Finite Group Databasebeta

← #26232712

Subgroups — #26232712

Order 12032.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689201C211yesmaximal, characteristic, complemented
2#20246317C211yesmaximal, characteristic, complemented
3#20244354C211yesmaximal, characteristic, complemented
4#20244346C211yesmaximal, characteristic, complemented
5#20243827C211yesmaximal, characteristic, complemented
6#20243827C211yesmaximal, characteristic, complemented
7#20243711C211yesmaximal, characteristic, complemented
8#20243706C211yesmaximal, characteristic, complemented
9#20243483C211yesmaximal, characteristic, complemented
10#20243474C211yesmaximal, characteristic, complemented
11#20243398C211yesmaximal, characteristic, complemented
12C4×#13093945C211yesmaximal, characteristic, complemented
13#20243109C211yesmaximal, characteristic, complemented
14#20243107C211yesmaximal, characteristic, complemented
15C2×C47×#553C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20#15689201—24no—
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×#13093945C2211yescharacteristic
23C2×#13093945C2211yescharacteristic
24C2×#13093945C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×C22⋊(C47⋊C8)C2211yescharacteristic
27C2×C22⋊(C47⋊C8)C2211yescharacteristic
28C2×C4×C47⋊C8C2211yescharacteristic
29#15689016—21no—
30#15689009—21no—
31#15689003—21no—
32#15688989C2211yescharacteristic
33#15688983C2211yescharacteristic
34#15688983C2211yescharacteristic
35C4×C4⋊Dic47C2211yescharacteristic
36C22⋊C4×Dic47—21no—
37#15688885C2211yescharacteristic
38#15688885C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49C47×#553—24no—
50C47×#553C418yescomplemented
51C2×#126×C47—21no—
52C2×#125×C47C2211yescharacteristic
53C2×#123×C47—21no—
54C2×#121×C47—21no—
55C2×#121×C47C2211yescharacteristic
56C2×#121×C47C2211yescharacteristic
57C2×C4×D4×C47—21no—
58C2×C4×D4×C47C2211yescharacteristic
59C2×C4×D4×C47C2211yescharacteristic
60C2×#117×C47C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C23×Dic47—21no—
63C2×#10625329—22no—
64C2×#10625329—22no—
65C2×#10625329—22no—
66C2×#10625329—22no—
67C2×#10625329—41no—
68C2×#10625329—41no—
69C22×C47⋊C8C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73#13093983—22no—
74#13093983—41no—
75C2×C4⋊Dic47—22no—
76C2×C4⋊Dic47—21no—
77C2×C4⋊Dic47—41no—
78C2×C4⋊Dic47C2311yescharacteristic
79C2×C4⋊Dic47C2311yescharacteristic
80C2×C4⋊Dic47C2311yescharacteristic
81C2×C4⋊Dic47C2311yescharacteristic
82C2×C22⋊Dic47—21no—
83C2×C22⋊Dic47—21no—
84C2×C22⋊Dic47—21no—
85C2×C4×Dic47—21no—
86C2×C4×Dic47—21no—
87C4⋊(C47⋊C8)—22no—
88#13093945—22no—
89#13093945—22no—
90#13093945—41no—
91#13093945—41no—
92C22⋊(C47⋊C8)—22no—
93C22⋊(C47⋊C8)—22no—
94C4×C47⋊C8—22no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C22×D4×C47—21no—
101C22×D4×C47—21no—
102C22×D4×C47D411yescharacteristic
103C22×D4×C47C2311yescharacteristic
104C23×C4×C47—21no—
105C23×C4×C47—21no—
106C23×C4×C47C2311yescharacteristic
107C23×C4×C47C2311yescharacteristic
