Finite Group Databasebeta

← #26215648

Subgroups — #26215648

Order 12032.

1582 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093981C211yesmaximal, characteristic
2C2×#15689148C212yesmaximal, complemented
3C2×#15689085C211yesmaximal, characteristic
4C2×C22⋊C8×D47C211yesmaximal, characteristic
5#20243371C212yesmaximal, complemented
6#20243369C212yesmaximal, complemented
7#20243368C211yesmaximal, characteristic, complemented
8#20243366C211yesmaximal, characteristic, complemented
9#20243366C211yesmaximal, characteristic, complemented
10#20243083C212yesmaximal, complemented
11C47×#1797C211yesmaximal, characteristic, complemented
12C23×C4×D47C2211yescharacteristic
13C22×#10625324C2212yes—
14C22×C8×D47C2212yes—
15C2×#13093981—28no—
16C2×#13093981C411yescharacteristic
17C2×#13093981C411yescharacteristic
18C2×#13093981C411yescharacteristic
19C2×#13093981C411yescharacteristic
20C2×#13093981C2211yescharacteristic
21C2×#13093981C2211yescharacteristic
22C2×#13093981C2211yescharacteristic
23C2×#13093981C2211yescharacteristic
24C22×Dic47⋊C4C411yescharacteristic
25C22×Dic47⋊C4C411yescharacteristic
26C22×(C2×D47)⋊C4C411yescharacteristic
27C22×(C2×D47)⋊C4C411yescharacteristic
28C22×C4×Dic47C2211yescharacteristic
29#15689148—28no—
30C2×C4⋊(C47⋊C8)C2212yescomplemented
31C2×Dic47⋊C8C2212yescomplemented
32C2×Dic47⋊C8C2212yescomplemented
33#15689085—24no—
34C2×C22⋊(C47⋊C8)C2211yescharacteristic
35C2×C22⋊(C47⋊C8)C2211yescharacteristic
36C2×(C2×D47)⋊C8C2212yes—
37C2×(C2×D47)⋊C8C2212yes—
38C22⋊C8×D47—24no—
39#15688878C2212yescomplemented
40#15688877C2212yescomplemented
41#15688877C2212yescomplemented
42C22×C42×C47C2211yescharacteristic
43C2×C4⋊C8×C47C2212yescomplemented
44C2×C22⋊C8×C47C2211yescharacteristic
45C2×C22⋊C8×C47C2211yescharacteristic
46C47×#336C2212yescomplemented
47C24×D47C2×C411yescharacteristic
48C23×Dic47C2×C411yescharacteristic
49C23×Dic47C2×C411yescharacteristic
50C23×Dic47C2×C411yescharacteristic
51C22×C4×D47—24no—
52C22×C4×D47—24no—
53C22×C4×D47C2×C411yescharacteristic
54C22×C4×D47C2×C411yescharacteristic
55C22×C4×D47D414yes—
56C22×C4×D47Q814yes—
57C22×C4×D47C2311yescharacteristic
58C22×C4×D47C2311yescharacteristic
59C2×#10625324—24no—
60C2×#10625324—24no—
61C2×#10625324—24no—
62C22×C47⋊C8C2312yes—
63C22×C47⋊C8C2312yes—
64C2×C8×D47—24no—
65C2×C8×D47—24no—
66C2×C8×D47—24no—
67#13093981—24no—
68#13093981—24no—
69#13093981—24no—
70#13093981—24no—
71#13093981—24no—
72#13093981—24no—
73#13093981—24no—
74#13093981D418yes—
75C2×Dic47⋊C4—24no—
76C2×Dic47⋊C4—24no—
77C2×Dic47⋊C4C2×C411yescharacteristic
78C2×Dic47⋊C4C2×C411yescharacteristic
79C2×Dic47⋊C4C2×C411yescharacteristic
80C2×Dic47⋊C4C2×C411yescharacteristic
