Finite Group Databasebeta

← #10826955

Subgroups — #10826955

Order 768.

1928 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#525C211yesmaximal, characteristic
2C22×#924C211yesmaximal, characteristic, complemented
3C2×#5239C212yesmaximal, complemented
4C2×#5050C211yesmaximal, characteristic, complemented
5C2×#5040C211yesmaximal, characteristic, complemented
6#72126C211yesmaximal, characteristic, complemented
7#71700C212yesmaximal, complemented
8#71692C211yesmaximal, characteristic, complemented
9#71685C212yesmaximal, complemented
10#71677C211yesmaximal, characteristic, complemented
11#71585C212yesmaximal, complemented
12#23922—31nomaximal, Sylow
13C22×C3×#41C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C23×Dic6C2211yescharacteristic
16C3×#525—24no—
17C3×#525—24no—
18C2×C3×#123—21no—
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic
23C2×C3×#120—21no—
24C2×C3×C4×D4—21no—
25C2×C3×C4×D4—21no—
26C2×C3×#117C2211yescharacteristic
27C22×#217—21no—
28C22×#216C2212yescomplemented
29C22×#214C2212yescomplemented
30C22×C4⋊Dic3C2211yescharacteristic
31C2×#924—21no—
32C2×#924—21no—
33C2×#924—28no—
34C2×#924C2212yes—
35C2×#924C2212yes—
36C22×Dic3⋊C4—21no—
37#5239—28no—
38C2×#835C2212yescomplemented
39C2×#832C2212yescomplemented
40C2×#830C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#830C2212yes—
43C2×#830C2212yes—
44#5050—24no—
45#5040—24no—
46C2×#810C2212yescomplemented
47C2×#810C2212yescomplemented
48#4529C2212yescomplemented
49#4529C2212yescomplemented
50C2×#525D311yescharacteristic
51C22×C22⋊Q8—31no—
52C2×#452—32no—
53C2×#451—31no—
54C2×#448—31no—
55#2001—32no—
56#2000—32no—
57#1874—31no—
58#1873—32no—
59#1872—31no—
60#1779—31no—
61C25×C3D411yescharacteristic
62C2×C3×#41—22no—
63C2×C3×#41—22no—
64C2×C3×#41—24no—
65C2×C3×#41—42no—
66C22×C3×Q8C2311yescharacteristic
67C22×C3×D4—21no—
68C22×C3×D4—21no—
69C22×C3×D4—21no—
70C22×C3×D4C2311yescharacteristic
71C23×C3×C4—24no—
72C23×C3×C4—22no—
73C23×C3×C4—22no—
74C23×C3×C4—21no—
75C23×C3×C4—42no—
76C23×C3×C4D411yescharacteristic
77C23×C3×C4D411yescharacteristic
78C23×C3×C4D411yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×Dic3—21no—
83C23×Dic3—21no—
84C22×Dic6—21no—
85C22×Dic6—24no—
86C22×Dic6—22no—
87C22×Dic6—22no—
88C22×Dic6—42no—
89C22×Dic6C2312yes—
90C3×#123—28no—
91C3×C22⋊Q8—22no—
92C3×C22⋊Q8—22no—
93C3×C22⋊Q8—22no—
94C3×C22⋊Q8D414yes—
95C3×#121—22no—
96C3×#121—22no—
97C3×#121—22no—
98C3×#121D414yes—
99C3×#120—28no—
100C3×C4×D4—28no—
101C3×C4×D4—28no—
102C3×#117—22no—
103C3×#117—22no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C42—21no—
114C2×#217—28no—
115C2×#217—22no—
116C2×#217—22no—
117C2×#216—24no—
118C2×#216—24no—
119C2×#216—42no—
120C2×#214—24no—
121C2×#214—24no—
122C2×#214—42no—
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3—24no—
125C2×C4⋊Dic3C2312yes—
126#924—28no—
127#924—28no—
128#924—24no—
129#924—24no—
130#924—24no—
131#924D418yescomplemented
132C2×Dic3⋊C4—28no—
133C2×Dic3⋊C4—22no—
134C2×Dic3⋊C4—22no—
135C22×C3⋊C8C2312yes—
136C22×C3⋊C8C2312yes—
137#835—24no—
138#832—24no—
139#830—24no—
140#830—22no—
141#830—22no—
142#830—42no—
143#810—24no—
144#810—24no—
145C22×#41C2×D311yescharacteristic
146C23×Q8—31no—
147C24×C4C2×D311yescharacteristic
148C22×Q16—32no—
149C22×SD16—32no—
150#525—24no—
151#525—24no—
152C2×#123—21no—
