Finite Group Databasebeta

← #26139640

Subgroups — #26139640

Order 12032.

2950 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D47C211yesmaximal, characteristic
2C2×#15689002C211yesmaximal, characteristic
3C2×#15689002C211yesmaximal, characteristic
4C2×#15688996C211yesmaximal, characteristic, complemented
5C2×#15688994C212yesmaximal, complemented
6#20241651C212yesmaximal, complemented
7#20241630C212yesmaximal, complemented
8#20241620C212yesmaximal, complemented
9#20241611C211yesmaximal, characteristic, complemented
10#20241611C211yesmaximal, characteristic, complemented
11C23×C4⋊C4×C47C211yesmaximal, characteristic, complemented
12C23×C22⋊D47C2211yescharacteristic
13C23×C4×D47C2211yescharacteristic
14C2×C4×C22⋊D47—24no—
15C2×C4×C22⋊D47—24no—
16C2×C4×C22⋊D47—24no—
17C22×Dic47⋊C4C2211yescharacteristic
18C22×Dic47⋊C4C2212yes—
19C22×C22⋊Dic47C2211yescharacteristic
20C22×C22⋊Dic47C2211yescharacteristic
21C22×C22⋊Dic47C2211yescharacteristic
22C22×(C2×D47)⋊C4C2211yescharacteristic
23C22×(C2×D47)⋊C4C2212yes—
24C22×(C2×D47)⋊C4C2212yes—
25C22×C4×Dic47C2211yescharacteristic
26#15689002—24no—
27#15689002C418yescomplemented
28#15688996—24no—
29#15688994—28no—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C2×C47⋊#95C2212yes—
37C24×C4×C47C2211yescharacteristic
38C24×C4×C47C2211yescharacteristic
39C24×C4×C47C2211yescharacteristic
40C22×C4⋊C4×C47—24no—
41C22×C4⋊C4×C47—28no—
42C22×C4⋊C4×C47C2212yes—
43C22×C4⋊C4×C47C2212yes—
44C24×D47C2311yescharacteristic
45C22×C22⋊D47—22no—
46C22×C22⋊D47—22no—
47C22×C22⋊D47—22no—
48C22×C22⋊D47—22no—
49C22×C22⋊D47C2×C414yes—
50C22×C22⋊D47D414yes—
51C22×C22⋊D47Q814yes—
52C23×Dic47C2312yes—
53C23×Dic47C2312yes—
54C23×Dic47C2311yescharacteristic
55C23×Dic47C2311yescharacteristic
56C23×Dic47C2311yescharacteristic
57C22×C4×D47—22no—
58C22×C4×D47—22no—
59C22×C4×D47—22no—
60C22×C4×D47—24no—
61C22×C4×D47—42no—
62C4×C22⋊D47—232no—
63C2×Dic47⋊C4—22no—
64C2×Dic47⋊C4—22no—
65C2×Dic47⋊C4—22no—
66C2×Dic47⋊C4—24no—
67C2×Dic47⋊C4—24no—
68C2×Dic47⋊C4—42no—
69C2×C22⋊Dic47—22no—
70C2×C22⋊Dic47—22no—
71C2×C22⋊Dic47—22no—
72C2×C22⋊Dic47—22no—
73C2×C22⋊Dic47—22no—
74C2×C22⋊Dic47—22no—
75C2×C22⋊Dic47—22no—
76C2×C22⋊Dic47C2×C414yescomplemented
77C2×C22⋊Dic47D414yes—
78C2×(C2×D47)⋊C4—22no—
79C2×(C2×D47)⋊C4—24no—
80C2×(C2×D47)⋊C4—22no—
81C2×(C2×D47)⋊C4—24no—
82C2×(C2×D47)⋊C4—22no—
83C2×(C2×D47)⋊C4—24no—
84C2×(C2×D47)⋊C4—24no—
85C2×(C2×D47)⋊C4—42no—
86C2×(C2×D47)⋊C4C2×C418yescomplemented
87C2×C4×Dic47—22no—
88C2×C4×Dic47—22no—
89C2×C4×Dic47—22no—
90C47⋊#95—24no—
91C47⋊#95—24no—
92C47⋊#95—24no—
93C47⋊#95—24no—
94C47⋊#95—24no—
95C47⋊#95—42no—
96C47⋊#95C2×C418yescomplemented
97C25×C47C2311yescharacteristic
98C23×C4×C47—22no—
99C23×C4×C47—22no—
100C23×C4×C47—24no—
101C23×C4×C47—24no—
102C23×C4×C47—22no—
103C23×C4×C47—22no—
104C23×C4×C47—22no—
105C23×C4×C47—24no—
106C23×C4×C47—24no—
107C23×C4×C47—22no—
108C23×C4×C47—22no—
