Finite Group Databasebeta

← #25118910

Subgroups — #25118910

Order 11008.

1158 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583092C211yesmaximal, characteristic
2C2×#14583008C211yesmaximal, characteristic, complemented
3#19137657C211yesmaximal, characteristic, complemented
4D4×Dic43⋊C4C211yesmaximal, characteristic, complemented
5#19135399C211yesmaximal, characteristic, complemented
6#19135355C211yesmaximal, characteristic, complemented
7#19135292C211yesmaximal, characteristic, complemented
8#19135289C211yesmaximal, characteristic, complemented
9#19134945C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic, complemented
11#19134856C211yesmaximal, characteristic, complemented
12#19134853C211yesmaximal, characteristic, complemented
13#19134463C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C2×C43×#442C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×#13063321C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21C2×C4×C22⋊D43—21no—
22C22×Dic43⋊C4—21no—
23#14583092C418yescomplemented
24#14583008—24no—
25C2×#13063256C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063235C2211yescharacteristic
34C2×C8×Dic43C2211yescharacteristic
35#14582802C2211yescharacteristic
36#14582801C2211yescharacteristic
37#14582799—21no—
38#14582797C2211yescharacteristic
39#14582795C2211yescharacteristic
40#14582778—21no—
41#14582775—21no—
42#14582772—21no—
43#14582771—21no—
44#14582768C2211yescharacteristic
45#14582757—21no—
46C4⋊C4×Dic43C2211yescharacteristic
47C4×Dic43⋊C4C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×D8×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C43×#442—24no—
58C2×#106×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#97×C43C2211yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C22×C22⋊D43—21no—
65C23×Dic43—21no—
66C23×Dic43—21no—
67C22×C4×D43—21no—
68C2×#10621882—22no—
69C2×#10621882—22no—
70C2×#10621882C2×C414yescomplemented
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063321—22no—
74#13063321C2×C414yescomplemented
75D4×Dic43—22no—
76D4×Dic43—22no—
77D4×Dic43—41no—
78D4×Dic43C2×C414yescomplemented
79#13063287—22no—
80#13063287—41no—
81C4×C22⋊D43—44no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—44no—
90C2×Dic43⋊C4D411yescharacteristic
91C2×Dic43⋊C4D411yescharacteristic
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102#13063256—22no—
103Dic43⋊C8C2×C414yescomplemented
104#13063247—22no—
105#13063247C2×C414yescomplemented
106#13063246—22no—
107#13063246—41no—
108#13063246C2×C414yescomplemented
109#13063245—41no—
110#13063235—22no—
111C8×Dic43—22no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C22×D4×C43C2311yescharacteristic
118C22×D4×C43C2311yescharacteristic
119C23×C4×C43—21no—
120C23×C4×C43—21no—
121C2×D8×C43—22no—
122C2×D8×C43—22no—
123C2×D8×C43C2×C414yescomplemented
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C4×D4×C43—22no—
127C4×D4×C43—22no—
128C4×D4×C43—41no—
129C4×D4×C43—41no—
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#106×C43—22no—
136#102×C43—22no—
137#102×C43D414yescomplemented
138#97×C43—22no—
139C24×C43—21no—
140C24×C43—21no—
141C23×D43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C22×C412yes—
151C2×D4×C43C22×C412yes—
152C2×D4×C43C2×D412yes—
153C2×D4×C43#4112yes—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43—42no—
159C22×C4×C43—42no—
160C22×C4×C43—81no—
161C22×C4×C43—81no—
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2411yescharacteristic
165C2×C22⋊D43—24no—
166C2×C22⋊D43—24no—
167C2×C22⋊D43—42no—
168C2×C22⋊D43—42no—
169C2×C22⋊D43—81no—
170C2×C22⋊D43—81no—
