Finite Group Databasebeta

← #26139194

Subgroups — #26139194

Order 12032.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689010C211yesmaximal, characteristic, complemented
2C2×#15688997C211yesmaximal, characteristic
3C2×#15688980C211yesmaximal, characteristic
4C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
5C2×#95×D47C211yesmaximal, characteristic
6#20241655C211yesmaximal, characteristic, complemented
7#20241648C211yesmaximal, characteristic, complemented
8#20241645C211yesmaximal, characteristic, complemented
9#20241638C211yesmaximal, characteristic, complemented
10#20241622C211yesmaximal, characteristic, complemented
11#20241615C211yesmaximal, characteristic, complemented
12(C2×D47)⋊#95C211yesmaximal, characteristic
13(C2×D47)⋊#95C211yesmaximal, characteristic
14(C2×D47)⋊#95C211yesmaximal, characteristic
15C47×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D47C2211yescharacteristic
17C23×C4×D47C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×(C2×D47)⋊C4C2211yescharacteristic
23C22×(C2×D47)⋊C4C2211yescharacteristic
24C22×(C2×D47)⋊C4C2211yescharacteristic
25C22×(C2×D47)⋊C4C2211yescharacteristic
26C22×C4×Dic47C2211yescharacteristic
27#15689010—24no—
28#15688997C418yescomplemented
29#15688980—24no—
30C4×(C2×D47)⋊C4—24no—
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2211yescharacteristic
35C2×C47⋊#95C2211yescharacteristic
36C2×C47⋊#95C2211yescharacteristic
37C2×C47⋊#95C2211yescharacteristic
38C2×C47⋊#95C2211yescharacteristic
39C2×C47⋊#95C2211yescharacteristic
40C2×C47⋊#95C2211yescharacteristic
41C2×C47⋊#95C2211yescharacteristic
42C2×C47⋊#95C2211yescharacteristic
43C2×C47⋊#95C2211yescharacteristic
44C2×C47⋊#95C2211yescharacteristic
45C2×C47⋊#95C2211yescharacteristic
46C2×C47⋊#95C2211yescharacteristic
47C2×C47⋊#95C2211yescharacteristic
48#95×D47—24no—
49C22×C4⋊C4×C47C2211yescharacteristic
50C22×C42×C47C2211yescharacteristic
51C2×#95×C47C2211yescharacteristic
52C2×#95×C47C2211yescharacteristic
53C2×#95×C47C2211yescharacteristic
54C2×#95×C47C2211yescharacteristic
55C2×#95×C47C2211yescharacteristic
56C24×D47C2311yescharacteristic
57C23×Dic47C2311yescharacteristic
58C23×Dic47C2311yescharacteristic
59C23×Dic47C2311yescharacteristic
60C23×Dic47C2311yescharacteristic
61C23×Dic47C2311yescharacteristic
62C23×Dic47C2311yescharacteristic
63C23×Dic47C2311yescharacteristic
64C22×C4×D47—22no—
65C22×C4×D47—22no—
66C22×C4×D47—22no—
67C22×C4×D47—22no—
68C22×C4×D47—22no—
69C22×C4×D47—22no—
70C22×C4×D47—22no—
71C22×C4×D47—22no—
72C22×C4×D47—22no—
73C22×C4×D47—22no—
74C22×C4×D47—22no—
75C22×C4×D47—22no—
76C22×C4×D47—22no—
77C22×C4×D47—41no—
78C22×C4×D47—41no—
79C22×C4×D47—41no—
80C22×C4×D47—41no—
81C22×C4×D47—41no—
82C22×C4×D47—41no—
83C22×C4×D47C2×C414yes—
84C22×C4×D47Q814yes—
85C2×C4⋊Dic47—22no—
86C2×C4⋊Dic47—22no—
87C2×C4⋊Dic47—41no—
88C2×C4⋊Dic47—41no—
89C2×C4⋊Dic47—41no—
90C2×C4⋊Dic47C2×C414yescomplemented
91C2×Dic47⋊C4—22no—