109C23×C4×C47—42no—
110C23×C4×C47—42no—
111C23×C4×C47C2×C414yescomplemented
112C23×C4×C47D414yes—
113C23×C4×C47C2312yes—
114C23×C4×C47C2311yescharacteristic
115C23×C4×C47C2312yes—
116C23×C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47—232no—
118C2×C4⋊C4×C47—24no—
119C2×C4⋊C4×C47—24no—
120C2×C4⋊C4×C47—24no—
121C2×C4⋊C4×C47—24no—
122C2×C4⋊C4×C47—24no—
123C2×C4⋊C4×C47D418yescomplemented
124C24×C47—22no—
125C24×C47—22no—
126C24×C47—22no—
127C24×C47—22no—
128C24×C47C22×C412yes—
129C24×C47C2×D412yes—
130C24×C47C2×D412yes—
131C24×C47C2×D412yes—
132C24×C47C2×Q812yes—
133C24×C47#4112yes—
134C24×C47#4112yes—
135C24×C47C2411yescharacteristic
136C23×D47—22no—
137C23×D47—21no—
138C23×D47—21no—
139C23×D47—22no—
140C23×D47—21no—
141C23×D47—21no—
142C23×D47—22no—
143C23×D47—22no—
144C23×D47C22×C412yes—
145C23×D47C2×D412yes—
146C23×D47C2×Q812yes—
147C22×C4×C47—28no—
148C22×C4×C47—216no—
149C22×C4×C47—28no—
150C22×C4×C47—28no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—216no—
159C22×C4×C47—28no—
160C22×C4×C47—28no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47—22no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—28no—
172C22×C4×C47—44no—
173C22×C4×C47—48no—
174C22×C4×C47—48no—
175C22×C4×C47—48no—
176C22×C4×C47—48no—
177C22×C4×C47—44no—
178C22×C4×C47—44no—
179C22×C4×C47C22×C414yes—
180C22×C4×C47C2×D412yes—
181C22×C4×C47C2×D414yes—
182C22×C4×C47C2×D414yes—
183C22×C4×C47C2×D412yes—
184C22×C4×C47C2×D414yes—
185C22×C4×C47#4114yes—
186C2×C22⋊D47—28no—
187C2×C22⋊D47—28no—
188C2×C22⋊D47—28no—
189C2×C22⋊D47—28no—
190C2×C22⋊D47—28no—
191C2×C22⋊D47—28no—
192C2×C22⋊D47C4⋊C4116yescomplemented
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—22no—
213C22×Dic47—22no—
214C22×Dic47—22no—
215C22×Dic47—22no—
216C22×Dic47—22no—
217C22×Dic47—22no—
218C22×Dic47C22×C414yes—
219C22×Dic47C22×C412yes—
220C22×Dic47C2×D412yes—
221C22×Dic47C2×D412yes—
222C22×Dic47C2×D412yes—
223C22×Dic47C2×Q812yes—
224C2×C4×D47—28no—
225C2×C4×D47—48no—
226C2×C4×D47—48no—
227C2×C4×D47—44no—
228C2×C4×D47—44no—
229C4⋊C4×C47—216no—
230C4⋊C4×C47—216no—
231C22⋊Dic47—28no—
232C22⋊Dic47—28no—
233C22⋊Dic47—44no—
234(C2×D47)⋊C4—28no—
235(C2×D47)⋊C4—216no—
236(C2×D47)⋊C4—48no—
237Dic47⋊C4—28no—
238Dic47⋊C4—48no—
239C4×Dic47—28no—
240C23×C47—24no—
241C23×C47—24no—
242C23×C47—22no—
243C23×C47—22no—
244C23×C47—24no—
245C23×C47—22no—
246C23×C47—22no—
247C23×C47—24no—
248C23×C47—24no—
249C23×C47—24no—
250C23×C47—24no—
251C23×C47—24no—
252C23×C47—24no—
253C23×C47—24no—
254C23×C47—24no—
255C23×C47—24no—
256C23×C47C2×C4⋊C414yes—
257C23×C47C4×D414yes—
258C23×C47C4×D414yes—
259C23×C47#12014yes—
260C23×C47C22⋊Q814yes—
261C23×C47C22⋊Q814yes—
262C23×C47#12314yes—
263C23×C47C23×C411yescharacteristic
264C23×C47C22×D411yescharacteristic
265C23×C47C22×D411yescharacteristic
266C23×C47C22×D411yescharacteristic
267C23×C47C22×D412yes—
268C23×C47C22×Q811yescharacteristic
269C23×C47C2×#4111yescharacteristic
