Finite Group Databasebeta

← C29×#14882 #20309782

Subgroups — C29×#14882 #20309782

Order 7424.

1742 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C29C211yesmaximal, characteristic, complemented
2C2×C29×#397C211yesmaximal, characteristic
3C2×C29×#393C211yesmaximal, characteristic
4C2×C29×#388C211yesmaximal, characteristic
5C29×#1446C211yesmaximal, characteristic, complemented
6C29×#1445C211yesmaximal, characteristic, complemented
7C29×#1442C212yesmaximal, complemented
8C29×#1439C212yesmaximal
9C29×#1437C212yesmaximal
10C29×#1436C212yesmaximal, complemented
11C29×#1434C211yesmaximal, characteristic, complemented
12C23×Q8×C29C2211yescharacteristic
13C2×C4×Q8×C29—24no—
14C2×C4×Q8×C29—24no—
15C2×C4×Q8×C29—24no—
16C22×C4⋊C4×C29C2211yescharacteristic
17C22×C4⋊C4×C29C2212yes—
18C22×C4⋊C4×C29C2211yescharacteristic
19C22×C22⋊C4×C29C2211yescharacteristic
20C22×C22⋊C4×C29C2212yes—
21C22×C22⋊C4×C29C2211yescharacteristic
22C22×C22⋊C4×C29C2211yescharacteristic
23C22×C22⋊C4×C29C2212yes—
24C22×C42×C29C2212yes—
25C22×C42×C29C2211yescharacteristic
26C29×#397—24no—
27C29×#393—24no—
28C29×#388—24no—
29C2×C29×#95C2212yes—
30C2×C29×#95C2211yescharacteristic
31C2×C29×#95C2211yescharacteristic
32C2×C29×#95C2212yes—
33C2×C29×#95C2212yes—
34C2×C29×#95C2212yes—
35C2×C29×#95C2212yes—
36C2×C29×#95C2212yes—
37C2×C29×#95C2211yescharacteristic
38C2×C29×#95C2211yescharacteristic
39C2×C29×#95C2212yes—
40C2×C29×#95C2212yes—
41C25×C29C2311yescharacteristic
42C22×Q8×C29—22no—
43C22×Q8×C29—22no—
44C22×Q8×C29—24no—
45C22×Q8×C29—24no—
46C22×Q8×C29D414yes—
47C23×C4×C29C2311yescharacteristic
48C23×C4×C29C2311yescharacteristic
49C23×C4×C29C2312yes—
50C23×C4×C29C2312yes—
51C23×C4×C29C2311yescharacteristic
52C23×C4×C29C2312yes—
53C23×C4×C29C2311yescharacteristic
54C23×C4×C29C2311yescharacteristic
55C23×C4×C29C2311yescharacteristic
56C23×C4×C29C2312yes—
57C4×Q8×C29—232no—
58C2×C4⋊C4×C29—24no—
59C2×C4⋊C4×C29—24no—
60C2×C4⋊C4×C29—24no—
61C2×C4⋊C4×C29—22no—
62C2×C4⋊C4×C29—22no—
63C2×C4⋊C4×C29—22no—
64C2×C4⋊C4×C29—24no—
65C2×C4⋊C4×C29D414yes—
66C2×C22⋊C4×C29—22no—
67C2×C22⋊C4×C29—22no—
68C2×C22⋊C4×C29—22no—
69C2×C22⋊C4×C29—24no—
70C2×C22⋊C4×C29—22no—
71C2×C22⋊C4×C29—22no—
72C2×C22⋊C4×C29—22no—
73C2×C22⋊C4×C29—24no—
74C2×C22⋊C4×C29—24no—
75C2×C22⋊C4×C29—22no—
76C2×C22⋊C4×C29—24no—
77C2×C22⋊C4×C29—24no—
78C2×C22⋊C4×C29—24no—
79C2×C22⋊C4×C29—42no—
80C2×C42×C29—24no—
81C2×C42×C29—24no—
82C2×C42×C29—24no—
83C2×C42×C29—22no—
84C2×C42×C29—22no—
85C2×C42×C29D414yes—
86C29×#95—22no—
87C29×#95—22no—
88C29×#95—22no—
89C29×#95—24no—
90C29×#95—24no—
91C29×#95—22no—
92C29×#95—24no—
93C29×#95—24no—
94C29×#95—24no—
95C29×#95—24no—
96C29×#95—42no—
