Finite Group Databasebeta

← #10944030

Subgroups — #10944030

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×C3×#463C211yesmaximal, characteristic, complemented
3C2×#5169C211yesmaximal, characteristic, complemented
4C2×#5156C211yesmaximal, characteristic
5#83008C211yesmaximal, characteristic, complemented
6C2×#5057C211yesmaximal, characteristic, complemented
7#72047C211yesmaximal, characteristic, complemented
8#72037C211yesmaximal, characteristic, complemented
9#71605C211yesmaximal, characteristic, complemented
10#70480C211yesmaximal, characteristic, complemented
11#70475C211yesmaximal, characteristic, complemented
12#70276C211yesmaximal, characteristic, complemented
13#70268C211yesmaximal, characteristic, complemented
14#70208C211yesmaximal, characteristic, complemented
15#70200C211yesmaximal, characteristic, complemented
16#32908—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C23×C4×D3—21no—
19C22×C3×SD16C2211yescharacteristic
20C22×C3×D8C2211yescharacteristic
21C2×C3×#124C2211yescharacteristic, complemented
22C2×C3×C4×D4C2211yescharacteristic
23C2×#946C2211yescharacteristic
24C22×#215C2211yescharacteristic
25C2×#938C2211yescharacteristic
26C2×D4×Dic3C2211yescharacteristic
27C22×#213C2211yescharacteristic
28C2×C4×#67—21no—
29C4×D3×D4—24no—
30C4×D3×D4—24no—
31C2×#893C2211yescharacteristic
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×#67⋊C4—21no—
34C2×D3×C22⋊C4—21no—
35C2×C4×D12C2211yescharacteristic
36C2×C42×D3C2211yescharacteristic
37C3×#463—24no—
38C2×C3×C4⋊C8C2211yescharacteristic, complemented
39C2×C3×#103C2211yescharacteristic, complemented
40C2×C3×#102C2211yescharacteristic, complemented
41#5229C2211yescharacteristic, complemented
42C2×#835C2211yescharacteristic, complemented
43#5221C2211yescharacteristic, complemented
44C2×#832C2211yescharacteristic
45C2×#832C2211yescharacteristic
46C2×#832C2211yescharacteristic, complemented
47#5169—24no—
48#5156—24no—
49C2×#821C2211yescharacteristic
50C2×#821C2211yescharacteristic
51C2×(C2×D3)⋊C8C2211yescharacteristic
52C2×(C2×D3)⋊C8C2211yescharacteristic
53#5057—24no—
54#4956—21no—
55#4956—21no—
56#4944—21no—
57#4944—21no—
58#4936C2211yescharacteristic, complemented
59C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
60#4551C2211yescharacteristic, complemented
61#4551C2211yescharacteristic, complemented
62#4550C2211yescharacteristic, complemented
63#4550C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C22×C4×D4—31no—
67C2×#463—31no—
68C2×#463D311yescharacteristic, complemented
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#1804—31no—
80#1797—31no—
81C24×D3—21no—
82C22×C3×Q8C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4—21no—
86C22×#67—21no—
87C22×#67—21no—
88C23×Dic3—21no—
89C2×D3×D4—22no—
90C2×D3×D4—22no—
91C2×D3×D4—22no—
92C2×D3×D4—22no—
93C2×D3×D4—22no—
94C2×D3×D4D414yes—
95C22×D12C2311yescharacteristic
96C22×C4×D3—28no—
97C22×C4×D3—21no—
98C22×C4×D3—21no—
99C22×C4×D3—21no—
100C22×C4×D3—44no—
101C22×C4×D3—44no—
102C22×C4×D3D411yescharacteristic
103C22×C4×D3D411yescharacteristic
104C22×C4×D3C2311yescharacteristic
105C2×C3×SD16—22no—
106C2×C3×SD16—22no—
107C2×C3×SD16—22no—
108C2×C3×D8—22no—
109C2×C3×D8—22no—
110C2×C3×D8—22no—
111C22×C3×C8C2311yescharacteristic
112C22×C3×C8C2311yescharacteristic
