Finite Group Databasebeta

← #10732612

Subgroups — #10732612

Order 768.

3142 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#940C211yesmaximal, characteristic
2C22×#885C212yesmaximal, complemented
3C2×#4957C212yesmaximal, complemented
4C2×#4646C211yesmaximal, characteristic, complemented
5C3×#1438C211yesmaximal, characteristic, complemented
6#72131C211yesmaximal, characteristic, complemented
7#71550C212yesmaximal, complemented
8#71550C212yesmaximal, complemented
9#69426C211yesmaximal, characteristic, complemented
10#69426C211yesmaximal, characteristic, complemented
11Dic3×#95C211yesmaximal, characteristic, complemented
12#15227—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×#67C2212yes—
15C23×#67C2212yes—
16C23×D12C2211yescharacteristic
17C23×Dic6C2211yescharacteristic
18C22×C3×C22⋊C4C2212yes—
19C22×C3×C22⋊C4C2212yes—
20C22×#217C2212yes—
21C22×#217C2212yes—
22C2×#940—28no—
23C2×#940—24no—
24C22×(C2×D3)⋊C4C2212yes—
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2212yes—
27C22×(C2×D3)⋊C4C2212yes—
28C22×Dic3⋊C4C2211yescharacteristic
29C22×C4×Dic3C2211yescharacteristic
30C22×C4×Dic3C2212yes—
31C2×#885—28no—
32C2×#885—28no—
33C2×#885—28no—
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41#4957—28no—
42#4646—24no—
43C22×#127—31no—
44C22×#124—32no—
45C2×#391—31no—
46C2×#390—32no—
47#1438—31no—
48#1438—31no—
49#1438—31no—
50#1438—32no—
51#1438—32no—
52#1438D311yescharacteristic, complemented
53C4×#95—31no—
54C25×C3C2312yes—
55C24×D3C2312yes—
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×C4C2311yescharacteristic
63C23×C3×C4C2312yes—
64C23×C3×C4C2311yescharacteristic
65C22×#67—24no—
66C22×#67—24no—
67C22×#67—24no—
68C22×#67—24no—
69C22×#67—24no—
70C22×#67—24no—
71C22×#67—24no—
72C22×#67—24no—
73C22×#67—24no—
74C22×#67—24no—
75C22×#67—24no—
76C22×#67—42no—
77C22×#67—42no—
78C22×#67D418yes—
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2312yes—
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C22×D12—24no—
85C22×D12—22no—
86C22×D12—22no—
87C22×D12—22no—
88C22×D12—42no—
89C22×Dic6—22no—
90C22×Dic6—24no—
91C22×Dic6—24no—
92C22×Dic6—22no—
93C22×Dic6D414yescomplemented
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—24no—
96C2×C3×C22⋊C4—24no—
97C2×C3×C22⋊C4—24no—
98C2×C3×C22⋊C4—42no—
99C2×C3×C22⋊C4—42no—
100C2×#217—24no—
101C2×#217—24no—
102C2×#217—24no—
103C2×#217—24no—
104C2×#217—42no—
105C2×#217—42no—
106#940—232no—
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—24no—
113C2×(C2×D3)⋊C4—24no—
114C2×(C2×D3)⋊C4—24no—
115C2×(C2×D3)⋊C4—42no—
116C2×(C2×D3)⋊C4—42no—
117C2×(C2×D3)⋊C4—42no—
118C2×(C2×D3)⋊C4—42no—
119C2×Dic3⋊C4—22no—
120C2×Dic3⋊C4—24no—
121C2×C4×Dic3—24no—
122C2×C4×Dic3—24no—
123C2×C4×Dic3—24no—
124C2×C4×Dic3D414yes—
125C2×C4×Dic3D418yescomplemented
126#885—264no—
127C3×#95—22no—
128C3×#95—22no—
129C3⋊#95—22no—
130C3⋊#95—22no—
131C3⋊#95—22no—
132C3⋊#95—22no—
133C3⋊#95—24no—
134C23×Q8—31no—
135C23×D4—32no—
136C23×D4—32no—
137C23×D4—31no—
138C23×D4C2×D311yescharacteristic
139C2×#127—64no—
140C2×#127—68no—
141C2×#124—68no—
142C2×#124—68no—
143C2×#124—68no—
144C22×C4⋊C4—31no—
