Finite Group Databasebeta

← C29×#14824 #20309724

Subgroups — C29×#14824 #20309724

Order 7424.

2238 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C29C211yesmaximal, characteristic
2C2×C29×#398C211yesmaximal, characteristic, complemented
3C2×C29×#397C211yesmaximal, characteristic, complemented
4C2×C29×#394C212yesmaximal
5C2×C29×#380C211yesmaximal, characteristic, complemented
6C29×#1441C211yesmaximal, characteristic, complemented
7C29×#1440C212yesmaximal, complemented
8C29×#1439C211yesmaximal, characteristic, complemented
9C29×#1436C212yesmaximal, complemented
10C29×C22⋊#95C212yesmaximal, complemented
11C29×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C29C2211yescharacteristic
13C24×C4×C29C2211yescharacteristic
14C24×C4×C29C2211yescharacteristic
15C2×C4×D4×C29—24no—
16C2×C4×D4×C29—24no—
17C2×C4×D4×C29—24no—
18C22×C4⋊C4×C29C2212yes—
19C22×C4⋊C4×C29C2211yescharacteristic
20C22×C4⋊C4×C29C2211yescharacteristic
21C22×C4⋊C4×C29C2211yescharacteristic
22C22×C22⋊C4×C29C2212yes—
23C22×C22⋊C4×C29C2211yescharacteristic
24C22×C22⋊C4×C29C2212yes—
25C22×C22⋊C4×C29C2212yes—
26C22×C22⋊C4×C29C2212yes—
27C22×C22⋊C4×C29C2211yescharacteristic
28C22×C42×C29C2211yescharacteristic
29C29×#398—24no—
30C29×#397—24no—
31C29×#394—28no—
32C29×#380—24no—
33C2×C29×#95C2212yes—
34C2×C29×#95C2212yes—
35C2×C29×#95C2211yescharacteristic
36C2×C29×#95C2212yes—
37C2×C29×#95C2211yescharacteristic
38C2×C29×#95C2212yes—
39C2×C29×#95C2212yes—
40C2×C29×#95C2212yes—
41C2×C29×#95C2212yes—
42C25×C29C2311yescharacteristic
43C25×C29C2311yescharacteristic
44C22×D4×C29—22no—
45C22×D4×C29—22no—
46C22×D4×C29—22no—
47C22×D4×C29—22no—
48C22×D4×C29—22no—
49C22×D4×C29—22no—
50C22×D4×C29D414yes—
51C23×C4×C29—22no—
52C23×C4×C29—22no—
53C23×C4×C29—22no—
54C23×C4×C29—22no—
55C23×C4×C29—22no—
56C23×C4×C29—24no—
57C23×C4×C29—24no—
58C23×C4×C29—42no—
59C23×C4×C29—42no—
60C23×C4×C29D414yes—
61C23×C4×C29C2312yes—
62C23×C4×C29C2312yes—
63C23×C4×C29C2312yes—
64C23×C4×C29C2311yescharacteristic
65C23×C4×C29C2311yescharacteristic
66C23×C4×C29C2312yes—
67C23×C4×C29C2311yescharacteristic
68C23×C4×C29C2311yescharacteristic
69C23×C4×C29C2311yescharacteristic
70C4×D4×C29—232no—
71C2×C4⋊C4×C29—22no—
72C2×C4⋊C4×C29—22no—
73C2×C4⋊C4×C29—22no—
74C2×C4⋊C4×C29—22no—
75C2×C4⋊C4×C29—24no—
76C2×C4⋊C4×C29—22no—
77C2×C4⋊C4×C29—22no—
78C2×C4⋊C4×C29—24no—
79C2×C4⋊C4×C29—24no—
80C2×C4⋊C4×C29—42no—
81C2×C4⋊C4×C29D414yes—
82C2×C22⋊C4×C29—22no—
83C2×C22⋊C4×C29—22no—
84C2×C22⋊C4×C29—22no—
85C2×C22⋊C4×C29—22no—
86C2×C22⋊C4×C29—22no—
87C2×C22⋊C4×C29—24no—
88C2×C22⋊C4×C29—24no—
89C2×C22⋊C4×C29—24no—
90C2×C22⋊C4×C29—24no—
91C2×C22⋊C4×C29—24no—
92C2×C22⋊C4×C29—24no—
93C2×C22⋊C4×C29—24no—
94C2×C22⋊C4×C29—24no—
95C2×C22⋊C4×C29—24no—
96C2×C22⋊C4×C29—24no—
97C2×C22⋊C4×C29—42no—
98C2×C22⋊C4×C29—42no—
99C2×C22⋊C4×C29D414yes—
100C2×C42×C29—22no—
101C2×C42×C29—22no—
102C2×C42×C29—22no—
103C29×#95—24no—
104C29×#95—24no—
105C29×#95—24no—
106C29×#95—22no—
107C29×#95—22no—
108C29×#95—24no—
109C29×#95—24no—
110C29×#95—24no—
111C29×#95—42no—
