Finite Group Databasebeta

← #10944006

Subgroups — #10944006

Order 768.

1868 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×D4C211yesmaximal, characteristic
2C2×#5169C211yesmaximal, characteristic
3C2×#5162C211yesmaximal, characteristic, complemented
4C2×#4818C211yesmaximal, characteristic, complemented
5C2×#4776C211yesmaximal, characteristic
6#76664C211yesmaximal, characteristic, complemented
7C3×#1877C211yesmaximal, characteristic, complemented
8#71612C211yesmaximal, characteristic, complemented
9#70268C211yesmaximal, characteristic, complemented
10#70153C211yesmaximal, characteristic, complemented
11#69687C211yesmaximal, characteristic, complemented
12#68892C211yesmaximal, characteristic, complemented
13#68878C211yesmaximal, characteristic, complemented
14#68672C211yesmaximal, characteristic, complemented
15#68662C211yesmaximal, characteristic, complemented
16#32905—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C23×C4×D3—21no—
19C22×C3×SD16C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×#944C2211yescharacteristic, complemented
23C22×#215C2211yescharacteristic
24C2×D4×Dic3C2211yescharacteristic
25C22×#214C2211yescharacteristic
26C2×C4×#67—21no—
27C22×#204C2211yescharacteristic
28C4×D3×D4—24no—
29C4×D3×D4—24no—
30C2×#897C2211yescharacteristic
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#5162—24no—
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×#816C2211yescharacteristic, complemented
48C2×Dic3⋊C8C2211yescharacteristic, complemented
49C2×Dic3⋊C8C2211yescharacteristic, complemented
50#4975C2211yescharacteristic, complemented
51C2×#810C2211yescharacteristic, complemented
52C2×#809C2211yescharacteristic
53#4929C2211yescharacteristic, complemented
54#4818—24no—
55#4776—24no—
56#4667—21no—
57#4667—21no—
58#4647—21no—
59#4647—21no—
60C3×#340C2211yescharacteristic, complemented
61C3×#336C2211yescharacteristic, complemented
62#4551C2211yescharacteristic, complemented
63#4529C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4524C2211yescharacteristic, complemented
66C22×C4×D4—31no—
67C2×#461—31no—
68C2×#461—31no—
69C2×#450—31no—
70C2×#450—31no—
71#2857—31no—
72#1877—31no—
73#1877—31no—
74#1877—31no—
75#1877D311yescharacteristic, complemented
76#1872—31no—
77#1872—31no—
78#1802—31no—
79#1802—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×D12C2311yescharacteristic
94C22×C4×D3—28no—
95C22×C4×D3—21no—
96C22×C4×D3—21no—
97C22×C4×D3—21no—
98C22×C4×D3—44no—
99C22×C4×D3—44no—
100C22×C4×D3D411yescharacteristic
101C22×C4×D3D411yescharacteristic
102C22×C4×D3C2311yescharacteristic
103C22×Dic6C2311yescharacteristic
104C2×C3×SD16—22no—
105C2×C3×SD16—22no—
106C2×C3×SD16—22no—
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×C42C2311yescharacteristic
115C2×#217—21no—
116#946—22no—
117#946—22no—
118#944—22no—
119#944—22no—
120C2×#215—22no—
121C2×#215—22no—
122C2×#215—22no—
123D4×Dic3—22no—
124D4×Dic3D414yes—
125C2×#214—22no—
126C2×#214—22no—
127C2×#214—22no—
128C4×#67—28no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×C4⋊Dic3—21no—
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4—21no—
141C2×Dic3⋊C4—21no—
