Finite Group Databasebeta

← #10728716

Subgroups — #10728716

Order 768.

2086 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#887C211yesmaximal, characteristic, complemented
2C2×#4991C211yesmaximal, characteristic
3C2×#4988C211yesmaximal, characteristic
4C2×#4673C212yesmaximal, complemented
5C2×#4672C211yesmaximal, characteristic
6C3×#1441C211yesmaximal, characteristic, complemented
7#71566C211yesmaximal, characteristic, complemented
8#69428C212yesmaximal, complemented
9#69408C212yesmaximal, complemented
10#69408C212yesmaximal, complemented
11#69402C211yesmaximal, characteristic, complemented
12#14883—31nomaximal, Sylow
13C23×D12C2211yescharacteristic
14C23×Dic6C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×(C2×D3)⋊C4C2212yes—
18C22×(C2×D3)⋊C4C2212yes—
19C22×(C2×D3)⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×Dic3⋊C4C2211yescharacteristic
24C22×Dic3⋊C4C2211yescharacteristic
25C22×C4×Dic3C2211yescharacteristic
26C22×C4×Dic3C2211yescharacteristic
27C22×C4×Dic3C2211yescharacteristic
28C2×#887—24no—
29C2×#887—24no—
30C2×#887—24no—
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2212yes—
33C2×C3×#95C2212yes—
34C2×C3⋊#95C2211yescharacteristic
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39#4991—24no—
40#4988—24no—
41#4673—28no—
42#4672—24no—
43C22×C4×Q8—31no—
44C2×#394—31no—
45C2×#394—31no—
46C2×#393—32no—
47C2×#390—31no—
48#1441—31no—
49#1441D311yescharacteristic, complemented
50#1439—32no—
51#1437—32no—
52#1437—32no—
53#1434—31no—
54C24×D3C2312yes—
55C23×C3×C4C2312yes—
56C23×C3×C4C2312yes—
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2311yescharacteristic
60C23×Dic3C2312yes—
61C23×Dic3C2311yescharacteristic
62C23×Dic3C2311yescharacteristic
63C23×Dic3C2311yescharacteristic
64C23×Dic3C2311yescharacteristic
65C22×D12—24no—
66C22×D12—22no—
67C22×D12—22no—
68C22×D12—22no—
69C22×D12—42no—
70C22×Dic6—22no—
71C22×Dic6—22no—
72C22×Dic6—22no—
73C22×Dic6—22no—
74C22×Dic6—22no—
75C22×Dic6—22no—
76C22×Dic6D414yescomplemented
77C2×C3×C4⋊C4—22no—
78C2×C3×C4⋊C4—22no—
79C2×C3×C4⋊C4—22no—
80C2×C3×C4⋊C4—42no—
81C2×C3×C4⋊C4D414yes—
82C2×(C2×D3)⋊C4—24no—
83C2×(C2×D3)⋊C4—24no—
84C2×(C2×D3)⋊C4—24no—
85C2×(C2×D3)⋊C4—24no—
86C2×(C2×D3)⋊C4—24no—
87C2×(C2×D3)⋊C4—24no—
88C2×(C2×D3)⋊C4—24no—
89C2×(C2×D3)⋊C4—24no—
90C2×(C2×D3)⋊C4—24no—
91C2×(C2×D3)⋊C4—24no—
92C2×(C2×D3)⋊C4—24no—
93C2×(C2×D3)⋊C4—24no—
94C2×(C2×D3)⋊C4—24no—
95C2×(C2×D3)⋊C4—24no—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—24no—
98C2×(C2×D3)⋊C4—42no—
99C2×(C2×D3)⋊C4—42no—
100C2×Dic3⋊C4—22no—
101C2×Dic3⋊C4—22no—
102C2×Dic3⋊C4—22no—
103C2×Dic3⋊C4—22no—
104C2×Dic3⋊C4—22no—
105C2×Dic3⋊C4D414yes—
106C2×C4×Dic3—22no—
107C2×C4×Dic3—22no—
108C2×C4×Dic3—22no—
109C2×C4×Dic3—22no—