81C2×Dic47⋊C4C2×C411yescharacteristic
82C2×Dic47⋊C4C2×C411yescharacteristic
83C2×Dic47⋊C4C2×C411yescharacteristic
84C2×Dic47⋊C4C2×C411yescharacteristic
85C2×(C2×D47)⋊C4—24no—
86C2×(C2×D47)⋊C4—24no—
87C2×(C2×D47)⋊C4C2×C411yescharacteristic
88C2×(C2×D47)⋊C4C2×C411yescharacteristic
89C2×(C2×D47)⋊C4C2×C411yescharacteristic
90C2×(C2×D47)⋊C4C2×C411yescharacteristic
91C2×(C2×D47)⋊C4C2×C411yescharacteristic
92C2×(C2×D47)⋊C4C2×C411yescharacteristic
93C2×(C2×D47)⋊C4C2×C411yescharacteristic
94C2×(C2×D47)⋊C4C2×C411yescharacteristic
95C2×C4×Dic47—24no—
96C2×C4×Dic47C2×C411yescharacteristic
97C2×C4×Dic47C2×C411yescharacteristic
98C2×C4×Dic47C2311yescharacteristic
99C2×C4×Dic47C2311yescharacteristic
100C4⋊(C47⋊C8)—24no—
101Dic47⋊C8—24no—
102Dic47⋊C8—24no—
103C22⋊(C47⋊C8)—22no—
104C22⋊(C47⋊C8)—22no—
105(C2×D47)⋊C8—24no—
106(C2×D47)⋊C8—24no—
107C23×C4×C47C2×C411yescharacteristic
108C23×C4×C47C2×C411yescharacteristic
109C23×C4×C47C2311yescharacteristic
110C22×C8×C47C2312yes—
111C22×C8×C47C2312yes—
112C2×C42×C47—24no—
113C2×C42×C47C2×C411yescharacteristic
114C2×C42×C47C2×C411yescharacteristic
115C2×C42×C47C2311yescharacteristic
116C2×C42×C47C2311yescharacteristic
117C4⋊C8×C47—24no—
118C22⋊C8×C47—22no—
119C22⋊C8×C47—22no—
120C24×C47C22×C411yescharacteristic
121C23×D47—22no—
122C23×D47—22no—
123C23×D47—22no—
124C23×D47—22no—
125C23×D47—41no—
126C23×D47—41no—
127C23×D47C4⋊C414yes—
128C23×D47C22×C411yescharacteristic
129C23×D47C22×C411yescharacteristic
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—41no—
137C22×C4×C47—41no—
138C22×C4×C47C22×C411yescharacteristic
139C22×C4×C47C22×C411yescharacteristic
140C22×C4×C47C22×C411yescharacteristic
141C22×C4×C47C22×C411yescharacteristic
142C22×C4×C47C22×C411yescharacteristic
143C22×C4×C47C2×D412yes—
144C22×C4×C47C2×Q812yes—
145C22×C4×C47C2411yescharacteristic
146C22×Dic47—22no—
147C22×Dic47—22no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47—22no—
152C22×Dic47—41no—
153C22×Dic47—41no—
154C22×Dic47C4⋊C414yes—
155C22×Dic47C22×C411yescharacteristic
156C22×Dic47C22×C411yescharacteristic
157C22×Dic47C22×C411yescharacteristic
158C22×Dic47C22×C411yescharacteristic
159C22×Dic47C22×C411yescharacteristic
160C22×Dic47C22×C411yescharacteristic
161C2×C4×D47—22no—
162C2×C4×D47—22no—
163C2×C4×D47—22no—
164C2×C4×D47—22no—
165C2×C4×D47—22no—
166C2×C4×D47—22no—
167C2×C4×D47—216no—
168C2×C4×D47—216no—
169C2×C4×D47C4⋊C414yes—
170C2×C4×D47C4⋊C414yes—
171C2×C4×D47C2×D412yes—
172C2×C4×D47C2×D412yes—
173C2×C4×D47C2×D414yes—
174C2×C4×D47C2×Q812yes—
175C2×C4×D47C2×Q812yes—
176C2×C4×D47#4114yes—
177C2×C8×C47—22no—
178C2×C8×C47—22no—
179C2×C8×C47—22no—
180C2×C8×C47—22no—