108#126×C47—28no—
109#125×C47—22no—
110#125×C47C2×C414yescomplemented
111#123×C47—28no—
112#121×C47—28no—
113#121×C47—22no—
114#121×C47—22no—
115#121×C47C2×C414yes—
116#121×C47C2×C414yescomplemented
117C4×D4×C47—28no—
118C4×D4×C47—22no—
119C4×D4×C47C2×C414yes—
120C4×D4×C47C2×C414yescomplemented
121C4×D4×C47D414yes—
122#117×C47—22no—
123#117×C47C2×C414yes—
124C2×C4⋊C4×C47—21no—
125C2×C4⋊C4×C47—22no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47—21no—
128C2×C4⋊C4×C47C2×C414yescomplemented
129C2×C4⋊C4×C47D411yescharacteristic
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×C47—21no—
136C2×C22⋊C4×C47—21no—
137C2×C22⋊C4×C47D411yescharacteristic
138C2×C22⋊C4×C47D411yescharacteristic
139C2×C42×C47—21no—
140C2×C42×C47C2311yescharacteristic
141C24×C47—21no—
142C24×C47C2×D411yescharacteristic
143C24×C47C2×D411yescharacteristic
144C2×D4×C47—24no—
145C2×D4×C47—24no—
146C2×D4×C47—21no—
147C2×D4×C47—21no—
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47—41no—
152C2×D4×C47—41no—
153C2×D4×C47—42no—
154C2×D4×C47—42no—
155C2×D4×C47—81no—
156C2×D4×C47—81no—
157C2×D4×C47C22⋊C414yes—
158C2×D4×C47C22×C412yes—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—24no—
171C22×C4×C47—24no—
172C22×C4×C47—81no—
173C22×C4×C47—81no—
174C22×C4×C47—81no—
175C22×C4×C47—81no—
176C22×C4×C47C22×C412yes—
177C22×C4×C47C22×C412yes—
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D412yes—
183C22×C4×C47C2×D412yes—
184C22×C4×C47C2411yescharacteristic
185C22×Dic47—21no—
186C22×Dic47—21no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189C22×Dic47—42no—
190C22×Dic47—42no—
191C22×Dic47—81no—
192C4⋊C4×C47—24no—
193C4⋊C4×C47—24no—
194C4⋊C4×C47—24no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—21no—
198C4⋊C4×C47C22⋊C414yes—
199C4⋊C4×C47C22×C412yes—
200C4⋊C4×C47C22×C412yes—
201C4⋊C4×C47C22×C412yes—
202C22⋊C4×C47—24no—
203C22⋊C4×C47—24no—
204C22⋊C4×C47—24no—
205C22⋊C4×C47—24no—
206C22⋊C4×C47C22⋊C414yes—
207C22⋊C4×C47C22⋊C414yes—
208C42×C47—24no—
209C42×C47C22×C412yes—
210C42×C47C2×D412yes—
211C22⋊Dic47—42no—
212C22⋊Dic47—42no—
213C22⋊Dic47—81no—
214C4⋊Dic47—21no—
215C4⋊Dic47—21no—
216C4⋊Dic47—21no—
217C4⋊Dic47—21no—
218C4⋊Dic47—21no—
219C4⋊Dic47—21no—
220C4⋊Dic47—21no—
221C4⋊Dic47—42no—
222C4⋊Dic47#4112yes—
223C4×Dic47—42no—
224C4×Dic47—81no—
225#10625329—44no—
226#10625329—44no—
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—21no—
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×C47—22no—
252C23×C47—41no—
253C23×C47—41no—
254C23×C47—41no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47—41no—
258C23×C47C2×C22⋊C412yes—
259C23×C47C2×C22⋊C412yes—
260C23×C47C22×D411yescharacteristic
261D4×C47—22no—
262D4×C47—22no—
263D4×C47—44no—
264D4×C47—48no—
265D4×C47—41no—
266D4×C47—41no—
267D4×C47—84no—
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—21no—
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—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
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—84no—
