Finite Group Databasebeta

← #26137439

Subgroups — #26137439

Order 12032.

2134 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689017C211yesmaximal, characteristic
2C2×#15689011C211yesmaximal, characteristic
3C2×#15688974C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic47C211yesmaximal, characteristic
5C2×C22⋊C4×Dic47C211yesmaximal, characteristic
6C2×C22⋊C4×Dic47C211yesmaximal, characteristic
7C2×C42×Dic47C211yesmaximal, characteristic, complemented
8#20241625C211yesmaximal, characteristic
9#20241621C211yesmaximal, characteristic, complemented
10#20241619C211yesmaximal, characteristic, complemented
11#20241614C211yesmaximal, characteristic, complemented
12#20241612C211yesmaximal, characteristic, complemented
13#95×Dic47C211yesmaximal, characteristic, complemented
14#95×Dic47C211yesmaximal, characteristic, complemented
15C47×#1437C211yesmaximal, characteristic
16C24×Dic47C2211yescharacteristic
17C22×Dic47⋊C4C2211yescharacteristic
18C22×Dic47⋊C4C2211yescharacteristic
19C22×C22⋊Dic47C2211yescharacteristic
20C22×C22⋊Dic47C2211yescharacteristic
21C22×C22⋊Dic47C2211yescharacteristic
22C22×C4×Dic47C2211yescharacteristic
23C22×C4×Dic47C2211yescharacteristic
24C22×C4×Dic47C2211yescharacteristic
25C22×C4×Dic47C2211yescharacteristic
26C22×C4×Dic47C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28C22×C4×Dic47C2211yescharacteristic
29C22×C4×Dic47C2211yescharacteristic
30C22×C4×Dic47C2211yescharacteristic
31#15689017C418yescomplemented
32#15689011C418yescomplemented
33#15688974—24no—
34C22⋊C4×Dic47—24no—
35C22⋊C4×Dic47—24no—
36C22⋊C4×Dic47C418yescomplemented
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
48C2×C47⋊#95C2211yescharacteristic
49C2×C47⋊#95C2211yescharacteristic
50C42×Dic47—24no—
51C22×C22⋊C4×C47C2211yescharacteristic
52C22×C22⋊C4×C47C2211yescharacteristic
53C22×C22⋊C4×C47C2211yescharacteristic
54C22×C42×C47C2211yescharacteristic
55C2×#95×C47C2211yescharacteristic
56C2×#95×C47C2211yescharacteristic
57C2×#95×C47C2211yescharacteristic
58C23×Dic47—22no—
59C23×Dic47—22no—
60C23×Dic47—22no—
61C23×Dic47—22no—
62C23×Dic47—22no—
63C23×Dic47—22no—
64C23×Dic47C2×C414yes—
65C23×Dic47C2311yescharacteristic
66C23×Dic47C2311yescharacteristic
67C23×Dic47C2311yescharacteristic
68C23×Dic47C2311yescharacteristic
69C23×Dic47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C2×Dic47⋊C4—22no—
74C2×Dic47⋊C4—22no—
75C2×Dic47⋊C4—22no—
76C2×Dic47⋊C4—22no—
77C2×Dic47⋊C4C2×C414yescomplemented
78C2×Dic47⋊C4C2×C414yescomplemented
79C2×C22⋊Dic47—22no—
80C2×C22⋊Dic47—22no—
81C2×C22⋊Dic47—22no—
82C2×C22⋊Dic47—22no—
83C2×C22⋊Dic47C2×C414yes—
84C2×C22⋊Dic47C2×C414yes—
85C2×C22⋊Dic47C2×C414yes—
86C2×C22⋊Dic47C2×C414yes—
87C2×C22⋊Dic47C2×C414yes—
88C2×C4×Dic47—22no—
89C2×C4×Dic47—22no—
90C2×C4×Dic47—22no—
91C2×C4×Dic47—22no—
92C2×C4×Dic47—22no—
93C2×C4×Dic47—22no—
94C2×C4×Dic47—22no—
95C2×C4×Dic47—22no—
96C2×C4×Dic47—22no—
97C2×C4×Dic47—22no—
98C2×C4×Dic47—22no—
99C2×C4×Dic47—22no—
100C2×C4×Dic47—22no—
101C2×C4×Dic47—22no—
