Finite Group Databasebeta

← #26231758

Subgroups — #26231758

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×#15689195C211yesmaximal, characteristic, complemented
2C2×#15689124C211yesmaximal, characteristic, complemented
3C22×#13093945C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic47C211yesmaximal, characteristic, complemented
5#20244321C211yesmaximal, characteristic, complemented
6#20244205C211yesmaximal, characteristic, complemented
7#20243827C211yesmaximal, characteristic, complemented
8#20243812C211yesmaximal, characteristic, complemented
9#20243706C211yesmaximal, characteristic, complemented
10#20243696C211yesmaximal, characteristic, complemented
11#20243388C211yesmaximal, characteristic, complemented
12#20243328C211yesmaximal, characteristic, complemented
13#20243319C211yesmaximal, characteristic, complemented
14#20243213C211yesmaximal, characteristic, complemented
15C2×C47×#546C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic, complemented
17C23×C47⋊C8C2211yescharacteristic
18C2×D4×Dic47—21no—
19C22×C4⋊Dic47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic, complemented
21#15689195—24no—
22C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
23#15689124—24no—
24C2×#13093948C2211yescharacteristic, complemented
25C2×#13093948C2211yescharacteristic, complemented
26C2×#13093948C2211yescharacteristic, complemented
27C2×#13093948C2211yescharacteristic, complemented
28C2×#13093945—24no—
29C2×#13093945C2211yescharacteristic
30C2×#13093945C2211yescharacteristic
31C2×#13093945C2211yescharacteristic
32C2×#13093945C2211yescharacteristic
33C2×#13093945C2211yescharacteristic
34C2×#13093945C2211yescharacteristic
35C2×#13093945C2211yescharacteristic
36C2×#13093945C2211yescharacteristic
37C2×C22⋊(C47⋊C8)C2211yescharacteristic
38C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
39C2×#13093935C2211yescharacteristic, complemented
40#15689022—21no—
41#15688998—21no—
42#15688998—21no—
43#15688993C2211yescharacteristic, complemented
44#15688983C2211yescharacteristic
45#15688983C2211yescharacteristic, complemented
46C4×C4⋊Dic47C2211yescharacteristic, complemented
47#15688885C2211yescharacteristic, complemented
48#15688885C2211yescharacteristic, complemented
49#15688885C2211yescharacteristic, complemented
50#15688885C2211yescharacteristic, complemented
51C22×#41×C47C2211yescharacteristic
52C23×D4×C47C2211yescharacteristic
53C47×#546—24no—
54C47×#546C418yescomplemented
55C2×#124×C47C2211yescharacteristic
56C2×#123×C47—21no—
57C2×C22⋊Q8×C47C2211yescharacteristic
58C2×#121×C47—21no—
59C2×#121×C47C2211yescharacteristic
60C2×#120×C47—21no—
61C2×C4×D4×C47C2211yescharacteristic
62C2×C4×D4×C47C2211yescharacteristic
63C22×C22⋊C4×C47—21no—
64C23×Dic47—21no—
65C23×Dic47—21no—
66C2×#10625329—22no—
67C2×#10625329—22no—
68C2×#10625329—41no—
69C22×C47⋊C8—22no—
70C22×C47⋊C8—22no—
71C22×C47⋊C8—41no—
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76D4×Dic47—44no—
77C2×C4⋊Dic47—22no—
78C2×C4⋊Dic47—22no—
79C2×C4⋊Dic47—21no—
80C2×C4⋊Dic47—21no—
