Finite Group Databasebeta

← C29×#19371 #20314271

Subgroups — C29×#19371 #20314271

Order 7424.

622 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3254C211yesmaximal, characteristic
2C29×#3235C211yesmaximal, characteristic
3C29×#3185C211yesmaximal, characteristic, complemented
4C29×#2935C211yesmaximal, 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×#1552C211yesmaximal, characteristic, complemented
15C29×#1550C211yesmaximal, characteristic, complemented
16C2×C29×#131—21no—
17C29×#533C2211yescharacteristic
18C29×#533C2211yescharacteristic
19C29×#532C2211yescharacteristic
20C29×#501—21no—
21C29×#498C2211yescharacteristic
22C29×#494C2211yescharacteristic
23C29×#490—21no—
24C29×#487C2211yescharacteristic
25C29×#487C2211yescharacteristic
26C29×#482—21no—
27C29×#482—21no—
28C29×#477—21no—
29C29×#476C2211yescharacteristic
30C29×#476C2211yescharacteristic
31C29×#474C2211yescharacteristic
32C29×#474C2211yescharacteristic
33C29×#474C2211yescharacteristic
34C29×#474C2211yescharacteristic
35C29×#470—21no—
36C29×#470—21no—
37C29×#468—21no—
38C29×#468—21no—
39C29×#461C2211yescharacteristic
40C29×#461C2211yescharacteristic
41C29×#460—21no—
42C29×#441—21no—
43C29×#441—21no—
44C29×#436C2211yescharacteristic
45C29×#436C2211yescharacteristic
46C29×#435—21no—
47C29×#435—21no—
48C8×D4×C29C2211yescharacteristic
49C8×D4×C29C2211yescharacteristic
50C29×#432C2211yescharacteristic
51C29×#423C2211yescharacteristic
52C2×C29×C4⋊C8C2211yescharacteristic
53C29×#408—21no—
54C4×M16×C29C2211yescharacteristic
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×#332C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#332C2211yescharacteristic
66C29×#332C2211yescharacteristic
67C2×#41×C29—21no—
68C2×Q16×C29—21no—
69C2×Q16×C29—21no—
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C29×#131—44no—
73C2×M16×C29—21no—
74C2×M16×C29—21no—
75C2×M16×C29—21no—
76C2×M16×C29D411yescharacteristic
77C2×M16×C29D411yescharacteristic
78C22×C8×C29—21no—
79C22×C8×C29—21no—
80C22×C8×C29—21no—
81C29×C4⋊Q8D411yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×C4⋊Q8C2311yescharacteristic
84C29×C4⋊Q8C2311yescharacteristic
85C29×C4⋊Q8C2311yescharacteristic
86C29×#127D411yescharacteristic
87C29×#125—21no—
88C29×#125—21no—
89C29×#124—21no—
90C29×C22⋊Q8—21no—
91C29×C22⋊Q8—21no—
92C29×C22⋊Q8—21no—
93C29×C22⋊Q8—21no—
94C29×#121—21no—
95C29×#121D411yescharacteristic
96C29×#121D411yescharacteristic
97C4×Q8×C29—21no—
98C4×Q8×C29—21no—
99C4×Q8×C29—21no—
100C4×Q8×C29—21no—
101C4×D4×C29—21no—
102C4×D4×C29C2311yescharacteristic
103C4×D4×C29C2311yescharacteristic
104C29×#117—21no—
105C29×#117—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
145#41×C29—42no—
146#41×C29—42no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×Q8×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29C2×D411yescharacteristic
157C2×D4×C29C2×D411yescharacteristic
158C22×C4×C29—21no—
159C22×C4×C29—21no—
160C22×C4×C29C2×D411yescharacteristic
161C22×C4×C29C2×D411yescharacteristic
162C22×C4×C29#4111yescharacteristic
163Q16×C29—42no—
164Q16×C29—42no—
165SD16×C29—81no—
166SD16×C29—81no—
167M16×C29—22no—
168M16×C29—41no—
169M16×C29—42no—
170M16×C29—42no—
171M16×C29—81no—
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×C29—42no—
180C2×C8×C29—42no—
181C2×C8×C29C2×D411yescharacteristic
182C2×C8×C29C2×D411yescharacteristic
183C2×C8×C29C2×D411yescharacteristic
184C2×C8×C29C2×D411yescharacteristic
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—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—21no—
194C4⋊C4×C29—41no—
195C4⋊C4×C29—41no—
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—41no—
205C22⋊C4×C29—41no—
206C42×C29—41no—
207C42×C29—41no—
208C42×C29C2×D411yescharacteristic
209C42×C29C2×D411yescharacteristic
210C42×C29#4111yescharacteristic
211C42×C29C2411yescharacteristic
212#19371C2911yesmaximal, characteristic, direct product factor, Sylow
213C23×C29—21no—
