Finite Group Databasebeta

← C29×#19253 #20314153

Subgroups — C29×#19253 #20314153

Order 7424.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3247C211yesmaximal, characteristic
2C29×#3233C211yesmaximal, characteristic, complemented
3C29×#3182C211yesmaximal, characteristic, complemented
4C29×#2969C211yesmaximal, characteristic, complemented
5C29×#1704C211yesmaximal, characteristic, complemented
6C29×#1698C211yesmaximal, characteristic, complemented
7C29×#1695C211yesmaximal, characteristic, complemented
8C29×#1685C211yesmaximal, characteristic, complemented
9C29×#1683C211yesmaximal, characteristic, complemented
10C29×#1677C211yesmaximal, characteristic, complemented
11C29×#1676C211yesmaximal, characteristic, complemented
12C29×#1666C211yesmaximal, characteristic, complemented
13C29×#1565C211yesmaximal, characteristic, complemented
14C29×#1543C211yesmaximal, characteristic, complemented
15C29×#1542C211yesmaximal, characteristic, complemented
16C29×#533C2211yescharacteristic
17C29×#532C2211yescharacteristic
18C29×#529C2211yescharacteristic
19C29×#500C2211yescharacteristic
20C29×#499—21no—
21C29×#492C2211yescharacteristic
22C29×#488—21no—
23C29×#487C2211yescharacteristic
24C29×#486C2211yescharacteristic
25C29×#485—21no—
26C29×#482—21no—
27C29×#478—21no—
28C29×#477C2211yescharacteristic
29C29×#477C2211yescharacteristic
30C29×#476C2211yescharacteristic
31C29×#476C2211yescharacteristic
32C29×#475C2211yescharacteristic
33C29×#474C2211yescharacteristic
34C29×#468—21no—
35C29×#468—21no—
36C29×#466—21no—
37C29×#465—21no—
38C29×#463—21no—
39C29×#460C2211yescharacteristic
40C29×#459C2211yescharacteristic
41C29×#446C2211yescharacteristic
42C8×Q8×C29C2211yescharacteristic
43C29×#440—21no—
44C29×#440—21no—
45C29×#436—21no—
46C29×#436C2211yescharacteristic
47C29×#435—21no—
48C8×D4×C29C2211yescharacteristic
49C29×#433—21no—
50C29×#431C2211yescharacteristic
51C29×#431C2211yescharacteristic
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×D8×C29—21no—
72C2×M16×C29—21no—
73C2×M16×C29D411yescharacteristic
74C2×M16×C29D411yescharacteristic
75C22×C8×C29—21no—
76C22×C8×C29—21no—
77C29×C4⋊Q8C2311yescharacteristic
78C29×C4⋊Q8C2311yescharacteristic
79C29×C4⋊Q8C2311yescharacteristic
80C29×#127C2311yescharacteristic
81C29×#126—21no—
82C29×#125—21no—
83C29×#125D411yescharacteristic
84C29×#124—21no—
85C29×#124D411yescharacteristic
86C29×#123—21no—
87C29×C22⋊Q8—21no—
88C29×C22⋊Q8—21no—
89C29×C22⋊Q8D411yescharacteristic
90C29×#121—21no—
91C29×#121—21no—
92C29×#121D411yescharacteristic
93C4×Q8×C29—21no—
94C4×Q8×C29—21no—
95C4×Q8×C29C2311yescharacteristic
96C4×D4×C29—21no—
97C4×D4×C29—21no—
98C4×D4×C29—21no—
99C4×D4×C29C2311yescharacteristic
100C29×#117—21no—
101C29×#117—21no—
102C2×C42×C29C2311yescharacteristic
103C29×#107—21no—
104C29×#107—21no—
105C29×#107—21no—
106C29×#107—21no—
107C29×#107—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×#106—21no—
111C29×C4⋊C8—21no—
112C29×C4⋊C8—21no—
113C29×C4⋊C8—21no—
114C29×C4⋊C8C2311yescharacteristic
115C29×C4⋊C8C2311yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×#103—21no—
121C29×#103—21no—
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#102—21no—
126C29×#102—21no—
