Finite Group Databasebeta

← #10944036

Subgroups — #10944036

Order 768.

1894 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×D4C211yesmaximal, characteristic, complemented
2C2×#5016C211yesmaximal, characteristic, complemented
3C2×#4844C211yesmaximal, characteristic, complemented
4C2×#4776C211yesmaximal, characteristic, complemented
5C2×#4773C211yesmaximal, characteristic
6#74256C211yesmaximal, characteristic, complemented
7C3×#1804C211yesmaximal, characteristic, complemented
8#70475C211yesmaximal, characteristic, complemented
9#70172C211yesmaximal, characteristic, complemented
10#70171C211yesmaximal, characteristic, complemented
11#69556C211yesmaximal, characteristic, complemented
12#68897C211yesmaximal, characteristic, complemented
13#68896C211yesmaximal, characteristic, complemented
14#68880C211yesmaximal, characteristic, complemented
15#68878C211yesmaximal, characteristic, complemented
16#32908—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C23×C4×D3—21no—
19C2×C3×C4×D4C2211yescharacteristic
20C2×D4×Dic3C2211yescharacteristic
21C22×#214C2211yescharacteristic
22C22×#213C2211yescharacteristic
23C2×C4×#67—21no—
24C22×D24C2211yescharacteristic
25C22×#204C2211yescharacteristic
26C4×D3×D4—24no—
27C4×D3×D4—24no—
28C2×#897C2211yescharacteristic
29C2×#895C2211yescharacteristic
30C2×#893C2211yescharacteristic
31C2×D3×C4⋊C4C2211yescharacteristic
32C2×#67⋊C4—21no—
33C2×D3×C22⋊C4—21no—
34C2×#875C2211yescharacteristic, complemented
35C2×C4×D12C2211yescharacteristic
36C2×C42×D3C2211yescharacteristic
37C2×C3×C4⋊C8C2211yescharacteristic, complemented
38C2×C3×#102C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C3×#382C2211yescharacteristic, complemented
41C2×#821C2211yescharacteristic, complemented
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×#816C2211yescharacteristic, complemented
45#5016—24no—
46#4988C2211yescharacteristic, complemented
47#4973C2211yescharacteristic, complemented
48C2×#810C2211yescharacteristic, complemented
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic, complemented
52C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
53#4844—24no—
54#4776—24no—
55#4773—24no—
56#4670—21no—
57#4670—21no—
58#4665—21no—
59#4665—21no—
60C3×#340C2211yescharacteristic, complemented
61C3×#340C2211yescharacteristic, complemented
62#4550C2211yescharacteristic, complemented
63#4550C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C22×C4×D4—31no—
67C2×#463—31no—
68C2×#463—31no—
69C2×#450—31no—
70C2×#447—31no—
71#2850—31no—
72#1879—31no—
73#1879—31no—
74#1877—31no—
75#1877—31no—
76#1874—31no—
77#1872—31no—
78#1804—31no—
79#1804D311yescharacteristic, complemented
80#1797—31no—
81C24×D3—21no—
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C22×#67—21no—
85C23×Dic3—21no—
86C2×D3×D4—22no—
87C2×D3×D4—22no—
88C2×D3×D4—22no—
89C2×D3×D4—22no—
90C2×D3×D4—22no—
91C2×D3×D4D414yes—
92C22×D12—21no—
93C22×D12C2311yescharacteristic
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
