Finite Group Databasebeta

← C29×#19382 #20314282

Subgroups — C29×#19382 #20314282

Order 7424.

594 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×#3251C211yesmaximal, characteristic
2C29×#3238C211yesmaximal, characteristic, complemented
3C29×#3141C211yesmaximal, characteristic, complemented
4C29×#2969C211yesmaximal, characteristic, complemented
5C29×#1704C211yesmaximal, characteristic, complemented
6C29×#1703C211yesmaximal, characteristic, complemented
7C29×#1698C211yesmaximal, characteristic, complemented
8C29×#1697C211yesmaximal, characteristic, complemented
9C29×#1684C211yesmaximal, characteristic, complemented
10C29×#1683C211yesmaximal, characteristic, complemented
11C29×#1678C211yesmaximal, characteristic, complemented
12C29×#1677C211yesmaximal, characteristic, complemented
13C29×#1569C211yesmaximal, characteristic, complemented
14C29×#1553C211yesmaximal, characteristic, complemented
15C29×#1548C211yesmaximal, characteristic, complemented
16C29×#532C2211yescharacteristic
17C2×C29×C4⋊Q8C2211yescharacteristic
18C29×#529C2211yescharacteristic
19C29×#501—21no—
20C29×#489—21no—
21C29×#489—21no—
22C29×#489—21no—
23C29×#487C2211yescharacteristic
24C29×#487C2211yescharacteristic
25C29×#486C2211yescharacteristic
26C29×#486C2211yescharacteristic
27C29×#483—21no—
28C29×#480—21no—
29C29×#478—21no—
30C29×#477C2211yescharacteristic
31C29×#477C2211yescharacteristic
32C29×#476C2211yescharacteristic
33C29×#476C2211yescharacteristic
34C29×#475C2211yescharacteristic
35C29×#474C2211yescharacteristic
36C29×#469—21no—
37C29×#468—21no—
38C29×#463—21no—
39C29×#460C2211yescharacteristic
40C29×#459C2211yescharacteristic
41C29×#446C2211yescharacteristic
42C8×Q8×C29C2211yescharacteristic
43C29×#436—21no—
44C29×#436C2211yescharacteristic
45C29×#435—21no—
46C8×D4×C29C2211yescharacteristic
47C29×#433—21no—
48C29×#432C2211yescharacteristic
49C29×#431C2211yescharacteristic
50C29×#423C2211yescharacteristic
51C29×#417—21no—
52C29×#417—21no—
53C29×#405—21no—
54C4×M16×C29C2211yescharacteristic
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#333C2211yescharacteristic
62C29×#333C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#331C2211yescharacteristic
66C29×#331C2211yescharacteristic
67C2×#41×C29—21no—
68C22×Q8×C29—21no—
69C2×SD16×C29—21no—
70C2×D8×C29—21no—
71C2×M16×C29—21no—
72C2×M16×C29—21no—
73C2×M16×C29D411yescharacteristic
74C2×M16×C29D411yescharacteristic
75C22×C8×C29—21no—
76C29×C4⋊Q8—21no—
77C29×C4⋊Q8—21no—
78C29×C4⋊Q8—21no—
79C29×C4⋊Q8C2311yescharacteristic
80C29×C4⋊Q8C2311yescharacteristic
81C29×C4⋊Q8C2311yescharacteristic
82C29×#127C2311yescharacteristic
83C29×#126—21no—
84C29×#125D411yescharacteristic
85C29×#124—21no—
86C29×#124D411yescharacteristic
87C29×#123—21no—
88C29×C22⋊Q8D411yescharacteristic
89C29×#121—21no—
90C29×#121—21no—
91C29×#121D411yescharacteristic
92C4×Q8×C29C2311yescharacteristic
93C4×D4×C29—21no—
94C4×D4×C29—21no—
95C4×D4×C29—21no—
96C4×D4×C29C2311yescharacteristic
97C29×#117—21no—
98C2×C4⋊C4×C29—21no—
99C2×C4⋊C4×C29—21no—
100C2×C42×C29C2311yescharacteristic
101C29×#107—21no—
102C29×#107—21no—
103C29×#107—21no—
104C29×#106—21no—
105C29×#106—21no—
106C29×#106—21no—
107C29×C4⋊C8—21no—
108C29×C4⋊C8—21no—
109C29×C4⋊C8—21no—
110C29×C4⋊C8C2311yescharacteristic
111C29×C4⋊C8C2311yescharacteristic
112C29×C4⋊C8C2311yescharacteristic
