Finite Group Databasebeta

← #26138462

Subgroups — #26138462

Order 12032.

2690 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D47C211yesmaximal, characteristic
2C2×#15688999C212yesmaximal
3C2×#15688994C212yesmaximal, complemented
4C2×#95×D47C211yesmaximal, characteristic, complemented
5#20241638C212yesmaximal, complemented
6#20241631C212yesmaximal, complemented
7Dic47⋊#95C211yesmaximal, characteristic, complemented
8#20241613C211yesmaximal, characteristic, complemented
9#20241611C211yesmaximal, characteristic, complemented
10(C2×D47)⋊#95C211yesmaximal, characteristic, complemented
11C2×C47×#380C211yesmaximal, characteristic, complemented
12C23×C22⋊D47C2211yescharacteristic
13C23×C4×D47C2212yes—
14C23×C4×D47C2211yescharacteristic
15C2×C4×C22⋊D47—28no—
16C2×C4×C22⋊D47C418yescomplemented
17C22×Dic47⋊C4C2212yes—
18C22×Dic47⋊C4C2211yescharacteristic
19C22×C22⋊Dic47C2212yes—
20C22×C22⋊Dic47C2211yescharacteristic
21C22×(C2×D47)⋊C4C2212yes—
22C22×(C2×D47)⋊C4C2211yescharacteristic
23C22×C4×Dic47C2211yescharacteristic
24#15688999—28no—
25#15688994—28no—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2211yescharacteristic
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34#95×D47—24no—
35C24×C4×C47C2211yescharacteristic
36C22×C4⋊C4×C47C2212yes—
37C22×C22⋊C4×C47C2212yes—
38C47×#380—24no—
39C2×#95×C47C2211yescharacteristic
40C2×#95×C47C2211yescharacteristic
41C24×D47C2311yescharacteristic
42C22×C22⋊D47—24no—
43C22×C22⋊D47—24no—
44C22×C22⋊D47C2×C414yes—
45C22×C22⋊D47D414yes—
46C22×C22⋊D47Q814yes—
47C23×Dic47C2312yes—
48C23×Dic47C2311yescharacteristic
49C23×Dic47C2312yes—
50C23×Dic47C2311yescharacteristic
51C23×Dic47C2311yescharacteristic
52C22×C4×D47—24no—
53C22×C4×D47—24no—
54C22×C4×D47—24no—
55C22×C4×D47—22no—
56C22×C4×D47—22no—
57C22×C4×D47—24no—
58C22×C4×D47—24no—
59C22×C4×D47—24no—
60C22×C4×D47—42no—
61C22×C4×D47—42no—
62C22×C4×D47—42no—
63C22×C4×D47C2×C414yes—
64C4×C22⋊D47—232no—
65C2×Dic47⋊C4—24no—
66C2×Dic47⋊C4—24no—
67C2×Dic47⋊C4—24no—
68C2×Dic47⋊C4—42no—
69C2×Dic47⋊C4C2×C414yescomplemented
70C2×C22⋊Dic47—24no—
71C2×C22⋊Dic47—24no—
72C2×C22⋊Dic47—24no—
73C2×C22⋊Dic47—42no—
74C2×C22⋊Dic47C2×C414yescomplemented
75C2×(C2×D47)⋊C4—24no—
76C2×(C2×D47)⋊C4—24no—
77C2×(C2×D47)⋊C4—24no—
78C2×(C2×D47)⋊C4C2×C414yes—
79C2×(C2×D47)⋊C4D418yes—
80C2×C4×Dic47—24no—
81C2×C4×Dic47C2×C414yescomplemented
82C47⋊#95—24no—
83C47⋊#95—22no—
84C47⋊#95—24no—
85C47⋊#95—22no—
86C47⋊#95—24no—
87C47⋊#95—24no—
88C47⋊#95—24no—
89C47⋊#95—42no—
90C25×C47C2311yescharacteristic
91C23×C4×C47—24no—
92C23×C4×C47—22no—
93C23×C4×C47—22no—
94C23×C4×C47—42no—
95C23×C4×C47C2×C414yescomplemented
96C23×C4×C47C2312yes—
97C23×C4×C47C2312yes—
98C23×C4×C47C2311yescharacteristic
99C23×C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47—24no—
101C2×C4⋊C4×C47—24no—
102C2×C4⋊C4×C47—42no—
103C2×C22⋊C4×C47—24no—
104C2×C22⋊C4×C47—24no—
105C2×C22⋊C4×C47—42no—
106#95×C47—22no—
107#95×C47D414yescomplemented
108C24×C47—21no—
109C24×C47—22no—
110C24×C47—21no—
111C24×C47—22no—
112C24×C47—22no—
113C24×C47—21no—
114C24×C47—22no—
115C24×C47—21no—
116C24×C47C22×C412yes—
117C24×C47C2×D412yes—
118C24×C47C2×Q812yes—
119C24×C47C2411yescharacteristic
