Finite Group Databasebeta

← C29×#18305 #20313205

Subgroups — C29×#18305 #20313205

Order 7424.

934 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3455C211yesmaximal, characteristic
2C29×#3209C211yesmaximal, characteristic, complemented
3C29×#3206C211yesmaximal, characteristic, complemented
4C29×#2628C211yesmaximal, characteristic, complemented
5C29×#1606C214yesmaximal, complemented
6C29×#1603C214yesmaximal, complemented
7C29×#1518C211yesmaximal, characteristic, complemented
8C29×#1517C211yesmaximal, characteristic, complemented
9C29×#1458C211yesmaximal, characteristic, complemented
10C29×#542—21no—
11C29×#542—21no—
12C29×#541—21no—
13C29×#540—21no—
14C29×#539—21no—
15C29×#539C2212yes—
16C29×#538—21no—
17C29×#538C2212yes—
18C29×#533C2211yescharacteristic
19C29×#532C2211yescharacteristic
20C2×C29×C4⋊Q8C2211yescharacteristic
21C29×#529—22no—
22C29×#529—22no—
23C29×#525—21no—
24C4×#41×C29—21no—
25C2×C29×#117C2211yescharacteristic
26C29×#494—21no—
27C29×#492—21no—
28C29×#487—21no—
29C29×#487—21no—
30C29×#462—22no—
31C29×#461—22no—
32C29×#451C2214yes—
33C29×#448C2214yes—
34C29×#431C2211yescharacteristic
35C29×#431C2211yescharacteristic
36C29×#400—21no—
37C29×#399—21no—
38C29×#395C2212yes—
39C29×#393C2212yes—
40C29×#389—21no—
41C29×#382C2211yescharacteristic
42C29×#380—21no—
43C29×#328C2214yes—
44C29×#327C2214yes—
45C29×#324C2212yes—
46C29×#323C2212yes—
47C2×#41×C29—21no—
48C22×Q8×C29C2312yes—
49C23×C4×C29D411yescharacteristic
50C2×Q16×C29—24no—
51C2×SD16×C29—24no—
52C29×C4⋊Q8—21no—
53C29×C4⋊Q8—21no—
54C29×C4⋊Q8—21no—
55C29×C4⋊Q8—21no—
56C29×C4⋊Q8D411yescharacteristic
57C29×C4⋊Q8D411yescharacteristic
58C29×C4⋊Q8D411yescharacteristic
59C29×#127D411yescharacteristic
60C29×#126—22no—
61C29×#126—22no—
62C29×#126—22no—
63C29×#126—22no—
64C29×#125—22no—
65C29×#125—22no—
66C29×#125—21no—
67C29×#124—22no—
68C29×#124—22no—
69C29×#124—21no—
70C29×#123—22no—
71C29×#123—22no—
72C29×#123—22no—
73C29×#123—22no—
74C29×#123—22no—
75C29×C22⋊Q8—21no—
76C29×C22⋊Q8—21no—
77C29×C22⋊Q8—22no—
78C29×C22⋊Q8—22no—
79C29×C22⋊Q8—21no—
80C29×C22⋊Q8C2312yes—
81C29×#121—21no—
82C29×#121—21no—
83C29×#121—22no—
84C29×#121—22no—
85C29×#121—21no—
86C29×#121C2312yes—
87C29×#120—22no—
88C4×Q8×C29—21no—
89C4×Q8×C29—21no—
90C4×Q8×C29—21no—
91C4×Q8×C29D412yes—
92C4×D4×C29—21no—
93C4×D4×C29—21no—
94C4×D4×C29—22no—
95C4×D4×C29—22no—
96C4×D4×C29—22no—
97C4×D4×C29—22no—
98C4×D4×C29—21no—
99C4×D4×C29D412yes—
100C29×#117—22no—
101C29×#117—21no—
102C29×#117—21no—
103C29×#117—21no—
104C29×#117—21no—
105C29×#117—21no—
106C2×C4⋊C4×C29—21no—
107C2×C4⋊C4×C29—21no—
108C2×C4⋊C4×C29—21no—
109C2×C4⋊C4×C29—22no—
110C2×C4⋊C4×C29D411yescharacteristic
111C2×C4⋊C4×C29C2311yescharacteristic
112C2×C22⋊C4×C29—22no—
113C2×C22⋊C4×C29D411yescharacteristic
114C2×C22⋊C4×C29C2311yescharacteristic
115C2×C42×C29—22no—
116C2×C42×C29D411yescharacteristic
117C2×C42×C29C2311yescharacteristic
118C29×C4⋊C8—21no—
119C29×C4⋊C8—21no—
120C29×#103—24no—
121C29×#103—24no—
122C29×C22⋊C8C2312yes—
123C29×C22⋊C8C2312yes—
124C4×C8×C29—21no—
125C4×C8×C29—21no—
126C29×#95—22no—
