Finite Group Databasebeta

← #26232671

Subgroups — #26232671

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×#15689195C211yesmaximal, characteristic, complemented
2#20246337C211yesmaximal, characteristic, complemented
3#20244358C211yesmaximal, characteristic, complemented
4#20244346C211yesmaximal, characteristic, complemented
5#20243827C211yesmaximal, characteristic, complemented
6#20243817C211yesmaximal, characteristic, complemented
7#20243711C211yesmaximal, characteristic, complemented
8#20243711C211yesmaximal, characteristic, complemented
9#20243483C211yesmaximal, characteristic, complemented
10#20243474C211yesmaximal, characteristic, complemented
11#20243388C211yesmaximal, characteristic, complemented
12#20243213C211yesmaximal, characteristic, complemented
13#20243107C211yesmaximal, characteristic, complemented
14#20243104C211yesmaximal, characteristic, complemented
15C2×C47×#553C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19C2×#13093983C2211yescharacteristic
20#15689195—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×#13093935C2211yescharacteristic
29#15689026—21no—
30#15689016—21no—
31#15689016—21no—
32#15688993C2211yescharacteristic
33#15688983C2211yescharacteristic
34#15688983C2211yescharacteristic
35C4⋊C4×Dic47—21no—
36C4×C4⋊Dic47C2211yescharacteristic
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
62C2×#10625329—22no—
63C2×#10625329—22no—
64C2×#10625329—41no—
65C22×C47⋊C8—22no—
66C22×C47⋊C8—22no—
67C22×C47⋊C8—41no—
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72#13093983—22no—
73#13093983—22no—
74#13093983—41no—
75#13093983—41no—
76C2×C4⋊Dic47—21no—
77C2×C4⋊Dic47—21no—
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×C22⋊Dic47—21no—
86C2×C4×Dic47—21no—
87C2×C4×Dic47—21no—
88C2×C4×Dic47—21no—
89C4⋊(C47⋊C8)—22no—
90#13093945—22no—
91#13093945—22no—
92#13093945—41no—
93#13093945—41no—
94C22⋊(C47⋊C8)—22no—
95C22⋊(C47⋊C8)—22no—
96#13093935—22no—
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×C414yes—
111#123×C47—28no—
112#121×C47—28no—
113#121×C47—22no—
114#121×C47—22no—
115#121×C47C2×C414yes—
116#121×C47C2×C414yes—
117C4×D4×C47—28no—
118C4×D4×C47—22no—
119C4×D4×C47C2×C414yes—
120C4×D4×C47C2×C414yes—
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×C414yes—
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—
189C4⋊C4×C47—24no—
190C4⋊C4×C47—24no—
191C4⋊C4×C47—24no—
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47C22⋊C414yes—
196C4⋊C4×C47C22×C412yes—
197C4⋊C4×C47C22×C412yes—
198C4⋊C4×C47C22×C412yes—
199C22⋊C4×C47—24no—
200C22⋊C4×C47—24no—
201C22⋊C4×C47—24no—
202C22⋊C4×C47—24no—
203C22⋊C4×C47C22⋊C414yes—
204C22⋊C4×C47C22⋊C414yes—
205C42×C47—24no—
206C42×C47C22×C412yes—
207C42×C47C2×D412yes—
208C22⋊Dic47—42no—
209C22⋊Dic47—42no—
210C22⋊Dic47—81no—
211C22⋊Dic47—81no—
212C4⋊Dic47—21no—
213C4⋊Dic47—21no—
214C4⋊Dic47—21no—
215C4⋊Dic47—21no—
216C4⋊Dic47—21no—
217C4⋊Dic47—21no—
218C4⋊Dic47—21no—
219C4⋊Dic47—42no—
220C4⋊Dic47—81no—
221C4⋊Dic47#4112yes—
222C4×Dic47—42no—
223C4×Dic47—42no—
224C4×Dic47—42no—
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×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—
