Finite Group Databasebeta

← #25118906

Subgroups — #25118906

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×#14583093C211yesmaximal, characteristic
2C2×#14583012C211yesmaximal, characteristic, complemented
3C2×#14583008C211yesmaximal, characteristic, complemented
4#19137656C211yesmaximal, characteristic, complemented
5#19137496C211yesmaximal, characteristic, complemented
6#19135399C211yesmaximal, characteristic, complemented
7#19135357C211yesmaximal, characteristic, complemented
8#19135293C211yesmaximal, characteristic, complemented
9#19134946C211yesmaximal, characteristic, complemented
10#19134944C211yesmaximal, characteristic, complemented
11#19134858C211yesmaximal, characteristic, complemented
12#19134855C211yesmaximal, characteristic, complemented
13#19134463C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1936C211yesmaximal, characteristic, complemented
16C22×D344C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063321C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23C2×#13063287C2211yescharacteristic
24C2×(C22⋊D43)⋊C4—21no—
25C2×C4⋊C4×D43—21no—
26#14583093C418yescomplemented
27#14583012—24no—
28#14583008—24no—
29C2×#13063257C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31C2×Dic43⋊C8C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063235C2211yescharacteristic
39C2×C8×Dic43C2211yescharacteristic
40#14582800C2211yescharacteristic
41#14582799—21no—
42#14582798C2211yescharacteristic
43#14582776—21no—
44#14582775—21no—
45#14582773—21no—
46#14582770—21no—
47#14582768C2211yescharacteristic
48#14582758—21no—
49C4⋊C4×Dic43C2211yescharacteristic
50C4×Dic43⋊C4C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#97×C43C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×D172C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C23×Dic43—21no—
67C22×C4×D43—21no—
68C22×C4×D43—21no—
69C22×C4×D43—21no—
70C22×C4×D43—21no—
71C2×D344—22no—
72C2×D344—22no—
73C2×D344C2×C414yescomplemented
74C2×#10621882—22no—
75C2×#10621882—22no—
76C2×#10621882C2×C414yescomplemented
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063321—22no—
80#13063321C2×C414yescomplemented
81C4×D172—22no—
82C4×D172—22no—
83C4×D172—41no—
84C4×D172—41no—
85D4×Dic43—22no—
86D4×Dic43—41no—
87#13063287—22no—
88#13063287—22no—
89#13063287—41no—
90#13063287C2×C414yescomplemented
91(C22⋊D43)⋊C4—44no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4D411yescharacteristic
98C2×Dic43⋊C4D411yescharacteristic
99C4⋊C4×D43—44no—
100C2×C22⋊Dic43—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43C2311yescharacteristic
109C2×C4×Dic43C2311yescharacteristic
110#13063257—22no—
111#13063256—22no—
112Dic43⋊C8C2×C414yescomplemented
113#13063247—22no—
114#13063247D414yescomplemented
115#13063246—41no—
116#13063245—22no—
117#13063245—41no—
118#13063245C2×C414yescomplemented
119#13063235—22no—
120C8×Dic43—22no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95D411yescharacteristic
124C43⋊#95D411yescharacteristic
125C22×D4×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#102×C43—22no—
136#102×C43C2×C414yescomplemented
137#97×C43—22no—
138#95×C43—21no—
139C24×C43—21no—
140C23×D43—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×C43C22×C412yes—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C2×C22⋊D43—24no—
155C2×C22⋊D43—24no—
