Finite Group Databasebeta

← C29×#14506 #20309406

Subgroups — C29×#14506 #20309406

Order 7424.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C29×#123C211yesmaximal, characteristic
2C2×C29×#388C212yesmaximal, complemented
3C29×#1445C212yesmaximal, complemented
4C29×#1439C212yesmaximal, complemented
5C29×#1438C211yesmaximal, characteristic
6C29×#1438C211yesmaximal, characteristic
7C29×#1437C212yesmaximal, complemented
8C29×C4⋊#95C212yesmaximal, complemented
9C29×C22⋊#95C212yesmaximal, complemented
10C23×D4×C29C2211yescharacteristic
11C24×C4×C29C2211yescharacteristic
12C2×C29×#123—28no—
13C2×C29×#123C418yescomplemented
14C22×C4⋊C4×C29C2212yes—
15C22×C4⋊C4×C29C2212yes—
16C22×C22⋊C4×C29C2212yes—
17C22×C22⋊C4×C29C2212yes—
18C22×C22⋊C4×C29C2211yescharacteristic
19C22×C22⋊C4×C29C2212yes—
20C22×C22⋊C4×C29C2212yes—
21C22×C22⋊C4×C29C2211yescharacteristic
22C22×C22⋊C4×C29C2211yescharacteristic
23C22×C42×C29C2212yes—
24C29×#388—28no—
25C2×C29×#95C2212yes—
26C2×C29×#95C2212yes—
27C2×C29×#95C2212yes—
28C2×C29×#95C2212yes—
29C2×C29×#95C2212yes—
30C2×C29×#95C2212yes—
31C2×C29×#95C2211yescharacteristic
32C2×C29×#95C2212yes—
33C2×C29×#95C2211yescharacteristic
34C25×C29C2311yescharacteristic
35C25×C29C2311yescharacteristic
36C22×D4×C29—24no—
37C22×D4×C29—42no—
38C22×D4×C29—41no—
39C22×D4×C29—41no—
40C22×D4×C29C2×C414yes—
41C23×C4×C29—24no—
42C23×C4×C29—42no—
43C23×C4×C29—41no—
44C23×C4×C29—41no—
45C23×C4×C29C2×C414yes—
46C23×C4×C29C2312yes—
47C23×C4×C29C2312yes—
48C23×C4×C29C2312yes—
49C23×C4×C29C2311yescharacteristic
50C23×C4×C29C2312yes—
51C23×C4×C29C2312yes—
52C23×C4×C29C2312yes—
53C29×#123—232no—
54C2×C4⋊C4×C29—24no—
55C2×C4⋊C4×C29—24no—
56C2×C4⋊C4×C29—24no—
57C2×C4⋊C4×C29—24no—
58C2×C4⋊C4×C29—42no—
59C2×C4⋊C4×C29C2×C418yes—
60C2×C22⋊C4×C29—24no—
61C2×C22⋊C4×C29—24no—
62C2×C22⋊C4×C29—24no—
63C2×C22⋊C4×C29—24no—
64C2×C22⋊C4×C29—24no—
65C2×C22⋊C4×C29—24no—
66C2×C22⋊C4×C29—24no—
67C2×C22⋊C4×C29—24no—
68C2×C22⋊C4×C29—41no—
69C2×C22⋊C4×C29—42no—
70C2×C22⋊C4×C29—42no—
71C2×C22⋊C4×C29—42no—
72C2×C22⋊C4×C29—42no—
73C2×C22⋊C4×C29—42no—
74C2×C22⋊C4×C29—41no—
75C2×C22⋊C4×C29C2×C418yes—
76C2×C22⋊C4×C29C2×C414yes—
77C2×C22⋊C4×C29D418yes—
78C2×C42×C29—24no—
79C2×C42×C29—24no—
80C2×C42×C29—42no—
81C29×#95—24no—
82C29×#95—24no—
83C29×#95—42no—
84C29×#95—42no—
85C29×#95—42no—
86C29×#95—42no—
87C29×#95—41no—
88C29×#95—42no—
89C29×#95—41no—
90C24×C29—22no—
91C24×C29—22no—
92C24×C29—22no—
93C24×C29—22no—
94C24×C29—21no—
95C24×C29—21no—
96C24×C29—22no—
97C24×C29—22no—
98C24×C29—22no—
99C24×C29—22no—
100C24×C29—22no—
101C24×C29—22no—
102C24×C29—21no—
103C24×C29—21no—
104C24×C29—22no—
105C24×C29C22×C412yes—
106C24×C29C22×C412yes—
107C24×C29C2×D414yes—
108C24×C29C2411yescharacteristic
109C2×D4×C29—28no—
110C2×D4×C29—44no—
111C2×D4×C29—44no—
112C2×D4×C29—48no—
113C2×D4×C29—48no—
114C22×C4×C29—22no—
115C22×C4×C29—22no—
116C22×C4×C29—22no—
117C22×C4×C29—22no—
118C22×C4×C29—28no—
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—22no—
126C22×C4×C29—22no—
127C22×C4×C29—22no—