120C23×D47—21no—
121C23×D47—21no—
122C23×D47—22no—
123C23×D47—22no—
124C23×D47—21no—
125C23×D47—21no—
126C23×D47C22×C412yes—
127C23×D47C2×D414yes—
128C23×D47C2×D412yes—
129C23×D47C2×Q812yes—
130C23×D47#4114yes—
131C22×C4×C47—21no—
132C22×C4×C47—22no—
133C22×C4×C47—21no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—28no—
143C22×C4×C47—28no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—44no—
152C22×C4×C47—48no—
153C22×C4×C47—48no—
154C22×C4×C47C22×C412yes—
155C22×C4×C47C22×C412yes—
156C22×C4×C47C2×D414yes—
157C22×C4×C47C2×D414yes—
158C22×C4×C47C2×D412yes—
159C22×C4×C47#4112yes—
160C2×C22⋊D47—28no—
161C2×C22⋊D47—28no—
162C2×C22⋊D47—216no—
163C2×C22⋊D47—216no—
164C2×C22⋊D47C4⋊C4116yescomplemented
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—21no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47C22×C412yes—
188C22×Dic47C22×C412yes—
189C22×Dic47C22×C412yes—
190C22×Dic47C2×D414yes—
191C22×Dic47C2×D412yes—
192C22×Dic47C2×Q812yes—
193C22×Dic47#4114yes—
194C2×C4×D47—216no—
195C2×C4×D47—28no—
196C2×C4×D47—28no—
197C2×C4×D47—44no—
198C2×C4×D47—48no—
199C2×C4×D47—48no—
200C2×C4×D47—48no—
201C2×C4×D47—48no—
202C2×C4×D47—48no—
203C2×C4×D47—48no—
204C2×C4×D47—48no—
205C2×C4×D47—48no—
206C4⋊C4×C47—48no—
207C22⋊C4×C47—48no—
208C22⋊Dic47—28no—
209C22⋊Dic47—48no—
210(C2×D47)⋊C4—48no—
211(C2×D47)⋊C4C22⋊C4116yescomplemented
212Dic47⋊C4—28no—
213Dic47⋊C4—48no—
214C4×Dic47—28no—
215C23×C47—22no—
216C23×C47—22no—
217C23×C47—22no—
218C23×C47—22no—
219C23×C47—22no—
220C23×C47—22no—
221C23×C47—24no—
222C23×C47—24no—
223C23×C47—22no—
224C23×C47—24no—
225C23×C47—22no—
226C23×C47—22no—
227C23×C47—24no—
228C23×C47—22no—
229C23×C47—42no—
230C23×C47—42no—
231C23×C47—42no—
232C23×C47—42no—
233C23×C47—42no—
234C23×C47—42no—
235C23×C47—42no—
236C23×C47—42no—
237C23×C47C2×C4⋊C414yes—
238C23×C47C23×C411yescharacteristic
239C23×C47C22×D412yes—
240C23×C47C22×D411yescharacteristic
241C23×C47C22×D411yescharacteristic
242C23×C47C22×Q811yescharacteristic
243C23×C47C2×#4112yes—
244C23×C47C2×#4112yes—
245C23×C47C2×#4111yescharacteristic
246C23×C47H(5,𝔽2)12yes—
247C23×C47H(5,𝔽2)11yescharacteristic
248C23×C472−1+411yescharacteristic
249C22×D47—22no—
250C22×D47—22no—
251C22×D47—22no—
252C22×D47—22no—
253C22×D47—24no—
254C22×D47—24no—
255C22×D47—24no—
256C22×D47—24no—
257C22×D47—24no—
258C22×D47—22no—
259C22×D47—24no—
260C22×D47—24no—
261C22×D47—24no—
262C22×D47—22no—
263C22×D47—24no—
264C22×D47—22no—
265C22×D47—24no—
266C22×D47—22no—
267C22×D47C2×C22⋊C414yes—
268C22×D47C2×C4⋊C414yes—
269C22×D47#11714yes—
270C22×D47#12118yes—
271C22×D47C22⋊Q818yes—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—24no—
277C2×C4×C47—24no—
278C2×C4×C47—24no—
279C2×C4×C47—24no—
280C2×C4×C47—24no—
281C2×C4×C47—24no—
282C2×C4×C47—24no—
283C2×C4×C47—416no—
284C2×C4×C47—42no—
285C2×C4×C47—42no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47—42no—
289C2×C4×C47—42no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47C2×C22⋊C414yes—
296C2×C4×C47C4×D414yes—
297C22⋊D47—232no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—24no—
303C2×Dic47—24no—
304C2×Dic47—24no—
305C2×Dic47—24no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—24no—
