Finite Group Databasebeta

← #26147568

Subgroups — #26147568

Order 12032.

2734 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094001C211yesmaximal, characteristic
2C23×C4×Dic47C211yesmaximal, characteristic
3C2×#15689027C212yesmaximal, complemented
4C2×#15688981C211yesmaximal, characteristic
5#20241622C212yesmaximal, complemented
6#20241619C212yesmaximal, complemented
7Dic47⋊#95C212yesmaximal, complemented
8#20241611C211yesmaximal, characteristic
9#20241610C211yesmaximal, characteristic
10#20241610C211yesmaximal, characteristic
11C47×C22⋊#95C211yesmaximal, characteristic
12C23×Dic94C2211yescharacteristic
13C24×Dic47C2211yescharacteristic
14C24×Dic47C2211yescharacteristic
15C2×#13094001—24no—
16C2×#13094001—24no—
17C2×#13094001C418yescomplemented
18C22×C4⋊Dic47C2211yescharacteristic
19C22×Dic47⋊C4C2212yes—
20C22×Dic47⋊C4C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×C22⋊Dic47C2211yescharacteristic
23C22×C22⋊Dic47C2211yescharacteristic
24C22×C4×Dic47—24no—
25C22×C4×Dic47—28no—
26C22×C4×Dic47C2212yes—
27C22×C4×Dic47C2212yes—
28#15689027—28no—
29#15688981—24no—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C2×C47⋊#95C2212yes—
37C24×C4×C47C2211yescharacteristic
38C22×C22⋊C4×C47C2211yescharacteristic
39C22×C22⋊C4×C47C2211yescharacteristic
40C2×#95×C47C2212yes—
41C2×#95×C47C2212yes—
42C22×Dic94—24no—
43C22×Dic94—22no—
44C22×Dic94—22no—
45C22×Dic94—24no—
46C22×Dic94C2×C414yescomplemented
47C23×Dic47—22no—
48C23×Dic47—22no—
49C23×Dic47—24no—
50C23×Dic47—24no—
51C23×Dic47—24no—
52C23×Dic47—24no—
53C23×Dic47C2×C414yes—
54C23×Dic47D414yes—
55C23×Dic47D414yes—
56C23×Dic47Q814yescomplemented
57C23×Dic47C2312yes—
58C23×Dic47C2311yescharacteristic
59C23×Dic47C2311yescharacteristic
60C23×Dic47C2311yescharacteristic
61C23×Dic47C2312yes—
62C23×Dic47C2311yescharacteristic
63#13094001—232no—
64C2×C4⋊Dic47—22no—
65C2×C4⋊Dic47—22no—
66C2×C4⋊Dic47C2×C414yescomplemented
67C2×Dic47⋊C4—22no—
68C2×Dic47⋊C4—22no—
69C2×Dic47⋊C4—22no—
70C2×Dic47⋊C4—22no—
71C2×Dic47⋊C4—24no—
72C2×Dic47⋊C4—24no—
73C2×Dic47⋊C4—24no—
74C2×Dic47⋊C4C2×C414yescomplemented
75C2×Dic47⋊C4C2×C414yescomplemented
76C2×C22⋊Dic47—22no—
77C2×C22⋊Dic47—22no—
78C2×C22⋊Dic47—22no—
79C2×C22⋊Dic47—22no—
80C2×C22⋊Dic47—22no—
81C2×C22⋊Dic47C2×C414yes—
82C2×C4×Dic47—232no—
83C2×C4×Dic47—24no—
84C2×C4×Dic47—24no—
85C2×C4×Dic47—24no—
86C2×C4×Dic47—24no—
87C2×C4×Dic47—24no—
88C2×C4×Dic47D418yes—
89C47⋊#95—24no—
90C47⋊#95—24no—
91C47⋊#95—24no—
92C47⋊#95—24no—
93C47⋊#95—24no—
94C47⋊#95—24no—
95C47⋊#95—24no—
96C25×C47C2311yescharacteristic
97C23×C4×C47—22no—
98C23×C4×C47—22no—
99C23×C4×C47—24no—
100C23×C4×C47—24no—
101C23×C4×C47Q814yescomplemented
102C23×C4×C47C2312yes—
103C23×C4×C47C2311yescharacteristic
104C23×C4×C47C2311yescharacteristic
105C23×C4×C47C2312yes—
106C2×C22⋊C4×C47—22no—
107C2×C22⋊C4×C47—22no—
108C2×C22⋊C4×C47—22no—
109C2×C22⋊C4×C47—22no—
110C2×C22⋊C4×C47—22no—
111C2×C22⋊C4×C47C2×C414yes—
112#95×C47—24no—
113#95×C47—24no—
114C24×C47—22no—
115C24×C47—22no—
116C24×C47—22no—
117C24×C47—22no—
118C24×C47C22×C412yes—
