Finite Group Databasebeta

← #26139639

Subgroups — #26139639

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×(C22⋊D47)⋊C4C211yesmaximal, characteristic
2C23×Dic47⋊C4C211yesmaximal, characteristic, complemented
3C2×#15689002C211yesmaximal, characteristic
4C2×#15689000C211yesmaximal, characteristic
5C2×#15688994C212yesmaximal, complemented
6#20241651C212yesmaximal, complemented
7#20241632C212yesmaximal, complemented
8#20241619C212yesmaximal, complemented
9#20241610C211yesmaximal, characteristic, complemented
10#20241610C211yesmaximal, characteristic, complemented
11C2×C47×#385C211yesmaximal, characteristic, complemented
12C23×C22⋊D47C2211yescharacteristic
13C24×Dic47C2211yescharacteristic
14C24×Dic47C2211yescharacteristic
15C23×C4×D47C2211yescharacteristic
16C2×(C22⋊D47)⋊C4—24no—
17C2×(C22⋊D47)⋊C4—24no—
18C2×(C22⋊D47)⋊C4—24no—
19C22×Dic47⋊C4—24no—
20C22×Dic47⋊C4—28no—
21C22×Dic47⋊C4C2212yes—
22C22×Dic47⋊C4C2211yescharacteristic
23C22×Dic47⋊C4C2212yes—
24C22×C22⋊Dic47C2211yescharacteristic
25C22×(C2×D47)⋊C4C2211yescharacteristic
26C22×(C2×D47)⋊C4C2212yes—
27C22×(C2×D47)⋊C4C2212yes—
28C22×C4×Dic47C2211yescharacteristic
29#15689002—24no—
30#15689000C418yescomplemented
31#15688994—28no—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C2×C47⋊#95C2212yes—
37C2×C47⋊#95C2212yes—
38C24×C4×C47C2211yescharacteristic
39C22×C4⋊C4×C47C2212yes—
40C22×C22⋊C4×C47C2211yescharacteristic
41C22×C22⋊C4×C47C2211yescharacteristic
42C47×#385—24no—
43C2×#95×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×Dic47—22no—
53C23×Dic47—22no—
54C23×Dic47—24no—
55C23×Dic47—24no—
56C23×Dic47—22no—
57C23×Dic47—22no—
58C23×Dic47—24no—
59C23×Dic47—42no—
60C23×Dic47C2×C414yescomplemented
61C23×Dic47D414yes—
62C23×Dic47C2312yes—
63C23×Dic47C2311yescharacteristic
64C23×Dic47C2311yescharacteristic
65C23×Dic47C2312yes—
66C23×Dic47C2311yescharacteristic
67C22×C4×D47—22no—
68C22×C4×D47—22no—
69C22×C4×D47—22no—
70C22×C4×D47—24no—
71C22×C4×D47—42no—
72(C22⋊D47)⋊C4—232no—
73C2×Dic47⋊C4—232no—
74C2×Dic47⋊C4—24no—
75C2×Dic47⋊C4—22no—
76C2×Dic47⋊C4—24no—
77C2×Dic47⋊C4—24no—
78C2×Dic47⋊C4—24no—
79C2×Dic47⋊C4—24no—
80C2×Dic47⋊C4—22no—
81C2×Dic47⋊C4—22no—
82C2×Dic47⋊C4D418yescomplemented
83C2×C22⋊Dic47—22no—
84C2×C22⋊Dic47—22no—
85C2×C22⋊Dic47—22no—
86C2×(C2×D47)⋊C4—22no—
87C2×(C2×D47)⋊C4—22no—
88C2×(C2×D47)⋊C4—24no—
89C2×(C2×D47)⋊C4—22no—
90C2×(C2×D47)⋊C4—24no—
91C2×(C2×D47)⋊C4—24no—
92C2×(C2×D47)⋊C4—24no—
93C2×(C2×D47)⋊C4—42no—
94C2×(C2×D47)⋊C4C2×C418yescomplemented
95C2×C4×Dic47—22no—
96C2×C4×Dic47—22no—
97C2×C4×Dic47—22no—
98C47⋊#95—24no—
99C47⋊#95—24no—
100C47⋊#95—24no—
101C47⋊#95—24no—
102C47⋊#95—42no—
103C47⋊#95C2×C418yescomplemented
104C25×C47C2311yescharacteristic
105C23×C4×C47—22no—
106C23×C4×C47—24no—
107C23×C4×C47—22no—
108C23×C4×C47—22no—
109C23×C4×C47—42no—
110C23×C4×C47C2312yes—
111C23×C4×C47C2311yescharacteristic
112C23×C4×C47C2311yescharacteristic
113C23×C4×C47C2312yes—
114C2×C4⋊C4×C47—24no—
115C2×C4⋊C4×C47—24no—
116C2×C4⋊C4×C47—42no—
117C2×C22⋊C4×C47—22no—
118C2×C22⋊C4×C47—22no—
119C2×C22⋊C4×C47—22no—
120C2×C22⋊C4×C47—22no—
121C2×C22⋊C4×C47C2×C414yescomplemented
122C2×C22⋊C4×C47D414yes—
