Finite Group Databasebeta

← C29×#19383 #20314283

Subgroups — C29×#19383 #20314283

Order 7424.

606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3251C211yesmaximal, characteristic
2C29×#3218C211yesmaximal, characteristic, complemented
3C29×#3141C211yesmaximal, characteristic, complemented
4C29×#2969C211yesmaximal, characteristic, complemented
5C29×#1702C211yesmaximal, characteristic, complemented
6C29×#1701C211yesmaximal, characteristic, complemented
7C29×#1700C211yesmaximal, characteristic, complemented
8C29×#1699C211yesmaximal, characteristic, complemented
9C29×#1682C211yesmaximal, characteristic, complemented
10C29×#1681C211yesmaximal, characteristic, complemented
11C29×#1680C211yesmaximal, characteristic, complemented
12C29×#1679C211yesmaximal, characteristic, complemented
13C29×#1569C211yesmaximal, characteristic, complemented
14C29×#1553C211yesmaximal, characteristic, complemented
15C29×#1546C211yesmaximal, characteristic, complemented
16C29×#532C2211yescharacteristic
17C2×C29×C4⋊Q8C2211yescharacteristic
18C29×#529C2211yescharacteristic
19C29×#497—21no—
20C29×#491—21no—
21C29×#489—21no—
22C29×#489—21no—
23C29×#487C2211yescharacteristic
24C29×#487C2211yescharacteristic
25C29×#486C2211yescharacteristic
26C29×#486C2211yescharacteristic
27C29×#478—21no—
28C29×#475C2211yescharacteristic
29C29×#474C2211yescharacteristic
30C29×#469—21no—
31C29×#468—21no—
32C29×#463—21no—
33C29×#462C2211yescharacteristic
34C29×#462C2211yescharacteristic
35C29×#461C2211yescharacteristic
36C29×#461C2211yescharacteristic
37C29×#460C2211yescharacteristic
38C29×#459C2211yescharacteristic
39C29×#451—21no—
40C29×#448—21no—
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×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×#332C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#331C2211yescharacteristic
66C29×#331C2211yescharacteristic
67C2×#41×C29—21no—
68C22×Q8×C29—21no—
69C2×Q16×C29—21no—
70C2×Q16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×D8×C29—21no—
75C2×M16×C29—21no—
76C2×M16×C29—21no—
77C2×M16×C29D411yescharacteristic
78C2×M16×C29D411yescharacteristic
79C22×C8×C29—21no—
80C29×C4⋊Q8—21no—
81C29×C4⋊Q8—21no—
82C29×C4⋊Q8—21no—
83C29×C4⋊Q8C2311yescharacteristic
84C29×C4⋊Q8C2311yescharacteristic
85C29×C4⋊Q8C2311yescharacteristic
86C29×#127C2311yescharacteristic
87C29×#126—21no—
88C29×#125D411yescharacteristic
89C29×#124—21no—
90C29×#124D411yescharacteristic
91C29×#123—21no—
92C29×C22⋊Q8D411yescharacteristic
93C29×#121—21no—
94C29×#121—21no—
95C29×#121D411yescharacteristic
96C4×Q8×C29C2311yescharacteristic
97C4×D4×C29—21no—
98C4×D4×C29—21no—
99C4×D4×C29—21no—
100C4×D4×C29C2311yescharacteristic
101C29×#117—21no—
102C2×C4⋊C4×C29—21no—
103C2×C4⋊C4×C29—21no—
104C2×C42×C29C2311yescharacteristic
105C29×#107—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×#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×#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—81no—
151C2×Q8×C29—81no—
152C2×Q8×C29C2×D411yescharacteristic
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29—41no—
158C2×D4×C29C2×D411yescharacteristic
159C22×C4×C29—21no—
160C22×C4×C29—41no—
