Finite Group Databasebeta

← C29×#19307 #20314207

Subgroups — C29×#19307 #20314207

Order 7424.

656 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3185C211yesmaximal, characteristic, complemented
2C29×#3110C211yesmaximal, characteristic
3C29×#3077C211yesmaximal, characteristic
4D4×M16×C29C211yesmaximal, characteristic
5C29×#1703C211yesmaximal, characteristic, complemented
6C29×#1699C211yesmaximal, characteristic, complemented
7C29×#1691C211yesmaximal, characteristic, complemented
8C29×#1689C211yesmaximal, characteristic, complemented
9C29×#1683C211yesmaximal, characteristic, complemented
10C29×#1679C211yesmaximal, characteristic, complemented
11C29×#1671C211yesmaximal, characteristic, complemented
12C29×#1669C211yesmaximal, characteristic, complemented
13C29×#1569C211yesmaximal, characteristic, complemented
14C29×#1561C211yesmaximal, characteristic, complemented
15C29×#1559C211yesmaximal, characteristic, complemented
16C22×M16×C29—21no—
17C29×#533C2211yescharacteristic
18C29×#533C2211yescharacteristic
19C2×C4×D4×C29C2211yescharacteristic
20C29×#498C2211yescharacteristic, complemented
21C29×#494C2211yescharacteristic, complemented
22C29×#487C2211yescharacteristic, complemented
23C29×#487C2211yescharacteristic, complemented
24C29×#484—21no—
25C29×#478—21no—
26C29×#478—21no—
27C29×#476C2211yescharacteristic
28C29×#476C2211yescharacteristic
29C29×#474C2211yescharacteristic
30C29×#474C2211yescharacteristic
31C29×#474C2211yescharacteristic
32C29×#474C2211yescharacteristic
33C29×#470—21no—
34C29×#470—21no—
35C29×#461C2211yescharacteristic
36C29×#461C2211yescharacteristic
37C29×#450—21no—
38C29×#441—21no—
39C29×#441—21no—
40C29×#440—21no—
41C29×#440—21no—
42C29×#436C2211yescharacteristic
43C29×#436C2211yescharacteristic
44C29×#435—21no—
45C29×#435—21no—
46C8×D4×C29C2211yescharacteristic
47C8×D4×C29C2211yescharacteristic
48C29×#432C2211yescharacteristic
49C29×#428—21no—
50C29×#423C2211yescharacteristic
51C29×#423C2211yescharacteristic
52C29×#418—21no—
53C29×#407—21no—
54C4×M16×C29C2211yescharacteristic
55C29×#335C2211yescharacteristic, complemented
56C29×#335C2211yescharacteristic, complemented
57C29×#334C2211yescharacteristic, complemented
58C29×#334C2211yescharacteristic, complemented
59C29×#333C2211yescharacteristic, complemented
60C29×#333C2211yescharacteristic, complemented
61C29×#332C2211yescharacteristic, complemented
62C29×#332C2211yescharacteristic, complemented
63C29×#332C2211yescharacteristic, complemented
64C29×#332C2211yescharacteristic, complemented
65C29×#332C2211yescharacteristic, complemented
66C29×#332C2211yescharacteristic, complemented
67C22×D4×C29D411yescharacteristic
68C23×C4×C29—21no—
69C2×Q16×C29—21no—
70C2×Q16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×M16×C29—21no—
74C2×M16×C29—21no—
75C2×M16×C29—21no—
76C2×M16×C29—21no—
77C2×M16×C29—44no—
78C2×M16×C29D411yescharacteristic
79C2×M16×C29D411yescharacteristic
80C22×C8×C29—21no—
81C22×C8×C29—21no—
82C29×C4⋊Q8C2311yescharacteristic
83C29×C4⋊Q8C2311yescharacteristic
84C29×C4⋊Q8C2311yescharacteristic
85C29×C4⋊Q8C2311yescharacteristic
86C29×#125—21no—
87C29×#125—21no—
88C29×C22⋊Q8—21no—
89C29×C22⋊Q8—21no—
90C29×C22⋊Q8—21no—
91C29×C22⋊Q8—21no—
92C4×Q8×C29—21no—
93C4×Q8×C29—21no—
94C4×Q8×C29—21no—
95C4×Q8×C29—21no—
96C4×D4×C29—21no—
97C4×D4×C29—21no—
98C4×D4×C29D411yescharacteristic
99C4×D4×C29D411yescharacteristic
100C4×D4×C29C2311yescharacteristic
101C4×D4×C29C2311yescharacteristic
102C29×#117—21no—
103C29×#117—21no—
104C2×C4⋊C4×C29D411yescharacteristic
105C2×C22⋊C4×C29—21no—
106C2×C42×C29C2311yescharacteristic
107C29×#107—21no—
108C29×#107—21no—
109C29×#107—21no—
110C29×#107—21no—
111C29×#106—21no—
112C29×#106—21no—
113C29×#106—21no—
114C29×#106—21no—
115C29×C4⋊C8—21no—
