Finite Group Databasebeta

← C29×#19032 #20313932

Subgroups — C29×#19032 #20313932

Order 7424.

896 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×#3561C211yesmaximal, characteristic
2C29×#3218C211yesmaximal, characteristic, complemented
3C29×#3165C211yesmaximal, characteristic, complemented
4C2×C29×#489C211yesmaximal, characteristic, complemented
5C29×#1664C214yesmaximal, complemented
6C29×#1661C214yesmaximal, complemented
7C29×#1531C211yesmaximal, characteristic, complemented
8C29×#1527C211yesmaximal, characteristic, complemented
9C29×#1524C211yesmaximal, characteristic, complemented
10C29×#563C2212yes—
11C29×#562C2212yes—
12C29×#556—21no—
13C29×#551—22no—
14D4×Q8×C29—21no—
15C29×#548—21no—
16C29×#546—21no—
17C29×#543—21no—
18C29×#542—21no—
19C29×#542—22no—
20C29×#538—21no—
21C29×#536—21no—
22C29×#533C2211yescharacteristic
23C2×C29×C4⋊Q8C2211yescharacteristic
24C29×#529C2211yescharacteristic
25C2×C29×#124C2211yescharacteristic
26C29×#501C2214yescomplemented
27C29×#500—21no—
28C29×#498—21no—
29C29×#497C2212yescomplemented
30C29×#491C2212yescomplemented
31C29×#489—22no—
32C29×#489C2214yes—
33C29×#462—21no—
34C29×#461—21no—
35C29×#451—21no—
36C29×#448—21no—
37C29×#432C2211yescharacteristic
38C29×#428—22no—
39C2×C29×#103—21no—
40C2×C29×#102—21no—
41C4×M16×C29C2211yescharacteristic
42C2×C29×#97C2211yescharacteristic
43C29×#330C2214yescomplemented
44C29×#330C2212yescomplemented
45C29×#329C2214yes—
46C29×#329C2212yescomplemented
47C2×#41×C29—21no—
48C22×Q8×C29—21no—
49C22×Q8×C29—21no—
50C22×Q8×C29D411yescharacteristic
51C22×D4×C29D411yescharacteristic
52C2×Q16×C29—22no—
53C2×SD16×C29—22no—
54C2×M16×C29—21no—
55C22×C8×C29—21no—
56C29×C4⋊Q8—21no—
57C29×C4⋊Q8—22no—
58C29×C4⋊Q8—21no—
59C29×C4⋊Q8—21no—
60C29×C4⋊Q8—21no—
61C29×C4⋊Q8D411yescharacteristic
62C29×C4⋊Q8D411yescharacteristic
63C29×C4⋊Q8C2312yes—
64C29×#126—22no—
65C29×#126—22no—
66C29×#126—22no—
67C29×#126—21no—
68C29×#125C2311yescharacteristic
69C29×#125C2312yes—
70C29×#124—21no—
71C29×#124—22no—
72C29×#124—22no—
73C29×#124—21no—
74C29×#124—21no—
75C29×#124D412yes—
76C29×#124C2312yes—
77C29×#124C2311yescharacteristic
78C29×#123—22no—
79C29×#123—22no—
80C29×#123—21no—
81C29×#123—22no—
82C29×#123—22no—
83C29×C22⋊Q8—22no—
84C29×C22⋊Q8—22no—
85C29×C22⋊Q8—21no—
86C29×C22⋊Q8—22no—
87C29×C22⋊Q8—22no—
88C29×C22⋊Q8—22no—
89C29×C22⋊Q8—21no—
90C29×C22⋊Q8—21no—
91C29×C22⋊Q8—22no—
92C29×C22⋊Q8—22no—
93C29×C22⋊Q8D411yescharacteristic
94C29×#121—21no—
95C29×#121—22no—
96C29×#121—22no—
97C29×#121D411yescharacteristic
98C29×#120—22no—
99C4×Q8×C29—21no—
100C4×Q8×C29—21no—
101C4×Q8×C29—21no—
102C4×Q8×C29D411yescharacteristic
103C4×D4×C29—22no—
104C4×D4×C29—21no—
105C4×D4×C29—22no—
106C4×D4×C29—21no—
107C4×D4×C29D411yescharacteristic
108C29×#117—22no—
109C29×#117—21no—
110C29×#117D412yes—
111C2×C4⋊C4×C29—21no—
112C2×C4⋊C4×C29—21no—
113C2×C22⋊C4×C29—22no—
114C2×C22⋊C4×C29—21no—
115C2×C22⋊C4×C29—21no—
116C2×C42×C29C2311yescharacteristic
117C29×#107—24no—
118C29×#106—24no—
119C29×C4⋊C8—21no—
120C29×#103—24no—
121C29×#103—22no—
122C29×#103—22no—
123C29×#102—24no—
124C29×C22⋊C8—21no—
