Finite Group Databasebeta

← C29×#19229 #20314129

Subgroups — C29×#19229 #20314129

Order 7424.

606 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×#3248C211yesmaximal, characteristic, complemented
2C29×#3247C211yesmaximal, characteristic
3C29×#3167C211yesmaximal, characteristic, complemented
4C29×#2966C211yesmaximal, characteristic, complemented
5C29×#1692C211yesmaximal, characteristic, complemented
6C29×#1691C211yesmaximal, characteristic, complemented
7C29×#1686C211yesmaximal, characteristic, complemented
8C29×#1685C211yesmaximal, characteristic, complemented
9C29×#1684C211yesmaximal, characteristic, complemented
10C29×#1683C211yesmaximal, characteristic, complemented
11C29×#1682C211yesmaximal, characteristic, complemented
12C29×#1681C211yesmaximal, characteristic, complemented
13C2×C29×#335C211yesmaximal, characteristic, complemented
14C29×#1552C211yesmaximal, characteristic, complemented
15C29×#1551C211yesmaximal, characteristic, complemented
16C29×#533C2211yescharacteristic
17C29×#532C2211yescharacteristic
18C29×#529C2211yescharacteristic
19C29×#498C2211yescharacteristic
20C29×#492C2211yescharacteristic
21C29×#487C2211yescharacteristic
22C29×#486C2211yescharacteristic
23C29×#479—21no—
24C29×#478—21no—
25C29×#477C2211yescharacteristic
26C29×#476C2211yescharacteristic
27C29×#475C2211yescharacteristic
28C29×#474C2211yescharacteristic
29C29×#467—21no—
30C29×#466—21no—
31C29×#465—21no—
32C29×#465—21no—
33C29×#465—21no—
34C29×#465—21no—
35C29×#464—21no—
36C29×#463—21no—
37C29×#462C2211yescharacteristic
38C29×#461C2211yescharacteristic
39C29×#460C2211yescharacteristic
40C29×#459C2211yescharacteristic
41C29×#446C2211yescharacteristic
42C8×Q8×C29C2211yescharacteristic
43C4×SD16×C29—21no—
44C4×SD16×C29—21no—
45C29×#436C2211yescharacteristic
46C29×#435—21no—
47C8×D4×C29—21no—
48C8×D4×C29C2211yescharacteristic
49C29×#433—21no—
50C29×#432C2211yescharacteristic
51C2×C29×C4⋊C8C2211yescharacteristic
52C2×C29×C4⋊C8C2211yescharacteristic
53C29×#405—21no—
54C2×C4×C8×C29C2211yescharacteristic
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#335C2211yescharacteristic
58C29×#335C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×#332C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#331C2211yescharacteristic
66C29×#331C2211yescharacteristic
67C2×#41×C29—21no—
68C2×Q16×C29—21no—
69C2×SD16×C29—21no—
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×D8×C29—21no—
74C2×M16×C29—21no—
75C22×C8×C29—21no—
76C22×C8×C29—21no—
77C22×C8×C29—21no—
78C22×C8×C29D411yescharacteristic
79C22×C8×C29D411yescharacteristic
80C29×C4⋊Q8C2311yescharacteristic
81C29×C4⋊Q8C2311yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×#127C2311yescharacteristic
84C29×#126—21no—
85C29×#125—21no—
86C29×#125D411yescharacteristic
87C29×#124—21no—
88C29×#124D411yescharacteristic
89C29×#123—21no—
90C29×C22⋊Q8—21no—
91C29×C22⋊Q8—21no—
92C29×C22⋊Q8D411yescharacteristic
93C29×#121—21no—
94C29×#121—21no—
95C29×#121D411yescharacteristic
96C4×Q8×C29—21no—
97C4×Q8×C29—21no—
98C4×Q8×C29C2311yescharacteristic
99C4×D4×C29—21no—
100C4×D4×C29—21no—
101C4×D4×C29—21no—
102C4×D4×C29C2311yescharacteristic
103C29×#117—21no—
104C29×#117—21no—
105C2×C42×C29C2311yescharacteristic
106C29×#107—21no—
107C29×#107—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×#106—21no—
111C29×#106—21no—
112C29×C4⋊C8—21no—
113C29×C4⋊C8—21no—
114C29×C4⋊C8—21no—
115C29×C4⋊C8—21no—
