Finite Group Databasebeta

← #25003549

Subgroups — #25003549

Order 11008.

1326 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063246C211yesmaximal, characteristic
2C2×#14582802C211yesmaximal, characteristic
3C2×#14582768C211yesmaximal, characteristic, complemented
4C2×#14582662C211yesmaximal, characteristic, complemented
5C2×#14582661C211yesmaximal, characteristic, complemented
6C2×#14582653C211yesmaximal, characteristic, complemented
7C22×#102×C43C211yesmaximal, characteristic
8C23×C43⋊C8C2211yescharacteristic
9C22×C4⋊Dic43C2211yescharacteristic
10C22×C4⋊Dic43C2211yescharacteristic
11C22×Dic43⋊C4—22no—
12C22×C22⋊Dic43—22no—
13C22×C4×Dic43C2211yescharacteristic
14C2×#13063246—22no—
15C2×#13063246—22no—
16C2×#13063246—22no—
17#14582802—22no—
18#14582802C414yescomplemented
19#14582768—22no—
20#14582768—22no—
21#14582662—22no—
22#14582661—22no—
23#14582653—22no—
24C23×D4×C43C2211yescharacteristic
25C23×C8×C43C2211yescharacteristic
26C22×C4⋊C4×C43C2211yescharacteristic
27C2×#102×C43—22no—
28C2×#102×C43—22no—
29C2×#102×C43—22no—
30C23×Dic43—21no—
31C23×Dic43—21no—
32C23×Dic43D412yes—
33C22×C43⋊C8—21no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36C22×C43⋊C8—21no—
37C22×C43⋊C8—21no—
38C22×C43⋊C8—21no—
39C22×C43⋊C8D412yes—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43—21no—
48C2×C4⋊Dic43—21no—
49C2×C4⋊Dic43—21no—
50C2×C4⋊Dic43C2×C412yes—
51C2×C4⋊Dic43D412yes—
52C2×Dic43⋊C4—28no—
53C2×Dic43⋊C4—44no—
54C2×Dic43⋊C4—44no—
55C2×C22⋊Dic43—28no—
56C2×C22⋊Dic43—44no—
57C2×C22⋊Dic43—44no—
58C2×C4×Dic43—21no—
59C2×C4×Dic43—21no—
60C2×C4×Dic43—21no—
61C2×C4×Dic43—21no—
62C2×C4×Dic43C2×C412yes—
63C2×C4×Dic43D412yes—
64#13063246—28no—
65C25×C43—21no—
66C22×D4×C43—21no—
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70C22×D4×C43—21no—
71C22×D4×C43—21no—
72C22×D4×C43—21no—
73C22×D4×C43—21no—
74C22×D4×C43—21no—
75C22×D4×C43—21no—
76C22×D4×C43—21no—
77C22×D4×C43C2×C412yes—
78C22×D4×C43D412yes—
79C22×D4×C43Q812yes—
80C23×C4×C43—21no—
81C23×C4×C43C2311yescharacteristic
82C22×C8×C43—21no—
83C22×C8×C43—21no—
84C22×C8×C43—21no—
85C22×C8×C43—21no—
86C22×C8×C43—21no—
87C22×C8×C43—21no—
88C22×C8×C43D412yes—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43D412yes—
95#102×C43—28no—
96C24×C43—22no—
97C24×C43—22no—
98C24×C43—22no—
99C24×C43—41no—
100C24×C43—41no—
101C24×C43—41no—
102C24×C43—41no—
103C24×C43—42no—
104C24×C43—42no—
105C24×C43—42no—
106C24×C43—42no—
107C24×C43C2×D411yescharacteristic
108C2×D4×C43—22no—
109C2×D4×C43—22no—
110C2×D4×C43—22no—
111C2×D4×C43—22no—
112C2×D4×C43—22no—
113C2×D4×C43—22no—
114C2×D4×C43—22no—
115C2×D4×C43—22no—
116C2×D4×C43—22no—
117C2×D4×C43—22no—
118C2×D4×C43—22no—
119C2×D4×C43—22no—
120C2×D4×C43—22no—
121C2×D4×C43—22no—
122C2×D4×C43—22no—
123C2×D4×C43—41no—
124C2×D4×C43—41no—
125C2×D4×C43—41no—
126C2×D4×C43—41no—
127C2×D4×C43—41no—
128C2×D4×C43—41no—
129C2×D4×C43—41no—
130C2×D4×C43—41no—
131C2×D4×C43—41no—
132C2×D4×C43—41no—
133C2×D4×C43—41no—
134C2×D4×C43—41no—
135C2×D4×C43C4⋊C414yescomplemented
136C22×C4×C43—22no—
137C22×C4×C43—41no—
138C22×C4×C43—41no—
139C22×C4×C43—42no—
140C22×C4×C43—42no—
