Finite Group Databasebeta

← #26121852

Subgroups — #26121852

Order 12032.

1426 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic47C211yesmaximal, characteristic
2C22×#13093951C211yesmaximal, characteristic
3C2×#15688884C211yesmaximal, characteristic, complemented
4C2×#15688883C211yesmaximal, characteristic, complemented
5#20243081C211yesmaximal, characteristic, complemented
6C4×C47⋊#95C211yesmaximal, characteristic, complemented
7C22×#104×C47C211yesmaximal, characteristic
8C22×#10625329C2211yescharacteristic
9#41×Dic47—22no—
10#41×Dic47—22no—
11#41×Dic47—22no—
12#41×Dic47—22no—
13C2×Q8×Dic47C412yescomplemented
14C2×D4×Dic47—22no—
15C2×D4×Dic47C412yescomplemented
16C2×#13093983—21no—
17C2×#13093983C2211yescharacteristic
18C22×C4×Dic47—21no—
19C22×C4×Dic47C2211yescharacteristic
20C22×C4×Dic47C2211yescharacteristic
21C2×#13093951—22no—
22C2×#13093951—22no—
23C2×#13093951C414yescomplemented
24C2×C47⋊#95—22no—
25#15688884—22no—
26#15688883—22no—
27#15688877—21no—
28#15688877—21no—
29C22×#41×C47C2211yescharacteristic
30C22×M16×C47C2211yescharacteristic
31C22×C42×C47C2211yescharacteristic
32C2×#104×C47—22no—
33C2×#104×C47—22no—
34C2×#104×C47C414yescomplemented
35C23×Dic47—21no—
36C23×Dic47—22no—
37C23×Dic47D412yes—
38C2×#10625329—21no—
39C2×#10625329—21no—
40C2×#10625329—21no—
41C2×#10625329—21no—
42C2×#10625329—21no—
43C2×#10625329C2×C412yescomplemented
44C22×C47⋊C8—21no—
45Q8×Dic47—24no—
46Q8×Dic47—24no—
47D4×Dic47—28no—
48D4×Dic47—28no—
49D4×Dic47—24no—
50D4×Dic47—24no—
51#13093983—24no—
52#13093983—24no—
53#13093983—21no—
54#13093983—21no—
55#13093983D412yes—
56#13093983D412yes—
57C2×C4⋊Dic47—22no—
58C2×C4⋊Dic47C2×C412yes—
59C2×C22⋊Dic47—21no—
60C2×C22⋊Dic47—22no—
61C2×C4×Dic47—24no—
62C2×C4×Dic47—24no—
63C2×C4×Dic47—21no—
64C2×C4×Dic47—21no—
65C2×C4×Dic47—21no—
66C2×C4×Dic47—21no—
67C2×C4×Dic47—21no—
68C2×C4×Dic47—22no—
69C2×C4×Dic47—21no—
70C2×C4×Dic47—21no—
71C2×C4×Dic47—21no—
72C2×C4×Dic47—21no—
73C2×C4×Dic47—21no—
74C2×C4×Dic47C2×C412yes—
75C2×C4×Dic47C2×C412yescomplemented
76C2×C4×Dic47D411yescharacteristic
77C2×C4×Dic47D411yescharacteristic
78#13093951—28no—
79C47⋊#95—28no—
80C2×#41×C47—21no—
81C2×#41×C47—21no—
82C2×#41×C47—21no—
83C2×#41×C47—21no—
84C2×#41×C47—21no—
85C2×#41×C47—21no—
86C2×#41×C47C2×C412yes—
87C2×#41×C47C2×C412yes—
88C2×#41×C47D412yes—
89C2×#41×C47D412yes—
90C2×#41×C47D412yes—
91C2×#41×C47Q812yes—
92C22×Q8×C47C2×C411yescharacteristic
93C22×D4×C47—21no—
94C22×D4×C47C2×C411yescharacteristic
95C23×C4×C47—21no—
96C23×C4×C47—21no—
97C23×C4×C47C2311yescharacteristic
98C2×M16×C47—21no—
99C2×M16×C47—21no—
100C2×M16×C47—21no—
101C2×M16×C47—21no—
102C2×M16×C47—21no—
103C2×M16×C47C2×C412yescomplemented
104C22×C8×C47—21no—
105C2×C42×C47—21no—
106C2×C42×C47—21no—
107C2×C42×C47—21no—
108C2×C42×C47—21no—
