Finite Group Databasebeta

← #26138249

Subgroups — #26138249

Order 12032.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093980C211yesmaximal, characteristic
2C2×#15688992C211yesmaximal, characteristic, complemented
3C2×#15688987C211yesmaximal, characteristic, complemented
4C2×#15688981C211yesmaximal, characteristic
5C2×C22⋊C4×Dic47C211yesmaximal, characteristic
6#20241633C211yesmaximal, characteristic
7#20241631C211yesmaximal, characteristic
8#20241631C211yesmaximal, characteristic
9#20241623C211yesmaximal, characteristic, complemented
10#20241622C211yesmaximal, characteristic, complemented
11#20241620C211yesmaximal, characteristic, complemented
12#20241619C211yesmaximal, characteristic, complemented
13Dic47⋊#95C211yesmaximal, characteristic, complemented
14Dic47⋊#95C211yesmaximal, characteristic, complemented
15C47×#1439C211yesmaximal, characteristic
16C24×Dic47C2211yescharacteristic
17C2×#13093980—24no—
18C2×#13093980—24no—
19C2×#13093980—24no—
20C22×C4⋊Dic47C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×Dic47⋊C4C2211yescharacteristic
23C22×Dic47⋊C4C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×C22⋊Dic47C2211yescharacteristic
28C22×C22⋊Dic47C2211yescharacteristic
29C22×C22⋊Dic47C2211yescharacteristic
30C22×C4×Dic47C2211yescharacteristic
31C22×C4×Dic47C2211yescharacteristic
32C22×C4×Dic47C2211yescharacteristic
33C22×C4×Dic47C2211yescharacteristic
34#15688992—24no—
35#15688987—24no—
36#15688981—24no—
37C22⋊C4×Dic47C418yescomplemented
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
48C2×C47⋊#95C2211yescharacteristic
49C2×C47⋊#95C2211yescharacteristic
50C2×C47⋊#95C2211yescharacteristic
51C22×C4⋊C4×C47C2211yescharacteristic
52C22×C22⋊C4×C47C2211yescharacteristic
53C22×C22⋊C4×C47C2211yescharacteristic
54C22×C22⋊C4×C47C2211yescharacteristic
55C2×#95×C47C2211yescharacteristic
56C2×#95×C47C2211yescharacteristic
57C2×#95×C47C2211yescharacteristic
58C23×Dic47—22no—
59C23×Dic47—22no—
60C23×Dic47—22no—
61C23×Dic47—22no—
62C23×Dic47C2×C414yes—
63C23×Dic47D414yes—
64C23×Dic47Q814yes—
65C23×Dic47C2311yescharacteristic
66C23×Dic47C2311yescharacteristic
67C23×Dic47C2311yescharacteristic
68C23×Dic47C2311yescharacteristic
69C23×Dic47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73#13093980—232no—
74C2×C4⋊Dic47—22no—
75C2×C4⋊Dic47—22no—
76C2×C4⋊Dic47—41no—
77C2×Dic47⋊C4—22no—
78C2×Dic47⋊C4—22no—
79C2×Dic47⋊C4—22no—
80C2×Dic47⋊C4—22no—
81C2×Dic47⋊C4—22no—
82C2×Dic47⋊C4—22no—
83C2×Dic47⋊C4—22no—
84C2×Dic47⋊C4—22no—
85C2×Dic47⋊C4—22no—
86C2×Dic47⋊C4—22no—
87C2×Dic47⋊C4—22no—
88C2×Dic47⋊C4—22no—
89C2×Dic47⋊C4—22no—
90C2×Dic47⋊C4—22no—
91C2×Dic47⋊C4—41no—
92C2×Dic47⋊C4—41no—
93C2×Dic47⋊C4D414yes—
94C2×Dic47⋊C4D414yes—
95C2×C22⋊Dic47—22no—
96C2×C22⋊Dic47—22no—
97C2×C22⋊Dic47—22no—
98C2×C22⋊Dic47—22no—
99C2×C22⋊Dic47—22no—
100C2×C22⋊Dic47—22no—
101C2×C22⋊Dic47—41no—
102C2×C22⋊Dic47—41no—
103C2×C22⋊Dic47C2×C414yes—
104C2×C4×Dic47—22no—
105C2×C4×Dic47—22no—
106C2×C4×Dic47—22no—
