Finite Group Databasebeta

← #25097549

Subgroups — #25097549

Order 11008.

1878 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D43C211yesmaximal, characteristic
2C2×#14582940C211yesmaximal, characteristic, complemented
3C2×#14582902C211yesmaximal, characteristic
4C2×#14582902C211yesmaximal, characteristic
5#19137076C211yesmaximal, characteristic, complemented
6#19134859C211yesmaximal, characteristic, complemented
7#19134858C211yesmaximal, characteristic, complemented
8#19134857C211yesmaximal, characteristic, complemented
9#19134856C211yesmaximal, characteristic, complemented
10#19134841C211yesmaximal, characteristic, complemented
11#19134840C211yesmaximal, characteristic, complemented
12#19134839C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#19134287C211yesmaximal, characteristic, complemented
15C43×#1862C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C23×C4×D43—21no—
18C22×#10621872C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23C2×C4×C22⋊D43—21no—
24C2×(C22⋊D43)⋊C4—21no—
25C4×D4×D43—24no—
26C4×D4×D43—24no—
27C2×#13063283C2211yescharacteristic
28C2×#13063283C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30C2×C22⋊C4×D43—21no—
31C2×C42×D43C2211yescharacteristic
32#14582940—24no—
33C2×#13063258C2211yescharacteristic, complemented
34C2×#13063257C2211yescharacteristic, complemented
35C2×#13063256C2211yescharacteristic, complemented
36#14582902—24no—
37#14582902C418yescomplemented
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44#14582798C2211yescharacteristic, complemented
45#14582797C2211yescharacteristic, complemented
46#14582795C2211yescharacteristic, complemented
47#14582773—21no—
48#14582770—21no—
49C4⋊C4×Dic43—21no—
50#14582750—21no—
51#14582662C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54#14582654C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56#14582653C2211yescharacteristic, complemented
57C2×C4×D4×C43C2211yescharacteristic
58C2×#107×C43C2211yescharacteristic, complemented
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C43×#389C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C43×#336C2211yescharacteristic, complemented
64C24×D43—21no—
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C2×D4×D43—22no—
68C2×D4×D43—22no—
69C2×D4×D43—22no—
70C2×D4×D43C2×C414yes—
71C2×D4×D43D414yes—
72C2×D4×D43Q814yes—
73C23×Dic43—21no—
74C22×C4×D43—28no—
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43—21no—
78C22×C4×D43—44no—
79C22×C4×D43—44no—
80C22×C4×D43D411yescharacteristic
81C22×C4×D43D411yescharacteristic
82C22×C4×D43C2311yescharacteristic
83C2×#10621872—22no—
84C2×#10621872—22no—
85C2×#10621872—22no—
86C2×#10621872—22no—
87C2×#10621872—22no—
88C2×#10621872C2×C414yescomplemented
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C4×D172—22no—
92C4×D172—22no—
93D4×Dic43—22no—
94D4×Dic43—22no—
95#13063287—22no—
96#13063287—22no—
97C4×C22⋊D43—28no—
98(C22⋊D43)⋊C4—28no—
99#13063283—22no—
100#13063283—22no—
101#13063283—22no—
102#13063283C2×C414yescomplemented
103C2×C4⋊Dic43—21no—
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4—21no—
110C4⋊C4×D43—22no—
111C4⋊C4×D43D414yes—
112C2×C22⋊Dic43—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C22⋊C4×D43—28no—
118C2×C4×Dic43—21no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43D411yescharacteristic
121C2×C4×Dic43D411yescharacteristic
122C2×C4×Dic43C2311yescharacteristic
123C42×D43—22no—
124C42×D43—22no—
125#13063258—22no—
126#13063257—22no—
127#13063256—22no—
128#13063247—22no—
129#13063247C2×C414yescomplemented
130#13063246—22no—
131#13063246C2×C414yescomplemented
132#13063245—22no—
