Finite Group Databasebeta

← C29×#20031 #20314931

Subgroups — C29×#20031 #20314931

Order 7424.

660 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×D8×C29C211yesmaximal, characteristic, complemented
2C29×#3330C211yesmaximal, characteristic
3C29×#3298C211yesmaximal, characteristic, complemented
4C29×#3276C211yesmaximal, characteristic, complemented
5C29×#1723C211yesmaximal, characteristic, complemented
6C29×#1699C211yesmaximal, characteristic, complemented
7C29×#1693C211yesmaximal, characteristic, complemented
8C29×#1680C211yesmaximal, characteristic, complemented
9C29×#1669C211yesmaximal, characteristic, complemented
10C29×#1654C211yesmaximal, characteristic, complemented
11C29×#1651C211yesmaximal, characteristic, complemented
12C29×#1649C211yesmaximal, characteristic, complemented
13C29×#1647C211yesmaximal, characteristic, complemented
14C29×#1588C211yesmaximal, characteristic, complemented
15C29×#1586C211yesmaximal, characteristic, complemented
16C2×C29×#137—21no—
17D4×Q8×C29C2211yescharacteristic
18D4×Q8×C29C2211yescharacteristic
19C29×#547C2211yescharacteristic
20C29×#547C2211yescharacteristic
21C29×#500—21no—
22C29×#500C2211yescharacteristic
23C29×#500C2211yescharacteristic
24C29×#498C2211yescharacteristic
25C29×#494C2211yescharacteristic
26C29×#487C2211yescharacteristic
27C29×#487C2211yescharacteristic
28C29×#484—21no—
29C29×#483—21no—
30C29×#475C2211yescharacteristic
31C29×#474—21no—
32C29×#474—21no—
33C29×#474C2211yescharacteristic
34C29×#474C2211yescharacteristic
35C29×#474C2211yescharacteristic
36C29×#470—21no—
37C29×#468—21no—
38C29×#465—21no—
39C29×#462C2211yescharacteristic
40C29×#461C2211yescharacteristic
41C29×#461C2211yescharacteristic
42C29×#461C2211yescharacteristic
43C29×#452—21no—
44C29×#451—21no—
45C29×#449—21no—
46C29×#448—21no—
47C8×Q8×C29C2211yescharacteristic
48C4×SD16×C29C2211yescharacteristic
49C4×D8×C29—21no—
50C4×D8×C29C2211yescharacteristic
51C29×#436C2211yescharacteristic
52C29×#436C2211yescharacteristic
53C8×D4×C29C2211yescharacteristic
54C29×#417—21no—
55C2×C29×#103—21no—
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#332C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×D4⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C29×#322C2211yescharacteristic
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C22×Q8×C29—21no—
70C22×Q8×C29—21no—
71C29×#137—44no—
72C2×Q16×C29—21no—
73C2×Q16×C29—21no—
74C2×Q16×C29—21no—
75C2×SD16×C29—21no—
76C2×SD16×C29—21no—
77C2×SD16×C29—21no—
78C2×SD16×C29D411yescharacteristic
79C2×D8×C29D411yescharacteristic
80C2×M16×C29—21no—
81C2×M16×C29—21no—
82C22×C8×C29—21no—
83C29×C4⋊Q8—21no—
84C29×C4⋊Q8—21no—
85C29×C4⋊Q8C2311yescharacteristic
86C29×C4⋊Q8C2311yescharacteristic
87C29×C4⋊Q8C2311yescharacteristic
88C29×C4⋊Q8C2311yescharacteristic
89C29×#123—41no—
90C29×#123—41no—
91C29×C22⋊Q8—21no—
92C29×C22⋊Q8—21no—
93C29×C22⋊Q8—21no—
94C29×C22⋊Q8—21no—
95C29×C22⋊Q8—41no—
96C29×C22⋊Q8—41no—
97C29×#121—21no—
98C29×#121—21no—
99C4×Q8×C29C2311yescharacteristic
100C4×D4×C29—21no—
101C4×D4×C29—21no—
102C4×D4×C29C2311yescharacteristic
103C4×D4×C29C2311yescharacteristic
104C4×D4×C29C2311yescharacteristic
105C2×C4⋊C4×C29—21no—
106C2×C4⋊C4×C29—21no—
107C29×#107—21no—
108C29×#107—21no—
109C29×#107—21no—
110C29×#107—21no—
111C29×#107—21no—
112C29×#107—41no—
113C29×#107D411yescharacteristic
114C29×#106—21no—
115C29×#106—41no—
116C29×#106D411yescharacteristic
117C29×C4⋊C8—21no—
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×#103—21no—
127C29×#103—21no—
128C29×#103—21no—
129C29×#103—21no—
130C29×#103—21no—
