Finite Group Databasebeta

← C29×#24263 #20319163

Subgroups — C29×#24263 #20319163

Order 7424.

1502 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3496C211yesmaximal, characteristic
2C2×C29×#458C212yesmaximal, complemented
3C29×#2618C212yesmaximal, complemented
4C29×#2322C211yesmaximal, characteristic, complemented
5C29×#2044C212yesmaximal, complemented
6C29×#2022C212yesmaximal, complemented
7C29×#1964C212yesmaximal, complemented
8C29×#1799C211yesmaximal, characteristic, complemented
9C29×#1790C212yesmaximal, complemented
10C2×C29×H(5,𝔽2)C2212yes—
11C29×#547—22no—
12C29×#546—24no—
13D42×C29—22no—
14C29×#537—21no—
15C29×#534—21no—
16C29×#534C2212yes—
17C29×#532—21no—
18C2×C29×#123C2211yescharacteristic
19C2×C29×#123C2214yescomplemented
20C2×C29×#121—21no—
21C2×C29×#121C2212yes—
22C2×C4×D4×C29C2211yescharacteristic
23C22×C4⋊C4×C29C2211yescharacteristic, complemented
24C29×#458—28no—
25C2×C29×#99C2212yes—
26C2×C29×#99C2214yescomplemented
27C2×C29×#99C2214yescomplemented
28C29×#398—22no—
29C29×#396—24no—
30C29×#394—22no—
31C29×#389—21no—
32C29×#388—21no—
33C29×#387—21no—
34C29×#386C2211yescharacteristic
35C29×#386C2214yescomplemented
36C29×#385—21no—
37C29×#385C2211yescharacteristic, complemented
38C29×#381C2211yescharacteristic, complemented
39C29×#380C2212yescomplemented
40C4×C22⋊C4×C29C2211yescharacteristic, complemented
41C29×#342C2212yescomplemented
42C29×H(5,𝔽2)—24no—
43C29×H(5,𝔽2)—24no—
44C29×H(5,𝔽2)—44no—
45C2×#41×C29—22no—
46C2×#41×C29—24no—
47C22×D4×C29—22no—
48C22×D4×C29—24no—
49C22×D4×C29—21no—
50C22×D4×C29D412yes—
51C22×D4×C29C2314yes—
52C22×D4×C29C2311yescharacteristic
53C23×C4×C29D411yescharacteristic
54C23×C4×C29C2311yescharacteristic
55C23×C4×C29C2311yescharacteristic
56C23×C4×C29C2311yescharacteristic
57C29×C4⋊Q8—21no—
58C29×#127—21no—
59C29×#124—22no—
60C29×#123—24no—
61C29×#123—22no—
62C29×#123—24no—
63C29×#123—28no—
64C29×#123—44no—
65C29×#123D414yescomplemented
66C29×C22⋊Q8—24no—
67C29×#121—22no—
68C29×#121—22no—
69C29×#121—24no—
70C29×#121—22no—
71C29×#121—22no—
72C29×#121—22no—
73C29×#121—22no—
74C29×#121—22no—
75C29×#121—22no—
76C29×#120—24no—
77C29×#120—24no—
78C4×D4×C29—22no—
79C4×D4×C29—22no—
80C4×D4×C29—22no—
81C4×D4×C29—22no—
82C2×C4⋊C4×C29—21no—
83C2×C4⋊C4×C29—21no—
84C2×C4⋊C4×C29—21no—
85C2×C4⋊C4×C29—21no—
86C2×C4⋊C4×C29—22no—
87C2×C4⋊C4×C29—22no—
88C2×C4⋊C4×C29—24no—
89C2×C4⋊C4×C29—22no—
90C2×C4⋊C4×C29—21no—
91C2×C4⋊C4×C29D411yescharacteristic
92C2×C4⋊C4×C29D412yes—
93C2×C22⋊C4×C29—22no—
94C2×C22⋊C4×C29—21no—
95C2×C22⋊C4×C29—24no—
96C2×C22⋊C4×C29—21no—
97C2×C22⋊C4×C29—24no—
98C2×C22⋊C4×C29D411yescharacteristic
99C2×C22⋊C4×C29D414yes—
100C2×C22⋊C4×C29C2314yes—
101C2×C22⋊C4×C29C2311yescharacteristic
102C2×C22⋊C4×C29C2311yescharacteristic
103C2×C22⋊C4×C29C2311yescharacteristic
104C2×C42×C29—21no—
105C2×C42×C29D411yescharacteristic
