Finite Group Databasebeta

← #26232665

Subgroups — #26232665

Order 12032.

1186 conjugacy classes of subgroups.

The subgroup lattice has 750 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#20243710C211yesmaximal, characteristic, complemented
8#20243710C211yesmaximal, characteristic, complemented
9#20243480C211yesmaximal, characteristic, complemented
10#20243472C211yesmaximal, characteristic, complemented
11#20243385C211yesmaximal, characteristic, complemented
12#20243216C211yesmaximal, characteristic, complemented
13#20243109C211yesmaximal, characteristic, complemented
14#20243104C211yesmaximal, characteristic, complemented
15C47×#2354C211yesmaximal, 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×C47C2211yescharacteristic
52C2×#117×C47C2211yescharacteristic
53C2×#117×C47C2211yescharacteristic
54C47×#390—21no—
55C47×#388—21no—
56C47×#388—21no—
57C47×#384C2211yescharacteristic
58C47×#380C2211yescharacteristic
59C47×#380C2211yescharacteristic
60C4×C4⋊C4×C47—21no—
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×C414yes—
80#13094006—28no—
81#13093998—22no—
82#13093998—22no—
83#13093998C2×C414yes—
84#13093998C2×C414yes—
85#13093996—28no—
86C4×D188—22no—
87C4×D188C2×C414yes—
88(C22⋊D47)⋊C4—28no—
89#13093983—22no—
90#13093983C2×C414yes—
91C2×C4⋊Dic47—22no—
92C2×C4⋊Dic47—21no—
93C2×C4⋊Dic47C2×C414yes—
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×C47C2311yescharacteristic
114C23×C4×C47C2311yescharacteristic
115C4×D4×C47C2×C414yes—
116C4×D4×C47D414yes—
117#117×C47—22no—
118#117×C47—22no—
119#117×C47—41no—
120#117×C47—41no—
121C2×C4⋊C4×C47—21no—
122C2×C4⋊C4×C47—21no—
123C2×C4⋊C4×C47D411yescharacteristic
124C2×C4⋊C4×C47C2311yescharacteristic
125C2×C4⋊C4×C47C2311yescharacteristic
126C2×C4⋊C4×C47C2311yescharacteristic
127C2×C4⋊C4×C47C2311yescharacteristic
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47D411yescharacteristic
133C2×C22⋊C4×C47D411yescharacteristic
134C2×C42×C47—21no—
135C2×C42×C47—21no—
136C2×C42×C47—21no—
137C2×C42×C47C2311yescharacteristic
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141C24×C47C2×D411yescharacteristic
142C24×C47C2×D411yescharacteristic
143C23×D47—21no—
144C2×D4×C47—41no—
145C2×D4×C47—41no—
146C2×D4×C47C22⋊C414yes—
147C22×C4×C47—21no—
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×C47C22×C412yes—
160C22×C4×C47C22×C412yes—
161C22×C4×C47C2×D411yescharacteristic
162C22×C4×C47C2×D411yescharacteristic
163C22×C4×C47C2×D411yescharacteristic
164C22×C4×C47C2×D411yescharacteristic
165C22×C4×C47C2×D412yes—
166C22×C4×C47C2×D412yes—
167C22×C4×C47C2411yescharacteristic
168C2×C22⋊D47—24no—
169C2×C22⋊D47—24no—
170C2×C22⋊D47—42no—
171C2×C22⋊D47—42no—
172C2×C22⋊D47—81no—
173C2×C22⋊D47—81no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C22×Dic47—24no—
178C22×Dic47—81no—
179C22×Dic47—81no—
180C2×D188—21no—
181C2×D188—21no—
182C2×D188—21no—
183C2×D188—21no—
184C2×D188—21no—
185C2×D188C22×C412yes—
186C2×C4×D47—24no—
187C2×C4×D47—81no—
188C2×C4×D47—81no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47—21no—
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—42no—
197C4⋊C4×C47—81no—
198C4⋊C4×C47C22⋊C414yes—
199C4⋊C4×C47#4112yes—
200C22⋊C4×C47—42no—
201C22⋊C4×C47—42no—
202C22⋊C4×C47—81no—
203C22⋊C4×C47—81no—
204C22⋊C4×C47C22⋊C414yes—
