Finite Group Databasebeta

← C29×#19372 #20314272

Subgroups — C29×#19372 #20314272

Order 7424.

588 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3255C211yesmaximal, characteristic, complemented
2C29×#3216C211yesmaximal, characteristic
3C29×#3182C211yesmaximal, characteristic
4C29×#2962C211yesmaximal, characteristic, complemented
5C29×#1702C211yesmaximal, characteristic, complemented
6C29×#1700C211yesmaximal, characteristic, complemented
7C29×#1694C211yesmaximal, characteristic, complemented
8C29×#1686C211yesmaximal, characteristic, complemented
9C29×#1682C211yesmaximal, characteristic, complemented
10C29×#1680C211yesmaximal, characteristic, complemented
11C29×#1674C211yesmaximal, characteristic, complemented
12C29×#1666C211yesmaximal, characteristic, complemented
13C29×#1569C211yesmaximal, characteristic, complemented
14C29×#1552C211yesmaximal, characteristic, complemented
15C29×#1547C211yesmaximal, characteristic
16C29×#533C2211yescharacteristic
17C29×#533C2211yescharacteristic
18C29×#532C2211yescharacteristic
19C29×#500C2211yescharacteristic
20C29×#497—21no—
21C29×#492C2211yescharacteristic
22C29×#489—21no—
23C29×#487C2211yescharacteristic
24C29×#486C2211yescharacteristic
25C29×#475—21no—
26C29×#475C2211yescharacteristic
27C29×#475C2211yescharacteristic
28C29×#470—21no—
29C29×#470—21no—
30C29×#468—21no—
31C29×#468—21no—
32C29×#462—21no—
33C29×#462C2211yescharacteristic
34C29×#462C2211yescharacteristic
35C29×#462C2211yescharacteristic
36C29×#462C2211yescharacteristic
37C29×#460C2211yescharacteristic
38C29×#460C2211yescharacteristic
39C29×#452—21no—
40C29×#452—21no—
41C29×#446—21no—
42C29×#446—21no—
43C29×#446C2211yescharacteristic
44C29×#446C2211yescharacteristic
45C8×Q8×C29C2211yescharacteristic
46C8×Q8×C29C2211yescharacteristic
47C29×#440—21no—
48C29×#440—21no—
49C29×#432C2211yescharacteristic
50C29×#424—21no—
51C29×#423C2211yescharacteristic
52C2×C29×C4⋊C8C2211yescharacteristic
53C29×#405—21no—
54C4×M16×C29C2211yescharacteristic
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×#332C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#331C2211yescharacteristic
66C29×#331C2211yescharacteristic
67C2×#41×C29—21no—
68C2×Q16×C29—21no—
69C2×Q16×C29—21no—
70C2×Q16×C29—21no—
71C2×Q16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×SD16×C29—21no—
75C2×SD16×C29—21no—
76C2×M16×C29—21no—
77C2×M16×C29D411yescharacteristic
78C2×M16×C29D411yescharacteristic
79C22×C8×C29—21no—
80C29×C4⋊Q8D411yescharacteristic
81C29×C4⋊Q8D411yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×C4⋊Q8C2311yescharacteristic
84C29×C4⋊Q8C2311yescharacteristic
85C29×#127C2311yescharacteristic
86C29×#125—21no—
87C29×#125—21no—
88C29×#124—21no—
89C29×C22⋊Q8—21no—
90C29×C22⋊Q8—21no—
91C29×C22⋊Q8—21no—
92C29×C22⋊Q8D411yescharacteristic
93C29×C22⋊Q8D411yescharacteristic
94C29×#121—21no—
95C29×#121—21no—
96C4×Q8×C29—21no—
97C4×Q8×C29—21no—
98C4×Q8×C29—21no—
99C4×Q8×C29C2311yescharacteristic
100C4×Q8×C29C2311yescharacteristic
101C4×D4×C29—21no—
102C4×D4×C29—21no—
103C29×#117—21no—
104C29×#117—21no—
105C2×C42×C29C2311yescharacteristic
106C29×#107—21no—
107C29×#107—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×C4⋊C8—21no—
111C29×C4⋊C8—21no—
