Finite Group Databasebeta

← #26222012

Subgroups — #26222012

Order 12032.

1560 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689274C211yesmaximal, characteristic
2C2×#15689223C211yesmaximal, characteristic, complemented
3C2×C4×#10625335C211yesmaximal, characteristic, complemented
4#20246070C211yesmaximal, characteristic, complemented
5#20243722C211yesmaximal, characteristic, complemented
6#20243722C211yesmaximal, characteristic, complemented
7#20243700C211yesmaximal, characteristic, complemented
8#20243649C211yesmaximal, characteristic, complemented
9#20243635C211yesmaximal, characteristic, complemented
10#20243587C211yesmaximal, characteristic, complemented
11#20243319C211yesmaximal, characteristic
12#20243213C211yesmaximal, characteristic, complemented
13C4×#13093945C211yesmaximal, characteristic, complemented
14#20243154C211yesmaximal, characteristic, complemented
15C2×C47×#518C211yesmaximal, characteristic
16C22×#10625335C2211yescharacteristic
17C22×#10625335C2211yescharacteristic
18C2×#13094003C2211yescharacteristic
19C2×C4×Dic94C2211yescharacteristic, complemented
20#15689274C418yescomplemented
21#15689223—24no—
22C4×#10625335—24no—
23C2×#13093957C2211yescharacteristic, complemented
24C2×#13093955C2211yescharacteristic, complemented
25C2×#13093947C2211yescharacteristic, complemented
26C2×#13093947C2211yescharacteristic, complemented
27C2×#13093945C2211yescharacteristic
28C2×#13093945C2211yescharacteristic
29C2×#13093945C2211yescharacteristic
30C2×#13093945C2211yescharacteristic
31C2×#13093945C2211yescharacteristic
32C2×#13093945C2211yescharacteristic
33C2×C22⋊(C47⋊C8)C2211yescharacteristic
34C2×C22⋊(C47⋊C8)C2211yescharacteristic
35C2×#13093935C2211yescharacteristic, complemented
36C2×C4×C47⋊C8C2211yescharacteristic, complemented
37#15689029C2211yescharacteristic, complemented
38#15689021C2211yescharacteristic, complemented
39#15689018—21no—
40#15689017—21no—
41#15689011—21no—
42#15689004—21no—
43#15688983C2211yescharacteristic
44C4×C4⋊Dic47C2211yescharacteristic, complemented
45#15688885C2211yescharacteristic, complemented
46#15688885C2211yescharacteristic, complemented
47#15688885C2211yescharacteristic, complemented
48#15688885C2211yescharacteristic, complemented
49#15688878C2211yescharacteristic, complemented
50#15688878C2211yescharacteristic, complemented
51C23×D4×C47C2211yescharacteristic
52C47×#518—24no—
53C47×#518—24no—
54C2×C4×D4×C47—21no—
55C2×C4×D4×C47—21no—
56C2×C4×D4×C47C2211yescharacteristic
57C2×C4×D4×C47C2211yescharacteristic
58C2×C4×D4×C47C2211yescharacteristic
59C2×C4×D4×C47C2211yescharacteristic
60C2×#117×C47C2211yescharacteristic
61C2×#117×C47C2211yescharacteristic
62C22×C22⋊C4×C47—21no—
63C22×C22⋊C4×C47—21no—
64C22×Dic94C2311yescharacteristic
65C2×#10625335—22no—
66C2×#10625335—22no—
67C2×#10625335—22no—
68C2×#10625335—22no—
69C2×#10625335C2×C414yescomplemented
70C2×#10625335C2×C414yescomplemented
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75#13094003—22no—
