Finite Group Databasebeta

← C29×#18332 #20313232

Subgroups — C29×#18332 #20313232

Order 7424.

1230 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×#3449C211yesmaximal, characteristic, complemented
2C29×#3213C212yesmaximal, complemented
3C29×#2610C211yesmaximal, characteristic, complemented
4C29×#1604C212yesmaximal, complemented
5C29×#1601C212yesmaximal, complemented
6C29×#1598C212yesmaximal, complemented
7C29×#1595C212yesmaximal, complemented
8C29×#1505C212yesmaximal, complemented
9C29×#1464C211yesmaximal, characteristic, complemented
10C22×#41×C29—21no—
11C29×#537—21no—
12C29×#537C2212yes—
13C29×#536—22no—
14C29×#535—22no—
15C29×#534—21no—
16C29×#534C2212yes—
17C29×#532—21no—
18C29×#532C2212yes—
19C2×C29×#124C2211yescharacteristic, complemented
20C29×#525—24no—
21C2×C29×#117C2211yescharacteristic
22C29×#496—22no—
23C29×#489—22no—
24C29×#463—24no—
25C29×#448C2214yescomplemented
26C29×#447C2214yescomplemented
27C29×#432C2212yescomplemented
28C29×#395C2211yescharacteristic, complemented
29C29×#394C2211yescharacteristic, complemented
30C29×#393C2211yescharacteristic
31C29×#392C2211yescharacteristic
32C29×#390—21no—
33C29×#388—21no—
34C29×#388—21no—
35C29×#386—21no—
36C29×#376C2211yescharacteristic, complemented
37C29×#327C2214yescomplemented
38C29×#327C2214yescomplemented
39C29×#324C2212yescomplemented
40C29×#323C2212yes—
41C2×#41×C29—22no—
42C2×#41×C29—22no—
43C2×#41×C29—22no—
44C2×#41×C29—22no—
45C2×#41×C29—44no—
46C2×#41×C29—44no—
47C22×Q8×C29—21no—
48C22×Q8×C29C2311yescharacteristic
49C22×D4×C29—21no—
50C22×D4×C29—22no—
51C22×D4×C29—21no—
52C22×D4×C29C2311yescharacteristic
53C23×C4×C29—22no—
54C23×C4×C29D411yescharacteristic
55C2×SD16×C29—24no—
56C2×D8×C29—24no—
57C29×C4⋊Q8—21no—
58C29×C4⋊Q8D412yescomplemented
59C29×#127—21no—
60C29×#127D412yescomplemented
61C29×#124—22no—
62C29×#124—22no—
63C29×#124—22no—
64C29×#124—22no—
65C29×#123—24no—
66C29×#123—24no—
67C29×C22⋊Q8—24no—
68C29×C22⋊Q8—24no—
69C29×#121—24no—
70C29×#121—24no—
71C29×#121—22no—
72C29×#121—22no—
73C29×#121—22no—
74C29×#121C2314yes—
75C29×#120—24no—
76C29×#120—24no—
77C4×D4×C29—22no—
78C4×D4×C29—22no—
79C4×D4×C29—22no—
80C4×D4×C29D414yescomplemented
81C29×#117—22no—
82C29×#117—22no—
83C2×C4⋊C4×C29—21no—
84C2×C4⋊C4×C29D411yescharacteristic
85C2×C4⋊C4×C29C2311yescharacteristic
86C2×C22⋊C4×C29—21no—
87C2×C22⋊C4×C29—21no—
88C2×C22⋊C4×C29—21no—
89C2×C22⋊C4×C29—21no—
90C2×C22⋊C4×C29—21no—
91C2×C22⋊C4×C29—21no—
92C2×C22⋊C4×C29D411yescharacteristic
93C2×C22⋊C4×C29C2311yescharacteristic
94C2×C42×C29—21no—
95C2×C42×C29D411yescharacteristic
96C2×C42×C29C2311yescharacteristic
97C29×C4⋊C8—22no—
98C29×#103—24no—
99C29×#102—24no—
100C29×C22⋊C8C2314yes—
101C29×#97—22no—
102C29×#95—21no—
103C29×#95—21no—
104C29×#95—21no—
105C29×#95C2311yescharacteristic
106C29×#95C2311yescharacteristic
107C24×C29—22no—
108C24×C29—21no—
109C24×C29C2×D411yescharacteristic
110#41×C29—48no—
111#41×C29—48no—
112#41×C29—44no—
113#41×C29—44no—
114#41×C29—44no—
115#41×C29—44no—
116C2×Q8×C29—22no—
117C2×Q8×C29—22no—
118C2×Q8×C29—22no—
119C2×Q8×C29—44no—
120C2×Q8×C29—81no—
121C2×D4×C29—24no—
122C2×D4×C29—22no—
123C2×D4×C29—24no—
124C2×D4×C29—22no—
125C2×D4×C29—22no—
126C2×D4×C29—22no—
127C2×D4×C29—22no—
128C2×D4×C29—22no—
