Finite Group Databasebeta

← C29×#19466 #20314366

Subgroups — C29×#19466 #20314366

Order 7424.

608 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3231C211yesmaximal, characteristic, complemented
2C29×#3101C211yesmaximal, characteristic
3C29×#3077C211yesmaximal, characteristic
4C29×#2974C211yesmaximal, characteristic
5C29×#1703C211yesmaximal, characteristic, complemented
6C29×#1699C211yesmaximal, characteristic, complemented
7C29×#1695C211yesmaximal, characteristic, complemented
8C29×#1691C211yesmaximal, characteristic, complemented
9C29×#1683C211yesmaximal, characteristic, complemented
10C29×#1679C211yesmaximal, characteristic, complemented
11C29×#1675C211yesmaximal, characteristic, complemented
12C29×#1671C211yesmaximal, characteristic, complemented
13C29×#1574C211yesmaximal, characteristic, complemented
14C29×#1559C211yesmaximal, characteristic, complemented
15C29×#1554C211yesmaximal, characteristic, complemented
16C29×#533C2211yescharacteristic
17C29×#533C2211yescharacteristic
18C2×C4×D4×C29C2211yescharacteristic
19C29×#500C2211yescharacteristic, complemented
20C29×#498C2211yescharacteristic, complemented
21C29×#487C2211yescharacteristic, complemented
22C29×#487C2211yescharacteristic, complemented
23C29×#485—21no—
24C29×#485—21no—
25C29×#483—21no—
26C29×#479—21no—
27C29×#479—21no—
28C29×#478—21no—
29C29×#478—21no—
30C29×#476C2211yescharacteristic
31C29×#476C2211yescharacteristic
32C29×#476C2211yescharacteristic
33C29×#476C2211yescharacteristic
34C29×#474C2211yescharacteristic
35C29×#474C2211yescharacteristic
36C29×#461C2211yescharacteristic
37C29×#461C2211yescharacteristic
38C29×#450—21no—
39C4×SD16×C29—21no—
40C4×SD16×C29—21no—
41C29×#436C2211yescharacteristic
42C29×#436C2211yescharacteristic
43C29×#435—21no—
44C29×#435—21no—
45C8×D4×C29C2211yescharacteristic
46C8×D4×C29C2211yescharacteristic
47C29×#432C2211yescharacteristic
48C29×#431C2211yescharacteristic
49C29×#431C2211yescharacteristic
50C29×#428—21no—
51C29×#423C2211yescharacteristic
52C29×#418—21no—
53C29×#407—21no—
54C2×C29×C22⋊C8—21no—
55C29×#335C2211yescharacteristic, complemented
56C29×#335C2211yescharacteristic, complemented
57C29×#334C2211yescharacteristic, complemented
58C29×#334C2211yescharacteristic, complemented
59C29×#333C2211yescharacteristic, complemented
60C29×#333C2211yescharacteristic, complemented
61C29×#333C2211yescharacteristic, complemented
62C29×#333C2211yescharacteristic, complemented
63C29×#332C2211yescharacteristic, complemented
64C29×#332C2211yescharacteristic, complemented
65C29×#332C2211yescharacteristic, complemented
66C29×#332C2211yescharacteristic, complemented
67C22×D4×C29D411yescharacteristic
68C23×C4×C29—21no—
69C2×SD16×C29—21no—
70C2×SD16×C29—21no—
71C2×M16×C29—21no—
72C2×M16×C29—21no—
73C2×M16×C29—21no—
74C22×C8×C29—21no—
75C22×C8×C29—21no—
76C29×C4⋊Q8C2311yescharacteristic
77C29×C4⋊Q8C2311yescharacteristic
78C29×C4⋊Q8C2311yescharacteristic
79C29×C4⋊Q8C2311yescharacteristic
80C29×#125—21no—
81C29×#125—21no—
82C29×C22⋊Q8—21no—
83C29×C22⋊Q8—21no—
84C29×C22⋊Q8—21no—
85C29×C22⋊Q8—21no—
86C4×Q8×C29—21no—
87C4×Q8×C29—21no—
88C4×Q8×C29—21no—
89C4×Q8×C29—21no—
90C4×D4×C29—21no—
91C4×D4×C29—21no—
92C4×D4×C29D411yescharacteristic
93C4×D4×C29D411yescharacteristic
94C4×D4×C29C2311yescharacteristic
95C4×D4×C29C2311yescharacteristic
96C29×#117—21no—
97C29×#117—21no—
98C2×C4⋊C4×C29D411yescharacteristic
99C2×C22⋊C4×C29—21no—
100C2×C42×C29C2311yescharacteristic
101C29×#107—21no—
102C29×#107—21no—
103C29×#107—21no—
104C29×#107—21no—
105C29×#106—21no—
106C29×#106—21no—
107C29×#106—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×#106—21no—
111C29×C4⋊C8—21no—