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×C4⋊C8C2311yescharacteristic
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—21no—
126C29×#103—21no—
127C29×#103—21no—
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×C22⋊C8—21no—
135C29×C22⋊C8—21no—
136C29×C22⋊C8—21no—
137C29×#97—21no—
138C29×#97—21no—
139C4×C8×C29—21no—
140C4×C8×C29D411yescharacteristic
141C4×C8×C29D411yescharacteristic
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144#41×C29—82no—
145C2×Q8×C29—21no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29C2×D411yescharacteristic
149C2×D4×C29—21no—
150C2×D4×C29—21no—
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—41no—
154C2×D4×C29C2×D411yescharacteristic
155C22×C4×C29—21no—
156C22×C4×C29—41no—
157C22×C4×C29C2×D411yescharacteristic
158C22×C4×C29C2×D411yescharacteristic
159C22×C4×C29#4111yescharacteristic
160Q16×C29—81no—
161SD16×C29—42no—
162SD16×C29—42no—
163SD16×C29—81no—
164SD16×C29—81no—
165D8×C29—81no—
166M16×C29—42no—
167C2×C8×C29—22no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C2×C8×C29—21no—
173C2×C8×C29—21no—
174C2×C8×C29—41no—
175C2×C8×C29—42no—
176C2×C8×C29—81no—
177C2×C8×C29—81no—
178C2×C8×C29C2×D411yescharacteristic
179C2×C8×C29C2×D411yescharacteristic
180C2×C8×C29C2×D411yescharacteristic
181C2×C8×C29C2×D411yescharacteristic
182C4⋊C4×C29—21no—
183C4⋊C4×C29—21no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
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—41no—
193C4⋊C4×C29—41no—
194C4⋊C4×C29C2×D411yescharacteristic
195C4⋊C4×C29C2×D411yescharacteristic
196C22⋊C4×C29—21no—
197C22⋊C4×C29—21no—
198C22⋊C4×C29—21no—
199C22⋊C4×C29—21no—
200C22⋊C4×C29—21no—
201C22⋊C4×C29—41no—
202C22⋊C4×C29—41no—
203C22⋊C4×C29—41no—
204C42×C29—21no—
205C42×C29—41no—
206C42×C29C2×D411yescharacteristic
207C42×C29C2×D411yescharacteristic
208C42×C29#4111yescharacteristic
209C42×C29C2411yescharacteristic
210#19229C2911yesmaximal, characteristic, direct product factor, Sylow
211C23×C29—21no—
212C23×C29—41no—
213C23×C29#12111yescharacteristic
214Q8×C29—21no—
215Q8×C29—21no—
216Q8×C29—41no—
217Q8×C29—41no—
218Q8×C29—41no—
219Q8×C29—41no—
220Q8×C29—81no—
221D4×C29—21no—
222D4×C29—21no—
223D4×C29—42no—
224D4×C29—41no—
225D4×C29—41no—
226D4×C29—41no—
227D4×C29—41no—
228D4×C29—81no—
229D4×C29—82no—
230C2×C4×C29—22no—
231C2×C4×C29—21no—
232C2×C4×C29—21no—
233C2×C4×C29—21no—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—41no—
239C2×C4×C29—41no—
240C2×C4×C29—41no—
241C2×C4×C29—41no—
242C2×C4×C29—41no—
243C2×C4×C29—82no—
244C2×C4×C29#12111yescharacteristic
245C2×C4×C29#12111yescharacteristic
246C2×C4×C29#12111yescharacteristic
247C2×C4×C29C22×D411yescharacteristic
248C2×C4×C29C22×D411yescharacteristic
249C2×C4×C29C2×#4111yescharacteristic
250C8×C29—21no—
251C8×C29—21no—
252C8×C29—21no—
253C8×C29—41no—
254C8×C29—41no—
255C8×C29—41no—
256C8×C29—41no—
257C8×C29—41no—
258C8×C29—41no—
259C8×C29#13512yes—
260#3248C2×C2911yescharacteristic, complemented
261#3247C2×C2911yescharacteristic
262#3167C2×C2911yescharacteristic, complemented
263#2966C2×C2911yescharacteristic, complemented
264#1692C2×C2911yescharacteristic, complemented
265#1691C2×C2911yescharacteristic, complemented
266#1686C2×C2911yescharacteristic, complemented
267#1685C2×C2911yescharacteristic, complemented
268#1684C2×C2911yescharacteristic, complemented
269#1683C2×C2911yescharacteristic, complemented
270#1682C2×C2911yescharacteristic, complemented
