Finite Group Databasebeta

← #10800833

Subgroups — #10800833

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×#5156C211yesmaximal, characteristic
3C2×#5152C211yesmaximal, characteristic, complemented
4C2×#4785C211yesmaximal, characteristic, complemented
5#76291C211yesmaximal, characteristic, complemented
6C3×#1879C211yesmaximal, characteristic, complemented
7#71607C211yesmaximal, characteristic, complemented
8#70200C211yesmaximal, characteristic, complemented
9#70198C211yesmaximal, characteristic, complemented
10#70152C211yesmaximal, characteristic, complemented
11#69657C211yesmaximal, characteristic, complemented
12#68875C211yesmaximal, characteristic, complemented
13#68782C211yesmaximal, characteristic, complemented
14#68671C211yesmaximal, characteristic, complemented
15#68600C211yesmaximal, characteristic, complemented
16#21452—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C23×C4×D3—21no—
19C22×C3×D8C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×#938C2211yescharacteristic
22C2×D4×Dic3C2211yescharacteristic
23C2×D4×Dic3C2211yescharacteristic, complemented
24C22×#213C2211yescharacteristic
25C2×C4×#67—21no—
26C4×D3×D4—24no—
27C4×D3×D4—24no—
28C2×#893C2211yescharacteristic
29C2×D3×C4⋊C4C2211yescharacteristic
30C2×#67⋊C4—21no—
31C2×#67⋊C4—21no—
32C2×D3×C22⋊C4—21no—
33C2×C4×D12C2211yescharacteristic
34C2×C42×D3C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic, complemented
37C3×#390C2211yescharacteristic, complemented
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic, complemented
41#5156C418yescomplemented
42#5152—24no—
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×#817C2211yescharacteristic, complemented
48C2×#815C2211yescharacteristic, complemented
49C2×#815C2211yescharacteristic, complemented
50#4987C2211yescharacteristic
51Dic3×C4⋊C4C2211yescharacteristic, complemented
52C2×#809C2211yescharacteristic
53C2×#808C2211yescharacteristic, complemented
54#4956—21no—
55#4945—21no—
56Dic3×C22⋊C4—21no—
57#4928C2211yescharacteristic, complemented
58#4785—24no—
59C3×#340C2211yescharacteristic, complemented
60C3×#336C2211yescharacteristic, complemented
61#4551C2211yescharacteristic, complemented
62#4529C2211yescharacteristic, complemented
63#4529C2211yescharacteristic, complemented
64#4524C2211yescharacteristic, complemented
65C22×C4×D4—31no—
66C2×#447—31no—
67C2×#442—31no—
68C2×#442—31no—
69C4×#121—31no—
70#1879—31no—
71#1879D311yescharacteristic, complemented
72#1874—31no—
73#1864—31no—
74#1864—31no—
75#1853—31no—
76#1786—31no—
77#1762—31no—
78#1762—31no—
79#1749—31no—
80C24×D3—21no—
81C22×C3×D4C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C22×#67—21no—
85C22×#67—21no—
86C23×Dic3—21no—
87C23×Dic3—21no—
88C2×D3×D4—22no—
89C2×D3×D4—22no—
90C2×D3×D4—22no—
91C2×D3×D4—22no—
92C2×D3×D4—22no—
93C2×D3×D4C2×C414yescomplemented
94C22×D12C2311yescharacteristic
95C22×C4×D3—28no—
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
104C2×C3×D8—22no—
105C2×C3×D8—22no—
106C2×C3×D8C2×C414yescomplemented
107C22×C3×C8C2311yescharacteristic
108C22×C3×C8C2311yescharacteristic
109C3×C4×D4—22no—
110C3×C4×D4—22no—
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C42C2311yescharacteristic
117C2×#217—21no—
118C2×#217—21no—
119C2×#217—21no—
120#938—22no—
121#938C2×C414yescomplemented
122D4×Dic3—22no—
