Finite Group Databasebeta

← C29×#19181 #20314081

Subgroups — C29×#19181 #20314081

Order 7424.

594 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3185C211yesmaximal, characteristic, complemented
2C29×#3107C211yesmaximal, characteristic
3C29×#3076C211yesmaximal, characteristic
4C29×#2970C211yesmaximal, characteristic
5C29×#1704C211yesmaximal, characteristic, complemented
6C29×#1700C211yesmaximal, characteristic, complemented
7C29×#1692C211yesmaximal, characteristic, complemented
8C29×#1690C211yesmaximal, characteristic, complemented
9C29×#1683C211yesmaximal, characteristic, complemented
10C29×#1679C211yesmaximal, characteristic, complemented
11C29×#1671C211yesmaximal, characteristic, complemented
12C29×#1669C211yesmaximal, characteristic, complemented
13C29×#1565C211yesmaximal, characteristic, complemented
14C29×#1554C211yesmaximal, characteristic, complemented
15C29×#1552C211yesmaximal, characteristic, complemented
16C29×#533C2211yescharacteristic
17C29×#533C2211yescharacteristic
18C4×#41×C29C2211yescharacteristic
19C29×#498C2211yescharacteristic
20C29×#494C2211yescharacteristic
21C29×#487C2211yescharacteristic
22C29×#487C2211yescharacteristic
23C29×#485—21no—
24C29×#479—21no—
25C29×#478—21no—
26C29×#477C2211yescharacteristic
27C29×#476C2211yescharacteristic
28C29×#475C2211yescharacteristic
29C29×#475C2211yescharacteristic
30C29×#474C2211yescharacteristic
31C29×#474C2211yescharacteristic
32C29×#470—21no—
33C29×#470—21no—
34C29×#462C2211yescharacteristic
35C29×#461C2211yescharacteristic
36C29×#452—21no—
37C29×#446C2211yescharacteristic
38C29×#446C2211yescharacteristic
39C29×#441—21no—
40C29×#441—21no—
41C4×Q16×C29—21no—
42C4×SD16×C29—21no—
43C29×#435—21no—
44C29×#435—21no—
45C8×D4×C29C2211yescharacteristic
46C8×D4×C29C2211yescharacteristic
47C29×#432—21no—
48C29×#432C2211yescharacteristic
49C29×#431C2211yescharacteristic
50C29×#427—21no—
51C2×C29×C4⋊C8C2211yescharacteristic
52C29×#416—21no—
53C4×M16×C29C2211yescharacteristic
54C2×C29×#97—21no—
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×#332C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#332C2211yescharacteristic
66C29×#332C2211yescharacteristic
67C2×#41×C29D411yescharacteristic
68C2×Q16×C29—21no—
69C2×Q16×C29—21no—
70C2×Q16×C29—21no—
71C2×SD16×C29—21no—
72C2×M16×C29D411yescharacteristic
73C2×M16×C29D411yescharacteristic
74C22×C8×C29—21no—
75C22×C8×C29—21no—
76C22×C8×C29—21no—
77C29×C4⋊Q8C2311yescharacteristic
78C29×C4⋊Q8C2311yescharacteristic
79C29×C4⋊Q8C2311yescharacteristic
80C29×C4⋊Q8C2311yescharacteristic
81C29×#125—21no—
82C29×#125—21no—
83C29×C22⋊Q8—21no—
84C29×C22⋊Q8—21no—
85C29×C22⋊Q8—21no—
86C29×C22⋊Q8—21no—
87C4×Q8×C29—21no—
88C4×Q8×C29—21no—
89C4×Q8×C29—21no—
90C4×Q8×C29—21no—
91C4×Q8×C29D411yescharacteristic
92C4×Q8×C29C2311yescharacteristic
93C4×D4×C29—21no—
94C4×D4×C29—21no—
95C4×D4×C29D411yescharacteristic
96C4×D4×C29C2311yescharacteristic
97C29×#117—21no—
98C29×#117—21no—
99C29×#117—21no—
100C29×#117D411yescharacteristic
101C2×C42×C29—21no—
102C2×C42×C29C2311yescharacteristic
103C29×#107—21no—
104C29×#107—21no—
105C29×#107—21no—
106C29×#106—21no—
107C29×#106—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×#106—21no—