119C24×C47C2×D412yes—
120C24×C47C2×D412yes—
121C24×C47C2×Q812yes—
122C24×C47C2×Q812yes—
123C24×C47#4112yes—
124C24×C47#4112yes—
125C24×C47C2411yescharacteristic
126C22×C4×C47—216no—
127C22×C4×C47—28no—
128C22×C4×C47—28no—
129C22×C4×C47—28no—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—216no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
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—22no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47C22×C412yes—
151C22×C4×C47C22×C412yes—
152C22×C4×C47C2×D414yes—
153C22×C4×C47C2×Q814yes—
154C22×C4×C47#4114yes—
155C22×Dic47—28no—
156C22×Dic47—216no—
157C22×Dic47—28no—
158C22×Dic47—28no—
159C22×Dic47—22no—
160C22×Dic47—22no—
161C22×Dic47—22no—
162C22×Dic47—22no—
163C22×Dic47—22no—
164C22×Dic47—22no—
165C22×Dic47—216no—
166C22×Dic47—28no—
167C22×Dic47—216no—
168C22×Dic47—216no—
169C22×Dic47—28no—
170C22×Dic47—22no—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—22no—
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×Dic47C22⋊C4116yes—
186C22×Dic47C22×C412yes—
187C22×Dic47C22×C412yes—
188C22×Dic47C22×C412yes—
189C22×Dic47C22×C412yes—
190C22×Dic47C2×D412yes—
191C22×Dic47C2×D412yes—
192C22×Dic47C2×D414yes—
193C22×Dic47C2×D412yes—
194C22×Dic47C2×D412yes—
195C22×Dic47C2×D414yes—
196C22×Dic47C2×Q814yes—
197C22×Dic47#4114yes—
198C22×Dic47#4114yes—
199C2×Dic94—28no—
200C2×Dic94—216no—
201C2×Dic94—44no—
202C2×Dic94—48no—
203C2×Dic94—44no—
204C22⋊C4×C47—28no—
205C22⋊C4×C47—44no—
206C22⋊Dic47—28no—
207C22⋊Dic47—44no—
208C4⋊Dic47—28no—
209Dic47⋊C4—28no—
210Dic47⋊C4—28no—
211Dic47⋊C4—48no—
212C4×Dic47—216no—
213C4×Dic47—216no—
214C23×C47—24no—
215C23×C47—24no—
216C23×C47—22no—
217C23×C47—24no—
218C23×C47—24no—
219C23×C47—24no—
220C23×C47—22no—
221C23×C47—22no—
222C23×C47—24no—
223C23×C47—22no—
224C23×C47—24no—
225C23×C47—24no—
226C23×C47—24no—
227C23×C47—24no—
228C23×C47—24no—
229C23×C47—24no—
230C23×C47C2×C22⋊C414yes—
231C23×C47C4×Q814yes—
232C23×C47C4×Q814yes—
233C23×C47C22⋊Q814yes—
234C23×C47C22⋊Q814yes—
235C23×C47#12414yes—
236C23×C47C4⋊Q814yes—
237C23×C47C23×C411yescharacteristic
238C23×C47C22×D411yescharacteristic
239C23×C47C22×D411yescharacteristic
240C23×C47C22×D412yes—
241C23×C47C22×Q811yescharacteristic
242C23×C47C22×Q811yescharacteristic
243C23×C47C2×#4112yes—
244C23×C47C2×#4112yes—
245C23×C47C2×#4111yescharacteristic
246C23×C47C2×#4112yes—
247C23×C47C2×#4111yescharacteristic
248C2×C4×C47—232no—
249C2×C4×C47—24no—
250C2×C4×C47—24no—
251C2×C4×C47—24no—
252C2×C4×C47—24no—
253C2×C4×C47—24no—
254C2×C4×C47—24no—
255C2×C4×C47—22no—
256C2×C4×C47—22no—
257C2×C4×C47—24no—
258C2×C4×C47—24no—
259C2×C4×C47—41no—
260C2×C4×C47—42no—
261C2×C4×C47—41no—
262C2×C4×C47—41no—
263C2×C4×C47—41no—
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—42no—
272C2×C4×C47C22⋊Q818yescomplemented
273C2×Dic47—232no—
274C2×Dic47—24no—
275C2×Dic47—24no—
276C2×Dic47—22no—
277C2×Dic47—24no—
278C2×Dic47—24no—
279C2×Dic47—24no—
280C2×Dic47—22no—
281C2×Dic47—24no—
282C2×Dic47—24no—
283C2×Dic47—24no—
284C2×Dic47—232no—
285C2×Dic47—22no—
286C2×Dic47—22no—