270C23×C47C2×#4112yes—
271C23×C47C2×#4111yescharacteristic
272C23×C47H(5,𝔽2)12yes—
273C23×C472−1+412yes—
274C22×D47—24no—
275C22×D47—22no—
276C22×D47—22no—
277C22×D47—24no—
278C22×D47—22no—
279C22×D47—22no—
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—24no—
283C22×D47—24no—
284C22×D47—24no—
285C22×D47—24no—
286C22×D47—41no—
287C22×D47—41no—
288C22×D47—42no—
289C22×D47—41no—
290C22×D47—41no—
291C22×D47—42no—
292C22×D47—42no—
293C22×D47—42no—
294C22×D47—42no—
295C22×D47—42no—
296C22×D47C2×C4⋊C414yescomplemented
297C2×C4×C47—232no—
298C2×C4×C47—24no—
299C2×C4×C47—24no—
300C2×C4×C47—22no—
301C2×C4×C47—24no—
302C2×C4×C47—24no—
303C2×C4×C47—24no—
304C2×C4×C47—24no—
305C2×C4×C47—22no—
306C2×C4×C47—24no—
307C2×C4×C47—24no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—24no—
311C2×C4×C47—22no—
312C2×C4×C47—24no—
313C2×C4×C47—24no—
314C2×C4×C47—416no—
315C2×C4×C47—416no—
316C2×C4×C47—42no—
317C2×C4×C47—42no—
318C2×C4×C47—42no—
319C2×C4×C47—42no—
320C2×C4×C47—42no—
321C2×C4×C47—42no—
322C2×C4×C47C4×D418yescomplemented
323C2×C4×C47#12014yes—
324C22⋊D47—232no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—24no—
332C2×Dic47—24no—
333C2×Dic47—24no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—24no—
337C2×Dic47—24no—
338C2×Dic47—41no—
339C2×Dic47—41no—
340C2×Dic47—41no—
341C2×Dic47—41no—
342C2×Dic47—42no—
343C2×Dic47—42no—
344C2×Dic47—42no—
345C2×Dic47—42no—
346C2×Dic47—42no—
347C2×Dic47—42no—
348C2×Dic47—42no—
349C2×Dic47—42no—
350C2×Dic47—42no—
351C2×Dic47—42no—
352C2×Dic47—42no—
353C2×Dic47—42no—
354C2×Dic47—42no—
355C2×Dic47C2×C4⋊C414yescomplemented
356C4×D47—416no—
357#14015—471nomaximal, Sylow
358C22×C47—24no—
359C22×C47—24no—
360C22×C47—28no—
361C22×C47—28no—
362C22×C47—24no—
363C22×C47—24no—
364C22×C47—24no—
365C22×C47—28no—
366C22×C47—28no—
367C22×C47—24no—
368C22×C47#38518yescomplemented
369C22×C47C22×C4⋊C411yescharacteristic
370C22×C47C2×C4×D411yescharacteristic
371C22×C47C2×C4×D412yes—
372C22×C47C2×C4×D411yescharacteristic
373C22×C47#52012yes—
374C22×C47C2×#12011yescharacteristic
375C22×C47C2×#12011yescharacteristic
376C22×C47C2×C22⋊Q811yescharacteristic
377C22×C47C2×C22⋊Q811yescharacteristic
378C22×C47C2×#12311yescharacteristic
379C22×C47#52511yescharacteristic
380C22×C47#52512yes—
381C22×C47#53411yescharacteristic
382C22×C47#53611yescharacteristic
383C22×C47#53912yes—
384C22×C47D4212yes—
385C22×C47D4212yes—
386C22×C47#54712yes—
387C22×C47#54712yes—
388C22×C47#54812yes—
389C22×C47D4×Q812yes—
390C22×C47#55312yes—
391C22×C47#55412yes—
392C2×D47—28no—
393C2×D47—24no—
394C2×D47—42no—
395C2×D47—42no—
396C2×D47—44no—
397C2×D47—42no—
398C2×D47—42no—
399C2×D47—42no—
400C2×D47—44no—
401C2×D47—44no—
402C2×D47—42no—
403C4×C47—24no—
404C4×C47—28no—
405C4×C47—42no—
406C4×C47—44no—
407Dic47—24no—
408Dic47—44no—
409Dic47—42no—
410Dic47—42no—
411Dic47—82no—
412C22×C4×D4—471no—
413C23×C4⋊C4D4711yescharacteristic, complemented