142C2×C4×Dic3D411yescharacteristic
143C2×C4×Dic3D411yescharacteristic
144C2×C4×Dic3C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C2×#204—22no—
148C2×#204—22no—
149C2×#204—22no—
150#897—22no—
151#897—22no—
152#893—22no—
153#893D414yes—
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(C2×D3)⋊C8—22no—
172(C2×D3)⋊C8—22no—
173#816—22no—
174Dic3⋊C8—22no—
175Dic3⋊C8—22no—
176#810—22no—
177#809—22no—
178C23×D4—31no—
179C24×C4—61no—
180C22×SD16—31no—
181C22×SD16—31no—
182C22×SD16—31no—
183C22×SD16C2×D311yescharacteristic
184C2×C4⋊Q8—31no—
185C2×C22⋊Q8—31no—
186C2×C22⋊Q8—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#461—64no—
199#461—64no—
200#450—64no—
201#450—64no—
202C2×C4⋊C8—31no—
203C2×C4⋊C8—31no—
204C2×#103—31no—
205C2×#103—31no—
206C2×#103—31no—
207C2×#103C2×D311yescharacteristic, complemented
208C2×#102—31no—
209C2×#102—31no—
210C2×#102—31no—
211C2×#102C2×D311yescharacteristic
212C2×C22⋊C8—31no—
213C2×C22⋊C8—31no—
214#391—31no—
215#391C2×D311yescharacteristic, complemented
216#389—61no—
217#389—61no—
218#384—31no—
219#380—61no—
220#380—61no—
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—42no—
233C23×D3—42no—
234C23×D3—42no—
235C23×D3—42no—
236C23×D3C2×D411yescharacteristic
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4C2×D412yes—
247C2×C3×D4C2×D412yes—
248C2×C3×D4#4112yes—
249C22×C3×C4—24no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—42no—
254C22×C3×C4—42no—
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2411yescharacteristic
258C2×#67—24no—
259C2×#67—24no—
260C2×#67—24no—
261C22×Dic3—21no—
262C22×Dic3—24no—
263C22×Dic3—21no—
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×D12C2×D412yes—
278C2×D12C2×D412yes—
279C2×D12#4112yes—
280C2×C4×D3—21no—
281C2×C4×D3—21no—
282C2×C4×D3—21no—
283C2×C4×D3—21no—
284C2×C4×D3—22no—
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×D3SD1614yescomplemented
300C2×C4×D3C2×D412yes—
301C2×C4×D3#4112yes—
302C2×Dic6—21no—
303C2×Dic6—21no—
304C2×Dic6—21no—
305C2×Dic6—21no—
306C2×Dic6—21no—
307C2×Dic6—21no—
308C3×SD16—44no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4C2×D412yes—
319C3×C22⋊C4—24no—
320C3×C42—21no—
321C3×C42—21no—
322#217—24no—
323#215—44no—
324#214—44no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—42no—
328(C2×D3)⋊C4—42no—
329C4⋊Dic3—21no—
330C4⋊Dic3—21no—
331C4⋊Dic3—21no—
332C4⋊Dic3—42no—
333C4⋊Dic3C2×D412yes—
334Dic3⋊C4—24no—
335Dic3⋊C4—42no—
336Dic3⋊C4—42no—
337Dic3⋊C4—42no—
338Dic3⋊C4—42no—
339Dic3⋊C4—42no—
340C4×Dic3—22no—
341C4×Dic3—22no—
342C4×Dic3C2×D412yes—
343C4×Dic3C2×D412yes—
344C2×C3⋊C8—21no—
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350#204—44no—
351C25—61no—
352C22×Q8—31no—
353C22×Q8C22×D311yescharacteristic
354C22×D4—34no—
355C22×D4—31no—
356C22×D4—62no—
357C22×D4—61no—
358C22×D4—62no—
359C22×D4—62no—
360C22×D4—62no—
361C22×D4—62no—
362C22×D4C22×D311yescharacteristic
363C23×C4—21no—
364C23×C4—31no—
365C23×C4—31no—
366C23×C4—31no—
367C23×C4—61no—
368C23×C4—61no—
369C23×C4—68no—
370C23×C4—61no—
371C23×C4—61no—
372C23×C4—124no—
373C23×C4—124no—
374C2×SD16—22no—
375C2×SD16—22no—
376C2×SD16—22no—
