Finite Group Databasebeta

← C29×#14718 #20309618

Subgroups — C29×#14718 #20309618

Order 7424.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C29×#120C211yesmaximal, characteristic
2C23×C22⋊C4×C29C211yesmaximal, characteristic, complemented
3C2×C29×#394C212yesmaximal, complemented
4C2×C29×#386C211yesmaximal, characteristic, complemented
5C2×C29×#386C211yesmaximal, characteristic, complemented
6C2×C29×#385C211yesmaximal, characteristic, complemented
7C2×C29×#379C211yesmaximal, characteristic, complemented
8C29×#1440C212yesmaximal, complemented
9C29×#1439C212yesmaximal, complemented
10C29×#1438C212yesmaximal, complemented
11C29×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C29C2211yescharacteristic
13C23×D4×C29C2211yescharacteristic
14C23×D4×C29C2211yescharacteristic
15C23×D4×C29C2211yescharacteristic
16C24×C4×C29C2211yescharacteristic
17C24×C4×C29C2211yescharacteristic
18C2×C29×#120—24no—
19C2×C29×#120—24no—
20C2×C29×#120—24no—
21C22×C4⋊C4×C29C2212yescomplemented
22C22×C22⋊C4×C29—24no—
23C22×C22⋊C4×C29—28no—
24C22×C22⋊C4×C29C2211yescharacteristic
25C22×C22⋊C4×C29C2212yes—
26C22×C22⋊C4×C29C2211yescharacteristic
27C22×C22⋊C4×C29C2211yescharacteristic
28C22×C22⋊C4×C29C2212yes—
29C22×C22⋊C4×C29C2212yes—
30C22×C22⋊C4×C29C2211yescharacteristic
31C22×C22⋊C4×C29C2212yes—
32C22×C22⋊C4×C29C2211yescharacteristic
33C22×C22⋊C4×C29C2212yescomplemented
34C22×C22⋊C4×C29C2212yescomplemented
35C29×#394—28no—
36C29×#386—24no—
37C29×#386—24no—
38C29×#385—24no—
39C29×#379—24no—
40C2×C29×#95C2212yescomplemented
41C2×C29×#95C2212yescomplemented
42C2×C29×#95C2212yescomplemented
43C2×C29×#95C2212yescomplemented
44C2×C29×#95C2212yescomplemented
45C25×C29—24no—
46C25×C29—24no—
47C25×C29—22no—
48C25×C29—22no—
49C25×C29—22no—
50C25×C29—22no—
51C25×C29—22no—
52C25×C29—22no—
53C25×C29—42no—
54C25×C29—42no—
55C25×C29D414yes—
56C25×C29C2311yescharacteristic
57C25×C29C2311yescharacteristic
58C25×C29C2311yescharacteristic
59C25×C29C2311yescharacteristic
60C22×D4×C29—22no—
61C22×D4×C29—22no—
62C22×D4×C29—22no—
63C22×D4×C29—22no—
64C22×D4×C29—22no—
65C22×D4×C29—22no—
66C22×D4×C29—22no—
67C22×D4×C29—22no—
68C22×D4×C29—22no—
69C22×D4×C29—22no—
70C22×D4×C29—24no—
71C22×D4×C29—24no—
72C22×D4×C29—22no—
73C22×D4×C29—22no—
74C22×D4×C29—42no—
75C22×D4×C29—42no—
76C22×D4×C29D414yes—
77C23×C4×C29—22no—
78C23×C4×C29—22no—
79C23×C4×C29—24no—
80C23×C4×C29—24no—
81C23×C4×C29—22no—
82C23×C4×C29—22no—
83C23×C4×C29—22no—
84C23×C4×C29—22no—
85C23×C4×C29—42no—
86C23×C4×C29—42no—
87C23×C4×C29C2312yes—
88C23×C4×C29C2312yes—
89C23×C4×C29C2312yes—
90C23×C4×C29C2312yes—
91C23×C4×C29C2311yescharacteristic
92C23×C4×C29C2311yescharacteristic