112C24×C29—21no—
113C24×C29—21no—
114C24×C29—21no—
115C24×C29—21no—
116C24×C29—22no—
117C24×C29—22no—
118C24×C29—22no—
119C24×C29—22no—
120C24×C29—21no—
121C24×C29—21no—
122C24×C29—21no—
123C24×C29—21no—
124C24×C29—22no—
125C24×C29—22no—
126C24×C29—22no—
127C24×C29—22no—
128C24×C29C2×D412yes—
129C24×C29C2×D412yes—
130C24×C29C2×D412yes—
131C24×C29C2×D412yes—
132C24×C29#4112yes—
133C24×C29#4112yes—
134C24×C29C2411yescharacteristic
135C2×D4×C29—28no—
136C2×D4×C29—28no—
137C2×D4×C29—28no—
138C2×D4×C29—28no—
139C2×D4×C29—28no—
140C2×D4×C29—28no—
141C2×D4×C29—28no—
142C22×C4×C29—21no—
143C22×C4×C29—21no—
144C22×C4×C29—21no—
145C22×C4×C29—21no—
146C22×C4×C29—22no—
147C22×C4×C29—21no—
148C22×C4×C29—21no—
149C22×C4×C29—22no—
150C22×C4×C29—22no—
151C22×C4×C29—28no—
152C22×C4×C29—21no—
153C22×C4×C29—21no—
154C22×C4×C29—22no—
155C22×C4×C29—21no—
156C22×C4×C29—21no—
157C22×C4×C29—22no—
158C22×C4×C29—22no—
159C22×C4×C29—22no—
160C22×C4×C29—22no—
161C22×C4×C29—22no—
162C22×C4×C29—22no—
163C22×C4×C29—22no—
164C22×C4×C29—22no—
165C22×C4×C29—22no—
166C22×C4×C29—28no—
167C22×C4×C29—28no—
168C22×C4×C29—22no—
169C22×C4×C29—22no—
170C22×C4×C29—22no—
171C22×C4×C29—22no—
172C22×C4×C29—22no—
173C22×C4×C29—22no—
174C22×C4×C29—22no—
175C22×C4×C29—22no—
176C22×C4×C29—22no—
177C22×C4×C29—22no—
178C22×C4×C29—22no—
179C22×C4×C29—22no—
180C22×C4×C29—22no—
181C22×C4×C29—22no—
182C22×C4×C29—22no—
183C22×C4×C29—22no—
184C22×C4×C29—22no—
185C22×C4×C29—22no—
186C22×C4×C29—22no—
187C22×C4×C29—22no—
188C22×C4×C29—22no—
189C22×C4×C29—44no—
190C22×C4×C29—48no—
191C22×C4×C29—48no—
192C22×C4×C29—48no—
193C22×C4×C29—48no—
194C22×C4×C29—44no—
195C22×C4×C29—44no—
196C22×C4×C29C2×D412yes—
197C22×C4×C29C2×D412yes—
198C22×C4×C29C2×D412yes—
199C22×C4×C29C2×D412yes—
200C22×C4×C29C2×D412yes—
201C22×C4×C29C2×D412yes—
202C22×C4×C29C2×D412yes—
203C22×C4×C29C2×D412yes—
204C22×C4×C29#4114yes—
205C22×C4×C29#4112yes—
206C22×C4×C29#4114yes—
207C4⋊C4×C29—28no—
208C4⋊C4×C29—44no—
209C4⋊C4×C29—44no—
210C4⋊C4×C29—48no—
211C22⋊C4×C29—28no—
212C22⋊C4×C29—28no—
213C22⋊C4×C29—48no—
214C22⋊C4×C29—48no—
215C22⋊C4×C29—48no—
216C22⋊C4×C29—48no—
217C42×C29—28no—
218#14824C2911yesmaximal, characteristic, direct product factor, Sylow
219C23×C29—22no—
220C23×C29—22no—
221C23×C29—22no—
222C23×C29—22no—
223C23×C29—22no—
224C23×C29—22no—
225C23×C29—22no—
226C23×C29—22no—
227C23×C29—22no—
228C23×C29—22no—
229C23×C29—22no—
230C23×C29—22no—
231C23×C29—22no—
232C23×C29—24no—
233C23×C29—22no—
234C23×C29—22no—
235C23×C29—22no—
236C23×C29—24no—
237C23×C29—24no—
238C23×C29—24no—
239C23×C29—24no—
240C23×C29—24no—
241C23×C29—24no—
242C23×C29—24no—
243C23×C29—24no—
244C23×C29—24no—
245C23×C29—41no—
246C23×C29—42no—
247C23×C29—42no—
248C23×C29—42no—
249C23×C29—41no—
250C23×C29—41no—
251C23×C29—41no—
252C23×C29—42no—
253C23×C29—42no—
254C23×C29—42no—
255C23×C29—42no—
256C23×C29—42no—
257C23×C29—42no—
258C23×C29—42no—
259C23×C29—42no—
260C23×C29—42no—
261C23×C29—42no—
262C23×C29—42no—
263C23×C29#12114yes—
264C23×C29#12114yes—
