Finite Group Databasebeta

← C29×#29470 #20324370

Subgroups — C29×#29470 #20324370

Order 7424.

700 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2625C211yesmaximal, characteristic
2C29×#2323C211yesmaximal, characteristic
3C29×#2075C211yesmaximal, characteristic
4C29×#2036C211yesmaximal, characteristic
5C29×#2036C211yesmaximal, characteristic
6C29×#2001C211yesmaximal, characteristic
7C29×#1969C211yesmaximal, characteristic, complemented
8C29×#1942C211yesmaximal, characteristic, complemented
9C29×#1935C211yesmaximal, characteristic, complemented
10C29×#1935C211yesmaximal, characteristic, complemented
11C29×#1928C211yesmaximal, characteristic, complemented
12C29×#1918C211yesmaximal, characteristic, complemented
13C29×#1878C211yesmaximal, characteristic, complemented
14C29×#1863C211yesmaximal, characteristic, complemented
15C29×#1750C211yesmaximal, characteristic
16C22×Q16×C29C2211yescharacteristic
17C2×C29×C22⋊Q8C2211yescharacteristic
18C2×C29×C22⋊Q8C2211yescharacteristic
19C2×C4×Q8×C29C2211yescharacteristic
20C2×C29×#117C2211yescharacteristic
21C2×C29×#107C2211yescharacteristic
22C2×C29×#107C2211yescharacteristic
23C2×C29×#107C2211yescharacteristic
24C2×C29×#103C2211yescharacteristic
25C2×C29×#103C2211yescharacteristic
26C2×C29×#103C2211yescharacteristic
27C2×C29×#103C2211yescharacteristic
28C2×C29×#103C2211yescharacteristic
29C2×C29×#103C2211yescharacteristic
30C2×C29×C22⋊C8C2211yescharacteristic
31C2×C29×C22⋊C8C2211yescharacteristic
32C2×C29×#97C2211yescharacteristic
33C2×C4×C8×C29C2211yescharacteristic
34C29×#400—21no—
35C29×#398—21no—
36C29×#397—21no—
37C29×#397—21no—
38C29×#391C2211yescharacteristic
39C29×#391C2211yescharacteristic
40C29×#391C2211yescharacteristic
41C29×#389—21no—
42C29×#389C2211yescharacteristic
43C29×#389C2211yescharacteristic
44C29×#389C2211yescharacteristic
45C29×#388—21no—
46C29×#388—21no—
47C29×#387—21no—
48C29×#380C2211yescharacteristic
49C29×#380C2211yescharacteristic
50C4×C4⋊C4×C29C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×Q8×C29C2311yescharacteristic
60C22×Q8×C29C2311yescharacteristic
61C23×C4×C29C2311yescharacteristic
62C2×Q16×C29—22no—
63C2×Q16×C29—22no—
64C2×Q16×C29—41no—
65C22×C8×C29C2311yescharacteristic
66C22×C8×C29C2311yescharacteristic
67C22×C8×C29C2311yescharacteristic
68C22×C8×C29C2311yescharacteristic
69C29×C22⋊Q8—22no—
70C29×C22⋊Q8—22no—
71C29×C22⋊Q8—41no—
72C29×C22⋊Q8—41no—
73C4×Q8×C29—41no—
74C4×Q8×C29—41no—
75C29×#117—41no—
76C29×#117—41no—
77C2×C4⋊C4×C29—21no—
78C2×C4⋊C4×C29—21no—
79C2×C4⋊C4×C29—21no—
80C2×C4⋊C4×C29—21no—
81C2×C4⋊C4×C29—21no—
82C2×C4⋊C4×C29—21no—
83C2×C4⋊C4×C29D411yescharacteristic
84C2×C4⋊C4×C29D411yescharacteristic
85C2×C4⋊C4×C29C2311yescharacteristic
86C2×C4⋊C4×C29C2311yescharacteristic
87C2×C4⋊C4×C29C2311yescharacteristic
88C2×C4⋊C4×C29C2311yescharacteristic
89C2×C4⋊C4×C29C2311yescharacteristic
90C2×C4⋊C4×C29C2311yescharacteristic
91C2×C22⋊C4×C29—21no—
92C2×C22⋊C4×C29—21no—
93C2×C22⋊C4×C29—21no—
94C2×C22⋊C4×C29—21no—
95C2×C22⋊C4×C29D411yescharacteristic
96C2×C22⋊C4×C29D411yescharacteristic
97C2×C42×C29—21no—
98C2×C42×C29—21no—
99C2×C42×C29C2311yescharacteristic
100C2×C42×C29C2311yescharacteristic
101C29×#107—22no—
102C29×#107—22no—
103C29×#107—41no—
104C29×#103—22no—
105C29×#103—22no—
106C29×#103—22no—
107C29×#103—22no—
108C29×#103—41no—
109C29×#103—41no—
110C29×C22⋊C8—22no—
