Finite Group Databasebeta

← #10826942

Subgroups — #10826942

Order 768.

2272 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5606C211yesmaximal, characteristic, complemented
2C22×#895C211yesmaximal, characteristic, complemented
3C2×#5036C211yesmaximal, characteristic, complemented
4C2×#4781C212yesmaximal, complemented
5C2×#4731C211yesmaximal, characteristic, complemented
6C3×#1874C211yesmaximal, characteristic, complemented
7#71559C211yesmaximal, characteristic, complemented
8#70204C212yesmaximal, complemented
9#69955C211yesmaximal, characteristic, complemented
10#68887C212yesmaximal, complemented
11#68881C212yesmaximal, complemented
12#23920—31nomaximal, Sylow
13C22×#237C2211yescharacteristic, complemented
14C23×D12—21no—
15C23×D12C2211yescharacteristic
16C23×C4×D3C2211yescharacteristic
17C2×C3×#121C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C2×#938C2211yescharacteristic, complemented
20C2×#937—21no—
21C2×D4×Dic3—21no—
22C22×#213C2212yescomplemented
23C22×(C2×D3)⋊C4—21no—
24C2×#924C2211yescharacteristic
25C22×#204C2212yescomplemented
26#5606—24no—
27#5606—24no—
28C2×#897C2211yescharacteristic, complemented
29C2×#895—21no—
30C2×#895—21no—
31C2×#895—28no—
32C2×#895C2212yes—
33C2×#895C2212yes—
34C2×#892C2211yescharacteristic, complemented
35C2×#883—21no—
36C2×#67⋊C4—21no—
37C2×C3×#102C2212yescomplemented
38C2×C3×C22⋊C8C2211yescharacteristic
39C2×#830C2211yescharacteristic
40C2×#821C2212yescomplemented
41C2×(C2×D3)⋊C8C2212yescomplemented
42C2×(C2×D3)⋊C8C2212yescomplemented
43#5036—24no—
44C2×#810C2212yescomplemented
45C2×#809C2212yescomplemented
46#4781—28no—
47#4731—24no—
48C3×#340C2212yescomplemented
49#4529C2212yescomplemented
50C2×#525—31no—
51C22×#121—31no—
52C2×#449—32no—
53C2×#450—31no—
54C2×#447—31no—
55#2000—32no—
56#1999—32no—
57#1875—32no—
58#1874D311yescharacteristic, complemented
59#1872—31no—
60#1779—31no—
61C24×D3—21no—
62C24×D3D411yescharacteristic
63C22×C3×D4—21no—
64C22×C3×D4C2311yescharacteristic
65C23×C3×C4—21no—
66C23×C3×C4C2311yescharacteristic
67C22×#67—21no—
68C22×#67—21no—
69C23×Dic3—21no—
70C23×Dic3D411yescharacteristic
71C2×#237—22no—
72C2×#237—24no—
73C2×#237—22no—
74C2×#237—42no—
75C22×D12—28no—
76C22×D12—22no—
77C22×D12—22no—
78C22×D12—21no—
79C22×D12—24no—
80C22×D12—22no—
81C22×D12—22no—
82C22×D12—42no—
83C22×D12—44no—
84C22×D12—44no—
85C22×D12C2312yes—
86C22×C4×D3—22no—
87C22×C4×D3—22no—
88C22×C4×D3—24no—
89C22×C4×D3—42no—
90C22×C4×D3D411yescharacteristic
91C22×C4×D3D411yescharacteristic
92C22×C4×D3C2311yescharacteristic
93C22×C4×D3C2311yescharacteristic
94C22×Dic6C2311yescharacteristic
95C22×C3×C8C2312yes—
96C3×#121—22no—
97C3×#121D414yescomplemented
98C2×C3×C4⋊C4—21no—
99C2×C3×C4⋊C4—24no—
100C2×C3×C4⋊C4C2312yes—
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C22⋊C4—21no—
103C2×#217—21no—
104C2×#217—21no—
105#938—22no—
106#938—22no—
107#937—28no—
108D4×Dic3—28no—
109C2×#213—24no—
110C2×#213—24no—
111C2×#213—42no—
112C2×(C2×D3)⋊C4—28no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—22no—
117C2×C4⋊Dic3—21no—
118C2×C4⋊Dic3C2311yescharacteristic
119#924—22no—
120#924D414yescomplemented
121C2×Dic3⋊C4—21no—
122C2×C4×Dic3—21no—
123C22×C3⋊C8C2312yes—
124C2×#204—24no—
125C2×#204—24no—
126C2×#204—42no—
127#897—22no—
128#897—22no—
129#895—28no—
130#895—28no—
131#895—24no—