294C2×C4×C47—84no—
295C2×C4×C47C2×C22⋊C412yes—
296C2×C4×C47C2×C22⋊C412yes—
297C2×C4×C47C2×C22⋊C412yes—
298C2×C4×C47C2×C22⋊C412yes—
299C2×C4×C47C23×C411yescharacteristic
300C2×C4×C47C22×D411yescharacteristic
301C2×C4×C47C2×#4111yescharacteristic
302C2×C4×C47C2×#4111yescharacteristic
303C2×C4×C47H(5,𝔽2)11yescharacteristic
304C2×C4×C472−1+411yescharacteristic
305C2×Dic47—22no—
306C2×Dic47—41no—
307C2×Dic47—41no—
308C2×Dic47—41no—
309C2×Dic47—41no—
310C2×Dic47—41no—
311C2×Dic47—41no—
312C2×Dic47—41no—
313C2×Dic47—41no—
314C2×Dic47—41no—
315C2×Dic47—41no—
316C2×Dic47—41no—
317C2×Dic47—84no—
318C47⋊C8—22no—
319C47⋊C8—41no—
320C47⋊C8—41no—
321C47⋊C8—41no—
322#22501—471nomaximal, Sylow
323C22×C47—22no—
324C22×C47—22no—
325C22×C47—22no—
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—41no—
330C22×C47—41no—
331C22×C47—41no—
332C22×C47—41no—
333C22×C47—41no—
334C22×C47—41no—
335C22×C47—41no—
336C22×C47—41no—
337C22×C47—42no—
338C22×C47—42no—
339C22×C47—42no—
340C22×C47—81no—
341C22×C47—81no—
342C22×C47—81no—
343C22×C47—81no—
344C22×C47C22×C22⋊C411yescharacteristic
345C22×C47#54611yescharacteristic
346C22×C47#54711yescharacteristic
347C22×C47#57511yescharacteristic
348C22×C47#57511yescharacteristic
349C22×C47#57611yescharacteristic
350C22×C47#57711yescharacteristic
351C4×C47—22no—
352C4×C47—22no—
353C4×C47—22no—
354C4×C47—22no—
355C4×C47—42no—
356C4×C47—42no—
357C4×C47—42no—
358C4×C47C4×#4111yescharacteristic
359C4×C47#52011yescharacteristic
360C4×C47#54611yescharacteristic
361C4×C47#54711yescharacteristic
362Dic47—42no—
363Dic47—81no—
364Dic47—81no—
365Dic47—81no—
366C2×#553D4711yescharacteristic
367C2×#436—471no—
368#2352—471no—
369#1991—471no—
370#1989—471no—
371#1895—471no—
372#1895—471no—
373#1875—471no—
374#1874—471no—
375#1825—471no—
376#1823—471no—
377#1804—471no—
378C4×#102—471no—
379#1736—471no—
380#1736—471no—
381C2×C47—42no—
382C2×C47—42no—
383C2×C47—82no—
384C2×C47#233911yescharacteristic
385C2×C47#289611yescharacteristic
386C2×C47#289711yescharacteristic
387C2×C47#332211yescharacteristic
388C2×C47#332611yescharacteristic
389C2×C47#335111yescharacteristic
390C2×C47#335511yescharacteristic
391C22×M16—471no—
392C22×M16—471no—
393#553—24no—
394#553Dic4718yescomplemented
395C2×#126—21no—
396C2×#125C2×D4711yescharacteristic
397C2×#123—21no—
398C2×#121—21no—
399C2×#121C2×D4711yescharacteristic
400C2×#121C2×D4711yescharacteristic
401C2×C4×D4—21no—
402C2×C4×D4C2×D4711yescharacteristic
403C2×C4×D4C2×D4711yescharacteristic
404C2×#117—471no—
405C2×#117C2×D4711yescharacteristic
406C22×C4⋊C4—471no—
407C22×C4⋊C4C2×D4711yescharacteristic
408#436—944no—
409C2×C4⋊C8—471no—
410C2×#102—471no—
411C2×#102—471no—
412C2×#102—471no—
413C2×#102—471no—
414C2×C22⋊C8—471no—
415C2×C22⋊C8—471no—
416C2×C4×C8—471no—
417#388—941no—
418#387—941no—
419#386—941no—
420#382—471no—
421#380—471no—
422#380—471no—
423C4×C4⋊C4—471no—
424C4×C22⋊C4—941no—
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—
436#340—471no—