109C2×C42×C47—21no—
110C2×C42×C47C2×C412yescomplemented
111#104×C47—28no—
112C24×C47—21no—
113C24×C47C2×D411yescharacteristic
114#41×C47—22no—
115#41×C47—22no—
116#41×C47—22no—
117#41×C47—22no—
118#41×C47—22no—
119#41×C47—22no—
120#41×C47—22no—
121#41×C47—22no—
122#41×C47—22no—
123#41×C47—22no—
124#41×C47—22no—
125#41×C47—22no—
126#41×C47C22⋊C414yes—
127#41×C47C22⋊C414yes—
128#41×C47C4⋊C414yes—
129#41×C47C4⋊C414yes—
130C2×Q8×C47—21no—
131C2×Q8×C47—21no—
132C2×Q8×C47—21no—
133C2×Q8×C47C4212yes—
134C2×Q8×C47C22⋊C412yes—
135C2×Q8×C47C4⋊C412yes—
136C2×D4×C47—22no—
137C2×D4×C47—22no—
138C2×D4×C47—22no—
139C2×D4×C47—22no—
140C2×D4×C47—22no—
141C2×D4×C47—22no—
142C2×D4×C47—21no—
143C2×D4×C47—21no—
144C2×D4×C47—21no—
145C2×D4×C47C4212yes—
146C2×D4×C47C22⋊C412yes—
147C2×D4×C47C4⋊C412yes—
148C22×C4×C47—21no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—24no—
156C22×C4×C47—22no—
157C22×C4×C47—42no—
158C22×C4×C47—41no—
159C22×C4×C47—41no—
160C22×C4×C47C22×C411yescharacteristic
161C22×C4×C47C22×C411yescharacteristic
162C22×C4×C47C22×C411yescharacteristic
163C22×C4×C47C2×D411yescharacteristic
164C22×C4×C47C2×D411yescharacteristic
165C22×C4×C47C2×D411yescharacteristic
166C22×C4×C47C2×D411yescharacteristic
167C22×C4×C47C2×D411yescharacteristic
168C22×C4×C47C2×D411yescharacteristic
169C22×C4×C47C2×Q811yescharacteristic
170C22×C4×C47#4111yescharacteristic
171C22×C4×C47#4111yescharacteristic
172C22×C4×C47#4111yescharacteristic
173C22×C4×C47#4111yescharacteristic
174C22×Dic47—24no—
175C22×Dic47—28no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—24no—
181C22×Dic47—42no—
182C22×Dic47—44no—
183C22×Dic47—42no—
184C22×Dic47—41no—
185C22×Dic47—41no—
186C22×Dic47—44no—
187C22×Dic47C22⋊C412yes—
188C22×Dic47C22⋊C412yes—
189M16×C47—22no—
190M16×C47—22no—
191M16×C47—41no—
192M16×C47—41no—
193C2×C8×C47—22no—
194C2×C8×C47—41no—
195C2×C8×C47—41no—
196C42×C47—22no—
197C42×C47—22no—
198C42×C47—41no—
199C42×C47—41no—
200C22⋊Dic47—28no—
201C22⋊Dic47—22no—
202C22⋊Dic47—22no—
203C4⋊Dic47—28no—
204C4⋊Dic47—22no—
205C4⋊Dic47C22⋊C414yes—
206C4×Dic47—28no—
207C4×Dic47—22no—
208C4×Dic47—22no—
209C4×Dic47—21no—
210C4×Dic47—21no—
211C4×Dic47—22no—
212C4×Dic47—22no—
213C4×Dic47—21no—
214C4×Dic47—21no—
215C4×Dic47—22no—
216C4×Dic47—22no—
217C4×Dic47—41no—
218C4×Dic47—41no—
219#10625329—22no—
220#10625329—22no—
221#10625329—41no—
222#10625329—41no—
223C2×C47⋊C8—22no—
224C2×C47⋊C8—41no—
225C2×C47⋊C8—41no—
226C23×C47—22no—
227C23×C47—22no—
228C23×C47—22no—
229C23×C47—22no—
230C23×C47—22no—
231C23×C47—42no—
232C23×C47—42no—
233C23×C47C2×C22⋊C411yescharacteristic
234C23×C47C4×D411yescharacteristic
235C23×C47C4×D411yescharacteristic
236C23×C47#12011yescharacteristic
237C23×C47#12011yescharacteristic
238C23×C47#12111yescharacteristic
239C23×C47C22⋊Q811yescharacteristic
