Finite Group Databasebeta

← C29×#29099 #20323999

Subgroups — C29×#29099 #20323999

Order 7424.

726 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2511C211yesmaximal, characteristic, complemented
2C29×#2452C211yesmaximal, characteristic
3C29×#2088C211yesmaximal, characteristic, complemented
4C29×#2071C211yesmaximal, characteristic
5C29×#2055C211yesmaximal, characteristic
6C29×#2024C211yesmaximal, characteristic, complemented
7C29×#1990C211yesmaximal, characteristic, complemented
8C29×#1968C211yesmaximal, characteristic
9C29×#1936C211yesmaximal, characteristic
10C29×#1935C211yesmaximal, characteristic, complemented
11C29×#1935C211yesmaximal, characteristic, complemented
12C29×#1920C211yesmaximal, characteristic, complemented
13C29×#1877C211yesmaximal, characteristic
14C29×#1771C211yesmaximal, characteristic, complemented
15C29×#1762C211yesmaximal, characteristic
16C22×SD16×C29C2211yescharacteristic
17C2×C29×C4⋊Q8C2211yescharacteristic
18C2×C29×C22⋊Q8—21no—
19C2×C4×D4×C29C2211yescharacteristic
20C2×C29×#106C2211yescharacteristic
21C2×C29×C4⋊C8C2211yescharacteristic
22C2×C29×#103C2211yescharacteristic
23C2×C29×#103C2211yescharacteristic
24C2×C29×#103C2211yescharacteristic
25C2×C29×#102C2211yescharacteristic
26C2×C29×#102C2211yescharacteristic
27C2×C29×#102C2211yescharacteristic
28C2×C29×#97C2211yescharacteristic
29C2×C29×#97C2211yescharacteristic
30C2×C4×C8×C29C2211yescharacteristic
31C29×#400—21no—
32C29×#400—21no—
33C29×#396—21no—
34C29×#393—21no—
35C29×#391C2211yescharacteristic
36C29×#391C2211yescharacteristic
37C29×#391C2211yescharacteristic
38C29×#390C2211yescharacteristic
39C29×#390C2211yescharacteristic
40C29×#389C2211yescharacteristic
41C29×#389C2211yescharacteristic
42C29×#389C2211yescharacteristic
43C29×#387—21no—
44C29×#387—21no—
45C29×#385—21no—
46C29×#384C2211yescharacteristic
47C4×C4⋊C4×C29C2211yescharacteristic
48C4×C4⋊C4×C29C2211yescharacteristic
49C29×#340C2211yescharacteristic
50C29×#340C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×Q8×C29—21no—
60C22×Q8×C29C2311yescharacteristic
61C22×D4×C29C2311yescharacteristic
62C23×C4×C29—21no—
63C2×SD16×C29—22no—
64C2×SD16×C29—22no—
65C2×SD16×C29—41no—
66C22×C8×C29C2311yescharacteristic
67C22×C8×C29C2311yescharacteristic
68C22×C8×C29C2311yescharacteristic
69C22×C8×C29C2311yescharacteristic
70C29×C4⋊Q8—22no—
71C29×C4⋊Q8—41no—
72C29×C22⋊Q8—44no—
73C4×D4×C29—22no—
74C4×D4×C29—41no—
75C2×C4⋊C4×C29—21no—
76C2×C4⋊C4×C29—21no—
77C2×C4⋊C4×C29—21no—
78C2×C4⋊C4×C29—21no—
79C2×C4⋊C4×C29—21no—
80C2×C4⋊C4×C29—21no—
81C2×C4⋊C4×C29D411yescharacteristic
82C2×C4⋊C4×C29D411yescharacteristic
83C2×C4⋊C4×C29C2311yescharacteristic
84C2×C4⋊C4×C29C2311yescharacteristic
85C2×C4⋊C4×C29C2311yescharacteristic
86C2×C4⋊C4×C29C2311yescharacteristic
87C2×C4⋊C4×C29C2311yescharacteristic
88C2×C4⋊C4×C29C2311yescharacteristic
89C2×C22⋊C4×C29—21no—
90C2×C22⋊C4×C29—21no—
91C2×C22⋊C4×C29—21no—
92C2×C22⋊C4×C29—21no—
93C2×C22⋊C4×C29—21no—
94C2×C42×C29—21no—
95C2×C42×C29C2311yescharacteristic
96C2×C42×C29C2311yescharacteristic
97C2×C42×C29C2311yescharacteristic
98C29×#106—22no—
99C29×C4⋊C8—22no—
100C29×#103—22no—
101C29×#103—22no—
102C29×#103—41no—
103C29×#102—22no—
104C29×#102—22no—
105C29×#102—22no—
106C29×#97—22no—
107C29×#97—41no—
108C4×C8×C29—41no—
109C29×#95—21no—
110C29×#95—21no—
111C29×#95—21no—
112C29×#95—21no—
113C29×#95—21no—
114C29×#95—21no—
115C29×#95—21no—
116C29×#95—21no—
117C29×#95—21no—
118C29×#95—21no—
119C29×#95D411yescharacteristic
