Finite Group Databasebeta

← #26231752

Subgroups — #26231752

Order 12032.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689769C211yesmaximal, characteristic
2C2×#15689195C211yesmaximal, characteristic, complemented
3C2×#15689122C211yesmaximal, characteristic, complemented
4C22×#13093944C211yesmaximal, characteristic, complemented
5#20244320C211yesmaximal, characteristic, complemented
6#20244202C211yesmaximal, characteristic, complemented
7#20243824C211yesmaximal, characteristic, complemented
8#20243809C211yesmaximal, characteristic, complemented
9#20243705C211yesmaximal, characteristic, complemented
10#20243695C211yesmaximal, characteristic, complemented
11#20243385C211yesmaximal, characteristic, complemented
12#20243326C211yesmaximal, characteristic, complemented
13#20243318C211yesmaximal, characteristic, complemented
14#20243216C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C47C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17C23×D188C2211yescharacteristic
18C22×#10625329C2211yescharacteristic, complemented
19C23×C47⋊C8C2211yescharacteristic
20#15689769—24no—
21#15689769C418yescomplemented
22C2×#13094012C2211yescharacteristic
23C2×#13094009—21no—
24C2×#13094003C2211yescharacteristic
25C2×#13093998C2211yescharacteristic
26C2×#13093997—21no—
27C2×#13093992—21no—
28C2×C4×D188C2211yescharacteristic
29C2×C22⋊C4×D47—21no—
30#15689195—24no—
31C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
32#15689122—24no—
33C2×#13093947C2211yescharacteristic, complemented
34C2×#13093947C2211yescharacteristic, complemented
35C2×#13093947C2211yescharacteristic, complemented
36C2×#13093947C2211yescharacteristic, complemented
37C2×#13093944—24no—
38C2×#13093944C2211yescharacteristic
39C2×#13093944C2211yescharacteristic
40C2×#13093944C2211yescharacteristic
41C2×#13093944C2211yescharacteristic
42C2×#13093944C2211yescharacteristic
43C2×#13093944C2211yescharacteristic
44C2×#13093944C2211yescharacteristic
45C2×#13093944C2211yescharacteristic
46C2×C22⋊(C47⋊C8)C2211yescharacteristic
47C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
48C2×#13093935C2211yescharacteristic, complemented
49#15688885C2211yescharacteristic, complemented
50#15688885C2211yescharacteristic, complemented
51#15688885C2211yescharacteristic, complemented
52#15688885C2211yescharacteristic, complemented
53C2×C4×D4×C47—21no—
54C2×C4×D4×C47C2211yescharacteristic
55C22×C4⋊C4×C47C2211yescharacteristic
56C22×C4⋊C4×C47C2211yescharacteristic, complemented
57C47×#389—21no—
58C47×#385—21no—
59C47×#385—21no—
60C47×#384C2211yescharacteristic, complemented
61C47×#380C2211yescharacteristic
62C47×#380C2211yescharacteristic, complemented
63C4×C4⋊C4×C47C2211yescharacteristic, complemented
64C24×D47—21no—
65C2×#10625350—22no—
66C2×#10625350—22no—
67C2×#10625350—22no—
68C2×#10625350—41no—