181C2×C8×C47—22no—
182C2×C8×C47—22no—
183C42×C47—22no—
184C42×C47—22no—
185C42×C47—22no—
186C42×C47C2×D414yes—
187(C2×D47)⋊C4—22no—
188(C2×D47)⋊C4—22no—
189(C2×D47)⋊C4—22no—
190(C2×D47)⋊C4—22no—
191(C2×D47)⋊C4—22no—
192(C2×D47)⋊C4—22no—
193(C2×D47)⋊C4C22⋊C414yes—
194(C2×D47)⋊C4C22⋊C414yes—
195Dic47⋊C4—22no—
196Dic47⋊C4—22no—
197Dic47⋊C4—22no—
198Dic47⋊C4—22no—
199Dic47⋊C4—22no—
200Dic47⋊C4—22no—
201Dic47⋊C4C22⋊C414yes—
202Dic47⋊C4C22⋊C414yes—
203C4×Dic47—22no—
204C4×Dic47—22no—
205C4×Dic47—22no—
206C4×Dic47C2×D414yes—
207C2×C47⋊C8—22no—
208C2×C47⋊C8—22no—
209C2×C47⋊C8—22no—
210C2×C47⋊C8—22no—
211C2×C47⋊C8—22no—
212C2×C47⋊C8—22no—
213#10625324—48no—
214C8×D47—48no—
215C23×C47—21no—
216C23×C47—21no—
217C23×C47—21no—
218C23×C47—21no—
219C23×C47C2×C4⋊C412yes—
220C23×C47#13112yes—
221C23×C47#13112yes—
222C23×C47C23×C411yescharacteristic
223C22×D47—21no—
224C22×D47—21no—
225C22×D47—21no—
226C22×D47—21no—
227C22×D47—21no—
228C22×D47—21no—
229C22×D47—21no—
230C22×D47—21no—
231C22×D47—21no—
232C22×D47—21no—
233C22×D47—28no—
234C22×D47—28no—
235C22×D47—44no—
236C22×D47—44no—
237C22×D47—44no—
238C22×D47—44no—
239C22×D47—44no—
240C22×D47C2×C22⋊C412yes—
241C22×D47C2×C4⋊C412yes—
242C22×D47C2×C4⋊C412yes—
243C22×D47#11712yes—
244C2×C4×C47—21no—
245C2×C4×C47—21no—
246C2×C4×C47—21no—
247C2×C4×C47—21no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—24no—
251C2×C4×C47—24no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—21no—
258C2×C4×C47—44no—
259C2×C4×C47—44no—
260C2×C4×C47C2×C22⋊C412yes—
261C2×C4×C47C2×C22⋊C412yes—
262C2×C4×C47C2×C4⋊C412yes—
263C2×C4×C47C22×D411yescharacteristic
264C2×C4×C47C22×D412yes—
265C2×C4×C47C22×Q811yescharacteristic
266C2×C4×C47C2×#4112yes—
267C2×Dic47—21no—
268C2×Dic47—21no—
269C2×Dic47—21no—
270C2×Dic47—21no—
271C2×Dic47—21no—
272C2×Dic47—21no—
273C2×Dic47—28no—
274C2×Dic47—21no—
275C2×Dic47—21no—
276C2×Dic47—21no—
277C2×Dic47—21no—
278C2×Dic47—21no—
279C2×Dic47—21no—
280C2×Dic47—44no—
281C2×Dic47—44no—
282C2×Dic47C2×C22⋊C412yes—
283C2×Dic47C2×C22⋊C412yes—
284C2×Dic47C2×C22⋊C412yes—
285C2×Dic47C2×C4⋊C412yes—
286C2×Dic47C2×C4⋊C412yes—
287C2×Dic47#11712yes—
288C4×D47—28no—
289C4×D47—24no—
290C4×D47—24no—
291C4×D47—28no—
292C4×D47#12118yes—
293C4×D47C22⋊Q818yes—
294C8×C47—42no—
295C8×C47—42no—
296C47⋊C8—42no—
297C47⋊C8—42no—
298#20628—471nomaximal, Sylow
299C22×C47—22no—
300C22×C47—22no—
301C22×C47—22no—
302C22×C47—22no—
303C22×C47—22no—
304C22×C47—22no—
305C22×C47#42414yescomplemented
306C22×C47C22×C22⋊C411yescharacteristic
307C22×C47C22×C4⋊C411yescharacteristic
308C22×C47C2×#11711yescharacteristic
309C22×C47C2×#13111yescharacteristic
310C22×C47C2×#13111yescharacteristic