214C23×C29—21no—
215C23×C29#12111yescharacteristic
216Q8×C29—42no—
217Q8×C29—41no—
218Q8×C29—41no—
219Q8×C29—41no—
220Q8×C29—41no—
221Q8×C29—41no—
222Q8×C29—41no—
223Q8×C29—81no—
224D4×C29—21no—
225D4×C29—21no—
226D4×C29—21no—
227D4×C29—21no—
228D4×C29—42no—
229D4×C29—42no—
230D4×C29—42no—
231D4×C29—81no—
232C2×C4×C29—21no—
233C2×C4×C29—21no—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—41no—
239C2×C4×C29—41no—
240C2×C4×C29—41no—
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#12111yescharacteristic
248C2×C4×C29#12111yescharacteristic
249C2×C4×C29#12111yescharacteristic
250C2×C4×C29C22×D411yescharacteristic
251C2×C4×C29C22×D411yescharacteristic
252C2×C4×C29C2×#4111yescharacteristic
253C8×C29—21no—
254C8×C29—21no—
255C8×C29—21no—
256C8×C29—41no—
257C8×C29—41no—
258C8×C29—41no—
259C8×C29—41no—
260C8×C29—41no—
261C8×C29—41no—
262C8×C29AGL(1,ℤ/8)12yes—
263#3254C2×C2911yescharacteristic
264#3235C2×C2911yescharacteristic
265#3185C2×C2911yescharacteristic, complemented
266#2935C2×C2911yescharacteristic
267#1703C2×C2911yescharacteristic, complemented
268#1699C2×C2911yescharacteristic, complemented
269#1691C2×C2911yescharacteristic, complemented
270#1689C2×C2911yescharacteristic, complemented
271#1683C2×C2911yescharacteristic, complemented
272#1679C2×C2911yescharacteristic, complemented
273#1671C2×C2911yescharacteristic, complemented
274#1669C2×C2911yescharacteristic, complemented
275#1569C2×C2911yescharacteristic, complemented
276#1552C2×C2911yescharacteristic, complemented
277#1550C2×C2911yescharacteristic, complemented
278C22×C29—21no—
279C22×C29—21no—
280C22×C29—21no—
281C22×C29—41no—
282C22×C29—41no—
283C22×C29—41no—
284C22×C29—41no—
285C22×C29—41no—
286C22×C29—41no—
287C22×C29C2×#12111yescharacteristic
288C4×C29—21no—
289C4×C29—21no—
290C4×C29—21no—
291C4×C29—21no—
292C4×C29—41no—
293C4×C29—41no—
294C4×C29—81no—
295C4×C29—81no—
296C4×C29—81no—
297C4×C29—81no—
298C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C29#57511yescharacteristic
300C4×C29#57711yescharacteristic
301C4×C29#57811yescharacteristic
302C2×#131—21no—
303#533C22×C2911yescharacteristic
304#533C22×C2911yescharacteristic
305#532C22×C2911yescharacteristic
306#501—21no—
307#498C22×C2911yescharacteristic
308#494C22×C2911yescharacteristic
309#490—21no—
310#487C22×C2911yescharacteristic
311#487C22×C2911yescharacteristic
312#482—21no—
313#482—21no—
314#477—21no—
315#476C22×C2911yescharacteristic
316#476C22×C2911yescharacteristic
317#474C22×C2911yescharacteristic
318#474C22×C2911yescharacteristic
319#474C22×C2911yescharacteristic
320#474C22×C2911yescharacteristic
321#470—21no—
322#470—21no—
323#468—21no—
324#468—21no—
325#461C22×C2911yescharacteristic
326#461C22×C2911yescharacteristic
327#460—21no—
328#441—21no—
329#441—21no—
330#436C22×C2911yescharacteristic
331#436C22×C2911yescharacteristic
332#435—21no—
333#435—21no—
334C8×D4C22×C2911yescharacteristic
335C8×D4C22×C2911yescharacteristic
336#432C22×C2911yescharacteristic
337#423C22×C2911yescharacteristic
338C2×C4⋊C8C22×C2911yescharacteristic
339#408—21no—
340C4×M16C22×C2911yescharacteristic
341#335C22×C2911yescharacteristic
342#335C22×C2911yescharacteristic
343#334C22×C2911yescharacteristic
344#334C22×C2911yescharacteristic
345#333C22×C2911yescharacteristic
346#333C22×C2911yescharacteristic
347#332C22×C2911yescharacteristic
348#332C22×C2911yescharacteristic
349#332C22×C2911yescharacteristic
350#332C22×C2911yescharacteristic
351#332C22×C2911yescharacteristic
352#332C22×C2911yescharacteristic
353C2×C29—41no—
354C2×C29—81no—
355C2×C29—81no—
356C2×C29#303611yescharacteristic
357C2×C29#306311yescharacteristic
358C2×C29#306911yescharacteristic
359C2×#41—21no—
360C2×Q16—21no—
361C2×Q16—21no—
362C2×SD16—21no—
363C2×SD16—21no—
364#131—44no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16D4×C2911yescharacteristic
369C2×M16D4×C2911yescharacteristic
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C4⋊Q8D4×C2911yescharacteristic
