Finite Group Databasebeta

← #26138665

Subgroups — #26138665

Order 12032.

4166 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Q8×D47C211yesmaximal, characteristic
2C2×#15689030C211yesmaximal, characteristic, complemented
3C2×#15689029C211yesmaximal, characteristic, complemented
4C2×#15689028C211yesmaximal, characteristic, complemented
5C2×#15688980C211yesmaximal, characteristic
6C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
7#20241658C214yesmaximal, complemented
8(C2×D47)⋊#95C214yesmaximal
9C2×C47×#391C211yesmaximal, characteristic, complemented
10C23×Dic94C2212yes—
11C23×Dic94C2211yescharacteristic
12C22×Q8×D47—24no—
13C22×Q8×D47—24no—
14C22×Q8×D47—24no—
15C22×Q8×D47—24no—
16C22×Q8×D47—24no—
17C22×Q8×D47—24no—
18C22×Q8×D47C418yescomplemented
19C23×C4×D47C2212yes—
20C23×C4×D47C2211yescharacteristic
21C22×C4⋊Dic47C2211yescharacteristic
22C22×(C2×D47)⋊C4C2212yes—
23C22×(C2×D47)⋊C4C2212yes—
24C22×C4×Dic47C2211yescharacteristic
25#15689030—24no—
26#15689029—24no—
27#15689028—24no—
28#15688980—24no—
29C4×(C2×D47)⋊C4—24no—
30C2×C47⋊#95C2214yes—
31C2×C47⋊#95C2214yes—
32C2×C47⋊#95C2214yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C23×Q8×C47C2211yescharacteristic
36C22×C4⋊C4×C47C2211yescharacteristic
37C22×C42×C47C2211yescharacteristic
38C47×#391—24no—
39C2×#95×C47C2214yes—
40C24×D47C2311yescharacteristic
41C22×Dic94—24no—
42C22×Dic94—24no—
43C22×Dic94—22no—
44C22×Dic94—22no—
45C22×Dic94—22no—
46C22×Dic94—22no—
47C22×Dic94—24no—
48C22×Dic94—24no—
49C22×Dic94—24no—
50C22×Dic94—24no—
51C22×Dic94C2×C418yes—
52C22×Dic94C2×C414yes—
53C22×Dic94D414yes—
54C22×Dic94D414yes—
55C2×Q8×D47—232no—
56C2×Q8×D47—232no—
57C2×Q8×D47—232no—
58C2×Q8×D47—232no—
59C2×Q8×D47—232no—
60C2×Q8×D47—232no—
61C2×Q8×D47—232no—
62C23×Dic47C2312yes—
63C23×Dic47C2312yes—
64C23×Dic47C2312yes—
65C23×Dic47C2311yescharacteristic
66C22×C4×D47—24no—
67C22×C4×D47—24no—
68C22×C4×D47—24no—
69C22×C4×D47—24no—
70C22×C4×D47—22no—
71C22×C4×D47—22no—
72C22×C4×D47—22no—
73C22×C4×D47—22no—
74C22×C4×D47—24no—
75C22×C4×D47—24no—
76C22×C4×D47C2×C418yes—
77C22×C4×D47C2×C414yes—
78C22×C4×D47D414yes—
79C22×C4×D47D414yes—
80C2×C4⋊Dic47—22no—
81C2×C4⋊Dic47—22no—
82C2×C4⋊Dic47—22no—
83C2×(C2×D47)⋊C4—24no—
84C2×(C2×D47)⋊C4—24no—
85C2×(C2×D47)⋊C4—24no—
86C2×(C2×D47)⋊C4—28no—
87C2×(C2×D47)⋊C4Q818yescomplemented
88C2×C4×Dic47—22no—
89C2×C4×Dic47—22no—
90C2×C4×Dic47—22no—
91C47⋊#95—28no—
92C47⋊#95—24no—
93C47⋊#95—24no—
94C47⋊#95—28no—
95C47⋊#95—28no—
96C22×Q8×C47—22no—
97C22×Q8×C47—22no—
98C22×Q8×C47—22no—
99C22×Q8×C47—22no—
100C22×Q8×C47C2×C414yes—