127C29×#95—21no—
128C29×#95—22no—
129C29×#95C2312yes—
130C24×C29C2×D411yescharacteristic
131#41×C29—42no—
132#41×C29—42no—
133C2×Q8×C29—21no—
134C2×Q8×C29—21no—
135C2×Q8×C29—22no—
136C2×Q8×C29—22no—
137C2×Q8×C29—82no—
138C2×Q8×C29C2×D412yes—
139C2×D4×C29—22no—
140C2×D4×C29—22no—
141C2×D4×C29—22no—
142C2×D4×C29—21no—
143C2×D4×C29—21no—
144C2×D4×C29C2×D412yes—
145C22×C4×C29—22no—
146C22×C4×C29—22no—
147C22×C4×C29—22no—
148C22×C4×C29—21no—
149C22×C4×C29—21no—
150C22×C4×C29—22no—
151C22×C4×C29—22no—
152C22×C4×C29—22no—
153C22×C4×C29—22no—
154C22×C4×C29C2×D411yescharacteristic
155C22×C4×C29C2×D411yescharacteristic
156C22×C4×C29C2×D411yescharacteristic
157C22×C4×C29C2×D411yescharacteristic
158C22×C4×C29C2×D411yescharacteristic
159C22×C4×C29C2411yescharacteristic
160Q16×C29—84no—
161SD16×C29—84no—
162C2×C8×C29—22no—
163C2×C8×C29—22no—
164C4⋊C4×C29—22no—
165C4⋊C4×C29—22no—
166C4⋊C4×C29—22no—
167C4⋊C4×C29—22no—
168C4⋊C4×C29—21no—
169C4⋊C4×C29—21no—
170C4⋊C4×C29—21no—
171C4⋊C4×C29—21no—
172C4⋊C4×C29—21no—
173C4⋊C4×C29—21no—
174C4⋊C4×C29—22no—
175C4⋊C4×C29—21no—
176C4⋊C4×C29—21no—
177C4⋊C4×C29—22no—
178C4⋊C4×C29—41no—
179C4⋊C4×C29—41no—
180C4⋊C4×C29—41no—
181C4⋊C4×C29—41no—
182C4⋊C4×C29—42no—
183C4⋊C4×C29—82no—
184C4⋊C4×C29C2×D412yes—
185C4⋊C4×C29C2×D412yes—
186C22⋊C4×C29—22no—
187C22⋊C4×C29—22no—
188C22⋊C4×C29—22no—
189C22⋊C4×C29—22no—
190C22⋊C4×C29—22no—
191C22⋊C4×C29—22no—
192C22⋊C4×C29—22no—
193C22⋊C4×C29—21no—
194C22⋊C4×C29—21no—
195C22⋊C4×C29—22no—
196C22⋊C4×C29—21no—
197C22⋊C4×C29—21no—
198C22⋊C4×C29—22no—
199C22⋊C4×C29—82no—
200C42×C29—22no—
201C42×C29—22no—
202C42×C29—21no—
203C42×C29—22no—
204C42×C29—21no—
205C42×C29C2×D411yescharacteristic
206C42×C29C2×D411yescharacteristic
207C42×C29C2×D411yescharacteristic
208C42×C29C2×D411yescharacteristic
209#18305C2911yesmaximal, characteristic, direct product factor, Sylow
210C23×C29—21no—
211C23×C29—22no—
212C23×C29—21no—
213C23×C29—21no—
214C23×C29—41no—
215C23×C29—41no—
216C23×C29C22×D411yescharacteristic
217Q8×C29—42no—
218Q8×C29—44no—
219Q8×C29—44no—
220Q8×C29—42no—
221Q8×C29—81no—
222D4×C29—42no—
223D4×C29—42no—
224D4×C29—42no—
225D4×C29—42no—
226D4×C29—81no—
227D4×C29—82no—
228D4×C29—82no—
229C2×C4×C29—21no—
230C2×C4×C29—21no—
231C2×C4×C29—22no—
232C2×C4×C29—22no—
233C2×C4×C29—22no—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—21no—
237C2×C4×C29—41no—
238C2×C4×C29—41no—
239C2×C4×C29—42no—
240C2×C4×C29—42no—
241C2×C4×C29—44no—
242C2×C4×C29—41no—
243C2×C4×C29—41no—
244C2×C4×C29—42no—
245C2×C4×C29—42no—
246C2×C4×C29—42no—
247C2×C4×C29—42no—
248C2×C4×C29—42no—
249C2×C4×C29—42no—
250C2×C4×C29—82no—
251C2×C4×C29—82no—
252C2×C4×C29#12011yescharacteristic
253C2×C4×C29#12011yescharacteristic
254C2×C4×C29#12011yescharacteristic
255C2×C4×C29#12011yescharacteristic
256C2×C4×C29#13512yes—
257C2×C4×C29#13712yes—
258C2×C4×C29C22×D411yescharacteristic
259C2×C4×C29C22×D411yescharacteristic
260C8×C29—42no—
261C8×C29—42no—
262#3455C2×C2911yescharacteristic
263#3209C2×C2911yescharacteristic, complemented
264#3206C2×C2911yescharacteristic, complemented