129C2×D4×C29—44no—
130C2×D4×C29—42no—
131C2×D4×C29—44no—
132C2×D4×C29—44no—
133C2×D4×C29—42no—
134C2×D4×C29—81no—
135C2×D4×C29—81no—
136C2×D4×C29C2×D414yes—
137C22×C4×C29—22no—
138C22×C4×C29—21no—
139C22×C4×C29—21no—
140C22×C4×C29—22no—
141C22×C4×C29—24no—
142C22×C4×C29—22no—
143C22×C4×C29—21no—
144C22×C4×C29—24no—
145C22×C4×C29—21no—
146C22×C4×C29—21no—
147C22×C4×C29—48no—
148C22×C4×C29C2×D411yescharacteristic
149C22×C4×C29C2×D411yescharacteristic
150C22×C4×C29C2×D411yescharacteristic
151C22×C4×C29C2×D411yescharacteristic
152C22×C4×C29C2×D411yescharacteristic
153C22×C4×C29C2411yescharacteristic
154SD16×C29—84no—
155D8×C29—84no—
156C2×C8×C29—24no—
157C4⋊C4×C29—22no—
158C4⋊C4×C29—22no—
159C4⋊C4×C29—22no—
160C4⋊C4×C29—22no—
161C4⋊C4×C29—22no—
162C4⋊C4×C29—81no—
163C4⋊C4×C29C2×D414yes—
164C22⋊C4×C29—24no—
165C22⋊C4×C29—24no—
166C22⋊C4×C29—22no—
167C22⋊C4×C29—24no—
168C22⋊C4×C29—22no—
169C22⋊C4×C29—24no—
170C22⋊C4×C29—42no—
171C22⋊C4×C29—41no—
172C22⋊C4×C29—41no—
173C22⋊C4×C29—42no—
174C22⋊C4×C29—42no—
175C22⋊C4×C29—81no—
176C22⋊C4×C29—81no—
177C42×C29—21no—
178C42×C29—21no—
179C42×C29—42no—
180C42×C29C2×D412yes—
181C42×C29C2×D412yes—
182#18332C2911yesmaximal, characteristic, direct product factor, Sylow
183C23×C29—21no—
184C23×C29—21no—
185C23×C29—24no—
186C23×C29—41no—
187C23×C29—41no—
188C23×C29—44no—
189C23×C29—41no—
190C23×C29—41no—
191C23×C29—41no—
192C23×C29—41no—
193C23×C29—41no—
194C23×C29—41no—
195C23×C29—41no—
196C23×C29—82no—
197C23×C29—82no—
198C23×C29AGL(1,ℤ/8)12yes—
199C23×C29C22×D411yescharacteristic
200Q8×C29—44no—
201Q8×C29—44no—
202Q8×C29—44no—
203D4×C29—44no—
204D4×C29—44no—
205D4×C29—44no—
206D4×C29—44no—
207D4×C29—48no—
208D4×C29—44no—
209D4×C29—44no—
210D4×C29—82no—
211D4×C29—82no—
212D4×C29—82no—
213D4×C29—84no—
214C2×C4×C29—24no—
215C2×C4×C29—24no—
216C2×C4×C29—21no—
217C2×C4×C29—21no—
218C2×C4×C29—21no—
219C2×C4×C29—21no—
220C2×C4×C29—22no—
221C2×C4×C29—21no—
222C2×C4×C29—21no—
223C2×C4×C29—24no—
224C2×C4×C29—41no—
225C2×C4×C29—41no—
226C2×C4×C29—48no—
227C2×C4×C29—48no—
228C2×C4×C29—41no—
229C2×C4×C29—44no—
230C2×C4×C29—41no—
231C2×C4×C29—41no—
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—41no—
239C2×C4×C29#12011yescharacteristic
240C2×C4×C29#12011yescharacteristic
241C2×C4×C29#12012yes—
242C2×C4×C29AGL(1,ℤ/8)12yes—
243C2×C4×C29C22×D412yes—
244C8×C29—44no—
245#3449C2×C2911yescharacteristic, complemented
246#3213C2×C2912yescomplemented
247#2610C2×C2911yescharacteristic, complemented
248#1604C2×C2912yescomplemented
249#1601C2×C2912yescomplemented
250#1598C2×C2912yescomplemented
251#1595C2×C2912yescomplemented
252#1505C2×C2912yescomplemented
253#1464C2×C2911yescharacteristic, complemented
254C22×C29—21no—
255C22×C29—21no—
256C22×C29—22no—
257C22×C29—42no—
258C22×C29—41no—
259C22×C29—41no—
260C22×C29—44no—
261C22×C29—44no—
262C22×C29—44no—
263C22×C29—81no—
264C22×C29—81no—
265C22×C29—81no—
266C22×C29—81no—
267C22×C29—81no—
268C22×C29—88no—
269C22×C29—81no—
270C22×C29—81no—
271C22×C29—81no—
272C22×C29C2×#12011yescharacteristic
273C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
274C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
275C4×C29—21no—
276C4×C29—22no—
277C4×C29—21no—
278C4×C29—22no—
279C4×C29—22no—