111C29×C22⋊C8—22no—
112C29×#97—41no—
113C4×C8×C29—41no—
114C29×#95—21no—
115C29×#95—21no—
116C29×#95—21no—
117C29×#95—21no—
118C29×#95—21no—
119C29×#95—21no—
120C29×#95—21no—
121C29×#95—21no—
122C29×#95—21no—
123C29×#95—21no—
124C29×#95—21no—
125C29×#95—21no—
126C24×C29C2×D411yescharacteristic
127C2×Q8×C29—21no—
128C2×Q8×C29—21no—
129C2×Q8×C29—21no—
130C2×Q8×C29—21no—
131C2×Q8×C29—21no—
132C2×Q8×C29—21no—
133C2×Q8×C29—21no—
134C2×Q8×C29—21no—
135C2×Q8×C29—21no—
136C2×Q8×C29—21no—
137C2×Q8×C29—21no—
138C2×Q8×C29#4112yes—
139C22×C4×C29—21no—
140C22×C4×C29—21no—
141C22×C4×C29—21no—
142C22×C4×C29—21no—
143C22×C4×C29—21no—
144C22×C4×C29—21no—
145C22×C4×C29—21no—
146C22×C4×C29—21no—
147C22×C4×C29—21no—
148C22×C4×C29—21no—
149C22×C4×C29—21no—
150C22×C4×C29—21no—
151C22×C4×C29—21no—
152C22×C4×C29—21no—
153C22×C4×C29C2×D411yescharacteristic
154C22×C4×C29C2×D411yescharacteristic
155C22×C4×C29C2×D411yescharacteristic
156C22×C4×C29C2×D411yescharacteristic
157C22×C4×C29C2×D411yescharacteristic
158C22×C4×C29C2411yescharacteristic
159Q16×C29—44no—
160C2×C8×C29—21no—
161C2×C8×C29—21no—
162C2×C8×C29—21no—
163C2×C8×C29—21no—
164C2×C8×C29—21no—
165C2×C8×C29—21no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29#4112yes—
171C2×C8×C29#4112yes—
172C4⋊C4×C29—24no—
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—21no—
181C4⋊C4×C29—21no—
182C4⋊C4×C29—21no—
183C4⋊C4×C29—21no—
184C4⋊C4×C29—41no—
185C4⋊C4×C29—41no—
186C4⋊C4×C29—42no—
187C4⋊C4×C29—42no—
188C4⋊C4×C29—81no—
189C4⋊C4×C29—81no—
190C4⋊C4×C29—81no—
191C4⋊C4×C29#4112yes—
192C22⋊C4×C29—24no—
193C22⋊C4×C29—41no—
194C22⋊C4×C29—41no—
195C22⋊C4×C29—42no—
196C22⋊C4×C29—81no—
197C22⋊C4×C29—81no—
198C42×C29—21no—
199C42×C29—21no—
200C42×C29—21no—
201C42×C29—21no—
202C42×C29—42no—
203C42×C29—81no—
204#29470C2911yesmaximal, characteristic, direct product factor, Sylow
205C23×C29—21no—
206C23×C29—21no—
207C23×C29—21no—
208C23×C29—21no—
209C23×C29—21no—
210C23×C29—21no—
211C23×C29—21no—
212C23×C29C22×D411yescharacteristic
213Q8×C29—22no—
214Q8×C29—22no—
215Q8×C29—41no—
216Q8×C29—41no—
217Q8×C29—41no—
218Q8×C29—41no—
219Q8×C29—41no—
220Q8×C29—41no—
221C2×C4×C29—22no—
222C2×C4×C29—22no—
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—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—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—41no—
255C2×C4×C29—41no—
256C2×C4×C29—41no—
257C2×C4×C29—41no—
258C2×C4×C29—41no—
259C2×C4×C29—41no—
260C2×C4×C29—41no—
261C2×C4×C29—41no—
262C2×C4×C29—41no—
263C2×C4×C29—41no—
264C2×C4×C29C2×#4111yescharacteristic
265C2×C4×C29C2×#4111yescharacteristic
266C2×C4×C29C2×#4111yescharacteristic
267C2×C4×C29C2×#4111yescharacteristic
268C2×C4×C29H(5,𝔽2)11yescharacteristic
269C2×C4×C29H(5,𝔽2)11yescharacteristic
270C8×C29—22no—
271C8×C29—22no—
272C8×C29—41no—
273C8×C29—41no—
274#2625C2×C2911yescharacteristic
275#2323C2×C2911yescharacteristic
276#2075C2×C2911yescharacteristic
277#2036C2×C2911yescharacteristic
278#2036C2×C2911yescharacteristic
279#2001C2×C2911yescharacteristic
280#1969C2×C2911yescharacteristic, complemented
281#1942C2×C2911yescharacteristic, complemented
282#1935C2×C2911yescharacteristic, complemented
283#1935C2×C2911yescharacteristic, complemented
284#1928C2×C2911yescharacteristic, complemented
285#1918C2×C2911yescharacteristic, complemented
286#1878C2×C2911yescharacteristic, complemented