120C29×#95D411yescharacteristic
121C24×C29—21no—
122C2×Q8×C29—21no—
123C2×Q8×C29—21no—
124C2×Q8×C29—21no—
125C2×Q8×C29—21no—
126C2×Q8×C29—21no—
127C2×Q8×C29—21no—
128C2×Q8×C29—42no—
129C2×Q8×C29—42no—
130C2×Q8×C29—81no—
131C2×D4×C29—21no—
132C2×D4×C29—21no—
133C2×D4×C29—21no—
134C2×D4×C29—21no—
135C2×D4×C29—21no—
136C2×D4×C29#4112yes—
137C22×C4×C29—21no—
138C22×C4×C29—21no—
139C22×C4×C29—21no—
140C22×C4×C29—21no—
141C22×C4×C29—21no—
142C22×C4×C29—21no—
143C22×C4×C29—21no—
144C22×C4×C29—42no—
145C22×C4×C29—42no—
146C22×C4×C29—81no—
147C22×C4×C29C2×D411yescharacteristic
148C22×C4×C29C2×D411yescharacteristic
149C22×C4×C29C2×D411yescharacteristic
150C22×C4×C29C2×D411yescharacteristic
151C22×C4×C29C2×D411yescharacteristic
152C22×C4×C29C2×D411yescharacteristic
153C22×C4×C29C2411yescharacteristic
154SD16×C29—44no—
155C2×C8×C29—21no—
156C2×C8×C29—21no—
157C2×C8×C29—21no—
158C2×C8×C29—21no—
159C2×C8×C29—21no—
160C2×C8×C29—21no—
161C2×C8×C29—21no—
162C2×C8×C29—21no—
163C2×C8×C29—21no—
164C2×C8×C29—21no—
165C2×C8×C29#4112yes—
166C2×C8×C29#4112yes—
167C4⋊C4×C29—22no—
168C4⋊C4×C29—22no—
169C4⋊C4×C29—21no—
170C4⋊C4×C29—21no—
171C4⋊C4×C29—21no—
172C4⋊C4×C29—21no—
173C4⋊C4×C29—21no—
174C4⋊C4×C29—21no—
175C4⋊C4×C29—21no—
176C4⋊C4×C29—21no—
177C4⋊C4×C29—21no—
178C4⋊C4×C29—21no—
179C4⋊C4×C29—21no—
180C4⋊C4×C29—42no—
181C4⋊C4×C29—42no—
182C4⋊C4×C29—42no—
183C4⋊C4×C29—42no—
184C4⋊C4×C29—81no—
185C4⋊C4×C29—81no—
186C4⋊C4×C29#4112yes—
187C22⋊C4×C29—42no—
188C22⋊C4×C29—42no—
189C22⋊C4×C29—42no—
190C22⋊C4×C29—42no—
191C22⋊C4×C29—81no—
192C42×C29—21no—
193C42×C29—21no—
194C42×C29—21no—
195C42×C29—21no—
196C42×C29—21no—
197C42×C29—21no—
198C42×C29—81no—
199#29099C2911yesmaximal, characteristic, direct product factor, Sylow
200C23×C29—22no—
201C23×C29—41no—
202C23×C29—41no—
203C23×C29—41no—
204C23×C29—41no—
205C23×C29—41no—
206C23×C29—41no—
207C23×C29C22×D411yescharacteristic
208Q8×C29—41no—
209Q8×C29—41no—
210Q8×C29—41no—
211Q8×C29—41no—
212Q8×C29—84no—
213D4×C29—22no—
214D4×C29—22no—
215D4×C29—41no—
216D4×C29—41no—
217C2×C4×C29—21no—
218C2×C4×C29—21no—
219C2×C4×C29—21no—
220C2×C4×C29—21no—
221C2×C4×C29—21no—
222C2×C4×C29—21no—
223C2×C4×C29—21no—
224C2×C4×C29—21no—
225C2×C4×C29—22no—
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—21no—
233C2×C4×C29—21no—
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—41no—
242C2×C4×C29—41no—
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—41no—
252C2×C4×C29—41no—
253C2×C4×C29—41no—
254C2×C4×C29—84no—
255C2×C4×C29AGL(1,ℤ/8)12yes—
256C2×C4×C29#13712yes—
257C2×C4×C29C2×#4111yescharacteristic
258C2×C4×C29C2×#4111yescharacteristic
259C2×C4×C29C2×#4111yescharacteristic
260C2×C4×C29C2×#4111yescharacteristic
261C2×C4×C29H(5,𝔽2)11yescharacteristic
262C2×C4×C292−1+411yescharacteristic
263C8×C29—22no—
264C8×C29—22no—
265C8×C29—41no—
266C8×C29—41no—
267#2511C2×C2911yescharacteristic, complemented
268#2452C2×C2911yescharacteristic
269#2088C2×C2911yescharacteristic, complemented
270#2071C2×C2911yescharacteristic
271#2055C2×C2911yescharacteristic
272#2024C2×C2911yescharacteristic, complemented
273#1990C2×C2911yescharacteristic, complemented
274#1968C2×C2911yescharacteristic
275#1936C2×C2911yescharacteristic
276#1935C2×C2911yescharacteristic, complemented
277#1935C2×C2911yescharacteristic, complemented
278#1920C2×C2911yescharacteristic, complemented
279#1877C2×C2911yescharacteristic
280#1771C2×C2911yescharacteristic, complemented
