Finite Group Databasebeta

← #25107756

Subgroups — #25107756

Order 11008.

1012 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×Dic43C211yesmaximal, characteristic, complemented
2#19137086C211yesmaximal, characteristic
3#19135457C211yesmaximal, characteristic, complemented
4#19135451C211yesmaximal, characteristic, complemented
5#19135280C211yesmaximal, characteristic, complemented
6#19135273C211yesmaximal, characteristic, complemented
7#19135231C211yesmaximal, characteristic, complemented
8#19135217C211yesmaximal, characteristic, complemented
9#19134952C211yesmaximal, characteristic, complemented
10#19134938C211yesmaximal, characteristic, complemented
11#19134908C211yesmaximal, characteristic, complemented
12#19134796C211yesmaximal, characteristic, complemented
13#19134535C211yesmaximal, characteristic
14C22⋊C8×Dic43C211yesmaximal, characteristic, complemented
15C2×C43×#452C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18C22×C4×Dic43C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582806C2211yescharacteristic
31#14582806C2211yescharacteristic
32#14582806C2211yescharacteristic
33#14582802C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582785—21no—
37#14582779—21no—
38#14582779—21no—
39#14582774—21no—
40#14582759C2211yescharacteristic
41C4⋊C4×Dic43—21no—
42C4⋊C4×Dic43C2211yescharacteristic
43C22⋊C4×Dic43—21no—
44C4×C22⋊Dic43—21no—
45C4×C22⋊Dic43—21no—
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×#41×C43C2211yescharacteristic
53C22×Q16×C43C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C2×C22⋊Q8×C43C2211yescharacteristic
56C43×#452C418yescomplemented
57C2×#103×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C23×Dic43D411yescharacteristic
61C23×Dic43D411yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64Q8×Dic43—41no—
65Q8×Dic43—41no—
66#13063284—41no—
67#13063284—41no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—41no—
84C2×C4×Dic43—41no—
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063259—41no—
90#13063257—41no—
91#13063249—41no—
92#13063249—41no—
93#13063249—41no—
94#13063249—41no—
95#13063246—41no—
96#13063246—41no—
97C22⋊(C43⋊C8)—22no—
98C8×Dic43—41no—
99C8×Dic43—41no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C2×#41×C43—22no—
110C2×#41×C43—41no—
111C2×#41×C43—41no—
112C2×#41×C43—41no—
113C2×#41×C43—41no—
114C2×#41×C43C2×C414yes—
115C22×Q8×C43C2311yescharacteristic
116C22×Q8×C43C2311yescharacteristic
117C22×D4×C43—21no—
118C22×D4×C43C2311yescharacteristic
119C23×C4×C43—21no—
120C23×C4×C43C2311yescharacteristic
121C2×Q16×C43—41no—
122C2×Q16×C43—41no—
123C2×Q16×C43C2×C414yescomplemented
124C2×SD16×C43—41no—
125C2×SD16×C43—41no—
126C2×SD16×C43C2×C414yescomplemented
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C22⋊Q8×C43—22no—
130C22⋊Q8×C43C2×C414yes—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C22⋊C4×C43—21no—
134#103×C43C2×C414yescomplemented
135#102×C43C2×C414yescomplemented
136C22⋊C8×C43C2×C414yes—
137C24×C43—21no—
138C24×C43C2×D411yescharacteristic
139#41×C43—44no—
140#41×C43—44no—
141#41×C43—44no—
142#41×C43—44no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43C22×C412yes—
154C2×Q8×C43C22×C412yes—
155C2×D4×C43—21no—
156C2×D4×C43—24no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43C22×C412yes—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—24no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—42no—
173C22×C4×C43—42no—
