Finite Group Databasebeta

← C29×#19816 #20314716

Subgroups — C29×#19816 #20314716

Order 7424.

564 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3385C211yesmaximal, characteristic
2C29×#3381C211yesmaximal, characteristic
3C29×#3363C211yesmaximal, characteristic, complemented
4C29×#3338C211yesmaximal, characteristic
5C29×#1723C211yesmaximal, characteristic, complemented
6C29×#1692C211yesmaximal, characteristic, complemented
7C29×#1683C211yesmaximal, characteristic
8C29×#1676C211yesmaximal, characteristic, complemented
9C29×#1676C211yesmaximal, characteristic, complemented
10C29×#1644C211yesmaximal, characteristic
11C29×#1636C211yesmaximal, characteristic, complemented
12C29×#1633C211yesmaximal, characteristic, complemented
13C29×#1632C211yesmaximal, characteristic
14C29×#1584C211yesmaximal, characteristic, complemented
15C29×SD16⋊C8C211yesmaximal, characteristic
16Q82×C29C2211yescharacteristic
17C29×#557C2211yescharacteristic
18C29×#554C2211yescharacteristic
19C29×#554C2211yescharacteristic
20C29×#501—21no—
21C29×#500C2211yescharacteristic
22C29×#500C2211yescharacteristic
23C29×#499—21no—
24C29×#498C2211yescharacteristic
25C29×#494C2211yescharacteristic
26C29×#487—21no—
27C29×#487C2211yescharacteristic
28C29×#487C2211yescharacteristic
29C29×#484—21no—
30C29×#484—21no—
31C29×#479—21no—
32C29×#479—21no—
33C29×#478—21no—
34C29×#477—21no—
35C29×#477C2211yescharacteristic
36C29×#477C2211yescharacteristic
37C29×#477C2211yescharacteristic
38C29×#477C2211yescharacteristic
39C29×#477C2211yescharacteristic
40C29×#476C2211yescharacteristic
41C29×#474—21no—
42C29×#474C2211yescharacteristic
43C29×#467—21no—
44C29×#462—21no—
45C29×#462C2211yescharacteristic
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×#107—21no—
56C29×#335C2211yescharacteristic
57C29×#335C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×Q8⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C29×#322C2211yescharacteristic
67C2×Q16×C29—21no—
68C2×Q16×C29—41no—
69C2×Q16×C29D411yescharacteristic
70C2×SD16×C29D411yescharacteristic
71C22×C8×C29—21no—
72C29×C4⋊Q8—21no—
73C29×C4⋊Q8—21no—
74C29×C4⋊Q8—21no—
75C29×C4⋊Q8—41no—
76C29×C4⋊Q8C2311yescharacteristic
77C29×C4⋊Q8C2311yescharacteristic
78C29×C4⋊Q8C2311yescharacteristic
79C29×C4⋊Q8C2311yescharacteristic
80C29×#125—21no—
81C29×#125—21no—
82C29×#125—21no—
83C29×#125—41no—
84C29×C22⋊Q8—21no—
85C29×C22⋊Q8—21no—
86C29×C22⋊Q8—41no—
87C29×C22⋊Q8—41no—
88C4×Q8×C29—21no—
89C4×Q8×C29—21no—
90C4×Q8×C29—21no—
91C4×Q8×C29—21no—
92C4×Q8×C29C2311yescharacteristic
93C4×Q8×C29C2311yescharacteristic
94C4×Q8×C29C2311yescharacteristic
95C4×D4×C29—21no—
96C4×D4×C29—21no—
97C4×D4×C29C2311yescharacteristic
98C2×C4⋊C4×C29—21no—
99C2×C4⋊C4×C29—21no—
100C29×#107—21no—
101C29×#107—21no—
102C29×#107—21no—
103C29×#107—21no—
104C29×#107—21no—
105C29×#107—21no—
106C29×#107—21no—
107C29×#107—21no—
108C29×#107—21no—
109C29×#107—21no—
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×C29C2×D411yescharacteristic