281#1762C2×C2911yescharacteristic
282C22×C29—42no—
283C22×C29—42no—
284C22×C29—42no—
285C22×C29—81no—
286C22×C29—81no—
287C22×C29—81no—
288C22×C29—81no—
289C22×C29#53211yescharacteristic
290C22×C29#54611yescharacteristic
291C22×C29#54811yescharacteristic
292C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C29C2×#13711yescharacteristic
294C22×C29#57711yescharacteristic
295C22×C29#57711yescharacteristic
296C4×C29—22no—
297C4×C29—22no—
298C4×C29—41no—
299C4×C29—41no—
300C4×C29—41no—
301C4×C29—42no—
302C4×C29—41no—
303C4×C29—81no—
304C4×C29—81no—
305C4×C29—81no—
306C4×C29—81no—
307C4×C29—81no—
308C4×C29—81no—
309C4×C29#52911yescharacteristic
310C4×C29#53911yescharacteristic
311C4×C29#55111yescharacteristic
312C4×C29#55611yescharacteristic
313C22×SD16C22×C2911yescharacteristic
314C2×C4⋊Q8C22×C2911yescharacteristic
315C2×C22⋊Q8—21no—
316C2×C4×D4C22×C2911yescharacteristic
317C2×#106C22×C2911yescharacteristic
318C2×C4⋊C8C22×C2911yescharacteristic
319C2×#103C22×C2911yescharacteristic
320C2×#103C22×C2911yescharacteristic
321C2×#103C22×C2911yescharacteristic
322C2×#102C22×C2911yescharacteristic
323C2×#102C22×C2911yescharacteristic
324C2×#102C22×C2911yescharacteristic
325C2×#97C22×C2911yescharacteristic
326C2×#97C22×C2911yescharacteristic
327C2×C4×C8C22×C2911yescharacteristic
328#400—21no—
329#400—21no—
330#396—21no—
331#393—21no—
332#391C22×C2911yescharacteristic
333#391C22×C2911yescharacteristic
334#391C22×C2911yescharacteristic
335#390C22×C2911yescharacteristic
336#390C22×C2911yescharacteristic
337#389C22×C2911yescharacteristic
338#389C22×C2911yescharacteristic
339#389C22×C2911yescharacteristic
340#387—21no—
341#387—21no—
342#385—21no—
343#384C22×C2911yescharacteristic
344C4×C4⋊C4C22×C2911yescharacteristic
345C4×C4⋊C4C22×C2911yescharacteristic
346#340C22×C2911yescharacteristic
347#340C22×C2911yescharacteristic
348#340C22×C2911yescharacteristic
349#340C22×C2911yescharacteristic
350#340C22×C2911yescharacteristic
351#340C22×C2911yescharacteristic
352#340C22×C2911yescharacteristic
353#340C22×C2911yescharacteristic
354#336C22×C2911yescharacteristic
355#336C22×C2911yescharacteristic
356C2×C29—82no—
357C2×C29#256011yescharacteristic
358C2×C29#317311yescharacteristic
359C2×C29#318211yescharacteristic
360C2×C29#331011yescharacteristic
361C2×C29#331611yescharacteristic
362C2×C29#337211yescharacteristic
363C2×C29#337311yescharacteristic
364C22×Q8—21no—
365C22×Q8C23×C2911yescharacteristic
366C22×D4C23×C2911yescharacteristic
367C23×C4—21no—
368C2×SD16—22no—
369C2×SD16—22no—
370C2×SD16—41no—
371C22×C8C23×C2911yescharacteristic
372C22×C8C23×C2911yescharacteristic
373C22×C8C23×C2911yescharacteristic
374C22×C8C23×C2911yescharacteristic
375C4⋊Q8—22no—
376C4⋊Q8—41no—
377C22⋊Q8—44no—
378C4×D4—22no—
379C4×D4—41no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4D4×C2911yescharacteristic
387C2×C4⋊C4D4×C2911yescharacteristic
388C2×C4⋊C4C23×C2911yescharacteristic
389C2×C4⋊C4C23×C2911yescharacteristic
390C2×C4⋊C4C23×C2911yescharacteristic
391C2×C4⋊C4C23×C2911yescharacteristic
392C2×C4⋊C4C23×C2911yescharacteristic
393C2×C4⋊C4C23×C2911yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C42—21no—
400C2×C42C23×C2911yescharacteristic
401C2×C42C23×C2911yescharacteristic
402C2×C42C23×C2911yescharacteristic
403#106—22no—
404C4⋊C8—22no—
405#103—22no—
406#103—22no—
407#103—41no—
408#102—22no—
409#102—22no—
410#102—22no—
411#97—22no—
412#97—41no—
413C4×C8—41no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95D4×C2911yescharacteristic