141C22×C4×C43C22×C411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×Q811yescharacteristic
149C22×C4×C43#4111yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C22×C4×C43#4111yescharacteristic
152C22×C4×C43#4111yescharacteristic
153C22×C4×C43#4111yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—41no—
162C22×Dic43—41no—
163C22×Dic43—41no—
164C22×Dic43—41no—
165C22×Dic43—42no—
166C22×Dic43—42no—
167C22×Dic43—42no—
168C22×Dic43—42no—
169C22×Dic43C22⋊C414yes—
170C22×Dic43D814yes—
171C22×Dic43SD1614yes—
172C2×C8×C43—22no—
173C2×C8×C43—22no—
174C2×C8×C43—22no—
175C2×C8×C43—41no—
176C2×C8×C43—41no—
177C2×C8×C43—41no—
178C2×C8×C43—41no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—41no—
182C4⋊C4×C43—41no—
183C22⋊Dic43—416no—
184C4⋊Dic43—22no—
185C4⋊Dic43—22no—
186C4⋊Dic43—22no—
187C4⋊Dic43—22no—
188C4⋊Dic43—41no—
189C4⋊Dic43—41no—
190C4⋊Dic43—41no—
191C4⋊Dic43—41no—
192Dic43⋊C4—416no—
193C4×Dic43—22no—
194C4×Dic43—22no—
195C4×Dic43—22no—
196C4×Dic43—22no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—22no—
200C2×C43⋊C8—41no—
201C2×C43⋊C8—41no—
202C2×C43⋊C8—41no—
203C2×C43⋊C8—41no—
204C23×C43—24no—
205C23×C43—42no—
206C23×C43—42no—
207C23×C43—42no—
208C23×C43—42no—
209C23×C43—42no—
210C23×C43—42no—
211C23×C43—44no—
212C23×C43—44no—
213C23×C43—44no—
214C23×C43—44no—
215C23×C43—44no—
216C23×C43—44no—
217C23×C43—82no—
218C23×C43—82no—
219C23×C43—82no—
220C23×C43—82no—
221C23×C43—82no—
222C23×C43—82no—
223C23×C43—81no—
224C23×C43—81no—
225C23×C43—81no—
226C23×C43—81no—
227C23×C43C2×C22⋊C411yescharacteristic
228C23×C43#12011yescharacteristic
229C23×C43#12111yescharacteristic
230C23×C43C22⋊Q811yescharacteristic
231C23×C43#12311yescharacteristic
232C23×C43#12411yescharacteristic
233C23×C43#12711yescharacteristic
234C23×C43C2×D812yes—
235C23×C43C2×SD1612yes—
236C23×C43AGL(1,ℤ/8)12yes—
237C23×C43#13712yes—
238D4×C43—24no—
239D4×C43—24no—
240D4×C43—42no—
241D4×C43—42no—
242D4×C43—42no—
243D4×C43—42no—
244D4×C43—42no—
245D4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—44no—
248C2×C4×C43—82no—
249C2×C4×C43—81no—
250C2×C4×C43—81no—
251C2×C4×C43C2×C4⋊C411yescharacteristic
252C2×C4×C43#11711yescharacteristic
253C2×C4×C43C4×D411yescharacteristic
254C2×C4×C43C4×D411yescharacteristic
255C2×C4×C43C4×D411yescharacteristic
256C2×C4×C43C4×D411yescharacteristic
257C2×C4×C43#12011yescharacteristic
258C2×C4×C43#12011yescharacteristic
259C2×C4×C43#12111yescharacteristic
260C2×C4×C43#12111yescharacteristic
261C2×C4×C43#12111yescharacteristic
262C2×C4×C43#12111yescharacteristic
263C2×C4×C43#12111yescharacteristic
264C2×C4×C43#12111yescharacteristic
265C2×C4×C43#12111yescharacteristic
266C2×C4×C43C22⋊Q811yescharacteristic
267C2×C4×C43C22⋊Q811yescharacteristic
268C2×C4×C43C22⋊Q811yescharacteristic
269C2×C4×C43C22⋊Q811yescharacteristic
270C2×C4×C43C22⋊Q811yescharacteristic
271C2×C4×C43#12311yescharacteristic
272C2×C4×C43#12311yescharacteristic
273C2×C4×C43#12311yescharacteristic
274C2×C4×C43#12311yescharacteristic
275C2×C4×C43#12411yescharacteristic
276C2×C4×C43#12411yescharacteristic
277C2×C4×C43#12611yescharacteristic
278C2×C4×C43#12611yescharacteristic
279C2×Dic43—24no—
