Finite Group Databasebeta

← #10727111

Subgroups — #10727111

Order 768.

2414 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#946C211yesmaximal, characteristic, complemented
2C2×#5231C211yesmaximal, characteristic, complemented
3C2×#4665C211yesmaximal, characteristic
4C2×#4665C212yesmaximal
5C2×D3×#95C211yesmaximal, characteristic, complemented
6C3×#1446C211yesmaximal, characteristic, complemented
7#69428C212yesmaximal, complemented
8#69427C211yesmaximal, characteristic, complemented
9(C2×D3)⋊#95C212yesmaximal, complemented
10#69415C211yesmaximal, characteristic, complemented
11#69414C212yesmaximal, complemented
12#14759—31nomaximal, Sylow
13C23×C3×Q8C2211yescharacteristic
14C23×D12C2211yescharacteristic
15C23×C4×D3C2212yes—
16C23×C4×D3C2211yescharacteristic
17C2×#946—24no—
18C2×#946—28no—
19C22×(C2×D3)⋊C4C2211yescharacteristic
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26C22×Dic3⋊C4C2212yes—
27C2×C3×#95C2212yes—
28C2×C3×#95C2211yescharacteristic
29C2×C3×#95C2211yescharacteristic
30C2×C3×#95C2212yes—
31#5231—24no—
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39#4665—24no—
40#4665—28no—
41D3×#95—24no—
42C22×C22⋊Q8—31no—
43C2×#393—31no—
44C2×#386—32no—
45C2×#386—31no—
46C22×#95—31no—
47#1446D311yescharacteristic, complemented
48#1442—32no—
49#1442—31no—
50#1439—31no—
51#1439—32no—
52C22⋊#95—32no—
53C24×D3C2311yescharacteristic
54C24×D3C2311yescharacteristic
55C22×C3×Q8—24no—
56C22×C3×Q8—22no—
57C22×C3×Q8—22no—
58C22×C3×Q8—22no—
59C22×C3×Q8—42no—
60C23×C3×C4C2311yescharacteristic
61C23×C3×C4C2312yes—
62C23×C3×C4C2311yescharacteristic
63C23×C3×C4C2312yes—
64C23×C3×C4C2311yescharacteristic
65C23×Dic3C2311yescharacteristic
66C23×Dic3C2312yes—
67C23×Dic3C2311yescharacteristic
68C23×Dic3C2312yes—
69C22×D12—22no—
70C22×D12—24no—
71C22×D12—24no—
72C22×D12—22no—
73C22×D12Q814yescomplemented
74C22×C4×D3—24no—
75C22×C4×D3—24no—
76C22×C4×D3—22no—
77C22×C4×D3—22no—
78C22×C4×D3—24no—
79C22×C4×D3—24no—
80C22×C4×D3—24no—
81C22×C4×D3—24no—
82C22×C4×D3—42no—
83C22×C4×D3—42no—
84C22×C4×D3—42no—
85C22×C4×D3D414yes—
86#946—232no—
87C2×(C2×D3)⋊C4—24no—
88C2×(C2×D3)⋊C4—24no—
89C2×(C2×D3)⋊C4—22no—
90C2×(C2×D3)⋊C4—24no—
91C2×(C2×D3)⋊C4—24no—
92C2×(C2×D3)⋊C4—22no—
93C2×(C2×D3)⋊C4—22no—
94C2×(C2×D3)⋊C4—22no—
95C2×(C2×D3)⋊C4—24no—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—22no—
98C2×(C2×D3)⋊C4—24no—
99C2×(C2×D3)⋊C4—42no—
100C2×(C2×D3)⋊C4—42no—
101C2×(C2×D3)⋊C4—42no—
102C2×(C2×D3)⋊C4D418yes—
103C2×C4⋊Dic3—22no—
104C2×C4⋊Dic3—24no—
105C2×Dic3⋊C4—24no—
106C2×Dic3⋊C4—24no—
107C2×Dic3⋊C4—24no—
108C3×#95—22no—
109C3×#95—24no—
110C3×#95—22no—
111C3×#95—42no—
112C3⋊#95—24no—
113C3⋊#95—24no—
114C3⋊#95—24no—
115C3⋊#95—22no—
116C3⋊#95—24no—
117C3⋊#95—42no—
118C3⋊#95D414yescomplemented
119C23×Q8C2×D311yescharacteristic
120C23×D4—31no—
121C24×C4—31no—
122C24×C4—32no—