156C2×C22⋊D43—42no—
157C2×C22⋊D43—42no—
158C2×C22⋊D43—81no—
159C2×C22⋊D43—81no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—42no—
163C22×Dic43—42no—
164C22×Dic43—81no—
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172C22×C412yes—
178C2×D172C22×C412yes—
179C2×D172C2×D412yes—
180C2×D172#4112yes—
181C2×C4×D43—24no—
182C2×C4×D43—42no—
183C2×C4×D43—42no—
184C2×C4×D43—42no—
185C2×C4×D43—42no—
186C2×C4×D43—42no—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×C4×D43—81no—
191C2×C4×D43—81no—
192C2×C4×D43—81no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43C22×C412yes—
198C2×C8×C43C2×D412yes—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—42no—
205C4⋊C4×C43C22×C412yes—
206C22⋊C4×C43—42no—
207C22⋊C4×C43—81no—
208C42×C43—21no—
209C42×C43—21no—
210C22⋊Dic43—42no—
211#10621882—28no—
212(C2×D43)⋊C4—24no—
213(C2×D43)⋊C4—42no—
214(C2×D43)⋊C4—42no—
215(C2×D43)⋊C4—42no—
216(C2×D43)⋊C4—42no—
217(C2×D43)⋊C4—81no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—42no—
222C4⋊Dic43C2×D412yes—
223Dic43⋊C4—22no—
224Dic43⋊C4—22no—
225Dic43⋊C4—42no—
226Dic43⋊C4—81no—
227C4×Dic43—21no—
228C4×Dic43—21no—
229C4×Dic43—42no—
230C4×Dic43C22×C412yes—
231C4×Dic43#4112yes—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8C22×C412yes—
238D344—28no—
239C23×C43—22no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43C22×D411yescharacteristic
247C22×D43—22no—
248C22×D43—22no—
249C22×D43—22no—
250C22×D43—22no—
251C22×D43—41no—
252C22×D43—41no—
253C22×D43—41no—
254C22×D43—41no—
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—41no—
264D4×C43—41no—
265C2×C4×C43—22no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43C23×C411yescharacteristic
281C2×C4×C43C22×D411yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43H(5,𝔽2)11yescharacteristic
285C2×C4×C432−1+411yescharacteristic
286C22⋊D43—48no—
287C22⋊D43—84no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—22no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—84no—
303C2×Dic43C4×D412yes—
304C2×Dic43C4×D412yes—
305C2×Dic43AGL(1,ℤ/8)12yes—
306C2×Dic43AGL(1,ℤ/8)12yes—
307D172—22no—
308D172—22no—
309D172—22no—
310D172—22no—
311D172—22no—
312D172—41no—
313D172—41no—
314D172C4×D414yescomplemented
315C4×D43—48no—
316C4×D43—84no—
317C4×D43—84no—
318C4×D43—84no—
319C8×C43—22no—
320C8×C43—22no—
321C43⋊C8—22no—
322C43⋊C8—41no—
323#23001—431nomaximal, Sylow
324C22×C43—42no—
325C22×C43—42no—
326C22×C43—42no—
327C22×C43—81no—
328C22×C43—81no—
329C22×C43—81no—
330C22×C43—81no—
331C22×C43C2×C4×D411yescharacteristic
332C22×C43D4211yescharacteristic
333C22×C43#54811yescharacteristic
334C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
335C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
336C22×C43#57611yescharacteristic
337C22×C43#57711yescharacteristic
338C2×D43—24no—
339C2×D43—42no—
340C2×D43—42no—
341C2×D43—42no—
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—42no—
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×C43—81no—
357C4×C43C2×C4×D411yescharacteristic
358C4×C43#52011yescharacteristic
359C4×C43#54711yescharacteristic
360C4×C43#55311yescharacteristic
361Dic43—22no—
362Dic43—42no—
363Dic43—41no—
364Dic43—41no—
365Dic43—81no—
366Dic43#44214yescomplemented
367C2×#459—431no—
368C2×#442—431no—
369C2×#442—431no—
370#2366—431no—