92C2×Dic47⋊C4—22no—
93C2×Dic47⋊C4C2×C414yescomplemented
94C2×(C2×D47)⋊C4—22no—
95C2×(C2×D47)⋊C4—22no—
96C2×(C2×D47)⋊C4—22no—
97C2×(C2×D47)⋊C4—22no—
98C2×(C2×D47)⋊C4—22no—
99C2×(C2×D47)⋊C4—22no—
100C2×(C2×D47)⋊C4—22no—
101C2×(C2×D47)⋊C4—22no—
102C2×(C2×D47)⋊C4—22no—
103C2×(C2×D47)⋊C4C2×C414yes—
104C2×(C2×D47)⋊C4C2×C414yes—
105C2×(C2×D47)⋊C4D414yes—
106C2×C4×Dic47—22no—
107C2×C4×Dic47—22no—
108C2×C4×Dic47—41no—
109C47⋊#95—22no—
110C47⋊#95—22no—
111C47⋊#95—22no—
112C47⋊#95—22no—
113C47⋊#95—22no—
114C47⋊#95—22no—
115C47⋊#95—22no—
116C47⋊#95—22no—
117C47⋊#95—22no—
118C47⋊#95—22no—
119C47⋊#95—22no—
120C47⋊#95—22no—
121C47⋊#95—41no—
122C47⋊#95—41no—
123C47⋊#95—41no—
124C47⋊#95—41no—
125C47⋊#95C2×C414yescomplemented
126C23×C4×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C23×C4×C47C2311yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C2×C4⋊C4×C47—22no—
134C2×C4⋊C4×C47—22no—
135C2×C4⋊C4×C47—41no—
136C2×C42×C47—22no—
137C2×C42×C47—22no—
138C2×C42×C47—41no—
139#95×C47—22no—
140#95×C47—41no—
141#95×C47—41no—
142#95×C47C2×C414yescomplemented
143#95×C47D414yes—
144C24×C47C2411yescharacteristic
145C23×D47—21no—
146C23×D47—21no—
147C23×D47—21no—
148C23×D47—21no—
149C23×D47—21no—
150C23×D47—21no—
151C23×D47—21no—
152C23×D47—21no—
153C23×D47C22×C412yes—
154C23×D47C2×D412yes—
155C23×D47C2×Q812yes—
156C23×D47#4112yes—
157C23×D47#4112yes—
158C23×D47#4112yes—
159C23×D47#4112yes—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47C22×C412yes—
200C22×C4×C47C22×C412yes—
201C22×C4×C47C22×C412yes—
202C22×C4×C47C2×D412yes—
203C22×C4×C47C2×D412yes—
204C22×C4×C47C2×D412yes—
205C22×C4×C47C2×D412yes—
206C22×C4×C47C2×Q812yes—
207C22×C4×C47#4112yes—
208C22×C4×C47#4112yes—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47—21no—
219C22×Dic47—21no—
220C22×Dic47—21no—
221C22×Dic47—21no—
222C22×Dic47—21no—
223C22×Dic47—21no—
224C22×Dic47—21no—
225C22×Dic47—21no—
226C22×Dic47—21no—
227C22×Dic47—21no—
228C22×Dic47—21no—
229C22×Dic47—21no—
230C22×Dic47—21no—
231C22×Dic47—21no—
232C22×Dic47—21no—
233C22×Dic47—21no—
234C22×Dic47—21no—
235C22×Dic47—21no—
236C22×Dic47—21no—
237C22×Dic47—21no—
238C22×Dic47—21no—
239C22×Dic47—21no—
240C22×Dic47—21no—
241C22×Dic47—21no—
242C22×Dic47—21no—
243C22×Dic47—21no—
244C22×Dic47—21no—
245C22×Dic47—21no—
246C22×Dic47—21no—
247C22×Dic47—21no—
248C22×Dic47—21no—
249C22×Dic47—21no—
250C22×Dic47—21no—
251C22×Dic47—21no—
252C22×Dic47C22×C412yes—
253C22×Dic47C22×C412yes—
254C22×Dic47C22×C412yes—
255C22×Dic47C2×D412yes—
256C22×Dic47C2×Q812yes—
257C22×Dic47#4112yes—
258C2×C4×D47—28no—
259C2×C4×D47—28no—
260C2×C4×D47—28no—
261C2×C4×D47—28no—
262C2×C4×D47—28no—
263C2×C4×D47—44no—
264C2×C4×D47—44no—
265C2×C4×D47—44no—
266C2×C4×D47—44no—
267C2×C4×D47—44no—
268C2×C4×D47—44no—
269C2×C4×D47—44no—
270C2×C4×D47—44no—
271C2×C4×D47—44no—
272C2×C4×D47—44no—
273C2×C4×D47—44no—
274C2×C4×D47—44no—
275C2×C4×D47—44no—
276C2×C4×D47—44no—
277C2×C4×D47—44no—
