Finite Group Databasebeta

← C29×#29025 #20323925

Subgroups — C29×#29025 #20323925

Order 7424.

688 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2506C211yesmaximal, characteristic, complemented
2C29×#2448C211yesmaximal, characteristic
3C29×#2100C211yesmaximal, characteristic, complemented
4C29×#2068C211yesmaximal, characteristic, complemented
5C29×#2065C211yesmaximal, characteristic
6C29×#2042C211yesmaximal, characteristic
7C29×#1959C211yesmaximal, characteristic
8C29×#1943C211yesmaximal, characteristic, complemented
9C29×#1936C211yesmaximal, characteristic
10C29×#1935C211yesmaximal, characteristic, complemented
11C29×#1934C211yesmaximal, characteristic
12C29×#1925C211yesmaximal, characteristic
13C29×#1865C211yesmaximal, characteristic, complemented
14C29×#1771C211yesmaximal, characteristic, complemented
15C4×C29×#103C211yesmaximal, characteristic, complemented
16C2×C29×#125—21no—
17C2×C29×#124C2211yescharacteristic
18C2×C4×Q8×C29C2211yescharacteristic
19C2×C29×#107C2211yescharacteristic
20C2×C29×#106C2211yescharacteristic
21C2×C29×C4⋊C8C2211yescharacteristic
22C2×C29×#103C2211yescharacteristic
23C2×C29×#103C2211yescharacteristic
24C2×C29×#103C2211yescharacteristic
25C2×C29×#103C2211yescharacteristic
26C2×C29×#102C2211yescharacteristic
27C2×C29×#102C2211yescharacteristic
28C2×C29×#102C2211yescharacteristic
29C2×C29×#102C2211yescharacteristic
30C2×C29×#97C2211yescharacteristic
31C2×C29×#97C2211yescharacteristic
32C2×C4×C8×C29C2211yescharacteristic
33C29×#400—21no—
34C29×#399—21no—
35C29×#398—21no—
36C29×#397—21no—
37C29×#391C2211yescharacteristic
38C29×#390C2211yescharacteristic
39C29×#390C2211yescharacteristic
40C29×#389C2211yescharacteristic
41C29×#389C2211yescharacteristic
42C29×#389C2211yescharacteristic
43C29×#389C2211yescharacteristic
44C29×#389C2211yescharacteristic
45C29×#388—21no—
46C29×#388—21no—
47C29×#387—21no—
48C29×#384C2211yescharacteristic
49C4×C4⋊C4×C29C2211yescharacteristic
50C4×C4⋊C4×C29C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×Q8×C29C2311yescharacteristic
60C22×D4×C29C2311yescharacteristic
61C22×C8×C29C2311yescharacteristic
62C22×C8×C29C2311yescharacteristic
63C22×C8×C29C2311yescharacteristic
64C22×C8×C29C2311yescharacteristic
65C29×#125—44no—
66C29×#124—22no—
67C29×#124—41no—
68C4×Q8×C29—22no—
69C4×Q8×C29—41no—
70C2×C4⋊C4×C29—21no—
71C2×C4⋊C4×C29—21no—
72C2×C4⋊C4×C29—21no—
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×C29D411yescharacteristic
79C2×C4⋊C4×C29D411yescharacteristic
80C2×C4⋊C4×C29C2311yescharacteristic
81C2×C4⋊C4×C29C2311yescharacteristic
82C2×C4⋊C4×C29C2311yescharacteristic
83C2×C4⋊C4×C29C2311yescharacteristic
84C2×C4⋊C4×C29C2311yescharacteristic
85C2×C4⋊C4×C29C2311yescharacteristic
86C2×C22⋊C4×C29—21no—
87C2×C22⋊C4×C29—21no—
88C2×C22⋊C4×C29—21no—
89C2×C22⋊C4×C29—21no—
90C2×C22⋊C4×C29—21no—
91C2×C22⋊C4×C29—21no—
92C2×C42×C29—21no—
93C2×C42×C29—21no—
94C2×C42×C29C2311yescharacteristic
95C2×C42×C29C2311yescharacteristic
96C2×C42×C29C2311yescharacteristic
97C29×#107—22no—
98C29×#106—41no—
99C29×C4⋊C8—22no—
100C29×#103—22no—
101C29×#103—22no—
102C29×#103—22no—
103C29×#103—22no—
104C29×#102—22no—
105C29×#102—22no—