97C29×#95—42no—
98C24×C29—21no—
99C24×C29—21no—
100C24×C29—21no—
101C24×C29—21no—
102C24×C29—22no—
103C24×C29—22no—
104C24×C29—22no—
105C24×C29—21no—
106C24×C29—21no—
107C24×C29—22no—
108C24×C29#4112yes—
109C24×C29C2411yescharacteristic
110C2×Q8×C29—28no—
111C2×Q8×C29—28no—
112C2×Q8×C29—216no—
113C2×Q8×C29—28no—
114C2×Q8×C29—216no—
115C22×C4×C29—21no—
116C22×C4×C29—21no—
117C22×C4×C29—22no—
118C22×C4×C29—22no—
119C22×C4×C29—22no—
120C22×C4×C29—22no—
121C22×C4×C29—22no—
122C22×C4×C29—22no—
123C22×C4×C29—22no—
124C22×C4×C29—22no—
125C22×C4×C29—21no—
126C22×C4×C29—22no—
127C22×C4×C29—21no—
128C22×C4×C29—21no—
129C22×C4×C29—21no—
130C22×C4×C29—21no—
131C22×C4×C29—21no—
132C22×C4×C29—22no—
133C22×C4×C29—22no—
134C22×C4×C29—22no—
135C22×C4×C29—22no—
136C22×C4×C29—22no—
137C22×C4×C29—21no—
138C22×C4×C29—21no—
139C22×C4×C29—22no—
140C22×C4×C29—21no—
141C22×C4×C29—21no—
142C22×C4×C29—21no—
143C22×C4×C29—22no—
144C22×C4×C29—21no—
145C22×C4×C29—22no—
146C22×C4×C29—22no—
147C22×C4×C29—22no—
148C22×C4×C29—22no—
149C22×C4×C29—22no—
150C22×C4×C29—22no—
151C22×C4×C29—22no—
152C22×C4×C29—22no—
153C22×C4×C29—22no—
154C22×C4×C29—22no—
155C22×C4×C29—22no—
156C22×C4×C29—22no—
157C22×C4×C29—22no—
158C22×C4×C29—21no—
159C22×C4×C29—22no—
160C22×C4×C29—22no—
161C22×C4×C29—21no—
162C22×C4×C29—22no—
163C22×C4×C29—22no—
164C22×C4×C29C2×D414yes—
165C22×C4×C29C2×D412yes—
166C22×C4×C29C2×D412yes—
167C22×C4×C29C2×D412yes—
168C22×C4×C29C2×D412yes—
169C22×C4×C29C2×D414yes—
170C22×C4×C29C2×D412yes—
171C22×C4×C29#4112yes—
172C22×C4×C29#4114yes—
173C22×C4×C29#4114yes—
174C22×C4×C29#4114yes—
175C4⋊C4×C29—216no—
176C4⋊C4×C29—28no—
177C4⋊C4×C29—44no—
178C22⋊C4×C29—28no—
179C22⋊C4×C29—48no—
180C22⋊C4×C29—44no—
181C22⋊C4×C29—48no—
182C22⋊C4×C29—44no—
183C42×C29—216no—
184C42×C29—28no—
185#14882C2911yesmaximal, characteristic, direct product factor, Sylow
186C23×C29—22no—
187C23×C29—24no—
188C23×C29—22no—
189C23×C29—22no—
190C23×C29—24no—
191C23×C29—41no—
192C23×C29—42no—
193C23×C29—41no—
194C23×C29—41no—
195C23×C29—42no—
196C23×C29—41no—
197C23×C29—42no—
198C23×C29—41no—
199C23×C29—41no—
200C23×C29—42no—
201C23×C29—42no—
202C23×C29—41no—
203C23×C29—42no—
204C23×C29—42no—
205C23×C29—41no—
206C23×C29—42no—
207C23×C29—42no—
208C23×C29—42no—
209C23×C29C22×D411yescharacteristic
210C23×C29C22×D411yescharacteristic
211C23×C29C22×D411yescharacteristic
212C23×C29C2×#4112yes—
213C23×C29C2×#4112yes—
214C23×C29C2×#4111yescharacteristic
215C23×C29C2×#4111yescharacteristic
216C23×C29C2×#4112yes—
217C23×C29H(5,𝔽2)11yescharacteristic
218C23×C292−1+412yes—
219C23×C292−1+411yescharacteristic
220Q8×C29—232no—
221C2×C4×C29—22no—
222C2×C4×C29—24no—
223C2×C4×C29—24no—