113C3×#124—22no—
114C3×#124—22no—
115C3×C4×D4—22no—
116C3×C4×D4D414yescomplemented
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C42C2311yescharacteristic
122C2×#217—21no—
123C2×#217—21no—
124C2×#217—21no—
125C2×#217—21no—
126#946—22no—
127#946—22no—
128C2×#215—22no—
129C2×#215—22no—
130C2×#215—22no—
131#938—22no—
132#938—22no—
133D4×Dic3—22no—
134D4×Dic3—22no—
135C2×#213—22no—
136C2×#213—22no—
137C2×#213—22no—
138C4×#67—28no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142C2×C4⋊Dic3C2311yescharacteristic
143C2×C4⋊Dic3C2311yescharacteristic
144C2×C4⋊Dic3C2311yescharacteristic
145C2×Dic3⋊C4—21no—
146C2×Dic3⋊C4—21no—
147C2×C4×Dic3D411yescharacteristic
148C2×C4×Dic3D411yescharacteristic
149C2×C4×Dic3C2311yescharacteristic
150C22×C3⋊C8C2311yescharacteristic
151C22×C3⋊C8C2311yescharacteristic
152#893—22no—
153#893—22no—
154D3×C4⋊C4—22no—
155D3×C4⋊C4—22no—
156#67⋊C4—28no—
157D3×C22⋊C4—28no—
158C4×D12—22no—
159C4×D12D414yescomplemented
160C42×D3—22no—
161C42×D3—22no—
162C3×C4⋊C8—22no—
163C3×#103—22no—
164C3×#102—22no—
165#835—22no—
166#832—22no—
167#832—22no—
168#832—22no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172C3⋊#95—21no—
173#821—22no—
174#821—22no—
175(C2×D3)⋊C8—22no—
176(C2×D3)⋊C8—22no—
177C4⋊(C3⋊C8)—22no—
178C23×D4—31no—
179C24×C4—61no—
180C22×SD16—31no—
181C22×SD16C2×D311yescharacteristic
182C22×D8—31no—
183C22×D8C2×D311yescharacteristic
184C2×#124C2×D311yescharacteristic, complemented
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—24no—
199#463—64no—
200#450—64no—
201#447—64no—
202C2×C4⋊C8—31no—
203C2×C4⋊C8C2×D311yescharacteristic, complemented
204C2×#103—31no—
205C2×#103C2×D311yescharacteristic, complemented
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102—31no—
210C2×#102—31no—
211C2×#102C2×D311yescharacteristic, complemented
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#382—31no—
221#340—31no—
222#340—31no—
223#340—31no—
224#340—31no—
225#336—31no—
226#336—31no—
227C24×C3—21no—
228C24×C3—21no—
229C23×D3—24no—
230C23×D3—24no—
231C23×D3—21no—
232C23×D3—24no—
233C23×D3—42no—
234C23×D3—42no—
235C23×D3—42no—
236C23×D3—42no—
237C23×D3C2×D411yescharacteristic
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4C2×D412yes—
254C2×C3×D4C2×D412yes—
255C2×C3×D4#4112yes—
256C22×C3×C4—21no—
257C22×C3×C4—24no—
258C22×C3×C4—21no—
259C22×C3×C4—42no—
260C22×C3×C4—42no—
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2411yescharacteristic
264C2×#67—24no—
265C2×#67—24no—
266C2×#67—24no—
267C2×#67—42no—
268C2×#67—42no—
269C2×#67—42no—
270C22×Dic3—24no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—42no—
275C22×Dic3—42no—
276C22×Dic3C2×D411yescharacteristic
277C22×Dic3C2×D411yescharacteristic
278C22×Dic3C2×D411yescharacteristic
279D3×D4—28no—
280D3×D4—28no—
281D3×D4—28no—
282D3×D4—28no—
283C2×D12—21no—
284C2×D12—21no—
285C2×D12—21no—
286C2×D12C2×D412yes—
287C2×D12C2×D412yes—
288C2×D12#4112yes—
289C2×C4×D3—22no—
290C2×C4×D3—22no—
291C2×C4×D3—21no—
292C2×C4×D3—21no—
293C2×C4×D3—21no—
294C2×C4×D3—21no—
295C2×C4×D3—22no—
296C2×C4×D3—24no—
297C2×C4×D3—24no—
298C2×C4×D3—22no—
299C2×C4×D3—22no—
300C2×C4×D3—24no—
301C2×C4×D3—432no—
302C2×C4×D3—41no—
303C2×C4×D3—42no—
304C2×C4×D3—42no—
305C2×C4×D3—42no—
306C2×C4×D3—42no—
307C2×C4×D3—42no—
308C2×C4×D3—42no—
