Finite Group Databasebeta

← C29×#20001 #20314901

Subgroups — C29×#20001 #20314901

Order 7424.

586 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3381C211yesmaximal, characteristic
2Q8×SD16×C29C211yesmaximal, characteristic
3C29×#3363C211yesmaximal, characteristic, complemented
4C29×#3299C211yesmaximal, characteristic
5C29×#1707C211yesmaximal, characteristic, complemented
6C29×#1684C211yesmaximal, characteristic, complemented
7C29×#1683C211yesmaximal, characteristic
8C29×#1672C211yesmaximal, characteristic, complemented
9C29×#1672C211yesmaximal, characteristic, complemented
10C29×#1649C211yesmaximal, characteristic
11C29×#1648C211yesmaximal, characteristic, complemented
12C29×#1633C211yesmaximal, characteristic, complemented
13C29×#1632C211yesmaximal, characteristic
14C8×Q16×C29C211yesmaximal, characteristic, complemented
15C8×SD16×C29C211yesmaximal, characteristic
16Q82×C29C2211yescharacteristic
17C29×#557C2211yescharacteristic
18C29×#554C2211yescharacteristic
19D4×Q8×C29C2211yescharacteristic
20C29×#500C2211yescharacteristic
21C29×#499—21no—
22C29×#498—21no—
23C29×#498C2211yescharacteristic
24C29×#498C2211yescharacteristic
25C29×#494C2211yescharacteristic
26C29×#487—21no—
27C29×#487C2211yescharacteristic
28C29×#487C2211yescharacteristic
29C29×#484—21no—
30C29×#479—21no—
31C29×#478—21no—
32C29×#477—21no—
33C29×#477C2211yescharacteristic
34C29×#477C2211yescharacteristic
35C29×#477C2211yescharacteristic
36C29×#476—21no—
37C29×#476C2211yescharacteristic
38C29×#475—21no—
39C29×#475C2211yescharacteristic
40C29×#474C2211yescharacteristic
41C29×#467—21no—
42C29×#462—21no—
43C29×#462C2211yescharacteristic
44C29×#462C2211yescharacteristic
45C29×#451—21no—
46C8×Q8×C29C2211yescharacteristic
47C8×Q8×C29C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C4×Q16×C29—21no—
50C4×Q16×C29C2211yescharacteristic
51C4×SD16×C29—21no—
52C4×SD16×C29—21no—
53C4×SD16×C29C2211yescharacteristic
54C8×D4×C29C2211yescharacteristic
55C2×C29×#103—21no—
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×Q8⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C82×C29C2211yescharacteristic
67C22×Q8×C29—21no—
68C2×Q16×C29—21no—
69C2×Q16×C29—21no—
70C2×Q16×C29—41no—
71C2×Q16×C29D411yescharacteristic
72C2×SD16×C29D411yescharacteristic
73C22×C8×C29—21no—
74C29×C4⋊Q8—21no—
75C29×C4⋊Q8—21no—
76C29×C4⋊Q8—21no—
77C29×C4⋊Q8—21no—
78C29×C4⋊Q8—41no—
79C29×C4⋊Q8C2311yescharacteristic
80C29×C4⋊Q8C2311yescharacteristic
81C29×C4⋊Q8C2311yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×#125—21no—
84C29×#125—21no—
85C29×#125—41no—
86C29×C22⋊Q8—21no—
87C29×C22⋊Q8—21no—
88C29×C22⋊Q8—41no—
89C29×C22⋊Q8—41no—
90C4×Q8×C29—21no—
91C4×Q8×C29—21no—
92C4×Q8×C29—21no—
93C4×Q8×C29—21no—
94C4×Q8×C29C2311yescharacteristic
95C4×Q8×C29C2311yescharacteristic
96C4×Q8×C29C2311yescharacteristic
97C4×D4×C29—21no—
98C4×D4×C29—21no—
99C4×D4×C29C2311yescharacteristic
100C2×C4⋊C4×C29—21no—
101C29×#107—21no—
102C29×#107—21no—
103C29×#107—21no—
104C29×#107—21no—
105C29×#107—41no—
106C29×#107D411yescharacteristic