131C29×#103D411yescharacteristic
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×#102D411yescharacteristic
136C29×#102D411yescharacteristic
137C29×#102D411yescharacteristic
138C29×C22⋊C8—21no—
139C29×C22⋊C8—21no—
140C29×C22⋊C8—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C4×C8×C29C2311yescharacteristic
145#41×C29—42no—
146#41×C29—42no—
147#41×C29—81no—
148#41×C29—81no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×Q8×C29—21no—
152C2×Q8×C29—21no—
153C2×Q8×C29—41no—
154C2×Q8×C29—41no—
155C2×Q8×C29—42no—
156C2×Q8×C29—42no—
157C2×Q8×C29—81no—
158C2×Q8×C29—81no—
159C2×Q8×C29C2×D411yescharacteristic
160C2×D4×C29—41no—
161C2×D4×C29—41no—
162C2×D4×C29C2×D411yescharacteristic
163C2×D4×C29C2×D411yescharacteristic
164C2×D4×C29C2×D411yescharacteristic
165C22×C4×C29—21no—
166C22×C4×C29—21no—
167C22×C4×C29—21no—
168C22×C4×C29—41no—
169C22×C4×C29—41no—
170C22×C4×C29—41no—
171C22×C4×C29—41no—
172Q16×C29—42no—
173Q16×C29—42no—
174Q16×C29—81no—
175SD16×C29—22no—
176SD16×C29—42no—
177SD16×C29—81no—
178SD16×C29—81no—
179D8×C29—22no—
180M16×C29—42no—
181M16×C29—81no—
182C2×C8×C29—21no—
183C2×C8×C29—21no—
184C2×C8×C29—21no—
185C2×C8×C29—21no—
186C2×C8×C29—21no—
187C2×C8×C29—81no—
188C2×C8×C29C2×D411yescharacteristic
189C2×C8×C29C2×D411yescharacteristic
190C2×C8×C29C2×D411yescharacteristic
191C2×C8×C29C2×D411yescharacteristic
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×C29—21no—
199C4⋊C4×C29—21no—
200C4⋊C4×C29—21no—
201C4⋊C4×C29—41no—
202C4⋊C4×C29—41no—
203C4⋊C4×C29—41no—
204C4⋊C4×C29—41no—
205C4⋊C4×C29C2×D411yescharacteristic
206C4⋊C4×C29C2×D411yescharacteristic
207C4⋊C4×C29C2×D411yescharacteristic
208C4⋊C4×C29C2×D411yescharacteristic
209C22⋊C4×C29—21no—
210C22⋊C4×C29—21no—
211C22⋊C4×C29—21no—
212C22⋊C4×C29—41no—
213C22⋊C4×C29—41no—
214C22⋊C4×C29—41no—
215C22⋊C4×C29—41no—
216C42×C29—21no—
217C42×C29C2411yescharacteristic
218#20031C2911yesmaximal, characteristic, direct product factor, Sylow
219C23×C29—21no—
220C23×C29—21no—
221C23×C29—21no—
222Q8×C29—21no—
223Q8×C29—41no—
224Q8×C29—41no—
225Q8×C29—41no—
226Q8×C29—41no—
227Q8×C29—41no—
228Q8×C29—41no—
229Q8×C29—41no—
230Q8×C29—41no—
231Q8×C29—82no—
232Q8×C29—82no—
233Q8×C29AGL(1,ℤ/8)12yes—
234D4×C29—21no—
235D4×C29—21no—
236D4×C29—21no—
237D4×C29—21no—
238D4×C29—21no—
239D4×C29—82no—
240D4×C29—82no—
241D4×C29#13712yescomplemented
242C2×C4×C29—21no—
243C2×C4×C29—21no—
244C2×C4×C29—21no—
245C2×C4×C29—21no—
246C2×C4×C29—21no—
247C2×C4×C29—41no—
248C2×C4×C29—41no—
249C2×C4×C29—41no—
250C2×C4×C29—41no—
251C2×C4×C29—41no—
252C2×C4×C29—41no—
253C2×C4×C29—41no—
254C2×C4×C29—41no—
255C2×C4×C29—41no—
256C2×C4×C29—41no—
257C2×C4×C29—82no—
258C2×C4×C29—82no—
259C2×C4×C29—82no—
260C2×C4×C29—82no—
261C2×C4×C29C22×D411yescharacteristic
262C2×C4×C29C22×D411yescharacteristic
263C2×C4×C29H(5,𝔽2)11yescharacteristic
264C8×C29—22no—
265C8×C29—21no—
266C8×C29—21no—
267C8×C29—21no—
268C8×C29—21no—
269C8×C29—41no—
270C8×C29—41no—
271C8×C29—41no—
272C8×C29—41no—
273Q8×D8C2×C2911yescharacteristic, complemented
274#3330C2×C2911yescharacteristic
275#3298C2×C2911yescharacteristic, complemented
276#3276C2×C2911yescharacteristic, complemented
277#1723C2×C2911yescharacteristic, complemented
278#1699C2×C2911yescharacteristic, complemented
279#1693C2×C2911yescharacteristic, complemented
280#1680C2×C2911yescharacteristic, complemented
281#1669C2×C2911yescharacteristic, complemented
282#1654C2×C2911yescharacteristic, complemented
283#1651C2×C2911yescharacteristic, complemented
284#1649C2×C2911yescharacteristic, complemented
285#1647C2×C2911yescharacteristic, complemented