132#895—24no—
133#895—24no—
134#895D418yescomplemented
135#892—22no—
136#892—22no—
137#883—28no—
138#67⋊C4—28no—
139C3×#102—24no—
140C3×C22⋊C8—22no—
141#830—22no—
142#821—24no—
143(C2×D3)⋊C8—24no—
144(C2×D3)⋊C8—42no—
145#810—24no—
146#809—24no—
147C22×#41—31no—
148C23×D4—31no—
149C23×D4—61no—
150C24×C4—31no—
151C22×SD16—32no—
152C22×D8—32no—
153#525—64no—
154#525—64no—
155C2×#123—61no—
156C2×C22⋊Q8—31no—
157C2×C22⋊Q8—31no—
158C2×#121—31no—
159C2×#121—32no—
160C2×#121—32no—
161C2×#121—68no—
162C2×#121—61no—
163C2×#121—61no—
164C2×#121C2×D311yescharacteristic
165C2×#120—61no—
166C2×C4×D4—61no—
167C2×C4×D4—61no—
168C2×#117—31no—
169C22×C4⋊C4C2×D311yescharacteristic
170C22×C22⋊C4—61no—
171#450—64no—
172#449—68no—
173#447—64no—
174C2×#103—32no—
175C2×#102—32no—
176C2×#102—32no—
177C2×#102C2×D312yescomplemented
178C2×C22⋊C8—31no—
179C2×C22⋊C8—32no—
180C2×C22⋊C8—32no—
181C2×C22⋊C8C2×D311yescharacteristic
182#340—32no—
183#340C2×D312yescomplemented
184C24×C3—21no—
185C24×C3C2×D411yescharacteristic
186C23×D3—22no—
187C23×D3—22no—
188C23×D3—22no—
189C23×D3—24no—
190C23×D3—22no—
191C23×D3—22no—
192C23×D3—22no—
193C23×D3—41no—
194C23×D3—41no—
195C23×D3—42no—
196C23×D3—42no—
197C23×D3—42no—
198C23×D3—42no—
199C23×D3—42no—
200C23×D3—42no—
201C23×D3C2×D411yescharacteristic
202C23×D3C2×D411yescharacteristic
203C2×C3×D4—24no—
204C2×C3×D4—22no—
205C2×C3×D4—21no—
206C2×C3×D4—22no—
207C2×C3×D4—42no—
208C2×C3×D4—42no—
209C2×C3×D4C2×D412yescomplemented
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—24no—
213C22×C3×C4—21no—
214C22×C3×C4—22no—
215C22×C3×C4—42no—
216C22×C3×C4—42no—
217C22×C3×C4C2×D412yes—
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2×D412yes—
220C22×C3×C4C2411yescharacteristic
221C2×#67—24no—
222C2×#67—24no—
223C2×#67—42no—
224C2×#67—42no—
225C2×#67—42no—
226C2×#67—42no—
227C22×Dic3—24no—
228C22×Dic3—22no—
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3—22no—
232C22×Dic3—41no—
233C22×Dic3—42no—
234C22×Dic3—42no—
235C22×Dic3C2×D411yescharacteristic
236C22×Dic3C2×D411yescharacteristic
237#237—48no—
238#237—48no—
239C2×D12—22no—
240C2×D12—22no—
241C2×D12—22no—
242C2×D12—22no—
243C2×D12—24no—
244C2×D12—28no—
245C2×D12—28no—
246C2×D12—22no—
247C2×D12—48no—
248C2×D12—48no—
249C2×D12—42no—
250C2×D12—432no—
251C2×D12—44no—
252C2×D12—44no—
253C2×D12—44no—
254C2×D12—44no—
255C2×D12—42no—
256C2×D12C2×D414yes—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—22no—
260C2×C4×D3—22no—
261C2×C4×D3—22no—
262C2×C4×D3—22no—
263C2×C4×D3—22no—
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—22no—
267C2×C4×D3—22no—
268C2×C4×D3—48no—
269C2×C4×D3—48no—
270C2×C4×D3—41no—
271C2×C4×D3—41no—
272C2×C4×D3C2×D414yes—
273C2×Dic6—22no—
274C2×Dic6—22no—
275C2×Dic6—21no—
276C2×Dic6C2×D412yescomplemented
277C2×C3×C8—22no—
278C2×C3×C8—22no—
279C2×C3×C8—22no—
280C3×C4⋊C4—24no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—22no—
283C3×C4⋊C4C2×D414yes—
284C3×C4⋊C4C2×D412yescomplemented
285C3×C22⋊C4—24no—
286#217—24no—
287#217—24no—
288#213—48no—
289(C2×D3)⋊C4—24no—
290(C2×D3)⋊C4—24no—
291(C2×D3)⋊C4—28no—
292(C2×D3)⋊C4—28no—
293C4⋊Dic3—24no—
294C4⋊Dic3—21no—
295C4⋊Dic3C2×D412yescomplemented
296Dic3⋊C4—24no—
297C4×Dic3—24no—
298C2×C3⋊C8—22no—
299C2×C3⋊C8—22no—
300C2×C3⋊C8—22no—
301#204—48no—
302C25—31no—
303C25—61no—
304C2×#41—64no—