265C23×C29C22×D411yescharacteristic
266C23×C29C22×D411yescharacteristic
267C23×C29C22×D411yescharacteristic
268C23×C29C22×D411yescharacteristic
269C23×C29C2×#4111yescharacteristic
270C23×C29C2×#4111yescharacteristic
271C23×C29C2×#4111yescharacteristic
272C23×C29C2×#4112yes—
273C23×C29C2×#4112yes—
274C23×C29H(5,𝔽2)12yes—
275C23×C292−1+412yes—
276D4×C29—232no—
277C2×C4×C29—22no—
278C2×C4×C29—22no—
279C2×C4×C29—22no—
280C2×C4×C29—22no—
281C2×C4×C29—22no—
282C2×C4×C29—22no—
283C2×C4×C29—22no—
284C2×C4×C29—22no—
285C2×C4×C29—22no—
286C2×C4×C29—22no—
287C2×C4×C29—24no—
288C2×C4×C29—24no—
289C2×C4×C29—24no—
290C2×C4×C29—24no—
291C2×C4×C29—22no—
292C2×C4×C29—22no—
293C2×C4×C29—24no—
294C2×C4×C29—24no—
295C2×C4×C29—24no—
296C2×C4×C29—24no—
297C2×C4×C29—24no—
298C2×C4×C29—416no—
299C2×C4×C29—416no—
300C2×C4×C29—42no—
301C2×C4×C29—41no—
302C2×C4×C29—41no—
303C2×C4×C29—41no—
304C2×C4×C29—41no—
305C2×C4×C29—42no—
306C2×C4×C29—42no—
307C2×C4×C29—42no—
308C2×C4×C29—42no—
309C2×C4×C29—42no—
310C2×C4×C29—42no—
311C2×C4×C29—42no—
312C2×C4×C29—42no—
313C2×C4×C29—42no—
314C2×C4×C29—42no—
315C2×C4×C29—42no—
316C2×C4×C29—42no—
317C2×C4×C29—42no—
318C2×C4×C29—42no—
319C2×C4×C29—42no—
320C2×C4×C29—42no—
321C2×C4×C29—42no—
322C2×C4×C29—42no—
323C2×C4×C29—42no—
324C2×C4×C29—42no—
325C2×C4×C29—42no—
326C2×C4×C29—42no—
327C2×C4×C29—42no—
328C2×C4×C29—42no—
329C2×C4×C29—42no—
330C2×C4×C29—42no—
331C2×C4×C29#12014yes—
332C2×C4×C29#12114yes—
333C2×C4×C29#12314yes—
334C22×C4×D4C2×C2911yescharacteristic
335C2×#398C2×C2911yescharacteristic, complemented
336C2×#397C2×C2911yescharacteristic, complemented
337C2×#394C2×C2912yes—
338C2×#380C2×C2911yescharacteristic, complemented
339#1441C2×C2911yescharacteristic, complemented
340#1440C2×C2912yescomplemented
341#1439C2×C2911yescharacteristic, complemented
342#1436C2×C2912yescomplemented
343C22⋊#95C2×C2912yescomplemented
344C22⋊#95C2×C2911yescharacteristic, complemented
345C22×C29—24no—
346C22×C29—24no—
347C22×C29—28no—
348C22×C29—24no—
349C22×C29—24no—
350C22×C29—42no—
351C22×C29—42no—
352C22×C29—42no—
353C22×C29—42no—
354C22×C29—42no—
355C22×C29—42no—
356C22×C29—44no—
357C22×C29—44no—
358C22×C29—44no—
359C22×C29—42no—
360C22×C29—42no—
361C22×C29—44no—
362C22×C29—44no—
363C22×C29—44no—
364C22×C29—44no—
365C22×C29—42no—
366C22×C29—42no—
367C22×C29C2×#12011yescharacteristic
368C22×C29C2×#12111yescharacteristic
369C22×C29C2×#12111yescharacteristic
370C22×C29C2×#12111yescharacteristic
371C22×C29C2×#12311yescharacteristic
372C22×C29#52511yescharacteristic
373C22×C29#52511yescharacteristic
374C22×C29#52511yescharacteristic
375C22×C29#52912yes—
376C22×C29#52912yes—
377C22×C29#53211yescharacteristic
378C22×C29#53411yescharacteristic
379C22×C29#53611yescharacteristic
380C22×C29#53912yes—
381C22×C29#54212yes—
382C22×C29#54612yes—
383C22×C29#54612yes—
384C22×C29#54612yes—
385C22×C29#54712yes—
386C22×C29#54712yes—
387C22×C29#54812yes—
388C22×C29#55212yes—
389C22×C29#55312yes—
390C4×C29—24no—
391C4×C29—24no—
392C4×C29—24no—
393C4×C29—42no—