278C2×C4×D47—44no—
279C4⋊C4×C47—44no—
280C42×C47—44no—
281(C2×D47)⋊C4—28no—
282(C2×D47)⋊C4—28no—
283(C2×D47)⋊C4—28no—
284(C2×D47)⋊C4—44no—
285C4⋊Dic47—44no—
286C4⋊Dic47—44no—
287Dic47⋊C4—28no—
288C4×Dic47—44no—
289C23×C47C23×C411yescharacteristic
290C23×C47C22×D411yescharacteristic
291C23×C47C22×D411yescharacteristic
292C23×C47C22×Q811yescharacteristic
293C23×C47C2×#4111yescharacteristic
294C23×C47C2×#4111yescharacteristic
295C23×C47C2×#4111yescharacteristic
296C23×C47C2×#4111yescharacteristic
297C23×C47C2×#4111yescharacteristic
298C23×C47C2×#4111yescharacteristic
299C23×C47C2×#4111yescharacteristic
300C23×C47H(5,𝔽2)11yescharacteristic
301C23×C47H(5,𝔽2)11yescharacteristic
302C23×C47H(5,𝔽2)11yescharacteristic
303C23×C472−1+411yescharacteristic
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—22no—
308C22×D47—22no—
309C22×D47—22no—
310C22×D47—22no—
311C22×D47—22no—
312C22×D47—22no—
313C22×D47—22no—
314C22×D47—22no—
315C22×D47—22no—
316C22×D47—22no—
317C22×D47—22no—
318C22×D47—22no—
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—22no—
324C22×D47—22no—
325C22×D47—22no—
326C22×D47—22no—
327C22×D47—22no—
328C22×D47—22no—
329C22×D47—22no—
330C22×D47—22no—
331C22×D47—22no—
332C22×D47#11714yes—
333C22×D47C4×D414yes—
334C22×D47C4×Q814yes—
335C22×D47C22⋊Q814yes—
336C22×D47#12314yes—
337C22×D47#12514yes—
338C22×D47#12614yes—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47—41no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—41no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47—41no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47C4×D414yes—
387C2×C4×C47C22⋊Q814yes—
388C2×Dic47—22no—
389C2×Dic47—22no—
390C2×Dic47—22no—
391C2×Dic47—22no—
392C2×Dic47—22no—
393C2×Dic47—22no—
394C2×Dic47—22no—
395C2×Dic47—22no—
396C2×Dic47—22no—
397C2×Dic47—22no—
398C2×Dic47—22no—
399C2×Dic47—22no—
400C2×Dic47—22no—
401C2×Dic47—22no—
402C2×Dic47—22no—
403C2×Dic47—22no—
404C2×Dic47—22no—
405C2×Dic47—22no—
406C2×Dic47—41no—
407C2×Dic47—41no—
408C2×Dic47—41no—
409C2×Dic47—41no—
410C2×Dic47—41no—
411C2×Dic47—41no—
412C2×Dic47—41no—
413C2×Dic47—41no—
414C2×Dic47—41no—
415C2×Dic47—41no—
416C2×Dic47—41no—
417C2×Dic47—41no—
418C2×Dic47—41no—
419C2×Dic47—41no—
420C2×Dic47—41no—
421C2×Dic47—41no—
422C2×Dic47—41no—
423C2×Dic47—41no—
424C2×Dic47—41no—
425C2×Dic47—41no—
426C2×Dic47—41no—
427C2×Dic47—41no—
428C2×Dic47—41no—
429C2×Dic47—41no—
430C2×Dic47—41no—
431C2×Dic47—41no—
432C2×Dic47—41no—
433C2×Dic47—41no—
434C2×Dic47—41no—
435C2×Dic47—41no—
436C2×Dic47—41no—
437C4×D47—416no—
438C4×D47—416no—
439C4×D47—416no—
440#13980—471nomaximal, Sylow
441C22×C47C2×#11711yescharacteristic
442C22×C47C2×C4×D411yescharacteristic
443C22×C47C2×C4×D411yescharacteristic
444C22×C47C2×C4×Q811yescharacteristic
445C22×C47C4×#4111yescharacteristic
446C22×C47#51811yescharacteristic
447C22×C47#52011yescharacteristic
448C22×C47C2×C22⋊Q811yescharacteristic
449C22×C47C2×C22⋊Q811yescharacteristic