102C2×C4×Dic47—22no—
103C2×C4×Dic47—22no—
104C2×C4×Dic47—22no—
105C2×C4×Dic47—22no—
106C2×C4×Dic47—22no—
107C2×C4×Dic47—22no—
108C2×C4×Dic47—22no—
109C2×C4×Dic47C2×C414yes—
110C2×C4×Dic47C2×C414yes—
111C2×C4×Dic47C2×C414yescomplemented
112C2×C4×Dic47C2×C414yescomplemented
113C2×C4×Dic47D414yes—
114C2×C4×Dic47D414yes—
115C47⋊#95—22no—
116C47⋊#95—22no—
117C47⋊#95—22no—
118C47⋊#95—22no—
119C47⋊#95—22no—
120C47⋊#95—22no—
121C47⋊#95—22no—
122C47⋊#95C2×C414yes—
123C47⋊#95C2×C414yes—
124C47⋊#95C2×C414yescomplemented
125C47⋊#95C2×C414yescomplemented
126C47⋊#95C2×C414yescomplemented
127C47⋊#95C2×C414yescomplemented
128C25×C47C2311yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C2×C22⋊C4×C47—22no—
136C2×C22⋊C4×C47—22no—
137C2×C22⋊C4×C47—22no—
138C2×C22⋊C4×C47—22no—
139C2×C22⋊C4×C47—22no—
140C2×C22⋊C4×C47—22no—
141C2×C22⋊C4×C47C2×C414yes—
142C2×C22⋊C4×C47C2×C414yes—
143C2×C22⋊C4×C47C2×C414yes—
144C2×C42×C47—22no—
145C2×C42×C47—22no—
146C2×C42×C47—22no—
147#95×C47—22no—
148#95×C47—22no—
149#95×C47—22no—
150C24×C47—21no—
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×C47C22×C412yes—
163C24×C47C22×C412yes—
164C24×C47C22×C412yes—
165C24×C47C2411yescharacteristic
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×C47C22×C412yes—
197C22×C4×C47C22×C412yes—
198C22×C4×C47C22×C412yes—
199C22×C4×C47C22×C412yes—
200C22×C4×C47C22×C412yes—
201C22×C4×C47C22×C412yes—
202C22×C4×C47C2×D412yes—
203C22×C4×C47C2×D412yes—
204C22×C4×C47#4112yes—
205C22×C4×C47#4112yes—
206C22×C4×C47#4112yes—
207C22×C4×C47#4112yes—
208C22×Dic47—21no—
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—28no—
243C22×Dic47—28no—
244C22×Dic47—28no—
245C22×Dic47—44no—
246C22×Dic47—44no—
247C22×Dic47—44no—
248C22×Dic47—44no—
249C22×Dic47C22×C412yes—
250C22×Dic47C22×C412yes—
251C22×Dic47C22×C412yes—
252C22×Dic47C22×C412yes—
253C22×Dic47C22×C412yes—
254C22×Dic47C22×C412yes—
255C22×Dic47C22×C412yes—
256C22×Dic47C22×C412yes—
257C22×Dic47C22×C412yes—
258C22×Dic47C22×C412yes—
259C22×Dic47C22×C412yes—
260C22×Dic47C22×C412yes—
261C22×Dic47C2×D412yes—
262C22×Dic47C2×D412yes—
263C22×Dic47C2×D412yes—
264C22×Dic47C2×D412yes—
265C22×Dic47#4112yes—
266C22×Dic47#4112yes—
267C22×Dic47#4112yes—
268C22×Dic47#4112yes—
269C22×Dic47#4112yes—
270C22×Dic47#4112yes—
271C22⋊C4×C47—28no—
272C22⋊C4×C47—28no—
273C22⋊C4×C47—28no—
274C42×C47—28no—
275C22⋊Dic47—28no—
276C22⋊Dic47—28no—
277C22⋊Dic47C42116yescomplemented
278Dic47⋊C4—28no—
279Dic47⋊C4—28no—
280C4×Dic47—28no—
281C4×Dic47—28no—
282C4×Dic47—28no—
283C4×Dic47—28no—
284C4×Dic47—28no—
285C4×Dic47—28no—
286C4×Dic47—28no—
287C4×Dic47—44no—
288C4×Dic47—44no—
289C23×C47—22no—
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—41no—
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×C47C2×C4214yes—
324C23×C47C23×C411yescharacteristic
325C23×C47C23×C411yescharacteristic
326C23×C47C23×C411yescharacteristic
327C23×C47C22×D411yescharacteristic
328C23×C47C22×D411yescharacteristic
329C23×C47C2×#4111yescharacteristic
