Finite Group Databasebeta

← #26122764

Subgroups — #26122764

Order 12032.

1902 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D47C211yesmaximal, characteristic
2C22×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
3C22×(C2×D47)⋊C8C212yesmaximal, complemented
4C2×#15688877C212yesmaximal, complemented
5C22×C22⋊C8×C47C211yesmaximal, characteristic, complemented
6C23×C22⋊D47C411yescharacteristic
7C23×C4×D47C2211yescharacteristic
8C23×C47⋊C8C2212yes—
9C2×C4×C22⋊D47—24no—
10C2×C4×C22⋊D47—24no—
11C2×C4×C22⋊D47—22no—
12C2×C4×C22⋊D47—22no—
13C22×Dic47⋊C4C411yescharacteristic
14C22×C22⋊Dic47C411yescharacteristic
15C22×(C2×D47)⋊C4C411yescharacteristic
16C22×C4×Dic47C2211yescharacteristic
17C2×C22⋊(C47⋊C8)—24no—
18C2×C22⋊(C47⋊C8)—22no—
19C2×(C2×D47)⋊C8—24no—
20C2×(C2×D47)⋊C8—24no—
21C2×(C2×D47)⋊C8—24no—
22#15688877—24no—
23C24×C4×C47C2211yescharacteristic
24C23×C8×C47C2212yes—
25C2×C22⋊C8×C47—22no—
26C2×C22⋊C8×C47—24no—
27C24×D47C2×C411yescharacteristic
28C22×C22⋊D47—22no—
29C22×C22⋊D47—22no—
30C22×C22⋊D47—22no—
31C22×C22⋊D47—22no—
32C22×C22⋊D47—22no—
33C22×C22⋊D47—22no—
34C22×C22⋊D47C814yescomplemented
35C23×Dic47C2×C411yescharacteristic
36C23×Dic47C2×C411yescharacteristic
37C23×Dic47C2×C411yescharacteristic
38C22×C4×D47—21no—
39C22×C4×D47—21no—
40C22×C4×D47—22no—
41C22×C4×D47—22no—
42C22×C4×D47—22no—
43C22×C4×D47—22no—
44C22×C4×D47—22no—
45C22×C4×D47D414yes—
46C22×C47⋊C8—22no—
47C22×C47⋊C8—22no—
48C22×C47⋊C8—22no—
49C22×C47⋊C8—22no—
50C22×C47⋊C8—22no—
51C22×C47⋊C8—22no—
52C22×C47⋊C8D414yescomplemented
53C4×C22⋊D47—216no—
54C4×C22⋊D47—216no—
55C2×Dic47⋊C4—22no—
56C2×Dic47⋊C4—22no—
57C2×Dic47⋊C4—22no—
58C2×C22⋊Dic47—22no—
59C2×C22⋊Dic47—22no—
60C2×C22⋊Dic47—22no—
61C2×(C2×D47)⋊C4—22no—
62C2×(C2×D47)⋊C4—22no—
63C2×(C2×D47)⋊C4—22no—
64C2×C4×Dic47—21no—
65C2×C4×Dic47—22no—
66C2×C4×Dic47—21no—
67C2×C4×Dic47D414yes—
68C22⋊(C47⋊C8)—28no—
69(C2×D47)⋊C8—216no—
70C25×C47C2×C411yescharacteristic
71C23×C4×C47—22no—
72C23×C4×C47—22no—
73C23×C4×C47—22no—
74C23×C4×C47—22no—
75C23×C4×C47—22no—
76C23×C4×C47—22no—
77C23×C4×C47C2×C411yescharacteristic
78C23×C4×C47D412yes—
79C23×C4×C47D412yes—
80C23×C4×C47C2311yescharacteristic
81C22×C8×C47—22no—
82C22×C8×C47—22no—
83C22×C8×C47—22no—
84C22×C8×C47—22no—
85C22×C8×C47—22no—
86C22×C8×C47—22no—
87C22×C8×C47D414yescomplemented
88C22⋊C8×C47—28no—
89C24×C47—21no—
90C24×C47—21no—
91C24×C47—22no—
92C24×C47—22no—
93C24×C47—21no—
94C24×C47—21no—
95C24×C47—22no—
96C24×C47—22no—
97C24×C47C22⋊C412yes—
98C24×C47C2×C812yes—
99C24×C47M1612yes—
100C24×C47C22×C411yescharacteristic
101C23×D47—21no—
