Finite Group Databasebeta

← C29×#19815 #20314715

Subgroups — C29×#19815 #20314715

Order 7424.

580 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3395C211yesmaximal, characteristic, complemented
2C29×#3386C211yesmaximal, characteristic
3C29×#3381C211yesmaximal, characteristic
4C29×#3299C211yesmaximal, characteristic
5C29×#1723C211yesmaximal, characteristic, complemented
6C29×#1692C211yesmaximal, characteristic, complemented
7C29×#1684C211yesmaximal, characteristic, complemented
8C29×#1674C211yesmaximal, characteristic, complemented
9C29×#1669C211yesmaximal, characteristic
10C29×#1649C211yesmaximal, characteristic
11C29×#1648C211yesmaximal, characteristic, complemented
12C29×#1644C211yesmaximal, characteristic
13C29×#1636C211yesmaximal, characteristic, complemented
14C29×#1584C211yesmaximal, characteristic, complemented
15C29×SD16⋊C8C211yesmaximal, characteristic
16C29×#557C2211yescharacteristic
17C29×#557C2211yescharacteristic
18C29×#554C2211yescharacteristic
19D4×Q8×C29C2211yescharacteristic
20C29×#501—21no—
21C29×#500C2211yescharacteristic
22C29×#500C2211yescharacteristic
23C29×#499—21no—
24C29×#498C2211yescharacteristic
25C29×#494—21no—
26C29×#494C2211yescharacteristic
27C29×#487C2211yescharacteristic
28C29×#487C2211yescharacteristic
29C29×#484—21no—
30C29×#479—21no—
31C29×#478—21no—
32C29×#478—21no—
33C29×#477—21no—
34C29×#477C2211yescharacteristic
35C29×#477C2211yescharacteristic
36C29×#475C2211yescharacteristic
37C29×#474C2211yescharacteristic
38C29×#474C2211yescharacteristic
39C29×#467—21no—
40C29×#462—21no—
41C29×#462—21no—
42C29×#462C2211yescharacteristic
43C29×#462C2211yescharacteristic
44C29×#462C2211yescharacteristic
45C29×#451—21no—
46C29×#446C2211yescharacteristic
47C8×Q8×C29C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C29×#440—21no—
50C4×Q16×C29—21no—
51C4×Q16×C29C2211yescharacteristic
52C4×SD16×C29—21no—
53C4×SD16×C29C2211yescharacteristic
54C8×D4×C29C2211yescharacteristic
55C2×C29×#103—21no—
56C29×#335C2211yescharacteristic
57C29×#335C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×Q8⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C29×#322C2211yescharacteristic
67C22×Q8×C29—21no—
68C2×Q16×C29—21no—
69C2×Q16×C29—21no—
70C2×Q16×C29—21no—
71C2×Q16×C29—21no—
72C2×Q16×C29—21no—
73C2×Q16×C29D411yescharacteristic
74C2×SD16×C29D411yescharacteristic
75C22×C8×C29—21no—
76C29×C4⋊Q8—21no—
77C29×C4⋊Q8—21no—
78C29×C4⋊Q8—21no—
79C29×C4⋊Q8C2311yescharacteristic
80C29×C4⋊Q8C2311yescharacteristic
81C29×C4⋊Q8C2311yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×#125—21no—
84C29×#125—21no—
85C29×#125—21no—
86C29×#125—41no—
87C29×#125—41no—
88C29×C22⋊Q8—21no—
89C29×C22⋊Q8—21no—
90C29×C22⋊Q8—41no—
91C29×C22⋊Q8—41no—
92C4×Q8×C29—21no—
93C4×Q8×C29—21no—
94C4×Q8×C29—21no—
95C4×Q8×C29—21no—
96C4×Q8×C29C2311yescharacteristic
97C4×Q8×C29C2311yescharacteristic
98C4×Q8×C29C2311yescharacteristic
99C4×D4×C29—21no—
100C4×D4×C29—21no—
101C4×D4×C29C2311yescharacteristic
102C2×C4⋊C4×C29—21no—
103C29×#107—21no—
104C29×#107—21no—
105C29×#107—21no—
106C29×#107—21no—
107C29×#107—21no—
108C29×#107—21no—
109C29×#107—41no—
110C29×#107D411yescharacteristic
111C29×#106—21no—
112C29×#106—21no—
113C29×#106—21no—
114C29×#106D411yescharacteristic
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×#103—21no—
129C29×#103—21no—
130C29×#103—41no—
131C29×#103D411yescharacteristic
132C29×#103D411yescharacteristic
133C29×#103D411yescharacteristic
134C29×#102—21no—
135C29×#102—21no—
136C29×#102D411yescharacteristic
137C29×C22⋊C8—21no—
138C29×#97—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—42no—
150C2×Q8×C29—81no—
151C2×Q8×C29C2×D411yescharacteristic
152C2×Q8×C29C2×D411yescharacteristic
153C2×Q8×C29C2×D411yescharacteristic
154C2×D4×C29C2×D411yescharacteristic
155C22×C4×C29—21no—
156C22×C4×C29—41no—
157C22×C4×C29—41no—
158Q16×C29—41no—
159Q16×C29—42no—
160Q16×C29—81no—
161Q16×C29—81no—
162Q16×C29—81no—
163Q16×C29—81no—
164SD16×C29Q1614yescomplemented