107C29×#106—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×#106—21no—
111C29×#106—21no—
112C29×#106—21no—
113C29×#106D411yescharacteristic
114C29×C4⋊C8—21no—
115C29×C4⋊C8—21no—
116C29×C4⋊C8—21no—
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×#103—21no—
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×#103—21no—
131C29×#103D411yescharacteristic
132C29×#103D411yescharacteristic
133C29×#103D411yescharacteristic
134C29×#102—21no—
135C29×#102—21no—
136C29×#102D411yescharacteristic
137C29×C22⋊C8—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×C29—21no—
148C2×Q8×C29—41no—
149C2×Q8×C29—41no—
150C2×Q8×C29—42no—
151C2×Q8×C29—81no—
152C2×Q8×C29C2×D411yescharacteristic
153C2×Q8×C29C2×D411yescharacteristic
154C2×Q8×C29C2×D411yescharacteristic
155C2×D4×C29C2×D411yescharacteristic
156C22×C4×C29—21no—
157C22×C4×C29—41no—
158C22×C4×C29—41no—
159Q16×C29—22no—
160Q16×C29—42no—
161Q16×C29—82no—
162Q16×C29—81no—
163SD16×C29Q1614yescomplemented
164C2×C8×C29—21no—
165C2×C8×C29—21no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—81no—
170C2×C8×C29C2×D411yescharacteristic
171C2×C8×C29C2×D411yescharacteristic
172C2×C8×C29C2×D411yescharacteristic
173C2×C8×C29C2×D411yescharacteristic
174C4⋊C4×C29—21no—
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×C29C2×D411yescharacteristic
194C4⋊C4×C29C2×D411yescharacteristic
195C4⋊C4×C29C2×D411yescharacteristic
196C4⋊C4×C29C2×D411yescharacteristic
197C22⋊C4×C29—21no—
198C22⋊C4×C29—41no—
199C22⋊C4×C29—41no—
200C42×C29—21no—
201C42×C29—21no—
202C42×C29—21no—
203C42×C29—41no—
204C42×C29—41no—
205C42×C29C2411yescharacteristic
206#20001C2911yesmaximal, characteristic, direct product factor, Sylow
207C23×C29—21no—
208Q8×C29—21no—
209Q8×C29—21no—
210Q8×C29—21no—
211Q8×C29—21no—
212Q8×C29—41no—
213Q8×C29—41no—
214Q8×C29—41no—
215Q8×C29—41no—
216Q8×C29—82no—
217Q8×C29—81no—
218Q8×C29—81no—
219Q8×C29—161no—
220Q8×C29C2×Q1612yes—
221Q8×C29#13512yes—
222D4×C29—21no—
223D4×C29C2×Q1612yes—
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—41no—
232C2×C4×C29—41no—
233C2×C4×C29—41no—
234C2×C4×C29—41no—
235C2×C4×C29—41no—
236C2×C4×C29—41no—
237C2×C4×C29—82no—
238C2×C4×C29—161no—
239C2×C4×C29C22×D411yescharacteristic
240C2×C4×C29C22×D411yescharacteristic
241C2×C4×C29H(5,𝔽2)11yescharacteristic
242C8×C29—22no—
243C8×C29—21no—
244C8×C29—21no—
245C8×C29—21no—
246C8×C29—41no—
247C8×C29—41no—
248C8×C29—41no—
249C8×C29—41no—
250C8×C29C2×Q1612yes—
251#3381C2×C2911yescharacteristic
252Q8×SD16C2×C2911yescharacteristic
253#3363C2×C2911yescharacteristic, complemented
254#3299C2×C2911yescharacteristic
255#1707C2×C2911yescharacteristic, complemented
256#1684C2×C2911yescharacteristic, complemented
257#1683C2×C2911yescharacteristic
258#1672C2×C2911yescharacteristic, complemented
259#1672C2×C2911yescharacteristic, complemented
260#1649C2×C2911yescharacteristic
261#1648C2×C2911yescharacteristic, complemented
262#1633C2×C2911yescharacteristic, complemented
263#1632C2×C2911yescharacteristic
264C8×Q16C2×C2911yescharacteristic, complemented
265C8×SD16C2×C2911yescharacteristic
266C22×C29—22no—
267C22×C29—41no—
