Finite Group Databasebeta

← C29×#19374 #20314274

Subgroups — C29×#19374 #20314274

Order 7424.

610 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×#3254C211yesmaximal, characteristic, complemented
2C29×#3216C211yesmaximal, characteristic, complemented
3C29×#3184C211yesmaximal, characteristic
4C29×#2962C211yesmaximal, characteristic, complemented
5C29×#1702C211yesmaximal, characteristic, complemented
6C29×#1698C211yesmaximal, characteristic, complemented
7C29×#1692C211yesmaximal, characteristic, complemented
8C29×#1688C211yesmaximal, characteristic, complemented
9C29×#1682C211yesmaximal, characteristic, complemented
10C29×#1678C211yesmaximal, characteristic, complemented
11C29×#1672C211yesmaximal, characteristic, complemented
12C29×#1668C211yesmaximal, characteristic, complemented
13C29×#1569C211yesmaximal, characteristic, complemented
14C29×#1551C211yesmaximal, characteristic, complemented
15C29×#1547C211yesmaximal, characteristic, complemented
16C29×#533C2211yescharacteristic
17C29×#532C2211yescharacteristic
18C29×#532C2211yescharacteristic
19C29×#498C2211yescharacteristic
20C29×#497—21no—
21C29×#493C2211yescharacteristic
22C29×#489—21no—
23C29×#486C2211yescharacteristic
24C29×#486C2211yescharacteristic
25C29×#477C2211yescharacteristic
26C29×#477C2211yescharacteristic
27C29×#474—21no—
28C29×#469—21no—
29C29×#469—21no—
30C29×#468—21no—
31C29×#468—21no—
32C29×#462C2211yescharacteristic
33C29×#462C2211yescharacteristic
34C29×#461—21no—
35C29×#460C2211yescharacteristic
36C29×#460C2211yescharacteristic
37C29×#460C2211yescharacteristic
38C29×#460C2211yescharacteristic
39C29×#452—21no—
40C29×#452—21no—
41C29×#446—21no—
42C29×#446—21no—
43C29×#446C2211yescharacteristic
44C29×#446C2211yescharacteristic
45C8×Q8×C29C2211yescharacteristic
46C8×Q8×C29C2211yescharacteristic
47C29×#442—21no—
48C29×#442—21no—
49C29×#432C2211yescharacteristic
50C29×#424—21no—
51C29×#423C2211yescharacteristic
52C2×C29×C4⋊C8C2211yescharacteristic
53C29×#405—21no—
54C4×M16×C29C2211yescharacteristic
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×#332C2211yescharacteristic
63C29×#331C2211yescharacteristic
64C29×#331C2211yescharacteristic
65C29×#331C2211yescharacteristic
66C29×#331C2211yescharacteristic
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C2×Q16×C29—21no—
70C2×Q16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×SD16×C29—21no—
75C2×D8×C29—21no—
76C2×D8×C29—21no—
77C2×M16×C29—21no—
78C2×M16×C29D411yescharacteristic
79C2×M16×C29D411yescharacteristic
80C22×C8×C29—21no—
81C29×C4⋊Q8D411yescharacteristic
82C29×C4⋊Q8D411yescharacteristic
83C29×C4⋊Q8C2311yescharacteristic
84C29×C4⋊Q8C2311yescharacteristic
85C29×#127C2311yescharacteristic
86C29×#127C2311yescharacteristic
87C29×#125—21no—
88C29×#124—21no—
89C29×#124—21no—
90C29×C22⋊Q8—21no—
91C29×C22⋊Q8D411yescharacteristic
92C29×C22⋊Q8D411yescharacteristic
93C29×#121—21no—
94C29×#121—21no—
95C29×#121—21no—
96C29×#121—21no—
97C4×Q8×C29—21no—
98C4×Q8×C29C2311yescharacteristic
99C4×Q8×C29C2311yescharacteristic
100C4×D4×C29—21no—
101C4×D4×C29—21no—
102C4×D4×C29—21no—
103C4×D4×C29—21no—
104C29×#117—21no—
105C2×C42×C29C2311yescharacteristic
106C29×#107—21no—
107C29×#107—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×C4⋊C8—21no—
111C29×C4⋊C8—21no—
112C29×C4⋊C8—21no—
113C29×C4⋊C8—21no—
114C29×C4⋊C8—21no—
115C29×C4⋊C8—21no—
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×C4⋊C8C2311yescharacteristic
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—21no—
126C29×#102—21no—
127C29×#102—21no—
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×C22⋊C8—21no—
135C29×#97—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—81no—
145#41×C29—81no—
146#41×C29—82no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29C2×D411yescharacteristic
151C2×Q8×C29C2×D411yescharacteristic
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29—21no—
158C2×D4×C29—41no—
159C2×D4×C29—41no—
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—
170SD16×C29—81no—
171D8×C29—42no—
172D8×C29—42no—
173M16×C29—22no—
174M16×C29—41no—
175M16×C29—81no—
176C2×C8×C29—21no—
