Finite Group Databasebeta

← C29×#27051 #20321951

Subgroups — C29×#27051 #20321951

Order 7424.

722 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
1C29×#2496C211yesmaximal, characteristic
2C29×#2360C211yesmaximal, characteristic
3C29×#2072C211yesmaximal, characteristic, complemented
4C29×#2068C211yesmaximal, characteristic, complemented
5C29×#2035C211yesmaximal, characteristic
6C29×#2035C211yesmaximal, characteristic
7C29×#1948C211yesmaximal, characteristic, complemented
8C29×#1944C211yesmaximal, characteristic, complemented
9C29×#1924C211yesmaximal, characteristic
10C29×#1921C211yesmaximal, characteristic, complemented
11C29×#1919C211yesmaximal, characteristic, complemented
12C29×#1863C211yesmaximal, characteristic, complemented
13C29×#1852C211yesmaximal, characteristic
14C29×#1823C211yesmaximal, characteristic
15C29×#1763C211yesmaximal, characteristic, complemented
16C2×C29×#126—21no—
17C2×C29×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C29C2211yescharacteristic
19C22×C4⋊C4×C29C2211yescharacteristic
20C2×C29×#107C2211yescharacteristic
21C2×C29×#107C2211yescharacteristic
22C2×C29×#106C2211yescharacteristic
23C2×C29×#106C2211yescharacteristic
24C2×C29×C4⋊C8C2211yescharacteristic
25C2×C29×#103C2211yescharacteristic
26C2×C29×#103C2211yescharacteristic
27C2×C29×#103C2211yescharacteristic
28C2×C29×#103C2211yescharacteristic
29C2×C29×C22⋊C8C2211yescharacteristic
30C2×C29×C22⋊C8C2211yescharacteristic
31C2×C29×#97C2211yescharacteristic
32C29×#400—21no—
33C29×#397—21no—
34C29×#391C2211yescharacteristic
35C29×#389—21no—
36C29×#389C2211yescharacteristic
37C29×#389C2211yescharacteristic
38C29×#389C2211yescharacteristic
39C29×#387—21no—
40C29×#387—21no—
41C29×#385—21no—
42C29×#384C2211yescharacteristic
43C29×#380C2211yescharacteristic
44C29×#380C2211yescharacteristic
45C4×C4⋊C4×C29C2211yescharacteristic
46C4×C4⋊C4×C29C2211yescharacteristic
47C4×C22⋊C4×C29—21no—
48C4×C22⋊C4×C29C2211yescharacteristic
49C29×#340C2211yescharacteristic
50C29×#340C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×Q8×C29C2311yescharacteristic
60C23×C4×C29—21no—
61C23×C4×C29C2311yescharacteristic
62C22×C8×C29C2311yescharacteristic
63C22×C8×C29C2311yescharacteristic
64C22×C8×C29C2311yescharacteristic
65C22×C8×C29C2311yescharacteristic
66C29×#126—44no—
67C29×C22⋊Q8—22no—
68C29×C22⋊Q8—22no—
69C4×Q8×C29—22no—
70C4×Q8×C29—41no—
71C2×C4⋊C4×C29—21no—
72C2×C4⋊C4×C29—22no—
73C2×C4⋊C4×C29—21no—
74C2×C4⋊C4×C29—21no—
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—41no—
81C2×C4⋊C4×C29C2311yescharacteristic
82C2×C4⋊C4×C29C2311yescharacteristic
83C2×C4⋊C4×C29C2311yescharacteristic
84C2×C4⋊C4×C29C2311yescharacteristic
85C2×C4⋊C4×C29C2311yescharacteristic
86C2×C4⋊C4×C29C2311yescharacteristic
87C2×C4⋊C4×C29C2311yescharacteristic
88C2×C22⋊C4×C29—21no—
89C2×C22⋊C4×C29—21no—
90C2×C22⋊C4×C29—21no—
91C2×C22⋊C4×C29D411yescharacteristic
92C2×C22⋊C4×C29D411yescharacteristic
93C2×C42×C29—21no—
94C2×C42×C29—21no—
95C2×C42×C29—21no—
96C2×C42×C29C2311yescharacteristic
97C2×C42×C29C2311yescharacteristic
98C29×#107—22no—
99C29×#107—41no—
100C29×#106—22no—
101C29×#106—22no—
102C29×C4⋊C8—22no—
103C29×#103—22no—
104C29×#103—22no—
105C29×#103—22no—
106C29×#103—41no—
107C29×C22⋊C8—22no—
108C29×C22⋊C8—41no—
109C29×#97—41no—
