Finite Group Databasebeta

← #25153680

Subgroups — #25153680

Order 11008.

1162 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#102×D43C211yesmaximal, characteristic
2#19138315C211yesmaximal, characteristic, complemented
3D4×(C2×D43)⋊C4C211yesmaximal, characteristic
4#19136113C211yesmaximal, characteristic, complemented
5#19135982C211yesmaximal, characteristic, complemented
6#19135964C211yesmaximal, characteristic, complemented
7#19135738C211yesmaximal, characteristic, complemented
8#19134856C211yesmaximal, characteristic, complemented
9#19134844C211yesmaximal, characteristic, complemented
10#19134786C211yesmaximal, characteristic, complemented
11#19134771C211yesmaximal, characteristic, complemented
12#19134621C211yesmaximal, characteristic, complemented
13#19134603C211yesmaximal, characteristic, complemented
14#19134524C211yesmaximal, characteristic
15C2×C43×#478C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×C4⋊C4×D43C2211yescharacteristic
20C22×(C2×D43)⋊C4—21no—
21C2×#13063259C2211yescharacteristic, complemented
22C2×#13063256C2211yescharacteristic, complemented
23C2×Dic43⋊C8C2211yescharacteristic, complemented
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30#102×D43—24no—
31C2×(C2×D43)⋊C8C2211yescharacteristic
32#14582837—21no—
33#14582832—21no—
34#14582801C2211yescharacteristic
35#14582800C2211yescharacteristic
36#14582798C2211yescharacteristic, complemented
37#14582797C2211yescharacteristic, complemented
38#14582778—21no—
39#14582776—21no—
40#14582770—21no—
41#14582764C2211yescharacteristic, complemented
42#14582756—21no—
43#14582756C2211yescharacteristic
44#14582756C2211yescharacteristic
45#14582754—21no—
46C4×(C2×D43)⋊C4C2211yescharacteristic
47#14582662C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582654C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53C2×#125×C43C2211yescharacteristic, complemented
54C2×C4×D4×C43C2211yescharacteristic
55C43×#478—24no—
56C2×#107×C43C2211yescharacteristic, complemented
57C2×#106×C43C2211yescharacteristic, complemented
58C2×C4⋊C8×C43C2211yescharacteristic, complemented
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C24×D43—21no—
62C22×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C2×D4×D43—22no—
65C2×D4×D43—22no—
66C2×D4×D43—22no—
67C2×D4×D43—41no—
68C2×D4×D43—41no—
69C2×D4×D43Q814yes—
70C23×Dic43—21no—
71C22×C4×D43—21no—
72C22×C4×D43C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C2×C8×D43—22no—
76C2×C8×D43—22no—
77C2×C8×D43—41no—
78D4×Dic43—22no—
79D4×Dic43—41no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C4⋊C4×D43—22no—
87C4⋊C4×D43—41no—
88C2×C22⋊Dic43—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—44no—
96C2×(C2×D43)⋊C4D411yescharacteristic
97C2×(C2×D43)⋊C4D411yescharacteristic
98C2×C4×Dic43C2311yescharacteristic
99#13063259—41no—
100#13063256—41no—
101Dic43⋊C8—41no—
102#13063247—22no—
103#13063247—41no—
104#13063246—22no—
105#13063246—22no—
106#13063245—22no—
107#13063245—41no—
108(C2×D43)⋊C8—22no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C22×D4×C43C2311yescharacteristic
118C23×C4×C43—21no—
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121#125×C43—22no—
122#125×C43—41no—
123C4×D4×C43—22no—
124C4×D4×C43—41no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131C2×C42×C43C2311yescharacteristic
132#107×C43—22no—
133#106×C43—22no—
134C4⋊C8×C43—22no—
135#102×C43—22no—
136#102×C43D414yes—
137C24×C43—21no—
138C23×D43—21no—
139C23×D43—24no—
140C23×D43—42no—
141C23×D43—42no—
142C23×D43—42no—
143C23×D43—42no—
144C23×D43—81no—
145C23×D43—81no—
146C23×D43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C2×D412yes—