271#1681C2×C2911yescharacteristic, complemented
272C2×#335C2×C2911yescharacteristic, complemented
273#1552C2×C2911yescharacteristic, complemented
274#1551C2×C2911yescharacteristic, complemented
275C22×C29—21no—
276C22×C29—21no—
277C22×C29—41no—
278C22×C29—41no—
279C22×C29—41no—
280C22×C29—81no—
281C22×C29—81no—
282C22×C29—81no—
283C22×C29#47112yes—
284C22×C29C2×#12111yescharacteristic
285C4×C29—21no—
286C4×C29—21no—
287C4×C29—21no—
288C4×C29—21no—
289C4×C29—41no—
290C4×C29—41no—
291C4×C29—41no—
292C4×C29—81no—
293C4×C29—81no—
294C4×C29—81no—
295C4×C29C2×#13511yescharacteristic
296C4×C29#57511yescharacteristic
297C4×C29#57611yescharacteristic
298C4×C29#57811yescharacteristic
299#533C22×C2911yescharacteristic
300#532C22×C2911yescharacteristic
301#529C22×C2911yescharacteristic
302#498C22×C2911yescharacteristic
303#492C22×C2911yescharacteristic
304#487C22×C2911yescharacteristic
305#486C22×C2911yescharacteristic
306#479—21no—
307#478—21no—
308#477C22×C2911yescharacteristic
309#476C22×C2911yescharacteristic
310#475C22×C2911yescharacteristic
311#474C22×C2911yescharacteristic
312#467—21no—
313#466—21no—
314#465—21no—
315#465—21no—
316#465—21no—
317#465—21no—
318#464—21no—
319#463—21no—
320#462C22×C2911yescharacteristic
321#461C22×C2911yescharacteristic
322#460C22×C2911yescharacteristic
323#459C22×C2911yescharacteristic
324#446C22×C2911yescharacteristic
325C8×Q8C22×C2911yescharacteristic
326C4×SD16—21no—
327C4×SD16—21no—
328#436C22×C2911yescharacteristic
329#435—21no—
330C8×D4—21no—
331C8×D4C22×C2911yescharacteristic
332#433—21no—
333#432C22×C2911yescharacteristic
334C2×C4⋊C8C22×C2911yescharacteristic
335C2×C4⋊C8C22×C2911yescharacteristic
336#405—21no—
337C2×C4×C8C22×C2911yescharacteristic
338#335C22×C2911yescharacteristic
339#335C22×C2911yescharacteristic
340#335C22×C2911yescharacteristic
341#335C22×C2911yescharacteristic
342#333C22×C2911yescharacteristic
343#333C22×C2911yescharacteristic
344#332C22×C2911yescharacteristic
345#332C22×C2911yescharacteristic
346#332C22×C2911yescharacteristic
347#332C22×C2911yescharacteristic
348#331C22×C2911yescharacteristic
349#331C22×C2911yescharacteristic
350C2×C29—22no—
351C2×C29—81no—
352C2×C29—161no—
353C2×C29#303511yescharacteristic
354C2×C29#306111yescharacteristic
355C2×C29C2×#47111yescharacteristic
356C2×#41—21no—
357C2×Q16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×D8—21no—
363C2×M16—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8D4×C2911yescharacteristic
368C22×C8D4×C2911yescharacteristic
369C4⋊Q8C23×C2911yescharacteristic
370C4⋊Q8C23×C2911yescharacteristic
371C4⋊Q8C23×C2911yescharacteristic
372#127C23×C2911yescharacteristic
373#126—21no—
374#125—21no—
375#125D4×C2911yescharacteristic
376#124—21no—
377#124D4×C2911yescharacteristic
378#123—21no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8D4×C2911yescharacteristic
382#121—21no—
383#121—21no—
384#121D4×C2911yescharacteristic
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8C23×C2911yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4C23×C2911yescharacteristic
392#117—21no—
393#117—21no—
394C2×C42C23×C2911yescharacteristic
395#107—21no—
396#107—21no—
397#106—21no—
398#106—21no—
399#106—21no—
400#106—21no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8C23×C2911yescharacteristic
406C4⋊C8C23×C2911yescharacteristic
407C4⋊C8C23×C2911yescharacteristic
408C4⋊C8C23×C2911yescharacteristic
409C4⋊C8C23×C2911yescharacteristic
