Finite Group Databasebeta

← #388×Dic47 #26137437

Subgroups — #388×Dic47 #26137437

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×#15689016C211yesmaximal, characteristic
2C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic47C211yesmaximal, characteristic
4C2×C22⋊C4×Dic47C211yesmaximal, characteristic
5C2×C22⋊C4×Dic47C211yesmaximal, characteristic
6C2×C42×Dic47C211yesmaximal, characteristic, complemented
7#20241625C211yesmaximal, characteristic
8#20241625C211yesmaximal, characteristic
9#20241622C211yesmaximal, characteristic, complemented
10#20241620C211yesmaximal, characteristic, complemented
11#20241615C211yesmaximal, characteristic, complemented
12#20241613C211yesmaximal, characteristic, complemented
13#95×Dic47C211yesmaximal, characteristic, complemented
14#95×Dic47C211yesmaximal, characteristic, complemented
15C2×C47×#388C211yesmaximal, characteristic
16C24×Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×C22⋊Dic47C2211yescharacteristic
19C22×C22⋊Dic47C2211yescharacteristic
20C22×C22⋊Dic47C2211yescharacteristic
21C22×C4×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
30#15689016C418yescomplemented
31C4⋊C4×Dic47—24no—
32C22⋊C4×Dic47—24no—
33C22⋊C4×Dic47—24no—
34C22⋊C4×Dic47C418yescomplemented
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
48C2×C47⋊#95C2211yescharacteristic
49C42×Dic47—24no—
50C22×C4⋊C4×C47C2211yescharacteristic
51C22×C22⋊C4×C47C2211yescharacteristic
52C22×C22⋊C4×C47C2211yescharacteristic
53C22×C22⋊C4×C47C2211yescharacteristic
54C22×C42×C47C2211yescharacteristic
55C47×#388C418yescomplemented
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×C4⋊Dic47—22no—
74C2×C4⋊Dic47—22no—
75C2×C4⋊Dic47C2×C414yescomplemented
76C2×C22⋊Dic47—22no—
77C2×C22⋊Dic47—22no—
78C2×C22⋊Dic47—22no—
79C2×C22⋊Dic47—22no—
80C2×C22⋊Dic47—22no—
81C2×C22⋊Dic47—22no—
82C2×C22⋊Dic47C2×C414yes—
83C2×C22⋊Dic47C2×C414yes—
84C2×C22⋊Dic47C2×C414yes—
85C2×C4×Dic47—22no—
86C2×C4×Dic47—22no—
87C2×C4×Dic47—22no—
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×Dic47C2×C414yes—
108C2×C4×Dic47C2×C414yes—
109C2×C4×Dic47C2×C414yescomplemented
110C2×C4×Dic47D414yes—
111C2×C4×Dic47D414yes—
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—22no—
122C47⋊#95C2×C414yes—
123C47⋊#95C2×C414yes—
124C47⋊#95C2×C414yescomplemented
125C47⋊#95C2×C414yescomplemented
126C25×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×C47C2×C414yescomplemented
136C2×C22⋊C4×C47—22no—
137C2×C22⋊C4×C47—22no—
138C2×C22⋊C4×C47—22no—
139C2×C22⋊C4×C47—22no—
140C2×C22⋊C4×C47C2×C414yes—
141C2×C22⋊C4×C47C2×C414yes—
142C2×C22⋊C4×C47C2×C414yes—
143C2×C22⋊C4×C47C2×C414yes—
144C2×C22⋊C4×C47C2×C414yes—
145C2×C42×C47—22no—
146C2×C42×C47—22no—
147C2×C42×C47C2×C414yescomplemented
148#95×C47C2×C414yescomplemented
149#95×C47C2×C414yescomplemented
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×C47C22×C412yes—
195C22×C4×C47C22×C412yes—
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×C47C22×C412yes—
203C22×C4×C47C22×C412yes—
204C22×C4×C47C2×D412yes—
205C22×C4×C47C2×D412yes—
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—21no—
243C22×Dic47—21no—
244C22×Dic47—28no—
245C22×Dic47—28no—
246C22×Dic47—28no—
247C22×Dic47—44no—
248C22×Dic47—44no—
249C22×Dic47—44no—
250C22×Dic47—44no—
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×Dic47C2×D412yes—
260C22×Dic47C2×D412yes—
261C22×Dic47C2×D412yes—
262C22×Dic47C2×D412yes—
263C22×Dic47#4112yes—
264C22×Dic47#4112yes—
265C22×Dic47#4112yes—
266C22×Dic47#4112yes—
267C22×Dic47#4112yes—
268C22×Dic47#4112yes—
269C22×Dic47#4112yes—
270C22×Dic47#4112yes—
271C4⋊C4×C47—28no—
272C22⋊C4×C47—28no—
273C22⋊C4×C47—28no—
274C22⋊C4×C47C42116yescomplemented