69C2×#10625350—41no—
70C2×#10625350C2×C414yescomplemented
71C22×Dic94C2311yescharacteristic
72C22×D188—22no—
73C22×D188—22no—
74C22×D188—22no—
75C22×D188—21no—
76C22×D188—41no—
77C22×D188—41no—
78C22×D188C2×C414yescomplemented
79C22×D188C2311yescharacteristic
80C22×D188C2311yescharacteristic
81C22×C22⋊D47—21no—
82C22×C22⋊D47—21no—
83C22×C4×D47—21no—
84C22×C4×D47—21no—
85C2×#10625329—22no—
86C2×#10625329—22no—
87C2×#10625329—41no—
88C22×C47⋊C8—22no—
89C22×C47⋊C8—22no—
90C22×C47⋊C8—41no—
91C22×C47⋊C8C2311yescharacteristic
92C22×C47⋊C8C2311yescharacteristic
93C22×C47⋊C8C2311yescharacteristic
94C22×C47⋊C8C2311yescharacteristic
95#13094012—22no—
96#13094012C2×C414yescomplemented
97#13094009—28no—
98#13094003—22no—
99#13094003C2×C414yescomplemented
100#13093998—22no—
101#13093998C2×C414yescomplemented
102#13093997—28no—
103#13093992—28no—
104C4×D188—22no—
105C4×D188C2×C414yescomplemented
106C2×C4⋊Dic47C2311yescharacteristic
107C2×Dic47⋊C4—21no—
108C2×C22⋊Dic47—21no—
109C2×(C2×D47)⋊C4—21no—
110C2×(C2×D47)⋊C4—21no—
111C2×(C2×D47)⋊C4—21no—
112C2×(C2×D47)⋊C4—21no—
113C22⋊C4×D47—28no—
114C4⋊(C47⋊C8)—22no—
115#13093947—22no—
116#13093947—22no—
117#13093947—41no—
118#13093947—41no—
119#13093944—22no—
120#13093944—22no—
121#13093944—22no—
122#13093944—22no—
123#13093944—22no—
124#13093944—41no—
125#13093944—41no—
126#13093944D414yescomplemented
127C22⋊(C47⋊C8)—22no—
128C22⋊(C47⋊C8)—22no—
129#13093935—22no—
130C22×D4×C47D411yescharacteristic
131C23×C4×C47—21no—
132C23×C4×C47—21no—
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C4×D4×C47—44no—
136C4×D4×C47C2×C414yes—
137C4×D4×C47D414yes—
138C2×C4⋊C4×C47—22no—
139C2×C4⋊C4×C47—22no—
140C2×C4⋊C4×C47—21no—
141C2×C4⋊C4×C47—21no—
142C2×C4⋊C4×C47—21no—
143C2×C4⋊C4×C47—21no—
144C2×C4⋊C4×C47—41no—
145C2×C4⋊C4×C47—41no—
146C2×C4⋊C4×C47D411yescharacteristic
147C2×C4⋊C4×C47C2311yescharacteristic
148C2×C4⋊C4×C47C2311yescharacteristic
149C2×C4⋊C4×C47C2311yescharacteristic
150C2×C4⋊C4×C47C2311yescharacteristic
151C2×C22⋊C4×C47—21no—
152C2×C22⋊C4×C47—21no—
153C2×C22⋊C4×C47D411yescharacteristic
154C2×C22⋊C4×C47D411yescharacteristic
155C2×C42×C47—21no—
156C2×C42×C47C2311yescharacteristic
157#95×C47—21no—
158#95×C47—21no—
159#95×C47—21no—
160C24×C47C2×D411yescharacteristic
161C24×C47C2×D411yescharacteristic
162C23×D47—21no—
163C23×D47—21no—
164C23×D47—24no—
165C23×D47—42no—
166C23×D47—42no—
167C23×D47—42no—
168C23×D47—42no—
169C23×D47—81no—
170C23×D47—81no—
171C2×D4×C47—22no—
172C2×D4×C47—22no—
173C2×D4×C47C22⋊C414yes—
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—42no—
187C22×C4×C47—42no—
188C22×C4×C47—42no—
189C22×C4×C47—42no—
190C22×C4×C47—81no—
191C22×C4×C47—81no—
192C22×C4×C47C22×C412yes—
193C22×C4×C47C22×C412yes—
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D412yes—
199C22×C4×C47C2×D412yes—
