Finite Group Databasebeta

← C29×#16250 #20311150

Subgroups — C29×#16250 #20311150

Order 7424.

2894 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C29×#123C211yesmaximal, characteristic, complemented
2C22×C29×#121C211yesmaximal, characteristic, complemented
3C2×C29×#394C211yesmaximal, characteristic, complemented
4C2×C29×#392C212yesmaximal, complemented
5C2×C29×#392C211yesmaximal, characteristic, complemented
6C29×#1441C211yesmaximal, characteristic, complemented
7C29×#1439C212yesmaximal, complemented
8C29×#1439C211yesmaximal, characteristic, complemented
9C29×#1438C212yesmaximal, complemented
10C29×#1438C212yesmaximal, complemented
11C29×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C29C2211yescharacteristic
13C23×D4×C29C2211yescharacteristic
14C23×D4×C29C2212yes—
15C23×D4×C29C2212yes—
16C24×C4×C29C2211yescharacteristic
17C2×C29×#123—24no—
18C2×C29×#123—24no—
19C2×C29×#123—24no—
20C2×C29×#121—28no—
21C2×C29×#121—24no—
22C22×C4⋊C4×C29C2211yescharacteristic
23C22×C4⋊C4×C29C2211yescharacteristic
24C22×C4⋊C4×C29C2211yescharacteristic
25C22×C22⋊C4×C29C2211yescharacteristic
26C22×C22⋊C4×C29C2211yescharacteristic
27C22×C22⋊C4×C29C2212yes—
28C22×C22⋊C4×C29C2212yes—
29C22×C22⋊C4×C29C2212yes—
30C22×C22⋊C4×C29C2212yes—
31C22×C22⋊C4×C29C2211yescharacteristic
32C22×C22⋊C4×C29C2212yes—
33C22×C22⋊C4×C29C2212yes—
34C29×#394—24no—
35C29×#392—28no—
36C29×#392—24no—
37C2×C29×#95C2211yescharacteristic
38C2×C29×#95C2211yescharacteristic
39C2×C29×#95C2212yes—
40C2×C29×#95C2212yes—
41C2×C29×#95C2212yes—
42C2×C29×#95C2212yes—
43C25×C29C2311yescharacteristic
44C25×C29C2312yes—
45C25×C29C2311yescharacteristic
46C22×D4×C29—24no—
47C22×D4×C29—24no—
48C22×D4×C29—24no—
49C22×D4×C29—22no—
50C22×D4×C29—22no—
51C22×D4×C29—24no—
52C22×D4×C29—24no—
53C22×D4×C29—24no—
54C22×D4×C29—22no—
55C22×D4×C29—22no—
56C22×D4×C29—22no—
57C22×D4×C29—22no—
58C22×D4×C29—24no—
59C22×D4×C29—42no—
60C22×D4×C29—42no—
61C22×D4×C29—42no—
62C22×D4×C29—42no—
63C22×D4×C29—42no—
64C22×D4×C29—42no—
65C22×D4×C29—42no—
66C22×D4×C29—42no—
67C22×D4×C29—42no—
68C22×D4×C29—42no—
69C22×D4×C29D418yescomplemented
70C23×C4×C29—24no—
71C23×C4×C29—22no—
72C23×C4×C29—22no—
73C23×C4×C29—42no—
74C23×C4×C29D414yescomplemented
75C23×C4×C29C2312yes—
76C23×C4×C29C2311yescharacteristic
77C23×C4×C29C2311yescharacteristic
78C23×C4×C29C2311yescharacteristic
79C23×C4×C29C2311yescharacteristic
80C23×C4×C29C2312yes—
81C23×C4×C29C2312yes—
82C23×C4×C29C2311yescharacteristic
83C29×#123—232no—
84C29×#121—232no—
85C2×C4⋊C4×C29—24no—
86C2×C4⋊C4×C29—22no—
87C2×C4⋊C4×C29—22no—
88C2×C4⋊C4×C29—22no—
89C2×C4⋊C4×C29—22no—
90C2×C4⋊C4×C29—22no—
91C2×C4⋊C4×C29—22no—