107C2×C4×Dic47—22no—
108C2×C4×Dic47—22no—
109C2×C4×Dic47—22no—
110C2×C4×Dic47—22no—
111C2×C4×Dic47—22no—
112C2×C4×Dic47—22no—
113C2×C4×Dic47—22no—
114C2×C4×Dic47C2×C414yes—
115C2×C4×Dic47C2×C414yes—
116C47⋊#95—22no—
117C47⋊#95—22no—
118C47⋊#95—22no—
119C47⋊#95—22no—
120C47⋊#95—22no—
121C47⋊#95—22no—
122C47⋊#95—22no—
123C47⋊#95—22no—
124C47⋊#95—41no—
125C47⋊#95—41no—
126C47⋊#95—41no—
127C47⋊#95C2×C414yes—
128C47⋊#95C2×C414yes—
129C25×C47C2311yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C2×C4⋊C4×C47—22no—
137C2×C4⋊C4×C47—22no—
138C2×C4⋊C4×C47—41no—
139C2×C22⋊C4×C47—22no—
140C2×C22⋊C4×C47—22no—
141C2×C22⋊C4×C47—22no—
142C2×C22⋊C4×C47—22no—
143C2×C22⋊C4×C47—22no—
144C2×C22⋊C4×C47—22no—
145C2×C22⋊C4×C47—41no—
146C2×C22⋊C4×C47—41no—
147C2×C22⋊C4×C47C2×C414yes—
148#95×C47—22no—
149#95×C47—22no—
150#95×C47—41no—
151C24×C47—21no—
152C24×C47—21no—
153C24×C47—21no—
154C24×C47—21no—
155C24×C47—21no—
156C24×C47—21no—
157C24×C47—21no—
158C24×C47—21no—
159C24×C47—21no—
160C24×C47—21no—
161C24×C47—21no—
162C24×C47—21no—
163C24×C47C22×C412yes—
164C24×C47C2×D412yes—
165C24×C47C2×Q812yes—
166C24×C47C2411yescharacteristic
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×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47C22×C412yes—
204C22×C4×C47C22×C412yes—
205C22×C4×C47C2×D412yes—
206C22×C4×C47C2×D412yes—
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—28no—
218C22×Dic47—28no—
219C22×Dic47—28no—
220C22×Dic47—28no—
221C22×Dic47—28no—
222C22×Dic47—28no—
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×Dic47—21no—
253C22×Dic47—21no—
254C22×Dic47—21no—
255C22×Dic47C4⋊C4116yescomplemented
256C22×Dic47C22×C412yes—
257C22×Dic47C22×C412yes—
258C22×Dic47C22×C412yes—
259C22×Dic47C22×C412yes—
260C22×Dic47C2×D412yes—
261C22×Dic47C2×D412yes—
262C22×Dic47C2×D412yes—
263C22×Dic47C2×D412yes—
264C22×Dic47C2×D412yes—
265C22×Dic47C2×D412yes—
266C22×Dic47C2×Q812yes—
267C22×Dic47C2×Q812yes—
268C22×Dic47#4112yes—
269C22×Dic47#4112yes—
270C22×Dic47#4112yes—
271C22×Dic47#4112yes—
272C4⋊C4×C47—44no—
273C22⋊C4×C47—28no—
274C22⋊C4×C47—28no—
275C22⋊C4×C47—44no—
276C22⋊Dic47—28no—
277C22⋊Dic47—28no—
278C22⋊Dic47—44no—
279C4⋊Dic47—44no—
280Dic47⋊C4—28no—
281Dic47⋊C4—28no—
282Dic47⋊C4—44no—
283Dic47⋊C4—44no—
284Dic47⋊C4—44no—
285Dic47⋊C4—44no—
286C4×Dic47—28no—
287C4×Dic47—28no—
288C4×Dic47—28no—
289C4×Dic47—28no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47—22no—
300C23×C47—22no—
301C23×C47—22no—
302C23×C47—22no—
303C23×C47—22no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—41no—
309C23×C47—41no—
310C23×C47—41no—
311C23×C47—41no—
312C23×C47—41no—
313C23×C47—41no—
314C23×C47—41no—
315C23×C47—41no—
316C23×C47—41no—
317C23×C47—41no—
318C23×C47—41no—
319C23×C47—41no—
320C23×C47—41no—
321C23×C47—41no—
322C23×C47—41no—
323C23×C47—41no—
324C23×C47C2×C4⋊C414yes—
325C23×C47C23×C411yescharacteristic
326C23×C47C22×D411yescharacteristic
327C23×C47C22×D411yescharacteristic