280C2×Dic43—24no—
281C2×Dic43—24no—
282C2×Dic43—24no—
283C2×Dic43—24no—
284C2×Dic43—24no—
285C2×Dic43—42no—
286C2×Dic43—42no—
287C2×Dic43—44no—
288C2×Dic43—44no—
289C2×Dic43—82no—
290C2×Dic43—82no—
291C2×Dic43—81no—
292C2×Dic43—81no—
293C2×Dic43—81no—
294C2×Dic43—81no—
295C2×Dic43#10218yescomplemented
296C8×C43—42no—
297C43⋊C8—42no—
298#11049—431nomaximal, Sylow
299C22×C43—48no—
300C22×C43—44no—
301C22×C43—84no—
302C22×C43—82no—
303C22×C43—82no—
304C22×C43—84no—
305C22×C43—82no—
306C22×C43—82no—
307C22×C43—82no—
308C22×C43—82no—
309C22×C43—84no—
310C22×C43#38011yescharacteristic
311C22×C43#38611yescharacteristic
312C22×C43#39011yescharacteristic
313C22×C43#39211yescharacteristic
314C22×C43#39311yescharacteristic
315C22×C43#39711yescharacteristic
316C22×C43#39911yescharacteristic
317C22×C43C2×#10212yes—
318C22×C43#41712yes—
319C22×C43#44712yes—
320C22×C43#44812yes—
321C22×C43#45912yes—
322C22×C43#46112yes—
323C22×C43#47412yes—
324C22×C43#47612yes—
325C22×C43#48012yes—
326C22×C43#48112yes—
327C22×C43#48612yes—
328C22×C43#48912yes—
329C22×C43#49211yescharacteristic
330C22×C43#49311yescharacteristic
331C22×C43#49611yescharacteristic
332C22×C43#49711yescharacteristic
333C4×C43—82no—
334C4×C43#38511yescharacteristic
335C4×C43#38511yescharacteristic
336C4×C43#38811yescharacteristic
337C4×C43#38811yescharacteristic
338C4×C43#39411yescharacteristic
339C4×C43#39411yescharacteristic
340C4×C43#39611yescharacteristic
341C4×C43#39611yescharacteristic
342Dic43—28no—
343Dic43—82no—
344Dic43—82no—
345C22×#102—431no—
346C22×#102D4311yescharacteristic
347C2×#390—431no—
348C2×#384—431no—
349C2×#340—431no—
350C2×#340—431no—
351C2×#336—431no—
352C2×C43—84no—
353C2×C43#143911yescharacteristic
354C2×C43#180212yes—
355C2×C43#187412yes—
356C2×C43#195711yescharacteristic
357C2×C43#195911yescharacteristic
358C2×C43#201111yescharacteristic
359C2×C43#201311yescharacteristic
360C2×C43#202312yes—
361C2×C43#207112yes—
362C2×C43#209311yescharacteristic
363C2×C43#209411yescharacteristic
364C23×D4C2×D4311yescharacteristic
365C23×C8—431no—
366C23×C8C2×D4311yescharacteristic
367C22×C4⋊C4—431no—
368C22×C4⋊C4—431no—
369C22×C4⋊C4—862no—
370C22×C4⋊C4C2×D4311yescharacteristic
371C22×C22⋊C4—862no—
372C22×C42—431no—
373C2×#102—22no—
374C2×#102—22no—
375C2×#102—22no—
376C2×#102—862no—
377C2×#102—862no—
378C2×#102—862no—
379#390—434no—
380#390—862no—
381#384—862no—
382#384—862no—
383#340—862no—
384#340—862no—
385#336—862no—
386C43#1104911yescharacteristic, complemented, Sylow
387C25—21no—
388C22×D4—21no—
389C22×D4—21no—
390C22×D4—21no—
391C22×D4—21no—
392C22×D4—21no—
393C22×D4—21no—
394C22×D4—21no—
395C22×D4—21no—
396C22×D4—21no—
397C22×D4—21no—
398C22×D4—21no—
399C22×D4Dic8612yes—
400C22×D4C4×D4312yes—
401C22×D4C22⋊D4312yes—
402C23×C4—21no—
403C23×C4—432no—
404C23×C4—861no—
405C23×C4—861no—
406C23×C4C22×D4311yescharacteristic
407C22×C8—21no—
408C22×C8—21no—
409C22×C8—21no—
410C22×C8—21no—
411C22×C8—21no—
412C22×C8—21no—
413C22×C8—432no—
414C22×C8—861no—
415C22×C8—861no—
416C22×C8—861no—
417C22×C8—861no—
418C22×C8—861no—
419C22×C8—861no—
420C22×C8C22⋊D4312yes—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—432no—