280C4×C29—42no—
281C4×C29—44no—
282C4×C29—41no—
283C4×C29—41no—
284C4×C29—81no—
285C4×C29—81no—
286C22×#41—21no—
287#537—21no—
288#537C22×C2912yes—
289#536—22no—
290#535—22no—
291#534—21no—
292#534C22×C2912yes—
293#532—21no—
294#532C22×C2912yes—
295C2×#124C22×C2911yescharacteristic, complemented
296#525—24no—
297C2×#117C22×C2911yescharacteristic
298#496—22no—
299#489—22no—
300#463—24no—
301#448C22×C2914yescomplemented
302#447C22×C2914yescomplemented
303#432C22×C2912yescomplemented
304#395C22×C2911yescharacteristic, complemented
305#394C22×C2911yescharacteristic, complemented
306#393C22×C2911yescharacteristic
307#392C22×C2911yescharacteristic
308#390—21no—
309#388—21no—
310#388—21no—
311#386—21no—
312#376C22×C2911yescharacteristic, complemented
313#327C22×C2914yescomplemented
314#327C22×C2914yescomplemented
315#324C22×C2912yescomplemented
316#323C22×C2912yes—
317C2×C29—21no—
318C2×C29—21no—
319C2×C29—42no—
320C2×C29—84no—
321C2×C29—161no—
322C2×C29#300311yescharacteristic
323C2×C29#301811yescharacteristic
324C2×C29#302711yescharacteristic
325C2×#41—22no—
326C2×#41—22no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—44no—
330C2×#41—44no—
331C22×Q8—21no—
332C22×Q8C23×C2911yescharacteristic
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—21no—
336C22×D4C23×C2911yescharacteristic
337C23×C4—22no—
338C23×C4D4×C2911yescharacteristic
339C2×SD16—24no—
340C2×D8—24no—
341C4⋊Q8—21no—
342C4⋊Q8D4×C2912yescomplemented
343#127—21no—
344#127D4×C2912yescomplemented
345#124—22no—
346#124—22no—
347#124—22no—
348#124—22no—
349#123—24no—
350#123—24no—
351C22⋊Q8—24no—
352C22⋊Q8—24no—
353#121—24no—
354#121—24no—
355#121—22no—
356#121—22no—
357#121—22no—
358#121C23×C2914yes—
359#120—24no—
360#120—24no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4D4×C2914yescomplemented
365#117—22no—
366#117—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4D4×C2911yescharacteristic
369C2×C4⋊C4C23×C2911yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4D4×C2911yescharacteristic
377C2×C22⋊C4C23×C2911yescharacteristic
378C2×C42—21no—
379C2×C42D4×C2911yescharacteristic
380C2×C42C23×C2911yescharacteristic
381C4⋊C8—22no—
382#103—24no—
383#102—24no—
384C22⋊C8C23×C2914yes—
385#97—22no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95C23×C2911yescharacteristic
390#95C23×C2911yescharacteristic
391C29#1833211yescharacteristic, direct product factor, Sylow
392C24—22no—
393C24—21no—
394C24C2×D4×C2911yescharacteristic
395#41—48no—
396#41—48no—
397#41—44no—
398#41—44no—
399#41—44no—
400#41—44no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—44no—
405C2×Q8—81no—
406C2×D4—24no—
407C2×D4—22no—
408C2×D4—24no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—44no—
415C2×D4—42no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—42no—
419C2×D4—81no—
420C2×D4—81no—
421C2×D4C2×D4×C2914yes—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—48no—
433C22×C4C2×D4×C2911yescharacteristic
434C22×C4C2×D4×C2911yescharacteristic
435C22×C4C2×D4×C2911yescharacteristic
436C22×C4C2×D4×C2911yescharacteristic
437C22×C4C2×D4×C2911yescharacteristic
438C22×C4C24×C2911yescharacteristic
439SD16—84no—
440D8—84no—
441C2×C8—24no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—81no—