171C22×Dic43—24no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—42no—
176C22×Dic43—42no—
177C22×Dic43—42no—
178C22×Dic43—42no—
179C22×Dic43—81no—
180C22×Dic43C2×D411yescharacteristic
181C22×Dic43C2×D411yescharacteristic
182C22×Dic43C2×D411yescharacteristic
183C22×Dic43C2×D411yescharacteristic
184C2×D172—21no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172C22×C412yes—
190C2×C4×D43—42no—
191C2×C4×D43—42no—
192C2×C4×D43—81no—
193D8×C43—28no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43C22×C412yes—
199C2×C8×C43C2×D412yes—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43C2×D412yes—
204C22⋊C4×C43—42no—
205C22⋊C4×C43—42no—
206C42×C43—21no—
207C42×C43—21no—
208C22⋊Dic43—24no—
209C22⋊Dic43—42no—
210C22⋊Dic43—42no—
211C22⋊Dic43—81no—
212#10621882—28no—
213(C2×D43)⋊C4—42no—
214(C2×D43)⋊C4—42no—
215(C2×D43)⋊C4—81no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43C22×C412yes—
222Dic43⋊C4—22no—
223Dic43⋊C4—22no—
224Dic43⋊C4—42no—
225Dic43⋊C4—42no—
226Dic43⋊C4—42no—
227Dic43⋊C4—81no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C4×Dic43—42no—
231C4×Dic43C22×C412yes—
232C4×Dic43#4112yes—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8C22×C412yes—
239C23×C43—22no—
240C23×C43—22no—
241C23×C43—22no—
242C23×C43—22no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43C22×D411yescharacteristic
254C22×D43—22no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261D4×C43—22no—
262D4×C43—22no—
263D4×C43—22no—
264D4×C43—22no—
265D4×C43—22no—
266D4×C43—41no—
267D4×C43—41no—
268D4×C43C4×D414yescomplemented
269C2×C4×C43—22no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—84no—
282C2×C4×C43—84no—
283C2×C4×C43C23×C411yescharacteristic
284C2×C4×C43C22×D411yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C43H(5,𝔽2)11yescharacteristic
288C2×C4×C432−1+411yescharacteristic
289C22⋊D43—48no—
290C22⋊D43—84no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—22no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—48no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—84no—
310C2×Dic43C4×D412yes—
311C2×Dic43C4×D412yes—
312C2×Dic43AGL(1,ℤ/8)12yes—
313C2×Dic43AGL(1,ℤ/8)12yes—
314D172—22no—
315D172—22no—
316D172—41no—
317D172—41no—
318C4×D43—84no—
319C8×C43—22no—
320C8×C43—22no—
321C43⋊C8—22no—
322C43⋊C8—41no—
323#23001—431nomaximal, Sylow
324C22×C43—24no—
325C22×C43—42no—
326C22×C43—42no—
327C22×C43—42no—
328C22×C43—42no—
329C22×C43—42no—
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—42no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43C2×C4×D411yescharacteristic
339C22×C43D4211yescharacteristic
340C22×C43#54811yescharacteristic
341C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
342C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C43#57611yescharacteristic
344C22×C43#57711yescharacteristic
345C2×D43—42no—
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—81no—
349C2×D43—81no—
350C2×D43—81no—
351C2×D43—81no—
352C4×C43—42no—
353C4×C43—41no—
354C4×C43—41no—
355C4×C43—81no—
356C4×C43C2×C4×D411yescharacteristic
357C4×C43#52011yescharacteristic
358C4×C43#54711yescharacteristic
359C4×C43#55311yescharacteristic
360Dic43—22no—
361Dic43—42no—
362Dic43—41no—
363Dic43—41no—
364Dic43—81no—
365Dic43—81no—
366Dic43#44214yescomplemented
367C2×#459—431no—
368C2×#442—431no—
369C2×#442D4311yescharacteristic, complemented
370#2366—431no—
371D4×C4⋊C4—431no—
372#1957—431no—
373#1948—431no—
374#1936—431no—
375#1936—431no—
376#1879—431no—
377#1879—431no—
378#1864—431no—
379#1864—431no—
380#1770—431no—
381C4×#102—431no—
382C2×C43—44no—
383C2×C43—82no—
384C2×C43#236111yescharacteristic