102C23×D47—21no—
103C23×D47—22no—
104C23×D47—22no—
105C23×D47—21no—
106C23×D47—21no—
107C23×D47—22no—
108C23×D47—22no—
109C23×D47C22⋊C412yes—
110C23×D47C2×C812yes—
111C23×D47M1612yes—
112C22×C4×C47—21no—
113C22×C4×C47—21no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—24no—
118C22×C4×C47—24no—
119C22×C4×C47—22no—
120C22×C4×C47—24no—
121C22×C4×C47—24no—
122C22×C4×C47—22no—
123C22×C4×C47—22no—
124C22×C4×C47—42no—
125C22×C4×C47—42no—
126C22×C4×C47—42no—
127C22×C4×C47—42no—
128C22×C4×C47—42no—
129C22×C4×C47—42no—
130C22×C4×C47—42no—
131C22×C4×C47—42no—
132C22×C4×C47C22⋊C412yes—
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D412yes—
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D412yes—
137C22×C4×C47C2×D412yes—
138C22×C4×C47C2×D412yes—
139C22×C4×C47#4112yes—
140C22×C4×C47#4112yes—
141C2×C22⋊D47—28no—
142C2×C22⋊D47—28no—
143C2×C22⋊D47—28no—
144C2×C22⋊D47—28no—
145C2×C22⋊D47—28no—
146C2×C22⋊D47—28no—
147C2×C22⋊D47—28no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151C22×Dic47—21no—
152C22×Dic47—21no—
153C22×Dic47—21no—
154C22×Dic47—21no—
155C22×Dic47—21no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—22no—
160C22×Dic47C22⋊C412yes—
161C22×Dic47C22⋊C412yes—
162C22×Dic47C22⋊C412yes—
163C22×Dic47C2×C812yes—
164C22×Dic47M1612yes—
165C2×C4×D47—24no—
166C2×C4×D47—24no—
167C2×C4×D47—24no—
168C2×C4×D47—24no—
169C2×C4×D47—24no—
170C2×C4×D47—24no—
171C2×C4×D47—41no—
172C2×C4×D47—41no—
173C2×C4×D47—42no—
174C2×C4×D47—42no—
175C2×C4×D47—42no—
176C2×C4×D47—42no—
177C2×C4×D47—41no—
178C2×C4×D47—41no—
179C2×C4×D47—42no—
180C2×C4×D47—42no—
181C2×C8×C47—24no—
182C2×C8×C47—24no—
183C2×C8×C47—24no—
184C2×C8×C47—42no—
185C2×C8×C47—42no—
186C2×C8×C47—42no—
187C2×C8×C47—42no—
188C22⋊Dic47—28no—
189(C2×D47)⋊C4—28no—
190Dic47⋊C4—28no—
191C4×Dic47—24no—
192C4×Dic47—24no—
193C2×C47⋊C8—24no—
194C2×C47⋊C8—24no—
195C2×C47⋊C8—24no—
196C2×C47⋊C8—42no—
197C2×C47⋊C8—42no—
198C2×C47⋊C8—42no—
199C2×C47⋊C8—42no—
200C23×C47—22no—
201C23×C47—22no—
202C23×C47—22no—
203C23×C47—22no—
204C23×C47—22no—
205C23×C47—22no—
206C23×C47—22no—
207C23×C47—22no—
208C23×C47—22no—
209C23×C47—22no—
210C23×C47—24no—
211C23×C47—24no—
212C23×C47—24no—
213C23×C47—24no—
214C23×C47—42no—
215C23×C47—42no—
216C23×C47—42no—
217C23×C47—42no—
218C23×C47—42no—
219C23×C47—42no—
220C23×C47—42no—
221C23×C47—42no—
222C23×C47C22⋊C814yescomplemented
223C23×C47C2×C22⋊C411yescharacteristic
224C23×C47C2×C22⋊C411yescharacteristic
225C23×C47C2×C22⋊C411yescharacteristic
226C23×C47C4×D412yes—
227C23×C47C4×D412yes—
228C23×C47C22×C811yescharacteristic
229C23×C47C2×M1611yescharacteristic