110C2×C4×Dic3—22no—
111C2×C4×Dic3—22no—
112C2×C4×Dic3—22no—
113C2×C4×Dic3—22no—
114C2×C4×Dic3D414yes—
115#887—232no—
116C3×#95—22no—
117C3×#95—24no—
118C3×#95—42no—
119C3⋊#95—22no—
120C3⋊#95—24no—
121C3⋊#95—24no—
122C3⋊#95—24no—
123C3⋊#95—42no—
124C23×Q8—31no—
125C23×D4—31no—
126C2×C4×Q8—64no—
127C2×C4×Q8—64no—
128C2×C4×Q8—64no—
129C22×C4⋊C4—31no—
130C22×C4⋊C4—31no—
131C22×C4⋊C4C2×D311yescharacteristic
132C22×C4⋊C4C2×D311yescharacteristic
133C22×C22⋊C4—32no—
134C22×C22⋊C4—32no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4—32no—
137C22×C22⋊C4—32no—
138C22×C22⋊C4—32no—
139C22×C42—31no—
140C22×C42—31no—
141C22×C42—31no—
142#394—64no—
143#394—64no—
144#393—68no—
145#390—64no—
146C2×#95—32no—
147C2×#95—32no—
148C2×#95—31no—
149C2×#95—32no—
150C2×#95—32no—
151C2×#95C2×D312yes—
152C2×#95C2×D311yescharacteristic
153C2×#95C2×D312yes—
154C24×C3C2411yescharacteristic
155C23×D3—22no—
156C23×D3—22no—
157C23×D3—22no—
158C23×D3—22no—
159C23×D3—22no—
160C23×D3—22no—
161C23×D3—22no—
162C23×D3—22no—
163C23×D3—22no—
164C23×D3—22no—
165C23×D3—22no—
166C23×D3—22no—
167C23×D3—22no—
168C23×D3—22no—
169C23×D3#4114yes—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
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—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4C2×D412yes—
195C22×C3×C4C2×D412yes—
196C22×C3×C4C2×D412yes—
197C22×C3×C4C2×D412yes—
198C22×C3×C4C2×D412yes—
199C22×C3×C4C2×D412yes—
200C22×C3×C4#4112yes—
201C22×Dic3—21no—
202C22×Dic3—21no—
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3—21no—
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—22no—
212C22×Dic3—21no—
213C22×Dic3—21no—
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×Dic3C2×D412yes—
224C22×Dic3C2×D412yes—
225C22×Dic3C2×D412yes—
226C22×Dic3C2×D412yes—
227C22×Dic3C2×D412yes—
228C22×Dic3C2×D412yes—
229C22×Dic3#4112yes—
230C22×Dic3#4112yes—
231C22×Dic3#4114yes—
232C2×D12—28no—
233C2×D12—48no—
234C2×D12—48no—
235C2×D12—44no—
236C2×D12—44no—
237C2×Dic6—28no—
238C2×Dic6—28no—
239C2×Dic6—28no—
240C2×Dic6—28no—
241C2×Dic6—28no—
242C2×Dic6—28no—
243C2×Dic6—28no—
244C3×C4⋊C4—28no—
245C3×C4⋊C4—44no—
246(C2×D3)⋊C4—48no—
247(C2×D3)⋊C4—48no—
248(C2×D3)⋊C4—48no—
249(C2×D3)⋊C4—48no—
250(C2×D3)⋊C4—48no—
251(C2×D3)⋊C4—48no—
252Dic3⋊C4—28no—
253Dic3⋊C4—28no—
254C4×Dic3—28no—
255C4×Dic3—28no—
256C4×Dic3—28no—
257C25—32no—
258C22×Q8—34no—
259C22×Q8—62no—
260C22×Q8—62no—
261C22×Q8—62no—
262C22×Q8—62no—
263C22×Q8—62no—
264C22×Q8—62no—
265C22×D4—64no—
266C22×D4—62no—
267C22×D4—62no—
268C22×D4—62no—
269C22×D4—122no—
270C23×C4—31no—
271C23×C4—31no—
272C23×C4—31no—
273C23×C4—31no—
274C23×C4—32no—
275C23×C4C22×D312yes—
276C23×C4C22×D312yes—
277C23×C4C22×D311yescharacteristic