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×C47—42no—
337C22×C47—42no—
338C22×C47—42no—
339C22×C47—81no—
340C22×C47—81no—
341C22×C47—81no—
342C22×C47—81no—
343C22×C47C22×C22⋊C411yescharacteristic
344C22×C47#54611yescharacteristic
345C22×C47#54711yescharacteristic
346C22×C47#57511yescharacteristic
347C22×C47#57511yescharacteristic
348C22×C47#57611yescharacteristic
349C22×C47#57711yescharacteristic
350C4×C47—22no—
351C4×C47—22no—
352C4×C47—22no—
353C4×C47—22no—
354C4×C47—42no—
355C4×C47—42no—
356C4×C47—42no—
357C4×C47C4×#4111yescharacteristic
358C4×C47#52011yescharacteristic
359C4×C47#54611yescharacteristic
360C4×C47#54711yescharacteristic
361Dic47—42no—
362Dic47—81no—
363Dic47—81no—
364Dic47—81no—
365C2×#553D4711yescharacteristic
366C2×#435—471no—
367#2354—471no—
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—82no—
383C2×C47#233911yescharacteristic
384C2×C47#289611yescharacteristic
385C2×C47#289711yescharacteristic
386C2×C47#330711yescharacteristic
387C2×C47#330911yescharacteristic
388C2×C47#334711yescharacteristic
389C2×C47#335011yescharacteristic
390C22×M16—471no—
391C23×C8—471no—
392#553—24no—
393#553Dic4718yescomplemented
394C2×#126—21no—
395C2×#125C2×D4711yescharacteristic
396C2×#123—21no—
397C2×#121—21no—
398C2×#121C2×D4711yescharacteristic
399C2×#121C2×D4711yescharacteristic
400C2×C4×D4—21no—
401C2×C4×D4C2×D4711yescharacteristic
402C2×C4×D4C2×D4711yescharacteristic
403C2×#117—471no—
404C2×#117—471no—
405C2×#117C2×D4711yescharacteristic
406C22×C4⋊C4C2×D4711yescharacteristic
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—941no—
417#388—941no—
418#388—941no—
419#384—471no—
420#380—471no—
421#380—471no—
422C4×C4⋊C4—471no—
423C4×C4⋊C4—941no—
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—21no—
438C22×D4—21no—
439C22×D4C22⋊D4711yescharacteristic
440C22×D4C22×D4711yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
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—28no—
456#125—22no—
457#125C2×Dic4714yes—
458#123—28no—
459#121—28no—
460#121—22no—
461#121—22no—
462#121C2×Dic4714yes—
463#121C2×Dic4714yes—
464C4×D4—28no—
465C4×D4—22no—
466C4×D4C2×Dic4714yes—
467C4×D4C2×Dic4714yes—
468C4×D4C22⋊D4714yes—
469#117—22no—
470#117—942no—
471#117—942no—
472#117—1881no—
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—941no—
484C2×C4⋊C4—941no—
485C2×C4⋊C4C2×Dic4714yes—
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—941no—
502C2×C42—941no—
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—941no—
514#95—941no—
515#95—941no—
516C24—21no—
517C24C2×C22⋊D4711yescharacteristic
518C24C2×C22⋊D4711yescharacteristic
519C2×D4—24no—
520C2×D4—24no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—81no—
531C2×D4—81no—
532C2×D4C22⋊Dic4714yes—
533C2×D4C22×Dic4712yes—
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—24no—
546C22×C4—24no—
547C22×C4—81no—
548C22×C4—81no—
549C22×C4—81no—
550C22×C4—81no—
551C22×C4—941no—
552C22×C4—941no—
553C22×C4—941no—
554C22×C4—941no—
555C22×C4C22×Dic4712yes—
556C22×C4C22×Dic4712yes—
557C22×C4C2×C22⋊D4711yescharacteristic
558C22×C4C2×C22⋊D4711yescharacteristic
559C22×C4C2×C22⋊D4711yescharacteristic
560C22×C4C2×C22⋊D4711yescharacteristic