240Q8×C47—22no—
241Q8×C47—22no—
242Q8×C47—22no—
243Q8×C47#9514yescomplemented
244D4×C47—24no—
245D4×C47—24no—
246D4×C47—24no—
247D4×C47—24no—
248D4×C47—22no—
249D4×C47—22no—
250D4×C47—22no—
251D4×C47#9514yescomplemented
252C2×C4×C47—22no—
253C2×C4×C47—22no—
254C2×C4×C47—22no—
255C2×C4×C47—24no—
256C2×C4×C47—24no—
257C2×C4×C47—24no—
258C2×C4×C47—24no—
259C2×C4×C47—24no—
260C2×C4×C47—44no—
261C2×C4×C47—42no—
262C2×C4×C47—44no—
263C2×C4×C47—42no—
264C2×C4×C47C2×C4211yescharacteristic
265C2×C4×C47C2×C22⋊C411yescharacteristic
266C2×C4×C47C2×C22⋊C411yescharacteristic
267C2×C4×C47C2×C22⋊C411yescharacteristic
268C2×C4×C47C2×C22⋊C411yescharacteristic
269C2×C4×C47C2×C4⋊C411yescharacteristic
270C2×C4×C47C2×C4⋊C411yescharacteristic
271C2×C4×C47C2×C4⋊C411yescharacteristic
272C2×C4×C47#11711yescharacteristic
273C2×C4×C47#11711yescharacteristic
274C2×C4×C47C4×D411yescharacteristic
275C2×C4×C47C4×D411yescharacteristic
276C2×C4×C47C4×D411yescharacteristic
277C2×C4×C47C4×D411yescharacteristic
278C2×C4×C47C4×D411yescharacteristic
279C2×C4×C47C4×D411yescharacteristic
280C2×C4×C47#12011yescharacteristic
281C2×C4×C47#12011yescharacteristic
282C2×C4×C47#12111yescharacteristic
283C2×C4×C47#12111yescharacteristic
284C2×C4×C47#12111yescharacteristic
285C2×C4×C47C22⋊Q811yescharacteristic
286C2×C4×C47C22⋊Q811yescharacteristic
287C2×C4×C47C22⋊Q811yescharacteristic
288C2×C4×C47#12311yescharacteristic
289C2×C4×C47#12311yescharacteristic
290C2×C4×C47#12311yescharacteristic
291C2×C4×C47#12311yescharacteristic
292C2×Dic47—22no—
293C2×Dic47—22no—
294C2×Dic47—24no—
295C2×Dic47—22no—
296C2×Dic47—24no—
297C2×Dic47—22no—
298C2×Dic47—22no—
299C2×Dic47—44no—
300C2×Dic47—44no—
301C2×Dic47—416no—
302C2×Dic47—44no—
303C2×Dic47—42no—
304C2×Dic47—44no—
305C2×Dic47—42no—
306C2×Dic47—42no—
307C2×Dic47—42no—
308C2×Dic47#10414yescomplemented
309C8×C47—42no—
310C47⋊C8—42no—
311#10790—471nomaximal, Sylow
312C22×C47—22no—
313C22×C47—22no—
314C22×C47—21no—
315C22×C47—21no—
316C22×C47—21no—
317C22×C47—21no—
318C22×C47—22no—
319C22×C47—22no—
320C22×C47—24no—
321C22×C47—44no—
322C22×C47—42no—
323C22×C47—42no—
324C22×C47—44no—
325C22×C47C4×C22⋊C411yescharacteristic
326C22×C47#37911yescharacteristic
327C22×C47#38011yescharacteristic
328C22×C47#38511yescharacteristic
329C22×C47#38511yescharacteristic
330C22×C47#38611yescharacteristic
331C22×C47#38611yescharacteristic
332C22×C47C2×#10412yes—
333C22×C47#42112yes—
334C4×C47—24no—
335C4×C47—44no—
336C4×C47C2×#9511yescharacteristic
337C4×C47C4×C22⋊C411yescharacteristic
338C4×C47#38011yescharacteristic
339C4×C47#38111yescharacteristic
340C4×C47#38511yescharacteristic
341C4×C47#38511yescharacteristic
342C4×C47#38611yescharacteristic
343C4×C47#38611yescharacteristic
344Dic47—24no—
345Dic47—44no—
346Dic47—42no—
347Dic47—44no—