310C2×Dic47—24no—
311C2×Dic47—24no—
312C2×Dic47—42no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47—42no—
318C2×Dic47—42no—
319C2×Dic47—42no—
320C2×Dic47—42no—
321C2×Dic47—42no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325C2×Dic47C2×C22⋊C414yes—
326C2×Dic47C2×C4⋊C414yes—
327C4×D47—416no—
328C4×D47—432no—
329#13899—471nomaximal, Sylow
330C22×C47—24no—
331C22×C47—24no—
332C22×C47—24no—
333C22×C47—42no—
334C22×C47—42no—
335C22×C47—42no—
336C22×C47—44no—
337C22×C47—44no—
338C22×C47—44no—
339C22×C47—44no—
340C22×C47—42no—
341C22×C47C22×C22⋊C411yescharacteristic
342C22×C47C22×C4⋊C411yescharacteristic
343C22×C47C2×#11711yescharacteristic
344C22×C47C2×C4×D411yescharacteristic
345C22×C47C4×#4111yescharacteristic
346C22×C47#51811yescharacteristic
347C22×C47#52011yescharacteristic
348C22×C47C2×#12112yes—
349C22×C47C2×C22⋊Q812yes—
350C22×C47#52512yes—
351C22×C47#52912yes—
352C22×C47#53812yes—
353C22×C47#53912yes—
354C22×C47D4212yes—
355C22×C47D4211yescharacteristic
356C22×C47#54612yes—
357C22×C47#54612yes—
358C22×C47#54612yes—
359C22×C47#54711yescharacteristic
360C22×C47#54712yes—
361C22×C47D4×Q811yescharacteristic
362C22×C47#55412yes—
363C22×C47#55411yescharacteristic
364C2×D47—24no—
365C2×D47—24no—
366C2×D47—24no—
367C2×D47—24no—
368C2×D47—24no—
369C2×D47—28no—
370C2×D47—28no—
371C2×D47—28no—
372C2×D47—28no—
373C2×D47—24no—
374C2×D47#38018yescomplemented
375C4×C47—24no—
376C4×C47—24no—
377C4×C47—44no—
378C4×C47—82no—
379Dic47—24no—
380Dic47—24no—
381Dic47—42no—
382Dic47—44no—
383Dic47—82no—
384C22×C4×D4—471no—
385C2×#386—472no—
386C2×#385—472no—
387C2×#380D4711yescharacteristic, complemented
388C22×#95—471no—
389#1441—472no—
390#1439—472no—
391C4⋊#95—471no—
392#1434—471no—
393C22⋊#95—471no—
394C22⋊#95—471no—
395C2×C47—44no—
396C2×C47C2×#38011yescharacteristic
397C2×C47#229011yescharacteristic
398C2×C47#231811yescharacteristic
399C2×C47D4×C22⋊C411yescharacteristic
400C2×C47#233911yescharacteristic
401C2×C47D4×C4⋊C411yescharacteristic
402C2×C47#234911yescharacteristic
403C2×C47#242412yes—
404C2×C47#242512yes—
405C2×C47#244912yes—
406C2×C47#245012yes—
407D47—28no—
408C23×D4—471no—
409C24×C4—471no—
410C24×C4—472no—
411C24×C4C2×D4711yescharacteristic
412C2×C4×D4—478no—
413C2×C4×D4—948no—
414C22×C4⋊C4—471no—
415C22×C4⋊C4—472no—
416C22×C4⋊C4C2×D4712yes—
417C22×C22⋊C4—471no—
418C22×C22⋊C4—471no—
419C22×C22⋊C4—472no—
420C22×C22⋊C4—472no—
421C22×C22⋊C4C2×D4712yes—
422C22×C42—471no—
423#386—948no—
424#385—948no—
425#380—24no—
426C2×#95—471no—
427C2×#95—471no—
428C2×#95—472no—
429C2×#95—472no—
430C2×#95—472no—
431C2×#95—472no—
432C2×#95—472no—
433C2×#95—472no—
434C2×#95—944no—
435C2×#95C2×D4711yescharacteristic
436C2×#95C2×D4711yescharacteristic
437C47#1389911yescharacteristic, complemented, Sylow
438C25—471no—
439C25C22×D4711yescharacteristic
440C22×D4—474no—
441C22×D4—474no—
442C22×D4—474no—
443C22×D4—944no—
444C22×D4—944no—
445C23×C4—22no—
446C23×C4—24no—
447C23×C4—22no—
448C23×C4—42no—
449C23×C4—471no—
450C23×C4—471no—
451C23×C4—471no—
452C23×C4—472no—
453C23×C4—474no—
454C23×C4—472no—
455C23×C4—944no—
456C23×C4—944no—
457C23×C4—944no—
458C23×C4—944no—
459C23×C4—944no—
460C23×C4—942no—
