Finite Group Databasebeta

← C29×#19183 #20314083

Subgroups — C29×#19183 #20314083

Order 7424.

614 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3182C211yesmaximal, characteristic, complemented
2C29×#3106C211yesmaximal, characteristic
3C29×#3076C211yesmaximal, characteristic, complemented
4C29×#2971C211yesmaximal, characteristic, complemented
5C29×#1703C211yesmaximal, characteristic, complemented
6C29×#1697C211yesmaximal, characteristic, complemented
7C29×#1695C211yesmaximal, characteristic, complemented
8C29×#1685C211yesmaximal, characteristic, complemented
9C29×#1684C211yesmaximal, characteristic, complemented
10C29×#1678C211yesmaximal, characteristic, complemented
11C29×#1676C211yesmaximal, characteristic, complemented
12C29×#1666C211yesmaximal, characteristic, complemented
13C29×#1565C211yesmaximal, characteristic, complemented
14C29×#1554C211yesmaximal, characteristic, complemented
15C29×#1551C211yesmaximal, characteristic, complemented
16C29×#533C2211yescharacteristic
17C29×#532C2211yescharacteristic
18C4×#41×C29C2211yescharacteristic
19C29×#500C2211yescharacteristic
20C29×#492C2211yescharacteristic
21C29×#487C2211yescharacteristic
22C29×#486C2211yescharacteristic
23C29×#482—21no—
24C29×#479—21no—
25C29×#478—21no—
26C29×#477C2211yescharacteristic
27C29×#477C2211yescharacteristic
28C29×#476C2211yescharacteristic
29C29×#476C2211yescharacteristic
30C29×#475C2211yescharacteristic
31C29×#474C2211yescharacteristic
32C29×#468—21no—
33C29×#468—21no—
34C29×#460C2211yescharacteristic
35C29×#459C2211yescharacteristic
36C29×#449—21no—
37C8×Q8×C29C2211yescharacteristic
38C8×Q8×C29C2211yescharacteristic
39C29×#440—21no—
40C29×#440—21no—
41C4×SD16×C29—21no—
42C4×D8×C29—21no—
43C29×#436—21no—
44C29×#436—21no—
45C29×#436C2211yescharacteristic
46C29×#436C2211yescharacteristic
47C29×#432—21no—
48C29×#432C2211yescharacteristic
49C29×#431C2211yescharacteristic
50C29×#427—21no—
51C2×C29×C4⋊C8C2211yescharacteristic
52C29×#416—21no—
53C4×M16×C29—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—
68C2×#41×C29D411yescharacteristic
69C2×SD16×C29—21no—
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C2×D8×C29—21no—
73C2×M16×C29—21no—
74C2×M16×C29—21no—
75C2×M16×C29D411yescharacteristic
76C2×M16×C29D411yescharacteristic
77C22×C8×C29—21no—
78C29×C4⋊Q8C2311yescharacteristic
79C29×C4⋊Q8C2311yescharacteristic
80C29×C4⋊Q8C2311yescharacteristic
81C29×#127C2311yescharacteristic
82C29×#125—21no—
83C29×#124—21no—
84C29×C22⋊Q8—21no—
85C29×C22⋊Q8—21no—
86C29×#121—21no—
87C29×#121—21no—
88C4×Q8×C29—21no—
89C4×Q8×C29—21no—
90C4×Q8×C29D411yescharacteristic
91C4×Q8×C29C2311yescharacteristic
92C4×D4×C29—21no—
93C4×D4×C29—21no—
94C4×D4×C29—21no—
95C4×D4×C29—21no—
96C4×D4×C29D411yescharacteristic
97C4×D4×C29C2311yescharacteristic
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×#107—21no—
107C29×#107—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×#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×#97D411yescharacteristic
138C29×#97D411yescharacteristic
139C4×C8×C29—21no—
140C4×C8×C29—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144#41×C29—22no—
145#41×C29—41no—