112C29×C4⋊C8D411yescharacteristic
113C29×C4⋊C8D411yescharacteristic
114C29×C4⋊C8C2311yescharacteristic
115C29×C4⋊C8C2311yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×#103—21no—
121C29×#103—21no—
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×C22⋊C8—21no—
133C29×C22⋊C8—21no—
134C29×C22⋊C8—21no—
135C29×C22⋊C8—21no—
136C29×C22⋊C8—21no—
137C29×C22⋊C8—21no—
138C29×C22⋊C8D411yescharacteristic
139C29×C22⋊C8D411yescharacteristic
140C29×#97—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C24×C29—21no—
145C2×Q8×C29—21no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×D4×C29—22no—
150C2×D4×C29—21no—
151C2×D4×C29—41no—
152C2×D4×C29C2×D411yescharacteristic
153C2×D4×C29C2×D411yescharacteristic
154C22×C4×C29—21no—
155C22×C4×C29—21no—
156C22×C4×C29—21no—
157C22×C4×C29—21no—
158C22×C4×C29—21no—
159C22×C4×C29—81no—
160C22×C4×C29—81no—
161C22×C4×C29C2×D411yescharacteristic
162C22×C4×C29C2×D411yescharacteristic
163C22×C4×C29#4111yescharacteristic
164SD16×C29—42no—
165SD16×C29—42no—
166M16×C29—42no—
167M16×C29—81no—
168M16×C29—81no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C2×C8×C29—21no—
173C2×C8×C29—21no—
174C2×C8×C29—21no—
175C2×C8×C29—81no—
176C2×C8×C29—81no—
177C2×C8×C29C2×D411yescharacteristic
178C2×C8×C29C2×D411yescharacteristic
179C2×C8×C29C2×D411yescharacteristic
180C2×C8×C29C2×D411yescharacteristic
181C4⋊C4×C29—21no—
182C4⋊C4×C29—21no—
183C4⋊C4×C29—21no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—41no—
191C4⋊C4×C29—41no—
192C4⋊C4×C29—41no—
193C4⋊C4×C29—41no—
194C4⋊C4×C29C2×D411yescharacteristic
195C4⋊C4×C29C2×D411yescharacteristic
196C22⋊C4×C29—21no—
197C22⋊C4×C29—21no—
198C22⋊C4×C29—21no—
199C22⋊C4×C29—21no—
200C22⋊C4×C29—41no—
201C22⋊C4×C29—41no—
202C42×C29—41no—
203C42×C29—41no—
204C42×C29C2×D411yescharacteristic
205C42×C29C2×D411yescharacteristic
206C42×C29#4111yescharacteristic
207C42×C29C2411yescharacteristic
208#19466C2911yesmaximal, characteristic, direct product factor, Sylow
209C23×C29—21no—
210C23×C29—21no—
211C23×C29—42no—
212C23×C29—42no—
213C23×C29—81no—
214C23×C29#12111yescharacteristic
215Q8×C29—41no—
216Q8×C29—41no—
217Q8×C29—41no—
218Q8×C29—41no—
219Q8×C29—81no—
220Q8×C29—81no—
221D4×C29—21no—
222D4×C29—21no—
223D4×C29—21no—
224D4×C29—42no—
225D4×C29#13712yes—
226C2×C4×C29—21no—
227C2×C4×C29—21no—
228C2×C4×C29—21no—
229C2×C4×C29—21no—
230C2×C4×C29—21no—
231C2×C4×C29—21no—
232C2×C4×C29—41no—
233C2×C4×C29—41no—
234C2×C4×C29—41no—
235C2×C4×C29—41no—
236C2×C4×C29—41no—
237C2×C4×C29—41no—
238C2×C4×C29—41no—
239C2×C4×C29—41no—
240C2×C4×C29—41no—
241C2×C4×C29—81no—
242C2×C4×C29—81no—
243C2×C4×C29—81no—
244C2×C4×C29#12111yescharacteristic
245C2×C4×C29#12111yescharacteristic
246C2×C4×C29#12111yescharacteristic
247C2×C4×C29C22×D411yescharacteristic
248C2×C4×C29C22×D411yescharacteristic
249C2×C4×C29C2×#4111yescharacteristic
250C8×C29—21no—
251C8×C29—21no—
252C8×C29—21no—
253C8×C29—21no—
254C8×C29—41no—
255C8×C29—41no—
256C8×C29—41no—
257C8×C29—41no—
258C8×C29—41no—
259C8×C29—41no—
260#3231C2×C2911yescharacteristic, complemented
261#3101C2×C2911yescharacteristic
262#3077C2×C2911yescharacteristic
263#2974C2×C2911yescharacteristic
264#1703C2×C2911yescharacteristic, complemented
265#1699C2×C2911yescharacteristic, complemented
266#1695C2×C2911yescharacteristic, complemented
267#1691C2×C2911yescharacteristic, complemented
268#1683C2×C2911yescharacteristic, complemented
269#1679C2×C2911yescharacteristic, complemented
270#1675C2×C2911yescharacteristic, complemented
271#1671C2×C2911yescharacteristic, complemented
272#1574C2×C2911yescharacteristic, complemented
273#1559C2×C2911yescharacteristic, complemented
274#1554C2×C2911yescharacteristic, complemented