461C23×C4—944no—
462C23×C4—942no—
463C23×C4—1882no—
464C23×C4—1882no—
465C23×C4—1882no—
466C23×C4C4×D4714yescomplemented
467C23×C4C22×D4712yes—
468C23×C4C22×D4712yes—
469C23×C4C22×D4711yescharacteristic
470C23×C4C22×D4711yescharacteristic
471C4×D4—9432no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—474no—
476C2×C4⋊C4—944no—
477C2×C4⋊C4—944no—
478C2×C4⋊C4—944no—
479C2×C4⋊C4—1882no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—474no—
484C2×C22⋊C4—478no—
485C2×C22⋊C4—474no—
486C2×C22⋊C4—944no—
487C2×C22⋊C4—944no—
488C2×C22⋊C4—944no—
489C2×C22⋊C4—944no—
490C2×C22⋊C4—944no—
491C2×C22⋊C4—944no—
492C2×C22⋊C4—1882no—
493C2×C42—474no—
494C2×C42—944no—
495#95—22no—
496#95—944no—
497#95—944no—
498#95—944no—
499#95—942no—
500#95—944no—
501#95—944no—
502#95—942no—
503#95—1882no—
504#95C22⋊D4714yescomplemented
505C24—22no—
506C24—21no—
507C24—22no—
508C24—22no—
509C24—21no—
510C24—21no—
511C24—22no—
512C24—21no—
513C24—472no—
514C24—474no—
515C24—472no—
516C24—472no—
517C24—474no—
518C24—941no—
519C24—942no—
520C24—941no—
521C24—942no—
522C24—941no—
523C24—941no—
524C24C2×C4×D4712yes—
525C24D4×D4712yes—
526C24Q8×D4712yes—
527C24C23×D4711yescharacteristic
528C2×D4—4716no—
529C2×D4—948no—
530C2×D4—948no—
531C2×D4—9416no—
532C2×D4—9416no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—44no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—472no—
557C22×C4—472no—
558C22×C4—472no—
559C22×C4—474no—
560C22×C4—472no—
561C22×C4—472no—
562C22×C4—474no—
563C22×C4—948no—
564C22×C4—9416no—
565C22×C4—942no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—941no—
569C22×C4—941no—
570C22×C4—942no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—941no—
574C22×C4—942no—
575C22×C4—942no—
576C22×C4—941no—
577C22×C4—942no—
578C22×C4—942no—
579C22×C4—942no—
580C22×C4—948no—
581C22×C4—942no—
582C22×C4—942no—
583C22×C4—942no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—1884no—
589C22×C4—1888no—
590C22×C4—1888no—
591C22×C4—1888no—
592C22×C4—1888no—
593C22×C4—1888no—
594C22×C4—1888no—
595C22×C4—1888no—
596C22×C4—1888no—
597C22×C4C2×C4×D4712yes—
598C22×C4C2×C4×D4712yes—
599C22×C4#1062535012yes—
600C22×C4D4×D4714yes—
601C22×C4C2×C22⋊D4714yes—
602C22×C4C2×C22⋊D4712yes—
603C4⋊C4—48no—
604C4⋊C4—948no—
605C4⋊C4—1888no—
606C22⋊C4—48no—
607C22⋊C4—4716no—
608C22⋊C4—948no—
609C22⋊C4—1888no—
610C22⋊C4—1888no—
611C42—948no—
612C23—22no—
613C23—24no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—24no—
625C23—24no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—474no—
635C23—474no—
636C23—474no—
637C23—478no—
638C23—478no—
639C23—942no—
640C23—944no—
641C23—944no—
642C23—944no—
643C23—944no—
644C23—942no—
645C23—944no—
646C23—942no—
647C23—944no—
648C23—942no—
649C23—942no—
650C23—942no—
651C23—942no—
652C23—942no—
653C23—944no—
654C23—944no—
655C23—944no—
656C23—944no—
657C23C4⋊C4×D4714yes—
658C23C22×C4×D4711yescharacteristic
659C23C2×D4×D4711yescharacteristic
660C23C2×D4×D4712yes—
661C23C22×C22⋊D4711yescharacteristic
662C23C2×Q8×D4711yescharacteristic
663C23#41×D4712yes—
664C23#41×D4712yes—
665C23C2×#1062535011yescharacteristic
666C23#1309406912yes—
667C23#1309406911yescharacteristic
