Finite Group Databasebeta

← #26221963

Subgroups — #26221963

Order 12032.

1552 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10625350C211yesmaximal, characteristic, complemented
2C2×#15689266C211yesmaximal, characteristic
3C2×#15689233C211yesmaximal, characteristic, complemented
4C2×#15689223C211yesmaximal, characteristic, complemented
5#20243746C211yesmaximal, characteristic, complemented
6#20243739C211yesmaximal, characteristic, complemented
7#20243711C211yesmaximal, characteristic, complemented
8#20243655C211yesmaximal, characteristic, complemented
9#20243634C211yesmaximal, characteristic, complemented
10#20243585C211yesmaximal, characteristic, complemented
11#20243326C211yesmaximal, characteristic, complemented
12#20243221C211yesmaximal, characteristic, complemented
13#20243216C211yesmaximal, characteristic, complemented
14#20243150C211yesmaximal, characteristic, complemented
15C4×#121×C47C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17C22×#10625335C2211yescharacteristic
18C22×#10625334C2211yescharacteristic
19C4×#10625350—24no—
20C4×#10625350—24no—
21C2×C4×Dic94C2211yescharacteristic
22C2×C4×Dic94C2211yescharacteristic
23C2×C4×D188C2211yescharacteristic
24C2×C4×D188C2211yescharacteristic
25C2×C4×C22⋊D47—21no—
26C2×C4×C22⋊D47—21no—
27C2×#13093983C2211yescharacteristic
28C2×#13093981—21no—
29C2×C42×D47—21no—
30#15689266C418yescomplemented
31#15689233—24no—
32#15689223—24no—
33C2×#13093957C2211yescharacteristic
34C2×#13093955C2211yescharacteristic
35C2×#13093947C2211yescharacteristic
36C2×#13093947C2211yescharacteristic
37C2×#13093947C2211yescharacteristic
38C2×#13093945C2211yescharacteristic
39C2×#13093945C2211yescharacteristic
40C2×#13093944C2211yescharacteristic
41C2×#13093944C2211yescharacteristic
42C2×#13093944C2211yescharacteristic
43C2×C22⋊(C47⋊C8)C2211yescharacteristic
44C2×C22⋊(C47⋊C8)C2211yescharacteristic
45C2×#13093935C2211yescharacteristic
46C2×#13093935C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688878C2211yescharacteristic
52#15688878C2211yescharacteristic
53C2×#121×C47C2211yescharacteristic
54C2×C4×D4×C47—21no—
55C2×C4×D4×C47C2211yescharacteristic
56C22×C42×C47C2211yescharacteristic
57C47×#390C2211yescharacteristic
58C47×#389C2211yescharacteristic
59C47×#388—21no—
60C47×#386—21no—
61C47×#380C2211yescharacteristic
62C4×C4⋊C4×C47C2211yescharacteristic
63C4×C22⋊C4×C47—21no—
64C2×#10625350—22no—
65C2×#10625350—22no—
66C2×#10625350—22no—
67C2×#10625350—22no—
68C2×#10625350—22no—
69C2×#10625350C2×C414yescomplemented
70C22×Dic94C2311yescharacteristic
71C22×D188C2311yescharacteristic
72C22×C22⋊D47—21no—
73C22×C4×D47—21no—
74C22×C4×D47—21no—
75C22×C4×D47—21no—
76C2×#10625335—22no—
77C2×#10625335—22no—
78C2×#10625335C2×C414yescomplemented
79C2×#10625334—22no—
80C2×#10625334—22no—
81C2×#10625334C2×C414yescomplemented
82C22×C47⋊C8C2311yescharacteristic
83C22×C47⋊C8C2311yescharacteristic
84C22×C47⋊C8C2311yescharacteristic
85C22×C47⋊C8C2311yescharacteristic
86C4×Dic94—22no—
87C4×Dic94—22no—
88C4×Dic94—22no—
89C4×Dic94D414yescomplemented
90C4×D188—22no—
91C4×D188—22no—
92C4×D188—22no—
93C4×D188D414yescomplemented
94C4×C22⋊D47—28no—
95C4×C22⋊D47—28no—
96#13093983—22no—
97#13093983—22no—
98#13093981—28no—
99C2×C4⋊Dic47C2311yescharacteristic
100C2×C4⋊Dic47C2311yescharacteristic
101C2×Dic47⋊C4—21no—
102C2×Dic47⋊C4—21no—