133#13063245C2×C414yescomplemented
134C43⋊#95—21no—
135C43⋊#95—21no—
136C43⋊#95—21no—
137C22×D4×C43C2311yescharacteristic
138C23×C4×C43—21no—
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C4×D4×C43—22no—
142C4×D4×C43—22no—
143C2×C4⋊C4×C43—21no—
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C22⋊C4×C43—21no—
148C2×C42×C43C2311yescharacteristic
149#107×C43—22no—
150#102×C43—22no—
151#102×C43C2×C414yescomplemented
152#95×C43—21no—
153C24×C43—21no—
154C23×D43—21no—
155C23×D43—24no—
156C23×D43—24no—
157C23×D43—24no—
158C23×D43—42no—
159C23×D43—42no—
160C23×D43—42no—
161C23×D43—42no—
162C23×D43C2×D411yescharacteristic
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43C22×C412yes—
167C2×D4×C43C2×D412yes—
168C2×D4×C43C2×Q812yes—
169C22×C4×C43—24no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—42no—
174C22×C4×C43—42no—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2411yescharacteristic
178C2×C22⋊D43—24no—
179C2×C22⋊D43—24no—
180C2×C22⋊D43—24no—
181C22×Dic43—24no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—42no—
186C22×Dic43—42no—
187C22×Dic43C2×D411yescharacteristic
188C22×Dic43C2×D411yescharacteristic
189C22×Dic43C2×D411yescharacteristic
190D4×D43—28no—
191D4×D43—28no—
192D4×D43—28no—
193D4×D43C4⋊C4116yescomplemented
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172C22×C412yes—
198C2×D172C2×D412yes—
199C2×D172C2×Q812yes—
200C2×C4×D43—22no—
201C2×C4×D43—22no—
202C2×C4×D43—24no—
203C2×C4×D43—24no—
204C2×C4×D43—22no—
205C2×C4×D43—22no—
206C2×C4×D43—24no—
207C2×C4×D43—41no—
208C2×C4×D43—41no—
209C2×C4×D43—42no—
210C2×C4×D43—42no—
211C2×C4×D43—432no—
212C2×C4×D43—42no—
213C2×C4×D43—42no—
214C2×C4×D43—42no—
215C2×C4×D43—42no—
216C2×C4×D43C22×C412yes—
217C2×C4×D43C2×D412yes—
218C2×C4×D43C2×D412yes—
219C2×C4×D43C2×Q812yes—
220C2×C4×D43#4112yes—
221C2×C4×D43#4112yes—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43C22×C412yescomplemented
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—42no—
233C4⋊C4×C43C22×C412yescomplemented
234C4⋊C4×C43C2×D412yes—
235C22⋊C4×C43—24no—
236C42×C43—21no—
237C42×C43—21no—
238C22⋊Dic43—24no—
239(C2×D43)⋊C4—24no—
240(C2×D43)⋊C4—24no—
241(C2×D43)⋊C4—24no—
242(C2×D43)⋊C4—42no—
243C4⋊Dic43—21no—
244C4⋊Dic43—21no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—42no—
248C4⋊Dic43C22×C412yescomplemented
249C4⋊Dic43C2×D412yes—
250Dic43⋊C4—24no—
251Dic43⋊C4—42no—
252Dic43⋊C4—42no—
253C4×Dic43—21no—
254C4×Dic43—21no—
255C4×Dic43—24no—
256C4×Dic43—22no—
257C4×Dic43—22no—
258C4×Dic43—42no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8C22×C412yescomplemented
265#10621872—28no—
266#10621872—44no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—22no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43C22×D411yescharacteristic
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—216no—
283C22×D43—48no—
284C22×D43—48no—
285C22×D43—48no—
286C22×D43—48no—
287C22×D43—48no—
288C22×D43—48no—
289C22×D43—41no—
290C22×D43—41no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43C4×D412yes—
294C22×D43#12012yes—
295C22×D43C22⋊Q812yes—
296D4×C43—22no—
297D4×C43—22no—
298D4×C43—22no—
299D4×C43C2×C4⋊C414yes—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—22no—
303C2×C4×C43—21no—
304C2×C4×C43—22no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—48no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43AGL(1,ℤ/8)12yes—
316C2×C4×C43C23×C411yescharacteristic
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C22×Q811yescharacteristic
320C2×C4×C43C2×#4111yescharacteristic
321C2×C4×C43C2×#4111yescharacteristic
322C22⋊D43—216no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—22no—