450C22×C47C2×#12311yescharacteristic
451C22×C47#52511yescharacteristic
452C22×C47C2×#12511yescharacteristic
453C22×C47C2×#12611yescharacteristic
454C22×C47#52911yescharacteristic
455C22×C47#53311yescharacteristic
456C22×C47#53811yescharacteristic
457C22×C47#53911yescharacteristic
458C22×C47#54311yescharacteristic
459C22×C47#54411yescharacteristic
460C22×C47D4211yescharacteristic
461C22×C47#54611yescharacteristic
462C22×C47#54611yescharacteristic
463C22×C47#54611yescharacteristic
464C22×C47#54611yescharacteristic
465C22×C47#54711yescharacteristic
466C22×C47#54811yescharacteristic
467C22×C47#55111yescharacteristic
468C22×C47#55111yescharacteristic
469C22×C47#55111yescharacteristic
470C22×C47#55111yescharacteristic
471C22×C47#55211yescharacteristic
472C22×C47#55211yescharacteristic
473C22×C47#55311yescharacteristic
474C22×C47#55311yescharacteristic
475C22×C47#55311yescharacteristic
476C2×D47—24no—
477C2×D47—24no—
478C2×D47—24no—
479C2×D47—24no—
480C2×D47—24no—
481C2×D47—24no—
482C2×D47—24no—
483C2×D47—24no—
484C2×D47—24no—
485C2×D47—24no—
486C2×D47—24no—
487C2×D47—24no—
488C2×D47—24no—
489C2×D47—24no—
490C2×D47#38718yescomplemented
491C4×C47—24no—
492C4×C47—24no—
493C4×C47—42no—
494C4×C47—42no—
495C4×C47—42no—
496C4×C47—42no—
497C4×C47—81no—
498Dic47—42no—
499Dic47—42no—
500Dic47—42no—
501Dic47—42no—
502Dic47—42no—
503Dic47—42no—
504Dic47—81no—
505C2×#387—471no—
506C2×#385—471no—
507C2×#380—471no—
508C2×C4×C22⋊C4—471no—
509C22×#95—471no—
510#1445—471no—
511#1443—471no—
512#1442—471no—
513#1441—471no—
514#1436—471no—
515#1436D4711yescharacteristic, complemented
516#1434—471no—
517C22⋊#95—471no—
518C22⋊#95—471no—
519C22⋊#95—471no—
520C2×C47C2×#38711yescharacteristic
521C2×C47C4×C22⋊Q811yescharacteristic
522C2×C47#232911yescharacteristic
523C2×C47#235211yescharacteristic
524C2×C47#235311yescharacteristic
525C2×C47#235811yescharacteristic
526C2×C47#235911yescharacteristic
527C2×C47#243711yescharacteristic
528C2×C47#243811yescharacteristic
529C2×C47#244211yescharacteristic
530C2×C47#244311yescharacteristic
531C2×C47#244411yescharacteristic
532C2×C47#248011yescharacteristic
533C2×C47#249311yescharacteristic
534C2×C47#256911yescharacteristic
535D47—28no—
536C24×C4—471no—
537C24×C4—471no—
538C24×C4—471no—
539C22×C4⋊C4—471no—
540C22×C4⋊C4—471no—
541C22×C4⋊C4—471no—
542C22×C4⋊C4C2×D4711yescharacteristic
543C22×C22⋊C4—471no—
544C22×C22⋊C4—471no—
545C22×C22⋊C4—471no—
546C22×C22⋊C4—471no—
547C22×C42—471no—
548C22×C42C2×D4711yescharacteristic
549#387—944no—
550#385—478no—
551#380—944no—
552C4×C22⋊C4—944no—
553C2×#95—471no—
554C2×#95—471no—
555C2×#95—471no—
556C2×#95—471no—
557C2×#95—471no—
558C2×#95—471no—
559C2×#95—471no—
560C2×#95—471no—
561C2×#95—471no—
562C2×#95—471no—
563C2×#95—471no—
564C2×#95—471no—
565C2×#95—471no—
566C2×#95—471no—
567C2×#95—471no—
568C2×#95—471no—
569C2×#95—471no—
570C2×#95—944no—
571C2×#95C2×D4711yescharacteristic