275C42×C47—28no—
276C22⋊Dic47—28no—
277C22⋊Dic47—28no—
278C22⋊Dic47—28no—
279C4⋊Dic47—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—22no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
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×C47C2×C4214yes—
378C2×C4×C47C2×C4214yes—
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—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—416no—
428C2×Dic47#11714yes—
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—24no—
493C4×C47—42no—
494C4×C47—42no—
495Dic47—24no—
496Dic47—24no—
497Dic47—24no—
498Dic47—42no—
499Dic47—42no—
500Dic47—42no—
501Dic47—42no—
502Dic47#38818yesdirect product factor
503C2×#388—471no—
504C2×#388D4711yescharacteristic
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#1437—471no—
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⋊C4C2×D4711yescharacteristic
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#388Dic4718yesdirect product factor
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×#95—471no—
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—474no—
583C23×C4—471no—
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—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—474no—
602C2×C4⋊C4—942no—
603C2×C4⋊C4—942no—
604C2×C4⋊C4C2×Dic4714yescomplemented
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—474no—
610C2×C22⋊C4—474no—
611C2×C22⋊C4—474no—
612C2×C22⋊C4—942no—
613C2×C22⋊C4—942no—
614C2×C22⋊C4—942no—
615C2×C22⋊C4—942no—
616C2×C22⋊C4—942no—
617C2×C22⋊C4—942no—
618C2×C22⋊C4C4×D4714yes—
619C2×C22⋊C4C4×D4714yes—
620C2×C22⋊C4C2×Dic4714yes—
621C2×C22⋊C4C2×Dic4714yes—
622C2×C22⋊C4C2×Dic4714yes—
623C2×C42—22no—
624C2×C42—22no—
625C2×C42—474no—
626C2×C42—474no—
627C2×C42—474no—
628C2×C42—474no—
629C2×C42—474no—
630C2×C42—942no—
631C2×C42—942no—
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×C42C2×Dic4714yescomplemented
653#95—474no—
654#95—474no—
655#95—474no—
656#95—474no—
657#95—942no—
658#95—942no—
659#95—942no—
660#95—942no—
661#95—942no—
662#95—942no—
663#95—942no—
664#95—942no—
665#95—942no—
666#95—942no—
667#95C2×Dic4714yescomplemented
668#95C2×Dic4714yescomplemented
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—
683C24C22×Dic4712yes—
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—472no—
714C22×C4—472no—
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—948no—
734C22×C4—948no—
735C22×C4—948no—
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—941no—
766C22×C4—941no—
767C22×C4—941no—
768C22×C4—941no—
769C22×C4—941no—
770C22×C4—941no—
771C22×C4—941no—
772C22×C4—1884no—
773C22×C4—1884no—
774C22×C4—1884no—
775C22×C4—1884no—
776C22×C4C2×C4×D4712yes—
777C22×C4C2×C4×D4712yes—
778C22×C4C2×C4×D4712yes—
779C22×C4C2×C4×D4712yes—
780C22×C4D4×D4712yes—
781C22×C4D4×D4712yes—
782C22×C4#1062535212yes—
783C22×C4#1062535212yes—
784C22×C4C22×Dic4712yes—
785C22×C4C22×Dic4712yes—
786C22×C4C22×Dic4712yes—
787C22×C4C22×Dic4712yes—
788C22×C4C22×Dic4712yes—
789C22×C4C22×Dic4712yes—
790C4⋊C4—28no—
791C4⋊C4—948no—
792C22⋊C4—28no—
793C22⋊C4—28no—
794C22⋊C4—948no—
795C22⋊C4—948no—
796C22⋊C4—948no—
797C22⋊C4C4×Dic47116yescomplemented
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—
842C23C2×C4×Dic4714yes—
843C23C22×C4×D4711yescharacteristic
844C23C22×C4×D4711yescharacteristic
845C23C23×Dic4711yescharacteristic
846C23C2×D4×D4711yescharacteristic
847C23C2×D4×D4711yescharacteristic
848C23#41×D4711yescharacteristic
849C23#41×D4711yescharacteristic
850C23#41×D4711yescharacteristic
851C23#41×D4711yescharacteristic
852C23#41×D4711yescharacteristic
853C23#41×D4711yescharacteristic
854C23#41×D4711yescharacteristic
855C23#41×D4711yescharacteristic
