Finite Group Databasebeta

← #10958713

Subgroups — #10958713

Order 768.

2766 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#535C211yesmaximal, characteristic
2#84087C211yesmaximal, characteristic, complemented
3#84086C211yesmaximal, characteristic, complemented
4D4×#217C212yesmaximal, complemented
5#83172C214yesmaximal, complemented
6#82957C212yesmaximal, complemented
7#82956C212yesmaximal, complemented
8#82637C212yesmaximal, complemented
9#82636C212yesmaximal, complemented
10#82633C212yesmaximal, complemented
11Dic3×#121C212yesmaximal, complemented
12#82580C212yesmaximal, complemented
13#82579C212yesmaximal, complemented
14#82578C214yesmaximal, complemented
15#82239C212yesmaximal, complemented
16#34415—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C3×#535C4116yescomplemented
20C2×C3×#127C2212yes—
21C2×C3×#124C2212yes—
22C2×C3×#121C2212yes—
23C2×C3×#121C2212yes—
24C2×C3×#120C2212yes—
25C2×C3×#120C2212yes—
26C2×C3×#117C2211yescharacteristic
27C22×#217C2214yes—
28C2×D4×Dic3C2212yes—
29C2×D4×Dic3C2212yes—
30C2×D4×Dic3C2214yescomplemented
31C2×D4×Dic3C2214yescomplemented
32C2×#926C2211yescharacteristic, complemented
33C2×#926C2211yescharacteristic, complemented
34C22×C4⋊Dic3C2211yescharacteristic, complemented
35C22×C4×Dic3C2211yescharacteristic, complemented
36#5247C2214yes—
37#5229C2211yescharacteristic, complemented
38#5229C2212yescomplemented
39#5229C2211yescharacteristic, complemented
40#5221C2212yes—
41#5221C2212yes—
42#5221C2211yescharacteristic
43#5221C2211yescharacteristic
44#5221C2212yes—
45#5221C2214yescomplemented
46#5221C2214yescomplemented
47#5220C2214yes—
48#5220C2214yes—
49#5220C2212yes—
50#5220C2212yes—
51#5220C2212yescomplemented
52#5220C2212yescomplemented
53#5220C2214yescomplemented
54#5220C2214yescomplemented
55#5220C2214yescomplemented
56#5220C2214yescomplemented
57#5212C2212yes—
58#5212C2212yescomplemented
59C4×#217C2212yes—
60C4×#217C2212yescomplemented
61#4984C2212yescomplemented
62#4984C2212yescomplemented
63Dic3×C4⋊C4C2212yescomplemented
64Dic3×C4⋊C4C2212yescomplemented
65#4951C2214yes—
66#4951C2214yes—
67#4951C2214yescomplemented
68#4951C2214yescomplemented
69#4951C2214yescomplemented
70#4951C2214yescomplemented
71#4950C2214yescomplemented
72#4950C2214yescomplemented
73Dic3×C22⋊C4C2214yescomplemented
74Dic3×C22⋊C4C2214yescomplemented
75#4936C2214yescomplemented
76#4932C2214yescomplemented
77C2×#535D311yescharacteristic
78#2379—32no—
79#2375—32no—
80#2372—32no—
81#2363—32no—
82#2361—32no—
83#2358—32no—
84#2346—32no—
85D4×C22⋊C4—32no—
86#2328—34no—
87#2324—32no—
88#2321—34no—
89#2311—31no—
90C4×#121—32no—
91#2297—31no—
92C25×C3C2312yes—
93C2×C3×#41—42no—
94C2×C3×#41—42no—
95C2×C3×#41C2×C418yescomplemented
96C22×C3×Q8C2311yescharacteristic
97C22×C3×D4—42no—
98C22×C3×D4—42no—
99C22×C3×D4C2×C418yescomplemented
100C22×C3×D4C2312yes—
