Finite Group Databasebeta

← #10729197

Subgroups — #10729197

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×#894C212yesmaximal, complemented
2C22×#895C211yesmaximal, characteristic
3C2×#4665C212yesmaximal, complemented
4C2×D3×#95C211yesmaximal, characteristic, complemented
5C3×#1444C211yesmaximal, characteristic, complemented
6#71570C212yesmaximal, complemented
7#71568C211yesmaximal, characteristic, complemented
8#69428C212yesmaximal, complemented
9#69426C211yesmaximal, characteristic, complemented
10#69426C211yesmaximal, characteristic, complemented
11(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
12#14926—31nomaximal, Sylow
13C23×D12C2212yes—
14C23×D12C2211yescharacteristic
15C23×C4×D3C2211yescharacteristic
16C23×C4×D3C2211yescharacteristic
17C23×C4×D3C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2212yes—
25C22×(C2×D3)⋊C4C2212yes—
26C22×Dic3⋊C4C2212yes—
27C2×#895—28no—
28C2×#895—24no—
29C2×#894—28no—
30C2×#894—28no—
31C2×#894—28no—
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2212yes—
41#4665—28no—
42D3×#95—24no—
43C22×#123—32no—
44C22×#121—31no—
45C2×#386—32no—
46C22×#95—31no—
47#1444—31no—
48#1444D311yescharacteristic, complemented
49#1439—32no—
50#1439—32no—
51#1438—31no—
52#1438—31no—
53C22⋊#95—31no—
54C24×D3C2312yes—
55C24×D3C2311yescharacteristic
56C23×C3×C4C2311yescharacteristic
57C23×C3×C4C2312yes—
58C23×C3×C4C2312yes—
59C23×C3×C4C2311yescharacteristic
60C23×C3×C4C2311yescharacteristic
61C23×Dic3C2311yescharacteristic
62C23×Dic3C2311yescharacteristic
63C23×Dic3C2312yes—
64C23×Dic3C2311yescharacteristic
65C22×D12—24no—
66C22×D12—24no—
67C22×D12—24no—
68C22×D12—24no—
69C22×D12—24no—
70C22×D12—24no—
71C22×D12—24no—
72C22×D12—22no—
73C22×D12—22no—
74C22×D12—22no—
75C22×D12—42no—
76C22×D12D418yes—
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×C4⋊C4—24no—
93C2×C3×C4⋊C4—24no—
94C2×C3×C4⋊C4—24no—
95C2×C3×C4⋊C4—24no—
96C2×C3×C4⋊C4—22no—
97C2×(C2×D3)⋊C4—24no—
98C2×(C2×D3)⋊C4—24no—
99C2×(C2×D3)⋊C4—24no—
100C2×(C2×D3)⋊C4—24no—
101C2×(C2×D3)⋊C4—24no—
102C2×(C2×D3)⋊C4—24no—
103C2×(C2×D3)⋊C4—24no—
104C2×(C2×D3)⋊C4—24no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—24no—
109C2×(C2×D3)⋊C4—24no—
110C2×(C2×D3)⋊C4—24no—
111C2×(C2×D3)⋊C4—24no—
112C2×(C2×D3)⋊C4—42no—
113C2×(C2×D3)⋊C4—42no—
114C2×(C2×D3)⋊C4D418yescomplemented
115C2×Dic3⋊C4—24no—
116C2×Dic3⋊C4—24no—
117C2×Dic3⋊C4—24no—
118#895—232no—
119#894—264no—
120C3×#95—22no—
121C3×#95—24no—
122C3×#95—22no—
123C3⋊#95—22no—
124C3⋊#95—22no—
125C3⋊#95—22no—
126C3⋊#95—22no—
127C3⋊#95—24no—
128C3⋊#95—42no—
129C23×D4—32no—
130C23×D4—31no—
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—32no—
140C22×C4⋊C4C2×D311yescharacteristic
141C22×C4⋊C4C2×D312yes—
142C22×C22⋊C4—32no—
143C22×C22⋊C4—32no—
144C22×C22⋊C4—32no—
145C22×C22⋊C4—32no—
146C22×C22⋊C4—32no—
147C22×C22⋊C4—32no—
148#386—68no—
149C2×#95—31no—
150C2×#95—31no—
151C2×#95—31no—
152C2×#95—31no—