93C23×C4×C29C2311yescharacteristic
94C29×#120—232no—
95C2×C4⋊C4×C29—24no—
96C2×C4⋊C4×C29—24no—
97C2×C4⋊C4×C29—42no—
98C2×C22⋊C4×C29—232no—
99C2×C22⋊C4×C29—24no—
100C2×C22⋊C4×C29—24no—
101C2×C22⋊C4×C29—24no—
102C2×C22⋊C4×C29—22no—
103C2×C22⋊C4×C29—22no—
104C2×C22⋊C4×C29—22no—
105C2×C22⋊C4×C29—22no—
106C2×C22⋊C4×C29—22no—
107C2×C22⋊C4×C29—22no—
108C2×C22⋊C4×C29—24no—
109C2×C22⋊C4×C29—24no—
110C2×C22⋊C4×C29—22no—
111C2×C22⋊C4×C29—22no—
112C2×C22⋊C4×C29—22no—
113C2×C22⋊C4×C29—22no—
114C2×C22⋊C4×C29—22no—
115C2×C22⋊C4×C29—22no—
116C2×C22⋊C4×C29—24no—
117C2×C22⋊C4×C29—24no—
118C2×C22⋊C4×C29—24no—
119C2×C22⋊C4×C29—22no—
120C2×C22⋊C4×C29—24no—
121C2×C22⋊C4×C29—24no—
122C2×C22⋊C4×C29—24no—
123C2×C22⋊C4×C29—24no—
124C2×C22⋊C4×C29—24no—
125C2×C22⋊C4×C29—42no—
126C2×C22⋊C4×C29—42no—
127C2×C22⋊C4×C29—42no—
128C2×C22⋊C4×C29—42no—
129C2×C22⋊C4×C29D414yes—
130C2×C22⋊C4×C29D418yescomplemented
131C2×C22⋊C4×C29D414yescomplemented
132C29×#95—24no—
133C29×#95—24no—
134C29×#95—24no—
135C29×#95—24no—
136C29×#95—42no—
137C24×C29—22no—
138C24×C29—22no—
139C24×C29—22no—
140C24×C29—22no—
141C24×C29—216no—
142C24×C29—216no—
143C24×C29—28no—
144C24×C29—28no—
145C24×C29—28no—
146C24×C29—22no—
147C24×C29—21no—
148C24×C29—21no—
149C24×C29—21no—
150C24×C29—21no—
151C24×C29—21no—
152C24×C29—21no—
153C24×C29—21no—
154C24×C29—21no—
155C24×C29—21no—
156C24×C29—21no—
157C24×C29—22no—
158C24×C29—21no—
159C24×C29—21no—
160C24×C29—22no—
161C24×C29—22no—
162C24×C29—22no—
163C24×C29—22no—
164C24×C29—28no—
165C24×C29—28no—
166C24×C29—21no—
167C24×C29—22no—
168C24×C29—21no—
169C24×C29—21no—
170C24×C29—21no—
171C24×C29—21no—
172C24×C29—21no—
173C24×C29—22no—
174C24×C29—22no—
175C24×C29—22no—
176C24×C29—44no—
177C24×C29—44no—
178C24×C29—48no—
179C24×C29—48no—
180C24×C29—48no—
181C24×C29—48no—
182C24×C29—48no—
183C24×C29—48no—
184C24×C29—48no—
185C24×C29—48no—
186C24×C29—48no—
187C24×C29—48no—
188C24×C29—44no—
189C24×C29—44no—
190C24×C29—44no—
191C24×C29—44no—
192C24×C29C2×D412yes—
193C24×C29C2×D412yes—
194C24×C29C2×D414yes—
195C24×C29C2×D412yes—
196C24×C29C2×D412yes—
197C24×C29C2×D412yes—
198C24×C29C2×D412yes—
199C24×C29C2×D412yes—
200C24×C29#4114yes—
201C24×C29#4112yes—
202C24×C29#4112yes—
203C24×C29#4112yes—
204C24×C29C2411yescharacteristic
205C2×D4×C29—28no—
206C2×D4×C29—28no—
207C2×D4×C29—28no—
208C2×D4×C29—28no—
209C2×D4×C29—28no—
210C2×D4×C29—48no—
211C2×D4×C29—48no—
212C2×D4×C29—48no—
213C2×D4×C29—48no—
214C2×D4×C29—44no—
215C2×D4×C29—44no—
216C2×D4×C29—44no—
217C2×D4×C29—44no—
218C2×D4×C29—44no—
219C2×D4×C29—44no—
220C2×D4×C29—44no—
221C2×D4×C29—44no—
222C22×C4×C29—28no—
223C22×C4×C29—28no—
224C22×C4×C29—22no—
225C22×C4×C29—22no—
226C22×C4×C29—22no—
