Finite Group Databasebeta

← #26123230

Subgroups — #26123230

Order 12032.

1326 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093945C211yesmaximal, characteristic
2C2×#15689026C211yesmaximal, characteristic
3C2×#15688992C211yesmaximal, characteristic, complemented
4C2×#15688886C211yesmaximal, characteristic, complemented
5C2×#15688885C211yesmaximal, characteristic, complemented
6C2×#15688877C211yesmaximal, characteristic, complemented
7C22×#102×C47C211yesmaximal, characteristic
8C23×C47⋊C8C2211yescharacteristic
9C22×C4⋊Dic47C2211yescharacteristic
10C22×C4⋊Dic47C2211yescharacteristic
11C22×Dic47⋊C4—22no—
12C22×C22⋊Dic47—22no—
13C22×C4×Dic47C2211yescharacteristic
14C2×#13093945—22no—
15C2×#13093945—22no—
16C2×#13093945—22no—
17#15689026—22no—
18#15689026C414yescomplemented
19#15688992—22no—
20#15688992—22no—
21#15688886—22no—
22#15688885—22no—
23#15688877—22no—
24C23×D4×C47C2211yescharacteristic
25C23×C8×C47C2211yescharacteristic
26C22×C4⋊C4×C47C2211yescharacteristic
27C2×#102×C47—22no—
28C2×#102×C47—22no—
29C2×#102×C47—22no—
30C23×Dic47—21no—
31C23×Dic47—21no—
32C23×Dic47D412yes—
33C22×C47⋊C8—21no—
34C22×C47⋊C8—21no—
35C22×C47⋊C8—21no—
36C22×C47⋊C8—21no—
37C22×C47⋊C8—21no—
38C22×C47⋊C8—21no—
39C22×C47⋊C8D412yes—
40C2×C4⋊Dic47—21no—
41C2×C4⋊Dic47—21no—
42C2×C4⋊Dic47—21no—
43C2×C4⋊Dic47—21no—
44C2×C4⋊Dic47—21no—
45C2×C4⋊Dic47—21no—
46C2×C4⋊Dic47—21no—
47C2×C4⋊Dic47—21no—
48C2×C4⋊Dic47—21no—
49C2×C4⋊Dic47—21no—
50C2×C4⋊Dic47C2×C412yes—
51C2×C4⋊Dic47D412yes—
52C2×Dic47⋊C4—28no—
53C2×Dic47⋊C4—44no—
54C2×Dic47⋊C4—44no—
55C2×C22⋊Dic47—28no—
56C2×C22⋊Dic47—44no—
57C2×C22⋊Dic47—44no—
58C2×C4×Dic47—21no—
59C2×C4×Dic47—21no—
60C2×C4×Dic47—21no—
61C2×C4×Dic47—21no—
62C2×C4×Dic47C2×C412yes—
63C2×C4×Dic47D412yes—
64#13093945—28no—
65C25×C47—21no—
66C22×D4×C47—21no—
67C22×D4×C47—21no—
68C22×D4×C47—21no—
69C22×D4×C47—21no—
70C22×D4×C47—21no—
71C22×D4×C47—21no—
72C22×D4×C47—21no—
73C22×D4×C47—21no—
74C22×D4×C47—21no—
75C22×D4×C47—21no—
76C22×D4×C47—21no—
77C22×D4×C47C2×C412yes—
78C22×D4×C47D412yes—
79C22×D4×C47Q812yes—
80C23×C4×C47—21no—
81C23×C4×C47C2311yescharacteristic
82C22×C8×C47—21no—
83C22×C8×C47—21no—
84C22×C8×C47—21no—
85C22×C8×C47—21no—
86C22×C8×C47—21no—
87C22×C8×C47—21no—
88C22×C8×C47D412yes—
89C2×C4⋊C4×C47—21no—
90C2×C4⋊C4×C47—21no—
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47—21no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47D412yes—
95#102×C47—28no—
96C24×C47—22no—
97C24×C47—22no—
98C24×C47—22no—
99C24×C47—41no—
100C24×C47—41no—
101C24×C47—41no—
102C24×C47—41no—
103C24×C47—42no—
104C24×C47—42no—
105C24×C47—42no—
106C24×C47—42no—
107C24×C47C2×D411yescharacteristic
108C2×D4×C47—22no—