200C22×C4×C47C2411yescharacteristic
201C2×C22⋊D47—24no—
202C2×C22⋊D47—24no—
203C2×C22⋊D47—42no—
204C2×C22⋊D47—42no—
205C2×C22⋊D47—81no—
206C2×C22⋊D47—81no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209#10625350—28no—
210#10625350—44no—
211#10625350—44no—
212#10625350—44no—
213C2×D188—21no—
214C2×D188—21no—
215C2×D188—21no—
216C2×D188—21no—
217C2×D188—21no—
218C2×D188—21no—
219C2×D188—21no—
220C2×D188—28no—
221C2×D188—24no—
222C2×D188—21no—
223C2×D188—44no—
224C2×D188—44no—
225C2×D188—44no—
226C2×D188—42no—
227C2×D188—42no—
228C2×D188C22×C412yes—
229C2×D188C22×C412yes—
230C2×D188C2×D412yes—
231C2×D188#4112yes—
232C2×C4×D47—24no—
233C2×C4×D47—24no—
234C2×C4×D47—42no—
235C2×C4×D47—42no—
236C2×C4×D47—81no—
237C2×C4×D47—81no—
238C2×Dic94—21no—
239C2×Dic94—21no—
240C2×Dic94—21no—
241C2×Dic94—21no—
242C2×Dic94—21no—
243C2×Dic94C22×C412yes—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47—42no—
252C4⋊C4×C47—42no—
253C4⋊C4×C47—42no—
254C4⋊C4×C47—81no—
255C4⋊C4×C47C22⋊C414yes—
256C4⋊C4×C47C2×D412yes—
257C22⋊C4×C47—42no—
258C22⋊C4×C47—42no—
259C22⋊C4×C47C22⋊C414yes—
260C22⋊C4×C47C22⋊C414yes—
261C42×C47—42no—
262C42×C47C22×C412yes—
263C42×C47C2×D412yes—
264C22⋊Dic47—24no—
265(C2×D47)⋊C4—24no—
266(C2×D47)⋊C4—24no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4—24no—
269C4⋊Dic47—21no—
270C4⋊Dic47C22×C412yes—
271Dic47⋊C4—24no—
272#10625329—44no—
273C2×C47⋊C8—21no—
274C2×C47⋊C8—21no—
275C2×C47⋊C8—21no—
276C2×C47⋊C8—21no—
277C2×C47⋊C8—21no—
278C2×C47⋊C8—21no—
279C2×C47⋊C8—21no—
280C2×C47⋊C8—21no—
281C2×C47⋊C8—21no—
282C2×C47⋊C8—21no—
283C2×C47⋊C8—21no—
284C2×C47⋊C8—44no—
285C2×C47⋊C8C2×D412yes—
286C23×C47—21no—
287C23×C47—21no—
288C23×C47—21no—
289C23×C47—21no—
290C23×C47—21no—
291C23×C47—21no—
292C23×C47—21no—
293C23×C47—21no—
294C23×C47—21no—
295C23×C47—21no—
296C23×C47C2×C22⋊C412yes—
297C23×C47C2×C22⋊C412yes—
298C23×C47AGL(1,ℤ/8)12yes—
299C23×C47#13712yes—
300C23×C47C22×D411yescharacteristic
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—48no—
306C22×D47—41no—
307C22×D47—41no—
308C22×D47—41no—
309C22×D47—41no—
310C22×D47—41no—
311C22×D47—41no—
312C22×D47—41no—
313C22×D47—41no—
314C22×D47—41no—
315C22×D47—41no—
316C22×D47—48no—
317C22×D47—84no—
318C22×D47—84no—
319C22×D47—84no—
320C22×D47—84no—
321C22×D47—84no—
322D4×C47—28no—
323C2×C4×C47—21no—
324C2×C4×C47—21no—
325C2×C4×C47—21no—
326C2×C4×C47—21no—
327C2×C4×C47—21no—
328C2×C4×C47—21no—
329C2×C4×C47—21no—
330C2×C4×C47—21no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47—84no—
352C2×C4×C47—84no—
353C2×C4×C47C2×C22⋊C412yes—
354C2×C4×C47C2×C22⋊C412yes—
355C2×C4×C47C2×C22⋊C412yes—
356C2×C4×C47C2×C22⋊C412yes—
357C2×C4×C47C23×C411yescharacteristic
358C2×C4×C47C22×D411yescharacteristic
359C2×C4×C47C22×D411yescharacteristic
360C2×C4×C47C2×#4111yescharacteristic
