Finite Group Databasebeta

← #10944039

Subgroups — #10944039

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×#5169C211yesmaximal, characteristic, complemented
3C2×#5165C211yesmaximal, characteristic, complemented
4C2×#4819C211yesmaximal, characteristic, complemented
5C2×#4773C211yesmaximal, characteristic
6#76662C211yesmaximal, characteristic, complemented
7C3×#1877C211yesmaximal, characteristic, complemented
8#71613C211yesmaximal, characteristic, complemented
9#70268C211yesmaximal, characteristic, complemented
10#70154C211yesmaximal, characteristic, complemented
11#69687C211yesmaximal, characteristic, complemented
12#68893C211yesmaximal, characteristic, complemented
13#68880C211yesmaximal, characteristic, complemented
14#68673C211yesmaximal, characteristic, complemented
15#68662C211yesmaximal, characteristic, complemented
16#32908—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C23×C4×D3—21no—
19C22×C3×SD16C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×#947C2211yescharacteristic, complemented
22C2×#946C2211yescharacteristic
23C22×#215C2211yescharacteristic
24C2×D4×Dic3C2211yescharacteristic
25C22×#213C2211yescharacteristic
26C2×C4×#67—21no—
27C22×D24C2211yescharacteristic
28C4×D3×D4—24no—
29C4×D3×D4—24no—
30C2×#895C2211yescharacteristic
31C2×#893C2211yescharacteristic
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×#67⋊C4—21no—
34C2×D3×C22⋊C4—21no—
35C2×C4×D12C2211yescharacteristic
36C2×C42×D3C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic, complemented
38C2×C3×#102C2211yescharacteristic
39C3×#391C2211yescharacteristic, complemented
40C2×#835C2211yescharacteristic, complemented
41C2×#832C2211yescharacteristic
42#5169—24no—
43#5165—24no—
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic, complemented
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×Dic3⋊C8C2211yescharacteristic, complemented
49C2×Dic3⋊C8C2211yescharacteristic, complemented
50#4977C2211yescharacteristic, complemented
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic, complemented
53#4939C2211yescharacteristic, complemented
54#4819—24no—
55#4773—24no—
56#4669—21no—
57#4669—21no—
58#4665—21no—
59#4665—21no—
60C3×#340C2211yescharacteristic, complemented
61C3×#336C2211yescharacteristic, complemented
62#4551C2211yescharacteristic, complemented
63#4529C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4524C2211yescharacteristic, 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#1877D311yescharacteristic, complemented
76#1874—31no—
77#1872—31no—
78#1804—31no—
79#1804—31no—
80#1797—31no—
81C24×D3—21no—
82C22×C3×Q8C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4—21no—
85C22×#67—21no—
86C23×Dic3—21no—
87C2×D3×D4—22no—
88C2×D3×D4—22no—
89C2×D3×D4—22no—
90C2×D3×D4—22no—
91C2×D3×D4—22no—
92C2×D3×D4D414yes—
93C22×D12—21no—
94C22×D12C2311yescharacteristic
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—
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C3×C4×D4—22no—
111C3×C4×D4—22no—
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C22⋊C4—21no—
115C2×C3×C42C2311yescharacteristic
116C2×#217—21no—
117#947—22no—
118#947—22no—
119#946—22no—
120#946—22no—
121C2×#215—22no—
122C2×#215—22no—
123C2×#215—22no—
124D4×Dic3—22no—
125D4×Dic3D414yescomplemented
126C2×#213—22no—
127C2×#213—22no—
128C2×#213—22no—
129C4×#67—28no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4—21no—
138C2×C4⋊Dic3C2311yescharacteristic
139C2×C4⋊Dic3C2311yescharacteristic
140C2×Dic3⋊C4—21no—
141C2×Dic3⋊C4—21no—
142C2×C4×Dic3D411yescharacteristic
143C2×C4×Dic3D411yescharacteristic
144C2×C4×Dic3C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C2×D24—22no—
148C2×D24—22no—
149C2×D24—22no—
150#895—22no—
151#895—22no—
152#893—22no—
153#893D414yescomplemented
154D3×C4⋊C4—22no—
155D3×C4⋊C4—22no—
156#67⋊C4—28no—
157D3×C22⋊C4—28no—
158C4×D12—22no—
