Finite Group Databasebeta

← #10726655

Subgroups — #10726655

Order 768.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
2C22×#882C211yesmaximal, characteristic
3C2×C3×#380C211yesmaximal, characteristic, complemented
4C2×#5213C211yesmaximal, characteristic, complemented
5C2×#4991C212yesmaximal, complemented
6C2×#4955C211yesmaximal, characteristic, complemented
7C2×#4958C211yesmaximal, characteristic, complemented
8#71570C212yesmaximal, complemented
9#71544C211yesmaximal, characteristic, complemented
10#69429C212yesmaximal, complemented
11#69426C212yesmaximal, complemented
12#14725—31nomaximal, Sylow
13C25×D3C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C23×#67C2211yescharacteristic
16C24×Dic3C2211yescharacteristic
17C23×D12C2212yes—
18C22×C3×C4⋊C4C2212yescomplemented
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×#217C2211yescharacteristic
22C22×(C2×D3)⋊C4—24no—
23C22×(C2×D3)⋊C4—28no—
24C22×(C2×D3)⋊C4C2212yes—
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2212yes—
27C22×(C2×D3)⋊C4C2212yes—
28C22×(C2×D3)⋊C4C2212yes—
29C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
30C22×(C2×D3)⋊C4C2212yescomplemented
31C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
32C2×#882—24no—
33C2×#882—24no—
34C2×#882—24no—
35C3×#380—24no—
36C2×C3×#95C2212yescomplemented
37#5213—24no—
38C2×C3⋊#95C2212yescomplemented
39C2×C3⋊#95C2211yescharacteristic, complemented
40C2×C3⋊#95C2212yescomplemented
41C2×C3⋊#95C2211yescharacteristic, complemented
42C2×C3⋊#95C2212yescomplemented
43#4991—28no—
44#4958—24no—
45#4955—24no—
46C22×#120—31no—
47C23×C22⋊C4—31no—
48C2×#394—32no—
49C2×#386—31no—
50C2×#386—31no—
51C2×#380D311yescharacteristic, complemented
52C2×#379—31no—
53#1440—32no—
54#1439—32no—
55#1438—32no—
56C22⋊#95—31no—
57C25×C3C2311yescharacteristic
58C24×D3—22no—
59C24×D3—22no—
60C24×D3—24no—
61C24×D3—24no—
62C24×D3—22no—
63C24×D3—22no—
64C24×D3—22no—
65C24×D3—22no—
66C24×D3—42no—
67C24×D3—42no—
68C24×D3D414yes—
69C24×D3C2311yescharacteristic
70C24×D3C2312yes—
71C23×C3×C4—22no—
72C23×C3×C4—22no—
73C23×C3×C4—24no—
74C23×C3×C4—42no—
75C23×C3×C4D414yescomplemented
76C23×C3×C4C2312yes—
77C23×C3×C4C2312yes—
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C22×#67—22no—
81C22×#67—22no—
82C22×#67—22no—
83C22×#67—22no—
84C22×#67—22no—
85C22×#67—22no—
86C22×#67D414yes—
87C23×Dic3—22no—
88C23×Dic3—24no—
89C23×Dic3—22no—
90C23×Dic3—22no—
91C23×Dic3—42no—
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2312yes—
95C23×Dic3C2311yescharacteristic
96C22×D12—24no—
97C22×D12—24no—
98C22×D12—24no—
99C22×D12—24no—
100C22×D12—24no—
101C22×D12—42no—
102C22×D12—42no—
103C2×C3×C4⋊C4—24no—
104C2×C3×C4⋊C4—24no—
105C2×C3×C4⋊C4—42no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4D414yes—
112C2×#217—22no—
113C2×#217—22no—
114C2×#217—22no—
115C2×(C2×D3)⋊C4—232no—