309C2×C4×D3C2×D412yes—
310C2×C4×D3#4112yes—
311C3×SD16—44no—
312C3×D8—44no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4C2×D412yes—
321C3×C22⋊C4—24no—
322C3×C22⋊C4—42no—
323C3×C22⋊C4—42no—
324C3×C42C2×D412yes—
325C3×C42C2×D412yes—
326#217—24no—
327#217—42no—
328#217—42no—
329#217—42no—
330#215—44no—
331#213—44no—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—42no—
335C4⋊Dic3—21no—
336C4⋊Dic3—21no—
337C4⋊Dic3—21no—
338C4⋊Dic3—21no—
339C4⋊Dic3—21no—
340C4⋊Dic3C2×D412yes—
341Dic3⋊C4—24no—
342Dic3⋊C4—42no—
343C4×Dic3—22no—
344C4×Dic3—22no—
345C4×Dic3—21no—
346C4×Dic3—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C25—61no—
354C22×Q8C22×D311yescharacteristic
355C22×D4—34no—
356C22×D4—31no—
357C22×D4—62no—
358C22×D4—61no—
359C22×D4—62no—
360C22×D4—62no—
361C22×D4—62no—
362C22×D4—62no—
363C22×D4—61no—
364C22×D4C22×D311yescharacteristic
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—22no—
378C2×SD16—22no—
379C2×SD16—22no—
380C2×SD16—62no—
381C2×SD16—62no—
382C2×SD16—62no—
383C2×D8—22no—
384C2×D8—22no—
385C2×D8—22no—
386C2×D8—62no—
387C2×D8—62no—
388C2×D8—62no—
389C22×C8—31no—
390C22×C8—31no—
391C22×C8C22×D311yescharacteristic
392C22×C8C22×D311yescharacteristic
393#124—22no—
394#124—22no—
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×D4#6714yescomplemented
409C2×C4⋊C4—31no—
410C2×C4⋊C4—31no—
411C2×C4⋊C4—31no—
412C2×C4⋊C4—62no—
413C2×C4⋊C4—61no—
414C2×C4⋊C4—62no—
415C2×C4⋊C4—61no—
416C2×C4⋊C4C22×D311yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—68no—
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—22no—
437#103—62no—
438#102—22no—
439#102—62no—
440#102—62no—
441#102—62no—
442#102—62no—
443#102—62no—
444C22⋊C8—62no—
445C22⋊C8—62no—
446#95—61no—
447#95—61no—
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×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3C22×D411yescharacteristic
465C22×D3—21no—
466C22×D3—21no—
467C22×D3—21no—
468C22×D3—21no—
469C22×D3—216no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—48no—
474C22×D3—48no—
475C22×D3—48no—
476C22×D3—48no—
477C22×D3—48no—
478C22×D3—41no—
479C22×D3—41no—
480C22×D3—41no—
481C22×D3—41no—
482C22×D3—48no—
483C22×D3#12112yes—
484C22×D3#13512yes—
485C22×D3AGL(1,ℤ/8)12yes—
486C3×Q8—41no—
487C3×Q8—41no—
488C3×Q8—41no—
489C3×Q8—41no—
490C3×D4—22no—
491C3×D4—22no—
492C3×D4—22no—
493C3×D4—41no—
494C3×D4—41no—
495C3×D4—41no—
496C3×D4—41no—
497C3×D4#12114yes—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—22no—
503C2×C3×C4—48no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4#12012yes—
510C2×C3×C4#12012yes—
511C2×C3×C4C22×D411yescharacteristic
512C2×C3×C4C22×D411yescharacteristic
513C2×C3×C4C22×D411yescharacteristic
514C2×C3×C4C2×#4111yescharacteristic
515C2×C3×C4C2×#4111yescharacteristic
516C2×C3×C4C2×#4111yescharacteristic
517#67—216no—
518#67—84no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—22no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—48no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3—41no—
532C2×Dic3—41no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3#12112yes—
537C2×Dic3AGL(1,ℤ/8)12yes—
538D12—22no—
539D12—22no—
540D12—22no—
541D12#12114yes—
542C4×D3—28no—
543C4×D3—22no—
544C4×D3—22no—
545C4×D3—22no—
546C4×D3—22no—
547C4×D3—48no—
548C4×D3—44no—