104C22×Dic6C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C3×C4×D4—22no—
108C3×C4×D4D414yescomplemented
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C22⋊C4—21no—
113C2×C3×C42C2311yescharacteristic
114C2×#217—21no—
115D4×Dic3—22no—
116D4×Dic3—22no—
117C2×#214—22no—
118C2×#214—22no—
119C2×#214—22no—
120C2×#213—22no—
121C2×#213—22no—
122C2×#213—22no—
123C4×#67—28no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×C4⋊Dic3—21no—
133C2×C4⋊Dic3C2311yescharacteristic
134C2×Dic3⋊C4—21no—
135C2×C4×Dic3D411yescharacteristic
136C2×C4×Dic3D411yescharacteristic
137C2×C4×Dic3C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C2×D24—22no—
141C2×D24—22no—
142C2×D24—22no—
143C2×#204—22no—
144C2×#204—22no—
145C2×#204—22no—
146#897—22no—
147#897—22no—
148#895—22no—
149#895—22no—
150#893—22no—
151#893—22no—
152D3×C4⋊C4—22no—
153D3×C4⋊C4—22no—
154#67⋊C4—28no—
155D3×C22⋊C4—28no—
156#875—22no—
157#875—22no—
158C4×D12—22no—
159C4×D12D414yescomplemented
160C42×D3—22no—
161C42×D3—22no—
162C3×C4⋊C8—22no—
163C3×#102—22no—
164C3×#102—22no—
165C3×#95—21no—
166C3×#95—21no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169#821—22no—
170(C2×D3)⋊C8—22no—
171(C2×D3)⋊C8—22no—
172#816—22no—
173#810—22no—
174#809—22no—
175#809—22no—
176#809—22no—
177C4⋊(C3⋊C8)—22no—
178C23×D4—31no—
179C24×C4—61no—
180C22×SD16—31no—
181C22×SD16—31no—
182C22×D8—31no—
183C22×D8—31no—
184C2×#124—31no—
185C2×C22⋊Q8—31no—
186C2×#121—31no—
187C2×C4×D4—31no—
188C2×C4×D4—31no—
189C2×C4×D4—31no—
190C2×C4×D4—61no—
191C2×C4×D4—61no—
192C2×C4×D4—64no—
193C2×C4×D4—64no—
194C2×C4×D4C2×D311yescharacteristic
195C22×C4⋊C4—31no—
196C22×C22⋊C4—61no—
197C22×C42—31no—
198#463—64no—
199#463—64no—
200#450—64no—
201#447—64no—
202C2×C4⋊C8—31no—
203C2×C4⋊C8C2×D311yescharacteristic, complemented
204C2×#103—31no—
205C2×#103—31no—
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102—31no—
210C2×#102C2×D311yescharacteristic
211C2×#102C2×D311yescharacteristic
212C2×C22⋊C8—31no—
213C2×C22⋊C8—31no—
214#391—31no—
215#390—31no—
216#388—61no—
217#388—61no—
218#386—61no—
219#386—61no—
220#382C2×D311yescharacteristic, complemented
221#340—31no—
222#340—31no—
223#340C2×D311yescharacteristic, complemented
224#340C2×D311yescharacteristic, complemented
225#336—31no—
226#336—31no—
227C24×C3—21no—
228C23×D3—24no—
229C23×D3—24no—
230C23×D3—21no—
231C23×D3—24no—
232C23×D3—21no—
233C23×D3—42no—
234C23×D3—42no—
235C23×D3—42no—
236C23×D3—42no—
237C23×D3C2×D411yescharacteristic
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4C2×D412yes—
242C2×C3×D4C2×D412yes—
243C2×C3×D4#4112yes—
244C22×C3×C4—21no—
245C22×C3×C4—24no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—42no—
249C22×C3×C4—42no—
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2411yescharacteristic
253C2×#67—24no—
254C2×#67—24no—
255C2×#67—24no—
256C22×Dic3—24no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—42no—
260C22×Dic3—42no—