394C4×C29—44no—
395C4×C29—42no—
396C4×C29—82no—
397C4×C29—82no—
398C4×C29—82no—
399C23×D4C22×C2911yescharacteristic
400C24×C4C22×C2911yescharacteristic
401C24×C4C22×C2911yescharacteristic
402C2×C4×D4—24no—
403C2×C4×D4—24no—
404C2×C4×D4—24no—
405C22×C4⋊C4C22×C2912yes—
406C22×C4⋊C4C22×C2911yescharacteristic
407C22×C4⋊C4C22×C2911yescharacteristic
408C22×C4⋊C4C22×C2911yescharacteristic
409C22×C22⋊C4C22×C2912yes—
410C22×C22⋊C4C22×C2912yes—
411C22×C22⋊C4C22×C2911yescharacteristic
412C22×C22⋊C4C22×C2912yes—
413C22×C22⋊C4C22×C2912yes—
414C22×C22⋊C4C22×C2911yescharacteristic
415C22×C42C22×C2911yescharacteristic
416#398—24no—
417#397—24no—
418#394—28no—
419#380—24no—
420C2×#95C22×C2912yes—
421C2×#95C22×C2911yescharacteristic
422C2×#95C22×C2912yes—
423C2×#95C22×C2911yescharacteristic
424C2×#95C22×C2912yes—
425C2×#95C22×C2912yes—
426C2×#95C22×C2912yes—
427C2×#95C22×C2912yes—
428C2×#95C22×C2912yes—
429C2×C29—44no—
430C2×C29—44no—
431C2×C29#239511yescharacteristic
432C2×C29#240511yescharacteristic
433C2×C29#242512yes—
434C2×C29#242712yes—
435C2×C29#243211yescharacteristic
436C2×C29#246012yes—
437C2×C29#246812yes—
438C2×C29#248611yescharacteristic
439C2×C29#254311yescharacteristic
440C2×C29#263811yescharacteristic
441C2×C29#284711yescharacteristic
442C25C23×C2911yescharacteristic
443C25C23×C2911yescharacteristic
444C22×D4—22no—
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—22no—
450C22×D4D4×C2914yes—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—24no—
457C23×C4—24no—
458C23×C4—42no—
459C23×C4—42no—
460C23×C4D4×C2914yes—
461C23×C4C23×C2912yes—
462C23×C4C23×C2912yes—
463C23×C4C23×C2912yes—
464C23×C4C23×C2911yescharacteristic
465C23×C4C23×C2911yescharacteristic
466C23×C4C23×C2912yes—
467C23×C4C23×C2911yescharacteristic
468C23×C4C23×C2911yescharacteristic
469C23×C4C23×C2911yescharacteristic
470C4×D4—232no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4D4×C2914yes—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4D4×C2914yes—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—22no—
503#95—24no—
504#95—24no—
505#95—22no—
506#95—24no—
507#95—22no—
508#95—24no—
509#95—24no—
510#95—24no—
511#95—42no—
512C29#1482411yescharacteristic, direct product factor, Sylow
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24C2×D4×C2912yes—
530C24C2×D4×C2912yes—
531C24C2×D4×C2912yes—
532C24C2×D4×C2912yes—
533C24#41×C2912yes—
534C24#41×C2912yes—
535C24C24×C2911yescharacteristic
536C2×D4—28no—
537C2×D4—28no—
538C2×D4—28no—
539C2×D4—28no—
540C2×D4—28no—
541C2×D4—28no—
542C2×D4—28no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—28no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—44no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4C2×D4×C2912yes—
598C22×C4C2×D4×C2912yes—
599C22×C4C2×D4×C2912yes—
600C22×C4C2×D4×C2912yes—
601C22×C4C2×D4×C2912yes—
602C22×C4C2×D4×C2912yes—
603C22×C4C2×D4×C2912yes—
604C22×C4C2×D4×C2912yes—
605C22×C4#41×C2914yes—
606C22×C4#41×C2912yes—
607C22×C4#41×C2914yes—
608C4⋊C4—28no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—48no—