101C22×Q8×C47D414yes—
102C22×Q8×C47D414yes—
103C23×C4×C47C2312yes—
104C23×C4×C47C2312yes—
105C23×C4×C47C2312yes—
106C23×C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47—22no—
108C2×C4⋊C4×C47—22no—
109C2×C4⋊C4×C47—22no—
110C2×C42×C47—22no—
111C2×C42×C47—22no—
112C2×C42×C47—22no—
113#95×C47—28no—
114C24×C47C2411yescharacteristic
115C23×D47—21no—
116C23×D47—21no—
117C23×D47—21no—
118C23×D47—21no—
119C23×D47—22no—
120C23×D47—22no—
121C23×D47C22×C412yes—
122C23×D47C2×D412yes—
123C23×D47C2×D412yes—
124C23×D47C2×Q814yes—
125C23×D47#4114yes—
126C2×Q8×C47—28no—
127C2×Q8×C47—28no—
128C2×Q8×C47—28no—
129C2×Q8×C47—28no—
130C2×Q8×C47—28no—
131C2×Q8×C47—28no—
132C2×Q8×C47C22⋊C4116yescomplemented
133C22×C4×C47—22no—
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—22no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—24no—
147C22×C4×C47—24no—
148C22×C4×C47C22×C414yes—
149C22×C4×C47C22×C412yes—
150C22×C4×C47C2×D414yes—
151C22×C4×C47C2×D414yes—
152C22×C4×C47C2×D412yes—
153C22×C4×C47C2×D412yes—
154C22×C4×C47C2×D412yes—
155C22×C4×C47C2×D412yes—
156C22×C4×C47C2×D412yes—
157C22×C4×C47C2×D412yes—
158C22×C4×C47C2×Q814yescomplemented
159C22×Dic47—22no—
160C22×Dic47—22no—
161C22×Dic47—21no—
162C22×Dic47—21no—
163C22×Dic47—21no—
164C22×Dic47—22no—
165C22×Dic47—21no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—24no—
177C22×Dic47—24no—
178C22×Dic47C22×C412yes—
179C22×Dic47C22×C414yes—
180C22×Dic47C2×D414yes—
181C22×Dic47C2×D414yes—
182C22×Dic47C2×D412yes—
183C22×Dic47C2×D412yes—
184C22×Dic47C2×Q814yescomplemented
185Q8×D47—2256no—
186C2×C4×D47—216no—
187C2×C4×D47—216no—
188C2×C4×D47—216no—
189C2×C4×D47—216no—
190C2×C4×D47—216no—
191C2×C4×D47—216no—
192C2×C4×D47—28no—
193C2×C4×D47—28no—
194C2×C4×D47—28no—
195C2×C4×D47—28no—
196C2×C4×D47—28no—
197C2×C4×D47—28no—
198C2×C4×D47—216no—
199C2×C4×D47C22⋊C4116yes—
200C2×Dic94—216no—
201C2×Dic94—216no—
202C2×Dic94—216no—
203C2×Dic94—216no—
204C2×Dic94—216no—
205C2×Dic94—28no—
206C2×Dic94—28no—
207C2×Dic94—28no—
208C2×Dic94—28no—
209C2×Dic94—28no—
210C2×Dic94—28no—
211C2×Dic94—216no—
212C2×Dic94—216no—
213C2×Dic94C22⋊C4116yescomplemented
214C4⋊C4×C47—44no—
215C42×C47—44no—
216(C2×D47)⋊C4—216no—
217(C2×D47)⋊C4—48no—
218C4⋊Dic47—44no—
219C4×Dic47—44no—
220C23×C47C23×C411yescharacteristic
221C23×C47C22×D411yescharacteristic
222C23×C47C22×D411yescharacteristic
223C23×C47C22×D411yescharacteristic
224C23×C47C22×D411yescharacteristic
225C23×C47C22×D411yescharacteristic
226C23×C47C22×D411yescharacteristic
227C23×C47C22×Q812yes—
228C23×C47C2×#4112yes—
229C23×C472−1+412yes—
230C23×C472−1+412yes—