286#1588C2×C2911yescharacteristic, complemented
287#1586C2×C2911yescharacteristic, complemented
288C22×C29—22no—
289C22×C29—41no—
290C22×C29—41no—
291C22×C29—41no—
292C22×C29—41no—
293C22×C29—41no—
294C22×C29—41no—
295C22×C29—41no—
296C22×C29—41no—
297C22×C29D4211yescharacteristic
298C4×C29—22no—
299C4×C29—21no—
300C4×C29—41no—
301C4×C29—41no—
302C4×C29—41no—
303C4×C29—41no—
304C4×C29—81no—
305C4×C29—81no—
306C4×C29—81no—
307C4×C29—81no—
308C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
309C4×C29C2×#13711yescharacteristic
310C4×C29#57611yescharacteristic
311C4×C29#57711yescharacteristic
312C2×#137—21no—
313D4×Q8C22×C2911yescharacteristic
314D4×Q8C22×C2911yescharacteristic
315#547C22×C2911yescharacteristic
316#547C22×C2911yescharacteristic
317#500—21no—
318#500C22×C2911yescharacteristic
319#500C22×C2911yescharacteristic
320#498C22×C2911yescharacteristic
321#494C22×C2911yescharacteristic
322#487C22×C2911yescharacteristic
323#487C22×C2911yescharacteristic
324#484—21no—
325#483—21no—
326#475C22×C2911yescharacteristic
327#474—21no—
328#474—21no—
329#474C22×C2911yescharacteristic
330#474C22×C2911yescharacteristic
331#474C22×C2911yescharacteristic
332#470—21no—
333#468—21no—
334#465—21no—
335#462C22×C2911yescharacteristic
336#461C22×C2911yescharacteristic
337#461C22×C2911yescharacteristic
338#461C22×C2911yescharacteristic
339#452—21no—
340#451—21no—
341#449—21no—
342#448—21no—
343C8×Q8C22×C2911yescharacteristic
344C4×SD16C22×C2911yescharacteristic
345C4×D8—21no—
346C4×D8C22×C2911yescharacteristic
347#436C22×C2911yescharacteristic
348#436C22×C2911yescharacteristic
349C8×D4C22×C2911yescharacteristic
350#417—21no—
351C2×#103—21no—
352#335C22×C2911yescharacteristic
353#334C22×C2911yescharacteristic
354#332C22×C2911yescharacteristic
355#332C22×C2911yescharacteristic
356#332C22×C2911yescharacteristic
357#332C22×C2911yescharacteristic
358Q8⋊C8C22×C2911yescharacteristic
359D4⋊C8C22×C2911yescharacteristic
360D4⋊C8C22×C2911yescharacteristic
361D4⋊C8C22×C2911yescharacteristic
362#322C22×C2911yescharacteristic
363C2×C29—42no—
364C2×C29—81no—
365C2×C29—81no—
366C2×C29#326411yescharacteristic
367C2×C29#326611yescharacteristic
368C2×C29#329311yescharacteristic
369C2×#41—21no—
370C2×#41—21no—
371C22×Q8—21no—
372C22×Q8—21no—
373#137—44no—
374C2×Q16—21no—
375C2×Q16—21no—
376C2×Q16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16D4×C2911yescharacteristic
381C2×D8D4×C2911yescharacteristic
382C2×M16—21no—
383C2×M16—21no—
384C22×C8—21no—
385C4⋊Q8—21no—
386C4⋊Q8—21no—
387C4⋊Q8C23×C2911yescharacteristic
388C4⋊Q8C23×C2911yescharacteristic
389C4⋊Q8C23×C2911yescharacteristic
390C4⋊Q8C23×C2911yescharacteristic
391#123—41no—
392#123—41no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—41no—
398C22⋊Q8—41no—
399#121—21no—
400#121—21no—
401C4×Q8C23×C2911yescharacteristic
402C4×D4—21no—
403C4×D4—21no—
404C4×D4C23×C2911yescharacteristic
405C4×D4C23×C2911yescharacteristic
406C4×D4C23×C2911yescharacteristic
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409#107—21no—
410#107—21no—
411#107—21no—
412#107—21no—
413#107—21no—
414#107—41no—
415#107D4×C2911yescharacteristic
416#106—21no—
417#106—41no—
418#106D4×C2911yescharacteristic
419C4⋊C8—21no—
420C4⋊C8C23×C2911yescharacteristic
421C4⋊C8C23×C2911yescharacteristic
422C4⋊C8C23×C2911yescharacteristic
423C4⋊C8C23×C2911yescharacteristic
424#103—21no—
425#103—21no—
426#103—21no—
427#103—21no—
428#103—21no—
429#103—21no—
430#103—21no—
431#103—21no—
432#103—21no—
433#103D4×C2911yescharacteristic
434#102—21no—
435#102—21no—
436#102—21no—
437#102D4×C2911yescharacteristic