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×C29C2×D411yescharacteristic
122C2×Q8×C29—21no—
123C2×Q8×C29—21no—
124C2×Q8×C29—21no—
125C2×Q8×C29—21no—
126C2×Q8×C29—21no—
127C2×Q8×C29#4112yes—
128C22×C4×C29—21no—
129C22×C4×C29—21no—
130C22×C4×C29—21no—
131C22×C4×C29—21no—
132C22×C4×C29—21no—
133C22×C4×C29—21no—
134C22×C4×C29—21no—
135C22×C4×C29—21no—
136C22×C4×C29—21no—
137C22×C4×C29—21no—
138C22×C4×C29—21no—
139C22×C4×C29—21no—
140C22×C4×C29—21no—
141C22×C4×C29—21no—
142C22×C4×C29—42no—
143C22×C4×C29—42no—
144C22×C4×C29—81no—
145C22×C4×C29C2×D411yescharacteristic
146C22×C4×C29C2×D411yescharacteristic
147C22×C4×C29C2×D411yescharacteristic
148C22×C4×C29C2×D411yescharacteristic
149C22×C4×C29C2×D411yescharacteristic
150C22×C4×C29C2411yescharacteristic
151C2×C8×C29—21no—
152C2×C8×C29—21no—
153C2×C8×C29—21no—
154C2×C8×C29—21no—
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#4112yes—
163C4⋊C4×C29—24no—
164C4⋊C4×C29—21no—
165C4⋊C4×C29—21no—
166C4⋊C4×C29—21no—
167C4⋊C4×C29—21no—
168C4⋊C4×C29—21no—
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—42no—
177C4⋊C4×C29—42no—
178C4⋊C4×C29—42no—
179C4⋊C4×C29—42no—
180C4⋊C4×C29—42no—
181C4⋊C4×C29—42no—
182C4⋊C4×C29—81no—
183C4⋊C4×C29#4112yes—
184C4⋊C4×C29#4112yes—
185C22⋊C4×C29—24no—
186C22⋊C4×C29—22no—
187C22⋊C4×C29—22no—
188C22⋊C4×C29—42no—
189C22⋊C4×C29—42no—
190C42×C29—21no—
191C42×C29—21no—
192C42×C29—21no—
193C42×C29—21no—
194C42×C29—42no—
195C42×C29—42no—
196C42×C29—81no—
197#27051C2911yesmaximal, characteristic, direct product factor, Sylow
198C23×C29—21no—
199C23×C29—21no—
200C23×C29—21no—
201C23×C29—21no—
202C23×C29—21no—
203C23×C29—21no—
204C23×C29AGL(1,ℤ/8)12yes—
205C23×C29C22×D411yescharacteristic
206Q8×C29—22no—
207Q8×C29—22no—
208Q8×C29—41no—
209Q8×C29—41no—
210C2×C4×C29—21no—
211C2×C4×C29—21no—
212C2×C4×C29—22no—
213C2×C4×C29—22no—
214C2×C4×C29—21no—
215C2×C4×C29—21no—
216C2×C4×C29—21no—
217C2×C4×C29—22no—
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—21no—
226C2×C4×C29—21no—
227C2×C4×C29—41no—
228C2×C4×C29—41no—
229C2×C4×C29—41no—
230C2×C4×C29—41no—
231C2×C4×C29—41no—
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—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—84no—
253C2×C4×C29#13712yes—
254C2×C4×C29C2×#4111yescharacteristic
255C2×C4×C29C2×#4111yescharacteristic
256C2×C4×C29C2×#4111yescharacteristic
257C2×C4×C29C2×#4111yescharacteristic
258C2×C4×C29H(5,𝔽2)11yescharacteristic
259C2×C4×C292−1+411yescharacteristic
260C8×C29—22no—
261C8×C29—41no—
262C8×C29—41no—
263C8×C29—41no—
264#2496C2×C2911yescharacteristic
265#2360C2×C2911yescharacteristic
266#2072C2×C2911yescharacteristic, complemented
267#2068C2×C2911yescharacteristic, complemented
268#2035C2×C2911yescharacteristic
269#2035C2×C2911yescharacteristic
270#1948C2×C2911yescharacteristic, complemented
271#1944C2×C2911yescharacteristic, complemented
272#1924C2×C2911yescharacteristic
273#1921C2×C2911yescharacteristic, complemented
274#1919C2×C2911yescharacteristic, complemented
275#1863C2×C2911yescharacteristic, complemented
276#1852C2×C2911yescharacteristic
277#1823C2×C2911yescharacteristic
278#1763C2×C2911yescharacteristic, complemented
279C22×C29—22no—
280C22×C29—22no—
281C22×C29—22no—
282C22×C29—41no—
283C22×C29—41no—
284C22×C29—41no—
