Finite Group Databasebeta

← C29×#18343 #20313243

Subgroups — C29×#18343 #20313243

Order 7424.

1034 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3459C211yesmaximal, characteristic
2C29×#3239C212yesmaximal, complemented
3C29×#2542C211yesmaximal, characteristic, complemented
4C29×#1618C214yesmaximal, complemented
5C29×#1614C212yesmaximal, complemented
6C29×#1613C212yesmaximal, complemented
7C29×#1509C212yesmaximal, complemented
8C29×#1466C211yesmaximal, characteristic, complemented
9C29×#543C2211yescharacteristic
10C29×#539—22no—
11C29×#539—21no—
12C29×#538—22no—
13C29×#538C2212yes—
14C29×#534—21no—
15C29×#534C2211yescharacteristic
16C2×C29×C4⋊Q8C2211yescharacteristic, complemented
17C29×#529—22no—
18C29×#529C2212yes—
19C29×#525—21no—
20C29×#525—22no—
21C2×C29×C22⋊Q8—21no—
22C2×C29×C22⋊Q8—21no—
23C2×C4×D4×C29—21no—
24C2×C4×D4×C29C2211yescharacteristic
25C29×#501—22no—
26C29×#489—22no—
27C29×#484C2214yescomplemented
28C29×#481C2214yes—
29C29×#475—22no—
30C29×#474—22no—
31C29×#432C2212yescomplemented
32C29×#399C2212yes—
33C29×#399C2212yescomplemented
34C29×#390—21no—
35C29×#384—21no—
36C4×C4⋊C4×C29C2211yescharacteristic, complemented
37C29×#328C2214yescomplemented
38C29×#327C2214yes—
39C29×#323C2212yes—
40C29×#323C2212yescomplemented
41C2×#41×C29—21no—
42C22×Q8×C29—21no—
43C22×D4×C29—21no—
44C22×D4×C29D411yescharacteristic
45C23×C4×C29—21no—
46C23×C4×C29D411yescharacteristic
47C23×C4×C29D411yescharacteristic
48C29×C4⋊Q8—22no—
49C29×C4⋊Q8—22no—
50C29×#126—22no—
51C29×#126—22no—
52C29×#126—22no—
53C29×#125—22no—
54C29×#125D412yes—
55C29×#124—22no—
56C29×#124D412yes—
57C29×#123—22no—
58C29×#123—22no—
59C29×#123—22no—
60C29×#123—22no—
61C29×#123—22no—
62C29×#123—22no—
63C29×C22⋊Q8—21no—
64C29×C22⋊Q8—22no—
65C29×C22⋊Q8—22no—
66C29×C22⋊Q8—21no—
67C29×C22⋊Q8—22no—
68C29×C22⋊Q8—44no—
69C29×C22⋊Q8—44no—
70C29×C22⋊Q8C2312yes—
71C29×#121—22no—
72C29×#121—21no—
73C29×#121—22no—
74C29×#121—22no—
75C29×#121—21no—
76C29×#121C2312yes—
77C29×#120—22no—
78C29×#120—22no—
79C29×#120—22no—
80C4×Q8×C29D412yes—
81C4×D4×C29—22no—
82C4×D4×C29—22no—
83C4×D4×C29—22no—
84C4×D4×C29—22no—
85C4×D4×C29—22no—
86C4×D4×C29—22no—
87C4×D4×C29—22no—
88C4×D4×C29D412yes—
89C29×#117—21no—
90C29×#117—22no—
91C2×C4⋊C4×C29—21no—
92C2×C4⋊C4×C29—21no—
93C2×C4⋊C4×C29—22no—
94C2×C4⋊C4×C29—22no—
95C2×C4⋊C4×C29—21no—
96C2×C4⋊C4×C29D411yescharacteristic
97C2×C4⋊C4×C29C2312yes—
98C2×C22⋊C4×C29—21no—
99C2×C22⋊C4×C29—21no—
100C2×C22⋊C4×C29—22no—
101C2×C22⋊C4×C29—22no—
102C2×C22⋊C4×C29C2311yescharacteristic
103C2×C22⋊C4×C29C2311yescharacteristic
104C2×C42×C29—21no—
105C2×C42×C29—21no—
106C2×C42×C29C2311yescharacteristic
107C29×#107—24no—
108C29×#106—24no—
109C29×C4⋊C8—22no—
110C29×#103—24no—
111C29×#102—24no—
112C29×C22⋊C8C2314yes—
113C29×#97—22no—
114C29×#95C2312yes—
115C24×C29—21no—
116C24×C29C2×D411yescharacteristic
117C24×C29C2×D411yescharacteristic
118#41×C29—82no—
119C2×Q8×C29—21no—
120C2×Q8×C29—42no—
121C2×Q8×C29—42no—
122C2×Q8×C29—41no—
123C2×Q8×C29—41no—
124C2×Q8×C29C2×D412yes—