92C2×C4⋊C4×C29D414yescomplemented
93C2×C22⋊C4×C29—24no—
94C2×C22⋊C4×C29—22no—
95C2×C22⋊C4×C29—22no—
96C2×C22⋊C4×C29—24no—
97C2×C22⋊C4×C29—24no—
98C2×C22⋊C4×C29—22no—
99C2×C22⋊C4×C29—22no—
100C2×C22⋊C4×C29—22no—
101C2×C22⋊C4×C29—22no—
102C2×C22⋊C4×C29—22no—
103C2×C22⋊C4×C29—22no—
104C2×C22⋊C4×C29—24no—
105C2×C22⋊C4×C29—24no—
106C2×C22⋊C4×C29—24no—
107C2×C22⋊C4×C29—24no—
108C2×C22⋊C4×C29—24no—
109C2×C22⋊C4×C29—24no—
110C2×C22⋊C4×C29—24no—
111C2×C22⋊C4×C29—24no—
112C2×C22⋊C4×C29—42no—
113C2×C22⋊C4×C29—42no—
114C2×C22⋊C4×C29—42no—
115C2×C22⋊C4×C29—42no—
116C2×C22⋊C4×C29—42no—
117C2×C22⋊C4×C29—42no—
118C2×C22⋊C4×C29—42no—
119C2×C22⋊C4×C29D414yescomplemented
120C29×#95—24no—
121C29×#95—22no—
122C29×#95—22no—
123C29×#95—42no—
124C29×#95—42no—
125C29×#95—42no—
126C24×C29—21no—
127C24×C29—21no—
128C24×C29—22no—
129C24×C29—21no—
130C24×C29—22no—
131C24×C29—21no—
132C24×C29—21no—
133C24×C29—22no—
134C24×C29—21no—
135C24×C29—21no—
136C24×C29—21no—
137C24×C29—22no—
138C24×C29—22no—
139C24×C29—22no—
140C24×C29—22no—
141C24×C29—22no—
142C24×C29—22no—
143C24×C29—22no—
144C24×C29—22no—
145C24×C29—21no—
146C24×C29—22no—
147C24×C29—22no—
148C24×C29—22no—
149C24×C29—22no—
150C24×C29—22no—
151C24×C29—22no—
152C24×C29—22no—
153C24×C29—21no—
154C24×C29—21no—
155C24×C29—22no—
156C24×C29—22no—
157C24×C29—21no—
158C24×C29—22no—
159C24×C29C2×D414yes—
160C24×C29C2×D412yes—
161C24×C29C2×D414yes—
162C24×C29C2×D412yes—
163C24×C29C2411yescharacteristic
164C2×D4×C29—28no—
165C2×D4×C29—28no—
166C2×D4×C29—216no—
167C2×D4×C29—48no—
168C2×D4×C29—48no—
169C2×D4×C29—48no—
170C2×D4×C29—48no—
171C2×D4×C29—48no—
172C2×D4×C29—48no—
173C2×D4×C29—48no—
174C2×D4×C29—44no—
175C2×D4×C29—48no—
176C2×D4×C29—48no—
177C2×D4×C29—48no—
178C2×D4×C29—44no—
179C2×D4×C29—48no—
180C2×D4×C29—48no—
181C2×D4×C29—48no—
182C2×D4×C29—48no—
183C2×D4×C29—48no—
184C2×D4×C29—48no—
185C2×D4×C29—48no—
186C2×D4×C29—44no—
187C2×D4×C29—44no—
188C22×C4×C29—22no—
189C22×C4×C29—22no—
190C22×C4×C29—28no—
191C22×C4×C29—21no—
192C22×C4×C29—21no—
193C22×C4×C29—21no—
194C22×C4×C29—21no—
195C22×C4×C29—22no—
196C22×C4×C29—21no—
197C22×C4×C29—21no—
198C22×C4×C29—22no—
199C22×C4×C29—22no—
200C22×C4×C29—22no—
201C22×C4×C29—22no—
202C22×C4×C29—22no—
203C22×C4×C29—21no—
204C22×C4×C29—21no—
205C22×C4×C29—22no—
206C22×C4×C29—21no—
207C22×C4×C29—21no—
208C22×C4×C29—22no—
209C22×C4×C29—22no—
210C22×C4×C29—22no—
211C22×C4×C29—22no—
212C22×C4×C29—22no—
213C22×C4×C29—22no—
214C22×C4×C29—22no—
215C22×C4×C29—22no—
216C22×C4×C29—22no—
217C22×C4×C29—22no—
218C22×C4×C29—22no—
219C22×C4×C29—21no—
220C22×C4×C29—21no—
221C22×C4×C29—28no—
222C22×C4×C29—22no—