103C2×C22⋊Dic47—21no—
104C2×(C2×D47)⋊C4—21no—
105C2×(C2×D47)⋊C4—21no—
106C2×C4×Dic47—21no—
107C2×C4×Dic47—21no—
108C2×C4×Dic47—21no—
109C42×D47—28no—
110#13093957—22no—
111#13093955—22no—
112#13093947—22no—
113#13093947—22no—
114#13093947C2×C414yescomplemented
115#13093945—22no—
116#13093945—22no—
117#13093944—22no—
118#13093944—22no—
119#13093944C2×C414yescomplemented
120C22⋊(C47⋊C8)—22no—
121C22⋊(C47⋊C8)C2×C414yescomplemented
122#13093935—22no—
123#13093935—22no—
124C22×D4×C47—21no—
125C22×D4×C47C2311yescharacteristic
126C23×C4×C47—21no—
127C23×C4×C47D411yescharacteristic
128C23×C4×C47D411yescharacteristic
129C23×C4×C47C2311yescharacteristic
130#121×C47—22no—
131#121×C47C2×C414yescomplemented
132C4×D4×C47—22no—
133C4×D4×C47—22no—
134C4×D4×C47—44no—
135C2×C4⋊C4×C47—21no—
136C2×C4⋊C4×C47C2311yescharacteristic
137C2×C4⋊C4×C47C2311yescharacteristic
138C2×C4⋊C4×C47C2311yescharacteristic
139C2×C22⋊C4×C47—21no—
140C2×C22⋊C4×C47—21no—
141C2×C22⋊C4×C47—21no—
142C2×C22⋊C4×C47—21no—
143C2×C22⋊C4×C47—21no—
144C2×C42×C47—22no—
145C2×C42×C47—22no—
146C2×C42×C47—21no—
147C2×C42×C47D411yescharacteristic
148C2×C42×C47D411yescharacteristic
149C2×C42×C47C2311yescharacteristic
150C2×C42×C47C2311yescharacteristic
151#95×C47—21no—
152#95×C47—21no—
153#95×C47—21no—
154C24×C47—21no—
155C24×C47C2×D411yescharacteristic
156C23×D47—21no—
157C2×D4×C47—24no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—21no—
163C2×D4×C47—42no—
164C2×D4×C47—42no—
165C2×D4×C47C22×C412yes—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—41no—
177C22×C4×C47—41no—
178C22×C4×C47—41no—
179C22×C4×C47—42no—
180C22×C4×C47—42no—
181C22×C4×C47—42no—
182C22×C4×C47C22×C412yes—
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47#4112yes—
189C22×C4×C47C2411yescharacteristic
190C2×C22⋊D47—24no—
191C2×C22⋊D47—24no—
192C2×C22⋊D47—24no—
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—21no—
196#10625350—28no—
197#10625350—28no—
198#10625350—28no—
199#10625350—28no—
200C2×D188—21no—
201C2×D188—21no—
202C2×D188—21no—
203C2×D188C22×C412yes—
204C2×D188C2×D412yes—
205C2×D188#4112yes—
206C2×C4×D47—24no—
207C2×C4×D47—24no—
208C2×C4×D47—24no—
209C2×C4×D47—24no—
210C2×C4×D47—24no—
211C2×C4×D47—42no—
212C2×C4×D47—42no—
213C2×C4×D47—42no—
214C2×C4×D47—42no—
215C2×Dic94—21no—
216C2×Dic94—21no—
217C2×Dic94—21no—
218C2×Dic94C22×C412yes—
219C2×Dic94C2×D412yes—
220C2×Dic94#4112yes—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—42no—
227C4⋊C4×C47C22×C412yes—
228C22⋊C4×C47—24no—
229C22⋊C4×C47—42no—
230C22⋊C4×C47—42no—
231C22⋊C4×C47—42no—
232C22⋊C4×C47—42no—
233C42×C47—22no—
234C42×C47—22no—
235C42×C47—21no—
236C42×C47—21no—
237C42×C47—42no—
238C42×C47C2×D412yes—
239C42×C47C2×D412yes—
240C22⋊Dic47—24no—
241#10625335—28no—
242#10625334—28no—
243(C2×D47)⋊C4—24no—
244(C2×D47)⋊C4—24no—
245C4⋊Dic47—21no—
246C4⋊Dic47—21no—
247C4⋊Dic47C2×D412yes—
248C4⋊Dic47C2×D412yes—
249Dic47⋊C4—24no—
250Dic47⋊C4—24no—
251C4×Dic47—24no—
252C4×Dic47—24no—
253C4×Dic47—24no—
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⋊C8—21no—
262C2×C47⋊C8—21no—
263C2×C47⋊C8—21no—
264C2×C47⋊C8C22×C412yes—
265C2×C47⋊C8C22×C412yes—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—22no—
273C23×C47—41no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—41no—
279C23×C47C4×D412yes—
280C23×C47C22×D411yescharacteristic