328C23×C47C22×D411yescharacteristic
329C23×C47C22×Q811yescharacteristic
330C23×C47C2×#4111yescharacteristic
331C23×C47C2×#4111yescharacteristic
332C23×C47C2×#4111yescharacteristic
333C23×C47C2×#4111yescharacteristic
334C23×C47C2×#4111yescharacteristic
335C23×C47C2×#4111yescharacteristic
336C23×C47H(5,𝔽2)11yescharacteristic
337C23×C47H(5,𝔽2)11yescharacteristic
338C23×C472−1+411yescharacteristic
339C23×C472−1+411yescharacteristic
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—41no—
356C2×C4×C47—41no—
357C2×C4×C47—41no—
358C2×C4×C47—41no—
359C2×C4×C47—41no—
360C2×C4×C47—41no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
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#11714yescomplemented
382C2×Dic47—22no—
383C2×Dic47—22no—
384C2×Dic47—22no—
385C2×Dic47—22no—
386C2×Dic47—22no—
387C2×Dic47—22no—
388C2×Dic47—22no—
389C2×Dic47—22no—
390C2×Dic47—22no—
391C2×Dic47—22no—
392C2×Dic47—22no—
393C2×Dic47—22no—
394C2×Dic47—232no—
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—41no—
405C2×Dic47—41no—
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×Dic47C2×C4⋊C414yes—
431C2×Dic47C2×C4⋊C414yes—
432C2×Dic47#11714yescomplemented
433C2×Dic47C4×D414yes—
434C2×Dic47C4×D414yes—
435C2×Dic47#12014yes—
436C2×Dic47C22⋊Q814yes—
437C2×Dic47C22⋊Q814yes—
438C2×Dic47#12314yes—
439#13879—471nomaximal, Sylow
440C22×C47—24no—
441C22×C47—24no—
442C22×C47—24no—
443C22×C47—42no—
444C22×C47—42no—
445C22×C47—42no—
446C22×C47—42no—
447C22×C47—42no—
448C22×C47—42no—
449C22×C47—42no—
450C22×C47—42no—
451C22×C47—42no—
452C22×C47—42no—
453C22×C47—42no—
454C22×C47—42no—
455C22×C47C22×C4⋊C411yescharacteristic
456C22×C47C2×#11711yescharacteristic
457C22×C47C2×#11711yescharacteristic
458C22×C47C2×C4×D411yescharacteristic
459C22×C47C2×C4×D411yescharacteristic
460C22×C47#52011yescharacteristic
461C22×C47#52011yescharacteristic
462C22×C47C2×#12011yescharacteristic
463C22×C47C2×C22⋊Q811yescharacteristic
464C22×C47C2×C22⋊Q811yescharacteristic
465C22×C47C2×#12311yescharacteristic
466C22×C47#53211yescharacteristic
467C22×C47#53211yescharacteristic
468C22×C47#53311yescharacteristic
469C22×C47#53311yescharacteristic
470C22×C47#53511yescharacteristic
471C22×C47#53611yescharacteristic
472C22×C47#54411yescharacteristic
473C22×C47#54411yescharacteristic
474C22×C47#54611yescharacteristic
475C22×C47#54611yescharacteristic
476C22×C47#54711yescharacteristic
477C22×C47#54711yescharacteristic
478C22×C47#54811yescharacteristic
479C22×C47#54811yescharacteristic
480C22×C47#55011yescharacteristic
481C22×C47#55011yescharacteristic
482C22×C47#55211yescharacteristic
483C22×C47#55211yescharacteristic
484C22×C47#55311yescharacteristic
485C22×C47#55311yescharacteristic
486C22×C47#55511yescharacteristic
487C22×C47#55511yescharacteristic
488C22×C47#55611yescharacteristic
489C22×C47#55611yescharacteristic
490C4×C47—24no—
491C4×C47—42no—
492C4×C47—42no—
493C4×C47—42no—
494C4×C47—81no—
495C4×C47—81no—
496Dic47—24no—
497Dic47—24no—
498Dic47—42no—