285C22×C29—41no—
286C22×C29#52511yescharacteristic
287C22×C29#54611yescharacteristic
288C22×C29#54711yescharacteristic
289C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C29C2×#13711yescharacteristic
291C22×C29#57711yescharacteristic
292C22×C29#57811yescharacteristic
293C4×C29—22no—
294C4×C29—41no—
295C4×C29—41no—
296C4×C29—42no—
297C4×C29—41no—
298C4×C29—42no—
299C4×C29—41no—
300C4×C29—42no—
301C4×C29—81no—
302C4×C29—81no—
303C4×C29—81no—
304C4×C29—81no—
305C4×C29—81no—
306C4×C29#52911yescharacteristic
307C4×C29#53911yescharacteristic
308C4×C29#55311yescharacteristic
309C4×C29#55611yescharacteristic
310C2×#126—21no—
311C2×C22⋊Q8C22×C2911yescharacteristic
312C2×C4×Q8C22×C2911yescharacteristic
313C22×C4⋊C4C22×C2911yescharacteristic
314C2×#107C22×C2911yescharacteristic
315C2×#107C22×C2911yescharacteristic
316C2×#106C22×C2911yescharacteristic
317C2×#106C22×C2911yescharacteristic
318C2×C4⋊C8C22×C2911yescharacteristic
319C2×#103C22×C2911yescharacteristic
320C2×#103C22×C2911yescharacteristic
321C2×#103C22×C2911yescharacteristic
322C2×#103C22×C2911yescharacteristic
323C2×C22⋊C8C22×C2911yescharacteristic
324C2×C22⋊C8C22×C2911yescharacteristic
325C2×#97C22×C2911yescharacteristic
326#400—21no—
327#397—21no—
328#391C22×C2911yescharacteristic
329#389—21no—
330#389C22×C2911yescharacteristic
331#389C22×C2911yescharacteristic
332#389C22×C2911yescharacteristic
333#387—21no—
334#387—21no—
335#385—21no—
336#384C22×C2911yescharacteristic
337#380C22×C2911yescharacteristic
338#380C22×C2911yescharacteristic
339C4×C4⋊C4C22×C2911yescharacteristic
340C4×C4⋊C4C22×C2911yescharacteristic
341C4×C22⋊C4—21no—
342C4×C22⋊C4C22×C2911yescharacteristic
343#340C22×C2911yescharacteristic
344#340C22×C2911yescharacteristic
345#340C22×C2911yescharacteristic
346#340C22×C2911yescharacteristic
347#340C22×C2911yescharacteristic
348#340C22×C2911yescharacteristic
349#340C22×C2911yescharacteristic
350#340C22×C2911yescharacteristic
351#336C22×C2911yescharacteristic
352#336C22×C2911yescharacteristic
353C2×C29—42no—
354C2×C29#246611yescharacteristic
355C2×C29#311211yescharacteristic
356C2×C29#312011yescharacteristic
357C2×C29#330611yescharacteristic
358C2×C29#332811yescharacteristic
359C2×C29#334311yescharacteristic
360C2×C29#334411yescharacteristic
361C22×Q8C23×C2911yescharacteristic
362C23×C4—21no—
363C23×C4C23×C2911yescharacteristic
364C22×C8C23×C2911yescharacteristic
365C22×C8C23×C2911yescharacteristic
366C22×C8C23×C2911yescharacteristic
367C22×C8C23×C2911yescharacteristic
368#126—44no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C4×Q8—22no—
372C4×Q8—41no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—41no—
383C2×C4⋊C4C23×C2911yescharacteristic
384C2×C4⋊C4C23×C2911yescharacteristic
385C2×C4⋊C4C23×C2911yescharacteristic
386C2×C4⋊C4C23×C2911yescharacteristic
387C2×C4⋊C4C23×C2911yescharacteristic
388C2×C4⋊C4C23×C2911yescharacteristic
389C2×C4⋊C4C23×C2911yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4D4×C2911yescharacteristic
394C2×C22⋊C4D4×C2911yescharacteristic
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42C23×C2911yescharacteristic
399C2×C42C23×C2911yescharacteristic
400#107—22no—
401#107—41no—
402#106—22no—
403#106—22no—
404C4⋊C8—22no—
405#103—22no—
406#103—22no—
407#103—22no—