106C29×#102—22no—
107C29×#102—41no—
108C29×#97—22no—
109C29×#97—41no—
110C4×C8×C29—41no—
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#4112yes—
128C2×D4×C29—21no—
129C2×D4×C29—21no—
130C2×D4×C29—21no—
131C2×D4×C29—21no—
132C2×D4×C29—21no—
133C2×D4×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×C29C2×D411yescharacteristic
142C22×C4×C29C2×D411yescharacteristic
143C22×C4×C29C2×D411yescharacteristic
144C22×C4×C29C2×D411yescharacteristic
145C22×C4×C29C2×D411yescharacteristic
146C22×C4×C29C2×D411yescharacteristic
147C22×C4×C29C2411yescharacteristic
148C2×C8×C29—21no—
149C2×C8×C29—21no—
150C2×C8×C29—21no—
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#4112yes—
159C2×C8×C29#4112yes—
160C4⋊C4×C29—22no—
161C4⋊C4×C29—21no—
162C4⋊C4×C29—21no—
163C4⋊C4×C29—21no—
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—41no—
173C4⋊C4×C29—42no—
174C4⋊C4×C29—42no—
175C4⋊C4×C29—42no—
176C4⋊C4×C29—42no—
177C4⋊C4×C29—42no—
178C4⋊C4×C29—42no—
179C4⋊C4×C29—42no—
180C4⋊C4×C29—81no—
181C4⋊C4×C29#4112yes—
182C22⋊C4×C29—42no—
183C22⋊C4×C29—42no—
184C22⋊C4×C29—42no—
185C22⋊C4×C29—42no—
186C22⋊C4×C29—81no—
187C22⋊C4×C29—81no—
188C42×C29—21no—
189C42×C29—21no—
190C42×C29—21no—
191C42×C29—21no—
192C42×C29—21no—
193C42×C29—21no—
194C42×C29—42no—
195C42×C29—42no—
196#29025C2911yesmaximal, characteristic, direct product factor, Sylow
197C23×C29—41no—
198C23×C29—41no—
199C23×C29—41no—
200C23×C29—41no—
201C23×C29—41no—
202C23×C29—41no—
203C23×C29—41no—
204C23×C29C22×D411yescharacteristic
205Q8×C29—22no—
206Q8×C29—22no—
207Q8×C29—41no—
208Q8×C29—41no—
209D4×C29—41no—
210D4×C29—41no—
211D4×C29—41no—
212D4×C29—41no—
213C2×C4×C29—21no—
214C2×C4×C29—21no—
215C2×C4×C29—21no—
216C2×C4×C29—21no—
217C2×C4×C29—21no—
218C2×C4×C29—21no—
219C2×C4×C29—21no—
220C2×C4×C29—22no—
221C2×C4×C29—22no—
222C2×C4×C29—21no—
223C2×C4×C29—21no—
224C2×C4×C29—21no—
225C2×C4×C29—21no—
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—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×C29AGL(1,ℤ/8)12yes—
252C2×C4×C29C2×#4111yescharacteristic
253C2×C4×C29C2×#4111yescharacteristic
254C2×C4×C29C2×#4111yescharacteristic
255C2×C4×C29C2×#4111yescharacteristic
256C2×C4×C29H(5,𝔽2)11yescharacteristic
257C2×C4×C292−1+411yescharacteristic
258C8×C29—22no—
259C8×C29—22no—
260C8×C29—41no—
261C8×C29—41no—
262#2506C2×C2911yescharacteristic, complemented
263#2448C2×C2911yescharacteristic
264#2100C2×C2911yescharacteristic, complemented
265#2068C2×C2911yescharacteristic, complemented
266#2065C2×C2911yescharacteristic
267#2042C2×C2911yescharacteristic
268#1959C2×C2911yescharacteristic
269#1943C2×C2911yescharacteristic, complemented
270#1936C2×C2911yescharacteristic
271#1935C2×C2911yescharacteristic, complemented
272#1934C2×C2911yescharacteristic
273#1925C2×C2911yescharacteristic
274#1865C2×C2911yescharacteristic, complemented
275#1771C2×C2911yescharacteristic, complemented
276C4×#103C2×C2911yescharacteristic, complemented
277C22×C29—81no—
278C22×C29—81no—
279C22×C29—81no—
280C22×C29—81no—
281C22×C29—81no—
282C22×C29—81no—
283C22×C29—81no—
284C22×C29#53211yescharacteristic
285C22×C29#54611yescharacteristic
286C22×C29#54811yescharacteristic