499Dic47—42no—
500Dic47—42no—
501Dic47—81no—
502Dic47—81no—
503Dic47#38518yes—
504C22×#117—471no—
505C2×#384—471no—
506C2×#382—471no—
507C2×#380—471no—
508C2×C4×C22⋊C4—471no—
509#1439—471no—
510#1439—471no—
511#1439—471no—
512#1439D4711yescharacteristic
513#1436—471no—
514#1436—471no—
515#1436—471no—
516#1436—471no—
517C4⋊#95—471no—
518C4⋊#95—471no—
519C2×C47—44no—
520C2×C47#228511yescharacteristic
521C2×C47C2×#38511yescharacteristic
522C2×C47#231711yescharacteristic
523C2×C47#235211yescharacteristic
524C2×C47#235211yescharacteristic
525C2×C47#235411yescharacteristic
526C2×C47#235411yescharacteristic
527C2×C47#243111yescharacteristic
528C2×C47#243211yescharacteristic
529C2×C47#243911yescharacteristic
530C2×C47#243911yescharacteristic
531C2×C47#244111yescharacteristic
532C2×C47#244111yescharacteristic
533C2×C47#249911yescharacteristic
534C2×C47#250011yescharacteristic
535C24×C4—471no—
536C2×#117—944no—
537C2×#117—944no—
538C2×#117—944no—
539C22×C4⋊C4—471no—
540C22×C4⋊C4—471no—
541C22×C4⋊C4—471no—
542C22×C4⋊C4—471no—
543C22×C4⋊C4—471no—
544C22×C4⋊C4—471no—
545C22×C4⋊C4—471no—
546C22×C4⋊C4C2×D4711yescharacteristic
547C22×C22⋊C4—471no—
548C22×C22⋊C4—471no—
549C22×C22⋊C4—471no—
550C22×C22⋊C4C2×D4711yescharacteristic
551C22×C22⋊C4C2×D4711yescharacteristic
552C22×C22⋊C4C2×D4711yescharacteristic
553C22×C42—471no—
554C22×C42—471no—
555C22×C42—471no—
556C22×C42—471no—
557#384—944no—
558#382—944no—
559#380—944no—
560C4×C22⋊C4—478no—
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—471no—
571C2×#95—471no—
572C2×#95—471no—
573C2×#95—471no—
574C2×#95C2×D4711yescharacteristic
575C2×#95C2×D4711yescharacteristic
576C2×#95C2×D4711yescharacteristic
577C47#1387911yescharacteristic, complemented, Sylow
578C25C22×D4711yescharacteristic
579C23×C4—471no—
580C23×C4—474no—
581C23×C4—474no—
582C23×C4—474no—
583C23×C4—471no—
584C23×C4—471no—
585C23×C4—471no—
586C23×C4—471no—
587C23×C4—471no—
588C23×C4—471no—
589C23×C4—471no—
590C23×C4—942no—
591C23×C4—942no—
592C23×C4—942no—
593C23×C4—942no—
594C23×C4C22×D4711yescharacteristic
595C23×C4C22×D4711yescharacteristic
596C23×C4C22×D4711yescharacteristic
597C23×C4C22×D4711yescharacteristic
598C23×C4C22×D4711yescharacteristic
599C23×C4C22×D4711yescharacteristic
600#117—9432no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—474no—
605C2×C4⋊C4—474no—
606C2×C4⋊C4—942no—
607C2×C4⋊C4—942no—
608C2×C4⋊C4—942no—
609C2×C4⋊C4—942no—
610C2×C4⋊C4—942no—
611C2×C4⋊C4—942no—
612C2×C4⋊C4—942no—
613C2×C4⋊C4—942no—
614C2×C4⋊C4—942no—
615C2×C4⋊C4—942no—
616C2×C4⋊C4—942no—
617C2×C4⋊C4—942no—
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—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—41no—
632C2×C22⋊C4—41no—
633C2×C22⋊C4—474no—
634C2×C22⋊C4—942no—
635C2×C22⋊C4—942no—
636C2×C22⋊C4—942no—
637C2×C22⋊C4—942no—
638C2×C22⋊C4—942no—
639C2×C22⋊C4—942no—
640C2×C22⋊C4—1881no—
641C2×C22⋊C4—1881no—
642C2×C22⋊C4C4×D4714yes—
643C2×C42—474no—
644C2×C42—474no—
645C2×C42—942no—
