Finite Group Databasebeta

← #10731724

Subgroups — #10731724

Order 768.

3458 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#893C211yesmaximal, characteristic, complemented
2C22×#884C212yesmaximal, complemented
3C2×#4960C211yesmaximal, characteristic, complemented
4C2×#4957C211yesmaximal, characteristic, complemented
5C2×#4671C211yesmaximal, characteristic, complemented
6C2×#4667C212yesmaximal, complemented
7C3×#1439C211yesmaximal, characteristic, complemented
8#71570C211yesmaximal, characteristic, complemented
9#71550C212yesmaximal, complemented
10#69426C212yesmaximal, complemented
11Dic3⋊#95C211yesmaximal, characteristic, complemented
12#15123—31nomaximal, Sylow
13C23×#67C2211yescharacteristic
14C23×#67C2212yes—
15C23×D12C2211yescharacteristic
16C23×D12C2212yes—
17C23×C4×D3C2212yes—
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2212yes—
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×#217C2211yescharacteristic
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2212yes—
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2212yes—
30C22×C4×Dic3C2211yescharacteristic
31C2×#893—28no—
32C2×#893—24no—
33C2×#884—28no—
34C2×#884—28no—
35C2×#884—28no—
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41#4960—24no—
42#4957—24no—
43#4671—24no—
44#4667—28no—
45C22×#121—32no—
46C22×C4×D4—31no—
47C2×#392—31no—
48C2×#392—31no—
49C2×#390—31no—
50C2×#380—32no—
51#1439—31no—
52#1439D311yescharacteristic, complemented
53#1438—32no—
54#1438—32no—
55C4⋊#95—31no—
56C25×C3C2311yescharacteristic
57C24×D3C2311yescharacteristic
58C24×D3C2312yes—
59C23×C3×C4C2311yescharacteristic
60C23×C3×C4C2312yes—
61C23×C3×C4C2312yes—
62C23×C3×C4C2311yescharacteristic
63C22×#67—24no—
64C22×#67—24no—
65C22×#67—24no—
66C22×#67—24no—
67C22×#67—22no—
68C22×#67—24no—
69C22×#67—24no—
70C22×#67—24no—
71C22×#67—22no—
72C22×#67—42no—
73C22×#67—42no—
74C22×#67D414yescomplemented
75C23×Dic3C2311yescharacteristic
76C23×Dic3C2312yes—
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2311yescharacteristic
79C22×D12—24no—
80C22×D12—24no—
81C22×D12—22no—
82C22×D12—22no—
83C22×D12—24no—
84C22×D12—24no—
85C22×D12—24no—
86C22×D12—24no—
87C22×D12—24no—
88C22×D12—42no—
89C22×D12—42no—
90C22×D12D414yescomplemented
91C22×C4×D3—24no—
92C22×C4×D3—24no—
93C22×C4×D3—24no—
94C22×C4×D3—24no—
95C22×C4×D3—24no—
96C22×C4×D3—24no—
97C22×C4×D3D418yescomplemented
98C2×C3×C4⋊C4—24no—
99C2×C3×C4⋊C4—22no—
100C2×C3×C22⋊C4—24no—
101C2×C3×C22⋊C4—24no—
102C2×C3×C22⋊C4—24no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×#217—22no—
107C2×#217—42no—
108C2×(C2×D3)⋊C4—24no—
109C2×(C2×D3)⋊C4—24no—
110C2×(C2×D3)⋊C4—24no—
111C2×(C2×D3)⋊C4—24no—
112C2×(C2×D3)⋊C4—24no—
113C2×(C2×D3)⋊C4—24no—
114C2×(C2×D3)⋊C4—24no—
115C2×(C2×D3)⋊C4—24no—
116C2×(C2×D3)⋊C4—24no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—24no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—42no—
123C2×(C2×D3)⋊C4—42no—
124C2×(C2×D3)⋊C4—42no—
125C2×Dic3⋊C4—24no—