371D4×C4⋊C4—431no—
372#1957—431no—
373#1948—431no—
374#1936—431no—
375#1936D4311yescharacteristic, complemented
376#1879—431no—
377#1879—431no—
378#1864—431no—
379#1864—431no—
380#1770—431no—
381C4×#102—431no—
382C2×C43—82no—
383C2×C43#236111yescharacteristic
384C2×C43C2×#44211yescharacteristic
385C2×C43#294611yescharacteristic
386C2×C43#327211yescharacteristic
387C2×C43#327411yescharacteristic
388C2×C43#336611yescharacteristic
389C2×C43#337311yescharacteristic
390D43—44no—
391D43—82no—
392C22×D8—431no—
393C22×D8—431no—
394C2×#127—431no—
395C2×C4×D4—431no—
396C2×C4×D4—431no—
397C2×C4×D4—431no—
398C2×C4×D4—431no—
399C2×C4×D4—431no—
400C2×C4×D4—861no—
401C22×C4⋊C4—861no—
402#459—438no—
403#442—864no—
404#442—864no—
405C2×#106—431no—
406C2×#106—431no—
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—861no—
421#390C2×D4311yescharacteristic
422#389—431no—
423#389C2×D4311yescharacteristic
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#340C2×D4311yescharacteristic
435#340C2×D4311yescharacteristic
436#336—431no—
437#336—431no—
438C43#2300111yescharacteristic, complemented, Sylow
439C22×D4—431no—
440C22×D4—431no—
441C22×D4—861no—
442C22×D4—861no—
443C22×D4C22×D4311yescharacteristic
444C23×C4—861no—
445C23×C4—861no—
446C23×C4—861no—
447C23×C4—861no—
448C23×C4—861no—
449C2×D8—434no—
450C2×D8—434no—
451C2×D8—862no—
452C2×D8—862no—
453C2×D8—862no—
454C2×D8—862no—
455C22×C8—431no—
456C22×C8—431no—
457C22×C8C22×D4311yescharacteristic
458C22×C8C22×D4311yescharacteristic
459#127—434no—
460#127—862no—
461C4×D4—434no—
462C4×D4—862no—
463C4×D4—862no—
464C4×D4—862no—
465C4×D4—862no—
466C4×D4—862no—
467C4×D4—1721no—
468C4×D4—1721no—
469C4×D4—1721no—
470C4×D4—1721no—
471C4×D4—1724no—
472C2×C4⋊C4—21no—
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—1724no—
481C2×C4⋊C4C22×D4311yescharacteristic
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—862no—
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#102C4×D4314yescomplemented
508#97—22no—
509#97—862no—
510C4×C8—862no—
511#95—21no—
512#95—431no—
513#95—431no—
514#95—861no—
515#95—861no—
516C24—21no—
517C24—861no—
518C24—861no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—432no—
525C2×D4—432no—
526C2×D4—432no—
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—861no—
536C2×D4—861no—
537C2×D4—861no—
538C2×D4—3441no—
539C2×D4—3441no—
540C2×D4—1722no—
541C2×D4—1722no—
542C2×D4C2×C4×D4312yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—431no—
547C22×C4—431no—
548C22×C4—431no—
549C22×C4—431no—
550C22×C4—864no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—3441no—
554C22×C4—3441no—
555C22×C4—3441no—
556C22×C4—3441no—
557C22×C4—1722no—
558C22×C4—1722no—
559C22×C4—1722no—
560C22×C4—1722no—
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—868no—
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×C8D4×D4312yes—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—42no—
590C4⋊C4—432no—
591C4⋊C4—862no—
592C4⋊C4—862no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—3441no—
597C4⋊C4—1722no—
598C4⋊C4—1722no—
599C4⋊C4C2×C4×D4312yes—
600C22⋊C4—42no—
601C22⋊C4—81no—
602C22⋊C4—864no—
603C22⋊C4—3441no—
604C22⋊C4—1722no—
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—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—862no—
624C23—862no—
625C23—862no—
