Finite Group Databasebeta

← C29×#19921 #20314821

Subgroups — C29×#19921 #20314821

Order 7424.

590 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3394C211yesmaximal, characteristic
2Q8×SD16×C29C211yesmaximal, characteristic, complemented
3C29×#3375C211yesmaximal, characteristic, complemented
4C29×#3328C211yesmaximal, characteristic, complemented
5C29×#1708C211yesmaximal, characteristic, complemented
6C29×#1700C211yesmaximal, characteristic, complemented
7C29×#1697C211yesmaximal, characteristic
8C29×#1672C211yesmaximal, characteristic, complemented
9C29×#1666C211yesmaximal, characteristic, complemented
10C29×#1645C211yesmaximal, characteristic, complemented
11C29×#1640C211yesmaximal, characteristic, complemented
12C29×#1638C211yesmaximal, characteristic, complemented
13C29×#1627C211yesmaximal, characteristic
14C29×#1590C211yesmaximal, characteristic, complemented
15C8×Q16×C29C211yesmaximal, characteristic, complemented
16C29×#559C2211yescharacteristic
17Q82×C29C2211yescharacteristic
18C29×#556C2211yescharacteristic
19D4×Q8×C29C2211yescharacteristic
20C29×#498—21no—
21C29×#498C2211yescharacteristic
22C29×#495—21no—
23C29×#492C2211yescharacteristic
24C29×#489—21no—
25C29×#487C2211yescharacteristic
26C29×#487C2211yescharacteristic
27C29×#486C2211yescharacteristic
28C29×#486C2211yescharacteristic
29C29×#485—21no—
30C29×#477C2211yescharacteristic
31C29×#476—21no—
32C29×#476C2211yescharacteristic
33C29×#475—21no—
34C29×#475C2211yescharacteristic
35C29×#475C2211yescharacteristic
36C29×#474—21no—
37C29×#470—21no—
38C29×#464—21no—
39C29×#464—21no—
40C29×#463—21no—
41C29×#462C2211yescharacteristic
42C29×#462C2211yescharacteristic
43C29×#460C2211yescharacteristic
44C29×#459C2211yescharacteristic
45C29×#451—21no—
46C29×#446C2211yescharacteristic
47C8×Q8×C29C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C29×#440—21no—
50C4×Q16×C29C2211yescharacteristic
51C4×SD16×C29—21no—
52C4×SD16×C29—21no—
53C4×SD16×C29C2211yescharacteristic
54C29×#436C2211yescharacteristic
55C29×#419—21no—
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#331C2211yescharacteristic
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×C29D411yescharacteristic
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×SD16×C29D411yescharacteristic
75C2×D8×C29—21no—
76C2×M16×C29—21no—
77C29×C4⋊Q8—21no—
78C29×C4⋊Q8—21no—
79C29×C4⋊Q8—21no—
80C29×C4⋊Q8—41no—
81C29×C4⋊Q8C2311yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×C4⋊Q8C2311yescharacteristic
84C29×#127C2311yescharacteristic
85C29×#126—41no—
86C29×#124—21no—
87C29×#124—21no—
88C29×#124—21no—
89C29×#123—41no—
90C29×C22⋊Q8—21no—
91C29×C22⋊Q8—21no—
92C29×C22⋊Q8—41no—
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×C29—21no—
102C4×D4×C29C2311yescharacteristic
103C29×#117—21no—
104C29×#107—21no—
105C29×#107D411yescharacteristic
106C29×#106—21no—
107C29×#106—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×#106—21no—
111C29×#106D411yescharacteristic
112C29×C4⋊C8—21no—
113C29×C4⋊C8—21no—
114C29×C4⋊C8—21no—
115C29×C4⋊C8C2311yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×#103—21no—
120C29×#103—21no—
121C29×#103—21no—