81C2×C4⋊Dic47—21no—
82C2×C4⋊Dic47—21no—
83C2×C4⋊Dic47—41no—
84C2×C4⋊Dic47—41no—
85C2×C4⋊Dic47C2311yescharacteristic
86C2×C4⋊Dic47C2311yescharacteristic
87C2×C4⋊Dic47C2311yescharacteristic
88C2×C4⋊Dic47C2311yescharacteristic
89C2×C22⋊Dic47—21no—
90C2×C22⋊Dic47—21no—
91C2×C4×Dic47—21no—
92C4⋊(C47⋊C8)—22no—
93#13093948—22no—
94#13093948—22no—
95#13093948—41no—
96#13093948—41no—
97#13093945—22no—
98#13093945—22no—
99#13093945—22no—
100#13093945—22no—
101#13093945—22no—
102#13093945—41no—
103#13093945—41no—
104#13093945D414yescomplemented
105C22⋊(C47⋊C8)—22no—
106C22⋊(C47⋊C8)—22no—
107#13093935—22no—
108C47⋊#95—21no—
109C47⋊#95—21no—
110C47⋊#95—21no—
111C25×C47—21no—
112C2×#41×C47—22no—
113C2×#41×C47—22no—
114C2×#41×C47—22no—
115C2×#41×C47—41no—
116C2×#41×C47—41no—
117C2×#41×C47C2×C414yescomplemented
118C22×Q8×C47C2311yescharacteristic
119C22×D4×C47—22no—
120C22×D4×C47—22no—
121C22×D4×C47—21no—
122C22×D4×C47—21no—
123C22×D4×C47—21no—
124C22×D4×C47—22no—
125C22×D4×C47—41no—
126C22×D4×C47—41no—
127C22×D4×C47C2×C414yescomplemented
128C22×D4×C47D411yescharacteristic
129C22×D4×C47C2311yescharacteristic
130C22×D4×C47C2311yescharacteristic
131C23×C4×C47—21no—
132C23×C4×C47—21no—
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135#124×C47—22no—
136#124×C47C2×C414yescomplemented
137#123×C47—28no—
138C22⋊Q8×C47—22no—
139C22⋊Q8×C47C2×C414yescomplemented
140#121×C47—22no—
141#121×C47—28no—
142#121×C47C2×C414yescomplemented
143#120×C47—28no—
144C4×D4×C47—22no—
145C4×D4×C47C2×C414yes—
146C4×D4×C47C2×C414yescomplemented
147C4×D4×C47D414yes—
148C2×C4⋊C4×C47—21no—
149C2×C4⋊C4×C47D411yescharacteristic
150C2×C4⋊C4×C47C2311yescharacteristic
151C2×C22⋊C4×C47—21no—
152C2×C22⋊C4×C47—21no—
153C2×C22⋊C4×C47—21no—
154C2×C22⋊C4×C47—21no—
155C2×C22⋊C4×C47—21no—
156C2×C22⋊C4×C47—28no—
157C2×C22⋊C4×C47D411yescharacteristic
158C2×C22⋊C4×C47D411yescharacteristic
159C2×C42×C47C2311yescharacteristic
160C24×C47—21no—
161C24×C47—21no—
162C24×C47—24no—
163C24×C47—42no—
164C24×C47—42no—
165C24×C47—42no—
166C24×C47—42no—
167C24×C47—81no—
168C24×C47—81no—
169C24×C47C2×D411yescharacteristic
170C24×C47C2×D411yescharacteristic
171#41×C47—28no—
172#41×C47—44no—
173#41×C47—44no—
174#41×C47—44no—
175C2×Q8×C47—21no—
176C2×Q8×C47—21no—
177C2×Q8×C47—21no—
178C2×Q8×C47—21no—
179C2×Q8×C47—21no—
180C2×Q8×C47C22×C412yes—
181C2×D4×C47—22no—
182C2×D4×C47—22no—
183C2×D4×C47—28no—
184C2×D4×C47—24no—
185C2×D4×C47—24no—
186C2×D4×C47—24no—
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—21no—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—21no—
193C2×D4×C47—21no—
194C2×D4×C47—21no—
195C2×D4×C47—44no—
196C2×D4×C47—44no—
197C2×D4×C47—44no—
198C2×D4×C47—42no—
199C2×D4×C47—42no—
200C2×D4×C47—42no—
201C2×D4×C47—42no—
202C2×D4×C47—81no—
203C2×D4×C47—81no—
204C2×D4×C47C22⋊C414yes—
205C2×D4×C47C22×C412yes—
206C2×D4×C47C22×C412yes—
207C2×D4×C47C2×D412yes—
208C2×D4×C47#4112yes—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—24no—
220C22×C4×C47—24no—
221C22×C4×C47—42no—
222C22×C4×C47—42no—