261C22×Dic3C2×D411yescharacteristic
262C22×Dic3C2×D411yescharacteristic
263C22×Dic3C2×D411yescharacteristic
264D3×D4—28no—
265D3×D4—28no—
266D3×D4—28no—
267D3×D4—28no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—42no—
278C2×D12—42no—
279C2×D12—42no—
280C2×D12C2×D412yes—
281C2×D12C2×D412yes—
282C2×D12#4112yes—
283C2×C4×D3—22no—
284C2×C4×D3—22no—
285C2×C4×D3—21no—
286C2×C4×D3—21no—
287C2×C4×D3—21no—
288C2×C4×D3—21no—
289C2×C4×D3—22no—
290C2×C4×D3—24no—
291C2×C4×D3—24no—
292C2×C4×D3—22no—
293C2×C4×D3—22no—
294C2×C4×D3—24no—
295C2×C4×D3—432no—
296C2×C4×D3—41no—
297C2×C4×D3—42no—
298C2×C4×D3—42no—
299C2×C4×D3—42no—
300C2×C4×D3—42no—
301C2×C4×D3—42no—
302C2×C4×D3—42no—
303C2×C4×D3C2×D412yes—
304C2×C4×D3#4112yes—
305C2×Dic6—21no—
306C2×Dic6—21no—
307C2×Dic6—21no—
308C2×Dic6—21no—
309C2×Dic6—21no—
310C2×Dic6—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4C2×D412yes—
323C3×C22⋊C4—24no—
324C3×C42C2×D412yes—
325C3×C42C2×D412yes—
326#217—24no—
327#214—44no—
328#213—44no—
329(C2×D3)⋊C4—24no—
330(C2×D3)⋊C4—24no—
331(C2×D3)⋊C4—42no—
332(C2×D3)⋊C4—42no—
333(C2×D3)⋊C4—42no—
334(C2×D3)⋊C4—42no—
335(C2×D3)⋊C4—42no—
336(C2×D3)⋊C4—42no—
337C4⋊Dic3—21no—
338C4⋊Dic3—42no—
339C4⋊Dic3C2×D412yes—
340Dic3⋊C4—24no—
341C4×Dic3—22no—
342C4×Dic3—22no—
343C4×Dic3—21no—
344C4×Dic3—21no—
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351D24—44no—
352#204—44no—
353C25—61no—
354C22×Q8—31no—
355C22×D4—34no—
356C22×D4—31no—
357C22×D4—31no—
358C22×D4—61no—
359C22×D4—62no—
360C22×D4—61no—
361C22×D4—62no—
362C22×D4—62no—
363C22×D4—62no—
364C22×D4—62no—
365C22×D4C22×D311yescharacteristic
366C23×C4—21no—
367C23×C4—31no—
368C23×C4—31no—
369C23×C4—31no—
370C23×C4—61no—
371C23×C4—61no—
372C23×C4—68no—
373C23×C4—61no—
374C23×C4—61no—
375C23×C4—124no—
376C23×C4—124no—
377C2×SD16—62no—
378C2×SD16—62no—
379C2×SD16—62no—
380C2×SD16—62no—
381C2×SD16—62no—
382C2×SD16—62no—
383C2×D8—62no—
384C2×D8—62no—
385C2×D8—62no—
386C2×D8—62no—
387C2×D8—62no—
388C2×D8—62no—
389C22×C8—31no—
390C22×C8—31no—
391C22×C8C22×D311yescharacteristic
392C22×C8C22×D311yescharacteristic
393#124—62no—
394#124—62no—
395C22⋊Q8—62no—
396C22⋊Q8—62no—
397#121—62no—
398#121—62no—
399C4×D4—22no—
400C4×D4—34no—
401C4×D4—68no—
402C4×D4—62no—
403C4×D4—62no—
404C4×D4—68no—
405C4×D4—62no—
406C4×D4—62no—
407C4×D4—62no—
408C4×D4D1214yescomplemented
409C2×C4⋊C4—31no—
410C2×C4⋊C4—62no—
411C2×C4⋊C4—61no—
412C2×C4⋊C4—62no—
413C2×C4⋊C4—61no—
414C2×C4⋊C4C22×D311yescharacteristic
415C2×C4⋊C4C22×D311yescharacteristic
416C2×C4⋊C4C22×D311yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—68no—
419C2×C22⋊C4—61no—
420C2×C22⋊C4—61no—
421C2×C22⋊C4—61no—
422C2×C22⋊C4—61no—
423C2×C22⋊C4—61no—
424C2×C22⋊C4—61no—
425C2×C22⋊C4—61no—
426C2×C22⋊C4—61no—
427C2×C22⋊C4—61no—
428C2×C42—31no—
429C2×C42—31no—
430C2×C42—31no—
431C2×C42—62no—
432C2×C42—62no—
433C2×C42C22×D311yescharacteristic
434C4⋊C8—22no—
435C4⋊C8—62no—
436#103—62no—
437#103—62no—
438#102—22no—
439#102—22no—
440#102—62no—