123#95×C47—24no—
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—22no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—22no—
159C22×C4×C47—22no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—48no—
169C22×C4×C47—48no—
170C22×C4×C47—44no—
171C22×C4×C47—44no—
172C22×C4×C47C22×C414yes—
173C22×C4×C47C2×D414yes—
174C22×C4×C47C2×D412yes—
175C22×C4×C47C2×D412yes—
176C2×C22⋊D47—28no—
177C2×C22⋊D47—28no—
178C2×C22⋊D47—28no—
179C2×C22⋊D47—28no—
180C2×C22⋊D47—28no—
181C2×C22⋊D47—28no—
182C2×C22⋊D47C4⋊C4116yescomplemented
183C22×Dic47—28no—
184C22×Dic47—216no—
185C22×Dic47—28no—
186C22×Dic47—28no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189C22×Dic47—21no—
190C22×Dic47—21no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47—22no—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—22no—
198C22×Dic47—216no—
199C22×Dic47—28no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—28no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—44no—
213C22×Dic47—48no—
214C22×Dic47—48no—
215C22×Dic47C22×C412yes—
216C22×Dic47C22×C414yes—
217C22×Dic47C2×D412yes—
218C22×Dic47C2×D412yes—
219C22×Dic47C2×D414yes—
220C22×Dic47C2×D414yes—
221C22×Dic47C2×D412yes—
222C22×Dic47C2×Q812yes—
223C22×Dic47#4114yes—
224C2×C4×D47—28no—
225C2×C4×D47—48no—
226C2×C4×D47—48no—
227C2×C4×D47—44no—
228C2×C4×D47—44no—
229C4⋊C4×C47—48no—
230C22⋊C4×C47—28no—
231C22⋊C4×C47—28no—
232C22⋊Dic47—44no—
233(C2×D47)⋊C4—28no—
234(C2×D47)⋊C4—216no—
235(C2×D47)⋊C4—48no—
236Dic47⋊C4—216no—
237Dic47⋊C4—28no—
238Dic47⋊C4—216no—
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×D412yes—
267C23×C47C22×D411yescharacteristic
268C23×C47C22×Q811yescharacteristic
269C23×C47C2×#4112yes—
270C23×C47C2×#4111yescharacteristic
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—24no—
298C2×C4×C47—24no—
299C2×C4×C47—24no—
300C2×C4×C47—22no—
301C2×C4×C47—24no—
302C2×C4×C47—22no—
303C2×C4×C47—24no—
304C2×C4×C47—24no—
305C2×C4×C47—24no—
306C2×C4×C47—24no—
307C2×C4×C47—416no—
308C2×C4×C47—41no—
309C2×C4×C47—42no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—42no—
313C2×C4×C47—41no—
314C2×C4×C47—42no—
315C2×C4×C47—42no—
316C2×C4×C47—42no—
317C2×C4×C47—42no—
318C2×C4×C47—42no—
319C2×C4×C47—42no—
320C2×C4×C47—42no—
321C2×C4×C47—42no—
322C22⋊D47—232no—
323C2×Dic47—232no—
324C2×Dic47—24no—
325C2×Dic47—24no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—24no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—24no—
335C2×Dic47—24no—
336C2×Dic47—24no—
337C2×Dic47—22no—
338C2×Dic47—24no—
339C2×Dic47—24no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—416no—
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×Dic47C2×C4⋊C414yescomplemented
354C2×Dic47C4×D418yescomplemented
355C2×Dic47#12014yes—
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×D412yes—
371C22×C47C2×C4×D411yescharacteristic
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—44no—
404C4×C47—42no—
405C4×C47—44no—
406C4×C47—42no—
407Dic47—24no—
408Dic47—24no—
409Dic47—28no—
410Dic47—42no—
411Dic47—82no—
412C22×C4×D4—471no—
413C23×C4⋊C4—471no—
414C2×#386—471no—
415C2×#386—471no—
416C2×#385—472no—
417C2×#385D4711yescharacteristic, complemented