165C2×C8×C29—21no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29—81no—
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—21no—
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×C29—41no—
195C4⋊C4×C29C2×D411yescharacteristic
196C4⋊C4×C29C2×D411yescharacteristic
197C4⋊C4×C29C2×D411yescharacteristic
198C4⋊C4×C29C2×D411yescharacteristic
199C22⋊C4×C29—21no—
200C22⋊C4×C29—41no—
201C22⋊C4×C29—41no—
202C42×C29—21no—
203C42×C29—21no—
204C42×C29—21no—
205C42×C29—41no—
206C42×C29—41no—
207C42×C29C2411yescharacteristic
208#19815C2911yesmaximal, characteristic, direct product factor, Sylow
209C23×C29—21no—
210Q8×C29—21no—
211Q8×C29—21no—
212Q8×C29—21no—
213Q8×C29—21no—
214Q8×C29—21no—
215Q8×C29—41no—
216Q8×C29—41no—
217Q8×C29—41no—
218Q8×C29—41no—
219Q8×C29—41no—
220Q8×C29—41no—
221Q8×C29—81no—
222Q8×C29—82no—
223Q8×C29C2×Q1612yes—
224D4×C29—21no—
225D4×C29C2×Q1612yes—
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—161no—
241C2×C4×C29C22×D411yescharacteristic
242C2×C4×C29C22×D411yescharacteristic
243C2×C4×C29H(5,𝔽2)11yescharacteristic
244C8×C29—21no—
245C8×C29—21no—
246C8×C29—21no—
247C8×C29—41no—
248C8×C29—41no—
249C8×C29—41no—
250C8×C29—41no—
251C8×C29—41no—
252C8×C29C2×Q1612yes—
253#3395C2×C2911yescharacteristic, complemented
254#3386C2×C2911yescharacteristic
255#3381C2×C2911yescharacteristic
256#3299C2×C2911yescharacteristic
257#1723C2×C2911yescharacteristic, complemented
258#1692C2×C2911yescharacteristic, complemented
259#1684C2×C2911yescharacteristic, complemented
260#1674C2×C2911yescharacteristic, complemented
261#1669C2×C2911yescharacteristic
262#1649C2×C2911yescharacteristic
263#1648C2×C2911yescharacteristic, complemented
264#1644C2×C2911yescharacteristic
265#1636C2×C2911yescharacteristic, complemented
266#1584C2×C2911yescharacteristic, complemented
267SD16⋊C8C2×C2911yescharacteristic
268C22×C29—22no—
269C22×C29—41no—
270C22×C29—41no—
271C22×C29D4211yescharacteristic
272C4×C29—22no—
273C4×C29—21no—
274C4×C29—41no—
275C4×C29—41no—
276C4×C29—41no—
277C4×C29—41no—
278C4×C29—41no—
279C4×C29—41no—
280C4×C29—81no—
281C4×C29—81no—
282C4×C29—81no—
283C4×C29—81no—
284C4×C29C22×Q1611yescharacteristic
285C4×C29#57511yescharacteristic
286C4×C29#57611yescharacteristic
287C4×C29#57811yescharacteristic
288#557C22×C2911yescharacteristic
289#557C22×C2911yescharacteristic
290#554C22×C2911yescharacteristic
291D4×Q8C22×C2911yescharacteristic
292#501—21no—
293#500C22×C2911yescharacteristic
294#500C22×C2911yescharacteristic
295#499—21no—
296#498C22×C2911yescharacteristic
297#494—21no—
298#494C22×C2911yescharacteristic
299#487C22×C2911yescharacteristic
300#487C22×C2911yescharacteristic
301#484—21no—
302#479—21no—
303#478—21no—
304#478—21no—
305#477—21no—
306#477C22×C2911yescharacteristic
307#477C22×C2911yescharacteristic
308#475C22×C2911yescharacteristic
309#474C22×C2911yescharacteristic
310#474C22×C2911yescharacteristic
311#467—21no—
312#462—21no—
313#462—21no—
314#462C22×C2911yescharacteristic
315#462C22×C2911yescharacteristic
316#462C22×C2911yescharacteristic
317#451—21no—
318#446C22×C2911yescharacteristic
319C8×Q8C22×C2911yescharacteristic
320C8×Q8C22×C2911yescharacteristic
321#440—21no—
322C4×Q16—21no—
323C4×Q16C22×C2911yescharacteristic
324C4×SD16—21no—
325C4×SD16C22×C2911yescharacteristic
326C8×D4C22×C2911yescharacteristic
327C2×#103—21no—
328#335C22×C2911yescharacteristic
329#335C22×C2911yescharacteristic
330#333C22×C2911yescharacteristic
331#332C22×C2911yescharacteristic
332#332C22×C2911yescharacteristic
333#332C22×C2911yescharacteristic
334Q8⋊C8C22×C2911yescharacteristic
335Q8⋊C8C22×C2911yescharacteristic
336Q8⋊C8C22×C2911yescharacteristic
337D4⋊C8C22×C2911yescharacteristic
338#322C22×C2911yescharacteristic
339C2×C29—42no—
340C2×C29#326811yescharacteristic
341C2×C29D4×Q1611yescharacteristic
342C2×C29#328911yescharacteristic
343C22×Q8—21no—
344C2×Q16—21no—
345C2×Q16—21no—
346C2×Q16—21no—
347C2×Q16—21no—
348C2×Q16—21no—