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—22no—
284C22×D47—41no—
285C22×D47—41no—
286C22×D47—41no—
287C22×D47—41no—
288D4×C47—22no—
289D4×C47—22no—
290D4×C47—48no—
291D4×C47—41no—
292D4×C47—41no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—44no—
310C2×C4×C47—44no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—84no—
320C2×C4×C47C4×D412yes—
321C2×C4×C47#12012yes—
322C2×C4×C47#12012yes—
323C2×C4×C47AGL(1,ℤ/8)12yes—
324C2×C4×C47C23×C411yescharacteristic
325C2×C4×C47C22×D411yescharacteristic
326C2×C4×C47C22×D411yescharacteristic
327C2×C4×C47C2×#4111yescharacteristic
328C2×C4×C47C2×#4111yescharacteristic
329C2×C4×C47C2×#4111yescharacteristic
330C22⋊D47—216no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—41no—
339C2×Dic47—41no—
340D188—22no—
341D188—22no—
342D188—22no—
343D188C4×D414yescomplemented
344C4×D47—216no—
345C4×D47—48no—
346C4×D47—48no—
347Dic94—22no—
348Dic94—22no—
349Dic94—22no—
350Dic94C4×D414yescomplemented
351C47⋊C8—22no—
352C47⋊C8—22no—
353C47⋊C8—41no—
354C47⋊C8—41no—
355#21456—471nomaximal, Sylow
356C22×C47—22no—
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—42no—
364C22×C47—42no—
365C22×C47—42no—
366C22×C47—81no—
367C22×C47—81no—
368C22×C47—81no—
369C22×C47—81no—
370C22×C47C2×C4×D411yescharacteristic
371C22×C47C2×#12011yescharacteristic
372C22×C47#52511yescharacteristic
373C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
374C22×C47#57511yescharacteristic
375C22×C47#57511yescharacteristic
376C22×C47#57511yescharacteristic
377C2×D47—24no—
378C2×D47—42no—
379C2×D47—42no—
380C2×D47—42no—
381C2×D47—42no—
382C2×D47—42no—
383C2×D47—42no—
384C4×C47—22no—
385C4×C47—22no—
386C4×C47—22no—
387C4×C47—22no—
388C4×C47—42no—
389C4×C47—41no—
390C4×C47—81no—
391C4×C47—81no—
392C4×C47C2×C4×D411yescharacteristic
393C4×C47C2×C4×D411yescharacteristic
394C4×C47#52511yescharacteristic
395C4×C47#52511yescharacteristic
396Dic47—24no—
397Dic47—42no—
398Dic47—42no—
399C2×C4×#41—471no—
400C2×#449—471no—
401C2×#442—471no—
402C2×#440—471no—
403C4×#121D4711yescharacteristic, complemented
404#1880—471no—
405#1879—471no—
406#1875—471no—
407#1865—471no—
408#1862—471no—
409#1854—471no—
410#1788—471no—
411#1763—471no—
412#1762—471no—
413#1749—471no—
414C2×C47—42no—
415C2×C47—82no—
416C2×C47C4×#12011yescharacteristic
417C2×C47#294311yescharacteristic
418C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
419C2×C47#300511yescharacteristic
420C2×C47#300611yescharacteristic
421C2×C47#311111yescharacteristic
422C2×C47#311511yescharacteristic
423D47—44no—
424C22×#41—471no—
425C22×SD16—471no—
426C22×D8—471no—
427C2×#121C2×D4711yescharacteristic
428C4×#41—944no—
429C4×#41—944no—
430C2×C4×Q8—471no—
431C2×C4×Q8—471no—
432C2×C4×D4—21no—
433C2×C4×D4—471no—
434C2×C4×D4—471no—
435C2×C4×D4—941no—
436C2×C4×D4—941no—
437C2×C4×D4C2×D4711yescharacteristic
438C2×#117—471no—
439C2×#117—941no—
440C22×C42—941no—
441C22×C42C2×D4711yescharacteristic
442#449—478no—
443#442—944no—
444#440—944no—
445C2×#107—471no—
446C2×#106—471no—
447C2×#103—471no—
448C2×#103—471no—
449C2×#103—471no—
450C2×#102—471no—
451C2×#102—471no—
452C2×#102—471no—
453C2×#102—471no—
454C2×#102—471no—
455C2×C22⋊C8—471no—
456C2×C22⋊C8—471no—
457C2×#97—471no—
458C2×#97—471no—
459#390C2×D4711yescharacteristic
460#389C2×D4711yescharacteristic
461#388—21no—
462#386—21no—
463#380C2×D4711yescharacteristic