125C29×#97—21no—
126C29×#97C2312yes—
127C29×#97C2312yes—
128C29×#97C2312yes—
129C4×C8×C29—21no—
130C24×C29—21no—
131#41×C29—82no—
132C2×Q8×C29—22no—
133C2×Q8×C29—21no—
134C2×Q8×C29—21no—
135C2×Q8×C29—21no—
136C2×Q8×C29—22no—
137C2×Q8×C29—42no—
138C2×Q8×C29—41no—
139C2×Q8×C29—82no—
140C2×Q8×C29—82no—
141C2×Q8×C29C2×D411yescharacteristic
142C2×Q8×C29C2×D412yes—
143C2×D4×C29—21no—
144C2×D4×C29—22no—
145C2×D4×C29—22no—
146C2×D4×C29—21no—
147C2×D4×C29—42no—
148C2×D4×C29C2×D411yescharacteristic
149C2×D4×C29C2×D412yes—
150C22×C4×C29—22no—
151C22×C4×C29—22no—
152C22×C4×C29—22no—
153C22×C4×C29—21no—
154C22×C4×C29—21no—
155C22×C4×C29—41no—
156C22×C4×C29C2×D411yescharacteristic
157C22×C4×C29C2×D411yescharacteristic
158C22×C4×C29C2×D411yescharacteristic
159Q16×C29—82no—
160SD16×C29—82no—
161M16×C29—24no—
162C2×C8×C29—22no—
163C2×C8×C29—22no—
164C2×C8×C29—22no—
165C2×C8×C29—42no—
166C4⋊C4×C29—22no—
167C4⋊C4×C29—22no—
168C4⋊C4×C29—22no—
169C4⋊C4×C29—22no—
170C4⋊C4×C29—21no—
171C4⋊C4×C29—21no—
172C4⋊C4×C29—21no—
173C4⋊C4×C29—21no—
174C4⋊C4×C29—21no—
175C4⋊C4×C29—21no—
176C4⋊C4×C29—22no—
177C4⋊C4×C29—22no—
178C4⋊C4×C29—22no—
179C4⋊C4×C29—22no—
180C4⋊C4×C29—41no—
181C4⋊C4×C29—41no—
182C4⋊C4×C29C2×D412yes—
183C4⋊C4×C29C2×D412yes—
184C4⋊C4×C29C2×D411yescharacteristic
185C4⋊C4×C29C2×D411yescharacteristic
186C22⋊C4×C29—22no—
187C22⋊C4×C29—22no—
188C22⋊C4×C29—22no—
189C22⋊C4×C29—22no—
190C22⋊C4×C29—22no—
191C22⋊C4×C29—21no—
192C22⋊C4×C29—22no—
193C22⋊C4×C29—22no—
194C22⋊C4×C29—22no—
195C22⋊C4×C29—21no—
196C22⋊C4×C29—21no—
197C22⋊C4×C29—22no—
198C22⋊C4×C29—22no—
199C22⋊C4×C29—21no—
200C22⋊C4×C29—21no—
201C42×C29—22no—
202C42×C29—22no—
203C42×C29—21no—
204C42×C29C2×D411yescharacteristic
205C42×C29C2×D411yescharacteristic
206C42×C29C2×D411yescharacteristic
207C42×C29C2411yescharacteristic
208#19032C2911yesmaximal, characteristic, direct product factor, Sylow
209C23×C29—22no—
210C23×C29—21no—
211C23×C29—42no—
212C23×C29—81no—
213C23×C29—81no—
214C23×C29#12011yescharacteristic
215Q8×C29—41no—
216Q8×C29—42no—
217Q8×C29—42no—
218Q8×C29—42no—
219Q8×C29—42no—
220Q8×C29—42no—
221Q8×C29—81no—
222Q8×C29—82no—
223Q8×C29—82no—
224D4×C29—41no—
225D4×C29—42no—
226D4×C29—42no—
227D4×C29—42no—
228D4×C29—82no—
229D4×C29—82no—
230C2×C4×C29—22no—
231C2×C4×C29—22no—
232C2×C4×C29—21no—
233C2×C4×C29—22no—
234C2×C4×C29—21no—
235C2×C4×C29—22no—
236C2×C4×C29—22no—
237C2×C4×C29—21no—
238C2×C4×C29—41no—
239C2×C4×C29—42no—
240C2×C4×C29—42no—
241C2×C4×C29—81no—
242C2×C4×C29—82no—
243C2×C4×C29—82no—
244C2×C4×C29—82no—
245C2×C4×C29—82no—
246C2×C4×C29#12011yescharacteristic
247C2×C4×C29#12011yescharacteristic
248C2×C4×C29#12011yescharacteristic
249C2×C4×C29C22×D411yescharacteristic
250C2×C4×C29C22×D411yescharacteristic
251C2×C4×C29C22×D411yescharacteristic
252C8×C29—24no—
253C8×C29—42no—
254C8×C29—42no—
255#3561C2×C2911yescharacteristic
256#3218C2×C2911yescharacteristic, complemented
257#3165C2×C2911yescharacteristic, complemented
258C2×#489C2×C2911yescharacteristic, complemented
259#1664C2×C2914yescomplemented
260#1661C2×C2914yescomplemented
261#1531C2×C2911yescharacteristic, complemented