106C29×#99—24no—
107C29×#99—28no—
108C29×#99—44no—
109C29×#95—21no—
110C29×#95—22no—
111C29×#95—21no—
112C29×#95—21no—
113C29×#95—21no—
114C29×#95—21no—
115C29×#95—24no—
116C24×C29—22no—
117C24×C29C2×D414yes—
118C24×C29C2×D411yescharacteristic
119C24×C29C2411yescharacteristic
120#41×C29—48no—
121#41×C29—48no—
122#41×C29—44no—
123#41×C29—44no—
124C2×Q8×C29—22no—
125C2×D4×C29—22no—
126C2×D4×C29—22no—
127C2×D4×C29—24no—
128C2×D4×C29—22no—
129C2×D4×C29—24no—
130C2×D4×C29—24no—
131C2×D4×C29—24no—
132C2×D4×C29—24no—
133C2×D4×C29—24no—
134C2×D4×C29—24no—
135C2×D4×C29—22no—
136C2×D4×C29—22no—
137C2×D4×C29—22no—
138C2×D4×C29—22no—
139C2×D4×C29—48no—
140C2×D4×C29—48no—
141C2×D4×C29—44no—
142C2×D4×C29—44no—
143C2×D4×C29—82no—
144C2×D4×C29—82no—
145C2×D4×C29C2×D412yes—
146C2×D4×C29#4112yes—
147C22×C4×C29—22no—
148C22×C4×C29—24no—
149C22×C4×C29—21no—
150C22×C4×C29—22no—
151C22×C4×C29—21no—
152C22×C4×C29—21no—
153C22×C4×C29—22no—
154C22×C4×C29—21no—
155C22×C4×C29—21no—
156C22×C4×C29—21no—
157C22×C4×C29—24no—
158C22×C4×C29—22no—
159C22×C4×C29—21no—
160C22×C4×C29—81no—
161C22×C4×C29—81no—
162C22×C4×C29—81no—
163C22×C4×C29C2×D414yes—
164C22×C4×C29C2×D411yescharacteristic
165C22×C4×C29C2×D411yescharacteristic
166C22×C4×C29C2×D411yescharacteristic
167C22×C4×C29C2×D411yescharacteristic
168C22×C4×C29C2×D411yescharacteristic
169C22×C4×C29C2×D412yes—
170C22×C4×C29C2×D412yes—
171C22×C4×C29C2×D412yescomplemented
172C4⋊C4×C29—22no—
173C4⋊C4×C29—22no—
174C4⋊C4×C29—22no—
175C4⋊C4×C29—22no—
176C4⋊C4×C29—22no—
177C4⋊C4×C29—24no—
178C4⋊C4×C29—48no—
179C4⋊C4×C29—41no—
180C4⋊C4×C29—41no—
181C4⋊C4×C29—42no—
182C4⋊C4×C29—82no—
183C4⋊C4×C29—81no—
184C22⋊C4×C29—24no—
185C22⋊C4×C29—24no—
186C22⋊C4×C29—24no—
187C22⋊C4×C29—22no—
188C22⋊C4×C29—21no—
189C22⋊C4×C29—24no—
190C22⋊C4×C29—22no—
191C22⋊C4×C29—24no—
192C22⋊C4×C29—24no—
193C22⋊C4×C29—24no—
194C22⋊C4×C29—22no—
195C22⋊C4×C29—48no—
196C22⋊C4×C29—81no—
197C22⋊C4×C29—84no—
198C22⋊C4×C29C2×D412yescomplemented
199C42×C29—21no—
200C42×C29—21no—
201C42×C29—81no—
202#24263C2911yesmaximal, characteristic, direct product factor, Sylow
203C23×C29—21no—
204C23×C29—21no—
205C23×C29—24no—
206C23×C29—24no—
207C23×C29—24no—
208C23×C29—41no—
209C23×C29—41no—
210C23×C29—41no—
211C23×C29—41no—
212C23×C29—44no—
213C23×C29—44no—
214C23×C29—44no—
215C23×C29—82no—
216C23×C29—82no—
217C23×C29#12112yes—
218C23×C29C22×D411yescharacteristic
219C23×C29C22×D412yes—
220C23×C29C22×D411yescharacteristic
221C23×C29C2×#4111yescharacteristic
222C23×C29H(5,𝔽2)12yes—
223Q8×C29—44no—
224D4×C29—24no—
225D4×C29—24no—
226D4×C29—44no—
227D4×C29—44no—
228D4×C29—48no—
229D4×C29—44no—
230D4×C29—44no—
231D4×C29—44no—
232D4×C29—44no—
233D4×C29—82no—
234D4×C29—82no—
235D4×C29—82no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—21no—
239C2×C4×C29—21no—
240C2×C4×C29—24no—