116C2×(C2×D3)⋊C4—24no—
117C2×(C2×D3)⋊C4—24no—
118C2×(C2×D3)⋊C4—24no—
119C2×(C2×D3)⋊C4—24no—
120C2×(C2×D3)⋊C4—24no—
121C2×(C2×D3)⋊C4—24no—
122C2×(C2×D3)⋊C4—24no—
123C2×(C2×D3)⋊C4—24no—
124C2×(C2×D3)⋊C4—24no—
125C2×(C2×D3)⋊C4—24no—
126C2×(C2×D3)⋊C4—24no—
127C2×(C2×D3)⋊C4—24no—
128C2×(C2×D3)⋊C4—24no—
129C2×(C2×D3)⋊C4—22no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—24no—
132C2×(C2×D3)⋊C4—24no—
133C2×(C2×D3)⋊C4—42no—
134C2×(C2×D3)⋊C4—42no—
135C2×(C2×D3)⋊C4—42no—
136C2×(C2×D3)⋊C4—42no—
137C2×(C2×D3)⋊C4D418yescomplemented
138#882—232no—
139C3×#95—24no—
140C3⋊#95—22no—
141C3⋊#95—22no—
142C3⋊#95—24no—
143C3⋊#95—24no—
144C3⋊#95—42no—
145C26—31no—
146C23×D4—31no—
147C23×D4—32no—
148C24×C4—31no—
149C24×C4C2×D311yescharacteristic
150C2×#120—64no—
151C2×#120—64no—
152C2×#120—64no—
153C22×C4⋊C4C2×D312yescomplemented
154C22×C22⋊C4—32no—
155C22×C22⋊C4—31no—
156C22×C22⋊C4—31no—
157C22×C22⋊C4—32no—
158C22×C22⋊C4—32no—
159C22×C22⋊C4—32no—
160C22×C22⋊C4—32no—
161C22×C22⋊C4—32no—
162C22×C22⋊C4—31no—
163C22×C22⋊C4—68no—
164C22×C22⋊C4—64no—
165C22×C22⋊C4C2×D311yescharacteristic
166C22×C22⋊C4C2×D311yescharacteristic
167#394—68no—
168#386—64no—
169#386—64no—
170#380—24no—
171#379—64no—
172C2×#95—32no—
173C2×#95—31no—
174C2×#95—32no—
175C2×#95—31no—
176C2×#95—32no—
177C2×#95C2×D312yescomplemented
178C24×C3—22no—
179C24×C3—22no—
180C24×C3—22no—
181C24×C3—22no—
182C24×C3C2×D412yes—
183C24×C3C2×D412yes—
184C24×C3C2×D412yes—
185C24×C3C2×D412yes—
186C24×C3#4112yes—
187C24×C3#4112yes—
188C24×C3#4112yes—
189C24×C3C2411yescharacteristic
190C23×D3—28no—
191C23×D3—216no—
192C23×D3—28no—
193C23×D3—28no—
194C23×D3—22no—
195C23×D3—22no—
196C23×D3—22no—
197C23×D3—22no—
198C23×D3—22no—
199C23×D3—22no—
200C23×D3—22no—
201C23×D3—22no—
202C23×D3—22no—
203C23×D3—22no—
204C23×D3—22no—
205C23×D3—22no—
206C23×D3—216no—
207C23×D3—28no—
208C23×D3—28no—
209C23×D3—22no—
210C23×D3—21no—
211C23×D3—21no—
212C23×D3—21no—
213C23×D3—22no—
214C23×D3—21no—
215C23×D3—21no—
216C23×D3—21no—
217C23×D3—22no—
218C23×D3—22no—
219C23×D3—48no—
220C23×D3—48no—
221C23×D3—48no—
222C23×D3—48no—
223C23×D3—48no—
224C23×D3—48no—
225C23×D3—48no—
226C23×D3—48no—
227C23×D3—48no—
228C23×D3—44no—
229C23×D3—44no—
230C23×D3—48no—
231C23×D3—44no—
232C23×D3—44no—
233C23×D3—44no—
234C23×D3—44no—
235C23×D3C2×D412yes—
236C23×D3C2×D414yes—
237C23×D3C2×D414yes—
238C23×D3#4114yes—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—22no—
242C22×C3×C4—28no—
243C22×C3×C4—22no—
244C22×C3×C4—21no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—21no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—28no—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—44no—
262C22×C3×C4—48no—
263C22×C3×C4—48no—
264C22×C3×C4C2×D412yes—
265C22×C3×C4C2×D412yes—
266C22×C3×C4C2×D414yes—
267C22×C3×C4C2×D414yes—
268C2×#67—28no—
269C2×#67—28no—