275C22×C29—21no—
276C22×C29—21no—
277C22×C29—22no—
278C22×C29—21no—
279C22×C29—41no—
280C22×C29—41no—
281C22×C29—41no—
282C22×C29—41no—
283C22×C29—41no—
284C22×C29—84no—
285C22×C29C2×#12111yescharacteristic
286C4×C29—21no—
287C4×C29—21no—
288C4×C29—21no—
289C4×C29—21no—
290C4×C29—41no—
291C4×C29—41no—
292C4×C29—81no—
293C4×C29—81no—
294C4×C29—81no—
295C4×C29—81no—
296C4×C29C2×#13711yescharacteristic
297C4×C29#57511yescharacteristic
298C4×C29#57711yescharacteristic
299C4×C29#57711yescharacteristic
300#533C22×C2911yescharacteristic
301#533C22×C2911yescharacteristic
302C2×C4×D4C22×C2911yescharacteristic
303#500C22×C2911yescharacteristic, complemented
304#498C22×C2911yescharacteristic, complemented
305#487C22×C2911yescharacteristic, complemented
306#487C22×C2911yescharacteristic, complemented
307#485—21no—
308#485—21no—
309#483—21no—
310#479—21no—
311#479—21no—
312#478—21no—
313#478—21no—
314#476C22×C2911yescharacteristic
315#476C22×C2911yescharacteristic
316#476C22×C2911yescharacteristic
317#476C22×C2911yescharacteristic
318#474C22×C2911yescharacteristic
319#474C22×C2911yescharacteristic
320#461C22×C2911yescharacteristic
321#461C22×C2911yescharacteristic
322#450—21no—
323C4×SD16—21no—
324C4×SD16—21no—
325#436C22×C2911yescharacteristic
326#436C22×C2911yescharacteristic
327#435—21no—
328#435—21no—
329C8×D4C22×C2911yescharacteristic
330C8×D4C22×C2911yescharacteristic
331#432C22×C2911yescharacteristic
332#431C22×C2911yescharacteristic
333#431C22×C2911yescharacteristic
334#428—21no—
335#423C22×C2911yescharacteristic
336#418—21no—
337#407—21no—
338C2×C22⋊C8—21no—
339#335C22×C2911yescharacteristic, complemented
340#335C22×C2911yescharacteristic, complemented
341#334C22×C2911yescharacteristic, complemented
342#334C22×C2911yescharacteristic, complemented
343#333C22×C2911yescharacteristic, complemented
344#333C22×C2911yescharacteristic, complemented
345#333C22×C2911yescharacteristic, complemented
346#333C22×C2911yescharacteristic, complemented
347#332C22×C2911yescharacteristic, complemented
348#332C22×C2911yescharacteristic, complemented
349#332C22×C2911yescharacteristic, complemented
350#332C22×C2911yescharacteristic, complemented
351C2×C29—41no—
352C2×C29—42no—
353C2×C29—81no—
354C2×C29#304211yescharacteristic
355C2×C29#305611yescharacteristic
356C2×C29#306711yescharacteristic
357C22×D4D4×C2911yescharacteristic
358C23×C4—21no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C22×C8—21no—
365C22×C8—21no—
366C4⋊Q8C23×C2911yescharacteristic
367C4⋊Q8C23×C2911yescharacteristic
368C4⋊Q8C23×C2911yescharacteristic
369C4⋊Q8C23×C2911yescharacteristic
370#125—21no—
371#125—21no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4D4×C2911yescharacteristic
383C4×D4D4×C2911yescharacteristic
384C4×D4C23×C2911yescharacteristic
385C4×D4C23×C2911yescharacteristic
386#117—21no—
387#117—21no—
388C2×C4⋊C4D4×C2911yescharacteristic
389C2×C22⋊C4—21no—
390C2×C42C23×C2911yescharacteristic
391#107—21no—
392#107—21no—
393#107—21no—
394#107—21no—
395#106—21no—
396#106—21no—
397#106—21no—
398#106—21no—
399#106—21no—
400#106—21no—
401C4⋊C8—21no—
402C4⋊C8D4×C2911yescharacteristic
403C4⋊C8D4×C2911yescharacteristic
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#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8D4×C2911yescharacteristic
429C22⋊C8D4×C2911yescharacteristic
430#97—21no—
431C4×C8—21no—
432C4×C8C23×C2911yescharacteristic
433C4×C8C23×C2911yescharacteristic
434C29#1946611yescharacteristic, direct product factor, Sylow
435C24—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—41no—
443C2×D4C2×D4×C2911yescharacteristic
444C2×D4C2×D4×C2911yescharacteristic