145C22×C22⋊C4—32no—
146C22×C22⋊C4—32no—
147C22×C22⋊C4—32no—
148C22×C22⋊C4—32no—
149C22×C22⋊C4—32no—
150C22×C22⋊C4—32no—
151C22×C22⋊C4C2×D312yes—
152C22×C22⋊C4C2×D312yes—
153C22×C42—32no—
154C22×C42—31no—
155#391—64no—
156#390—68no—
157C2×#95—32no—
158C2×#95—31no—
159C2×#95—31no—
160C2×#95—31no—
161C2×#95—31no—
162C2×#95C2×D311yescharacteristic
163C2×#95C2×D311yescharacteristic
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×C3—22no—
174C24×C3—22no—
175C24×C3—22no—
176C24×C3—22no—
177C24×C3—22no—
178C24×C3C2×D414yes—
179C24×C3C2411yescharacteristic
180C23×D3—22no—
181C23×D3—22no—
182C23×D3—22no—
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×D3C2×D414yes—
195C2×C3×D4—28no—
196C2×C3×D4—48no—
197C2×C3×D4—48no—
198C2×C3×D4—44no—
199C2×C3×D4—44no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—21no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—21no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—21no—
213C22×C3×C4—22no—
214C22×C3×C4—21no—
215C22×C3×C4—22no—
216C22×C3×C4—21no—
217C22×C3×C4C2×D414yes—
218C22×C3×C4C2×D412yes—
219C22×C3×C4C2×D412yes—
220C22×C3×C4#4112yes—
221C22×C3×C4#4112yes—
222C2×#67—216no—
223C2×#67—216no—
224C2×#67—216no—
225C2×#67—216no—
226C2×#67—48no—
227C2×#67—48no—
228C2×#67—48no—
229C2×#67—48no—
230C2×#67—48no—
231C2×#67—48no—
232C2×#67—48no—
233C2×#67—48no—
234C2×#67—48no—
235C2×#67—48no—
236C22×Dic3—22no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3—21no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—21no—
250C22×Dic3—22no—
251C22×Dic3—21no—
252C22×Dic3—22no—
253C22×Dic3—21no—
254C22×Dic3C2×D414yes—
255C22×Dic3C2×D412yes—
256C22×Dic3C2×D412yes—
257C22×Dic3C2×D414yes—
258C22×Dic3C2×D412yes—
259C22×Dic3C2×D412yes—
260C22×Dic3C2×D414yes—
261C22×Dic3#4114yes—
262C22×Dic3#4112yes—
263C2×D12—28no—
264C2×D12—48no—
265C2×D12—48no—
266C2×D12—44no—
267C2×D12—44no—
268C2×Dic6—216no—
269C2×Dic6—28no—
270C2×Dic6—44no—
271C2×Dic6—48no—
272C2×Dic6—44no—
273C3×C22⋊C4—216no—
274C3×C22⋊C4—48no—
275#217—216no—
276#217—48no—
277(C2×D3)⋊C4—216no—
278(C2×D3)⋊C4—216no—
279(C2×D3)⋊C4—48no—
280(C2×D3)⋊C4—48no—
281Dic3⋊C4—44no—
282C4×Dic3—216no—
283C4×Dic3—28no—
284C25—32no—
285C25C22×D312yes—
286C22×Q8—34no—
287C22×Q8—64no—
288C22×Q8—64no—
289C22×Q8—62no—
290C22×Q8—62no—
291C22×D4—24no—
292C22×D4—22no—
293C22×D4—22no—
294C22×D4—22no—
295C22×D4—38no—
296C22×D4—42no—
297C22×D4—64no—
298C22×D4—64no—
299C22×D4—64no—
300C22×D4—64no—
301C22×D4—64no—
302C22×D4—64no—
303C22×D4—64no—
304C22×D4—64no—
305C22×D4—64no—
306C22×D4—64no—
307C22×D4—64no—
308C22×D4—64no—
309C22×D4—62no—
310C22×D4—62no—
311C22×D4—62no—
312C22×D4—122no—
313C22×D4—122no—
314C22×D4—122no—
315C23×C4—31no—
316C23×C4—31no—
317C23×C4—31no—
318C23×C4—32no—
319C23×C4—31no—
320C23×C4C22×D311yescharacteristic
321C23×C4C22×D311yescharacteristic
322C23×C4C22×D312yes—
323C23×C4C22×D311yescharacteristic
324#127—632no—
325#124—664no—
326C2×C4⋊C4—64no—
327C2×C4⋊C4—62no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—64no—
335C2×C22⋊C4—64no—
336C2×C22⋊C4—64no—
337C2×C22⋊C4—64no—
338C2×C22⋊C4—64no—
339C2×C22⋊C4—64no—
