Finite Group Databasebeta

← #26232590

Subgroups — #26232590

Order 12032.

1258 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689819C211yesmaximal, characteristic
2C2×#15689195C211yesmaximal, characteristic, complemented
3#20244356C211yesmaximal, characteristic, complemented
4#20244345C211yesmaximal, characteristic, complemented
5#20243824C211yesmaximal, characteristic, complemented
6#20243814C211yesmaximal, characteristic, complemented
7#20243705C211yesmaximal, characteristic, complemented
8#20243705C211yesmaximal, characteristic, complemented
9#20243480C211yesmaximal, characteristic, complemented
10#20243476C211yesmaximal, characteristic, complemented
11#20243385C211yesmaximal, characteristic, complemented
12#20243216C211yesmaximal, characteristic, complemented
13#20243107C211yesmaximal, characteristic, complemented
14C2×#15688885C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C47C211yesmaximal, characteristic, complemented
16C22×#10625329C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic
18#15689819—24no—
19#15689819C418yescomplemented
20C2×#13094019—21no—
21C2×#13094016C2211yescharacteristic
22C2×#13094006—21no—
23C2×#13093998C2211yescharacteristic
24C2×#13093998C2211yescharacteristic
25C2×#13093996—21no—
26C2×C4×D188C2211yescharacteristic
27C2×(C22⋊D47)⋊C4—21no—
28C2×#13093983C2211yescharacteristic
29C22×C4⋊Dic47C2211yescharacteristic
30#15689195—24no—
31C2×C4⋊(C47⋊C8)C2211yescharacteristic
32C2×#13093944C2211yescharacteristic
33C2×#13093944C2211yescharacteristic
34C2×#13093944C2211yescharacteristic
35C2×#13093944C2211yescharacteristic
36C2×C22⋊(C47⋊C8)C2211yescharacteristic
37C2×C22⋊(C47⋊C8)C2211yescharacteristic
38C2×#13093935C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51C2×C4×D4×C47—21no—
52C2×C4×D4×C47C2211yescharacteristic
53C22×C4⋊C4×C47C2211yescharacteristic
54C22×C4⋊C4×C47C2211yescharacteristic
55C47×#389—21no—
56C47×#385—21no—
57C47×#385—21no—
58C47×#384C2211yescharacteristic
59C47×#380C2211yescharacteristic
60C47×#380C2211yescharacteristic
61C4×C4⋊C4×C47C2211yescharacteristic
62C22×D188C2311yescharacteristic
63C22×C22⋊D47—21no—
64C22×C22⋊D47—21no—
65C23×Dic47—21no—
66C22×C4×D47—21no—
67C2×#10625329—22no—
68C2×#10625329—22no—
69C2×#10625329—41no—
70C22×C47⋊C8—22no—
71C22×C47⋊C8—22no—
72C22×C47⋊C8—41no—
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77#13094019—28no—
78#13094016—22no—
79#13094016C2×C414yescomplemented
80#13094006—28no—
81#13093998—22no—
82#13093998—22no—
83#13093998C2×C414yescomplemented
84#13093998C2×C414yescomplemented
85#13093996—28no—
86C4×D188—22no—
87C4×D188C2×C414yescomplemented
88(C22⋊D47)⋊C4—28no—
89#13093983—22no—
90#13093983C2×C414yescomplemented
91C2×C4⋊Dic47—22no—
92C2×C4⋊Dic47—21no—
93C2×C4⋊Dic47C2×C414yescomplemented
94C2×C4⋊Dic47C2311yescharacteristic
95C2×C4⋊Dic47C2311yescharacteristic
96C2×C4⋊Dic47C2311yescharacteristic
97C2×Dic47⋊C4—21no—
98C2×Dic47⋊C4—21no—
99C2×C22⋊Dic47—21no—
100C2×(C2×D47)⋊C4—21no—
101C2×(C2×D47)⋊C4—21no—
102C2×(C2×D47)⋊C4—21no—
103C2×C4×Dic47—21no—
104C4⋊(C47⋊C8)—22no—
105#13093944—22no—
106#13093944—22no—
107#13093944—41no—
108#13093944—41no—
