Finite Group Databasebeta

← #25132961

Subgroups — #25132961

Order 11008.

1330 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583564C211yesmaximal, characteristic, complemented
2C2×#14583177C211yesmaximal, characteristic, complemented
3C2×#14582979C211yesmaximal, characteristic
4#19139515C211yesmaximal, characteristic, complemented
5#19135922C211yesmaximal, characteristic, complemented
6#19135920C211yesmaximal, characteristic, complemented
7#19135729C211yesmaximal, characteristic, complemented
8#19135554C211yesmaximal, characteristic, complemented
9#19135529C211yesmaximal, characteristic, complemented
10#19134946C211yesmaximal, characteristic
11#19134940C211yesmaximal, characteristic
12#19134845C211yesmaximal, characteristic, complemented
13#19134843C211yesmaximal, characteristic, complemented
14#19134594C211yesmaximal, characteristic, complemented
15C43×#2023C211yesmaximal, characteristic, complemented
16C22×Q8×D43—21no—
17C22×#10621882C2211yescharacteristic
18#14583564—24no—
19#14583564—24no—
20C2×#13063324C2211yescharacteristic
21C2×#13063324C2211yescharacteristic
22C2×#13063303—21no—
23C2×#13063303—21no—
24C2×#13063302—21no—
25C2×#13063301—21no—
26C2×C4×Dic86C2211yescharacteristic
27C2×C4×D172C2211yescharacteristic
28C2×D4×Dic43C2211yescharacteristic
29C2×#13063287C2211yescharacteristic
30C2×#13063287C2211yescharacteristic
31#14583177—24no—
32#14582979—24no—
33C2×#13063259C2211yescharacteristic
34C2×#13063258C2211yescharacteristic
35C2×#13063258C2211yescharacteristic
36C2×Dic43⋊C8C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×C8×Dic43C2211yescharacteristic
42#14582822—21no—
43#14582822—21no—
44#14582802C2211yescharacteristic
45#14582798C2211yescharacteristic
46#14582797C2211yescharacteristic
47#14582768C2211yescharacteristic
48#14582757—21no—
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×C4⋊Q8×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86—21no—
65C22×Dic86D411yescharacteristic
66C2×Q8×D43—28no—
67C2×Q8×D43—44no—
68C2×Q8×D43—44no—
69C22×D172C2311yescharacteristic
70C23×Dic43—21no—
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C2×#10621882—22no—
75C2×#10621882—22no—
76C2×#10621882Q814yescomplemented
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063324—22no—
80#13063324—22no—
81#13063324—22no—
82#13063324D414yes—
83#13063303—28no—
84#13063303—28no—
85#13063302—44no—
86#13063301—28no—
87C4×Dic86—22no—
88C4×Dic86—22no—
89C4×D172—22no—
90C4×D172—22no—
91D4×Dic43—22no—
92D4×Dic43—22no—
93#13063287—22no—
94#13063287—22no—
95#13063287—22no—
96#13063287D414yes—
97C2×C4⋊Dic43—21no—
98C2×C4⋊Dic43D411yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4D411yescharacteristic
108C2×Dic43⋊C4D411yescharacteristic
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×C4×Dic43C2311yescharacteristic
116C2×C4×Dic43C2311yescharacteristic
117#13063259—22no—
118#13063258—22no—
119#13063258—22no—
120Dic43⋊C8—22no—
121#13063247—22no—
122#13063247—22no—
123#13063246—22no—
124#13063245—22no—
125C8×Dic43—22no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C22×Q8×C43—21no—
129C22×D4×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C4⋊Q8×C43—22no—
133C4⋊Q8×C43—22no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C42×C43C2311yescharacteristic
141#102×C43—22no—
142#102×C43—22no—
143C24×C43—21no—
144C23×D43—21no—
145C2×Q8×C43—24no—
146C2×Q8×C43—42no—
147C2×Q8×C43—42no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43C2×Q812yescomplemented
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2411yescharacteristic