227C22×C4×C29—22no—
228C22×C4×C29—22no—
229C22×C4×C29—21no—
230C22×C4×C29—21no—
231C22×C4×C29—21no—
232C22×C4×C29—21no—
233C22×C4×C29—21no—
234C22×C4×C29—21no—
235C22×C4×C29—22no—
236C22×C4×C29—22no—
237C22×C4×C29—22no—
238C22×C4×C29—22no—
239C22×C4×C29—22no—
240C22×C4×C29—21no—
241C22×C4×C29—22no—
242C22×C4×C29—22no—
243C22×C4×C29—22no—
244C22×C4×C29—21no—
245C22×C4×C29—21no—
246C22×C4×C29—21no—
247C22×C4×C29—22no—
248C22×C4×C29—22no—
249C22×C4×C29—22no—
250C22×C4×C29—22no—
251C22×C4×C29—22no—
252C22×C4×C29—22no—
253C22×C4×C29—22no—
254C22×C4×C29—22no—
255C22×C4×C29—22no—
256C22×C4×C29—22no—
257C22×C4×C29—22no—
258C22×C4×C29—22no—
259C22×C4×C29—22no—
260C22×C4×C29—22no—
261C22×C4×C29—22no—
262C22×C4×C29—22no—
263C22×C4×C29—48no—
264C22×C4×C29—48no—
265C22×C4×C29—48no—
266C22×C4×C29—48no—
267C22×C4×C29—44no—
268C22×C4×C29—44no—
269C22×C4×C29—44no—
270C22×C4×C29—44no—
271C22×C4×C29C2×D414yes—
272C22×C4×C29C2×D414yes—
273C22×C4×C29C2×D414yes—
274C22×C4×C29C2×D412yes—
275C22×C4×C29C2×D412yes—
276C22×C4×C29C2×D412yes—
277C4⋊C4×C29—48no—
278C22⋊C4×C29—216no—
279C22⋊C4×C29—28no—
280C22⋊C4×C29—28no—
281C22⋊C4×C29—216no—
282C22⋊C4×C29—28no—
283C22⋊C4×C29—28no—
284C22⋊C4×C29—48no—
285C22⋊C4×C29—48no—
286C22⋊C4×C29—48no—
287C22⋊C4×C29—48no—
288C22⋊C4×C29—44no—
289#14718C2911yesmaximal, characteristic, direct product factor, Sylow
290C23×C29—22no—
291C23×C29—22no—
292C23×C29—24no—
293C23×C29—24no—
294C23×C29—22no—
295C23×C29—22no—
296C23×C29—24no—
297C23×C29—24no—
298C23×C29—24no—
299C23×C29—24no—
300C23×C29—24no—
301C23×C29—24no—
302C23×C29—24no—
303C23×C29—24no—
304C23×C29—24no—
305C23×C29—24no—
306C23×C29—232no—
307C23×C29—22no—
308C23×C29—22no—
309C23×C29—22no—
310C23×C29—22no—
311C23×C29—22no—
312C23×C29—22no—
313C23×C29—22no—
314C23×C29—22no—
315C23×C29—24no—
316C23×C29—24no—
317C23×C29—24no—
318C23×C29—24no—
319C23×C29—22no—
320C23×C29—22no—
321C23×C29—22no—
322C23×C29—22no—
323C23×C29—24no—
324C23×C29—24no—
325C23×C29—24no—
326C23×C29—24no—
327C23×C29—24no—
328C23×C29—24no—
329C23×C29—24no—
330C23×C29—24no—
331C23×C29—22no—
332C23×C29—22no—
333C23×C29—22no—
334C23×C29—24no—
335C23×C29—24no—
336C23×C29—416no—
337C23×C29—416no—
338C23×C29—416no—
339C23×C29—416no—
340C23×C29—416no—
341C23×C29—432no—
342C23×C29—432no—
343C23×C29—432no—
344C23×C29—432no—
345C23×C29—41no—
346C23×C29—41no—
347C23×C29—41no—
348C23×C29—41no—
349C23×C29—41no—
350C23×C29—41no—
351C23×C29—41no—
352C23×C29—41no—
353C23×C29—42no—
354C23×C29—42no—
355C23×C29—42no—
356C23×C29—42no—
357C23×C29—42no—
358C23×C29—42no—
359C23×C29—42no—
360C23×C29—42no—
361C23×C29—42no—
362C23×C29—42no—
363C23×C29—42no—
364C23×C29—42no—
365C23×C29—416no—
