Finite Group Databasebeta

← C29×#19373 #20314273

Subgroups — C29×#19373 #20314273

Order 7424.

576 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3254C211yesmaximal, characteristic
2C29×#3237C211yesmaximal, characteristic, complemented
3C29×#3182C211yesmaximal, characteristic
4C29×#2962C211yesmaximal, characteristic, complemented
5C29×#1704C211yesmaximal, characteristic, complemented
6C29×#1698C211yesmaximal, characteristic, complemented
7C29×#1696C211yesmaximal, characteristic, complemented
8C29×#1686C211yesmaximal, characteristic, complemented
9C29×#1684C211yesmaximal, characteristic, complemented
10C29×#1678C211yesmaximal, characteristic, complemented
11C29×#1676C211yesmaximal, characteristic, complemented
12C29×#1666C211yesmaximal, characteristic, complemented
13C29×#1569C211yesmaximal, characteristic, complemented
14C29×#1551C211yesmaximal, characteristic
15C29×#1550C211yesmaximal, characteristic, complemented
16C29×#533C2211yescharacteristic
17C29×#533C2211yescharacteristic
18C29×#532C2211yescharacteristic
19C29×#501—21no—
20C29×#500C2211yescharacteristic
21C29×#492C2211yescharacteristic
22C29×#491—21no—
23C29×#487C2211yescharacteristic
24C29×#486C2211yescharacteristic
25C29×#485—21no—
26C29×#485—21no—
27C29×#477C2211yescharacteristic
28C29×#477C2211yescharacteristic
29C29×#477C2211yescharacteristic
30C29×#477C2211yescharacteristic
31C29×#475C2211yescharacteristic
32C29×#475C2211yescharacteristic
33C29×#474—21no—
34C29×#468—21no—
35C29×#468—21no—
36C29×#468—21no—
37C29×#468—21no—
38C29×#461—21no—
39C29×#460C2211yescharacteristic
40C29×#460C2211yescharacteristic
41C29×#446—21no—
42C29×#446—21no—
43C29×#446C2211yescharacteristic
44C29×#446C2211yescharacteristic
45C8×Q8×C29C2211yescharacteristic
46C8×Q8×C29C2211yescharacteristic
47C29×#440—21no—
48C29×#440—21no—
49C29×#432C2211yescharacteristic
50C29×#424—21no—
51C29×#423C2211yescharacteristic
52C2×C29×C4⋊C8C2211yescharacteristic
53C29×#405—21no—
54C4×M16×C29C2211yescharacteristic
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#333C2211yescharacteristic
62C29×#333C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#331C2211yescharacteristic
66C29×#331C2211yescharacteristic
67C2×#41×C29—21no—
68C2×SD16×C29—21no—
69C2×SD16×C29—21no—
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C2×M16×C29—21no—
73C2×M16×C29D411yescharacteristic
74C2×M16×C29D411yescharacteristic
75C22×C8×C29—21no—
76C29×C4⋊Q8D411yescharacteristic
77C29×C4⋊Q8D411yescharacteristic
78C29×C4⋊Q8C2311yescharacteristic
79C29×C4⋊Q8C2311yescharacteristic
80C29×C4⋊Q8C2311yescharacteristic
81C29×#127C2311yescharacteristic
82C29×#125—21no—
83C29×#125—21no—
84C29×#124—21no—
85C29×C22⋊Q8—21no—
86C29×C22⋊Q8—21no—
87C29×C22⋊Q8—21no—
88C29×C22⋊Q8D411yescharacteristic
89C29×C22⋊Q8D411yescharacteristic
90C29×#121—21no—
91C29×#121—21no—
92C4×Q8×C29—21no—
93C4×Q8×C29—21no—
94C4×Q8×C29—21no—
95C4×Q8×C29C2311yescharacteristic
96C4×Q8×C29C2311yescharacteristic
97C4×D4×C29—21no—
98C4×D4×C29—21no—
99C29×#117—21no—
100C29×#117—21no—
101C2×C42×C29C2311yescharacteristic
102C29×#107—21no—
103C29×#107—21no—
104C29×#107—21no—
105C29×#107—21no—
106C29×#107—21no—
107C29×#107—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×C4⋊C8—21no—