287C2×Dic47—24no—
288C2×Dic47—24no—
289C2×Dic47—41no—
290C2×Dic47—42no—
291C2×Dic47—41no—
292C2×Dic47—41no—
293C2×Dic47—41no—
294C2×Dic47—42no—
295C2×Dic47—42no—
296C2×Dic47—42no—
297C2×Dic47—42no—
298C2×Dic47—42no—
299C2×Dic47—42no—
300C2×Dic47—42no—
301C2×Dic47—42no—
302C2×Dic47C2×C22⋊C414yes—
303C2×Dic47C2×C22⋊C414yes—
304C2×Dic47C4×D418yes—
305C2×Dic47#12014yes—
306C2×Dic47#12118yes—
307C2×Dic47C22⋊Q818yescomplemented
308C2×Dic47#12314yes—
309Dic94—416no—
310#14702—471nomaximal, Sylow
311C22×C47—24no—
312C22×C47—24no—
313C22×C47—28no—
314C22×C47—24no—
315C22×C47—24no—
316C22×C47—28no—
317C22×C47—24no—
318C22×C47—24no—
319C22×C47—28no—
320C22×C47—28no—
321C22×C47#39118yescomplemented
322C22×C47C22×C22⋊C411yescharacteristic
323C22×C47C2×C4×D412yes—
324C22×C47C2×C4×Q811yescharacteristic
325C22×C47C2×C4×Q811yescharacteristic
326C22×C47C4×#4112yes—
327C22×C47C2×#12011yescharacteristic
328C22×C47C2×#12112yes—
329C22×C47C2×C22⋊Q812yes—
330C22×C47C2×C22⋊Q811yescharacteristic
331C22×C47C2×C22⋊Q812yes—
332C22×C47C2×C22⋊Q811yescharacteristic
333C22×C47C2×#12311yescharacteristic
334C22×C47#52512yes—
335C22×C47#52511yescharacteristic
336C22×C47#52511yescharacteristic
337C22×C47#52512yes—
338C22×C47C2×#12411yescharacteristic
339C22×C47#52912yes—
340C22×C47#52912yes—
341C22×C47C2×C4⋊Q811yescharacteristic
342C22×C47#53212yes—
343C22×C47#53312yes—
344C22×C47#53312yes—
345C4×C47—28no—
346C4×C47—42no—
347C4×C47—42no—
348C4×C47—82no—
349Dic47—28no—
350Dic47—24no—
351Dic47—42no—
352Dic47—42no—
353Dic47—82no—
354Dic47#38618yes—
355C22×C22⋊Q8—471no—
356C23×C42—471no—
357C2×#391—472no—
358C2×#380—471no—
359#1436—472no—
360#1436—472no—
361C4⋊#95—472no—
362C22⋊#95—471no—
363C22⋊#95—471no—
364C22⋊#95—471no—
365C22⋊#95D4711yescharacteristic
366C2×C47—28no—
367C2×C47C2×#38611yescharacteristic
368C2×C47C2×#39111yescharacteristic
369C2×C47#229711yescharacteristic
370C2×C47C4×C22⋊Q812yes—
371C2×C47C4×C22⋊Q812yes—
372C2×C47#284811yescharacteristic
373C2×C47#284811yescharacteristic
374C2×C47#285012yes—
375C2×C47#285511yescharacteristic
376C2×C47#285511yescharacteristic
377C2×C47#285712yes—
378C23×Q8—471no—
379C24×C4—471no—
380C24×C4—471no—
381C24×C4C2×D4711yescharacteristic
382C2×C22⋊Q8—478no—
383C2×C22⋊Q8—944no—
384C2×C22⋊Q8—944no—
385C22×C4⋊C4—471no—
386C22×C4⋊C4—471no—
387C22×C4⋊C4—471no—
388C22×C4⋊C4—472no—
389C22×C22⋊C4—471no—
390C22×C22⋊C4—471no—
391C22×C22⋊C4C2×D4711yescharacteristic
392C22×C22⋊C4C2×D4711yescharacteristic
393C22×C42—472no—
394C22×C42—472no—
395C22×C42—948no—
396C22×C42—944no—
397#391—948no—
398#380—944no—
399C2×#95—472no—
400C2×#95—472no—
401C2×#95—472no—
402C2×#95—472no—
403C2×#95—472no—
404C2×#95—472no—
405C2×#95—472no—
406C2×#95C2×D4712yes—
407C2×#95C2×D4712yes—
408C47#1470211yescharacteristic, complemented, Sylow
409C25C22×D4711yescharacteristic
410C22×Q8—474no—
411C22×Q8—942no—
412C22×Q8—942no—
413C22×Q8—944no—
414C22×Q8—944no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—24no—
418C23×C4—24no—
419C23×C4—471no—
420C23×C4—474no—
421C23×C4—474no—
422C23×C4—474no—
423C23×C4—471no—