230C23×C47C2×M1611yescharacteristic
231C23×C47C2×M1611yescharacteristic
232C23×C47#13112yes—
233C23×C47#13112yes—
234C22×D47—22no—
235C22×D47—24no—
236C22×D47—22no—
237C22×D47—22no—
238C22×D47—22no—
239C22×D47—22no—
240C22×D47—22no—
241C22×D47—24no—
242C22×D47—24no—
243C22×D47—24no—
244C22×D47—24no—
245C22×D47—24no—
246C22×D47—41no—
247C22×D47—41no—
248C22×D47—42no—
249C22×D47—42no—
250C22×D47—41no—
251C22×D47—41no—
252C22×D47—42no—
253C22×D47—42no—
254C22×D47—42no—
255C22×D47—42no—
256C22×D47C22⋊C814yescomplemented
257C2×C4×C47—22no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—42no—
261C2×C4×C47—42no—
262C2×C4×C47—44no—
263C2×C4×C47—44no—
264C2×C4×C47—44no—
265C2×C4×C47—44no—
266C2×C4×C47#12012yes—
267C2×C4×C47#12012yes—
268C2×C4×C47#12011yescharacteristic
269C2×C4×C47#12011yescharacteristic
270C2×C4×C47#12012yes—
271C2×C4×C47#12112yes—
272C2×C4×C47#12112yes—
273C2×C4×C47#12112yes—
274C2×C4×C47#12112yes—
275C2×C4×C47#12112yes—
276C2×C4×C47#12112yes—
277C2×C4×C47#12312yes—
278C2×C4×C47#12311yescharacteristic
279C2×C4×C47#12311yescharacteristic
280C2×C4×C47#12412yes—
281C2×C4×C47#12712yes—
282C22⋊D47—232no—
283C2×Dic47—22no—
284C2×Dic47—22no—
285C2×Dic47—22no—
286C2×Dic47—22no—
287C2×Dic47—22no—
288C2×Dic47—22no—
289C2×Dic47—22no—
290C2×Dic47—22no—
291C2×Dic47—24no—
292C2×Dic47—24no—
293C2×Dic47—41no—
294C2×Dic47—41no—
295C2×Dic47—42no—
296C2×Dic47—42no—
297C2×Dic47—41no—
298C2×Dic47—41no—
299C2×Dic47C22⋊C814yescomplemented
300C4×D47—44no—
301C4×D47—44no—
302C4×D47—44no—
303C4×D47—44no—
304C8×C47—44no—
305C47⋊C8—44no—
306#10964—471nomaximal, Sylow
307C22×C47—24no—
308C22×C47—24no—
309C22×C47—24no—
310C22×C47—44no—
311C22×C47—44no—
312C22×C47—42no—
313C22×C47—42no—
314C22×C47—42no—
315C22×C47—44no—
316C22×C47—44no—
317C22×C47—42no—
318C22×C47#37911yescharacteristic
319C22×C47#38612yes—
320C22×C47#38611yescharacteristic
321C22×C47#38611yescharacteristic
322C22×C47#39012yes—
323C22×C47C2×C22⋊C811yescharacteristic
324C22×C47C2×C22⋊C811yescharacteristic
325C22×C47C2×C22⋊C811yescharacteristic
326C22×C47#40711yescharacteristic
327C22×C47#40711yescharacteristic
328C22×C47#40711yescharacteristic
329C22×C47#40812yes—
330C22×C47#40812yes—
331C22×C47#40811yescharacteristic
332C22×C47#40811yescharacteristic
333C22×C47C8×D412yes—
334C22×C47C8×D412yes—
335C22×C47#43512yes—
336C22×C47#43512yes—
337C22×C47#43512yes—
338C22×C47#43512yes—
339C22×C47#43612yes—
340C22×C47#43612yes—
341C2×D47—28no—
342C2×D47—24no—
343C2×D47—42no—
344C2×D47—42no—
345C2×D47—44no—
346C2×D47—42no—
347C2×D47—42no—
348C2×D47—42no—
349C2×D47—44no—