425#95D4×C2911yescharacteristic
426C29#2909911yescharacteristic, direct product factor, Sylow
427C24—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—42no—
435C2×Q8—42no—
436C2×Q8—81no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4#41×C2912yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—81no—
453C22×C4C2×D4×C2911yescharacteristic
454C22×C4C2×D4×C2911yescharacteristic
455C22×C4C2×D4×C2911yescharacteristic
456C22×C4C2×D4×C2911yescharacteristic
457C22×C4C2×D4×C2911yescharacteristic
458C22×C4C2×D4×C2911yescharacteristic
459C22×C4C24×C2911yescharacteristic
460SD16—44no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8#41×C2912yes—
472C2×C8#41×C2912yes—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
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—42no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—81no—
491C4⋊C4—81no—
492C4⋊C4#41×C2912yes—
493C22⋊C4—42no—
494C22⋊C4—42no—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C22⋊C4—81no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—81no—
505C23—22no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23C22×D4×C2911yescharacteristic
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—84no—
518D4—22no—
519D4—22no—
520D4—41no—
521D4—41no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
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×C4—41no—
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—84no—
560C2×C4C29×AGL(1,ℤ/8)12yes—
561C2×C4C29×#13712yes—
562C2×C4C2×#41×C2911yescharacteristic
563C2×C4C2×#41×C2911yescharacteristic
564C2×C4C2×#41×C2911yescharacteristic
565C2×C4C2×#41×C2911yescharacteristic
566C2×C4C29×H(5,𝔽2)11yescharacteristic
567C2×C4C29×2−1+411yescharacteristic
568C8—22no—
569C8—22no—
570C8—41no—
571C8—41no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22C29×#53211yescharacteristic
580C22C29×#54611yescharacteristic
581C22C29×#54811yescharacteristic
582C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
583C22C2×C29×#13711yescharacteristic
584C22C29×#57711yescharacteristic
585C22C29×#57711yescharacteristic
586C4—22no—
587C4—22no—
588C4—41no—
589C4—41no—
590C4—42no—
591C4—41no—
592C4—41no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4C29×#52911yescharacteristic
600C4C29×#53911yescharacteristic
601C4C29×#55111yescharacteristic
602C4C29×#55611yescharacteristic
603C2—82no—
604C2C29×#256011yescharacteristic
605C2C29×#317311yescharacteristic
606C2C29×#318211yescharacteristic
607C2C29×#331011yescharacteristic
608C2C29×#331611yescharacteristic
609C2C29×#337211yescharacteristic
610C2C29×#337311yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC22×D4×C29C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C4×C4⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#2511C2semidirect
3. C29×#2088C2semidirect
6. C29×#2024C2semidirect
7. C29×#1990C2semidirect
10. C29×#1935C2semidirect
11. C29×#1935C2semidirect
12. C29×#1920C2semidirect
14. C29×#1771C2semidirect
199. #29099C29direct (N × H)
267. #2511C2×C29semidirect
269. #2088C2×C29semidirect
272. #2024C2×C29semidirect
273. #1990C2×C29semidirect
276. #1935C2×C29semidirect
277. #1935C2×C29semidirect
278. #1920C2×C29semidirect
280. #1771C2×C29semidirect
426. C29#29099direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#25112
C29×#24522
C29×#20882
C29×#20712
C29×#20552
C29×#20242
C29×#19902
C29×#19682
C29×#19362
C29×#19352
C29×#19202
C29×#18772
C29×#17712
C29×#17622
#2909929