174C22×C4×C43C22×C412yes—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43#4112yes—
177C22×C4×C43C2411yescharacteristic
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—41no—
186C22×Dic43—41no—
187C22×Dic43—41no—
188C22×Dic43C2×D411yescharacteristic
189C22×Dic43C2×D411yescharacteristic
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192Q16×C43—44no—
193SD16×C43—44no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43C22×C412yes—
199C2×C8×C43C22×C412yes—
200C4⋊C4×C43—24no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43C22×C412yes—
203C22⋊C4×C43—24no—
204C22⋊Dic43—42no—
205C22⋊Dic43—42no—
206C22⋊Dic43—42no—
207C22⋊Dic43—42no—
208C22⋊Dic43—42no—
209C22⋊Dic43—42no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—42no—
219C4⋊Dic43—42no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—41no—
225C4×Dic43—41no—
226C4×Dic43—42no—
227C4×Dic43—42no—
228C4×Dic43—42no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—22no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43C4×D412yes—
249C23×C43C22×D411yescharacteristic
250Q8×C43—22no—
251Q8×C43—22no—
252Q8×C43—22no—
253Q8×C43—22no—
254Q8×C43—41no—
255Q8×C43—41no—
256Q8×C43—41no—
257Q8×C43—41no—
258D4×C43—22no—
259D4×C43—22no—
260D4×C43—48no—
261D4×C43—41no—
262D4×C43—41no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—48no—
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×C43C4×D412yes—
280C2×C4×C43C23×C411yescharacteristic
281C2×C4×C43C2×#4111yescharacteristic
282C2×C4×C43H(5,𝔽2)11yescharacteristic
283C2×C4×C43H(5,𝔽2)11yescharacteristic
284C2×C4×C43H(5,𝔽2)11yescharacteristic
285C2×C4×C43H(5,𝔽2)11yescharacteristic
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—44no—
296C2×Dic43—44no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
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#13512yes—
310C2×Dic43#13512yes—
311C2×Dic43#13712yes—
312C8×C43—22no—
313C8×C43—22no—
314C43⋊C8—41no—
315C43⋊C8—41no—
316#22042—431nomaximal, Sylow
317C22×C43—22no—
318C22×C43—22no—
319C22×C43—22no—
320C22×C43—41no—
321C22×C43—41no—
322C22×C43—41no—
323C22×C43—41no—
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×C43#53411yescharacteristic
333C22×C43#53511yescharacteristic
334C22×C43C2×#13511yescharacteristic
335C22×C43C2×#13511yescharacteristic
336C22×C43C2×#13711yescharacteristic
337C22×C43#57511yescharacteristic
338C4×C43—22no—
339C4×C43—42no—
340C4×C43—42no—
341C4×C43—42no—
342C4×C43#51811yescharacteristic
343C4×C43#51811yescharacteristic
344C4×C43#53811yescharacteristic
345C4×C43#53811yescharacteristic
346Dic43—22no—
347Dic43—22no—
348Dic43—22no—
349Dic43—41no—
350Dic43—81no—
351Dic43—81no—
352Dic43—81no—
353Dic43—81no—
354C2×#452D4311yescharacteristic
355C4×C22⋊Q8—431no—
356#2297—431no—
357#1969—431no—
358#1968—431no—
359#1934—431no—
360#1933—431no—
361#1927—431no—
362#1925—431no—
363#1880—431no—
364#1878—431no—
365#1873—431no—
366#1854—431no—
367#1788—431no—
368C4×C22⋊C8—431no—
369C2×C43—42no—
370C2×C43—82no—
371C2×C43#232111yescharacteristic
372C2×C43C4×#13511yescharacteristic
373C2×C43C4×#13711yescharacteristic
374C2×C43#319011yescharacteristic
375C2×C43#319111yescharacteristic
376C2×C43#321011yescharacteristic
377C2×C43#321211yescharacteristic
378C22×#41C2×D4311yescharacteristic
379C22×Q16C2×D4311yescharacteristic
380C22×SD16C2×D4311yescharacteristic
381C2×C22⋊Q8C2×D4311yescharacteristic
382C2×C4×Q8—431no—
383C2×#117—431no—