265#2628C2×C2911yescharacteristic, complemented
266#1606C2×C2914yescomplemented
267#1603C2×C2914yescomplemented
268#1518C2×C2911yescharacteristic, complemented
269#1517C2×C2911yescharacteristic, complemented
270#1458C2×C2911yescharacteristic, complemented
271C22×C29—21no—
272C22×C29—21no—
273C22×C29—42no—
274C22×C29—41no—
275C22×C29—42no—
276C22×C29—42no—
277C22×C29—41no—
278C22×C29—42no—
279C22×C29—41no—
280C22×C29—81no—
281C22×C29C2×#12011yescharacteristic
282C22×C29C2×#13511yescharacteristic
283C22×C29C2×#13711yescharacteristic
284C4×C29—21no—
285C4×C29—21no—
286C4×C29—21no—
287C4×C29—21no—
288C4×C29—41no—
289C4×C29—42no—
290C4×C29—41no—
291C4×C29—42no—
292C4×C29—41no—
293C4×C29—42no—
294C4×C29—82no—
295C4×C29—82no—
296C4×C29#45212yes—
297C4×C29#45212yes—
298#542—21no—
299#542—21no—
300#541—21no—
301#540—21no—
302#539—21no—
303#539C22×C2912yes—
304#538—21no—
305#538C22×C2912yes—
306#533C22×C2911yescharacteristic
307#532C22×C2911yescharacteristic
308C2×C4⋊Q8C22×C2911yescharacteristic
309#529—22no—
310#529—22no—
311#525—21no—
312C4×#41—21no—
313C2×#117C22×C2911yescharacteristic
314#494—21no—
315#492—21no—
316#487—21no—
317#487—21no—
318#462—22no—
319#461—22no—
320#451C22×C2914yes—
321#448C22×C2914yes—
322#431C22×C2911yescharacteristic
323#431C22×C2911yescharacteristic
324#400—21no—
325#399—21no—
326#395C22×C2912yes—
327#393C22×C2912yes—
328#389—21no—
329#382C22×C2911yescharacteristic
330#380—21no—
331#328C22×C2914yes—
332#327C22×C2914yes—
333#324C22×C2912yes—
334#323C22×C2912yes—
335C2×C29—21no—
336C2×C29—21no—
337C2×C29—82no—
338C2×C29—81no—
339C2×C29C2×#45211yescharacteristic
340C2×C29#302211yescharacteristic
341C2×C29#302711yescharacteristic
342C2×#41—21no—
343C22×Q8C23×C2912yes—
344C23×C4D4×C2911yescharacteristic
345C2×Q16—24no—
346C2×SD16—24no—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8D4×C2911yescharacteristic
352C4⋊Q8D4×C2911yescharacteristic
353C4⋊Q8D4×C2911yescharacteristic
354#127D4×C2911yescharacteristic
355#126—22no—
356#126—22no—
357#126—22no—
358#126—22no—
359#125—22no—
360#125—22no—
361#125—21no—
362#124—22no—
363#124—22no—
364#124—21no—
365#123—22no—
366#123—22no—
367#123—22no—
368#123—22no—
369#123—22no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8—21no—
375C22⋊Q8C23×C2912yes—
376#121—21no—
377#121—21no—
378#121—22no—
379#121—22no—
380#121—21no—
381#121C23×C2912yes—
382#120—22no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8D4×C2912yes—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—21no—
394C4×D4D4×C2912yes—
395#117—22no—
396#117—21no—
397#117—21no—
398#117—21no—
399#117—21no—
400#117—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4D4×C2911yescharacteristic
406C2×C4⋊C4C23×C2911yescharacteristic
407C2×C22⋊C4—22no—
408C2×C22⋊C4D4×C2911yescharacteristic
409C2×C22⋊C4C23×C2911yescharacteristic
410C2×C42—22no—
411C2×C42D4×C2911yescharacteristic
412C2×C42C23×C2911yescharacteristic
413C4⋊C8—21no—
414C4⋊C8—21no—
415#103—24no—
416#103—24no—
417C22⋊C8C23×C2912yes—
418C22⋊C8C23×C2912yes—
419C4×C8—21no—
420C4×C8—21no—
421#95—22no—
422#95—21no—
423#95—22no—
424#95C23×C2912yes—
