Finite Group Databasebeta

← #10800832

Subgroups — #10800832

Order 768.

1952 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×D4C211yesmaximal, characteristic, complemented
2C2×#5014C211yesmaximal, characteristic, complemented
3C2×#4773C211yesmaximal, characteristic
4C2×#4711C211yesmaximal, characteristic, complemented
5C4×#895C211yesmaximal, characteristic, complemented
6C3×#1762C211yesmaximal, characteristic, complemented
7#70198C211yesmaximal, characteristic, complemented
8#70172C211yesmaximal, characteristic, complemented
9#70170C211yesmaximal, characteristic, complemented
10#69807C211yesmaximal, characteristic, complemented
11#69474C211yesmaximal, characteristic, complemented
12#68897C211yesmaximal, characteristic, complemented
13#68895C211yesmaximal, characteristic, complemented
14#68880C211yesmaximal, characteristic, complemented
15#68875C211yesmaximal, characteristic, complemented
16#21452—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C23×C4×D3—21no—
19C2×C3×C4×D4C2211yescharacteristic
20C2×D4×Dic3C2211yescharacteristic
21C22×#213C2211yescharacteristic
22C2×C4×#67—21no—
23C22×D24C2211yescharacteristic
24C4×D3×D4—24no—
25C4×D3×D4—24no—
26C2×#895C2211yescharacteristic
27C2×#893C2211yescharacteristic
28C2×D3×C4⋊C4C2211yescharacteristic
29C2×#67⋊C4—21no—
30C2×D3×C22⋊C4—21no—
31C2×C4×D12—21no—
32C2×C4×D12C2211yescharacteristic
33C2×C4×D12C2211yescharacteristic, complemented
34C2×C42×D3C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#97C2211yescharacteristic, complemented
38C3×C4×C4⋊C4C2211yescharacteristic, complemented
39C2×#832C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×#821C2211yescharacteristic, complemented
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×#817C2211yescharacteristic, complemented
45#5014—24no—
46#4988C2211yescharacteristic, complemented
47#4987C2211yescharacteristic
48#4984C2211yescharacteristic, complemented
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic, complemented
52C2×#808C2211yescharacteristic, complemented
53C4×(C2×D3)⋊C4—21no—
54C2×#803C2211yescharacteristic, complemented
55#4773C418yescomplemented
56#4711—24no—
57#4670—21no—
58#4665—21no—
59C3×#340C2211yescharacteristic, complemented
60C3×#340C2211yescharacteristic, complemented
61#4550C2211yescharacteristic, complemented
62#4550C2211yescharacteristic, complemented
63#4529C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65C22×C4×D4—31no—
66C2×#447—31no—
67C2×#442—31no—
68C2×#442—31no—
69C4×#121—31no—
70#1879—31no—
71#1879—31no—
72#1874—31no—
73#1864—31no—
74#1864—31no—
75#1853—31no—
76#1786—31no—
77#1762—31no—
78#1762D311yescharacteristic, complemented
79#1749—31no—
80C24×D3—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C22×#67—21no—
84C23×Dic3—21no—
85C2×D3×D4—22no—
86C2×D3×D4—22no—
87C2×D3×D4—22no—
88C2×D3×D4—22no—
89C2×D3×D4—22no—
90C2×D3×D4C2×C414yescomplemented
91C22×D12—21no—
92C22×D12C2311yescharacteristic
93C22×D12C2311yescharacteristic
94C22×C4×D3—28no—
95C22×C4×D3—21no—
96C22×C4×D3—21no—
97C22×C4×D3—21no—
98C22×C4×D3—21no—
99C22×C4×D3—44no—
100C22×C4×D3—44no—
101C22×C4×D3D411yescharacteristic