223C22×C4×C47—81no—
224C22×C4×C47—81no—
225C22×C4×C47C22×C412yes—
226C22×C4×C47C22×C412yes—
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2×D411yescharacteristic
230C22×C4×C47C2×D411yescharacteristic
231C22×C4×C47C2×D412yes—
232C22×C4×C47C2×D412yes—
233C22×C4×C47C2411yescharacteristic
234C22×Dic47—21no—
235C22×Dic47—21no—
236C22×Dic47—21no—
237C22×Dic47—21no—
238C22×Dic47—42no—
239C22×Dic47—42no—
240C22×Dic47—42no—
241C22×Dic47—42no—
242C22×Dic47—81no—
243C22×Dic47—81no—
244C4⋊C4×C47—24no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47C22⋊C414yes—
247C4⋊C4×C47C22×C412yes—
248C22⋊C4×C47—24no—
249C22⋊C4×C47—24no—
250C22⋊C4×C47—24no—
251C22⋊C4×C47—24no—
252C22⋊C4×C47—24no—
253C22⋊C4×C47C22⋊C414yes—
254C22⋊C4×C47C22⋊C414yes—
255C42×C47C22×C412yes—
256C42×C47C2×D412yes—
257C22⋊Dic47—42no—
258C22⋊Dic47—42no—
259C4⋊Dic47—21no—
260C4⋊Dic47—21no—
261C4⋊Dic47—21no—
262C4⋊Dic47—21no—
263C4⋊Dic47—21no—
264C4⋊Dic47—21no—
265C4⋊Dic47—21no—
266C4⋊Dic47—42no—
267C4⋊Dic47—42no—
268C4⋊Dic47—42no—
269C4⋊Dic47—81no—
270C4⋊Dic47C2×D412yes—
271C4×Dic47—42no—
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—22no—
291C23×C47—21no—
292C23×C47—22no—
293C23×C47—21no—
294C23×C47—22no—
295C23×C47—21no—
296C23×C47—21no—
297C23×C47—21no—
298C23×C47—21no—
299C23×C47—22no—
300C23×C47—48no—
301C23×C47—41no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47—41no—
308C23×C47—41no—
309C23×C47—41no—
310C23×C47—41no—
311C23×C47—48no—
312C23×C47—84no—
313C23×C47—84no—
314C23×C47—84no—
315C23×C47—84no—
316C23×C47—84no—
317C23×C47C2×C22⋊C412yes—
318C23×C47C2×C22⋊C412yes—
319C23×C47AGL(1,ℤ/8)12yes—
320C23×C47#13712yes—
321C23×C47C22×D411yescharacteristic
322Q8×C47—22no—
323Q8×C47—22no—
324Q8×C47—41no—
325Q8×C47—41no—
326D4×C47—28no—
327D4×C47—22no—
328D4×C47—22no—
329D4×C47—22no—
330D4×C47—22no—
331D4×C47—22no—
332D4×C47—48no—
333D4×C47—48no—
334D4×C47—41no—
335D4×C47—41no—
336D4×C47—84no—
337D4×C47C4×D414yescomplemented
338C2×C4×C47—21no—
339C2×C4×C47—21no—
340C2×C4×C47—21no—
341C2×C4×C47—21no—
342C2×C4×C47—21no—
343C2×C4×C47—21no—
344C2×C4×C47—21no—
345C2×C4×C47—21no—
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—48no—
357C2×C4×C47—41no—
358C2×C4×C47—41no—
359C2×C4×C47—41no—
360C2×C4×C47—41no—
361C2×C4×C47—84no—
362C2×C4×C47C2×C22⋊C412yes—
363C2×C4×C47C2×C22⋊C412yes—
364C2×C4×C47C2×C22⋊C412yes—
365C2×C4×C47C2×C22⋊C412yes—
366C2×C4×C47C23×C411yescharacteristic
367C2×C4×C47C22×D411yescharacteristic
368C2×C4×C47C22×D411yescharacteristic
369C2×C4×C47C2×#4111yescharacteristic
370C2×C4×C47H(5,𝔽2)11yescharacteristic
371C2×C4×C47H(5,𝔽2)11yescharacteristic
372C2×Dic47—22no—
373C2×Dic47—41no—
374C2×Dic47—41no—
375C2×Dic47—41no—
376C2×Dic47—41no—
377C2×Dic47—41no—
378C2×Dic47—41no—
379C2×Dic47—41no—
380C2×Dic47—41no—
381C2×Dic47—41no—
382C2×Dic47—41no—
383C2×Dic47—41no—
384C2×Dic47—84no—
385C2×Dic47—84no—
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—24no—
399C22×C47—22no—
400C22×C47—22no—
401C22×C47—42no—
402C22×C47—42no—
403C22×C47—41no—
404C22×C47—42no—