270C2×#67—28no—
271C2×#67—44no—
272C2×#67—44no—
273C2×#67—44no—
274C2×#67—44no—
275C22×Dic3—28no—
276C22×Dic3—21no—
277C22×Dic3—22no—
278C22×Dic3—22no—
279C22×Dic3—22no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—22no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—22no—
287C22×Dic3—22no—
288C22×Dic3—22no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—22no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—22no—
297C22×Dic3—22no—
298C22×Dic3—48no—
299C22×Dic3—48no—
300C22×Dic3—44no—
301C22×Dic3—44no—
302C22×Dic3C2×D412yes—
303C22×Dic3C2×D414yes—
304C2×D12—216no—
305C2×D12—48no—
306C2×D12—48no—
307C2×D12—48no—
308C2×D12—48no—
309C2×D12—48no—
310C2×D12—48no—
311C3×C4⋊C4—48no—
312C3×C22⋊C4—28no—
313C3×C22⋊C4—44no—
314#217—44no—
315(C2×D3)⋊C4—216no—
316(C2×D3)⋊C4—216no—
317(C2×D3)⋊C4—216no—
318(C2×D3)⋊C4—48no—
319(C2×D3)⋊C4—44no—
320(C2×D3)⋊C4—48no—
321(C2×D3)⋊C4—48no—
322(C2×D3)⋊C4—44no—
323C25—32no—
324C25—31no—
325C25—34no—
326C25—64no—
327C25—64no—
328C25—62no—
329C25—62no—
330C25—62no—
331C25—62no—
332C25—62no—
333C25—62no—
334C25—122no—
335C25—122no—
336C25C22×D311yescharacteristic
337C22×D4—34no—
338C22×D4—64no—
339C22×D4—64no—
340C22×D4—64no—
341C22×D4—64no—
342C22×D4—62no—
343C22×D4—62no—
344C22×D4—62no—
345C22×D4—62no—
346C22×D4—62no—
347C22×D4—62no—
348C22×D4—64no—
349C22×D4—122no—
350C22×D4—122no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—24no—
354C23×C4—32no—
355C23×C4—31no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—42no—
359C23×C4—64no—
360C23×C4—62no—
361C23×C4—62no—
362C23×C4—62no—
363C23×C4—122no—
364C23×C4D1214yescomplemented
365C23×C4C22×D312yes—
366C23×C4C22×D311yescharacteristic
367C23×C4C22×D312yes—
368C23×C4C22×D311yescharacteristic
369#120—632no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—42no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—38no—
379C2×C22⋊C4—64no—
380C2×C22⋊C4—64no—
381C2×C22⋊C4—64no—
382C2×C22⋊C4—64no—
383C2×C22⋊C4—632no—
384C2×C22⋊C4—64no—
385C2×C22⋊C4—64no—
386C2×C22⋊C4—64no—
387C2×C22⋊C4—64no—
388C2×C22⋊C4—64no—
389C2×C22⋊C4—64no—
390C2×C22⋊C4—64no—
391C2×C22⋊C4—64no—
392C2×C22⋊C4—64no—
393C2×C22⋊C4—64no—
394C2×C22⋊C4—62no—
395C2×C22⋊C4—62no—
396C2×C22⋊C4—62no—
397C2×C22⋊C4—62no—
398C2×C22⋊C4—62no—
399C2×C22⋊C4—64no—
400C2×C22⋊C4—122no—
401C2×C22⋊C4—122no—
402C2×C22⋊C4—122no—
403C2×C22⋊C4—122no—
404C2×C22⋊C4#6714yes—
405#95—24no—
406#95—64no—
407#95—64no—
408#95—62no—
409#95—62no—
410#95—122no—
411C23×C3—22no—
412C23×C3—24no—
413C23×C3—22no—
414C23×C3—24no—
415C23×C3—22no—
416C23×C3—24no—
417C23×C3—22no—
418C23×C3—24no—
419C23×C3—24no—
420C23×C3—24no—
421C23×C3—24no—
422C23×C3—24no—
423C23×C3—24no—
424C23×C3—24no—
425C23×C3—24no—
426C23×C3—24no—
427C23×C3#12014yes—
428C23×C3#12114yes—
429C23×C3#12114yes—
430C23×C3#12114yes—
431C23×C3#12314yes—
