Finite Group Databasebeta

← #26231818

Subgroups — #26231818

Order 12032.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689195C211yesmaximal, characteristic, complemented
2C2×#15689128C211yesmaximal, characteristic, complemented
3C22×#13093945C211yesmaximal, characteristic, complemented
4#20246317C211yesmaximal, characteristic, complemented
5#20244316C211yesmaximal, characteristic, complemented
6#20244213C211yesmaximal, characteristic, complemented
7#20243827C211yesmaximal, characteristic, complemented
8#20243817C211yesmaximal, characteristic, complemented
9#20243711C211yesmaximal, characteristic, complemented
10#20243706C211yesmaximal, characteristic, complemented
11#20243398C211yesmaximal, characteristic, complemented
12#20243319C211yesmaximal, characteristic, complemented
13#20243319C211yesmaximal, characteristic, complemented
14#20243213C211yesmaximal, characteristic, complemented
15C2×D42×C47C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic, complemented
17C23×C47⋊C8C2211yescharacteristic, complemented
18C2×#13093983C2211yescharacteristic, complemented
19C22×C4⋊Dic47C2211yescharacteristic, complemented
20#15689195—24no—
21C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
22#15689128—24no—
23C2×#13093945—24no—
24C2×#13093945C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×#13093945C2211yescharacteristic, complemented
29C2×#13093945C2211yescharacteristic, complemented
30C2×#13093945C2211yescharacteristic, complemented
31C2×#13093945C2211yescharacteristic, complemented
32C2×#13093945C2211yescharacteristic, complemented
33C2×#13093945C2211yescharacteristic, complemented
34C2×#13093945C2211yescharacteristic, complemented
35C2×#13093945C2211yescharacteristic, complemented
36C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
37C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
38C2×#13093935C2211yescharacteristic, complemented
39#15689016—21no—
40#15689009—21no—
41#15689003—21no—
42#15688989C2211yescharacteristic, complemented
43#15688983C2211yescharacteristic, complemented
44#15688983C2211yescharacteristic, complemented
45C4×C4⋊Dic47C2211yescharacteristic, complemented
46C22⋊C4×Dic47—21no—
47#15688885C2211yescharacteristic, complemented
48#15688885C2211yescharacteristic, complemented
49#15688885C2211yescharacteristic, complemented
50#15688885C2211yescharacteristic, complemented
51C23×D4×C47—21no—
52C23×D4×C47C2211yescharacteristic
53C23×D4×C47C2211yescharacteristic
54D42×C47—24no—
55D42×C47C418yescomplemented
56C2×#127×C47C2211yescharacteristic
57C2×#121×C47—21no—
58C2×#121×C47C2211yescharacteristic
59C2×#121×C47C2211yescharacteristic
60C2×#120×C47—21no—
61C2×#120×C47—21no—
62C2×C4×D4×C47C2211yescharacteristic
63C2×C4×D4×C47C2211yescharacteristic
64C23×Dic47—21no—
65C2×#10625329—22no—
66C2×#10625329—22no—
67C2×#10625329—41no—
68C22×C47⋊C8—22no—
69C22×C47⋊C8—22no—
70C22×C47⋊C8—41no—
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75#13093983—22no—