549C4×D3—48no—
550C4×D3—48no—
551C3×C8—41no—
552C3×C8—41no—
553C3⋊C8—41no—
554C3⋊C8—41no—
555C24—21no—
556C24—21no—
557C24—31no—
558C24—64no—
559C24—64no—
560C24—64no—
561C24—61no—
562C24—122no—
563C24—122no—
564C24—122no—
565C24—122no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—32no—
582C2×D4—32no—
583C2×D4—32no—
584C2×D4—64no—
585C2×D4—68no—
586C2×D4—68no—
587C2×D4—68no—
588C2×D4—64no—
589C2×D4—64no—
590C2×D4—68no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—122no—
595C2×D4—122no—
596C2×D4—122no—
597C2×D4D3×D412yes—
598C2×D4#23712yes—
599C2×D4C2×#6712yes—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—21no—
603C22×C4—31no—
604C22×C4—31no—
605C22×C4—32no—
606C22×C4—32no—
607C22×C4—31no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—62no—
611C22×C4—62no—
612C22×C4—62no—
613C22×C4—64no—
614C22×C4—64no—
615C22×C4—62no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—64no—
621C22×C4—61no—
622C22×C4—62no—
623C22×C4—64no—
624C22×C4—61no—
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—44no—
640SD16—124no—
641D8—44no—
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—32no—
657C4⋊C4—64no—
658C4⋊C4—61no—
659C4⋊C4—61no—
660C4⋊C4—61no—
661C4⋊C4—61no—
662C4⋊C4—61no—
663C4⋊C4—122no—
664C4⋊C4C2×#6712yes—
665C22⋊C4—24no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—64no—
669C22⋊C4—64no—
670C22⋊C4—64no—
671C22⋊C4—122no—
672C22⋊C4—122no—
673C22⋊C4—122no—
674C22⋊C4—122no—
675C42—62no—
676C42—62no—
677C42—61no—
678C42—61no—
679C42D3×D412yes—
680C42C2×#6712yes—
681C22×C3—24no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—42no—
687C22×C3—42no—
688C22×C3—81no—
689C22×C3—81no—
690C22×C3—81no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3—81no—
694C22×C3—81no—
695C22×C3C2×#12011yescharacteristic
696C22×C3C2×#12111yescharacteristic
697C22×C3#52511yescharacteristic
698C22×C3C2×#13511yescharacteristic
699C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
700C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
701C22×C3#57511yescharacteristic
702C2×D3—22no—
703C2×D3—22no—
704C2×D3—22no—
705C2×D3—22no—
706C2×D3—22no—
707C2×D3—22no—
708C2×D3—24no—
709C2×D3—432no—
710C2×D3—42no—
711C2×D3—42no—
712C2×D3—42no—
713C2×D3—42no—
714C2×D3—42no—
715C2×D3—42no—
716C2×D3#46314yescomplemented
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—42no—
720C3×C4—81no—
721C3×C4C2×#12111yescharacteristic
722C3×C4C2×#12111yescharacteristic
723C3×C4#52511yescharacteristic
724C3×C4#52511yescharacteristic
725Dic3—22no—
726Dic3—22no—
727Dic3—41no—
728Dic3—42no—
729Dic3—81no—
730Dic3—81no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—32no—
735C23—32no—
736C23—32no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—616no—
749C23—61no—
750C23—61no—
751C23—61no—
752C23—61no—
753C23—62no—
754C23—62no—
755C23—62no—
756C23—128no—
757C23—128no—
758C23—128no—
759C23—128no—
760C23—128no—
761C23—128no—
762C23—121no—
763C23—121no—
764C23—121no—
765C23—121no—
766C23C2×D3×D411yescharacteristic
767Q8—41no—
768Q8—41no—
769Q8—41no—
770Q8—41no—
771D4—22no—
772D4—22no—
773D4—22no—
774D4—34no—
775D4—41no—
776D4—41no—
777D4—41no—
778D4—41no—
779D4—616no—
780D4—62no—
781D4—62no—
782D4—62no—
783D4—244no—
784D4#93814yes—
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—68no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—62no—