102C22×C4×D3D411yescharacteristic
103C22×C4×D3C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C3×C4×D4—22no—
107C3×C4×D4D414yescomplemented
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C22⋊C4—21no—
112C2×C3×C42—21no—
113C2×C3×C42C2311yescharacteristic
114C2×#217—21no—
115D4×Dic3—22no—
116D4×Dic3—22no—
117C2×#213—22no—
118C2×#213—22no—
119C2×#213C2×C414yescomplemented
120C4×#67—28no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×C4⋊Dic3—21no—
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×Dic3⋊C4—21no—
132C2×C4×Dic3D411yescharacteristic
133C2×C4×Dic3D411yescharacteristic
134C2×C4×Dic3C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137C2×D24—22no—
138C2×D24—22no—
139C2×D24C2×C414yescomplemented
140#895—22no—
141#895C2×C414yescomplemented
142#893—22no—
143#893—22no—
144D3×C4⋊C4—22no—
145D3×C4⋊C4—22no—
146#67⋊C4—28no—
147D3×C22⋊C4—28no—
148C4×D12—22no—
149C4×D12—22no—
150C4×D12—22no—
151C4×D12—44no—
152C4×D12D414yescomplemented
153C42×D3—22no—
154C42×D3—22no—
155C3×#102—22no—
156C3×#102C2×C414yescomplemented
157C3×#97—22no—
158C3×#95—21no—
159#832—22no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162#821—22no—
163#821—22no—
164(C2×D3)⋊C8—22no—
165(C2×D3)⋊C8C2×C414yescomplemented
166#817—22no—
167#809—22no—
168#809—22no—
169#809C2×C414yescomplemented
170#808—22no—
171#803—22no—
172C23×D4—31no—
173C24×C4—61no—
174C22×D8—31no—
175C22×D8—31no—
176C2×#121—31no—
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179C2×C4×D4—31no—
180C2×C4×D4—31no—
181C2×C4×D4—61no—
182C2×C4×D4—61no—
183C2×C4×D4—61no—
184C2×C4×D4—64no—
185C2×C4×D4—64no—
186C2×C4×D4C2×D311yescharacteristic
187C22×C4⋊C4—31no—
188C22×C22⋊C4—61no—
189C22×C42—31no—
190#447—38no—
191#442—64no—
192#442—64no—
193C2×#106—31no—
194C2×#106—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×#102—31no—
200C2×#102—31no—
201C2×#102C2×D311yescharacteristic
202C2×#102C2×D311yescharacteristic
203C2×C22⋊C8—31no—
204C2×C22⋊C8—31no—
205C2×#97—31no—
206C2×#97C2×D311yescharacteristic, complemented
207#390—31no—
208#389—31no—
209#388—61no—
210#386—61no—
211#380—31no—
212C4×C4⋊C4C2×D311yescharacteristic, complemented
213C4×C22⋊C4—61no—
214#340—31no—
215#340—31no—
216#340C2×D311yescharacteristic, complemented
217#340C2×D311yescharacteristic, complemented
218#336—31no—
219#336—31no—
220C24×C3—21no—
221C23×D3—24no—
222C23×D3—24no—
223C23×D3—21no—
224C23×D3—24no—
225C23×D3—21no—
226C23×D3—42no—
227C23×D3—42no—
228C23×D3—42no—
229C23×D3—42no—
230C23×D3C2×D411yescharacteristic
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4C22×C412yes—
235C2×C3×D4C2×D412yes—
236C2×C3×D4#4112yes—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—24no—
240C22×C3×C4—21no—
241C22×C3×C4—42no—
242C22×C3×C4—42no—
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2411yescharacteristic
246C2×#67—24no—
247C2×#67—24no—
248C2×#67—24no—
249C22×Dic3—24no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—42no—
253C22×Dic3—42no—
254C22×Dic3C2×D411yescharacteristic
255C22×Dic3C2×D411yescharacteristic
256C22×Dic3C2×D411yescharacteristic
257D3×D4—28no—
258D3×D4—28no—