366C23×C29—41no—
367C23×C29—41no—
368C23×C29—41no—
369C23×C29—41no—
370C23×C29—41no—
371C23×C29—42no—
372C23×C29—42no—
373C23×C29—41no—
374C23×C29—41no—
375C23×C29—41no—
376C23×C29—42no—
377C23×C29—42no—
378C23×C29—42no—
379C23×C29—42no—
380C23×C29—42no—
381C23×C29—42no—
382C23×C29—42no—
383C23×C29—42no—
384C23×C29#12014yes—
385C23×C29#12014yes—
386C23×C29#12114yes—
387C23×C29#12114yes—
388C23×C29#12114yes—
389C23×C29#12314yes—
390C23×C29#12314yes—
391C23×C29#12314yes—
392C23×C29#12414yes—
393C23×C29C22×D411yescharacteristic
394C23×C29C22×D411yescharacteristic
395C23×C29C22×D411yescharacteristic
396C23×C29C22×D412yes—
397C23×C29C22×D411yescharacteristic
398C23×C29C2×#4111yescharacteristic
399C23×C29C2×#4111yescharacteristic
400C23×C29C2×#4111yescharacteristic
401C23×C29C2×#4112yes—
402C23×C29H(5,𝔽2)12yes—
403C23×C29H(5,𝔽2)12yes—
404D4×C29—416no—
405D4×C29—416no—
406D4×C29—416no—
407C2×C4×C29—24no—
408C2×C4×C29—24no—
409C2×C4×C29—22no—
410C2×C4×C29—22no—
411C2×C4×C29—22no—
412C2×C4×C29—24no—
413C2×C4×C29—22no—
414C2×C4×C29—22no—
415C2×C4×C29—24no—
416C2×C4×C29—24no—
417C2×C4×C29—24no—
418C2×C4×C29—24no—
419C2×C4×C29—24no—
420C2×C4×C29—24no—
421C2×C4×C29—24no—
422C2×C4×C29—24no—
423C2×C4×C29—416no—
424C2×C4×C29—416no—
425C2×C4×C29—42no—
426C2×C4×C29—41no—
427C2×C4×C29—42no—
428C2×C4×C29—41no—
429C2×C4×C29—41no—
430C2×C4×C29—41no—
431C2×C4×C29—41no—
432C2×C4×C29—42no—
433C2×C4×C29—41no—
434C2×C4×C29—42no—
435C2×C4×C29—42no—
436C2×C4×C29—41no—
437C2×C4×C29—41no—
438C2×C4×C29—42no—
439C2×C4×C29—42no—
440C2×C4×C29—42no—
441C2×C4×C29—42no—
442C2×C4×C29—42no—
443C2×C4×C29—42no—
444C2×C4×C29—42no—
445C2×C4×C29—42no—
446C2×C4×C29—42no—
447C2×C4×C29—42no—
448C2×C4×C29—42no—
449C2×C4×C29—42no—
450C2×C4×C29—42no—
451C2×C4×C29—42no—
452C2×C4×C29—42no—
453C2×C4×C29—42no—
454C22×#120C2×C2911yescharacteristic
455C23×C22⋊C4C2×C2911yescharacteristic, complemented
456C2×#394C2×C2912yescomplemented
457C2×#386C2×C2911yescharacteristic, complemented
458C2×#386C2×C2911yescharacteristic, complemented
459C2×#385C2×C2911yescharacteristic, complemented
460C2×#379C2×C2911yescharacteristic, complemented
461#1440C2×C2912yescomplemented
462#1439C2×C2912yescomplemented
463#1438C2×C2912yescomplemented
464C22⋊#95C2×C2911yescharacteristic, complemented
465C22×C29—24no—
466C22×C29—24no—
467C22×C29—24no—
468C22×C29—24no—
469C22×C29—24no—
470C22×C29—24no—
471C22×C29—28no—
472C22×C29—28no—
473C22×C29—28no—
474C22×C29—28no—
475C22×C29—24no—
476C22×C29—24no—
477C22×C29—24no—
478C22×C29—24no—
479C22×C29—24no—
480C22×C29—24no—
481C22×C29—464no—
482C22×C29—42no—
483C22×C29—42no—
484C22×C29—42no—
485C22×C29—42no—
486C22×C29—42no—
487C22×C29—42no—