340C2×C22⋊C4—64no—
341C2×C22⋊C4—64no—
342C2×C22⋊C4—64no—
343C2×C22⋊C4—64no—
344C2×C22⋊C4—64no—
345C2×C22⋊C4—64no—
346C2×C22⋊C4—122no—
347C2×C22⋊C4—122no—
348C2×C22⋊C4—122no—
349C2×C22⋊C4—122no—
350C2×C22⋊C4—122no—
351C2×C22⋊C4—122no—
352C2×C42—38no—
353C2×C42—34no—
354C2×C42—64no—
355C2×C42—64no—
356C2×C42—64no—
357#95—22no—
358#95—22no—
359#95—64no—
360#95—62no—
361#95—62no—
362#95—62no—
363#95—62no—
364C23×C3—24no—
365C23×C3—24no—
366C23×C3—24no—
367C23×C3—24no—
368C23×C3—24no—
369C23×C3—24no—
370C23×C3—24no—
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×C3—42no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3—42no—
389C23×C3—42no—
390C23×C3—42no—
391C23×C3—42no—
392C23×C3—42no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3C22×D412yes—
400C23×C3C22×D411yescharacteristic
401C23×C3C22×D411yescharacteristic
402C23×C3C22×D412yes—
403C23×C3C2×#4111yescharacteristic
404C23×C3C2×#4111yescharacteristic
405C23×C3C2×#4111yescharacteristic
406C23×C3C2×#4112yes—
407C23×C3H(5,𝔽2)12yes—
408C23×C3H(5,𝔽2)11yescharacteristic
409C23×C3H(5,𝔽2)11yescharacteristic
410C22×D3—24no—
411C22×D3—24no—
412C22×D3—24no—
413C22×D3—24no—
414C22×D3—24no—
415C22×D3—24no—
416C22×D3—24no—
417C22×D3—42no—
418C22×D3—42no—
419C22×D3—42no—
420C22×D3—42no—
421C22×D3—42no—
422C22×D3—42no—
423C22×D3—42no—
424C22×D3—42no—
425C22×D3—42no—
426C22×D3—42no—
427C22×D3—42no—
428C22×D3—42no—
429C22×D3—42no—
430C22×D3—42no—
431C22×D3—42no—
432C22×D3—42no—
433C22×D3—42no—
434C22×D3—42no—
435C22×D3—42no—
436C22×D3—42no—
437C22×D3—42no—
438C22×D3—42no—
439C22×D3—42no—
440C22×D3—42no—
441C22×D3—42no—
442C22×D3—42no—
443C22×D3—42no—
444C22×D3—42no—
445C3×D4—416no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—24no—
449C2×C3×C4—24no—
450C2×C3×C4—24no—
451C2×C3×C4—24no—
452C2×C3×C4—22no—
453C2×C3×C4—24no—
454C2×C3×C4—24no—
455C2×C3×C4—41no—
456C2×C3×C4—42no—
457C2×C3×C4—41no—
458C2×C3×C4—42no—
459C2×C3×C4—42no—
460C2×C3×C4—42no—
461C2×C3×C4—42no—
462C2×C3×C4—41no—
463C2×C3×C4—42no—
464C2×C3×C4—42no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4#12414yescomplemented
468#67—432no—
469#67—432no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—24no—
473C2×Dic3—24no—
474C2×Dic3—24no—
475C2×Dic3—24no—
476C2×Dic3—22no—
477C2×Dic3—24no—
478C2×Dic3—24no—
479C2×Dic3—41no—
480C2×Dic3—42no—
481C2×Dic3—41no—
482C2×Dic3—42no—
483C2×Dic3—42no—
484C2×Dic3—42no—
485C2×Dic3—42no—
486C2×Dic3—41no—
487C2×Dic3—42no—
488C2×Dic3—42no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3#12018yes—
492C2×Dic3#12014yes—
493C2×Dic3#12114yes—
494C2×Dic3#12118yes—
495C2×Dic3#12414yescomplemented
496C2×Dic3#12714yes—
497D12—416no—
498Dic6—416no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—34no—
514C24—62no—
515C24—62no—
516C24—62no—
517C24—62no—
518C24—62no—
519C24—62no—
520C24—62no—
521C24—62no—
522C24—62no—
523C24—62no—
524C24—62no—
525C24—62no—
526C24—62no—
527C24—62no—
528C24D3×D414yes—
529C24C23×D311yescharacteristic
530C2×Q8—616no—
531C2×Q8—68no—
532C2×Q8—124no—
533C2×Q8—124no—
534C2×Q8—128no—
535C2×D4—28no—
536C2×D4—48no—