224C2×C4×C29—24no—
225C2×C4×C29—22no—
226C2×C4×C29—22no—
227C2×C4×C29—24no—
228C2×C4×C29—24no—
229C2×C4×C29—24no—
230C2×C4×C29—24no—
231C2×C4×C29—24no—
232C2×C4×C29—22no—
233C2×C4×C29—24no—
234C2×C4×C29—24no—
235C2×C4×C29—24no—
236C2×C4×C29—22no—
237C2×C4×C29—22no—
238C2×C4×C29—22no—
239C2×C4×C29—24no—
240C2×C4×C29—22no—
241C2×C4×C29—24no—
242C2×C4×C29—24no—
243C2×C4×C29—41no—
244C2×C4×C29—42no—
245C2×C4×C29—41no—
246C2×C4×C29—42no—
247C2×C4×C29—42no—
248C2×C4×C29—41no—
249C2×C4×C29—41no—
250C2×C4×C29—41no—
251C2×C4×C29—42no—
252C2×C4×C29—41no—
253C2×C4×C29—42no—
254C2×C4×C29—41no—
255C2×C4×C29—42no—
256C2×C4×C29—41no—
257C2×C4×C29—42no—
258C2×C4×C29—41no—
259C2×C4×C29—41no—
260C2×C4×C29—42no—
261C2×C4×C29—42no—
262C2×C4×C29—41no—
263C2×C4×C29—41no—
264C2×C4×C29—42no—
265C2×C4×C29—42no—
266C2×C4×C29—42no—
267C2×C4×C29—42no—
268C2×C4×C29—42no—
269C2×C4×C29—42no—
270C2×C4×C29—42no—
271C2×C4×C29—42no—
272C2×C4×C29—42no—
273C2×C4×C29—42no—
274C2×C4×C29—42no—
275C2×C4×C29—42no—
276C2×C4×C29—42no—
277C2×C4×C29—42no—
278C2×C4×C29#12014yes—
279C2×C4×C29#12318yes—
280C2×C4×C29#12414yes—
281C22×C4×Q8C2×C2911yescharacteristic, complemented
282C2×#397C2×C2911yescharacteristic
283C2×#393C2×C2911yescharacteristic
284C2×#388C2×C2911yescharacteristic
285#1446C2×C2911yescharacteristic, complemented
286#1445C2×C2911yescharacteristic, complemented
287#1442C2×C2912yescomplemented
288#1439C2×C2912yes—
289#1437C2×C2912yes—
290#1436C2×C2912yescomplemented
291#1434C2×C2911yescharacteristic, complemented
292C22×C29—42no—
293C22×C29—42no—
294C22×C29—42no—
295C22×C29—44no—
296C22×C29—44no—
297C22×C29—81no—
298C22×C29—81no—
299C22×C29—81no—
300C22×C29—81no—
301C22×C29—82no—
302C22×C29—82no—
303C22×C29C2×#12011yescharacteristic
304C22×C29C2×#12312yes—
305C22×C29#52511yescharacteristic
306C22×C29#52511yescharacteristic
307C22×C29#52512yes—
308C22×C29#52511yescharacteristic
309C22×C29C2×#12411yescharacteristic
310C22×C29#52912yes—
311C22×C29#52912yes—
312C22×C29#53611yescharacteristic
313C22×C29#53711yescharacteristic
314C22×C29#54112yes—
315C22×C29#54212yes—
316C22×C29#54611yescharacteristic
317C22×C29#54711yescharacteristic
318C22×C29#54811yescharacteristic
319C22×C29#54812yes—
320C22×C29#54812yes—
321C22×C29#55011yescharacteristic
322C22×C29#55212yes—
323C22×C29#55612yes—
324C22×C29#55612yes—
325C22×C29#55912yes—
326C4×C29—24no—
327C4×C29—28no—
328C4×C29—24no—
329C4×C29—42no—
330C4×C29—42no—
331C4×C29—44no—
332C4×C29—81no—
333C4×C29—81no—
334C4×C29—82no—
335C4×C29—82no—
336C23×Q8C22×C2911yescharacteristic
337C2×C4×Q8—24no—
338C2×C4×Q8—24no—
339C2×C4×Q8—24no—
340C22×C4⋊C4C22×C2912yes—
341C22×C4⋊C4C22×C2911yescharacteristic