153C2×C22⋊Q8—32no—
154C2×C22⋊Q8—32no—
155C2×C22⋊Q8—68no—
156C2×C22⋊Q8—61no—
157C2×C22⋊Q8—61no—
158C2×C22⋊Q8C2×D311yescharacteristic
159C2×C22⋊Q8C2×D311yescharacteristic
160C2×#121C2×D311yescharacteristic
161C2×#121C2×D311yescharacteristic
162C2×#120—21no—
163C2×C4×D4—21no—
164C2×C4×D4—21no—
165C2×#117C2×D311yescharacteristic
166C22×C4⋊C4—31no—
167C22×C4⋊C4—61no—
168C22×C22⋊C4—61no—
169#452—68no—
170#451—64no—
171#448—64no—
172C2×#103—32no—
173C2×#103—32no—
174C2×#103—32no—
175C2×#102—32no—
176C2×C22⋊C8—31no—
177C2×C22⋊C8—32no—
178C2×C22⋊C8—31no—
179C2×C22⋊C8—32no—
180#340—32no—
181#340—32no—
182C24×C3—22no—
183C24×C3—22no—
184C24×C3—22no—
185C24×C3—22no—
186C24×C3—22no—
187C24×C3—21no—
188C24×C3—41no—
189C24×C3—41no—
190C24×C3C2×D411yescharacteristic
191C24×C3C2×D411yescharacteristic
192C24×C3C2×D411yescharacteristic
193C3×#41—48no—
194C3×#41—48no—
195C2×C3×Q8—21no—
196C2×C3×Q8—22no—
197C2×C3×Q8—22no—
198C2×C3×Q8C2×D412yes—
199C2×C3×D4—24no—
200C2×C3×D4—24no—
201C2×C3×D4—24no—
202C2×C3×D4—22no—
203C2×C3×D4—21no—
204C2×C3×D4—22no—
205C2×C3×D4—42no—
206C2×C3×D4—42no—
207C2×C3×D4—42no—
208C2×C3×D4—42no—
209C2×C3×D4—42no—
210C2×C3×D4—42no—
211C2×C3×D4C2×D412yes—
212C22×C3×C4—22no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—24no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—22no—
231C22×C3×C4—41no—
232C22×C3×C4—41no—
233C22×C3×C4—41no—
234C22×C3×C4—48no—
235C22×C3×C4—48no—
236C22×C3×C4—42no—
237C22×C3×C4—42no—
238C22×C3×C4C2×D414yes—
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D412yes—
243C22×C3×C4C2×D412yes—
244C22×C3×C4C2411yescharacteristic
245C22×Dic3—24no—
246C22×Dic3—24no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—42no—
250C22×Dic3—42no—
251C22×Dic3—42no—
252C22×Dic3—42no—
253C2×Dic6—22no—
254C2×Dic6—22no—
255C2×Dic6—22no—
256C2×Dic6—22no—
257C2×Dic6—24no—
258C2×Dic6—22no—
259C2×Dic6—48no—
260C2×Dic6—48no—
261C2×Dic6—42no—
262C2×Dic6—42no—
263C2×Dic6C2×D414yes—
264C3×C4⋊C4—24no—
265C3×C4⋊C4—24no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4C2×D412yes—
269C3×C4⋊C4C2×D412yes—
270C3×C22⋊C4—24no—
271C3×C22⋊C4—24no—
272C3×C22⋊C4—24no—
273C3×C22⋊C4—24no—
274C3×C22⋊C4—24no—
275C3×C42—24no—
276#217—28no—
277#217—28no—
278#216—48no—
279#214—48no—
280C4⋊Dic3—24no—
281C4⋊Dic3—22no—
282C4⋊Dic3C2×D414yes—
283Dic3⋊C4—28no—
284Dic3⋊C4—28no—
285C2×C3⋊C8—22no—
286C2×C3⋊C8—22no—
287C2×C3⋊C8—22no—
288C2×C3⋊C8—22no—
289C2×C3⋊C8—22no—
290C2×C3⋊C8—22no—
291C25#6711yescharacteristic
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—24no—
295C2×#41—42no—
296C22×Q8—32no—
297C22×Q8—64no—
298C22×Q8—61no—
299C22×Q8—62no—
300C22×Q8—62no—
301C22×Q8—122no—
302C22×Q8C22×D311yescharacteristic
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4C22×D311yescharacteristic
307C23×C4—24no—
308C23×C4—21no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—42no—
312C23×C4—61no—
313C23×C4—61no—
314C23×C4#6711yescharacteristic
315C23×C4#6711yescharacteristic
316C23×C4#6711yescharacteristic
317C23×C4C22×D311yescharacteristic
318C23×C4C22×D311yescharacteristic
319C23×C4C22×D311yescharacteristic
320C2×Q16—64no—
321C2×Q16—64no—
322C2×Q16—122no—
323C2×SD16—64no—
324C2×SD16—64no—
325C2×SD16—122no—
326C22×C8—32no—
327C22×C8—32no—
328#123—28no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—38no—
333C22⋊Q8—64no—
334C22⋊Q8—64no—