668C23#1309407211yescharacteristic
669D4—9432no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—416no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—474no—
694C2×C4—474no—
695C2×C4—944no—
696C2×C4—944no—
697C2×C4—942no—
698C2×C4—942no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—944no—
702C2×C4—944no—
703C2×C4—944no—
704C2×C4—944no—
705C2×C4—942no—
706C2×C4—942no—
707C2×C4—942no—
708C2×C4—944no—
709C2×C4—18816no—
710C2×C4—18832no—
711C2×C4—1882no—
712C2×C4—1882no—
713C2×C4—1882no—
714C2×C4—1882no—
715C2×C4—1882no—
716C2×C4—1882no—
717C2×C4—1882no—
718C2×C4—1882no—
719C2×C4—1882no—
720C2×C4—1882no—
721C2×C4—1882no—
722C2×C4—1882no—
723C2×C4—1882no—
724C2×C4C22⋊C4×D4714yes—
725C2×C4C4×C22⋊D4714yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—42no—
730C22—42no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—44no—
735C22—42no—
736C22—42no—
737C22—478no—
738C22—944no—
739C22—944no—
740C22—944no—
741C22—944no—
742C22—948no—
743C22—948no—
744C22—948no—
745C22—948no—
746C22—944no—
747C22—944no—
748C22C2×C22⋊C4×D4711yescharacteristic
749C22C2×C4⋊C4×D4711yescharacteristic
750C22#117×D4711yescharacteristic
751C22C2×C4×C22⋊D4711yescharacteristic
752C22#1568959111yescharacteristic
753C22#1568959611yescharacteristic
754C22#1568960411yescharacteristic
755C22#121×D4712yes—
756C22C22⋊Q8×D4712yes—
757C22#1568963012yes—
758C22#1568965112yes—
759C22#1568970512yes—
760C22#1568971912yes—
761C22D4×C22⋊D4711yescharacteristic
762C22D4×C22⋊D4712yes—
763C22#1568976212yes—
764C22#1568976312yes—
765C22#1568977012yes—
766C22#1568977411yescharacteristic
767C22#1568977512yes—
768C22Q8×C22⋊D4711yescharacteristic
769C22#1568982712yes—
770C22#1568982811yescharacteristic
771C4—24no—
772C4—24no—
773C4—44no—
774C4—82no—
775C4—944no—
776C4—944no—
777C4—3762no—
778C4—1884no—
779C4—1882no—
780C2—44no—
781C2—948no—
782C2#380×D4711yescharacteristic
783C2#2024582511yescharacteristic
784C2#2024602311yescharacteristic
785C2C22⋊C4×C22⋊D4711yescharacteristic
786C2#2024621611yescharacteristic
787C2C4⋊C4×C22⋊D4711yescharacteristic
788C2#2024629211yescharacteristic
789C2#2024692112yes—
790C2#2024693612yes—
791C2#2024719412yes—
792C2#2024721912yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#380C2
socle, cosocleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC2×#380D47
hypocenterC47#13899
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
3. C2×#15688994C2semidirect
4. C2×#95×D47C2semidirect
5. #20241638C2semidirect
6. #20241631C2semidirect
7. Dic47⋊#95C2semidirect
8. #20241613C2semidirect
9. #20241611C2semidirect
10. (C2×D47)⋊#95C2semidirect
11. C2×C47×#380C2semidirect
16. C2×C4×C22⋊D47C4semidirect
69. C2×Dic47⋊C4C2×C4semidirect
74. C2×C22⋊Dic47C2×C4semidirect
81. C2×C4×Dic47C2×C4semidirect
95. C23×C4×C47C2×C4semidirect
107. #95×C47D4semidirect
164. C2×C22⋊D47C4⋊C4semidirect
211. (C2×D47)⋊C4C22⋊C4semidirect
374. C2×D47#380semidirect
387. C2×#380D47semidirect
437. C47#13899semidirect
466. C23×C4C4×D47semidirect
504. #95C22⋊D47semidirect

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×#156889992
C2×#156889942
C2×#95×D472
#202416382
#202416312
Dic47⋊#952
#202416132
#202416112
(C2×D47)⋊#952
C2×C47×#3802
#1389947