111C29×C4⋊C8—21no—
112C29×C4⋊C8—21no—
113C29×C4⋊C8—21no—
114C29×C4⋊C8C2311yescharacteristic
115C29×C4⋊C8C2311yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×#103—21no—
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×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×C22⋊C8—21no—
133C29×C22⋊C8—21no—
134C29×C22⋊C8—21no—
135C29×C22⋊C8—21no—
136C29×#97—21no—
137C29×#97—21no—
138C29×#97—21no—
139C29×#97D411yescharacteristic
140C29×#97D411yescharacteristic
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144#41×C29—22no—
145#41×C29—41no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29C2×D411yescharacteristic
151C2×D4×C29—21no—
152C2×D4×C29C2×D411yescharacteristic
153C22×C4×C29—21no—
154C22×C4×C29—21no—
155C22×C4×C29—21no—
156C22×C4×C29C2×D411yescharacteristic
157C22×C4×C29C2×D411yescharacteristic
158C22×C4×C29#4111yescharacteristic
159Q16×C29—42no—
160Q16×C29—42no—
161Q16×C29—42no—
162SD16×C29—42no—
163M16×C29—22no—
164M16×C29—41no—
165C2×C8×C29—21no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—42no—
172C2×C8×C29—42no—
173C2×C8×C29—42no—
174C2×C8×C29C2×D411yescharacteristic
175C2×C8×C29C2×D411yescharacteristic
176C2×C8×C29C2×D411yescharacteristic
177C2×C8×C29C2×D411yescharacteristic
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—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
194C22⋊C4×C29—21no—
195C22⋊C4×C29—21no—
196C22⋊C4×C29—21no—
197C22⋊C4×C29—41no—
198C22⋊C4×C29—41no—
199C42×C29—21no—
200C42×C29—21no—
201C42×C29—21no—
202C42×C29—41no—
203C42×C29—41no—
204C42×C29C2×D411yescharacteristic
205C42×C29C2×D411yescharacteristic
206C42×C29#4111yescharacteristic
207C42×C29C2411yescharacteristic
208#19181C2911yesmaximal, characteristic, direct product factor, Sylow
209C23×C29—21no—
210C23×C29#12111yescharacteristic
211Q8×C29—21no—
212Q8×C29—21no—
213Q8×C29—41no—
214Q8×C29—41no—
215Q8×C29—41no—
216Q8×C29—41no—
217Q8×C29—41no—
218Q8×C29—41no—
219Q8×C29—81no—
220D4×C29—21no—
221D4×C29—42no—
222D4×C29#13712yes—
223C2×C4×C29—21no—
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—41no—
231C2×C4×C29—42no—
232C2×C4×C29—41no—
233C2×C4×C29—41no—
234C2×C4×C29—41no—
235C2×C4×C29—41no—
236C2×C4×C29—41no—
237C2×C4×C29—41no—
238C2×C4×C29—81no—
239C2×C4×C29#12111yescharacteristic
240C2×C4×C29#12111yescharacteristic
241C2×C4×C29#12111yescharacteristic
242C2×C4×C29C22×D411yescharacteristic
243C2×C4×C29C22×D411yescharacteristic
244C2×C4×C29C2×#4111yescharacteristic
245C8×C29—21no—
246C8×C29—21no—
247C8×C29—21no—
248C8×C29—41no—
249C8×C29—41no—
250C8×C29—41no—
251C8×C29—41no—
252C8×C29—41no—
253C8×C29—41no—
254C8×C29#13512yes—
255#3185C2×C2911yescharacteristic, complemented
256#3107C2×C2911yescharacteristic
257#3076C2×C2911yescharacteristic
258#2970C2×C2911yescharacteristic
259#1704C2×C2911yescharacteristic, complemented
260#1700C2×C2911yescharacteristic, complemented
261#1692C2×C2911yescharacteristic, complemented
262#1690C2×C2911yescharacteristic, complemented
263#1683C2×C2911yescharacteristic, complemented
264#1679C2×C2911yescharacteristic, complemented
265#1671C2×C2911yescharacteristic, complemented
266#1669C2×C2911yescharacteristic, complemented
267#1565C2×C2911yescharacteristic, complemented