408#103—41no—
409C22⋊C8—22no—
410C22⋊C8—41no—
411#97—41no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95D4×C2911yescharacteristic
422#95D4×C2911yescharacteristic
423C29#2705111yescharacteristic, direct product factor, Sylow
424C24C2×D4×C2911yescharacteristic
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8#41×C2912yes—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—81no—
448C22×C4C2×D4×C2911yescharacteristic
449C22×C4C2×D4×C2911yescharacteristic
450C22×C4C2×D4×C2911yescharacteristic
451C22×C4C2×D4×C2911yescharacteristic
452C22×C4C2×D4×C2911yescharacteristic
453C22×C4C24×C2911yescharacteristic
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8#41×C2912yes—
466C4⋊C4—24no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C4⋊C4—42no—
484C4⋊C4—42no—
485C4⋊C4—81no—
486C4⋊C4#41×C2912yes—
487C4⋊C4#41×C2912yes—
488C22⋊C4—24no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—42no—
498C42—42no—
499C42—81no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23C29×AGL(1,ℤ/8)12yes—
507C23C22×D4×C2911yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—41no—
511Q8—41no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
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×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—84no—
555C2×C4C29×#13712yes—
556C2×C4C2×#41×C2911yescharacteristic
557C2×C4C2×#41×C2911yescharacteristic
558C2×C4C2×#41×C2911yescharacteristic
559C2×C4C2×#41×C2911yescharacteristic
560C2×C4C29×H(5,𝔽2)11yescharacteristic
561C2×C4C29×2−1+411yescharacteristic
562C8—22no—
563C8—41no—
564C8—41no—
565C8—41no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22C29×#52511yescharacteristic
574C22C29×#54611yescharacteristic
575C22C29×#54711yescharacteristic
576C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
577C22C2×C29×#13711yescharacteristic
578C22C29×#57711yescharacteristic
579C22C29×#57811yescharacteristic
580C4—22no—
581C4—41no—
582C4—42no—
583C4—41no—
584C4—42no—
585C4—41no—
586C4—41no—
587C4—42no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4C29×#52911yescharacteristic
594C4C29×#53911yescharacteristic
595C4C29×#55311yescharacteristic
596C4C29×#55611yescharacteristic
597C2—42no—
598C2C29×#246611yescharacteristic
599C2C29×#311211yescharacteristic
600C2C29×#312011yescharacteristic
601C2C29×#330611yescharacteristic
602C2C29×#332811yescharacteristic
603C2C29×#334311yescharacteristic
604C2C29×#334411yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC24×C29C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C4×C22⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#2072C2semidirect
4. C29×#2068C2semidirect
7. C29×#1948C2semidirect
8. C29×#1944C2semidirect
10. C29×#1921C2semidirect
11. C29×#1919C2semidirect
12. C29×#1863C2semidirect
15. C29×#1763C2semidirect
197. #27051C29direct (N × H)
266. #2072C2×C29semidirect
267. #2068C2×C29semidirect
270. #1948C2×C29semidirect
271. #1944C2×C29semidirect
273. #1921C2×C29semidirect
274. #1919C2×C29semidirect
275. #1863C2×C29semidirect
278. #1763C2×C29semidirect
423. C29#27051direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#24962
C29×#23602
C29×#20722
C29×#20682
C29×#20352
C29×#19482
C29×#19442
C29×#19242
C29×#19212
C29×#19192
C29×#18632
C29×#18522
C29×#18232
C29×#17632
#2705129