278C23×C4C22×D311yescharacteristic
279C23×C4C22×D311yescharacteristic
280C4×Q8—632no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—34no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—62no—
287C2×C4⋊C4—62no—
288C2×C4⋊C4—62no—
289C2×C4⋊C4—62no—
290C2×C4⋊C4—62no—
291C2×C4⋊C4D1214yes—
292C2×C22⋊C4—64no—
293C2×C22⋊C4—64no—
294C2×C22⋊C4—64no—
295C2×C22⋊C4—64no—
296C2×C22⋊C4—64no—
297C2×C22⋊C4—64no—
298C2×C22⋊C4—64no—
299C2×C22⋊C4—64no—
300C2×C22⋊C4—64no—
301C2×C22⋊C4—64no—
302C2×C22⋊C4—64no—
303C2×C22⋊C4—64no—
304C2×C22⋊C4—64no—
305C2×C22⋊C4—64no—
306C2×C22⋊C4—64no—
307C2×C22⋊C4—64no—
308C2×C22⋊C4—122no—
309C2×C22⋊C4—122no—
310C2×C42—34no—
311C2×C42—62no—
312C2×C42—62no—
313C2×C42—62no—
314C2×C42—62no—
315C2×C42—62no—
316C2×C42—62no—
317C2×C42—62no—
318C2×C42—62no—
319#95—24no—
320#95—22no—
321#95—42no—
322#95—64no—
323#95—64no—
324#95—64no—
325#95—62no—
326#95—122no—
327C23×C3C22×D411yescharacteristic
328C23×C3C22×D411yescharacteristic
329C23×C3C22×D411yescharacteristic
330C23×C3C22×D411yescharacteristic
331C23×C3C2×#4111yescharacteristic
332C23×C3C2×#4111yescharacteristic
333C23×C3C2×#4111yescharacteristic
334C23×C3C2×#4112yes—
335C23×C3C2×#4112yes—
336C23×C3H(5,𝔽2)12yes—
337C23×C32−1+412yes—
338C22×D3—24no—
339C22×D3—24no—
340C22×D3—24no—
341C22×D3—24no—
342C22×D3—24no—
343C22×D3—24no—
344C22×D3—24no—
345C22×D3—42no—
346C22×D3—42no—
347C22×D3—42no—
348C22×D3—42no—
349C22×D3—42no—
350C22×D3—42no—
351C22×D3—42no—
352C22×D3—42no—
353C22×D3—42no—
354C22×D3—42no—
355C22×D3—42no—
356C22×D3—42no—
357C22×D3—42no—
358C22×D3—42no—
359C22×D3—42no—
360C22×D3—42no—
361C22×D3—42no—
362C22×D3—42no—
363C22×D3—42no—
364C22×D3—42no—
365C22×D3—42no—
366C22×D3—42no—
367C22×D3—42no—
368C22×D3—42no—
369C22×D3—42no—
370C22×D3—42no—
371C22×D3—42no—
372C22×D3—42no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—24no—
382C2×C3×C4—24no—
383C2×C3×C4—22no—
384C2×C3×C4—24no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
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—42no—
402C2×C3×C4#12014yes—
403C2×C3×C4#12114yes—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—24no—
419C2×Dic3—24no—
420C2×Dic3—22no—
421C2×Dic3—24no—
422C2×Dic3—41no—
423C2×Dic3—41no—
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#12114yes—
433C2×Dic3#12114yes—
434C2×Dic3#12414yes—
435D12—416no—
436Dic6—232no—
437C24—34no—
438C24—62no—
439C24—62no—
440C24—62no—
441C24—62no—
442C24—62no—
443C24—62no—
444C24—62no—
445C24—62no—
446C24—62no—
447C24—62no—
448C24—62no—
449C24—62no—
450C24—62no—
451C24—62no—
452C24C23×D311yescharacteristic
453C2×Q8—68no—
454C2×Q8—68no—
455C2×Q8—68no—
456C2×Q8—68no—
457C2×Q8—68no—
458C2×Q8—68no—
459C2×Q8—68no—
460C2×D4—68no—
461C2×D4—128no—
462C2×D4—128no—