405C22×C47—41no—
406C22×C47—42no—
407C22×C47—41no—
408C22×C47—42no—
409C22×C47—41no—
410C22×C47—42no—
411C22×C47—42no—
412C22×C47—42no—
413C22×C47—42no—
414C22×C47—816no—
415C22×C47—81no—
416C22×C47—81no—
417C22×C47—81no—
418C22×C47—81no—
419C22×C47#41714yescomplemented
420C22×C47C22×C22⋊C411yescharacteristic
421C22×C47D4211yescharacteristic
422C22×C47#54611yescharacteristic
423C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C47C2×#13711yescharacteristic
425C22×C47#57611yescharacteristic
426C22×C47#57711yescharacteristic
427C4×C47—22no—
428C4×C47—22no—
429C4×C47—22no—
430C4×C47—22no—
431C4×C47—42no—
432C4×C47—42no—
433C4×C47C2×C4×D411yescharacteristic
434C4×C47#51811yescharacteristic
435C4×C47D4211yescharacteristic
436C4×C47#54611yescharacteristic
437Dic47—42no—
438Dic47—81no—
439Dic47—81no—
440Dic47—81no—
441C2×#546D4711yescharacteristic
442C2×#435—471no—
443C2×#417—471no—
444C22×#102—471no—
445D4×C4⋊C4—471no—
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×C47—44no—
459C2×C47—82no—
460C2×C47D4×C22⋊C411yescharacteristic
461C2×C47C2×#41711yescharacteristic
462C2×C47#289711yescharacteristic
463C2×C47#326411yescharacteristic
464C2×C47#326611yescharacteristic
465C2×C47#330611yescharacteristic
466C2×C47#331411yescharacteristic
467C22×#41C2×D4711yescharacteristic
468C23×D4C2×D4711yescharacteristic
469C22×M16—471no—
470C23×C8—471no—
471#546—24no—
472#546Dic4718yescomplemented
473C2×#124C2×D4711yescharacteristic
474C2×#123—21no—
475C2×C22⋊Q8C2×D4711yescharacteristic
476C2×#121—21no—
477C2×#121C2×D4711yescharacteristic
478C2×#120—21no—
479C2×C4×D4—941no—
480C2×C4×D4C2×D4711yescharacteristic
481C2×C4×D4C2×D4711yescharacteristic
482C22×C4⋊C4—471no—
483C22×C4⋊C4—471no—
484C22×C22⋊C4—21no—
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—941no—
505#385—941no—
506#385—941no—
507#384—471no—
508#380—471no—
509#380—471no—
510C4×C4⋊C4—471no—
511#340—471no—
512#340—471no—
513#340—471no—
514#340—471no—
515C47#2241911yescharacteristic, complemented, Sylow
516C25—21no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41C2×Dic4714yescomplemented
523C22×Q8C22×D4711yescharacteristic
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C2×Dic4714yescomplemented
533C22×D4C22⋊D4711yescharacteristic
534C22×D4C22×D4711yescharacteristic
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—22no—
553#124C2×Dic4714yescomplemented
554#123—28no—
555C22⋊Q8—22no—
556C22⋊Q8C2×Dic4714yescomplemented
557#121—22no—
558#121—28no—
559#121C2×Dic4714yescomplemented
560#120—28no—
561C4×D4—22no—
562C4×D4—1884no—
563C4×D4C2×Dic4714yes—
564C4×D4C2×Dic4714yescomplemented
565C4×D4C22⋊D4714yes—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—471no—
568C2×C4⋊C4—471no—
569C2×C4⋊C4—471no—
570C2×C4⋊C4—471no—
571C2×C4⋊C4—942no—
572C2×C4⋊C4—942no—
573C2×C4⋊C4—941no—
574C2×C4⋊C4—941no—
575C2×C4⋊C4—941no—
576C2×C4⋊C4—941no—
577C2×C4⋊C4—1881no—
578C2×C4⋊C4—1881no—
579C2×C4⋊C4C22⋊D4711yescharacteristic
580C2×C4⋊C4C22×D4711yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—28no—