262#1527C2×C2911yescharacteristic, complemented
263#1524C2×C2911yescharacteristic, complemented
264C22×C29—21no—
265C22×C29—21no—
266C22×C29—41no—
267C22×C29—42no—
268C22×C29—41no—
269C22×C29—42no—
270C22×C29—42no—
271C22×C29—41no—
272C22×C29—162no—
273C22×C29#45612yes—
274C22×C29C2×#12011yescharacteristic
275C4×C29—21no—
276C4×C29—21no—
277C4×C29—21no—
278C4×C29—21no—
279C4×C29—21no—
280C4×C29—41no—
281C4×C29—42no—
282C4×C29—42no—
283C4×C29—41no—
284C4×C29—41no—
285C4×C29—42no—
286C4×C29—82no—
287C4×C29#45512yes—
288#563C22×C2912yes—
289#562C22×C2912yes—
290#556—21no—
291#551—22no—
292D4×Q8—21no—
293#548—21no—
294#546—21no—
295#543—21no—
296#542—21no—
297#542—22no—
298#538—21no—
299#536—21no—
300#533C22×C2911yescharacteristic
301C2×C4⋊Q8C22×C2911yescharacteristic
302#529C22×C2911yescharacteristic
303C2×#124C22×C2911yescharacteristic
304#501C22×C2914yescomplemented
305#500—21no—
306#498—21no—
307#497C22×C2912yescomplemented
308#491C22×C2912yescomplemented
309#489—22no—
310#489C22×C2914yes—
311#462—21no—
312#461—21no—
313#451—21no—
314#448—21no—
315#432C22×C2911yescharacteristic
316#428—22no—
317C2×#103—21no—
318C2×#102—21no—
319C4×M16C22×C2911yescharacteristic
320C2×#97C22×C2911yescharacteristic
321#330C22×C2914yescomplemented
322#330C22×C2912yescomplemented
323#329C22×C2914yes—
324#329C22×C2912yescomplemented
325C2×C29—22no—
326C2×C29—81no—
327C2×C29—82no—
328C2×C29C2×#45511yescharacteristic
329C2×C29C2×#45611yescharacteristic
330C2×C29#302111yescharacteristic
331C2×#41—21no—
332C22×Q8—21no—
333C22×Q8—21no—
334C22×Q8D4×C2911yescharacteristic
335C22×D4D4×C2911yescharacteristic
336C2×Q16—22no—
337C2×SD16—22no—
338C2×M16—21no—
339C22×C8—21no—
340C4⋊Q8—21no—
341C4⋊Q8—22no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8D4×C2911yescharacteristic
346C4⋊Q8D4×C2911yescharacteristic
347C4⋊Q8C23×C2912yes—
348#126—22no—
349#126—22no—
350#126—22no—
351#126—21no—
352#125C23×C2911yescharacteristic
353#125C23×C2912yes—
354#124—21no—
355#124—22no—
356#124—22no—
357#124—21no—
358#124—21no—
359#124D4×C2912yes—
360#124C23×C2912yes—
361#124C23×C2911yescharacteristic
362#123—22no—
363#123—22no—
364#123—21no—
365#123—22no—
366#123—22no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8—21no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377C22⋊Q8D4×C2911yescharacteristic
378#121—21no—
379#121—22no—
380#121—22no—
381#121D4×C2911yescharacteristic
382#120—22no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8D4×C2911yescharacteristic
387C4×D4—22no—
388C4×D4—21no—
389C4×D4—22no—
390C4×D4—21no—
391C4×D4D4×C2911yescharacteristic
392#117—22no—
393#117—21no—
394#117D4×C2912yes—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C42C23×C2911yescharacteristic
401#107—24no—
402#106—24no—
403C4⋊C8—21no—
404#103—24no—
405#103—22no—
406#103—22no—
407#102—24no—
408C22⋊C8—21no—
409#97—21no—
410#97C23×C2912yes—
411#97C23×C2912yes—
412#97C23×C2912yes—
413C4×C8—21no—
414C29#1903211yescharacteristic, direct product factor, Sylow
415C24—21no—
416#41—82no—
417C2×Q8—22no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—22no—
422C2×Q8—42no—