127C29×#102—21no—
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×C22⋊C8—21no—
133C29×C22⋊C8—21no—
134C29×C22⋊C8—21no—
135C29×C22⋊C8—21no—
136C29×#97—21no—
137C29×#97D411yescharacteristic
138C29×#97D411yescharacteristic
139C4×C8×C29—21no—
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×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
160SD16×C29—42no—
161SD16×C29—42no—
162SD16×C29—81no—
163D8×C29—81no—
164M16×C29—22no—
165M16×C29—41no—
166M16×C29—42no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C2×C8×C29—21no—
173C2×C8×C29—42no—
174C2×C8×C29—81no—
175C2×C8×C29C2×D411yescharacteristic
176C2×C8×C29C2×D411yescharacteristic
177C2×C8×C29C2×D411yescharacteristic
178C2×C8×C29C2×D411yescharacteristic
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—41no—
190C4⋊C4×C29—41no—
191C4⋊C4×C29C2×D411yescharacteristic
192C4⋊C4×C29C2×D411yescharacteristic
193C22⋊C4×C29—21no—
194C22⋊C4×C29—21no—
195C22⋊C4×C29—21no—
196C22⋊C4×C29—21no—
197C22⋊C4×C29—21no—
198C22⋊C4×C29—41no—
199C22⋊C4×C29—41no—
200C22⋊C4×C29—41no—
201C42×C29—21no—
202C42×C29—41no—
203C42×C29C2×D411yescharacteristic
204C42×C29C2×D411yescharacteristic
205C42×C29#4111yescharacteristic
206C42×C29C2411yescharacteristic
207#19253C2911yesmaximal, characteristic, direct product factor, Sylow
208C23×C29—21no—
209C23×C29—41no—
210C23×C29#12111yescharacteristic
211Q8×C29—21no—
212Q8×C29—21no—
213Q8×C29—41no—
214Q8×C29—41no—
215Q8×C29—81no—
216Q8×C29—81no—
217D4×C29—21no—
218D4×C29—21no—
219D4×C29—41no—
220D4×C29—41no—
221D4×C29—41no—
222D4×C29—41no—
223D4×C29—81no—
224D4×C29—81no—
225D4×C29—82no—
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—21no—
233C2×C4×C29—41no—
234C2×C4×C29—41no—
235C2×C4×C29—41no—
236C2×C4×C29—41no—
237C2×C4×C29—41no—
238C2×C4×C29—41no—
239C2×C4×C29—82no—
240C2×C4×C29#12111yescharacteristic
241C2×C4×C29#12111yescharacteristic
242C2×C4×C29#12111yescharacteristic
243C2×C4×C29C22×D411yescharacteristic
244C2×C4×C29C22×D411yescharacteristic
245C2×C4×C29C2×#4111yescharacteristic
246C8×C29—21no—
247C8×C29—21no—
248C8×C29—21no—
249C8×C29—41no—
250C8×C29—41no—
251C8×C29—41no—
252C8×C29—41no—
253C8×C29—41no—
254C8×C29—41no—
255C8×C29#13512yes—
256#3247C2×C2911yescharacteristic
257#3233C2×C2911yescharacteristic, complemented
258#3182C2×C2911yescharacteristic, complemented
259#2969C2×C2911yescharacteristic, complemented
260#1704C2×C2911yescharacteristic, complemented
261#1698C2×C2911yescharacteristic, complemented
262#1695C2×C2911yescharacteristic, complemented
263#1685C2×C2911yescharacteristic, complemented
264#1683C2×C2911yescharacteristic, complemented
265#1677C2×C2911yescharacteristic, complemented
266#1676C2×C2911yescharacteristic, complemented
267#1666C2×C2911yescharacteristic, complemented
268#1565C2×C2911yescharacteristic, complemented
269#1543C2×C2911yescharacteristic, complemented
270#1542C2×C2911yescharacteristic, complemented
271C22×C29—21no—
272C22×C29—21no—
273C22×C29—21no—
274C22×C29—41no—
275C22×C29—41no—
276C22×C29—41no—
277C22×C29—81no—
278C22×C29—81no—
279C22×C29—81no—
280C22×C29C2×#12111yescharacteristic
281C4×C29—21no—
282C4×C29—21no—
283C4×C29—21no—
284C4×C29—21no—
285C4×C29—41no—
286C4×C29—41no—