326C2×Dic43—21no—
327C2×Dic43—22no—
328C2×Dic43—21no—
329C2×Dic43—21no—
330C2×Dic43—48no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43C4×D412yes—
339C2×Dic43#12012yes—
340C2×Dic43C22⋊Q812yes—
341C2×Dic43AGL(1,ℤ/8)12yes—
342D172—22no—
343D172—22no—
344D172—22no—
345D172C2×C4⋊C414yes—
346C4×D43—28no—
347C4×D43—48no—
348C4×D43—48no—
349C4×D43—44no—
350C4×D43—48no—
351C4×D43C2×C4⋊C414yes—
352C4×D43C4×D414yes—
353C4×D43C22⋊Q814yes—
354C4×D43#12314yes—
355C8×C43—22no—
356C8×C43—41no—
357C43⋊C8—22no—
358C43⋊C8—41no—
359#20873—431nomaximal, Sylow
360C22×C43—24no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43C2×C4×D411yescharacteristic
368C22×C43C2×#12011yescharacteristic
369C22×C43C2×C22⋊Q811yescharacteristic
370C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
372C22×C43#57511yescharacteristic
373C22×C43#57511yescharacteristic
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—22no—
378C2×D43—22no—
379C2×D43—22no—
380C2×D43—24no—
381C2×D43—432no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43#38514yes—
389C4×C43—22no—
390C4×C43—42no—
391C4×C43—42no—
392C4×C43—41no—
393C4×C43—81no—
394C4×C43C22×C4⋊C411yescharacteristic
395C4×C43C2×C4×D411yescharacteristic
396C4×C43C2×C22⋊Q811yescharacteristic
397C4×C43C2×#12311yescharacteristic
398Dic43—22no—
399Dic43—42no—
400Dic43—42no—
401Dic43—41no—
402Dic43—81no—
403Dic43#38514yes—
404C22×C4×D4—431no—
405C2×#428—431no—
406C2×#418—431no—
407C2×#418—431no—
408#2296—431no—
409#1864—431no—
410#1864—431no—
411#1864—431no—
412#1864—431no—
413#1862—431no—
414#1862—431no—
415#1862—431no—
416#1862D4311yescharacteristic, complemented
417#1736—431no—
418#1728—431no—
419C2×C43—44no—
420C2×C43C2×#38511yescharacteristic
421C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
422C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
423C2×C43#300311yescharacteristic
424C2×C43#300511yescharacteristic
425C2×C43#307711yescharacteristic
426C2×C43#307711yescharacteristic
427D43—24no—
428D43—44no—
429C23×D4—431no—
430C24×C4—861no—
431C22×M16—431no—
432C22×M16—431no—
433C2×C4×D4—431no—
434C2×C4×D4—431no—
435C2×C4×D4—431no—
436C2×C4×D4—861no—
437C2×C4×D4—861no—
438C2×C4×D4—864no—
439C2×C4×D4—864no—
440C2×C4×D4C2×D4311yescharacteristic
441C2×#117—431no—
442C2×#117—431no—
443C22×C4⋊C4—431no—
444C22×C22⋊C4—861no—
445C22×C42—431no—
446#428—864no—
447C2×#107—431no—
448C2×#107C2×D4311yescharacteristic, complemented
449C2×#106—431no—
450C2×#106—431no—
451#418—438no—
452#418—864no—
453C2×#102—431no—
454C2×#102—431no—
455C2×#102—431no—
456C2×#102—431no—
457C2×#102—431no—
458C2×#102—431no—
459C2×#102C2×D4311yescharacteristic
460C2×#102C2×D4311yescharacteristic
461#389—431no—
462#389—431no—
463#389—431no—
464#389C2×D4311yescharacteristic, complemented
465#385—861no—
466#385—861no—
467C4×C4⋊C4—861no—
468C4×C4⋊C4—861no—
469#340—431no—
470#340—431no—
471#340—431no—
472#340C2×D4311yescharacteristic, complemented
473#336—431no—
474#336—431no—
475#336—431no—
476#336C2×D4311yescharacteristic, complemented
477C43#2087311yescharacteristic, complemented, Sylow
478C25—861no—
479C22×D4—434no—
480C22×D4—434no—
481C22×D4—434no—
482C22×D4—431no—
483C22×D4—862no—
484C22×D4—862no—
485C22×D4—862no—
486C22×D4—861no—
487C22×D4C22×D4311yescharacteristic
488C23×C4—21no—
489C23×C4—431no—
490C23×C4—431no—
491C23×C4—431no—
492C23×C4—861no—
493C23×C4—861no—
494C23×C4—868no—
495C23×C4—861no—
496C23×C4—861no—
497C23×C4—1724no—
498C23×C4—1724no—
499C2×M16—434no—
500C2×M16—862no—
501C2×M16—862no—
502C2×M16—862no—
503C2×M16—862no—
504C2×M16—862no—
505C22×C8—431no—
506C22×C8—431no—
507C22×C8C22×D4311yescharacteristic