330C23×C47C2×#4111yescharacteristic
331C23×C47C2×#4111yescharacteristic
332C23×C47C2×#4111yescharacteristic
333C23×C47C2×#4111yescharacteristic
334C23×C47C2×#4111yescharacteristic
335C23×C47C2×#4111yescharacteristic
336C23×C47C2×#4111yescharacteristic
337C23×C47C2×#4111yescharacteristic
338C23×C47C2×#4111yescharacteristic
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—22no—
364C2×C4×C47—22no—
365C2×C4×C47—22no—
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#11714yes—
379C2×C4×C47C4×D414yes—
380C2×C4×C47C4×D414yes—
381C2×Dic47—22no—
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—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—22no—
407C2×Dic47—22no—
408C2×Dic47—22no—
409C2×Dic47—22no—
410C2×Dic47—22no—
411C2×Dic47—22no—
412C2×Dic47—22no—
413C2×Dic47—22no—
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—416no—
427C2×Dic47C2×C4214yes—
428C2×Dic47C2×C4214yes—
429C2×Dic47#11714yes—
430C2×Dic47C4×D414yes—
431C2×Dic47C4×D414yes—
432C2×Dic47C4×D414yes—
433C2×Dic47C4×D414yes—
434C2×Dic47#12114yes—
435C2×Dic47#12314yes—
436C2×Dic47#12414yes—
437C2×Dic47#12614yes—
438C4×#388—471nomaximal, Sylow
439C22×C47—24no—
440C22×C47—24no—
441C22×C47—24no—
442C22×C47—42no—
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×C47C22×C4211yescharacteristic
455C22×C47C2×#11711yescharacteristic
456C22×C47C2×#11711yescharacteristic
457C22×C47C2×C4×D411yescharacteristic
458C22×C47C2×C4×D411yescharacteristic
459C22×C47C2×C4×D411yescharacteristic
460C22×C47C2×C4×D411yescharacteristic
461C22×C47C2×C4×D411yescharacteristic
462C22×C47C2×C4×D411yescharacteristic
463C22×C47C4×#4111yescharacteristic
464C22×C47C4×#4111yescharacteristic
465C22×C47C4×#4111yescharacteristic
466C22×C47C4×#4111yescharacteristic
467C22×C47C4×#4111yescharacteristic
468C22×C47C4×#4111yescharacteristic
469C22×C47C4×#4111yescharacteristic
470C22×C47C4×#4111yescharacteristic
471C22×C47C4×#4111yescharacteristic
472C22×C47C4×#4111yescharacteristic
473C22×C47C2×#12111yescharacteristic
474C22×C47C2×#12311yescharacteristic
475C22×C47#52511yescharacteristic
476C22×C47#52511yescharacteristic
477C22×C47C2×#12411yescharacteristic
478C22×C47C2×#12611yescharacteristic
479C22×C47#52911yescharacteristic
480C22×C47#52911yescharacteristic
481C22×C47#52911yescharacteristic
482C22×C47#52911yescharacteristic
483C22×C47#52911yescharacteristic
484C22×C47#52911yescharacteristic
485C22×C47#52911yescharacteristic
486C22×C47#52911yescharacteristic
487C22×C47#53211yescharacteristic
488C22×C47#53211yescharacteristic
489C4×C47—24no—
490C4×C47—24no—
491C4×C47—24no—
492C4×C47—42no—
493C4×C47—42no—
494C4×C47—42no—
495Dic47—24no—
496Dic47—24no—
497Dic47—24no—
498Dic47—24no—
499Dic47—42no—
500Dic47—42no—
501Dic47—42no—
502Dic47#38818yescomplemented
503C2×#388—471no—
504C2×#388—471no—
505C2×C4×C4⋊C4—471no—
506C2×C4×C22⋊C4—471no—
507C2×C4×C22⋊C4—471no—
508C2×C4×C22⋊C4—471no—
509C2×C43—471no—
510#1437—471no—
511#1437D4711yescharacteristic
512#1436—471no—
513#1436—471no—
514#1434—471no—
