Finite Group Databasebeta

← #10729191

Subgroups — #10729191

Order 768.

3030 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#938C211yesmaximal, characteristic
2C22×#883C212yesmaximal, complemented
3C2×#4956C212yesmaximal, complemented
4C2×D3×#95C211yesmaximal, characteristic, complemented
5C3×#1438C211yesmaximal, characteristic, complemented
6#72131C211yesmaximal, characteristic, complemented
7#71547C212yesmaximal, complemented
8#71546C212yesmaximal, complemented
9(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
10#69420C211yesmaximal, characteristic, complemented
11#69419C211yesmaximal, characteristic, complemented
12#14926—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×#67C2212yes—
15C23×C4×D3C2211yescharacteristic
16C23×C4×D3C2211yescharacteristic
17C23×C4×D3C2211yescharacteristic
18C22×C3×C22⋊C4C2212yes—
19C22×C3×C22⋊C4C2212yes—
20C22×#217C2212yes—
21C22×#217C2212yes—
22C22×#217C2212yes—
23C2×#938—28no—
24C2×#938—24no—
25C22×(C2×D3)⋊C4C2212yes—
26C22×C4⋊Dic3C2211yescharacteristic
27C22×C4⋊Dic3C2212yes—
28C22×Dic3⋊C4C2212yes—
29C2×#883—28no—
30C2×#883—28no—
31C2×#883—28no—
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2211yescharacteristic
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2212yes—
41#4956—28no—
42D3×#95—24no—
43C22×#123—32no—
44C22×#121—31no—
45C2×#386—32no—
46C22×#95—31no—
47#1444—31no—
48#1444—31no—
49#1439—32no—
50#1439—32no—
51#1438—31no—
52#1438D311yescharacteristic, complemented
53C22⋊#95—31no—
54C25×C3C2312yes—
55C24×D3C2311yescharacteristic
56C22×C3×D4—24no—
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—42no—
61C23×C3×C4C2311yescharacteristic
62C23×C3×C4C2312yes—
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2311yescharacteristic
65C22×#67—24no—
66C22×#67—24no—
67C22×#67—24no—
68C22×#67—24no—
69C22×#67—24no—
70C22×#67—24no—
71C22×#67D418yes—
72C23×Dic3C2311yescharacteristic
73C23×Dic3C2311yescharacteristic
74C23×Dic3C2312yes—
75C23×Dic3C2312yes—
76C23×Dic3C2311yescharacteristic
77C22×C4×D3—22no—
78C22×C4×D3—22no—
79C22×C4×D3—24no—
80C22×C4×D3—24no—
81C22×C4×D3—24no—
82C22×C4×D3—22no—
83C22×C4×D3—22no—
84C22×C4×D3—22no—
85C22×C4×D3—22no—
86C22×C4×D3—22no—
87C22×C4×D3—24no—
88C22×C4×D3—42no—
89C22×C4×D3—42no—
90C22×C4×D3D414yes—
91C22×C4×D3D414yescomplemented
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—24no—
96C2×C3×C22⋊C4—24no—
97C2×C3×C22⋊C4—42no—
98C2×#217—24no—
99C2×#217—24no—
100C2×#217—24no—
101C2×#217—24no—
102C2×#217—24no—
103C2×#217—24no—
104C2×#217—24no—
105C2×#217—24no—
106C2×#217—42no—
107#938—232no—
108C2×(C2×D3)⋊C4—24no—
109C2×(C2×D3)⋊C4—24no—
110C2×(C2×D3)⋊C4D418yescomplemented
111C2×C4⋊Dic3—24no—
112C2×C4⋊Dic3—22no—
113C2×C4⋊Dic3—24no—
114C2×C4⋊Dic3—24no—
115C2×C4⋊Dic3—24no—
116C2×Dic3⋊C4—24no—
117C2×Dic3⋊C4—24no—
118C2×Dic3⋊C4—24no—