241C2×C4×C29—22no—
242C2×C4×C29—22no—
243C2×C4×C29—24no—
244C2×C4×C29—24no—
245C2×C4×C29—24no—
246C2×C4×C29—41no—
247C2×C4×C29—42no—
248C2×C4×C29—41no—
249C2×C4×C29—42no—
250C2×C4×C29—42no—
251C2×C4×C29—48no—
252C2×C4×C29—41no—
253C2×C4×C29—41no—
254C2×C4×C29—44no—
255C2×C4×C29—41no—
256C2×C4×C29—41no—
257C2×C4×C29—42no—
258C2×C4×C29—41no—
259C2×C4×C29—41no—
260C2×C4×C29—41no—
261C2×C4×C29—44no—
262C2×C4×C29—41no—
263C2×C4×C29—44no—
264C2×C4×C29—41no—
265C2×C4×C29—41no—
266C2×C4×C29—44no—
267C2×C4×C29—41no—
268C2×C4×C29—41no—
269C2×C4×C29—44no—
270C2×C4×C29—81no—
271C2×C4×C29#12011yescharacteristic
272C2×C4×C29#12011yescharacteristic
273C2×C4×C29#12012yes—
274C2×C4×C29#12112yes—
275#3496C2×C2911yescharacteristic
276C2×#458C2×C2912yescomplemented
277#2618C2×C2912yescomplemented
278#2322C2×C2911yescharacteristic, complemented
279#2044C2×C2912yescomplemented
280#2022C2×C2912yescomplemented
281#1964C2×C2912yescomplemented
282#1799C2×C2911yescharacteristic, complemented
283#1790C2×C2912yescomplemented
284C22×C29—21no—
285C22×C29—22no—
286C22×C29—21no—
287C22×C29—22no—
288C22×C29—22no—
289C22×C29—41no—
290C22×C29—41no—
291C22×C29—42no—
292C22×C29—42no—
293C22×C29—41no—
294C22×C29—41no—
295C22×C29—44no—
296C22×C29—44no—
297C22×C29—44no—
298C22×C29—81no—
299C22×C29—84no—
300C22×C29—84no—
301C22×C29—164no—
302C22×C29C2×#12011yescharacteristic
303C22×C29C2×#12111yescharacteristic
304C22×C29#53511yescharacteristic
305C22×C29D4212yes—
306C22×C29#54612yes—
307C4×C29—22no—
308C4×C29—21no—
309C4×C29—21no—
310C4×C29—22no—
311C4×C29—42no—
312C4×C29—42no—
313C4×C29—44no—
314C4×C29—41no—
315C4×C29—41no—
316C4×C29—84no—
317C4×C29—81no—
318C4×C29—81no—
319C2×H(5,𝔽2)C22×C2912yes—
320#547—22no—
321#546—24no—
322D42—22no—
323#537—21no—
324#534—21no—
325#534C22×C2912yes—
326#532—21no—
327C2×#123C22×C2911yescharacteristic
328C2×#123C22×C2914yescomplemented
329C2×#121—21no—
330C2×#121C22×C2912yes—
331C2×C4×D4C22×C2911yescharacteristic
332C22×C4⋊C4C22×C2911yescharacteristic, complemented
333#458—28no—
334C2×#99C22×C2912yes—
335C2×#99C22×C2914yescomplemented
336C2×#99C22×C2914yescomplemented
337#398—22no—
338#396—24no—
339#394—22no—
340#389—21no—
341#388—21no—
342#387—21no—
343#386C22×C2911yescharacteristic
344#386C22×C2914yescomplemented
345#385—21no—
346#385C22×C2911yescharacteristic, complemented
347#381C22×C2911yescharacteristic, complemented
348#380C22×C2912yescomplemented
349C4×C22⋊C4C22×C2911yescharacteristic, complemented
350#342C22×C2912yescomplemented
351C2×C29—21no—
352C2×C29—22no—
353C2×C29—21no—
354C2×C29—22no—
355C2×C29—42no—
356C2×C29—84no—
357C2×C29#240811yescharacteristic
358C2×C29#302611yescharacteristic
359C2×C29#302811yescharacteristic
360H(5,𝔽2)—24no—
361H(5,𝔽2)—24no—
362H(5,𝔽2)—44no—
363C2×#41—22no—
364C2×#41—24no—
365C22×D4—22no—
366C22×D4—24no—