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—21no—
126C29×#103—41no—
127C29×#103D411yescharacteristic
128C29×#103D411yescharacteristic
129C29×#103D411yescharacteristic
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×#102—41no—
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—41no—
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×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29C2×D411yescharacteristic
158C22×C4×C29—21no—
159C22×C4×C29—41no—
160C22×C4×C29—41no—
161Q16×C29—22no—
162Q16×C29—81no—
163Q16×C29—81no—
164SD16×C29—22no—
165SD16×C29—42no—
166SD16×C29—42no—
167SD16×C29—81no—
168D8×C29—81no—
169M16×C29—81no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C2×C8×C29—21no—
173C2×C8×C29—21no—
174C2×C8×C29—21no—
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—41no—
189C4⋊C4×C29—41no—
190C4⋊C4×C29—41no—
191C4⋊C4×C29—41no—
192C4⋊C4×C29C2×D411yescharacteristic
193C4⋊C4×C29C2×D411yescharacteristic
194C4⋊C4×C29C2×D411yescharacteristic
195C4⋊C4×C29C2×D411yescharacteristic
196C22⋊C4×C29—21no—
197C22⋊C4×C29—41no—
198C22⋊C4×C29—41no—
199C22⋊C4×C29—41no—
200C22⋊C4×C29—41no—
201C22⋊C4×C29—41no—
202C22⋊C4×C29—41no—
203C42×C29—21no—
204C42×C29—21no—
205C42×C29—21no—
206C42×C29—41no—
207C42×C29—41no—
208C42×C29C2411yescharacteristic
209#19921C2911yesmaximal, characteristic, direct product factor, Sylow
210C23×C29—21no—
211C23×C29—41no—
212Q8×C29—21no—
213Q8×C29—21no—
214Q8×C29—21no—
215Q8×C29—21no—
216Q8×C29—21no—
217Q8×C29—41no—
218Q8×C29—41no—
219Q8×C29—41no—
220Q8×C29—41no—
221Q8×C29—82no—
222Q8×C29—81no—
223Q8×C29—161no—
224Q8×C29#13512yes—
225D4×C29—21no—
226D4×C29—21no—
227D4×C29—41no—
228D4×C29—41no—
229D4×C29—41no—
230D4×C29—41no—
231D4×C29—81no—
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—21no—
239C2×C4×C29—41no—
240C2×C4×C29—41no—
241C2×C4×C29—41no—
242C2×C4×C29—41no—
243C2×C4×C29—41no—
244C2×C4×C29—82no—
245C2×C4×C29—161no—
246C2×C4×C29C22×D411yescharacteristic
247C2×C4×C29C22×D411yescharacteristic
248C2×C4×C29H(5,𝔽2)11yescharacteristic
249C8×C29—21no—
250C8×C29—21no—
251C8×C29—21no—
252C8×C29—41no—
253C8×C29—41no—
254C8×C29—41no—
255C8×C29—41no—
256C8×C29—41no—
257C8×C29#13712yes—
258#3394C2×C2911yescharacteristic
259Q8×SD16C2×C2911yescharacteristic, complemented
260#3375C2×C2911yescharacteristic, complemented
261#3328C2×C2911yescharacteristic, complemented
262#1708C2×C2911yescharacteristic, complemented
263#1700C2×C2911yescharacteristic, complemented
264#1697C2×C2911yescharacteristic
265#1672C2×C2911yescharacteristic, complemented
266#1666C2×C2911yescharacteristic, complemented
267#1645C2×C2911yescharacteristic, complemented
268#1640C2×C2911yescharacteristic, complemented
269#1638C2×C2911yescharacteristic, complemented
270#1627C2×C2911yescharacteristic
271#1590C2×C2911yescharacteristic, complemented
272C8×Q16C2×C2911yescharacteristic, complemented
273C22×C29—41no—
274C22×C29—41no—
275C22×C29—41no—
276C22×C29—81no—
277C22×C29—81no—
278C22×C29—81no—
279C22×C29D4211yescharacteristic
280C4×C29—22no—
281C4×C29—21no—
282C4×C29—41no—
283C4×C29—41no—
284C4×C29—41no—
285C4×C29—41no—
286C4×C29—41no—
287C4×C29—41no—