116C29×C4⋊C8—21no—
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×C4⋊C8C2311yescharacteristic
122C29×C4⋊C8C2311yescharacteristic
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—21no—
126C29×#103—21no—
127C29×#103—21no—
128C29×#103—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×C22⋊C8—21no—
136C29×C22⋊C8—21no—
137C29×C22⋊C8—21no—
138C29×C22⋊C8—21no—
139C29×C22⋊C8—21no—
140C29×#97—21no—
141C29×#97D411yescharacteristic
142C29×#97D411yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C4×C8×C29C2311yescharacteristic
145C24×C29—21no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×D4×C29—22no—
151C2×D4×C29—21no—
152C2×D4×C29—41no—
153C2×D4×C29C2×D411yescharacteristic
154C2×D4×C29C2×D411yescharacteristic
155C22×C4×C29—21no—
156C22×C4×C29—21no—
157C22×C4×C29—21no—
158C22×C4×C29—21no—
159C22×C4×C29—21no—
160C22×C4×C29—42no—
161C22×C4×C29—42no—
162C22×C4×C29C2×D411yescharacteristic
163C22×C4×C29C2×D411yescharacteristic
164C22×C4×C29#4111yescharacteristic
165Q16×C29—42no—
166Q16×C29—42no—
167SD16×C29—42no—
168SD16×C29—42no—
169M16×C29—22no—
170M16×C29—41no—
171M16×C29—42no—
172M16×C29—42no—
173M16×C29—42no—
174M16×C29—42no—
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×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—41no—
197C4⋊C4×C29—41no—
198C4⋊C4×C29—41no—
199C4⋊C4×C29—41no—
200C4⋊C4×C29C2×D411yescharacteristic
201C4⋊C4×C29C2×D411yescharacteristic
202C22⋊C4×C29—21no—
203C22⋊C4×C29—21no—
204C22⋊C4×C29—21no—
205C22⋊C4×C29—21no—
206C22⋊C4×C29—41no—
207C22⋊C4×C29—41no—
208C42×C29—41no—
209C42×C29—41no—
210C42×C29C2×D411yescharacteristic
211C42×C29C2×D411yescharacteristic
212C42×C29#4111yescharacteristic
213C42×C29C2411yescharacteristic
214#19307C2911yesmaximal, characteristic, direct product factor, Sylow
215C23×C29—21no—
216C23×C29—21no—
217C23×C29—42no—
218C23×C29—42no—
219C23×C29—81no—
220C23×C29#12111yescharacteristic
221Q8×C29—41no—
222Q8×C29—41no—
223Q8×C29—41no—
224Q8×C29—41no—
225Q8×C29—41no—
226Q8×C29—41no—
227Q8×C29—81no—
228D4×C29—21no—
229D4×C29—21no—
230D4×C29—21no—
231D4×C29—42no—
232D4×C29#13712yes—
233C2×C4×C29—21no—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—21no—
239C2×C4×C29—41no—
240C2×C4×C29—42no—
241C2×C4×C29—42no—
242C2×C4×C29—42no—
243C2×C4×C29—41no—
244C2×C4×C29—41no—
245C2×C4×C29—41no—
246C2×C4×C29—41no—
247C2×C4×C29—41no—
248C2×C4×C29—41no—
249C2×C4×C29—41no—
250C2×C4×C29—41no—
251C2×C4×C29#12111yescharacteristic
252C2×C4×C29#12111yescharacteristic
253C2×C4×C29#12111yescharacteristic
254C2×C4×C29C22×D411yescharacteristic
255C2×C4×C29C22×D411yescharacteristic
256C2×C4×C29C2×#4111yescharacteristic
257C8×C29—21no—
258C8×C29—21no—
259C8×C29—21no—
260C8×C29—41no—
261C8×C29—41no—
262C8×C29—41no—
263C8×C29—41no—
264C8×C29—41no—
265C8×C29—41no—
266C8×C29AGL(1,ℤ/8)12yes—
267#3185C2×C2911yescharacteristic, complemented
268#3110C2×C2911yescharacteristic
269#3077C2×C2911yescharacteristic
270D4×M16C2×C2911yescharacteristic
271#1703C2×C2911yescharacteristic, complemented
272#1699C2×C2911yescharacteristic, complemented
273#1691C2×C2911yescharacteristic, complemented
274#1689C2×C2911yescharacteristic, complemented
275#1683C2×C2911yescharacteristic, complemented
276#1679C2×C2911yescharacteristic, complemented
277#1671C2×C2911yescharacteristic, complemented
278#1669C2×C2911yescharacteristic, complemented
279#1569C2×C2911yescharacteristic, complemented
280#1561C2×C2911yescharacteristic, complemented
281#1559C2×C2911yescharacteristic, complemented
282C22×C29—21no—
283C22×C29—21no—
284C22×C29—22no—
285C22×C29—21no—
286C22×C29—41no—
287C22×C29—41no—
288C22×C29—41no—
289C22×C29—41no—
290C22×C29—41no—
291C22×C29—84no—
292C22×C29C2×#12111yescharacteristic
293C4×C29—21no—
294C4×C29—21no—
295C4×C29—21no—
296C4×C29—21no—