128C22×C4×C29—22no—
129C22×C4×C29—22no—
130C22×C4×C29—22no—
131C22×C4×C29—22no—
132C22×C4×C29—22no—
133C22×C4×C29—22no—
134C22×C4×C29—22no—
135C22×C4×C29—22no—
136C22×C4×C29—21no—
137C22×C4×C29—21no—
138C22×C4×C29—22no—
139C22×C4×C29—22no—
140C22×C4×C29—22no—
141C22×C4×C29—22no—
142C22×C4×C29—22no—
143C22×C4×C29—22no—
144C22×C4×C29—22no—
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—44no—
156C22×C4×C29—44no—
157C22×C4×C29—48no—
158C22×C4×C29—48no—
159C22×C4×C29C22×C414yes—
160C22×C4×C29C22×C412yes—
161C22×C4×C29C22×C414yes—
162C22×C4×C29C2×D414yes—
163C22×C4×C29C2×D414yes—
164C22×C4×C29#4114yes—
165C22×C4×C29#4114yes—
166C4⋊C4×C29—216no—
167C4⋊C4×C29—48no—
168C22⋊C4×C29—216no—
169C22⋊C4×C29—44no—
170C22⋊C4×C29—48no—
171C22⋊C4×C29—48no—
172C22⋊C4×C29—48no—
173C22⋊C4×C29—44no—
174C22⋊C4×C29C22⋊C4116yescomplemented
175C42×C29—48no—
176#14506C2911yesmaximal, characteristic, direct product factor, Sylow
177C23×C29—24no—
178C23×C29—22no—
179C23×C29—22no—
180C23×C29—24no—
181C23×C29—24no—
182C23×C29—24no—
183C23×C29—24no—
184C23×C29—24no—
185C23×C29—24no—
186C23×C29—24no—
187C23×C29—22no—
188C23×C29—24no—
189C23×C29—22no—
190C23×C29—22no—
191C23×C29—24no—
192C23×C29—42no—
193C23×C29—42no—
194C23×C29—42no—
195C23×C29—42no—
196C23×C29—41no—
197C23×C29—42no—
198C23×C29—41no—
199C23×C29—41no—
200C23×C29—42no—
201C23×C29—41no—
202C23×C29—42no—
203C23×C29—42no—
204C23×C29—42no—
205C23×C29—42no—
206C23×C29—42no—
207C23×C29—42no—
208C23×C29—42no—
209C23×C29—42no—
210C23×C29—42no—
211C23×C29—42no—
212C23×C29—41no—
213C23×C29—42no—
214C23×C29—41no—
215C23×C29—41no—
216C23×C29—42no—
217C23×C29—41no—
218C23×C29C2×C22⋊C414yes—
219C23×C29C23×C411yescharacteristic
220C23×C29C22×D412yes—
221C23×C29C2×#4112yes—
222C23×C29C2×#4112yes—
223C23×C29H(5,𝔽2)12yes—
224C23×C29H(5,𝔽2)11yescharacteristic
225C23×C29H(5,𝔽2)11yescharacteristic
226C23×C29H(5,𝔽2)12yes—
227C23×C292−1+412yes—
228D4×C29—416no—
229C2×C4×C29—24no—
230C2×C4×C29—24no—
231C2×C4×C29—24no—
232C2×C4×C29—24no—
233C2×C4×C29—24no—
234C2×C4×C29—24no—
235C2×C4×C29—24no—
236C2×C4×C29—22no—
237C2×C4×C29—24no—
238C2×C4×C29—24no—
239C2×C4×C29—22no—
240C2×C4×C29—22no—
241C2×C4×C29—24no—
242C2×C4×C29—24no—
243C2×C4×C29—24no—
244C2×C4×C29—24no—
245C2×C4×C29—24no—
246C2×C4×C29—24no—
247C2×C4×C29—416no—
248C2×C4×C29—42no—
249C2×C4×C29—42no—
250C2×C4×C29—42no—
251C2×C4×C29—42no—
252C2×C4×C29—42no—
253C2×C4×C29—42no—
254C2×C4×C29—42no—
255C2×C4×C29—42no—
256C2×C4×C29—42no—
257C2×C4×C29—42no—
258C2×C4×C29—42no—
259C2×C4×C29—42no—
260C2×C4×C29—42no—
261C2×C4×C29—42no—
262C2×C4×C29—42no—
263C2×C4×C29—42no—
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×C29C2×C22⋊C418yes—
277C22×#123C2×C2911yescharacteristic
278C2×#388C2×C2912yescomplemented
279#1445C2×C2912yescomplemented
280#1439C2×C2912yescomplemented
281#1438C2×C2911yescharacteristic
282#1438C2×C2911yescharacteristic
283#1437C2×C2912yescomplemented
284C4⋊#95C2×C2912yescomplemented
285C22⋊#95C2×C2912yescomplemented
286C22×C29—24no—
287C22×C29—28no—
288C22×C29—44no—
289C22×C29—42no—
