Finite Group Databasebeta

← C29×#26713 #20321613

Subgroups — C29×#26713 #20321613

Order 7424.

694 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×#2447C211yesmaximal, characteristic
2C29×#2370C211yesmaximal, characteristic, complemented
3C29×#2087C211yesmaximal, characteristic, complemented
4C29×#2042C211yesmaximal, characteristic
5C29×#2026C211yesmaximal, characteristic, complemented
6C29×#2025C211yesmaximal, characteristic
7C29×#1983C211yesmaximal, characteristic
8C29×#1935C211yesmaximal, characteristic, complemented
9C29×#1928C211yesmaximal, characteristic, complemented
10C29×#1928C211yesmaximal, characteristic, complemented
11C29×#1925C211yesmaximal, characteristic
12C29×#1918C211yesmaximal, characteristic, complemented
13C29×#1917C211yesmaximal, characteristic, complemented
14C29×#1862C211yesmaximal, characteristic
15C29×#1762C211yesmaximal, characteristic
16C2×C29×#125C2211yescharacteristic
17C2×C29×#124C2211yescharacteristic
18C2×C4×D4×C29C2211yescharacteristic
19C2×C29×#107C2211yescharacteristic
20C2×C29×#107C2211yescharacteristic
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
31C29×#397—21no—
32C29×#397—21no—
33C29×#391C2211yescharacteristic
34C29×#391C2211yescharacteristic
35C29×#390C2211yescharacteristic
36C29×#389—21no—
37C29×#389C2211yescharacteristic
38C29×#389C2211yescharacteristic
39C29×#389C2211yescharacteristic
40C29×#387—21no—
41C29×#387—21no—
42C29×#385—21no—
43C29×#381—21no—
44C4×C4⋊C4×C29—21no—
45C4×C4⋊C4×C29C2211yescharacteristic
46C4×C4⋊C4×C29C2211yescharacteristic
47C4×C4⋊C4×C29C2211yescharacteristic
48C4×C4⋊C4×C29C2211yescharacteristic
49C29×#340C2211yescharacteristic
50C29×#340C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#336C2211yescharacteristic
56C29×#336C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×Q8×C29C2311yescharacteristic
60C22×D4×C29C2311yescharacteristic
61C23×C4×C29—21no—
62C22×C8×C29C2311yescharacteristic
63C22×C8×C29C2311yescharacteristic
64C22×C8×C29C2311yescharacteristic
65C22×C8×C29C2311yescharacteristic
66C29×#125—22no—
67C29×#125—22no—
68C29×#124—22no—
69C29×#124—41no—
70C4×D4×C29—22no—
71C4×D4×C29—41no—
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×C29D411yescharacteristic
78C2×C4⋊C4×C29D411yescharacteristic
79C2×C4⋊C4×C29C2311yescharacteristic
80C2×C4⋊C4×C29C2311yescharacteristic
81C2×C4⋊C4×C29C2311yescharacteristic
82C2×C4⋊C4×C29C2311yescharacteristic
83C2×C4⋊C4×C29C2311yescharacteristic
84C2×C4⋊C4×C29C2311yescharacteristic
85C2×C22⋊C4×C29—21no—
86C2×C22⋊C4×C29—21no—
87C2×C22⋊C4×C29—21no—
88C2×C22⋊C4×C29—21no—
89C2×C22⋊C4×C29—21no—
90C2×C42×C29—21no—
91C2×C42×C29—21no—
92C2×C42×C29—21no—
93C2×C42×C29C2311yescharacteristic
94C2×C42×C29C2311yescharacteristic
95C2×C42×C29C2311yescharacteristic
96C29×#107—22no—
97C29×#107—41no—
98C29×C4⋊C8—41no—
99C29×#103—22no—
100C29×#103—22no—
101C29×#103—22no—
102C29×#103—41no—
103C29×#102—22no—
104C29×#102—22no—
105C29×#102—22no—
106C29×#102—22no—
107C29×#97—41no—
108C29×#95—21no—
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×#95D411yescharacteristic
119C29×#95D411yescharacteristic
120C24×C29—21no—
121C2×Q8×C29—21no—
122C2×Q8×C29—21no—
123C2×Q8×C29—21no—
124C2×Q8×C29—21no—
125C2×Q8×C29—21no—
126C2×Q8×C29—21no—
127C2×D4×C29—21no—
128C2×D4×C29—21no—
129C2×D4×C29—21no—
130C2×D4×C29—21no—
131C2×D4×C29—21no—
132C2×D4×C29#4112yes—
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—42no—
141C22×C4×C29—42no—
142C22×C4×C29—81no—
143C22×C4×C29C2×D411yescharacteristic
144C22×C4×C29C2×D411yescharacteristic
145C22×C4×C29C2×D411yescharacteristic
146C22×C4×C29C2×D411yescharacteristic
147C22×C4×C29C2×D411yescharacteristic
148C22×C4×C29C2×D411yescharacteristic
149C22×C4×C29C2411yescharacteristic
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—21no—
159C2×C8×C29—21no—
160C2×C8×C29—21no—
161C2×C8×C29—21no—
162C4⋊C4×C29—24no—
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—41no—
174C4⋊C4×C29—41no—
175C4⋊C4×C29—42no—
176C4⋊C4×C29—81no—