488C22×C29—42no—
489C22×C29—42no—
490C22×C29—44no—
491C22×C29—44no—
492C22×C29—44no—
493C22×C29—44no—
494C22×C29—44no—
495C22×C29—44no—
496C22×C29—44no—
497C22×C29—44no—
498C22×C29—42no—
499C22×C29—42no—
500C22×C29—42no—
501C22×C29—44no—
502C22×C29—44no—
503C22×C29—81no—
504C22×C29—81no—
505C22×C29—81no—
506C22×C29—81no—
507C22×C29—82no—
508C22×C29—82no—
509C22×C29#39418yescomplemented
510C22×C29C2×#12011yescharacteristic
511C22×C29C2×#12011yescharacteristic
512C22×C29C2×#12111yescharacteristic
513C22×C29C2×#12111yescharacteristic
514C22×C29C2×#12111yescharacteristic
515C22×C29C2×#12311yescharacteristic
516C22×C29C2×#12311yescharacteristic
517C22×C29C2×#12311yescharacteristic
518C22×C29#52512yes—
519C22×C29#52512yes—
520C22×C29C2×#12411yescharacteristic
521C22×C29#53411yescharacteristic
522C22×C29#53411yescharacteristic
523C22×C29#53812yes—
524C22×C29#53812yes—
525C22×C29D4212yes—
526C22×C29D4212yes—
527C22×C29D4212yes—
528C22×C29#54612yes—
529C22×C29#54612yes—
530C22×C29#54612yes—
531C22×C29#54612yes—
532C22×C29#55112yes—
533C4×C29—42no—
534C4×C29—44no—
535C4×C29—42no—
536C4×C29—42no—
537C4×C29—44no—
538C4×C29—44no—
539C4×C29—82no—
540C26C22×C2911yescharacteristic
541C23×D4C22×C2911yescharacteristic
542C23×D4C22×C2911yescharacteristic
543C23×D4C22×C2911yescharacteristic
544C24×C4C22×C2911yescharacteristic
545C24×C4C22×C2911yescharacteristic
546C2×#120—24no—
547C2×#120—24no—
548C2×#120—24no—
549C22×C4⋊C4C22×C2912yescomplemented
550C22×C22⋊C4—24no—
551C22×C22⋊C4—28no—
552C22×C22⋊C4C22×C2912yes—
553C22×C22⋊C4C22×C2911yescharacteristic
554C22×C22⋊C4C22×C2911yescharacteristic
555C22×C22⋊C4C22×C2911yescharacteristic
556C22×C22⋊C4C22×C2912yes—
557C22×C22⋊C4C22×C2912yes—
558C22×C22⋊C4C22×C2911yescharacteristic
559C22×C22⋊C4C22×C2912yes—
560C22×C22⋊C4C22×C2911yescharacteristic
561C22×C22⋊C4C22×C2912yescomplemented
562C22×C22⋊C4C22×C2912yescomplemented
563#394—28no—
564#386—24no—
565#386—24no—
566#385—24no—
567#379—24no—
568C2×#95C22×C2912yescomplemented
569C2×#95C22×C2912yescomplemented
570C2×#95C22×C2912yescomplemented
571C2×#95C22×C2912yescomplemented
572C2×#95C22×C2912yescomplemented
573C2×C29—28no—
574C2×C29—44no—
575C2×C29—44no—
576C2×C29—82no—
577C2×C29C2×#39411yescharacteristic
578C2×C29#240311yescharacteristic
579C2×C29#240511yescharacteristic
580C2×C29#241011yescharacteristic
581C2×C29#241211yescharacteristic
582C2×C29#241812yes—
583C2×C29#242412yes—
584C2×C29#242412yes—
585C2×C29#247212yes—
586C2×C29#262211yescharacteristic
587C2×C29#284911yescharacteristic
588C25—24no—
589C25—24no—
590C25—22no—
591C25—22no—
592C25—22no—
593C25—22no—
594C25—22no—
595C25—22no—
596C25—42no—
597C25—42no—
598C25D4×C2914yes—