161C22×C4×C29—41no—
162C22×C4×C29C2×D411yescharacteristic
163C22×C4×C29C2×D411yescharacteristic
164C22×C4×C29#4111yescharacteristic
165Q16×C29—81no—
166Q16×C29—81no—
167SD16×C29—81no—
168SD16×C29—81no—
169SD16×C29—81no—
170D8×C29—81no—
171M16×C29—41no—
172M16×C29—41no—
173M16×C29—42no—
174M16×C29—81no—
175C2×C8×C29—21no—
176C2×C8×C29—21no—
177C2×C8×C29—21no—
178C2×C8×C29—21no—
179C2×C8×C29—21no—
180C2×C8×C29—21no—
181C2×C8×C29—42no—
182C2×C8×C29C2×D411yescharacteristic
183C2×C8×C29C2×D411yescharacteristic
184C2×C8×C29C2×D411yescharacteristic
185C2×C8×C29C2×D411yescharacteristic
186C4⋊C4×C29—21no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—21no—
194C4⋊C4×C29—21no—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—41no—
197C4⋊C4×C29—41no—
198C4⋊C4×C29C2×D411yescharacteristic
199C4⋊C4×C29C2×D411yescharacteristic
200C22⋊C4×C29—21no—
201C22⋊C4×C29—21no—
202C22⋊C4×C29—21no—
203C22⋊C4×C29—21no—
204C22⋊C4×C29—21no—
205C22⋊C4×C29—41no—
206C22⋊C4×C29—41no—
207C42×C29—21no—
208C42×C29C2×D411yescharacteristic
209C42×C29C2×D411yescharacteristic
210C42×C29#4111yescharacteristic
211C42×C29C2411yescharacteristic
212#19383C2911yesmaximal, characteristic, direct product factor, Sylow
213C23×C29—21no—
214C23×C29—41no—
215C23×C29#12111yescharacteristic
216Q8×C29—21no—
217Q8×C29—21no—
218Q8×C29—41no—
219Q8×C29—41no—
220Q8×C29—41no—
221Q8×C29—41no—
222Q8×C29—41no—
223Q8×C29—41no—
224Q8×C29—82no—
225D4×C29—21no—
226D4×C29—21no—
227D4×C29—41no—
228D4×C29—41no—
229D4×C29—41no—
230D4×C29—41no—
231D4×C29—81no—
232D4×C29—81no—
233D4×C29—82no—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—21no—
239C2×C4×C29—21no—
240C2×C4×C29—21no—
241C2×C4×C29—41no—
242C2×C4×C29—41no—
243C2×C4×C29—41no—
244C2×C4×C29—41no—
245C2×C4×C29—41no—
246C2×C4×C29—41no—
247C2×C4×C29—82no—
248C2×C4×C29—82no—
249C2×C4×C29#12111yescharacteristic
250C2×C4×C29#12111yescharacteristic
251C2×C4×C29#12111yescharacteristic
252C2×C4×C29C22×D411yescharacteristic
253C2×C4×C29C22×D411yescharacteristic
254C2×C4×C29C2×#4111yescharacteristic
255C8×C29—21no—
256C8×C29—21no—
257C8×C29—21no—
258C8×C29—21no—
259C8×C29—41no—
260C8×C29—41no—
261C8×C29—41no—
262C8×C29—41no—
263C8×C29—41no—
264C8×C29—41no—
265#3251C2×C2911yescharacteristic
266#3218C2×C2911yescharacteristic, complemented
267#3141C2×C2911yescharacteristic, complemented
268#2969C2×C2911yescharacteristic, complemented
269#1702C2×C2911yescharacteristic, complemented
270#1701C2×C2911yescharacteristic, complemented
271#1700C2×C2911yescharacteristic, complemented
272#1699C2×C2911yescharacteristic, complemented
273#1682C2×C2911yescharacteristic, complemented
274#1681C2×C2911yescharacteristic, complemented
275#1680C2×C2911yescharacteristic, complemented
276#1679C2×C2911yescharacteristic, complemented
277#1569C2×C2911yescharacteristic, complemented
278#1553C2×C2911yescharacteristic, complemented
279#1546C2×C2911yescharacteristic, complemented
280C22×C29—21no—
281C22×C29—21no—
282C22×C29—21no—
283C22×C29—41no—
284C22×C29—41no—
285C22×C29—41no—
286C22×C29—81no—
287C22×C29—81no—
288C22×C29—81no—
289C22×C29C2×#12111yescharacteristic
290C4×C29—21no—
291C4×C29—21no—