76#13094003C2×C414yescomplemented
77C4×Dic94—22no—
78C4×Dic94—22no—
79C2×C4⋊Dic47C2311yescharacteristic
80C2×C4⋊Dic47C2311yescharacteristic
81C2×C4⋊Dic47C2311yescharacteristic
82C2×Dic47⋊C4—21no—
83C2×Dic47⋊C4—21no—
84C2×Dic47⋊C4—21no—
85C2×C22⋊Dic47—21no—
86C2×C22⋊Dic47—21no—
87C2×C4×Dic47—21no—
88C2×C4×Dic47—21no—
89#13093957—22no—
90#13093955—22no—
91#13093947—22no—
92#13093947—22no—
93#13093945—22no—
94#13093945—22no—
95#13093945—22no—
96#13093945—22no—
97#13093945C2×C414yescomplemented
98#13093945C2×C414yescomplemented
99C22⋊(C47⋊C8)—22no—
100C22⋊(C47⋊C8)C2×C414yescomplemented
101#13093935—22no—
102C4×C47⋊C8—22no—
103C47⋊#95—21no—
104C47⋊#95—21no—
105C47⋊#95—21no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C25×C47—21no—
109C22×D4×C47—22no—
110C22×D4×C47—22no—
111C22×D4×C47—22no—
112C22×D4×C47—22no—
113C22×D4×C47—21no—
114C22×D4×C47—22no—
115C22×D4×C47C2×C414yes—
116C22×D4×C47C2311yescharacteristic
117C22×D4×C47C2311yescharacteristic
118C23×C4×C47—21no—
119C23×C4×C47—21no—
120C23×C4×C47—21no—
121C23×C4×C47—21no—
122C23×C4×C47C2311yescharacteristic
123C4×D4×C47—28no—
124C4×D4×C47—28no—
125C4×D4×C47—22no—
126C4×D4×C47—22no—
127C4×D4×C47—22no—
128C4×D4×C47—22no—
129C4×D4×C47—22no—
130C4×D4×C47—22no—
131C4×D4×C47D414yes—
132C4×D4×C47D414yes—
133#117×C47—22no—
134#117×C47—22no—
135#117×C47—22no—
136#117×C47—22no—
137C2×C4⋊C4×C47D411yescharacteristic
138C2×C4⋊C4×C47D411yescharacteristic
139C2×C4⋊C4×C47C2311yescharacteristic
140C2×C4⋊C4×C47C2311yescharacteristic
141C2×C22⋊C4×C47—28no—
142C2×C22⋊C4×C47—28no—
143C2×C22⋊C4×C47—21no—
144C2×C22⋊C4×C47—21no—
145C2×C22⋊C4×C47—21no—
146C2×C22⋊C4×C47—21no—
147C2×C22⋊C4×C47—21no—
148C2×C22⋊C4×C47D411yescharacteristic
149C2×C22⋊C4×C47D411yescharacteristic
150C2×C42×C47—21no—
151C2×C42×C47C2311yescharacteristic
152C2×C42×C47C2311yescharacteristic
153C24×C47—24no—
154C24×C47—24no—
155C24×C47—21no—
156C24×C47—21no—
157C24×C47—24no—
158C24×C47—81no—
159C24×C47—81no—
160C24×C47—81no—
161C24×C47—81no—
162C24×C47C2×D411yescharacteristic
163C2×D4×C47—24no—
164C2×D4×C47—24no—
165C2×D4×C47—28no—
166C2×D4×C47—28no—
167C2×D4×C47—28no—
168C2×D4×C47—28no—
169C2×D4×C47—24no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—21no—
175C2×D4×C47—21no—
176C2×D4×C47C22×C412yes—
177C2×D4×C47C22×C412yes—
178C2×D4×C47C2×D412yes—
179C2×D4×C47C2×D412yes—
180C2×D4×C47#4112yes—
181C2×D4×C47#4112yes—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—24no—
189C22×C4×C47—24no—
190C22×C4×C47—24no—
191C22×C4×C47—24no—
192C22×C4×C47—81no—
193C22×C4×C47—81no—
194C22×C4×C47—81no—
195C22×C4×C47—81no—
196C22×C4×C47—81no—
197C22×C4×C47—81no—
198C22×C4×C47—81no—
199C22×C4×C47—81no—
200C22×C4×C47C22×C412yes—
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47#4112yes—
207C22×C4×C47C2411yescharacteristic
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C2×Dic94—21no—
213C2×Dic94—21no—
214C2×Dic94—21no—
215C2×Dic94—21no—