599C25C23×C2911yescharacteristic
600C25C23×C2911yescharacteristic
601C25C23×C2911yescharacteristic
602C25C23×C2911yescharacteristic
603C22×D4—22no—
604C22×D4—22no—
605C22×D4—22no—
606C22×D4—22no—
607C22×D4—22no—
608C22×D4—22no—
609C22×D4—22no—
610C22×D4—22no—
611C22×D4—22no—
612C22×D4—22no—
613C22×D4—24no—
614C22×D4—24no—
615C22×D4—22no—
616C22×D4—22no—
617C22×D4—42no—
618C22×D4—42no—
619C22×D4D4×C2914yes—
620C23×C4—22no—
621C23×C4—22no—
622C23×C4—24no—
623C23×C4—24no—
624C23×C4—22no—
625C23×C4—22no—
626C23×C4—22no—
627C23×C4—22no—
628C23×C4—42no—
629C23×C4—42no—
630C23×C4C23×C2912yes—
631C23×C4C23×C2912yes—
632C23×C4C23×C2912yes—
633C23×C4C23×C2912yes—
634C23×C4C23×C2911yescharacteristic
635C23×C4C23×C2911yescharacteristic
636C23×C4C23×C2911yescharacteristic
637#120—232no—
638C2×C4⋊C4—24no—
639C2×C4⋊C4—24no—
640C2×C4⋊C4—42no—
641C2×C22⋊C4—232no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—24no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—24no—
660C2×C22⋊C4—24no—
661C2×C22⋊C4—24no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—24no—
664C2×C22⋊C4—24no—
665C2×C22⋊C4—24no—
666C2×C22⋊C4—24no—
667C2×C22⋊C4—24no—
668C2×C22⋊C4—42no—
669C2×C22⋊C4—42no—
670C2×C22⋊C4—42no—
671C2×C22⋊C4—42no—
672C2×C22⋊C4D4×C2914yes—
673C2×C22⋊C4D4×C2918yescomplemented
674C2×C22⋊C4D4×C2914yescomplemented
675#95—24no—
676#95—24no—
677#95—24no—
678#95—24no—
679#95—42no—
680C29#1471811yescharacteristic, direct product factor, Sylow
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—216no—
686C24—216no—
687C24—28no—
688C24—28no—
689C24—28no—
690C24—22no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—22no—
702C24—21no—
703C24—21no—
704C24—22no—
705C24—22no—
706C24—22no—
707C24—22no—
708C24—28no—
709C24—28no—
710C24—21no—
711C24—22no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—22no—
718C24—22no—
719C24—22no—
720C24—44no—
721C24—44no—
722C24—48no—
723C24—48no—
724C24—48no—
725C24—48no—
726C24—48no—
727C24—48no—
728C24—48no—
729C24—48no—
730C24—48no—
731C24—48no—
732C24—44no—
733C24—44no—
734C24—44no—
735C24—44no—
736C24C2×D4×C2912yes—
737C24C2×D4×C2912yes—
738C24C2×D4×C2914yes—
739C24C2×D4×C2912yes—
740C24C2×D4×C2912yes—
741C24C2×D4×C2912yes—
742C24C2×D4×C2912yes—
743C24C2×D4×C2912yes—
744C24#41×C2914yes—
745C24#41×C2912yes—
746C24#41×C2912yes—
747C24#41×C2912yes—
748C24C24×C2911yescharacteristic
749C2×D4—28no—
750C2×D4—28no—
751C2×D4—28no—
752C2×D4—28no—
753C2×D4—28no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—48no—
808C22×C4—48no—
809C22×C4—48no—
810C22×C4—48no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4C2×D4×C2912yes—
816C22×C4C2×D4×C2912yes—
817C22×C4C2×D4×C2914yes—