441#102—62no—
442#102—62no—
443#102—62no—
444C22⋊C8—62no—
445C22⋊C8—62no—
446#95—21no—
447#95—21no—
448#95—61no—
449#95—61no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3C22×D411yescharacteristic
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—216no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—48no—
467C22×D3—48no—
468C22×D3—48no—
469C22×D3—48no—
470C22×D3—48no—
471C22×D3—41no—
472C22×D3—41no—
473C22×D3—41no—
474C22×D3—41no—
475C22×D3—48no—
476C22×D3—41no—
477C22×D3—41no—
478C22×D3—41no—
479C22×D3—41no—
480C22×D3—41no—
481C22×D3—41no—
482C22×D3—41no—
483C22×D3#12112yes—
484C22×D3#13512yes—
485C22×D3AGL(1,ℤ/8)12yes—
486C3×D4—22no—
487C3×D4—22no—
488C3×D4—22no—
489C3×D4#12114yes—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—22no—
495C2×C3×C4—48no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4#12012yes—
505C2×C3×C4#12012yes—
506C2×C3×C4C22×D411yescharacteristic
507C2×C3×C4C22×D411yescharacteristic
508C2×C3×C4C22×D411yescharacteristic
509C2×C3×C4C2×#4111yescharacteristic
510C2×C3×C4C2×#4111yescharacteristic
511C2×C3×C4C2×#4111yescharacteristic
512#67—216no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—22no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—48no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3#12112yes—
528C2×Dic3AGL(1,ℤ/8)12yes—
529D12—22no—
530D12—22no—
531D12—22no—
532D12—41no—
533D12—41no—
534D12—41no—
535D12—41no—
536D12—84no—
537D12#12114yes—
538C4×D3—28no—
539C4×D3—22no—
540C4×D3—22no—
541C4×D3—22no—
542C4×D3—22no—
543C4×D3—48no—
544C4×D3—44no—
545C4×D3—48no—
546C4×D3—48no—
547Dic6—41no—
548Dic6—41no—
549Dic6—41no—
550Dic6—41no—
551C3×C8—41no—
552C3×C8—41no—
553C3⋊C8—41no—
554C3⋊C8—41no—
555C24—21no—
556C24—31no—
557C24—64no—
558C24—64no—
559C24—64no—
560C24—61no—
561C24—61no—
562C24—122no—
563C24—122no—
564C24—122no—
565C24—122no—
566C2×Q8—61no—
567C2×Q8—61no—
568C2×Q8—61no—
569C2×Q8—61no—
570C2×Q8—61no—
571C2×Q8—61no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—32no—
576C2×D4—32no—
577C2×D4—32no—
578C2×D4—64no—
579C2×D4—68no—
580C2×D4—68no—
581C2×D4—68no—
582C2×D4—64no—
583C2×D4—64no—
584C2×D4—68no—
585C2×D4—61no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—122no—
595C2×D4—122no—
596C2×D4—122no—
597C2×D4C2×D1212yes—
598C2×D4D3×D412yes—
599C2×D4#23912yes—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—32no—
607C22×C4—32no—
608C22×C4—31no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—62no—
612C22×C4—62no—
613C22×C4—62no—
614C22×C4—64no—
615C22×C4—64no—
616C22×C4—62no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—64no—
622C22×C4—61no—
623C22×C4—62no—
624C22×C4—64no—
625C22×C4—61no—
626C22×C4—121no—
627C22×C4—122no—
628C22×C4—122no—
629C22×C4—122no—
630C22×C4—122no—
631C22×C4—1232no—
632C22×C4—122no—
633C22×C4—122no—
634C22×C4—122no—
635C22×C4—122no—
636C22×C4D3×D411yescharacteristic
637C22×C4D3×D411yescharacteristic
638C22×C4C23×D311yescharacteristic
639SD16—124no—
640SD16—124no—