464C4×C4⋊C4C2×D4711yescharacteristic
465C4×C22⋊C4—21no—
466#340—471no—
467#340—471no—
468#340—471no—
469#340—471no—
470#336—471no—
471#336—471no—
472C47#2145611yescharacteristic, complemented, Sylow
473C2×#41—474no—
474C2×#41—942no—
475C2×#41—942no—
476C2×#41—942no—
477C2×#41—942no—
478C2×#41—942no—
479C22×Q8—471no—
480C22×D4—21no—
481C22×D4—471no—
482C22×D4—941no—
483C22×D4C22×D4711yescharacteristic
484C23×C4—21no—
485C23×C4—941no—
486C23×C4—941no—
487C23×C4—941no—
488C23×C4C22⋊D4711yescharacteristic
489C23×C4C22⋊D4711yescharacteristic
490C23×C4C22×D4711yescharacteristic
491C2×SD16—474no—
492C2×SD16—942no—
493C2×SD16—942no—
494C2×D8—474no—
495C2×D8—942no—
496C2×D8—942no—
497C22×C8—471no—
498C22×C8—471no—
499C22×C8—471no—
500C22×C8—471no—
501#121—22no—
502#121C4×D4714yescomplemented
503C4×Q8—474no—
504C4×Q8—942no—
505C4×Q8—942no—
506C4×Q8—942no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—44no—
510C4×D4—474no—
511C4×D4—942no—
512C4×D4—942no—
513C4×D4—948no—
514C4×D4—948no—
515C4×D4—942no—
516#117—948no—
517#117—942no—
518#117—942no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—941no—
524C2×C4⋊C4C22×D4711yescharacteristic
525C2×C4⋊C4C22×D4711yescharacteristic
526C2×C4⋊C4C22×D4711yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—941no—
533C2×C22⋊C4—941no—
534C2×C22⋊C4—941no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—21no—
538C2×C42—948no—
539C2×C42—941no—
540C2×C42—941no—
541C2×C42—941no—
542C2×C42C22⋊D4711yescharacteristic
543C2×C42C22⋊D4711yescharacteristic
544C2×C42C22×D4711yescharacteristic
545C2×C42C22×D4711yescharacteristic
546#107—942no—
547#106—942no—
548#103—474no—
549#103—942no—
550#103—942no—
551#102—474no—
552#102—942no—
553#102—942no—
554#102—942no—
555#102—942no—
556C22⋊C8—474no—
557C22⋊C8—942no—
558#97—942no—
559#97—942no—
560#95—21no—
561#95—21no—
562#95—21no—
563C24—21no—
564C24—941no—
565C24C2×C22⋊D4711yescharacteristic
566#41—948no—
567#41—948no—
568#41—948no—
569#41—948no—
570C2×Q8—472no—
571C2×Q8—472no—
572C2×Q8—472no—
573C2×Q8—941no—
574C2×Q8—941no—
575C2×Q8—941no—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—472no—
585C2×D4—472no—
586C2×D4—472no—
587C2×D4—944no—
588C2×D4—944no—
589C2×D4—944no—
590C2×D4—941no—
591C2×D4—941no—
592C2×D4—941no—
593C2×D4C2×C4×D4712yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—944no—
611C22×C4—944no—
612C22×C4—944no—
613C22×C4—941no—
614C22×C4—944no—
615C22×C4—941no—
616C22×C4—941no—
617C22×C4—944no—
618C22×C4—1882no—
619C22×C4—1882no—
620C22×C4—1882no—
621C22×C4—1882no—
622C22×C4C2×C4×D4712yes—
623C22×C4#1062535012yes—
624C22×C4C2×C22⋊D4711yescharacteristic
625C22×C4C2×C22⋊D4711yescharacteristic
626C22×C4C2×C22⋊D4711yescharacteristic
627C22×C4C2×C22⋊D4711yescharacteristic
628C22×C4C2×C22⋊D4711yescharacteristic
629C22×C4C23×D4711yescharacteristic
630SD16—948no—
631D8—948no—
632C2×C8—472no—
633C2×C8—472no—
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—
643C2×C8—941no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—42no—
650C4⋊C4—472no—
651C4⋊C4—472no—
652C4⋊C4—944no—
653C4⋊C4—944no—
654C4⋊C4—941no—
655C4⋊C4—941no—
656C4⋊C4C2×C4×D4712yes—
657C22⋊C4—24no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—944no—
663C22⋊C4—944no—
664C22⋊C4—944no—
665C42—22no—
666C42—22no—
667C42—21no—
668C42—21no—
669C42—42no—
670C42—944no—
671C42—944no—