335C22⋊Q8—68no—
336C22⋊Q8—68no—
337C22⋊Q8—64no—
338C22⋊Q8#6714yes—
339#121—22no—
340#121—22no—
341#121—22no—
342#121#6714yes—
343#120—28no—
344C4×D4—28no—
345C4×D4—28no—
346#117—22no—
347#117—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—32no—
351C2×C4⋊C4—64no—
352C2×C4⋊C4—68no—
353C2×C4⋊C4—61no—
354C2×C4⋊C4—62no—
355C2×C4⋊C4—62no—
356C2×C4⋊C4C22×D311yescharacteristic
357C2×C4⋊C4C22×D311yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—68no—
364C2×C22⋊C4—62no—
365C2×C22⋊C4—62no—
366C2×C42—21no—
367#103—64no—
368#103—64no—
369#103—64no—
370#102—64no—
371C22⋊C8—64no—
372C22⋊C8—62no—
373C22⋊C8—62no—
374C22⋊C8—122no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—28no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—22no—
393C23×C3—44no—
394C23×C3—44no—
395C23×C3—44no—
396C23×C3—44no—
397C23×C3—44no—
398C23×C3—44no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3#12012yes—
406C23×C3#12012yes—
407C23×C3#13512yes—
408C23×C3#13712yes—
409C23×C3#13712yes—
410C23×C3C22×D411yescharacteristic
411C3×Q8—24no—
412C3×Q8—42no—
413C3×D4—24no—
414C3×D4—48no—
415C3×D4—48no—
416C3×D4—48no—
417C3×D4—42no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
425C2×C3×C4—24no—
426C2×C3×C4—21no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—21no—
430C2×C3×C4—22no—
431C2×C3×C4—21no—
432C2×C3×C4—44no—
433C2×C3×C4—44no—
434C2×C3×C4—44no—
435C2×C3×C4—48no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—42no—
443C2×C3×C4—42no—
444C2×C3×C4#12012yes—
445C2×C3×C4#12012yes—
446C2×C3×C4C22×D412yes—
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4H(5,𝔽2)12yes—
450C2×Dic3—24no—
451C2×Dic3—24no—
452C2×Dic3—48no—
453C2×Dic3—48no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456C2×Dic3—42no—
457C2×Dic3—42no—
458Dic6—24no—
459Dic6—24no—
460Dic6—48no—
461Dic6—42no—
462Dic6—42no—
463C3⋊C8—42no—
464C3⋊C8—42no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—21no—
471C24—41no—
472C24—41no—
473C24C2×#6711yescharacteristic
474C24C2×#6711yescharacteristic
475C24C2×#6711yescharacteristic
476#41—48no—
477#41—48no—
478C2×Q8—21no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—34no—
482C2×Q8—64no—
483C2×Q8—62no—
484C2×Q8—62no—
485C2×Q8—62no—
486C2×Q8—62no—
487C2×Q8—62no—
488C2×Q8—128no—
489C2×Q8—128no—
490C2×Q8—122no—
491C2×Q8—122no—
492C2×Q8C2×#6712yes—
493C2×D4—24no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—21no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4C2×#6712yes—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—64no—
533C22×C4—64no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—122no—
537C22×C4—122no—
538C22×C4—122no—
539C22×C4—122no—
540C22×C4D3×D414yes—
541C22×C4C2×#6711yescharacteristic
542C22×C4C2×#6711yescharacteristic
543C22×C4C2×#6711yescharacteristic
544C22×C4C2×#6712yes—
545C22×C4C2×#6712yes—
546C22×C4C23×D311yescharacteristic
547Q16—128no—
548SD16—128no—
549C2×C8—62no—
550C2×C8—62no—
551C2×C8—62no—
552C2×C8—62no—
553C2×C8—62no—
554C2×C8—62no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—34no—
560C4⋊C4—68no—
561C4⋊C4—64no—
562C4⋊C4—68no—
563C4⋊C4—62no—
564C4⋊C4C2×#6712yes—
565C4⋊C4C2×#6712yes—
566C22⋊C4—24no—
567C22⋊C4—24no—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—24no—
571C22⋊C4—68no—
572C22⋊C4—68no—