377C2×SD16—62no—
378C2×SD16—62no—
379C2×SD16—62no—
380C2×SD16—62no—
381C2×SD16—62no—
382C2×SD16—62no—
383C2×SD16—62no—
384C2×SD16—62no—
385C2×SD16—62no—
386C22×C8—31no—
387C22×C8—31no—
388C22×C8C22×D311yescharacteristic
389C22×C8C22×D311yescharacteristic
390C4⋊Q8—62no—
391C4⋊Q8—62no—
392C22⋊Q8—62no—
393C22⋊Q8—62no—
394C22⋊Q8—62no—
395C22⋊Q8—62no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—34no—
399C4×D4—34no—
400C4×D4—62no—
401C4×D4—62no—
402C4×D4—62no—
403C4×D4—62no—
404C4×D4—68no—
405C4×D4—68no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4—31no—
408C2×C4⋊C4—62no—
409C2×C4⋊C4—61no—
410C2×C4⋊C4—62no—
411C2×C4⋊C4—61no—
412C2×C4⋊C4—61no—
413C2×C4⋊C4—61no—
414C2×C4⋊C4—61no—
415C2×C4⋊C4—61no—
416C2×C4⋊C4—61no—
417C2×C4⋊C4C22×D311yescharacteristic
418C2×C4⋊C4C22×D311yescharacteristic
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×C42—31no—
427C2×C42—31no—
428C2×C42—31no—
429C2×C42—62no—
430C2×C42—62no—
431C2×C42C22×D311yescharacteristic
432C4⋊C8—62no—
433C4⋊C8—62no—
434#103—22no—
435#103—62no—
436#103—62no—
437#103—62no—
438#102—22no—
439#102—62no—
440#102—62no—
441#102—62no—
442C22⋊C8—62no—
443C22⋊C8—62no—
444#95—21no—
445#95—21no—
446#95—61no—
447#95—61no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3C22×D411yescharacteristic
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—216no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—48no—
465C22×D3—48no—
466C22×D3—48no—
467C22×D3—48no—
468C22×D3—48no—
469C22×D3—41no—
470C22×D3—41no—
471C22×D3—41no—
472C22×D3—41no—
473C22×D3—48no—
474C22×D3#12112yes—
475C22×D3C2×SD1612yes—
476C22×D3#13712yes—
477C3×Q8—41no—
478C3×Q8—41no—
479C3×Q8—41no—
480C3×Q8—41no—
481C3×D4—22no—
482C3×D4—22no—
483C3×D4—22no—
484C3×D4#12114yes—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—22no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—48no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4C2×SD1612yes—
501C2×C3×C4C22×D411yescharacteristic
502C2×C3×C4C22×D411yescharacteristic
503C2×C3×C4C22×D411yescharacteristic
504C2×C3×C4C2×#4111yescharacteristic
505C2×C3×C4C2×#4111yescharacteristic
506C2×C3×C4C2×#4111yescharacteristic
507#67—216no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—22no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—48no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3#12012yes—
523C2×Dic3#12012yes—
524C2×Dic3#12112yes—
525C2×Dic3C2×SD1612yes—
526C2×Dic3AGL(1,ℤ/8)12yes—
527D12—22no—
528D12—22no—
529D12—22no—
530D12#12114yes—
531C4×D3—22no—
532C4×D3—22no—
533C4×D3—22no—
534C4×D3—22no—
535C4×D3—28no—
536C4×D3—44no—
537C4×D3—48no—
538C4×D3—48no—
539C4×D3—48no—
540Dic6—41no—
541Dic6—41no—
542Dic6—41no—
543Dic6—41no—
544C3×C8—41no—
545C3×C8—41no—
546C3⋊C8—41no—
547C3⋊C8—41no—
548C24—21no—
549C24—31no—
550C24—64no—
551C24—64no—
552C24—64no—
553C24—61no—
554C24—122no—
555C24—122no—
556C24—122no—
557C24—122no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—61no—
565C2×Q8—61no—
566C2×Q8—61no—
567C2×Q8—61no—
568C2×Q8—61no—
569C2×Q8—61no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—32no—
574C2×D4—32no—
575C2×D4—32no—
576C2×D4—64no—