424C23×C4—472no—
425C23×C4—474no—
426C23×C4—471no—
427C23×C4—471no—
428C23×C4—472no—
429C23×C4—944no—
430C23×C4—944no—
431C23×C4—944no—
432C23×C4—944no—
433C23×C4—942no—
434C23×C4—942no—
435C23×C4Dic9414yescomplemented
436C23×C4C22×D4712yes—
437C23×C4C22×D4711yescharacteristic
438C23×C4C22×D4711yescharacteristic
439C23×C4C22×D4712yes—
440C22⋊Q8—9432no—
441C2×C4⋊C4—474no—
442C2×C4⋊C4—474no—
443C2×C4⋊C4—474no—
444C2×C4⋊C4—942no—
445C2×C4⋊C4—942no—
446C2×C4⋊C4—942no—
447C2×C4⋊C4—942no—
448C2×C4⋊C4—942no—
449C2×C4⋊C4—942no—
450C2×C4⋊C4—944no—
451C2×C4⋊C4—944no—
452C2×C4⋊C4—944no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—474no—
459C2×C22⋊C4—942no—
460C2×C22⋊C4—942no—
461C2×C22⋊C4—942no—
462C2×C22⋊C4—942no—
463C2×C22⋊C4—942no—
464C2×C22⋊C4C4×D4714yes—
465C2×C42—478no—
466C2×C42—944no—
467C2×C42—944no—
468C2×C42—944no—
469C2×C42—944no—
470C2×C42—9432no—
471C2×C42—944no—
472#95—24no—
473#95—24no—
474#95—944no—
475#95—944no—
476#95—944no—
477#95—944no—
478#95—944no—
479#95—944no—
480#95—944no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24C2×Dic9412yes—
486C24C2×C4×D4712yes—
487C24#1062535012yes—
488C24D4×D4712yes—
489C24D4×D4712yes—
490C24#1062535212yes—
491C24Q8×D4712yes—
492C24C23×D4711yescharacteristic
493C2×Q8—948no—
494C2×Q8—9416no—
495C2×Q8—1884no—
496C2×Q8—1888no—
497C2×Q8—1884no—
498C22×C4—28no—
499C22×C4—216no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—216no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
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—472no—
523C22×C4—474no—
524C22×C4—472no—
525C22×C4—472no—
526C22×C4—474no—
527C22×C4—4716no—
528C22×C4—472no—
529C22×C4—474no—
530C22×C4—472no—
531C22×C4—472no—
532C22×C4—474no—
533C22×C4—474no—
534C22×C4—472no—
535C22×C4—472no—
536C22×C4—948no—
537C22×C4—9416no—
538C22×C4—9416no—
539C22×C4—948no—
540C22×C4—9416no—
541C22×C4—948no—
542C22×C4—948no—
543C22×C4—9416no—
544C22×C4—948no—
545C22×C4—942no—
546C22×C4—942no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4—942no—
550C22×C4—942no—
551C22×C4—942no—
552C22×C4—941no—
553C22×C4—941no—
554C22×C4—941no—
555C22×C4—941no—
556C22×C4—942no—
557C22×C4—942no—
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×C4C2×Dic9414yes—
567C22×C4C2×C4×D4712yes—
568C22×C4C2×C4×D4712yes—
569C22×C4D4×D4714yes—
570C22×C4#1062535214yes—
571C4⋊C4—948no—
572C4⋊C4—948no—
573C4⋊C4—948no—
574C4⋊C4—1888no—
575C22⋊C4—28no—
576C22⋊C4—44no—
577C22⋊C4—948no—
578C22⋊C4—1884no—
579C42—9416no—
580C42—9416no—
581C23—24no—
582C23—24no—
583C23—22no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—22no—
588C23—22no—
589C23—24no—
590C23—22no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23C22⋊C4×D4714yes—
598C23#1309398914yes—
599C23C4×Dic9414yes—
600C23#1309400114yes—
601C23#1309400214yes—
602C23#1309401014yes—
603C23#1309402314yes—
604C23C22×C4×D4711yescharacteristic
605C23C2×D4×D4711yescharacteristic
606C23C2×D4×D4711yescharacteristic
607C23C2×D4×D4712yes—
608C23C2×Q8×D4711yescharacteristic
609C23C22×Dic9411yescharacteristic
610C23#41×D4712yes—