268#1554C2×C2911yescharacteristic, complemented
269#1552C2×C2911yescharacteristic, complemented
270C22×C29—21no—
271C22×C29—21no—
272C22×C29—22no—
273C22×C29—21no—
274C22×C29—41no—
275C22×C29—41no—
276C22×C29C2×#12111yescharacteristic
277C4×C29—21no—
278C4×C29—21no—
279C4×C29—21no—
280C4×C29—21no—
281C4×C29—41no—
282C4×C29—41no—
283C4×C29—41no—
284C4×C29—81no—
285C4×C29—81no—
286C4×C29—81no—
287C4×C29—81no—
288C4×C29C2×#13511yescharacteristic
289C4×C29C2×#13711yescharacteristic
290C4×C29#57511yescharacteristic
291C4×C29#57511yescharacteristic
292#533C22×C2911yescharacteristic
293#533C22×C2911yescharacteristic
294C4×#41C22×C2911yescharacteristic
295#498C22×C2911yescharacteristic
296#494C22×C2911yescharacteristic
297#487C22×C2911yescharacteristic
298#487C22×C2911yescharacteristic
299#485—21no—
300#479—21no—
301#478—21no—
302#477C22×C2911yescharacteristic
303#476C22×C2911yescharacteristic
304#475C22×C2911yescharacteristic
305#475C22×C2911yescharacteristic
306#474C22×C2911yescharacteristic
307#474C22×C2911yescharacteristic
308#470—21no—
309#470—21no—
310#462C22×C2911yescharacteristic
311#461C22×C2911yescharacteristic
312#452—21no—
313#446C22×C2911yescharacteristic
314#446C22×C2911yescharacteristic
315#441—21no—
316#441—21no—
317C4×Q16—21no—
318C4×SD16—21no—
319#435—21no—
320#435—21no—
321C8×D4C22×C2911yescharacteristic
322C8×D4C22×C2911yescharacteristic
323#432—21no—
324#432C22×C2911yescharacteristic
325#431C22×C2911yescharacteristic
326#427—21no—
327C2×C4⋊C8C22×C2911yescharacteristic
328#416—21no—
329C4×M16C22×C2911yescharacteristic
330C2×#97—21no—
331#335C22×C2911yescharacteristic
332#335C22×C2911yescharacteristic
333#334C22×C2911yescharacteristic
334#334C22×C2911yescharacteristic
335#333C22×C2911yescharacteristic
336#333C22×C2911yescharacteristic
337#332C22×C2911yescharacteristic
338#332C22×C2911yescharacteristic
339#332C22×C2911yescharacteristic
340#332C22×C2911yescharacteristic
341#332C22×C2911yescharacteristic
342#332C22×C2911yescharacteristic
343C2×C29—41no—
344C2×C29—42no—
345C2×C29#303511yescharacteristic
346C2×C29#305611yescharacteristic
347C2×C29#306911yescharacteristic
348C2×#41D4×C2911yescharacteristic
349C2×Q16—21no—
350C2×Q16—21no—
351C2×Q16—21no—
352C2×SD16—21no—
353C2×M16D4×C2911yescharacteristic
354C2×M16D4×C2911yescharacteristic
355C22×C8—21no—
356C22×C8—21no—
357C22×C8—21no—
358C4⋊Q8C23×C2911yescharacteristic
359C4⋊Q8C23×C2911yescharacteristic
360C4⋊Q8C23×C2911yescharacteristic
361C4⋊Q8C23×C2911yescharacteristic
362#125—21no—
363#125—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8D4×C2911yescharacteristic
373C4×Q8C23×C2911yescharacteristic
374C4×D4—21no—
375C4×D4—21no—
376C4×D4D4×C2911yescharacteristic
377C4×D4C23×C2911yescharacteristic
378#117—21no—
379#117—21no—
380#117—21no—
381#117D4×C2911yescharacteristic
382C2×C42—21no—
383C2×C42C23×C2911yescharacteristic
384#107—21no—
385#107—21no—
386#107—21no—
387#106—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8C23×C2911yescharacteristic
396C4⋊C8C23×C2911yescharacteristic
397C4⋊C8C23×C2911yescharacteristic
398C4⋊C8C23×C2911yescharacteristic
399C4⋊C8C23×C2911yescharacteristic
400C4⋊C8C23×C2911yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#102—21no—
