Finite Group Databasebeta

← C29×#19873 #20314773

Subgroups — C29×#19873 #20314773

Order 7424.

572 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3400C211yesmaximal, characteristic
2C29×#3395C211yesmaximal, characteristic, complemented
3C29×#3383C211yesmaximal, characteristic, complemented
4C29×#3365C211yesmaximal, characteristic
5C29×#1722C211yesmaximal, characteristic
6C29×#1690C211yesmaximal, characteristic, complemented
7C29×#1682C211yesmaximal, characteristic
8C29×#1674C211yesmaximal, characteristic, complemented
9C29×#1666C211yesmaximal, characteristic
10C29×#1648C211yesmaximal, characteristic, complemented
11C29×#1648C211yesmaximal, characteristic, complemented
12C29×#1640C211yesmaximal, characteristic
13C29×#1626C211yesmaximal, characteristic
14C29×#1584C211yesmaximal, characteristic, complemented
15C29×#1579C211yesmaximal, characteristic, complemented
16C29×#559C2211yescharacteristic
17C29×#557C2211yescharacteristic
18C29×#557C2211yescharacteristic
19C29×#557C2211yescharacteristic
20C29×#500C2211yescharacteristic
21C29×#500C2211yescharacteristic
22C29×#499—21no—
23C29×#497—21no—
24C29×#494—21no—
25C29×#494C2211yescharacteristic
26C29×#492C2211yescharacteristic
27C29×#488—21no—
28C29×#486C2211yescharacteristic
29C29×#486C2211yescharacteristic
30C29×#479—21no—
31C29×#479—21no—
32C29×#478—21no—
33C29×#475C2211yescharacteristic
34C29×#475C2211yescharacteristic
35C29×#475C2211yescharacteristic
36C29×#464—21no—
37C29×#464—21no—
38C29×#462—21no—
39C29×#462—21no—
40C29×#462C2211yescharacteristic
41C29×#462C2211yescharacteristic
42C29×#462C2211yescharacteristic
43C29×#461—21no—
44C29×#460C2211yescharacteristic
45C29×#460C2211yescharacteristic
46C29×#446C2211yescharacteristic
47C8×Q8×C29C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C8×Q8×C29C2211yescharacteristic
50C29×#440—21no—
51C4×Q16×C29—21no—
52C4×Q16×C29—21no—
53C4×Q16×C29C2211yescharacteristic
54C4×Q16×C29C2211yescharacteristic
55C4×SD16×C29—21no—
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#332C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×Q8⋊C8C2211yescharacteristic
65C29×Q8⋊C8C2211yescharacteristic
66C29×#322C2211yescharacteristic
67C2×Q16×C29—21no—
68C2×Q16×C29—21no—
69C2×Q16×C29—21no—
70C2×Q16×C29—21no—
71C2×Q16×C29—21no—
72C2×Q16×C29D411yescharacteristic
73C2×Q16×C29D411yescharacteristic
74C2×SD16×C29—21no—
75C2×SD16×C29—21no—
76C2×SD16×C29—21no—
77C2×SD16×C29—21no—
78C29×C4⋊Q8—21no—
79C29×C4⋊Q8—21no—
80C29×C4⋊Q8—21no—
81C29×C4⋊Q8C2311yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×C4⋊Q8C2311yescharacteristic
84C29×#127C2311yescharacteristic
85C29×#125—21no—
86C29×#125—21no—
87C29×#125—21no—
88C29×#125—41no—
89C29×#125—41no—
90C29×#125—41no—
91C29×#124—21no—
92C29×#124—21no—
93C29×#123—41no—
94C4×Q8×C29—21no—
95C4×Q8×C29—21no—
96C4×Q8×C29—21no—
97C4×Q8×C29—21no—
98C4×Q8×C29—21no—
99C4×Q8×C29—21no—
100C4×Q8×C29C2311yescharacteristic
101C4×Q8×C29C2311yescharacteristic
102C4×Q8×C29C2311yescharacteristic
103C4×Q8×C29C2311yescharacteristic
104C4×D4×C29—21no—
105C4×D4×C29—21no—
106C29×#107—21no—
107C29×#107—21no—