146#41×C29—82no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29C2×D411yescharacteristic
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—41no—
156C2×D4×C29C2×D411yescharacteristic
157C22×C4×C29—21no—
158C22×C4×C29—21no—
159C22×C4×C29—21no—
160C22×C4×C29—41no—
161C22×C4×C29C2×D411yescharacteristic
162C22×C4×C29C2×D411yescharacteristic
163C22×C4×C29#4111yescharacteristic
164SD16×C29—42no—
165SD16×C29—42no—
166SD16×C29—42no—
167D8×C29—42no—
168M16×C29—22no—
169M16×C29—41no—
170M16×C29—42no—
171M16×C29—42no—
172C2×C8×C29—21no—
173C2×C8×C29—21no—
174C2×C8×C29—21no—
175C2×C8×C29—21no—
176C2×C8×C29—21no—
177C2×C8×C29—21no—
178C2×C8×C29—42no—
179C2×C8×C29C2×D411yescharacteristic
180C2×C8×C29C2×D411yescharacteristic
181C2×C8×C29C2×D411yescharacteristic
182C2×C8×C29C2×D411yescharacteristic
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—41no—
199C22⋊C4×C29—41no—
200C22⋊C4×C29—41no—
201C42×C29—21no—
202C42×C29—21no—
203C42×C29—21no—
204C42×C29—41no—
205C42×C29C2×D411yescharacteristic
206C42×C29C2×D411yescharacteristic
207C42×C29#4111yescharacteristic
208C42×C29C2411yescharacteristic
209#19183C2911yesmaximal, characteristic, direct product factor, Sylow
210C23×C29—21no—
211C23×C29—41no—
212C23×C29#12111yescharacteristic
213Q8×C29—21no—
214Q8×C29—41no—
215Q8×C29—41no—
216Q8×C29—81no—
217Q8×C29—81no—
218Q8×C29#13712yes—
219D4×C29—21no—
220D4×C29—21no—
221D4×C29—42no—
222D4×C29—41no—
223D4×C29—41no—
224D4×C29—41no—
225D4×C29—41no—
226D4×C29—81no—
227D4×C29—82no—
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—21no—
235C2×C4×C29—41no—
236C2×C4×C29—42no—
237C2×C4×C29—41no—
238C2×C4×C29—41no—
239C2×C4×C29—41no—
240C2×C4×C29—41no—
241C2×C4×C29—41no—
242C2×C4×C29—81no—
243C2×C4×C29—82no—
244C2×C4×C29#12111yescharacteristic
245C2×C4×C29#12111yescharacteristic
246C2×C4×C29#12111yescharacteristic
247C2×C4×C29C22×D411yescharacteristic
248C2×C4×C29C22×D411yescharacteristic
249C2×C4×C29C2×#4111yescharacteristic
250C8×C29—21no—
251C8×C29—21no—
252C8×C29—21no—
253C8×C29—41no—
254C8×C29—41no—
255C8×C29—41no—
256C8×C29—41no—
257C8×C29—41no—
258C8×C29—41no—
259C8×C29#13512yes—
260#3182C2×C2911yescharacteristic, complemented
261#3106C2×C2911yescharacteristic
262#3076C2×C2911yescharacteristic, complemented
263#2971C2×C2911yescharacteristic, complemented
264#1703C2×C2911yescharacteristic, complemented
265#1697C2×C2911yescharacteristic, complemented
266#1695C2×C2911yescharacteristic, complemented
267#1685C2×C2911yescharacteristic, complemented
268#1684C2×C2911yescharacteristic, complemented
269#1678C2×C2911yescharacteristic, complemented
270#1676C2×C2911yescharacteristic, complemented
271#1666C2×C2911yescharacteristic, complemented
272#1565C2×C2911yescharacteristic, complemented
273#1554C2×C2911yescharacteristic, complemented
274#1551C2×C2911yescharacteristic, complemented
275C22×C29—21no—
276C22×C29—21no—
277C22×C29—21no—
278C22×C29—41no—
279C22×C29—41no—
280C22×C29—41no—
281C22×C29—81no—
282C22×C29—81no—
283C22×C29—81no—
284C22×C29C2×#12111yescharacteristic
285C4×C29—21no—
286C4×C29—21no—
287C4×C29—22no—
288C4×C29—21no—
289C4×C29—21no—
290C4×C29—41no—
291C4×C29—41no—
292C4×C29—81no—
293C4×C29—81no—
294C4×C29—81no—