259D3×D4—28no—
260D3×D4—28no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—24no—
269C2×D12—21no—
270C2×D12—42no—
271C2×D12—42no—
272C2×D12C22×C412yes—
273C2×D12C22×C412yescomplemented
274C2×D12C2×D412yes—
275C2×D12#4112yes—
276C2×C4×D3—22no—
277C2×C4×D3—22no—
278C2×C4×D3—21no—
279C2×C4×D3—21no—
280C2×C4×D3—21no—
281C2×C4×D3—21no—
282C2×C4×D3—22no—
283C2×C4×D3—24no—
284C2×C4×D3—24no—
285C2×C4×D3—22no—
286C2×C4×D3—22no—
287C2×C4×D3—24no—
288C2×C4×D3—432no—
289C2×C4×D3—41no—
290C2×C4×D3—42no—
291C2×C4×D3—42no—
292C2×C4×D3—42no—
293C2×C4×D3—42no—
294C2×C4×D3—42no—
295C2×C4×D3—42no—
296C2×C4×D3—42no—
297C2×C4×D3—42no—
298C2×C4×D3—42no—
299C2×C4×D3C22×C412yes—
300C2×C4×D3#4112yes—
301C2×C3×C8—21no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C2×C3×C8C22×C412yescomplemented
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4C22×C412yescomplemented
312C3×C4⋊C4C2×D412yes—
313C3×C22⋊C4—24no—
314C3×C42—42no—
315C3×C42C2×D412yes—
316C3×C42C2×D412yes—
317#217—24no—
318#213—28no—
319(C2×D3)⋊C4—24no—
320(C2×D3)⋊C4—24no—
321(C2×D3)⋊C4—24no—
322(C2×D3)⋊C4—42no—
323(C2×D3)⋊C4—42no—
324(C2×D3)⋊C4—42no—
325(C2×D3)⋊C4—42no—
326C4⋊Dic3—21no—
327C4⋊Dic3—21no—
328C4⋊Dic3—21no—
329C4⋊Dic3—42no—
330C4⋊Dic3C2×D412yes—
331Dic3⋊C4—24no—
332C4×Dic3—22no—
333C4×Dic3—22no—
334C4×Dic3—21no—
335C4×Dic3—21no—
336C2×C3⋊C8—21no—
337C2×C3⋊C8—21no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8C22×C412yescomplemented
342D24—28no—
343C25—61no—
344C22×D4—34no—
345C22×D4—31no—
346C22×D4—31no—
347C22×D4—61no—
348C22×D4—62no—
349C22×D4—61no—
350C22×D4—62no—
351C22×D4—62no—
352C22×D4—62no—
353C22×D4—62no—
354C22×D4C22×D311yescharacteristic
355C23×C4—21no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—31no—
359C23×C4—61no—
360C23×C4—61no—
361C23×C4—68no—
362C23×C4—61no—
363C23×C4—61no—
364C23×C4—61no—
365C23×C4—124no—
366C23×C4—124no—
367C2×D8—34no—
368C2×D8—34no—
369C2×D8—62no—
370C2×D8—62no—
371C2×D8—62no—
372C2×D8—62no—
373C22×C8—31no—
374C22×C8—31no—
375C22×C8C22×D311yescharacteristic
376C22×C8C22×D311yescharacteristic
377#121—34no—
378#121—62no—
379C4×D4—22no—
380C4×D4—34no—
381C4×D4—68no—
382C4×D4—62no—
383C4×D4—62no—
384C4×D4—68no—
385C4×D4—62no—
386C4×D4—62no—
387C4×D4—62no—
388C4×D4—62no—
389C4×D4—62no—
390C4×D4—124no—
391C4×D4D1214yescomplemented
392C2×C4⋊C4—31no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—62no—
395C2×C4⋊C4—61no—
396C2×C4⋊C4—62no—
397C2×C4⋊C4—61no—
398C2×C4⋊C4C22×D311yescharacteristic
399C2×C4⋊C4C22×D311yescharacteristic
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—68no—
403C2×C22⋊C4—61no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C22⋊C4—61no—
408C2×C22⋊C4—61no—
409C2×C22⋊C4—61no—
410C2×C22⋊C4—61no—
411C2×C42—21no—
412C2×C42—31no—
413C2×C42—31no—
414C2×C42—31no—
415C2×C42—62no—
416C2×C42—62no—
417C2×C42C22×D311yescharacteristic
418#106—62no—
419#106—62no—
420#102—22no—
421#102—34no—
422#102—62no—
423#102—62no—
424#102—62no—
425#102—62no—
426#102—62no—
427#102C4×D314yescomplemented
428C22⋊C8—34no—
429C22⋊C8—62no—
430#97—22no—
431#97—62no—
432#95—21no—
433#95—61no—