342C22×C4⋊C4C22×C2911yescharacteristic
343C22×C22⋊C4C22×C2911yescharacteristic
344C22×C22⋊C4C22×C2912yes—
345C22×C22⋊C4C22×C2911yescharacteristic
346C22×C22⋊C4C22×C2911yescharacteristic
347C22×C22⋊C4C22×C2912yes—
348C22×C42C22×C2912yes—
349C22×C42C22×C2911yescharacteristic
350#397—24no—
351#393—24no—
352#388—24no—
353C2×#95C22×C2911yescharacteristic
354C2×#95C22×C2912yes—
355C2×#95C22×C2911yescharacteristic
356C2×#95C22×C2912yes—
357C2×#95C22×C2912yes—
358C2×#95C22×C2912yes—
359C2×#95C22×C2912yes—
360C2×#95C22×C2912yes—
361C2×#95C22×C2911yescharacteristic
362C2×#95C22×C2911yescharacteristic
363C2×#95C22×C2912yes—
364C2×#95C22×C2912yes—
365C2×C29—82no—
366C2×C29#239811yescharacteristic
367C2×C29#240711yescharacteristic
368C2×C29#242112yes—
369C2×C29#243611yescharacteristic
370C2×C29#244812yes—
371C2×C29#245812yes—
372C2×C29#246912yes—
373C2×C29#259211yescharacteristic
374C2×C29#259911yescharacteristic
375C2×C29#263711yescharacteristic
376C2×C29#284911yescharacteristic
377C25C23×C2911yescharacteristic
378C22×Q8—22no—
379C22×Q8—22no—
380C22×Q8—24no—
381C22×Q8—24no—
382C22×Q8D4×C2914yes—
383C23×C4C23×C2911yescharacteristic
384C23×C4C23×C2912yes—
385C23×C4C23×C2912yes—
386C23×C4C23×C2911yescharacteristic
387C23×C4C23×C2912yes—
388C23×C4C23×C2911yescharacteristic
389C23×C4C23×C2911yescharacteristic
390C23×C4C23×C2911yescharacteristic
391C23×C4C23×C2912yes—
392C23×C4C23×C2911yescharacteristic
393C4×Q8—232no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4D4×C2914yes—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—42no—
416C2×C42—24no—
417C2×C42—24no—
418C2×C42—24no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42D4×C2914yes—
422#95—22no—
423#95—22no—
424#95—22no—
425#95—24no—
426#95—24no—
427#95—22no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—42no—
433#95—42no—
434C29#1488211yescharacteristic, direct product factor, Sylow
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—21no—
443C24—21no—
444C24—22no—
445C24#41×C2912yes—
446C24C24×C2911yescharacteristic
447C2×Q8—216no—
448C2×Q8—28no—
449C2×Q8—28no—
450C2×Q8—28no—
451C2×Q8—216no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4C2×D4×C2914yes—
502C22×C4C2×D4×C2912yes—
503C22×C4C2×D4×C2912yes—
504C22×C4C2×D4×C2912yes—
505C22×C4C2×D4×C2912yes—
506C22×C4C2×D4×C2914yes—
507C22×C4C2×D4×C2912yes—
508C22×C4#41×C2912yes—
509C22×C4#41×C2914yes—
510C22×C4#41×C2914yes—
511C22×C4#41×C2914yes—
512C4⋊C4—216no—
513C4⋊C4—28no—
514C4⋊C4—44no—
515C22⋊C4—28no—
516C22⋊C4—48no—
517C22⋊C4—44no—
518C22⋊C4—48no—
519C22⋊C4—44no—
520C42—216no—
521C42—28no—
522C23—22no—
523C23—24no—
524C23—22no—
525C23—22no—
526C23—24no—
527C23—41no—