561C22×C4C2×C22⋊D4712yes—
562C22×C4C2×C22⋊D4712yes—
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—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—472no—
585C4⋊C4—941no—
586C4⋊C4—941no—
587C4⋊C4—941no—
588C4⋊C4—941no—
589C4⋊C4—941no—
590C4⋊C4—941no—
591C4⋊C4—941no—
592C4⋊C4—3761no—
593C4⋊C4—1882no—
594C4⋊C4C22⋊Dic4714yes—
595C4⋊C4C22×Dic4712yes—
596C4⋊C4C22×Dic4712yes—
597C4⋊C4C22×Dic4712yes—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—3761no—
603C22⋊C4—3761no—
604C22⋊C4—1882no—
605C22⋊C4—1882no—
606C22⋊C4C22⋊Dic4714yes—
607C22⋊C4C22⋊Dic4714yes—
608C42—24no—
609C42—1882no—
610C42—1882no—
611C42—1882no—
612C42C22×Dic4712yes—
613C42C2×C22⋊D4712yes—
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—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23C2×C22⋊Dic4712yes—
634C23C2×C22⋊Dic4712yes—
635C23C22×C22⋊D4711yescharacteristic
636D4—22no—
637D4—22no—
638D4—44no—
639D4—48no—
640D4—41no—
641D4—41no—
642D4—84no—
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—22no—
661C2×C4—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—84no—
669C2×C4—84no—
670C2×C4—942no—
671C2×C4—1881no—
672C2×C4—1881no—
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×C4C2×C22⋊Dic4712yes—
683C2×C4C2×C22⋊Dic4712yes—
684C2×C4C2×C22⋊Dic4712yes—
685C2×C4C2×C22⋊Dic4712yes—
686C2×C4C23×Dic4711yescharacteristic
687C2×C4C22×C22⋊D4711yescharacteristic
688C2×C4#41×D4711yescharacteristic
689C2×C4#41×D4711yescharacteristic
690C2×C4#1309407011yescharacteristic
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—42no—
711C22—42no—
712C22—42no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22C22×C22⋊Dic4711yescharacteristic
718C22#1568976111yescharacteristic
719C22#1568977211yescharacteristic
720C22#1568992111yescharacteristic
721C22#1568992111yescharacteristic
722C22#1568992611yescharacteristic
723C22#1568993411yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—3761no—
732C4—3761no—
733C4—3761no—
734C4—1882no—
735C4#41×Dic4711yescharacteristic
736C4#1568960611yescharacteristic
737C4#1568976111yescharacteristic
738C4#1568977211yescharacteristic
739C2—42no—
740C2—42no—
741C2—82no—
742C2#2024621811yescharacteristic
743C2#2025190711yescharacteristic
744C2#2025191411yescharacteristic
745C2#2025535811yescharacteristic
746C2#2025538811yescharacteristic
747C2#2025588211yescharacteristic
748C2#2025592711yescharacteristic
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#22498
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×#15689195C2semidirect
2. #20246337C2semidirect
3. #20244358C2semidirect
4. #20244346C2semidirect
5. #20243827C2semidirect
6. #20243817C2semidirect
7. #20243711C2semidirect
8. #20243711C2semidirect
9. #20243483C2semidirect
10. #20243474C2semidirect
11. #20243388C2semidirect
12. #20243213C2semidirect
13. #20243107C2semidirect
14. #20243104C2semidirect
50. C47×#553C4semidirect
393. #553Dic47semidirect
436. C47#22498semidirect

Maximal subgroups

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

subgroupindex
C2×#156891952
#202463372
#202443582
#202443462
#202438272
#202438172
#202437112
#202434832
#202434742
#202433882
#202432132
#202431072
#202431042
C2×C47×#5532
#2249847