350C2×D47—44no—
351C2×D47—42no—
352C4×C47—42no—
353C4×C47#39212yes—
354C4×C47#39212yes—
355C4×C47#39412yes—
356C4×C47#39412yes—
357Dic47—24no—
358Dic47—42no—
359Dic47—42no—
360C22×C4×D4—471no—
361C22×C22⋊C8—471no—
362C22×C22⋊C8—472no—
363C22×C22⋊C8D4711yescharacteristic, complemented
364C2×#336—472no—
365C2×C47—44no—
366C2×C47#143811yescharacteristic
367C2×C47#177911yescharacteristic
368C2×C47#178011yescharacteristic
369C2×C47#186912yes—
370C2×C47#186911yescharacteristic
371C2×C47#186911yescharacteristic
372C2×C47#187012yes—
373C2×C47#187011yescharacteristic
374C2×C47#187011yescharacteristic
375C2×C47#195412yes—
376C2×C47#195512yes—
377D47—44no—
378C23×D4—471no—
379C24×C4—471no—
380C24×C4C2×D4711yescharacteristic
381C23×C8—472no—
382C23×C8C2×D4712yes—
383C2×C4×D4—944no—
384C2×C4×D4—944no—
385C2×C4×D4—942no—
386C2×C4×D4—942no—
387C22×C4⋊C4—471no—
388C22×C22⋊C4—471no—
389C22×C22⋊C4—471no—
390C22×C42—471no—
391C2×C22⋊C8—22no—
392C2×C22⋊C8—24no—
393C2×C22⋊C8—944no—
394C2×C22⋊C8—944no—
395C2×C22⋊C8—944no—
396C2×C22⋊C8—942no—
397C2×C22⋊C8—944no—
398#336—944no—
399C47#1096411yescharacteristic, complemented, Sylow
400C25—471no—
401C25C4×D4711yescharacteristic
402C22×D4—474no—
403C22×D4—942no—
404C22×D4—942no—
405C22×D4—942no—
406C22×D4—942no—
407C22×D4—942no—
408C22×D4—942no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—471no—
416C23×C4—471no—
417C23×C4—471no—
418C23×C4—474no—
419C23×C4—941no—
420C23×C4—942no—
421C23×C4—942no—
422C23×C4—942no—
423C23×C4—942no—
424C23×C4—941no—
425C23×C4—942no—
426C23×C4C4×D4711yescharacteristic
427C23×C4D18812yes—
428C23×C4C22⋊D4712yes—
429C23×C4C22×D4711yescharacteristic
430C22×C8—22no—
431C22×C8—22no—
432C22×C8—22no—
433C22×C8—22no—
434C22×C8—22no—
435C22×C8—22no—
436C22×C8—474no—
437C22×C8—942no—
438C22×C8—942no—
439C22×C8—942no—
440C22×C8—942no—
441C22×C8—942no—
442C22×C8—942no—
443C22×C8C22⋊D4714yescomplemented
444C4×D4—9416no—
445C4×D4—9416no—
446C2×C4⋊C4—942no—
447C2×C4⋊C4—942no—
448C2×C4⋊C4—942no—
449C2×C22⋊C4—942no—
450C2×C22⋊C4—942no—
451C2×C22⋊C4—942no—
452C2×C22⋊C4—942no—
453C2×C22⋊C4—942no—
454C2×C22⋊C4—942no—
455C2×C42—474no—
456C2×C42—941no—
457C2×C42—942no—
458C2×C42—941no—
459C22⋊C8—28no—
460C22⋊C8—9416no—
461C22⋊C8—948no—
462C24—21no—
463C24—21no—
464C24—22no—
465C24—22no—
466C24—21no—
467C24—21no—
468C24—22no—
469C24—22no—
470C24—472no—
471C24—472no—
472C24—472no—
473C24—941no—
474C24—941no—
475C24—942no—
476C24—942no—
477C24—941no—
478C24—941no—
479C24—942no—
480C24—942no—
481C24C8×D4712yes—
482C24#1062532412yes—
483C24(C2×D47)⋊C412yes—
484C24C2×C4×D4711yescharacteristic