125C2×D4×C29—22no—
126C2×D4×C29—22no—
127C2×D4×C29—22no—
128C2×D4×C29—22no—
129C2×D4×C29—21no—
130C2×D4×C29—22no—
131C2×D4×C29—22no—
132C2×D4×C29—41no—
133C2×D4×C29—42no—
134C2×D4×C29—42no—
135C2×D4×C29C2×D412yes—
136C22×C4×C29—21no—
137C22×C4×C29—22no—
138C22×C4×C29—21no—
139C22×C4×C29—21no—
140C22×C4×C29—22no—
141C22×C4×C29—21no—
142C22×C4×C29—21no—
143C22×C4×C29—22no—
144C22×C4×C29—21no—
145C22×C4×C29—21no—
146C22×C4×C29—22no—
147C22×C4×C29—42no—
148C22×C4×C29—42no—
149C22×C4×C29—82no—
150C22×C4×C29C2×D411yescharacteristic
151C22×C4×C29C2×D411yescharacteristic
152C22×C4×C29C2×D411yescharacteristic
153C22×C4×C29C2×D411yescharacteristic
154C22×C4×C29C2411yescharacteristic
155C2×C8×C29—24no—
156C4⋊C4×C29—22no—
157C4⋊C4×C29—24no—
158C4⋊C4×C29—21no—
159C4⋊C4×C29—21no—
160C4⋊C4×C29—22no—
161C4⋊C4×C29—22no—
162C4⋊C4×C29—22no—
163C4⋊C4×C29—22no—
164C4⋊C4×C29—22no—
165C4⋊C4×C29—22no—
166C4⋊C4×C29—24no—
167C4⋊C4×C29—44no—
168C4⋊C4×C29—44no—
169C4⋊C4×C29—42no—
170C4⋊C4×C29C2×D412yes—
171C4⋊C4×C29C2×D412yes—
172C22⋊C4×C29—22no—
173C22⋊C4×C29—22no—
174C22⋊C4×C29—22no—
175C22⋊C4×C29—22no—
176C22⋊C4×C29—22no—
177C22⋊C4×C29—22no—
178C22⋊C4×C29—22no—
179C22⋊C4×C29—22no—
180C22⋊C4×C29—22no—
181C22⋊C4×C29—22no—
182C22⋊C4×C29—22no—
183C22⋊C4×C29—22no—
184C22⋊C4×C29—44no—
185C22⋊C4×C29—44no—
186C42×C29—22no—
187C42×C29—22no—
188C42×C29—42no—
189C42×C29C2×D412yes—
190C42×C29C2×D412yes—
191#18343C2911yesmaximal, characteristic, direct product factor, Sylow
192C23×C29—21no—
193C23×C29—21no—
194C23×C29—21no—
195C23×C29—22no—
196C23×C29—21no—
197C23×C29—21no—
198C23×C29—41no—
199C23×C29—41no—
200C23×C29—41no—
201C23×C29—41no—
202C23×C29—42no—
203C23×C29—81no—
204C23×C29—81no—
205C23×C29#13712yes—
206C23×C29C22×D411yescharacteristic
207Q8×C29—42no—
208Q8×C29—82no—
209Q8×C29—81no—
210Q8×C29—82no—
211D4×C29—44no—
212D4×C29—42no—
213D4×C29—44no—
214D4×C29—42no—
215D4×C29—42no—
216D4×C29—82no—
217D4×C29—81no—
218D4×C29—82no—
219C2×C4×C29—21no—
220C2×C4×C29—21no—
221C2×C4×C29—22no—
222C2×C4×C29—24no—
223C2×C4×C29—22no—
224C2×C4×C29—22no—
225C2×C4×C29—21no—
226C2×C4×C29—21no—
227C2×C4×C29—22no—
228C2×C4×C29—41no—
229C2×C4×C29—42no—
230C2×C4×C29—42no—
231C2×C4×C29—42no—
232C2×C4×C29—42no—
233C2×C4×C29—42no—
234C2×C4×C29—44no—
235C2×C4×C29—41no—
236C2×C4×C29—41no—
237C2×C4×C29—42no—
238C2×C4×C29—42no—
239C2×C4×C29—42no—
240C2×C4×C29—81no—
241C2×C4×C29—81no—
242C2×C4×C29—81no—
243C2×C4×C29—82no—
244C2×C4×C29—81no—
245C2×C4×C29#12012yes—
246C2×C4×C29#12011yescharacteristic
247C2×C4×C29#12011yescharacteristic
248C2×C4×C29C22×D412yes—
249C8×C29—44no—
250#3459C2×C2911yescharacteristic
251#3239C2×C2912yescomplemented
252#2542C2×C2911yescharacteristic, complemented
253#1618C2×C2914yescomplemented
254#1614C2×C2912yescomplemented
255#1613C2×C2912yescomplemented
256#1509C2×C2912yescomplemented
257#1466C2×C2911yescharacteristic, complemented
258C22×C29—21no—
259C22×C29—21no—
260C22×C29—22no—
261C22×C29—42no—
262C22×C29—42no—
263C22×C29—41no—
264C22×C29—41no—
265C22×C29—41no—