287C4×C29—41no—
288C4×C29—81no—
289C4×C29—81no—
290C4×C29—81no—
291C4×C29C2×#13511yescharacteristic
292C4×C29#57511yescharacteristic
293C4×C29#57711yescharacteristic
294C4×C29#57811yescharacteristic
295#533C22×C2911yescharacteristic
296#532C22×C2911yescharacteristic
297#529C22×C2911yescharacteristic
298#500C22×C2911yescharacteristic
299#499—21no—
300#492C22×C2911yescharacteristic
301#488—21no—
302#487C22×C2911yescharacteristic
303#486C22×C2911yescharacteristic
304#485—21no—
305#482—21no—
306#478—21no—
307#477C22×C2911yescharacteristic
308#477C22×C2911yescharacteristic
309#476C22×C2911yescharacteristic
310#476C22×C2911yescharacteristic
311#475C22×C2911yescharacteristic
312#474C22×C2911yescharacteristic
313#468—21no—
314#468—21no—
315#466—21no—
316#465—21no—
317#463—21no—
318#460C22×C2911yescharacteristic
319#459C22×C2911yescharacteristic
320#446C22×C2911yescharacteristic
321C8×Q8C22×C2911yescharacteristic
322#440—21no—
323#440—21no—
324#436—21no—
325#436C22×C2911yescharacteristic
326#435—21no—
327C8×D4C22×C2911yescharacteristic
328#433—21no—
329#431C22×C2911yescharacteristic
330#431C22×C2911yescharacteristic
331C2×C4⋊C8C22×C2911yescharacteristic
332#405—21no—
333C4×M16C22×C2911yescharacteristic
334#335C22×C2911yescharacteristic
335#335C22×C2911yescharacteristic
336#334C22×C2911yescharacteristic
337#334C22×C2911yescharacteristic
338#333C22×C2911yescharacteristic
339#333C22×C2911yescharacteristic
340#333C22×C2911yescharacteristic
341#333C22×C2911yescharacteristic
342#332C22×C2911yescharacteristic
343#332C22×C2911yescharacteristic
344#331C22×C2911yescharacteristic
345#331C22×C2911yescharacteristic
346C2×C29—41no—
347C2×C29—81no—
348C2×C29—161no—
349C2×C29#303511yescharacteristic
350C2×C29#306311yescharacteristic
351C2×C29#306811yescharacteristic
352C2×#41—21no—
353C2×SD16—21no—
354C2×SD16—21no—
355C2×SD16—21no—
356C2×D8—21no—
357C2×M16—21no—
358C2×M16D4×C2911yescharacteristic
359C2×M16D4×C2911yescharacteristic
360C22×C8—21no—
361C22×C8—21no—
362C4⋊Q8C23×C2911yescharacteristic
363C4⋊Q8C23×C2911yescharacteristic
364C4⋊Q8C23×C2911yescharacteristic
365#127C23×C2911yescharacteristic
366#126—21no—
367#125—21no—
368#125D4×C2911yescharacteristic
369#124—21no—
370#124D4×C2911yescharacteristic
371#123—21no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8D4×C2911yescharacteristic
375#121—21no—
376#121—21no—
377#121D4×C2911yescharacteristic
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8C23×C2911yescharacteristic
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4C23×C2911yescharacteristic
385#117—21no—
386#117—21no—
387C2×C42C23×C2911yescharacteristic
388#107—21no—
389#107—21no—
390#107—21no—
391#107—21no—
392#107—21no—
393#106—21no—
394#106—21no—
395#106—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8C23×C2911yescharacteristic
400C4⋊C8C23×C2911yescharacteristic
401C4⋊C8C23×C2911yescharacteristic
402C4⋊C8C23×C2911yescharacteristic
403C4⋊C8C23×C2911yescharacteristic
404C4⋊C8C23×C2911yescharacteristic
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#102—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421#97—21no—
422#97D4×C2911yescharacteristic
423#97D4×C2911yescharacteristic