528C23—42no—
529C23—42no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—42no—
534C23—41no—
535C23—41no—
536C23—42no—
537C23—42no—
538C23—41no—
539C23—42no—
540C23—42no—
541C23—41no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23C22×D4×C2911yescharacteristic
546C23C22×D4×C2911yescharacteristic
547C23C22×D4×C2911yescharacteristic
548C23C2×#41×C2912yes—
549C23C2×#41×C2912yes—
550C23C2×#41×C2911yescharacteristic
551C23C2×#41×C2911yescharacteristic
552C23C2×#41×C2912yes—
553C23C29×H(5,𝔽2)11yescharacteristic
554C23C29×2−1+412yes—
555C23C29×2−1+411yescharacteristic
556Q8—232no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4C29×#12014yes—
615C2×C4C29×#12318yes—
616C2×C4C29×#12414yes—
617C22—44no—
618C22—44no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—81no—
623C22—82no—
624C22—82no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22C2×C29×#12011yescharacteristic
629C22C2×C29×#12312yes—
630C22C29×#52512yes—
631C22C29×#52511yescharacteristic
632C22C29×#52511yescharacteristic
633C22C29×#52511yescharacteristic
634C22C2×C29×#12411yescharacteristic
635C22C29×#52912yes—
636C22C29×#52912yes—
637C22C29×#53611yescharacteristic
638C22C29×#53711yescharacteristic
639C22C29×#54112yes—
640C22C29×#54212yes—
641C22C29×#54611yescharacteristic
642C22C29×#54711yescharacteristic
643C22C29×#54811yescharacteristic
644C22C29×#54812yes—
645C22C29×#54812yes—
646C22C29×#55011yescharacteristic
647C22C29×#55212yes—
648C22C29×#55612yes—
649C22C29×#55612yes—
650C22C29×#55912yes—
651C4—24no—
652C4—24no—
653C4—28no—
654C4—42no—
655C4—42no—
656C4—44no—
657C4—81no—
658C4—82no—
659C4—82no—
660C4—81no—
661C2—82no—
662C2C29×#239811yescharacteristic
663C2C29×#240711yescharacteristic
664C2C29×#242112yes—
665C2C29×#243611yescharacteristic
666C2C29×#244812yes—
667C2C29×#245812yes—
668C2C29×#246912yes—
669C2C29×#259211yescharacteristic
670C2C29×#259911yescharacteristic
671C2C29×#263711yescharacteristic
672C2C29×#284911yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutator, Frattini, cosocleC24C24×C29
prime radicalC25×C29C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C4×Q8×C29C2semidirect
5. C29×#1446C2semidirect
6. C29×#1445C2semidirect
7. C29×#1442C2semidirect
10. C29×#1436C2semidirect
11. C29×#1434C2semidirect
185. #14882C29direct (N × H)
281. C22×C4×Q8C2×C29semidirect
285. #1446C2×C29semidirect
286. #1445C2×C29semidirect
287. #1442C2×C29semidirect
290. #1436C2×C29semidirect
291. #1434C2×C29semidirect
434. C29#14882direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C292
C2×C29×#3972
C2×C29×#3932
C2×C29×#3882
C29×#14462
C29×#14452
C29×#14422
C29×#14392
C29×#14372
C29×#14362
C29×#14342
#1488229