287C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
288C22×C29#57511yescharacteristic
289C22×C29#57711yescharacteristic
290C22×C29#57811yescharacteristic
291C4×C29—22no—
292C4×C29—42no—
293C4×C29—41no—
294C4×C29—41no—
295C4×C29—41no—
296C4×C29—41no—
297C4×C29—41no—
298C4×C29—42no—
299C4×C29—81no—
300C4×C29—81no—
301C4×C29—81no—
302C4×C29—81no—
303C4×C29—81no—
304C4×C29#52911yescharacteristic
305C4×C29#53911yescharacteristic
306C4×C29#55211yescharacteristic
307C4×C29#55311yescharacteristic
308C2×#125—21no—
309C2×#124C22×C2911yescharacteristic
310C2×C4×Q8C22×C2911yescharacteristic
311C2×#107C22×C2911yescharacteristic
312C2×#106C22×C2911yescharacteristic
313C2×C4⋊C8C22×C2911yescharacteristic
314C2×#103C22×C2911yescharacteristic
315C2×#103C22×C2911yescharacteristic
316C2×#103C22×C2911yescharacteristic
317C2×#103C22×C2911yescharacteristic
318C2×#102C22×C2911yescharacteristic
319C2×#102C22×C2911yescharacteristic
320C2×#102C22×C2911yescharacteristic
321C2×#102C22×C2911yescharacteristic
322C2×#97C22×C2911yescharacteristic
323C2×#97C22×C2911yescharacteristic
324C2×C4×C8C22×C2911yescharacteristic
325#400—21no—
326#399—21no—
327#398—21no—
328#397—21no—
329#391C22×C2911yescharacteristic
330#390C22×C2911yescharacteristic
331#390C22×C2911yescharacteristic
332#389C22×C2911yescharacteristic
333#389C22×C2911yescharacteristic
334#389C22×C2911yescharacteristic
335#389C22×C2911yescharacteristic
336#389C22×C2911yescharacteristic
337#388—21no—
338#388—21no—
339#387—21no—
340#384C22×C2911yescharacteristic
341C4×C4⋊C4C22×C2911yescharacteristic
342C4×C4⋊C4C22×C2911yescharacteristic
343#340C22×C2911yescharacteristic
344#340C22×C2911yescharacteristic
345#340C22×C2911yescharacteristic
346#340C22×C2911yescharacteristic
347#340C22×C2911yescharacteristic
348#340C22×C2911yescharacteristic
349#336C22×C2911yescharacteristic
350#336C22×C2911yescharacteristic
351C2×C29—161no—
352C2×C29#255811yescharacteristic
353C2×C29#317111yescharacteristic
354C2×C29#317811yescharacteristic
355C2×C29#330811yescharacteristic
356C2×C29#331711yescharacteristic
357C2×C29#337311yescharacteristic
358C2×C29#337711yescharacteristic
359C22×Q8C23×C2911yescharacteristic
360C22×D4C23×C2911yescharacteristic
361C22×C8C23×C2911yescharacteristic
362C22×C8C23×C2911yescharacteristic
363C22×C8C23×C2911yescharacteristic
364C22×C8C23×C2911yescharacteristic
365#125—44no—
366#124—22no—
367#124—41no—
368C4×Q8—22no—
369C4×Q8—41no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4D4×C2911yescharacteristic
379C2×C4⋊C4D4×C2911yescharacteristic
380C2×C4⋊C4C23×C2911yescharacteristic
381C2×C4⋊C4C23×C2911yescharacteristic
382C2×C4⋊C4C23×C2911yescharacteristic
383C2×C4⋊C4C23×C2911yescharacteristic
384C2×C4⋊C4C23×C2911yescharacteristic
385C2×C4⋊C4C23×C2911yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42C23×C2911yescharacteristic
395C2×C42C23×C2911yescharacteristic
396C2×C42C23×C2911yescharacteristic
397#107—22no—
398#106—41no—
399C4⋊C8—22no—
400#103—22no—
401#103—22no—
402#103—22no—
403#103—22no—
404#102—22no—
405#102—22no—
406#102—22no—
407#102—41no—
408#97—22no—
409#97—41no—
410C4×C8—41no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95D4×C2911yescharacteristic