438#102D4×C2911yescharacteristic
439#102D4×C2911yescharacteristic
440C22⋊C8—21no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443C4×C8—21no—
444C4×C8C23×C2911yescharacteristic
445C4×C8C23×C2911yescharacteristic
446C4×C8C23×C2911yescharacteristic
447C29#2003111yescharacteristic, direct product factor, Sylow
448#41—42no—
449#41—42no—
450#41—81no—
451#41—81no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—41no—
457C2×Q8—41no—
458C2×Q8—42no—
459C2×Q8—42no—
460C2×Q8—81no—
461C2×Q8—81no—
462C2×Q8C2×D4×C2911yescharacteristic
463C2×D4—41no—
464C2×D4—41no—
465C2×D4C2×D4×C2911yescharacteristic
466C2×D4C2×D4×C2911yescharacteristic
467C2×D4C2×D4×C2911yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475Q16—42no—
476Q16—42no—
477Q16—81no—
478SD16—22no—
479SD16—42no—
480SD16—81no—
481SD16—81no—
482D8—22no—
483M16—42no—
484M16—81no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—81no—
491C2×C8C2×D4×C2911yescharacteristic
492C2×C8C2×D4×C2911yescharacteristic
493C2×C8C2×D4×C2911yescharacteristic
494C2×C8C2×D4×C2911yescharacteristic
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4C2×D4×C2911yescharacteristic
509C4⋊C4C2×D4×C2911yescharacteristic
510C4⋊C4C2×D4×C2911yescharacteristic
511C4⋊C4C2×D4×C2911yescharacteristic
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C42—21no—
520C42C24×C2911yescharacteristic
521C23—21no—
522C23—21no—
523C23—21no—
524Q8—21no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533Q8—82no—
534Q8—82no—
535Q8C29×AGL(1,ℤ/8)12yes—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—82no—
542D4—82no—
543D4C29×#13712yescomplemented
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4—82no—
563C2×C4C22×D4×C2911yescharacteristic
564C2×C4C22×D4×C2911yescharacteristic
565C2×C4C29×H(5,𝔽2)11yescharacteristic
566C8—22no—
567C8—21no—
568C8—21no—
569C8—21no—
570C8—21no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—41no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22D42×C2911yescharacteristic
585C4—22no—
586C4—21no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
596C4C2×C29×#13711yescharacteristic
597C4C29×#57611yescharacteristic
598C4C29×#57711yescharacteristic
599C2—42no—
600C2—81no—
601C2—81no—
602C2C29×#326411yescharacteristic
603C2C29×#326611yescharacteristic
604C2C29×#329311yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3330C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C42×C29 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. Q8×D8×C29C2semidirect
3. C29×#3298C2semidirect
4. C29×#3276C2semidirect
5. C29×#1723C2semidirect
6. C29×#1699C2semidirect
7. C29×#1693C2semidirect
8. C29×#1680C2semidirect
9. C29×#1669C2semidirect
10. C29×#1654C2semidirect
11. C29×#1651C2semidirect
12. C29×#1649C2semidirect
13. C29×#1647C2semidirect
14. C29×#1588C2semidirect
15. C29×#1586C2semidirect
218. #20031C29direct (N × H)
241. D4×C29#137semidirect
273. Q8×D8C2×C29semidirect
275. #3298C2×C29semidirect
276. #3276C2×C29semidirect
277. #1723C2×C29semidirect
278. #1699C2×C29semidirect
279. #1693C2×C29semidirect
280. #1680C2×C29semidirect
281. #1669C2×C29semidirect
282. #1654C2×C29semidirect
283. #1651C2×C29semidirect
284. #1649C2×C29semidirect
285. #1647C2×C29semidirect
286. #1588C2×C29semidirect
287. #1586C2×C29semidirect
447. C29#20031direct (N × H)
543. D4C29×#137semidirect

Maximal subgroups

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

subgroupindex
Q8×D8×C292
C29×#33302
C29×#32982
C29×#32762
C29×#17232
C29×#16992
C29×#16932
C29×#16802
C29×#16692
C29×#16542
C29×#16512
C29×#16492
C29×#16472
C29×#15882
C29×#15862
#2003129