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—42no—
164C22×Dic43—42no—
165C22×Dic43—42no—
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170Q8×D43—432no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172C2×D412yes—
175C2×D172C2×Q812yes—
176C2×D172#4112yes—
177C2×C4×D43—24no—
178C2×C4×D43—24no—
179C2×C4×D43—24no—
180C2×C4×D43—42no—
181C2×C4×D43—42no—
182C2×C4×D43—42no—
183C2×C4×D43—42no—
184C2×C4×D43—42no—
185C2×C4×D43—42no—
186C2×Dic86—22no—
187C2×Dic86—22no—
188C2×Dic86—24no—
189C2×Dic86—24no—
190C2×Dic86—42no—
191C2×Dic86—42no—
192C2×Dic86—42no—
193C2×Dic86—42no—
194C2×Dic86D814yescomplemented
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C4⋊C4×C43—24no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43C2×D412yes—
207C4⋊C4×C43C2×D412yes—
208C22⋊C4×C43—42no—
209C22⋊C4×C43—81no—
210C42×C43—21no—
211C42×C43—21no—
212C22⋊Dic43—42no—
213C22⋊Dic43—42no—
214C22⋊Dic43—81no—
215#10621882—28no—
216(C2×D43)⋊C4—24no—
217(C2×D43)⋊C4—24no—
218(C2×D43)⋊C4—24no—
219C4⋊Dic43—21no—
220C4⋊Dic43—22no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—42no—
226C4⋊Dic43C2×D412yes—
227Dic43⋊C4—24no—
228Dic43⋊C4—24no—
229Dic43⋊C4—22no—
230Dic43⋊C4—22no—
231Dic43⋊C4—42no—
232Dic43⋊C4—42no—
233Dic43⋊C4—81no—
234C4×Dic43—21no—
235C4×Dic43—21no—
236C4×Dic43C2×D412yes—
237C4×Dic43C2×D412yes—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8C2×Q812yescomplemented
244C23×C43—22no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43C22×D411yescharacteristic
252C22×D43—22no—
253C22×D43—22no—
254C22×D43—22no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259Q8×C43—48no—
260D4×C43—22no—
261D4×C43—22no—
262D4×C43—41no—
263D4×C43—41no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—41no—
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×C43C2×D812yes—
279C2×C4×C43C22×D411yescharacteristic
280C2×C4×C43C22×D411yescharacteristic
281C2×C4×C43C22×Q811yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C432−1+411yescharacteristic
284C2×C4×C432−1+411yescharacteristic
285C2×Dic43—21no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—22no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—84no—
302C2×Dic43#12012yes—
303C2×Dic43#12012yes—
304C2×Dic43C2×D812yes—
305C2×Dic43C2×D812yes—
306C2×Dic43AGL(1,ℤ/8)12yes—
307D172—22no—
308D172—22no—
309D172—22no—
310D172C22⋊Q814yescomplemented
311C4×D43—48no—
312C4×D43—48no—
313C4×D43—48no—
314Dic86—28no—
315Dic86—48no—
316Dic86—48no—
317C8×C43—41no—
318C8×C43—41no—
319C43⋊C8—22no—
320C43⋊C8—41no—
321#24326—431nomaximal, Sylow
322C22×C43—42no—
323C22×C43—42no—
324C22×C43—42no—
325C22×C43—81no—
326C22×C43—81no—
327C22×C43—81no—
328C22×C43—81no—
329C22×C43C2×#12011yescharacteristic
330C22×C43#54811yescharacteristic
331C22×C43D4×Q811yescharacteristic
332C22×C43C22×D811yescharacteristic
333C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
334C22×C43#57711yescharacteristic
335C22×C43#57811yescharacteristic
336C2×D43—24no—
337C2×D43—42no—
338C2×D43—42no—
339C2×D43—42no—
340C2×D43—42no—
341C2×D43—42no—
342C2×D43—42no—
343C4×C43—22no—
344C4×C43—42no—
345C4×C43—42no—
346C4×C43—41no—
347C4×C43—81no—
348C4×C43C2×C22⋊Q811yescharacteristic
349C4×C43#53611yescharacteristic
350C4×C43#54811yescharacteristic
351C4×C43D4×Q811yescharacteristic
352Dic43—22no—
353Dic43—22no—
354Dic43—42no—
355Dic43—41no—
356Dic43—81no—
357Dic43—81no—
358Dic43#44714yes—
359C2×D4×Q8—431no—
360C2×#474—431no—
361C2×C4×D8—431no—
362#2538—431no—
363#2057—431no—
364#2057—431no—
365#2023—431no—