641D8—124no—
642D8—124no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—61no—
650C2×C8—61no—
651C2×C8—61no—
652C2×C8—61no—
653C2×C8—61no—
654C2×C8—61no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—32no—
661C4⋊C4—64no—
662C4⋊C4—61no—
663C4⋊C4—122no—
664C4⋊C4C2×D1212yes—
665C22⋊C4—24no—
666C22⋊C4—64no—
667C22⋊C4—64no—
668C22⋊C4—64no—
669C22⋊C4—122no—
670C22⋊C4—122no—
671C22⋊C4—122no—
672C22⋊C4—122no—
673C22⋊C4—122no—
674C22⋊C4—122no—
675C42—62no—
676C42—62no—
677C42—61no—
678C42—61no—
679C42C2×D1212yes—
680C42D3×D412yes—
681C22×C3—24no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—42no—
687C22×C3—42no—
688C22×C3C2×#12011yescharacteristic
689C22×C3C2×#12111yescharacteristic
690C22×C3#52511yescharacteristic
691C22×C3C2×#13511yescharacteristic
692C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
693C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
694C22×C3#57511yescharacteristic
695C2×D3—22no—
696C2×D3—22no—
697C2×D3—22no—
698C2×D3—22no—
699C2×D3—22no—
700C2×D3—22no—
701C2×D3—24no—
702C2×D3—432no—
703C2×D3—42no—
704C2×D3—42no—
705C2×D3—42no—
706C2×D3—42no—
707C2×D3—42no—
708C2×D3—42no—
709C2×D3—81no—
710C2×D3—81no—
711C2×D3—81no—
712C2×D3—81no—
713C2×D3—81no—
714C2×D3—81no—
715C2×D3—81no—
716C2×D3#46314yescomplemented
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—42no—
720C3×C4—81no—
721C3×C4—81no—
722C3×C4C2×#12111yescharacteristic
723C3×C4C2×#12111yescharacteristic
724C3×C4#52511yescharacteristic
725C3×C4#52511yescharacteristic
726Dic3—22no—
727Dic3—22no—
728Dic3—41no—
729Dic3—42no—
730Dic3—81no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—32no—
735C23—32no—
736C23—32no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—616no—
742C23—61no—
743C23—61no—
744C23—61no—
745C23—61no—
746C23—62no—
747C23—62no—
748C23—62no—
749C23—128no—
750C23—128no—
751C23—128no—
752C23—128no—
753C23—128no—
754C23—128no—
755C23—121no—
756C23—121no—
757C23—121no—
758C23—121no—
759C23—121no—
760C23—121no—
761C23—121no—
762C23—121no—
763C23—121no—
764C23—121no—
765C23—121no—
766C23C2×D3×D411yescharacteristic
767Q8—121no—
768Q8—121no—
769Q8—121no—
770Q8—121no—
771D4—22no—
772D4—22no—
773D4—22no—
774D4—34no—
775D4—616no—
776D4—62no—
777D4—62no—
778D4—62no—
779D4—121no—
780D4—121no—
781D4—121no—
782D4—121no—
783D4—244no—
784D4#89514yes—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—32no—
791C2×C4—32no—
792C2×C4—48no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—68no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—62no—
807C2×C4—62no—
808C2×C4—62no—
809C2×C4—62no—
810C2×C4—61no—
811C2×C4—62no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—124no—
815C2×C4—128no—
816C2×C4—128no—
817C2×C4—128no—
818C2×C4—128no—
819C2×C4—121no—
820C2×C4—121no—
821C2×C4—121no—
822C2×C4—121no—
823C2×C4—121no—
824C2×C4#88212yes—
825C2×C4#88212yes—
826C2×C4C22×D1211yescharacteristic
827C2×C4C2×D3×D411yescharacteristic
828C2×C4C2×D3×D411yescharacteristic