216C2×Dic94—21no—
217C2×Dic94C22×C412yes—
218C4⋊C4×C47—22no—
219C4⋊C4×C47—22no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47C2×D412yes—
223C4⋊C4×C47C2×D412yes—
224C22⋊C4×C47—24no—
225C22⋊C4×C47—24no—
226C22⋊C4×C47—24no—
227C22⋊C4×C47—22no—
228C22⋊C4×C47—22no—
229C22⋊C4×C47—24no—
230C22⋊C4×C47—24no—
231C42×C47—24no—
232C42×C47—21no—
233C42×C47—21no—
234C42×C47C2×D412yes—
235C42×C47C2×D412yes—
236C22⋊Dic47—24no—
237C22⋊Dic47—81no—
238#10625335—28no—
239#10625335—28no—
240C4⋊Dic47—21no—
241C4⋊Dic47—21no—
242C4⋊Dic47—21no—
243C4⋊Dic47—21no—
244C4⋊Dic47—21no—
245C4⋊Dic47C22×C412yes—
246Dic47⋊C4—24no—
247Dic47⋊C4—42no—
248Dic47⋊C4—81no—
249C4×Dic47—42no—
250C4×Dic47—81no—
251C2×C47⋊C8—21no—
252C2×C47⋊C8—21no—
253C2×C47⋊C8—21no—
254C2×C47⋊C8—21no—
255C2×C47⋊C8—21no—
256C2×C47⋊C8—21no—
257C2×C47⋊C8—21no—
258C2×C47⋊C8—21no—
259C2×C47⋊C8—21no—
260C2×C47⋊C8—21no—
261C2×C47⋊C8C22×C412yes—
262C2×C47⋊C8C22×C412yes—
263C23×C47—216no—
264C23×C47—22no—
265C23×C47—22no—
266C23×C47—21no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47—21no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—21no—
275C23×C47—21no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—41no—
279C23×C47—41no—
280C23×C47—41no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—84no—
285C23×C47—84no—
286C23×C47—84no—
287C23×C47—84no—
288C23×C47—84no—
289C23×C47—84no—
290C23×C47C4×D412yes—
291C23×C47C22×D411yescharacteristic
292D4×C47—216no—
293D4×C47—22no—
294D4×C47—22no—
295D4×C47—22no—
296D4×C47—22no—
297D4×C47—22no—
298D4×C47—22no—
299D4×C47C4×D414yes—
300D4×C47C4×D414yes—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—84no—
324C2×C4×C47—84no—
325C2×C4×C47—84no—
326C2×C4×C47—84no—
327C2×C4×C47C4×D412yes—
328C2×C4×C47#12012yes—
329C2×C4×C47#12012yes—
330C2×C4×C47C23×C411yescharacteristic
331C2×C4×C47C22×D411yescharacteristic
332C2×C4×C47C22×D411yescharacteristic
333C2×C4×C47C2×#4111yescharacteristic
334C2×C4×C47C2×#4111yescharacteristic
335C2×C4×C47C2×#4111yescharacteristic
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—41no—
339C2×Dic47—41no—
340C2×Dic47—41no—
341C2×Dic47—41no—
342C2×Dic47—41no—
343C2×Dic47—41no—
344C2×Dic47—41no—
345C2×Dic47—41no—
346C2×Dic47—41no—
347C2×Dic47—41no—
348Dic94—22no—
349Dic94—22no—
350Dic94—41no—
351Dic94—41no—
352C47⋊C8—22no—
353C47⋊C8—22no—
354C47⋊C8—41no—
355C47⋊C8—41no—
356#21459—471nomaximal, Sylow
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—22no—
360C22×C47—24no—
361C22×C47—24no—
362C22×C47—41no—
363C22×C47—42no—
364C22×C47—42no—
365C22×C47—41no—
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—42no—
369C22×C47—42no—
370C22×C47—42no—
371C22×C47—42no—
372C22×C47—42no—
373C22×C47—42no—
374C22×C47—41no—
375C22×C47—42no—
376C22×C47—42no—
377C22×C47—41no—
378C22×C47—816no—
379C22×C47C2×C4×D411yescharacteristic
380C22×C47C2×#12011yescharacteristic
381C22×C47#52511yescharacteristic
382C22×C47#57611yescharacteristic
383C22×C47#57711yescharacteristic