223C22×C4×C29—22no—
224C22×C4×C29—22no—
225C22×C4×C29—22no—
226C22×C4×C29—22no—
227C22×C4×C29—22no—
228C22×C4×C29—22no—
229C22×C4×C29—44no—
230C22×C4×C29—48no—
231C22×C4×C29—48no—
232C22×C4×C29C2×D412yes—
233C22×C4×C29C2×D412yes—
234C22×C4×C29C2×D412yes—
235C22×C4×C29C2×D412yes—
236C22×C4×C29C2×D414yes—
237C22×C4×C29C2×D412yes—
238C22×C4×C29C2×D412yes—
239C22×C4×C29C2×D412yes—
240C22×C4×C29#4114yes—
241C4⋊C4×C29—28no—
242C4⋊C4×C29—28no—
243C4⋊C4×C29—28no—
244C22⋊C4×C29—216no—
245C22⋊C4×C29—28no—
246C22⋊C4×C29—28no—
247C22⋊C4×C29—28no—
248C22⋊C4×C29—48no—
249C22⋊C4×C29—48no—
250C22⋊C4×C29—48no—
251C22⋊C4×C29—48no—
252C22⋊C4×C29—48no—
253#16250C2911yesmaximal, characteristic, direct product factor, Sylow
254C23×C29—22no—
255C23×C29—22no—
256C23×C29—22no—
257C23×C29—24no—
258C23×C29—24no—
259C23×C29—22no—
260C23×C29—22no—
261C23×C29—22no—
262C23×C29—24no—
263C23×C29—24no—
264C23×C29—24no—
265C23×C29—24no—
266C23×C29—22no—
267C23×C29—24no—
268C23×C29—24no—
269C23×C29—24no—
270C23×C29—22no—
271C23×C29—22no—
272C23×C29—24no—
273C23×C29—24no—
274C23×C29—24no—
275C23×C29—24no—
276C23×C29—24no—
277C23×C29—24no—
278C23×C29—41no—
279C23×C29—41no—
280C23×C29—41no—
281C23×C29—41no—
282C23×C29—42no—
283C23×C29—42no—
284C23×C29—42no—
285C23×C29—42no—
286C23×C29—42no—
287C23×C29—42no—
288C23×C29—41no—
289C23×C29—42no—
290C23×C29—42no—
291C23×C29—41no—
292C23×C29—42no—
293C23×C29—42no—
294C23×C29—42no—
295C23×C29—42no—
296C23×C29—41no—
297C23×C29—42no—
298C23×C29—42no—
299C23×C29—42no—
300C23×C29—42no—
301C23×C29—42no—
302C23×C29—41no—
303C23×C29—41no—
304C23×C29—41no—
305C23×C29—41no—
306C23×C29—41no—
307C23×C29—42no—
308C23×C29—42no—
309C23×C29—42no—
310C23×C29—42no—
311C23×C29—42no—
312C23×C29—42no—
313C23×C29—42no—
314C23×C29—42no—
315C23×C29—42no—
316C23×C29—42no—
317C23×C29—42no—
318C23×C29—42no—
319C23×C29—42no—
320C23×C29—42no—
321C23×C29—42no—
322C23×C29—42no—
323C23×C29—42no—
324C23×C29—42no—
325C23×C29—42no—
326C23×C29—42no—
327C23×C29—42no—
328C23×C29—42no—
329C23×C29—42no—
330C23×C29—42no—
331C23×C29—42no—
332C23×C29—42no—
333C23×C29—42no—
334C23×C29#12014yes—
335C23×C29C22×D411yescharacteristic
336C23×C29C22×D412yes—
337C23×C29C22×D411yescharacteristic
338C23×C29C22×D411yescharacteristic
339C23×C29C2×#4112yes—
340C23×C29H(5,𝔽2)11yescharacteristic
341C23×C29H(5,𝔽2)11yescharacteristic
342C23×C29H(5,𝔽2)12yes—
343C23×C29H(5,𝔽2)12yes—
344C23×C29H(5,𝔽2)11yescharacteristic
345C23×C292−1+411yescharacteristic
346D4×C29—416no—
347D4×C29—432no—
348D4×C29—416no—
349D4×C29—432no—
350C2×C4×C29—22no—
351C2×C4×C29—22no—
352C2×C4×C29—24no—
353C2×C4×C29—24no—
354C2×C4×C29—22no—
355C2×C4×C29—22no—