411#102—21no—
412#102—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417#97—21no—
418#97—21no—
419#97—21no—
420#97D4×C2911yescharacteristic
421#97D4×C2911yescharacteristic
422C4×C8—21no—
423C4×C8C23×C2911yescharacteristic
424C4×C8C23×C2911yescharacteristic
425C29#1918111yescharacteristic, direct product factor, Sylow
426#41—22no—
427#41—41no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8C2×D4×C2911yescharacteristic
433C2×D4—21no—
434C2×D4C2×D4×C2911yescharacteristic
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4C2×D4×C2911yescharacteristic
439C22×C4C2×D4×C2911yescharacteristic
440C22×C4#41×C2911yescharacteristic
441Q16—42no—
442Q16—42no—
443Q16—42no—
444SD16—42no—
445M16—22no—
446M16—41no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—42no—
454C2×C8—42no—
455C2×C8—42no—
456C2×C8C2×D4×C2911yescharacteristic
457C2×C8C2×D4×C2911yescharacteristic
458C2×C8C2×D4×C2911yescharacteristic
459C2×C8C2×D4×C2911yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4C2×D4×C2911yescharacteristic
475C4⋊C4C2×D4×C2911yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—41no—
485C42—41no—
486C42C2×D4×C2911yescharacteristic
487C42C2×D4×C2911yescharacteristic
488C42#41×C2911yescharacteristic
489C42C24×C2911yescharacteristic
490C23—21no—
491C23C29×#12111yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501D4—21no—
502D4—42no—
503D4C29×#13712yes—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—81no—
520C2×C4C29×#12111yescharacteristic
521C2×C4C29×#12111yescharacteristic
522C2×C4C29×#12111yescharacteristic
523C2×C4C22×D4×C2911yescharacteristic
524C2×C4C22×D4×C2911yescharacteristic
525C2×C4C2×#41×C2911yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8C29×#13512yes—
536C22—21no—
537C22—21no—
538C22—22no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22C2×C29×#12111yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—81no—
551C4—81no—
552C4—81no—
553C4—81no—
554C4C2×C29×#13511yescharacteristic
555C4C2×C29×#13711yescharacteristic
556C4C29×#57511yescharacteristic
557C4C29×#57511yescharacteristic
558C2—41no—
559C2—42no—
560C2C29×#303511yescharacteristic
561C2C29×#305611yescharacteristic
562C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC2×#41×C29D4
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×#3185C2semidirect
5. C29×#1704C2semidirect
6. C29×#1700C2semidirect
7. C29×#1692C2semidirect
8. C29×#1690C2semidirect
9. C29×#1683C2semidirect
10. C29×#1679C2semidirect
11. C29×#1671C2semidirect
12. C29×#1669C2semidirect
13. C29×#1565C2semidirect
14. C29×#1554C2semidirect
15. C29×#1552C2semidirect
208. #19181C29direct (N × H)
255. #3185C2×C29semidirect
259. #1704C2×C29semidirect
260. #1700C2×C29semidirect
261. #1692C2×C29semidirect
262. #1690C2×C29semidirect
263. #1683C2×C29semidirect
264. #1679C2×C29semidirect
265. #1671C2×C29semidirect
266. #1669C2×C29semidirect
267. #1565C2×C29semidirect
268. #1554C2×C29semidirect
269. #1552C2×C29semidirect
425. C29#19181direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31852
C29×#31072
C29×#30762
C29×#29702
C29×#17042
C29×#17002
C29×#16922
C29×#16902
C29×#16832
C29×#16792
C29×#16712
C29×#16692
C29×#15652
C29×#15542
C29×#15522
#1918129