266C22×C29—42no—
267C22×C29—41no—
268C22×C29—42no—
269C22×C29—42no—
270C22×C29—41no—
271C22×C29—81no—
272C22×C29—81no—
273C22×C29—84no—
274C22×C29C2×#12011yescharacteristic
275C22×C29C2×#13711yescharacteristic
276C22×C29#57511yescharacteristic
277C4×C29—22no—
278C4×C29—21no—
279C4×C29—22no—
280C4×C29—44no—
281C4×C29—42no—
282C4×C29—41no—
283C4×C29—41no—
284C4×C29—42no—
285C4×C29—42no—
286C4×C29—82no—
287C4×C29#45312yes—
288#543C22×C2911yescharacteristic
289#539—22no—
290#539—21no—
291#538—22no—
292#538C22×C2912yes—
293#534—21no—
294#534C22×C2911yescharacteristic
295C2×C4⋊Q8C22×C2911yescharacteristic, complemented
296#529—22no—
297#529C22×C2912yes—
298#525—21no—
299#525—22no—
300C2×C22⋊Q8—21no—
301C2×C22⋊Q8—21no—
302C2×C4×D4—21no—
303C2×C4×D4C22×C2911yescharacteristic
304#501—22no—
305#489—22no—
306#484C22×C2914yescomplemented
307#481C22×C2914yes—
308#475—22no—
309#474—22no—
310#432C22×C2912yescomplemented
311#399C22×C2912yes—
312#399C22×C2912yescomplemented
313#390—21no—
314#384—21no—
315C4×C4⋊C4C22×C2911yescharacteristic, complemented
316#328C22×C2914yescomplemented
317#327C22×C2914yes—
318#323C22×C2912yes—
319#323C22×C2912yescomplemented
320C2×C29—21no—
321C2×C29—21no—
322C2×C29—42no—
323C2×C29—81no—
324C2×C29—82no—
325C2×C29#300711yescharacteristic
326C2×C29C2×#45311yescharacteristic
327C2×C29#302811yescharacteristic
328C2×#41—21no—
329C22×Q8—21no—
330C22×D4—21no—
331C22×D4D4×C2911yescharacteristic
332C23×C4—21no—
333C23×C4D4×C2911yescharacteristic
334C23×C4D4×C2911yescharacteristic
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337#126—22no—
338#126—22no—
339#126—22no—
340#125—22no—
341#125D4×C2912yes—
342#124—22no—
343#124D4×C2912yes—
344#123—22no—
345#123—22no—
346#123—22no—
347#123—22no—
348#123—22no—
349#123—22no—
350C22⋊Q8—21no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—21no—
354C22⋊Q8—22no—
355C22⋊Q8—44no—
356C22⋊Q8—44no—
357C22⋊Q8C23×C2912yes—
358#121—22no—
359#121—21no—
360#121—22no—
361#121—22no—
362#121—21no—
363#121C23×C2912yes—
364#120—22no—
365#120—22no—
366#120—22no—
367C4×Q8D4×C2912yes—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4—22no—
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4D4×C2912yes—
376#117—21no—
377#117—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4D4×C2911yescharacteristic
384C2×C4⋊C4C23×C2912yes—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4C23×C2911yescharacteristic
390C2×C22⋊C4C23×C2911yescharacteristic
391C2×C42—21no—
392C2×C42—21no—
393C2×C42C23×C2911yescharacteristic
394#107—24no—
395#106—24no—
396C4⋊C8—22no—
397#103—24no—
398#102—24no—
399C22⋊C8C23×C2914yes—
400#97—22no—
401#95C23×C2912yes—
402C29#1834311yescharacteristic, direct product factor, Sylow
403C24—21no—
404C24C2×D4×C2911yescharacteristic
405C24C2×D4×C2911yescharacteristic
406#41—82no—
407C2×Q8—21no—
408C2×Q8—42no—
409C2×Q8—42no—
410C2×Q8—41no—
411C2×Q8—41no—
412C2×Q8C2×D4×C2912yes—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—41no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4C2×D4×C2912yes—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—82no—