123C2×C22⋊Q8—68no—
124C2×C22⋊Q8—64no—
125C22×C4⋊C4—32no—
126C22×C4⋊C4—31no—
127C22×C22⋊C4—32no—
128C22×C22⋊C4—31no—
129C22×C22⋊C4—31no—
130C22×C22⋊C4—32no—
131C22×C22⋊C4—32no—
132C22×C22⋊C4—31no—
133#393—64no—
134#386—68no—
135#386—64no—
136C2×#95—31no—
137C2×#95—32no—
138C2×#95—32no—
139C2×#95—32no—
140C2×#95—32no—
141C2×#95—31no—
142C2×#95—32no—
143C2×#95—64no—
144C2×#95C2×D311yescharacteristic
145C2×#95C2×D311yescharacteristic
146C2×#95C2×D312yes—
147C2×#95C2×D312yes—
148C24×C3C2411yescharacteristic
149C23×D3—21no—
150C23×D3—21no—
151C23×D3—22no—
152C23×D3—22no—
153C23×D3—21no—
154C23×D3—21no—
155C23×D3—21no—
156C23×D3—21no—
157C23×D3—22no—
158C23×D3—21no—
159C23×D3—22no—
160C23×D3—22no—
161C23×D3—21no—
162C23×D3—22no—
163C23×D3—21no—
164C23×D3—21no—
165C23×D3C2×D412yes—
166C23×D3C2×D414yes—
167C23×D3C2×Q812yes—
168C23×D3C2×Q812yes—
169C23×D3#4114yes—
170C23×D3#4112yes—
171C2×C3×Q8—28no—
172C2×C3×Q8—48no—
173C2×C3×Q8—48no—
174C2×C3×Q8—44no—
175C2×C3×Q8—44no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—21no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C22×C3×C4—22no—
198C22×C3×C4—21no—
199C22×C3×C4C2×D414yes—
200C22×C3×C4C2×D412yes—
201C22×C3×C4C2×D412yes—
202C22×C3×C4C2×Q812yes—
203C22×C3×C4#4112yes—
204C22×C3×C4#4114yes—
205C22×Dic3—21no—
206C22×Dic3—22no—
207C22×Dic3—22no—
208C22×Dic3—22no—
209C22×Dic3—22no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—21no—
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—21no—
222C22×Dic3—21no—
223C22×Dic3—22no—
224C22×Dic3—21no—
225C22×Dic3—22no—
226C22×Dic3C2×D414yes—
227C22×Dic3C2×D412yes—
228C22×Dic3C2×D414yes—
229C2×D12—28no—
230C2×D12—216no—
231C2×D12—44no—
232C2×D12—44no—
233C2×D12—48no—
234C2×C4×D3—216no—
235C2×C4×D3—28no—
236C2×C4×D3—28no—
237C2×C4×D3—44no—
238C2×C4×D3—48no—
239C2×C4×D3—48no—
240C2×C4×D3—48no—
241C2×C4×D3—48no—
242C2×C4×D3—48no—
243C2×C4×D3—48no—
244C2×C4×D3—48no—
245C2×C4×D3—48no—
246(C2×D3)⋊C4—216no—
247(C2×D3)⋊C4—48no—
248(C2×D3)⋊C4—48no—
249(C2×D3)⋊C4—44no—
250(C2×D3)⋊C4—44no—
251(C2×D3)⋊C4—44no—
252C4⋊Dic3—28no—
253Dic3⋊C4—216no—
254C25—31no—
255C25—31no—
256C22×Q8—22no—
257C22×Q8—24no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—42no—
261C22×D4—34no—
262C22×D4—64no—
263C22×D4—62no—
264C22×D4—64no—
265C22×D4—62no—
266C23×C4—32no—
267C23×C4—31no—
268C23×C4—32no—
269C23×C4—34no—
270C23×C4—31no—
271C23×C4—64no—
272C23×C4—64no—
273C23×C4—64no—
274C23×C4—64no—
275C23×C4—64no—
276C23×C4—62no—
277C23×C4—62no—
278C23×C4—64no—
279C23×C4—122no—
280C23×C4—122no—
281C23×C4—122no—
282C23×C4C22×D311yescharacteristic
283C23×C4C22×D312yes—
284C23×C4C22×D311yescharacteristic
285C23×C4C22×D312yes—
286C23×C4C22×D311yescharacteristic
287C22⋊Q8—632no—
288C2×C4⋊C4—64no—
289C2×C4⋊C4—64no—
290C2×C4⋊C4—64no—
291C2×C4⋊C4—64no—
292C2×C4⋊C4—62no—
293C2×C22⋊C4—38no—
294C2×C22⋊C4—64no—
295C2×C22⋊C4—64no—