150C2×Q8×C29C2×D411yescharacteristic
151C2×Q8×C29C2×D411yescharacteristic
152C2×D4×C29C2×D411yescharacteristic
153C22×C4×C29—21no—
154C22×C4×C29—41no—
155C22×C4×C29—41no—
156Q16×C29—41no—
157Q16×C29—42no—
158Q16×C29—82no—
159SD16×C29Q1614yescomplemented
160C2×C8×C29—21no—
161C2×C8×C29—21no—
162C2×C8×C29—21no—
163C2×C8×C29—21no—
164C2×C8×C29—21no—
165C2×C8×C29—42no—
166C2×C8×C29C2×D411yescharacteristic
167C2×C8×C29C2×D411yescharacteristic
168C2×C8×C29C2×D411yescharacteristic
169C2×C8×C29C2×D411yescharacteristic
170C4⋊C4×C29—21no—
171C4⋊C4×C29—21no—
172C4⋊C4×C29—21no—
173C4⋊C4×C29—21no—
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—41no—
182C4⋊C4×C29—41no—
183C4⋊C4×C29—41no—
184C4⋊C4×C29—41no—
185C4⋊C4×C29—41no—
186C4⋊C4×C29—41no—
187C4⋊C4×C29—41no—
188C4⋊C4×C29—41no—
189C4⋊C4×C29—41no—
190C4⋊C4×C29C2×D411yescharacteristic
191C4⋊C4×C29C2×D411yescharacteristic
192C4⋊C4×C29C2×D411yescharacteristic
193C4⋊C4×C29C2×D411yescharacteristic
194C22⋊C4×C29—21no—
195C22⋊C4×C29—41no—
196C22⋊C4×C29—41no—
197C42×C29—21no—
198C42×C29—21no—
199C42×C29—21no—
200C42×C29—41no—
201C42×C29—41no—
202C42×C29C2411yescharacteristic
203#19816C2911yesmaximal, characteristic, direct product factor, Sylow
204C23×C29—21no—
205Q8×C29—21no—
206Q8×C29—21no—
207Q8×C29—21no—
208Q8×C29—21no—
209Q8×C29—21no—
210Q8×C29—41no—
211Q8×C29—41no—
212Q8×C29—81no—
213Q8×C29—81no—
214Q8×C29—81no—
215Q8×C29—161no—
216Q8×C29C2×Q1612yes—
217D4×C29—21no—
218D4×C29C2×Q1612yes—
219C2×C4×C29—21no—
220C2×C4×C29—21no—
221C2×C4×C29—21no—
222C2×C4×C29—21no—
223C2×C4×C29—21no—
224C2×C4×C29—21no—
225C2×C4×C29—21no—
226C2×C4×C29—41no—
227C2×C4×C29—41no—
228C2×C4×C29—41no—
229C2×C4×C29—41no—
230C2×C4×C29—41no—
231C2×C4×C29—41no—
232C2×C4×C29—161no—
233C2×C4×C29—161no—
234C2×C4×C29C22×D411yescharacteristic
235C2×C4×C29C22×D411yescharacteristic
236C2×C4×C29H(5,𝔽2)11yescharacteristic
237C8×C29—21no—
238C8×C29—21no—
239C8×C29—21no—
240C8×C29—41no—
241C8×C29—41no—
242C8×C29—41no—
243C8×C29—41no—
244C8×C29—41no—
245C8×C29C2×Q1612yes—
246#3385C2×C2911yescharacteristic
247#3381C2×C2911yescharacteristic
248#3363C2×C2911yescharacteristic, complemented
249#3338C2×C2911yescharacteristic
250#1723C2×C2911yescharacteristic, complemented
251#1692C2×C2911yescharacteristic, complemented
252#1683C2×C2911yescharacteristic
253#1676C2×C2911yescharacteristic, complemented
254#1676C2×C2911yescharacteristic, complemented
255#1644C2×C2911yescharacteristic
256#1636C2×C2911yescharacteristic, complemented
257#1633C2×C2911yescharacteristic, complemented
258#1632C2×C2911yescharacteristic
259#1584C2×C2911yescharacteristic, complemented
260SD16⋊C8C2×C2911yescharacteristic
261C22×C29—22no—
262C22×C29—41no—
263C22×C29—41no—
264C22×C29D4211yescharacteristic
265C4×C29—22no—
266C4×C29—21no—
267C4×C29—41no—
268C4×C29—41no—
269C4×C29—41no—
270C4×C29—41no—
271C4×C29—41no—
272C4×C29—41no—
273C4×C29—81no—
274C4×C29—81no—
275C4×C29—81no—
276C4×C29—81no—