367C22×D4—21no—
368C22×D4D4×C2912yes—
369C22×D4C23×C2914yes—
370C22×D4C23×C2911yescharacteristic
371C23×C4D4×C2911yescharacteristic
372C23×C4C23×C2911yescharacteristic
373C23×C4C23×C2911yescharacteristic
374C23×C4C23×C2911yescharacteristic
375C4⋊Q8—21no—
376#127—21no—
377#124—22no—
378#123—24no—
379#123—22no—
380#123—24no—
381#123—28no—
382#123—44no—
383#123D4×C2914yescomplemented
384C22⋊Q8—24no—
385#121—22no—
386#121—22no—
387#121—24no—
388#121—22no—
389#121—22no—
390#121—22no—
391#121—22no—
392#121—22no—
393#121—22no—
394#120—24no—
395#120—24no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4D4×C2911yescharacteristic
410C2×C4⋊C4D4×C2912yes—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4D4×C2911yescharacteristic
417C2×C22⋊C4D4×C2914yes—
418C2×C22⋊C4C23×C2914yes—
419C2×C22⋊C4C23×C2911yescharacteristic
420C2×C22⋊C4C23×C2911yescharacteristic
421C2×C22⋊C4C23×C2911yescharacteristic
422C2×C42—21no—
423C2×C42D4×C2911yescharacteristic
424#99—24no—
425#99—28no—
426#99—44no—
427#95—21no—
428#95—22no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—24no—
434C29#2426311yescharacteristic, direct product factor, Sylow
435C24—22no—
436C24C2×D4×C2914yes—
437C24C2×D4×C2911yescharacteristic
438C24C24×C2911yescharacteristic
439#41—48no—
440#41—48no—
441#41—44no—
442#41—44no—
443C2×Q8—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—24no—
447C2×D4—22no—
448C2×D4—24no—
449C2×D4—24no—
450C2×D4—24no—
451C2×D4—24no—
452C2×D4—24no—
453C2×D4—24no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—48no—
459C2×D4—48no—
460C2×D4—44no—
461C2×D4—44no—
462C2×D4—82no—
463C2×D4—82no—
464C2×D4C2×D4×C2912yes—
465C2×D4#41×C2912yes—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—81no—
480C22×C4—81no—
481C22×C4—81no—
482C22×C4C2×D4×C2914yes—
483C22×C4C2×D4×C2911yescharacteristic
484C22×C4C2×D4×C2911yescharacteristic
485C22×C4C2×D4×C2911yescharacteristic
486C22×C4C2×D4×C2911yescharacteristic
487C22×C4C2×D4×C2912yes—
488C22×C4C2×D4×C2911yescharacteristic
489C22×C4C2×D4×C2912yes—
490C22×C4C2×D4×C2912yescomplemented
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—24no—
497C4⋊C4—48no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—42no—
501C4⋊C4—82no—
502C4⋊C4—81no—
503C22⋊C4—24no—
504C22⋊C4—24no—
505C22⋊C4—24no—
506C22⋊C4—22no—
507C22⋊C4—21no—
508C22⋊C4—24no—
509C22⋊C4—22no—
510C22⋊C4—24no—
511C22⋊C4—24no—
512C22⋊C4—22no—
513C22⋊C4—24no—
514C22⋊C4—48no—
515C22⋊C4—81no—
516C22⋊C4—84no—
517C22⋊C4C2×D4×C2912yescomplemented
518C42—21no—
519C42—21no—
520C42—81no—
521C23—21no—
522C23—21no—
523C23—24no—
524C23—24no—
525C23—24no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—44no—
531C23—44no—
532C23—44no—
533C23—82no—
534C23—82no—
535C23C29×#12112yes—
536C23C22×D4×C2911yescharacteristic
537C23C22×D4×C2912yes—
538C23C22×D4×C2911yescharacteristic
539C23C2×#41×C2911yescharacteristic