818C22×C4C2×D4×C2914yes—
819C22×C4C2×D4×C2914yes—
820C22×C4C2×D4×C2912yes—
821C4⋊C4—48no—
822C22⋊C4—216no—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—216no—
826C22⋊C4—28no—
827C22⋊C4—28no—
828C22⋊C4—48no—
829C22⋊C4—48no—
830C22⋊C4—48no—
831C22⋊C4—48no—
832C22⋊C4—44no—
833C23—22no—
834C23—22no—
835C23—24no—
836C23—24no—
837C23—22no—
838C23—22no—
839C23—24no—
840C23—24no—
841C23—24no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—232no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—24no—
867C23—24no—
868C23—24no—
869C23—24no—
870C23—24no—
871C23—24no—
872C23—24no—
873C23—24no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—24no—
878C23—24no—
879C23—416no—
880C23—416no—
881C23—416no—
882C23—416no—
883C23—432no—
884C23—432no—
885C23—432no—
886C23—432no—
887C23—416no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—42no—
905C23—42no—
906C23—42no—
907C23—42no—
908C23—416no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—42no—
915C23—42no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—42no—
920C23—42no—
921C23—42no—
922C23—42no—
923C23—42no—
924C23—42no—
925C23—42no—
926C23—42no—
927C23C29×#12014yes—
928C23C29×#12014yes—
929C23C29×#12114yes—
930C23C29×#12114yes—
931C23C29×#12114yes—
932C23C29×#12314yes—
933C23C29×#12314yes—
934C23C29×#12314yes—
935C23C29×#12414yes—
936C23C22×D4×C2911yescharacteristic
937C23C22×D4×C2911yescharacteristic
938C23C22×D4×C2911yescharacteristic
939C23C22×D4×C2912yes—
940C23C22×D4×C2911yescharacteristic
941C23C2×#41×C2911yescharacteristic
942C23C2×#41×C2911yescharacteristic
943C23C2×#41×C2911yescharacteristic
944C23C2×#41×C2912yes—
945C23C29×H(5,𝔽2)12yes—
946C23C29×H(5,𝔽2)12yes—
947D4—416no—
948D4—416no—
949D4—416no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—416no—
967C2×C4—416no—
968C2×C4—42no—
969C2×C4—41no—
970C2×C4—42no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—42no—
976C2×C4—41no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—42no—
997C22—28no—
998C22—28no—
999C22—28no—
1000C22—28no—
1001C22—24no—
1002C22—24no—
1003C22—24no—
1004C22—24no—
1005C22—24no—
1006C22—24no—
1007C22—24no—
1008C22—24no—
1009C22—24no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—464no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—44no—
1020C22—44no—
1021C22—44no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—44no—
1031C22—44no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—82no—
1036C22—82no—
1037C22—81no—
1038C22—81no—
1039C22—81no—
1040C22—81no—
1041C22C29×#39418yescomplemented
1042C22C2×C29×#12011yescharacteristic
1043C22C2×C29×#12011yescharacteristic
1044C22C2×C29×#12111yescharacteristic
1045C22C2×C29×#12111yescharacteristic