577C2×D4—68no—
578C2×D4—68no—
579C2×D4—68no—
580C2×D4—64no—
581C2×D4—64no—
582C2×D4—68no—
583C2×D4—61no—
584C2×D4—61no—
585C2×D4—61no—
586C2×D4#23512yes—
587C2×D4D3×D412yes—
588C2×D4D3×D412yes—
589C22×C4—24no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—34no—
597C22×C4—32no—
598C22×C4—32no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—62no—
602C22×C4—62no—
603C22×C4—62no—
604C22×C4—64no—
605C22×C4—62no—
606C22×C4—64no—
607C22×C4—64no—
608C22×C4—64no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—121no—
617C22×C4—122no—
618C22×C4—122no—
619C22×C4—122no—
620C22×C4—122no—
621C22×C4—122no—
622C22×C4—1232no—
623C22×C4—122no—
624C22×C4—122no—
625C22×C4—122no—
626C22×C4D3×D411yescharacteristic
627C22×C4D3×D411yescharacteristic
628C22×C4C23×D311yescharacteristic
629SD16—44no—
630SD16—124no—
631SD16—124no—
632SD16—124no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—61no—
640C2×C8—61no—
641C2×C8—61no—
642C2×C8—61no—
643C2×C8—61no—
644C2×C8—61no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—32no—
649C4⋊C4—64no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—61no—
653C4⋊C4—122no—
654C4⋊C4—122no—
655C4⋊C4—122no—
656C4⋊C4—122no—
657C4⋊C4—122no—
658C4⋊C4—122no—
659C4⋊C4D3×D412yes—
660C22⋊C4—24no—
661C22⋊C4—64no—
662C22⋊C4—64no—
663C22⋊C4—64no—
664C22⋊C4—122no—
665C22⋊C4—122no—
666C42—21no—
667C42—21no—
668C42—32no—
669C42—32no—
670C42—62no—
671C42—62no—
672C22×C3—24no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3—42no—
676C22×C3—42no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3C2×#12011yescharacteristic
680C22×C3C2×#12111yescharacteristic
681C22×C3#52511yescharacteristic
682C22×C3C22×SD1611yescharacteristic
683C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
684C22×C3C2×#13711yescharacteristic
685C22×C3#57511yescharacteristic
686C2×D3—22no—
687C2×D3—22no—
688C2×D3—22no—
689C2×D3—22no—
690C2×D3—22no—
691C2×D3—22no—
692C2×D3—24no—
693C2×D3—432no—
694C2×D3—42no—
695C2×D3—42no—
696C2×D3—42no—
697C2×D3—42no—
698C2×D3—42no—
699C2×D3—42no—
700C2×D3#46114yescomplemented
701C3×C4—22no—
702C3×C4—42no—
703C3×C4—41no—
704C3×C4—81no—
705C3×C4—81no—
706C3×C4C2×#12111yescharacteristic
707C3×C4C2×#12111yescharacteristic
708C3×C4#52511yescharacteristic
709C3×C4#52511yescharacteristic
710Dic3—22no—
711Dic3—22no—
712Dic3—42no—
713Dic3—81no—
714Dic3—81no—
715Dic3#45014yescomplemented
716C23—22no—
717C23—22no—
718C23—22no—
719C23—32no—
720C23—32no—
721C23—32no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—616no—
727C23—61no—
728C23—61no—
729C23—61no—
730C23—61no—
731C23—62no—
732C23—62no—
733C23—62no—
734C23—128no—
735C23—128no—
736C23—128no—
737C23—128no—
738C23—128no—
739C23—128no—
740C23—121no—
741C23—121no—
742C23—121no—
743C23—121no—
744C23C2×D3×D411yescharacteristic
745Q8—41no—
746Q8—41no—
747Q8—41no—
748Q8—41no—
749Q8—121no—
750Q8—121no—
751Q8—121no—
752Q8—121no—
753D4—22no—
754D4—22no—
755D4—22no—
756D4—34no—
757D4—616no—
758D4—62no—
759D4—62no—
760D4—62no—
761D4#88414yes—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—32no—
769C2×C4—32no—
770C2×C4—32no—
771C2×C4—32no—
772C2×C4—32no—