101C22×C3×D4C2312yes—
102C22×C3×D4C2311yescharacteristic
103C22×C3×D4C2311yescharacteristic
104C22×C3×D4C2311yescharacteristic
105C22×C3×D4C2314yes—
106C22×C3×D4C2314yes—
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C23×Dic3C2314yes—
111C23×Dic3C2312yes—
112C23×Dic3C2314yes—
113C23×Dic3C2312yes—
114C3×#127C2×C4116yescomplemented
115C3×#124C2×C4116yescomplemented
116C3×#121C2×C4116yescomplemented
117C3×#121C2×C4116yescomplemented
118C3×#120C2×C4116yescomplemented
119C3×#120C2×C4116yescomplemented
120C3×#117C2×C418yescomplemented
121C2×C3×C4⋊C4C2312yes—
122C2×C3×C22⋊C4C2314yes—
123C2×C3×C22⋊C4C2314yes—
124C2×C3×C22⋊C4C2312yes—
125C2×C3×C42C2312yes—
126C2×#217—48no—
127C2×#217C2314yes—
128C2×#217C2312yes—
129C2×#217C2312yes—
130C2×#217C2314yes—
131C2×#217C2314yes—
132C2×#217C2314yes—
133C2×#217C2312yes—
134C2×#217C2314yes—
135C2×#217C2314yes—
136C2×#217C2314yes—
137C2×#217C2312yes—
138C2×#217C2314yes—
139C2×#217C2312yes—
140C2×#217C2312yes—
141D4×Dic3—44no—
142D4×Dic3—44no—
143D4×Dic3—48no—
144D4×Dic3—48no—
145#926—42no—
146#926—42no—
147C2×C4⋊Dic3—42no—
148C2×C4⋊Dic3C2312yes—
149C2×C4⋊Dic3C2312yes—
150C2×C4⋊Dic3C2314yes—
151C2×C4⋊Dic3C2314yes—
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2312yes—
154C2×C4⋊Dic3C2311yescharacteristic
155C2×C4×Dic3—42no—
156C2×C4×Dic3C2314yes—
157C2×C4×Dic3C2312yes—
158C2×C4×Dic3C2312yes—
159C2×C4×Dic3C2314yes—
160C2×C4×Dic3C2311yescharacteristic
161C2×C4×Dic3C2312yes—
162C2×C4×Dic3C2311yescharacteristic
163C3⋊#95C2312yes—
164C3⋊#95C2314yes—
165C3⋊#95C2314yes—
166C3⋊#95C2314yes—
167C3⋊#95C2312yes—
168C3⋊#95C2314yes—
169C3⋊#95C2314yes—
170C3⋊#95C2312yes—
171C3⋊#95C2314yes—
172C3⋊#95C2312yes—
173C22×#41C2×D311yescharacteristic
174C23×D4C2×D311yescharacteristic
175#535Dic3116yescomplemented
176C2×#127C2×D312yes—
177C2×#124C2×D312yes—
178C2×#121C2×D312yes—
179C2×#121C2×D312yes—
180C2×#120C2×D312yes—
181C2×#120C2×D312yes—
182C2×C4×D4—34no—
183C2×C4×D4—32no—
184C2×C4×D4—34no—
185C2×C4×D4—32no—
186C2×#117—31no—
187C2×#117—31no—
188C2×#117C2×D311yescharacteristic
189C22×C4⋊C4—31no—
190C22×C22⋊C4—34no—
191C22×C42—31no—
192#391—32no—
193#391—31no—
194#391—31no—
195#390—32no—
196#390—34no—
197#390—32no—
198#390—34no—
199#390—32no—
200#390—31no—
201#390—31no—
202#389—32no—
203#389—32no—
204#388—34no—
205#388—34no—
206#388—34no—
207#388—34no—
208#388—34no—
209#388—34no—
210#386—32no—
211#386—32no—
212#386—32no—
213#386—34no—
214#386—34no—
215#386—32no—
216#386—34no—
217#386—34no—
218#386—34no—
219#386—34no—
220#385—34no—
221#385—34no—
222#382—34no—
223#380—32no—
224#380—32no—
225#379—34no—
226C4×C4⋊C4—32no—
227C4×C4⋊C4—32no—
228C4×C22⋊C4—32no—
229C4×C22⋊C4—32no—
230C4×C22⋊C4—34no—
231C4×C22⋊C4—34no—
232#376—34no—
233C24×C3—44no—
234C24×C3—44no—
235C24×C3—42no—
236C24×C3—42no—
237C24×C3C22×C418yes—
238C24×C3C2411yescharacteristic
239C24×C3C2414yes—