109C2×D4×C47—22no—
110C2×D4×C47—22no—
111C2×D4×C47—22no—
112C2×D4×C47—22no—
113C2×D4×C47—22no—
114C2×D4×C47—22no—
115C2×D4×C47—22no—
116C2×D4×C47—22no—
117C2×D4×C47—22no—
118C2×D4×C47—22no—
119C2×D4×C47—22no—
120C2×D4×C47—22no—
121C2×D4×C47—22no—
122C2×D4×C47—22no—
123C2×D4×C47—41no—
124C2×D4×C47—41no—
125C2×D4×C47—41no—
126C2×D4×C47—41no—
127C2×D4×C47—41no—
128C2×D4×C47—41no—
129C2×D4×C47—41no—
130C2×D4×C47—41no—
131C2×D4×C47—41no—
132C2×D4×C47—41no—
133C2×D4×C47—41no—
134C2×D4×C47—41no—
135C2×D4×C47C4⋊C414yescomplemented
136C22×C4×C47—22no—
137C22×C4×C47—41no—
138C22×C4×C47—41no—
139C22×C4×C47—42no—
140C22×C4×C47—42no—
141C22×C4×C47C22×C411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×Q811yescharacteristic
149C22×C4×C47#4111yescharacteristic
150C22×C4×C47#4111yescharacteristic
151C22×C4×C47#4111yescharacteristic
152C22×C4×C47#4111yescharacteristic
153C22×C4×C47#4111yescharacteristic
154C22×C4×C47#4111yescharacteristic
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—22no—
160C22×Dic47—22no—
161C22×Dic47—41no—
162C22×Dic47—41no—
163C22×Dic47—41no—
164C22×Dic47—41no—
165C22×Dic47—42no—
166C22×Dic47—42no—
167C22×Dic47—42no—
168C22×Dic47—42no—
169C22×Dic47C22⋊C414yes—
170C22×Dic47D814yes—
171C22×Dic47SD1614yes—
172C2×C8×C47—22no—
173C2×C8×C47—22no—
174C2×C8×C47—22no—
175C2×C8×C47—41no—
176C2×C8×C47—41no—
177C2×C8×C47—41no—
178C2×C8×C47—41no—
179C4⋊C4×C47—22no—
180C4⋊C4×C47—22no—
181C4⋊C4×C47—41no—
182C4⋊C4×C47—41no—
183C22⋊Dic47—416no—
184C4⋊Dic47—22no—
185C4⋊Dic47—22no—
186C4⋊Dic47—22no—
187C4⋊Dic47—22no—
188C4⋊Dic47—41no—
189C4⋊Dic47—41no—
190C4⋊Dic47—41no—
191C4⋊Dic47—41no—
192Dic47⋊C4—416no—
193C4×Dic47—22no—
194C4×Dic47—22no—
195C4×Dic47—22no—
196C4×Dic47—22no—
197C2×C47⋊C8—22no—
198C2×C47⋊C8—22no—
199C2×C47⋊C8—22no—
200C2×C47⋊C8—41no—
201C2×C47⋊C8—41no—
202C2×C47⋊C8—41no—
203C2×C47⋊C8—41no—
204C23×C47—24no—
205C23×C47—42no—
206C23×C47—42no—
207C23×C47—42no—
208C23×C47—42no—
209C23×C47—42no—
210C23×C47—42no—
211C23×C47—44no—
212C23×C47—44no—
213C23×C47—44no—
214C23×C47—44no—
215C23×C47—44no—
216C23×C47—44no—
217C23×C47—82no—
218C23×C47—82no—
219C23×C47—82no—
220C23×C47—82no—
221C23×C47—82no—
222C23×C47—82no—
223C23×C47—81no—
224C23×C47—81no—
225C23×C47—81no—
226C23×C47—81no—
227C23×C47C2×C22⋊C411yescharacteristic
228C23×C47#12011yescharacteristic
229C23×C47#12111yescharacteristic
230C23×C47C22⋊Q811yescharacteristic
231C23×C47#12311yescharacteristic
232C23×C47#12411yescharacteristic
233C23×C47#12711yescharacteristic
234C23×C47C2×D812yes—
235C23×C47C2×SD1612yes—
236C23×C47AGL(1,ℤ/8)12yes—
237C23×C47#13712yes—
238D4×C47—24no—
239D4×C47—24no—
240D4×C47—42no—
241D4×C47—42no—
242D4×C47—42no—