515#1434—471no—
516C4×#95—471no—
517C4×#95—471no—
518C2×C47—44no—
519C2×C47C4×#11711yescharacteristic
520C2×C47C42×D411yescharacteristic
521C2×C47C42×D411yescharacteristic
522C2×C47C2×#38811yescharacteristic
523C2×C47#229011yescharacteristic
524C2×C47#229311yescharacteristic
525C2×C47#229811yescharacteristic
526C2×C47C4×#12111yescharacteristic
527C2×C47C4×#12111yescharacteristic
528C2×C47C4×#12311yescharacteristic
529C2×C47C4×#12311yescharacteristic
530C2×C47C4×#12411yescharacteristic
531C2×C47C4×#12411yescharacteristic
532C2×C47C4×#12611yescharacteristic
533C2×C47C4×#12611yescharacteristic
534C24×C4—471no—
535C22×C4⋊C4—471no—
536C22×C4⋊C4—471no—
537C22×C22⋊C4—471no—
538C22×C22⋊C4—471no—
539C22×C22⋊C4—471no—
540C22×C22⋊C4C2×D4711yescharacteristic
541C22×C22⋊C4C2×D4711yescharacteristic
542C22×C22⋊C4C2×D4711yescharacteristic
543C22×C42—471no—
544C22×C42—471no—
545C22×C42—471no—
546C22×C42—471no—
547C22×C42—471no—
548C22×C42—471no—
549C22×C42—471no—
550C22×C42—471no—
551C22×C42—471no—
552C22×C42C2×D4711yescharacteristic
553#388—478no—
554#388—478no—
555C4×C4⋊C4—944no—
556C4×C22⋊C4—478no—
557C4×C22⋊C4—944no—
558C4×C22⋊C4—944no—
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—471no—
571C2×#95—471no—
572C2×#95C2×D4711yescharacteristic
573C2×#95C2×D4711yescharacteristic
574C2×#95C2×D4711yescharacteristic
575C43—944no—
576C47C4×#38811yescharacteristic, complemented, Sylow
577C25C22×D4711yescharacteristic
578C23×C4—471no—
579C23×C4—471no—
580C23×C4—471no—
581C23×C4—471no—
582C23×C4—471no—
583C23×C4—474no—
584C23×C4—471no—
585C23×C4—471no—
586C23×C4—471no—
587C23×C4—942no—
588C23×C4—942no—
589C23×C4—942no—
590C23×C4—942no—
591C23×C4—942no—
592C23×C4—942no—
593C23×C4C22×D4711yescharacteristic
594C23×C4C22×D4711yescharacteristic
595C23×C4C22×D4711yescharacteristic
596C23×C4C22×D4711yescharacteristic
597C23×C4C22×D4711yescharacteristic
598C23×C4C22×D4711yescharacteristic
599C2×C4⋊C4—474no—
600C2×C4⋊C4—474no—
601C2×C4⋊C4—942no—
602C2×C4⋊C4—942no—
603C2×C4⋊C4—942no—
604C2×C4⋊C4—942no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—474no—
612C2×C22⋊C4—474no—
613C2×C22⋊C4—474no—
614C2×C22⋊C4—474no—
615C2×C22⋊C4—474no—
616C2×C22⋊C4—942no—
617C2×C22⋊C4—942no—
618C2×C22⋊C4—942no—
619C2×C22⋊C4—942no—
620C2×C22⋊C4C4×D4714yes—
621C2×C22⋊C4C4×D4714yes—
622C2×C22⋊C4C4×D4714yes—
623C2×C42—22no—
624C2×C42—22no—
625C2×C42—22no—
626C2×C42—474no—
627C2×C42—474no—
628C2×C42—474no—
629C2×C42—474no—
630C2×C42—474no—
631C2×C42—474no—
632C2×C42—942no—
633C2×C42—942no—
634C2×C42—942no—
635C2×C42—942no—
636C2×C42—942no—
637C2×C42—942no—
638C2×C42—942no—
639C2×C42—942no—
640C2×C42—942no—
641C2×C42—942no—
642C2×C42—942no—
643C2×C42—942no—
644C2×C42—942no—
645C2×C42—942no—
646C2×C42—942no—
647C2×C42—942no—
648C2×C42—942no—
649C2×C42—942no—
650C2×C42—942no—
651C2×C42—942no—
652C2×C42—942no—
653#95—22no—
654#95—22no—
655#95—22no—
656#95—474no—
657#95—474no—
658#95—474no—
659#95—474no—
660#95—474no—
661#95—474no—
662#95—942no—
663#95—942no—