361C2×C4×C47H(5,𝔽2)11yescharacteristic
362C2×C4×C47H(5,𝔽2)11yescharacteristic
363C22⋊D47—48no—
364C22⋊D47—84no—
365C2×Dic47—22no—
366C2×Dic47—22no—
367C2×Dic47—41no—
368C2×Dic47—41no—
369C2×Dic47—41no—
370C2×Dic47—41no—
371D188—22no—
372D188—22no—
373D188—22no—
374D188—22no—
375D188—22no—
376D188—48no—
377D188—41no—
378D188—41no—
379D188C4×D414yescomplemented
380C4×D47—48no—
381C4×D47—84no—
382Dic94—22no—
383Dic94—22no—
384Dic94—41no—
385Dic94—41no—
386C47⋊C8—22no—
387C47⋊C8—41no—
388C47⋊C8—41no—
389C47⋊C8—41no—
390#22419—471nomaximal, Sylow
391C22×C47—22no—
392C22×C47—22no—
393C22×C47—22no—
394C22×C47—22no—
395C22×C47—22no—
396C22×C47—22no—
397C22×C47—22no—
398C22×C47—22no—
399C22×C47—22no—
400C22×C47—41no—
401C22×C47—41no—
402C22×C47—41no—
403C22×C47—41no—
404C22×C47#41714yescomplemented
405C22×C47C22×C22⋊C411yescharacteristic
406C22×C47D4211yescharacteristic
407C22×C47#54611yescharacteristic
408C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C47C2×#13711yescharacteristic
410C22×C47#57611yescharacteristic
411C22×C47#57711yescharacteristic
412C2×D47—24no—
413C2×D47—42no—
414C2×D47—42no—
415C2×D47—42no—
416C2×D47—42no—
417C2×D47—42no—
418C2×D47—42no—
419C2×D47—42no—
420C2×D47—42no—
421C2×D47—42no—
422C2×D47—816no—
423C2×D47—81no—
424C2×D47—81no—
425C2×D47—81no—
426C2×D47—81no—
427C4×C47—22no—
428C4×C47—22no—
429C4×C47—22no—
430C4×C47—22no—
431C4×C47—42no—
432C4×C47—81no—
433C4×C47—81no—
434C4×C47—81no—
435C4×C47C2×C4×D411yescharacteristic
436C4×C47#51811yescharacteristic
437C4×C47D4211yescharacteristic
438C4×C47#54611yescharacteristic
439Dic47—42no—
440Dic47—42no—
441C2×#546—471no—
442C2×#435—471no—
443C2×#417—471no—
444C22×#102—471no—
445D4×C4⋊C4D4711yescharacteristic, complemented
446#1983—471no—
447#1959—471no—
448#1895—471no—
449#1892—471no—
450#1874—471no—
451#1872—471no—
452#1802—471no—
453#1788—471no—
454#1786—471no—
455#1762—471no—
456C2×C47—24no—
457C2×C47—42no—
458C2×C47D4×C22⋊C411yescharacteristic
459C2×C47C2×#41711yescharacteristic
460C2×C47#289711yescharacteristic
461C2×C47#326411yescharacteristic
462C2×C47#326611yescharacteristic
463C2×C47#330611yescharacteristic
464C2×C47#331411yescharacteristic
465D47—44no—
466D47—82no—
467C22×#41—471no—
468C23×D4—471no—
469C22×M16—471no—
470C23×C8—471no—
471#546—478no—
472#546—944no—
473C2×#124—471no—
474C2×#123—941no—
475C2×C22⋊Q8—471no—
476C2×#121—471no—
477C2×#121—941no—
478C2×#120—941no—
479C2×C4×D4—21no—
480C2×C4×D4—471no—
481C2×C4×D4C2×D4711yescharacteristic
482C22×C4⋊C4C2×D4711yescharacteristic
483C22×C4⋊C4C2×D4711yescharacteristic, complemented
484C22×C22⋊C4—941no—
485#435—944no—
486C2×C4⋊C8—471no—
487#417—944no—
488C2×#103—471no—
489C2×#103—471no—
490C2×#103—471no—
491C2×#103—471no—
492C2×#102—471no—
493C2×#102—471no—
494C2×#102—471no—
495C2×#102—471no—
496C2×#102—471no—