177C4⋊C4×C29—81no—
178C4⋊C4×C29#4112yes—
179C4⋊C4×C29#4112yes—
180C4⋊C4×C29#4112yes—
181C22⋊C4×C29—42no—
182C22⋊C4×C29—42no—
183C22⋊C4×C29—42no—
184C22⋊C4×C29—42no—
185C22⋊C4×C29—81no—
186C42×C29—21no—
187C42×C29—21no—
188C42×C29—21no—
189C42×C29—21no—
190C42×C29—21no—
191C42×C29—21no—
192C42×C29—42no—
193C42×C29—81no—
194C42×C29—81no—
195#26713C2911yesmaximal, characteristic, direct product factor, Sylow
196C23×C29—22no—
197C23×C29—41no—
198C23×C29—41no—
199C23×C29—41no—
200C23×C29—41no—
201C23×C29—41no—
202C23×C29—41no—
203C23×C29C22×D411yescharacteristic
204Q8×C29—41no—
205Q8×C29—41no—
206Q8×C29—41no—
207Q8×C29—41no—
208D4×C29—22no—
209D4×C29—22no—
210D4×C29—41no—
211D4×C29—41no—
212C2×C4×C29—21no—
213C2×C4×C29—21no—
214C2×C4×C29—22no—
215C2×C4×C29—22no—
216C2×C4×C29—21no—
217C2×C4×C29—21no—
218C2×C4×C29—21no—
219C2×C4×C29—21no—
220C2×C4×C29—22no—
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—21no—
228C2×C4×C29—21no—
229C2×C4×C29—21no—
230C2×C4×C29—21no—
231C2×C4×C29—21no—
232C2×C4×C29—21no—
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—84no—
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—41no—
259C8×C29—41no—
260C8×C29—41no—
261C8×C29—41no—
262#2447C2×C2911yescharacteristic
263#2370C2×C2911yescharacteristic, complemented
264#2087C2×C2911yescharacteristic, complemented
265#2042C2×C2911yescharacteristic
266#2026C2×C2911yescharacteristic, complemented
267#2025C2×C2911yescharacteristic
268#1983C2×C2911yescharacteristic
269#1935C2×C2911yescharacteristic, complemented
270#1928C2×C2911yescharacteristic, complemented
271#1928C2×C2911yescharacteristic, complemented
272#1925C2×C2911yescharacteristic
273#1918C2×C2911yescharacteristic, complemented
274#1917C2×C2911yescharacteristic, complemented
275#1862C2×C2911yescharacteristic
276#1762C2×C2911yescharacteristic
277C22×C29—42no—
278C22×C29—42no—
279C22×C29—42no—
280C22×C29—81no—
281C22×C29—81no—
282C22×C29—81no—
283C22×C29—81no—
284C22×C29#52511yescharacteristic
285C22×C29#54611yescharacteristic
286C22×C29#54811yescharacteristic
287C22×C29#57511yescharacteristic
288C22×C29#57511yescharacteristic
289C22×C29#57611yescharacteristic
290C22×C29#57811yescharacteristic
291C4×C29—41no—
292C4×C29—42no—
293C4×C29—42no—
294C4×C29—41no—
295C4×C29—42no—
296C4×C29—41no—
297C4×C29—41no—
298C4×C29—41no—
299C4×C29—41no—
300C4×C29—81no—
301C4×C29—81no—
302C4×C29—81no—
303C4×C29—81no—
304C4×C29#52911yescharacteristic
305C4×C29#54211yescharacteristic
306C4×C29#55211yescharacteristic
307C4×C29#55911yescharacteristic
308C2×#125C22×C2911yescharacteristic
309C2×#124C22×C2911yescharacteristic
310C2×C4×D4C22×C2911yescharacteristic
311C2×#107C22×C2911yescharacteristic
312C2×#107C22×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
323#397—21no—
324#397—21no—
325#391C22×C2911yescharacteristic
326#391C22×C2911yescharacteristic
327#390C22×C2911yescharacteristic
328#389—21no—
329#389C22×C2911yescharacteristic
330#389C22×C2911yescharacteristic
331#389C22×C2911yescharacteristic
332#387—21no—
333#387—21no—
334#385—21no—
335#381—21no—
336C4×C4⋊C4—21no—
337C4×C4⋊C4C22×C2911yescharacteristic
338C4×C4⋊C4C22×C2911yescharacteristic
339C4×C4⋊C4C22×C2911yescharacteristic
340C4×C4⋊C4C22×C2911yescharacteristic
341#340C22×C2911yescharacteristic
342#340C22×C2911yescharacteristic
343#340C22×C2911yescharacteristic
344#340C22×C2911yescharacteristic
345#340C22×C2911yescharacteristic
346#340C22×C2911yescharacteristic
347#336C22×C2911yescharacteristic
348#336C22×C2911yescharacteristic
349#336C22×C2911yescharacteristic
350#336C22×C2911yescharacteristic
351C2×C29—82no—
352C2×C29#245811yescharacteristic
353C2×C29#311111yescharacteristic
354C2×C29#312411yescharacteristic
355C2×C29#331511yescharacteristic
356C2×C29#332211yescharacteristic
357C2×C29#337011yescharacteristic
358C2×C29#337711yescharacteristic
359C22×Q8C23×C2911yescharacteristic
360C22×D4C23×C2911yescharacteristic
361C23×C4—21no—
362C22×C8C23×C2911yescharacteristic