305C2×#41—62no—
306C2×#41—62no—
307C2×#41—122no—
308C22×Q8—31no—
309C22×D4—21no—
310C22×D4—32no—
311C22×D4—64no—
312C22×D4—62no—
313C22×D4—62no—
314C22×D4—68no—
315C22×D4—61no—
316C22×D4—61no—
317C22×D4—62no—
318C22×D4—61no—
319C22×D4—62no—
320C22×D4—122no—
321C22×D4—124no—
322C22×D4—124no—
323C22×D4C22×D311yescharacteristic
324C23×C4—21no—
325C23×C4—31no—
326C23×C4—31no—
327C23×C4—31no—
328C23×C4—31no—
329C23×C4—31no—
330C23×C4—64no—
331C23×C4—61no—
332C23×C4—62no—
333C23×C4—62no—
334C23×C4—122no—
335C23×C4C22×D311yescharacteristic
336C2×SD16—64no—
337C2×SD16—64no—
338C2×SD16—122no—
339C2×D8—64no—
340C2×D8—64no—
341C2×D8—122no—
342C22×C8—32no—
343C22×C8C22×D312yes—
344#123—68no—
345C22⋊Q8—34no—
346C22⋊Q8—62no—
347C22⋊Q8—62no—
348C22⋊Q8—62no—
349#121—22no—
350#121—38no—
351#121—64no—
352#121—64no—
353#121—68no—
354#121—68no—
355#121—62no—
356#121—62no—
357#121—64no—
358#121D1214yescomplemented
359#120—68no—
360C4×D4—68no—
361C4×D4—68no—
362#117—62no—
363#117—62no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C4⋊C4C22×D312yes—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—62no—
373C2×C22⋊C4—62no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—68no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C42—61no—
380#103—64no—
381#102—24no—
382#102—64no—
383#102—64no—
384C22⋊C8—22no—
385C22⋊C8—64no—
386C22⋊C8—62no—
387C22⋊C8—122no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—22no—
393C23×C3—41no—
394C23×C3—41no—
395C23×C3—41no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3#12012yes—
400C23×C3#13512yes—
401C23×C3AGL(1,ℤ/8)12yes—
402C23×C3C22×D411yescharacteristic
403C22×D3—28no—
404C22×D3—21no—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—21no—
408C22×D3—21no—
409C22×D3—21no—
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—21no—
416C22×D3—24no—
417C22×D3—44no—
418C22×D3—44no—
419C22×D3—44no—
420C22×D3—44no—
421C22×D3—44no—
422C22×D3—44no—
423C22×D3—48no—
424C22×D3—48no—
425C22×D3—48no—
426C22×D3—42no—
427C22×D3—42no—
428C22×D3—42no—
429C22×D3—42no—
430C22×D3—42no—
431C22×D3—42no—
432C22×D3—84no—
433C22×D3—84no—
434C22×D3—84no—
435C22×D3—84no—
436C22×D3#12012yes—
437C22×D3AGL(1,ℤ/8)12yes—
438C3×D4—24no—
439C3×D4—48no—
440C3×D4—42no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—24no—
444C2×C3×C4—24no—
445C2×C3×C4—22no—
446C2×C3×C4—24no—
447C2×C3×C4—48no—
448C2×C3×C4—41no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4—41no—
452C2×C3×C4#12012yes—
453C2×C3×C4C22×D411yescharacteristic
454C2×C3×C4C22×D412yes—
455C2×C3×C4C22×D411yescharacteristic
456C2×C3×C4H(5,𝔽2)12yes—
457#67—48no—
458#67—48no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—44no—
467C2×Dic3—48no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3#12012yes—
473D12—24no—
474D12—24no—
475D12—48no—
476D12—416no—
477D12—416no—
478D12—42no—
479D12—42no—
480C4×D3—24no—
481C4×D3—24no—
482C4×D3—44no—
483C4×D3—44no—
484C4×D3—42no—
485C4×D3—42no—
486Dic6—24no—
487Dic6—42no—
488C3×C8—42no—
489C3⋊C8—42no—
490C24—21no—
491C24—31no—
492C24—31no—
493C24—62no—
494C24—62no—
495C24—64no—
496C24—62no—
497C24—62no—
498C24—62no—
499C24—62no—
500C24—121no—
501C24—121no—
502C24—122no—
503C24—122no—
504C24—122no—
505C24—122no—
506C24—122no—
507C24—122no—
508C24D3×D411yescharacteristic
509#41—128no—
510#41—128no—