348C2×C4×#41—471no—
349C22×#104—471no—
350C22×#104D4711yescharacteristic
351C2×#339—471no—
352C2×#339—471no—
353#1728—471no—
354C4×#95—471no—
355C2×C47—21no—
356C2×C47—21no—
357C2×C47—21no—
358C2×C47—21no—
359C2×C47—44no—
360C2×C47C22⋊#9511yescharacteristic
361C2×C47C4×#10411yescharacteristic
362C2×C47#175911yescharacteristic
363C2×C47#178912yes—
364C2×C47#180612yes—
365C22×#41C2×D4711yescharacteristic
366C22×M16—471no—
367C22×M16C2×D4711yescharacteristic
368C4×#41—942no—
369C4×#41—942no—
370C4×#41—942no—
371C4×#41—942no—
372C2×C4×Q8—472no—
373C2×C4×D4—472no—
374C2×C4×D4—942no—
375C2×#117—471no—
376C2×#117—941no—
377C22×C42—471no—
378C22×C42—471no—
379C22×C42—941no—
380C22×C42C2×D4711yescharacteristic
381C2×#104—22no—
382C2×#104—22no—
383C2×#104—474no—
384C2×#104—942no—
385C2×#104—942no—
386C2×#104Dic4714yescomplemented
387C2×#95—942no—
388#339—942no—
389#339—942no—
390#336—941no—
391#336—941no—
392C47#1079011yescharacteristic, complemented, Sylow
393C2×#41—21no—
394C2×#41—21no—
395C2×#41—21no—
396C2×#41—21no—
397C2×#41—21no—
398C2×#41—21no—
399C2×#41Dic9412yes—
400C2×#41C4×D4712yes—
401C2×#41D18812yes—
402C2×#41C2×Dic4712yes—
403C2×#41C22⋊D4712yes—
404C2×#41C22⋊D4712yes—
405C22×Q8C4×D4711yescharacteristic
406C22×D4—21no—
407C22×D4C4×D4711yescharacteristic
408C23×C4—21no—
409C23×C4—21no—
410C23×C4—472no—
411C23×C4—942no—
412C23×C4—941no—
413C23×C4C22×D4711yescharacteristic
414C2×M16—21no—
415C2×M16—21no—
416C2×M16—21no—
417C2×M16—21no—
418C2×M16—21no—
419C2×M16—472no—
420C2×M16—941no—
421C2×M16—941no—
422C2×M16—941no—
423C2×M16—941no—
424C2×M16—941no—
425C2×M16C2×Dic4712yescomplemented
426C22×C8—21no—
427C22×C8—941no—
428C4×Q8—944no—
429C4×Q8—944no—
430C4×D4—944no—
431C4×D4—948no—
432C4×D4—948no—
433C4×D4—944no—
434#117—472no—
435#117—472no—
436#117—944no—
437#117—944no—
438#117—941no—
439#117—941no—
440C2×C4⋊C4—472no—
441C2×C4⋊C4—942no—
442C2×C22⋊C4—942no—
443C2×C22⋊C4—941no—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—472no—
450C2×C42—471no—
451C2×C42—471no—
452C2×C42—472no—
453C2×C42—942no—
454C2×C42—944no—
455C2×C42—944no—
456C2×C42—941no—
457C2×C42—941no—
458C2×C42—941no—
459C2×C42—941no—
460C2×C42—941no—
461C2×C42—941no—
462C2×C42—941no—
463C2×C42—941no—
464C2×C42—941no—
465C2×C42—941no—
466C2×C42C2×Dic4712yescomplemented
467#104—28no—
468#104—948no—
469#95—948no—
470C24—21no—
471C24D4×D4711yescharacteristic
472#41—22no—
473#41—22no—
474#41—22no—
475#41—22no—
476#41—22no—
477#41—22no—
478#41—22no—
479#41—22no—
480#41—22no—
481#41—22no—
482#41—22no—
483#41—22no—
484#41Dic47⋊C414yes—
485#41C4⋊Dic4714yes—
486#41(C2×D47)⋊C414yes—
487#41C22⋊Dic4714yes—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8C4×Dic4712yes—
492C2×Q8Dic47⋊C412yes—
493C2×Q8(C2×D47)⋊C412yes—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4C4×Dic4712yes—