829C2×C4C2×#23911yescharacteristic
830C2×C4D3×#4111yescharacteristic
831C2×C4D3×#4111yescharacteristic
832C8—41no—
833C8—41no—
834C8—121no—
835C8—121no—
836C2×C3—44no—
837C2×C3#284711yescharacteristic
838C2×C3#300211yescharacteristic
839C2×C3#300311yescharacteristic
840C2×C3C2×#46311yescharacteristic
841C2×C3#303611yescharacteristic
842C2×C3#310511yescharacteristic
843C2×C3#311411yescharacteristic
844D3—24no—
845D3—44no—
846D3—161no—
847C22—24no—
848C22—34no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—62no—
856C22—62no—
857C22—62no—
858C22—62no—
859C22—62no—
860C22—62no—
861C22—64no—
862C22—1232no—
863C22—122no—
864C22—122no—
865C22—122no—
866C22—122no—
867C22—122no—
868C22—122no—
869C22—241no—
870C22—241no—
871C22—241no—
872C22—241no—
873C22—241no—
874C22—241no—
875C22—241no—
876C22C2×#88211yescharacteristic
877C22D3×#12111yescharacteristic
878C22#562711yescharacteristic
879C22D3×#13511yescharacteristic
880C22#576811yescharacteristic
881C22D3×AGL(1,ℤ/8)11yescharacteristic
882C22D3×AGL(1,ℤ/8)11yescharacteristic
883C4—22no—
884C4—22no—
885C4—42no—
886C4—62no—
887C4—62no—
888C4—81no—
889C4—81no—
890C4—122no—
891C4—121no—
892C4—241no—
893C4C2×#89511yescharacteristic
894C4#552411yescharacteristic
895C4D3×#12111yescharacteristic
896C4#562711yescharacteristic
897C3#3290811yescharacteristic, complemented, Sylow
898C2—44no—
899C2—64no—
900C2—124no—
901C2—481no—
902C2#7404811yescharacteristic
903C2#7883311yescharacteristic
904C2#7892611yescharacteristic
905C2D3×#46311yescharacteristic
906C2#8053411yescharacteristic
907C2#8114111yescharacteristic
908C2#8114311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1804C2
socleC23×C3C22×D4
prime radicalC2×#4773C2
hypercenter#1804D3
hypocenterC3#32908
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
1. C2×C4×D3×D4C2semidirect
2. C2×#5016C2semidirect
3. C2×#4844C2semidirect
4. C2×#4776C2semidirect
6. #74256C2semidirect
7. C3×#1804C2semidirect
8. #70475C2semidirect
9. #70172C2semidirect
10. #70171C2semidirect
11. #69556C2semidirect
12. #68897C2semidirect
13. #68896C2semidirect
14. #68880C2semidirect
15. #68878C2semidirect
34. C2×#875C22semidirect
37. C2×C3×C4⋊C8C22semidirect
40. C3×#382C22semidirect
41. C2×#821C22semidirect
44. C2×#816C22semidirect
46. #4988C22semidirect
47. #4973C22semidirect
48. C2×#810C22semidirect
51. C2×#809C22semidirect
52. C2×C4⋊(C3⋊C8)C22semidirect
60. C3×#340C22semidirect
61. C3×#340C22semidirect
62. #4550C22semidirect
63. #4550C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
79. #1804D3semidirect
108. C3×C4×D4D4semidirect
159. C4×D12D4semidirect
203. C2×C4⋊C8C2×D3semidirect
220. #382C2×D3semidirect
223. #340C2×D3semidirect
224. #340C2×D3semidirect
408. C4×D4D12semidirect
716. C2×D3#463semidirect
897. C3#32908semidirect

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×#50162
C2×#48442
C2×#47762
C2×#47732
#742562
C3×#18042
#704752
#701722
#701712
#695562
#688972
#688962
#688802
#688782
#329083