437C47#2250111yescharacteristic, complemented, Sylow
438C22×D4—21no—
439C22×D4—21no—
440C22×D4C22⋊D4711yescharacteristic
441C22×D4C22×D4711yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
444C23×C4—941no—
445C23×C4C22×D4711yescharacteristic
446C23×C4C22×D4711yescharacteristic
447C2×M16—942no—
448C2×M16—942no—
449C2×M16—942no—
450C2×M16—942no—
451C2×M16—1881no—
452C2×M16—1881no—
453C22×C8—471no—
454C22×C8—471no—
455C22×C8—471no—
456C22×C8—471no—
457#126—28no—
458#125—22no—
459#125C2×Dic4714yescomplemented
460#123—28no—
461#121—28no—
462#121—22no—
463#121—22no—
464#121C2×Dic4714yes—
465#121C2×Dic4714yescomplemented
466C4×D4—28no—
467C4×D4—22no—
468C4×D4C2×Dic4714yes—
469C4×D4C2×Dic4714yescomplemented
470C4×D4C22⋊D4714yes—
471#117—22no—
472#117—942no—
473#117—1881no—
474#117C2×Dic4714yes—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—471no—
480C2×C4⋊C4—471no—
481C2×C4⋊C4—471no—
482C2×C4⋊C4—471no—
483C2×C4⋊C4—942no—
484C2×C4⋊C4—941no—
485C2×C4⋊C4—1881no—
486C2×C4⋊C4C2×Dic4714yescomplemented
487C2×C4⋊C4C22⋊D4711yescharacteristic
488C2×C4⋊C4C22×D4711yescharacteristic
489C2×C4⋊C4C22×D4711yescharacteristic
490C2×C4⋊C4C22×D4711yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
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—941no—
502C2×C42—941no—
503C2×C42C22×D4711yescharacteristic
504C4⋊C8—942no—
505#102—942no—
506#102—942no—
507#102—1881no—
508#102—1881no—
509C22⋊C8—942no—
510C22⋊C8—942no—
511C4×C8—942no—
512#95—941no—
513#95—941no—
514#95—941no—
515#95—941no—
516#95—941no—
517C24—21no—
518C24C2×C22⋊D4711yescharacteristic
519C24C2×C22⋊D4711yescharacteristic
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—81no—
532C2×D4—81no—
533C2×D4C22⋊Dic4714yes—
534C2×D4C22×Dic4712yes—
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—24no—
547C22×C4—24no—
548C22×C4—81no—
549C22×C4—81no—
550C22×C4—81no—
551C22×C4—81no—
552C22×C4—941no—
553C22×C4—941no—
554C22×C4—941no—
555C22×C4—941no—
556C22×C4—3761no—
557C22×C4—1882no—
558C22×C4—1882no—
559C22×C4C22×Dic4712yes—
560C22×C4C22×Dic4712yes—
561C22×C4C2×C22⋊D4711yescharacteristic
562C22×C4C2×C22⋊D4711yescharacteristic
563C22×C4C2×C22⋊D4711yescharacteristic
564C22×C4C2×C22⋊D4711yescharacteristic
565C22×C4C2×C22⋊D4712yes—
566C22×C4C2×C22⋊D4712yes—
567C22×C4C23×D4711yescharacteristic
568M16—1884no—
569M16—1884no—
570C2×C8—472no—
571C2×C8—941no—
572C2×C8—941no—
573C2×C8—941no—
574C2×C8—941no—
575C2×C8—941no—
576C2×C8—941no—
577C2×C8—941no—
578C2×C8—941no—
579C2×C8—941no—
580C2×C8—941no—
581C2×C8—941no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—472no—
589C4⋊C4—941no—
590C4⋊C4—941no—
591C4⋊C4—941no—
592C4⋊C4—941no—
593C4⋊C4—941no—
594C4⋊C4—941no—
595C4⋊C4—941no—
596C4⋊C4—1882no—
597C4⋊C4C22⋊Dic4714yes—
598C4⋊C4C22×Dic4712yes—
599C4⋊C4C22×Dic4712yes—
600C4⋊C4C22×Dic4712yes—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—3761no—
606C22⋊C4—1882no—
607C22⋊C4—1882no—
608C22⋊C4C22⋊Dic4714yes—
609C22⋊C4C22⋊Dic4714yes—
610C42—24no—
611C42—3761no—
612C42—1882no—