485C2×D4—948no—
486C2×D4—948no—
487C2×D4—948no—
488C2×D4—948no—
489C2×D4—948no—
490C2×D4—948no—
491C2×D4—948no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—472no—
513C22×C4—472no—
514C22×C4—472no—
515C22×C4—472no—
516C22×C4—472no—
517C22×C4—941no—
518C22×C4—941no—
519C22×C4—941no—
520C22×C4—941no—
521C22×C4—941no—
522C22×C4—941no—
523C22×C4—941no—
524C22×C4—941no—
525C22×C4—942no—
526C22×C4—942no—
527C22×C4—942no—
528C22×C4—942no—
529C22×C4—944no—
530C22×C4—944no—
531C22×C4—944no—
532C22×C4—944no—
533C22×C4—944no—
534C22×C4—944no—
535C22×C4—1881no—
536C22×C4—1881no—
537C22×C4—1882no—
538C22×C4—1882no—
539C22×C4—1882no—
540C22×C4—1882no—
541C22×C4—1881no—
542C22×C4—1881no—
543C22×C4—1882no—
544C22×C4—1882no—
545C22×C4(C2×D47)⋊C412yes—
546C22×C4C2×D18811yescharacteristic
547C22×C4#1062535012yes—
548C22×C4D4×D4712yes—
549C22×C4D4×D4712yes—
550C22×C4D4×D4712yes—
551C22×C4#1062535212yes—
552C22×C4C2×C22⋊D4711yescharacteristic
553C22×C4C2×C22⋊D4712yes—
554C2×C8—24no—
555C2×C8—24no—
556C2×C8—24no—
557C2×C8—42no—
558C2×C8—42no—
559C2×C8—42no—
560C2×C8—42no—
561C2×C8—944no—
562C2×C8—944no—
563C2×C8—944no—
564C2×C8—1882no—
565C2×C8—1882no—
566C2×C8—1882no—
567C2×C8—1882no—
568C4⋊C4—948no—
569C22⋊C4—948no—
570C22⋊C4—948no—
571C42—944no—
572C42—944no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—474no—
596C23—942no—
597C23—944no—
598C23—942no—
599C23—942no—
600C23—942no—
601C23—942no—
602C23—942no—
603C23—944no—
604C23—944no—
605C23—944no—
606C23—944no—
607C23—944no—
608C23—1881no—
609C23—1881no—
610C23—1882no—
611C23—1882no—
612C23—1881no—
613C23—1881no—
614C23—1882no—
615C23—1882no—
616C23—1882no—
617C23—1882no—
618C23(C2×D47)⋊C814yescomplemented
619C23C22⋊C4×D4711yescharacteristic
620C23C22⋊C4×D4711yescharacteristic
621C23C2×(C2×D47)⋊C411yescharacteristic
622C23(C22⋊D47)⋊C412yes—
623C23C4×C22⋊D4712yes—
624C23C2×C8×D4711yescharacteristic
625C23M16×D4711yescharacteristic
626C23M16×D4711yescharacteristic
627C23C2×#1062532411yescharacteristic
628C23#1309403012yes—
629C23#1309403212yes—
630D4—9432no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—474no—
641C2×C4—942no—
642C2×C4—942no—
643C2×C4—942no—
644C2×C4—942no—
645C2×C4—942no—
646C2×C4—942no—
647C2×C4—942no—
648C2×C4—942no—
649C2×C4—944no—
650C2×C4—944no—
651C2×C4—1881no—
652C2×C4—1881no—
653C2×C4—1882no—
654C2×C4—1882no—
655C2×C4—1881no—
656C2×C4—1881no—
657C2×C4—1884no—
658C2×C4—1884no—
659C2×C4—1884no—
660C2×C4—1884no—
661C2×C4#1309399212yes—
662C2×C4#1309399212yes—
663C2×C4#1309399311yescharacteristic
664C2×C4#1309399411yescharacteristic