240C24×C3C2411yescharacteristic
241C24×C3C2411yescharacteristic
242C3×#41—416no—
243C2×C3×Q8—41no—
244C2×C3×Q8—41no—
245C2×C3×Q8C22×C414yes—
246C2×C3×D4—24no—
247C2×C3×D4—24no—
248C2×C3×D4—416no—
249C2×C3×D4—44no—
250C2×C3×D4—44no—
251C2×C3×D4—42no—
252C2×C3×D4—42no—
253C2×C3×D4—44no—
254C2×C3×D4—44no—
255C2×C3×D4—41no—
256C2×C3×D4—41no—
257C2×C3×D4—41no—
258C2×C3×D4—41no—
259C2×C3×D4—41no—
260C2×C3×D4—41no—
261C2×C3×D4C22×C418yes—
262C2×C3×D4C22×C414yes—
263C2×C3×D4C22×C414yes—
264C2×C3×D4C22×C4116yes—
265C2×C3×D4C22×C4116yes—
266C2×C3×D4C22×C418yes—
267C2×C3×D4C22×C414yes—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4C22×C414yes—
275C22×C3×C4C22×C414yes—
276C22×C3×C4C22×C414yes—
277C22×C3×C4C2411yescharacteristic
278C22×C3×C4C2414yes—
279C22×C3×C4C2411yescharacteristic
280C22×C3×C4C2411yescharacteristic
281C22×C3×C4C2411yescharacteristic
282C22×Dic3—24no—
283C22×Dic3—28no—
284C22×Dic3—42no—
285C22×Dic3—42no—
286C22×Dic3—42no—
287C22×Dic3—44no—
288C22×Dic3—44no—
289C22×Dic3—44no—
290C22×Dic3—44no—
291C22×Dic3—44no—
292C22×Dic3—44no—
293C22×Dic3C2412yes—
294C22×Dic3C2412yes—
295C22×Dic3C2414yes—
296C22×Dic3C2412yes—
297C22×Dic3C2414yes—
298C22×Dic3C2412yes—
299C3×C4⋊C4C22×C418yes—
300C3×C22⋊C4C22×C418yes—
301C3×C22⋊C4C22×C4116yes—
302C3×C22⋊C4C22×C4116yes—
303C3×C42C22×C418yes—
304#217—24no—
305#217—28no—
306#217—24no—
307#217—42no—
308#217—42no—
309#217—44no—
310#217—44no—
311#217—44no—
312#217—44no—
313#217—44no—
314#217—44no—
315#217—42no—
316#217—44no—
317#217—42no—
318C4⋊Dic3—24no—
319C4⋊Dic3—24no—
320C4⋊Dic3—42no—
321C4⋊Dic3—41no—
322C4⋊Dic3—41no—
323C4⋊Dic3—44no—
324C4⋊Dic3—44no—
325C4×Dic3—24no—
326C4×Dic3—24no—
327C4×Dic3—28no—
328C4×Dic3—41no—
329C4×Dic3—41no—
330C4×Dic3—44no—
331C4×Dic3—42no—
332C25C22×D312yes—
333C2×#41—42no—
334C2×#41—42no—
335C2×#41C2×Dic318yescomplemented
336C22×Q8C22×D311yescharacteristic
337C22×D4—42no—
338C22×D4—42no—
339C22×D4C2×Dic318yescomplemented
340C22×D4C22×D312yes—
341C22×D4C22×D314yes—
342C22×D4C22×D314yes—
343C22×D4C22×D311yescharacteristic
344C22×D4C22×D311yescharacteristic
345C22×D4C22×D312yes—
346C22×D4C22×D311yescharacteristic
347C23×C4—34no—
348C23×C4—32no—
349C23×C4—34no—
350C23×C4—32no—
351C23×C4C22×D311yescharacteristic
352C23×C4C22×D311yescharacteristic
353C23×C4C22×D311yescharacteristic
354#127C2×Dic3116yescomplemented
355#124C2×Dic3116yescomplemented
356#121C2×Dic3116yescomplemented
357#121C2×Dic3116yescomplemented
358#120C2×Dic3116yescomplemented
359#120C2×Dic3116yescomplemented
360C4×D4—128no—
361C4×D4—124no—
362C4×D4—124no—
363C4×D4—128no—
364#117—122no—
365#117—122no—
366#117C2×Dic318yescomplemented
367C2×C4⋊C4—32no—
368C2×C4⋊C4—32no—
369C2×C4⋊C4—32no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—34no—
373C2×C4⋊C4—34no—
374C2×C4⋊C4—122no—
375C2×C4⋊C4C22×D312yes—
376C2×C22⋊C4—32no—
377C2×C22⋊C4—34no—