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×C4—471no—
439C24×C4—471no—
440C24×C4C2×D4711yescharacteristic
441C2×C4×D4—944no—
442C2×C4×D4—944no—
443C2×C4×D4—944no—
444C22×C4⋊C4—472no—
445C22×C4⋊C4—472no—
446C22×C4⋊C4—471no—
447C22×C4⋊C4—948no—
448C22×C4⋊C4—944no—
449C22×C4⋊C4C2×D4712yes—
450C22×C22⋊C4—472no—
451C22×C22⋊C4—471no—
452C22×C22⋊C4—471no—
453C22×C22⋊C4—472no—
454C22×C22⋊C4C2×D4711yescharacteristic
455C22×C22⋊C4C2×D4711yescharacteristic
456C22×C42—471no—
457#386—478no—
458#386—944no—
459#385—24no—
460#385—948no—
461C2×#95—472no—
462C2×#95—472no—
463C2×#95—472no—
464C2×#95—472no—
465C2×#95—472no—
466C2×#95—472no—
467C2×#95C2×D4712yes—
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—24no—
480C23×C4—22no—
481C23×C4—22no—
482C23×C4—42no—
483C23×C4—472no—
484C23×C4—471no—
485C23×C4—471no—
486C23×C4—474no—
487C23×C4—471no—
488C23×C4—474no—
489C23×C4—472no—
490C23×C4—942no—
491C23×C4—944no—
492C23×C4—942no—
493C23×C4—944no—
494C23×C4—944no—
495C23×C4—944no—
496C23×C4—942no—
497C23×C4—942no—
498C23×C4—942no—
499C23×C4—942no—
500C23×C4—942no—
501C23×C4—1882no—
502C23×C4—1882no—
503C23×C4C22×D4712yes—
504C23×C4C22×D4712yes—
505C23×C4C22×D4711yescharacteristic
506C23×C4C22×D4711yescharacteristic
507C4×D4—9432no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—42no—
511C2×C4⋊C4—478no—
512C2×C4⋊C4—944no—
513C2×C4⋊C4—944no—
514C2×C4⋊C4—944no—
515C2×C4⋊C4—944no—
516C2×C4⋊C4—942no—
517C2×C4⋊C4—942no—
518C2×C4⋊C4—9432no—
519C2×C4⋊C4—944no—
520C2×C4⋊C4—942no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—478no—
526C2×C22⋊C4—942no—
527C2×C22⋊C4—944no—
528C2×C22⋊C4—944no—
529C2×C22⋊C4—942no—
530C2×C22⋊C4—942no—
531C2×C22⋊C4—944no—
532C2×C22⋊C4—942no—
533C2×C22⋊C4—942no—
534C2×C22⋊C4—942no—
535C2×C22⋊C4—944no—
536C2×C22⋊C4—1882no—
537C2×C22⋊C4C4×D4714yescomplemented
538C2×C22⋊C4C22⋊D4714yes—
539C2×C42—942no—
540C2×C42—942no—
541C2×C42—942no—
542#95—24no—
543#95—478no—
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—942no—
557C24—941no—
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—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—472no—
605C22×C4—474no—
606C22×C4—472no—
607C22×C4—474no—
608C22×C4—474no—
609C22×C4—472no—
610C22×C4—472no—
611C22×C4—474no—
612C22×C4—472no—
613C22×C4—948no—
614C22×C4—9416no—
615C22×C4—948no—
616C22×C4—948no—
617C22×C4—948no—
618C22×C4—9416no—
619C22×C4—948no—
620C22×C4—941no—
621C22×C4—941no—
622C22×C4—942no—
623C22×C4—942no—
624C22×C4—941no—
625C22×C4—941no—
626C22×C4—942no—
627C22×C4—941no—
628C22×C4—942no—
629C22×C4—941no—
630C22×C4—942no—
631C22×C4—948no—
632C22×C4—941no—
633C22×C4—942no—
634C22×C4—941no—
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—1884no—
645C22×C4—1888no—
646C22×C4—1884no—
647C22×C4—1884no—
648C22×C4—1888no—
649C22×C4—1888no—
650C22×C4C2×C4×D4714yes—
651C22×C4D4×D4714yes—
652C22×C4C2×C22⋊D4712yes—
653C22×C4C2×C22⋊D4712yes—
654C4⋊C4—48no—
655C4⋊C4—9416no—
656C4⋊C4—9416no—
657C4⋊C4—948no—
658C22⋊C4—28no—
659C22⋊C4—28no—
660C22⋊C4—9416no—
661C22⋊C4—948no—
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—22no—
677C23—24no—
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—1881no—