420#95D4×C2911yescharacteristic
421C29#2902511yescharacteristic, direct product factor, Sylow
422C24—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8#41×C2912yes—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4C2×D4×C2911yescharacteristic
443C22×C4C2×D4×C2911yescharacteristic
444C22×C4C2×D4×C2911yescharacteristic
445C22×C4C2×D4×C2911yescharacteristic
446C22×C4C2×D4×C2911yescharacteristic
447C22×C4C2×D4×C2911yescharacteristic
448C22×C4C24×C2911yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8#41×C2912yes—
460C2×C8#41×C2912yes—
461C4⋊C4—22no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—41no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—81no—
482C4⋊C4#41×C2912yes—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C22⋊C4—81no—
488C22⋊C4—81no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—42no—
496C42—42no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23C22×D4×C2911yescharacteristic
505Q8—22no—
506Q8—22no—
507Q8—41no—
508Q8—41no—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—41no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
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—21no—
531C2×C4—21no—
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×C4C29×AGL(1,ℤ/8)12yes—
552C2×C4C2×#41×C2911yescharacteristic
553C2×C4C2×#41×C2911yescharacteristic
554C2×C4C2×#41×C2911yescharacteristic
555C2×C4C2×#41×C2911yescharacteristic
556C2×C4C29×H(5,𝔽2)11yescharacteristic
557C2×C4C29×2−1+411yescharacteristic
558C8—22no—
559C8—22no—
560C8—41no—
561C8—41no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22C29×#53211yescharacteristic
570C22C29×#54611yescharacteristic
571C22C29×#54811yescharacteristic
572C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
573C22C29×#57511yescharacteristic
574C22C29×#57711yescharacteristic
575C22C29×#57811yescharacteristic
576C4—22no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—42no—
581C4—42no—
582C4—41no—
583C4—41no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4C29×#52911yescharacteristic
590C4C29×#53911yescharacteristic
591C4C29×#55211yescharacteristic
592C4C29×#55311yescharacteristic
593C2—161no—
594C2C29×#255811yescharacteristic
595C2C29×#317111yescharacteristic
596C2C29×#317811yescharacteristic
597C2C29×#330811yescharacteristic
598C2C29×#331711yescharacteristic
599C2C29×#337311yescharacteristic
600C2C29×#337711yescharacteristic
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×#2506C2semidirect
3. C29×#2100C2semidirect
4. C29×#2068C2semidirect
8. C29×#1943C2semidirect
10. C29×#1935C2semidirect
13. C29×#1865C2semidirect
14. C29×#1771C2semidirect
15. C4×C29×#103C2semidirect
196. #29025C29direct (N × H)
262. #2506C2×C29semidirect
264. #2100C2×C29semidirect
265. #2068C2×C29semidirect
269. #1943C2×C29semidirect
271. #1935C2×C29semidirect
274. #1865C2×C29semidirect
275. #1771C2×C29semidirect
276. C4×#103C2×C29semidirect
421. C29#29025direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#25062
C29×#24482
C29×#21002
C29×#20682
C29×#20652
C29×#20422
C29×#19592
C29×#19432
C29×#19362
C29×#19352
C29×#19342
C29×#19252
C29×#18652
C29×#17712
C4×C29×#1032
#2902529