363C22×C8C23×C2911yescharacteristic
364C22×C8C23×C2911yescharacteristic
365C22×C8C23×C2911yescharacteristic
366#125—22no—
367#125—22no—
368#124—22no—
369#124—41no—
370C4×D4—22no—
371C4×D4—41no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4D4×C2911yescharacteristic
378C2×C4⋊C4D4×C2911yescharacteristic
379C2×C4⋊C4C23×C2911yescharacteristic
380C2×C4⋊C4C23×C2911yescharacteristic
381C2×C4⋊C4C23×C2911yescharacteristic
382C2×C4⋊C4C23×C2911yescharacteristic
383C2×C4⋊C4C23×C2911yescharacteristic
384C2×C4⋊C4C23×C2911yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42C23×C2911yescharacteristic
394C2×C42C23×C2911yescharacteristic
395C2×C42C23×C2911yescharacteristic
396#107—22no—
397#107—41no—
398C4⋊C8—41no—
399#103—22no—
400#103—22no—
401#103—22no—
402#103—41no—
403#102—22no—
404#102—22no—
405#102—22no—
406#102—22no—
407#97—41no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95D4×C2911yescharacteristic
419#95D4×C2911yescharacteristic
420C29#2671311yescharacteristic, direct product factor, Sylow
421C24—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4#41×C2912yes—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—81no—
444C22×C4C2×D4×C2911yescharacteristic
445C22×C4C2×D4×C2911yescharacteristic
446C22×C4C2×D4×C2911yescharacteristic
447C22×C4C2×D4×C2911yescharacteristic
448C22×C4C2×D4×C2911yescharacteristic
449C22×C4C2×D4×C2911yescharacteristic
450C22×C4C24×C2911yescharacteristic
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—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C4⋊C4—24no—
464C4⋊C4—24no—
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—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—42no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4#41×C2912yes—
480C4⋊C4#41×C2912yes—
481C4⋊C4#41×C2912yes—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—81no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—42no—
494C42—81no—
495C42—81no—
496C23—22no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23C22×D4×C2911yescharacteristic
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508D4—22no—
509D4—22no—
510D4—41no—
511D4—41no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
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—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
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—84no—
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—41no—
559C8—41no—
560C8—41no—
561C8—41no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22C29×#52511yescharacteristic
570C22C29×#54611yescharacteristic
571C22C29×#54811yescharacteristic
572C22C29×#57511yescharacteristic
573C22C29×#57511yescharacteristic
574C22C29×#57611yescharacteristic
575C22C29×#57811yescharacteristic
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—42no—
582C4—42no—
583C4—41no—
584C4—42no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4C29×#52911yescharacteristic
590C4C29×#54211yescharacteristic
591C4C29×#55211yescharacteristic
592C4C29×#55911yescharacteristic
593C2—82no—
594C2C29×#245811yescharacteristic
595C2C29×#311111yescharacteristic
596C2C29×#312411yescharacteristic
597C2C29×#331511yescharacteristic
598C2C29×#332211yescharacteristic
599C2C29×#337011yescharacteristic
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
2. C29×#2370C2semidirect
3. C29×#2087C2semidirect
5. C29×#2026C2semidirect
8. C29×#1935C2semidirect
9. C29×#1928C2semidirect
10. C29×#1928C2semidirect
12. C29×#1918C2semidirect
13. C29×#1917C2semidirect
195. #26713C29direct (N × H)
263. #2370C2×C29semidirect
264. #2087C2×C29semidirect
266. #2026C2×C29semidirect
269. #1935C2×C29semidirect
270. #1928C2×C29semidirect
271. #1928C2×C29semidirect
273. #1918C2×C29semidirect
274. #1917C2×C29semidirect
420. C29#26713direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#24472
C29×#23702
C29×#20872
C29×#20422
C29×#20262
C29×#20252
C29×#19832
C29×#19352
C29×#19282
C29×#19252
C29×#19182
C29×#19172
C29×#18622
C29×#17622
#2671329