572C2×#95C2×D4711yescharacteristic
573C2×#95C2×D4711yescharacteristic
574C2×#95C2×D4711yescharacteristic
575C2×#95C2×D4711yescharacteristic
576C47#1398011yescharacteristic, complemented, Sylow
577C25—471no—
578C23×C4—471no—
579C23×C4—471no—
580C23×C4—471no—
581C23×C4—471no—
582C23×C4—471no—
583C23×C4—471no—
584C23×C4—474no—
585C23×C4—474no—
586C23×C4—471no—
587C23×C4—942no—
588C23×C4—942no—
589C23×C4—942no—
590C23×C4—942no—
591C23×C4—942no—
592C23×C4—942no—
593C23×C4—942no—
594C23×C4—942no—
595C23×C4—942no—
596C23×C4—942no—
597C23×C4—942no—
598C23×C4—942no—
599C23×C4—942no—
600C23×C4—1881no—
601C23×C4—1881no—
602C23×C4—1881no—
603C23×C4—1881no—
604C23×C4—1881no—
605C23×C4—1881no—
606C23×C4C22×D4711yescharacteristic
607C23×C4C22×D4711yescharacteristic
608C23×C4C22×D4711yescharacteristic
609C23×C4C22×D4711yescharacteristic
610C23×C4C22×D4711yescharacteristic
611C23×C4C22×D4711yescharacteristic
612C23×C4C22×D4711yescharacteristic
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4—474no—
617C2×C4⋊C4—474no—
618C2×C4⋊C4—942no—
619C2×C4⋊C4—942no—
620C2×C4⋊C4—942no—
621C2×C4⋊C4—942no—
622C2×C4⋊C4—1881no—
623C2×C4⋊C4—1881no—
624C2×C4⋊C4—1881no—
625C2×C22⋊C4—474no—
626C2×C22⋊C4—474no—
627C2×C22⋊C4—474no—
628C2×C22⋊C4—942no—
629C2×C22⋊C4—942no—
630C2×C22⋊C4—942no—
631C2×C22⋊C4—942no—
632C2×C22⋊C4—942no—
633C2×C22⋊C4—942no—
634C2×C22⋊C4—942no—
635C2×C22⋊C4—942no—
636C2×C22⋊C4—942no—
637C2×C42—22no—
638C2×C42—22no—
639C2×C42—41no—
640C2×C42—942no—
641C2×C42—942no—
642C2×C42—1881no—
643#95—22no—
644#95—41no—
645#95—41no—
646#95—474no—
647#95—942no—
648#95—942no—
649#95—942no—
650#95—942no—
651#95—942no—
652#95—942no—
653#95—942no—
654#95—942no—
655#95—942no—
656#95—942no—
657#95—942no—
658#95—942no—
659#95—1881no—
660#95—1881no—
661#95—1881no—
662#95—1881no—
663#95C4×D4714yescomplemented
664#95D18814yes—
665C24—472no—
666C24—472no—
667C24—472no—
668C24—472no—
669C24—472no—
670C24—472no—
671C24—472no—
672C24—941no—
673C24—941no—
674C24—941no—
675C24—941no—
676C24—941no—
677C24—941no—
678C24—941no—
679C24—941no—
680C24C23×D4711yescharacteristic
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—472no—
721C22×C4—472no—
722C22×C4—472no—
723C22×C4—472no—
724C22×C4—472no—
725C22×C4—472no—
726C22×C4—948no—
727C22×C4—948no—
728C22×C4—948no—
729C22×C4—941no—
730C22×C4—941no—
731C22×C4—941no—
732C22×C4—941no—
733C22×C4—941no—
734C22×C4—941no—
735C22×C4—941no—
736C22×C4—941no—
737C22×C4—941no—
738C22×C4—941no—
739C22×C4—941no—
740C22×C4—941no—
741C22×C4—941no—
742C22×C4—941no—
743C22×C4—941no—
744C22×C4—941no—
745C22×C4—941no—
746C22×C4—941no—
747C22×C4—941no—
748C22×C4—941no—
749C22×C4—941no—
750C22×C4—941no—
751C22×C4—941no—
752C22×C4—941no—
753C22×C4—941no—
754C22×C4—941no—
755C22×C4—941no—
756C22×C4—941no—
757C22×C4—941no—
758C22×C4—941no—
759C22×C4—941no—
760C22×C4—941no—
761C22×C4—941no—
762C22×C4—941no—
763C22×C4—941no—
764C22×C4—941no—
765C22×C4—948no—
766C22×C4—948no—