109C22⋊(C47⋊C8)—22no—
110C22⋊(C47⋊C8)—22no—
111#13093935—22no—
112C22×D4×C47D411yescharacteristic
113C23×C4×C47—21no—
114C23×C4×C47—21no—
115C23×C4×C47C2311yescharacteristic
116C23×C4×C47C2311yescharacteristic
117C4×D4×C47—44no—
118C4×D4×C47C2×C414yes—
119C4×D4×C47D414yes—
120C2×C4⋊C4×C47—22no—
121C2×C4⋊C4×C47—22no—
122C2×C4⋊C4×C47—21no—
123C2×C4⋊C4×C47—21no—
124C2×C4⋊C4×C47—21no—
125C2×C4⋊C4×C47—21no—
126C2×C4⋊C4×C47—41no—
127C2×C4⋊C4×C47—41no—
128C2×C4⋊C4×C47D411yescharacteristic
129C2×C4⋊C4×C47C2311yescharacteristic
130C2×C4⋊C4×C47C2311yescharacteristic
131C2×C4⋊C4×C47C2311yescharacteristic
132C2×C4⋊C4×C47C2311yescharacteristic
133C2×C22⋊C4×C47—21no—
134C2×C22⋊C4×C47—21no—
135C2×C22⋊C4×C47D411yescharacteristic
136C2×C22⋊C4×C47D411yescharacteristic
137C2×C42×C47—21no—
138C2×C42×C47C2311yescharacteristic
139#95×C47—21no—
140#95×C47—21no—
141#95×C47—21no—
142C24×C47C2×D411yescharacteristic
143C24×C47C2×D411yescharacteristic
144C23×D47—21no—
145C2×D4×C47—22no—
146C2×D4×C47—22no—
147C2×D4×C47C22⋊C414yes—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—42no—
161C22×C4×C47—42no—
162C22×C4×C47—42no—
163C22×C4×C47—42no—
164C22×C4×C47—81no—
165C22×C4×C47—81no—
166C22×C4×C47C22×C412yes—
167C22×C4×C47C22×C412yes—
168C22×C4×C47C2×D411yescharacteristic
169C22×C4×C47C2×D411yescharacteristic
170C22×C4×C47C2×D411yescharacteristic
171C22×C4×C47C2×D411yescharacteristic
172C22×C4×C47C2×D412yes—
173C22×C4×C47C2×D412yes—
174C22×C4×C47C2411yescharacteristic
175C2×C22⋊D47—24no—
176C2×C22⋊D47—24no—
177C2×C22⋊D47—42no—
178C2×C22⋊D47—42no—
179C2×C22⋊D47—81no—
180C2×C22⋊D47—81no—
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—21no—
184C22×Dic47—24no—
185C22×Dic47—81no—
186C22×Dic47—81no—
187C2×D188—21no—
188C2×D188—21no—
189C2×D188—21no—
190C2×D188—21no—
191C2×D188—21no—
192C2×D188C22×C412yes—
193C2×C4×D47—24no—
194C2×C4×D47—81no—
195C2×C4×D47—81no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—21no—
198C4⋊C4×C47—21no—
199C4⋊C4×C47—21no—
200C4⋊C4×C47—21no—
201C4⋊C4×C47—21no—
202C4⋊C4×C47—21no—
203C4⋊C4×C47—42no—
204C4⋊C4×C47—42no—
205C4⋊C4×C47—42no—
206C4⋊C4×C47—81no—
207C4⋊C4×C47C22⋊C414yes—
208C4⋊C4×C47#4112yes—
209C22⋊C4×C47—42no—
210C22⋊C4×C47—42no—
211C22⋊C4×C47C22⋊C414yes—
212C22⋊C4×C47C22⋊C414yes—
213C42×C47—42no—
214C42×C47C22×C412yes—
215C42×C47C2×D412yes—
216C22⋊Dic47—24no—
217(C2×D47)⋊C4—24no—
218(C2×D47)⋊C4—24no—
219(C2×D47)⋊C4—24no—
220C4⋊Dic47—24no—
221C4⋊Dic47—21no—
222C4⋊Dic47—21no—
223C4⋊Dic47—21no—
224C4⋊Dic47C22×C412yes—
225C4⋊Dic47C22×C412yes—
226C4⋊Dic47C22×C412yes—
227Dic47⋊C4—24no—
228Dic47⋊C4—24no—
229C4×Dic47—24no—
230#10625329—44no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—21no—
237C2×C47⋊C8—21no—
238C2×C47⋊C8—21no—
239C2×C47⋊C8—21no—
240C2×C47⋊C8—21no—
241C2×C47⋊C8—21no—
242C2×C47⋊C8—44no—
243C2×C47⋊C8#4112yes—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47C2×C22⋊C412yes—
255C23×C47C2×C22⋊C412yes—
256C23×C47AGL(1,ℤ/8)12yes—
257C23×C47#13712yes—
258C23×C47C22×D411yescharacteristic
259C22×D47—22no—
260C22×D47—41no—
261C22×D47—41no—
262C22×D47—41no—
263C22×D47—41no—
264C22×D47—41no—
265C22×D47—41no—