384C22×C42—431no—
385#452Dic4318yescomplemented
386C2×#107—431no—
387C2×#106—431no—
388C2×#103—431no—
389C2×#103—431no—
390C2×#103—431no—
391C2×#103—431no—
392C2×#103C2×D4311yescharacteristic
393C2×#102—431no—
394C2×#102—431no—
395C2×#102C2×D4311yescharacteristic
396C2×C22⋊C8—431no—
397C2×C22⋊C8C2×D4311yescharacteristic
398C2×C4×C8—431no—
399C2×C4×C8—431no—
400#391—431no—
401#391—431no—
402#391—431no—
403#390—431no—
404#390—431no—
405#389—431no—
406#387—861no—
407#386—861no—
408#386—861no—
409#385—861no—
410#380—431no—
411C4×C4⋊C4—431no—
412C4×C4⋊C4—861no—
413C4×C22⋊C4—861no—
414C4×C22⋊C4—861no—
415C4×C22⋊C4—861no—
416#340—431no—
417#340—431no—
418#340—431no—
419#340—431no—
420#336—431no—
421#336—431no—
422C43#2204211yescharacteristic, complemented, Sylow
423C2×#41—22no—
424C2×#41—41no—
425C2×#41—41no—
426C2×#41—41no—
427C2×#41—41no—
428C2×#41C2×Dic4314yes—
429C22×Q8C22×D4311yescharacteristic
430C22×Q8C22×D4311yescharacteristic
431C22×D4—21no—
432C22×D4C22×D4311yescharacteristic
433C23×C4—21no—
434C23×C4—431no—
435C23×C4—431no—
436C23×C4C22×D4311yescharacteristic
437C2×Q16—41no—
438C2×Q16—41no—
439C2×Q16C2×Dic4314yescomplemented
440C2×SD16—41no—
441C2×SD16—41no—
442C2×SD16C2×Dic4314yescomplemented
443C22×C8—431no—
444C22×C8—431no—
445C22×C8C22×D4311yescharacteristic
446C22×C8C22×D4311yescharacteristic
447C22⋊Q8—22no—
448C22⋊Q8C2×Dic4314yes—
449C4×Q8—1721no—
450C4×Q8—1721no—
451#117—1721no—
452#117—1721no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—431no—
455C2×C4⋊C4—431no—
456C2×C4⋊C4—431no—
457C2×C4⋊C4—431no—
458C2×C4⋊C4—861no—
459C2×C4⋊C4—861no—
460C2×C4⋊C4C22×D4311yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—861no—
463C2×C22⋊C4—861no—
464C2×C22⋊C4—861no—
465C2×C22⋊C4—861no—
466C2×C22⋊C4—861no—
467C2×C22⋊C4—861no—
468C2×C42—431no—
469C2×C42—431no—
470C2×C42—431no—
471C2×C42—431no—
472C2×C42—861no—
473C2×C42—861no—
474C2×C42—861no—
475C2×C42—1721no—
476C2×C42—1721no—
477#107—1721no—
478#106—1721no—
479#103—1721no—
480#103—1721no—
481#103—1721no—
482#103—1721no—
483#103C2×Dic4314yescomplemented
484#102—1721no—
485#102—1721no—
486#102C2×Dic4314yescomplemented
487C22⋊C8—862no—
488C22⋊C8C2×Dic4314yes—
489C4×C8—1721no—
490C4×C8—1721no—
491#95—861no—
492#95—861no—
493#95—861no—
494#95—861no—
495#95—861no—
496#95—861no—
497#95—861no—
498#95—861no—
499#95—861no—
500C24—21no—
501C24D4×D4311yescharacteristic
502#41—44no—
503#41—44no—
504#41—44no—
505#41—44no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8C22×Dic4312yes—
517C2×Q8C22×Dic4312yes—
518C2×D4—24no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4C22×Dic4312yes—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—24no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—431no—
538C22×C4—431no—
539C22×C4—431no—
540C22×C4—431no—
541C22×C4—862no—
542C22×C4—862no—
543C22×C4—862no—
544C22×C4—861no—
545C22×C4—861no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—1721no—
549C22×C4—1721no—
550C22×C4—1721no—
551C22×C4D4×D4311yescharacteristic
552C22×C4#1062190012yes—
553C22×C4C22×Dic4312yes—
554C22×C4C23×D4311yescharacteristic
555Q16—44no—
556SD16—44no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—861no—
562C2×C8—861no—
563C2×C8—861no—
564C2×C8—861no—
565C2×C8—861no—
566C2×C8—861no—
567C2×C8C22×Dic4312yes—
568C2×C8C22×Dic4312yes—
569C4⋊C4—24no—
570C4⋊C4—21no—
571C4⋊C4—861no—
572C4⋊C4—861no—
573C4⋊C4—861no—
574C4⋊C4—861no—
575C4⋊C4—861no—