112C29×C4⋊C8—21no—
113C29×C4⋊C8—21no—
114C29×C4⋊C8—21no—
115C29×C4⋊C8—21no—
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
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×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×C22⋊C8—21no—
135C29×#97—21no—
136C29×#97—21no—
137C29×#97—21no—
138C29×#97D411yescharacteristic
139C29×#97D411yescharacteristic
140C4×C8×C29—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144#41×C29—81no—
145#41×C29—81no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29C2×D411yescharacteristic
151C2×Q8×C29C2×D411yescharacteristic
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—41no—
156C22×C4×C29—41no—
157C22×C4×C29C2×D411yescharacteristic
158C22×C4×C29C2×D411yescharacteristic
159C22×C4×C29#4111yescharacteristic
160Q16×C29—81no—
161Q16×C29—81no—
162Q16×C29—81no—
163Q16×C29—81no—
164SD16×C29—42no—
165SD16×C29—42no—
166SD16×C29—81no—
167SD16×C29—81no—
168M16×C29—22no—
169M16×C29—41no—
170M16×C29—81no—
171C2×C8×C29—21no—
172C2×C8×C29—21no—
173C2×C8×C29—21no—
174C2×C8×C29—21no—
175C2×C8×C29—21no—
176C2×C8×C29—21no—
177C2×C8×C29—42no—
178C2×C8×C29C2×D411yescharacteristic
179C2×C8×C29C2×D411yescharacteristic
180C2×C8×C29C2×D411yescharacteristic
181C2×C8×C29C2×D411yescharacteristic
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—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—21no—
194C4⋊C4×C29—21no—
195C4⋊C4×C29—41no—
196C4⋊C4×C29—41no—
197C4⋊C4×C29C2×D411yescharacteristic
198C4⋊C4×C29C2×D411yescharacteristic
199C22⋊C4×C29—21no—
200C22⋊C4×C29—21no—
201C22⋊C4×C29—41no—
202C22⋊C4×C29—41no—
203C22⋊C4×C29—41no—
204C42×C29—21no—
205C42×C29—21no—
206C42×C29—41no—
207C42×C29C2×D411yescharacteristic
208C42×C29C2×D411yescharacteristic
209C42×C29#4111yescharacteristic
210C42×C29C2411yescharacteristic
211#19372C2911yesmaximal, characteristic, direct product factor, Sylow
212C23×C29—41no—
213C23×C29#12111yescharacteristic
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—81no—
225D4×C29—41no—
226D4×C29—41no—
227D4×C29—41no—
228D4×C29—41no—
229D4×C29—81no—
230D4×C29—82no—
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—21no—
239C2×C4×C29—41no—
240C2×C4×C29—41no—
241C2×C4×C29—41no—
242C2×C4×C29—41no—
243C2×C4×C29—82no—
244C2×C4×C29#12111yescharacteristic
245C2×C4×C29#12111yescharacteristic
246C2×C4×C29#12111yescharacteristic
247C2×C4×C29C22×D411yescharacteristic
248C2×C4×C29C22×D411yescharacteristic
249C2×C4×C29C2×#4111yescharacteristic
250C8×C29—21no—
251C8×C29—21no—
252C8×C29—21no—
253C8×C29—41no—
254C8×C29—41no—
255C8×C29—41no—
256C8×C29—41no—
257C8×C29—41no—
258C8×C29—41no—
259C8×C29#13712yes—
260#3255C2×C2911yescharacteristic, complemented
261#3216C2×C2911yescharacteristic
262#3182C2×C2911yescharacteristic
263#2962C2×C2911yescharacteristic, complemented
264#1702C2×C2911yescharacteristic, complemented
265#1700C2×C2911yescharacteristic, complemented
266#1694C2×C2911yescharacteristic, complemented
267#1686C2×C2911yescharacteristic, complemented
268#1682C2×C2911yescharacteristic, complemented
269#1680C2×C2911yescharacteristic, complemented
270#1674C2×C2911yescharacteristic, complemented
271#1666C2×C2911yescharacteristic, complemented
272#1569C2×C2911yescharacteristic, complemented
