Finite Group Databasebeta

← #10943998

Subgroups — #10943998

Order 768.

1608 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#239C211yesmaximal, characteristic, complemented
2C2×#5172C211yesmaximal, characteristic, complemented
3C2×#5163C211yesmaximal, characteristic, complemented
4C2×#4810C211yesmaximal, characteristic, complemented
5C2×#4786C211yesmaximal, characteristic, complemented
6#76476C211yesmaximal, characteristic, complemented
7C3×#1880C211yesmaximal, characteristic, complemented
8#71633C211yesmaximal, characteristic, complemented
9#70221C211yesmaximal, characteristic, complemented
10#70201C211yesmaximal, characteristic, complemented
11#69657C211yesmaximal, characteristic, complemented
12#68892C211yesmaximal, characteristic, complemented
13#68881C211yesmaximal, characteristic, complemented
14#68673C211yesmaximal, characteristic, complemented
15#68662C211yesmaximal, characteristic, complemented
16#32904—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×Q8×Dic3C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C2×#940C2211yescharacteristic
23C2×#938C2211yescharacteristic
24C22×#213C2211yescharacteristic
25C22×D24C2211yescharacteristic
26C4×#239—24no—
27C4×#239—24no—
28C2×#895C2211yescharacteristic
29C2×#893—21no—
30C2×#893C2211yescharacteristic
31C2×#892—21no—
32C2×#892C2211yescharacteristic
33C2×#884—21no—
34C2×#884—21no—
35C2×C4×D12—21no—
36C2×C4×D12C2211yescharacteristic
37C2×C42×D3—21no—
38C2×C42×D3C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C3×#390C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#832C2211yescharacteristic
44#5172—24no—
45#5163—24no—
46C2×#821C2211yescharacteristic
47C2×#821C2211yescharacteristic
48C2×(C2×D3)⋊C8C2211yescharacteristic
49C2×(C2×D3)⋊C8C2211yescharacteristic
50C2×Dic3⋊C8C2211yescharacteristic
51C2×Dic3⋊C8C2211yescharacteristic
52#4975C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#809C2211yescharacteristic
55#4957—21no—
56#4957—21no—
57#4939C2211yescharacteristic
58#4810—24no—
59#4786—24no—
60C3×#340C2211yescharacteristic
61C3×#336C2211yescharacteristic
62#4551C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65#4524C2211yescharacteristic
66C2×C4×#41—31no—
67C2×#460—31no—
68C2×#459—31no—
69C2×#449—31no—
70C2×#449—31no—
71#2856—31no—
72#1880—31no—
73#1880D311yescharacteristic, complemented
74#1879—31no—
75#1879—31no—
76#1875—31no—
77#1875—31no—
78#1803—31no—
79#1802—31no—
80#1797—31no—
81C22×C3×Q8C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C2×#239—22no—
87C2×#239—22no—
88C2×#239—22no—
89C2×#239—22no—
90C2×#239—22no—
91C2×#239D414yescomplemented
92C22×D12—21no—
93C22×D12—21no—
94C22×D12C2311yescharacteristic
95C22×D12C2311yescharacteristic
96C22×C4×D3—21no—
97C22×C4×D3—21no—
98C22×C4×D3—21no—
99C22×C4×D3D411yescharacteristic
100C22×C4×D3D411yescharacteristic
101C22×C4×D3C2311yescharacteristic
102C2×C3×SD16—22no—
103C2×C3×SD16—22no—
104C2×C3×SD16—22no—
105C22×C3×C8C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C3×C4×Q8—22no—
108C3×C4×Q8—22no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C42—21no—
115C2×C3×C42C2311yescharacteristic
116C2×#217—21no—
117Q8×Dic3—22no—
118Q8×Dic3D414yescomplemented
119C2×#215—22no—
120C2×#215—22no—
121C2×#215—22no—
122#940—22no—
123#940—22no—