311C22×C47#56811yescharacteristic
312C22×C47#56811yescharacteristic
313C2×D47—22no—
314C2×D47—22no—
315C2×D47—22no—
316C2×D47—22no—
317C2×D47—22no—
318C2×D47—22no—
319C2×D47—22no—
320C2×D47—22no—
321C2×D47—22no—
322C2×D47—416no—
323C2×D47—41no—
324C2×D47—41no—
325C2×D47—41no—
326C2×D47—41no—
327C2×D47#38014yes—
328C4×C47—22no—
329C4×C47—22no—
330C4×C47—22no—
331C4×C47—41no—
332C4×C47—41no—
333C4×C47C2×#12112yes—
334C4×C47C2×C22⋊Q812yes—
335Dic47—22no—
336Dic47—22no—
337Dic47—22no—
338Dic47—41no—
339Dic47—41no—
340Dic47#38014yes—
341C22×#117—471no—
342C2×#424—472no—
343C2×#407—471no—
344C22×C22⋊C8—471no—
345#1798—472no—
346#1798—472no—
347#1797—471no—
348#1797—471no—
349#1797—471no—
350#1797D4711yescharacteristic, complemented
351#1729—472no—
352C2×C47—24no—
353C2×C47C2×#38011yescharacteristic
354C2×C47#288011yescharacteristic
355C2×C47#288011yescharacteristic
356C2×C47C2×#42411yescharacteristic
357C2×C47#290511yescharacteristic
358C2×C47#292411yescharacteristic
359C2×C47#292411yescharacteristic
360D47—24no—
361D47—42no—
362C24×C4—471no—
363C22×M16—472no—
364C23×C8—472no—
365C2×#117—471no—
366C2×#117—471no—
367C2×#117—471no—
368C2×#117—471no—
369C2×#117—471no—
370C2×#117—471no—
371C2×#117—471no—
372C2×#117—471no—
373C2×#117—948no—
374C22×C4⋊C4—471no—
375C22×C4⋊C4—471no—
376C22×C22⋊C4—471no—
377C22×C22⋊C4—471no—
378C22×C42—471no—
379C22×C42C2×D4711yescharacteristic
380#424—948no—
381C2×C4⋊C8—472no—
382C2×C4⋊C8—472no—
383C2×C4⋊C8—472no—
384C2×C4⋊C8C2×D4712yescomplemented
385#407—944no—
386C2×C22⋊C8—471no—
387C2×C22⋊C8—471no—
388C2×C22⋊C8—472no—
389C2×C22⋊C8—472no—
390C2×C22⋊C8—944no—
391C2×C22⋊C8C2×D4711yescharacteristic
392C2×C22⋊C8C2×D4711yescharacteristic
393#336—472no—
394#336—472no—
395#336—472no—
396#336C2×D4712yescomplemented
397C47#2062811yescharacteristic, complemented, Sylow
398C25—471no—
399C23×C4—471no—
400C23×C4—471no—
401C23×C4—471no—
402C23×C4—471no—
403C23×C4—474no—
404C23×C4—474no—
405C23×C4—471no—
406C23×C4—471no—
407C23×C4—471no—
408C23×C4—944no—
409C23×C4—944no—
410C23×C4C4×D4711yescharacteristic
411C23×C4C4×D4711yescharacteristic
412C23×C4C22×D4711yescharacteristic
413C2×M16—944no—
414C2×M16—944no—
415C2×M16—944no—
416C22×C8—472no—
417C22×C8—472no—
418C22×C8—944no—
419C22×C8—944no—
420C22×C8—944no—
421C22×C8C22×D4712yes—
422C22×C8C22×D4712yes—
423#117—478no—
424#117—944no—
425#117—944no—
426#117—944no—
427#117—944no—
428#117—944no—
429#117—944no—
430#117—944no—
431C2×C4⋊C4—471no—
432C2×C4⋊C4—471no—
433C2×C4⋊C4—471no—
434C2×C4⋊C4—471no—
435C2×C4⋊C4—471no—
436C2×C4⋊C4—471no—
437C2×C4⋊C4—471no—
438C2×C4⋊C4—471no—
439C2×C4⋊C4—944no—
440C2×C4⋊C4—944no—
441C2×C22⋊C4—471no—
442C2×C22⋊C4—471no—