273#1552C2×C2911yescharacteristic, complemented
274#1547C2×C2911yescharacteristic
275C22×C29—21no—
276C22×C29—21no—
277C22×C29—21no—
278C22×C29—81no—
279C22×C29—81no—
280C22×C29—81no—
281C22×C29C2×#12111yescharacteristic
282C4×C29—21no—
283C4×C29—21no—
284C4×C29—21no—
285C4×C29—21no—
286C4×C29—41no—
287C4×C29—41no—
288C4×C29—41no—
289C4×C29—41no—
290C4×C29—81no—
291C4×C29—81no—
292C4×C29—81no—
293C4×C29C2×#13711yescharacteristic
294C4×C29#57511yescharacteristic
295C4×C29#57611yescharacteristic
296C4×C29#57711yescharacteristic
297#533C22×C2911yescharacteristic
298#533C22×C2911yescharacteristic
299#532C22×C2911yescharacteristic
300#500C22×C2911yescharacteristic
301#497—21no—
302#492C22×C2911yescharacteristic
303#489—21no—
304#487C22×C2911yescharacteristic
305#486C22×C2911yescharacteristic
306#475—21no—
307#475C22×C2911yescharacteristic
308#475C22×C2911yescharacteristic
309#470—21no—
310#470—21no—
311#468—21no—
312#468—21no—
313#462—21no—
314#462C22×C2911yescharacteristic
315#462C22×C2911yescharacteristic
316#462C22×C2911yescharacteristic
317#462C22×C2911yescharacteristic
318#460C22×C2911yescharacteristic
319#460C22×C2911yescharacteristic
320#452—21no—
321#452—21no—
322#446—21no—
323#446—21no—
324#446C22×C2911yescharacteristic
325#446C22×C2911yescharacteristic
326C8×Q8C22×C2911yescharacteristic
327C8×Q8C22×C2911yescharacteristic
328#440—21no—
329#440—21no—
330#432C22×C2911yescharacteristic
331#424—21no—
332#423C22×C2911yescharacteristic
333C2×C4⋊C8C22×C2911yescharacteristic
334#405—21no—
335C4×M16C22×C2911yescharacteristic
336#335C22×C2911yescharacteristic
337#335C22×C2911yescharacteristic
338#334C22×C2911yescharacteristic
339#334C22×C2911yescharacteristic
340#332C22×C2911yescharacteristic
341#332C22×C2911yescharacteristic
342#332C22×C2911yescharacteristic
343#332C22×C2911yescharacteristic
344#332C22×C2911yescharacteristic
345#332C22×C2911yescharacteristic
346#331C22×C2911yescharacteristic
347#331C22×C2911yescharacteristic
348C2×C29—41no—
349C2×C29—161no—
350C2×C29#303711yescharacteristic
351C2×C29#306211yescharacteristic
352C2×C29#306911yescharacteristic
353C2×#41—21no—
354C2×Q16—21no—
355C2×Q16—21no—
356C2×Q16—21no—
357C2×Q16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×M16—21no—
363C2×M16D4×C2911yescharacteristic
364C2×M16D4×C2911yescharacteristic
365C22×C8—21no—
366C4⋊Q8D4×C2911yescharacteristic
367C4⋊Q8D4×C2911yescharacteristic
368C4⋊Q8C23×C2911yescharacteristic
369C4⋊Q8C23×C2911yescharacteristic
370C4⋊Q8C23×C2911yescharacteristic
371#127C23×C2911yescharacteristic
372#125—21no—
373#125—21no—
374#124—21no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—21no—
378C22⋊Q8D4×C2911yescharacteristic
379C22⋊Q8D4×C2911yescharacteristic
380#121—21no—
381#121—21no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8C23×C2911yescharacteristic
386C4×Q8C23×C2911yescharacteristic
387C4×D4—21no—
388C4×D4—21no—
389#117—21no—
390#117—21no—
391C2×C42C23×C2911yescharacteristic
392#107—21no—
393#107—21no—
394#106—21no—
395#106—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8—21no—
402C4⋊C8C23×C2911yescharacteristic
403C4⋊C8C23×C2911yescharacteristic
404C4⋊C8C23×C2911yescharacteristic
405C4⋊C8C23×C2911yescharacteristic