287#1863C2×C2911yescharacteristic, complemented
288#1750C2×C2911yescharacteristic
289C22×C29—41no—
290C22×C29—41no—
291C22×C29—41no—
292C22×C29—41no—
293C22×C29—41no—
294C22×C29—41no—
295C22×C29—41no—
296C22×C29#52511yescharacteristic
297C22×C29#53211yescharacteristic
298C22×C29#53411yescharacteristic
299C22×C29#57611yescharacteristic
300C22×C29#57811yescharacteristic
301C22×C29#57811yescharacteristic
302C22×C29#57811yescharacteristic
303C4×C29—41no—
304C4×C29—42no—
305C4×C29—42no—
306C4×C29—41no—
307C4×C29—41no—
308C4×C29—41no—
309C4×C29—41no—
310C4×C29—81no—
311C4×C29—81no—
312C4×C29—81no—
313C4×C29—81no—
314C4×C29—81no—
315C4×C29—81no—
316C4×C29#55111yescharacteristic
317C4×C29#55311yescharacteristic
318C4×C29#55311yescharacteristic
319C4×C29#55911yescharacteristic
320C22×Q16C22×C2911yescharacteristic
321C2×C22⋊Q8C22×C2911yescharacteristic
322C2×C22⋊Q8C22×C2911yescharacteristic
323C2×C4×Q8C22×C2911yescharacteristic
324C2×#117C22×C2911yescharacteristic
325C2×#107C22×C2911yescharacteristic
326C2×#107C22×C2911yescharacteristic
327C2×#107C22×C2911yescharacteristic
328C2×#103C22×C2911yescharacteristic
329C2×#103C22×C2911yescharacteristic
330C2×#103C22×C2911yescharacteristic
331C2×#103C22×C2911yescharacteristic
332C2×#103C22×C2911yescharacteristic
333C2×#103C22×C2911yescharacteristic
334C2×C22⋊C8C22×C2911yescharacteristic
335C2×C22⋊C8C22×C2911yescharacteristic
336C2×#97C22×C2911yescharacteristic
337C2×C4×C8C22×C2911yescharacteristic
338#400—21no—
339#398—21no—
340#397—21no—
341#397—21no—
342#391C22×C2911yescharacteristic
343#391C22×C2911yescharacteristic
344#391C22×C2911yescharacteristic
345#389—21no—
346#389C22×C2911yescharacteristic
347#389C22×C2911yescharacteristic
348#389C22×C2911yescharacteristic
349#388—21no—
350#388—21no—
351#387—21no—
352#380C22×C2911yescharacteristic
353#380C22×C2911yescharacteristic
354C4×C4⋊C4C22×C2911yescharacteristic
355#340C22×C2911yescharacteristic
356#340C22×C2911yescharacteristic
357#340C22×C2911yescharacteristic
358#340C22×C2911yescharacteristic
359#340C22×C2911yescharacteristic
360#340C22×C2911yescharacteristic
361#336C22×C2911yescharacteristic
362#336C22×C2911yescharacteristic
363C2×C29—81no—
364C2×C29#260211yescharacteristic
365C2×C29#312411yescharacteristic
366C2×C29#312711yescharacteristic
367C2×C29#317511yescharacteristic
368C2×C29#317711yescharacteristic
369C2×C29#320211yescharacteristic
370C2×C29#320311yescharacteristic
371C22×Q8C23×C2911yescharacteristic
372C22×Q8C23×C2911yescharacteristic
373C23×C4C23×C2911yescharacteristic
374C2×Q16—22no—
375C2×Q16—22no—
376C2×Q16—41no—
377C22×C8C23×C2911yescharacteristic
378C22×C8C23×C2911yescharacteristic
379C22×C8C23×C2911yescharacteristic
380C22×C8C23×C2911yescharacteristic
381C22⋊Q8—22no—
382C22⋊Q8—22no—
383C22⋊Q8—41no—
384C22⋊Q8—41no—
385C4×Q8—41no—
386C4×Q8—41no—
387#117—41no—
388#117—41no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4D4×C2911yescharacteristic
396C2×C4⋊C4D4×C2911yescharacteristic
397C2×C4⋊C4C23×C2911yescharacteristic
398C2×C4⋊C4C23×C2911yescharacteristic
399C2×C4⋊C4C23×C2911yescharacteristic
400C2×C4⋊C4C23×C2911yescharacteristic
401C2×C4⋊C4C23×C2911yescharacteristic
402C2×C4⋊C4C23×C2911yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4D4×C2911yescharacteristic
408C2×C22⋊C4D4×C2911yescharacteristic
409C2×C42—21no—
410C2×C42—21no—