295C4×C29C2×#13511yescharacteristic
296C4×C29C2×#13711yescharacteristic
297C4×C29#57511yescharacteristic
298C4×C29#57511yescharacteristic
299#533C22×C2911yescharacteristic
300#532C22×C2911yescharacteristic
301C4×#41C22×C2911yescharacteristic
302#500C22×C2911yescharacteristic
303#492C22×C2911yescharacteristic
304#487C22×C2911yescharacteristic
305#486C22×C2911yescharacteristic
306#482—21no—
307#479—21no—
308#478—21no—
309#477C22×C2911yescharacteristic
310#477C22×C2911yescharacteristic
311#476C22×C2911yescharacteristic
312#476C22×C2911yescharacteristic
313#475C22×C2911yescharacteristic
314#474C22×C2911yescharacteristic
315#468—21no—
316#468—21no—
317#460C22×C2911yescharacteristic
318#459C22×C2911yescharacteristic
319#449—21no—
320C8×Q8C22×C2911yescharacteristic
321C8×Q8C22×C2911yescharacteristic
322#440—21no—
323#440—21no—
324C4×SD16—21no—
325C4×D8—21no—
326#436—21no—
327#436—21no—
328#436C22×C2911yescharacteristic
329#436C22×C2911yescharacteristic
330#432—21no—
331#432C22×C2911yescharacteristic
332#431C22×C2911yescharacteristic
333#427—21no—
334C2×C4⋊C8C22×C2911yescharacteristic
335#416—21no—
336C4×M16—21no—
337C4×M16C22×C2911yescharacteristic
338#335C22×C2911yescharacteristic
339#335C22×C2911yescharacteristic
340#334C22×C2911yescharacteristic
341#334C22×C2911yescharacteristic
342#333C22×C2911yescharacteristic
343#333C22×C2911yescharacteristic
344#333C22×C2911yescharacteristic
345#333C22×C2911yescharacteristic
346#332C22×C2911yescharacteristic
347#332C22×C2911yescharacteristic
348#331C22×C2911yescharacteristic
349#331C22×C2911yescharacteristic
350C2×C29—41no—
351C2×C29—81no—
352C2×C29—161no—
353C2×C29#303511yescharacteristic
354C2×C29#305611yescharacteristic
355C2×C29#306811yescharacteristic
356C2×#41—21no—
357C2×#41D4×C2911yescharacteristic
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×D8—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16D4×C2911yescharacteristic
365C2×M16D4×C2911yescharacteristic
366C22×C8—21no—
367C4⋊Q8C23×C2911yescharacteristic
368C4⋊Q8C23×C2911yescharacteristic
369C4⋊Q8C23×C2911yescharacteristic
370#127C23×C2911yescharacteristic
371#125—21no—
372#124—21no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375#121—21no—
376#121—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8D4×C2911yescharacteristic
380C4×Q8C23×C2911yescharacteristic
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4D4×C2911yescharacteristic
386C4×D4C23×C2911yescharacteristic
387#117—21no—
388#117—21no—
389#117D4×C2911yescharacteristic
390C2×C42—21no—
391C2×C42C23×C2911yescharacteristic
392#107—21no—
393#107—21no—
394#107—21no—
395#107—21no—
396#107—21no—
397#106—21no—
398#106—21no—
399#106—21no—
400C4⋊C8—21no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8C23×C2911yescharacteristic
404C4⋊C8C23×C2911yescharacteristic
405C4⋊C8C23×C2911yescharacteristic
406C4⋊C8C23×C2911yescharacteristic
407C4⋊C8C23×C2911yescharacteristic
408C4⋊C8C23×C2911yescharacteristic
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425#97—21no—
426#97D4×C2911yescharacteristic
427#97D4×C2911yescharacteristic
428C4×C8—21no—
429C4×C8—21no—
430C4×C8—21no—
431C4×C8C23×C2911yescharacteristic
432C4×C8C23×C2911yescharacteristic