126C2×Dic3⋊C4—24no—
127C2×Dic3⋊C4—24no—
128C2×Dic3⋊C4—22no—
129C2×Dic3⋊C4D418yescomplemented
130C2×C4×Dic3—24no—
131C2×C4×Dic3D414yescomplemented
132#893—232no—
133#884—264no—
134C3×#95—24no—
135C3×#95—22no—
136C3⋊#95—22no—
137C3⋊#95—24no—
138C3⋊#95—42no—
139C23×D4—31no—
140C23×D4—32no—
141C23×D4—31no—
142C23×D4—32no—
143C24×C4—32no—
144C2×#121—68no—
145C2×#121—68no—
146C2×#121—68no—
147C2×C4×D4—64no—
148C2×C4×D4—68no—
149C22×C4⋊C4—32no—
150C22×C4⋊C4—31no—
151C22×C4⋊C4C2×D311yescharacteristic
152C22×C22⋊C4—31no—
153C22×C22⋊C4—32no—
154C22×C22⋊C4—32no—
155C22×C22⋊C4—32no—
156C22×C22⋊C4—32no—
157C22×C22⋊C4—31no—
158C22×C22⋊C4—31no—
159C22×C22⋊C4C2×D311yescharacteristic
160C22×C22⋊C4C2×D312yes—
161C22×C42—31no—
162#392—64no—
163#392—64no—
164#390—64no—
165#380—68no—
166C2×#95—31no—
167C2×#95—32no—
168C2×#95—32no—
169C2×#95C2×D311yescharacteristic
170C2×#95C2×D312yes—
171C24×C3—21no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3—21no—
175C24×C3—21no—
176C24×C3—21no—
177C24×C3—22no—
178C24×C3—22no—
179C24×C3—21no—
180C24×C3—21no—
181C24×C3C2×D412yes—
182C24×C3C2411yescharacteristic
183C23×D3—22no—
184C23×D3—22no—
185C23×D3—22no—
186C23×D3—22no—
187C23×D3—22no—
188C23×D3—22no—
189C23×D3—22no—
190C23×D3—22no—
191C23×D3—22no—
192C23×D3—22no—
193C23×D3—22no—
194C23×D3—22no—
195C23×D3—21no—
196C23×D3—21no—
197C23×D3—22no—
198C23×D3—22no—
199C23×D3—21no—
200C23×D3—22no—
201C23×D3—21no—
202C23×D3—22no—
203C23×D3—21no—
204C23×D3—21no—
205C23×D3C2×D412yes—
206C23×D3C2×D414yes—
207C23×D3C2×D414yes—
208C23×D3#4114yes—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—22no—
228C22×C3×C4C2×D414yes—
229C22×C3×C4C2×D414yes—
230C22×C3×C4C2×D412yes—
231C22×C3×C4C2×D412yes—
232C22×C3×C4#4112yes—
233C2×#67—216no—
234C2×#67—216no—
235C2×#67—28no—
236C2×#67—48no—
237C2×#67—48no—
238C2×#67—48no—
239C2×#67—48no—
240C2×#67—48no—
241C2×#67—48no—
242C2×#67—44no—
243C2×#67—48no—
244C2×#67—44no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—22no—
250C22×Dic3—21no—
251C22×Dic3—22no—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—21no—
255C22×Dic3—22no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—22no—
260C22×Dic3C2×D414yes—
261C22×Dic3C2×D412yes—
262C22×Dic3C2×D414yes—
263C22×Dic3C2×D412yes—
264C22×Dic3C2×D412yes—
265C22×Dic3C2×D414yes—
266C22×Dic3#4112yes—
267C2×D12—28no—
268C2×D12—28no—
269C2×D12—216no—
270C2×D12—216no—
271C2×D12—28no—
272C2×D12—216no—
273C2×D12—48no—
274C2×D12—48no—
275C2×D12—48no—
276C2×D12—48no—
277C2×D12—48no—
278C2×D12—48no—
279C2×C4×D3—216no—
280C2×C4×D3—216no—
281C2×C4×D3—216no—
282C2×C4×D3—48no—
283C2×C4×D3—48no—
284C2×C4×D3—48no—
285C2×C4×D3—48no—
286C3×C4⋊C4—28no—
287C3×C22⋊C4—216no—
288C3×C22⋊C4—44no—
289#217—44no—
290(C2×D3)⋊C4—216no—
291(C2×D3)⋊C4—216no—
292(C2×D3)⋊C4—48no—
293(C2×D3)⋊C4—44no—
294(C2×D3)⋊C4—48no—
295(C2×D3)⋊C4—44no—
296Dic3⋊C4—216no—
297Dic3⋊C4—44no—
298C4×Dic3—28no—
299C25—32no—
300C25—31no—
301C25C22×D311yescharacteristic