626C23—862no—
627C23—1721no—
628C23—1721no—
629C23—1721no—
630C23—1721no—
631C23—1721no—
632C23—1721no—
633C23—1721no—
634C23—1721no—
635C23—1721no—
636C23—1721no—
637C23C2×D4×D4311yescharacteristic
638D4—22no—
639D4—22no—
640D4—41no—
641D4—41no—
642D4—434no—
643D4—862no—
644D4—862no—
645D4—862no—
646D4—862no—
647D4—862no—
648D4—3444no—
649D4—1728no—
650D4—1721no—
651D4—1721no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—432no—
668C2×C4—432no—
669C2×C4—432no—
670C2×C4—432no—
671C2×C4—861no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—861no—
675C2×C4—861no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—861no—
679C2×C4—862no—
680C2×C4—3444no—
681C2×C4—3444no—
682C2×C4—3444no—
683C2×C4—3444no—
684C2×C4—1728no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4C22×C4×D4311yescharacteristic
691C2×C4C2×D4×D4311yescharacteristic
692C2×C4#41×D4311yescharacteristic
693C2×C4#41×D4311yescharacteristic
694C2×C4#1306337111yescharacteristic
695C2×C4#1306337211yescharacteristic
696C8—22no—
697C8—22no—
698C8—862no—
699C8—1721no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—864no—
708C22—3441no—
709C22—3441no—
710C22—3441no—
711C22—3441no—
712C22—1722no—
713C22—1722no—
714C22—1722no—
715C22—1722no—
716C22—1722no—
717C22—1722no—
718C22—1722no—
719C22—1722no—
720C22—1722no—
721C22C4×D4×D4311yescharacteristic
722C22#1458353311yescharacteristic
723C22#1458355711yescharacteristic
724C22AGL(1,ℤ/8)×D4311yescharacteristic
725C22AGL(1,ℤ/8)×D4311yescharacteristic
726C22#1458370311yescharacteristic
727C22#1458370811yescharacteristic
728C4—41no—
729C4—42no—
730C4—41no—
731C4—81no—
732C4—81no—
733C4—434no—
734C4—862no—
735C4—3441no—
736C4—1721no—
737C4—1722no—
738C4—1721no—
739C4C4×D4×D4311yescharacteristic
740C4#1458337911yescharacteristic
741C4#1458354711yescharacteristic
742C4#1458360011yescharacteristic
743C2—82no—
744C2—3442no—
745C2—1724no—
746C2#1913760811yescharacteristic
747C2#442×D4311yescharacteristic
748C2#1914342611yescharacteristic
749C2#1914619211yescharacteristic
750C2#1914621211yescharacteristic
751C2#1914729911yescharacteristic
752C2#1914738411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1936C2
socleC23×C43C22×D4
prime radicalC2×#14583093C2
cosocleC22×C4×C43C24
hypercenter#1936D43
hypocenterC43#23001
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
2. C2×#14583012C2semidirect
3. C2×#14583008C2semidirect
4. #19137656C2semidirect
5. #19137496C2semidirect
6. #19135399C2semidirect
7. #19135357C2semidirect
8. #19135293C2semidirect
9. #19134946C2semidirect
10. #19134944C2semidirect
11. #19134858C2semidirect
12. #19134855C2semidirect
13. #19134463C2semidirect
14. #19134409C2semidirect
15. C43×#1936C2semidirect
26. #14583093C4semidirect
73. C2×D344C2×C4semidirect
76. C2×#10621882C2×C4semidirect
80. #13063321C2×C4semidirect
90. #13063287C2×C4semidirect
112. Dic43⋊C8C2×C4semidirect
114. #13063247D4semidirect
118. #13063245C2×C4semidirect
136. #102×C43C2×C4semidirect
314. D172C4×D4semidirect
366. Dic43#442semidirect
375. #1936D43semidirect
438. C43#23001semidirect
507. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830932
C2×#145830122
C2×#145830082
#191376562
#191374962
#191353992
#191353572
#191352932
#191349462
#191349442
#191348582
#191348552
#191344632
#191344092
C43×#19362
#2300143