427C2×C4⋊C4—432no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—868no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—1724no—
440C2×C4⋊C4—1724no—
441C2×C4⋊C4C22⋊D4312yes—
442C2×C22⋊C4—868no—
443C2×C22⋊C4—1724no—
444C2×C22⋊C4—1724no—
445C2×C42—432no—
446C2×C42—432no—
447C2×C42—861no—
448C2×C42—861no—
449C2×C42—861no—
450C2×C42—861no—
451#102—28no—
452#102—868no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—41no—
457C24—41no—
458C24—41no—
459C24—41no—
460C24—42no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24D4×D4311yescharacteristic
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4Dic43⋊C414yescomplemented
493C22×C4—22no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—434no—
499C22×C4—434no—
500C22×C4—434no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—862no—
504C22×C4—862no—
505C22×C4—862no—
506C22×C4—862no—
507C22×C4—1721no—
508C22×C4—1721no—
509C22×C4—1721no—
510C22×C4—1721no—
511C22×C4—1722no—
512C22×C4—1722no—
513C22×C4—1722no—
514C22×C4—1722no—
515C22×C4C2×Dic8611yescharacteristic
516C22×C4C2×C4×D4311yescharacteristic
517C22×C4#1062189811yescharacteristic
518C22×C4#1062189811yescharacteristic
519C22×C4D4×D4311yescharacteristic
520C22×C4D4×D4311yescharacteristic
521C22×C4D4×D4311yescharacteristic
522C22×C4#1062190011yescharacteristic
523C22×C4#1062190011yescharacteristic
524C22×C4#1062190011yescharacteristic
525C22×C4#1062190011yescharacteristic
526C22×C4C2×C22⋊D4311yescharacteristic
527C22×C4C2×C22⋊D4311yescharacteristic
528C22×C4C2×C22⋊D4311yescharacteristic
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—862no—
537C2×C8—862no—
538C2×C8—862no—
539C2×C8—1721no—
540C2×C8—1721no—
541C2×C8—1721no—
542C2×C8—1721no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—862no—
548C4⋊C4—862no—
549C4⋊C4—862no—
550C4⋊C4—862no—
551C4⋊C4—17216no—
552C4⋊C4—1721no—
553C4⋊C4—1721no—
554C4⋊C4—1721no—
555C4⋊C4—1721no—
556C22⋊C4—17216no—
557C42—862no—
558C42—862no—
559C42—862no—
560C42—862no—
561C23—24no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—44no—
568C23—44no—
569C23—44no—
570C23—44no—
571C23—44no—
572C23—44no—
573C23—42no—
574C23—82no—
575C23—82no—
576C23—82no—
577C23—82no—
578C23—81no—
579C23—81no—
580C23—82no—
581C23—81no—
582C23—81no—
583C23—82no—
584C23C22⋊C4×D4311yescharacteristic
585C23#1306329311yescharacteristic
586C23#1306329711yescharacteristic
587C23#1306330211yescharacteristic
588C23#1306330711yescharacteristic
589C23#1306331111yescharacteristic
590C23#1306332111yescharacteristic
591C23D8×D4312yes—
592C23SD16×D4312yes—
593C23#1306334912yes—
594C23#1306335412yes—
595D4—24no—
596D4—24no—
597D4—42no—
598D4—42no—
599D4—42no—
600D4—42no—
601D4—42no—
602D4—42no—
603C2×C4—42no—
604C2×C4—44no—
605C2×C4—82no—
606C2×C4—81no—
607C2×C4—81no—
608C2×C4—438no—
609C2×C4—864no—
610C2×C4—864no—
611C2×C4—864no—
612C2×C4—864no—
613C2×C4—864no—
614C2×C4—864no—
615C2×C4—3442no—
616C2×C4—3442no—
617C2×C4—3441no—
618C2×C4—3441no—
619C2×C4—3441no—
620C2×C4—3441no—
621C2×C4—1722no—
622C2×C4—1722no—
623C2×C4—1724no—
624C2×C4—1724no—
625C2×C4C2×Dic43⋊C411yescharacteristic
626C2×C4#1306328111yescharacteristic