302C22×D4—34no—
303C22×D4—34no—
304C22×D4—64no—
305C22×D4—64no—
306C22×D4—64no—
307C22×D4—64no—
308C22×D4—64no—
309C22×D4—64no—
310C22×D4—64no—
311C22×D4—64no—
312C22×D4—64no—
313C22×D4—62no—
314C22×D4—62no—
315C22×D4—64no—
316C22×D4—64no—
317C22×D4—64no—
318C22×D4—64no—
319C22×D4—62no—
320C22×D4—62no—
321C22×D4—64no—
322C22×D4—122no—
323C22×D4—122no—
324C22×D4—122no—
325C22×D4—122no—
326C23×C4—31no—
327C23×C4—31no—
328C23×C4—32no—
329C23×C4—38no—
330C23×C4—31no—
331C23×C4—64no—
332C23×C4—64no—
333C23×C4—64no—
334C23×C4—64no—
335C23×C4—64no—
336C23×C4—64no—
337C23×C4C22×D311yescharacteristic
338C23×C4C22×D312yes—
339C23×C4C22×D312yes—
340C23×C4C22×D311yescharacteristic
341#121—664no—
342C4×D4—632no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—38no—
346C2×C4⋊C4—64no—
347C2×C4⋊C4—64no—
348C2×C4⋊C4—64no—
349C2×C4⋊C4—62no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—64no—
357C2×C22⋊C4—64no—
358C2×C22⋊C4—64no—
359C2×C22⋊C4—64no—
360C2×C22⋊C4—64no—
361C2×C22⋊C4—64no—
362C2×C22⋊C4—64no—
363C2×C22⋊C4—62no—
364C2×C22⋊C4—64no—
365C2×C22⋊C4—64no—
366C2×C22⋊C4—62no—
367C2×C22⋊C4—62no—
368C2×C22⋊C4—64no—
369C2×C22⋊C4—62no—
370C2×C22⋊C4—62no—
371C2×C22⋊C4—122no—
372C2×C22⋊C4—122no—
373C2×C22⋊C4—122no—
374C2×C22⋊C4—122no—
375C2×C42—34no—
376C2×C42—64no—
377#95—24no—
378#95—22no—
379#95—64no—
380#95—62no—
381#95—122no—
382C23×C3—24no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—24no—
386C23×C3—22no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3—42no—
390C23×C3—42no—
391C23×C3—41no—
392C23×C3—42no—
393C23×C3—41no—
394C23×C3—41no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3—41no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—41no—
401C23×C3—42no—
402C23×C3—42no—
403C23×C3—42no—
404C23×C3—41no—
405C23×C3C22×D412yes—
406C23×C3C22×D411yescharacteristic
407C23×C3C22×D411yescharacteristic
408C23×C3C22×D412yes—
409C23×C3C22×D411yescharacteristic
410C23×C3C2×#4111yescharacteristic
411C23×C3C2×#4111yescharacteristic
412C23×C3C2×#4112yes—
413C23×C3H(5,𝔽2)11yescharacteristic
414C23×C3H(5,𝔽2)12yes—
415C23×C32−1+411yescharacteristic
416C22×D3—24no—
417C22×D3—24no—
418C22×D3—24no—
419C22×D3—24no—
420C22×D3—24no—
421C22×D3—24no—
422C22×D3—24no—
423C22×D3—24no—
424C22×D3—24no—
425C22×D3—24no—
426C22×D3—24no—
427C22×D3—24no—
428C22×D3—24no—
429C22×D3—24no—
430C22×D3—24no—
431C22×D3—24no—
432C22×D3—24no—
433C22×D3—24no—
434C22×D3—24no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—24no—
438C22×D3—22no—
439C22×D3—42no—
440C22×D3—42no—
441C22×D3—42no—
442C22×D3—42no—
443C22×D3—42no—
444C22×D3—42no—
445C22×D3—42no—
446C22×D3—42no—
447C22×D3—42no—
448C22×D3—42no—
449C22×D3—42no—
450C22×D3—42no—
451C22×D3—42no—
452C22×D3—42no—
453C22×D3—42no—
454C22×D3—42no—
455C22×D3—41no—
456C22×D3—41no—
457C22×D3—42no—
458C22×D3—42no—
459C22×D3—41no—
460C22×D3—42no—
461C22×D3—41no—
462C22×D3—41no—
463C22×D3—42no—
464C22×D3—42no—
465C22×D3—41no—
466C22×D3—42no—
467C22×D3—42no—