432C23×C3#12314yes—
433C23×C3#12414yes—
434C23×C3C22×D411yescharacteristic
435C23×C3C22×D411yescharacteristic
436C23×C3C22×D411yescharacteristic
437C23×C3C22×D412yes—
438C23×C3C22×D411yescharacteristic
439C23×C3C2×#4111yescharacteristic
440C23×C3C2×#4111yescharacteristic
441C23×C3C2×#4111yescharacteristic
442C23×C3C2×#4112yes—
443C23×C3H(5,𝔽2)12yes—
444C23×C3H(5,𝔽2)12yes—
445C22×D3—232no—
446C22×D3—24no—
447C22×D3—24no—
448C22×D3—24no—
449C22×D3—24no—
450C22×D3—24no—
451C22×D3—24no—
452C22×D3—24no—
453C22×D3—24no—
454C22×D3—24no—
455C22×D3—24no—
456C22×D3—24no—
457C22×D3—24no—
458C22×D3—24no—
459C22×D3—24no—
460C22×D3—24no—
461C22×D3—24no—
462C22×D3—24no—
463C22×D3—24no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—24no—
468C22×D3—24no—
469C22×D3—432no—
470C22×D3—432no—
471C22×D3—416no—
472C22×D3—416no—
473C22×D3—416no—
474C22×D3—416no—
475C22×D3—432no—
476C22×D3—432no—
477C22×D3—416no—
478C22×D3—42no—
479C22×D3—42no—
480C22×D3—42no—
481C22×D3—42no—
482C22×D3—42no—
483C22×D3—42no—
484C22×D3—42no—
485C22×D3—42no—
486C22×D3—42no—
487C22×D3—42no—
488C22×D3—42no—
489C22×D3—42no—
490C22×D3—42no—
491C22×D3—42no—
492C22×D3—42no—
493C22×D3—42no—
494C22×D3—416no—
495C22×D3—41no—
496C22×D3—42no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—42no—
502C22×D3—41no—
503C22×D3—41no—
504C22×D3—42no—
505C22×D3—41no—
506C22×D3—42no—
507C22×D3—42no—
508C22×D3—42no—
509C22×D3—42no—
510C22×D3—42no—
511C22×D3—42no—
512C22×D3—42no—
513C22×D3#12118yes—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—24no—
517C2×C3×C4—24no—
518C2×C3×C4—22no—
519C2×C3×C4—24no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—24no—
523C2×C3×C4—24no—
524C2×C3×C4—416no—
525C2×C3×C4—42no—
526C2×C3×C4—42no—
527C2×C3×C4—42no—
528C2×C3×C4—42no—
529C2×C3×C4—42no—
530C2×C3×C4—42no—
531C2×C3×C4—42no—
532C2×C3×C4—42no—
533C2×C3×C4—42no—
534C2×C3×C4—42no—
535C2×C3×C4—42no—
536C2×C3×C4—42no—
537C2×C3×C4—42no—
538C2×C3×C4#12014yescomplemented
539#67—416no—
540C2×Dic3—24no—
541C2×Dic3—22no—
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3—24no—
545C2×Dic3—24no—
546C2×Dic3—416no—
547C2×Dic3—42no—
548C2×Dic3—41no—
549C2×Dic3—41no—
550C2×Dic3—41no—
551C2×Dic3—41no—
552C2×Dic3—42no—
553C2×Dic3—42no—
554C2×Dic3—42no—
555C2×Dic3—41no—
556C2×Dic3—42no—
557C2×Dic3—41no—
558C2×Dic3—41no—
559C2×Dic3—41no—
560C2×Dic3—42no—
561C2×Dic3—41no—
562C2×Dic3—42no—
563C2×Dic3—41no—
564C2×Dic3—42no—
565D12—432no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—34no—
571C24—34no—
572C24—34no—
573C24—32no—
574C24—616no—
575C24—68no—
576C24—68no—
577C24—616no—
578C24—68no—
579C24—62no—
580C24—62no—
581C24—62no—
582C24—62no—
583C24—62no—
584C24—62no—
585C24—62no—
586C24—62no—
587C24—62no—
588C24—62no—
589C24—62no—
590C24—62no—
591C24—68no—
592C24—68no—
593C24—61no—
594C24—61no—
595C24—62no—
596C24—61no—