153C2×#95—32no—
154C2×#95—32no—
155C2×#95—64no—
156C2×#95C2×D311yescharacteristic
157C2×#95C2×D311yescharacteristic
158C2×#95C2×D312yes—
159C24×C3C2411yescharacteristic
160C23×D3—21no—
161C23×D3—21no—
162C23×D3—21no—
163C23×D3—21no—
164C23×D3—22no—
165C23×D3—22no—
166C23×D3—22no—
167C23×D3—22no—
168C23×D3—22no—
169C23×D3—22no—
170C23×D3—22no—
171C23×D3—22no—
172C23×D3—22no—
173C23×D3—22no—
174C23×D3—22no—
175C23×D3—22no—
176C23×D3—22no—
177C23×D3—22no—
178C23×D3—22no—
179C23×D3—22no—
180C23×D3C2×D414yes—
181C23×D3C2×D412yes—
182C23×D3C2×D414yes—
183C23×D3C2×D414yes—
184C23×D3C2×D412yes—
185C23×D3#4112yes—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
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×C4—22no—
208C22×C3×C4C2×D414yes—
209C22×C3×C4C2×D414yes—
210C22×C3×C4C2×D412yes—
211C22×C3×C4C2×D412yes—
212C22×C3×C4#4112yes—
213C22×C3×C4#4112yes—
214C22×C3×C4#4112yes—
215C22×Dic3—21no—
216C22×Dic3—21no—
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—21no—
226C22×Dic3—21no—
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3C2×D412yes—
234C22×Dic3C2×D414yes—
235C22×Dic3C2×D412yes—
236C22×Dic3#4112yes—
237C2×D12—28no—
238C2×D12—216no—
239C2×D12—216no—
240C2×D12—216no—
241C2×D12—48no—
242C2×D12—48no—
243C2×D12—44no—
244C2×D12—48no—
245C2×D12—48no—
246C2×D12—48no—
247C2×D12—48no—
248C2×D12—44no—
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×C4⋊C4—216no—
265C3×C4⋊C4—28no—
266(C2×D3)⋊C4—216no—
267(C2×D3)⋊C4—216no—
268(C2×D3)⋊C4—216no—
269(C2×D3)⋊C4—216no—
270(C2×D3)⋊C4—48no—
271(C2×D3)⋊C4—48no—
272Dic3⋊C4—216no—
273C25—31no—
274C25—32no—
275C22×D4—38no—
276C22×D4—64no—
277C22×D4—64no—
278C22×D4—64no—
279C22×D4—64no—
280C22×D4—64no—
281C22×D4—64no—
282C22×D4—64no—
283C22×D4—62no—
284C22×D4—62no—
285C22×D4—62no—
286C22×D4—122no—
287C23×C4—32no—
288C23×C4—31no—
289C23×C4—31no—
290C23×C4—31no—
291C23×C4—34no—
292C23×C4—34no—
293C23×C4—62no—
294C23×C4—64no—
295C23×C4—64no—
296C23×C4—64no—
297C23×C4—62no—
298C23×C4—62no—
299C23×C4—62no—
300C23×C4—64no—
301C23×C4—62no—
302C23×C4—62no—
303C23×C4—62no—
304C23×C4—122no—
305C23×C4—122no—
306C23×C4C22×D312yes—
307C23×C4C22×D311yescharacteristic
308C23×C4C22×D312yes—
309C23×C4C22×D311yescharacteristic
310C23×C4C22×D311yescharacteristic
311#123—664no—
312#121—632no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—64no—
319C2×C4⋊C4—64no—
320C2×C4⋊C4—64no—
321C2×C22⋊C4—38no—
322C2×C22⋊C4—64no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—64no—
326C2×C22⋊C4—64no—
327C2×C22⋊C4—64no—
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—122no—
338C2×C22⋊C4—122no—
339#95—22no—
340#95—22no—
341#95—24no—
342#95—62no—
343#95—62no—
344#95—64no—
345#95—62no—
346#95—62no—
347#95—122no—
348C23×C3C22×D411yescharacteristic
349C23×C3C22×D412yes—
350C23×C3C22×D411yescharacteristic
351C23×C3C22×D412yes—
352C23×C3C2×#4111yescharacteristic
353C23×C3C2×#4111yescharacteristic