113C29×C4⋊C8C2311yescharacteristic
114C29×C4⋊C8C2311yescharacteristic
115C29×C4⋊C8C2311yescharacteristic
116C29×#103—21no—
117C29×#103—21no—
118C29×#103—21no—
119C29×#103—21no—
120C29×#103—21no—
121C29×#103—21no—
122C29×#103—21no—
123C29×#102—21no—
124C29×#102—21no—
125C29×#102—21no—
126C29×#102—21no—
127C29×#102—21no—
128C29×#102—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×#97D411yescharacteristic
139C29×#97D411yescharacteristic
140C4×C8×C29—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144#41×C29—42no—
145#41×C29—42no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—41no—
150C2×Q8×C29—82no—
151C2×Q8×C29C2×D411yescharacteristic
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—41no—
157C2×D4×C29C2×D411yescharacteristic
158C22×C4×C29—21no—
159C22×C4×C29—41no—
160C22×C4×C29—41no—
161C22×C4×C29C2×D411yescharacteristic
162C22×C4×C29C2×D411yescharacteristic
163C22×C4×C29#4111yescharacteristic
164SD16×C29—81no—
165D8×C29—81no—
166M16×C29—41no—
167M16×C29—41no—
168M16×C29—42no—
169M16×C29—81no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C2×C8×C29—21no—
173C2×C8×C29—21no—
174C2×C8×C29—21no—
175C2×C8×C29—21no—
176C2×C8×C29—42no—
177C2×C8×C29C2×D411yescharacteristic
178C2×C8×C29C2×D411yescharacteristic
179C2×C8×C29C2×D411yescharacteristic
180C2×C8×C29C2×D411yescharacteristic
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—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—41no—
192C4⋊C4×C29—41no—
193C4⋊C4×C29C2×D411yescharacteristic
194C4⋊C4×C29C2×D411yescharacteristic
195C22⋊C4×C29—21no—
196C22⋊C4×C29—21no—
197C22⋊C4×C29—21no—
198C22⋊C4×C29—21no—
199C22⋊C4×C29—21no—
200C22⋊C4×C29—41no—
201C22⋊C4×C29—41no—
202C42×C29—21no—
203C42×C29C2×D411yescharacteristic
204C42×C29C2×D411yescharacteristic
205C42×C29#4111yescharacteristic
206C42×C29C2411yescharacteristic
207#19382C2911yesmaximal, characteristic, direct product factor, Sylow
208C23×C29—21no—
209C23×C29—41no—
210C23×C29#12111yescharacteristic
211Q8×C29—21no—
212Q8×C29—21no—
213Q8×C29—41no—
214Q8×C29—41no—
215Q8×C29—81no—
216Q8×C29—81no—
217Q8×C29—82no—
218D4×C29—21no—
219D4×C29—21no—
220D4×C29—41no—
221D4×C29—41no—
222D4×C29—41no—
223D4×C29—41no—
224D4×C29—81no—
225D4×C29—81no—
226D4×C29—82no—
227C2×C4×C29—21no—
228C2×C4×C29—21no—
229C2×C4×C29—21no—
230C2×C4×C29—21no—
231C2×C4×C29—21no—
232C2×C4×C29—21no—
233C2×C4×C29—21no—
234C2×C4×C29—41no—
235C2×C4×C29—41no—
236C2×C4×C29—41no—
237C2×C4×C29—41no—
238C2×C4×C29—41no—
239C2×C4×C29—41no—
240C2×C4×C29—82no—
241C2×C4×C29—82no—
242C2×C4×C29#12111yescharacteristic
243C2×C4×C29#12111yescharacteristic
244C2×C4×C29#12111yescharacteristic
245C2×C4×C29C22×D411yescharacteristic
246C2×C4×C29C22×D411yescharacteristic
247C2×C4×C29C2×#4111yescharacteristic
248C8×C29—21no—
249C8×C29—21no—
250C8×C29—21no—
251C8×C29—21no—
252C8×C29—41no—
253C8×C29—41no—
254C8×C29—41no—
255C8×C29—41no—
256C8×C29—41no—
257C8×C29—41no—
258#3251C2×C2911yescharacteristic
259#3238C2×C2911yescharacteristic, complemented
260#3141C2×C2911yescharacteristic, complemented
261#2969C2×C2911yescharacteristic, complemented
262#1704C2×C2911yescharacteristic, complemented
263#1703C2×C2911yescharacteristic, complemented
264#1698C2×C2911yescharacteristic, complemented
265#1697C2×C2911yescharacteristic, complemented
266#1684C2×C2911yescharacteristic, complemented