123D4×Dic3—22no—
124D4×Dic3—22no—
125D4×Dic3D414yescomplemented
126C2×#213—22no—
127C2×#213—22no—
128C2×#213C2×C414yescomplemented
129C4×#67—28no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×C4×Dic3—21no—
139C2×C4×Dic3D411yescharacteristic
140C2×C4×Dic3D411yescharacteristic
141C2×C4×Dic3C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144#893—22no—
145#893D414yescomplemented
146D3×C4⋊C4—22no—
147D3×C4⋊C4—22no—
148#67⋊C4—28no—
149#67⋊C4—44no—
150D3×C22⋊C4—28no—
151C4×D12—22no—
152C4×D12—22no—
153C42×D3—22no—
154C42×D3—22no—
155C3×#102—22no—
156C3×#102—22no—
157#832—22no—
158#832—22no—
159#832C2×C414yescomplemented
160C3⋊#95—21no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163#821—22no—
164#821C2×C414yescomplemented
165(C2×D3)⋊C8—22no—
166(C2×D3)⋊C8C2×C414yescomplemented
167#817—22no—
168#815—22no—
169#815—22no—
170#809—22no—
171#808—22no—
172C23×D4—31no—
173C24×C4—61no—
174C22×D8—31no—
175C22×D8C2×D311yescharacteristic
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, complemented
203C2×C22⋊C8—31no—
204C2×C22⋊C8—31no—
205C2×#97—31no—
206C2×#97—31no—
207#390C2×D311yescharacteristic, complemented
208#389—31no—
209#388—61no—
210#386—61no—
211#380—31no—
212C4×C4⋊C4—31no—
213C4×C22⋊C4—61no—
214#340—31no—
215#340—31no—
216#340—31no—
217#340C2×D311yescharacteristic, complemented
218#336—31no—
219#336C2×D311yescharacteristic, complemented
220C24×C3—21no—
221C24×C3—21no—
222C23×D3—24no—
223C23×D3—24no—
224C23×D3—21no—
225C23×D3—24no—
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×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4C22×C412yes—
240C2×C3×D4C22×C412yescomplemented
241C2×C3×D4C2×D412yes—
242C2×C3×D4#4112yes—
243C22×C3×C4—24no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—42no—
247C22×C3×C4—42no—
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2411yescharacteristic
251C2×#67—24no—
252C2×#67—24no—
253C2×#67—24no—
254C2×#67—24no—
255C2×#67—42no—
256C2×#67—42no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—24no—
260C22×Dic3—21no—
261C22×Dic3—42no—
262C22×Dic3—42no—
263C22×Dic3—42no—
264C22×Dic3—42no—
265C22×Dic3—42no—
266C22×Dic3C2×D411yescharacteristic
267C22×Dic3C2×D411yescharacteristic
268C22×Dic3C2×D411yescharacteristic
269D3×D4—28no—
270D3×D4—28no—
271D3×D4—28no—
272D3×D4—28no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12C22×C412yes—
277C2×D12C2×D412yes—
278C2×D12#4112yes—
279C2×C4×D3—22no—
280C2×C4×D3—22no—
281C2×C4×D3—21no—
282C2×C4×D3—21no—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×C4×D3—22no—
286C2×C4×D3—24no—
287C2×C4×D3—24no—
288C2×C4×D3—22no—
289C2×C4×D3—22no—
290C2×C4×D3—24no—
291C2×C4×D3—432no—
292C2×C4×D3—41no—
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—
301C3×D8—28no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C2×C3×C8—21no—
307C2×C3×C8C22×C412yescomplemented
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4C2×D412yes—
312C3×C22⋊C4—24no—
313C3×C22⋊C4—42no—
314C3×C22⋊C4—42no—
315C3×C42—21no—
316C3×C42—21no—
317#217—24no—
318#217—24no—
319#217—42no—
320#213—28no—
321(C2×D3)⋊C4—24no—
322(C2×D3)⋊C4—24no—
323(C2×D3)⋊C4—42no—
324C4⋊Dic3—21no—
325C4⋊Dic3—21no—
326C4⋊Dic3—21no—
327C4⋊Dic3—21no—
328C4⋊Dic3C22×C412yescomplemented
329C4⋊Dic3C2×D412yes—
330Dic3⋊C4—24no—
331Dic3⋊C4—42no—
332C4×Dic3—22no—
333C4×Dic3—22no—