384C22×C47#57711yescharacteristic
385C22×C47#57711yescharacteristic
386C4×C47—22no—
387C4×C47—22no—
388C4×C47—22no—
389C4×C47—41no—
390C4×C47—42no—
391C4×C47—41no—
392C4×C47—42no—
393C4×C47C2×C4×D411yescharacteristic
394C4×C47C2×C4×D411yescharacteristic
395C4×C47#52511yescharacteristic
396C4×C47#52511yescharacteristic
397Dic47—42no—
398Dic47—42no—
399Dic47—81no—
400Dic47—81no—
401C2×#518D4711yescharacteristic
402C2×#450—471no—
403C2×#440—471no—
404C2×C4×SD16—471no—
405#2323—471no—
406#1877—471no—
407#1877—471no—
408#1873—471no—
409#1864—471no—
410#1862—471no—
411#1854—471no—
412#1786—471no—
413#1762—471no—
414C4×#102—471no—
415#1750—471no—
416C2×C47—42no—
417C2×C47—44no—
418C2×C47—44no—
419C2×C47C4×#12011yescharacteristic
420C2×C47#294611yescharacteristic
421C2×C47#294911yescharacteristic
422C2×C47#300911yescharacteristic
423C2×C47#301211yescharacteristic
424C2×C47#311811yescharacteristic
425C2×C47#312311yescharacteristic
426C23×D4C2×D4711yescharacteristic
427C22×SD16—471no—
428C22×SD16—471no—
429C2×C22⋊Q8—471no—
430#518—24no—
431#518—24no—
432C2×C4×Q8—471no—
433C2×C4×D4—21no—
434C2×C4×D4—21no—
435C2×C4×D4C2×D4711yescharacteristic
436C2×C4×D4C2×D4711yescharacteristic
437C2×C4×D4C2×D4711yescharacteristic
438C2×C4×D4C2×D4711yescharacteristic
439C2×#117C2×D4711yescharacteristic
440C2×#117C2×D4711yescharacteristic
441C22×C22⋊C4—21no—
442C22×C22⋊C4—21no—
443#450—478no—
444#440—944no—
445C4×SD16—944no—
446C2×#107—471no—
447C2×#106—471no—
448C2×#103—471no—
449C2×#103—471no—
450C2×#102—471no—
451C2×#102—471no—
452C2×#102—471no—
453C2×#102—471no—
454C2×#102—471no—
455C2×#102—471no—
456C2×C22⋊C8—471no—
457C2×C22⋊C8—471no—
458C2×#97—471no—
459C2×C4×C8—471no—
460#391—471no—
461#389—471no—
462#389—941no—
463#388—941no—
464#388—941no—
465#387—941no—
466#380—471no—
467C4×C4⋊C4—471no—
468#340—471no—
469#340—471no—
470#340—471no—
471#340—471no—
472#336—471no—
473#336—471no—
474C47#2145911yescharacteristic, complemented, Sylow
475C25—21no—
476C22×Q8—471no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—22no—
480C22×D4—22no—
481C22×D4—22no—
482C22×D4—21no—
483C22×D4C4×D4714yes—
484C22×D4C22×D4711yescharacteristic
485C22×D4C22×D4711yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—21no—
490C23×C4C22×D4711yescharacteristic
491C2×SD16—474no—
492C2×SD16—474no—
493C2×SD16—942no—
494C2×SD16—942no—
495C2×SD16—942no—
496C2×SD16—942no—
497C22×C8—471no—
498C22×C8—471no—
499C22×C8—471no—
500C22×C8—471no—
501C22⋊Q8—474no—
502C22⋊Q8—942no—
503C4×Q8—942no—
504C4×Q8—942no—
505C4×D4—28no—
506C4×D4—28no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4C22⋊D4714yes—
514C4×D4C22⋊D4714yes—
515#117—22no—
516#117—22no—
517#117—22no—
518#117—22no—
519C2×C4⋊C4—471no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—941no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4C22⋊D4711yescharacteristic
526C2×C4⋊C4C22⋊D4711yescharacteristic
527C2×C4⋊C4C22×D4711yescharacteristic