627C2×C4(C22⋊D43)⋊C411yescharacteristic
628C2×C4(C22⋊D43)⋊C411yescharacteristic
629C2×C4C4×C22⋊D4311yescharacteristic
630C2×C4C4×C22⋊D4311yescharacteristic
631C2×C4#1306329311yescharacteristic
632C2×C4#1306329411yescharacteristic
633C2×C4#1306329611yescharacteristic
634C2×C4#1306329611yescharacteristic
635C2×C4#1306329711yescharacteristic
636C2×C4#1306329711yescharacteristic
637C2×C4#1306329711yescharacteristic
638C2×C4#1306329811yescharacteristic
639C2×C4#1306329811yescharacteristic
640C2×C4#1306330211yescharacteristic
641C2×C4#1306330211yescharacteristic
642C2×C4#1306330211yescharacteristic
643C2×C4#1306330411yescharacteristic
644C2×C4#1306330411yescharacteristic
645C2×C4#1306330611yescharacteristic
646C2×C4#1306330611yescharacteristic
647C2×C4#1306330711yescharacteristic
648C2×C4#1306330811yescharacteristic
649C2×C4#1306331111yescharacteristic
650C2×C4#1306331211yescharacteristic
651C2×C4#1306331811yescharacteristic
652C2×C4#1306331811yescharacteristic
653C8—42no—
654C8—1722no—
655C22—48no—
656C22—44no—
657C22—84no—
658C22—82no—
659C22—82no—
660C22—82no—
661C22—82no—
662C22—82no—
663C22—82no—
664C22—84no—
665C22—84no—
666C22#1458275711yescharacteristic
667C22#1458277511yescharacteristic
668C22#1458279911yescharacteristic
669C22#1458280711yescharacteristic
670C22#1458281111yescharacteristic
671C22#1458282711yescharacteristic
672C22#1458283511yescharacteristic
673C22#102×D4312yes—
674C22#1458289712yes—
675C22#1458303112yes—
676C22#1458303612yes—
677C22#1458309212yes—
678C22#1458310212yes—
679C22#1458317712yes—
680C22#1458318712yes—
681C22#1458321112yes—
682C22#1458321612yes—
683C22#1458324412yes—
684C22#1458325712yes—
685C22#1458327011yescharacteristic
686C22#1458327411yescharacteristic
687C22#1458328711yescharacteristic
688C22#1458329011yescharacteristic
689C4—82no—
690C4—868no—
691C4—3442no—
692C4—3442no—
693C4#1458277111yescharacteristic
694C4#1458277211yescharacteristic
695C4#1458278711yescharacteristic
696C4#1458279311yescharacteristic
697C4#1458281311yescharacteristic
698C4#1458281411yescharacteristic
699C4#1458282211yescharacteristic
700C4#1458282211yescharacteristic
701C2—84no—
702C2#1913283811yescharacteristic
703C2#1913459312yes—
704C2#1913490912yes—
705C2#1913539911yescharacteristic
706C2#1913541011yescharacteristic
707C2#1913566411yescharacteristic
708C2#1913567611yescharacteristic
709C2#1913572912yes—
710C2#1913600112yes—
711C2#1913612111yescharacteristic
712C2#1913612611yescharacteristic
subgroupG/H
centerC24D4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC22×#102×C43C2
socleC24×C43C2×D4
prime radicalC23×D4×C43C22
cosocleC23×C4×C43C23
hypercenterC22×#102D43
hypocenterC43#11049
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
3. C2×#14582768C2semidirect
4. C2×#14582662C2semidirect
5. C2×#14582661C2semidirect
6. C2×#14582653C2semidirect
18. #14582802C4semidirect
135. C2×D4×C43C4⋊C4semidirect
295. C2×Dic43#102semidirect
386. C43#11049semidirect
492. C2×D4Dic43⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130632462
C2×#145828022
C2×#145827682
C2×#145826622
C2×#145826612
C2×#145826532
C22×#102×C432
#1104943