414C2×#386—471no—
415C2×#386—471no—
416C2×#385—471no—
417C2×#385—472no—
418#1444—472no—
419#1439—472no—
420#1436—472no—
421C22⋊#95—471no—
422C22⋊#95—471no—
423C2×C47—28no—
424C2×C47C2×#38511yescharacteristic
425C2×C47C4×#12011yescharacteristic
426C2×C47#232211yescharacteristic
427C2×C47D4×C4⋊C412yes—
428C2×C47#236112yes—
429C2×C47#240311yescharacteristic
430C2×C47#240611yescharacteristic
431C2×C47#240911yescharacteristic
432C2×C47#244312yes—
433C2×C47#244912yes—
434C2×C47#257911yescharacteristic
435D47—44no—
436C23×D4—471no—
437C24×C4—471no—
438C24×C4C2×D4711yescharacteristic
439C24×C4C2×D4711yescharacteristic
440C24×C4C2×D4711yescharacteristic
441C2×C4×D4—944no—
442C2×C4×D4—944no—
443C2×C4×D4—944no—
444C22×C4⋊C4—24no—
445C22×C4⋊C4—28no—
446C22×C4⋊C4—471no—
447C22×C4⋊C4—472no—
448C22×C4⋊C4C2×D4712yes—
449C22×C4⋊C4C2×D4712yes—
450C22×C22⋊C4—471no—
451C22×C22⋊C4—471no—
452C22×C22⋊C4—472no—
453C22×C22⋊C4—471no—
454C22×C22⋊C4—471no—
455C22×C22⋊C4—472no—
456C22×C42—471no—
457#386—478no—
458#386—944no—
459#385—944no—
460#385—948no—
461C2×#95—472no—
462C2×#95—472no—
463C2×#95—472no—
464C2×#95—472no—
465C2×#95—472no—
466C2×#95—472no—
467C2×#95—472no—
468C47#1401511yescharacteristic, complemented, Sylow
469C25—471no—
470C25C22×D4711yescharacteristic
471C22×D4—474no—
472C22×D4—474no—
473C22×D4—474no—
474C22×D4—942no—
475C22×D4—942no—
476C22×D4—942no—
477C22×D4—942no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—22no—
485C23×C4—24no—
486C23×C4—24no—
487C23×C4—22no—
488C23×C4—22no—
489C23×C4—42no—
490C23×C4—42no—
491C23×C4—471no—
492C23×C4—472no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—472no—
496C23×C4—942no—
497C23×C4—942no—
498C23×C4—942no—
499C23×C4—944no—
500C23×C4—1882no—
501C23×C4C4×D4714yescomplemented
502C23×C4C22⋊D4714yes—
503C23×C4C22×D4712yes—
504C23×C4C22×D4711yescharacteristic
505C23×C4C22×D4712yes—
506C23×C4C22×D4711yescharacteristic
507C4×D4—9432no—
508C2×C4⋊C4—232no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—24no—
512C2×C4⋊C4—24no—
513C2×C4⋊C4—24no—
514C2×C4⋊C4—942no—
515C2×C4⋊C4—942no—
516C2×C4⋊C4—942no—
517C2×C4⋊C4—944no—
518C2×C4⋊C4—944no—
519C2×C4⋊C4—1882no—
520C2×C4⋊C4C22⋊D4718yescomplemented
521C2×C22⋊C4—474no—
522C2×C22⋊C4—474no—
523C2×C22⋊C4—478no—
524C2×C22⋊C4—942no—
525C2×C22⋊C4—942no—
526C2×C22⋊C4—942no—
527C2×C22⋊C4—942no—
528C2×C22⋊C4—942no—
529C2×C22⋊C4—942no—
530C2×C22⋊C4—944no—
531C2×C22⋊C4—942no—
532C2×C22⋊C4—944no—
533C2×C22⋊C4—944no—
534C2×C22⋊C4—942no—
535C2×C22⋊C4—942no—
536C2×C22⋊C4—942no—
537C2×C22⋊C4—944no—
538C2×C22⋊C4—1882no—
539C2×C42—942no—
540C2×C42—942no—
541C2×C42—942no—
542#95—478no—
543#95—944no—
544#95—944no—
545#95—944no—
546#95—944no—
547#95—944no—
548#95—1882no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—472no—
554C24—472no—
555C24—472no—
556C24—941no—
557C24—942no—
558C24—941no—
559C24—942no—
560C24—941no—
561C24—941no—
562C24—942no—