76#13093983—41no—
77C2×C4⋊Dic47—22no—
78C2×C4⋊Dic47—21no—
79C2×C4⋊Dic47—41no—
80C2×C4⋊Dic47C2311yescharacteristic
81C2×C4⋊Dic47C2311yescharacteristic
82C2×C4⋊Dic47C2311yescharacteristic
83C2×C4⋊Dic47C2311yescharacteristic
84C2×C22⋊Dic47—21no—
85C2×C22⋊Dic47—21no—
86C2×C22⋊Dic47—21no—
87C2×C4×Dic47—21no—
88C2×C4×Dic47—21no—
89C4⋊(C47⋊C8)—22no—
90#13093945—22no—
91#13093945—22no—
92#13093945—22no—
93#13093945—22no—
94#13093945—22no—
95#13093945—22no—
96#13093945—22no—
97#13093945—41no—
98#13093945—41no—
99#13093945—41no—
100#13093945—41no—
101#13093945D414yescomplemented
102C22⋊(C47⋊C8)—22no—
103C22⋊(C47⋊C8)—22no—
104#13093935—22no—
105C47⋊#95—21no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C47⋊#95—21no—
109C47⋊#95—21no—
110C25×C47—21no—
111C25×C47—21no—
112C22×D4×C47—22no—
113C22×D4×C47—22no—
114C22×D4×C47—22no—
115C22×D4×C47—22no—
116C22×D4×C47—21no—
117C22×D4×C47—21no—
118C22×D4×C47—28no—
119C22×D4×C47—21no—
120C22×D4×C47—21no—
121C22×D4×C47—21no—
122C22×D4×C47—22no—
123C22×D4×C47—22no—
124C22×D4×C47—21no—
125C22×D4×C47—41no—
126C22×D4×C47—41no—
127C22×D4×C47—41no—
128C22×D4×C47—41no—
129C22×D4×C47—44no—
130C22×D4×C47—44no—
131C22×D4×C47C2×C414yes—
132C22×D4×C47C2×C414yescomplemented
133C22×D4×C47D411yescharacteristic
134C22×D4×C47C2311yescharacteristic
135C22×D4×C47C2311yescharacteristic
136C22×D4×C47C2311yescharacteristic
137C23×C4×C47—21no—
138C23×C4×C47C2311yescharacteristic
139C23×C4×C47C2311yescharacteristic
140#127×C47—22no—
141#127×C47C2×C414yescomplemented
142#121×C47—22no—
143#121×C47—22no—
144#121×C47—28no—
145#121×C47C2×C414yes—
146#121×C47C2×C414yescomplemented
147#120×C47—28no—
148#120×C47—28no—
149C4×D4×C47—22no—
150C4×D4×C47C2×C414yes—
151C4×D4×C47C2×C414yescomplemented
152C4×D4×C47D414yes—
153C2×C4⋊C4×C47D411yescharacteristic
154C2×C4⋊C4×C47C2311yescharacteristic
155C2×C22⋊C4×C47—21no—
156C2×C22⋊C4×C47—21no—
157C2×C22⋊C4×C47—21no—
158C2×C22⋊C4×C47D411yescharacteristic
159C2×C22⋊C4×C47D411yescharacteristic
160C2×C42×C47C2311yescharacteristic
161C24×C47—21no—
162C24×C47—21no—
163C24×C47—21no—
164C24×C47—24no—
165C24×C47—24no—
166C24×C47—42no—
167C24×C47—42no—
168C24×C47—42no—
169C24×C47—42no—
170C24×C47—42no—
171C24×C47—42no—
172C24×C47—42no—
173C24×C47—42no—
174C24×C47—81no—
175C24×C47—81no—
176C24×C47—81no—
177C24×C47—81no—
178C24×C47C2×D411yescharacteristic
179C24×C47C2×D411yescharacteristic
180C2×D4×C47—22no—
181C2×D4×C47—22no—
182C2×D4×C47—28no—
183C2×D4×C47—28no—
184C2×D4×C47—24no—
185C2×D4×C47—24no—
186C2×D4×C47—24no—
187C2×D4×C47—24no—
188C2×D4×C47—24no—
189C2×D4×C47—24no—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—21no—
193C2×D4×C47—21no—
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47—21no—
197C2×D4×C47—21no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—21no—
201C2×D4×C47—21no—
202C2×D4×C47—21no—
203C2×D4×C47—44no—
204C2×D4×C47—44no—
205C2×D4×C47—44no—
206C2×D4×C47—44no—