124#938—22no—
125#938—22no—
126C2×#213—22no—
127C2×#213—22no—
128C2×#213—22no—
129C2×(C2×D3)⋊C4—21no—
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×C4⋊Dic3—21no—
136C2×C4⋊Dic3C2311yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×C4×Dic3—21no—
141C2×C4×Dic3—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—28no—
153#893—22no—
154#893D414yescomplemented
155#892—28no—
156#892—22no—
157#892—22no—
158#884—44no—
159#884—44no—
160C4×D12—28no—
161C4×D12—22no—
162C4×D12—22no—
163C42×D3—28no—
164C42×D3—22no—
165C42×D3—22no—
166C3×#103—22no—
167C3×#102—22no—
168#835—22no—
169#832—22no—
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—
178C22×#41—31no—
179C22×SD16—31no—
180C22×SD16C2×D311yescharacteristic
181C22×D8—31no—
182C22×D8—31no—
183C2×#127—31no—
184C2×#121—31no—
185C2×#121—31no—
186C2×#121—61no—
187C2×#121—61no—
188C4×#41—64no—
189C4×#41—64no—
190C2×C4×Q8—31no—
191C2×C4×Q8C2×D311yescharacteristic
192C2×C4×D4—31no—
193C2×C4×D4—31no—
194C2×C4×D4—61no—
195C2×C4×D4—61no—
196C2×#117—31no—
197C2×#117—61no—
198C22×C42—31no—
199C22×C42—61no—
200#460—64no—
201#459—64no—
202#449—64no—
203#449—64no—
204C2×C4⋊C8—31no—
205C2×C4⋊C8—31no—
206C2×#103—31no—
207C2×#103C2×D311yescharacteristic
208C2×#102—31no—
209C2×#102—31no—
210C2×#102—31no—
211C2×#102—31no—
212C2×#102—31no—
213C2×#102C2×D311yescharacteristic
214C2×C22⋊C8—31no—
215C2×C22⋊C8—31no—
216#390—31no—
217#390—61no—
218#390—61no—
219#390C2×D311yescharacteristic
220#384—31no—
221#340—31no—
222#340—31no—
223#340—31no—
224#340C2×D311yescharacteristic
225#336—31no—
226#336C2×D311yescharacteristic
227C24×C3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3C2×D411yescharacteristic
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8C2×D412yes—
235C2×C3×Q8C2×D412yes—
236C2×C3×Q8#4112yes—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2411yescharacteristic
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—42no—
252C2×#67—42no—
253C2×#67—42no—
254C2×#67—42no—
255C2×#67—42no—
256C2×#67—42no—
257C2×#67—42no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3C2×D411yescharacteristic
261C22×Dic3C2×D411yescharacteristic
262C22×Dic3C2×D411yescharacteristic
263#239—28no—
264#239—28no—
265#239—28no—
266#239—28no—
267C2×D12—24no—
268C2×D12—24no—
269C2×D12—24no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—42no—
280C2×D12—42no—
281C2×D12—42no—
282C2×D12C2×D412yes—
283C2×D12C2×D412yes—
284C2×D12#4112yes—
285C2×C4×D3—24no—
286C2×C4×D3—24no—
287C2×C4×D3—21no—
288C2×C4×D3—21no—
289C2×C4×D3—21no—
290C2×C4×D3—21no—
291C2×C4×D3—24no—
292C2×C4×D3—24no—
293C2×C4×D3—22no—
294C2×C4×D3—22no—
295C2×C4×D3—22no—
296C2×C4×D3—24no—
297C2×C4×D3—22no—
298C2×C4×D3—22no—
299C2×C4×D3—41no—
300C2×C4×D3—42no—
301C2×C4×D3—42no—
302C2×C4×D3—42no—
303C2×C4×D3—42no—
304C2×C4×D3C2×D412yes—
305C2×C4×D3#4112yes—
306C3×SD16—44no—
307C2×C3×C8—21no—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C3×C4⋊C4—24no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4C2×D412yes—
318C3×C22⋊C4—42no—
319C3×C22⋊C4—42no—
320C3×C42—24no—
321C3×C42—21no—
322C3×C42—21no—
323#217—42no—
324#215—44no—
325#213—44no—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—24no—
328(C2×D3)⋊C4—24no—
329(C2×D3)⋊C4—42no—
330(C2×D3)⋊C4—42no—
331(C2×D3)⋊C4—42no—
332C4⋊Dic3—21no—