356C2×C4×C29—22no—
357C2×C4×C29—22no—
358C2×C4×C29—24no—
359C2×C4×C29—22no—
360C2×C4×C29—24no—
361C2×C4×C29—22no—
362C2×C4×C29—24no—
363C2×C4×C29—22no—
364C2×C4×C29—22no—
365C2×C4×C29—24no—
366C2×C4×C29—24no—
367C2×C4×C29—24no—
368C2×C4×C29—24no—
369C2×C4×C29—24no—
370C2×C4×C29—416no—
371C2×C4×C29—41no—
372C2×C4×C29—41no—
373C2×C4×C29—42no—
374C2×C4×C29—42no—
375C2×C4×C29—41no—
376C2×C4×C29—42no—
377C2×C4×C29—41no—
378C2×C4×C29—41no—
379C2×C4×C29—41no—
380C2×C4×C29—42no—
381C2×C4×C29—42no—
382C2×C4×C29—42no—
383C2×C4×C29—41no—
384C2×C4×C29—41no—
385C2×C4×C29—42no—
386C2×C4×C29—42no—
387C2×C4×C29—42no—
388C2×C4×C29—42no—
389C2×C4×C29—42no—
390C2×C4×C29—42no—
391C2×C4×C29—42no—
392C2×C4×C29—42no—
393C2×C4×C29—42no—
394C2×C4×C29—42no—
395C2×C4×C29—42no—
396C2×C4×C29—42no—
397C2×C4×C29—42no—
398C2×C4×C29#12014yes—
399C22×#123C2×C2911yescharacteristic, complemented
400C22×#121C2×C2911yescharacteristic, complemented
401C2×#394C2×C2911yescharacteristic, complemented
402C2×#392C2×C2912yescomplemented
403C2×#392C2×C2911yescharacteristic, complemented
404#1441C2×C2911yescharacteristic, complemented
405#1439C2×C2912yescomplemented
406#1439C2×C2911yescharacteristic, complemented
407#1438C2×C2912yescomplemented
408#1438C2×C2912yescomplemented
409C22⋊#95C2×C2911yescharacteristic, complemented
410C22×C29—24no—
411C22×C29—24no—
412C22×C29—24no—
413C22×C29—42no—
414C22×C29—42no—
415C22×C29—44no—
416C22×C29—44no—
417C22×C29—44no—
418C22×C29—44no—
419C22×C29—42no—
420C22×C29—42no—
421C22×C29—44no—
422C22×C29—42no—
423C22×C29—44no—
424C22×C29—42no—
425C22×C29—44no—
426C22×C29—44no—
427C22×C29—44no—
428C22×C29—44no—
429C22×C29—44no—
430C22×C29—44no—
431C22×C29—44no—
432C22×C29—42no—
433C22×C29—81no—
434C22×C29—82no—
435C22×C29—82no—
436C22×C29—81no—
437C22×C29—82no—
438C22×C29—82no—
439C22×C29—82no—
440C22×C29—82no—
441C22×C29—82no—
442C22×C29—82no—
443C22×C29—81no—
444C22×C29—82no—
445C22×C29—82no—
446C22×C29—81no—
447C22×C29C2×#12011yescharacteristic
448C22×C29C2×#12011yescharacteristic
449C22×C29#53211yescharacteristic
450C22×C29#53412yes—
451C22×C29#53412yes—
452C22×C29#53411yescharacteristic
453C22×C29#53511yescharacteristic
454C22×C29#53511yescharacteristic
455C22×C29#53511yescharacteristic
456C22×C29#53511yescharacteristic
457C22×C29#53711yescharacteristic
458C22×C29#53711yescharacteristic
459C22×C29#53711yescharacteristic
460C22×C29#53812yes—
461C22×C29#54012yes—
462C22×C29D4212yes—
463C22×C29D4212yes—
464C22×C29#54612yes—
465C22×C29#54612yes—
466C22×C29#54712yes—
467C22×C29#55012yes—
468C22×C29#56012yes—
469C22×C29#56212yes—
470C4×C29—24no—
471C4×C29—44no—
472C4×C29—42no—
473C4×C29—42no—