385C2×C43C2×#44211yescharacteristic
386C2×C43#294611yescharacteristic
387C2×C43#327211yescharacteristic
388C2×C43#327411yescharacteristic
389C2×C43#336611yescharacteristic
390C2×C43#337311yescharacteristic
391D43—82no—
392C22×D8—431no—
393C22×D8C2×D4311yescharacteristic
394C2×#127—431no—
395C2×C4×D4—431no—
396C2×C4×D4—431no—
397C2×C4×D4—431no—
398C2×C4×D4—861no—
399C2×C4×D4C2×D4311yescharacteristic
400C2×C4×D4C2×D4311yescharacteristic
401C22×C4⋊C4—861no—
402#459—438no—
403#442—24no—
404#442—864no—
405C2×#106—431no—
406C2×#106C2×D4311yescharacteristic
407C2×C4⋊C8—431no—
408C2×#102—431no—
409C2×#102—431no—
410C2×#102—431no—
411C2×#102—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×#102C2×D4311yescharacteristic
415C2×#102C2×D4311yescharacteristic
416C2×#97—431no—
417C2×#97C2×D4311yescharacteristic
418C2×C4×C8—431no—
419#390—431no—
420#390—431no—
421#390—861no—
422#389—431no—
423#389—431no—
424#386—861no—
425#386—861no—
426#385—861no—
427#385—861no—
428#384—431no—
429#380—861no—
430C4×C4⋊C4—431no—
431C4×C4⋊C4—431no—
432#340—431no—
433#340—431no—
434#340—431no—
435#340—431no—
436#336—431no—
437#336—431no—
438C43#2300111yescharacteristic, complemented, Sylow
439C22×D4—431no—
440C22×D4—861no—
441C22×D4—861no—
442C22×D4C22×D4311yescharacteristic
443C22×D4C22×D4311yescharacteristic
444C23×C4—21no—
445C23×C4—21no—
446C23×C4—861no—
447C23×C4—861no—
448C23×C4—861no—
449C2×D8—22no—
450C2×D8—22no—
451C2×D8—434no—
452C2×D8—862no—
453C2×D8—862no—
454C2×D8C4×D4314yescomplemented
455C22×C8—431no—
456C22×C8—431no—
457C22×C8C22×D4311yescharacteristic
458C22×C8C22×D4311yescharacteristic
459#127—434no—
460#127—862no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—41no—
464C4×D4—41no—
465C4×D4—434no—
466C4×D4—862no—
467C4×D4—862no—
468C4×D4—862no—
469C4×D4—1721no—
470C4×D4—1721no—
471C4×D4—1724no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—1724no—
482C2×C4⋊C4C22×D4311yescharacteristic
483C2×C4⋊C4C22×D4311yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C42—431no—
494C2×C42—431no—
495C2×C42—861no—
496C2×C42C22×D4311yescharacteristic
497#106—22no—
498#106—862no—
499C4⋊C8—434no—
500#102—22no—
501#102—434no—
502#102—434no—
503#102—862no—
504#102—862no—
505#102—1721no—
506#102—1721no—
507#102C22⋊D4314yescomplemented
508#97—22no—
509#97—862no—
510C4×C8—862no—
511#95—431no—
512#95—431no—
513#95—861no—
514#95—861no—
515#95—861no—
516C24—21no—
517C24—21no—
518C24—861no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—432no—
528C2×D4—864no—
529C2×D4—864no—
530C2×D4—861no—
531C2×D4—861no—
532C2×D4—861no—
533C2×D4—861no—
534C2×D4—861no—
535C2×D4—3441no—
536C2×D4—3441no—
537C2×D4—1722no—
538C2×D4—1722no—
539C2×D4C2×C4×D4312yes—
540C2×D4C2×C4×D4312yes—
541C2×D4#1062189812yes—
542C2×D4C2×C22⋊D4312yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—81no—
550C22×C4—81no—
551C22×C4—431no—
552C22×C4—431no—
553C22×C4—431no—
554C22×C4—431no—
555C22×C4—864no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—3441no—
560C22×C4—3441no—
561C22×C4—1722no—
562C22×C4—1722no—
563C22×C4—1722no—
564C22×C4—1722no—
565C22×C4—1722no—
566C22×C4—1722no—
567C22×C4D4×D4311yescharacteristic
568C22×C4D4×D4311yescharacteristic
569C22×C4C23×D4311yescharacteristic
570D8—28no—
571D8—868no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—432no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8C2×C4×D4312yes—
583C2×C8C2×C22⋊D4312yes—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—432no—
588C4⋊C4—862no—
589C4⋊C4—862no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—3441no—
596C4⋊C4—1722no—
597C4⋊C4—1722no—