378C2×C22⋊C4—32no—
379C2×C22⋊C4—34no—
380C2×C22⋊C4—34no—
381C2×C22⋊C4—32no—
382C2×C22⋊C4—32no—
383C2×C22⋊C4—34no—
384C2×C22⋊C4—34no—
385C2×C22⋊C4—34no—
386C2×C22⋊C4—34no—
387C2×C22⋊C4—32no—
388C2×C22⋊C4—34no—
389C2×C22⋊C4—32no—
390C2×C22⋊C4—128no—
391C2×C22⋊C4C22×D312yes—
392C2×C22⋊C4C22×D314yes—
393C2×C22⋊C4C22×D314yes—
394C2×C42—32no—
395C2×C42—34no—
396C2×C42—32no—
397C2×C42—32no—
398C2×C42—34no—
399C2×C42—31no—
400C2×C42—31no—
401C2×C42—122no—
402C2×C42C22×D312yes—
403#95—32no—
404#95—34no—
405#95—34no—
406#95—34no—
407#95—32no—
408#95—34no—
409#95—32no—
410#95—32no—
411#95—34no—
412#95—34no—
413C23×C3—22no—
414C23×C3—24no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—24no—
420C23×C3—24no—
421C23×C3—24no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—22no—
427C23×C3—24no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—24no—
431C23×C3—48no—
432C23×C3—416no—
433C23×C3—88no—
434C23×C3—84no—
435C23×C3—84no—
436C23×C3C23×C412yes—
437C23×C3C23×C418yes—
438C23×C3C23×C412yes—
439C23×C3C23×C412yes—
440C23×C3C2511yescharacteristic
441C3×Q8—44no—
442C3×D4—216no—
443C3×D4—48no—
444C3×D4—416no—
445C3×D4—416no—
446C3×D4—44no—
447C3×D4—44no—
448C3×D4—44no—
449C2×C3×C4—24no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—24no—
457C2×C3×C4—28no—
458C2×C3×C4—28no—
459C2×C3×C4—28no—
460C2×C3×C4C23×C412yes—
461C2×C3×C4C23×C418yes—
462C2×C3×C4C23×C412yes—
463C2×C3×C4C23×C412yes—
464C2×C3×C4C23×C412yes—
465C2×C3×C4H(5,𝔽2)12yes—
466C2×C3×C4H(5,𝔽2)12yes—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—24no—
473C2×Dic3—24no—
474C2×Dic3—24no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—24no—
478C2×Dic3—24no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—24no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—48no—
485C2×Dic3—88no—
486C2×Dic3—84no—
487C2×Dic3—88no—
488C2×Dic3H(5,𝔽2)14yes—
489C24—44no—
490C24—42no—
491C24—42no—
492C24—44no—
493C24C22×Dic318yes—
494C24C23×D311yescharacteristic
495C24C23×D314yes—
496C24C23×D311yescharacteristic
497C24C23×D311yescharacteristic
498#41—416no—
499C2×Q8—41no—
500C2×Q8—41no—
501C2×Q8C22×Dic314yes—
502C2×D4—24no—
503C2×D4—24no—
504C2×D4—416no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—41no—
510C2×D4—41no—
511C2×D4—41no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4C22×Dic318yes—
518C2×D4C22×Dic314yes—
519C2×D4C22×Dic314yes—
520C2×D4C22×Dic3116yes—
521C2×D4C22×Dic3116yes—
522C2×D4C22×Dic318yes—
523C2×D4C22×Dic314yes—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—32no—
531C22×C4—32no—
532C22×C4—32no—
533C22×C4—34no—
534C22×C4—32no—
535C22×C4—34no—
536C22×C4—64no—
537C22×C4—68no—
538C22×C4—122no—
539C22×C4—122no—
540C22×C4—124no—
541C22×C4—122no—
542C22×C4—124no—
543C22×C4—124no—
544C22×C4—124no—
545C22×C4—124no—
546C22×C4—124no—
547C22×C4C22×Dic314yes—
548C22×C4C22×Dic314yes—