468C22×D3—41no—
469C22×D3—42no—
470C22×D3—42no—
471C22×D3—42no—
472C22×D3—41no—
473C22×D3#12118yescomplemented
474C2×C3×C4—22no—
475C2×C3×C4—24no—
476C2×C3×C4—22no—
477C2×C3×C4—24no—
478C2×C3×C4—24no—
479C2×C3×C4—24no—
480C2×C3×C4—24no—
481C2×C3×C4—24no—
482C2×C3×C4—24no—
483C2×C3×C4—24no—
484C2×C3×C4—42no—
485C2×C3×C4—42no—
486C2×C3×C4—42no—
487C2×C3×C4—42no—
488C2×C3×C4—42no—
489C2×C3×C4—42no—
490C2×C3×C4—42no—
491C2×C3×C4—42no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—42no—
496C2×C3×C4—42no—
497C2×C3×C4#12114yescomplemented
498#67—432no—
499#67—416no—
500C2×Dic3—22no—
501C2×Dic3—24no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—24no—
505C2×Dic3—24no—
506C2×Dic3—42no—
507C2×Dic3—42no—
508C2×Dic3—42no—
509C2×Dic3—42no—
510C2×Dic3—42no—
511C2×Dic3—42no—
512C2×Dic3—41no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—42no—
516C2×Dic3—42no—
517C2×Dic3#12014yes—
518C2×Dic3#12018yes—
519C2×Dic3#12118yes—
520C2×Dic3#12114yes—
521C2×Dic3#12714yes—
522D12—232no—
523D12—432no—
524C4×D3—432no—
525C24—21no—
526C24—21no—
527C24—22no—
528C24—22no—
529C24—21no—
530C24—21no—
531C24—22no—
532C24—21no—
533C24—22no—
534C24—21no—
535C24—34no—
536C24—34no—
537C24—34no—
538C24—32no—
539C24—62no—
540C24—62no—
541C24—62no—
542C24—62no—
543C24—62no—
544C24—62no—
545C24—62no—
546C24—62no—
547C24—62no—
548C24—62no—
549C24—62no—
550C24—62no—
551C24—61no—
552C24—61no—
553C24—62no—
554C24—62no—
555C24—61no—
556C24—61no—
557C24—62no—
558C24—61no—
559C24—62no—
560C24—61no—
561C24D3×D412yes—
562C24C23×D311yescharacteristic
563C2×D4—616no—
564C2×D4—68no—
565C2×D4—68no—
566C2×D4—616no—
567C2×D4—616no—
568C2×D4—616no—
569C2×D4—68no—
570C2×D4—616no—
571C2×D4—68no—
572C2×D4—128no—
573C2×D4—128no—
574C2×D4—124no—
575C2×D4—124no—
576C2×D4—128no—
577C2×D4—128no—
578C2×D4—128no—
579C2×D4—128no—
580C2×D4—128no—
581C2×D4—128no—
582C2×D4—128no—
583C2×D4—128no—
584C2×D4—128no—
585C2×D4—128no—
586C2×D4—128no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—32no—
607C22×C4—34no—
608C22×C4—34no—
609C22×C4—32no—
610C22×C4—32no—
611C22×C4—34no—
612C22×C4—32no—
613C22×C4—616no—
614C22×C4—616no—
615C22×C4—616no—
616C22×C4—62no—
617C22×C4—62no—
618C22×C4—62no—
619C22×C4—62no—
620C22×C4—61no—
621C22×C4—62no—
622C22×C4—61no—
623C22×C4—62no—
624C22×C4—62no—
625C22×C4—62no—
626C22×C4—61no—
627C22×C4—62no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4—62no—
631C22×C4—128no—
632C22×C4—128no—
633C22×C4—128no—
634C22×C4—128no—
635C22×C4#23512yes—
636C22×C4D3×D414yes—
637C22×C4D3×D414yes—
638C22×C4D3×D412yes—
639C22×C4D3×D412yes—
640C4⋊C4—28no—
641C4⋊C4—616no—
642C4⋊C4—124no—
643C22⋊C4—216no—
644C22⋊C4—44no—
645C22⋊C4—616no—
646C22⋊C4—616no—
647C22⋊C4—128no—
648C22⋊C4—128no—
649C22⋊C4—124no—
650C22⋊C4—124no—
651C22⋊C4—124no—
652C42—68no—
653C22×C3—42no—
654C22×C3—44no—
655C22×C3—44no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—82no—
661C22×C3—82no—
662C22×C3—81no—
663C22×C3—81no—