119#883—264no—
120C3×#95—22no—
121C3×#95—22no—
122C3⋊#95—22no—
123C3⋊#95—24no—
124C3⋊#95—22no—
125C3⋊#95—22no—
126C3⋊#95—22no—
127C3⋊#95—24no—
128C3⋊#95—42no—
129C23×D4—32no—
130C23×D4C2×D311yescharacteristic
131C24×C4—31no—
132C24×C4—31no—
133C24×C4—31no—
134C2×#123—68no—
135C2×#123—68no—
136C2×#123—68no—
137C2×#121—64no—
138C2×#121—68no—
139C22×C4⋊C4—31no—
140C22×C4⋊C4—32no—
141C22×C4⋊C4—32no—
142C22×C22⋊C4—32no—
143C22×C22⋊C4—32no—
144C22×C22⋊C4—32no—
145C22×C22⋊C4—32no—
146C22×C22⋊C4C2×D312yes—
147C22×C22⋊C4C2×D312yes—
148#386—68no—
149C2×#95—31no—
150C2×#95—31no—
151C2×#95—31no—
152C2×#95—31no—
153C2×#95—32no—
154C2×#95—32no—
155C2×#95—32no—
156C2×#95—64no—
157C2×#95C2×D311yescharacteristic
158C2×#95C2×D311yescharacteristic
159C24×C3—22no—
160C24×C3—22no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3C2×D414yes—
174C24×C3C2411yescharacteristic
175C23×D3—21no—
176C23×D3—21no—
177C23×D3—21no—
178C23×D3—21no—
179C23×D3—22no—
180C23×D3—22no—
181C23×D3C2×D412yes—
182C23×D3C2×D414yes—
183C23×D3C2×D414yes—
184C23×D3C2×D412yes—
185C23×D3#4112yes—
186C2×C3×D4—28no—
187C2×C3×D4—48no—
188C2×C3×D4—48no—
189C2×C3×D4—44no—
190C2×C3×D4—44no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4C2×D414yes—
208C22×C3×C4C2×D412yes—
209C22×C3×C4C2×D412yes—
210C22×C3×C4#4112yes—
211C22×C3×C4#4112yes—
212C22×C3×C4#4112yes—
213C2×#67—216no—
214C2×#67—216no—
215C2×#67—216no—
216C2×#67—48no—
217C2×#67—48no—
218C2×#67—48no—
219C2×#67—48no—
220C22×Dic3—21no—
221C22×Dic3—21no—
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—22no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3C2×D412yes—
245C22×Dic3C2×D414yes—
246C22×Dic3C2×D414yes—
247C22×Dic3C2×D412yes—
248C22×Dic3#4112yes—
249C2×C4×D3—28no—
250C2×C4×D3—216no—
251C2×C4×D3—28no—
252C2×C4×D3—28no—
253C2×C4×D3—28no—
254C2×C4×D3—44no—
255C2×C4×D3—48no—
256C2×C4×D3—48no—
257C2×C4×D3—48no—
258C2×C4×D3—48no—
259C2×C4×D3—44no—
260C2×C4×D3—44no—
261C2×C4×D3—48no—
262C2×C4×D3—44no—
263C2×C4×D3—44no—
264C3×C22⋊C4—216no—
265C3×C22⋊C4—48no—
266#217—216no—
267#217—216no—
268#217—48no—
269(C2×D3)⋊C4—216no—
270C4⋊Dic3—216no—
271C4⋊Dic3—28no—
272Dic3⋊C4—216no—
273C25—31no—
274C25C22×D312yes—
275C22×D4—24no—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—38no—
280C22×D4—42no—
281C22×D4—64no—
282C22×D4—64no—
283C22×D4—64no—
284C22×D4—64no—
285C22×D4—64no—
286C22×D4—64no—
287C23×C4—32no—
288C23×C4—31no—
289C23×C4—31no—
290C23×C4—31no—
291C23×C4—32no—
292C23×C4—34no—
293C23×C4—34no—
294C23×C4—62no—
295C23×C4—64no—
296C23×C4—64no—
297C23×C4—64no—
298C23×C4—62no—
299C23×C4—62no—
300C23×C4—62no—
301C23×C4—64no—
302C23×C4—62no—
303C23×C4—62no—
304C23×C4—62no—
305C23×C4—122no—
306C23×C4—122no—
307C23×C4C22×D312yes—
308C23×C4C22×D311yescharacteristic
309C23×C4C22×D311yescharacteristic
310C23×C4C22×D311yescharacteristic