366#2023D4311yescharacteristic, complemented
367#1990—431no—
368#1984—431no—
369#1879—431no—
370#1879—431no—
371#1862—431no—
372#1862—431no—
373#1802—431no—
374C2×C43—82no—
375C2×C43#240911yescharacteristic
376C2×C43C2×#44711yescharacteristic
377C2×C43#301311yescharacteristic
378C2×C43#335811yescharacteristic
379C2×C43#336711yescharacteristic
380C2×C43Q8×D811yescharacteristic
381C2×C43#338411yescharacteristic
382D43—44no—
383C23×Q8—861no—
384C22×D8—431no—
385D4×Q8—864no—
386D4×Q8—864no—
387C2×C4⋊Q8—431no—
388C2×C4⋊Q8—431no—
389C2×C4⋊Q8C2×D4311yescharacteristic
390C2×C22⋊Q8—861no—
391C2×C22⋊Q8—861no—
392C2×C22⋊Q8—861no—
393C2×C22⋊Q8—861no—
394C2×C4×Q8—431no—
395C2×C4×D4—431no—
396C2×C4×D4—431no—
397C2×C4×D4—431no—
398C2×C4×D4—431no—
399#474—864no—
400C4×D8—864no—
401C2×#107—431no—
402C2×#107—431no—
403C2×#107—431no—
404C2×C4⋊C8—431no—
405C2×#102—431no—
406C2×#102—431no—
407C2×#102—431no—
408C2×#102—431no—
409C2×#102C2×D4311yescharacteristic
410C2×#102C2×D4311yescharacteristic
411C2×C4×C8—431no—
412#396—861no—
413#396—861no—
414#390—431no—
415#390C2×D4311yescharacteristic
416#389—431no—
417#389—431no—
418#384—431no—
419#380—861no—
420#340—431no—
421#340—431no—
422#340—431no—
423#340—431no—
424#340C2×D4311yescharacteristic
425#340C2×D4311yescharacteristic
426#336—431no—
427#336—431no—
428#336—431no—
429#336C2×D4311yescharacteristic
430C43#2432611yescharacteristic, complemented, Sylow
431C22×Q8—21no—
432C22×Q8—431no—
433C22×Q8—861no—
434C22×Q8—861no—
435C22×Q8—868no—
436C22×Q8—1724no—
437C22×Q8—1724no—
438C22×D4—431no—
439C22×D4C22×D4311yescharacteristic
440C23×C4—861no—
441C23×C4—861no—
442C23×C4—861no—
443C23×C4—861no—
444C2×D8—434no—
445C2×D8—862no—
446C2×D8—862no—
447C22×C8—431no—
448C22×C8—431no—
449C22×C8C22×D4311yescharacteristic
450C22×C8C22×D4311yescharacteristic
451C4⋊Q8—22no—
452C4⋊Q8—22no—
453C4⋊Q8—434no—
454C4⋊Q8—862no—
455C4⋊Q8—862no—
456C4⋊Q8—862no—
457C22⋊Q8—868no—
458C22⋊Q8—868no—
459C22⋊Q8—868no—
460C22⋊Q8—1724no—
461C4×Q8—862no—
462C4×Q8—862no—
463C4×D4—434no—
464C4×D4—862no—
465C4×D4—862no—
466C4×D4—862no—
467C4×D4—862no—
468C4×D4—862no—
469C4×D4—862no—
470C4×D4—862no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4C22×D4311yescharacteristic
485C2×C4⋊C4C22×D4311yescharacteristic
486C2×C4⋊C4C22×D4311yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C42—431no—
496C2×C42—431no—
497C2×C42C22×D4311yescharacteristic
498#107—862no—
499#107—862no—
500#107—862no—
501C4⋊C8—862no—
502#102—22no—
503#102—22no—
504#102—862no—
505#102—862no—
506#102—862no—
507#102—862no—
508C4×C8—862no—
509#95—861no—
510#95—861no—
511C24—21no—
512C24—861no—
513C2×Q8—24no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8—434no—
517C2×Q8—862no—
518C2×Q8—862no—
519C2×Q8—864no—
520C2×Q8—864no—
521C2×Q8—1722no—
522C2×Q8—1722no—
523C2×Q8—1722no—
524C2×Q8—1722no—
525C2×Q8—17232no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—432no—
532C2×D4—432no—
533C2×D4—432no—
534C2×D4—861no—
535C2×D4—861no—
536C2×D4—861no—
537C2×D4Q8×D4312yescomplemented
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—431no—
542C22×C4—431no—
543C22×C4—431no—
544C22×C4—431no—
545C22×C4—864no—
546C22×C4—864no—
547C22×C4—864no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—1722no—
552C22×C4—1722no—
553C22×C4—1722no—
554C22×C4—1722no—
555C22×C4—1722no—
556C22×C4—1722no—
557C22×C4—1722no—
558C22×C4—1722no—
559C22×C4—1722no—
560C22×C4D4×D4311yescharacteristic
561C22×C4D4×D4311yescharacteristic
562C22×C4C23×D4311yescharacteristic