277C4×C29C22×Q1611yescharacteristic
278C4×C29#57511yescharacteristic
279C4×C29#57811yescharacteristic
280C4×C29#57811yescharacteristic
281Q82C22×C2911yescharacteristic
282#557C22×C2911yescharacteristic
283#554C22×C2911yescharacteristic
284#554C22×C2911yescharacteristic
285#501—21no—
286#500C22×C2911yescharacteristic
287#500C22×C2911yescharacteristic
288#499—21no—
289#498C22×C2911yescharacteristic
290#494C22×C2911yescharacteristic
291#487—21no—
292#487C22×C2911yescharacteristic
293#487C22×C2911yescharacteristic
294#484—21no—
295#484—21no—
296#479—21no—
297#479—21no—
298#478—21no—
299#477—21no—
300#477C22×C2911yescharacteristic
301#477C22×C2911yescharacteristic
302#477C22×C2911yescharacteristic
303#477C22×C2911yescharacteristic
304#477C22×C2911yescharacteristic
305#476C22×C2911yescharacteristic
306#474—21no—
307#474C22×C2911yescharacteristic
308#467—21no—
309#462—21no—
310#462C22×C2911yescharacteristic
311#446C22×C2911yescharacteristic
312C8×Q8C22×C2911yescharacteristic
313C8×Q8C22×C2911yescharacteristic
314#440—21no—
315C4×Q16—21no—
316C4×Q16C22×C2911yescharacteristic
317C4×SD16—21no—
318C4×SD16C22×C2911yescharacteristic
319C8×D4C22×C2911yescharacteristic
320C2×#107—21no—
321#335C22×C2911yescharacteristic
322#335C22×C2911yescharacteristic
323#333C22×C2911yescharacteristic
324#333C22×C2911yescharacteristic
325#333C22×C2911yescharacteristic
326#332C22×C2911yescharacteristic
327Q8⋊C8C22×C2911yescharacteristic
328Q8⋊C8C22×C2911yescharacteristic
329Q8⋊C8C22×C2911yescharacteristic
330D4⋊C8C22×C2911yescharacteristic
331#322C22×C2911yescharacteristic
332C2×C29—42no—
333C2×C29#326911yescharacteristic
334C2×C29D4×Q1611yescharacteristic
335C2×C29#328811yescharacteristic
336C2×Q16—21no—
337C2×Q16—41no—
338C2×Q16D4×C2911yescharacteristic
339C2×SD16D4×C2911yescharacteristic
340C22×C8—21no—
341C4⋊Q8—21no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8—41no—
345C4⋊Q8C23×C2911yescharacteristic
346C4⋊Q8C23×C2911yescharacteristic
347C4⋊Q8C23×C2911yescharacteristic
348C4⋊Q8C23×C2911yescharacteristic
349#125—21no—
350#125—21no—
351#125—21no—
352#125—41no—
353C22⋊Q8—21no—
354C22⋊Q8—21no—
355C22⋊Q8—41no—
356C22⋊Q8—41no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8C23×C2911yescharacteristic
362C4×Q8C23×C2911yescharacteristic
363C4×Q8C23×C2911yescharacteristic
364C4×D4—21no—
365C4×D4—21no—
366C4×D4C23×C2911yescharacteristic
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369#107—21no—
370#107—21no—
371#107—21no—
372#107—21no—
373#107—21no—
374#107—21no—
375#107—21no—
376#107—21no—
377#107—21no—
378#107—21no—
379#107D4×C2911yescharacteristic
380#106—21no—
381#106—21no—
382#106—21no—
383#106D4×C2911yescharacteristic
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8C23×C2911yescharacteristic
388C4⋊C8C23×C2911yescharacteristic
389C4⋊C8C23×C2911yescharacteristic
390C4⋊C8C23×C2911yescharacteristic
391#103—21no—
392#103—21no—
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—41no—
400#103D4×C2911yescharacteristic