311#123—664no—
312#121—632no—
313C2×C4⋊C4—64no—
314C2×C4⋊C4—64no—
315C2×C4⋊C4—64no—
316C2×C4⋊C4—64no—
317C2×C4⋊C4—64no—
318C2×C4⋊C4—62no—
319C2×C4⋊C4—64no—
320C2×C4⋊C4—64no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—38no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—64no—
329C2×C22⋊C4—64no—
330C2×C22⋊C4—64no—
331C2×C22⋊C4—64no—
332C2×C22⋊C4—64no—
333C2×C22⋊C4—64no—
334C2×C22⋊C4—64no—
335C2×C22⋊C4—64no—
336C2×C22⋊C4—64no—
337C2×C22⋊C4—64no—
338C2×C22⋊C4—122no—
339#95—22no—
340#95—22no—
341#95—62no—
342#95—62no—
343#95—64no—
344#95—62no—
345#95—62no—
346#95—64no—
347#95—122no—
348C23×C3—24no—
349C23×C3—24no—
350C23×C3—24no—
351C23×C3—24no—
352C23×C3—24no—
353C23×C3—24no—
354C23×C3—24no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3C22×D411yescharacteristic
384C23×C3C22×D412yes—
385C23×C3C22×D411yescharacteristic
386C23×C3C22×D412yes—
387C23×C3C2×#4111yescharacteristic
388C23×C3C2×#4111yescharacteristic
389C23×C3C2×#4111yescharacteristic
390C23×C3C2×#4111yescharacteristic
391C23×C3C2×#4111yescharacteristic
392C23×C3H(5,𝔽2)12yes—
393C23×C32−1+412yes—
394C22×D3—22no—
395C22×D3—22no—
396C22×D3—22no—
397C22×D3—22no—
398C22×D3—22no—
399C22×D3—22no—
400C22×D3—22no—
401C22×D3—22no—
402C22×D3—24no—
403C22×D3—24no—
404C22×D3—24no—
405C22×D3—24no—
406C22×D3—24no—
407C22×D3—24no—
408C22×D3—24no—
409C22×D3—24no—
410C22×D3—24no—
411C22×D3—24no—
412C22×D3#12018yes—
413C22×D3#12014yes—
414C22×D3#12114yes—
415C22×D3#12118yes—
416C22×D3#12714yes—
417C3×D4—416no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—24no—
427C2×C3×C4—24no—
428C2×C3×C4—24no—
429C2×C3×C4—41no—
430C2×C3×C4—42no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—42no—
434C2×C3×C4—41no—
435C2×C3×C4—42no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4#12314yescomplemented
440#67—432no—
441C2×Dic3—24no—
442C2×Dic3—24no—
443C2×Dic3—24no—
444C2×Dic3—24no—
445C2×Dic3—22no—
446C2×Dic3—22no—
447C2×Dic3—24no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—24no—
452C2×Dic3—24no—
453C2×Dic3—24no—
454C2×Dic3—41no—
455C2×Dic3—42no—
456C2×Dic3—42no—
457C2×Dic3—42no—
458C2×Dic3—42no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—42no—
462C2×Dic3—42no—
463C2×Dic3—41no—
464C2×Dic3—42no—
465C2×Dic3—42no—
466C2×Dic3—42no—
467C2×Dic3—42no—
468C2×Dic3—42no—
469C2×Dic3—42no—
470C4×D3—416no—
471C4×D3—416no—
472C4×D3—416no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—34no—
488C24—32no—
489C24—34no—
490C24—32no—
491C24—32no—
492C24—61no—
493C24—61no—
494C24—61no—
495C24—62no—
496C24—61no—
497C24—62no—
498C24D3×D414yes—
499C24C23×D311yescharacteristic
500C2×D4—28no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—616no—
506C2×D4—616no—
507C2×D4—616no—
508C2×D4—128no—
509C2×D4—128no—
510C2×D4—128no—
511C2×D4—128no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—32no—