597C24—62no—
598C24—61no—
599C24—61no—
600C24—62no—
601C24—62no—
602C24—61no—
603C24—128no—
604C24—128no—
605C24—128no—
606C24—128no—
607C24—128no—
608C24—128no—
609C24—128no—
610C24—128no—
611C24—128no—
612C24—128no—
613C24—124no—
614C24—124no—
615C24—124no—
616C24—124no—
617C24—124no—
618C24—124no—
619C24C2×D1212yes—
620C24#23512yes—
621C24D3×D412yes—
622C24D3×D412yes—
623C24#23912yes—
624C24#23912yes—
625C24C2×#6712yes—
626C24C23×D311yescharacteristic
627C2×D4—616no—
628C2×D4—68no—
629C2×D4—68no—
630C2×D4—68no—
631C2×D4—128no—
632C2×D4—128no—
633C2×D4—128no—
634C2×D4—128no—
635C2×D4—128no—
636C2×D4—128no—
637C2×D4—124no—
638C2×D4—124no—
639C2×D4—124no—
640C2×D4—124no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—21no—
644C22×C4—28no—
645C22×C4—21no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—28no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—32no—
664C22×C4—34no—
665C22×C4—44no—
666C22×C4—48no—
667C22×C4—48no—
668C22×C4—68no—
669C22×C4—61no—
670C22×C4—62no—
671C22×C4—61no—
672C22×C4—62no—
673C22×C4—62no—
674C22×C4—61no—
675C22×C4—62no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—62no—
679C22×C4—62no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—62no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4—62no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—62no—
690C22×C4—62no—
691C22×C4—128no—
692C22×C4—128no—
693C22×C4—124no—
694C22×C4—124no—
695C22×C4C2×D1212yes—
696C22×C4C2×D1212yes—
697C22×C4D3×D414yes—
698C22×C4C2×#6714yes—
699C4⋊C4—48no—
700C22⋊C4—28no—
701C22⋊C4—44no—
702C22⋊C4—616no—
703C22⋊C4—616no—
704C22⋊C4—616no—
705C22⋊C4—124no—
706C22⋊C4—128no—
707C22⋊C4—128no—
708C22⋊C4—128no—
709C22⋊C4—124no—
710C22⋊C4—124no—
711C22×C3—24no—
712C22×C3—24no—
713C22×C3—24no—
714C22×C3—24no—
715C22×C3—28no—
716C22×C3—24no—
717C22×C3—28no—
718C22×C3—28no—
719C22×C3—28no—
720C22×C3—24no—
721C22×C3#39418yescomplemented
722C22×C3C2×#12011yescharacteristic
723C22×C3C2×#12011yescharacteristic
724C22×C3C2×#12111yescharacteristic
725C22×C3C2×#12111yescharacteristic
726C22×C3C2×#12111yescharacteristic
727C22×C3C2×#12112yes—
728C22×C3C2×#12311yescharacteristic
729C22×C3C2×#12311yescharacteristic
730C22×C3#52511yescharacteristic
731C22×C3#52512yes—
732C22×C3C2×#12411yescharacteristic
733C22×C3#53411yescharacteristic
734C22×C3#53412yes—
735C22×C3#53511yescharacteristic
736C22×C3#53812yes—
737C22×C3D4212yes—
738C22×C3D4212yes—
739C22×C3#54612yes—
740C22×C3#54612yes—
741C22×C3#54612yes—
742C22×C3#54612yes—
743C22×C3#55112yes—
744C22×C3#55112yes—
745C2×D3—28no—
746C2×D3—28no—
747C2×D3—28no—
748C2×D3—464no—
749C2×D3—44no—
750C2×D3—44no—
751C2×D3—44no—
752C2×D3—44no—
753C2×D3—44no—
754C2×D3—44no—
755C2×D3—44no—
756C2×D3—44no—
757C2×D3—44no—
758C2×D3—44no—
759C2×D3—44no—
760C2×D3—44no—
761C2×D3—42no—
762C2×D3—42no—
763C2×D3—44no—