598C4⋊C4—1722no—
599C4⋊C4C2×C22⋊D4312yes—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—864no—
603C22⋊C4—3441no—
604C22⋊C4—3441no—
605C22⋊C4—1722no—
606C22⋊C4—1722no—
607C22⋊C4—1722no—
608C22⋊C4—1722no—
609C42—21no—
610C42—21no—
611C42—432no—
612C42—432no—
613C42—861no—
614C42—861no—
615C42—1722no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—862no—
631C23—1721no—
632C23—1721no—
633C23—1721no—
634C23—1721no—
635C23—1721no—
636C23—1721no—
637C23C2×D4×D4311yescharacteristic
638D4—22no—
639D4—22no—
640D4—22no—
641D4—22no—
642D4—22no—
643D4—41no—
644D4—41no—
645D4—862no—
646D4—862no—
647D4—3444no—
648D4—1728no—
649D4—1721no—
650D4—1721no—
651D4C4×C22⋊D4314yescomplemented
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—84no—
665C2×C4—84no—
666C2×C4—432no—
667C2×C4—432no—
668C2×C4—432no—
669C2×C4—432no—
670C2×C4—861no—
671C2×C4—861no—
672C2×C4—862no—
673C2×C4—861no—
674C2×C4—861no—
675C2×C4—861no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—861no—
679C2×C4—3444no—
680C2×C4—3444no—
681C2×C4—1728no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4C22×C4×D4311yescharacteristic
691C2×C4C22×C22⋊D4311yescharacteristic
692C2×C4#41×D4311yescharacteristic
693C2×C4C2×#1062189811yescharacteristic
694C2×C4#1306337011yescharacteristic
695C2×C4#1306337211yescharacteristic
696C8—22no—
697C8—22no—
698C8—862no—
699C8—1721no—
700C22—24no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—3441no—
715C22—3441no—
716C22—3441no—
717C22—3441no—
718C22—1722no—
719C22—1722no—
720C22—1722no—
721C22C4×D4×D4311yescharacteristic
722C22D4×C22⋊D4311yescharacteristic
723C22#1458355811yescharacteristic
724C22AGL(1,ℤ/8)×D4311yescharacteristic
725C22AGL(1,ℤ/8)×D4311yescharacteristic
726C22#1458370311yescharacteristic
727C22#1458370911yescharacteristic
728C4—41no—
729C4—42no—
730C4—41no—
731C4—81no—
732C4—434no—
733C4—862no—
734C4—3441no—
735C4—3441no—
736C4—1721no—
737C4—1722no—
738C4—1721no—
739C4C2×C4×C22⋊D4311yescharacteristic
740C4#1458337811yescharacteristic
741C4#1458354811yescharacteristic
742C4#1458359811yescharacteristic
743C2—44no—
744C2—82no—
745C2—3442no—
746C2#1913761211yescharacteristic
747C2#442×D4311yescharacteristic
748C2#1914342411yescharacteristic
749C2#1914618911yescharacteristic
750C2#1914620911yescharacteristic
751C2#1914730311yescharacteristic
752C2#1914738811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#442C2
socleC23×C43C22×D4
prime radicalC2×#14583092C2
cosocleC22×C4×C43C24
hypercenterC2×#442D43
hypocenterC43#23001
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
2. C2×#14583008C2semidirect
3. #19137657C2semidirect
4. D4×Dic43⋊C4C2semidirect
5. #19135399C2semidirect
6. #19135355C2semidirect
7. #19135292C2semidirect
8. #19135289C2semidirect
9. #19134945C2semidirect
10. #19134943C2semidirect
11. #19134856C2semidirect
12. #19134853C2semidirect
13. #19134463C2semidirect
14. #102×Dic43C2semidirect
15. C2×C43×#442C2semidirect
23. #14583092C4semidirect
70. C2×#10621882C2×C4semidirect
74. #13063321C2×C4semidirect
78. D4×Dic43C2×C4semidirect
103. Dic43⋊C8C2×C4semidirect
105. #13063247C2×C4semidirect
108. #13063246C2×C4semidirect
123. C2×D8×C43C2×C4semidirect
137. #102×C43D4semidirect
268. D4×C43C4×D4semidirect
366. Dic43#442semidirect
369. C2×#442D43semidirect
438. C43#23001semidirect
454. C2×D8C4×D43semidirect
507. #102C22⋊D43semidirect
651. D4C4×C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830922
C2×#145830082
#191376572
D4×Dic43⋊C42
#191353992
#191353552
#191352922
#191352892
#191349452
#191349432
#191348562
#191348532
#191344632
#102×Dic432
C2×C43×#4422
#2300143