267#1683C2×C2911yescharacteristic, complemented
268#1678C2×C2911yescharacteristic, complemented
269#1677C2×C2911yescharacteristic, complemented
270#1569C2×C2911yescharacteristic, complemented
271#1553C2×C2911yescharacteristic, complemented
272#1548C2×C2911yescharacteristic, complemented
273C22×C29—21no—
274C22×C29—21no—
275C22×C29—21no—
276C22×C29—41no—
277C22×C29—41no—
278C22×C29—41no—
279C22×C29—81no—
280C22×C29—81no—
281C22×C29—81no—
282C22×C29C2×#12111yescharacteristic
283C4×C29—21no—
284C4×C29—21no—
285C4×C29—21no—
286C4×C29—21no—
287C4×C29—41no—
288C4×C29—41no—
289C4×C29—41no—
290C4×C29—81no—
291C4×C29—81no—
292C4×C29—81no—
293C4×C29#57511yescharacteristic
294C4×C29#57511yescharacteristic
295C4×C29#57711yescharacteristic
296C4×C29#57811yescharacteristic
297#532C22×C2911yescharacteristic
298C2×C4⋊Q8C22×C2911yescharacteristic
299#529C22×C2911yescharacteristic
300#501—21no—
301#489—21no—
302#489—21no—
303#489—21no—
304#487C22×C2911yescharacteristic
305#487C22×C2911yescharacteristic
306#486C22×C2911yescharacteristic
307#486C22×C2911yescharacteristic
308#483—21no—
309#480—21no—
310#478—21no—
311#477C22×C2911yescharacteristic
312#477C22×C2911yescharacteristic
313#476C22×C2911yescharacteristic
314#476C22×C2911yescharacteristic
315#475C22×C2911yescharacteristic
316#474C22×C2911yescharacteristic
317#469—21no—
318#468—21no—
319#463—21no—
320#460C22×C2911yescharacteristic
321#459C22×C2911yescharacteristic
322#446C22×C2911yescharacteristic
323C8×Q8C22×C2911yescharacteristic
324#436—21no—
325#436C22×C2911yescharacteristic
326#435—21no—
327C8×D4C22×C2911yescharacteristic
328#433—21no—
329#432C22×C2911yescharacteristic
330#431C22×C2911yescharacteristic
331#423C22×C2911yescharacteristic
332#417—21no—
333#417—21no—
334#405—21no—
335C4×M16C22×C2911yescharacteristic
336#335C22×C2911yescharacteristic
337#335C22×C2911yescharacteristic
338#334C22×C2911yescharacteristic
339#334C22×C2911yescharacteristic
340#333C22×C2911yescharacteristic
341#333C22×C2911yescharacteristic
342#333C22×C2911yescharacteristic
343#333C22×C2911yescharacteristic
344#332C22×C2911yescharacteristic
345#332C22×C2911yescharacteristic
346#331C22×C2911yescharacteristic
347#331C22×C2911yescharacteristic
348C2×C29—41no—
349C2×C29—81no—
350C2×C29—161no—
351C2×C29#304011yescharacteristic
352C2×C29#306311yescharacteristic
353C2×C29#306811yescharacteristic
354C2×#41—21no—
355C22×Q8—21no—
356C2×SD16—21no—
357C2×D8—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16D4×C2911yescharacteristic
361C2×M16D4×C2911yescharacteristic
362C22×C8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8C23×C2911yescharacteristic
367C4⋊Q8C23×C2911yescharacteristic
368C4⋊Q8C23×C2911yescharacteristic
369#127C23×C2911yescharacteristic
370#126—21no—
371#125D4×C2911yescharacteristic
372#124—21no—
373#124D4×C2911yescharacteristic
374#123—21no—
375C22⋊Q8D4×C2911yescharacteristic
376#121—21no—
377#121—21no—
378#121D4×C2911yescharacteristic
379C4×Q8C23×C2911yescharacteristic
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4C23×C2911yescharacteristic
384#117—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C42C23×C2911yescharacteristic
388#107—21no—
389#107—21no—
390#107—21no—
391#106—21no—
392#106—21no—
393#106—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8C23×C2911yescharacteristic