764C2×D3—44no—
765C2×D3—42no—
766C2×D3—81no—
767C2×D3—81no—
768C2×D3—81no—
769C2×D3—81no—
770C2×D3—82no—
771C2×D3—82no—
772C3×C4—24no—
773C3×C4—44no—
774C3×C4—42no—
775C3×C4—82no—
776Dic3—42no—
777Dic3—44no—
778Dic3—81no—
779Dic3—81no—
780C23—24no—
781C23—24no—
782C23—22no—
783C23—24no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—24no—
791C23—24no—
792C23—24no—
793C23—24no—
794C23—24no—
795C23—24no—
796C23—38no—
797C23—632no—
798C23—64no—
799C23—64no—
800C23—64no—
801C23—64no—
802C23—64no—
803C23—64no—
804C23—64no—
805C23—64no—
806C23—64no—
807C23—64no—
808C23—64no—
809C23—64no—
810C23—64no—
811C23—64no—
812C23—64no—
813C23—64no—
814C23—64no—
815C23—64no—
816C23—62no—
817C23—62no—
818C23—62no—
819C23—64no—
820C23—64no—
821C23—1232no—
822C23—1232no—
823C23—1216no—
824C23—1232no—
825C23—1216no—
826C23—1216no—
827C23—1232no—
828C23—1216no—
829C23—1216no—
830C23—122no—
831C23—122no—
832C23—122no—
833C23—122no—
834C23—122no—
835C23—1216no—
836C23—122no—
837C23—122no—
838C23—122no—
839C23—122no—
840C23—122no—
841C23—122no—
842C23—122no—
843C23—122no—
844C23—122no—
845C23—122no—
846C23—122no—
847C23—122no—
848C23—122no—
849C23—121no—
850C23—122no—
851C23—121no—
852C23—121no—
853C23—121no—
854C23—121no—
855C23—121no—
856C23—122no—
857C23—121no—
858C23—122no—
859C23—121no—
860C23—122no—
861C23—122no—
862C23—122no—
863C23—122no—
864C23—122no—
865C23#89414yes—
866C23#89414yes—
867C23#89514yes—
868C23#89514yes—
869C23#93014yes—
870C23#93714yes—
871C23#94714yes—
872C23C22×D1211yescharacteristic
873C23C2×#23511yescharacteristic
874C23C2×D3×D412yes—
875C23C2×D3×D411yescharacteristic
876C23C2×D3×D411yescharacteristic
877C23#100412yes—
878C23C2×#23911yescharacteristic
879C23C2×#23911yescharacteristic
880C23D3×#4112yes—
881C23#100912yes—
882C23C22×#6711yescharacteristic
883D4—1232no—
884D4—1216no—
885C2×C4—24no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—24no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—416no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—64no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—64no—
914C2×C4—64no—
915C2×C4—1216no—
916C2×C4—121no—
917C2×C4—122no—
918C2×C4—121no—
919C2×C4—122no—
920C2×C4—121no—
921C2×C4—121no—
922C2×C4—122no—
923C2×C4—122no—
924C2×C4—122no—
925C2×C4—121no—
926C2×C4—121no—
927C2×C4—121no—
928C2×C4—121no—
929C2×C4—121no—
930C2×C4—121no—
931C2×C4—122no—
932C2×C4—122no—
933C2×C4—122no—
934C2×C4#88214yescomplemented
935C2×C3—28no—
936C2×C3C2×#39411yescharacteristic
937C2×C3#240811yescharacteristic
938C2×C3#241012yes—
939C2×C3#241011yescharacteristic
940C2×C3#241111yescharacteristic
941C2×C3#241212yes—
942C2×C3#241812yes—
943C2×C3#247212yes—
944C2×C3#253411yescharacteristic
945C2×C3#261711yescharacteristic
946C2×C3#284711yescharacteristic
947D3—48no—
948D3—82no—
949C22—28no—
950C22—24no—