508C22×C8C22×D4311yescharacteristic
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—862no—
512C4×D4—862no—
513C4×D4—868no—
514C4×D4—862no—
515C4×D4—862no—
516C4×D4—868no—
517C4×D4—862no—
518C4×D4—862no—
519#117—434no—
520#117—862no—
521#117—862no—
522#117—862no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—431no—
525C2×C4⋊C4—431no—
526C2×C4⋊C4—434no—
527C2×C4⋊C4—431no—
528C2×C4⋊C4—862no—
529C2×C4⋊C4—861no—
530C2×C4⋊C4—861no—
531C2×C4⋊C4—861no—
532C2×C4⋊C4—861no—
533C2×C4⋊C4C22×D4311yescharacteristic
534C2×C4⋊C4C22×D4311yescharacteristic
535C2×C4⋊C4C22×D4311yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—868no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—861no—
542C2×C22⋊C4—861no—
543C2×C42—431no—
544C2×C42—431no—
545C2×C42—431no—
546C2×C42—862no—
547C2×C42—862no—
548C2×C42—861no—
549C2×C42—861no—
550C2×C42C22×D4311yescharacteristic
551#107—22no—
552#107—862no—
553#106—862no—
554#106—862no—
555#102—22no—
556#102—434no—
557#102—434no—
558#102—434no—
559#102—862no—
560#102—862no—
561#102—862no—
562#102C4×D4314yescomplemented
563#95—21no—
564#95—861no—
565#95—861no—
566#95—861no—
567C24—21no—
568C24—431no—
569C24—864no—
570C24—864no—
571C24—864no—
572C24—861no—
573C24—1722no—
574C24—1722no—
575C24—1722no—
576C24—1722no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—4316no—
581C2×D4—432no—
582C2×D4—432no—
583C2×D4—432no—
584C2×D4—868no—
585C2×D4—868no—
586C2×D4—868no—
587C2×D4—864no—
588C2×D4—864no—
589C2×D4—864no—
590C2×D4—861no—
591C2×D4—861no—
592C2×D4—861no—
593C2×D4C2×C4×D4312yes—
594C2×D4D4×D4312yes—
595C2×D4Q8×D4312yes—
596C22×C4—24no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—431no—
603C22×C4—432no—
604C22×C4—432no—
605C22×C4—432no—
606C22×C4—432no—
607C22×C4—432no—
608C22×C4—432no—
609C22×C4—431no—
610C22×C4—431no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4—862no—
614C22×C4—864no—
615C22×C4—864no—
616C22×C4—864no—
617C22×C4—862no—
618C22×C4—864no—
619C22×C4—861no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—1721no—
623C22×C4—1721no—
624C22×C4—1722no—
625C22×C4—1722no—
626C22×C4—17232no—
627C22×C4—1722no—
628C22×C4—1722no—
629C22×C4—1722no—
630C22×C4—1722no—
631C22×C4—1722no—
632C22×C4—1722no—
633C22×C4D4×D4311yescharacteristic
634C22×C4D4×D4311yescharacteristic
635C22×C4C23×D4311yescharacteristic
636M16—868no—
637M16—1724no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—432no—
644C2×C8—861no—
645C2×C8—861no—
646C2×C8—861no—
647C2×C8—861no—
648C2×C8—861no—
649C2×C8C2×C4×D4312yescomplemented
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—42no—
655C4⋊C4—432no—
656C4⋊C4—432no—
657C4⋊C4—864no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C4⋊C4—1722no—
663C4⋊C4—1722no—
664C4⋊C4—1722no—
665C4⋊C4C2×C4×D4312yescomplemented
666C4⋊C4D4×D4312yes—
667C22⋊C4—24no—
668C22⋊C4—864no—
669C22⋊C4—864no—
670C22⋊C4—864no—
671C22⋊C4—864no—
672C22⋊C4—1722no—
673C42—21no—
674C42—21no—
675C42—862no—
676C42—862no—
677C42—864no—
678C42—861no—
679C42—861no—
680C42—1722no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—432no—
689C23—432no—
690C23—432no—
691C23—8616no—
692C23—861no—
693C23—861no—
694C23—861no—
695C23—861no—
696C23—862no—
697C23—862no—
698C23—862no—
699C23—1728no—
700C23—1728no—
701C23—1728no—
702C23—1728no—
703C23—1728no—
704C23—1728no—
705C23—1721no—
706C23—1721no—
707C23—1721no—
708C23—1721no—
709C23C2×D4×D4311yescharacteristic
710D4—22no—
711D4—22no—
712D4—22no—
713D4—434no—
714D4—8616no—
715D4—862no—
716D4—862no—
717D4—862no—
718D4C4⋊C4×D4314yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—48no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—432no—