664C22×C3C2×#12011yescharacteristic
665C22×C3C2×#12012yes—
666C22×C3C2×#12111yescharacteristic
667C22×C3C2×#12112yes—
668C22×C3C2×#12112yes—
669C22×C3C2×#12111yescharacteristic
670C22×C3#52511yescharacteristic
671C22×C3#52512yes—
672C22×C3C2×#12711yescharacteristic
673C22×C3#53512yes—
674C22×C3#53511yescharacteristic
675C22×C3#53712yes—
676C22×C3#53711yescharacteristic
677C22×C3D4211yescharacteristic
678C22×C3D4212yes—
679C22×C3#54612yes—
680C22×C3#54612yes—
681C22×C3#54711yescharacteristic
682C22×C3#54711yescharacteristic
683C22×C3#54812yes—
684C22×C3#55012yes—
685C22×C3#55312yes—
686C22×C3#55511yescharacteristic
687C2×D3—28no—
688C2×D3—28no—
689C2×D3—28no—
690C2×D3—44no—
691C2×D3—44no—
692C2×D3—44no—
693C2×D3—44no—
694C2×D3—44no—
695C2×D3—44no—
696C2×D3—44no—
697C2×D3—44no—
698C2×D3—44no—
699C2×D3—44no—
700C2×D3—44no—
701C2×D3—44no—
702C2×D3—42no—
703C2×D3—44no—
704C2×D3—44no—
705C2×D3—42no—
706C2×D3—42no—
707C2×D3—81no—
708C2×D3—81no—
709C2×D3—82no—
710C2×D3—82no—
711C2×D3—81no—
712C2×D3—81no—
713C3×C4—24no—
714C3×C4—44no—
715C3×C4—44no—
716C3×C4—81no—
717Dic3—42no—
718Dic3—44no—
719Dic3—81no—
720Dic3#39218yescomplemented
721C23—24no—
722C23—22no—
723C23—24no—
724C23—22no—
725C23—22no—
726C23—38no—
727C23—42no—
728C23—42no—
729C23—41no—
730C23—41no—
731C23—42no—
732C23—42no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—42no—
737C23—42no—
738C23—41no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—41no—
744C23—41no—
745C23—64no—
746C23—64no—
747C23—64no—
748C23—64no—
749C23—64no—
750C23—64no—
751C23—64no—
752C23—64no—
753C23—64no—
754C23—64no—
755C23—64no—
756C23—64no—
757C23—64no—
758C23—64no—
759C23—64no—
760C23—64no—
761C23—64no—
762C23—64no—
763C23—64no—
764C23—62no—
765C23—64no—
766C23—62no—
767C23—62no—
768C23—122no—
769C23—122no—
770C23—122no—
771C23—122no—
772C23—122no—
773C23—122no—
774C23—122no—
775C23—122no—
776C23—122no—
777C23—122no—
778C23—122no—
779C23—122no—
780C23—122no—
781C23—122no—
782C23—122no—
783C23—122no—
784C23—122no—
785C23—122no—
786C23—121no—
787C23—121no—
788C23—122no—
789C23—122no—
790C23—121no—
791C23—121no—
792C23—121no—
793C23—122no—
794C23—122no—
795C23—121no—
796C23—122no—
797C23—122no—
798C23—122no—
799C23—122no—
800C23—121no—
801C23—121no—
802C23C2×#23511yescharacteristic
803C23C2×D3×D412yes—
804C23C2×D3×D411yescharacteristic
805C23C2×D3×D411yescharacteristic
806C23C2×D3×D412yes—
807C23C2×D3×D411yescharacteristic
808C23#100711yescharacteristic
809C23D3×#4112yes—
810C23D3×#4111yescharacteristic
811C23#100911yescharacteristic
812C23#100912yes—
813D4—632no—
814D4—1216no—
815D4—1232no—
816D4—1232no—
817C2×C4—22no—
818C2×C4—24no—
819C2×C4—22no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—34no—
828C2×C4—34no—
829C2×C4—38no—
830C2×C4—38no—
831C2×C4—34no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—64no—
846C2×C4—62no—
847C2×C4—62no—
848C2×C4—64no—
849C2×C4—64no—
850C2×C4—62no—
851C2×C4—1232no—
852C2×C4—122no—
853C2×C4—122no—
854C2×C4—122no—