613C42C22×Dic4712yes—
614C42C2×C22⋊D4712yes—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—22no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23C2×C22⋊Dic4712yes—
635C23C2×C22⋊Dic4712yes—
636C23C22×C22⋊D4711yescharacteristic
637D4—22no—
638D4—22no—
639D4—44no—
640D4—48no—
641D4—41no—
642D4—41no—
643D4—84no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
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—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—84no—
670C2×C4—84no—
671C2×C4—942no—
672C2×C4—3764no—
673C2×C4—1881no—
674C2×C4—1881no—
675C2×C4—1881no—
676C2×C4—1881no—
677C2×C4—1881no—
678C2×C4—1881no—
679C2×C4—1881no—
680C2×C4—1881no—
681C2×C4—1881no—
682C2×C4—1881no—
683C2×C4—1881no—
684C2×C4C2×C22⋊Dic4712yes—
685C2×C4C2×C22⋊Dic4712yes—
686C2×C4C2×C22⋊Dic4712yes—
687C2×C4C2×C22⋊Dic4712yes—
688C2×C4C23×Dic4711yescharacteristic
689C2×C4C22×C22⋊D4711yescharacteristic
690C2×C4#41×D4711yescharacteristic
691C2×C4#41×D4711yescharacteristic
692C2×C4#1309407011yescharacteristic
693C2×C4#1309407111yescharacteristic
694C8—942no—
695C8—1881no—
696C8—1881no—
697C8—1881no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22C22×C22⋊Dic4711yescharacteristic
720C22#1568976111yescharacteristic
721C22#1568977211yescharacteristic
722C22#1568992111yescharacteristic
723C22#1568992111yescharacteristic
724C22#1568992611yescharacteristic
725C22#1568993411yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—3761no—
734C4—3761no—
735C4—3761no—
736C4—1882no—
737C4#41×Dic4711yescharacteristic
738C4#1568960611yescharacteristic
739C4#1568976111yescharacteristic
740C4#1568977211yescharacteristic
741C2—42no—
742C2—42no—
743C2—82no—
744C2#2024621811yescharacteristic
745C2#2025190711yescharacteristic
746C2#2025191411yescharacteristic
747C2#2025558311yescharacteristic
748C2#2025563511yescharacteristic
749C2#2025594211yescharacteristic
750C2#2025598811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC2×C47×#553C2
socleC23×C47C22×D4
cosocleC22×C4×C47C24
hypercenterC2×#553D47
hypocenterC47#22501
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#15689201C2semidirect
2. #20246317C2semidirect
3. #20244354C2semidirect
4. #20244346C2semidirect
5. #20243827C2semidirect
6. #20243827C2semidirect
7. #20243711C2semidirect
8. #20243706C2semidirect
9. #20243483C2semidirect
10. #20243474C2semidirect
11. #20243398C2semidirect
12. C4×#13093945C2semidirect
13. #20243109C2semidirect
14. #20243107C2semidirect
50. C47×#553C4semidirect
110. #125×C47C2×C4semidirect
116. #121×C47C2×C4semidirect
120. C4×D4×C47C2×C4semidirect
128. C2×C4⋊C4×C47C2×C4semidirect
394. #553Dic47semidirect
437. C47#22501semidirect
459. #125C2×Dic47semidirect
465. #121C2×Dic47semidirect
469. C4×D4C2×Dic47semidirect
486. C2×C4⋊C4C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156892012
#202463172
#202443542
#202443462
#202438272
#202437112
#202437062
#202434832
#202434742
#202433982
C4×#130939452
#202431092
#202431072
C2×C47×#5532
#2250147