504C2×D4Dic47⋊C412yes—
505C2×D4(C2×D47)⋊C412yes—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—42no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—472no—
519C22×C4—472no—
520C22×C4—944no—
521C22×C4—944no—
522C22×C4—948no—
523C22×C4—942no—
524C22×C4—942no—
525C22×C4—942no—
526C22×C4—942no—
527C22×C4—1884no—
528C22×C4—1882no—
529C22×C4—1884no—
530C22×C4—1882no—
531C22×C4—1881no—
532C22×C4—1881no—
533C22×C4C2×Dic9411yescharacteristic
534C22×C4C2×C4×D4711yescharacteristic
535C22×C4C2×C4×D4711yescharacteristic
536C22×C4C2×D18811yescharacteristic
537C22×C4D4×D4711yescharacteristic
538C22×C4D4×D4711yescharacteristic
539C22×C4D4×D4711yescharacteristic
540C22×C4#1062535211yescharacteristic
541C22×C4#1062535211yescharacteristic
542C22×C4#1062535211yescharacteristic
543C22×C4#1062535211yescharacteristic
544C22×C4C22×Dic4711yescharacteristic
545C22×C4C2×C22⋊D4711yescharacteristic
546C22×C4C2×C22⋊D4711yescharacteristic
547M16—22no—
548M16—22no—
549M16—41no—
550M16—41no—
551M16—942no—
552M16—942no—
553M16—1881no—
554M16—1881no—
555C2×C8—22no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—942no—
559C2×C8—1881no—
560C2×C8—1881no—
561C4⋊C4—474no—
562C4⋊C4—948no—
563C4⋊C4—942no—
564C22⋊C4—948no—
565C22⋊C4—942no—
566C22⋊C4—942no—
567C42—22no—
568C42—22no—
569C42—41no—
570C42—41no—
571C42—948no—
572C42—942no—
573C42—942no—
574C42—941no—
575C42—941no—
576C42—942no—
577C42—941no—
578C42—941no—
579C42—942no—
580C42—942no—
581C42—942no—
582C42—1881no—
583C42—1881no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—42no—
590C23—42no—
591C23C22⋊C4×D4711yescharacteristic
592C23(C22⋊D47)⋊C411yescharacteristic
593C23D4×Dic4711yescharacteristic
594C23#1309399211yescharacteristic
595C23#1309399411yescharacteristic
596C23#1309399611yescharacteristic
597C23#1309400111yescharacteristic
598Q8—22no—
599Q8—22no—
600Q8—22no—
601Q8C47⋊#9514yescomplemented
602D4—24no—
603D4—24no—
604D4—24no—
605D4—24no—
606D4—22no—
607D4—22no—
608D4—22no—
609D4C47⋊#9514yescomplemented
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—42no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—42no—
622C2×C4—474no—
623C2×C4—942no—
624C2×C4—942no—
625C2×C4—944no—
626C2×C4—944no—
627C2×C4—942no—
628C2×C4—942no—
629C2×C4—942no—
630C2×C4—1884no—
631C2×C4—1884no—
632C2×C4—18816no—
633C2×C4—1882no—
634C2×C4—1884no—
635C2×C4—1884no—
636C2×C4—1882no—
637C2×C4—1882no—
638C2×C4—1882no—
639C2×C4C2×C4×Dic4711yescharacteristic
640C2×C4C22⋊C4×D4711yescharacteristic
641C2×C4C2×(C2×D47)⋊C411yescharacteristic
642C2×C4C2×(C2×D47)⋊C411yescharacteristic
643C2×C4C2×C22⋊Dic4711yescharacteristic
644C2×C4C2×Dic47⋊C411yescharacteristic
645C2×C4C2×Dic47⋊C411yescharacteristic
646C2×C4C2×C4⋊Dic4711yescharacteristic
647C2×C4#1309398011yescharacteristic