587C2×C22⋊C4—941no—
588C2×C22⋊C4—941no—
589C2×C22⋊C4C22⋊D4711yescharacteristic
590C2×C22⋊C4C22⋊D4711yescharacteristic
591C2×C42—941no—
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—941no—
610#95—941no—
611#95—941no—
612C24—21no—
613C24—21no—
614C24—24no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24C2×C22⋊D4711yescharacteristic
622C24C2×C22⋊D4711yescharacteristic
623#41—28no—
624#41—44no—
625#41—44no—
626#41—44no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C22×Dic4712yes—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—28no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—81no—
655C2×D4—81no—
656C2×D4C22⋊Dic4714yes—
657C2×D4D4×D4712yes—
658C2×D4#1062535212yes—
659C2×D4C22×Dic4712yes—
660C2×D4C22×Dic4712yes—
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—24no—
672C22×C4—24no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4—81no—
677C22×C4—941no—
678C22×C4—941no—
679C22×C4—941no—
680C22×C4—941no—
681C22×C4—3761no—
682C22×C4—3761no—
683C22×C4—1882no—
684C22×C4—1882no—
685C22×C4—1882no—
686C22×C4—1882no—
687C22×C4C22×Dic4712yes—
688C22×C4C22×Dic4712yes—
689C22×C4C2×C22⋊D4711yescharacteristic
690C22×C4C2×C22⋊D4711yescharacteristic
691C22×C4C2×C22⋊D4711yescharacteristic
692C22×C4C2×C22⋊D4711yescharacteristic
693C22×C4C2×C22⋊D4712yes—
694C22×C4C2×C22⋊D4712yes—
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—24no—
711C4⋊C4—21no—
712C4⋊C4—472no—
713C4⋊C4—941no—
714C4⋊C4—941no—
715C4⋊C4—941no—
716C4⋊C4—941no—
717C4⋊C4—941no—
718C4⋊C4—941no—
719C4⋊C4—941no—
720C4⋊C4—3761no—
721C4⋊C4—1882no—
722C4⋊C4—1882no—
723C4⋊C4—1882no—
724C4⋊C4C22⋊Dic4714yes—
725C4⋊C4C22×Dic4712yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—1882no—
732C22⋊C4—1882no—
733C22⋊C4C22⋊Dic4714yes—
734C22⋊C4C22⋊Dic4714yes—
735C42—1882no—
736C42C22×Dic4712yes—
737C42C2×C22⋊D4712yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—22no—
744C23—21no—
745C23—22no—
746C23—22no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—22no—
752C23—48no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—48no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23C2×C22⋊Dic4712yes—
770C23C2×C22⋊Dic4712yes—
771C23#1309404912yes—
772C23#1309405412yes—
773C23C22×C22⋊D4711yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—28no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4D4×Dic4714yescomplemented
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—22no—
808C2×C4—48no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—84no—
814C2×C4—942no—
815C2×C4—3764no—
816C2×C4—3764no—
817C2×C4—1881no—
818C2×C4—1881no—
819C2×C4—1881no—
820C2×C4—1881no—
821C2×C4—1881no—
822C2×C4—1881no—
823C2×C4—1881no—
824C2×C4—1881no—
825C2×C4—1881no—
826C2×C4—1881no—
827C2×C4—1881no—
828C2×C4C2×C22⋊Dic4712yes—
829C2×C4C2×C22⋊Dic4712yes—
830C2×C4C2×C22⋊Dic4712yes—
831C2×C4C2×C22⋊Dic4712yes—
832C2×C4C23×Dic4711yescharacteristic
833C2×C4C2×D4×D4711yescharacteristic
834C2×C4C22×C22⋊D4711yescharacteristic
835C2×C4C2×#1062535211yescharacteristic
836C2×C4#1309406911yescharacteristic