151C2×D4×C43C2×Q812yes—
152C2×D4×C43#4112yes—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43—81no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C2×C22⋊D43—24no—
163C2×C22⋊D43—42no—
164C2×C22⋊D43—42no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—42no—
169C22×Dic43—42no—
170C22×Dic43—81no—
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174D4×D43—28no—
175D4×D43—44no—
176D4×D43—44no—
177D4×D43—44no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172C2×Q812yes—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×C4×D43—81no—
191C2×C4×D43C2×Q812yes—
192C2×C4×D43#4112yes—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
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×C43—42no—
206C4⋊C4×C43C2×D412yes—
207C22⋊C4×C43—42no—
208C42×C43—21no—
209C42×C43—21no—
210C22⋊Dic43—42no—
211(C2×D43)⋊C4—22no—
212(C2×D43)⋊C4—22no—
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—
218(C2×D43)⋊C4—81no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—81no—
226Dic43⋊C4—42no—
227Dic43⋊C4—81no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C8×D43—44no—
237C23×C43—22no—
238C23×C43—22no—
239C23×C43—22no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43C22×D411yescharacteristic
245C22×D43—21no—
246C22×D43—21no—
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—22no—
250C22×D43—48no—
251C22×D43—41no—
252C22×D43—41no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—48no—
258C22×D43—84no—
259C22×D43—84no—
260C22×D43—84no—
261C22×D43—84no—
262C22×D43—84no—
263C22×D43C22⋊Q812yes—
264C22×D43#13512yes—
265C22×D43AGL(1,ℤ/8)12yes—
266D4×C43—22no—
267D4×C43—22no—
268D4×C43—22no—
269D4×C43C22⋊Q814yes—
270C2×C4×C43—22no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—84no—
286C2×C4×C43C22×D411yescharacteristic
287C2×C4×C43C22×Q811yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43H(5,𝔽2)11yescharacteristic
291C2×C4×C43H(5,𝔽2)11yescharacteristic
292C22⋊D43—48no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—84no—
311C2×Dic43C22⋊Q812yes—
312D172—22no—
313D172—22no—
314D172—41no—
315D172—41no—
316C4×D43—22no—
317C4×D43—22no—
318C4×D43—22no—
319C4×D43—22no—
320C4×D43—84no—
321C8×C43—22no—
322C8×C43—41no—
323C43⋊C8—41no—
324C43⋊C8—41no—
325#25952—431nomaximal, Sylow
326C22×C43—24no—
327C22×C43—42no—
328C22×C43—42no—
329C22×C43—42no—
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43C2×C22⋊Q811yescharacteristic
334C22×C43D4211yescharacteristic
335C22×C43#54611yescharacteristic
336C22×C43C2×#13511yescharacteristic
337C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
338C22×C43#57611yescharacteristic
339C22×C43#57711yescharacteristic
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—22no—
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—816no—
350C2×D43—81no—
351C2×D43—81no—
352C2×D43—81no—
353C2×D43—81no—
354C2×D43#47814yescomplemented
355C4×C43—41no—
356C4×C43—42no—
357C4×C43—41no—
358C4×C43—81no—
359C4×C43—81no—
360C4×C43C2×C22⋊Q811yescharacteristic
361C4×C43#54311yescharacteristic
362C4×C43#54611yescharacteristic
363C4×C43#55111yescharacteristic
364Dic43—22no—
365Dic43—41no—
366Dic43—41no—
367Dic43—81no—
368Dic43—81no—
369Dic43—81no—
370C2×#478D4311yescharacteristic, complemented
371C22×#102—431no—
372#2442—431no—
373D4×C22⋊C4—431no—
374#2092—431no—
375#2067—431no—
376#2065—431no—
377#2025—431no—
378#1864—431no—
379#1862—431no—
380#1853—431no—
381#1850—431no—
382#1808—431no—
383#1804—431no—
384#1786—431no—
385C2×C43—44no—
386C2×C43#243711yescharacteristic
387C2×C43C2×#47811yescharacteristic
388C2×C43#308111yescharacteristic
389C2×C43#326511yescharacteristic