398C4⋊C8C23×C2911yescharacteristic
399C4⋊C8C23×C2911yescharacteristic
400C4⋊C8C23×C2911yescharacteristic
401C4⋊C8C23×C2911yescharacteristic
402C4⋊C8C23×C2911yescharacteristic
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—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423#97—21no—
424#97—21no—
425#97D4×C2911yescharacteristic
426#97D4×C2911yescharacteristic
427C4×C8—21no—
428C4×C8—21no—
429C4×C8C23×C2911yescharacteristic
430C4×C8C23×C2911yescharacteristic
431C29#1938211yescharacteristic, direct product factor, Sylow
432#41—42no—
433#41—42no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—41no—
438C2×Q8—82no—
439C2×Q8C2×D4×C2911yescharacteristic
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4C2×D4×C2911yescharacteristic
446C22×C4—21no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4C2×D4×C2911yescharacteristic
450C22×C4C2×D4×C2911yescharacteristic
451C22×C4#41×C2911yescharacteristic
452SD16—81no—
453D8—81no—
454M16—41no—
455M16—41no—
456M16—42no—
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—41no—
480C4⋊C4—41no—
481C4⋊C4C2×D4×C2911yescharacteristic
482C4⋊C4C2×D4×C2911yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C42—21no—
491C42C2×D4×C2911yescharacteristic
492C42C2×D4×C2911yescharacteristic
493C42#41×C2911yescharacteristic
494C42C24×C2911yescharacteristic
495C23—21no—
496C23—41no—
497C23C29×#12111yescharacteristic
498Q8—21no—
499Q8—21no—
500Q8—41no—
501Q8—41no—
502Q8—81no—
503Q8—81no—
504Q8—82no—
505D4—21no—
506D4—21no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—81no—
512D4—81no—
513D4—82no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4C29×#12111yescharacteristic
530C2×C4C29×#12111yescharacteristic
531C2×C4C29×#12111yescharacteristic
532C2×C4C22×D4×C2911yescharacteristic
533C2×C4C22×D4×C2911yescharacteristic
534C2×C4C2×#41×C2911yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22C2×C29×#12111yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4C29×#57511yescharacteristic
566C4C29×#57511yescharacteristic
567C4C29×#57711yescharacteristic
568C4C29×#57811yescharacteristic
569C2—41no—
570C2—81no—
571C2—161no—
572C2C29×#304011yescharacteristic
573C2C29×#306311yescharacteristic
574C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3251C2
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×#3238C2semidirect
3. C29×#3141C2semidirect
4. C29×#2969C2semidirect
5. C29×#1704C2semidirect
6. C29×#1703C2semidirect
7. C29×#1698C2semidirect
8. C29×#1697C2semidirect
9. C29×#1684C2semidirect
10. C29×#1683C2semidirect
11. C29×#1678C2semidirect
12. C29×#1677C2semidirect
13. C29×#1569C2semidirect
14. C29×#1553C2semidirect
15. C29×#1548C2semidirect
207. #19382C29direct (N × H)
259. #3238C2×C29semidirect
260. #3141C2×C29semidirect
261. #2969C2×C29semidirect
262. #1704C2×C29semidirect
263. #1703C2×C29semidirect
264. #1698C2×C29semidirect
265. #1697C2×C29semidirect
266. #1684C2×C29semidirect
267. #1683C2×C29semidirect
268. #1678C2×C29semidirect
269. #1677C2×C29semidirect
270. #1569C2×C29semidirect
271. #1553C2×C29semidirect
272. #1548C2×C29semidirect
431. C29#19382direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32512
C29×#32382
C29×#31412
C29×#29692
C29×#17042
C29×#17032
C29×#16982
C29×#16972
C29×#16842
C29×#16832
C29×#16782
C29×#16772
C29×#15692
C29×#15532
C29×#15482
#1938229