537C2×D4—48no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—68no—
541C2×D4—616no—
542C2×D4—616no—
543C2×D4—616no—
544C2×D4—616no—
545C2×D4—128no—
546C2×D4—128no—
547C2×D4—124no—
548C2×D4—128no—
549C2×D4—128no—
550C2×D4—128no—
551C2×D4—128no—
552C2×D4—128no—
553C2×D4—128no—
554C2×D4—128no—
555C2×D4—128no—
556C2×D4—128no—
557C2×D4—128no—
558C2×D4—124no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—32no—
577C22×C4—34no—
578C22×C4—34no—
579C22×C4—32no—
580C22×C4—32no—
581C22×C4—32no—
582C22×C4—34no—
583C22×C4—34no—
584C22×C4—32no—
585C22×C4—62no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—62no—
589C22×C4—61no—
590C22×C4—62no—
591C22×C4—62no—
592C22×C4—62no—
593C22×C4—62no—
594C22×C4—62no—
595C22×C4—62no—
596C22×C4—61no—
597C22×C4—62no—
598C22×C4—61no—
599C22×C4—62no—
600C22×C4—61no—
601C22×C4—62no—
602C22×C4—61no—
603C22×C4#23512yes—
604C22×C4D3×D414yes—
605C22×C4D3×D412yes—
606C22×C4D3×D412yes—
607C22×C4#23712yes—
608C4⋊C4—124no—
609C22⋊C4—216no—
610C22⋊C4—48no—
611C22⋊C4—616no—
612C22⋊C4—616no—
613C22⋊C4—616no—
614C22⋊C4—128no—
615C22⋊C4—128no—
616C22⋊C4—128no—
617C42—616no—
618C42—68no—
619C22×C3—44no—
620C22×C3—44no—
621C22×C3—44no—
622C22×C3—44no—
623C22×C3—44no—
624C22×C3—44no—
625C22×C3—44no—
626C22×C3—82no—
627C22×C3—82no—
628C22×C3—82no—
629C22×C3—82no—
630C22×C3—82no—
631C22×C3—82no—
632C22×C3—82no—
633C22×C3—82no—
634C22×C3C2×#12012yes—
635C22×C3C2×#12011yescharacteristic
636C22×C3C2×#12112yes—
637C22×C3C2×#12111yescharacteristic
638C22×C3C2×#12411yescharacteristic
639C22×C3C2×#12411yescharacteristic
640C22×C3C2×#12711yescharacteristic
641C22×C3#53212yes—
642C22×C3#53212yes—
643C22×C3#53512yes—
644C22×C3#53511yescharacteristic
645C22×C3#53512yes—
646C22×C3#53511yescharacteristic
647C22×C3#54612yes—
648C22×C3#54612yes—
649C22×C3#54612yes—
650C22×C3#54612yes—
651C22×C3#55011yescharacteristic
652C22×C3#55011yescharacteristic
653C22×C3#55012yes—
654C22×C3#55912yes—
655C22×C3#55911yescharacteristic
656C22×C3#55911yescharacteristic
657C2×D3—44no—
658C2×D3—44no—
659C2×D3—44no—
660C2×D3—44no—
661C2×D3—44no—
662C2×D3—44no—
663C2×D3—44no—
664C2×D3—82no—
665C2×D3—82no—
666C2×D3—82no—
667C2×D3—82no—
668C2×D3—82no—
669C2×D3—82no—
670C2×D3—82no—
671C2×D3—82no—
672C3×C4—24no—
673C3×C4—42no—
674C3×C4—44no—
675C3×C4—81no—
676Dic3—24no—
677Dic3—42no—
678Dic3—44no—
679Dic3—81no—
680Dic3#39218yes—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—64no—
717C23—64no—
718C23—64no—
719C23—64no—
720C23—64no—
721C23—64no—
722C23—64no—
723C23—122no—
724C23—122no—
725C23—122no—
726C23—122no—
727C23—122no—
728C23—122no—
729C23—122no—
730C23—122no—
731C23—122no—
732C23—122no—
733C23—122no—
734C23—122no—
735C23—122no—
736C23—122no—
737C23—122no—
738C23—122no—
739C23—122no—
740C23—122no—
741C23—122no—
742C23—122no—
743C23—122no—
744C23—122no—
745C23—122no—
746C23—122no—
747C23—122no—
748C23—122no—
749C23—122no—
750C23—122no—
751C23C2×#23511yescharacteristic
752C23C2×D3×D412yes—
753C23C2×D3×D411yescharacteristic
754C23C2×D3×D412yes—
755C23C2×D3×D411yescharacteristic
756C23C2×#23711yescharacteristic
757C23#100412yes—
758C23#100411yescharacteristic