511C2×Q8—32no—
512C2×Q8—61no—
513C2×Q8—62no—
514C2×Q8—62no—
515C2×D4—24no—
516C2×D4—22no—
517C2×D4—21no—
518C2×D4—22no—
519C2×D4—34no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—68no—
523C2×D4—64no—
524C2×D4—68no—
525C2×D4—64no—
526C2×D4—64no—
527C2×D4—62no—
528C2×D4—62no—
529C2×D4—62no—
530C2×D4—62no—
531C2×D4—62no—
532C2×D4—128no—
533C2×D4—128no—
534C2×D4—122no—
535C2×D4—124no—
536C2×D4—1232no—
537C2×D4—124no—
538C2×D4—124no—
539C2×D4—124no—
540C2×D4—122no—
541C2×D4—122no—
542C2×D4—122no—
543C2×D4—122no—
544C2×D4—122no—
545C2×D4C2×D1212yescomplemented
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—31no—
552C22×C4—34no—
553C22×C4—31no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—62no—
562C22×C4—64no—
563C22×C4—62no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—61no—
569C22×C4—62no—
570C22×C4—61no—
571C22×C4—62no—
572C22×C4—121no—
573C22×C4—121no—
574C22×C4—128no—
575C22×C4—128no—
576C22×C4—122no—
577C22×C4—121no—
578C22×C4—122no—
579C22×C4C2×D1212yes—
580C22×C4D3×D411yescharacteristic
581C22×C4D3×D412yes—
582C22×C4C23×D311yescharacteristic
583SD16—128no—
584D8—128no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—62no—
589C2×C8—62no—
590C2×C8—62no—
591C4⋊C4—24no—
592C4⋊C4—22no—
593C4⋊C4—21no—
594C4⋊C4—32no—
595C4⋊C4—64no—
596C4⋊C4—64no—
597C4⋊C4—61no—
598C4⋊C4C2×D1212yescomplemented
599C4⋊C4D3×D414yes—
600C22⋊C4—24no—
601C22⋊C4—68no—
602C22⋊C4—68no—
603C22⋊C4—64no—
604C22⋊C4—64no—
605C22⋊C4—64no—
606C22⋊C4—64no—
607C42—64no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—81no—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3#44914yescomplemented
622C22×C3C2×#12011yescharacteristic
623C22×C3C2×#12011yescharacteristic
624C22×C3#53411yescharacteristic
625C22×C3C2×#13511yescharacteristic
626C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
627C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
628C22×C3#57511yescharacteristic
629C2×D3—22no—
630C2×D3—22no—
631C2×D3—22no—
632C2×D3—22no—
633C2×D3—22no—
634C2×D3—22no—
635C2×D3—416no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—41no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—44no—
645C2×D3—44no—
646C2×D3—44no—
647C2×D3—816no—
648C2×D3—82no—
649C2×D3—82no—
650C2×D3—82no—
651C2×D3—82no—
652C3×C4—22no—
653C3×C4—42no—
654C3×C4—44no—
655C3×C4D4212yes—
656C3×C4D4212yes—
657Dic3—22no—
658Dic3—42no—
659Dic3—41no—
660Dic3—42no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—22no—
666C23—32no—
667C23—32no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—68no—
675C23—61no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—61no—
681C23—61no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—61no—
686C23—61no—
687C23—64no—
688C23—124no—
689C23—124no—
690C23—124no—
691C23—124no—
692C23—124no—
693C23—128no—
694C23—128no—
695C23—128no—
696C23—124no—
697C23—122no—
698C23—122no—
699C23—122no—
700C23—122no—
701C23—122no—
702C23—122no—
703C23—244no—
704C23—244no—
705C23—244no—
706C23—244no—
707C23#88212yes—
708C23#91112yes—
709C23#91612yes—
710C23C2×D3×D411yescharacteristic
711Q8—64no—
712Q8—122no—
713D4—24no—
714D4—48no—
715D4—42no—
716D4—64no—
717D4—64no—
718D4—128no—
719D4—1216no—
720D4—1216no—
721D4—128no—
722D4—128no—
723D4—122no—
724D4—122no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—32no—