354C23×C3C2×#4111yescharacteristic
355C23×C3C2×#4111yescharacteristic
356C23×C3C2×#4111yescharacteristic
357C23×C3H(5,𝔽2)12yes—
358C23×C32−1+412yes—
359C22×D3—22no—
360C22×D3—22no—
361C22×D3—22no—
362C22×D3—22no—
363C22×D3—22no—
364C22×D3—22no—
365C22×D3—22no—
366C22×D3—22no—
367C22×D3—24no—
368C22×D3—24no—
369C22×D3—24no—
370C22×D3—24no—
371C22×D3—24no—
372C22×D3—24no—
373C22×D3—24no—
374C22×D3—24no—
375C22×D3—24no—
376C22×D3—24no—
377C22×D3—24no—
378C22×D3—24no—
379C22×D3—24no—
380C22×D3—24no—
381C22×D3—24no—
382C22×D3—24no—
383C22×D3—24no—
384C22×D3—42no—
385C22×D3—42no—
386C22×D3—42no—
387C22×D3—42no—
388C22×D3—42no—
389C22×D3—42no—
390C22×D3—42no—
391C22×D3—42no—
392C22×D3—42no—
393C22×D3—42no—
394C22×D3—42no—
395C22×D3—42no—
396C22×D3—42no—
397C22×D3—42no—
398C22×D3—42no—
399C22×D3—42no—
400C22×D3—42no—
401C22×D3—42no—
402C22×D3—42no—
403C22×D3—42no—
404C22×D3—42no—
405C22×D3—42no—
406C22×D3—42no—
407C22×D3—42no—
408C22×D3—42no—
409C22×D3—42no—
410C22×D3—42no—
411C22×D3—42no—
412C22×D3#12018yes—
413C22×D3#12014yes—
414C22×D3#12114yes—
415C22×D3#12118yes—
416C22×D3#12714yes—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—24no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
425C2×C3×C4—22no—
426C2×C3×C4—24no—
427C2×C3×C4—22no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—24no—
431C2×C3×C4—41no—
432C2×C3×C4—42no—
433C2×C3×C4—42no—
434C2×C3×C4—42no—
435C2×C3×C4—42no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—41no—
441C2×C3×C4—42no—
442C2×C3×C4—42no—
443C2×C3×C4—42no—
444C2×C3×C4—42no—
445C2×C3×C4#12314yescomplemented
446C2×Dic3—24no—
447C2×Dic3—24no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—24no—
454C2×Dic3—24no—
455C2×Dic3—24no—
456C2×Dic3—41no—
457C2×Dic3—42no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—42no—
461C2×Dic3—41no—
462C2×Dic3—42no—
463C2×Dic3—42no—
464C2×Dic3—42no—
465C2×Dic3—42no—
466C2×Dic3—42no—
467C2×Dic3—42no—
468D12—416no—
469D12—432no—
470C4×D3—416no—
471C4×D3—416no—
472C4×D3—416no—
473C24—34no—
474C24—32no—
475C24—34no—
476C24—32no—
477C24—32no—
478C24—34no—
479C24—61no—
480C24—61no—
481C24—61no—
482C24—62no—
483C24—61no—
484C24—62no—
485C24—62no—
486C24—62no—
487C24—62no—
488C24—62no—
489C24—62no—
490C24—62no—
491C24—62no—
492C24—62no—
493C24—62no—
494C24—62no—
495C24—62no—
496C24—62no—
497C24—62no—
498C24—62no—
499C24C23×D311yescharacteristic
500C2×D4—616no—
501C2×D4—616no—
502C2×D4—616no—
503C2×D4—68no—
504C2×D4—128no—
505C2×D4—128no—
506C2×D4—124no—
507C2×D4—128no—
508C2×D4—128no—
509C2×D4—128no—
510C2×D4—128no—
511C2×D4—124no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
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—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—32no—
535C22×C4—34no—
536C22×C4—32no—
537C22×C4—32no—
538C22×C4—68no—
539C22×C4—616no—
540C22×C4—68no—
541C22×C4—68no—
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—62no—