334C4×Dic3—42no—
335C4×Dic3C2×D412yes—
336C4×Dic3C2×D412yes—
337C2×C3⋊C8—21no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—21no—
342C2×C3⋊C8C22×C412yescomplemented
343C25—61no—
344C22×D4—34no—
345C22×D4—31no—
346C22×D4—62no—
347C22×D4—61no—
348C22×D4—62no—
349C22×D4—62no—
350C22×D4—62no—
351C22×D4—62no—
352C22×D4—61no—
353C22×D4C22×D311yescharacteristic
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—22no—
368C2×D8—22no—
369C2×D8—34no—
370C2×D8—62no—
371C2×D8—62no—
372C2×D8C4×D314yescomplemented
373C22×C8—31no—
374C22×C8—31no—
375C22×C8C22×D311yescharacteristic
376C22×C8C22×D311yescharacteristic
377#121—34no—
378#121—62no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—34no—
382C4×D4—34no—
383C4×D4—62no—
384C4×D4—62no—
385C4×D4—62no—
386C4×D4—62no—
387C4×D4—62no—
388C4×D4—62no—
389C4×D4—68no—
390C4×D4—68no—
391C4×D4—124no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—62no—
396C2×C4⋊C4—61no—
397C2×C4⋊C4—62no—
398C2×C4⋊C4—61no—
399C2×C4⋊C4C22×D311yescharacteristic
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—68no—
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—31no—
412C2×C42—31no—
413C2×C42—31no—
414C2×C42—62no—
415C2×C42—62no—
416C2×C42—61no—
417C2×C42C22×D311yescharacteristic
418#106—62no—
419#106—62no—
420#102—22no—
421#102—22no—
422#102—34no—
423#102—34no—
424#102—62no—
425#102—62no—
426#102—62no—
427#102—62no—
428C22⋊C8—34no—
429C22⋊C8—62no—
430#97—62no—
431#97—62no—
432#95—61no—
433#95—61no—
434#95—61no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3C22×D411yescharacteristic
450C22×D3—21no—
451C22×D3—21no—
452C22×D3—21no—
453C22×D3—21no—
454C22×D3—216no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—48no—
459C22×D3—48no—
460C22×D3—48no—
461C22×D3—48no—
462C22×D3—48no—
463C22×D3—41no—
464C22×D3—41no—
465C22×D3—41no—
466C22×D3—41no—
467C22×D3—48no—
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×D4—22no—
475C3×D4—22no—
476C3×D4—41no—
477C3×D4—41no—
478C3×D4C4×D414yescomplemented
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—22no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—48no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4AGL(1,ℤ/8)12yes—
492C2×C3×C4C23×C411yescharacteristic
493C2×C3×C4C22×D411yescharacteristic
494C2×C3×C4C22×D411yescharacteristic
495C2×C3×C4C2×#4111yescharacteristic
496C2×C3×C4C2×#4111yescharacteristic
497C2×C3×C4C2×#4111yescharacteristic
498#67—216no—
499#67—48no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—48no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3—84no—
517C2×Dic3C4×D412yes—
518C2×Dic3#12012yes—
519C2×Dic3#12012yes—
520D12—22no—
521D12—22no—
522D12—22no—
523D12C4×D414yescomplemented
524C4×D3—28no—
525C4×D3—22no—
526C4×D3—22no—
527C4×D3—22no—
528C4×D3—22no—
529C4×D3—44no—
530C4×D3—48no—
531C4×D3—48no—
532C4×D3—48no—
533C3×C8—22no—
534C3×C8—41no—
535C3⋊C8—22no—
536C3⋊C8—41no—
537C24—21no—
538C24—21no—
539C24—31no—
540C24—64no—
541C24—64no—
542C24—64no—
543C24—61no—
544C24—122no—
545C24—122no—
546C24—122no—
547C24—122no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—32no—
557C2×D4—32no—
558C2×D4—32no—
559C2×D4—64no—
560C2×D4—68no—
561C2×D4—68no—
562C2×D4—68no—
563C2×D4—64no—
564C2×D4—64no—
565C2×D4—68no—
566C2×D4—64no—
567C2×D4—61no—
568C2×D4—61no—
569C2×D4—61no—
570C2×D4—122no—