837C2×C4#1309406911yescharacteristic
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—24no—
851C22—22no—
852C22—42no—
853C22—41no—
854C22—42no—
855C22—41no—
856C22—42no—
857C22—41no—
858C22—42no—
859C22—41no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—816no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22#1568912414yescomplemented
871C22C22×C22⋊Dic4711yescharacteristic
872C22D4×C22⋊D4711yescharacteristic
873C22#1568976711yescharacteristic
874C22C2×#1309404911yescharacteristic
875C22C2×#1309405411yescharacteristic
876C22#1568992611yescharacteristic
877C22#1568993411yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—3761no—
885C4—3761no—
886C4—3761no—
887C4—1882no—
888C4C2×D4×Dic4711yescharacteristic
889C4#1568959811yescharacteristic
890C4D4×C22⋊D4711yescharacteristic
891C4#1568976711yescharacteristic
892C2—24no—
893C2—42no—
894C2—44no—
895C2—82no—
896C2D4×C22⋊Dic4711yescharacteristic
897C2C2×#1568912411yescharacteristic
898C2#2025191411yescharacteristic
899C2#2025486911yescharacteristic
900C2#2025489411yescharacteristic
901C2#2025534911yescharacteristic
902C2#2025546911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC2×C47×#546C2
socleC23×C47C22×D4
cosocleC22×C4×C47C24
hypercenterC2×#546D47
hypocenterC47#22419
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#15689195C2semidirect
2. C2×#15689124C2semidirect
3. C22×#13093945C2semidirect
4. D4×C4⋊Dic47C2semidirect
5. #20244321C2semidirect
6. #20244205C2semidirect
7. #20243827C2semidirect
8. #20243812C2semidirect
9. #20243706C2semidirect
10. #20243696C2semidirect
11. #20243388C2semidirect
12. #20243328C2semidirect
13. #20243319C2semidirect
14. #20243213C2semidirect
16. C22×#10625329C22semidirect
20. C22×C4⋊Dic47C22semidirect
22. C2×C4⋊(C47⋊C8)C22semidirect
24. C2×#13093948C22semidirect
25. C2×#13093948C22semidirect
26. C2×#13093948C22semidirect
27. C2×#13093948C22semidirect
38. C2×C22⋊(C47⋊C8)C22semidirect
39. C2×#13093935C22semidirect
43. #15688993C22semidirect
45. #15688983C22semidirect
46. C4×C4⋊Dic47C22semidirect
47. #15688885C22semidirect
48. #15688885C22semidirect
49. #15688885C22semidirect
50. #15688885C22semidirect
54. C47×#546C4semidirect
104. #13093945D4semidirect
117. C2×#41×C47C2×C4semidirect
127. C22×D4×C47C2×C4semidirect
136. #124×C47C2×C4semidirect
139. C22⋊Q8×C47C2×C4semidirect
142. #121×C47C2×C4semidirect
146. C4×D4×C47C2×C4semidirect
337. D4×C47C4×D4semidirect
419. C22×C47#417semidirect
472. #546Dic47semidirect
515. C47#22419semidirect
522. C2×#41C2×Dic47semidirect
532. C22×D4C2×Dic47semidirect
553. #124C2×Dic47semidirect
556. C22⋊Q8C2×Dic47semidirect
559. #121C2×Dic47semidirect
564. C4×D4C2×Dic47semidirect
789. D4D4×Dic47semidirect
870. C22#15689124semidirect

Maximal subgroups

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

subgroupindex
C2×#156891952
C2×#156891242
C22×#130939452
D4×C4⋊Dic472
#202443212
#202442052
#202438272
#202438122
#202437062
#202436962
#202433882
#202433282
#202433192
#202432132
C2×C47×#5462
#2241947