Finite Group Databasebeta

← #10718607

Subgroups — #10718607

Order 768.

2178 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#386C211yesmaximal, characteristic
2C2×#5220C211yesmaximal, characteristic
3C2×#5220C211yesmaximal, characteristic
4C2×C4×#217C211yesmaximal, characteristic, complemented
5C22×C3⋊#95C211yesmaximal, characteristic, complemented
6#71549C212yesmaximal, complemented
7#71545C212yesmaximal, complemented
8#71544C211yesmaximal, characteristic, complemented
9#71544C211yesmaximal, characteristic, complemented
10#69418C212yesmaximal, complemented
11#69403C212yesmaximal, complemented
12#14020—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C24×Dic3C2211yescharacteristic
16C24×Dic3C2211yescharacteristic
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×#217C2212yes—
21C22×#217C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2212yes—
24C22×C4×Dic3C2212yes—
25C3×#386—24no—
26C2×C3×#95C2211yescharacteristic
27C2×C3×#95C2211yescharacteristic
28#5220—24no—
29#5220C418yescomplemented
30C4×#217—24no—
31C2×C3⋊#95—24no—
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×#386—31no—
42C2×#386—31no—
43C2×#386D311yescharacteristic
44C2×C4×C22⋊C4—31no—
45C22×#95—31no—
46#1443—32no—
47#1440—32no—
48#1437—32no—
49#1434—32no—
50C22⋊#95—31no—
51C22⋊#95—31no—
52C25×C3C2311yescharacteristic
53C25×C3C2311yescharacteristic
54C22×C3×D4—22no—
55C22×C3×D4—22no—
56C22×C3×D4—22no—
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4C2×C414yes—
61C23×C3×C4—22no—
62C23×C3×C4—22no—
63C23×C3×C4—24no—
64C23×C3×C4—42no—
65C23×C3×C4D414yes—
66C23×C3×C4C2311yescharacteristic
67C23×C3×C4C2311yescharacteristic
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×Dic3—22no—
72C23×Dic3—22no—
73C23×Dic3—22no—
74C23×Dic3—24no—
75C23×Dic3—22no—
76C23×Dic3—22no—
77C23×Dic3—42no—
78C23×Dic3—42no—
79C23×Dic3—42no—
80C23×Dic3C2×C414yes—
81C23×Dic3C2312yes—
82C23×Dic3C2312yes—
83C23×Dic3C2312yes—
84C23×Dic3C2312yes—
85C2×C3×C22⋊C4—22no—
86C2×C3×C22⋊C4—22no—
87C2×C3×C22⋊C4—22no—
88C2×C3×C22⋊C4—22no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—42no—
92C2×#217—22no—
93C2×#217—22no—
94C2×#217—22no—
95C2×#217—22no—
96C2×#217—24no—
97C2×#217—24no—
98C2×#217—42no—
99C2×#217—42no—
100C2×#217—42no—
101C2×#217C2×C414yes—
102C2×#217C2×C418yescomplemented
103C2×#217D414yes—
104C2×C4×Dic3—24no—
105C2×C4×Dic3—24no—
106C2×C4×Dic3—42no—
107C3×#95—22no—
108C3×#95—22no—
109C3⋊#95—24no—
110C3⋊#95—24no—
111C3⋊#95—24no—
112C3⋊#95—24no—
113C3⋊#95—24no—
114C3⋊#95—42no—
115C3⋊#95—42no—
116C3⋊#95—42no—
117C3⋊#95C2×C418yescomplemented
118C23×D4C2×D311yescharacteristic
119C24×C4—31no—
120C24×C4—31no—
121C24×C4C2×D311yescharacteristic
122C22×C22⋊C4—31no—
123C22×C22⋊C4—31no—
124C22×C22⋊C4—32no—
125C22×C22⋊C4—32no—
126C22×C22⋊C4C2×D311yescharacteristic
127C22×C22⋊C4C2×D311yescharacteristic
128C22×C22⋊C4C2×D311yescharacteristic
129C22×C42—32no—
130#386—24no—
131#386—38no—
132#386—64no—
133C4×C22⋊C4—64no—
134C2×#95—32no—
135C2×#95—32no—
136C2×#95—32no—
137C2×#95—32no—
138C2×#95—32no—
139C2×#95—32no—
140C2×#95—32no—
141C2×#95—32no—
142C2×#95—32no—
143C2×#95—64no—
144C2×#95C2×D311yescharacteristic
145C2×#95C2×D311yescharacteristic
146C24×C3—22no—
147C24×C3—22no—
148C24×C3—22no—
149C24×C3—22no—
150C24×C3—21no—
151C24×C3—21no—
152C24×C3—22no—
153C24×C3—22no—
154C24×C3—21no—
155C24×C3—21no—
156C24×C3—21no—
157C24×C3—21no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3C22×C412yes—