207C2×D4×C47—44no—
208C2×D4×C47—44no—
209C2×D4×C47—42no—
210C2×D4×C47—42no—
211C2×D4×C47—42no—
212C2×D4×C47—42no—
213C2×D4×C47—42no—
214C2×D4×C47—42no—
215C2×D4×C47—432no—
216C2×D4×C47—42no—
217C2×D4×C47—42no—
218C2×D4×C47—42no—
219C2×D4×C47—42no—
220C2×D4×C47—81no—
221C2×D4×C47—81no—
222C2×D4×C47C22⋊C414yes—
223C2×D4×C47C22×C412yes—
224C2×D4×C47C22×C412yes—
225C2×D4×C47C22×C412yes—
226C2×D4×C47C2×D412yes—
227C2×D4×C47#4112yes—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47—21no—
231C22×C4×C47—21no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47—21no—
237C22×C4×C47—24no—
238C22×C4×C47—42no—
239C22×C4×C47—42no—
240C22×C4×C47C22×C412yes—
241C22×C4×C47C22×C412yes—
242C22×C4×C47C2×D411yescharacteristic
243C22×C4×C47C2×D411yescharacteristic
244C22×C4×C47C2×D411yescharacteristic
245C22×C4×C47C2×D411yescharacteristic
246C22×C4×C47C2×D412yes—
247C22×C4×C47C2×D412yes—
248C22×C4×C47C2411yescharacteristic
249C22×Dic47—21no—
250C22×Dic47—21no—
251C22×Dic47—21no—
252C22×Dic47—21no—
253C22×Dic47—42no—
254C22×Dic47—42no—
255C22×Dic47—81no—
256C4⋊C4×C47—21no—
257C4⋊C4×C47C22⋊C414yes—
258C4⋊C4×C47C22×C412yes—
259C22⋊C4×C47—24no—
260C22⋊C4×C47—24no—
261C22⋊C4×C47—24no—
262C22⋊C4×C47C22⋊C414yes—
263C22⋊C4×C47C22⋊C414yes—
264C42×C47C22×C412yes—
265C42×C47C2×D412yes—
266C22⋊Dic47—42no—
267C22⋊Dic47—42no—
268C22⋊Dic47—81no—
269C4⋊Dic47—21no—
270C4⋊Dic47—21no—
271C4⋊Dic47—21no—
272C4⋊Dic47—21no—
273C4⋊Dic47—21no—
274C4⋊Dic47—21no—
275C4⋊Dic47—21no—
276C4⋊Dic47—42no—
277C4⋊Dic47C2×D412yescomplemented
278C4×Dic47—42no—
279C4×Dic47—81no—
280#10625329—44no—
281C2×C47⋊C8—21no—
282C2×C47⋊C8—21no—
283C2×C47⋊C8—21no—
284C2×C47⋊C8—21no—
285C2×C47⋊C8—21no—
286C2×C47⋊C8—21no—
287C2×C47⋊C8—21no—
288C2×C47⋊C8—21no—
289C2×C47⋊C8—21no—
290C2×C47⋊C8—21no—
291C2×C47⋊C8—21no—
292C2×C47⋊C8—44no—
293C2×C47⋊C8C2×D412yescomplemented
294C23×C47—21no—
295C23×C47—21no—
296C23×C47—21no—
297C23×C47—21no—
298C23×C47—22no—
299C23×C47—21no—
300C23×C47—22no—
301C23×C47—21no—
302C23×C47—22no—
303C23×C47—21no—
304C23×C47—21no—
305C23×C47—21no—
306C23×C47—21no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—48no—
310C23×C47—48no—
311C23×C47—48no—
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×C47—41no—
325C23×C47—41no—
326C23×C47—41no—
327C23×C47—41no—
328C23×C47—48no—
329C23×C47—84no—
330C23×C47—84no—
331C23×C47—84no—
332C23×C47—84no—
333C23×C47—84no—
334C23×C47—84no—
335C23×C47—84no—
336C23×C47—84no—
337C23×C47—84no—
338C23×C47—84no—
339C23×C47C2×C22⋊C412yes—
340C23×C47C2×C22⋊C412yes—
341C23×C47AGL(1,ℤ/8)12yes—
342C23×C47AGL(1,ℤ/8)12yes—
343C23×C47C22×D411yescharacteristic
344D4×C47—28no—
345D4×C47—22no—
346D4×C47—22no—
347D4×C47—22no—
348D4×C47—22no—
349D4×C47—22no—
350D4×C47—22no—
351D4×C47—22no—
352D4×C47—48no—
353D4×C47—48no—
354D4×C47—48no—
355D4×C47—48no—
356D4×C47—48no—
357D4×C47—41no—
358D4×C47—41no—
359D4×C47—41no—
360D4×C47—41no—
361D4×C47—84no—
362D4×C47C4×D414yes—
