×C8C23×C2912yes—
435C29#1896111yescharacteristic, direct product factor, Sylow
436C2×Q8—22no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—22no—
440C2×Q8—41no—
441C2×Q8—82no—
442C2×Q8C2×D4×C2911yescharacteristic
443C2×Q8C2×D4×C2911yescharacteristic
444C2×Q8C2×D4×C2911yescharacteristic
445C2×Q8C2×D4×C2912yes—
446C2×D4—21no—
447C2×D4C2×D4×C2911yescharacteristic
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—41no—
451C22×C4C2×D4×C2911yescharacteristic
452C22×C4C2×D4×C2911yescharacteristic
453C22×C4C2×D4×C2911yescharacteristic
454Q16—84no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—22no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4C2×D4×C2912yes—
487C4⋊C4C2×D4×C2911yescharacteristic
488C4⋊C4C2×D4×C2911yescharacteristic
489C4⋊C4C2×D4×C2911yescharacteristic
490C4⋊C4C2×D4×C2911yescharacteristic
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—21no—
495C22⋊C4—22no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C42—22no—
503C42—22no—
504C42—22no—
505C42—22no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42C2×D4×C2911yescharacteristic
510C42C2×D4×C2911yescharacteristic
511C42C2×D4×C2911yescharacteristic
512C42C24×C2911yescharacteristic
513C23—21no—
514C23C29×#12011yescharacteristic
515Q8—22no—
516Q8—22no—
517Q8—22no—
518Q8—42no—
519Q8—44no—
520Q8—42no—
521Q8—81no—
522Q8—82no—
523Q8—82no—
524D4—22no—
525D4—81no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4C29×#12011yescharacteristic
543C2×C4C29×#12011yescharacteristic
544C2×C4C29×#12011yescharacteristic
545C2×C4C22×D4×C2911yescharacteristic
546C2×C4C22×D4×C2911yescharacteristic
547C2×C4C22×D4×C2911yescharacteristic
548C8—42no—
549C8—42no—
550C8—42no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22C2×C29×#12011yescharacteristic
558C4—21no—
559C4—21no—
560C4—21no—
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—42no—
567C4—41no—
568C4—42no—
569C4—41no—
570C4—41no—
571C4—82no—
572C4C29×#57812yes—
573C4C29×#57812yes—
574C2—41no—
575C2—81no—
576C2C29×#301111yescharacteristic
577C2C29×#301111yescharacteristic
578C2C29×#302111yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#121D4
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. C29×#3230C2semidirect
4. C29×#3209C2semidirect
5. C29×#1638C2semidirect
6. C29×#1636C2semidirect
7. C29×#1633C2semidirect
8. C29×#1632C2semidirect
9. C29×#1554C2semidirect
10. C29×#1497C2semidirect
223. #18961C29direct (N × H)
264. #3230C2×C29semidirect
265. #3209C2×C29semidirect
266. #1638C2×C29semidirect
267. #1636C2×C29semidirect
268. #1633C2×C29semidirect
269. #1632C2×C29semidirect
270. #1554C2×C29semidirect
271. #1497C2×C29semidirect
435. C29#18961direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35552
C29×#32382
C29×#32302
C29×#32092
C29×#16382
C29×#16362
C29×#16332
C29×#16322
C29×#15542
C29×#14972
C29×#14822
#1896129