266D4×C47—28no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—84no—
296C2×C4×C47—84no—
297C2×C4×C47C2×C22⋊C412yes—
298C2×C4×C47C2×C22⋊C412yes—
299C2×C4×C47C2×C22⋊C412yes—
300C2×C4×C47C2×C22⋊C412yes—
301C2×C4×C47C23×C411yescharacteristic
302C2×C4×C47C22×D411yescharacteristic
303C2×C4×C47C2×#4111yescharacteristic
304C2×C4×C47C2×#4111yescharacteristic
305C2×C4×C47H(5,𝔽2)11yescharacteristic
306C2×C4×C472−1+411yescharacteristic
307C22⋊D47—48no—
308C22⋊D47—84no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—41no—
313C2×Dic47—41no—
314C2×Dic47—41no—
315C2×Dic47—41no—
316C2×Dic47—41no—
317C2×Dic47—41no—
318C2×Dic47—84no—
319D188—22no—
320D188—22no—
321D188—41no—
322D188—41no—
323C4×D47—84no—
324C47⋊C8—22no—
325C47⋊C8—41no—
326C47⋊C8—41no—
327C47⋊C8—41no—
328#22493—471nomaximal, Sylow
329C22×C47—22no—
330C22×C47—22no—
331C22×C47—22no—
332C22×C47—22no—
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—22no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47—41no—
341C22×C47—41no—
342C22×C47#41714yes—
343C22×C47C22×C22⋊C411yescharacteristic
344C22×C47#54611yescharacteristic
345C22×C47#54711yescharacteristic
346C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C47C2×#13711yescharacteristic
348C22×C47#57611yescharacteristic
349C22×C47#57711yescharacteristic
350C2×D47—42no—
351C2×D47—42no—
352C2×D47—42no—
353C2×D47—81no—
354C2×D47—81no—
355C2×D47—81no—
356C2×D47—81no—
357C4×C47—22no—
358C4×C47—22no—
359C4×C47—22no—
360C4×C47—22no—
361C4×C47—42no—
362C4×C47—81no—
363C4×C47—81no—
364C4×C47—81no—
365C4×C47C4×#4111yescharacteristic
366C4×C47#52011yescharacteristic
367C4×C47#54611yescharacteristic
368C4×C47#54711yescharacteristic
369Dic47—42no—
370Dic47—42no—
371Dic47—42no—
372C2×#553—471no—
373C2×#435—471no—
374D4×C4⋊C4D4711yescharacteristic, complemented
375#1992—471no—
376#1989—471no—
377#1895—471no—
378#1893—471no—
379#1874—471no—
380#1874—471no—
381#1825—471no—
382#1824—471no—
383#1802—471no—
384#1762—471no—
385#1736—471no—
386C2×#340—471no—
387C2×C47—24no—
388C2×C47—42no—
389C2×C47#233911yescharacteristic
390C2×C47C2×#41711yescharacteristic
391C2×C47#289711yescharacteristic
392C2×C47#331811yescharacteristic
393C2×C47#332011yescharacteristic
394C2×C47#334511yescharacteristic
395C2×C47#334611yescharacteristic
396D47—82no—
397C22×M16—471no—
398C23×C8—471no—
399#553—478no—
400#553—944no—
401C2×#126—941no—
402C2×#125—471no—
403C2×#123—941no—
404C2×#121—471no—
405C2×#121—471no—
406C2×#121—941no—
407C2×C4×D4—21no—
408C2×C4×D4—471no—
409C2×C4×D4—941no—
410C2×C4×D4C2×D4711yescharacteristic
411C2×#117—471no—
412C22×C4⋊C4—471no—
413C22×C4⋊C4C2×D4711yescharacteristic
414C22×C4⋊C4C2×D4711yescharacteristic
415#435—944no—
416C2×C4⋊C8—471no—
417C2×#102—471no—
418C2×#102—471no—
419C2×#102—471no—
420C2×#102—471no—
421C2×C22⋊C8—471no—
422C2×C22⋊C8—471no—
423C2×#97—471no—
424#389—21no—
425#385—21no—
426#385—21no—
427#384C2×D4711yescharacteristic
428#380C2×D4711yescharacteristic
429#380C2×D4711yescharacteristic
430C4×C4⋊C4C2×D4711yescharacteristic
431#340—471no—
432#340—471no—
433#340—471no—
434#340—471no—
435#340—471no—
436#340—471no—
437#340—471no—
438#340—471no—
439#340—471no—
440#340—471no—
441#340—471no—