159C4×D12—22no—
160C42×D3—22no—
161C42×D3—22no—
162C3×#103—22no—
163C3×#102—22no—
164C3×#95—21no—
165C3×#95—21no—
166#835—22no—
167#832—22no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170#821—22no—
171#821—22no—
172(C2×D3)⋊C8—22no—
173(C2×D3)⋊C8—22no—
174Dic3⋊C8—22no—
175Dic3⋊C8—22no—
176#809—22no—
177#809—22no—
178C23×D4—31no—
179C24×C4—61no—
180C22×SD16—31no—
181C22×SD16C2×D311yescharacteristic
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⋊C8—31no—
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
212C2×C22⋊C8—31no—
213C2×C22⋊C8—31no—
214#391C2×D311yescharacteristic, complemented
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#340C2×D311yescharacteristic, complemented
225#336—31no—
226#336C2×D311yescharacteristic, complemented
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×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×D4C2×D412yes—
248C2×C3×D4C2×D412yes—
249C2×C3×D4#4112yes—
250C22×C3×C4—24no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—42no—
255C22×C3×C4—42no—
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2411yescharacteristic
259C2×#67—24no—
260C2×#67—24no—
261C2×#67—24no—
262C22×Dic3—21no—
263C22×Dic3—24no—
264C22×Dic3—21no—
265C22×Dic3—42no—
266C22×Dic3—42no—
267C22×Dic3C2×D411yescharacteristic
268C22×Dic3C2×D411yescharacteristic
269C22×Dic3C2×D411yescharacteristic
270D3×D4—28no—
271D3×D4—28no—
272D3×D4—28no—
273D3×D4—28no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12—21no—
281C2×D12—21no—
282C2×D12—21no—
283C2×D12—42no—
284C2×D12—42no—
285C2×D12—42no—
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—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4C2×D412yes—
322C3×C22⋊C4—24no—
323C3×C42—21no—
324C3×C42—21no—
325#217—24no—
326#215—44no—
327#213—44no—
328(C2×D3)⋊C4—24no—
329(C2×D3)⋊C4—24no—
330(C2×D3)⋊C4—42no—
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—
336C4⋊Dic3—21no—
337C4⋊Dic3—21no—
338C4⋊Dic3—21no—
339C4⋊Dic3C2×D412yes—
340Dic3⋊C4—24no—
341Dic3⋊C4—42no—
342C4×Dic3—22no—
343C4×Dic3—22no—
344C4×Dic3C2×D412yes—
345C4×Dic3C2×D412yes—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352D24—44no—
353C25—61no—
354C22×Q8C22×D311yescharacteristic
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—22no—
378C2×SD16—22no—
379C2×SD16—22no—
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—22no—
401C4×D4—34no—
402C4×D4—34no—
403C4×D4—62no—
404C4×D4—62no—
405C4×D4—62no—
406C4×D4—62no—
407C4×D4—68no—
408C4×D4—68no—
409C2×C4⋊C4—31no—
410C2×C4⋊C4—31no—
411C2×C4⋊C4—62no—
412C2×C4⋊C4—61no—
413C2×C4⋊C4—62no—
414C2×C4⋊C4—61no—
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—62no—
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—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×Q8—41no—
487C3×Q8—41no—
488C3×Q8—41no—
489C3×Q8—41no—
490C3×D4—22no—
491C3×D4—22no—
492C3×D4—22no—
493C3×D4#12114yes—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—22no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—48no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4AGL(1,ℤ/8)12yes—
510C2×C3×C4C22×D411yescharacteristic
511C2×C3×C4C22×D411yescharacteristic
512C2×C3×C4C22×D411yescharacteristic
513C2×C3×C4C2×#4111yescharacteristic
514C2×C3×C4C2×#4111yescharacteristic
515C2×C3×C4C2×#4111yescharacteristic
516#67—216no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—22no—
524C2×Dic3—48no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3#12012yes—
531C2×Dic3#12012yes—
532C2×Dic3#12112yes—
533D12—22no—
534D12—22no—
535D12—22no—
536D12—41no—
537D12—41no—
538D12—41no—
539D12—41no—
540D12—84no—
541D12#12114yes—
542C4×D3—28no—
543C4×D3—22no—
544C4×D3—22no—
545C4×D3—22no—
546C4×D3—22no—
547C4×D3—44no—
548C4×D3—48no—
549C4×D3—48no—
550C4×D3—48no—
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—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—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×D4#23512yes—