205C22⋊C4×C47C22⋊C414yes—
206C42×C47—42no—
207C42×C47—42no—
208C42×C47—42no—
209C42×C47C22×C412yes—
210C42×C47C2×D412yes—
211C22⋊Dic47—24no—
212(C2×D47)⋊C4—24no—
213(C2×D47)⋊C4—24no—
214(C2×D47)⋊C4—24no—
215C4⋊Dic47—24no—
216C4⋊Dic47—21no—
217C4⋊Dic47—21no—
218C4⋊Dic47—21no—
219C4⋊Dic47C22×C412yes—
220C4⋊Dic47C22×C412yes—
221C4⋊Dic47C22×C412yes—
222Dic47⋊C4—24no—
223Dic47⋊C4—24no—
224C4×Dic47—24no—
225#10625329—44no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
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—44no—
238C2×C47⋊C8#4112yes—
239C23×C47—21no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47C2×C22⋊C412yes—
252C23×C47C2×C22⋊C412yes—
253C23×C47C22×D411yescharacteristic
254C22×D47—22no—
255C22×D47—41no—
256C22×D47—41no—
257C22×D47—41no—
258C22×D47—41no—
259C22×D47—41no—
260C22×D47—41no—
261D4×C47—44no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
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×C47C2×C22⋊C412yes—
291C2×C4×C47C2×C22⋊C412yes—
292C2×C4×C47C2×C22⋊C412yes—
293C2×C4×C47C2×C22⋊C412yes—
294C2×C4×C47C23×C411yescharacteristic
295C2×C4×C47C22×D411yescharacteristic
296C2×C4×C47C2×#4111yescharacteristic
297C2×C4×C47C2×#4111yescharacteristic
298C2×C4×C47H(5,𝔽2)11yescharacteristic
299C2×C4×C472−1+411yescharacteristic
300C22⋊D47—48no—
301C22⋊D47—84no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—41no—
306C2×Dic47—41no—
307C2×Dic47—41no—
308C2×Dic47—41no—
309C2×Dic47—41no—
310C2×Dic47—41no—
311C2×Dic47—84no—
312D188—22no—
313D188—22no—
314D188—41no—
315D188—41no—
316C4×D47—84no—
317C47⋊C8—22no—
318C47⋊C8—41no—
319C47⋊C8—41no—
320C47⋊C8—41no—
321#22498—471nomaximal, Sylow
322C22×C47—22no—
323C22×C47—22no—
324C22×C47—22no—
325C22×C47—22no—
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—41no—
329C22×C47—41no—
330C22×C47—41no—
331C22×C47—41no—
332C22×C47—41no—
333C22×C47—41no—
334C22×C47—41no—
335C22×C47—41no—
336C22×C47C22×C22⋊C411yescharacteristic
337C22×C47#54611yescharacteristic
338C22×C47#54711yescharacteristic
339C22×C47#57511yescharacteristic
340C22×C47#57511yescharacteristic
341C22×C47#57611yescharacteristic
342C22×C47#57711yescharacteristic
343C2×D47—42no—
344C2×D47—42no—
345C2×D47—42no—
346C2×D47—81no—
347C2×D47—81no—
348C2×D47—81no—
349C2×D47—81no—
350C4×C47—22no—
351C4×C47—22no—
352C4×C47—22no—
353C4×C47—22no—
354C4×C47—42no—
355C4×C47—81no—
356C4×C47—81no—
357C4×C47—81no—
358C4×C47C4×#4111yescharacteristic
359C4×C47#52011yescharacteristic
360C4×C47#54611yescharacteristic
361C4×C47#54711yescharacteristic
362Dic47—42no—
363Dic47—42no—
364Dic47—42no—
365C2×#553—471no—
366C2×#435—471no—
367#2354D4711yescharacteristic, complemented
368#1992—471no—
369#1989—471no—
370#1895—471no—
371#1893—471no—
372#1875—471no—
373#1875—471no—
374#1825—471no—
375#1823—471no—
376#1802—471no—
377#1762—471no—
378#1736—471no—
379#1735—471no—
380C2×C47—42no—
381C2×C47—42no—
382C2×C47#233911yescharacteristic
383C2×C47#289611yescharacteristic
384C2×C47#289711yescharacteristic
385C2×C47#330711yescharacteristic
386C2×C47#330911yescharacteristic
387C2×C47#334711yescharacteristic
388C2×C47#335011yescharacteristic
389D47—82no—
390C22×M16—471no—
391C23×C8—471no—
392#553—478no—
393#553—944no—
394C2×#126—941no—
395C2×#125—471no—
396C2×#123—941no—
397C2×#121—471no—
398C2×#121—471no—