611C23#41×D4712yes—
612C23C2×#1062535211yescharacteristic
613C23C2×#1062535212yes—
614C23C2×#1062535011yescharacteristic
615Q8—18816no—
616C2×C4—232no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—474no—
641C2×C4—478no—
642C2×C4—474no—
643C2×C4—478no—
644C2×C4—474no—
645C2×C4—474no—
646C2×C4—478no—
647C2×C4—9432no—
648C2×C4—9432no—
649C2×C4—944no—
650C2×C4—944no—
651C2×C4—942no—
652C2×C4—944no—
653C2×C4—944no—
654C2×C4—944no—
655C2×C4—942no—
656C2×C4—944no—
657C2×C4—944no—
658C2×C4—944no—
659C2×C4—942no—
660C2×C4—942no—
661C2×C4—944no—
662C2×C4—944no—
663C2×C4—1882no—
664C2×C4—1882no—
665C2×C4—1882no—
666C2×C4—1882no—
667C2×C4—1882no—
668C2×C4—1882no—
669C2×C4—1882no—
670C2×C4—1881no—
671C2×C4—1882no—
672C2×C4—1881no—
673C2×C4—1881no—
674C2×C4—1881no—
675C2×C4—1882no—
676C2×C4#1309400118yescomplemented
677C22—24no—
678C22—24no—
679C22—28no—
680C22—24no—
681C22—24no—
682C22—24no—
683C22—28no—
684C22—24no—
685C22—28no—
686C22—28no—
687C22#1568902718yescomplemented
688C22C2×C22⋊C4×D4711yescharacteristic
689C22C4×D4×D4712yes—
690C22C2×#1309398911yescharacteristic
691C22C2×C4×Dic9411yescharacteristic
692C22C4×#1062535212yes—
693C22#120×D4711yescharacteristic
694C22#121×D4712yes—
695C22C22⋊Q8×D4712yes—
696C22C2×#1309400111yescharacteristic
697C22C2×#1309400112yes—
698C22C2×#1309400211yescharacteristic
699C22#123×D4711yescharacteristic
700C22#1568962912yes—
701C22#1568962911yescharacteristic
702C22#1568963111yescharacteristic
703C22#1568963212yes—
704C22C2×#1309401011yescharacteristic
705C22#1568965012yes—
706C22#1568965312yes—
707C22C2×#1309402311yescharacteristic
708C22#1568966812yes—
709C22#1568967512yes—
710C22#1568967612yes—
711C4—28no—
712C4—42no—
713C4—42no—
714C4—82no—
715C4—478no—
716C4—948no—
717C4—944no—
718C4—3762no—
719C4—1882no—
720C4—1882no—
721C2—28no—
722C2#386×D4711yescharacteristic
723C2C2×#1568902711yescharacteristic
724C2#2024587311yescharacteristic
725C2C4×#1309400112yes—
726C2#2024592012yes—
727C2#2025167311yescharacteristic
728C2#2025167411yescharacteristic
729C2#2025168512yes—
730C2#2025172411yescharacteristic
731C2#2025172511yescharacteristic
732C2#2025173812yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×C22⋊#95C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC22⋊#95D47
hypocenterC47#14702
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#15689027C2semidirect
5. #20241622C2semidirect
6. #20241619C2semidirect
7. Dic47⋊#95C2semidirect
17. C2×#13094001C4semidirect
46. C22×Dic94C2×C4semidirect
56. C23×Dic47Q8semidirect
66. C2×C4⋊Dic47C2×C4semidirect
74. C2×Dic47⋊C4C2×C4semidirect
75. C2×Dic47⋊C4C2×C4semidirect
101. C23×C4×C47Q8semidirect
272. C2×C4×C47C22⋊Q8semidirect
307. C2×Dic47C22⋊Q8semidirect
321. C22×C47#391semidirect
408. C47#14702semidirect
435. C23×C4Dic94semidirect
676. C2×C4#13094001semidirect
687. C22#15689027semidirect

Maximal subgroups

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

subgroupindex
C22×#130940012
C23×C4×Dic472
C2×#156890272
C2×#156889812
#202416222
#202416192
Dic47⋊#952
#202416112
#202416102
C47×C22⋊#952
#1470247