612C22⋊C4—28no—
613C22⋊C4—28no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C42—28no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—24no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—41no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23C29×#12114yes—
664C23C29×#12114yes—
665C23C22×D4×C2911yescharacteristic
666C23C22×D4×C2911yescharacteristic
667C23C22×D4×C2911yescharacteristic
668C23C22×D4×C2911yescharacteristic
669C23C2×#41×C2911yescharacteristic
670C23C2×#41×C2911yescharacteristic
671C23C2×#41×C2911yescharacteristic
672C23C2×#41×C2912yes—
673C23C2×#41×C2912yes—
674C23C29×H(5,𝔽2)12yes—
675C23C29×2−1+412yes—
676D4—232no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—416no—
699C2×C4—416no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4C29×#12014yes—
732C2×C4C29×#12114yes—
733C2×C4C29×#12314yes—
734C22—28no—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—24no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—42no—
743C22—42no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22C2×C29×#12011yescharacteristic
757C22C2×C29×#12111yescharacteristic
758C22C2×C29×#12111yescharacteristic
759C22C2×C29×#12111yescharacteristic
760C22C2×C29×#12311yescharacteristic
761C22C29×#52511yescharacteristic
762C22C29×#52511yescharacteristic
763C22C29×#52511yescharacteristic
764C22C29×#52912yes—
765C22C29×#52912yes—
766C22C29×#53211yescharacteristic
767C22C29×#53411yescharacteristic
768C22C29×#53611yescharacteristic
769C22C29×#53912yes—
770C22C29×#54212yes—
771C22C29×#54612yes—
772C22C29×#54612yes—
773C22C29×#54612yes—
774C22C29×#54712yes—
775C22C29×#54712yes—
776C22C29×#54812yes—
777C22C29×#55212yes—
778C22C29×#55312yes—
779C4—24no—
780C4—24no—
781C4—24no—
782C4—44no—
783C4—42no—
784C4—42no—
785C4—82no—
786C4—82no—
787C4—82no—
788C2—44no—
789C2—44no—
790C2C29×#239511yescharacteristic
791C2C29×#240511yescharacteristic
792C2C29×#242512yes—
793C2C29×#242712yes—
794C2C29×#243211yescharacteristic
795C2C29×#246012yes—
796C2C29×#246812yes—
797C2C29×#248611yescharacteristic
798C2C29×#254311yescharacteristic
799C2C29×#263811yescharacteristic
800C2C29×#284711yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutator, Frattini, cosocleC24C24×C29
prime radicalC23×D4×C29C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#398C2semidirect
3. C2×C29×#397C2semidirect
5. C2×C29×#380C2semidirect
6. C29×#1441C2semidirect
7. C29×#1440C2semidirect
8. C29×#1439C2semidirect
9. C29×#1436C2semidirect
10. C29×C22⋊#95C2semidirect
11. C29×C22⋊#95C2semidirect
218. #14824C29direct (N × H)
335. C2×#398C2×C29semidirect
336. C2×#397C2×C29semidirect
338. C2×#380C2×C29semidirect
339. #1441C2×C29semidirect
340. #1440C2×C29semidirect
341. #1439C2×C29semidirect
342. #1436C2×C29semidirect
343. C22⋊#95C2×C29semidirect
344. C22⋊#95C2×C29semidirect
512. C29#14824direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D4×C292
C2×C29×#3982
C2×C29×#3972
C2×C29×#3942
C2×C29×#3802
C29×#14412
C29×#14402
C29×#14392
C29×#14362
C29×C22⋊#952
#1482429