549C22×C4C22×Dic314yes—
550C22×C4C23×D311yescharacteristic
551C22×C4C23×D314yes—
552C22×C4C23×D311yescharacteristic
553C22×C4C23×D311yescharacteristic
554C22×C4C23×D311yescharacteristic
555C4⋊C4—64no—
556C4⋊C4—64no—
557C4⋊C4—122no—
558C4⋊C4—121no—
559C4⋊C4—121no—
560C4⋊C4—124no—
561C4⋊C4—124no—
562C4⋊C4C22×Dic318yes—
563C22⋊C4—64no—
564C22⋊C4—68no—
565C22⋊C4—64no—
566C22⋊C4—124no—
567C22⋊C4—124no—
568C22⋊C4—122no—
569C22⋊C4—122no—
570C22⋊C4—124no—
571C22⋊C4—124no—
572C22⋊C4—124no—
573C22⋊C4—124no—
574C22⋊C4—122no—
575C22⋊C4—124no—
576C22⋊C4—122no—
577C22⋊C4C22×Dic318yes—
578C22⋊C4C22×Dic3116yes—
579C22⋊C4C22×Dic3116yes—
580C42—68no—
581C42—64no—
582C42—64no—
583C42—121no—
584C42—121no—
585C42—122no—
586C42—124no—
587C42C22×Dic318yes—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—28no—
592C22×C3—24no—
593C22×C3—24no—
594C22×C3—28no—
595C22×C3—28no—
596C22×C3—24no—
597C22×C3—42no—
598C22×C3—44no—
599C22×C3—42no—
600C22×C3—44no—
601C22×C3—42no—
602C22×C3—41no—
603C22×C3—44no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—41no—
608C22×C3—44no—
609C22×C3—41no—
610C22×C3—816no—
611C22×C3C24×C411yescharacteristic
612C22×C3C2×H(5,𝔽2)11yescharacteristic
613C22×C3C2×H(5,𝔽2)11yescharacteristic
614C22×C3C2×H(5,𝔽2)12yes—
615C22×C3#58512yes—
616C3×C4—22no—
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—28no—
620C3×C4#51814yes—
621Dic3—24no—
622Dic3—42no—
623Dic3—44no—
624Dic3—42no—
625Dic3—44no—
626Dic3—42no—
627C23—21no—
628C23—21no—
629C23—24no—
630C23—24no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—22no—
636C23—24no—
637C23—22no—
638C23—22no—
639C23—24no—
640C23—22no—
641C23—24no—
642C23—22no—
643C23—22no—
644C23—24no—
645C23—48no—
646C23—416no—
647C23—84no—
648C23—84no—
649C23—88no—
650C23C23×Dic312yes—
651C23C23×Dic318yes—
652C23C23×Dic312yes—
653C23C23×Dic312yes—
654C23C24×D311yescharacteristic
655Q8—44no—
656D4—216no—
657D4—48no—
658D4—44no—
659D4—44no—
660D4—44no—
661D4—416no—
662D4—416no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—28no—
672C2×C4—28no—
673C2×C4—28no—
674C2×C4—34no—
675C2×C4—62no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—64no—
681C2×C4—64no—
682C2×C4—64no—
683C2×C4—62no—
684C2×C4—64no—
685C2×C4—62no—
686C2×C4—64no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—64no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—128no—
693C2×C4—248no—
694C2×C4—244no—
695C2×C4—248no—
696C2×C4#100412yes—
697C2×C4#100412yes—
698C2×C4C23×Dic312yes—
699C2×C4C23×Dic318yes—
700C2×C4C23×Dic312yes—
701C2×C4C23×Dic312yes—
702C2×C4C23×Dic312yes—
703C2×C3—42no—
704C2×C3—42no—
705C2×C3—48no—
706C2×C3—42no—
707C2×C3C2×#51811yescharacteristic
708C2×C3C4×H(5,𝔽2)12yes—
709C2×C3#354212yes—
710C2×C3#354911yescharacteristic
711C2×C3#355111yescharacteristic
712C22—22no—
713C22—22no—
714C22—22no—
715C22—28no—
716C22—24no—
717C22—24no—
718C22—28no—