288C4×C29—81no—
289C4×C29—81no—
290C4×C29—81no—
291C4×C29C2×#13511yescharacteristic
292C4×C29C2×#13711yescharacteristic
293C4×C29#57711yescharacteristic
294C4×C29#57711yescharacteristic
295#559C22×C2911yescharacteristic
296Q82C22×C2911yescharacteristic
297#556C22×C2911yescharacteristic
298D4×Q8C22×C2911yescharacteristic
299#498—21no—
300#498C22×C2911yescharacteristic
301#495—21no—
302#492C22×C2911yescharacteristic
303#489—21no—
304#487C22×C2911yescharacteristic
305#487C22×C2911yescharacteristic
306#486C22×C2911yescharacteristic
307#486C22×C2911yescharacteristic
308#485—21no—
309#477C22×C2911yescharacteristic
310#476—21no—
311#476C22×C2911yescharacteristic
312#475—21no—
313#475C22×C2911yescharacteristic
314#475C22×C2911yescharacteristic
315#474—21no—
316#470—21no—
317#464—21no—
318#464—21no—
319#463—21no—
320#462C22×C2911yescharacteristic
321#462C22×C2911yescharacteristic
322#460C22×C2911yescharacteristic
323#459C22×C2911yescharacteristic
324#451—21no—
325#446C22×C2911yescharacteristic
326C8×Q8C22×C2911yescharacteristic
327C8×Q8C22×C2911yescharacteristic
328#440—21no—
329C4×Q16C22×C2911yescharacteristic
330C4×SD16—21no—
331C4×SD16—21no—
332C4×SD16C22×C2911yescharacteristic
333#436C22×C2911yescharacteristic
334#419—21no—
335#335C22×C2911yescharacteristic
336#334C22×C2911yescharacteristic
337#333C22×C2911yescharacteristic
338#332C22×C2911yescharacteristic
339#332C22×C2911yescharacteristic
340#331C22×C2911yescharacteristic
341Q8⋊C8C22×C2911yescharacteristic
342Q8⋊C8C22×C2911yescharacteristic
343Q8⋊C8C22×C2911yescharacteristic
344D4⋊C8C22×C2911yescharacteristic
345C82C22×C2911yescharacteristic
346C2×C29—81no—
347C2×C29—161no—
348C2×C29#327811yescharacteristic
349C2×C29#328211yescharacteristic
350C2×C29#329011yescharacteristic
351C22×Q8—21no—
352C2×Q16—21no—
353C2×Q16—21no—
354C2×Q16D4×C2911yescharacteristic
355C2×SD16—21no—
356C2×SD16—21no—
357C2×SD16—21no—
358C2×SD16D4×C2911yescharacteristic
359C2×D8—21no—
360C2×M16—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—41no—
365C4⋊Q8C23×C2911yescharacteristic
366C4⋊Q8C23×C2911yescharacteristic
367C4⋊Q8C23×C2911yescharacteristic
368#127C23×C2911yescharacteristic
369#126—41no—
370#124—21no—
371#124—21no—
372#124—21no—
373#123—41no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—41no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8C23×C2911yescharacteristic
381C4×Q8C23×C2911yescharacteristic
382C4×Q8C23×C2911yescharacteristic
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4C23×C2911yescharacteristic
387#117—21no—
388#107—21no—
389#107D4×C2911yescharacteristic
390#106—21no—
391#106—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395#106D4×C2911yescharacteristic
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8C23×C2911yescharacteristic
400C4⋊C8C23×C2911yescharacteristic
401C4⋊C8C23×C2911yescharacteristic
402C4⋊C8C23×C2911yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—41no—
411#103D4×C2911yescharacteristic
412#103D4×C2911yescharacteristic
413#103D4×C2911yescharacteristic
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—41no—
420#102D4×C2911yescharacteristic
421C22⋊C8—21no—