672C42—944no—
673C42D4×D4712yes—
674C42D4×D4712yes—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—22no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—942no—
689C23—942no—
690C23—942no—
691C23—1881no—
692C23—1881no—
693C23—1881no—
694C23—1881no—
695C23C4×C22⋊D4712yes—
696C23C22×C22⋊D4711yescharacteristic
697Q8—474no—
698Q8—942no—
699Q8—942no—
700Q8—942no—
701D4—22no—
702D4—22no—
703D4—48no—
704D4—41no—
705D4—41no—
706D4—474no—
707D4—9416no—
708D4—942no—
709D4—942no—
710D4—942no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—84no—
738C2×C4—9416no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—942no—
743C2×C4—942no—
744C2×C4—1888no—
745C2×C4—1888no—
746C2×C4—1881no—
747C2×C4—1881no—
748C2×C4—1881no—
749C2×C4—1881no—
750C2×C4C4×C22⋊D4712yes—
751C2×C4#1309399212yes—
752C2×C4#1309399212yes—
753C2×C4#1309405012yes—
754C2×C4C22×C4×D4711yescharacteristic
755C2×C4C2×D4×D4711yescharacteristic
756C2×C4C2×D4×D4711yescharacteristic
757C2×C4#41×D4711yescharacteristic
758C2×C4#41×D4711yescharacteristic
759C2×C4C2×#1062535011yescharacteristic
760C8—942no—
761C8—942no—
762C8—1881no—
763C8—1881no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—944no—
779C22—1882no—
780C22—1882no—
781C22—1882no—
782C22—1882no—
783C22—1882no—
784C22—1882no—
785C22C2×C4×C22⋊D4711yescharacteristic
786C22C2×#1309399211yescharacteristic
787C22#1568963011yescharacteristic
788C22C2×#1309405011yescharacteristic
789C22#1568992111yescharacteristic
790C22#1568992111yescharacteristic
791C22#1568992111yescharacteristic
792C4—22no—
793C4—22no—
794C4—22no—
795C4—22no—
796C4—42no—
797C4—41no—
798C4—81no—
799C4—81no—
800C4—944no—
801C4—1882no—
802C4—1882no—
803C4C4×D4×D4711yescharacteristic
804C4C4×D4×D4711yescharacteristic
805C4#1568963211yescharacteristic
806C4#1568963211yescharacteristic
807C2—42no—
808C2—82no—
809C2—1884no—
810C2C4×#1309399211yescharacteristic
811C2#2025218611yescharacteristic
812C2C4×#1309405011yescharacteristic
813C2#2025262811yescharacteristic
814C2#2025263811yescharacteristic
815C2#2025349111yescharacteristic
816C2#2025353311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×#121×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689266C2
cosocleC22×C4×C47C24
hypercenterC4×#121D47
hypocenterC47#21456
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×C4×#10625350C2semidirect
3. C2×#15689233C2semidirect
4. C2×#15689223C2semidirect
5. #20243746C2semidirect
6. #20243739C2semidirect
7. #20243711C2semidirect
8. #20243655C2semidirect
9. #20243634C2semidirect
10. #20243585C2semidirect
11. #20243326C2semidirect
12. #20243221C2semidirect
13. #20243216C2semidirect
14. #20243150C2semidirect
15. C4×#121×C47C2semidirect
30. #15689266C4semidirect
69. C2×#10625350C2×C4semidirect
78. C2×#10625335C2×C4semidirect
81. C2×#10625334C2×C4semidirect
89. C4×Dic94D4semidirect
93. C4×D188D4semidirect
114. #13093947C2×C4semidirect
119. #13093944C2×C4semidirect
121. C22⋊(C47⋊C8)C2×C4semidirect
131. #121×C47C2×C4semidirect
343. D188C4×D4semidirect
350. Dic94C4×D4semidirect
403. C4×#121D47semidirect
472. C47#21456semidirect
502. #121C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106253502
C2×#156892662
C2×#156892332
C2×#156892232
#202437462
#202437392
#202437112
#202436552
#202436342
#202435852
#202433262
#202432212
#202432162
#202431502
C4×#121×C472
#2145647