529C22×C4—34no—
530C22×C4—32no—
531C22×C4—34no—
532C22×C4—32no—
533C22×C4—68no—
534C22×C4—616no—
535C22×C4—68no—
536C22×C4—68no—
537C22×C4—62no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—61no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—68no—
562C22×C4—124no—
563C22×C4—128no—
564C22×C4—128no—
565C22×C4—128no—
566C22×C4—128no—
567C22×C4—124no—
568C22×C4—124no—
569C22×C4—124no—
570C22×C4—128no—
571C22×C4—124no—
572C22×C4#23512yes—
573C22×C4D3×D414yes—
574C22×C4D3×D412yes—
575C22×C4D3×D412yes—
576C22×C4#23712yes—
577C22×C4#23712yes—
578C4⋊C4—68no—
579C4⋊C4—616no—
580C4⋊C4—616no—
581C22⋊C4—216no—
582C22⋊C4—48no—
583C22⋊C4—616no—
584C22⋊C4—616no—
585C22⋊C4—616no—
586C22⋊C4—128no—
587C22×C3—44no—
588C22×C3—44no—
589C22×C3—44no—
590C22×C3—44no—
591C22×C3—44no—
592C22×C3—44no—
593C22×C3—44no—
594C22×C3—82no—
595C22×C3—82no—
596C22×C3—82no—
597C22×C3—82no—
598C22×C3—82no—
599C22×C3—82no—
600C22×C3—82no—
601C22×C3—82no—
602C22×C3C2×#12011yescharacteristic
603C22×C3C2×#12012yes—
604C22×C3C2×#12111yescharacteristic
605C22×C3C2×#12112yes—
606C22×C3C2×#12311yescharacteristic
607C22×C3#52511yescharacteristic
608C22×C3#52911yescharacteristic
609C22×C3#52911yescharacteristic
610C22×C3C2×#12711yescharacteristic
611C22×C3#53211yescharacteristic
612C22×C3#53211yescharacteristic
613C22×C3#53411yescharacteristic
614C22×C3#53611yescharacteristic
615C22×C3#53712yes—
616C22×C3#53912yes—
617C22×C3#54612yes—
618C22×C3#54612yes—
619C22×C3#54612yes—
620C22×C3#54612yes—
621C22×C3#54712yes—
622C22×C3#54712yes—
623C22×C3#54712yes—
624C22×C3#54712yes—
625C2×D3—24no—
626C2×D3—24no—
627C2×D3—24no—
628C2×D3—24no—
629C2×D3—28no—
630C2×D3—28no—
631C2×D3—28no—
632C2×D3—28no—
633C2×D3—24no—
634C2×D3—24no—
635C2×D3#39218yes—
636C3×C4—24no—
637C3×C4—42no—
638C3×C4—44no—
639C3×C4—42no—
640Dic3—42no—
641Dic3—44no—
642Dic3—42no—
643Dic3—44no—
644Dic3—42no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—34no—
653C23—38no—
654C23—34no—
655C23—34no—
656C23—38no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—64no—
686C23—64no—
687C23—62no—
688C23—62no—
689C23—62no—
690C23—62no—
691C23—64no—
692C23—62no—
693C23—64no—
694C23—62no—
695C23—62no—
696C23—64no—
697C23—64no—
698C23—62no—
699C23—64no—
700C23—64no—
701C23—64no—
702C23—64no—
703C23C2×#23511yescharacteristic
704C23C2×D3×D412yes—
705C23C2×D3×D411yescharacteristic
706C23C2×D3×D412yes—
707C23C2×D3×D411yescharacteristic
708C23C2×#23711yescharacteristic
709C23C2×#23711yescharacteristic
710C23#100412yes—
711C23D3×#4111yescharacteristic
712C23D3×#4111yescharacteristic
713C23#101012yes—
714D4—416no—
715D4—1232no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—62no—
738C2×C4—64no—
739C2×C4—64no—
740C2×C4—62no—
741C2×C4—64no—
742C2×C4—64no—
743C2×C4—64no—
744C2×C4—62no—