290C22×C29—42no—
291C22×C29—44no—
292C22×C29—44no—
293C22×C29—44no—
294C22×C29—44no—
295C22×C29—42no—
296C22×C29—44no—
297C22×C29—44no—
298C22×C29—42no—
299C22×C29—42no—
300C22×C29—82no—
301C22×C29—82no—
302C22×C29—82no—
303C22×C29—82no—
304C22×C29C22×C22⋊C411yescharacteristic
305C22×C29C4×#4112yes—
306C22×C29#51811yescharacteristic
307C22×C29#51811yescharacteristic
308C22×C29#52012yes—
309C22×C29#53512yes—
310C22×C29#53512yes—
311C22×C29#53812yes—
312C22×C29#53912yes—
313C22×C29#54012yes—
314C22×C29#54212yes—
315C22×C29#54612yes—
316C22×C29#54612yes—
317C22×C29#54712yes—
318C22×C29#54712yes—
319C22×C29#55111yescharacteristic
320C22×C29#55312yes—
321C22×C29#55911yescharacteristic
322C22×C29#56011yescharacteristic
323C22×C29#56212yes—
324C22×C29#56311yescharacteristic
325C4×C29—28no—
326C4×C29—44no—
327C4×C29—42no—
328C4×C29—44no—
329C4×C29—44no—
330C4×C29—82no—
331C4×C29—82no—
332C23×D4C22×C2911yescharacteristic
333C24×C4C22×C2911yescharacteristic
334C2×#123—28no—
335C2×#123C4×C2918yescomplemented
336C22×C4⋊C4C22×C2912yes—
337C22×C4⋊C4C22×C2912yes—
338C22×C22⋊C4C22×C2912yes—
339C22×C22⋊C4C22×C2912yes—
340C22×C22⋊C4C22×C2911yescharacteristic
341C22×C22⋊C4C22×C2912yes—
342C22×C22⋊C4C22×C2912yes—
343C22×C22⋊C4C22×C2911yescharacteristic
344C22×C22⋊C4C22×C2911yescharacteristic
345C22×C42C22×C2912yes—
346#388—28no—
347C2×#95C22×C2912yes—
348C2×#95C22×C2912yes—
349C2×#95C22×C2912yes—
350C2×#95C22×C2912yes—
351C2×#95C22×C2912yes—
352C2×#95C22×C2912yes—
353C2×#95C22×C2911yescharacteristic
354C2×#95C22×C2912yes—
355C2×#95C22×C2911yescharacteristic
356C2×C29—44no—
357C2×C29—82no—
358C2×C29#230911yescharacteristic
359C2×C29#233512yes—
360C2×C29#233912yes—
361C2×C29#237411yescharacteristic
362C2×C29#237611yescharacteristic
363C2×C29#270312yes—
364C2×C29#270612yes—
365C2×C29#271012yes—
366C2×C29#271812yes—
367C25C23×C2911yescharacteristic
368C25C23×C2911yescharacteristic
369C22×D4—24no—
370C22×D4—42no—
371C22×D4—41no—
372C22×D4—41no—
373C22×D4C2×C4×C2914yes—
374C23×C4—24no—
375C23×C4—42no—
376C23×C4—41no—
377C23×C4—41no—
378C23×C4C2×C4×C2914yes—
379C23×C4C23×C2912yes—
380C23×C4C23×C2912yes—
381C23×C4C23×C2912yes—
382C23×C4C23×C2911yescharacteristic
383C23×C4C23×C2912yes—
384C23×C4C23×C2912yes—
385C23×C4C23×C2912yes—
386#123—232no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—42no—
392C2×C4⋊C4C2×C4×C2918yes—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—41no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—41no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4C2×C4×C2918yes—
409C2×C22⋊C4C2×C4×C2914yes—
410C2×C22⋊C4D4×C2918yes—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—42no—
414#95—24no—
415#95—24no—
416#95—41no—
417#95—42no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—41no—
423C29#1450611yescharacteristic, direct product factor, Sylow
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24C22×C4×C2912yes—
440C24C22×C4×C2912yes—
441C24C2×D4×C2914yes—
442C24C24×C2911yescharacteristic
443C2×D4—28no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4C22×C4×C2914yes—