648C2×C4#1309398011yescharacteristic
649C2×C4(C22⋊D47)⋊C411yescharacteristic
650C2×C4(C22⋊D47)⋊C411yescharacteristic
651C2×C4(C22⋊D47)⋊C411yescharacteristic
652C2×C4D4×Dic4711yescharacteristic
653C2×C4D4×Dic4711yescharacteristic
654C2×C4D4×Dic4711yescharacteristic
655C2×C4#1309399211yescharacteristic
656C2×C4#1309399411yescharacteristic
657C2×C4#1309399611yescharacteristic
658C2×C4#1309399611yescharacteristic
659C2×C4#1309399611yescharacteristic
660C2×C4#1309400111yescharacteristic
661C2×C4#1309400111yescharacteristic
662C2×C4#1309400111yescharacteristic
663C2×C4#1309400511yescharacteristic
664C2×C4#1309400511yescharacteristic
665C2×C4#1309400811yescharacteristic
666C2×C4#1309400811yescharacteristic
667C8—42no—
668C8—1882no—
669C22—21no—
670C22—21no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—21no—
676C22—21no—
677C22—24no—
678C22—42no—
679C22—44no—
680C22—44no—
681C22—42no—
682C22C22⋊C4×Dic4711yescharacteristic
683C22#1568897811yescharacteristic
684C22#1568898111yescharacteristic
685C22#1568899511yescharacteristic
686C22#1568899811yescharacteristic
687C22#1568900011yescharacteristic
688C22#1568900311yescharacteristic
689C22#104×D4712yes—
690C22#1568913812yes—
691C4—24no—
692C4—44no—
693C4—944no—
694C4—1884no—
695C4—1882no—
696C4—1884no—
697C4C2×C47⋊#9511yescharacteristic
698C4C22⋊C4×Dic4711yescharacteristic
699C4#1568898111yescharacteristic
700C4#1568898411yescharacteristic
701C4#1568899511yescharacteristic
702C4#1568899811yescharacteristic
703C4#1568900011yescharacteristic
704C4#1568900311yescharacteristic
705C2—21no—
706C2—21no—
707C2—21no—
708C2—21no—
709C2—44no—
710C2#2024161011yescharacteristic
711C2#104×Dic4711yescharacteristic
712C2#2024320011yescharacteristic
713C2#2024333012yes—
714C2#2024340612yes—
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC22×#104×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC22×#41×C47C22
cosocleC23×C4×C47C23
hypercenterC22×#104D47
hypocenterC47#10790
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
3. C2×#15688884C2semidirect
4. C2×#15688883C2semidirect
5. #20243081C2semidirect
6. C4×C47⋊#95C2semidirect
13. C2×Q8×Dic47C4semidirect
15. C2×D4×Dic47C4semidirect
23. C2×#13093951C4semidirect
34. C2×#104×C47C4semidirect
43. C2×#10625329C2×C4semidirect
75. C2×C4×Dic47C2×C4semidirect
103. C2×M16×C47C2×C4semidirect
110. C2×C42×C47C2×C4semidirect
243. Q8×C47#95semidirect
251. D4×C47#95semidirect
308. C2×Dic47#104semidirect
386. C2×#104Dic47semidirect
392. C47#10790semidirect
425. C2×M16C2×Dic47semidirect
466. C2×C42C2×Dic47semidirect
601. Q8C47⋊#95semidirect
609. D4C47⋊#95semidirect

Maximal subgroups

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

subgroupindex
C2×#41×Dic472
C22×#130939512
C2×#156888842
C2×#156888832
#202430812
C4×C47⋊#952
C22×#104×C472
#1079047