951C22—28no—
952C22—28no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—28no—
957C22—24no—
958C22—24no—
959C22—68no—
960C22—68no—
961C22—68no—
962C22—1264no—
963C22—124no—
964C22—124no—
965C22—124no—
966C22—124no—
967C22—124no—
968C22—124no—
969C22—124no—
970C22—124no—
971C22—124no—
972C22—124no—
973C22—124no—
974C22—124no—
975C22—122no—
976C22—124no—
977C22—122no—
978C22—124no—
979C22—122no—
980C22—242no—
981C22—241no—
982C22—241no—
983C22—242no—
984C22—241no—
985C22—241no—
986C22#499118yescomplemented
987C22C2×#88211yescharacteristic
988C22#549012yes—
989C22#549311yescharacteristic
990C22C2×#89411yescharacteristic
991C22C2×#89411yescharacteristic
992C22C2×#89511yescharacteristic
993C22C2×#89511yescharacteristic
994C22#552411yescharacteristic
995C22#552511yescharacteristic
996C22#552712yes—
997C22D3×#12112yes—
998C22#560512yes—
999C22#560912yes—
1000C22#561012yes—
1001C22#562712yes—
1002C22#563012yes—
1003C22#563712yes—
1004C22#564412yes—
1005C22C2×#93011yescharacteristic
1006C22C2×#93711yescharacteristic
1007C22D4×#6712yes—
1008C22C2×#94711yescharacteristic
1009C22#582912yes—
1010C4—24no—
1011C4—44no—
1012C4—42no—
1013C4—82no—
1014C4—122no—
1015C4—124no—
1016C4—241no—
1017C4—241no—
1018C3#1472511yescharacteristic, complemented, Sylow
1019C2—28no—
1020C2—128no—
1021C2—242no—
1022C2#7401611yescharacteristic
1023C2#7401812yes—
1024C2#7402112yes—
1025C2#7402911yescharacteristic
1026C2#7403111yescharacteristic
1027C2#7404811yescharacteristic
1028C2#8212711yescharacteristic
1029C2C2×#499111yescharacteristic
1030C2#8227511yescharacteristic
1031C2#8270212yes—
1032C2#8276912yes—
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#380C2
prime radicalC22×#882C2
hypercenterC2×#380D3
hypocenterC3#14725
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C23×(C2×D3)⋊C4C2semidirect
3. C2×C3×#380C2semidirect
4. C2×#5213C2semidirect
5. C2×#4991C2semidirect
6. C2×#4955C2semidirect
7. C2×#4958C2semidirect
8. #71570C2semidirect
9. #71544C2semidirect
10. #69429C2semidirect
11. #69426C2semidirect
18. C22×C3×C4⋊C4C22semidirect
29. C22×(C2×D3)⋊C4C22semidirect
30. C22×(C2×D3)⋊C4C22semidirect
31. C22×(C2×D3)⋊C4C22semidirect
36. C2×C3×#95C22semidirect
38. C2×C3⋊#95C22semidirect
39. C2×C3⋊#95C22semidirect
40. C2×C3⋊#95C22semidirect
41. C2×C3⋊#95C22semidirect
42. C2×C3⋊#95C22semidirect
51. C2×#380D3semidirect
75. C23×C3×C4D4semidirect
137. C2×(C2×D3)⋊C4D4semidirect
153. C22×C4⋊C4C2×D3semidirect
177. C2×#95C2×D3semidirect
364. C23×C4D12semidirect
538. C2×C3×C4#120semidirect
721. C22×C3#394semidirect
934. C2×C4#882semidirect
986. C22#4991semidirect
1018. C3#14725semidirect

Maximal subgroups

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

subgroupindex
C23×(C2×D3)⋊C42
C22×#8822
C2×C3×#3802
C2×#52132
C2×#49912
C2×#49552
C2×#49582
#715702
#715442
#694292
#694262
#147253