598C2×D4D3×D412yes—
599C2×D4D3×D412yes—
600C22×C4—24no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—32no—
608C22×C4—32no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—62no—
612C22×C4—62no—
613C22×C4—64no—
614C22×C4—62no—
615C22×C4—62no—
616C22×C4—64no—
617C22×C4—64no—
618C22×C4—64no—
619C22×C4—62no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—121no—
627C22×C4—122no—
628C22×C4—1232no—
629C22×C4—122no—
630C22×C4—122no—
631C22×C4—122no—
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—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—32no—
659C4⋊C4—64no—
660C4⋊C4—61no—
661C4⋊C4—61no—
662C4⋊C4—61no—
663C4⋊C4—122no—
664C4⋊C4D3×D412yes—
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—21no—
676C42—21no—
677C42—32no—
678C42—32no—
679C42—62no—
680C42—62no—
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—41no—
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—22no—
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—41no—
768Q8—41no—
769Q8—41no—
770Q8—41no—
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#88414yes—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—22no—
791C2×C4—32no—
792C2×C4—32no—
793C2×C4—32no—
794C2×C4—48no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—68no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—62no—
814C2×C4—62no—
815C2×C4—128no—
816C2×C4—124no—
817C2×C4—128no—
818C2×C4—128no—
819C2×C4—128no—
820C2×C4—121no—
821C2×C4—121no—
822C2×C4—121no—
823C2×C4—121no—
824C2×C4—121no—
825C2×C4#91412yes—
826C2×C4C2×#23511yescharacteristic
827C2×C4C2×D3×D411yescharacteristic
828C2×C4C2×D3×D411yescharacteristic
829C2×C4C2×D3×D411yescharacteristic
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—
876C22#554711yescharacteristic
877C22D3×#12011yescharacteristic
878C22D3×#12111yescharacteristic
879C22C2×#91411yescharacteristic
880C22D3×#13511yescharacteristic
881C22D3×AGL(1,ℤ/8)11yescharacteristic
882C22#577711yescharacteristic
883C4—22no—
884C4—42no—
885C4—41no—
886C4—62no—
887C4—62no—
888C4—62no—
889C4—81no—
890C4—81no—
891C4—122no—
892C4—241no—
893C4C2×#88411yescharacteristic
894C4#554711yescharacteristic
895C4D3×#12111yescharacteristic
896C4#565611yescharacteristic
897C3#3290811yescharacteristic, complemented, Sylow
898C2—44no—
899C2—64no—
900C2—124no—
901C2—481no—
902C2#7493511yescharacteristic
903C2#7965411yescharacteristic
904C2#7978211yescharacteristic
905C2#8014611yescharacteristic
906C2#8022611yescharacteristic
907C2#8042811yescharacteristic
908C2D3×#46311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1877C2
socleC23×C3C22×D4
prime radicalC2×#4773C2
hypercenter#1877D3
hypocenterC3#32908
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
1. C2×C4×D3×D4C2semidirect
2. C2×#5169C2semidirect
3. C2×#5165C2semidirect
4. C2×#4819C2semidirect
6. #76662C2semidirect
7. C3×#1877C2semidirect
8. #71613C2semidirect
9. #70268C2semidirect
10. #70154C2semidirect
11. #69687C2semidirect
12. #68893C2semidirect
13. #68880C2semidirect
14. #68673C2semidirect
15. #68662C2semidirect
21. C2×#947C22semidirect
37. C2×C3×#103C22semidirect
39. C3×#391C22semidirect
40. C2×#835C22semidirect
45. C2×#821C22semidirect
48. C2×Dic3⋊C8C22semidirect
49. C2×Dic3⋊C8C22semidirect
50. #4977C22semidirect
52. C2×#809C22semidirect
53. #4939C22semidirect
60. C3×#340C22semidirect
61. C3×#336C22semidirect
62. #4551C22semidirect
63. #4529C22semidirect
64. #4529C22semidirect
65. #4524C22semidirect
75. #1877D3semidirect
125. D4×Dic3D4semidirect
153. #893D4semidirect
205. C2×#103C2×D3semidirect
214. #391C2×D3semidirect
224. #340C2×D3semidirect
226. #336C2×D3semidirect
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×#51692
C2×#51652
C2×#48192
C2×#47732
#766622
C3×#18772
#716132
#702682
#701542
#696872
#688932
#688802
#686732
#686622
#329083