401#103D4×C2911yescharacteristic
402#103D4×C2911yescharacteristic
403#102—21no—
404#102—21no—
405#102D4×C2911yescharacteristic
406C22⋊C8—21no—
407#97—21no—
408C4×C8—21no—
409C4×C8—21no—
410C4×C8C23×C2911yescharacteristic
411C4×C8C23×C2911yescharacteristic
412C4×C8C23×C2911yescharacteristic
413C29#1981611yescharacteristic, direct product factor, Sylow
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—41no—
419C2×Q8C2×D4×C2911yescharacteristic
420C2×Q8C2×D4×C2911yescharacteristic
421C2×Q8C2×D4×C2911yescharacteristic
422C2×D4C2×D4×C2911yescharacteristic
423C22×C4—21no—
424C22×C4—41no—
425C22×C4—41no—
426Q16—41no—
427Q16—42no—
428Q16—82no—
429SD16Q16×C2914yescomplemented
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—42no—
436C2×C8C2×D4×C2911yescharacteristic
437C2×C8C2×D4×C2911yescharacteristic
438C2×C8C2×D4×C2911yescharacteristic
439C2×C8C2×D4×C2911yescharacteristic
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4C2×D4×C2911yescharacteristic
461C4⋊C4C2×D4×C2911yescharacteristic
462C4⋊C4C2×D4×C2911yescharacteristic
463C4⋊C4C2×D4×C2911yescharacteristic
464C22⋊C4—21no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—41no—
471C42—41no—
472C42C24×C2911yescharacteristic
473C23—21no—
474Q8—21no—
475Q8—21no—
476Q8—21no—
477Q8—21no—
478Q8—21no—
479Q8—41no—
480Q8—41no—
481Q8—81no—
482Q8—81no—
483Q8—81no—
484Q8—161no—
485Q8C2×Q16×C2912yes—
486D4—21no—
487D4C2×Q16×C2912yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—161no—
502C2×C4—161no—
503C2×C4C22×D4×C2911yescharacteristic
504C2×C4C22×D4×C2911yescharacteristic
505C2×C4C29×H(5,𝔽2)11yescharacteristic
506C8—21no—
507C8—21no—
508C8—21no—
509C8—41no—
510C8—41no—
511C8—41no—
512C8—41no—
513C8—41no—
514C8C2×Q16×C2912yes—
515C22—22no—
516C22—41no—
517C22—41no—
518C22D42×C2911yescharacteristic
519C4—22no—
520C4—21no—
521C4—41no—
522C4—41no—
523C4—41no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—81no—
528C4—81no—
529C4—81no—
530C4—81no—
531C4C22×Q16×C2911yescharacteristic
532C4C29×#57511yescharacteristic
533C4C29×#57811yescharacteristic
534C4C29×#57811yescharacteristic
535C2—42no—
536C2C29×#326911yescharacteristic
537C2D4×Q16×C2911yescharacteristic
538C2C29×#328811yescharacteristic
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×#1723C2semidirect
6. C29×#1692C2semidirect
8. C29×#1676C2semidirect
9. C29×#1676C2semidirect
11. C29×#1636C2semidirect
12. C29×#1633C2semidirect
14. C29×#1584C2semidirect
159. SD16×C29Q16semidirect
203. #19816C29direct (N × H)
248. #3363C2×C29semidirect
250. #1723C2×C29semidirect
251. #1692C2×C29semidirect
253. #1676C2×C29semidirect
254. #1676C2×C29semidirect
256. #1636C2×C29semidirect
257. #1633C2×C29semidirect
259. #1584C2×C29semidirect
413. C29#19816direct (N × H)
429. SD16Q16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#33852
C29×#33812
C29×#33632
C29×#33382
C29×#17232
C29×#16922
C29×#16832
C29×#16762
C29×#16442
C29×#16362
C29×#16332
C29×#16322
C29×#15842
C29×SD16⋊C82
#1981629