292C4×C29—21no—
293C4×C29—21no—
294C4×C29—41no—
295C4×C29—41no—
296C4×C29—41no—
297C4×C29—81no—
298C4×C29—81no—
299C4×C29—81no—
300C4×C29#57511yescharacteristic
301C4×C29#57511yescharacteristic
302C4×C29#57611yescharacteristic
303C4×C29#57711yescharacteristic
304#532C22×C2911yescharacteristic
305C2×C4⋊Q8C22×C2911yescharacteristic
306#529C22×C2911yescharacteristic
307#497—21no—
308#491—21no—
309#489—21no—
310#489—21no—
311#487C22×C2911yescharacteristic
312#487C22×C2911yescharacteristic
313#486C22×C2911yescharacteristic
314#486C22×C2911yescharacteristic
315#478—21no—
316#475C22×C2911yescharacteristic
317#474C22×C2911yescharacteristic
318#469—21no—
319#468—21no—
320#463—21no—
321#462C22×C2911yescharacteristic
322#462C22×C2911yescharacteristic
323#461C22×C2911yescharacteristic
324#461C22×C2911yescharacteristic
325#460C22×C2911yescharacteristic
326#459C22×C2911yescharacteristic
327#451—21no—
328#448—21no—
329#446C22×C2911yescharacteristic
330C8×Q8C22×C2911yescharacteristic
331#436—21no—
332#436C22×C2911yescharacteristic
333#435—21no—
334C8×D4C22×C2911yescharacteristic
335#433—21no—
336#432C22×C2911yescharacteristic
337#431C22×C2911yescharacteristic
338#423C22×C2911yescharacteristic
339#417—21no—
340#417—21no—
341#405—21no—
342C4×M16C22×C2911yescharacteristic
343#335C22×C2911yescharacteristic
344#335C22×C2911yescharacteristic
345#334C22×C2911yescharacteristic
346#334C22×C2911yescharacteristic
347#332C22×C2911yescharacteristic
348#332C22×C2911yescharacteristic
349#332C22×C2911yescharacteristic
350#332C22×C2911yescharacteristic
351#332C22×C2911yescharacteristic
352#332C22×C2911yescharacteristic
353#331C22×C2911yescharacteristic
354#331C22×C2911yescharacteristic
355C2×C29—41no—
356C2×C29—81no—
357C2×C29—161no—
358C2×C29#304011yescharacteristic
359C2×C29#306211yescharacteristic
360C2×C29#306911yescharacteristic
361C2×#41—21no—
362C22×Q8—21no—
363C2×Q16—21no—
364C2×Q16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×D8—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16D4×C2911yescharacteristic
372C2×M16D4×C2911yescharacteristic
373C22×C8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376C4⋊Q8—21no—
377C4⋊Q8C23×C2911yescharacteristic
378C4⋊Q8C23×C2911yescharacteristic
379C4⋊Q8C23×C2911yescharacteristic
380#127C23×C2911yescharacteristic
381#126—21no—
382#125D4×C2911yescharacteristic
383#124—21no—
384#124D4×C2911yescharacteristic
385#123—21no—
386C22⋊Q8D4×C2911yescharacteristic
387#121—21no—
388#121—21no—
389#121D4×C2911yescharacteristic
390C4×Q8C23×C2911yescharacteristic
391C4×D4—21no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4C23×C2911yescharacteristic
395#117—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C42C23×C2911yescharacteristic
399#107—21no—
400#106—21no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8C23×C2911yescharacteristic
405C4⋊C8C23×C2911yescharacteristic
406C4⋊C8C23×C2911yescharacteristic
407C4⋊C8C23×C2911yescharacteristic
408C4⋊C8C23×C2911yescharacteristic
409C4⋊C8C23×C2911yescharacteristic
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430#97—21no—
431#97—21no—
432#97D4×C2911yescharacteristic
433#97D4×C2911yescharacteristic