576C4⋊C4—861no—
577C4⋊C4—861no—
578C4⋊C4—861no—
579C4⋊C4—1722no—
580C4⋊C4—1722no—
581C4⋊C4C22×Dic4312yes—
582C22⋊C4—24no—
583C22⋊C4—1722no—
584C22⋊C4—1722no—
585C22⋊C4—1722no—
586C22⋊C4—1722no—
587C22⋊C4—1722no—
588C22⋊C4—1722no—
589C42—861no—
590C42—861no—
591C42—861no—
592C42—861no—
593C42—1721no—
594C42—1721no—
595C42—1722no—
596C42—1722no—
597C42—1722no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—22no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23D4×Dic4312yes—
612C23C2×D4×D4311yescharacteristic
613Q8—22no—
614Q8—22no—
615Q8—22no—
616Q8—22no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620Q8—41no—
621D4—22no—
622D4—22no—
623D4—48no—
624D4—41no—
625D4—41no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—48no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—432no—
643C2×C4—432no—
644C2×C4—432no—
645C2×C4—861no—
646C2×C4—861no—
647C2×C4—861no—
648C2×C4—861no—
649C2×C4—861no—
650C2×C4—861no—
651C2×C4—861no—
652C2×C4—861no—
653C2×C4—861no—
654C2×C4—1724no—
655C2×C4—1724no—
656C2×C4—1721no—
657C2×C4—1721no—
658C2×C4—1721no—
659C2×C4—1721no—
660C2×C4—1721no—
661C2×C4—1721no—
662C2×C4—1721no—
663C2×C4—1721no—
664C2×C4—1721no—
665C2×C4—1721no—
666C2×C4—1721no—
667C2×C4—1721no—
668C2×C4D4×Dic4312yes—
669C2×C4C23×Dic4311yescharacteristic
670C2×C4C2×#1062190011yescharacteristic
671C2×C4#1306337011yescharacteristic
672C2×C4#1306337011yescharacteristic
673C2×C4#1306337011yescharacteristic
674C2×C4#1306337011yescharacteristic
675C8—22no—
676C8—22no—
677C8—1721no—
678C8—1721no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22C2×D4×Dic4311yescharacteristic
694C22#1458345911yescharacteristic
695C22#1458346411yescharacteristic
696C22#135×D4311yescharacteristic
697C22#135×D4311yescharacteristic
698C22#137×D4311yescharacteristic
699C22#1458369811yescharacteristic
700C4—22no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—862no—
705C4—862no—
706C4—862no—
707C4—3441no—
708C4—3441no—
709C4—3441no—
710C4—3441no—
711C4—1721no—
712C4#1458337411yescharacteristic
713C4#1458337411yescharacteristic
714C4#1458348411yescharacteristic
715C4#1458348411yescharacteristic
716C2—42no—
717C2—82no—
718C2#1913725611yescharacteristic
719C2#135×Dic4311yescharacteristic
720C2#137×Dic4311yescharacteristic
721C2#1914537411yescharacteristic
722C2#1914538711yescharacteristic
723C2#1914554911yescharacteristic
724C2#1914557411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#452C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#452D43
hypocenterC43#22042
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C22⋊Q8×Dic43C2semidirect
3. #19135457C2semidirect
4. #19135451C2semidirect
5. #19135280C2semidirect
6. #19135273C2semidirect
7. #19135231C2semidirect
8. #19135217C2semidirect
9. #19134952C2semidirect
10. #19134938C2semidirect
11. #19134908C2semidirect
12. #19134796C2semidirect
14. C22⋊C8×Dic43C2semidirect
56. C43×#452C4semidirect
123. C2×Q16×C43C2×C4semidirect
126. C2×SD16×C43C2×C4semidirect
134. #103×C43C2×C4semidirect
135. #102×C43C2×C4semidirect
385. #452Dic43semidirect
422. C43#22042semidirect
439. C2×Q16C2×Dic43semidirect
442. C2×SD16C2×Dic43semidirect
483. #103C2×Dic43semidirect
486. #102C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×Dic432
#191370862
#191354572
#191354512
#191352802
#191352732
#191352312
#191352172
#191349522
#191349382
#191349082
#191347962
#191345352
C22⋊C8×Dic432
C2×C43×#4522
#2204243