374C4⋊Q8C23×C2911yescharacteristic
375C4⋊Q8C23×C2911yescharacteristic
376C4⋊Q8C23×C2911yescharacteristic
377C4⋊Q8C23×C2911yescharacteristic
378#127D4×C2911yescharacteristic
379#125—21no—
380#125—21no—
381#124—21no—
382C22⋊Q8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386#121—21no—
387#121D4×C2911yescharacteristic
388#121D4×C2911yescharacteristic
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×D4—21no—
394C4×D4C23×C2911yescharacteristic
395C4×D4C23×C2911yescharacteristic
396#117—21no—
397#117—21no—
398C2×C42C23×C2911yescharacteristic
399#107—21no—
400#107—21no—
401#107—21no—
402#107—21no—
403#106—21no—
404#106—21no—
405#106—21no—
406#106—21no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8C23×C2911yescharacteristic
410C4⋊C8C23×C2911yescharacteristic
411C4⋊C8C23×C2911yescharacteristic
412C4⋊C8C23×C2911yescharacteristic
413C4⋊C8C23×C2911yescharacteristic
414C4⋊C8C23×C2911yescharacteristic
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432#97—21no—
433#97D4×C2911yescharacteristic
434#97D4×C2911yescharacteristic
435C4×C8C23×C2911yescharacteristic
436C4×C8C23×C2911yescharacteristic
437C29#1937111yescharacteristic, direct product factor, Sylow
438#41—42no—
439#41—42no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4C2×D4×C2911yescharacteristic
450C2×D4C2×D4×C2911yescharacteristic
451C22×C4—21no—
452C22×C4—21no—
453C22×C4C2×D4×C2911yescharacteristic
454C22×C4C2×D4×C2911yescharacteristic
455C22×C4#41×C2911yescharacteristic
456Q16—42no—
457Q16—42no—
458SD16—81no—
459SD16—81no—
460M16—22no—
461M16—41no—
462M16—42no—
463M16—42no—
464M16—81no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—42no—
472C2×C8—42no—
473C2×C8—42no—
474C2×C8C2×D4×C2911yescharacteristic
475C2×C8C2×D4×C2911yescharacteristic
476C2×C8C2×D4×C2911yescharacteristic
477C2×C8C2×D4×C2911yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4C2×D4×C2911yescharacteristic
492C4⋊C4C2×D4×C2911yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—41no—
500C42—41no—
501C42C2×D4×C2911yescharacteristic
502C42C2×D4×C2911yescharacteristic
503C42#41×C2911yescharacteristic
504C42C24×C2911yescharacteristic
505C23—21no—
506C23—21no—
507C23C29×#12111yescharacteristic
508Q8—42no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—81no—
516D4—21no—
517D4—21no—
518D4—21no—
519D4—21no—
520D4—42no—
521D4—42no—
522D4—42no—
523D4—81no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4C29×#12111yescharacteristic
540C2×C4C29×#12111yescharacteristic
541C2×C4C29×#12111yescharacteristic
542C2×C4C22×D4×C2911yescharacteristic
543C2×C4C22×D4×C2911yescharacteristic
544C2×C4C2×#41×C2911yescharacteristic
545C8—21no—
546C8—21no—
547C8—21no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8C29×AGL(1,ℤ/8)12yes—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22C2×C29×#12111yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
576C4C29×#57511yescharacteristic
577C4C29×#57711yescharacteristic
578C4C29×#57811yescharacteristic
579C2—41no—
580C2—81no—
581C2—81no—
582C2C29×#303611yescharacteristic
583C2C29×#306311yescharacteristic
584C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#532C22
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
3. 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×#1552C2semidirect
15. C29×#1550C2semidirect
212. #19371C29direct (N × H)
265. #3185C2×C29semidirect
267. #1703C2×C29semidirect
268. #1699C2×C29semidirect
269. #1691C2×C29semidirect
270. #1689C2×C29semidirect
271. #1683C2×C29semidirect
272. #1679C2×C29semidirect
273. #1671C2×C29semidirect
274. #1669C2×C29semidirect
275. #1569C2×C29semidirect
276. #1552C2×C29semidirect
277. #1550C2×C29semidirect
437. C29#19371direct (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×#32352
C29×#31852
C29×#29352
C29×#17032
C29×#16992
C29×#16912
C29×#16892
C29×#16832
C29×#16792
C29×#16712
C29×#16692
C29×#15692
C29×#15522
C29×#15502
#1937129