243D4×C47—42no—
244D4×C47—42no—
245D4×C47—42no—
246C2×C4×C47—42no—
247C2×C4×C47—44no—
248C2×C4×C47—82no—
249C2×C4×C47—81no—
250C2×C4×C47—81no—
251C2×C4×C47C2×C4⋊C411yescharacteristic
252C2×C4×C47#11711yescharacteristic
253C2×C4×C47C4×D411yescharacteristic
254C2×C4×C47C4×D411yescharacteristic
255C2×C4×C47C4×D411yescharacteristic
256C2×C4×C47C4×D411yescharacteristic
257C2×C4×C47#12011yescharacteristic
258C2×C4×C47#12011yescharacteristic
259C2×C4×C47#12111yescharacteristic
260C2×C4×C47#12111yescharacteristic
261C2×C4×C47#12111yescharacteristic
262C2×C4×C47#12111yescharacteristic
263C2×C4×C47#12111yescharacteristic
264C2×C4×C47#12111yescharacteristic
265C2×C4×C47#12111yescharacteristic
266C2×C4×C47C22⋊Q811yescharacteristic
267C2×C4×C47C22⋊Q811yescharacteristic
268C2×C4×C47C22⋊Q811yescharacteristic
269C2×C4×C47C22⋊Q811yescharacteristic
270C2×C4×C47C22⋊Q811yescharacteristic
271C2×C4×C47#12311yescharacteristic
272C2×C4×C47#12311yescharacteristic
273C2×C4×C47#12311yescharacteristic
274C2×C4×C47#12311yescharacteristic
275C2×C4×C47#12411yescharacteristic
276C2×C4×C47#12411yescharacteristic
277C2×C4×C47#12611yescharacteristic
278C2×C4×C47#12611yescharacteristic
279C2×Dic47—24no—
280C2×Dic47—24no—
281C2×Dic47—24no—
282C2×Dic47—24no—
283C2×Dic47—24no—
284C2×Dic47—24no—
285C2×Dic47—42no—
286C2×Dic47—42no—
287C2×Dic47—44no—
288C2×Dic47—44no—
289C2×Dic47—82no—
290C2×Dic47—82no—
291C2×Dic47—81no—
292C2×Dic47—81no—
293C2×Dic47—81no—
294C2×Dic47—81no—
295C2×Dic47#10218yescomplemented
296C8×C47—42no—
297C47⋊C8—42no—
298#11049—471nomaximal, Sylow
299C22×C47—48no—
300C22×C47—44no—
301C22×C47—84no—
302C22×C47—82no—
303C22×C47—82no—
304C22×C47—84no—
305C22×C47—82no—
306C22×C47—82no—
307C22×C47—82no—
308C22×C47—82no—
309C22×C47—84no—
310C22×C47#38011yescharacteristic
311C22×C47#38611yescharacteristic
312C22×C47#39011yescharacteristic
313C22×C47#39211yescharacteristic
314C22×C47#39311yescharacteristic
315C22×C47#39711yescharacteristic
316C22×C47#39911yescharacteristic
317C22×C47C2×#10212yes—
318C22×C47#41712yes—
319C22×C47#44712yes—
320C22×C47#44812yes—
321C22×C47#45912yes—
322C22×C47#46112yes—
323C22×C47#47412yes—
324C22×C47#47612yes—
325C22×C47#48012yes—
326C22×C47#48112yes—
327C22×C47#48612yes—
328C22×C47#48912yes—
329C22×C47#49211yescharacteristic
330C22×C47#49311yescharacteristic
331C22×C47#49611yescharacteristic
332C22×C47#49711yescharacteristic
333C4×C47—82no—
334C4×C47#38511yescharacteristic
335C4×C47#38511yescharacteristic
336C4×C47#38811yescharacteristic
337C4×C47#38811yescharacteristic
338C4×C47#39411yescharacteristic
339C4×C47#39411yescharacteristic
340C4×C47#39611yescharacteristic
341C4×C47#39611yescharacteristic