497C2×#102—471no—
498C2×#102—471no—
499C2×#102—471no—
500C2×#102—944no—
501C2×C22⋊C8—471no—
502C2×C22⋊C8—471no—
503C2×#97—471no—
504#389—21no—
505#385—21no—
506#385—21no—
507#384C2×D4711yescharacteristic, complemented
508#380C2×D4711yescharacteristic
509#380C2×D4711yescharacteristic, complemented
510C4×C4⋊C4C2×D4711yescharacteristic, complemented
511#340—471no—
512#340—471no—
513#340—471no—
514#340—471no—
515C47#2241911yescharacteristic, complemented, Sylow
516C25—941no—
517C2×#41—474no—
518C2×#41—942no—
519C2×#41—942no—
520C2×#41—942no—
521C2×#41—1881no—
522C2×#41—1881no—
523C22×Q8—471no—
524C22×D4—474no—
525C22×D4—471no—
526C22×D4—471no—
527C22×D4—942no—
528C22×D4—942no—
529C22×D4—941no—
530C22×D4—941no—
531C22×D4—942no—
532C22×D4—941no—
533C22×D4—1881no—
534C22×D4—1881no—
535C22×D4C22⋊D4711yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—941no—
539C23×C4—941no—
540C23×C4C22×D4711yescharacteristic
541C23×C4C22×D4711yescharacteristic
542C2×M16—942no—
543C2×M16—942no—
544C2×M16—1881no—
545C22×C8—471no—
546C22×C8—471no—
547C22×C8—471no—
548C22×C8—471no—
549C22×C8—942no—
550C22×C8—942no—
551C22×C8—1881no—
552#124—474no—
553#124—942no—
554#123—948no—
555C22⋊Q8—474no—
556C22⋊Q8—942no—
557#121—474no—
558#121—942no—
559#121—948no—
560#120—948no—
561C4×D4—44no—
562C4×D4—474no—
563C4×D4—942no—
564C4×D4C4×D4714yes—
565C4×D4D18814yes—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—471no—
575C2×C4⋊C4—941no—
576C2×C4⋊C4C22⋊D4711yescharacteristic
577C2×C4⋊C4C22×D4711yescharacteristic
578C2×C4⋊C4C22×D4711yescharacteristic
579C2×C4⋊C4C22×D4711yescharacteristic
580C2×C4⋊C4C22×D4711yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—941no—
584C2×C22⋊C4—941no—
585C2×C22⋊C4—941no—
586C2×C22⋊C4—941no—
587C2×C22⋊C4—941no—
588C2×C22⋊C4—948no—
589C2×C22⋊C4C22⋊D4711yescharacteristic
590C2×C22⋊C4C22⋊D4711yescharacteristic
591C2×C42—21no—
592C2×C42C22×D4711yescharacteristic
593C4⋊C8—942no—
594#103—942no—
595#103—942no—
596#103—1881no—
597#103—1881no—
598#102—474no—
599#102—942no—
600#102—942no—
601#102—942no—
602#102—942no—
603#102—942no—
604#102—1881no—
605#102—1881no—
606C22⋊C8—942no—
607C22⋊C8—942no—
608#97—942no—
609#95—21no—
610#95—21no—
611#95—21no—
612C24—941no—
613C24—944no—
614C24—941no—
615C24—3761no—
616C24—3761no—
617C24—1882no—
618C24—1882no—
619C24—1882no—
620C24—1882no—
621C24C2×C22⋊D4711yescharacteristic
622C24C2×C22⋊D4711yescharacteristic
623#41—948no—
624#41—1884no—
625#41—1884no—
626#41—1884no—
627C2×Q8—472no—
628C2×Q8—941no—
629C2×Q8—941no—
630C2×Q8—941no—
631C2×Q8—941no—
632C2×Q8—941no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—472no—
636C2×D4—472no—
637C2×D4—472no—
638C2×D4—472no—
639C2×D4—948no—
640C2×D4—944no—
641C2×D4—944no—
642C2×D4—944no—
643C2×D4—941no—
644C2×D4—941no—
645C2×D4—941no—
646C2×D4—941no—
647C2×D4—941no—