1046C22C2×C29×#12111yescharacteristic
1047C22C2×C29×#12311yescharacteristic
1048C22C2×C29×#12311yescharacteristic
1049C22C2×C29×#12311yescharacteristic
1050C22C29×#52512yes—
1051C22C29×#52512yes—
1052C22C2×C29×#12411yescharacteristic
1053C22C29×#53411yescharacteristic
1054C22C29×#53411yescharacteristic
1055C22C29×#53812yes—
1056C22C29×#53812yes—
1057C22D42×C2912yes—
1058C22D42×C2912yes—
1059C22D42×C2912yes—
1060C22C29×#54612yes—
1061C22C29×#54612yes—
1062C22C29×#54612yes—
1063C22C29×#54612yes—
1064C22C29×#55112yes—
1065C4—44no—
1066C4—42no—
1067C4—44no—
1068C4—42no—
1069C4—42no—
1070C4—44no—
1071C4—82no—
1072C2—28no—
1073C2—44no—
1074C2—44no—
1075C2—82no—
1076C2C2×C29×#39411yescharacteristic
1077C2C29×#240311yescharacteristic
1078C2C29×#240511yescharacteristic
1079C2C29×#241011yescharacteristic
1080C2C29×#241211yescharacteristic
1081C2C29×#241812yes—
1082C2C29×#242412yes—
1083C2C29×#242412yes—
1084C2C29×#247212yes—
1085C2C29×#262211yescharacteristic
1086C2C29×#284911yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutator, Frattini, cosocleC24C24×C29
prime radicalC22×C29×#120C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C29C2semidirect
3. C2×C29×#394C2semidirect
4. C2×C29×#386C2semidirect
5. C2×C29×#386C2semidirect
6. C2×C29×#385C2semidirect
7. C2×C29×#379C2semidirect
8. C29×#1440C2semidirect
9. C29×#1439C2semidirect
10. C29×#1438C2semidirect
11. C29×C22⋊#95C2semidirect
21. C22×C4⋊C4×C29C22semidirect
33. C22×C22⋊C4×C29C22semidirect
34. C22×C22⋊C4×C29C22semidirect
40. C2×C29×#95C22semidirect
41. C2×C29×#95C22semidirect
42. C2×C29×#95C22semidirect
43. C2×C29×#95C22semidirect
44. C2×C29×#95C22semidirect
130. C2×C22⋊C4×C29D4semidirect
131. C2×C22⋊C4×C29D4semidirect
289. #14718C29direct (N × H)
455. C23×C22⋊C4C2×C29semidirect
456. C2×#394C2×C29semidirect
457. C2×#386C2×C29semidirect
458. C2×#386C2×C29semidirect
459. C2×#385C2×C29semidirect
460. C2×#379C2×C29semidirect
461. #1440C2×C29semidirect
462. #1439C2×C29semidirect
463. #1438C2×C29semidirect
464. C22⋊#95C2×C29semidirect
509. C22×C29#394semidirect
549. C22×C4⋊C4C22×C29semidirect
561. C22×C22⋊C4C22×C29semidirect
562. C22×C22⋊C4C22×C29semidirect
568. C2×#95C22×C29semidirect
569. C2×#95C22×C29semidirect
570. C2×#95C22×C29semidirect
571. C2×#95C22×C29semidirect
572. C2×#95C22×C29semidirect
673. C2×C22⋊C4D4×C29semidirect
674. C2×C22⋊C4D4×C29semidirect
680. C29#14718direct (N × H)
1041. C22C29×#394semidirect

Maximal subgroups

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

subgroupindex
C22×C29×#1202
C23×C22⋊C4×C292
C2×C29×#3942
C2×C29×#3862
C2×C29×#3852
C2×C29×#3792
C29×#14402
C29×#14392
C29×#14382
C29×C22⋊#952
#1471829