745C2×C4—62no—
746C2×C4—64no—
747C2×C4—62no—
748C2×C4—64no—
749C2×C4—64no—
750C2×C4—1216no—
751C2×C4—1216no—
752C2×C4—1216no—
753C2×C4—122no—
754C2×C4—121no—
755C2×C4—121no—
756C2×C4—122no—
757C2×C4—122no—
758C2×C4—122no—
759C2×C4—122no—
760C2×C4—121no—
761C2×C4—122no—
762C2×C4—121no—
763C2×C4—122no—
764C2×C4—122no—
765C2×C4—122no—
766C2×C4—122no—
767C2×C4—122no—
768C2×C4—122no—
769C2×C4#88314yescomplemented
770C2×C3—84no—
771C2×C3C2×#39211yescharacteristic
772C2×C3#240511yescharacteristic
773C2×C3#240611yescharacteristic
774C2×C3#242512yes—
775C2×C3#242512yes—
776C2×C3#243012yes—
777C2×C3#243012yes—
778C2×C3#250111yescharacteristic
779C2×C3#253911yescharacteristic
780C2×C3#261811yescharacteristic
781C2×C3#285411yescharacteristic
782D3—28no—
783C22—38no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—64no—
792C22—64no—
793C22—68no—
794C22—64no—
795C22—64no—
796C22—68no—
797C22—68no—
798C22—64no—
799C22—68no—
800C22—64no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22C2×#88311yescharacteristic
810C22#549012yes—
811C22#554811yescharacteristic
812C22#555112yes—
813C22#555711yescharacteristic
814C22D3×#12011yescharacteristic
815C22D3×#12012yes—
816C22#558911yescharacteristic
817C22#559112yes—
818C22#559112yes—
819C22D3×#12112yes—
820C22D3×#12111yescharacteristic
821C22#560611yescharacteristic
822C22#560812yes—
823C22#561112yes—
824C22#561112yes—
825C22#561212yes—
826C22#565512yes—
827C22#566012yes—
828C22#567511yescharacteristic
829C22#568011yescharacteristic
830C22D3×#12711yescharacteristic
831C22#571611yescharacteristic
832C4—24no—
833C4—42no—
834C4—44no—
835C4—42no—
836C4—122no—
837C4—124no—
838C4—122no—
839C4—124no—
840C4—122no—
841C3#1492611yescharacteristic, complemented, Sylow
842C2—68no—
843C2—84no—
844C2#7385311yescharacteristic
845C2#7489512yes—
846C2#7489612yes—
847C2#7633511yescharacteristic
848C2#7647511yescharacteristic
849C2D3×#39211yescharacteristic
850C2#7675712yes—
851C2#7675811yescharacteristic
852C2#7710711yescharacteristic
853C2#7711512yes—
854C2#7712411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1438C2
prime radicalC22×#938C2
hypercenter#1438D3
hypocenterC3#14926
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C22×#883C2semidirect
3. C2×#4956C2semidirect
4. C2×D3×#95C2semidirect
5. C3×#1438C2semidirect
6. #72131C2semidirect
7. #71547C2semidirect
8. #71546C2semidirect
9. (C2×D3)⋊#95C2semidirect
10. #69420C2semidirect
11. #69419C2semidirect
52. #1438D3semidirect
91. C22×C4×D3D4semidirect
110. C2×(C2×D3)⋊C4D4semidirect
439. C2×C3×C4#123semidirect
769. C2×C4#883semidirect
841. C3#14926semidirect

Maximal subgroups

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

subgroupindex
C22×#9382
C22×#8832
C2×#49562
C2×D3×#952
C3×#14382
#721312
#715472
#715462
(C2×D3)⋊#952
#694202
#694192
#149263