161C24×C3C22×C412yes—
162C24×C3C2×D412yes—
163C24×C3C2×D412yes—
164C24×C3#4112yes—
165C24×C3#4112yes—
166C24×C3#4112yes—
167C24×C3#4112yes—
168C24×C3C2411yescharacteristic
169C2×C3×D4—28no—
170C2×C3×D4—28no—
171C2×C3×D4—28no—
172C2×C3×D4—44no—
173C2×C3×D4—44no—
174C2×C3×D4—44no—
175C2×C3×D4—44no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—22no—
179C22×C3×C4—28no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—22no—
190C22×C3×C4—28no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—44no—
202C22×C3×C4—48no—
203C22×C3×C4—48no—
204C22×C3×C4C22×C412yes—
205C22×C3×C4C2×D412yes—
206C22×C3×C4C2×D412yes—
207C22×C3×C4#4114yes—
208C22×Dic3—28no—
209C22×Dic3—28no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—22no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—48no—
235C22×Dic3—48no—
236C22×Dic3—48no—
237C22×Dic3—44no—
238C22×Dic3—44no—
239C22×Dic3—44no—
240C22×Dic3—48no—
241C22×Dic3—44no—
242C22×Dic3C22×C414yes—
243C22×Dic3C22×C414yes—
244C22×Dic3C2×D414yes—
245C22×Dic3#4114yes—
246C3×C22⋊C4—44no—
247C3×C22⋊C4—44no—
248C3×C22⋊C4—44no—
249#217—28no—
250#217—28no—
251#217—48no—
252#217—48no—
253C4×Dic3—48no—
254C25C22×D311yescharacteristic
255C25C22×D311yescharacteristic
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4C4×D314yes—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—24no—
266C23×C4—32no—
267C23×C4—32no—
268C23×C4—32no—
269C23×C4—32no—
270C23×C4—34no—
271C23×C4—42no—
272C23×C4—64no—
273C23×C4—62no—
274C23×C4—62no—
275C23×C4—62no—
276C23×C4—62no—
277C23×C4—62no—
278C23×C4—122no—
279C23×C4—122no—
280C23×C4—122no—
281C23×C4#6714yes—
282C23×C4C22×D311yescharacteristic
283C23×C4C22×D311yescharacteristic
284C23×C4C22×D311yescharacteristic
285C23×C4C22×D311yescharacteristic
286C23×C4C22×D311yescharacteristic
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—34no—
294C2×C22⋊C4—34no—
295C2×C22⋊C4—38no—
296C2×C22⋊C4—42no—
297C2×C22⋊C4—62no—
298C2×C22⋊C4—62no—
299C2×C22⋊C4—62no—
300C2×C22⋊C4—62no—
301C2×C22⋊C4—64no—
302C2×C22⋊C4—64no—
303C2×C22⋊C4—122no—
304C2×C22⋊C4—122no—
305C2×C22⋊C4—122no—
306C2×C42—64no—
307C2×C42—64no—
308C2×C42—122no—
309#95—22no—
310#95—22no—
311#95—38no—
312#95—64no—
313#95—64no—
314#95—64no—
315#95—64no—
316#95—64no—
317#95—122no—
318#95—122no—
319#95—122no—
320C23×C3—24no—
321C23×C3—24no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—24no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—24no—
328C23×C3—24no—
329C23×C3—24no—
330C23×C3—24no—
331C23×C3—24no—
332C23×C3—24no—
333C23×C3—24no—
334C23×C3—24no—
335C23×C3—24no—
336C23×C3—22no—
337C23×C3—22no—
338C23×C3—22no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—41no—
342C23×C3—41no—
343C23×C3—41no—
344C23×C3—41no—
345C23×C3—41no—
346C23×C3—41no—
347C23×C3—42no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3#11714yes—
360C23×C3C4×D414yes—
361C23×C3C4×D414yes—
362C23×C3#12114yes—
363C23×C3#12314yes—
364C23×C3#12414yes—
365C23×C3#12614yes—
366C23×C3C23×C411yescharacteristic
367C23×C3C22×D411yescharacteristic
368C23×C3C22×D411yescharacteristic
369C23×C3C2×#4111yescharacteristic
370C23×C3C2×#4111yescharacteristic
371C23×C3C2×#4111yescharacteristic
372C23×C3C2×#4111yescharacteristic
373C23×C3C2×#4112yes—
374C23×C3C2×#4112yes—
375C23×C3H(5,𝔽2)12yes—
376C23×C3H(5,𝔽2)12yes—
377C3×D4—416no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—24no—
381C2×C3×C4—24no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—416no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4#12314yes—