333C4⋊Dic3—24no—
334C4⋊Dic3—21no—
335C4⋊Dic3—21no—
336C4⋊Dic3C2×D412yes—
337Dic3⋊C4—42no—
338Dic3⋊C4—42no—
339C4×Dic3—24no—
340C4×Dic3—22no—
341C4×Dic3—22no—
342C4×Dic3—24no—
343C4×Dic3C2×D412yes—
344C4×Dic3C2×D412yes—
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—
352C2×#41—34no—
353C2×#41—62no—
354C2×#41—62no—
355C2×#41—62no—
356C2×#41—62no—
357C2×#41—62no—
358C22×Q8C22×D311yescharacteristic
359C22×D4—31no—
360C22×D4—31no—
361C22×D4—61no—
362C22×D4—61no—
363C22×D4—61no—
364C22×D4—61no—
365C22×D4—61no—
366C22×D4C22×D311yescharacteristic
367C23×C4—31no—
368C23×C4—31no—
369C23×C4—31no—
370C23×C4—61no—
371C23×C4—61no—
372C23×C4—61no—
373C2×SD16—22no—
374C2×SD16—22no—
375C2×SD16—22no—
376C2×SD16—62no—
377C2×SD16—62no—
378C2×SD16—62no—
379C2×D8—62no—
380C2×D8—62no—
381C2×D8—62no—
382C2×D8—62no—
383C2×D8—62no—
384C2×D8—62no—
385C22×C8—31no—
386C22×C8—31no—
387C22×C8C22×D311yescharacteristic
388C22×C8C22×D311yescharacteristic
389#127—62no—
390#127—62no—
391#121—62no—
392#121—62no—
393#121—62no—
394#121—62no—
395#121—124no—
396#121—124no—
397C4×Q8—22no—
398C4×Q8—22no—
399C4×Q8—34no—
400C4×Q8—62no—
401C4×D4—34no—
402C4×D4—62no—
403C4×D4—62no—
404C4×D4—68no—
405C4×D4—62no—
406C4×D4—68no—
407#117—62no—
408#117—68no—
409#117—62no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—31no—
412C2×C4⋊C4—31no—
413C2×C4⋊C4—61no—
414C2×C4⋊C4—61no—
415C2×C4⋊C4—61no—
416C2×C4⋊C4C22×D311yescharacteristic
417C2×C4⋊C4C22×D311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
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×C42—21no—
428C2×C42—31no—
429C2×C42—31no—
430C2×C42—31no—
431C2×C42—62no—
432C2×C42—62no—
433C2×C42—68no—
434C2×C42—61no—
435C2×C42—61no—
436C2×C42C22×D311yescharacteristic
437C4⋊C8—62no—
438C4⋊C8—62no—
439#103—22no—
440#103—62no—
441#102—22no—
442#102—62no—
443#102—62no—
444#102—62no—
445#102—62no—
446#102—62no—
447C22⋊C8—62no—
448C22⋊C8—62no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3C22×D411yescharacteristic
457C22×D3—21no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—21no—
461C22×D3—22no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3—21no—
465C22×D3—21no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3—41no—
470C22×D3—41no—
471C22×D3—41no—
472C22×D3—41no—
473C22×D3—41no—
474C22×D3—41no—
475C22×D3—41no—
476C22×D3—41no—
477C22×D3#12112yes—
478C3×Q8—22no—
479C3×Q8—22no—
480C3×Q8—22no—
481C3×Q8#12114yescomplemented
482C3×D4—41no—
483C3×D4—41no—
484C3×D4—41no—
485C3×D4—41no—
486C2×C3×C4—22no—
487C2×C3×C4—21no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—22no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4AGL(1,ℤ/8)12yes—
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—84no—
508#67—84no—
509#67—84no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—22no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3—41no—
520C2×Dic3#12012yes—
521C2×Dic3#12012yes—
522C2×Dic3#12112yes—
523C2×Dic3#13512yes—
524C2×Dic3AGL(1,ℤ/8)12yes—
525D12—216no—
526D12—22no—
527D12—22no—
528D12—22no—
529D12—41no—
530D12—41no—
531D12—41no—
532D12—41no—
533D12—84no—
534D12#12114yescomplemented
535C4×D3—216no—
536C4×D3—22no—
537C4×D3—22no—
538C4×D3—22no—
539C4×D3—22no—
540C4×D3—44no—
541C4×D3—48no—
542C4×D3—44no—
543C4×D3—48no—
544C3×C8—41no—