342Dic47—28no—
343Dic47—82no—
344Dic47—82no—
345C22×#102—471no—
346C22×#102D4711yescharacteristic
347C2×#390—471no—
348C2×#384—471no—
349C2×#340—471no—
350C2×#340—471no—
351C2×#336—471no—
352C2×C47—84no—
353C2×C47#143911yescharacteristic
354C2×C47#180212yes—
355C2×C47#187412yes—
356C2×C47#195711yescharacteristic
357C2×C47#195911yescharacteristic
358C2×C47#201111yescharacteristic
359C2×C47#201311yescharacteristic
360C2×C47#202312yes—
361C2×C47#207112yes—
362C2×C47#209311yescharacteristic
363C2×C47#209411yescharacteristic
364C23×D4C2×D4711yescharacteristic
365C23×C8—471no—
366C23×C8C2×D4711yescharacteristic
367C22×C4⋊C4—471no—
368C22×C4⋊C4—471no—
369C22×C4⋊C4—942no—
370C22×C4⋊C4C2×D4711yescharacteristic
371C22×C22⋊C4—942no—
372C22×C42—471no—
373C2×#102—22no—
374C2×#102—22no—
375C2×#102—22no—
376C2×#102—942no—
377C2×#102—942no—
378C2×#102—942no—
379#390—474no—
380#390—942no—
381#384—942no—
382#384—942no—
383#340—942no—
384#340—942no—
385#336—942no—
386C47#1104911yescharacteristic, complemented, Sylow
387C25—21no—
388C22×D4—21no—
389C22×D4—21no—
390C22×D4—21no—
391C22×D4—21no—
392C22×D4—21no—
393C22×D4—21no—
394C22×D4—21no—
395C22×D4—21no—
396C22×D4—21no—
397C22×D4—21no—
398C22×D4—21no—
399C22×D4Dic9412yes—
400C22×D4C4×D4712yes—
401C22×D4C22⋊D4712yes—
402C23×C4—21no—
403C23×C4—472no—
404C23×C4—941no—
405C23×C4—941no—
406C23×C4C22×D4711yescharacteristic
407C22×C8—21no—
408C22×C8—21no—
409C22×C8—21no—
410C22×C8—21no—
411C22×C8—21no—
412C22×C8—21no—
413C22×C8—472no—
414C22×C8—941no—
415C22×C8—941no—
416C22×C8—941no—
417C22×C8—941no—
418C22×C8—941no—
419C22×C8—941no—
420C22×C8C22⋊D4712yes—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—472no—
427C2×C4⋊C4—472no—
428C2×C4⋊C4—941no—
429C2×C4⋊C4—941no—
430C2×C4⋊C4—941no—
431C2×C4⋊C4—941no—
432C2×C4⋊C4—941no—
433C2×C4⋊C4—941no—
434C2×C4⋊C4—941no—
435C2×C4⋊C4—941no—
436C2×C4⋊C4—948no—
437C2×C4⋊C4—941no—
438C2×C4⋊C4—941no—
439C2×C4⋊C4—1884no—
440C2×C4⋊C4—1884no—
441C2×C4⋊C4C22⋊D4712yes—
442C2×C22⋊C4—948no—
443C2×C22⋊C4—1884no—
444C2×C22⋊C4—1884no—
445C2×C42—472no—
446C2×C42—472no—
447C2×C42—941no—
448C2×C42—941no—
449C2×C42—941no—
450C2×C42—941no—
451#102—28no—
452#102—948no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—41no—
457C24—41no—
458C24—41no—
459C24—41no—
460C24—42no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24D4×D4711yescharacteristic
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4Dic47⋊C414yescomplemented
493C22×C4—22no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—474no—
499C22×C4—474no—
500C22×C4—474no—
501C22×C4—942no—
502C22×C4—942no—
503C22×C4—942no—
504C22×C4—942no—
505C22×C4—942no—
506C22×C4—942no—
507C22×C4—1881no—