434#95—61no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3C22×D411yescharacteristic
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—21no—
446C22×D3—21no—
447C22×D3—216no—
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—48no—
453C22×D3—48no—
454C22×D3—48no—
455C22×D3—48no—
456C22×D3—48no—
457C22×D3—41no—
458C22×D3—41no—
459C22×D3—41no—
460C22×D3—41no—
461C22×D3—48no—
462C22×D3—41no—
463C22×D3—41no—
464C22×D3—41no—
465C22×D3—41no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3C4×D412yes—
469C22×D3AGL(1,ℤ/8)12yes—
470C22×D3AGL(1,ℤ/8)12yes—
471C3×D4—22no—
472C3×D4—22no—
473C3×D4—22no—
474C3×D4C4×D414yescomplemented
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—48no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4#12012yes—
490C2×C3×C4#12012yes—
491C2×C3×C4C23×C411yescharacteristic
492C2×C3×C4C22×D411yescharacteristic
493C2×C3×C4C22×D411yescharacteristic
494C2×C3×C4C2×#4111yescharacteristic
495C2×C3×C4C2×#4111yescharacteristic
496C2×C3×C4C2×#4111yescharacteristic
497#67—216no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—22no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—48no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3C4×D412yes—
513C2×Dic3AGL(1,ℤ/8)12yes—
514D12—22no—
515D12—22no—
516D12—22no—
517D12—22no—
518D12—22no—
519D12—48no—
520D12—41no—
521D12—41no—
522D12C4×D414yescomplemented
523C4×D3—28no—
524C4×D3—22no—
525C4×D3—22no—
526C4×D3—22no—
527C4×D3—22no—
528C4×D3—48no—
529C4×D3—44no—
530C4×D3—48no—
531C4×D3—48no—
532C4×D3—84no—
533C3×C8—22no—
534C3×C8—41no—
535C3⋊C8—22no—
536C3⋊C8—41no—
537C24—21no—
538C24—31no—
539C24—64no—
540C24—64no—
541C24—64no—
542C24—61no—
543C24—61no—
544C24—122no—
545C24—122no—
546C24—122no—
547C24—122no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—32no—
552C2×D4—32no—
553C2×D4—32no—
554C2×D4—32no—
555C2×D4—64no—
556C2×D4—64no—
557C2×D4—68no—
558C2×D4—68no—
559C2×D4—68no—
560C2×D4—64no—
561C2×D4—64no—
562C2×D4—68no—
563C2×D4—61no—
564C2×D4—61no—
565C2×D4—61no—
566C2×D4—61no—
567C2×D4—61no—
568C2×D4—61no—
569C2×D4—61no—
570C2×D4—61no—
571C2×D4—122no—
572C2×D4—122no—
573C2×D4C2×C4×D312yes—
574C2×D4C2×D1212yes—
575C2×D4#23512yes—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—21no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—32no—
583C22×C4—32no—
584C22×C4—31no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—62no—
588C22×C4—62no—
589C22×C4—62no—
590C22×C4—64no—
591C22×C4—64no—
592C22×C4—62no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—64no—
598C22×C4—61no—
599C22×C4—62no—
600C22×C4—64no—
601C22×C4—61no—
602C22×C4—121no—
603C22×C4—122no—
604C22×C4—122no—
605C22×C4—122no—
606C22×C4—122no—
607C22×C4—122no—
608C22×C4—122no—
609C22×C4—1232no—
610C22×C4—122no—
611C22×C4—122no—
612C22×C4—122no—
613C22×C4—122no—
614C22×C4—122no—
615C22×C4D3×D411yescharacteristic
616C22×C4D3×D411yescharacteristic
617C22×C4C23×D311yescharacteristic
618D8—68no—
619D8—68no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—32no—
626C2×C8—61no—
627C2×C8—61no—
628C2×C8—61no—
629C2×C8—61no—
630C2×C8—61no—
631C2×C8C2×C4×D312yescomplemented