563D8—868no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—432no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C4⋊C4—24no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—432no—
582C4⋊C4—862no—
583C4⋊C4—862no—
584C4⋊C4—862no—
585C4⋊C4—864no—
586C4⋊C4—864no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—3441no—
593C4⋊C4—1722no—
594C4⋊C4—1722no—
595C4⋊C4—1722no—
596C4⋊C4D4×D4312yes—
597C4⋊C4D4×D4312yes—
598C22⋊C4—42no—
599C22⋊C4—81no—
600C22⋊C4—864no—
601C22⋊C4—864no—
602C22⋊C4—864no—
603C22⋊C4—3441no—
604C22⋊C4—1722no—
605C22⋊C4—1722no—
606C42—21no—
607C42—21no—
608C42—432no—
609C42—432no—
610C42—861no—
611C42—861no—
612C23—22no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—862no—
620C23—862no—
621C23—862no—
622C23—1721no—
623C23—1721no—
624C23—1721no—
625C23—1721no—
626C23C2×D4×D4311yescharacteristic
627Q8—48no—
628Q8—868no—
629Q8—1728no—
630Q8—1728no—
631D4—22no—
632D4—22no—
633D4—41no—
634D4—41no—
635D4—434no—
636D4—862no—
637D4—862no—
638D4—862no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—432no—
654C2×C4—432no—
655C2×C4—432no—
656C2×C4—432no—
657C2×C4—432no—
658C2×C4—861no—
659C2×C4—861no—
660C2×C4—861no—
661C2×C4—861no—
662C2×C4—861no—
663C2×C4—862no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—3444no—
667C2×C4—1728no—
668C2×C4—1728no—
669C2×C4—1728no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4D8×D4312yes—
679C2×C4C2×D4×D4311yescharacteristic
680C2×C4C2×D4×D4311yescharacteristic
681C2×C4C2×Q8×D4311yescharacteristic
682C2×C4#41×D4311yescharacteristic
683C2×C4#1306337211yescharacteristic
684C2×C4#1306337211yescharacteristic
685C8—41no—
686C8—41no—
687C8—862no—
688C8—1721no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—864no—
697C22—1722no—
698C22—1722no—
699C22—1722no—
700C22—1722no—
701C22—1722no—
702C22—1722no—
703C22#120×D4311yescharacteristic
704C22#1458355711yescharacteristic
705C22#1458356211yescharacteristic
706C22C2×D8×D4311yescharacteristic
707C22AGL(1,ℤ/8)×D4311yescharacteristic
708C22#1458370511yescharacteristic
709C22#1458371511yescharacteristic
710C4—22no—
711C4—42no—
712C4—42no—
713C4—41no—
714C4—81no—
715C4—434no—
716C4—862no—
717C4—862no—
718C4—3441no—
719C4—3441no—
720C4—1722no—
721C4—1721no—
722C4C22⋊Q8×D4311yescharacteristic
723C4#1458346911yescharacteristic
724C4#1458355711yescharacteristic
725C4#1458356211yescharacteristic
726C2—82no—
727C2—1724no—
728C2#1913795311yescharacteristic
729C2#447×D4311yescharacteristic
730C2#1914390511yescharacteristic
731C2#1914722711yescharacteristic
732C2#1914731011yescharacteristic
733C2#1914744511yescharacteristic
734C2#1914748911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2023C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenter#2023D43
hypocenterC43#24326
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
1. C2×#14583564C2semidirect
2. C2×#14583177C2semidirect
4. #19139515C2semidirect
5. #19135922C2semidirect
6. #19135920C2semidirect
7. #19135729C2semidirect
8. #19135554C2semidirect
9. #19135529C2semidirect
12. #19134845C2semidirect
13. #19134843C2semidirect
14. #19134594C2semidirect
15. C43×#2023C2semidirect
76. C2×#10621882Q8semidirect
153. C2×D4×C43C2×Q8semidirect
194. C2×Dic86D8semidirect
243. C2×C43⋊C8C2×Q8semidirect
310. D172C22⋊Q8semidirect
366. #2023D43semidirect
430. C43#24326semidirect
537. C2×D4Q8×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835642
C2×#145831772
C2×#145829792
#191395152
#191359222
#191359202
#191357292
#191355542
#191355292
#191349462
#191349402
#191348452
#191348432
#191345942
C43×#20232
#2432643