108C29×#107—41no—
109C29×#107D411yescharacteristic
110C29×#107D411yescharacteristic
111C29×#106—21no—
112C29×#106—21no—
113C29×#106—21no—
114C29×C4⋊C8—21no—
115C29×C4⋊C8—21no—
116C29×C4⋊C8—21no—
117C29×C4⋊C8—21no—
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×#103D411yescharacteristic
129C29×#103D411yescharacteristic
130C29×#103D411yescharacteristic
131C29×#103D411yescharacteristic
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×#102—21no—
136C29×#102—41no—
137C29×#97—21no—
138C4×C8×C29—21no—
139C4×C8×C29—21no—
140C4×C8×C29—21no—
141C4×C8×C29C2311yescharacteristic
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C2×Q8×C29—21no—
145C2×Q8×C29—21no—
146C2×Q8×C29—21no—
147C2×Q8×C29C2×D411yescharacteristic
148C2×Q8×C29C2×D411yescharacteristic
149C2×Q8×C29C2×D411yescharacteristic
150C2×Q8×C29C2×D411yescharacteristic
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C22×C4×C29—41no—
155Q16×C29—22no—
156Q16×C29—22no—
157Q16×C29—42no—
158Q16×C29—81no—
159Q16×C29—81no—
160Q16×C29—81no—
161Q16×C29—81no—
162SD16×C29—42no—
163SD16×C29—42no—
164SD16×C29—81no—
165SD16×C29—81no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29C2×D411yescharacteristic
172C2×C8×C29C2×D411yescharacteristic
173C2×C8×C29C2×D411yescharacteristic
174C2×C8×C29C2×D411yescharacteristic
175C4⋊C4×C29—21no—
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—21no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—41no—
186C4⋊C4×C29—41no—
187C4⋊C4×C29—41no—
188C4⋊C4×C29—41no—
189C4⋊C4×C29—41no—
190C4⋊C4×C29—41no—
191C4⋊C4×C29—41no—
192C4⋊C4×C29—41no—
193C4⋊C4×C29—41no—
194C4⋊C4×C29C2×D411yescharacteristic
195C4⋊C4×C29C2×D411yescharacteristic
196C4⋊C4×C29C2×D411yescharacteristic
197C4⋊C4×C29C2×D411yescharacteristic
198C22⋊C4×C29—41no—
199C22⋊C4×C29—41no—
200C22⋊C4×C29—41no—
201C42×C29—21no—
202C42×C29—21no—
203C42×C29—21no—
204C42×C29—21no—
205C42×C29—41no—
206C42×C29—41no—
207C42×C29—41no—
208C42×C29C2411yescharacteristic
209#19873C2911yesmaximal, characteristic, direct product factor, Sylow
210C23×C29—41no—
211Q8×C29—21no—
212Q8×C29—21no—
213Q8×C29—21no—
214Q8×C29—21no—
215Q8×C29—21no—
216Q8×C29—21no—
217Q8×C29—21no—
218Q8×C29—41no—
219Q8×C29—41no—
220Q8×C29—41no—
221Q8×C29—41no—
222Q8×C29—41no—
223Q8×C29—41no—
224Q8×C29#13712yes—
225D4×C29—41no—
226D4×C29—41no—
227D4×C29—41no—
228D4×C29—41no—
229D4×C29—81no—
230C2×C4×C29—21no—
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—161no—
242C2×C4×C29C22×D411yescharacteristic
243C2×C4×C29C22×D411yescharacteristic
244C2×C4×C29H(5,𝔽2)11yescharacteristic
245C8×C29—21no—
246C8×C29—21no—
247C8×C29—21no—
248C8×C29—41no—
249C8×C29—41no—
250C8×C29—41no—
251C8×C29—41no—
252C8×C29—41no—
253C8×C29#13512yes—
254#3400C2×C2911yescharacteristic
255#3395C2×C2911yescharacteristic, complemented
256#3383C2×C2911yescharacteristic, complemented
257#3365C2×C2911yescharacteristic
258#1722C2×C2911yescharacteristic
259#1690C2×C2911yescharacteristic, complemented
260#1682C2×C2911yescharacteristic
261#1674C2×C2911yescharacteristic, complemented
262#1666C2×C2911yescharacteristic