735C2×C4—432no—
736C2×C4—432no—
737C2×C4—434no—
738C2×C4—434no—
739C2×C4—434no—
740C2×C4—434no—
741C2×C4—432no—
742C2×C4—868no—
743C2×C4—861no—
744C2×C4—861no—
745C2×C4—862no—
746C2×C4—861no—
747C2×C4—862no—
748C2×C4—861no—
749C2×C4—861no—
750C2×C4—1728no—
751C2×C4—1728no—
752C2×C4—1728no—
753C2×C4—1724no—
754C2×C4—1728no—
755C2×C4—1721no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1721no—
759C2×C4—1721no—
760C2×C4—1721no—
761C2×C4—1721no—
762C2×C4#1306334912yes—
763C2×C4C22×C4×D4311yescharacteristic
764C2×C4C2×D4×D4311yescharacteristic
765C2×C4C2×D4×D4311yescharacteristic
766C2×C4C2×Q8×D4311yescharacteristic
767C2×C4#41×D4311yescharacteristic
768C2×C4#41×D4311yescharacteristic
769C8—22no—
770C8—41no—
771C8—862no—
772C8—1721no—
773C22—24no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—434no—
781C22—862no—
782C22—862no—
783C22—862no—
784C22—862no—
785C22—862no—
786C22—862no—
787C22—864no—
788C22—17232no—
789C22—1722no—
790C22—1722no—
791C22—1722no—
792C22—1722no—
793C22—1722no—
794C22—1722no—
795C22C4×D4×D4311yescharacteristic
796C22#120×D4311yescharacteristic
797C22C22⋊Q8×D4311yescharacteristic
798C22AGL(1,ℤ/8)×D4311yescharacteristic
799C22C2×#1306334911yescharacteristic
800C22#1458369611yescharacteristic
801C22#1458369811yescharacteristic
802C4—22no—
803C4—42no—
804C4—41no—
805C4—42no—
806C4—81no—
807C4—434no—
808C4—862no—
809C4—3441no—
810C4—1722no—
811C4—1721no—
812C4—1722no—
813C4C2×C4⋊C4×D4311yescharacteristic
814C4C4×D4×D4311yescharacteristic
815C4C22⋊Q8×D4311yescharacteristic
816C4#123×D4311yescharacteristic
817C2—44no—
818C2—864no—
819C2—1724no—
820C2#385×D4311yescharacteristic
821C2C4×#1306334911yescharacteristic
822C2#1914340011yescharacteristic
823C2#1914381911yescharacteristic
824C2#1914383811yescharacteristic
825C2#1914438711yescharacteristic
826C2#1914439011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1862C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1862D43
hypocenterC43#20873
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
2. C2×#14582940C2semidirect
5. #19137076C2semidirect
6. #19134859C2semidirect
7. #19134858C2semidirect
8. #19134857C2semidirect
9. #19134856C2semidirect
10. #19134841C2semidirect
11. #19134840C2semidirect
12. #19134839C2semidirect
13. #19134313C2semidirect
14. #19134287C2semidirect
15. C43×#1862C2semidirect
33. C2×#13063258C22semidirect
34. C2×#13063257C22semidirect
35. C2×#13063256C22semidirect
37. #14582902C4semidirect
44. #14582798C22semidirect
45. #14582797C22semidirect
46. #14582795C22semidirect
51. #14582662C22semidirect
52. #14582661C22semidirect
53. #14582661C22semidirect
54. #14582654C22semidirect
55. #14582653C22semidirect
56. #14582653C22semidirect
58. C2×#107×C43C22semidirect
61. C43×#389C22semidirect
62. C43×#340C22semidirect
63. C43×#336C22semidirect
88. C2×#10621872C2×C4semidirect
102. #13063283C2×C4semidirect
129. #13063247C2×C4semidirect
131. #13063246C2×C4semidirect
133. #13063245C2×C4semidirect
151. #102×C43C2×C4semidirect
193. D4×D43C4⋊C4semidirect
227. C2×C8×C43C22×C4semidirect
233. C4⋊C4×C43C22×C4semidirect
248. C4⋊Dic43C22×C4semidirect
264. C2×C43⋊C8C22×C4semidirect
416. #1862D43semidirect
448. C2×#107C2×D43semidirect
464. #389C2×D43semidirect
472. #340C2×D43semidirect
476. #336C2×D43semidirect
477. C43#20873semidirect
562. #102C4×D43semidirect
649. C2×C8C2×C4×D43semidirect
665. C4⋊C4C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D432
C2×#145829402
C2×#145829022
#191370762
#191348592
#191348582
#191348572
#191348562
#191348412
#191348402
#191348392
#191343132
#191342872
C43×#18622
#2087343