390C2×C43#328011yescharacteristic
391C2×C43#329611yescharacteristic
392C2×C43#331811yescharacteristic
393D43—24no—
394D43—82no—
395C23×D4—431no—
396C23×C8—431no—
397C2×#125C2×D4311yescharacteristic, complemented
398C2×C4×D4—431no—
399C2×C4×D4C2×D4311yescharacteristic
400C22×C4⋊C4—431no—
401C22×C22⋊C4—861no—
402#478—24no—
403C2×#107—431no—
404C2×#107C2×D4311yescharacteristic, complemented
405C2×#106—431no—
406C2×#106C2×D4311yescharacteristic, complemented
407C2×C4⋊C8—431no—
408C2×C4⋊C8C2×D4311yescharacteristic, complemented
409C2×#102—431no—
410C2×#102—431no—
411C2×#102—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×#102—431no—
415C2×#102—864no—
416C2×#102C2×D4311yescharacteristic
417C2×#102C2×D4311yescharacteristic
418C2×C22⋊C8—431no—
419#400—861no—
420#398—861no—
421#390—431no—
422#390—431no—
423#389—431no—
424#389—431no—
425#386—861no—
426#386—861no—
427#385—861no—
428#382—431no—
429#380—431no—
430#380—431no—
431#380—861no—
432#379—861no—
433C4×C22⋊C4—431no—
434#340—431no—
435#340—431no—
436#340—431no—
437#340—431no—
438#336—431no—
439#336—431no—
440C43#2595211yescharacteristic, complemented, Sylow
441C25—861no—
442C22×D4—434no—
443C22×D4—431no—
444C22×D4—862no—
445C22×D4—861no—
446C22×D4—862no—
447C22×D4—862no—
448C22×D4—1721no—
449C22×D4—1721no—
450C22×D4C22×D4311yescharacteristic
451C23×C4—21no—
452C23×C4—431no—
453C23×C4—861no—
454C23×C4—861no—
455C22×C8—431no—
456C22×C8—431no—
457C22×C8—862no—
458C22×C8—862no—
459C22×C8—1721no—
460C22×C8C22×D4311yescharacteristic
461C22×C8C22×D4311yescharacteristic
462#125—22no—
463#125—41no—
464C4×D4—22no—
465C4×D4—41no—
466C4×D4—862no—
467C4×D4—1721no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—862no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—1721no—
478C2×C4⋊C4C22×D4311yescharacteristic
479C2×C4⋊C4C22×D4311yescharacteristic
480C2×C4⋊C4C22×D4311yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—431no—
483C2×C22⋊C4—431no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—1724no—
492C2×C42—431no—
493C2×C42C22×D4311yescharacteristic
494#107—22no—
495#107—1721no—
496#106—22no—
497#106—1721no—
498C4⋊C8—22no—
499C4⋊C8—1721no—
500#102—22no—
501#102—862no—
502#102—862no—
503#102—862no—
504#102—862no—
505#102—1721no—
506#102—1721no—
507#102C22⋊D4314yes—
508C22⋊C8—862no—
509#95—431no—
510#95—431no—
511#95—861no—
512#95—861no—
513#95—861no—
514#95—861no—
515#95—861no—
516#95—861no—
517C24—21no—
518C24—431no—
519C24—864no—
520C24—861no—
521C24—3441no—
522C24—3441no—
523C24—1722no—
524C24—1722no—
525C24—1722no—
526C24—1722no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—432no—
531C2×D4—864no—
532C2×D4—868no—
533C2×D4—861no—
534C2×D4—861no—
535C2×D4—861no—
536C2×D4—861no—
537C2×D4—861no—
538C2×D4—1724no—
539C2×D4—1724no—
540C2×D4—1724no—
541C2×D4—1722no—
542C2×D4—1722no—
543C2×D4Q8×D4312yes—
544C2×D4#1062190212yes—
545C2×D4C2×C22⋊D4312yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—81no—
552C22×C4—431no—
553C22×C4—432no—
554C22×C4—432no—
555C22×C4—431no—
556C22×C4—431no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—3441no—
565C22×C4—3441no—
566C22×C4—1722no—
567C22×C4—1722no—
568C22×C4—1722no—
569C22×C4—1722no—
570C22×C4D4×D4311yescharacteristic
571C22×C4D4×D4311yescharacteristic
572C22×C4C23×D4311yescharacteristic
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—1724no—
585C2×C8C2×C22⋊D4312yes—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—3441no—
600C4⋊C4—3441no—
601C4⋊C4—1722no—
602C4⋊C4C2×C22⋊D4312yes—
603C22⋊C4—42no—
604C22⋊C4—862no—
605C22⋊C4—862no—
606C22⋊C4—3441no—
607C22⋊C4—3441no—
608C22⋊C4—1722no—
609C22⋊C4—1722no—
610C22⋊C4—1722no—