268C22×C29—41no—
269C22×C29D4211yescharacteristic
270C4×C29—22no—
271C4×C29—22no—
272C4×C29—21no—
273C4×C29—41no—
274C4×C29—41no—
275C4×C29—41no—
276C4×C29—41no—
277C4×C29—41no—
278C4×C29—81no—
279C4×C29—81no—
280C4×C29—81no—
281C4×C29—81no—
282C4×C29C22×Q1611yescharacteristic
283C4×C29C2×#13511yescharacteristic
284C4×C29#57711yescharacteristic
285C4×C29#57811yescharacteristic
286Q82C22×C2911yescharacteristic
287#557C22×C2911yescharacteristic
288#554C22×C2911yescharacteristic
289D4×Q8C22×C2911yescharacteristic
290#500C22×C2911yescharacteristic
291#499—21no—
292#498—21no—
293#498C22×C2911yescharacteristic
294#498C22×C2911yescharacteristic
295#494C22×C2911yescharacteristic
296#487—21no—
297#487C22×C2911yescharacteristic
298#487C22×C2911yescharacteristic
299#484—21no—
300#479—21no—
301#478—21no—
302#477—21no—
303#477C22×C2911yescharacteristic
304#477C22×C2911yescharacteristic
305#477C22×C2911yescharacteristic
306#476—21no—
307#476C22×C2911yescharacteristic
308#475—21no—
309#475C22×C2911yescharacteristic
310#474C22×C2911yescharacteristic
311#467—21no—
312#462—21no—
313#462C22×C2911yescharacteristic
314#462C22×C2911yescharacteristic
315#451—21no—
316C8×Q8C22×C2911yescharacteristic
317C8×Q8C22×C2911yescharacteristic
318C8×Q8C22×C2911yescharacteristic
319C4×Q16—21no—
320C4×Q16C22×C2911yescharacteristic
321C4×SD16—21no—
322C4×SD16—21no—
323C4×SD16C22×C2911yescharacteristic
324C8×D4C22×C2911yescharacteristic
325C2×#103—21no—
326#335C22×C2911yescharacteristic
327#334C22×C2911yescharacteristic
328#333C22×C2911yescharacteristic
329#333C22×C2911yescharacteristic
330#332C22×C2911yescharacteristic
331#332C22×C2911yescharacteristic
332Q8⋊C8C22×C2911yescharacteristic
333Q8⋊C8C22×C2911yescharacteristic
334Q8⋊C8C22×C2911yescharacteristic
335D4⋊C8C22×C2911yescharacteristic
336C82C22×C2911yescharacteristic
337C2×C29—42no—
338C2×C29#328211yescharacteristic
339C2×C29D4×Q1611yescharacteristic
340C2×C29#329111yescharacteristic
341C22×Q8—21no—
342C2×Q16—21no—
343C2×Q16—21no—
344C2×Q16—41no—
345C2×Q16D4×C2911yescharacteristic
346C2×SD16D4×C2911yescharacteristic
347C22×C8—21no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—41no—
353C4⋊Q8C23×C2911yescharacteristic
354C4⋊Q8C23×C2911yescharacteristic
355C4⋊Q8C23×C2911yescharacteristic
356C4⋊Q8C23×C2911yescharacteristic
357#125—21no—
358#125—21no—
359#125—41no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C22⋊Q8—41no—
363C22⋊Q8—41no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8C23×C2911yescharacteristic
369C4×Q8C23×C2911yescharacteristic
370C4×Q8C23×C2911yescharacteristic
371C4×D4—21no—
372C4×D4—21no—
373C4×D4C23×C2911yescharacteristic
374C2×C4⋊C4—21no—
375#107—21no—
376#107—21no—
377#107—21no—
378#107—21no—
379#107—41no—
380#107D4×C2911yescharacteristic
381#106—21no—
382#106—21no—
383#106—21no—
384#106—21no—
385#106—21no—
386#106—21no—
387#106D4×C2911yescharacteristic
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8C23×C2911yescharacteristic
392C4⋊C8C23×C2911yescharacteristic
393C4⋊C8C23×C2911yescharacteristic
394C4⋊C8C23×C2911yescharacteristic