406C4⋊C8C23×C2911yescharacteristic
407C4⋊C8C23×C2911yescharacteristic
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420C22⋊C8—21no—
421#97—21no—
422#97—21no—
423#97—21no—
424#97D4×C2911yescharacteristic
425#97D4×C2911yescharacteristic
426C4×C8—21no—
427C4×C8—21no—
428C4×C8C23×C2911yescharacteristic
429C4×C8C23×C2911yescharacteristic
430C29#1937211yescharacteristic, direct product factor, Sylow
431#41—81no—
432#41—81no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8C2×D4×C2911yescharacteristic
438C2×Q8C2×D4×C2911yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—41no—
443C22×C4—41no—
444C22×C4C2×D4×C2911yescharacteristic
445C22×C4C2×D4×C2911yescharacteristic
446C22×C4#41×C2911yescharacteristic
447Q16—81no—
448Q16—81no—
449Q16—81no—
450Q16—81no—
451SD16—42no—
452SD16—42no—
453SD16—81no—
454SD16—81no—
455M16—22no—
456M16—41no—
457M16—81no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—42no—
465C2×C8C2×D4×C2911yescharacteristic
466C2×C8C2×D4×C2911yescharacteristic
467C2×C8C2×D4×C2911yescharacteristic
468C2×C8C2×D4×C2911yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4C2×D4×C2911yescharacteristic
485C4⋊C4C2×D4×C2911yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C42—21no—
492C42—21no—
493C42—41no—
494C42C2×D4×C2911yescharacteristic
495C42C2×D4×C2911yescharacteristic
496C42#41×C2911yescharacteristic
497C42C24×C2911yescharacteristic
498C23—41no—
499C23C29×#12111yescharacteristic
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—81no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—81no—
516D4—82no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—82no—
530C2×C4C29×#12111yescharacteristic
531C2×C4C29×#12111yescharacteristic
532C2×C4C29×#12111yescharacteristic
533C2×C4C22×D4×C2911yescharacteristic
534C2×C4C22×D4×C2911yescharacteristic
535C2×C4C2×#41×C2911yescharacteristic
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8C29×#13712yes—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22C2×C29×#12111yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4C2×C29×#13711yescharacteristic
565C4C29×#57511yescharacteristic
566C4C29×#57611yescharacteristic
567C4C29×#57711yescharacteristic
568C2—41no—
569C2—161no—
570C2C29×#303711yescharacteristic
571C2C29×#306211yescharacteristic
572C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3255C2semidirect
4. C29×#2962C2semidirect
5. C29×#1702C2semidirect
6. C29×#1700C2semidirect
7. C29×#1694C2semidirect
8. C29×#1686C2semidirect
9. C29×#1682C2semidirect
10. C29×#1680C2semidirect
11. C29×#1674C2semidirect
12. C29×#1666C2semidirect
13. C29×#1569C2semidirect
14. C29×#1552C2semidirect
211. #19372C29direct (N × H)
260. #3255C2×C29semidirect
263. #2962C2×C29semidirect
264. #1702C2×C29semidirect
265. #1700C2×C29semidirect
266. #1694C2×C29semidirect
267. #1686C2×C29semidirect
268. #1682C2×C29semidirect
269. #1680C2×C29semidirect
270. #1674C2×C29semidirect
271. #1666C2×C29semidirect
272. #1569C2×C29semidirect
273. #1552C2×C29semidirect
430. C29#19372direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32552
C29×#32162
C29×#31822
C29×#29622
C29×#17022
C29×#17002
C29×#16942
C29×#16862
C29×#16822
C29×#16802
C29×#16742
C29×#16662
C29×#15692
C29×#15522
C29×#15472
#1937229