463C2×D4—124no—
464C2×D4—124no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
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—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—32no—
490C22×C4—32no—
491C22×C4—32no—
492C22×C4—32no—
493C22×C4—32no—
494C22×C4—34no—
495C22×C4—32no—
496C22×C4—32no—
497C22×C4—32no—
498C22×C4—61no—
499C22×C4—61no—
500C22×C4—61no—
501C22×C4—61no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4—61no—
505C22×C4—61no—
506C22×C4—62no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—61no—
510C22×C4—61no—
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×C4C2×D1212yes—
521C22×C4C2×D1212yes—
522C22×C4C2×D1212yes—
523C22×C4D3×D412yes—
524C22×C4D3×D412yes—
525C22×C4D3×D412yes—
526C22×C4#23912yes—
527C4⋊C4—28no—
528C4⋊C4—44no—
529C4⋊C4—68no—
530C4⋊C4—68no—
531C22⋊C4—128no—
532C22⋊C4—128no—
533C22⋊C4—128no—
534C22⋊C4—128no—
535C22⋊C4—128no—
536C22⋊C4—128no—
537C42—68no—
538C42—68no—
539C42—68no—
540C22×C3C2×#12011yescharacteristic
541C22×C3C2×#12111yescharacteristic
542C22×C3C2×#12111yescharacteristic
543C22×C3C2×#12111yescharacteristic
544C22×C3#52511yescharacteristic
545C22×C3#52511yescharacteristic
546C22×C3#52511yescharacteristic
547C22×C3#52511yescharacteristic
548C22×C3C2×#12411yescharacteristic
549C22×C3#52912yes—
550C22×C3#52912yes—
551C22×C3#53511yescharacteristic
552C22×C3#53611yescharacteristic
553C22×C3#54212yes—
554C22×C3#54212yes—
555C22×C3#54612yes—
556C22×C3#54612yes—
557C22×C3#54812yes—
558C22×C3#54812yes—
559C22×C3#54812yes—
560C22×C3#55012yes—
561C22×C3#55212yes—
562C22×C3#55912yes—
563C2×D3—44no—
564C2×D3—44no—
565C2×D3—44no—
566C2×D3—44no—
567C2×D3—44no—
568C2×D3—44no—
569C2×D3—44no—
570C2×D3—82no—
571C2×D3—82no—
572C2×D3—82no—
573C2×D3—82no—
574C2×D3—82no—
575C2×D3—82no—
576C2×D3—82no—
577C2×D3—82no—
578C3×C4—24no—
579C3×C4—24no—
580C3×C4—42no—
581C3×C4—82no—
582C3×C4—82no—
583Dic3—24no—
584Dic3—24no—
585Dic3—24no—
586Dic3—42no—
587Dic3—82no—
588C23—64no—
589C23—64no—
590C23—64no—
591C23—64no—
592C23—64no—
593C23—64no—
594C23—64no—
595C23—122no—
596C23—122no—
597C23—122no—
598C23—122no—
599C23—122no—
600C23—122no—
601C23—122no—
602C23—122no—
603C23—122no—
604C23—122no—
605C23—122no—
606C23—122no—
607C23—122no—
608C23—122no—
609C23—122no—
610C23—122no—
611C23—122no—
612C23—122no—
613C23—122no—
614C23—122no—
615C23—122no—
616C23—122no—
617C23—122no—
618C23—122no—
619C23—122no—
620C23—122no—
621C23—122no—
622C23—122no—
623C23C22×D1211yescharacteristic
624C23C2×D3×D411yescharacteristic
625C23C2×D3×D411yescharacteristic
626C23C2×D3×D411yescharacteristic
627C23#100412yes—
628C23C2×#23911yescharacteristic
629C23#100712yes—
630C23D3×#4112yes—
631C23D3×#4112yes—
632C23D3×#4111yescharacteristic