474C4×C29—42no—
475C4×C29—44no—
476C4×C29—42no—
477C4×C29—82no—
478C23×D4C22×C2911yescharacteristic
479C23×D4C22×C2911yescharacteristic
480C23×D4C22×C2912yes—
481C23×D4C22×C2912yes—
482C24×C4C22×C2911yescharacteristic
483C2×#123—24no—
484C2×#123—24no—
485C2×#123—24no—
486C2×#121—28no—
487C2×#121—24no—
488C22×C4⋊C4C22×C2911yescharacteristic
489C22×C4⋊C4C22×C2911yescharacteristic
490C22×C4⋊C4C22×C2911yescharacteristic
491C22×C22⋊C4C22×C2912yes—
492C22×C22⋊C4C22×C2911yescharacteristic
493C22×C22⋊C4C22×C2911yescharacteristic
494C22×C22⋊C4C22×C2912yes—
495C22×C22⋊C4C22×C2912yes—
496C22×C22⋊C4C22×C2912yes—
497C22×C22⋊C4C22×C2911yescharacteristic
498C22×C22⋊C4C22×C2912yes—
499C22×C22⋊C4C22×C2912yes—
500#394—24no—
501#392—28no—
502#392—24no—
503C2×#95C22×C2911yescharacteristic
504C2×#95C22×C2912yes—
505C2×#95C22×C2911yescharacteristic
506C2×#95C22×C2912yes—
507C2×#95C22×C2912yes—
508C2×#95C22×C2912yes—
509C2×C29—44no—
510C2×C29—84no—
511C2×C29—82no—
512C2×C29#240311yescharacteristic
513C2×C29#243011yescharacteristic
514C2×C29#243111yescharacteristic
515C2×C29#261311yescharacteristic
516C2×C29#261511yescharacteristic
517C2×C29#266111yescharacteristic
518C2×C29#267112yes—
519C2×C29#267312yes—
520C2×C29#267812yes—
521C2×C29#268212yes—
522C2×C29#281311yescharacteristic
523C25C23×C2911yescharacteristic
524C25C23×C2912yes—
525C25C23×C2911yescharacteristic
526C22×D4—24no—
527C22×D4—24no—
528C22×D4—24no—
529C22×D4—22no—
530C22×D4—22no—
531C22×D4—24no—
532C22×D4—24no—
533C22×D4—24no—
534C22×D4—22no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—24no—
539C22×D4—42no—
540C22×D4—42no—
541C22×D4—42no—
542C22×D4—42no—
543C22×D4—42no—
544C22×D4—42no—
545C22×D4—42no—
546C22×D4—42no—
547C22×D4—42no—
548C22×D4—42no—
549C22×D4D4×C2918yescomplemented
550C23×C4—24no—
551C23×C4—22no—
552C23×C4—22no—
553C23×C4—42no—
554C23×C4D4×C2914yescomplemented
555C23×C4C23×C2912yes—
556C23×C4C23×C2911yescharacteristic
557C23×C4C23×C2911yescharacteristic
558C23×C4C23×C2911yescharacteristic
559C23×C4C23×C2911yescharacteristic
560C23×C4C23×C2912yes—
561C23×C4C23×C2912yes—
562C23×C4C23×C2911yescharacteristic
563#123—232no—
564#121—232no—
565C2×C4⋊C4—24no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4D4×C2914yescomplemented
573C2×C22⋊C4—24no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—24no—
587C2×C22⋊C4—24no—
588C2×C22⋊C4—24no—
589C2×C22⋊C4—24no—
590C2×C22⋊C4—24no—
591C2×C22⋊C4—24no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4—42no—
596C2×C22⋊C4—42no—
597C2×C22⋊C4—42no—
598C2×C22⋊C4—42no—
599C2×C22⋊C4D4×C2914yescomplemented
600#95—24no—
601#95—22no—
602#95—22no—
603#95—42no—
604#95—42no—