664#95—942no—
665#95—942no—
666#95—942no—
667#95—942no—
668#95—942no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C2×C4×D4712yes—
682C24C2×C4×D4712yes—
683C24C2×C4×D4712yes—
684C24C23×D4711yescharacteristic
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—472no—
716C22×C4—472no—
717C22×C4—472no—
718C22×C4—472no—
719C22×C4—472no—
720C22×C4—472no—
721C22×C4—472no—
722C22×C4—472no—
723C22×C4—472no—
724C22×C4—472no—
725C22×C4—472no—
726C22×C4—472no—
727C22×C4—472no—
728C22×C4—472no—
729C22×C4—472no—
730C22×C4—472no—
731C22×C4—472no—
732C22×C4—472no—
733C22×C4—472no—
734C22×C4—472no—
735C22×C4—472no—
736C22×C4—472no—
737C22×C4—948no—
738C22×C4—948no—
739C22×C4—948no—
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—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—1884no—
775C22×C4—1884no—
776C22×C4—1884no—
777C22×C4—1884no—
778C22×C4C2×C4×D4712yes—
779C22×C4C2×C4×D4712yes—
780C22×C4C2×C4×D4712yes—
781C22×C4C2×C4×D4712yes—
782C22×C4C2×C4×D4712yes—
783C22×C4C2×C4×D4712yes—
784C22×C4D4×D4712yes—
785C22×C4D4×D4712yes—
786C22×C4#1062535212yes—
787C22×C4#1062535212yes—
788C22×C4#1062535212yes—
789C22×C4#1062535212yes—
790C4⋊C4—948no—
791C4⋊C4—948no—
792C22⋊C4—28no—
793C22⋊C4—28no—
794C22⋊C4—28no—
795C22⋊C4—4716no—
796C22⋊C4—948no—
797C22⋊C4—948no—
798C42—28no—
799C42—948no—
800C42—948no—
801C42—948no—
802C42—948no—
803C42—948no—
804C42—948no—
805C42—948no—
806C42—1884no—
807C42—1884no—
808C23—22no—
809C23—22no—
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—41no—
827C23—41no—
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—
842C23C42×D4714yes—
843C23C22×C4×D4711yescharacteristic
844C23C22×C4×D4711yescharacteristic
845C23C22×C4×D4711yescharacteristic
846C23C2×D4×D4711yescharacteristic
847C23C2×D4×D4711yescharacteristic
848C23#41×D4711yescharacteristic
849C23#41×D4711yescharacteristic
850C23#41×D4711yescharacteristic
851C23#41×D4711yescharacteristic
852C23#41×D4711yescharacteristic
853C23#41×D4711yescharacteristic
854C23C2×#1062535211yescharacteristic
855C23C2×#1062535211yescharacteristic
856C23C2×#1062535211yescharacteristic
857C23C2×#1062535211yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
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—22no—
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—474no—
898C2×C4—474no—
899C2×C4—474no—
900C2×C4—474no—
901C2×C4—474no—
902C2×C4—474no—
903C2×C4—474no—
904C2×C4—474no—
905C2×C4—474no—
906C2×C4—474no—
907C2×C4—474no—
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—942no—
926C2×C4—942no—
927C2×C4—942no—
928C2×C4—942no—
929C2×C4—942no—
930C2×C4—942no—
931C2×C4—942no—
932C2×C4—942no—
933C2×C4—942no—
934C2×C4—942no—
935C2×C4—942no—
936C2×C4—942no—
937C2×C4—942no—
938C2×C4—942no—
939C2×C4—942no—
940C2×C4—942no—
941C2×C4—18816no—
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#1309398014yes—
955C2×C4(C22⋊D47)⋊C414yes—
956C2×C4(C22⋊D47)⋊C414yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C2×C42×D4711yescharacteristic