296C2×C22⋊C4—64no—
297C2×C22⋊C4—62no—
298C2×C22⋊C4—64no—
299C2×C22⋊C4—62no—
300C2×C22⋊C4—64no—
301C2×C22⋊C4—62no—
302C2×C22⋊C4—64no—
303C2×C22⋊C4—62no—
304C2×C22⋊C4—62no—
305C2×C22⋊C4—64no—
306C2×C22⋊C4—122no—
307C2×C22⋊C4—122no—
308C2×C22⋊C4—122no—
309#95—22no—
310#95—24no—
311#95—22no—
312#95—34no—
313#95—42no—
314#95—64no—
315#95—64no—
316#95—62no—
317#95—64no—
318#95—64no—
319#95—122no—
320C23×C3C22×D411yescharacteristic
321C23×C3C22×D412yes—
322C23×C3C22×D411yescharacteristic
323C23×C3C22×Q811yescharacteristic
324C23×C3C2×#4111yescharacteristic
325C23×C3C2×#4112yes—
326C23×C3C2×#4112yes—
327C23×C3C2×#4111yescharacteristic
328C23×C3H(5,𝔽2)12yes—
329C23×C3H(5,𝔽2)11yescharacteristic
330C23×C32−1+411yescharacteristic
331C22×D3—22no—
332C22×D3—24no—
333C22×D3—24no—
334C22×D3—22no—
335C22×D3—22no—
336C22×D3—22no—
337C22×D3—24no—
338C22×D3—24no—
339C22×D3—24no—
340C22×D3—22no—
341C22×D3—24no—
342C22×D3—24no—
343C22×D3—24no—
344C22×D3—22no—
345C22×D3—24no—
346C22×D3—22no—
347C22×D3—24no—
348C22×D3—22no—
349C22×D3—22no—
350C22×D3—24no—
351C22×D3—22no—
352C22×D3—24no—
353C22×D3—22no—
354C22×D3—41no—
355C22×D3—41no—
356C22×D3—42no—
357C22×D3—41no—
358C22×D3—42no—
359C22×D3—42no—
360C22×D3—41no—
361C22×D3—41no—
362C22×D3—41no—
363C22×D3—42no—
364C22×D3—42no—
365C22×D3—42no—
366C22×D3—42no—
367C22×D3—41no—
368C22×D3—42no—
369C22×D3—42no—
370C22×D3—42no—
371C22×D3—41no—
372C22×D3#12014yes—
373C22×D3C22⋊Q814yes—
374C22×D3C22⋊Q818yes—
375C22×D3#12414yes—
376C22×D3#12418yes—
377C3×Q8—416no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—24no—
381C2×C3×C4—24no—
382C2×C3×C4—24no—
383C2×C3×C4—22no—
384C2×C3×C4—24no—
385C2×C3×C4—24no—
386C2×C3×C4—24no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—24no—
390C2×C3×C4—41no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—41no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4#12114yes—
407C2×Dic3—22no—
408C2×Dic3—24no—
409C2×Dic3—22no—
410C2×Dic3—24no—
411C2×Dic3—22no—
412C2×Dic3—24no—
413C2×Dic3—24no—
414C2×Dic3—24no—
415C2×Dic3—24no—
416C2×Dic3—42no—
417C2×Dic3—42no—
418C2×Dic3—42no—
419C2×Dic3—42no—
420C2×Dic3—42no—
421C2×Dic3—42no—
422C2×Dic3—42no—
423C2×Dic3—42no—
424C2×Dic3—42no—
425C2×Dic3—42no—
426C2×Dic3—41no—
427C2×Dic3—42no—
428C2×Dic3—41no—
429C2×Dic3—42no—
430C2×Dic3—41no—
431D12—416no—
432C4×D3—416no—
433C4×D3—432no—
434C24—34no—
435C24—32no—
436C24—32no—
437C24—34no—
438C24—32no—
439C24—32no—
440C24—61no—
441C24—61no—
442C24—62no—
443C24—62no—
444C24—61no—
445C24—61no—
446C24—61no—
447C24—61no—
448C24—61no—
449C24—62no—
450C24—62no—
451C24—62no—
452C24—61no—
453C24—61no—
454C24—62no—
455C24—61no—
456C24C23×D311yescharacteristic
457C2×Q8—28no—
458C2×Q8—48no—
459C2×Q8—48no—
460C2×Q8—44no—
461C2×Q8—44no—
462C2×D4—68no—
463C2×D4—616no—
464C2×D4—124no—
465C2×D4—128no—
466C2×D4—124no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—34no—