528C2×C4⋊C4C22×D4711yescharacteristic
529C2×C22⋊C4—28no—
530C2×C22⋊C4—28no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—941no—
537C2×C22⋊C4—941no—
538C2×C22⋊C4C22⋊D4711yescharacteristic
539C2×C22⋊C4C22⋊D4711yescharacteristic
540C2×C42—21no—
541C2×C42—941no—
542C2×C42—941no—
543C2×C42C22×D4711yescharacteristic
544C2×C42C22×D4711yescharacteristic
545#107—942no—
546#106—942no—
547#103—942no—
548#103—942no—
549#102—474no—
550#102—474no—
551#102—942no—
552#102—942no—
553#102—942no—
554#102—942no—
555C22⋊C8—474no—
556C22⋊C8—942no—
557#97—942no—
558C4×C8—942no—
559#95—941no—
560#95—941no—
561#95—941no—
562#95—941no—
563#95—941no—
564C24—24no—
565C24—24no—
566C24—21no—
567C24—21no—
568C24—24no—
569C24—81no—
570C24—81no—
571C24—81no—
572C24—81no—
573C24C2×C22⋊D4711yescharacteristic
574C2×Q8—472no—
575C2×Q8—941no—
576C2×Q8—941no—
577C2×Q8—941no—
578C2×Q8—941no—
579C2×Q8—941no—
580C2×D4—24no—
581C2×D4—24no—
582C2×D4—28no—
583C2×D4—28no—
584C2×D4—28no—
585C2×D4—28no—
586C2×D4—24no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4C2×C4×D4712yes—
594C2×D4C2×C4×D4712yes—
595C2×D4#1062535012yes—
596C2×D4#1062535012yes—
597C2×D4C2×C22⋊D4712yes—
598C2×D4C2×C22⋊D4712yes—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—941no—
618C22×C4—941no—
619C22×C4—941no—
620C22×C4—941no—
621C22×C4C2×C4×D4712yes—
622C22×C4#1062535012yes—
623C22×C4C2×C22⋊D4711yescharacteristic
624C22×C4C2×C22⋊D4711yescharacteristic
625C22×C4C2×C22⋊D4711yescharacteristic
626C22×C4C2×C22⋊D4711yescharacteristic
627C22×C4C2×C22⋊D4711yescharacteristic
628C22×C4C23×D4711yescharacteristic
629SD16—948no—
630SD16—948no—
631C2×C8—472no—
632C2×C8—472no—
633C2×C8—941no—
634C2×C8—941no—
635C2×C8—941no—
636C2×C8—941no—
637C2×C8—941no—
638C2×C8—941no—
639C2×C8—941no—
640C2×C8—941no—
641C2×C8—941no—
642C2×C8—941no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—472no—
648C4⋊C4—944no—
649C4⋊C4—941no—
650C4⋊C4—941no—
651C4⋊C4—941no—
652C4⋊C4—941no—
653C4⋊C4—941no—
654C4⋊C4—3761no—
655C4⋊C4—1882no—
656C4⋊C4C2×C22⋊D4712yes—
657C4⋊C4C2×C22⋊D4712yes—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—24no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—944no—
666C22⋊C4—3761no—
667C42—24no—
668C42—21no—
669C42—21no—
670C42—3761no—
671C42—1882no—
672C42C2×C22⋊D4712yes—
673C42C2×C22⋊D4712yes—
674C23—216no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—84no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23C4×C22⋊D4712yes—
702C23C22×C22⋊D4711yescharacteristic
703Q8—942no—
704Q8—942no—
705Q8—1881no—
706Q8—1881no—
707D4—216no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4C4×C22⋊D4714yes—
715D4C4×C22⋊D4714yes—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4—84no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—942no—
743C2×C4—942no—
744C2×C4—1881no—
745C2×C4—1881no—
746C2×C4—1881no—
747C2×C4—1881no—
748C2×C4—1881no—
749C2×C4—1881no—
750C2×C4—1881no—
751C2×C4—1881no—
752C2×C4—1881no—
753C2×C4—1881no—