973C22#117×D4711yescharacteristic
974C22C2×#1309398011yescharacteristic
975C22C4×D4×D4711yescharacteristic
976C22C4×D4×D4711yescharacteristic
977C22C4×D4×D4711yescharacteristic
978C22C4×D4×D4711yescharacteristic
979C22C2×(C22⋊D47)⋊C411yescharacteristic
980C22C2×(C22⋊D47)⋊C411yescharacteristic
981C22C4×#1062535211yescharacteristic
982C22C4×#1062535211yescharacteristic
983C22C4×#1062535211yescharacteristic
984C22C4×#1062535211yescharacteristic
985C22C4×#1062535211yescharacteristic
986C22C4×#1062535211yescharacteristic
987C22C4×#1062535211yescharacteristic
988C22C4×#1062535211yescharacteristic
989C22#1568959111yescharacteristic
990C22#1568959111yescharacteristic
991C22#121×D4711yescharacteristic
992C22#123×D4711yescharacteristic
993C22#1568962911yescharacteristic
994C22#1568963311yescharacteristic
995C22#124×D4711yescharacteristic
996C22#126×D4711yescharacteristic
997C22#1568965011yescharacteristic
998C22#1568965011yescharacteristic
999C22#1568965211yescharacteristic
1000C22#1568965211yescharacteristic
1001C22#1568965411yescharacteristic
1002C22#1568965411yescharacteristic
1003C22#1568965411yescharacteristic
1004C22#1568965611yescharacteristic
1005C22#1568966811yescharacteristic
1006C22#1568967111yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—478no—
1014C4—944no—
1015C4—944no—
1016C4—944no—
1017C4—944no—
1018C4—1882no—
1019C4—1882no—
1020C4—1882no—
1021C2—44no—
1022C2C4×#1309398011yescharacteristic
1023C2C4×(C22⋊D47)⋊C411yescharacteristic
1024C2C4×(C22⋊D47)⋊C411yescharacteristic
1025C2#388×D4711yescharacteristic
1026C2#2024582811yescharacteristic
1027C2#2024585011yescharacteristic
1028C2#2024588211yescharacteristic
1029C2#2024589811yescharacteristic
1030C2#2024590411yescharacteristic
1031C2#2024591311yescharacteristic
1032C2#2024591511yescharacteristic
1033C2#2024592911yescharacteristic
1034C2#2024593511yescharacteristic
1035C2#2024594211yescharacteristic
1036C2#2024594211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC47×#1437C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenter#1437D47
hypocenterC47C4×#388
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
3. C2×#15688974C2semidirect
7. C2×C42×Dic47C2semidirect
9. #20241621C2semidirect
10. #20241619C2semidirect
11. #20241614C2semidirect
12. #20241612C2semidirect
13. #95×Dic47C2semidirect
14. #95×Dic47C2semidirect
31. #15689017C4semidirect
32. #15689011C4semidirect
36. C22⋊C4×Dic47C4semidirect
77. C2×Dic47⋊C4C2×C4semidirect
78. C2×Dic47⋊C4C2×C4semidirect
111. C2×C4×Dic47C2×C4semidirect
112. C2×C4×Dic47C2×C4semidirect
124. C47⋊#95C2×C4semidirect
125. C47⋊#95C2×C4semidirect
126. C47⋊#95C2×C4semidirect
127. C47⋊#95C2×C4semidirect
277. C22⋊Dic47C42semidirect
502. Dic47#388semidirect
576. C47C4×#388semidirect

Maximal subgroups

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

subgroupindex
C2×#156890172
C2×#156890112
C2×#156889742
C2×C22⋊C4×Dic472
C2×C42×Dic472
#202416252
#202416212
#202416192
#202416142
#202416122
#95×Dic472
C47×#14372
C4×#38847