231C22×D47—22no—
232C22×D47—22no—
233C22×D47—24no—
234C22×D47—22no—
235C22×D47—22no—
236C22×D47—22no—
237C22×D47—22no—
238C22×D47—22no—
239C22×D47—24no—
240C22×D47—22no—
241C22×D47—24no—
242C22×D47—24no—
243C22×D47—24no—
244C22×D47—24no—
245C22×D47—24no—
246C22×D47—24no—
247C22×D47—24no—
248C22×D47—24no—
249C22×D47C2×C22⋊C414yes—
250C22×D47C4×Q818yes—
251C22×D47C22⋊Q818yes—
252C22×D47#12414yes—
253C22×D47C4⋊Q814yes—
254Q8×C47—232no—
255C2×C4×C47—24no—
256C2×C4×C47—24no—
257C2×C4×C47—24no—
258C2×C4×C47—24no—
259C2×C4×C47—24no—
260C2×C4×C47—24no—
261C2×C4×C47—24no—
262C2×C4×C47—24no—
263C2×C4×C47—24no—
264C2×C4×C47—42no—
265C2×C4×C47—42no—
266C2×C4×C47—42no—
267C2×C4×C47—42no—
268C2×C4×C47—42no—
269C2×C4×C47—42no—
270C2×C4×C47—42no—
271C2×C4×C47—44no—
272C2×C4×C47—44no—
273C2×C4×C47C2×C22⋊C414yes—
274C2×C4×C47C2×C22⋊C414yes—
275C2×C4×C47C2×C22⋊C418yes—
276C2×C4×C47C2×C22⋊C414yes—
277C2×C4×C47#12014yes—
278C2×C4×C47#12014yes—
279C2×C4×C47#12014yes—
280C2×C4×C47#12014yes—
281C2×Dic47—24no—
282C2×Dic47—22no—
283C2×Dic47—22no—
284C2×Dic47—24no—
285C2×Dic47—22no—
286C2×Dic47—24no—
287C2×Dic47—22no—
288C2×Dic47—24no—
289C2×Dic47—22no—
290C2×Dic47—24no—
291C2×Dic47—22no—
292C2×Dic47—24no—
293C2×Dic47—24no—
294C2×Dic47—24no—
295C2×Dic47—24no—
296C2×Dic47—42no—
297C2×Dic47—42no—
298C2×Dic47—42no—
299C2×Dic47—42no—
300C2×Dic47—42no—
301C2×Dic47—42no—
302C2×Dic47—42no—
303C2×Dic47—44no—
304C2×Dic47—44no—
305C2×Dic47C2×C22⋊C414yes—
306C2×Dic47C2×C22⋊C418yes—
307C4×D47—264no—
308C4×D47—232no—
309Dic94—264no—
310Dic94—232no—
311#13922—471nomaximal, Sylow
312C22×C47C22×C22⋊C411yescharacteristic
313C22×C47C22×C22⋊C411yescharacteristic
314C22×C47C22×C22⋊C411yescharacteristic
315C22×C47C2×C4×Q812yes—
316C22×C47#51912yes—
317C22×C47C2×#12011yescharacteristic
318C22×C47C2×#12011yescharacteristic
319C22×C47C2×#12011yescharacteristic
320C22×C47C2×#12011yescharacteristic
321C22×C47C2×C22⋊Q812yes—
322C22×C47C2×#12411yescharacteristic
323C22×C47C2×C4⋊Q811yescharacteristic
324C22×C47#53611yescharacteristic
325C22×C47#53612yes—
326C22×C47#53611yescharacteristic
327C22×C47#54812yes—
328C22×C47#54812yes—
329C22×C47#54812yes—
330C22×C47#54812yes—
331C22×C47D4×Q812yes—
332C22×C47D4×Q812yes—
333C22×C47D4×Q812yes—
334C22×C47D4×Q812yes—
335C2×D47—24no—
336C2×D47—28no—
337C2×D47—28no—
338C2×D47—28no—
339C2×D47—28no—
340C2×D47—24no—
341C2×D47—24no—
342C2×D47—24no—
343C2×D47—24no—
344C2×D47—24no—
345C2×D47#39118yescomplemented
346C4×C47—28no—
347C4×C47—44no—
348C4×C47—82no—
349C4×C47#37918yes—
350Dic47—24no—
351Dic47—28no—
352Dic47—44no—