571C2×D4—122no—
572C2×D4C2×C4×D312yes—
573C2×D4C2×C4×D312yescomplemented
574C2×D4D3×D412yes—
575C2×D4#23712yes—
576C22×C4—24no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—32no—
583C22×C4—32no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—62no—
587C22×C4—62no—
588C22×C4—64no—
589C22×C4—62no—
590C22×C4—62no—
591C22×C4—64no—
592C22×C4—64no—
593C22×C4—64no—
594C22×C4—62no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—121no—
603C22×C4—122no—
604C22×C4—122no—
605C22×C4—1232no—
606C22×C4—122no—
607C22×C4—122no—
608C22×C4—122no—
609C22×C4—122no—
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—28no—
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—32no—
636C4⋊C4—32no—
637C4⋊C4—64no—
638C4⋊C4—61no—
639C4⋊C4—61no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—122no—
643C4⋊C4D3×D412yes—
644C22⋊C4—24no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—64no—
648C22⋊C4—64no—
649C22⋊C4—64no—
650C22⋊C4—64no—
651C22⋊C4—122no—
652C22⋊C4—122no—
653C42—21no—
654C42—21no—
655C42—32no—
656C42—32no—
657C42—62no—
658C42—62no—
659C42—122no—
660C22×C3—24no—
661C22×C3—42no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—81no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—81no—
674C22×C3C2×C4×D411yescharacteristic
675C22×C3C2×#12011yescharacteristic
676C22×C3#52511yescharacteristic
677C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
678C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
679C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
680C22×C3#57511yescharacteristic
681C2×D3—22no—
682C2×D3—22no—
683C2×D3—22no—
684C2×D3—22no—
685C2×D3—22no—
686C2×D3—22no—
687C2×D3—24no—
688C2×D3—432no—
689C2×D3—42no—
690C2×D3—42no—
691C2×D3—42no—
692C2×D3—42no—
693C2×D3—42no—
694C2×D3—42no—
695C2×D3#44214yescomplemented
696C3×C4—22no—
697C3×C4—42no—
698C3×C4—41no—
699C3×C4—81no—
700C3×C4C2×C4×D411yescharacteristic
701C3×C4C2×C4×D411yescharacteristic
702C3×C4#52511yescharacteristic
703C3×C4#52511yescharacteristic
704Dic3—22no—
705Dic3—22no—
706Dic3—22no—
707Dic3—42no—
708Dic3—42no—
709Dic3—81no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—32no—
715C23—32no—
716C23—32no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—616no—
728C23—61no—
729C23—61no—
730C23—61no—
731C23—61no—
732C23—62no—
733C23—62no—
734C23—62no—
735C23—128no—
736C23—128no—
737C23—128no—
738C23—128no—
739C23—128no—
740C23—128no—
741C23—121no—
742C23—121no—
743C23—121no—
744C23—121no—
745C23C2×D3×D411yescharacteristic
746D4—22no—
747D4—22no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—34no—
752D4—41no—
753D4—41no—
754D4—616no—
755D4—62no—
756D4—62no—
757D4—62no—
758D4—128no—
759D4#67⋊C414yescomplemented
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—32no—
767C2×C4—32no—
768C2×C4—32no—
769C2×C4—48no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—68no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—128no—
789C2×C4—124no—
790C2×C4—128no—
791C2×C4—128no—
792C2×C4—128no—
793C2×C4—121no—
794C2×C4—121no—
795C2×C4—121no—
796C2×C4—121no—
797C2×C4—121no—
798C2×C4—121no—
799C2×C4—121no—
800C2×C4—244no—
801C2×C4#91112yes—
802C2×C4C22×C4×D311yescharacteristic
803C2×C4C2×D3×D411yescharacteristic
804C2×C4C2×D3×D411yescharacteristic
805C2×C4C2×#23711yescharacteristic
806C2×C4D3×#4111yescharacteristic