556C22×C4—61no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—62no—
560C22×C4—68no—
561C22×C4—124no—
562C22×C4—128no—
563C22×C4—128no—
564C22×C4—128no—
565C22×C4—128no—
566C22×C4—124no—
567C22×C4—124no—
568C22×C4—124no—
569C22×C4—128no—
570C22×C4—124no—
571C22×C4#23512yes—
572C22×C4D3×D414yes—
573C22×C4D3×D412yes—
574C22×C4D3×D414yes—
575C22×C4D3×D412yes—
576C22×C4#23912yes—
577C22×C4#23912yes—
578C4⋊C4—28no—
579C4⋊C4—216no—
580C4⋊C4—616no—
581C22⋊C4—616no—
582C22⋊C4—616no—
583C22⋊C4—616no—
584C22⋊C4—616no—
585C22⋊C4—128no—
586C22⋊C4—128no—
587C22×C3C2×#12011yescharacteristic
588C22×C3C2×#12012yes—
589C22×C3C2×#12111yescharacteristic
590C22×C3C2×#12112yes—
591C22×C3C2×#12311yescharacteristic
592C22×C3#52511yescharacteristic
593C22×C3#52911yescharacteristic
594C22×C3#52911yescharacteristic
595C22×C3C2×#12711yescharacteristic
596C22×C3#53211yescharacteristic
597C22×C3#53211yescharacteristic
598C22×C3#53411yescharacteristic
599C22×C3#53611yescharacteristic
600C22×C3#53712yes—
601C22×C3#53912yes—
602C22×C3#54612yes—
603C22×C3#54612yes—
604C22×C3#54612yes—
605C22×C3#54612yes—
606C22×C3#54712yes—
607C22×C3#54712yes—
608C22×C3#54712yes—
609C22×C3#54712yes—
610C2×D3—24no—
611C2×D3—24no—
612C2×D3—24no—
613C2×D3—24no—
614C2×D3—28no—
615C2×D3—28no—
616C2×D3—28no—
617C2×D3—28no—
618C2×D3—24no—
619C2×D3—24no—
620C2×D3—44no—
621C2×D3—44no—
622C2×D3—44no—
623C2×D3—44no—
624C2×D3—44no—
625C2×D3—44no—
626C2×D3—44no—
627C2×D3—82no—
628C2×D3—82no—
629C2×D3—82no—
630C2×D3—82no—
631C2×D3—82no—
632C2×D3—82no—
633C2×D3—82no—
634C2×D3—82no—
635C2×D3#39218yes—
636C3×C4—24no—
637C3×C4—42no—
638C3×C4—44no—
639C3×C4—44no—
640C3×C4—42no—
641Dic3—42no—
642Dic3—42no—
643Dic3—44no—
644Dic3—42no—
645C23—34no—
646C23—38no—
647C23—34no—
648C23—34no—
649C23—38no—
650C23—62no—
651C23—64no—
652C23—62no—
653C23—64no—
654C23—62no—
655C23—62no—
656C23—64no—
657C23—64no—
658C23—62no—
659C23—64no—
660C23—62no—
661C23—64no—
662C23—62no—
663C23—62no—
664C23—64no—
665C23—64no—
666C23—64no—
667C23—64no—
668C23—64no—
669C23—64no—
670C23—64no—
671C23—64no—
672C23—64no—
673C23—64no—
674C23—64no—
675C23—122no—
676C23—122no—
677C23—122no—
678C23—122no—
679C23—122no—
680C23—122no—
681C23—122no—
682C23—122no—
683C23—122no—
684C23—122no—
685C23—122no—
686C23—122no—
687C23—122no—
688C23—122no—
689C23—122no—
690C23—122no—
691C23—122no—
692C23—122no—
693C23—122no—
694C23—122no—
695C23—122no—
696C23—122no—
697C23—122no—
698C23—122no—
699C23—122no—
700C23—122no—
701C23—122no—
702C23—122no—
703C23C2×#23511yescharacteristic
704C23C2×D3×D411yescharacteristic
705C23C2×D3×D412yes—
706C23C2×D3×D411yescharacteristic
707C23C2×D3×D412yes—
708C23C2×#23911yescharacteristic
709C23C2×#23911yescharacteristic
710C23#100712yes—
711C23D3×#4111yescharacteristic
712C23D3×#4111yescharacteristic
713C23#100912yes—
714D4—1216no—
715D4—1232no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—62no—
745C2×C4—64no—