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—81no—
451C22×C4—81no—
452C22×C4C2×D4×C2911yescharacteristic
453C22×C4C2×D4×C2911yescharacteristic
454C22×C4#41×C2911yescharacteristic
455SD16—42no—
456SD16—42no—
457M16—42no—
458M16—81no—
459M16—81no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—81no—
467C2×C8—81no—
468C2×C8C2×D4×C2911yescharacteristic
469C2×C8C2×D4×C2911yescharacteristic
470C2×C8C2×D4×C2911yescharacteristic
471C2×C8C2×D4×C2911yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4C2×D4×C2911yescharacteristic
486C4⋊C4C2×D4×C2911yescharacteristic
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C42—41no—
494C42—41no—
495C42C2×D4×C2911yescharacteristic
496C42C2×D4×C2911yescharacteristic
497C42#41×C2911yescharacteristic
498C42C24×C2911yescharacteristic
499C23—21no—
500C23—21no—
501C23—42no—
502C23—42no—
503C23—81no—
504C23C29×#12111yescharacteristic
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—81no—
510Q8—81no—
511D4—21no—
512D4—21no—
513D4—21no—
514D4—42no—
515D4C29×#13712yes—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4C29×#12111yescharacteristic
535C2×C4C29×#12111yescharacteristic
536C2×C4C29×#12111yescharacteristic
537C2×C4C22×D4×C2911yescharacteristic
538C2×C4C22×D4×C2911yescharacteristic
539C2×C4C2×#41×C2911yescharacteristic
540C8—21no—
541C8—21no—
542C8—21no—
543C8—21no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C22—21no—
551C22—21no—
552C22—22no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—84no—
560C22C2×C29×#12111yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4C2×C29×#13711yescharacteristic
572C4C29×#57511yescharacteristic
573C4C29×#57711yescharacteristic
574C4C29×#57711yescharacteristic
575C2—41no—
576C2—42no—
577C2—81no—
578C2C29×#304211yescharacteristic
579C2C29×#305611yescharacteristic
580C2C29×#306711yescharacteristic
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×#3231C2semidirect
5. C29×#1703C2semidirect
6. C29×#1699C2semidirect
7. C29×#1695C2semidirect
8. C29×#1691C2semidirect
9. C29×#1683C2semidirect
10. C29×#1679C2semidirect
11. C29×#1675C2semidirect
12. C29×#1671C2semidirect
13. C29×#1574C2semidirect
14. C29×#1559C2semidirect
15. C29×#1554C2semidirect
19. C29×#500C22semidirect
20. C29×#498C22semidirect
21. C29×#487C22semidirect
22. C29×#487C22semidirect
55. C29×#335C22semidirect
56. C29×#335C22semidirect
57. C29×#334C22semidirect
58. C29×#334C22semidirect
59. C29×#333C22semidirect
60. C29×#333C22semidirect
61. C29×#333C22semidirect
62. C29×#333C22semidirect
63. C29×#332C22semidirect
64. C29×#332C22semidirect
65. C29×#332C22semidirect
66. C29×#332C22semidirect
208. #19466C29direct (N × H)
260. #3231C2×C29semidirect
264. #1703C2×C29semidirect
265. #1699C2×C29semidirect
266. #1695C2×C29semidirect
267. #1691C2×C29semidirect
268. #1683C2×C29semidirect
269. #1679C2×C29semidirect
270. #1675C2×C29semidirect
271. #1671C2×C29semidirect
272. #1574C2×C29semidirect
273. #1559C2×C29semidirect
274. #1554C2×C29semidirect
303. #500C22×C29semidirect
304. #498C22×C29semidirect
305. #487C22×C29semidirect
306. #487C22×C29semidirect
339. #335C22×C29semidirect
340. #335C22×C29semidirect
341. #334C22×C29semidirect
342. #334C22×C29semidirect
343. #333C22×C29semidirect
344. #333C22×C29semidirect
345. #333C22×C29semidirect
346. #333C22×C29semidirect
347. #332C22×C29semidirect
348. #332C22×C29semidirect
349. #332C22×C29semidirect
350. #332C22×C29semidirect
434. C29#19466direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32312
C29×#31012
C29×#30772
C29×#29742
C29×#17032
C29×#16992
C29×#16952
C29×#16912
C29×#16832
C29×#16792
C29×#16752
C29×#16712
C29×#15742
C29×#15592
C29×#15542
#1946629