363C2×C4×C47—21no—
364C2×C4×C47—21no—
365C2×C4×C47—21no—
366C2×C4×C47—21no—
367C2×C4×C47—21no—
368C2×C4×C47—21no—
369C2×C4×C47—21no—
370C2×C4×C47—21no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—22no—
376C2×C4×C47—22no—
377C2×C4×C47—22no—
378C2×C4×C47—22no—
379C2×C4×C47—22no—
380C2×C4×C47—48no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47C2×C22⋊C412yes—
384C2×C4×C47C2×C22⋊C412yes—
385C2×C4×C47C2×C22⋊C412yes—
386C2×C4×C47C2×C22⋊C412yes—
387C2×C4×C47C23×C411yescharacteristic
388C2×C4×C47C22×D411yescharacteristic
389C2×C4×C47C22×D411yescharacteristic
390C2×C4×C47C2×#4111yescharacteristic
391C2×C4×C47H(5,𝔽2)11yescharacteristic
392C2×C4×C47H(5,𝔽2)11yescharacteristic
393C2×Dic47—22no—
394C2×Dic47—41no—
395C2×Dic47—41no—
396C2×Dic47—41no—
397C2×Dic47—41no—
398C2×Dic47—41no—
399C2×Dic47—41no—
400C2×Dic47—41no—
401C2×Dic47—41no—
402C2×Dic47—41no—
403C2×Dic47—41no—
404C2×Dic47—41no—
405C2×Dic47—84no—
406C47⋊C8—22no—
407C47⋊C8—41no—
408C47⋊C8—41no—
409C47⋊C8—41no—
410#22423—471nomaximal, Sylow
411C22×C47—22no—
412C22×C47—22no—
413C22×C47—22no—
414C22×C47—22no—
415C22×C47—22no—
416C22×C47—22no—
417C22×C47—22no—
418C22×C47—24no—
419C22×C47—22no—
420C22×C47—22no—
421C22×C47—42no—
422C22×C47—42no—
423C22×C47—41no—
424C22×C47—42no—
425C22×C47—41no—
426C22×C47—42no—
427C22×C47—41no—
428C22×C47—42no—
429C22×C47—41no—
430C22×C47—42no—
431C22×C47—42no—
432C22×C47—42no—
433C22×C47—42no—
434C22×C47—42no—
435C22×C47—42no—
436C22×C47—42no—
437C22×C47—816no—
438C22×C47—816no—
439C22×C47—81no—
440C22×C47—81no—
441C22×C47—81no—
442C22×C47—81no—
443C22×C47—81no—
444C22×C47—81no—
445C22×C47—81no—
446C22×C47—81no—
447C22×C47#41814yescomplemented
448C22×C47C22×C22⋊C411yescharacteristic
449C22×C47D4211yescharacteristic
450C22×C47#54611yescharacteristic
451C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
452C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
453C22×C47#57611yescharacteristic
454C22×C47#57711yescharacteristic
455C4×C47—22no—
456C4×C47—22no—
457C4×C47—22no—
458C4×C47—22no—
459C4×C47—42no—
460C4×C47C2×C4×D411yescharacteristic
461C4×C47#51811yescharacteristic
462C4×C47D4211yescharacteristic
463C4×C47#54611yescharacteristic
464Dic47—42no—
465Dic47—81no—
466Dic47—81no—
467Dic47—81no—
468C2×D42D4711yescharacteristic
469C2×#435—471no—
470C2×#418—471no—
471C22×#102—471no—
472#2352—471no—
473#1982—471no—
474#1961—471no—
475#1895—471no—
476#1893—471no—
477#1875—471no—
478#1874—471no—
479#1804—471no—
480#1786—471no—
481#1786—471no—
482#1762—471no—
483C2×C47—24no—
484C2×C47—42no—
485C2×C47—44no—
486C2×C47—82no—
487C2×C47—82no—
488C2×C47D4×C22⋊C411yescharacteristic
489C2×C47C2×#41811yescharacteristic
490C2×C47#289711yescharacteristic
491C2×C47#326411yescharacteristic
492C2×C47#326511yescharacteristic
493C2×C47#331011yescharacteristic
494C2×C47#331811yescharacteristic
495C23×D4—21no—
496C23×D4C2×D4711yescharacteristic
497C23×D4C2×D4711yescharacteristic