573C42—24no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—416no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—81no—
599C22×C3—81no—
600C22×C3—81no—
601C22×C3—81no—
602C22×C3#45214yescomplemented
603C22×C3C2×#12011yescharacteristic
604C22×C3C2×#12011yescharacteristic
605C22×C3#53411yescharacteristic
606C22×C3C2×#13511yescharacteristic
607C22×C3C2×#13711yescharacteristic
608C22×C3C2×#13711yescharacteristic
609C22×C3#57511yescharacteristic
610C3×C4—22no—
611C3×C4—22no—
612C3×C4—41no—
613C3×C4—42no—
614C3×C4—42no—
615C3×C4—42no—
616C3×C4D4212yes—
617C3×C4D4212yes—
618Dic3—44no—
619Dic3—44no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—28no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23#93712yes—
651C23#95012yes—
652C23#95112yes—
653C23#95112yes—
654C23#95312yes—
655C23C22×#6711yescharacteristic
656Q8—24no—
657Q8—42no—
658Q8—64no—
659Q8—64no—
660Q8—128no—
661Q8—122no—
662Q8—122no—
663D4—24no—
664D4—48no—
665D4—48no—
666D4—48no—
667D4—42no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—48no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—64no—
695C2×C4—64no—
696C2×C4—128no—
697C2×C4—128no—
698C2×C4—122no—
699C2×C4—122no—
700C2×C4—122no—
701C2×C4—122no—
702C2×C4#93712yes—
703C2×C4#95312yes—
704C2×C4C2×D3×D412yes—
705C2×C4#100412yes—
706C2×C4C22×#6711yescharacteristic
707C2×C4C22×#6711yescharacteristic
708C8—122no—
709C8—122no—
710C2×C3—24no—
711C2×C3—42no—
712C2×C3—42no—
713C2×C3—82no—
714C2×C3#240311yescharacteristic
715C2×C3C2×#45211yescharacteristic
716C2×C3#300211yescharacteristic
717C2×C3#300411yescharacteristic
718C2×C3#300711yescharacteristic
719C2×C3#319011yescharacteristic
720C2×C3#319611yescharacteristic
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—416no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22#523914yescomplemented
750C22C2×#93711yescharacteristic
751C22#580411yescharacteristic
752C22C2×#95011yescharacteristic
753C22#582211yescharacteristic
754C22C2×#95111yescharacteristic
755C22C2×#95111yescharacteristic
756C22C2×#95311yescharacteristic
757C4—22no—
758C4—22no—
759C4—41no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—124no—
764C4—124no—
765C4D4×#6712yes—
766C4D4×#6712yes—
767C3#2392211yescharacteristic, complemented, Sylow
768C2—24no—
769C2—42no—
770C2—42no—
771C2—82no—
772C2#8292611yescharacteristic
773C2#8293311yescharacteristic
774C2#8293411yescharacteristic
775C2#8293511yescharacteristic
776C2#8405211yescharacteristic
777C2C2×#523911yescharacteristic
778C2#8408411yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC2×C3×#525C2
socleC23×C3C22×D4
hypercenterC2×#525D3
hypocenterC3#23922
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
2. C22×#924C2semidirect
3. C2×#5239C2semidirect
4. C2×#5050C2semidirect
5. C2×#5040C2semidirect
6. #72126C2semidirect
7. #71700C2semidirect
8. #71692C2semidirect
9. #71685C2semidirect
10. #71677C2semidirect
11. #71585C2semidirect
28. C22×#216C22semidirect
29. C22×#214C22semidirect
38. C2×#835C22semidirect
39. C2×#832C22semidirect
46. C2×#810C22semidirect
47. C2×#810C22semidirect
48. #4529C22semidirect
49. #4529C22semidirect
131. #924D4semidirect
602. C22×C3#452semidirect
749. C22#5239semidirect
767. C3#23922semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5252
C22×#9242
C2×#52392
C2×#50502
C2×#50402
#721262
#717002
#716922
#716852
#716772
#715852
#239223