353Dic47—82no—
354C24×Q8—471no—
355C2×#391—471no—
356C2×#391—471no—
357C2×#391—471no—
358C2×#391D4711yescharacteristic, complemented
359C2×#380—471no—
360C2×C4×C22⋊C4—471no—
361#1446—474no—
362C22⋊#95—474no—
363C2×C47C2×#37911yescharacteristic
364C2×C47C2×#39111yescharacteristic
365C2×C47#231011yescharacteristic
366C2×C47Q8×C22⋊C412yes—
367C2×C47Q8×C22⋊C412yes—
368C2×C47#240912yes—
369C2×C47#240912yes—
370C2×C47#243411yescharacteristic
371C2×C47#243411yescharacteristic
372C2×C47#243611yescharacteristic
373C2×C47#243611yescharacteristic
374D47—28no—
375C23×Q8—478no—
376C23×Q8—471no—
377C23×Q8—472no—
378C23×Q8—944no—
379C23×Q8—944no—
380C23×Q8—944no—
381C23×Q8—944no—
382C23×Q8—944no—
383C23×Q8—944no—
384C23×Q8C2×D4711yescharacteristic
385C24×C4—471no—
386C24×C4—472no—
387C22×C4⋊C4—471no—
388C22×C4⋊C4C2×D4711yescharacteristic
389C22×C22⋊C4—472no—
390C22×C22⋊C4—472no—
391C22×C42—471no—
392C22×C42C2×D4711yescharacteristic
393#391—24no—
394#391—944no—
395#391—944no—
396#391—944no—
397#380—944no—
398C4×C22⋊C4—944no—
399C2×#95—474no—
400C2×#95—474no—
401C2×#95—474no—
402C2×#95—472no—
403C2×#95—472no—
404C2×#95C2×D4714yes—
405C47#1392211yescharacteristic, complemented, Sylow
406C25—471no—
407C22×Q8—22no—
408C22×Q8—22no—
409C22×Q8—22no—
410C22×Q8—22no—
411C22×Q8—474no—
412C22×Q8—478no—
413C22×Q8—474no—
414C22×Q8—474no—
415C22×Q8—944no—
416C22×Q8—944no—
417C22×Q8—944no—
418C22×Q8—944no—
419C22×Q8—9432no—
420C22×Q8—9432no—
421C22×Q8—9432no—
422C22×Q8—9432no—
423C22×Q8—9432no—
424C22×Q8—9432no—
425C22×Q8—9432no—
426C22×Q8—944no—
427C22×Q8—942no—
428C22×Q8—942no—
429C22×Q8—942no—
430C22×Q8—944no—
431C22×Q8—942no—
432C22×Q8C4×D4714yes—
433C22×Q8D18814yes—
434C22×Q8C22⋊D4714yes—
435C23×C4—471no—
436C23×C4—472no—
437C23×C4—474no—
438C23×C4—474no—
439C23×C4—474no—
440C23×C4—472no—
441C23×C4—478no—
442C23×C4—472no—
443C23×C4—944no—
444C23×C4—944no—
445C23×C4—944no—
446C23×C4—944no—
447C23×C4—944no—
448C23×C4—942no—
449C23×C4—942no—
450C23×C4—942no—
451C23×C4—944no—
452C23×C4—942no—
453C23×C4C22×D4712yes—
454C23×C4C22×D4712yes—
455C23×C4C22×D4712yes—
456C23×C4C22×D4711yescharacteristic
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—942no—
461C2×C4⋊C4—942no—
462C2×C4⋊C4—942no—
463C2×C22⋊C4—478no—
464C2×C22⋊C4—944no—
465C2×C22⋊C4—944no—
466C2×C22⋊C4—948no—
467C2×C22⋊C4—944no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—942no—
472C2×C42—942no—
473C2×C42—942no—
474#95—28no—
475#95—944no—
476#95—944no—
477#95—948no—
478#95—948no—
479#95—948no—
480C24—472no—
481C24—472no—
482C24—472no—
483C24—474no—
484C24—474no—
485C24—941no—