508C22×C4—1881no—
509C22×C4—1881no—
510C22×C4—1881no—
511C22×C4—1882no—
512C22×C4—1882no—
513C22×C4—1882no—
514C22×C4—1882no—
515C22×C4C2×Dic9411yescharacteristic
516C22×C4C2×C4×D4711yescharacteristic
517C22×C4#1062535011yescharacteristic
518C22×C4#1062535011yescharacteristic
519C22×C4D4×D4711yescharacteristic
520C22×C4D4×D4711yescharacteristic
521C22×C4D4×D4711yescharacteristic
522C22×C4#1062535211yescharacteristic
523C22×C4#1062535211yescharacteristic
524C22×C4#1062535211yescharacteristic
525C22×C4#1062535211yescharacteristic
526C22×C4C2×C22⋊D4711yescharacteristic
527C22×C4C2×C22⋊D4711yescharacteristic
528C22×C4C2×C22⋊D4711yescharacteristic
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—942no—
537C2×C8—942no—
538C2×C8—942no—
539C2×C8—1881no—
540C2×C8—1881no—
541C2×C8—1881no—
542C2×C8—1881no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—942no—
548C4⋊C4—942no—
549C4⋊C4—942no—
550C4⋊C4—942no—
551C4⋊C4—18816no—
552C4⋊C4—1881no—
553C4⋊C4—1881no—
554C4⋊C4—1881no—
555C4⋊C4—1881no—
556C22⋊C4—18816no—
557C42—942no—
558C42—942no—
559C42—942no—
560C42—942no—
561C23—24no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—44no—
569C23—44no—
570C23—44no—
571C23—44no—
572C23—44no—
573C23—44no—
574C23—82no—
575C23—81no—
576C23—81no—
577C23—82no—
578C23—81no—
579C23—81no—
580C23—82no—
581C23—82no—
582C23—82no—
583C23—82no—
584C23C22⋊C4×D4711yescharacteristic
585C23#1309399211yescharacteristic
586C23#1309399611yescharacteristic
587C23#1309400111yescharacteristic
588C23#1309400611yescharacteristic
589C23#1309401011yescharacteristic
590C23#1309402011yescharacteristic
591C23D8×D4712yes—
592C23SD16×D4712yes—
593C23#1309404812yes—
594C23#1309405312yes—
595D4—24no—
596D4—24no—
597D4—42no—
598D4—42no—
599D4—42no—
600D4—42no—
601D4—42no—
602D4—42no—
603C2×C4—44no—
604C2×C4—42no—
605C2×C4—81no—
606C2×C4—81no—
607C2×C4—82no—
608C2×C4—478no—
609C2×C4—944no—
610C2×C4—944no—
611C2×C4—944no—
612C2×C4—944no—
613C2×C4—944no—
614C2×C4—944no—
615C2×C4—3761no—
616C2×C4—3761no—
617C2×C4—3761no—
618C2×C4—3761no—
619C2×C4—3762no—
620C2×C4—3762no—
621C2×C4—1884no—
622C2×C4—1882no—
623C2×C4—1882no—
624C2×C4—1884no—
625C2×C4C2×Dic47⋊C411yescharacteristic
626C2×C4#1309398011yescharacteristic
627C2×C4(C22⋊D47)⋊C411yescharacteristic
628C2×C4(C22⋊D47)⋊C411yescharacteristic
629C2×C4C4×C22⋊D4711yescharacteristic
630C2×C4C4×C22⋊D4711yescharacteristic
631C2×C4#1309399211yescharacteristic
632C2×C4#1309399311yescharacteristic
633C2×C4#1309399511yescharacteristic
634C2×C4#1309399511yescharacteristic
635C2×C4#1309399611yescharacteristic
636C2×C4#1309399611yescharacteristic
637C2×C4#1309399611yescharacteristic
638C2×C4#1309399711yescharacteristic