177C2×C8×C29—21no—
178C2×C8×C29—21no—
179C2×C8×C29—21no—
180C2×C8×C29—21no—
181C2×C8×C29—21no—
182C2×C8×C29—42no—
183C2×C8×C29C2×D411yescharacteristic
184C2×C8×C29C2×D411yescharacteristic
185C2×C8×C29C2×D411yescharacteristic
186C2×C8×C29C2×D411yescharacteristic
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—21no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29C2×D411yescharacteristic
199C4⋊C4×C29C2×D411yescharacteristic
200C22⋊C4×C29—21no—
201C22⋊C4×C29—21no—
202C22⋊C4×C29—41no—
203C22⋊C4×C29—41no—
204C22⋊C4×C29—41no—
205C22⋊C4×C29—41no—
206C42×C29—21no—
207C42×C29—21no—
208C42×C29C2×D411yescharacteristic
209C42×C29C2×D411yescharacteristic
210C42×C29#4111yescharacteristic
211C42×C29C2411yescharacteristic
212#19374C2911yesmaximal, characteristic, direct product factor, Sylow
213C23×C29—41no—
214C23×C29—41no—
215C23×C29#12111yescharacteristic
216Q8×C29—21no—
217Q8×C29—21no—
218Q8×C29—21no—
219Q8×C29—21no—
220Q8×C29—41no—
221Q8×C29—41no—
222Q8×C29—81no—
223Q8×C29—81no—
224D4×C29—41no—
225D4×C29—41no—
226D4×C29—41no—
227D4×C29—41no—
228D4×C29—41no—
229D4×C29—41no—
230D4×C29—41no—
231D4×C29—41no—
232D4×C29—81no—
233D4×C29—81no—
234D4×C29—82no—
235D4×C29—82no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—21no—
239C2×C4×C29—21no—
240C2×C4×C29—21no—
241C2×C4×C29—21no—
242C2×C4×C29—21no—
243C2×C4×C29—21no—
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—41no—
259C8×C29—41no—
260C8×C29—41no—
261C8×C29—41no—
262C8×C29—41no—
263C8×C29—41no—
264C8×C29#13712yes—
265#3254C2×C2911yescharacteristic, complemented
266#3216C2×C2911yescharacteristic, complemented
267#3184C2×C2911yescharacteristic
268#2962C2×C2911yescharacteristic, complemented
269#1702C2×C2911yescharacteristic, complemented
270#1698C2×C2911yescharacteristic, complemented
271#1692C2×C2911yescharacteristic, complemented
272#1688C2×C2911yescharacteristic, complemented
273#1682C2×C2911yescharacteristic, complemented
274#1678C2×C2911yescharacteristic, complemented
275#1672C2×C2911yescharacteristic, complemented
276#1668C2×C2911yescharacteristic, complemented
277#1569C2×C2911yescharacteristic, complemented
278#1551C2×C2911yescharacteristic, complemented
279#1547C2×C2911yescharacteristic, complemented
280C22×C29—21no—
281C22×C29—21no—
282C22×C29—21no—
283C22×C29—81no—
284C22×C29—81no—
285C22×C29—81no—
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—41no—
298C4×C29—81no—
299C4×C29—81no—
300C4×C29C2×#13711yescharacteristic
301C4×C29#57511yescharacteristic
302C4×C29#57611yescharacteristic
303C4×C29#57711yescharacteristic
304#533C22×C2911yescharacteristic
305#532C22×C2911yescharacteristic
306#532C22×C2911yescharacteristic
307#498C22×C2911yescharacteristic
308#497—21no—
309#493C22×C2911yescharacteristic
310#489—21no—
311#486C22×C2911yescharacteristic
312#486C22×C2911yescharacteristic
313#477C22×C2911yescharacteristic
314#477C22×C2911yescharacteristic
315#474—21no—
316#469—21no—
317#469—21no—
318#468—21no—
319#468—21no—
320#462C22×C2911yescharacteristic
321#462C22×C2911yescharacteristic
322#461—21no—
323#460C22×C2911yescharacteristic
324#460C22×C2911yescharacteristic
325#460C22×C2911yescharacteristic
326#460C22×C2911yescharacteristic
327#452—21no—
328#452—21no—
329#446—21no—
330#446—21no—
331#446C22×C2911yescharacteristic
332#446C22×C2911yescharacteristic
333C8×Q8C22×C2911yescharacteristic
334C8×Q8C22×C2911yescharacteristic
335#442—21no—
336#442—21no—
337#432C22×C2911yescharacteristic
338#424—21no—
339#423C22×C2911yescharacteristic
340C2×C4⋊C8C22×C2911yescharacteristic
341#405—21no—
342C4×M16C22×C2911yescharacteristic
343#335C22×C2911yescharacteristic
344#335C22×C2911yescharacteristic
345#334C22×C2911yescharacteristic
346#334C22×C2911yescharacteristic
347#333C22×C2911yescharacteristic
348#333C22×C2911yescharacteristic
349#332C22×C2911yescharacteristic
350#332C22×C2911yescharacteristic
351#331C22×C2911yescharacteristic
352#331C22×C2911yescharacteristic
353#331C22×C2911yescharacteristic
354#331C22×C2911yescharacteristic
355C2×C29—41no—
356C2×C29—161no—
357C2×C29—161no—
358C2×C29#303711yescharacteristic
359C2×C29#306211yescharacteristic