263#1648C2×C2911yescharacteristic, complemented
264#1648C2×C2911yescharacteristic, complemented
265#1640C2×C2911yescharacteristic
266#1626C2×C2911yescharacteristic
267#1584C2×C2911yescharacteristic, complemented
268#1579C2×C2911yescharacteristic, complemented
269C22×C29—81no—
270C22×C29—81no—
271C22×C29—81no—
272C22×C29D4211yescharacteristic
273C4×C29—22no—
274C4×C29—21no—
275C4×C29—41no—
276C4×C29—41no—
277C4×C29—41no—
278C4×C29—41no—
279C4×C29—41no—
280C4×C29—41no—
281C4×C29—41no—
282C4×C29—81no—
283C4×C29—81no—
284C4×C29—81no—
285C4×C29C2×#13511yescharacteristic
286C4×C29C2×#13711yescharacteristic
287C4×C29#57611yescharacteristic
288C4×C29#57811yescharacteristic
289#559C22×C2911yescharacteristic
290#557C22×C2911yescharacteristic
291#557C22×C2911yescharacteristic
292#557C22×C2911yescharacteristic
293#500C22×C2911yescharacteristic
294#500C22×C2911yescharacteristic
295#499—21no—
296#497—21no—
297#494—21no—
298#494C22×C2911yescharacteristic
299#492C22×C2911yescharacteristic
300#488—21no—
301#486C22×C2911yescharacteristic
302#486C22×C2911yescharacteristic
303#479—21no—
304#479—21no—
305#478—21no—
306#475C22×C2911yescharacteristic
307#475C22×C2911yescharacteristic
308#475C22×C2911yescharacteristic
309#464—21no—
310#464—21no—
311#462—21no—
312#462—21no—
313#462C22×C2911yescharacteristic
314#462C22×C2911yescharacteristic
315#462C22×C2911yescharacteristic
316#461—21no—
317#460C22×C2911yescharacteristic
318#460C22×C2911yescharacteristic
319#446C22×C2911yescharacteristic
320C8×Q8C22×C2911yescharacteristic
321C8×Q8C22×C2911yescharacteristic
322C8×Q8C22×C2911yescharacteristic
323#440—21no—
324C4×Q16—21no—
325C4×Q16—21no—
326C4×Q16C22×C2911yescharacteristic
327C4×Q16C22×C2911yescharacteristic
328C4×SD16—21no—
329#335C22×C2911yescharacteristic
330#334C22×C2911yescharacteristic
331#332C22×C2911yescharacteristic
332#332C22×C2911yescharacteristic
333#332C22×C2911yescharacteristic
334#331C22×C2911yescharacteristic
335Q8⋊C8C22×C2911yescharacteristic
336Q8⋊C8C22×C2911yescharacteristic
337Q8⋊C8C22×C2911yescharacteristic
338Q8⋊C8C22×C2911yescharacteristic
339#322C22×C2911yescharacteristic
340C2×C29—161no—
341C2×C29#327011yescharacteristic
342C2×C29#328711yescharacteristic
343C2×C29#328911yescharacteristic
344C2×Q16—21no—
345C2×Q16—21no—
346C2×Q16—21no—
347C2×Q16—21no—
348C2×Q16—21no—
349C2×Q16D4×C2911yescharacteristic
350C2×Q16D4×C2911yescharacteristic
351C2×SD16—21no—
352C2×SD16—21no—
353C2×SD16—21no—
354C2×SD16—21no—
355C4⋊Q8—21no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8C23×C2911yescharacteristic
359C4⋊Q8C23×C2911yescharacteristic
360C4⋊Q8C23×C2911yescharacteristic
361#127C23×C2911yescharacteristic
362#125—21no—
363#125—21no—
364#125—21no—
365#125—41no—
366#125—41no—
367#125—41no—
368#124—21no—
369#124—21no—
370#123—41no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8C23×C2911yescharacteristic
378C4×Q8C23×C2911yescharacteristic
379C4×Q8C23×C2911yescharacteristic
380C4×Q8C23×C2911yescharacteristic
381C4×D4—21no—
382C4×D4—21no—
383#107—21no—
384#107—21no—
385#107—41no—
386#107D4×C2911yescharacteristic
387#107D4×C2911yescharacteristic