443C2×C22⋊C4—471no—
444C2×C22⋊C4—471no—
445C2×C22⋊C4—471no—
446C2×C22⋊C4—471no—
447C2×C22⋊C4—471no—
448C2×C22⋊C4—471no—
449C2×C22⋊C4—944no—
450C2×C22⋊C4—944no—
451C2×C42—24no—
452C2×C42—471no—
453C2×C42—471no—
454C2×C42—471no—
455C2×C42—471no—
456C2×C42—944no—
457C2×C42C4×D4711yescharacteristic
458C2×C42C4×D4711yescharacteristic
459C2×C42C22×D4711yescharacteristic
460C2×C42C22×D4711yescharacteristic
461C4⋊C8—24no—
462C4⋊C8—944no—
463C4⋊C8—944no—
464C4⋊C8—944no—
465C22⋊C8—22no—
466C22⋊C8—22no—
467C22⋊C8—944no—
468C22⋊C8—944no—
469C22⋊C8—942no—
470C22⋊C8—942no—
471C24—471no—
472C24—471no—
473C24—474no—
474C24—942no—
475C24—942no—
476C24—942no—
477C24—942no—
478C24—1881no—
479C24—1881no—
480C24C2×C4×D4711yescharacteristic
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—471no—
490C22×C4—474no—
491C22×C4—472no—
492C22×C4—472no—
493C22×C4—474no—
494C22×C4—474no—
495C22×C4—471no—
496C22×C4—471no—
497C22×C4—471no—
498C22×C4—474no—
499C22×C4—474no—
500C22×C4—472no—
501C22×C4—472no—
502C22×C4—471no—
503C22×C4—471no—
504C22×C4—942no—
505C22×C4—942no—
506C22×C4—9416no—
507C22×C4—9416no—
508C22×C4—942no—
509C22×C4—942no—
510C22×C4—942no—
511C22×C4—942no—
512C22×C4—942no—
513C22×C4—942no—
514C22×C4—942no—
515C22×C4—942no—
516C22×C4—942no—
517C22×C4—942no—
518C22×C4—1881no—
519C22×C4—1881no—
520C22×C4C2×C4×D4711yescharacteristic
521C22×C4C2×C4×D4711yescharacteristic
522C22×C4C2×C4×D4711yescharacteristic
523C22×C4C2×C4×D4711yescharacteristic
524C22×C4C2×C4×D4711yescharacteristic
525C22×C4D4×D4712yes—
526C22×C4Q8×D4712yes—
527C22×C4C23×D4711yescharacteristic
528M16—1888no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—942no—
536C2×C8—942no—
537C2×C8—942no—
538C2×C8—942no—
539C2×C8—942no—
540C2×C8—942no—
541C2×C8—1888no—
542C4⋊C4—474no—
543C4⋊C4—474no—
544C4⋊C4—942no—
545C4⋊C4—942no—
546C4⋊C4—942no—
547C4⋊C4—942no—
548C4⋊C4—942no—
549C4⋊C4—942no—
550C22⋊C4—474no—
551C22⋊C4—474no—
552C22⋊C4—942no—
553C22⋊C4—942no—
554C22⋊C4—942no—
555C22⋊C4—942no—
556C22⋊C4—942no—
557C22⋊C4—942no—
558C42—22no—
559C42—22no—
560C42—22no—
561C42—474no—
562C42—942no—
563C42—942no—
564C42—942no—
565C42D4×D4714yes—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—472no—
571C23—472no—
572C23—472no—
573C23—472no—
574C23—948no—
575C23—941no—
576C23—941no—
577C23—941no—
578C23—941no—
579C23—941no—
580C23—941no—
581C23—941no—
582C23—941no—
583C23—941no—
584C23—941no—
585C23—948no—
586C23—1884no—
587C23—1884no—
588C23—1884no—
589C23—1884no—
590C23—1884no—
591C23C4⋊C4×D4712yes—
592C23#1309403012yes—
593C23#1309403212yes—
594C23C22×C4×D4711yescharacteristic
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—472no—
612C2×C4—472no—