494C22×C4C22×C4×C2912yes—
495C22×C4C22×C4×C2914yes—
496C22×C4C2×D4×C2914yes—
497C22×C4C2×D4×C2914yes—
498C22×C4#41×C2914yes—
499C22×C4#41×C2914yes—
500C4⋊C4—216no—
501C4⋊C4—48no—
502C22⋊C4—216no—
503C22⋊C4—44no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C22⋊C4—48no—
507C22⋊C4—44no—
508C22⋊C4C22⋊C4×C29116yescomplemented
509C42—48no—
510C23—24no—
511C23—22no—
512C23—22no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—24no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—41no—
548C23—41no—
549C23—42no—
550C23—41no—
551C23C2×C22⋊C4×C2914yes—
552C23C23×C4×C2911yescharacteristic
553C23C22×D4×C2912yes—
554C23C2×#41×C2912yes—
555C23C2×#41×C2912yes—
556C23C29×H(5,𝔽2)12yes—
557C23C29×H(5,𝔽2)11yescharacteristic
558C23C29×H(5,𝔽2)11yescharacteristic
559C23C29×H(5,𝔽2)12yes—
560C23C29×2−1+412yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—416no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
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×C4C2×C22⋊C4×C2918yes—
610C22—24no—
611C22—28no—
612C22—44no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22—44no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—44no—
621C22—44no—
622C22—42no—
623C22—42no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22C22×C22⋊C4×C2911yescharacteristic
629C22C4×#41×C2912yes—
630C22C29×#51811yescharacteristic
631C22C29×#51811yescharacteristic
632C22C29×#52012yes—
633C22C29×#53512yes—
634C22C29×#53512yes—
635C22C29×#53812yes—
636C22C29×#53912yes—
637C22C29×#54012yes—
638C22C29×#54212yes—
639C22C29×#54612yes—
640C22C29×#54612yes—
641C22C29×#54712yes—
642C22C29×#54712yes—
643C22C29×#55111yescharacteristic
644C22C29×#55312yes—
645C22C29×#55911yescharacteristic
646C22C29×#56011yescharacteristic
647C22C29×#56212yes—
648C22C29×#56311yescharacteristic
649C4—28no—
650C4—44no—
651C4—44no—
652C4—44no—
653C4—42no—
654C4—82no—
655C4—82no—
656C2—44no—
657C2—82no—
658C2C29×#230911yescharacteristic
659C2C29×#233512yes—
660C2C29×#233912yes—
661C2C29×#237411yescharacteristic
662C2C29×#237611yescharacteristic
663C2C29×#270312yes—
664C2C29×#270612yes—
665C2C29×#271012yes—
666C2C29×#271812yes—
subgroupG/H
center, socleC24×C29C24
commutatorC23C23×C4×C29
Frattini, cosocleC24C24×C29
prime radicalC23×D4×C29C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#388C2semidirect
3. C29×#1445C2semidirect
4. C29×#1439C2semidirect
7. C29×#1437C2semidirect
8. C29×C4⋊#95C2semidirect
9. C29×C22⋊#95C2semidirect
13. C2×C29×#123C4semidirect
174. C22⋊C4×C29C22⋊C4semidirect
176. #14506C29direct (N × H)
278. C2×#388C2×C29semidirect
279. #1445C2×C29semidirect
280. #1439C2×C29semidirect
283. #1437C2×C29semidirect
284. C4⋊#95C2×C29semidirect
285. C22⋊#95C2×C29semidirect
335. C2×#123C4×C29semidirect
423. C29#14506direct (N × H)
508. C22⋊C4C22⋊C4×C29semidirect

Maximal subgroups

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

subgroupindex
C22×C29×#1232
C2×C29×#3882
C29×#14452
C29×#14392
C29×#14382
C29×#14372
C29×C4⋊#952
C29×C22⋊#952
#1450629