767C22×C4—941no—
768C22×C4—941no—
769C22×C4—941no—
770C22×C4—941no—
771C22×C4—941no—
772C22×C4—941no—
773C22×C4—941no—
774C22×C4—1884no—
775C22×C4—1884no—
776C22×C4—1884no—
777C22×C4—1884no—
778C22×C4—1884no—
779C22×C4—1884no—
780C22×C4—1884no—
781C22×C4—1884no—
782C22×C4—1884no—
783C22×C4—1884no—
784C22×C4—1884no—
785C22×C4—1884no—
786C22×C4—1884no—
787C22×C4—1884no—
788C22×C4—1884no—
789C22×C4—1884no—
790C22×C4C2×C4×D4712yes—
791C22×C4C2×C4×D4712yes—
792C22×C4C2×C4×D4712yes—
793C22×C4C2×D18812yes—
794C22×C4C2×D18812yes—
795C22×C4C2×D18812yes—
796C22×C4#1062535012yes—
797C22×C4D4×D4712yes—
798C22×C4#1062535212yes—
799C22×C4Q8×D4712yes—
800C4⋊C4—44no—
801C4⋊C4—948no—
802C4⋊C4—1884no—
803C4⋊C4—1884no—
804C22⋊C4—948no—
805C22⋊C4—948no—
806C22⋊C4—948no—
807C22⋊C4—1884no—
808C42—44no—
809C42—1884no—
810C23—474no—
811C23—474no—
812C23—474no—
813C23—474no—
814C23—474no—
815C23—474no—
816C23—474no—
817C23—942no—
818C23—942no—
819C23—942no—
820C23—942no—
821C23—942no—
822C23—942no—
823C23—942no—
824C23—942no—
825C23—942no—
826C23—942no—
827C23—942no—
828C23—942no—
829C23—942no—
830C23—942no—
831C23—942no—
832C23—942no—
833C23—942no—
834C23—942no—
835C23—942no—
836C23—942no—
837C23—942no—
838C23—942no—
839C23—942no—
840C23—942no—
841C23—942no—
842C23—942no—
843C23—942no—
844C23—942no—
845C23C22×C4×D4711yescharacteristic
846C23C2×D4×D4711yescharacteristic
847C23C22×D18811yescharacteristic
848C23C2×Q8×D4711yescharacteristic
849C23#41×D4711yescharacteristic
850C23#41×D4711yescharacteristic
851C23#41×D4711yescharacteristic
852C23#41×D4711yescharacteristic
853C23#41×D4711yescharacteristic
854C23C2×#1062535211yescharacteristic
855C23C2×#1062535011yescharacteristic
856C23#1309406911yescharacteristic
857C23#1309406911yescharacteristic
858C23#1309407011yescharacteristic
859C23#1309407211yescharacteristic
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—942no—
908C2×C4—942no—
909C2×C4—942no—
910C2×C4—942no—
911C2×C4—942no—
912C2×C4—942no—
913C2×C4—942no—
914C2×C4—942no—
915C2×C4—942no—
916C2×C4—942no—
917C2×C4—942no—
918C2×C4—942no—
919C2×C4—942no—
920C2×C4—942no—
921C2×C4—942no—
922C2×C4—942no—
923C2×C4—942no—
924C2×C4—942no—
925C2×C4—18816no—
926C2×C4—18816no—
927C2×C4—18816no—
928C2×C4—1881no—
929C2×C4—1881no—
930C2×C4—1881no—
931C2×C4—1881no—
932C2×C4—1881no—
933C2×C4—1881no—
934C2×C4—1881no—
935C2×C4—1881no—
936C2×C4—1881no—
937C2×C4—1881no—
938C2×C4—1881no—
939C2×C4—1881no—
940C2×C4—1881no—
941C2×C4—1881no—
942C2×C4—1881no—
943C2×C4—1881no—
944C2×C4—1881no—
945C2×C4—1881no—
946C2×C4—1881no—
947C2×C4—1881no—
948C2×C4—1881no—
949C2×C4—1881no—
950C2×C4—1881no—
951C2×C4—1881no—
952C2×C4—1881no—
953C2×C4—1881no—
954C2×C4—1881no—
955C2×C4—1881no—
956C2×C4—1881no—
957C2×C4—1881no—
958C2×C4—1881no—
959C2×C4C4×D18814yes—
960C2×C4#1309400414yes—
961C22—478no—
962C22—944no—
963C22—944no—
964C22—944no—
965C22—944no—
966C22—944no—
967C22—944no—
968C22—944no—