111C29×C4⋊C8—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×#103—21no—
129C29×#103—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×C22⋊C8—21no—
135C29×#97—21no—
136C29×#97—21no—
137C29×#97—21no—
138C29×#97D411yescharacteristic
139C29×#97D411yescharacteristic
140C4×C8×C29—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144#41×C29—82no—
145C2×Q8×C29—21no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29C2×D411yescharacteristic
150C2×Q8×C29C2×D411yescharacteristic
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—41no—
155C22×C4×C29—41no—
156C22×C4×C29C2×D411yescharacteristic
157C22×C4×C29C2×D411yescharacteristic
158C22×C4×C29#4111yescharacteristic
159SD16×C29—42no—
160SD16×C29—42no—
161SD16×C29—81no—
162SD16×C29—81no—
163M16×C29—22no—
164M16×C29—41no—
165M16×C29—81no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C2×C8×C29—42no—
173C2×C8×C29C2×D411yescharacteristic
174C2×C8×C29C2×D411yescharacteristic
175C2×C8×C29C2×D411yescharacteristic
176C2×C8×C29C2×D411yescharacteristic
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—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—41no—
191C4⋊C4×C29—41no—
192C4⋊C4×C29C2×D411yescharacteristic
193C4⋊C4×C29C2×D411yescharacteristic
194C22⋊C4×C29—21no—
195C22⋊C4×C29—21no—
196C22⋊C4×C29—41no—
197C22⋊C4×C29—41no—
198C22⋊C4×C29—41no—
199C42×C29—21no—
200C42×C29—21no—
201C42×C29—41no—
202C42×C29C2×D411yescharacteristic
203C42×C29C2×D411yescharacteristic
204C42×C29#4111yescharacteristic
205C42×C29C2411yescharacteristic
206#19373C2911yesmaximal, characteristic, direct product factor, Sylow
207C23×C29—41no—
208C23×C29#12111yescharacteristic
209Q8×C29—21no—
210Q8×C29—21no—
211Q8×C29—21no—
212Q8×C29—21no—
213Q8×C29—41no—
214Q8×C29—41no—
215Q8×C29—81no—
216Q8×C29—81no—
217Q8×C29—81no—
218D4×C29—41no—
219D4×C29—41no—
220D4×C29—41no—
221D4×C29—41no—
222D4×C29—81no—
223D4×C29—82no—
224C2×C4×C29—21no—
225C2×C4×C29—21no—
226C2×C4×C29—21no—
227C2×C4×C29—21no—
228C2×C4×C29—21no—
229C2×C4×C29—21no—
230C2×C4×C29—21no—
231C2×C4×C29—21no—
232C2×C4×C29—41no—
233C2×C4×C29—41no—
234C2×C4×C29—41no—
235C2×C4×C29—41no—
236C2×C4×C29—82no—
237C2×C4×C29#12111yescharacteristic
238C2×C4×C29#12111yescharacteristic
239C2×C4×C29#12111yescharacteristic
240C2×C4×C29C22×D411yescharacteristic
241C2×C4×C29C22×D411yescharacteristic
242C2×C4×C29C2×#4111yescharacteristic
243C8×C29—21no—
244C8×C29—21no—
245C8×C29—21no—
246C8×C29—41no—
247C8×C29—41no—
248C8×C29—41no—
249C8×C29—41no—
250C8×C29—41no—
251C8×C29—41no—
252C8×C29#13712yes—
253#3254C2×C2911yescharacteristic
254#3237C2×C2911yescharacteristic, complemented
255#3182C2×C2911yescharacteristic
256#2962C2×C2911yescharacteristic, complemented
257#1704C2×C2911yescharacteristic, complemented
258#1698C2×C2911yescharacteristic, complemented
259#1696C2×C2911yescharacteristic, complemented
260#1686C2×C2911yescharacteristic, complemented
261#1684C2×C2911yescharacteristic, complemented
262#1678C2×C2911yescharacteristic, complemented
263#1676C2×C2911yescharacteristic, complemented
264#1666C2×C2911yescharacteristic, complemented
265#1569C2×C2911yescharacteristic, complemented
266#1551C2×C2911yescharacteristic