540C23C29×H(5,𝔽2)12yes—
541Q8—44no—
542D4—24no—
543D4—24no—
544D4—44no—
545D4—44no—
546D4—48no—
547D4—44no—
548D4—44no—
549D4—44no—
550D4—44no—
551D4—82no—
552D4—82no—
553D4—82no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—48no—
570C2×C4—41no—
571C2×C4—44no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—44no—
580C2×C4—41no—
581C2×C4—44no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—44no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—44no—
588C2×C4—81no—
589C2×C4C29×#12011yescharacteristic
590C2×C4C29×#12011yescharacteristic
591C2×C4C29×#12012yes—
592C2×C4C29×#12112yes—
593C22—21no—
594C22—22no—
595C22—21no—
596C22—22no—
597C22—22no—
598C22—41no—
599C22—41no—
600C22—42no—
601C22—42no—
602C22—41no—
603C22—41no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—81no—
608C22—84no—
609C22—84no—
610C22—164no—
611C22C2×C29×#12011yescharacteristic
612C22C2×C29×#12111yescharacteristic
613C22C29×#53511yescharacteristic
614C22D42×C2912yes—
615C22C29×#54612yes—
616C4—21no—
617C4—21no—
618C4—22no—
619C4—22no—
620C4—42no—
621C4—41no—
622C4—41no—
623C4—44no—
624C4—42no—
625C4—84no—
626C4—81no—
627C4—81no—
628C2—21no—
629C2—22no—
630C2—21no—
631C2—22no—
632C2—42no—
633C2—84no—
634C2C29×#240811yescharacteristic
635C2C29×#302611yescharacteristic
636C2C29×#302811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC24C24×C29
prime radicalC29×#3496C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#458C2semidirect
3. C29×#2618C2semidirect
4. C29×#2322C2semidirect
5. C29×#2044C2semidirect
6. C29×#2022C2semidirect
7. C29×#1964C2semidirect
8. C29×#1799C2semidirect
9. C29×#1790C2semidirect
19. C2×C29×#123C22semidirect
23. C22×C4⋊C4×C29C22semidirect
26. C2×C29×#99C22semidirect
27. C2×C29×#99C22semidirect
35. C29×#386C22semidirect
37. C29×#385C22semidirect
38. C29×#381C22semidirect
39. C29×#380C22semidirect
40. C4×C22⋊C4×C29C22semidirect
41. C29×#342C22semidirect
65. C29×#123D4semidirect
171. C22×C4×C29C2×D4semidirect
198. C22⋊C4×C29C2×D4semidirect
202. #24263C29direct (N × H)
276. C2×#458C2×C29semidirect
277. #2618C2×C29semidirect
278. #2322C2×C29semidirect
279. #2044C2×C29semidirect
280. #2022C2×C29semidirect
281. #1964C2×C29semidirect
282. #1799C2×C29semidirect
283. #1790C2×C29semidirect
328. C2×#123C22×C29semidirect
332. C22×C4⋊C4C22×C29semidirect
335. C2×#99C22×C29semidirect
336. C2×#99C22×C29semidirect
344. #386C22×C29semidirect
346. #385C22×C29semidirect
347. #381C22×C29semidirect
348. #380C22×C29semidirect
349. C4×C22⋊C4C22×C29semidirect
350. #342C22×C29semidirect
383. #123D4×C29semidirect
434. C29#24263direct (N × H)
490. C22×C4C2×D4×C29semidirect
517. C22⋊C4C2×D4×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#34962
C2×C29×#4582
C29×#26182
C29×#23222
C29×#20442
C29×#20222
C29×#19642
C29×#17992
C29×#17902
#2426329