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—32no—
637C4⋊C4—64no—
638C4⋊C4—61no—
639C4⋊C4—61no—
640C4⋊C4—61no—
641C4⋊C4—122no—
642C4⋊C4C2×C4×D312yescomplemented
643C4⋊C4C2×D1212yes—
644C22⋊C4—24no—
645C22⋊C4—64no—
646C22⋊C4—64no—
647C22⋊C4—64no—
648C22⋊C4—64no—
649C22⋊C4—122no—
650C22⋊C4—122no—
651C22⋊C4—122no—
652C22⋊C4—122no—
653C42—42no—
654C42—62no—
655C42—62no—
656C42—61no—
657C42—61no—
658C42C2×D1212yes—
659C42D3×D412yes—
660C22×C3—24no—
661C22×C3—42no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3C2×C4×D411yescharacteristic
668C22×C3C2×#12011yescharacteristic
669C22×C3#52511yescharacteristic
670C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
671C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
672C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
673C22×C3#57511yescharacteristic
674C2×D3—22no—
675C2×D3—22no—
676C2×D3—22no—
677C2×D3—22no—
678C2×D3—22no—
679C2×D3—22no—
680C2×D3—24no—
681C2×D3—432no—
682C2×D3—42no—
683C2×D3—42no—
684C2×D3—42no—
685C2×D3—42no—
686C2×D3—42no—
687C2×D3—42no—
688C2×D3—42no—
689C2×D3—42no—
690C2×D3—42no—
691C2×D3—81no—
692C2×D3—81no—
693C2×D3—81no—
694C2×D3—81no—
695C2×D3#44214yescomplemented
696C3×C4—22no—
697C3×C4—22no—
698C3×C4—42no—
699C3×C4—42no—
700C3×C4—81no—
701C3×C4C2×C4×D411yescharacteristic
702C3×C4C2×C4×D411yescharacteristic
703C3×C4#52511yescharacteristic
704C3×C4#52511yescharacteristic
705Dic3—22no—
706Dic3—22no—
707Dic3—42no—
708Dic3—41no—
709Dic3—81no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—32no—
714C23—32no—
715C23—32no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—616no—
721C23—61no—
722C23—61no—
723C23—61no—
724C23—61no—
725C23—62no—
726C23—62no—
727C23—62no—
728C23—62no—
729C23—128no—
730C23—128no—
731C23—128no—
732C23—128no—
733C23—128no—
734C23—128no—
735C23—121no—
736C23—121no—
737C23—121no—
738C23—121no—
739C23—121no—
740C23—121no—
741C23—121no—
742C23—121no—
743C23—121no—
744C23—121no—
745C23C2×D3×D411yescharacteristic
746D4—22no—
747D4—22no—
748D4—22no—
749D4—34no—
750D4—616no—
751D4—62no—
752D4—62no—
753D4—62no—
754D4—62no—
755D4—62no—
756D4—128no—
757D4—121no—
758D4—121no—
759D4C4×D1214yescomplemented
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—32no—
767C2×C4—32no—
768C2×C4—48no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—68no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—61no—
786C2×C4—62no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—124no—
790C2×C4—128no—
791C2×C4—128no—
792C2×C4—128no—
793C2×C4—128no—
794C2×C4—121no—
795C2×C4—121no—
796C2×C4—121no—
797C2×C4—121no—
798C2×C4—121no—
799C2×C4—244no—
800C2×C4#88212yes—
801C2×C4#88212yes—
802C2×C4C22×C4×D311yescharacteristic
803C2×C4C22×D1211yescharacteristic
804C2×C4C2×#23511yescharacteristic
805C2×C4C2×D3×D411yescharacteristic
806C2×C4D3×#4111yescharacteristic
807C2×C4D3×#4111yescharacteristic
808C8—22no—
809C8—41no—
810C8—62no—
811C8—121no—
812C2×C3—44no—
813C2×C3C4×#12011yescharacteristic
814C2×C3C2×#44211yescharacteristic
815C2×C3C4×AGL(1,ℤ/8)11yescharacteristic
816C2×C3#300311yescharacteristic
817C2×C3#300611yescharacteristic
818C2×C3#310911yescharacteristic