665C2×C4#1309399412yes—
666C2×C4#1309399512yes—
667C2×C4#1309399612yes—
668C2×C4#1309399612yes—
669C2×C4#1309399712yes—
670C2×C4#1309399712yes—
671C2×C4#1309399812yes—
672C2×C4#1309400612yes—
673C2×C4#1309400711yescharacteristic
674C2×C4#1309400811yescharacteristic
675C2×C4#1309401012yes—
676C2×C4#1309402012yes—
677C8—44no—
678C8—1884no—
679C22—24no—
680C22—24no—
681C22—24no—
682C22—42no—
683C22—44no—
684C22—44no—
685C22—42no—
686C22—44no—
687C22—44no—
688C22—42no—
689C22—42no—
690C22—944no—
691C22—948no—
692C22—1882no—
693C22—1884no—
694C22—1884no—
695C22—1882no—
696C22—1882no—
697C22—1882no—
698C22—1884no—
699C22—1882no—
700C22—1882no—
701C22#1568897811yescharacteristic
702C22#1568899912yes—
703C22#1568900011yescharacteristic
704C22#1568900211yescharacteristic
705C22#1568902312yes—
706C22C22⋊C8×D4711yescharacteristic
707C22C22⋊C8×D4711yescharacteristic
708C22C2×(C2×D47)⋊C811yescharacteristic
709C22#1568908511yescharacteristic
710C22#1568908511yescharacteristic
711C22#1568908611yescharacteristic
712C22#1568908812yes—
713C22#1568908812yes—
714C22#1568908911yescharacteristic
715C22#1568909111yescharacteristic
716C22(C22⋊D47)⋊C812yes—
717C22C8×C22⋊D4712yes—
718C22#1568919112yes—
719C22#1568919212yes—
720C22#1568919412yes—
721C22#1568919712yes—
722C22#1568919812yes—
723C22#1568919912yes—
724C4—42no—
725C4—944no—
726C4—1882no—
727C4—1882no—
728C4#1568903112yes—
729C4#1568903212yes—
730C4#1568903812yes—
731C4#1568903912yes—
732C2—44no—
733C2—1884no—
734C2#2024162711yescharacteristic
735C2#2024329711yescharacteristic
736C2#2024329911yescharacteristic
737C2#2024367712yes—
738C2#2024367811yescharacteristic
739C2#2024368011yescharacteristic
740C2#2024368212yes—
741C2#2024368311yescharacteristic
742C2#2024368511yescharacteristic
743C2#2024418012yes—
744C2#2024418412yes—
subgroupG/H
center, FrattiniC23×C4C22×D47
commutatorC23×C47C22×C8
FittingC22×C22⋊C8×C47C2
socleC24×C47C22×C4
prime radicalC23×C22⋊D47C4
cosocleC23×C4×C47C23
hypercenterC22×C22⋊C8D47
hypocenterC47#10964
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊(C47⋊C8)C2semidirect
3. C22×(C2×D47)⋊C8C2semidirect
4. C2×#15688877C2semidirect
5. C22×C22⋊C8×C47C2semidirect
34. C22×C22⋊D47C8semidirect
52. C22×C47⋊C8D4semidirect
87. C22×C8×C47D4semidirect
222. C23×C47C22⋊C8semidirect
256. C22×D47C22⋊C8semidirect
299. C2×Dic47C22⋊C8semidirect
363. C22×C22⋊C8D47semidirect
399. C47#10964semidirect
443. C22×C8C22⋊D47semidirect
618. C23(C2×D47)⋊C8semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D472
C22×C22⋊(C47⋊C8)2
C22×(C2×D47)⋊C82
C2×#156888772
C22×C22⋊C8×C472
#1096447