425C29#1830511yescharacteristic, direct product factor, Sylow
426C24C2×D4×C2911yescharacteristic
427#41—42no—
428#41—42no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—82no—
434C2×Q8C2×D4×C2912yes—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C2×D4×C2912yes—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4C2×D4×C2911yescharacteristic
451C22×C4C2×D4×C2911yescharacteristic
452C22×C4C2×D4×C2911yescharacteristic
453C22×C4C2×D4×C2911yescharacteristic
454C22×C4C2×D4×C2911yescharacteristic
455C22×C4C24×C2911yescharacteristic
456Q16—84no—
457SD16—84no—
458C2×C8—22no—
459C2×C8—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—22no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—42no—
479C4⋊C4—82no—
480C4⋊C4C2×D4×C2912yes—
481C4⋊C4C2×D4×C2912yes—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—22no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—22no—
495C22⋊C4—82no—
496C42—22no—
497C42—22no—
498C42—21no—
499C42—22no—
500C42—21no—
501C42C2×D4×C2911yescharacteristic
502C42C2×D4×C2911yescharacteristic
503C42C2×D4×C2911yescharacteristic
504C42C2×D4×C2911yescharacteristic
505C23—21no—
506C23—22no—
507C23—21no—
508C23—21no—
509C23—41no—
510C23—41no—
511C23C22×D4×C2911yescharacteristic
512Q8—42no—
513Q8—44no—
514Q8—44no—
515Q8—42no—
516Q8—81no—
517D4—42no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—81no—
522D4—82no—
523D4—82no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—44no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4C29×#12011yescharacteristic
548C2×C4C29×#12011yescharacteristic
549C2×C4C29×#12011yescharacteristic
550C2×C4C29×#12011yescharacteristic
551C2×C4C29×#13512yes—
552C2×C4C29×#13712yes—
553C2×C4C22×D4×C2911yescharacteristic
554C2×C4C22×D4×C2911yescharacteristic
555C8—42no—
556C8—42no—
557C22—21no—
558C22—21no—
559C22—42no—
560C22—41no—
561C22—42no—
562C22—42no—
563C22—41no—
564C22—42no—
565C22—41no—
566C22—81no—
567C22C2×C29×#12011yescharacteristic
568C22C2×C29×#13511yescharacteristic
569C22C2×C29×#13711yescharacteristic
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—41no—
575C4—42no—
576C4—41no—
577C4—42no—
578C4—41no—
579C4—42no—
580C4—82no—
581C4—82no—
582C4C29×#45212yes—
583C4C29×#45212yes—
584C2—21no—
585C2—21no—
586C2—81no—
587C2—82no—
588C2C2×C29×#45211yescharacteristic
589C2C29×#302211yescharacteristic
590C2C29×#302711yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#3455C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3209C2semidirect
3. C29×#3206C2semidirect
4. C29×#2628C2semidirect
5. C29×#1606C2semidirect
6. C29×#1603C2semidirect
7. C29×#1518C2semidirect
8. C29×#1517C2semidirect
9. C29×#1458C2semidirect
209. #18305C29direct (N × H)
263. #3209C2×C29semidirect
264. #3206C2×C29semidirect
265. #2628C2×C29semidirect
266. #1606C2×C29semidirect
267. #1603C2×C29semidirect
268. #1518C2×C29semidirect
269. #1517C2×C29semidirect
270. #1458C2×C29semidirect
425. C29#18305direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34552
C29×#32092
C29×#32062
C29×#26282
C29×#16062
C29×#16032
C29×#15182
C29×#15172
C29×#14582
#1830529