807C2×C4D3×#4111yescharacteristic
808C8—22no—
809C8—41no—
810C8—62no—
811C8—121no—
812C2×C3—44no—
813C2×C3—82no—
814C2×C3C4×#12011yescharacteristic
815C2×C3C2×#44211yescharacteristic
816C2×C3C4×AGL(1,ℤ/8)11yescharacteristic
817C2×C3#300311yescharacteristic
818C2×C3#300611yescharacteristic
819C2×C3#310911yescharacteristic
820C2×C3#311411yescharacteristic
821D3—24no—
822D3—44no—
823C22—24no—
824C22—34no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—62no—
835C22—62no—
836C22—62no—
837C22—62no—
838C22—62no—
839C22—62no—
840C22—64no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—1232no—
846C22—122no—
847C22—122no—
848C22—122no—
849C22—122no—
850C22—122no—
851C22—122no—
852C22C4×D3×D411yescharacteristic
853C22D3×#12011yescharacteristic
854C22#560611yescharacteristic
855C22C2×#91111yescharacteristic
856C22#576811yescharacteristic
857C22D3×AGL(1,ℤ/8)11yescharacteristic
858C22D3×AGL(1,ℤ/8)11yescharacteristic
859C4—22no—
860C4—42no—
861C4—41no—
862C4—62no—
863C4—62no—
864C4—62no—
865C4—81no—
866C4—122no—
867C4—122no—
868C4—241no—
869C4C2×#67⋊C411yescharacteristic
870C4C4×D3×D411yescharacteristic
871C4#560611yescharacteristic
872C4#565611yescharacteristic
873C3#2145211yescharacteristic, complemented, Sylow
874C2—44no—
875C2—64no—
876C2—82no—
877C2—124no—
878C2#7465911yescharacteristic
879C2C4×#91111yescharacteristic
880C2D3×#44211yescharacteristic
881C2#8000211yescharacteristic
882C2#8008411yescharacteristic
883C2#8031411yescharacteristic
884C2#8050711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1879C2
socleC23×C3C22×D4
prime radicalC2×#5156C2
cosocleC22×C3×C4C24
hypercenter#1879D3
hypocenterC3#21452
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
1. C2×C4×D3×D4C2semidirect
3. C2×#5152C2semidirect
4. C2×#4785C2semidirect
5. #76291C2semidirect
6. C3×#1879C2semidirect
7. #71607C2semidirect
8. #70200C2semidirect
9. #70198C2semidirect
10. #70152C2semidirect
11. #69657C2semidirect
12. #68875C2semidirect
13. #68782C2semidirect
14. #68671C2semidirect
15. #68600C2semidirect
23. C2×D4×Dic3C22semidirect
36. C2×C3×#102C22semidirect
37. C3×#390C22semidirect
40. C2×#832C22semidirect
41. #5156C4semidirect
47. C2×#817C22semidirect
48. C2×#815C22semidirect
49. C2×#815C22semidirect
51. Dic3×C4⋊C4C22semidirect
53. C2×#808C22semidirect
57. #4928C22semidirect
59. C3×#340C22semidirect
60. C3×#336C22semidirect
61. #4551C22semidirect
62. #4529C22semidirect
63. #4529C22semidirect
64. #4524C22semidirect
71. #1879D3semidirect
93. C2×D3×D4C2×C4semidirect
106. C2×C3×D8C2×C4semidirect
121. #938C2×C4semidirect
125. D4×Dic3D4semidirect
128. C2×#213C2×C4semidirect
145. #893D4semidirect
159. #832C2×C4semidirect
164. #821C2×C4semidirect
166. (C2×D3)⋊C8C2×C4semidirect
202. C2×#102C2×D3semidirect
207. #390C2×D3semidirect
217. #340C2×D3semidirect
219. #336C2×D3semidirect
240. C2×C3×D4C22×C4semidirect
307. C2×C3×C8C22×C4semidirect
328. C4⋊Dic3C22×C4semidirect
342. C2×C3⋊C8C22×C4semidirect
372. C2×D8C4×D3semidirect
478. C3×D4C4×D4semidirect
523. D12C4×D4semidirect
573. C2×D4C2×C4×D3semidirect
631. C2×C8C2×C4×D3semidirect
695. C2×D3#442semidirect
759. D4#67⋊C4semidirect
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×#51562
C2×#51522
C2×#47852
#762912
C3×#18792
#716072
#702002
#701982
#701522
#696572
#688752
#687822
#686712
#686002
#214523