545C3×C8—41no—
546C3⋊C8—41no—
547C3⋊C8—41no—
548C24—21no—
549C24—31no—
550C24—61no—
551C24—61no—
552#41—68no—
553#41—68no—
554#41—68no—
555#41—68no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8#23512yes—
560C2×Q8D3×D412yes—
561C2×Q8D3×D412yes—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—32no—
569C2×D4—32no—
570C2×D4—32no—
571C2×D4—64no—
572C2×D4—64no—
573C2×D4—64no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4—61no—
580C2×D4—61no—
581C2×D4—61no—
582C2×D4—61no—
583C2×D4—122no—
584C2×D4—122no—
585C2×D4—122no—
586C2×D4—122no—
587C2×D4—122no—
588C2×D4—122no—
589C2×D4—122no—
590C2×D4—122no—
591C2×D4—122no—
592C2×D4—122no—
593C2×D4—122no—
594C2×D4—122no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—32no—
602C22×C4—32no—
603C22×C4—64no—
604C22×C4—64no—
605C22×C4—62no—
606C22×C4—62no—
607C22×C4—62no—
608C22×C4—62no—
609C22×C4—64no—
610C22×C4—64no—
611C22×C4—64no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—62no—
618C22×C4—61no—
619C22×C4—121no—
620C22×C4—122no—
621C22×C4—122no—
622C22×C4—122no—
623C22×C4—122no—
624C22×C4D3×D411yescharacteristic
625C22×C4D3×D411yescharacteristic
626C22×C4C23×D311yescharacteristic
627SD16—44no—
628SD16—124no—
629D8—124no—
630D8—124no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—61no—
638C2×C8—61no—
639C2×C8—61no—
640C2×C8—61no—
641C2×C8—61no—
642C2×C8—61no—
643C4⋊C4—24no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—32no—
648C4⋊C4—64no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—122no—
653C4⋊C4—122no—
654C4⋊C4D3×D412yes—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—64no—
658C22⋊C4—64no—
659C22⋊C4—64no—
660C22⋊C4—122no—
661C22⋊C4—122no—
662C22⋊C4—122no—
663C22⋊C4—122no—
664C42—24no—
665C42—21no—
666C42—21no—
667C42—32no—
668C42—32no—
669C42—62no—
670C42—62no—
671C42—64no—
672C42—64no—
673C22×C3—81no—
674C22×C3—81no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3—81no—
680C22×C3C2×#12011yescharacteristic
681C22×C3C2×#12111yescharacteristic
682C22×C3#52511yescharacteristic
683C22×C3C2×#13511yescharacteristic
684C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
685C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
686C22×C3#57511yescharacteristic
687C2×D3—22no—
688C2×D3—24no—
689C2×D3—22no—
690C2×D3—22no—
691C2×D3—41no—
692C2×D3—42no—
693C2×D3—41no—
694C2×D3—42no—
695C2×D3—41no—
696C2×D3—42no—
697C2×D3—41no—
698C2×D3—42no—
699C2×D3—42no—
700C2×D3—42no—
701C2×D3—81no—
702C2×D3—81no—
703C2×D3—81no—
704C2×D3—81no—
705C2×D3—81no—
706C2×D3—81no—
707C2×D3—81no—
708C3×C4—24no—
709C3×C4—22no—
710C3×C4—41no—
711C3×C4—42no—
712C3×C4—81no—
713C3×C4C2×#12111yescharacteristic
714C3×C4C2×#12111yescharacteristic
715C3×C4#52511yescharacteristic
716C3×C4#52511yescharacteristic
717Dic3—22no—
718Dic3—22no—
719Dic3—42no—
720Dic3—81no—
721Dic3#44914yescomplemented
722C23—32no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—61no—
731C23—61no—
732C23—61no—
733C23—61no—
734C23—62no—
735C23—61no—
736C23—62no—
737C23—61no—
738C23—62no—
739C23—121no—
740C23—121no—
741C23—121no—
742C23—121no—
743C23—121no—
744C23—121no—
745C23—121no—
746C23—121no—
747C23—121no—
748C23—121no—
749C23—121no—
750C23C2×D3×D411yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8#88414yescomplemented