969C22—944no—
970C22—944no—
971C22—944no—
972C22—944no—
973C22—944no—
974C22—944no—
975C22—944no—
976C22#117×D4711yescharacteristic
977C22C4×D4×D4711yescharacteristic
978C22C2×C4×D18811yescharacteristic
979C22C4×Q8×D4711yescharacteristic
980C22C4×#1062535211yescharacteristic
981C22#1568959511yescharacteristic
982C22#1568960411yescharacteristic
983C22C22⋊Q8×D4711yescharacteristic
984C22C2×#1309400411yescharacteristic
985C22#123×D4711yescharacteristic
986C22#1568963511yescharacteristic
987C22#125×D4711yescharacteristic
988C22#126×D4711yescharacteristic
989C22#1568965511yescharacteristic
990C22#1568967711yescharacteristic
991C22#1568970511yescharacteristic
992C22#1568972111yescharacteristic
993C22#1568974811yescharacteristic
994C22#1568975011yescharacteristic
995C22D4×D18811yescharacteristic
996C22#1568976011yescharacteristic
997C22#1568976311yescharacteristic
998C22#1568976811yescharacteristic
999C22#1568976811yescharacteristic
1000C22#1568977511yescharacteristic
1001C22#1568978511yescharacteristic
1002C22#1568979611yescharacteristic
1003C22#1568979711yescharacteristic
1004C22#1568980111yescharacteristic
1005C22#1568980311yescharacteristic
1006C22#1568980711yescharacteristic
1007C22#1568981411yescharacteristic
1008C22#1568982011yescharacteristic
1009C22#1568982311yescharacteristic
1010C22#1568982411yescharacteristic
1011C4—24no—
1012C4—24no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—81no—
1018C4—3761no—
1019C4—1882no—
1020C4—1882no—
1021C4—1882no—
1022C4—1882no—
1023C4—1882no—
1024C4—1882no—
1025C2—948no—
1026C2#387×D4711yescharacteristic
1027C2C4×#1309400411yescharacteristic
1028C2#2024612211yescharacteristic
1029C2#2024632011yescharacteristic
1030C2#2024632311yescharacteristic
1031C2#2024637011yescharacteristic
1032C2#2024638311yescharacteristic
1033C2#2024705211yescharacteristic
1034C2#2024706111yescharacteristic
1035C2#2024711011yescharacteristic
1036C2#2024712811yescharacteristic
1037C2#2024713511yescharacteristic
1038C2#2024763211yescharacteristic
1039C2#2024777211yescharacteristic
1040C2#2024861011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1436C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenter#1436D47
hypocenterC47#13980
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C2×#15689010C2semidirect
6. #20241655C2semidirect
7. #20241648C2semidirect
8. #20241645C2semidirect
9. #20241638C2semidirect
10. #20241622C2semidirect
11. #20241615C2semidirect
15. C47×#1436C2semidirect
28. #15688997C4semidirect
90. C2×C4⋊Dic47C2×C4semidirect
93. C2×Dic47⋊C4C2×C4semidirect
125. C47⋊#95C2×C4semidirect
142. #95×C47C2×C4semidirect
490. C2×D47#387semidirect
515. #1436D47semidirect
576. C47#13980semidirect
663. #95C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156890102
C2×#156889972
C2×#156889802
C2×C4×(C2×D47)⋊C42
C2×#95×D472
#202416552
#202416482
#202416452
#202416382
#202416222
#202416152
(C2×D47)⋊#952
C47×#14362
#1398047