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—22no—
886C2×C4—22no—
887C2×C4—22no—
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—474no—
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—942no—
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—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—18816no—
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×C4C2×C4×Dic4714yes—
954C2×C4C2×C4×Dic4714yes—
955C2×C4D4×Dic4714yes—
956C2×C4D4×Dic4714yes—
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—
972C22C22×C4×Dic4711yescharacteristic
973C22#117×D4711yescharacteristic
974C22#117×D4711yescharacteristic
975C22C4×D4×D4711yescharacteristic
976C22C4×D4×D4711yescharacteristic
977C22C4×D4×D4711yescharacteristic
978C22C4×D4×D4711yescharacteristic
979C22C2×D4×Dic4711yescharacteristic
980C22C2×D4×Dic4711yescharacteristic
981C22C4×#1062535211yescharacteristic
982C22C4×#1062535211yescharacteristic
983C22C4×#1062535211yescharacteristic
984C22C4×#1062535211yescharacteristic
985C22#1568959111yescharacteristic
986C22#1568959111yescharacteristic
987C22#41×Dic4711yescharacteristic
988C22#41×Dic4711yescharacteristic
989C22#41×Dic4711yescharacteristic
990C22#41×Dic4711yescharacteristic
991C22#121×D4711yescharacteristic
992C22#123×D4711yescharacteristic
993C22#1568963111yescharacteristic
994C22#1568963311yescharacteristic
995C22#124×D4711yescharacteristic
996C22#126×D4711yescharacteristic
997C22#1568965011yescharacteristic
998C22#1568965011yescharacteristic
999C22#1568965211yescharacteristic
1000C22#1568965211yescharacteristic
1001C22#1568965411yescharacteristic
1002C22#1568965611yescharacteristic
1003C22#1568965611yescharacteristic
1004C22#1568965611yescharacteristic
1005C22#1568966811yescharacteristic
1006C22#1568967211yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—478no—
1014C4—944no—
1015C4—944no—
1016C4—944no—
1017C4—1882no—
1018C4—1882no—
1019C4—1882no—
1020C4—1882no—
1021C2—44no—
1022C2#117×Dic4711yescharacteristic
1023C2C4×D4×Dic4711yescharacteristic
1024C2C4×D4×Dic4711yescharacteristic
1025C2#388×D4711yescharacteristic
1026C2#2024583011yescharacteristic
1027C2#2024584811yescharacteristic
1028C2#2024588211yescharacteristic
1029C2#2024590011yescharacteristic
1030C2#121×Dic4711yescharacteristic
1031C2#123×Dic4711yescharacteristic
1032C2#2024591511yescharacteristic
1033C2#2024592911yescharacteristic
1034C2#124×Dic4711yescharacteristic
1035C2#126×Dic4711yescharacteristic
1036C2#2024594211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC2×C47×#388C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#388D47
hypocenterC47C4×#388
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic47C2semidirect
6. C2×C42×Dic47C2semidirect
9. #20241622C2semidirect
10. #20241620C2semidirect
11. #20241615C2semidirect
12. #20241613C2semidirect
13. #95×Dic47C2semidirect
14. #95×Dic47C2semidirect
30. #15689016C4semidirect
34. C22⋊C4×Dic47C4semidirect
55. C47×#388C4semidirect
75. C2×C4⋊Dic47C2×C4semidirect
109. C2×C4×Dic47C2×C4semidirect
124. C47⋊#95C2×C4semidirect
125. C47⋊#95C2×C4semidirect
135. C2×C4⋊C4×C47C2×C4semidirect
147. C2×C42×C47C2×C4semidirect
148. #95×C47C2×C4semidirect
149. #95×C47C2×C4semidirect
274. C22⋊C4×C47C42semidirect
502. Dic47#388direct (N × H)
554. #388Dic47direct (N × H)
576. C47C4×#388semidirect
604. C2×C4⋊C4C2×Dic47semidirect
652. C2×C42C2×Dic47semidirect
667. #95C2×Dic47semidirect
668. #95C2×Dic47semidirect
797. C22⋊C4C4×Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156890162
C2×C4⋊C4×Dic472
C2×C22⋊C4×Dic472
C2×C42×Dic472
#202416252
#202416222
#202416202
#202416152
#202416132
#95×Dic472
C2×C47×#3882
C4×#38847