433C29#1918311yescharacteristic, direct product factor, Sylow
434#41—22no—
435#41—41no—
436#41—82no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8C2×D4×C2911yescharacteristic
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—41no—
446C2×D4C2×D4×C2911yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—41no—
451C22×C4C2×D4×C2911yescharacteristic
452C22×C4C2×D4×C2911yescharacteristic
453C22×C4#41×C2911yescharacteristic
454SD16—42no—
455SD16—42no—
456SD16—42no—
457D8—42no—
458M16—22no—
459M16—41no—
460M16—42no—
461M16—42no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—42no—
469C2×C8C2×D4×C2911yescharacteristic
470C2×C8C2×D4×C2911yescharacteristic
471C2×C8C2×D4×C2911yescharacteristic
472C2×C8C2×D4×C2911yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4C2×D4×C2911yescharacteristic
484C4⋊C4C2×D4×C2911yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—41no—
495C42C2×D4×C2911yescharacteristic
496C42C2×D4×C2911yescharacteristic
497C42#41×C2911yescharacteristic
498C42C24×C2911yescharacteristic
499C23—21no—
500C23—41no—
501C23C29×#12111yescharacteristic
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—81no—
506Q8—81no—
507Q8C29×#13712yes—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—81no—
516D4—82no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—81no—
532C2×C4—82no—
533C2×C4C29×#12111yescharacteristic
534C2×C4C29×#12111yescharacteristic
535C2×C4C29×#12111yescharacteristic
536C2×C4C22×D4×C2911yescharacteristic
537C2×C4C22×D4×C2911yescharacteristic
538C2×C4C2×#41×C2911yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8C29×#13512yes—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22C2×C29×#12111yescharacteristic
559C4—21no—
560C4—21no—
561C4—22no—
562C4—21no—
563C4—21no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4C2×C29×#13511yescharacteristic
570C4C2×C29×#13711yescharacteristic
571C4C29×#57511yescharacteristic
572C4C29×#57511yescharacteristic
573C2—41no—
574C2—81no—
575C2—161no—
576C2C29×#303511yescharacteristic
577C2C29×#305611yescharacteristic
578C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3106C2
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×#3182C2semidirect
3. C29×#3076C2semidirect
4. C29×#2971C2semidirect
5. C29×#1703C2semidirect
6. C29×#1697C2semidirect
7. C29×#1695C2semidirect
8. C29×#1685C2semidirect
9. C29×#1684C2semidirect
10. C29×#1678C2semidirect
11. C29×#1676C2semidirect
12. C29×#1666C2semidirect
13. C29×#1565C2semidirect
14. C29×#1554C2semidirect
15. C29×#1551C2semidirect
209. #19183C29direct (N × H)
260. #3182C2×C29semidirect
262. #3076C2×C29semidirect
263. #2971C2×C29semidirect
264. #1703C2×C29semidirect
265. #1697C2×C29semidirect
266. #1695C2×C29semidirect
267. #1685C2×C29semidirect
268. #1684C2×C29semidirect
269. #1678C2×C29semidirect
270. #1676C2×C29semidirect
271. #1666C2×C29semidirect
272. #1565C2×C29semidirect
273. #1554C2×C29semidirect
274. #1551C2×C29semidirect
433. C29#19183direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31822
C29×#31062
C29×#30762
C29×#29712
C29×#17032
C29×#16972
C29×#16952
C29×#16852
C29×#16842
C29×#16782
C29×#16762
C29×#16662
C29×#15652
C29×#15542
C29×#15512
#1918329