498C22×M16—471no—
499C23×C8—471no—
500D42—24no—
501D42Dic4718yescomplemented
502C2×#127C2×D4711yescharacteristic
503C2×#121—21no—
504C2×#121C2×D4711yescharacteristic
505C2×#121C2×D4711yescharacteristic
506C2×#120—21no—
507C2×#120—21no—
508C2×C4×D4C2×D4711yescharacteristic
509C2×C4×D4C2×D4711yescharacteristic
510C2×#117—471no—
511C22×C4⋊C4—471no—
512#435—944no—
513C2×C4⋊C8—471no—
514#418—944no—
515C2×#102—471no—
516C2×#102—471no—
517C2×#102—471no—
518C2×#102—471no—
519C2×#102—471no—
520C2×#102—471no—
521C2×#102—471no—
522C2×#102—471no—
523C2×#102—471no—
524C2×#102—471no—
525C2×#102—471no—
526C2×#102—471no—
527C2×#102—944no—
528C2×C22⋊C8—471no—
529C2×C22⋊C8—471no—
530C2×#97—471no—
531#388—941no—
532#387—941no—
533#386—941no—
534#382—471no—
535#380—471no—
536#380—471no—
537C4×C4⋊C4—471no—
538C4×C22⋊C4—941no—
539#340—471no—
540#340—471no—
541#340—471no—
542#340—471no—
543C47#2242311yescharacteristic, complemented, Sylow
544C25—21no—
545C25—21no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—28no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—21no—
559C22×D4—41no—
560C22×D4—41no—
561C22×D4—41no—
562C22×D4—41no—
563C22×D4—44no—
564C22×D4—44no—
565C22×D4C2×Dic4714yes—
566C22×D4C2×Dic4714yescomplemented
567C22×D4C22⋊D4711yescharacteristic
568C22×D4C22×D4711yescharacteristic
569C22×D4C22×D4711yescharacteristic
570C22×D4C22×D4711yescharacteristic
571C23×C4—21no—
572C23×C4—941no—
573C23×C4C22×D4711yescharacteristic
574C23×C4C22×D4711yescharacteristic
575C2×M16—942no—
576C2×M16—942no—
577C2×M16—1881no—
578C22×C8—471no—
579C22×C8—471no—
580C22×C8—471no—
581C22×C8—471no—
582C22×C8—942no—
583C22×C8—942no—
584C22×C8—1881no—
585#127—22no—
586#127C2×Dic4714yescomplemented
587#121—22no—
588#121—22no—
589#121—28no—
590#121C2×Dic4714yes—
591#121C2×Dic4714yescomplemented
592#120—28no—
593#120—28no—
594C4×D4—22no—
595C4×D4C2×Dic4714yes—
596C4×D4C2×Dic4714yescomplemented
597C4×D4C22⋊D4714yes—
598#117—942no—
599#117—1881no—
600C2×C4⋊C4—471no—
601C2×C4⋊C4—471no—
602C2×C4⋊C4—471no—
603C2×C4⋊C4—471no—
604C2×C4⋊C4—942no—
605C2×C4⋊C4—941no—
606C2×C4⋊C4—1881no—
607C2×C4⋊C4C22⋊D4711yescharacteristic
608C2×C4⋊C4C22×D4711yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—941no—
613C2×C22⋊C4—941no—
614C2×C22⋊C4—941no—
615C2×C22⋊C4C22⋊D4711yescharacteristic
616C2×C22⋊C4C22⋊D4711yescharacteristic
617C2×C42—941no—
618C2×C42—941no—
619C2×C42C22×D4711yescharacteristic
620C4⋊C8—942no—
621#102—474no—
622#102—942no—
623#102—942no—
624#102—942no—
625#102—942no—
626#102—942no—
627#102—942no—
628#102—942no—
629#102—1881no—
630#102—1881no—
631#102—1881no—
632#102—1881no—
633C22⋊C8—942no—
634C22⋊C8—942no—
635#97—942no—
636#95—941no—
637#95—941no—
638#95—941no—
639#95—941no—
640#95—941no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—24no—
645C24—24no—
646C24—42no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24C2×C22⋊D4711yescharacteristic
659C24C2×C22⋊D4711yescharacteristic