759C23D3×#4112yes—
760C23D3×#4111yescharacteristic
761C23#100911yescharacteristic
762Q8—1216no—
763D4—416no—
764D4—1216no—
765D4—1232no—
766D4—1232no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—34no—
777C2×C4—34no—
778C2×C4—38no—
779C2×C4—38no—
780C2×C4—34no—
781C2×C4—34no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—64no—
795C2×C4—62no—
796C2×C4—62no—
797C2×C4—64no—
798C2×C4—64no—
799C2×C4—64no—
800C2×C4—64no—
801C2×C4—62no—
802C2×C4—64no—
803C2×C4—122no—
804C2×C4—121no—
805C2×C4—122no—
806C2×C4—122no—
807C2×C4—121no—
808C2×C4—122no—
809C2×C4—122no—
810C2×C4—121no—
811C2×C4—122no—
812C2×C4—121no—
813C2×C4—122no—
814C2×C4—121no—
815C2×C4#88514yescomplemented
816C2×C3—84no—
817C2×C3C2×#39211yescharacteristic
818C2×C3#243112yes—
819C2×C3#243112yes—
820C2×C3#243511yescharacteristic
821C2×C3#243511yescharacteristic
822C2×C3#254412yes—
823C2×C3#254412yes—
824C2×C3#254811yescharacteristic
825C2×C3#254811yescharacteristic
826C2×C3#265711yescharacteristic
827C2×C3#285811yescharacteristic
828D3—84no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—124no—
845C22—124no—
846C22—124no—
847C22—124no—
848C22—124no—
849C22—124no—
850C22—124no—
851C22—242no—
852C22—242no—
853C22—242no—
854C22—242no—
855C22—242no—
856C22—242no—
857C22—242no—
858C22—242no—
859C22#549012yes—
860C22C2×#88511yescharacteristic
861C22#554812yes—
862C22#555311yescharacteristic
863C22#555911yescharacteristic
864C22D3×#12011yescharacteristic
865C22D3×#12012yes—
866C22#559112yes—
867C22#559212yes—
868C22#559211yescharacteristic
869C22#559612yes—
870C22#559912yes—
871C22D3×#12112yes—
872C22D3×#12111yescharacteristic
873C22#560711yescharacteristic
874C22#560712yes—
875C22#561012yes—
876C22#565412yes—
877C22#566412yes—
878C22D3×#12411yescharacteristic
879C22#568111yescharacteristic
880C22D3×#12711yescharacteristic
881C22#571811yescharacteristic
882C4—24no—
883C4—38no—
884C4—44no—
885C4—42no—
886C4—64no—
887C4—81no—
888C4—124no—
889C4—122no—
890C4—241no—
891C3#1522711yescharacteristic, complemented, Sylow
892C2—84no—
893C2—244no—
894C2#7382711yescharacteristic
895C2#7470012yes—
896C2#7475312yes—
897C2#7635311yescharacteristic
898C2#7642411yescharacteristic
899C2#7667212yes—
900C2#7670611yescharacteristic
901C2D3×#39211yescharacteristic
902C2#7690511yescharacteristic
903C2#7694512yes—
904C2#7694611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1438C2
prime radicalC22×#940C2
hypercenter#1438D3
hypocenterC3#15227
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C22×#885C2semidirect
3. C2×#4957C2semidirect
4. C2×#4646C2semidirect
5. C3×#1438C2semidirect
6. #72131C2semidirect
7. #71550C2semidirect
8. #71550C2semidirect
9. #69426C2semidirect
10. #69426C2semidirect
11. Dic3×#95C2semidirect
52. #1438D3semidirect
93. C22×Dic6D4semidirect
125. C2×C4×Dic3D4semidirect
467. C2×C3×C4#124semidirect
495. C2×Dic3#124semidirect
815. C2×C4#885semidirect
891. C3#15227semidirect

Maximal subgroups

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

subgroupindex
C22×#9402
C22×#8852
C2×#49572
C2×#46462
C3×#14382
#721312
#715502
#694262
Dic3×#952
#152273