399C2×#121—941no—
400C2×C4×D4—471no—
401C2×C4×D4—941no—
402C2×C4×D4C2×D4711yescharacteristic
403C2×#117—471no—
404C2×#117C2×D4711yescharacteristic
405C2×#117C2×D4711yescharacteristic
406C22×C4⋊C4—471no—
407#435—944no—
408C2×C4⋊C8—471no—
409C2×#102—471no—
410C2×#102—471no—
411C2×#102—471no—
412C2×#102—471no—
413C2×C22⋊C8—471no—
414C2×C22⋊C8—471no—
415C2×#97—471no—
416#390—21no—
417#388—21no—
418#388—21no—
419#384C2×D4711yescharacteristic
420#380C2×D4711yescharacteristic
421#380C2×D4711yescharacteristic
422C4×C4⋊C4—21no—
423C4×C4⋊C4C2×D4711yescharacteristic
424#340—471no—
425#340—471no—
426#340—471no—
427#340—471no—
428#340—471no—
429#340—471no—
430#340—471no—
431#340—471no—
432#340—471no—
433#340—471no—
434#340—471no—
435#340—471no—
436C47#2249811yescharacteristic, complemented, Sylow
437C22×D4—471no—
438C22×D4—941no—
439C22×D4—941no—
440C22×D4C22⋊D4711yescharacteristic
441C23×C4—941no—
442C23×C4—941no—
443C23×C4C22×D4711yescharacteristic
444C23×C4C22×D4711yescharacteristic
445C2×M16—942no—
446C2×M16—942no—
447C2×M16—1881no—
448C22×C8—471no—
449C22×C8—471no—
450C22×C8—471no—
451C22×C8—471no—
452C22×C8—942no—
453C22×C8—942no—
454C22×C8—1881no—
455#126—948no—
456#125—474no—
457#125—942no—
458#123—948no—
459#121—474no—
460#121—474no—
461#121—948no—
462#121—942no—
463#121—942no—
464C4×D4—474no—
465C4×D4—948no—
466C4×D4—942no—
467C4×D4C4×D4714yes—
468C4×D4D18814yes—
469#117—22no—
470#117—22no—
471#117—41no—
472#117—41no—
473#117—474no—
474#117—942no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—474no—
478C2×C4⋊C4—471no—
479C2×C4⋊C4—471no—
480C2×C4⋊C4—471no—
481C2×C4⋊C4—942no—
482C2×C4⋊C4—941no—
483C2×C4⋊C4—941no—
484C2×C4⋊C4—941no—
485C2×C4⋊C4C22⋊D4711yescharacteristic
486C2×C4⋊C4C22×D4711yescharacteristic
487C2×C4⋊C4C22×D4711yescharacteristic
488C2×C4⋊C4C22×D4711yescharacteristic
489C2×C4⋊C4C22×D4711yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—941no—
495C2×C22⋊C4—941no—
496C2×C22⋊C4—941no—
497C2×C22⋊C4—941no—
498C2×C22⋊C4C22⋊D4711yescharacteristic
499C2×C22⋊C4C22⋊D4711yescharacteristic
500C2×C42—21no—
501C2×C42—21no—
502C2×C42—21no—
503C2×C42—941no—
504C2×C42C22×D4711yescharacteristic
505C4⋊C8—942no—
506#102—942no—
507#102—942no—
508#102—1881no—
509#102—1881no—
510C22⋊C8—942no—
511C22⋊C8—942no—
512#97—942no—
513#95—21no—
514#95—21no—
515#95—21no—
516C24—941no—
517C24C2×C22⋊D4711yescharacteristic
518C24C2×C22⋊D4711yescharacteristic
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—472no—
522C2×D4—944no—
523C2×D4—944no—
524C2×D4—941no—
525C2×D4—941no—
526C2×D4—941no—
527C2×D4—941no—
528C2×D4—941no—
529C2×D4—3761no—
530C2×D4—3761no—
531C2×D4—1882no—
532C2×D4—1882no—
533C2×D4(C2×D47)⋊C414yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—944no—
547C22×C4—941no—
548C22×C4—941no—
549C22×C4—941no—
550C22×C4—944no—
551C22×C4—3761no—
552C22×C4—3761no—
553C22×C4—3761no—
554C22×C4—3761no—
555C22×C4C2×C4×D4712yes—
556C22×C4C2×C4×D4712yes—
557C22×C4C2×D18812yes—
558C22×C4C2×D18812yes—
559C22×C4C2×C22⋊D4711yescharacteristic
560C22×C4C2×C22⋊D4711yescharacteristic
561C22×C4C2×C22⋊D4711yescharacteristic
562C22×C4C2×C22⋊D4711yescharacteristic
563C22×C4C23×D4711yescharacteristic
564M16—1884no—
565C2×C8—472no—
566C2×C8—941no—
567C2×C8—941no—
568C2×C8—941no—
569C2×C8—941no—
570C2×C8—941no—
571C2×C8—941no—