700C23—1882no—
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×D4712yes—
714C23C2×D4×D4711yescharacteristic
715C23C22×C22⋊D4711yescharacteristic
716C23C2×Q8×D4711yescharacteristic
717C23#41×D4712yes—
718C23C2×#1062535011yescharacteristic
719C23C2×#1062535411yescharacteristic
720C23#1309406912yes—
721C23#1309407112yes—
722D4—9432no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—416no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—474no—
749C2×C4—478no—
750C2×C4—474no—
751C2×C4—9432no—
752C2×C4—944no—
753C2×C4—944no—
754C2×C4—944no—
755C2×C4—942no—
756C2×C4—944no—
757C2×C4—942no—
758C2×C4—944no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—944no—
765C2×C4—944no—
766C2×C4—944no—
767C2×C4—942no—
768C2×C4—942no—
769C2×C4—942no—
770C2×C4—942no—
771C2×C4—18816no—
772C2×C4—18816no—
773C2×C4—1882no—
774C2×C4—1882no—
775C2×C4—1882no—
776C2×C4—1882no—
777C2×C4—1882no—
778C2×C4—1882no—
779C2×C4—1882no—
780C2×C4—1882no—
781C2×C4—1882no—
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
805C22C4×D4×D4712yes—
806C22C2×C4×C22⋊D4711yescharacteristic
807C22C2×#1309398611yescharacteristic
808C22#1568960212yes—
809C22#120×D4711yescharacteristic
810C22C2×#1309399211yescharacteristic
811C22C2×#1309400011yescharacteristic
812C22C2×#1309400211yescharacteristic
813C22C2×#1309400911yescharacteristic
814C22#1568963111yescharacteristic
815C22#1568963612yes—
816C22#1568968311yescharacteristic
817C22#1568969511yescharacteristic
818C22#1568972212yes—
819C22#1568975512yes—
820C22D4×C22⋊D4712yes—
821C22#1568977112yes—
822C22#1568977212yes—
823C22#1568978212yes—
824C22#1568978612yes—
825C22#1568982212yes—
826C22#1568982712yes—
827C4—44no—
828C4—44no—
829C4—42no—
830C4—42no—
831C4—944no—
832C4—948no—
833C4—944no—
834C4—3762no—
835C4—1882no—
836C2—28no—
837C2—1884no—
838C2C2×#1568899411yescharacteristic
839C2#2024588911yescharacteristic
840C2#2024605611yescharacteristic
841C2#2024628612yes—
842C2#2024640512yes—
843C2#2024669911yescharacteristic
844C2#2024672011yescharacteristic
845C2#2024675211yescharacteristic
846C2#2024712712yes—
847C2#2024719312yes—
848C2#2024874011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#385C2
socle, cosocleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC2×#385D47
hypocenterC47#14015
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C23×Dic47⋊C4C2semidirect
5. C2×#15688994C2semidirect
6. #20241651C2semidirect
7. #20241632C2semidirect
8. #20241619C2semidirect
9. #20241610C2semidirect
10. #20241610C2semidirect
11. C2×C47×#385C2semidirect
30. #15689000C4semidirect
60. C23×Dic47C2×C4semidirect
82. C2×Dic47⋊C4D4semidirect
94. C2×(C2×D47)⋊C4C2×C4semidirect
103. C47⋊#95C2×C4semidirect
121. C2×C22⋊C4×C47C2×C4semidirect
182. C2×C22⋊D47C4⋊C4semidirect
296. C22×D47C2×C4⋊C4semidirect
353. C2×Dic47C2×C4⋊C4semidirect
354. C2×Dic47C4×D4semidirect
368. C22×C47#385semidirect
417. C2×#385D47semidirect
468. C47#14015semidirect
537. C2×C22⋊C4C4×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×(C22⋊D47)⋊C42
C23×Dic47⋊C42
C2×#156890022
C2×#156890002
C2×#156889942
#202416512
#202416322
#202416192
#202416102
C2×C47×#3852
#1401547