410C4⋊C8C23×C2911yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426#97—21no—
427#97—21no—
428C4×C8—21no—
429C4×C8D4×C2911yescharacteristic
430C4×C8D4×C2911yescharacteristic
431C4×C8C23×C2911yescharacteristic
432C4×C8C23×C2911yescharacteristic
433C29#1922911yescharacteristic, direct product factor, Sylow
434#41—82no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C2×D4×C2911yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4C2×D4×C2911yescharacteristic
445C22×C4—21no—
446C22×C4—41no—
447C22×C4C2×D4×C2911yescharacteristic
448C22×C4C2×D4×C2911yescharacteristic
449C22×C4#41×C2911yescharacteristic
450Q16—81no—
451SD16—42no—
452SD16—42no—
453SD16—81no—
454SD16—81no—
455D8—81no—
456M16—42no—
457C2×C8—22no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—41no—
465C2×C8—42no—
466C2×C8—81no—
467C2×C8—81no—
468C2×C8C2×D4×C2911yescharacteristic
469C2×C8C2×D4×C2911yescharacteristic
470C2×C8C2×D4×C2911yescharacteristic
471C2×C8C2×D4×C2911yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4C2×D4×C2911yescharacteristic
485C4⋊C4C2×D4×C2911yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C42—21no—
495C42—41no—
496C42C2×D4×C2911yescharacteristic
497C42C2×D4×C2911yescharacteristic
498C42#41×C2911yescharacteristic
499C42C24×C2911yescharacteristic
500C23—21no—
501C23—41no—
502C23C29×#12111yescharacteristic
503Q8—21no—
504Q8—21no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—81no—
510D4—21no—
511D4—21no—
512D4—42no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—41no—
517D4—81no—
518D4—82no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—82no—
533C2×C4C29×#12111yescharacteristic
534C2×C4C29×#12111yescharacteristic
535C2×C4C29×#12111yescharacteristic
536C2×C4C22×D4×C2911yescharacteristic
537C2×C4C22×D4×C2911yescharacteristic
538C2×C4C2×#41×C2911yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8C29×#13512yes—
549C22—21no—
550C22—21no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C29×#47112yes—
558C22C2×C29×#12111yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4C2×C29×#13511yescharacteristic
570C4C29×#57511yescharacteristic
571C4C29×#57611yescharacteristic
572C4C29×#57811yescharacteristic
573C2—22no—
574C2—81no—
575C2—161no—
576C2C29×#303511yescharacteristic
577C2C29×#306111yescharacteristic
578C2C2×C29×#47111yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3247C2
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
1. C29×#3248C2semidirect
3. C29×#3167C2semidirect
4. C29×#2966C2semidirect
5. C29×#1692C2semidirect
6. C29×#1691C2semidirect
7. C29×#1686C2semidirect
8. C29×#1685C2semidirect
9. C29×#1684C2semidirect
10. C29×#1683C2semidirect
11. C29×#1682C2semidirect
12. C29×#1681C2semidirect
13. C2×C29×#335C2semidirect
14. C29×#1552C2semidirect
15. C29×#1551C2semidirect
210. #19229C29direct (N × H)
260. #3248C2×C29semidirect
262. #3167C2×C29semidirect
263. #2966C2×C29semidirect
264. #1692C2×C29semidirect
265. #1691C2×C29semidirect
266. #1686C2×C29semidirect
267. #1685C2×C29semidirect
268. #1684C2×C29semidirect
269. #1683C2×C29semidirect
270. #1682C2×C29semidirect
271. #1681C2×C29semidirect
272. C2×#335C2×C29semidirect
273. #1552C2×C29semidirect
274. #1551C2×C29semidirect
433. C29#19229direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32482
C29×#32472
C29×#31672
C29×#29662
C29×#16922
C29×#16912
C29×#16862
C29×#16852
C29×#16842
C29×#16832
C29×#16822
C29×#16812
C2×C29×#3352
C29×#15522
C29×#15512
#1922929