297C4×C29—41no—
298C4×C29—41no—
299C4×C29—81no—
300C4×C29—81no—
301C4×C29—81no—
302C4×C29—81no—
303C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
304C4×C29C2×#13711yescharacteristic
305C4×C29#57511yescharacteristic
306C4×C29#57511yescharacteristic
307C22×M16—21no—
308#533C22×C2911yescharacteristic
309#533C22×C2911yescharacteristic
310C2×C4×D4C22×C2911yescharacteristic
311#498C22×C2911yescharacteristic, complemented
312#494C22×C2911yescharacteristic, complemented
313#487C22×C2911yescharacteristic, complemented
314#487C22×C2911yescharacteristic, complemented
315#484—21no—
316#478—21no—
317#478—21no—
318#476C22×C2911yescharacteristic
319#476C22×C2911yescharacteristic
320#474C22×C2911yescharacteristic
321#474C22×C2911yescharacteristic
322#474C22×C2911yescharacteristic
323#474C22×C2911yescharacteristic
324#470—21no—
325#470—21no—
326#461C22×C2911yescharacteristic
327#461C22×C2911yescharacteristic
328#450—21no—
329#441—21no—
330#441—21no—
331#440—21no—
332#440—21no—
333#436C22×C2911yescharacteristic
334#436C22×C2911yescharacteristic
335#435—21no—
336#435—21no—
337C8×D4C22×C2911yescharacteristic
338C8×D4C22×C2911yescharacteristic
339#432C22×C2911yescharacteristic
340#428—21no—
341#423C22×C2911yescharacteristic
342#423C22×C2911yescharacteristic
343#418—21no—
344#407—21no—
345C4×M16C22×C2911yescharacteristic
346#335C22×C2911yescharacteristic, complemented
347#335C22×C2911yescharacteristic, complemented
348#334C22×C2911yescharacteristic, complemented
349#334C22×C2911yescharacteristic, complemented
350#333C22×C2911yescharacteristic, complemented
351#333C22×C2911yescharacteristic, complemented
352#332C22×C2911yescharacteristic, complemented
353#332C22×C2911yescharacteristic, complemented
354#332C22×C2911yescharacteristic, complemented
355#332C22×C2911yescharacteristic, complemented
356#332C22×C2911yescharacteristic, complemented
357#332C22×C2911yescharacteristic, complemented
358C2×C29—41no—
359C2×C29—42no—
360C2×C29—81no—
361C2×C29#303611yescharacteristic
362C2×C29#305611yescharacteristic
363C2×C29#306911yescharacteristic
364C22×D4D4×C2911yescharacteristic
365C23×C4—21no—
366C2×Q16—21no—
367C2×Q16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—44no—
375C2×M16D4×C2911yescharacteristic
376C2×M16D4×C2911yescharacteristic
377C22×C8—21no—
378C22×C8—21no—
379C4⋊Q8C23×C2911yescharacteristic
380C4⋊Q8C23×C2911yescharacteristic
381C4⋊Q8C23×C2911yescharacteristic
382C4⋊Q8C23×C2911yescharacteristic
383#125—21no—
384#125—21no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4D4×C2911yescharacteristic
396C4×D4D4×C2911yescharacteristic
397C4×D4C23×C2911yescharacteristic
398C4×D4C23×C2911yescharacteristic
399#117—21no—
400#117—21no—
401C2×C4⋊C4D4×C2911yescharacteristic
402C2×C22⋊C4—21no—
403C2×C42C23×C2911yescharacteristic
404#107—21no—
405#107—21no—
406#107—21no—
407#107—21no—
408#106—21no—
409#106—21no—
410#106—21no—
411#106—21no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8C23×C2911yescharacteristic
415C4⋊C8C23×C2911yescharacteristic
416C4⋊C8C23×C2911yescharacteristic
417C4⋊C8C23×C2911yescharacteristic
418C4⋊C8C23×C2911yescharacteristic
419C4⋊C8C23×C2911yescharacteristic
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432C22⋊C8—21no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437#97—21no—
438#97D4×C2911yescharacteristic
439#97D4×C2911yescharacteristic
440C4×C8C23×C2911yescharacteristic
441C4×C8C23×C2911yescharacteristic
442C29#1930711yescharacteristic, direct product factor, Sylow
443C24—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×D4—22no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4C2×D4×C2911yescharacteristic
452C2×D4C2×D4×C2911yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4C2×D4×C2911yescharacteristic