746C2×C4—64no—
747C2×C4—62no—
748C2×C4—64no—
749C2×C4—62no—
750C2×C4—64no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—64no—
754C2×C4—1216no—
755C2×C4—1216no—
756C2×C4—1216no—
757C2×C4—121no—
758C2×C4—121no—
759C2×C4—121no—
760C2×C4—122no—
761C2×C4—122no—
762C2×C4—122no—
763C2×C4—121no—
764C2×C4—122no—
765C2×C4—122no—
766C2×C4—122no—
767C2×C4—122no—
768C2×C4—122no—
769C2×C4#89414yescomplemented
770C2×C3C2×#39211yescharacteristic
771C2×C3#240511yescharacteristic
772C2×C3#240611yescharacteristic
773C2×C3#242512yes—
774C2×C3#242512yes—
775C2×C3#243012yes—
776C2×C3#243012yes—
777C2×C3#250111yescharacteristic
778C2×C3#253911yescharacteristic
779C2×C3#261811yescharacteristic
780C2×C3#285411yescharacteristic
781D3—28no—
782D3—84no—
783C22—38no—
784C22—64no—
785C22—64no—
786C22—64no—
787C22—68no—
788C22—68no—
789C22—64no—
790C22—68no—
791C22—64no—
792C22—68no—
793C22—64no—
794C22—124no—
795C22—124no—
796C22—124no—
797C22—124no—
798C22—124no—
799C22—124no—
800C22—124no—
801C22—242no—
802C22—242no—
803C22—242no—
804C22—242no—
805C22—242no—
806C22—242no—
807C22—242no—
808C22—242no—
809C22C2×#89411yescharacteristic
810C22#550712yes—
811C22#554811yescharacteristic
812C22#555012yes—
813C22#558011yescharacteristic
814C22D3×#12011yescharacteristic
815C22D3×#12012yes—
816C22D3×#12112yes—
817C22D3×#12111yescharacteristic
818C22#562711yescharacteristic
819C22#562912yes—
820C22#563012yes—
821C22#563012yes—
822C22#563112yes—
823C22#565311yescharacteristic
824C22#565412yes—
825C22#569111yescharacteristic
826C22#569212yes—
827C22D3×#12711yescharacteristic
828C22#572411yescharacteristic
829C22#572511yescharacteristic
830C22#572612yes—
831C22#572612yes—
832C4—24no—
833C4—42no—
834C4—44no—
835C4—42no—
836C4—44no—
837C4—122no—
838C4—122no—
839C4—124no—
840C4—122no—
841C3#1492611yescharacteristic, complemented, Sylow
842C2—68no—
843C2—244no—
844C2#7432811yescharacteristic
845C2#7459911yescharacteristic
846C2#7460612yes—
847C2#7621712yes—
848C2#7628611yescharacteristic
849C2D3×#39211yescharacteristic
850C2#7724911yescharacteristic
851C2#7725012yes—
852C2#7794812yes—
853C2#7796211yescharacteristic
854C2#7810711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1444C2
prime radicalC22×#895C2
hypercenter#1444D3
hypocenterC3#14926
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
1. C22×#894C2semidirect
3. C2×#4665C2semidirect
4. C2×D3×#95C2semidirect
5. C3×#1444C2semidirect
6. #71570C2semidirect
7. #71568C2semidirect
8. #69428C2semidirect
9. #69426C2semidirect
10. #69426C2semidirect
11. (C2×D3)⋊#95C2semidirect
48. #1444D3semidirect
91. C22×C4×D3D4semidirect
114. C2×(C2×D3)⋊C4D4semidirect
445. C2×C3×C4#123semidirect
769. C2×C4#894semidirect
841. C3#14926semidirect

Maximal subgroups

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

subgroupindex
C22×#8942
C22×#8952
C2×#46652
C2×D3×#952
C3×#14442
#715702
#715682
#694282
#694262
(C2×D3)⋊#952
#149263