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—432no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C22⋊Dic4714yes—
703C2×D4D4×D4712yes—
704C2×D4#1062535212yes—
705C2×D4C22×Dic4712yes—
706C2×D4C22×Dic4712yes—
707C2×D4C22×Dic4712yes—
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—24no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—941no—
721C22×C4—941no—
722C22×C4—941no—
723C22×C4—941no—
724C22×C4—3761no—
725C22×C4—1882no—
726C22×C4—1882no—
727C22×C4C22×Dic4712yes—
728C22×C4C22×Dic4712yes—
729C22×C4C2×C22⋊D4711yescharacteristic
730C22×C4C2×C22⋊D4711yescharacteristic
731C22×C4C2×C22⋊D4711yescharacteristic
732C22×C4C2×C22⋊D4711yescharacteristic
733C22×C4C2×C22⋊D4712yes—
734C22×C4C2×C22⋊D4712yes—
735C22×C4C23×D4711yescharacteristic
736M16—1884no—
737C2×C8—472no—
738C2×C8—941no—
739C2×C8—941no—
740C2×C8—941no—
741C2×C8—941no—
742C2×C8—941no—
743C2×C8—941no—
744C2×C8—941no—
745C2×C8—941no—
746C2×C8—941no—
747C2×C8—941no—
748C2×C8—941no—
749C2×C8—1884no—
750C4⋊C4—21no—
751C4⋊C4—472no—
752C4⋊C4—941no—
753C4⋊C4—941no—
754C4⋊C4—941no—
755C4⋊C4—941no—
756C4⋊C4—941no—
757C4⋊C4—941no—
758C4⋊C4—941no—
759C4⋊C4—1882no—
760C4⋊C4C22⋊Dic4714yes—
761C4⋊C4C22×Dic4712yes—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—3761no—
766C22⋊C4—1882no—
767C22⋊C4—1882no—
768C22⋊C4C22⋊Dic4714yes—
769C22⋊C4C22⋊Dic4714yes—
770C42—3761no—
771C42—1882no—
772C42C22×Dic4712yes—
773C42C2×C22⋊D4712yes—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—21no—
781C23—22no—
782C23—22no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—22no—
788C23—22no—
789C23—48no—
790C23—48no—
791C23—48no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—48no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—84no—
810C23—84no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23C2×C22⋊Dic4712yes—
820C23C2×C22⋊Dic4712yes—
821C23#1309405012yes—
822C23#1309405012yes—
823C23C22×C22⋊D4711yescharacteristic
824D4—28no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—48no—
833D4—48no—
834D4—48no—
835D4—48no—
836D4—48no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—84no—
842D4D4×Dic4714yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—48no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—942no—
864C2×C4—3764no—
865C2×C4—1881no—
866C2×C4—1881no—
867C2×C4—1881no—
868C2×C4—1881no—
869C2×C4—1881no—
870C2×C4—1881no—
871C2×C4—1881no—
872C2×C4—1881no—
873C2×C4—1881no—
874C2×C4—1881no—
875C2×C4—1881no—
876C2×C4C2×C22⋊Dic4712yes—
877C2×C4C2×C22⋊Dic4712yes—
878C2×C4C2×C22⋊Dic4712yes—
879C2×C4C2×C22⋊Dic4712yes—
880C2×C4C23×Dic4711yescharacteristic
881C2×C4C2×D4×D4711yescharacteristic
882C2×C4C22×C22⋊D4711yescharacteristic
883C2×C4C2×#1062535211yescharacteristic
884C2×C4#1309406911yescharacteristic
885C2×C4#1309406911yescharacteristic
886C8—942no—
887C8—1881no—
888C8—1881no—
889C8—1881no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—24no—