349C2×Q16D4×C2911yescharacteristic
350C2×SD16D4×C2911yescharacteristic
351C22×C8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—21no—
355C4⋊Q8C23×C2911yescharacteristic
356C4⋊Q8C23×C2911yescharacteristic
357C4⋊Q8C23×C2911yescharacteristic
358C4⋊Q8C23×C2911yescharacteristic
359#125—21no—
360#125—21no—
361#125—21no—
362#125—41no—
363#125—41no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—41no—
367C22⋊Q8—41no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8C23×C2911yescharacteristic
373C4×Q8C23×C2911yescharacteristic
374C4×Q8C23×C2911yescharacteristic
375C4×D4—21no—
376C4×D4—21no—
377C4×D4C23×C2911yescharacteristic
378C2×C4⋊C4—21no—
379#107—21no—
380#107—21no—
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#107—41no—
386#107D4×C2911yescharacteristic
387#106—21no—
388#106—21no—
389#106—21no—
390#106D4×C2911yescharacteristic
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8C23×C2911yescharacteristic
395C4⋊C8C23×C2911yescharacteristic
396C4⋊C8C23×C2911yescharacteristic
397C4⋊C8C23×C2911yescharacteristic
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—41no—
407#103D4×C2911yescharacteristic
408#103D4×C2911yescharacteristic
409#103D4×C2911yescharacteristic
410#102—21no—
411#102—21no—
412#102D4×C2911yescharacteristic
413C22⋊C8—21no—
414#97—21no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8C23×C2911yescharacteristic
418C4×C8C23×C2911yescharacteristic
419C4×C8C23×C2911yescharacteristic
420C29#1981511yescharacteristic, direct product factor, Sylow
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—41no—
426C2×Q8—42no—
427C2×Q8—81no—
428C2×Q8C2×D4×C2911yescharacteristic
429C2×Q8C2×D4×C2911yescharacteristic
430C2×Q8C2×D4×C2911yescharacteristic
431C2×D4C2×D4×C2911yescharacteristic
432C22×C4—21no—
433C22×C4—41no—
434C22×C4—41no—
435Q16—41no—
436Q16—42no—
437Q16—81no—
438Q16—81no—
439Q16—81no—
440Q16—81no—
441SD16Q16×C2914yescomplemented
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—81no—
448C2×C8C2×D4×C2911yescharacteristic
449C2×C8C2×D4×C2911yescharacteristic
450C2×C8C2×D4×C2911yescharacteristic
451C2×C8C2×D4×C2911yescharacteristic
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—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—21no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42—41no—
484C42C24×C2911yescharacteristic
485C23—21no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—81no—
498Q8—82no—
499Q8C2×Q16×C2912yes—
500D4—21no—
501D4C2×Q16×C2912yes—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—82no—
516C2×C4—161no—
517C2×C4C22×D4×C2911yescharacteristic
518C2×C4C22×D4×C2911yescharacteristic
519C2×C4C29×H(5,𝔽2)11yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8C2×Q16×C2912yes—
529C22—22no—
530C22—41no—
531C22—41no—
532C22D42×C2911yescharacteristic
533C4—22no—
534C4—21no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—81no—
542C4—81no—
543C4—81no—
544C4—81no—
545C4C22×Q16×C2911yescharacteristic
546C4C29×#57511yescharacteristic
547C4C29×#57611yescharacteristic
548C4C29×#57811yescharacteristic
549C2—42no—
550C2C29×#326811yescharacteristic
551C2D4×Q16×C2911yescharacteristic
552C2C29×#328911yescharacteristic
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
1. C29×#3395C2semidirect
5. C29×#1723C2semidirect
6. C29×#1692C2semidirect
7. C29×#1684C2semidirect
8. C29×#1674C2semidirect
11. C29×#1648C2semidirect
13. C29×#1636C2semidirect
14. C29×#1584C2semidirect
164. SD16×C29Q16semidirect
208. #19815C29direct (N × H)
253. #3395C2×C29semidirect
257. #1723C2×C29semidirect
258. #1692C2×C29semidirect
259. #1684C2×C29semidirect
260. #1674C2×C29semidirect
263. #1648C2×C29semidirect
265. #1636C2×C29semidirect
266. #1584C2×C29semidirect
420. C29#19815direct (N × H)
441. SD16Q16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#33952
C29×#33862
C29×#33812
C29×#32992
C29×#17232
C29×#16922
C29×#16842
C29×#16742
C29×#16692
C29×#16492
C29×#16482
C29×#16442
C29×#16362
C29×#15842
C29×SD16⋊C82
#1981529