563C24—942no—
564C24C2×C4×D4712yes—
565C24#1062535012yes—
566C24D4×D4712yes—
567C24D4×D4712yes—
568C24Q8×D4712yes—
569C24#1062535412yes—
570C24C2×C22⋊D4712yes—
571C24C23×D4711yescharacteristic
572C2×D4—4716no—
573C2×D4—948no—
574C2×D4—948no—
575C2×D4—948no—
576C2×D4—948no—
577C2×D4—948no—
578C2×D4—948no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—216no—
582C22×C4—28no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—216no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—28no—
604C22×C4—44no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—472no—
612C22×C4—472no—
613C22×C4—472no—
614C22×C4—474no—
615C22×C4—472no—
616C22×C4—472no—
617C22×C4—948no—
618C22×C4—941no—
619C22×C4—941no—
620C22×C4—941no—
621C22×C4—941no—
622C22×C4—942no—
623C22×C4—941no—
624C22×C4—941no—
625C22×C4—942no—
626C22×C4—942no—
627C22×C4—941no—
628C22×C4—941no—
629C22×C4—942no—
630C22×C4—942no—
631C22×C4—942no—
632C22×C4—942no—
633C22×C4—942no—
634C22×C4—942no—
635C22×C4—942no—
636C22×C4—942no—
637C22×C4—942no—
638C22×C4—942no—
639C22×C4—942no—
640C22×C4—942no—
641C22×C4—942no—
642C22×C4—942no—
643C22×C4—1888no—
644C22×C4—1888no—
645C22×C4—1884no—
646C22×C4—1884no—
647C22×C4C2×C4×D4714yes—
648C22×C4#1062535014yes—
649C22×C4C2×C22⋊D4712yes—
650C22×C4C2×C22⋊D4714yes—
651C22×C4C2×C22⋊D4714yes—
652C22×C4C2×C22⋊D4714yes—
653C22×C4C2×C22⋊D4712yes—
654C4⋊C4—216no—
655C4⋊C4—216no—
656C4⋊C4—948no—
657C4⋊C4—1888no—
658C22⋊C4—948no—
659C22⋊C4—948no—
660C22⋊C4—948no—
661C22⋊C4—9416no—
662C22⋊C4—1888no—
663C22⋊C4—1884no—
664C42—948no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—22no—
676C23—24no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—24no—
681C23—474no—
682C23—944no—
683C23—944no—
684C23—944no—
685C23—944no—
686C23—944no—
687C23—942no—
688C23—942no—
689C23—944no—
690C23—942no—
691C23—942no—
692C23—942no—
693C23—942no—
694C23—1882no—
695C23—1882no—
696C23—1882no—
697C23—1882no—
698C23—1881no—
699C23—1882no—
700C23—1881no—
701C23—1881no—
702C23—1881no—
703C23—1882no—
704C23C4⋊C4×D4714yes—
705C23C4×C22⋊D4714yes—
706C23#1309398614yes—
707C23#1309399214yes—
708C23#1309400014yes—
709C23#1309400214yes—
710C23#1309400914yes—
711C23C22×C4×D4711yescharacteristic
712C23C2×D4×D4711yescharacteristic
713C23C2×D4×D4711yescharacteristic
714C23C22×C22⋊D4712yes—
715C23C22×C22⋊D4711yescharacteristic
716C23C2×Q8×D4711yescharacteristic
717C23C2×#1062535012yes—
718C23C2×#1062535011yescharacteristic
719C23C2×#1062535411yescharacteristic
720C23#1309406912yes—
721C23#1309407212yes—
722D4—9432no—
723C2×C4—232no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—416no—
741C2×C4—416no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—474no—
749C2×C4—942no—
750C2×C4—942no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—944no—
756C2×C4—944no—
757C2×C4—944no—
758C2×C4—944no—
759C2×C4—944no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—18816no—