605#95—42no—
606C29#1625011yescharacteristic, direct product factor, Sylow
607C24—21no—
608C24—21no—
609C24—22no—
610C24—21no—
611C24—22no—
612C24—21no—
613C24—21no—
614C24—22no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—21no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—21no—
635C24—21no—
636C24—22no—
637C24—22no—
638C24—21no—
639C24—22no—
640C24C2×D4×C2914yes—
641C24C2×D4×C2912yes—
642C24C2×D4×C2914yes—
643C24C2×D4×C2912yes—
644C24C24×C2911yescharacteristic
645C2×D4—28no—
646C2×D4—28no—
647C2×D4—216no—
648C2×D4—48no—
649C2×D4—48no—
650C2×D4—48no—
651C2×D4—48no—
652C2×D4—48no—
653C2×D4—48no—
654C2×D4—48no—
655C2×D4—44no—
656C2×D4—48no—
657C2×D4—48no—
658C2×D4—48no—
659C2×D4—44no—
660C2×D4—48no—
661C2×D4—48no—
662C2×D4—48no—
663C2×D4—48no—
664C2×D4—48no—
665C2×D4—48no—
666C2×D4—48no—
667C2×D4—44no—
668C2×D4—44no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—28no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—22no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—21no—
702C22×C4—28no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—44no—
711C22×C4—48no—
712C22×C4—48no—
713C22×C4C2×D4×C2914yes—
714C22×C4C2×D4×C2912yes—
715C22×C4C2×D4×C2912yes—
716C22×C4C2×D4×C2912yes—
717C22×C4C2×D4×C2912yes—
718C22×C4C2×D4×C2912yes—
719C22×C4C2×D4×C2912yes—
720C22×C4C2×D4×C2912yes—
721C22×C4#41×C2914yes—
722C4⋊C4—28no—
723C4⋊C4—28no—
724C4⋊C4—28no—
725C22⋊C4—216no—
726C22⋊C4—28no—
727C22⋊C4—28no—
728C22⋊C4—28no—
729C22⋊C4—48no—
730C22⋊C4—48no—
731C22⋊C4—48no—
732C22⋊C4—48no—
733C22⋊C4—48no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—24no—
738C23—24no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23—24no—
746C23—22no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—22no—
751C23—22no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—41no—
769C23—42no—
770C23—42no—
771C23—41no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—41no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23C29×#12014yes—
815C23C22×D4×C2911yescharacteristic
816C23C22×D4×C2912yes—
817C23C22×D4×C2911yescharacteristic
818C23C22×D4×C2911yescharacteristic
819C23C2×#41×C2912yes—
820C23C29×H(5,𝔽2)11yescharacteristic
821C23C29×H(5,𝔽2)11yescharacteristic
822C23C29×H(5,𝔽2)12yes—
823C23C29×H(5,𝔽2)12yes—
824C23C29×H(5,𝔽2)11yescharacteristic
825C23C29×2−1+411yescharacteristic
826D4—416no—
827D4—432no—
828D4—416no—
829D4—432no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—24no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—416no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4C29×#12014yes—
879C22—24no—
880C22—24no—
881C22—24no—