646C2×C42—942no—
647C2×C42—942no—
648C2×C42—942no—
649C2×C42—942no—
650C2×C42—942no—
651C2×C42—942no—
652C2×C42—942no—
653C2×C42—942no—
654C2×C42—942no—
655#95—22no—
656#95—22no—
657#95—41no—
658#95—474no—
659#95—474no—
660#95—942no—
661#95—942no—
662#95—942no—
663#95—942no—
664#95—942no—
665#95—942no—
666#95—942no—
667#95—942no—
668#95—1881no—
669#95—1881no—
670#95—1881no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24C2×C4×D4712yes—
684C24D4×D4712yes—
685C24Q8×D4712yes—
686C24C23×D4711yescharacteristic
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—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—472no—
724C22×C4—472no—
725C22×C4—472no—
726C22×C4—472no—
727C22×C4—472no—
728C22×C4—472no—
729C22×C4—472no—
730C22×C4—4716no—
731C22×C4—472no—
732C22×C4—472no—
733C22×C4—472no—
734C22×C4—472no—
735C22×C4—472no—
736C22×C4—472no—
737C22×C4—472no—
738C22×C4—472no—
739C22×C4—472no—
740C22×C4—948no—
741C22×C4—948no—
742C22×C4—948no—
743C22×C4—948no—
744C22×C4—948no—
745C22×C4—948no—
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—941no—
766C22×C4—941no—
767C22×C4—941no—
768C22×C4—941no—
769C22×C4—941no—
770C22×C4—941no—
771C22×C4—941no—
772C22×C4—941no—
773C22×C4—941no—
774C22×C4—941no—
775C22×C4—941no—
776C22×C4—941no—
777C22×C4—941no—
778C22×C4—941no—
779C22×C4—941no—
780C22×C4—941no—
781C22×C4—941no—
782C22×C4—941no—
783C22×C4—941no—
784C22×C4—941no—
785C22×C4—941no—
786C22×C4C2×C4×D4712yes—
787C22×C4C2×C4×D4712yes—
788C22×C4D4×D4712yes—
789C22×C4D4×D4712yes—
790C22×C4#1062535212yes—
791C22×C4#1062535212yes—
792C4⋊C4—44no—
793C4⋊C4—948no—
794C4⋊C4—948no—
795C4⋊C4—1884no—
796C4⋊C4—1884no—
797C4⋊C4—1884no—
798C4⋊C4—1884no—
799C4⋊C4—1884no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—44no—
803C22⋊C4—948no—
804C22⋊C4—948no—
805C22⋊C4—1884no—
806C42—948no—
807C42—948no—
808C42—948no—
809C42—948no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23C4⋊C4×D4714yes—
845C23C22×C4×D4711yescharacteristic
846C23C2×D4×D4711yescharacteristic
847C23C2×D4×D4711yescharacteristic
848C23C2×D4×D4711yescharacteristic
849C23C2×Q8×D4711yescharacteristic
850C23#41×D4711yescharacteristic
851C23#41×D4711yescharacteristic
852C23#41×D4711yescharacteristic
853C23#41×D4711yescharacteristic
854C23C2×#1062535211yescharacteristic
855C23C2×#1062535211yescharacteristic
856C23#1309406911yescharacteristic
857C23#1309406911yescharacteristic
858C23#1309407111yescharacteristic
859C23#1309407111yescharacteristic
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—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
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—474no—
902C2×C4—474no—
903C2×C4—474no—
904C2×C4—474no—
905C2×C4—474no—
906C2×C4—474no—
907C2×C4—474no—
908C2×C4—474no—
909C2×C4—474no—
910C2×C4—9432no—
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—942no—
926C2×C4—942no—
927C2×C4—942no—
928C2×C4—942no—
929C2×C4—942no—
930C2×C4—942no—
931C2×C4—942no—