899C22—22no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—816no—
917C22—816no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22#1568912814yescomplemented
927C22C22×C22⋊Dic4711yescharacteristic
928C22D4×C22⋊D4711yescharacteristic
929C22#1568976711yescharacteristic
930C22C2×#1309405011yescharacteristic
931C22C2×#1309405011yescharacteristic
932C22#1568992611yescharacteristic
933C22#1568993411yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—42no—
939C4—3761no—
940C4—3761no—
941C4—3761no—
942C4—1882no—
943C4C2×D4×Dic4711yescharacteristic
944C4#1568959811yescharacteristic
945C4D4×C22⋊D4711yescharacteristic
946C4#1568976711yescharacteristic
947C2—24no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—82no—
952C2D4×C22⋊Dic4711yescharacteristic
953C2C2×#1568912811yescharacteristic
954C2#2025191411yescharacteristic
955C2#2025486411yescharacteristic
956C2#2025487911yescharacteristic
957C2#2025540911yescharacteristic
958C2#2025552911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC2×D42×C47C2
socleC23×C47C22×D4
cosocleC22×C4×C47C24
hypercenterC2×D42D47
hypocenterC47#22423
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C2×#15689195C2semidirect
2. C2×#15689128C2semidirect
3. C22×#13093945C2semidirect
4. #20246317C2semidirect
5. #20244316C2semidirect
6. #20244213C2semidirect
7. #20243827C2semidirect
8. #20243817C2semidirect
9. #20243711C2semidirect
10. #20243706C2semidirect
11. #20243398C2semidirect
12. #20243319C2semidirect
13. #20243319C2semidirect
14. #20243213C2semidirect
16. C22×#10625329C22semidirect
17. C23×C47⋊C8C22semidirect
18. C2×#13093983C22semidirect
19. C22×C4⋊Dic47C22semidirect
21. C2×C4⋊(C47⋊C8)C22semidirect
28. C2×#13093945C22semidirect
29. C2×#13093945C22semidirect
30. C2×#13093945C22semidirect
31. C2×#13093945C22semidirect
32. C2×#13093945C22semidirect
33. C2×#13093945C22semidirect
34. C2×#13093945C22semidirect
35. C2×#13093945C22semidirect
36. C2×C22⋊(C47⋊C8)C22semidirect
37. C2×C22⋊(C47⋊C8)C22semidirect
38. C2×#13093935C22semidirect
42. #15688989C22semidirect
43. #15688983C22semidirect
44. #15688983C22semidirect
45. C4×C4⋊Dic47C22semidirect
47. #15688885C22semidirect
48. #15688885C22semidirect
49. #15688885C22semidirect
50. #15688885C22semidirect
55. D42×C47C4semidirect
101. #13093945D4semidirect
132. C22×D4×C47C2×C4semidirect
141. #127×C47C2×C4semidirect
146. #121×C47C2×C4semidirect
151. C4×D4×C47C2×C4semidirect
277. C4⋊Dic47C2×D4semidirect
293. C2×C47⋊C8C2×D4semidirect
447. C22×C47#418semidirect
501. D42Dic47semidirect
543. C47#22423semidirect
566. C22×D4C2×Dic47semidirect
586. #127C2×Dic47semidirect
591. #121C2×Dic47semidirect
596. C4×D4C2×Dic47semidirect
926. C22#15689128semidirect

Maximal subgroups

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

subgroupindex
C2×#156891952
C2×#156891282
C22×#130939452
#202463172
#202443162
#202442132
#202438272
#202438172
#202437112
#202437062
#202433982
#202433192
#202432132
C2×D42×C472
#2242347