438C22×C4C2×D4×C2911yescharacteristic
439C22×C4C2×D4×C2911yescharacteristic
440C22×C4C2×D4×C2911yescharacteristic
441C22×C4C2×D4×C2911yescharacteristic
442C22×C4C24×C2911yescharacteristic
443C2×C8—24no—
444C4⋊C4—22no—
445C4⋊C4—24no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—24no—
455C4⋊C4—44no—
456C4⋊C4—44no—
457C4⋊C4—42no—
458C4⋊C4C2×D4×C2912yes—
459C4⋊C4C2×D4×C2912yes—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—44no—
473C22⋊C4—44no—
474C42—22no—
475C42—22no—
476C42—42no—
477C42C2×D4×C2912yes—
478C42C2×D4×C2912yes—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—22no—
483C23—21no—
484C23—21no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—42no—
490C23—81no—
491C23—81no—
492C23C29×#13712yes—
493C23C22×D4×C2911yescharacteristic
494Q8—42no—
495Q8—82no—
496Q8—81no—
497Q8—82no—
498D4—44no—
499D4—42no—
500D4—44no—
501D4—42no—
502D4—42no—
503D4—81no—
504D4—82no—
505D4—82no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—44no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—81no—
528C2×C4—81no—
529C2×C4—82no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4C29×#12012yes—
533C2×C4C29×#12011yescharacteristic
534C2×C4C29×#12011yescharacteristic
535C2×C4C22×D4×C2912yes—
536C8—44no—
537C22—21no—
538C22—21no—
539C22—22no—
540C22—42no—
541C22—42no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—42no—
546C22—41no—
547C22—42no—
548C22—42no—
549C22—41no—
550C22—81no—
551C22—81no—
552C22—84no—
553C22C2×C29×#12011yescharacteristic
554C22C2×C29×#13711yescharacteristic
555C22C29×#57511yescharacteristic
556C4—22no—
557C4—21no—
558C4—22no—
559C4—44no—
560C4—42no—
561C4—41no—
562C4—41no—
563C4—42no—
564C4—42no—
565C4—82no—
566C4C29×#45312yes—
567C2—21no—
568C2—21no—
569C2—42no—
570C2—81no—
571C2—82no—
572C2C29×#300711yescharacteristic
573C2C2×C29×#45311yescharacteristic
574C2C29×#302811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#3459C2
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
2. C29×#3239C2semidirect
3. C29×#2542C2semidirect
4. C29×#1618C2semidirect
5. C29×#1614C2semidirect
6. C29×#1613C2semidirect
7. C29×#1509C2semidirect
8. C29×#1466C2semidirect
16. C2×C29×C4⋊Q8C22semidirect
27. C29×#484C22semidirect
31. C29×#432C22semidirect
33. C29×#399C22semidirect
36. C4×C4⋊C4×C29C22semidirect
37. C29×#328C22semidirect
40. C29×#323C22semidirect
191. #18343C29direct (N × H)
251. #3239C2×C29semidirect
252. #2542C2×C29semidirect
253. #1618C2×C29semidirect
254. #1614C2×C29semidirect
255. #1613C2×C29semidirect
256. #1509C2×C29semidirect
257. #1466C2×C29semidirect
295. C2×C4⋊Q8C22×C29semidirect
306. #484C22×C29semidirect
310. #432C22×C29semidirect
312. #399C22×C29semidirect
315. C4×C4⋊C4C22×C29semidirect
316. #328C22×C29semidirect
319. #323C22×C29semidirect
402. C29#18343direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34592
C29×#32392
C29×#25422
C29×#16182
C29×#16142
C29×#16132
C29×#15092
C29×#14662
#1834329