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
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#102—21no—
409#102—21no—
410#102D4×C2911yescharacteristic
411C22⋊C8—21no—
412C4×C8—21no—
413C4×C8—21no—
414C4×C8—21no—
415C4×C8C23×C2911yescharacteristic
416C4×C8C23×C2911yescharacteristic
417C4×C8C23×C2911yescharacteristic
418C29#2000111yescharacteristic, direct product factor, Sylow
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—41no—
424C2×Q8—41no—
425C2×Q8—42no—
426C2×Q8—81no—
427C2×Q8C2×D4×C2911yescharacteristic
428C2×Q8C2×D4×C2911yescharacteristic
429C2×Q8C2×D4×C2911yescharacteristic
430C2×D4C2×D4×C2911yescharacteristic
431C22×C4—21no—
432C22×C4—41no—
433C22×C4—41no—
434Q16—22no—
435Q16—42no—
436Q16—82no—
437Q16—81no—
438SD16Q16×C2914yescomplemented
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—81no—
445C2×C8C2×D4×C2911yescharacteristic
446C2×C8C2×D4×C2911yescharacteristic
447C2×C8C2×D4×C2911yescharacteristic
448C2×C8C2×D4×C2911yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4C2×D4×C2911yescharacteristic
469C4⋊C4C2×D4×C2911yescharacteristic
470C4⋊C4C2×D4×C2911yescharacteristic
471C4⋊C4C2×D4×C2911yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—41no—
479C42—41no—
480C42C24×C2911yescharacteristic
481C23—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—41no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—82no—
491Q8—81no—
492Q8—81no—
493Q8—161no—
494Q8C2×Q16×C2912yes—
495Q8C29×#13512yes—
496D4—21no—
497D4C2×Q16×C2912yes—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—82no—
512C2×C4—161no—
513C2×C4C22×D4×C2911yescharacteristic
514C2×C4C22×D4×C2911yescharacteristic
515C2×C4C29×H(5,𝔽2)11yescharacteristic
516C8—22no—
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8C2×Q16×C2912yes—
525C22—22no—
526C22—41no—
527C22—41no—
528C22D42×C2911yescharacteristic
529C4—22no—
530C4—22no—
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—81no—
538C4—81no—
539C4—81no—
540C4—81no—
541C4C22×Q16×C2911yescharacteristic
542C4C2×C29×#13511yescharacteristic
543C4C29×#57711yescharacteristic
544C4C29×#57811yescharacteristic
545C2—42no—
546C2C29×#328211yescharacteristic
547C2D4×Q16×C2911yescharacteristic
548C2C29×#329111yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC2×D4×C29C2×D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#3363C2semidirect
5. C29×#1707C2semidirect
6. C29×#1684C2semidirect
8. C29×#1672C2semidirect
9. C29×#1672C2semidirect
11. C29×#1648C2semidirect
12. C29×#1633C2semidirect
14. C8×Q16×C29C2semidirect
163. SD16×C29Q16semidirect
206. #20001C29direct (N × H)
253. #3363C2×C29semidirect
255. #1707C2×C29semidirect
256. #1684C2×C29semidirect
258. #1672C2×C29semidirect
259. #1672C2×C29semidirect
261. #1648C2×C29semidirect
262. #1633C2×C29semidirect
264. C8×Q16C2×C29semidirect
418. C29#20001direct (N × H)
438. SD16Q16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#33812
Q8×SD16×C292
C29×#33632
C29×#32992
C29×#17072
C29×#16842
C29×#16832
C29×#16722
C29×#16492
C29×#16482
C29×#16332
C29×#16322
C8×Q16×C292
C8×SD16×C292
#2000129