360C2×C29#306811yescharacteristic
361C2×#41—21no—
362C2×#41—21no—
363C2×Q16—21no—
364C2×Q16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×D8—21no—
370C2×D8—21no—
371C2×M16—21no—
372C2×M16D4×C2911yescharacteristic
373C2×M16D4×C2911yescharacteristic
374C22×C8—21no—
375C4⋊Q8D4×C2911yescharacteristic
376C4⋊Q8D4×C2911yescharacteristic
377C4⋊Q8C23×C2911yescharacteristic
378C4⋊Q8C23×C2911yescharacteristic
379#127C23×C2911yescharacteristic
380#127C23×C2911yescharacteristic
381#125—21no—
382#124—21no—
383#124—21no—
384C22⋊Q8—21no—
385C22⋊Q8D4×C2911yescharacteristic
386C22⋊Q8D4×C2911yescharacteristic
387#121—21no—
388#121—21no—
389#121—21no—
390#121—21no—
391C4×Q8—21no—
392C4×Q8C23×C2911yescharacteristic
393C4×Q8C23×C2911yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398#117—21no—
399C2×C42C23×C2911yescharacteristic
400#107—21no—
401#107—21no—
402#106—21no—
403#106—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8C23×C2911yescharacteristic
411C4⋊C8C23×C2911yescharacteristic
412C4⋊C8C23×C2911yescharacteristic
413C4⋊C8C23×C2911yescharacteristic
414C4⋊C8C23×C2911yescharacteristic
415C4⋊C8C23×C2911yescharacteristic
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428C22⋊C8—21no—
429#97—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#1937411yescharacteristic, direct product factor, Sylow
439#41—81no—
440#41—81no—
441#41—82no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8C2×D4×C2911yescharacteristic
446C2×Q8C2×D4×C2911yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4—41no—
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—
465SD16—81no—
466D8—42no—
467D8—42no—
468M16—22no—
469M16—41no—
470M16—81no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—42no—
478C2×C8C2×D4×C2911yescharacteristic
479C2×C8C2×D4×C2911yescharacteristic
480C2×C8C2×D4×C2911yescharacteristic
481C2×C8C2×D4×C2911yescharacteristic
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—21no—
492C4⋊C4—21no—
493C4⋊C4C2×D4×C2911yescharacteristic
494C4⋊C4C2×D4×C2911yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C42—21no—
502C42—21no—
503C42C2×D4×C2911yescharacteristic
504C42C2×D4×C2911yescharacteristic
505C42#41×C2911yescharacteristic
506C42C24×C2911yescharacteristic
507C23—41no—
508C23—41no—
509C23C29×#12111yescharacteristic
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—81no—
517Q8—81no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—81no—
527D4—81no—
528D4—82no—
529D4—82no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
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—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8C29×#13712yes—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22C2×C29×#12111yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4C2×C29×#13711yescharacteristic
580C4C29×#57511yescharacteristic
581C4C29×#57611yescharacteristic
582C4C29×#57711yescharacteristic
583C2—41no—
584C2—161no—
585C2—161no—
586C2C29×#303711yescharacteristic
587C2C29×#306211yescharacteristic
588C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3184C2
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×#3254C2semidirect
2. C29×#3216C2semidirect
4. C29×#2962C2semidirect
5. C29×#1702C2semidirect
6. C29×#1698C2semidirect
7. C29×#1692C2semidirect
8. C29×#1688C2semidirect
9. C29×#1682C2semidirect
10. C29×#1678C2semidirect
11. C29×#1672C2semidirect
12. C29×#1668C2semidirect
13. C29×#1569C2semidirect
14. C29×#1551C2semidirect
15. C29×#1547C2semidirect
212. #19374C29direct (N × H)
265. #3254C2×C29semidirect
266. #3216C2×C29semidirect
268. #2962C2×C29semidirect
269. #1702C2×C29semidirect
270. #1698C2×C29semidirect
271. #1692C2×C29semidirect
272. #1688C2×C29semidirect
273. #1682C2×C29semidirect
274. #1678C2×C29semidirect
275. #1672C2×C29semidirect
276. #1668C2×C29semidirect
277. #1569C2×C29semidirect
278. #1551C2×C29semidirect
279. #1547C2×C29semidirect
438. C29#19374direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32542
C29×#32162
C29×#31842
C29×#29622
C29×#17022
C29×#16982
C29×#16922
C29×#16882
C29×#16822
C29×#16782
C29×#16722
C29×#16682
C29×#15692
C29×#15512
C29×#15472
#1937429