267#1550C2×C2911yescharacteristic, complemented
268C22×C29—21no—
269C22×C29—21no—
270C22×C29—21no—
271C22×C29—81no—
272C22×C29—81no—
273C22×C29—81no—
274C22×C29C2×#12111yescharacteristic
275C4×C29—21no—
276C4×C29—21no—
277C4×C29—21no—
278C4×C29—21no—
279C4×C29—41no—
280C4×C29—41no—
281C4×C29—41no—
282C4×C29—41no—
283C4×C29—81no—
284C4×C29—81no—
285C4×C29—81no—
286C4×C29C2×#13711yescharacteristic
287C4×C29#57511yescharacteristic
288C4×C29#57711yescharacteristic
289C4×C29#57811yescharacteristic
290#533C22×C2911yescharacteristic
291#533C22×C2911yescharacteristic
292#532C22×C2911yescharacteristic
293#501—21no—
294#500C22×C2911yescharacteristic
295#492C22×C2911yescharacteristic
296#491—21no—
297#487C22×C2911yescharacteristic
298#486C22×C2911yescharacteristic
299#485—21no—
300#485—21no—
301#477C22×C2911yescharacteristic
302#477C22×C2911yescharacteristic
303#477C22×C2911yescharacteristic
304#477C22×C2911yescharacteristic
305#475C22×C2911yescharacteristic
306#475C22×C2911yescharacteristic
307#474—21no—
308#468—21no—
309#468—21no—
310#468—21no—
311#468—21no—
312#461—21no—
313#460C22×C2911yescharacteristic
314#460C22×C2911yescharacteristic
315#446—21no—
316#446—21no—
317#446C22×C2911yescharacteristic
318#446C22×C2911yescharacteristic
319C8×Q8C22×C2911yescharacteristic
320C8×Q8C22×C2911yescharacteristic
321#440—21no—
322#440—21no—
323#432C22×C2911yescharacteristic
324#424—21no—
325#423C22×C2911yescharacteristic
326C2×C4⋊C8C22×C2911yescharacteristic
327#405—21no—
328C4×M16C22×C2911yescharacteristic
329#335C22×C2911yescharacteristic
330#335C22×C2911yescharacteristic
331#334C22×C2911yescharacteristic
332#334C22×C2911yescharacteristic
333#333C22×C2911yescharacteristic
334#333C22×C2911yescharacteristic
335#333C22×C2911yescharacteristic
336#333C22×C2911yescharacteristic
337#332C22×C2911yescharacteristic
338#332C22×C2911yescharacteristic
339#331C22×C2911yescharacteristic
340#331C22×C2911yescharacteristic
341C2×C29—41no—
342C2×C29—161no—
343C2×C29#303711yescharacteristic
344C2×C29#306311yescharacteristic
345C2×C29#306811yescharacteristic
346C2×#41—21no—
347C2×SD16—21no—
348C2×SD16—21no—
349C2×SD16—21no—
350C2×SD16—21no—
351C2×M16—21no—
352C2×M16D4×C2911yescharacteristic
353C2×M16D4×C2911yescharacteristic
354C22×C8—21no—
355C4⋊Q8D4×C2911yescharacteristic
356C4⋊Q8D4×C2911yescharacteristic
357C4⋊Q8C23×C2911yescharacteristic
358C4⋊Q8C23×C2911yescharacteristic
359C4⋊Q8C23×C2911yescharacteristic
360#127C23×C2911yescharacteristic
361#125—21no—
362#125—21no—
363#124—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8D4×C2911yescharacteristic
368C22⋊Q8D4×C2911yescharacteristic
369#121—21no—
370#121—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8C23×C2911yescharacteristic
375C4×Q8C23×C2911yescharacteristic
376C4×D4—21no—
377C4×D4—21no—
378#117—21no—
379#117—21no—
380C2×C42C23×C2911yescharacteristic
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—21no—
387#106—21no—
388#106—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8C23×C2911yescharacteristic
396C4⋊C8C23×C2911yescharacteristic
397C4⋊C8C23×C2911yescharacteristic
398C4⋊C8C23×C2911yescharacteristic
399C4⋊C8C23×C2911yescharacteristic
400C4⋊C8C23×C2911yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#102—21no—