732C2×C4—48no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—64no—
740C2×C4—64no—
741C2×C4—61no—
742C2×C4—62no—
743C2×C4—61no—
744C2×C4—62no—
745C2×C4—61no—
746C2×C4—124no—
747C2×C4—124no—
748C2×C4—124no—
749C2×C4—128no—
750C2×C4—121no—
751C2×C4—121no—
752C2×C4—121no—
753C2×C4—121no—
754C2×C4—122no—
755C2×C4—122no—
756C2×C4#88212yes—
757C2×C4C22×D1211yescharacteristic
758C2×C4C2×D3×D412yes—
759C2×C4C2×D3×D411yescharacteristic
760C2×C4#100912yes—
761C8—42no—
762C8—122no—
763C2×C3—24no—
764C2×C3—82no—
765C2×C3#240311yescharacteristic
766C2×C3C2×#44911yescharacteristic
767C2×C3#300211yescharacteristic
768C2×C3#300311yescharacteristic
769C2×C3#300611yescharacteristic
770C2×C3#318811yescharacteristic
771C2×C3#319411yescharacteristic
772D3—42no—
773D3—42no—
774D3—84no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—62no—
785C22—62no—
786C22—62no—
787C22—62no—
788C22—62no—
789C22—62no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—1216no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—121no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22—121no—
803C22—124no—
804C22—124no—
805C22—124no—
806C22—2416no—
807C22—242no—
808C22—242no—
809C22—242no—
810C22—242no—
811C22#478114yescomplemented
812C22C2×#88211yescharacteristic
813C22D3×#12011yescharacteristic
814C22#565311yescharacteristic
815C22C2×#91111yescharacteristic
816C22C2×#91611yescharacteristic
817C22D3×AGL(1,ℤ/8)11yescharacteristic
818C22#577711yescharacteristic
819C4—22no—
820C4—44no—
821C4—42no—
822C4—62no—
823C4—122no—
824C4—121no—
825C4—122no—
826C4D4×D1212yes—
827C4#560912yes—
828C3#2392011yescharacteristic, complemented, Sylow
829C2—24no—
830C2—82no—
831C2—122no—
832C2—122no—
833C2—244no—
834C2#7488411yescharacteristic
835C2C2×#478111yescharacteristic
836C2#7888411yescharacteristic
837C2#8000211yescharacteristic
838C2#8003811yescharacteristic
839C2#8130011yescharacteristic
840C2#8133911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1874C2
socleC23×C3C22×D4
hypercenter#1874D3
hypocenterC3#23920
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C2×#5606C2semidirect
2. C22×#895C2semidirect
3. C2×#5036C2semidirect
4. C2×#4781C2semidirect
5. C2×#4731C2semidirect
6. C3×#1874C2semidirect
7. #71559C2semidirect
8. #70204C2semidirect
9. #69955C2semidirect
10. #68887C2semidirect
11. #68881C2semidirect
13. C22×#237C22semidirect
19. C2×#938C22semidirect
22. C22×#213C22semidirect
25. C22×#204C22semidirect
28. C2×#897C22semidirect
34. C2×#892C22semidirect
37. C2×C3×#102C22semidirect
40. C2×#821C22semidirect
41. C2×(C2×D3)⋊C8C22semidirect
42. C2×(C2×D3)⋊C8C22semidirect
44. C2×#810C22semidirect
45. C2×#809C22semidirect
48. C3×#340C22semidirect
49. #4529C22semidirect
58. #1874D3semidirect
97. C3×#121D4semidirect
120. #924D4semidirect
134. #895D4semidirect
177. C2×#102C2×D3semidirect
183. #340C2×D3semidirect
209. C2×C3×D4C2×D4semidirect
276. C2×Dic6C2×D4semidirect
284. C3×C4⋊C4C2×D4semidirect
295. C4⋊Dic3C2×D4semidirect
358. #121D12semidirect
545. C2×D4C2×D12semidirect
598. C4⋊C4C2×D12semidirect
621. C22×C3#449semidirect
811. C22#4781semidirect
828. C3#23920semidirect

Maximal subgroups

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

subgroupindex
C2×#56062
C22×#8952
C2×#50362
C2×#47812
C2×#47312
C3×#18742
#715592
#702042
#699552
#688872
#688812
#239203