611C22⋊C4—1722no—
612C22⋊C4—1722no—
613C42—21no—
614C42—21no—
615C42—861no—
616C42—861no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—432no—
625C23—432no—
626C23—432no—
627C23—861no—
628C23—861no—
629C23—861no—
630C23—861no—
631C23—862no—
632C23—3444no—
633C23—3444no—
634C23—3444no—
635C23—3444no—
636C23—3444no—
637C23—1728no—
638C23—1728no—
639C23—1721no—
640C23—1721no—
641C23—1721no—
642C23—1721no—
643C23—1721no—
644C23—1721no—
645C23C2×D4×D4311yescharacteristic
646D4—22no—
647D4—22no—
648D4—22no—
649D4—862no—
650D4—862no—
651D4—1728no—
652D4—1721no—
653D4—1721no—
654D4#1306330114yes—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—84no—
671C2×C4—432no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4—861no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—861no—
684C2×C4—3444no—
685C2×C4—3444no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4C22×C22⋊D4311yescharacteristic
696C2×C4C2×Q8×D4311yescharacteristic
697C2×C4#41×D4311yescharacteristic
698C2×C4C2×#1062190211yescharacteristic
699C2×C4#1306337011yescharacteristic
700C2×C4#1306337111yescharacteristic
701C8—22no—
702C8—41no—
703C8—1721no—
704C8—1721no—
705C22—24no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—434no—
713C22—862no—
714C22—862no—
715C22—862no—
716C22—862no—
717C22—862no—
718C22—862no—
719C22—34416no—
720C22—3441no—
721C22—3441no—
722C22—3441no—
723C22—3441no—
724C22—1722no—
725C22—1722no—
726C22—1722no—
727C22C22⋊Q8×D4311yescharacteristic
728C22D4×C22⋊D4311yescharacteristic
729C22#1458354011yescharacteristic
730C22#135×D4311yescharacteristic
731C22AGL(1,ℤ/8)×D4311yescharacteristic
732C22#1458370111yescharacteristic
733C22#1458370911yescharacteristic
734C4—41no—
735C4—42no—
736C4—41no—
737C4—81no—
738C4—81no—
739C4—862no—
740C4—3441no—
741C4—3441no—
742C4—3441no—
743C4—1721no—
744C4—1721no—
745C4C2×#1306330111yescharacteristic
746C4#1458352411yescharacteristic
747C4#1458353711yescharacteristic
748C4#1458357611yescharacteristic
749C2—44no—
750C2—864no—
751C2—3442no—
752C2#1913825811yescharacteristic
753C2#478×D4311yescharacteristic
754C2#1914442311yescharacteristic
755C2#1914608411yescharacteristic
756C2#1914627411yescharacteristic
757C2#1914642711yescharacteristic
758C2#1914673311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#478C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
hypercenterC2×#478D43
hypocenterC43#25952
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
2. #19138315C2semidirect
4. #19136113C2semidirect
5. #19135982C2semidirect
6. #19135964C2semidirect
7. #19135738C2semidirect
8. #19134856C2semidirect
9. #19134844C2semidirect
10. #19134786C2semidirect
11. #19134771C2semidirect
12. #19134621C2semidirect
13. #19134603C2semidirect
15. C2×C43×#478C2semidirect
21. C2×#13063259C22semidirect
22. C2×#13063256C22semidirect
23. C2×Dic43⋊C8C22semidirect
36. #14582798C22semidirect
37. #14582797C22semidirect
41. #14582764C22semidirect
47. #14582662C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582654C22semidirect
52. #14582653C22semidirect
53. C2×#125×C43C22semidirect
56. C2×#107×C43C22semidirect
57. C2×#106×C43C22semidirect
58. C2×C4⋊C8×C43C22semidirect
354. C2×D43#478semidirect
370. C2×#478D43semidirect
397. C2×#125C2×D43semidirect
404. C2×#107C2×D43semidirect
406. C2×#106C2×D43semidirect
408. C2×C4⋊C8C2×D43semidirect
440. C43#25952semidirect

Maximal subgroups

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

subgroupindex
C2×#102×D432
#191383152
D4×(C2×D43)⋊C42
#191361132
#191359822
#191359642
#191357382
#191348562
#191348442
#191347862
#191347712
#191346212
#191346032
#191345242
C2×C43×#4782
#2595243