755D4—34no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—616no—
761D4—62no—
762D4—62no—
763D4—62no—
764D4—121no—
765D4—121no—
766D4—121no—
767D4—121no—
768D4—244no—
769D4—244no—
770D4—244no—
771D4—244no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—32no—
782C2×C4—32no—
783C2×C4—32no—
784C2×C4—32no—
785C2×C4—32no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—616no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—62no—
797C2×C4—62no—
798C2×C4—62no—
799C2×C4—62no—
800C2×C4—62no—
801C2×C4—124no—
802C2×C4—128no—
803C2×C4—124no—
804C2×C4—128no—
805C2×C4—121no—
806C2×C4—121no—
807C2×C4—121no—
808C2×C4—121no—
809C2×C4—121no—
810C2×C4#91412yes—
811C2×C4C2×#23511yescharacteristic
812C2×C4C2×D3×D411yescharacteristic
813C2×C4C2×D3×D411yescharacteristic
814C2×C4C2×D3×D411yescharacteristic
815C2×C4D3×#4111yescharacteristic
816C2×C4D3×#4111yescharacteristic
817C8—41no—
818C8—41no—
819C8—121no—
820C8—121no—
821C2×C3—161no—
822C2×C3#284711yescharacteristic
823C2×C3C2×#44911yescharacteristic
824C2×C3#300611yescharacteristic
825C2×C3#303511yescharacteristic
826C2×C3#303811yescharacteristic
827C2×C3#310611yescharacteristic
828C2×C3#311511yescharacteristic
829D3—42no—
830D3—44no—
831D3—161no—
832C22—62no—
833C22—64no—
834C22—62no—
835C22—62no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—122no—
844C22—121no—
845C22—122no—
846C22—121no—
847C22—122no—
848C22—121no—
849C22—122no—
850C22—121no—
851C22—122no—
852C22—122no—
853C22—241no—
854C22—241no—
855C22—241no—
856C22—241no—
857C22—241no—
858C22—241no—
859C22—241no—
860C22#554711yescharacteristic
861C22D3×#12011yescharacteristic
862C22D3×#12111yescharacteristic
863C22C2×#91411yescharacteristic
864C22D3×#13511yescharacteristic
865C22D3×AGL(1,ℤ/8)11yescharacteristic
866C22#577711yescharacteristic
867C4—22no—
868C4—24no—
869C4—34no—
870C4—41no—
871C4—42no—
872C4—62no—
873C4—62no—
874C4—81no—
875C4—122no—
876C4—241no—
877C4C2×#88411yescharacteristic
878C4#554711yescharacteristic
879C4D3×#12111yescharacteristic
880C4#565611yescharacteristic
881C3#3290411yescharacteristic, complemented, Sylow
882C2—122no—
883C2—124no—
884C2—161no—
885C2—481no—
886C2#7493511yescharacteristic
887C2#7969511yescharacteristic
888C2#7981111yescharacteristic
889C2#8004011yescharacteristic
890C2D3×#44911yescharacteristic
891C2#8038411yescharacteristic
892C2#8059711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1880C2
socleC23×C3C22×D4
hypercenter#1880D3
hypocenterC3#32904
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
1. C2×C4×#239C2semidirect
2. C2×#5172C2semidirect
3. C2×#5163C2semidirect
4. C2×#4810C2semidirect
5. C2×#4786C2semidirect
6. #76476C2semidirect
7. C3×#1880C2semidirect
8. #71633C2semidirect
9. #70221C2semidirect
10. #70201C2semidirect
11. #69657C2semidirect
12. #68892C2semidirect
13. #68881C2semidirect
14. #68673C2semidirect
15. #68662C2semidirect
73. #1880D3semidirect
91. C2×#239D4semidirect
118. Q8×Dic3D4semidirect
154. #893D4semidirect
481. C3×Q8#121semidirect
534. D12#121semidirect
721. Dic3#449semidirect
754. Q8#884semidirect
881. C3#32904semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C4×#2392
C2×#51722
C2×#51632
C2×#48102
C2×#47862
#764762
C3×#18802
#716332
#702212
#702012
#696572
#688922
#688812
#686732
#686622
#329043