486C24—941no—
487C24—941no—
488C24—941no—
489C24—942no—
490C24—942no—
491C24C23×D4711yescharacteristic
492C2×Q8—28no—
493C2×Q8—28no—
494C2×Q8—28no—
495C2×Q8—28no—
496C2×Q8—28no—
497C2×Q8—28no—
498C2×Q8—4716no—
499C2×Q8—9416no—
500C2×Q8—9416no—
501C2×Q8—9416no—
502C2×Q8—9416no—
503C2×Q8—9416no—
504C2×Q8—9416no—
505C2×Q8—94256no—
506C2×Q8—948no—
507C2×Q8—9416no—
508C2×Q8—948no—
509C2×Q8—948no—
510C2×Q8—948no—
511C2×Q8—948no—
512C2×Q8—948no—
513C2×Q8(C2×D47)⋊C4116yescomplemented
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—472no—
530C22×C4—474no—
531C22×C4—472no—
532C22×C4—472no—
533C22×C4—474no—
534C22×C4—474no—
535C22×C4—4716no—
536C22×C4—474no—
537C22×C4—9416no—
538C22×C4—9416no—
539C22×C4—9416no—
540C22×C4—9416no—
541C22×C4—9416no—
542C22×C4—9416no—
543C22×C4—941no—
544C22×C4—941no—
545C22×C4—942no—
546C22×C4—942no—
547C22×C4—941no—
548C22×C4—942no—
549C22×C4—941no—
550C22×C4—942no—
551C22×C4—948no—
552C22×C4—9416no—
553C22×C4—948no—
554C22×C4—948no—
555C22×C4—948no—
556C22×C4—948no—
557C22×C4—948no—
558C22×C4—942no—
559C22×C4—942no—
560C22×C4—942no—
561C22×C4—942no—
562C22×C4—942no—
563C22×C4—942no—
564C22×C4—942no—
565C22×C4—942no—
566C22×C4—942no—
567C22×C4—944no—
568C22×C4—944no—
569C22×C4C2×C4×D4714yes—
570C22×C4C2×C4×D4712yes—
571C22×C4C2×D18814yes—
572C22×C4C2×D18812yes—
573C22×C4D4×D4712yes—
574C22×C4D4×D4712yes—
575C22×C4D4×D4712yes—
576C22×C4D4×D4712yes—
577C22×C4Q8×D4714yescomplemented
578C22×C4C2×C22⋊D4714yes—
579C22×C4C2×C22⋊D4712yes—
580C4⋊C4—44no—
581C4⋊C4—1884no—
582C22⋊C4—9416no—
583C22⋊C4—1888no—
584C42—44no—
585C42—1884no—
586C23—474no—
587C23—478no—
588C23—478no—
589C23—474no—
590C23—474no—
591C23—944no—
592C23—944no—
593C23—944no—
594C23—944no—
595C23—944no—
596C23—944no—
597C23—944no—
598C23—944no—
599C23—942no—
600C23—942no—
601C23—944no—
602C23—942no—
603C23—942no—
604C23—942no—
605C23—942no—
606C23—942no—
607C23—944no—
608C23—942no—
609C23C22×C4×D4711yescharacteristic
610C23C2×D4×D4711yescharacteristic
611C23C2×D4×D4711yescharacteristic
612C23C2×D4×D4711yescharacteristic
613C23C2×D4×D4711yescharacteristic
614C23C22×C22⋊D4711yescharacteristic
615C23C22×D18811yescharacteristic
616C23C2×Q8×D4712yes—
617C23#41×D4712yes—
618C23#1309407112yes—
619C23#1309407212yes—
620Q8—232no—
621Q8—9464no—
622Q8—9432no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—474no—
642C2×C4—478no—
643C2×C4—9464no—
644C2×C4—944no—
645C2×C4—942no—
646C2×C4—942no—
647C2×C4—944no—
648C2×C4—942no—
649C2×C4—944no—
650C2×C4—942no—
651C2×C4—944no—
652C2×C4—942no—
653C2×C4—944no—
654C2×C4—942no—
655C2×C4—944no—