648C2×D4—941no—
649C2×D4—941no—
650C2×D4—941no—
651C2×D4—3761no—
652C2×D4—3761no—
653C2×D4—1884no—
654C2×D4—1884no—
655C2×D4—1884no—
656C2×D4—1882no—
657C2×D4—1882no—
658C2×D4—1882no—
659C2×D4—1882no—
660C2×D4(C2×D47)⋊C414yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—81no—
678C22×C4—81no—
679C22×C4—941no—
680C22×C4—941no—
681C22×C4—944no—
682C22×C4—944no—
683C22×C4—3761no—
684C22×C4—3761no—
685C22×C4—1882no—
686C22×C4—1882no—
687C22×C4C2×C4×D4712yes—
688C22×C4C2×C4×D4712yes—
689C22×C4C2×D18812yes—
690C22×C4C2×D18812yes—
691C22×C4C2×C22⋊D4711yescharacteristic
692C22×C4C2×C22⋊D4711yescharacteristic
693C22×C4C2×C22⋊D4711yescharacteristic
694C22×C4C2×C22⋊D4711yescharacteristic
695C22×C4C23×D4711yescharacteristic
696M16—1884no—
697C2×C8—472no—
698C2×C8—941no—
699C2×C8—941no—
700C2×C8—941no—
701C2×C8—941no—
702C2×C8—941no—
703C2×C8—941no—
704C2×C8—941no—
705C2×C8—941no—
706C2×C8—941no—
707C2×C8—941no—
708C2×C8—941no—
709C2×C8—1884no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—42no—
718C4⋊C4—42no—
719C4⋊C4—42no—
720C4⋊C4—81no—
721C4⋊C4—472no—
722C4⋊C4—944no—
723C4⋊C4—941no—
724C4⋊C4(C2×D47)⋊C414yes—
725C4⋊C4D4×D4712yes—
726C22⋊C4—42no—
727C22⋊C4—42no—
728C22⋊C4—944no—
729C22⋊C4—944no—
730C22⋊C4—944no—
731C22⋊C4—944no—
732C22⋊C4—944no—
733C22⋊C4(C2×D47)⋊C414yes—
734C22⋊C4(C2×D47)⋊C414yes—
735C42—42no—
736C42C2×C4×D4712yes—
737C42C2×D18812yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—942no—
749C23—942no—
750C23—942no—
751C23—942no—
752C23—3764no—
753C23—3764no—
754C23—3764no—
755C23—3764no—
756C23—3764no—
757C23—1888no—
758C23—1881no—
759C23—1881no—
760C23—1888no—
761C23—1881no—
762C23—1881no—
763C23—1881no—
764C23—1881no—
765C23—1881no—
766C23—1881no—
767C23—1881no—
768C23—1881no—
769C23C2×(C2×D47)⋊C412yes—
770C23C2×(C2×D47)⋊C412yes—
771C23#1309405012yes—
772C23#1309405512yes—
773C23C22×C22⋊D4711yescharacteristic
774Q8—942no—
775Q8—942no—
776Q8—1881no—
777Q8—1881no—
778D4—28no—
779D4—474no—
780D4—942no—
781D4—942no—
782D4—942no—
783D4—942no—
784D4—942no—
785D4—3764no—
786D4—1888no—
787D4—1888no—
788D4—1881no—
789D4—1881no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—84no—
819C2×C4—84no—
820C2×C4—942no—
821C2×C4—942no—
822C2×C4—3764no—
823C2×C4—1888no—
824C2×C4—1881no—
825C2×C4—1881no—
826C2×C4—1881no—
827C2×C4—1881no—
828C2×C4C2×(C2×D47)⋊C412yes—
829C2×C4C2×(C2×D47)⋊C412yes—
830C2×C4C2×(C2×D47)⋊C412yes—
831C2×C4C2×(C2×D47)⋊C412yes—
832C2×C4C22×C4×D4711yescharacteristic
833C2×C4C2×D4×D4711yescharacteristic
834C2×C4C22×D18811yescharacteristic
835C2×C4#41×D4711yescharacteristic
836C2×C4#1309406911yescharacteristic
837C2×C4#1309407011yescharacteristic
838C8—942no—
839C8—1881no—
840C8—1881no—
841C8—1881no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—944no—
856C22—37616no—
857C22—3761no—
858C22—3761no—