424C4×C8—21no—
425C4×C8—21no—
426C4×C8—21no—
427C4×C8C23×C2911yescharacteristic
428C4×C8C23×C2911yescharacteristic
429C29#1925311yescharacteristic, direct product factor, Sylow
430#41—82no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8C2×D4×C2911yescharacteristic
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—41no—
440C2×D4C2×D4×C2911yescharacteristic
441C22×C4—21no—
442C22×C4—41no—
443C22×C4C2×D4×C2911yescharacteristic
444C22×C4C2×D4×C2911yescharacteristic
445C22×C4#41×C2911yescharacteristic
446SD16—42no—
447SD16—42no—
448SD16—81no—
449D8—81no—
450M16—22no—
451M16—41no—
452M16—42no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—42no—
460C2×C8—81no—
461C2×C8C2×D4×C2911yescharacteristic
462C2×C8C2×D4×C2911yescharacteristic
463C2×C8C2×D4×C2911yescharacteristic
464C2×C8C2×D4×C2911yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4C2×D4×C2911yescharacteristic
478C4⋊C4C2×D4×C2911yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C42—21no—
488C42—41no—
489C42C2×D4×C2911yescharacteristic
490C42C2×D4×C2911yescharacteristic
491C42#41×C2911yescharacteristic
492C42C24×C2911yescharacteristic
493C23—21no—
494C23—41no—
495C23C29×#12111yescharacteristic
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—81no—
502D4—21no—
503D4—21no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—81no—
509D4—81no—
510D4—82no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—82no—
525C2×C4C29×#12111yescharacteristic
526C2×C4C29×#12111yescharacteristic
527C2×C4C29×#12111yescharacteristic
528C2×C4C22×D4×C2911yescharacteristic
529C2×C4C22×D4×C2911yescharacteristic
530C2×C4C2×#41×C2911yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8C29×#13512yes—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22C2×C29×#12111yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—81no—
559C4—81no—
560C4—81no—
561C4C2×C29×#13511yescharacteristic
562C4C29×#57511yescharacteristic
563C4C29×#57711yescharacteristic
564C4C29×#57811yescharacteristic
565C2—41no—
566C2—81no—
567C2—161no—
568C2C29×#303511yescharacteristic
569C2C29×#306311yescharacteristic
570C2C29×#306811yescharacteristic
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
2. C29×#3233C2semidirect
3. C29×#3182C2semidirect
4. C29×#2969C2semidirect
5. C29×#1704C2semidirect
6. C29×#1698C2semidirect
7. C29×#1695C2semidirect
8. C29×#1685C2semidirect
9. C29×#1683C2semidirect
10. C29×#1677C2semidirect
11. C29×#1676C2semidirect
12. C29×#1666C2semidirect
13. C29×#1565C2semidirect
14. C29×#1543C2semidirect
15. C29×#1542C2semidirect
207. #19253C29direct (N × H)
257. #3233C2×C29semidirect
258. #3182C2×C29semidirect
259. #2969C2×C29semidirect
260. #1704C2×C29semidirect
261. #1698C2×C29semidirect
262. #1695C2×C29semidirect
263. #1685C2×C29semidirect
264. #1683C2×C29semidirect
265. #1677C2×C29semidirect
266. #1676C2×C29semidirect
267. #1666C2×C29semidirect
268. #1565C2×C29semidirect
269. #1543C2×C29semidirect
270. #1542C2×C29semidirect
429. C29#19253direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32472
C29×#32332
C29×#31822
C29×#29692
C29×#17042
C29×#16982
C29×#16952
C29×#16852
C29×#16832
C29×#16772
C29×#16762
C29×#16662
C29×#15652
C29×#15432
C29×#15422
#1925329