613C2×C4—472no—
614C2×C4—478no—
615C2×C4—478no—
616C2×C4—472no—
617C2×C4—472no—
618C2×C4—472no—
619C2×C4—948no—
620C2×C4—948no—
621C2×C4—948no—
622C2×C4—941no—
623C2×C4—941no—
624C2×C4—941no—
625C2×C4—941no—
626C2×C4—941no—
627C2×C4—941no—
628C2×C4—944no—
629C2×C4—944no—
630C2×C4—941no—
631C2×C4—941no—
632C2×C4—941no—
633C2×C4—941no—
634C2×C4—941no—
635C2×C4—941no—
636C2×C4—1884no—
637C2×C4—1884no—
638C2×C4C22⋊C4×D4712yes—
639C2×C4C22⋊C4×D4712yes—
640C2×C4C4⋊C4×D4712yes—
641C2×C4C2×D4×D4711yescharacteristic
642C2×C4C2×D4×D4712yes—
643C2×C4C2×Q8×D4711yescharacteristic
644C2×C4#41×D4712yes—
645C8—42no—
646C8—42no—
647C8—1882no—
648C8—1882no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—474no—
656C22—942no—
657C22—942no—
658C22—942no—
659C22—942no—
660C22—942no—
661C22—942no—
662C22—942no—
663C22—942no—
664C22—942no—
665C22—18816no—
666C22—1881no—
667C22—1881no—
668C22—1881no—
669C22—1881no—
670C22#1568914814yescomplemented
671C22C2×C22⋊C4×D4711yescharacteristic
672C22C2×C4⋊C4×D4711yescharacteristic
673C22#117×D4711yescharacteristic
674C22C2×#1309403011yescharacteristic
675C22C2×#1309403211yescharacteristic
676C22#1568988911yescharacteristic
677C22#1568988911yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—41no—
682C4—41no—
683C4—474no—
684C4—942no—
685C4—942no—
686C4—942no—
687C4—1881no—
688C4—1881no—
689C4#121×D4712yes—
690C4C22⋊Q8×D4712yes—
691C2—24no—
692C2—944no—
693C2—1882no—
694C2#380×D4711yescharacteristic
695C2#2025183411yescharacteristic
696C2#2025183811yescharacteristic
697C2C2×#1568914811yescharacteristic
698C2#2025195011yescharacteristic
699C2#2025204111yescharacteristic
700C2#2025204711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1797C2
prime radicalC24×D47C2×C4
cosocleC22×C4×C47C24
hypercenter#1797D47
hypocenterC47#20628
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C2×#15689148C2semidirect
5. #20243371C2semidirect
6. #20243369C2semidirect
7. #20243368C2semidirect
8. #20243366C2semidirect
9. #20243366C2semidirect
10. #20243083C2semidirect
11. C47×#1797C2semidirect
30. C2×C4⋊(C47⋊C8)C22semidirect
31. C2×Dic47⋊C8C22semidirect
32. C2×Dic47⋊C8C22semidirect
39. #15688878C22semidirect
40. #15688877C22semidirect
41. #15688877C22semidirect
43. C2×C4⋊C8×C47C22semidirect
46. C47×#336C22semidirect
305. C22×C47#424semidirect
350. #1797D47semidirect
384. C2×C4⋊C8C2×D47semidirect
396. #336C2×D47semidirect
397. C47#20628semidirect
670. C22#15689148semidirect

Maximal subgroups

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

subgroupindex
C22×#130939812
C2×#156891482
C2×#156890852
C2×C22⋊C8×D472
#202433712
#202433692
#202433682
#202433662
#202430832
C47×#17972
#2062847