804C2×C4—62no—
805C2×C4—62no—
806C2×C4—62no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—62no—
811C2×C4—124no—
812C2×C4—128no—
813C2×C4—128no—
814C2×C4—128no—
815C2×C4—128no—
816C2×C4—121no—
817C2×C4—121no—
818C2×C4—121no—
819C2×C4—121no—
820C2×C4—121no—
821C2×C4—121no—
822C2×C4—121no—
823C2×C4—121no—
824C2×C4#93712yes—
825C2×C4#93712yes—
826C2×C4C2×D3×D411yescharacteristic
827C2×C4C2×D3×D411yescharacteristic
828C2×C4C2×#23711yescharacteristic
829C2×C4D3×#4111yescharacteristic
830C2×C4D3×#4111yescharacteristic
831C2×C4C22×#6711yescharacteristic
832C8—41no—
833C8—41no—
834C8—121no—
835C8—121no—
836C2×C3—44no—
837C2×C3—161no—
838C2×C3#284711yescharacteristic
839C2×C3#300211yescharacteristic
840C2×C3#300311yescharacteristic
841C2×C3C2×#46311yescharacteristic
842C2×C3#303611yescharacteristic
843C2×C3#310511yescharacteristic
844C2×C3#311411yescharacteristic
845D3—24no—
846D3—44no—
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—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—1232no—
870C22—122no—
871C22—122no—
872C22—122no—
873C22—122no—
874C22—122no—
875C22—122no—
876C22D3×#12111yescharacteristic
877C22#560611yescharacteristic
878C22D3×#13511yescharacteristic
879C22#576811yescharacteristic
880C22D3×AGL(1,ℤ/8)11yescharacteristic
881C22D3×AGL(1,ℤ/8)11yescharacteristic
882C22C2×#93711yescharacteristic
883C4—22no—
884C4—22no—
885C4—42no—
886C4—62no—
887C4—62no—
888C4—81no—
889C4—121no—
890C4—122no—
891C4—241no—
892C4—241no—
893C4D3×#12111yescharacteristic
894C4#560611yescharacteristic
895C4C2×#93811yescharacteristic
896C4#582811yescharacteristic
897C3#3290811yescharacteristic, complemented, Sylow
898C2—44no—
899C2—64no—
900C2—124no—
901C2—161no—
902C2#8050511yescharacteristic
903C2#8050711yescharacteristic
904C2D3×#46311yescharacteristic
905C2#8053411yescharacteristic
906C2#8272311yescharacteristic
907C2#8391111yescharacteristic
908C2#8394411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#463C2
socleC23×C3C22×D4
prime radicalC2×#5156C2
hypercenterC2×#463D3
hypocenterC3#32908
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×C4×D3×D4C2semidirect
2. C2×C3×#463C2semidirect
3. C2×#5169C2semidirect
5. #83008C2semidirect
6. C2×#5057C2semidirect
7. #72047C2semidirect
8. #72037C2semidirect
9. #71605C2semidirect
10. #70480C2semidirect
11. #70475C2semidirect
12. #70276C2semidirect
13. #70268C2semidirect
14. #70208C2semidirect
15. #70200C2semidirect
21. C2×C3×#124C22semidirect
38. C2×C3×C4⋊C8C22semidirect
39. C2×C3×#103C22semidirect
40. C2×C3×#102C22semidirect
41. #5229C22semidirect
42. C2×#835C22semidirect
43. #5221C22semidirect
46. C2×#832C22semidirect
58. #4936C22semidirect
59. C2×C4⋊(C3⋊C8)C22semidirect
60. #4551C22semidirect
61. #4551C22semidirect
62. #4550C22semidirect
63. #4550C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
68. C2×#463D3semidirect
116. C3×C4×D4D4semidirect
159. C4×D12D4semidirect
184. C2×#124C2×D3semidirect
203. C2×C4⋊C8C2×D3semidirect
205. C2×#103C2×D3semidirect
211. C2×#102C2×D3semidirect
408. C4×D4#67semidirect
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×C3×#4632
C2×#51692
C2×#51562
#830082
C2×#50572
#720472
#720372
#716052
#704802
#704752
#702762
#702682
#702082
#702002
#329083