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#1309398014yescomplemented
959C22—24no—
960C22—24no—
961C22—24no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22C2×C4⋊C4×D4711yescharacteristic
975C22#117×D4711yescharacteristic
976C22C2×#1309398011yescharacteristic
977C22C4×D4×D4711yescharacteristic
978C22C4×D4×D4711yescharacteristic
979C22#1568960211yescharacteristic
980C22#1568960211yescharacteristic
981C22#120×D4711yescharacteristic
982C22C22⋊Q8×D4711yescharacteristic
983C22C22⋊Q8×D4711yescharacteristic
984C22#123×D4711yescharacteristic
985C22#1568966811yescharacteristic
986C22#1568966811yescharacteristic
987C22#1568967511yescharacteristic
988C22#1568967511yescharacteristic
989C22#1568968811yescharacteristic
990C22#1568969511yescharacteristic
991C22#1568975211yescharacteristic
992C22#1568975211yescharacteristic
993C22#1568976011yescharacteristic
994C22#1568976211yescharacteristic
995C22#1568977111yescharacteristic
996C22#1568977311yescharacteristic
997C22#1568977911yescharacteristic
998C22#1568978111yescharacteristic
999C22#1568979111yescharacteristic
1000C22#1568979311yescharacteristic
1001C22#1568980911yescharacteristic
1002C22#1568981011yescharacteristic
1003C22#1568981611yescharacteristic
1004C22#1568981811yescharacteristic
1005C22#1568983511yescharacteristic
1006C22#1568983711yescharacteristic
1007C22#1568984011yescharacteristic
1008C22#1568984211yescharacteristic
1009C4—24no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—81no—
1014C4—81no—
1015C4—478no—
1016C4—944no—
1017C4—944no—
1018C4—3761no—
1019C4—3761no—
1020C4—1882no—
1021C4—1882no—
1022C4—1882no—
1023C2—44no—
1024C2#2024579011yescharacteristic
1025C2#385×D4711yescharacteristic
1026C2#2024600711yescharacteristic
1027C2#2024631511yescharacteristic
1028C2#2024631611yescharacteristic
1029C2#2024633411yescharacteristic
1030C2#2024633611yescharacteristic
1031C2#2024700211yescharacteristic
1032C2#2024701111yescharacteristic
1033C2#2024707211yescharacteristic
1034C2#2024707411yescharacteristic
1035C2#2024709411yescharacteristic
1036C2#2024709611yescharacteristic
1037C2#2024783611yescharacteristic
1038C2#2024784511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1439C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenter#1439D47
hypocenterC47#13879
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#15688992C2semidirect
3. C2×#15688987C2semidirect
9. #20241623C2semidirect
10. #20241622C2semidirect
11. #20241620C2semidirect
12. #20241619C2semidirect
13. Dic47⋊#95C2semidirect
14. Dic47⋊#95C2semidirect
37. C22⋊C4×Dic47C4semidirect
255. C22×Dic47C4⋊C4semidirect
381. C2×C4×C47#117semidirect
432. C2×Dic47#117semidirect
577. C47#13879semidirect
958. C2×C4#13093980semidirect

Maximal subgroups

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

subgroupindex
C22×#130939802
C2×#156889922
C2×#156889872
C2×#156889812
C2×C22⋊C4×Dic472
#202416332
#202416312
#202416232
#202416222
#202416202
#202416192
Dic47⋊#952
C47×#14392
#1387947