406C2×Dic3—24no—
407C2×Dic3—24no—
408C2×Dic3—24no—
409C2×Dic3—24no—
410C2×Dic3—24no—
411C2×Dic3—24no—
412C2×Dic3—24no—
413C2×Dic3—24no—
414C2×Dic3—24no—
415C2×Dic3—24no—
416C2×Dic3—24no—
417C2×Dic3—24no—
418C2×Dic3—416no—
419C2×Dic3—416no—
420C2×Dic3—42no—
421C2×Dic3—42no—
422C2×Dic3—42no—
423C2×Dic3—42no—
424C2×Dic3—42no—
425C2×Dic3—42no—
426C2×Dic3—42no—
427C2×Dic3—42no—
428C2×Dic3—42no—
429C2×Dic3—42no—
430C2×Dic3—42no—
431C2×Dic3—42no—
432C2×Dic3—42no—
433C2×Dic3—42no—
434C2×Dic3—42no—
435C2×Dic3—42no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—21no—
441C24—21no—
442C24—22no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—21no—
450C24C2×C4×D312yes—
451C24C2×C4×D312yes—
452C24#23512yes—
453C24D3×D412yes—
454C24#23712yes—
455C24#23712yes—
456C24#23712yes—
457C24C2×#6712yes—
458C24C23×D311yescharacteristic
459C2×D4—28no—
460C2×D4—28no—
461C2×D4—28no—
462C2×D4—44no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—44no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—28no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—28no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—34no—
492C22×C4—34no—
493C22×C4—34no—
494C22×C4—34no—
495C22×C4—44no—
496C22×C4—48no—
497C22×C4—48no—
498C22×C4—68no—
499C22×C4—68no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—62no—
503C22×C4—62no—
504C22×C4—62no—
505C22×C4—62no—
506C22×C4—62no—
507C22×C4—62no—
508C22×C4—62no—
509C22×C4—62no—
510C22×C4—62no—
511C22×C4—62no—
512C22×C4—62no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4—62no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—128no—
525C22×C4—128no—
526C22×C4—128no—
527C22×C4—124no—
528C22×C4—128no—
529C22×C4—124no—
530C22×C4—124no—
531C22×C4—124no—
532C22×C4C2×C4×D312yes—
533C22×C4#23714yes—
534C22×C4C2×#6712yes—
535C22×C4C2×#6712yes—
536C22⋊C4—44no—
537C22⋊C4—44no—
538C22⋊C4—44no—
539C22⋊C4—68no—
540C22⋊C4—68no—
541C22⋊C4—128no—
542C22⋊C4—128no—
543C42—128no—
544C22×C3—24no—
545C22×C3—24no—
546C22×C3—28no—
547C22×C3—28no—
548C22×C3—24no—
549C22×C3—24no—
550C22×C3—28no—
551C22×C3—24no—
552C22×C3—28no—
553C22×C3—24no—
554C22×C3—42no—
555C22×C3—44no—
556C22×C3—44no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—81no—
560C22×C3—81no—
561C22×C3—81no—
562C22×C3—82no—
563C22×C3—81no—
564C22×C3—82no—
565C22×C3#38818yes—
566C22×C3C2×#11711yescharacteristic
567C22×C3C2×C4×D411yescharacteristic
568C22×C3C2×C4×D411yescharacteristic
569C22×C3C4×#4112yes—
570C22×C3#51812yes—
571C22×C3C2×#12111yescharacteristic
572C22×C3C2×#12311yescharacteristic
573C22×C3C2×#12311yescharacteristic
574C22×C3#52511yescharacteristic
575C22×C3C2×#12411yescharacteristic
576C22×C3C2×#12611yescharacteristic
577C22×C3#52912yes—
578C22×C3#53411yescharacteristic
579C22×C3#53511yescharacteristic
580C22×C3#53812yes—
581C22×C3#54612yes—
582C22×C3#54612yes—
583C22×C3#55112yes—
584C22×C3#55112yes—
585C22×C3#55312yes—
586C22×C3#55312yes—
587C22×C3#55312yes—
588C22×C3#55312yes—
589C3×C4—24no—
590C3×C4—42no—
591C3×C4—42no—
592C3×C4—81no—
593C3×C4—81no—
594Dic3—44no—
595Dic3—44no—
596Dic3—44no—
597Dic3—44no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—22no—
603C23—24no—
604C23—22no—
605C23—24no—
606C23—22no—
607C23—22no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—24no—
619C23—42no—
620C23—42no—
621C23—41no—
622C23—41no—
623C23—42no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—42no—