859C22—3761no—
860C22—3761no—
861C22—1882no—
862C22—1882no—
863C22—1882no—
864C22—1882no—
865C22—1882no—
866C22—1882no—
867C22—1882no—
868C22—1882no—
869C22—1882no—
870C22#1568912214yescomplemented
871C22C22×(C2×D47)⋊C411yescharacteristic
872C22D4×C22⋊D4711yescharacteristic
873C22#1568976111yescharacteristic
874C22C2×#1309405011yescharacteristic
875C22C2×#1309405511yescharacteristic
876C22#1568992611yescharacteristic
877C22#1568993111yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—81no—
884C4—81no—
885C4—81no—
886C4—1882no—
887C4—1882no—
888C4C4×D4×D4711yescharacteristic
889C4#1568959511yescharacteristic
890C4D4×D18811yescharacteristic
891C4#1568976811yescharacteristic
892C2—24no—
893C2—42no—
894C2—3762no—
895C2—1884no—
896C2D4×(C2×D47)⋊C411yescharacteristic
897C2C2×#1568912211yescharacteristic
898C2#2025191111yescharacteristic
899C2#2025486411yescharacteristic
900C2#2025489911yescharacteristic
901C2#2025534311yescharacteristic
902C2#2025546311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingD4×C4⋊C4×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689769C2
cosocleC22×C4×C47C24
hypercenterD4×C4⋊C4D47
hypocenterC47#22419
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#15689195C2semidirect
3. C2×#15689122C2semidirect
4. C22×#13093944C2semidirect
5. #20244320C2semidirect
6. #20244202C2semidirect
7. #20243824C2semidirect
8. #20243809C2semidirect
9. #20243705C2semidirect
10. #20243695C2semidirect
11. #20243385C2semidirect
12. #20243326C2semidirect
13. #20243318C2semidirect
14. #20243216C2semidirect
15. D4×C4⋊C4×C47C2semidirect
18. C22×#10625329C22semidirect
21. #15689769C4semidirect
31. C2×C4⋊(C47⋊C8)C22semidirect
33. C2×#13093947C22semidirect
34. C2×#13093947C22semidirect
35. C2×#13093947C22semidirect
36. C2×#13093947C22semidirect
47. C2×C22⋊(C47⋊C8)C22semidirect
48. C2×#13093935C22semidirect
49. #15688885C22semidirect
50. #15688885C22semidirect
51. #15688885C22semidirect
52. #15688885C22semidirect
56. C22×C4⋊C4×C47C22semidirect
60. C47×#384C22semidirect
62. C47×#380C22semidirect
63. C4×C4⋊C4×C47C22semidirect
70. C2×#10625350C2×C4semidirect
78. C22×D188C2×C4semidirect
96. #13094012C2×C4semidirect
99. #13094003C2×C4semidirect
101. #13093998C2×C4semidirect
105. C4×D188C2×C4semidirect
126. #13093944D4semidirect
379. D188C4×D4semidirect
404. C22×C47#417semidirect
445. D4×C4⋊C4D47semidirect
483. C22×C4⋊C4C2×D47semidirect
507. #384C2×D47semidirect
509. #380C2×D47semidirect
510. C4×C4⋊C4C2×D47semidirect
515. C47#22419semidirect
870. C22#15689122semidirect

Maximal subgroups

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

subgroupindex
C2×#156897692
C2×#156891952
C2×#156891222
C22×#130939442
#202443202
#202442022
#202438242
#202438092
#202437052
#202436952
#202433852
#202433262
#202433182
#202432162
D4×C4⋊C4×C472
#2241947