819C2×C3#311411yescharacteristic
820D3—24no—
821D3—44no—
822D3—82no—
823C22—24no—
824C22—34no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—62no—
832C22—62no—
833C22—62no—
834C22—62no—
835C22—62no—
836C22—62no—
837C22—64no—
838C22—1232no—
839C22—122no—
840C22—122no—
841C22—122no—
842C22—122no—
843C22—122no—
844C22—122no—
845C22—122no—
846C22—122no—
847C22—122no—
848C22—241no—
849C22—241no—
850C22—241no—
851C22—241no—
852C22C2×#88211yescharacteristic
853C22C4×D3×D411yescharacteristic
854C22#554711yescharacteristic
855C22D3×AGL(1,ℤ/8)11yescharacteristic
856C22D3×AGL(1,ℤ/8)11yescharacteristic
857C22D3×AGL(1,ℤ/8)11yescharacteristic
858C22#577711yescharacteristic
859C4—22no—
860C4—22no—
861C4—42no—
862C4—42no—
863C4—62no—
864C4—62no—
865C4—81no—
866C4—121no—
867C4—122no—
868C4—241no—
869C4C2×C4×D1211yescharacteristic
870C4#552411yescharacteristic
871C4C4×D3×D411yescharacteristic
872C4#554711yescharacteristic
873C3#2145211yescharacteristic, complemented, Sylow
874C2—44no—
875C2—64no—
876C2—124no—
877C2—242no—
878C2C4×#88211yescharacteristic
879C2#7888411yescharacteristic
880C2#7892611yescharacteristic
881C2#7977311yescharacteristic
882C2#7978211yescharacteristic
883C2D3×#44211yescharacteristic
884C2#7986911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1762C2
socleC23×C3C22×D4
prime radicalC2×#4773C2
cosocleC22×C3×C4C24
hypercenter#1762D3
hypocenterC3#21452
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
1. C2×C4×D3×D4C2semidirect
2. C2×#5014C2semidirect
4. C2×#4711C2semidirect
5. C4×#895C2semidirect
6. C3×#1762C2semidirect
7. #70198C2semidirect
8. #70172C2semidirect
9. #70170C2semidirect
10. #69807C2semidirect
11. #69474C2semidirect
12. #68897C2semidirect
13. #68895C2semidirect
14. #68880C2semidirect
15. #68875C2semidirect
33. C2×C4×D12C22semidirect
37. C2×C3×#97C22semidirect
38. C3×C4×C4⋊C4C22semidirect
41. C2×#821C22semidirect
44. C2×#817C22semidirect
46. #4988C22semidirect
48. #4984C22semidirect
51. C2×#809C22semidirect
52. C2×#808C22semidirect
54. C2×#803C22semidirect
55. #4773C4semidirect
59. C3×#340C22semidirect
60. C3×#340C22semidirect
61. #4550C22semidirect
62. #4550C22semidirect
63. #4529C22semidirect
64. #4529C22semidirect
78. #1762D3semidirect
90. C2×D3×D4C2×C4semidirect
107. C3×C4×D4D4semidirect
119. C2×#213C2×C4semidirect
139. C2×D24C2×C4semidirect
141. #895C2×C4semidirect
152. C4×D12D4semidirect
156. C3×#102C2×C4semidirect
165. (C2×D3)⋊C8C2×C4semidirect
169. #809C2×C4semidirect
206. C2×#97C2×D3semidirect
212. C4×C4⋊C4C2×D3semidirect
216. #340C2×D3semidirect
217. #340C2×D3semidirect
273. C2×D12C22×C4semidirect
306. C2×C3×C8C22×C4semidirect
311. C3×C4⋊C4C22×C4semidirect
341. C2×C3⋊C8C22×C4semidirect
391. C4×D4D12semidirect
427. #102C4×D3semidirect
474. C3×D4C4×D4semidirect
522. D12C4×D4semidirect
631. C2×C8C2×C4×D3semidirect
642. C4⋊C4C2×C4×D3semidirect
695. C2×D3#442semidirect
759. D4C4×D12semidirect
873. C3#21452semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×D42
C2×#50142
C2×#47732
C2×#47112
C4×#8952
C3×#17622
#701982
#701722
#701702
#698072
#694742
#688972
#688952
#688802
#688752
#214523