388#106—21no—
389#106—21no—
390#106—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
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103D4×C2911yescharacteristic
406#103D4×C2911yescharacteristic
407#103D4×C2911yescharacteristic
408#103D4×C2911yescharacteristic
409#102—21no—
410#102—21no—
411#102—21no—
412#102—21no—
413#102—41no—
414#97—21no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8—21no—
418C4×C8C23×C2911yescharacteristic
419C4×C8C23×C2911yescharacteristic
420C4×C8C23×C2911yescharacteristic
421C29#1987311yescharacteristic, direct product factor, Sylow
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8C2×D4×C2911yescharacteristic
426C2×Q8C2×D4×C2911yescharacteristic
427C2×Q8C2×D4×C2911yescharacteristic
428C2×Q8C2×D4×C2911yescharacteristic
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C22×C4—41no—
433Q16—22no—
434Q16—22no—
435Q16—42no—
436Q16—81no—
437Q16—81no—
438Q16—81no—
439Q16—81no—
440SD16—42no—
441SD16—42no—
442SD16—81no—
443SD16—81no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8C2×D4×C2911yescharacteristic
450C2×C8C2×D4×C2911yescharacteristic
451C2×C8C2×D4×C2911yescharacteristic
452C2×C8C2×D4×C2911yescharacteristic
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4C2×D4×C2911yescharacteristic
473C4⋊C4C2×D4×C2911yescharacteristic
474C4⋊C4C2×D4×C2911yescharacteristic
475C4⋊C4C2×D4×C2911yescharacteristic
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—41no—
484C42—41no—
485C42—41no—
486C42C24×C2911yescharacteristic
487C23—41no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8C29×#13712yes—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—81no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—161no—
519C2×C4C22×D4×C2911yescharacteristic
520C2×C4C22×D4×C2911yescharacteristic
521C2×C4C29×H(5,𝔽2)11yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8C29×#13512yes—
531C22—81no—
532C22—81no—
533C22—81no—
534C22D42×C2911yescharacteristic
535C4—22no—
536C4—21no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—81no—
545C4—81no—
546C4—81no—
547C4C2×C29×#13511yescharacteristic
548C4C2×C29×#13711yescharacteristic
549C4C29×#57611yescharacteristic
550C4C29×#57811yescharacteristic
551C2—161no—
552C2C29×#327011yescharacteristic
553C2C29×#328711yescharacteristic
554C2C29×#328911yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#127C23
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3395C2semidirect
3. C29×#3383C2semidirect
6. C29×#1690C2semidirect
8. C29×#1674C2semidirect
10. C29×#1648C2semidirect
11. C29×#1648C2semidirect
14. C29×#1584C2semidirect
15. C29×#1579C2semidirect
209. #19873C29direct (N × H)
255. #3395C2×C29semidirect
256. #3383C2×C29semidirect
259. #1690C2×C29semidirect
261. #1674C2×C29semidirect
263. #1648C2×C29semidirect
264. #1648C2×C29semidirect
267. #1584C2×C29semidirect
268. #1579C2×C29semidirect
421. C29#19873direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34002
C29×#33952
C29×#33832
C29×#33652
C29×#17222
C29×#16902
C29×#16822
C29×#16742
C29×#16662
C29×#16482
C29×#16402
C29×#16262
C29×#15842
C29×#15792
#1987329