572C2×C8—941no—
573C2×C8—941no—
574C2×C8—941no—
575C2×C8—941no—
576C2×C8—941no—
577C2×C8—1884no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—42no—
586C4⋊C4—81no—
587C4⋊C4—472no—
588C4⋊C4—472no—
589C4⋊C4—472no—
590C4⋊C4—944no—
591C4⋊C4—944no—
592C4⋊C4—944no—
593C4⋊C4—941no—
594C4⋊C4—941no—
595C4⋊C4—941no—
596C4⋊C4(C2×D47)⋊C414yes—
597C4⋊C4#1062535212yes—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—81no—
601C22⋊C4—81no—
602C22⋊C4—944no—
603C22⋊C4—944no—
604C22⋊C4—944no—
605C22⋊C4—944no—
606C22⋊C4(C2×D47)⋊C414yes—
607C22⋊C4(C2×D47)⋊C414yes—
608C42—42no—
609C42—42no—
610C42—42no—
611C42—944no—
612C42C2×C4×D4712yes—
613C42C2×D18812yes—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—942no—
627C23—1881no—
628C23—1881no—
629C23—1881no—
630C23—1881no—
631C23—1881no—
632C23—1881no—
633C23C2×(C2×D47)⋊C412yes—
634C23C2×(C2×D47)⋊C412yes—
635C23C22×C22⋊D4711yescharacteristic
636D4—44no—
637D4—942no—
638D4—942no—
639D4—3764no—
640D4—1888no—
641D4—1881no—
642D4—1881no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—942no—
672C2×C4—942no—
673C2×C4—942no—
674C2×C4—3764no—
675C2×C4—3764no—
676C2×C4—1881no—
677C2×C4—1881no—
678C2×C4—1881no—
679C2×C4—1881no—
680C2×C4—1881no—
681C2×C4—1881no—
682C2×C4C2×(C2×D47)⋊C412yes—
683C2×C4C2×(C2×D47)⋊C412yes—
684C2×C4C2×(C2×D47)⋊C412yes—
685C2×C4C2×(C2×D47)⋊C412yes—
686C2×C4C22×C4×D4711yescharacteristic
687C2×C4C22×D18811yescharacteristic
688C2×C4#41×D4711yescharacteristic
689C2×C4C2×#1062535211yescharacteristic
690C2×C4#1309406911yescharacteristic
691C2×C4#1309407111yescharacteristic
692C8—942no—
693C8—1881no—
694C8—1881no—
695C8—1881no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—3761no—
711C22—3761no—
712C22—3761no—
713C22—3761no—
714C22—1882no—
715C22—1882no—
716C22—1882no—
717C22C22×(C2×D47)⋊C411yescharacteristic
718C22#1568976711yescharacteristic
719C22#1568977211yescharacteristic
720C22#1568992111yescharacteristic
721C22#1568992111yescharacteristic
722C22#1568992611yescharacteristic
723C22#1568993111yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—42no—
729C4—81no—
730C4—81no—
731C4—81no—
732C4—1882no—
733C4—1882no—
734C4—1882no—
735C4C4×#1062535211yescharacteristic
736C4#1568960211yescharacteristic
737C4#1568976811yescharacteristic
738C4#1568977711yescharacteristic
739C2—42no—
740C2—42no—
741C2—3762no—
742C2#2024621311yescharacteristic
743C2#2025190511yescharacteristic
744C2#2025191111yescharacteristic
745C2#2025536411yescharacteristic
746C2#2025539411yescharacteristic
747C2#2025588811yescharacteristic
748C2#2025593311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2354C2
socleC23×C47C22×D4
prime radicalC2×#15689819C2
cosocleC22×C4×C47C24
hypercenter#2354D47
hypocenterC47#22498
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

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. #20243710C2semidirect
8. #20243710C2semidirect
9. #20243480C2semidirect
10. #20243472C2semidirect
11. #20243385C2semidirect
12. #20243216C2semidirect
13. #20243109C2semidirect
14. #20243104C2semidirect
15. C47×#2354C2semidirect
19. #15689819C4semidirect
367. #2354D47semidirect
436. C47#22498semidirect

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
#202437102
#202434802
#202434722
#202433852
#202432162
#202431092
#202431042
C47×#23542
#2249847