442#340—471no—
443C47#2249311yescharacteristic, complemented, Sylow
444C22×D4—471no—
445C22×D4—941no—
446C22×D4—941no—
447C22×D4C22⋊D4711yescharacteristic
448C23×C4—21no—
449C23×C4—21no—
450C23×C4—941no—
451C23×C4—941no—
452C23×C4C22×D4711yescharacteristic
453C23×C4C22×D4711yescharacteristic
454C2×M16—942no—
455C2×M16—942no—
456C2×M16—1881no—
457C22×C8—471no—
458C22×C8—471no—
459C22×C8—471no—
460C22×C8—471no—
461C22×C8—942no—
462C22×C8—942no—
463C22×C8—1881no—
464#126—948no—
465#125—474no—
466#125—942no—
467#123—948no—
468#121—474no—
469#121—474no—
470#121—948no—
471#121—942no—
472#121—942no—
473C4×D4—44no—
474C4×D4—474no—
475C4×D4—948no—
476C4×D4—942no—
477C4×D4C4×D4714yes—
478C4×D4D18814yes—
479#117—474no—
480#117—942no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—41no—
488C2×C4⋊C4—41no—
489C2×C4⋊C4—474no—
490C2×C4⋊C4—471no—
491C2×C4⋊C4—471no—
492C2×C4⋊C4—471no—
493C2×C4⋊C4—942no—
494C2×C4⋊C4—941no—
495C2×C4⋊C4—941no—
496C2×C4⋊C4—941no—
497C2×C4⋊C4C22⋊D4711yescharacteristic
498C2×C4⋊C4C22×D4711yescharacteristic
499C2×C4⋊C4C22×D4711yescharacteristic
500C2×C4⋊C4C22×D4711yescharacteristic
501C2×C4⋊C4C22×D4711yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—941no—
505C2×C22⋊C4—941no—
506C2×C22⋊C4—941no—
507C2×C22⋊C4—941no—
508C2×C22⋊C4C22⋊D4711yescharacteristic
509C2×C22⋊C4C22⋊D4711yescharacteristic
510C2×C42—21no—
511C2×C42—941no—
512C2×C42C22×D4711yescharacteristic
513C4⋊C8—942no—
514#102—942no—
515#102—942no—
516#102—1881no—
517#102—1881no—
518C22⋊C8—942no—
519C22⋊C8—942no—
520#97—942no—
521#95—21no—
522#95—21no—
523#95—21no—
524C24—941no—
525C24C2×C22⋊D4711yescharacteristic
526C24C2×C22⋊D4711yescharacteristic
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—472no—
530C2×D4—944no—
531C2×D4—944no—
532C2×D4—941no—
533C2×D4—941no—
534C2×D4—941no—
535C2×D4—941no—
536C2×D4—941no—
537C2×D4—3761no—
538C2×D4—3761no—
539C2×D4—1882no—
540C2×D4—1882no—
541C2×D4(C2×D47)⋊C414yes—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—81no—
559C22×C4—81no—
560C22×C4—944no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—941no—
564C22×C4—944no—
565C22×C4—3761no—
566C22×C4—3761no—
567C22×C4—3761no—
568C22×C4—3761no—
569C22×C4C2×C4×D4712yes—
570C22×C4C2×C4×D4712yes—
571C22×C4C2×D18812yes—
572C22×C4C2×D18812yes—
573C22×C4C2×C22⋊D4711yescharacteristic
574C22×C4C2×C22⋊D4711yescharacteristic
575C22×C4C2×C22⋊D4711yescharacteristic
576C22×C4C2×C22⋊D4711yescharacteristic
577C22×C4C23×D4711yescharacteristic
578M16—1884no—
579C2×C8—472no—
580C2×C8—941no—
581C2×C8—941no—
582C2×C8—941no—
583C2×C8—941no—
584C2×C8—941no—
585C2×C8—941no—
586C2×C8—941no—
587C2×C8—941no—
588C2×C8—941no—
589C2×C8—941no—
590C2×C8—941no—
591C2×C8—1884no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—81no—
603C4⋊C4—472no—
604C4⋊C4—472no—
605C4⋊C4—472no—
606C4⋊C4—944no—
607C4⋊C4—944no—
608C4⋊C4—944no—
609C4⋊C4—941no—
610C4⋊C4—941no—
611C4⋊C4—941no—
612C4⋊C4(C2×D47)⋊C414yes—
613C4⋊C4#1062535212yes—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—944no—
617C22⋊C4—944no—
618C22⋊C4—944no—
619C22⋊C4—944no—
620C22⋊C4(C2×D47)⋊C414yes—
621C22⋊C4(C2×D47)⋊C414yes—
622C42—42no—
623C42—944no—