719C22—28no—
720C22—24no—
721C22—41no—
722C22—44no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—44no—
727C22—41no—
728C22—41no—
729C22—42no—
730C22—44no—
731C22—42no—
732C22—44no—
733C22—42no—
734C22—816no—
735C22C2×#100411yescharacteristic
736C22C2×#100411yescharacteristic
737C22D3×H(5,𝔽2)12yes—
738C22#596612yes—
739C22C24×Dic311yescharacteristic
740C4—22no—
741C4—22no—
742C4—22no—
743C4—28no—
744C4—64no—
745C4—122no—
746C4—124no—
747C4—122no—
748C4—122no—
749C4—124no—
750C4#579814yes—
751C3#3441511yescharacteristic, complemented, Sylow
752C2—42no—
753C2—48no—
754C2—42no—
755C2—42no—
756C2#8632611yescharacteristic
757C2#8632711yescharacteristic
758C2#8633512yes—
759C2C2×#579811yescharacteristic
760C2Dic3×H(5,𝔽2)12yes—
subgroupG/H
center, FrattiniC23C24×D3
commutatorC22×C3C24×C4
Fitting, prime radicalC2×C3×#535C2
socle, cosocleC23×C3C25
hypercenterC2×#535D3
hypocenterC3#34415
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
2. #84087C2semidirect
3. #84086C2semidirect
4. D4×#217C2semidirect
5. #83172C2semidirect
6. #82957C2semidirect
7. #82956C2semidirect
8. #82637C2semidirect
9. #82636C2semidirect
10. #82633C2semidirect
11. Dic3×#121C2semidirect
12. #82580C2semidirect
13. #82579C2semidirect
14. #82578C2semidirect
15. #82239C2semidirect
19. C3×#535C4semidirect
30. C2×D4×Dic3C22semidirect
31. C2×D4×Dic3C22semidirect
32. C2×#926C22semidirect
33. C2×#926C22semidirect
34. C22×C4⋊Dic3C22semidirect
35. C22×C4×Dic3C22semidirect
37. #5229C22semidirect
38. #5229C22semidirect
39. #5229C22semidirect
45. #5221C22semidirect
46. #5221C22semidirect
51. #5220C22semidirect
52. #5220C22semidirect
53. #5220C22semidirect
54. #5220C22semidirect
55. #5220C22semidirect
56. #5220C22semidirect
58. #5212C22semidirect
60. C4×#217C22semidirect
61. #4984C22semidirect
62. #4984C22semidirect
63. Dic3×C4⋊C4C22semidirect
64. Dic3×C4⋊C4C22semidirect
67. #4951C22semidirect
68. #4951C22semidirect
69. #4951C22semidirect
70. #4951C22semidirect
71. #4950C22semidirect
72. #4950C22semidirect
73. Dic3×C22⋊C4C22semidirect
74. Dic3×C22⋊C4C22semidirect
75. #4936C22semidirect
76. #4932C22semidirect
95. C2×C3×#41C2×C4semidirect
99. C22×C3×D4C2×C4semidirect
114. C3×#127C2×C4semidirect
115. C3×#124C2×C4semidirect
116. C3×#121C2×C4semidirect
117. C3×#121C2×C4semidirect
118. C3×#120C2×C4semidirect
119. C3×#120C2×C4semidirect
120. C3×#117C2×C4semidirect
175. #535Dic3semidirect
335. C2×#41C2×Dic3semidirect
339. C22×D4C2×Dic3semidirect
354. #127C2×Dic3semidirect
355. #124C2×Dic3semidirect
356. #121C2×Dic3semidirect
357. #121C2×Dic3semidirect
358. #120C2×Dic3semidirect
359. #120C2×Dic3semidirect
366. #117C2×Dic3semidirect
751. C3#34415semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5352
#840872
#840862
D4×#2172
#831722
#829572
#829562
#826372
#826362
#826332
Dic3×#1212
#825802
#825792
#825782
#822392
#344153