423C2×Q8—41no—
424C2×Q8—82no—
425C2×Q8—82no—
426C2×Q8C2×D4×C2912yes—
427C2×Q8C2×D4×C2911yescharacteristic
428C2×D4—21no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4—42no—
433C2×D4C2×D4×C2912yes—
434C2×D4C2×D4×C2911yescharacteristic
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—41no—
441C22×C4C2×D4×C2911yescharacteristic
442C22×C4C2×D4×C2911yescharacteristic
443C22×C4C2×D4×C2911yescharacteristic
444Q16—82no—
445SD16—82no—
446M16—24no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—42no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4C2×D4×C2911yescharacteristic
468C4⋊C4C2×D4×C2911yescharacteristic
469C4⋊C4C2×D4×C2912yes—
470C4⋊C4C2×D4×C2912yes—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—21no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C42—22no—
487C42—22no—
488C42—21no—
489C42C2×D4×C2911yescharacteristic
490C42C2×D4×C2911yescharacteristic
491C42C2×D4×C2911yescharacteristic
492C42C24×C2911yescharacteristic
493C23—22no—
494C23—21no—
495C23—42no—
496C23—81no—
497C23—81no—
498C23C29×#12011yescharacteristic
499Q8—41no—
500Q8—42no—
501Q8—42no—
502Q8—42no—
503Q8—42no—
504Q8—42no—
505Q8—81no—
506Q8—82no—
507Q8—82no—
508D4—41no—
509D4—42no—
510D4—42no—
511D4—42no—
512D4—82no—
513D4—82no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—81no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4C29×#12011yescharacteristic
531C2×C4C29×#12011yescharacteristic
532C2×C4C29×#12011yescharacteristic
533C2×C4C22×D4×C2911yescharacteristic
534C2×C4C22×D4×C2911yescharacteristic
535C2×C4C22×D4×C2911yescharacteristic
536C8—24no—
537C8—42no—
538C8—42no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—42no—
543C22—41no—
544C22—42no—
545C22—42no—
546C22—41no—
547C22—162no—
548C22C29×#45612yes—
549C22C2×C29×#12011yescharacteristic
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—41no—
559C4—41no—
560C4—42no—
561C4—82no—
562C4C29×#45512yes—
563C2—22no—
564C2—82no—
565C2—81no—
566C2C2×C29×#45511yescharacteristic
567C2C2×C29×#45611yescharacteristic
568C2C29×#302111yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3561C2
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
2. C29×#3218C2semidirect
3. C29×#3165C2semidirect
4. C2×C29×#489C2semidirect
5. C29×#1664C2semidirect
6. C29×#1661C2semidirect
7. C29×#1531C2semidirect
8. C29×#1527C2semidirect
9. C29×#1524C2semidirect
26. C29×#501C22semidirect
29. C29×#497C22semidirect
30. C29×#491C22semidirect
43. C29×#330C22semidirect
44. C29×#330C22semidirect
46. C29×#329C22semidirect
208. #19032C29direct (N × H)
256. #3218C2×C29semidirect
257. #3165C2×C29semidirect
258. C2×#489C2×C29semidirect
259. #1664C2×C29semidirect
260. #1661C2×C29semidirect
261. #1531C2×C29semidirect
262. #1527C2×C29semidirect
263. #1524C2×C29semidirect
304. #501C22×C29semidirect
307. #497C22×C29semidirect
308. #491C22×C29semidirect
321. #330C22×C29semidirect
322. #330C22×C29semidirect
324. #329C22×C29semidirect
414. C29#19032direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35612
C29×#32182
C29×#31652
C2×C29×#4892
C29×#16642
C29×#16612
C29×#15312
C29×#15272
C29×#15242
#1903229