410#102—21no—
411#102—21no—
412#102—21no—
413C22⋊C8—21no—
414#97—21no—
415#97—21no—
416#97—21no—
417#97D4×C2911yescharacteristic
418#97D4×C2911yescharacteristic
419C4×C8—21no—
420C4×C8—21no—
421C4×C8C23×C2911yescharacteristic
422C4×C8C23×C2911yescharacteristic
423C29#1937311yescharacteristic, direct product factor, Sylow
424#41—82no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8C2×D4×C2911yescharacteristic
430C2×Q8C2×D4×C2911yescharacteristic
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—41no—
435C22×C4—41no—
436C22×C4C2×D4×C2911yescharacteristic
437C22×C4C2×D4×C2911yescharacteristic
438C22×C4#41×C2911yescharacteristic
439SD16—42no—
440SD16—42no—
441SD16—81no—
442SD16—81no—
443M16—22no—
444M16—41no—
445M16—81no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—42no—
453C2×C8C2×D4×C2911yescharacteristic
454C2×C8C2×D4×C2911yescharacteristic
455C2×C8C2×D4×C2911yescharacteristic
456C2×C8C2×D4×C2911yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4C2×D4×C2911yescharacteristic
473C4⋊C4C2×D4×C2911yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C42—21no—
480C42—21no—
481C42—41no—
482C42C2×D4×C2911yescharacteristic
483C42C2×D4×C2911yescharacteristic
484C42#41×C2911yescharacteristic
485C42C24×C2911yescharacteristic
486C23—41no—
487C23C29×#12111yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8—81no—
496Q8—81no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—41no—
501D4—81no—
502D4—82no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—82no—
516C2×C4C29×#12111yescharacteristic
517C2×C4C29×#12111yescharacteristic
518C2×C4C29×#12111yescharacteristic
519C2×C4C22×D4×C2911yescharacteristic
520C2×C4C22×D4×C2911yescharacteristic
521C2×C4C2×#41×C2911yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8C29×#13712yes—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22C2×C29×#12111yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4C2×C29×#13711yescharacteristic
551C4C29×#57511yescharacteristic
552C4C29×#57711yescharacteristic
553C4C29×#57811yescharacteristic
554C2—41no—
555C2—161no—
556C2C29×#303711yescharacteristic
557C2C29×#306311yescharacteristic
558C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#532C22
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
2. C29×#3237C2semidirect
4. C29×#2962C2semidirect
5. C29×#1704C2semidirect
6. C29×#1698C2semidirect
7. C29×#1696C2semidirect
8. C29×#1686C2semidirect
9. C29×#1684C2semidirect
10. C29×#1678C2semidirect
11. C29×#1676C2semidirect
12. C29×#1666C2semidirect
13. C29×#1569C2semidirect
15. C29×#1550C2semidirect
206. #19373C29direct (N × H)
254. #3237C2×C29semidirect
256. #2962C2×C29semidirect
257. #1704C2×C29semidirect
258. #1698C2×C29semidirect
259. #1696C2×C29semidirect
260. #1686C2×C29semidirect
261. #1684C2×C29semidirect
262. #1678C2×C29semidirect
263. #1676C2×C29semidirect
264. #1666C2×C29semidirect
265. #1569C2×C29semidirect
267. #1550C2×C29semidirect
423. C29#19373direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32542
C29×#32372
C29×#31822
C29×#29622
C29×#17042
C29×#16982
C29×#16962
C29×#16862
C29×#16842
C29×#16782
C29×#16762
C29×#16662
C29×#15692
C29×#15512
C29×#15502
#1937329