422#97—21no—
423C4×C8—21no—
424C4×C8—21no—
425C4×C8C23×C2911yescharacteristic
426C4×C8C23×C2911yescharacteristic
427C4×C8C23×C2911yescharacteristic
428C29#1992111yescharacteristic, direct product factor, Sylow
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—41no—
433C2×Q8—41no—
434C2×Q8—42no—
435C2×Q8—81no—
436C2×Q8C2×D4×C2911yescharacteristic
437C2×Q8C2×D4×C2911yescharacteristic
438C2×Q8C2×D4×C2911yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4C2×D4×C2911yescharacteristic
443C22×C4—21no—
444C22×C4—41no—
445C22×C4—41no—
446Q16—22no—
447Q16—81no—
448Q16—81no—
449SD16—22no—
450SD16—42no—
451SD16—42no—
452SD16—81no—
453D8—81no—
454M16—81no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8C2×D4×C2911yescharacteristic
461C2×C8C2×D4×C2911yescharacteristic
462C2×C8C2×D4×C2911yescharacteristic
463C2×C8C2×D4×C2911yescharacteristic
464C4⋊C4—21no—
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—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4C2×D4×C2911yescharacteristic
478C4⋊C4C2×D4×C2911yescharacteristic
479C4⋊C4C2×D4×C2911yescharacteristic
480C4⋊C4C2×D4×C2911yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—41no—
492C42—41no—
493C42C24×C2911yescharacteristic
494C23—21no—
495C23—41no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—82no—
506Q8—81no—
507Q8—161no—
508Q8C29×#13512yes—
509D4—21no—
510D4—21no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—81no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—82no—
529C2×C4—161no—
530C2×C4C22×D4×C2911yescharacteristic
531C2×C4C22×D4×C2911yescharacteristic
532C2×C4C29×H(5,𝔽2)11yescharacteristic
533C8—21no—
534C8—21no—
535C8—21no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8C29×#13712yes—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22D42×C2911yescharacteristic
549C4—22no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4C2×C29×#13511yescharacteristic
561C4C2×C29×#13711yescharacteristic
562C4C29×#57711yescharacteristic
563C4C29×#57711yescharacteristic
564C2—81no—
565C2—161no—
566C2C29×#327811yescharacteristic
567C2C29×#328211yescharacteristic
568C2C29×#329011yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#459C22
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. Q8×SD16×C29C2semidirect
3. C29×#3375C2semidirect
4. C29×#3328C2semidirect
5. C29×#1708C2semidirect
6. C29×#1700C2semidirect
8. C29×#1672C2semidirect
9. C29×#1666C2semidirect
10. C29×#1645C2semidirect
11. C29×#1640C2semidirect
12. C29×#1638C2semidirect
14. C29×#1590C2semidirect
15. C8×Q16×C29C2semidirect
209. #19921C29direct (N × H)
259. Q8×SD16C2×C29semidirect
260. #3375C2×C29semidirect
261. #3328C2×C29semidirect
262. #1708C2×C29semidirect
263. #1700C2×C29semidirect
265. #1672C2×C29semidirect
266. #1666C2×C29semidirect
267. #1645C2×C29semidirect
268. #1640C2×C29semidirect
269. #1638C2×C29semidirect
271. #1590C2×C29semidirect
272. C8×Q16C2×C29semidirect
428. C29#19921direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33942
Q8×SD16×C292
C29×#33752
C29×#33282
C29×#17082
C29×#17002
C29×#16972
C29×#16722
C29×#16662
C29×#16452
C29×#16402
C29×#16382
C29×#16272
C29×#15902
C8×Q16×C292
#1992129