491C22×C4—34no—
492C22×C4—32no—
493C22×C4—68no—
494C22×C4—616no—
495C22×C4—61no—
496C22×C4—61no—
497C22×C4—62no—
498C22×C4—62no—
499C22×C4—62no—
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—68no—
512C22×C4—61no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—62no—
516C22×C4—62no—
517C22×C4—124no—
518C22×C4—128no—
519C22×C4—128no—
520C22×C4—128no—
521C22×C4—128no—
522C22×C4—128no—
523C22×C4—128no—
524C22×C4—128no—
525C22×C4—128no—
526C22×C4#23512yes—
527C22×C4D3×D414yes—
528C22×C4D3×D412yes—
529C22×C4D3×D412yes—
530C22×C4D3×Q812yes—
531C22×C4#23914yes—
532C4⋊C4—616no—
533C4⋊C4—68no—
534C22⋊C4—616no—
535C22⋊C4—128no—
536C22⋊C4—128no—
537C22⋊C4—124no—
538C22⋊C4—124no—
539C22⋊C4—124no—
540C22×C3C2×#12011yescharacteristic
541C22×C3C2×#12111yescharacteristic
542C22×C3C2×C22⋊Q811yescharacteristic
543C22×C3C2×C22⋊Q812yes—
544C22×C3#52512yes—
545C22×C3C2×#12411yescharacteristic
546C22×C3C2×#12412yes—
547C22×C3#52912yes—
548C22×C3#53211yescharacteristic
549C22×C3#53411yescharacteristic
550C22×C3#53711yescharacteristic
551C22×C3#53812yes—
552C22×C3#53912yes—
553C22×C3D4212yes—
554C22×C3#54611yescharacteristic
555C22×C3#54612yes—
556C22×C3#54612yes—
557C22×C3#54712yes—
558C22×C3D4×Q811yescharacteristic
559C22×C3#55112yes—
560C22×C3#55211yescharacteristic
561C22×C3#55412yes—
562C22×C3#55411yescharacteristic
563C2×D3—24no—
564C2×D3—24no—
565C2×D3—24no—
566C2×D3—24no—
567C2×D3—24no—
568C2×D3—24no—
569C2×D3—28no—
570C2×D3—28no—
571C2×D3—28no—
572C2×D3—28no—
573C2×D3—42no—
574C2×D3—42no—
575C2×D3—42no—
576C2×D3—44no—
577C2×D3—44no—
578C2×D3—81no—
579C2×D3—81no—
580C2×D3—81no—
581C2×D3—81no—
582C2×D3—82no—
583C2×D3—82no—
584C2×D3#39318yescomplemented
585C3×C4—24no—
586C3×C4—42no—
587C3×C4—44no—
588C3×C4—44no—
589C3×C4—81no—
590Dic3—42no—
591Dic3—44no—
592Dic3—44no—
593Dic3—81no—
594C23—34no—
595C23—38no—
596C23—34no—
597C23—34no—
598C23—38no—
599C23—64no—
600C23—64no—
601C23—62no—
602C23—64no—
603C23—62no—
604C23—64no—
605C23—62no—
606C23—64no—
607C23—62no—
608C23—64no—
609C23—62no—
610C23—64no—
611C23—62no—
612C23—62no—
613C23—64no—
614C23—64no—
615C23—62no—
616C23—64no—
617C23—62no—
618C23—64no—
619C23—62no—
620C23—62no—
621C23—64no—
622C23—122no—
623C23—122no—
624C23—121no—
625C23—122no—
626C23—121no—
627C23—122no—
628C23—121no—
629C23—122no—
630C23—121no—
631C23—122no—
632C23—122no—
633C23—121no—
634C23—121no—
635C23—121no—
636C23—122no—
637C23—122no—
638C23—121no—
639C23—122no—
640C23C2×#23511yescharacteristic
641C23C2×D3×D411yescharacteristic
642C23C2×D3×D412yes—
643C23C2×D3×D411yescharacteristic
644C23#100412yes—
645C23C2×D3×Q811yescharacteristic
646C23C2×#23912yes—
647C23#100711yescharacteristic
648C23D3×#4111yescharacteristic
649C23D3×#4112yes—
650C23#100911yescharacteristic
651Q8—416no—
652D4—1216no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—64no—