754C2×C4C4×C22⋊D4712yes—
755C2×C4#1309399312yes—
756C2×C4#1309399312yes—
757C2×C4C22×C4×D4711yescharacteristic
758C2×C4C22×C22⋊D4711yescharacteristic
759C2×C4C22×C22⋊D4711yescharacteristic
760C2×C4C2×#1062535011yescharacteristic
761C2×C4C2×#1062535011yescharacteristic
762C2×C4C2×#1062535011yescharacteristic
763C8—942no—
764C8—942no—
765C8—1881no—
766C8—1881no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—24no—
771C22—24no—
772C22—42no—
773C22—42no—
774C22—41no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—42no—
782C22—41no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—41no—
788C22—816no—
789C22C2×C4×C22⋊D4711yescharacteristic
790C22C2×#1309399311yescharacteristic
791C22#1568963411yescharacteristic
792C22#1568992611yescharacteristic
793C22#1568993411yescharacteristic
794C22#1568993411yescharacteristic
795C22#1568993411yescharacteristic
796C4—22no—
797C4—22no—
798C4—22no—
799C4—41no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—3761no—
804C4—3761no—
805C4—1882no—
806C4—1882no—
807C4C2×C4×C22⋊D4711yescharacteristic
808C4C2×C4×C22⋊D4711yescharacteristic
809C4#1568963411yescharacteristic
810C4#1568963411yescharacteristic
811C2—42no—
812C2—44no—
813C2—44no—
814C2C4×#1309399311yescharacteristic
815C2#2025222011yescharacteristic
816C2#2025224511yescharacteristic
817C2#2025266511yescharacteristic
818C2#2025269211yescharacteristic
819C2#2025357211yescharacteristic
820C2#2025364011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#518C2
socleC23×C47C22×D4
prime radicalC23×D4×C47C22
cosocleC22×C4×C47C24
hypercenterC2×#518D47
hypocenterC47#21459
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
2. C2×#15689223C2semidirect
3. C2×C4×#10625335C2semidirect
4. #20246070C2semidirect
5. #20243722C2semidirect
6. #20243722C2semidirect
7. #20243700C2semidirect
8. #20243649C2semidirect
9. #20243635C2semidirect
10. #20243587C2semidirect
12. #20243213C2semidirect
13. C4×#13093945C2semidirect
14. #20243154C2semidirect
19. C2×C4×Dic94C22semidirect
20. #15689274C4semidirect
23. C2×#13093957C22semidirect
24. C2×#13093955C22semidirect
25. C2×#13093947C22semidirect
26. C2×#13093947C22semidirect
35. C2×#13093935C22semidirect
36. C2×C4×C47⋊C8C22semidirect
37. #15689029C22semidirect
38. #15689021C22semidirect
44. C4×C4⋊Dic47C22semidirect
45. #15688885C22semidirect
46. #15688885C22semidirect
47. #15688885C22semidirect
48. #15688885C22semidirect
49. #15688878C22semidirect
50. #15688878C22semidirect
69. C2×#10625335C2×C4semidirect
70. C2×#10625335C2×C4semidirect
76. #13094003C2×C4semidirect
97. #13093945C2×C4semidirect
98. #13093945C2×C4semidirect
100. C22⋊(C47⋊C8)C2×C4semidirect
474. C47#21459semidirect

Maximal subgroups

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

subgroupindex
C2×#156892742
C2×#156892232
C2×C4×#106253352
#202460702
#202437222
#202437002
#202436492
#202436352
#202435872
#202433192
#202432132
C4×#130939452
#202431542
C2×C47×#5182
#2145947