639C2×C4#1309399711yescharacteristic
640C2×C4#1309400111yescharacteristic
641C2×C4#1309400111yescharacteristic
642C2×C4#1309400111yescharacteristic
643C2×C4#1309400311yescharacteristic
644C2×C4#1309400311yescharacteristic
645C2×C4#1309400511yescharacteristic
646C2×C4#1309400511yescharacteristic
647C2×C4#1309400611yescharacteristic
648C2×C4#1309400711yescharacteristic
649C2×C4#1309401011yescharacteristic
650C2×C4#1309401111yescharacteristic
651C2×C4#1309401711yescharacteristic
652C2×C4#1309401711yescharacteristic
653C8—42no—
654C8—1882no—
655C22—48no—
656C22—44no—
657C22—84no—
658C22—84no—
659C22—82no—
660C22—82no—
661C22—82no—
662C22—82no—
663C22—82no—
664C22—82no—
665C22—84no—
666C22#1568898111yescharacteristic
667C22#1568899911yescharacteristic
668C22#1568902311yescharacteristic
669C22#1568903111yescharacteristic
670C22#1568903511yescharacteristic
671C22#1568905111yescharacteristic
672C22#1568905911yescharacteristic
673C22#102×D4712yes—
674C22#1568912112yes—
675C22#1568925512yes—
676C22#1568926012yes—
677C22#1568931612yes—
678C22#1568932612yes—
679C22#1568940112yes—
680C22#1568941112yes—
681C22#1568943512yes—
682C22#1568944012yes—
683C22#1568946812yes—
684C22#1568948112yes—
685C22#1568949411yescharacteristic
686C22#1568949811yescharacteristic
687C22#1568951111yescharacteristic
688C22#1568951411yescharacteristic
689C4—82no—
690C4—948no—
691C4—3762no—
692C4—3762no—
693C4#1568899511yescharacteristic
694C4#1568899611yescharacteristic
695C4#1568901111yescharacteristic
696C4#1568901711yescharacteristic
697C4#1568903711yescharacteristic
698C4#1568903811yescharacteristic
699C4#1568904611yescharacteristic
700C4#1568904611yescharacteristic
701C2—84no—
702C2#2024163111yescharacteristic
703C2#2024338612yes—
704C2#2024370212yes—
705C2#2024419211yescharacteristic
706C2#2024420311yescharacteristic
707C2#2024445711yescharacteristic
708C2#2024446911yescharacteristic
709C2#2024452212yes—
710C2#2024479412yes—
711C2#2024491411yescharacteristic
712C2#2024491911yescharacteristic
subgroupG/H
centerC24D4×D47
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC22×#102×C47C2
socleC24×C47C2×D4
prime radicalC23×D4×C47C22
cosocleC23×C4×C47C23
hypercenterC22×#102D47
hypocenterC47#11049
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
3. C2×#15688992C2semidirect
4. C2×#15688886C2semidirect
5. C2×#15688885C2semidirect
6. C2×#15688877C2semidirect
18. #15689026C4semidirect
135. C2×D4×C47C4⋊C4semidirect
295. C2×Dic47#102semidirect
386. C47#11049semidirect
492. C2×D4Dic47⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130939452
C2×#156890262
C2×#156889922
C2×#156888862
C2×#156888852
C2×#156888772
C22×#102×C472
#1104947