682C2×C4—64no—
683C2×C4—62no—
684C2×C4—64no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—64no—
688C2×C4—64no—
689C2×C4—64no—
690C2×C4—1216no—
691C2×C4—1232no—
692C2×C4—122no—
693C2×C4—122no—
694C2×C4—122no—
695C2×C4—122no—
696C2×C4—122no—
697C2×C4—122no—
698C2×C4—122no—
699C2×C4—122no—
700C2×C4—122no—
701C2×C4—122no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—122no—
706C2×C4—122no—
707C2×C4#88414yes—
708C2×C3C2×#39311yescharacteristic
709C2×C3#241011yescharacteristic
710C2×C3#241711yescharacteristic
711C2×C3#243011yescharacteristic
712C2×C3#244912yes—
713C2×C3#245012yes—
714C2×C3#247212yes—
715C2×C3#248812yes—
716C2×C3#256411yescharacteristic
717C2×C3#263911yescharacteristic
718C2×C3#285011yescharacteristic
719D3—28no—
720D3—82no—
721C22—38no—
722C22—64no—
723C22—64no—
724C22—68no—
725C22—68no—
726C22—64no—
727C22—64no—
728C22—64no—
729C22—68no—
730C22—64no—
731C22—68no—
732C22—122no—
733C22—122no—
734C22—124no—
735C22—124no—
736C22—122no—
737C22—241no—
738C22—242no—
739C22—241no—
740C22—241no—
741C22—241no—
742C22—242no—
743C22C2×#88411yescharacteristic
744C22#549012yes—
745C22#557911yescharacteristic
746C22#558012yes—
747C22#558111yescharacteristic
748C22D3×#12011yescharacteristic
749C22#558911yescharacteristic
750C22#559012yes—
751C22D3×C22⋊Q811yescharacteristic
752C22D3×C22⋊Q812yes—
753C22#562712yes—
754C22#562911yescharacteristic
755C22#563012yes—
756C22#563712yes—
757C22#563812yes—
758C22D3×#12411yescharacteristic
759C22D3×#12412yes—
760C22#567611yescharacteristic
761C22#567812yes—
762C22#572511yescharacteristic
763C22#572612yes—
764C22#572711yescharacteristic
765C22#573012yes—
766C4—24no—
767C4—42no—
768C4—44no—
769C4—44no—
770C4—81no—
771C4—122no—
772C4—124no—
773C4—124no—
774C4—241no—
775C3#1475911yescharacteristic, complemented, Sylow
776C2—68no—
777C2—242no—
778C2#7385411yescharacteristic
779C2#7662111yescharacteristic
780C2#7662812yes—
781C2#7662912yes—
782C2#7666211yescharacteristic
783C2#7679012yes—
784C2D3×#39311yescharacteristic
785C2#7687211yescharacteristic
786C2#7725011yescharacteristic
787C2#7725212yes—
788C2#7725411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1446C2
prime radicalC23×D12C22
hypercenter#1446D3
hypocenterC3#14759
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
1. C22×#946C2semidirect
2. C2×#5231C2semidirect
5. C2×D3×#95C2semidirect
6. C3×#1446C2semidirect
7. #69428C2semidirect
8. #69427C2semidirect
9. (C2×D3)⋊#95C2semidirect
10. #69415C2semidirect
11. #69414C2semidirect
47. #1446D3semidirect
73. C22×D12Q8semidirect
118. C3⋊#95D4semidirect
584. C2×D3#393semidirect
775. C3#14759semidirect

Maximal subgroups

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

subgroupindex
C22×#9462
C2×#52312
C2×#46652
C2×D3×#952
C3×#14462
#694282
#694272
(C2×D3)⋊#952
#694152
#694142
#147593