434C4×C8—21no—
435C4×C8—21no—
436C4×C8C23×C2911yescharacteristic
437C4×C8C23×C2911yescharacteristic
438C29#1938311yescharacteristic, direct product factor, Sylow
439#41—42no—
440#41—42no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—41no—
445C2×Q8—81no—
446C2×Q8—81no—
447C2×Q8C2×D4×C2911yescharacteristic
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4C2×D4×C2911yescharacteristic
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4C2×D4×C2911yescharacteristic
458C22×C4C2×D4×C2911yescharacteristic
459C22×C4#41×C2911yescharacteristic
460Q16—81no—
461Q16—81no—
462SD16—81no—
463SD16—81no—
464SD16—81no—
465D8—81no—
466M16—41no—
467M16—41no—
468M16—42no—
469M16—81no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—42no—
477C2×C8C2×D4×C2911yescharacteristic
478C2×C8C2×D4×C2911yescharacteristic
479C2×C8C2×D4×C2911yescharacteristic
480C2×C8C2×D4×C2911yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4C2×D4×C2911yescharacteristic
494C4⋊C4C2×D4×C2911yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C42—21no—
503C42C2×D4×C2911yescharacteristic
504C42C2×D4×C2911yescharacteristic
505C42#41×C2911yescharacteristic
506C42C24×C2911yescharacteristic
507C23—21no—
508C23—41no—
509C23C29×#12111yescharacteristic
510Q8—21no—
511Q8—21no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—82no—
519D4—21no—
520D4—21no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—81no—
526D4—81no—
527D4—82no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4C29×#12111yescharacteristic
544C2×C4C29×#12111yescharacteristic
545C2×C4C29×#12111yescharacteristic
546C2×C4C22×D4×C2911yescharacteristic
547C2×C4C22×D4×C2911yescharacteristic
548C2×C4C2×#41×C2911yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22C2×C29×#12111yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4C29×#57511yescharacteristic
580C4C29×#57511yescharacteristic
581C4C29×#57611yescharacteristic
582C4C29×#57711yescharacteristic
583C2—41no—
584C2—81no—
585C2—161no—
586C2C29×#304011yescharacteristic
587C2C29×#306211yescharacteristic
588C2C29×#306911yescharacteristic
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×#3218C2semidirect
3. C29×#3141C2semidirect
4. C29×#2969C2semidirect
5. C29×#1702C2semidirect
6. C29×#1701C2semidirect
7. C29×#1700C2semidirect
8. C29×#1699C2semidirect
9. C29×#1682C2semidirect
10. C29×#1681C2semidirect
11. C29×#1680C2semidirect
12. C29×#1679C2semidirect
13. C29×#1569C2semidirect
14. C29×#1553C2semidirect
15. C29×#1546C2semidirect
212. #19383C29direct (N × H)
266. #3218C2×C29semidirect
267. #3141C2×C29semidirect
268. #2969C2×C29semidirect
269. #1702C2×C29semidirect
270. #1701C2×C29semidirect
271. #1700C2×C29semidirect
272. #1699C2×C29semidirect
273. #1682C2×C29semidirect
274. #1681C2×C29semidirect
275. #1680C2×C29semidirect
276. #1679C2×C29semidirect
277. #1569C2×C29semidirect
278. #1553C2×C29semidirect
279. #1546C2×C29semidirect
438. C29#19383direct (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×#32182
C29×#31412
C29×#29692
C29×#17022
C29×#17012
C29×#17002
C29×#16992
C29×#16822
C29×#16812
C29×#16802
C29×#16792
C29×#15692
C29×#15532
C29×#15462
#1938329