763C2×C4—1882no—
764C2×C4—1882no—
765C2×C4—1882no—
766C2×C4—1882no—
767C2×C4—1882no—
768C2×C4—1882no—
769C2×C4—1882no—
770C2×C4—1882no—
771C2×C4—1882no—
772C2×C4—1882no—
773C2×C4—1882no—
774C2×C4—1882no—
775C2×C4—1882no—
776C2×C4—1881no—
777C2×C4—1881no—
778C2×C4—1881no—
779C2×C4—1881no—
780C2×C4C4×C22⋊D4718yescomplemented
781C2×C4#1309399314yes—
782C22—28no—
783C22—24no—
784C22—28no—
785C22—24no—
786C22—28no—
787C22—28no—
788C22—24no—
789C22—24no—
790C22—24no—
791C22—24no—
792C22—948no—
793C22—944no—
794C22—1882no—
795C22—1884no—
796C22—1882no—
797C22—1884no—
798C22—1884no—
799C22—1882no—
800C22—1882no—
801C22—1882no—
802C22—1882no—
803C22#1568899418yescomplemented
804C22C2×C4⋊C4×D4711yescharacteristic
805C22C2×C4×C22⋊D4712yes—
806C22C2×C4×C22⋊D4711yescharacteristic
807C22C2×#1309398611yescharacteristic
808C22#1568960412yes—
809C22C2×#1309399211yescharacteristic
810C22C2×#1309399311yescharacteristic
811C22C2×#1309400011yescharacteristic
812C22C2×#1309400211yescharacteristic
813C22C2×#1309400911yescharacteristic
814C22#1568963412yes—
815C22#1568963411yescharacteristic
816C22#1568968211yescharacteristic
817C22#1568969711yescharacteristic
818C22#1568972012yes—
819C22D4×C22⋊D4712yes—
820C22D4×C22⋊D4712yes—
821C22#1568977412yes—
822C22#1568977412yes—
823C22#1568978412yes—
824C22Q8×C22⋊D4712yes—
825C22#1568982112yes—
826C22#1568982812yes—
827C4—28no—
828C4—24no—
829C4—44no—
830C4—42no—
831C4—944no—
832C4—3762no—
833C4—1884no—
834C4—1882no—
835C4—1882no—
836C2—28no—
837C2—1884no—
838C2C2×#1568899411yescharacteristic
839C2C4×#1309399311yescharacteristic
840C2#2024605711yescharacteristic
841C2C4⋊C4×C22⋊D4712yes—
842C2#2024640412yes—
843C2#2024669811yescharacteristic
844C2#2024672311yescharacteristic
845C2#2024674711yescharacteristic
846C2#2024712312yes—
847C2#2024719712yes—
848C2#2024873511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC23×C4⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC23×C4⋊C4D47
hypocenterC47#14015
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#15688996C2semidirect
5. C2×#15688994C2semidirect
6. #20241651C2semidirect
7. #20241630C2semidirect
8. #20241620C2semidirect
9. #20241611C2semidirect
10. #20241611C2semidirect
11. C23×C4⋊C4×C47C2semidirect
27. #15689002C4semidirect
76. C2×C22⋊Dic47C2×C4semidirect
86. C2×(C2×D47)⋊C4C2×C4semidirect
96. C47⋊#95C2×C4semidirect
111. C23×C4×C47C2×C4semidirect
123. C2×C4⋊C4×C47D4semidirect
192. C2×C22⋊D47C4⋊C4semidirect
296. C22×D47C2×C4⋊C4semidirect
322. C2×C4×C47C4×D4semidirect
355. C2×Dic47C2×C4⋊C4semidirect
368. C22×C47#385semidirect
413. C23×C4⋊C4D47semidirect
468. C47#14015semidirect
501. C23×C4C4×D47semidirect
520. C2×C4⋊C4C22⋊D47semidirect
780. C2×C4C4×C22⋊D47semidirect
803. C22#15688994semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D472
C2×#156890022
C2×#156889962
C2×#156889942
#202416512
#202416302
#202416202
#202416112
C23×C4⋊C4×C472
#1401547