656C2×C4—9432no—
657C2×C4—944no—
658C2×C4—944no—
659C2×C4—944no—
660C2×C4—1884no—
661C2×C4—1884no—
662C2×C4—1882no—
663C2×C4—1882no—
664C2×C4—1882no—
665C2×C4—1882no—
666C2×C4—1882no—
667C2×C4—1882no—
668C2×C4—1882no—
669C2×C4C22⋊C4×D4714yes—
670C2×C4C22⋊C4×D4714yes—
671C2×C4C2×(C2×D47)⋊C418yes—
672C2×C4C2×(C2×D47)⋊C414yes—
673C2×C4#1309399214yes—
674C2×C4#1309399214yes—
675C2×C4#1309399414yes—
676C2×C4#1309399414yes—
677C22—478no—
678C22—944no—
679C22—944no—
680C22—948no—
681C22—948no—
682C22—944no—
683C22—948no—
684C22—948no—
685C22—944no—
686C22—944no—
687C22—944no—
688C22C2×C22⋊C4×D4711yescharacteristic
689C22C2×C22⋊C4×D4711yescharacteristic
690C22C22×(C2×D47)⋊C411yescharacteristic
691C22C4×Q8×D4712yes—
692C22#1568959912yes—
693C22C2×#1309399211yescharacteristic
694C22C2×#1309399211yescharacteristic
695C22C2×#1309399411yescharacteristic
696C22C2×#1309399411yescharacteristic
697C22C22⋊Q8×D4712yes—
698C22#124×D4711yescharacteristic
699C22C4⋊Q8×D4711yescharacteristic
700C22#1568969311yescharacteristic
701C22#1568969612yes—
702C22#1568969811yescharacteristic
703C22#1568978012yes—
704C22#1568978112yes—
705C22#1568978312yes—
706C22#1568978512yes—
707C22#1568978612yes—
708C22Q8×C22⋊D4712yes—
709C22#1568978812yes—
710C22Q8×D18812yes—
711C4—28no—
712C4—44no—
713C4—82no—
714C4—944no—
715C4—948no—
716C4—3762no—
717C4—1884no—
718C4#1568897818yes—
719C2—948no—
720C2C2×#1568897811yescharacteristic
721C2#391×D4711yescharacteristic
722C2#2024597111yescharacteristic
723C2Q8×(C2×D47)⋊C412yes—
724C2#2024622212yes—
725C2#2024674912yes—
726C2#2024675112yes—
727C2#2024702911yescharacteristic
728C2#2024703111yescharacteristic
729C2#2024704311yescharacteristic
730C2#2024704511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#391C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenterC2×#391D47
hypocenterC47#13922
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×#15689030C2semidirect
3. C2×#15689029C2semidirect
4. C2×#15689028C2semidirect
7. #20241658C2semidirect
9. C2×C47×#391C2semidirect
18. C22×Q8×D47C4semidirect
87. C2×(C2×D47)⋊C4Q8semidirect
132. C2×Q8×C47C22⋊C4semidirect
158. C22×C4×C47C2×Q8semidirect
184. C22×Dic47C2×Q8semidirect
213. C2×Dic94C22⋊C4semidirect
345. C2×D47#391semidirect
358. C2×#391D47semidirect
405. C47#13922semidirect
513. C2×Q8(C2×D47)⋊C4semidirect
577. C22×C4Q8×D47semidirect

Maximal subgroups

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

subgroupindex
C23×Q8×D472
C2×#156890302
C2×#156890292
C2×#156890282
C2×#156889802
C2×C4×(C2×D47)⋊C42
#202416582
(C2×D47)⋊#952
C2×C47×#3912
#1392247