461C22×C4C2×D4×C2911yescharacteristic
462C22×C4#41×C2911yescharacteristic
463Q16—42no—
464Q16—42no—
465SD16—42no—
466SD16—42no—
467M16—22no—
468M16—41no—
469M16—42no—
470M16—42no—
471M16—42no—
472M16—42no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—42no—
480C2×C8—42no—
481C2×C8C2×D4×C2911yescharacteristic
482C2×C8C2×D4×C2911yescharacteristic
483C2×C8C2×D4×C2911yescharacteristic
484C2×C8C2×D4×C2911yescharacteristic
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⋊C4—21no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4C2×D4×C2911yescharacteristic
499C4⋊C4C2×D4×C2911yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C42—41no—
507C42—41no—
508C42C2×D4×C2911yescharacteristic
509C42C2×D4×C2911yescharacteristic
510C42#41×C2911yescharacteristic
511C42C24×C2911yescharacteristic
512C23—21no—
513C23—21no—
514C23—42no—
515C23—42no—
516C23—81no—
517C23C29×#12111yescharacteristic
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—81no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—42no—
529D4C29×#13712yes—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4C29×#12111yescharacteristic
549C2×C4C29×#12111yescharacteristic
550C2×C4C29×#12111yescharacteristic
551C2×C4C22×D4×C2911yescharacteristic
552C2×C4C22×D4×C2911yescharacteristic
553C2×C4C2×#41×C2911yescharacteristic
554C8—21no—
555C8—21no—
556C8—21no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8C29×AGL(1,ℤ/8)12yes—
564C22—21no—
565C22—21no—
566C22—22no—
567C22—21no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—84no—
574C22C2×C29×#12111yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—21no—
579C4—41no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
586C4C2×C29×#13711yescharacteristic
587C4C29×#57511yescharacteristic
588C4C29×#57511yescharacteristic
589C2—41no—
590C2—42no—
591C2—81no—
592C2C29×#303611yescharacteristic
593C2C29×#305611yescharacteristic
594C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC22×D4×C29D4
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×#3185C2semidirect
5. C29×#1703C2semidirect
6. C29×#1699C2semidirect
7. C29×#1691C2semidirect
8. C29×#1689C2semidirect
9. C29×#1683C2semidirect
10. C29×#1679C2semidirect
11. C29×#1671C2semidirect
12. C29×#1669C2semidirect
13. C29×#1569C2semidirect
14. C29×#1561C2semidirect
15. C29×#1559C2semidirect
20. C29×#498C22semidirect
21. C29×#494C22semidirect
22. C29×#487C22semidirect
23. C29×#487C22semidirect
55. C29×#335C22semidirect
56. C29×#335C22semidirect
57. C29×#334C22semidirect
58. C29×#334C22semidirect
59. C29×#333C22semidirect
60. C29×#333C22semidirect
61. C29×#332C22semidirect
62. C29×#332C22semidirect
63. C29×#332C22semidirect
64. C29×#332C22semidirect
65. C29×#332C22semidirect
66. C29×#332C22semidirect
214. #19307C29direct (N × H)
267. #3185C2×C29semidirect
271. #1703C2×C29semidirect
272. #1699C2×C29semidirect
273. #1691C2×C29semidirect
274. #1689C2×C29semidirect
275. #1683C2×C29semidirect
276. #1679C2×C29semidirect
277. #1671C2×C29semidirect
278. #1669C2×C29semidirect
279. #1569C2×C29semidirect
280. #1561C2×C29semidirect
281. #1559C2×C29semidirect
311. #498C22×C29semidirect
312. #494C22×C29semidirect
313. #487C22×C29semidirect
314. #487C22×C29semidirect
346. #335C22×C29semidirect
347. #335C22×C29semidirect
348. #334C22×C29semidirect
349. #334C22×C29semidirect
350. #333C22×C29semidirect
351. #333C22×C29semidirect
352. #332C22×C29semidirect
353. #332C22×C29semidirect
354. #332C22×C29semidirect
355. #332C22×C29semidirect
356. #332C22×C29semidirect
357. #332C22×C29semidirect
442. C29#19307direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31852
C29×#31102
C29×#30772
D4×M16×C292
C29×#17032
C29×#16992
C29×#16912
C29×#16892
C29×#16832
C29×#16792
C29×#16712
C29×#16692
C29×#15692
C29×#15612
C29×#15592
#1930729