773C2×C4—48no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—68no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—128no—
793C2×C4—128no—
794C2×C4—128no—
795C2×C4—124no—
796C2×C4—128no—
797C2×C4—121no—
798C2×C4—121no—
799C2×C4—121no—
800C2×C4—121no—
801C2×C4—121no—
802C2×C4—121no—
803C2×C4—121no—
804C2×C4—121no—
805C2×C4D3×SD1612yes—
806C2×C4C2×#23511yescharacteristic
807C2×C4C2×D3×D411yescharacteristic
808C2×C4C2×D3×D411yescharacteristic
809C2×C4C2×D3×D411yescharacteristic
810C2×C4D3×#4111yescharacteristic
811C2×C4D3×#4111yescharacteristic
812C8—41no—
813C8—41no—
814C8—121no—
815C8—121no—
816C2×C3—44no—
817C2×C3#284711yescharacteristic
818C2×C3C2×#45011yescharacteristic
819C2×C3#300711yescharacteristic
820C2×C3C2×#46111yescharacteristic
821C2×C3#303611yescharacteristic
822C2×C3#310111yescharacteristic
823C2×C3#311011yescharacteristic
824D3—24no—
825D3—44no—
826C22—24no—
827C22—34no—
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—1232no—
842C22—122no—
843C22—122no—
844C22—122no—
845C22—122no—
846C22—122no—
847C22—122no—
848C22#554711yescharacteristic
849C22D3×#12011yescharacteristic
850C22D3×#12111yescharacteristic
851C22C2×D3×SD1611yescharacteristic
852C22#576811yescharacteristic
853C22D3×AGL(1,ℤ/8)11yescharacteristic
854C22D3×#13711yescharacteristic
855C4—22no—
856C4—34no—
857C4—42no—
858C4—41no—
859C4—62no—
860C4—62no—
861C4—81no—
862C4—81no—
863C4—122no—
864C4—241no—
865C4—241no—
866C4C2×#88411yescharacteristic
867C4#554711yescharacteristic
868C4D3×#12111yescharacteristic
869C4#565611yescharacteristic
870C3#3290511yescharacteristic, complemented, Sylow
871C2—44no—
872C2—64no—
873C2—124no—
874C2#7493511yescharacteristic
875C2#7965111yescharacteristic
876C2#7977911yescharacteristic
877C2D3×#45011yescharacteristic
878C2#8022811yescharacteristic
879C2D3×#46111yescharacteristic
880C2#8053411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1877C2
socleC23×C3C22×D4
prime radicalC22×D3×D4C22
hypercenter#1877D3
hypocenterC3#32905
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
3. C2×#5162C2semidirect
4. C2×#4818C2semidirect
6. #76664C2semidirect
7. C3×#1877C2semidirect
8. #71612C2semidirect
9. #70268C2semidirect
10. #70153C2semidirect
11. #69687C2semidirect
12. #68892C2semidirect
13. #68878C2semidirect
14. #68672C2semidirect
15. #68662C2semidirect
22. C2×#944C22semidirect
37. C2×C3×#103C22semidirect
39. C3×#391C22semidirect
40. C2×#835C22semidirect
47. C2×#816C22semidirect
48. C2×Dic3⋊C8C22semidirect
49. C2×Dic3⋊C8C22semidirect
50. #4975C22semidirect
51. C2×#810C22semidirect
53. #4929C22semidirect
60. C3×#340C22semidirect
61. C3×#336C22semidirect
62. #4551C22semidirect
63. #4529C22semidirect
64. #4529C22semidirect
65. #4524C22semidirect
75. #1877D3semidirect
207. C2×#103C2×D3semidirect
215. #391C2×D3semidirect
224. #340C2×D3semidirect
226. #336C2×D3semidirect
299. C2×C4×D3SD16semidirect
700. C2×D3#461semidirect
715. Dic3#450semidirect
870. C3#32905semidirect

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×#51622
C2×#48182
C2×#47762
#766642
C3×#18772
#716122
#702682
#701532
#696872
#688922
#688782
#686722
#686622
#329053