633C23D3×#4111yescharacteristic
634Q8—632no—
635D4—1216no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—34no—
649C2×C4—34no—
650C2×C4—34no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—64no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—62no—
677C2×C4—64no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—64no—
686C2×C4—121no—
687C2×C4—122no—
688C2×C4—121no—
689C2×C4—122no—
690C2×C4—122no—
691C2×C4—122no—
692C2×C4—122no—
693C2×C4—122no—
694C2×C4—122no—
695C2×C4—122no—
696C2×C4#88214yes—
697C2×C4#89514yes—
698C2×C3#239811yescharacteristic
699C2×C3#240411yescharacteristic
700C2×C3#242612yes—
701C2×C3#242612yes—
702C2×C3#243611yescharacteristic
703C2×C3#245812yes—
704C2×C3#245812yes—
705C2×C3#253611yescharacteristic
706C2×C3#254811yescharacteristic
707C2×C3#263211yescharacteristic
708C2×C3#284711yescharacteristic
709D3—84no—
710C22—124no—
711C22—124no—
712C22—124no—
713C22—124no—
714C22—124no—
715C22—124no—
716C22—124no—
717C22—242no—
718C22—242no—
719C22—242no—
720C22—242no—
721C22—242no—
722C22—242no—
723C22—242no—
724C22—242no—
725C22C2×#88211yescharacteristic
726C22C2×#89511yescharacteristic
727C22#552411yescharacteristic
728C22#555412yes—
729C22#557612yes—
730C22#559211yescharacteristic
731C22#559912yes—
732C22D3×#12111yescharacteristic
733C22D3×#12111yescharacteristic
734C22#561012yes—
735C22#562711yescharacteristic
736C22#562711yescharacteristic
737C22#563312yes—
738C22#563312yes—
739C22#564012yes—
740C22#565611yescharacteristic
741C22#566412yes—
742C22D3×#12411yescharacteristic
743C22#569112yes—
744C22#569312yes—
745C22#570612yes—
746C22#572411yescharacteristic
747C22#573312yes—
748C4—24no—
749C4—24no—
750C4—42no—
751C4—64no—
752C4—64no—
753C4—64no—
754C4—82no—
755C4—82no—
756C4—122no—
757C4—242no—
758C3#1488311yescharacteristic, complemented, Sylow
759C2—244no—
760C2#7404811yescharacteristic
761C2#7488511yescharacteristic
762C2#7532512yes—
763C2#7621812yes—
764C2#7650011yescharacteristic
765C2#7694611yescharacteristic
766C2#7720311yescharacteristic
767C2#7728612yes—
768C2#7775012yes—
769C2#7778411yescharacteristic
770C2#7813111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1441C2
prime radicalC23×D12C22
hypercenter#1441D3
hypocenterC3#14883
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
1. C22×#887C2semidirect
4. C2×#4673C2semidirect
6. C3×#1441C2semidirect
7. #71566C2semidirect
8. #69428C2semidirect
9. #69408C2semidirect
10. #69408C2semidirect
11. #69402C2semidirect
49. #1441D3semidirect
76. C22×Dic6D4semidirect
758. C3#14883semidirect

Maximal subgroups

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

subgroupindex
C22×#8872
C2×#49912
C2×#49882
C2×#46732
C2×#46722
C3×#14412
#715662
#694282
#694082
#694022
#148833