855C2×C4—122no—
856C2×C4—122no—
857C2×C4—122no—
858C2×C4—121no—
859C2×C4—121no—
860C2×C4—121no—
861C2×C4—122no—
862C2×C4—122no—
863C2×C4#88414yescomplemented
864C2×C3—82no—
865C2×C3C2×#39211yescharacteristic
866C2×C3#240712yes—
867C2×C3#240812yes—
868C2×C3#241412yes—
869C2×C3#241612yes—
870C2×C3#253511yescharacteristic
871C2×C3#253711yescharacteristic
872C2×C3#254011yescharacteristic
873C2×C3#254111yescharacteristic
874C2×C3#261511yescharacteristic
875C2×C3#284711yescharacteristic
876D3—48no—
877D3—82no—
878C22—44no—
879C22—44no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—68no—
884C22—68no—
885C22—68no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—82no—
891C22—82no—
892C22—124no—
893C22—124no—
894C22—124no—
895C22—124no—
896C22—124no—
897C22—124no—
898C22—124no—
899C22—124no—
900C22—124no—
901C22—124no—
902C22—124no—
903C22—124no—
904C22—124no—
905C22—124no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—241no—
910C22—241no—
911C22—241no—
912C22—241no—
913C22—242no—
914C22—242no—
915C22C2×#88411yescharacteristic
916C22#550711yescharacteristic
917C22#553211yescharacteristic
918C22#554712yes—
919C22#555312yes—
920C22D3×#12011yescharacteristic
921C22D3×#12012yes—
922C22D3×#12112yes—
923C22D3×#12111yescharacteristic
924C22D3×#12112yes—
925C22#560912yes—
926C22#560911yescharacteristic
927C22#562912yes—
928C22#562911yescharacteristic
929C22#563111yescharacteristic
930C22#563312yes—
931C22#565412yes—
932C22#565412yes—
933C22#565611yescharacteristic
934C22#567411yescharacteristic
935C22#567412yes—
936C22#570912yes—
937C22D3×#12711yescharacteristic
938C4—24no—
939C4—38no—
940C4—44no—
941C4—44no—
942C4—81no—
943C4—122no—
944C4—124no—
945C4—241no—
946C3#1512311yescharacteristic, complemented, Sylow
947C2—82no—
948C2—128no—
949C2—242no—
950C2#7393511yescharacteristic
951C2#7440412yes—
952C2#7493511yescharacteristic
953C2#7549512yes—
954C2#7634811yescharacteristic
955C2D3×#39211yescharacteristic
956C2#7680911yescharacteristic
957C2#7689512yes—
958C2#7728412yes—
959C2#7751311yescharacteristic
960C2#7803611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
hypercenter#1439D3
hypocenterC3#15123
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#893C2semidirect
2. C22×#884C2semidirect
3. C2×#4960C2semidirect
4. C2×#4957C2semidirect
5. C2×#4671C2semidirect
6. C2×#4667C2semidirect
7. C3×#1439C2semidirect
8. #71570C2semidirect
9. #71550C2semidirect
10. #69426C2semidirect
11. Dic3⋊#95C2semidirect
52. #1439D3semidirect
74. C22×#67D4semidirect
90. C22×D12D4semidirect
97. C22×C4×D3D4semidirect
129. C2×Dic3⋊C4D4semidirect
131. C2×C4×Dic3D4semidirect
473. C22×D3#121semidirect
497. C2×C3×C4#121semidirect
720. Dic3#392semidirect
863. C2×C4#884semidirect
946. C3#15123semidirect

Maximal subgroups

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

subgroupindex
C22×#8932
C22×#8842
C2×#49602
C2×#49572
C2×#46712
C2×#46672
C3×#14392
#715702
#715502
#694262
Dic3⋊#952
#151233