624C42C2×C4×D4712yes—
625C42C2×D18812yes—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—942no—
637C23—1881no—
638C23—1881no—
639C23—1881no—
640C23—1881no—
641C23—1881no—
642C23—1881no—
643C23C2×(C2×D47)⋊C412yes—
644C23C2×(C2×D47)⋊C412yes—
645C23#1309405012yes—
646C23#1309405512yes—
647C23C22×C22⋊D4711yescharacteristic
648D4—28no—
649D4—942no—
650D4—942no—
651D4—3764no—
652D4—1888no—
653D4—1881no—
654D4—1881no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—84no—
684C2×C4—84no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—942no—
688C2×C4—3764no—
689C2×C4—3764no—
690C2×C4—1881no—
691C2×C4—1881no—
692C2×C4—1881no—
693C2×C4—1881no—
694C2×C4—1881no—
695C2×C4—1881no—
696C2×C4C2×(C2×D47)⋊C412yes—
697C2×C4C2×(C2×D47)⋊C412yes—
698C2×C4C2×(C2×D47)⋊C412yes—
699C2×C4C2×(C2×D47)⋊C412yes—
700C2×C4C22×C4×D4711yescharacteristic
701C2×C4C22×D18811yescharacteristic
702C2×C4#41×D4711yescharacteristic
703C2×C4C2×#1062535211yescharacteristic
704C2×C4#1309406911yescharacteristic
705C2×C4#1309407111yescharacteristic
706C8—942no—
707C8—1881no—
708C8—1881no—
709C8—1881no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—3761no—
724C22—3761no—
725C22—3761no—
726C22—3761no—
727C22—1882no—
728C22—1882no—
729C22—1882no—
730C22#1568912214yes—
731C22C22×(C2×D47)⋊C411yescharacteristic
732C22#1568976711yescharacteristic
733C22#1568977211yescharacteristic
734C22C2×#1309405011yescharacteristic
735C22C2×#1309405511yescharacteristic
736C22#1568992611yescharacteristic
737C22#1568993111yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—81no—
744C4—81no—
745C4—81no—
746C4—1882no—
747C4—1882no—
748C4—1882no—
749C4C4×#1062535211yescharacteristic
750C4#1568960211yescharacteristic
751C4#1568976811yescharacteristic
752C4#1568977711yescharacteristic
753C2—24no—
754C2—42no—
755C2—3762no—
756C2#2024621311yescharacteristic
757C2C2×#1568912211yescharacteristic
758C2#2025191111yescharacteristic
759C2#2025552911yescharacteristic
760C2#2025555911yescharacteristic
761C2#2025585811yescharacteristic
762C2#2025586711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingD4×C4⋊C4×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689819C2
cosocleC22×C4×C47C24
hypercenterD4×C4⋊C4D47
hypocenterC47#22493
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. #20244356C2semidirect
4. #20244345C2semidirect
5. #20243824C2semidirect
6. #20243814C2semidirect
7. #20243705C2semidirect
8. #20243705C2semidirect
9. #20243480C2semidirect
10. #20243476C2semidirect
11. #20243385C2semidirect
12. #20243216C2semidirect
13. #20243107C2semidirect
14. C2×#15688885C2semidirect
15. D4×C4⋊C4×C47C2semidirect
19. #15689819C4semidirect
79. #13094016C2×C4semidirect
83. #13093998C2×C4semidirect
84. #13093998C2×C4semidirect
87. C4×D188C2×C4semidirect
90. #13093983C2×C4semidirect
93. C2×C4⋊Dic47C2×C4semidirect
374. D4×C4⋊C4D47semidirect
443. C47#22493semidirect

Maximal subgroups

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

subgroupindex
C2×#156898192
C2×#156891952
#202443562
#202443452
#202438242
#202438142
#202437052
#202434802
#202434762
#202433852
#202432162
#202431072
C2×#156888852
D4×C4⋊C4×C472
#2249347