448C4⋊C4C2×D4×C2914yes—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—22no—
452C22⋊C4—24no—
453C22⋊C4—22no—
454C22⋊C4—24no—
455C22⋊C4—42no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—42no—
459C22⋊C4—42no—
460C22⋊C4—81no—
461C22⋊C4—81no—
462C42—21no—
463C42—21no—
464C42—42no—
465C42C2×D4×C2912yes—
466C42C2×D4×C2912yes—
467C23—21no—
468C23—21no—
469C23—24no—
470C23—41no—
471C23—41no—
472C23—44no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—82no—
481C23—82no—
482C23C29×AGL(1,ℤ/8)12yes—
483C23C22×D4×C2911yescharacteristic
484Q8—44no—
485Q8—44no—
486Q8—44no—
487D4—44no—
488D4—44no—
489D4—44no—
490D4—44no—
491D4—48no—
492D4—44no—
493D4—44no—
494D4—82no—
495D4—82no—
496D4—82no—
497D4—84no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—24no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—48no—
511C2×C4—48no—
512C2×C4—41no—
513C2×C4—44no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4C29×#12011yescharacteristic
524C2×C4C29×#12011yescharacteristic
525C2×C4C29×#12012yes—
526C2×C4C29×AGL(1,ℤ/8)12yes—
527C2×C4C22×D4×C2912yes—
528C8—44no—
529C22—21no—
530C22—21no—
531C22—22no—
532C22—42no—
533C22—41no—
534C22—41no—
535C22—44no—
536C22—44no—
537C22—44no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—88no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22C2×C29×#12011yescharacteristic
548C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
549C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
550C4—21no—
551C4—22no—
552C4—21no—
553C4—22no—
554C4—22no—
555C4—42no—
556C4—44no—
557C4—41no—
558C4—41no—
559C4—81no—
560C4—81no—
561C2—21no—
562C2—21no—
563C2—42no—
564C2—84no—
565C2—161no—
566C2C29×#300311yescharacteristic
567C2C29×#301811yescharacteristic
568C2C29×#302711yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
LCSG ▷ C22×C4 ▷ 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×#3449C2semidirect
2. C29×#3213C2semidirect
3. C29×#2610C2semidirect
4. C29×#1604C2semidirect
5. C29×#1601C2semidirect
6. C29×#1598C2semidirect
7. C29×#1595C2semidirect
8. C29×#1505C2semidirect
9. C29×#1464C2semidirect
19. C2×C29×#124C22semidirect
25. C29×#448C22semidirect
26. C29×#447C22semidirect
27. C29×#432C22semidirect
28. C29×#395C22semidirect
29. C29×#394C22semidirect
36. C29×#376C22semidirect
37. C29×#327C22semidirect
38. C29×#327C22semidirect
39. C29×#324C22semidirect
58. C29×C4⋊Q8D4semidirect
60. C29×#127D4semidirect
80. C4×D4×C29D4semidirect
182. #18332C29direct (N × H)
245. #3449C2×C29semidirect
246. #3213C2×C29semidirect
247. #2610C2×C29semidirect
248. #1604C2×C29semidirect
249. #1601C2×C29semidirect
250. #1598C2×C29semidirect
251. #1595C2×C29semidirect
252. #1505C2×C29semidirect
253. #1464C2×C29semidirect
295. C2×#124C22×C29semidirect
301. #448C22×C29semidirect
302. #447C22×C29semidirect
303. #432C22×C29semidirect
304. #395C22×C29semidirect
305. #394C22×C29semidirect
312. #376C22×C29semidirect
313. #327C22×C29semidirect
314. #327C22×C29semidirect
315. #324C22×C29semidirect
342. C4⋊Q8D4×C29semidirect
344. #127D4×C29semidirect
364. C4×D4D4×C29semidirect
391. C29#18332direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34492
C29×#32132
C29×#26102
C29×#16042
C29×#16012
C29×#15982
C29×#15952
C29×#15052
C29×#14642
#1833229