882C22—44no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—44no—
891C22—44no—
892C22—44no—
893C22—44no—
894C22—44no—
895C22—44no—
896C22—44no—
897C22—42no—
898C22—44no—
899C22—42no—
900C22—44no—
901C22—42no—
902C22—82no—
903C22—82no—
904C22—82no—
905C22—82no—
906C22—82no—
907C22—82no—
908C22—81no—
909C22—82no—
910C22—82no—
911C22—81no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—81no—
916C22C2×C29×#12011yescharacteristic
917C22C2×C29×#12011yescharacteristic
918C22C29×#53211yescharacteristic
919C22C29×#53412yes—
920C22C29×#53412yes—
921C22C29×#53411yescharacteristic
922C22C29×#53511yescharacteristic
923C22C29×#53511yescharacteristic
924C22C29×#53511yescharacteristic
925C22C29×#53511yescharacteristic
926C22C29×#53711yescharacteristic
927C22C29×#53711yescharacteristic
928C22C29×#53711yescharacteristic
929C22C29×#53812yes—
930C22C29×#54012yes—
931C22D42×C2912yes—
932C22D42×C2912yes—
933C22C29×#54612yes—
934C22C29×#54612yes—
935C22C29×#54712yes—
936C22C29×#55012yes—
937C22C29×#56012yes—
938C22C29×#56212yes—
939C4—24no—
940C4—44no—
941C4—42no—
942C4—44no—
943C4—42no—
944C4—42no—
945C4—42no—
946C4—82no—
947C2—44no—
948C2—82no—
949C2—84no—
950C2C29×#240311yescharacteristic
951C2C29×#243011yescharacteristic
952C2C29×#243111yescharacteristic
953C2C29×#261311yescharacteristic
954C2C29×#261511yescharacteristic
955C2C29×#266111yescharacteristic
956C2C29×#267112yes—
957C2C29×#267312yes—
958C2C29×#267812yes—
959C2C29×#268212yes—
960C2C29×#281311yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutator, Frattini, cosocleC24C24×C29
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C29×#123C2semidirect
2. C22×C29×#121C2semidirect
3. C2×C29×#394C2semidirect
4. C2×C29×#392C2semidirect
5. C2×C29×#392C2semidirect
6. C29×#1441C2semidirect
7. C29×#1439C2semidirect
8. C29×#1439C2semidirect
9. C29×#1438C2semidirect
10. C29×#1438C2semidirect
11. C29×C22⋊#95C2semidirect
69. C22×D4×C29D4semidirect
74. C23×C4×C29D4semidirect
92. C2×C4⋊C4×C29D4semidirect
119. C2×C22⋊C4×C29D4semidirect
253. #16250C29direct (N × H)
399. C22×#123C2×C29semidirect
400. C22×#121C2×C29semidirect
401. C2×#394C2×C29semidirect
402. C2×#392C2×C29semidirect
403. C2×#392C2×C29semidirect
404. #1441C2×C29semidirect
405. #1439C2×C29semidirect
406. #1439C2×C29semidirect
407. #1438C2×C29semidirect
408. #1438C2×C29semidirect
409. C22⋊#95C2×C29semidirect
549. C22×D4D4×C29semidirect
554. C23×C4D4×C29semidirect
572. C2×C4⋊C4D4×C29semidirect
599. C2×C22⋊C4D4×C29semidirect
606. C29#16250direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C29×#1232
C22×C29×#1212
C2×C29×#3942
C2×C29×#3922
C29×#14412
C29×#14392
C29×#14382
C29×C22⋊#952
#1625029