629C23—41no—
630C23—41no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23#87714yes—
638C23#87914yes—
639C23#67⋊C414yes—
640C23#88314yes—
641C23C4×#6714yes—
642C23#93614yes—
643C23#93914yes—
644C23C22×C4×D311yescharacteristic
645C23C2×#23511yescharacteristic
646C23C2×D3×D411yescharacteristic
647C23C2×#23711yescharacteristic
648C23C2×#23711yescharacteristic
649C23C2×#23711yescharacteristic
650C23C2×#23712yes—
651C23#100412yes—
652C23D3×#4112yes—
653C23#100912yes—
654C23C22×#6711yescharacteristic
655D4—416no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—416no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—64no—
684C2×C4—64no—
685C2×C4—64no—
686C2×C4—64no—
687C2×C4—64no—
688C2×C4—64no—
689C2×C4—64no—
690C2×C4—64no—
691C2×C4—64no—
692C2×C4—64no—
693C2×C4—64no—
694C2×C4—64no—
695C2×C4—1216no—
696C2×C4—1216no—
697C2×C4—122no—
698C2×C4—122no—
699C2×C4—122no—
700C2×C4—122no—
701C2×C4—122no—
702C2×C4—122no—
703C2×C4—122no—
704C2×C4—122no—
705C2×C4—122no—
706C2×C4—122no—
707C2×C4—122no—
708C2×C4—122no—
709C2×C4—122no—
710C2×C4—122no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4#93514yes—
714C2×C3—28no—
715C2×C3—82no—
716C2×C3C2×#38811yescharacteristic
717C2×C3C4×#12311yescharacteristic
718C2×C3#232111yescharacteristic
719C2×C3#235312yes—
720C2×C3#236412yes—
721C2×C3#241111yescharacteristic
722C2×C3#241211yescharacteristic
723C2×C3#244412yes—
724C2×C3#250411yescharacteristic
725C2×C3#251012yes—
726C2×C3#259111yescharacteristic
727C22—24no—
728C22—24no—
729C22—28no—
730C22—28no—
731C22—24no—
732C22—28no—
733C22—24no—
734C22—24no—
735C22—24no—
736C22—28no—
737C22—42no—
738C22—42no—
739C22—44no—
740C22—44no—
741C22—42no—
742C22—81no—
743C22—81no—
744C22—82no—
745C22—81no—
746C22—81no—
747C22—82no—
748C22#494518yes—
749C22C2×#87711yescharacteristic
750C22C2×#87911yescharacteristic
751C22C2×#67⋊C411yescharacteristic
752C22C2×#88311yescharacteristic
753C22C4×#23712yes—
754C22#553812yes—
755C22#554512yes—
756C22#556012yes—
757C22#558712yes—
758C22#559112yes—
759C22#560112yes—
760C22#560112yes—
761C22#561812yes—
762C22#561812yes—
763C22#565412yes—
764C22#565812yes—
765C22C2×C4×#6711yescharacteristic
766C22C2×#93511yescharacteristic
767C22C2×#93611yescharacteristic
768C22C2×#93911yescharacteristic
769C22#580411yescharacteristic
770C22#582811yescharacteristic
771C22#583011yescharacteristic
772C4—24no—
773C4—42no—
774C4—42no—
775C4—81no—
776C4—81no—
777C4—124no—
778C4—124no—
779C4—124no—
780C4—124no—
781C3#1402011yescharacteristic, complemented, Sylow
782C2—28no—
783C2—82no—
784C2#7467412yes—
785C2#7467812yes—
786C2#7470512yes—
787C2#7474412yes—
788C2C2×#494511yescharacteristic
789C2C4×#93511yescharacteristic
790C2#8239511yescharacteristic
791C2#8258411yescharacteristic
792C2#8266511yescharacteristic
793C2#8267411yescharacteristic
794C2#8289411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#386C2
socle, cosocleC24×C3C24
prime radicalC23×C3×D4C22
hypercenterC2×#386D3
hypocenterC3#14020
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
4. C2×C4×#217C2semidirect
5. C22×C3⋊#95C2semidirect
6. #71549C2semidirect
7. #71545C2semidirect
8. #71544C2semidirect
9. #71544C2semidirect
10. #69418C2semidirect
11. #69403C2semidirect
29. #5220C4semidirect
102. C2×#217C2×C4semidirect
117. C3⋊#95C2×C4semidirect
781. C3#14020semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3862
C2×#52202
C2×C4×#2172
C22×C3⋊#952
#715492
#715452
#715442
#694182
#694032
#140203