411C2×C42C23×C2911yescharacteristic
412C2×C42C23×C2911yescharacteristic
413#107—22no—
414#107—22no—
415#107—41no—
416#103—22no—
417#103—22no—
418#103—22no—
419#103—22no—
420#103—41no—
421#103—41no—
422C22⋊C8—22no—
423C22⋊C8—22no—
424#97—41no—
425C4×C8—41no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438C29#2947011yescharacteristic, direct product factor, Sylow
439C24C2×D4×C2911yescharacteristic
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8#41×C2912yes—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4C2×D4×C2911yescharacteristic
467C22×C4C2×D4×C2911yescharacteristic
468C22×C4C2×D4×C2911yescharacteristic
469C22×C4C2×D4×C2911yescharacteristic
470C22×C4C2×D4×C2911yescharacteristic
471C22×C4C24×C2911yescharacteristic
472Q16—44no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8#41×C2912yes—
484C2×C8#41×C2912yes—
485C4⋊C4—24no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—81no—
502C4⋊C4—81no—
503C4⋊C4—81no—
504C4⋊C4#41×C2912yes—
505C22⋊C4—24no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—42no—
509C22⋊C4—81no—
510C22⋊C4—81no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—42no—
516C42—81no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23C22×D4×C2911yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
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—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4C2×#41×C2911yescharacteristic
577C2×C4C2×#41×C2911yescharacteristic
578C2×C4C2×#41×C2911yescharacteristic
579C2×C4C2×#41×C2911yescharacteristic
580C2×C4C29×H(5,𝔽2)11yescharacteristic
581C2×C4C29×H(5,𝔽2)11yescharacteristic
582C8—22no—
583C8—22no—
584C8—41no—
585C8—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22C29×#52511yescharacteristic
594C22C29×#53211yescharacteristic
595C22C29×#53411yescharacteristic
596C22C29×#57611yescharacteristic
597C22C29×#57811yescharacteristic
598C22C29×#57811yescharacteristic
599C22C29×#57811yescharacteristic
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—42no—
606C4—42no—
607C4—81no—
608C4—81no—
609C4—81no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4C29×#55111yescharacteristic
614C4C29×#55311yescharacteristic
615C4C29×#55311yescharacteristic
616C4C29×#55911yescharacteristic
617C2—81no—
618C2C29×#260211yescharacteristic
619C2C29×#312411yescharacteristic
620C2C29×#312711yescharacteristic
621C2C29×#317511yescharacteristic
622C2C29×#317711yescharacteristic
623C2C29×#320211yescharacteristic
624C2C29×#320311yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC24×C29C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C29×#117 ◁ G

Complements

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

NH ≅ G/Ntype
7. C29×#1969C2semidirect
8. C29×#1942C2semidirect
9. C29×#1935C2semidirect
10. C29×#1935C2semidirect
11. C29×#1928C2semidirect
12. C29×#1918C2semidirect
13. C29×#1878C2semidirect
14. C29×#1863C2semidirect
204. #29470C29direct (N × H)
280. #1969C2×C29semidirect
281. #1942C2×C29semidirect
282. #1935C2×C29semidirect
283. #1935C2×C29semidirect
284. #1928C2×C29semidirect
285. #1918C2×C29semidirect
286. #1878C2×C29semidirect
287. #1863C2×C29semidirect
438. C29#29470direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#26252
C29×#23232
C29×#20752
C29×#20362
C29×#20012
C29×#19692
C29×#19422
C29×#19352
C29×#19282
C29×#19182
C29×#18782
C29×#18632
C29×#17502
#2947029