Finite Group Databasebeta

← #10848689

Subgroups — #10848689

Order 768.

1298 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5622C211yesmaximal, characteristic, complemented
2C2×#5175C211yesmaximal, characteristic, complemented
3#82700C211yesmaximal, characteristic
4C2×#4760C211yesmaximal, characteristic, complemented
5C3×#2000C211yesmaximal, characteristic, complemented
6#72048C211yesmaximal, characteristic, complemented
7#71699C211yesmaximal, characteristic, complemented
8#71685C211yesmaximal, characteristic, complemented
9#70240C211yesmaximal, characteristic, complemented
10#70225C211yesmaximal, characteristic, complemented
11#70213C211yesmaximal, characteristic, complemented
12#69962C211yesmaximal, characteristic, complemented
13Dic3×C22⋊C8C211yesmaximal, characteristic, complemented
14#68909C211yesmaximal, characteristic, complemented
15#68803C211yesmaximal, characteristic, complemented
16#25598—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×Q8×Dic3C2211yescharacteristic
21C2×#944C2211yescharacteristic
22C22×#215C2211yescharacteristic
23C2×#940C2211yescharacteristic
24C2×#939—21no—
25C2×#939—21no—
26C22×#214C2211yescharacteristic
27C2×#930C2211yescharacteristic
28C2×#924C2211yescharacteristic
29C22×C4×Dic3C2211yescharacteristic
30C22×#204C2211yescharacteristic
31#5622—24no—
32#5622—24no—
33C2×#889—21no—
34C2×#888C2211yescharacteristic
35C2×#887—21no—
36C2×#887C2211yescharacteristic
37C2×#878—21no—
38C2×#877—21no—
39C2×C3×#103C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C2×C3×C22⋊C8C2211yescharacteristic
42C2×#835C2211yescharacteristic
43#5221C2211yescharacteristic
44C2×#832C2211yescharacteristic
45C2×#830C2211yescharacteristic
46#5175—24no—
47C2×#821C2211yescharacteristic
48C2×#816C2211yescharacteristic
49C2×C8×Dic3C2211yescharacteristic
50C2×C8×Dic3C2211yescharacteristic
51#4988C2211yescharacteristic
52#4975C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#809C2211yescharacteristic
55#4957—21no—
56#4957—21no—
57#4760—24no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#533—31no—
65C2×#492—31no—
66C2×#486—31no—
67#2856—31no—
68#2000—31no—
69#2000—31no—
70#2000—31no—
71#2000D311yescharacteristic, complemented
72#1990—31no—
73#1956—31no—
74#1880—31no—
75#1880—31no—
76#1880—31no—
77#1880—31no—
78C4×C22⋊C8—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C23×Dic3D411yescharacteristic
87C23×Dic3D411yescharacteristic
88C22×D12C2311yescharacteristic
89C22×Dic6—21no—
90C22×Dic6C2311yescharacteristic
91C2×C3×SD16—22no—
92C2×C3×SD16—22no—
93C2×C3×SD16—41no—
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C3×C22⋊Q8—22no—
97C3×C22⋊Q8—22no—
98C3×#121—41no—
99C3×#121—41no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C22⋊C4—21no—
104C2×C3×C22⋊C4—21no—
105C2×#217—21no—
106C2×#217—21no—
107C2×#217—21no—
108Q8×Dic3—22no—
109Q8×Dic3—22no—
110#944—22no—
111#944D414yescomplemented
112C2×#215—22no—
113C2×#215—22no—
114C2×#215—41no—
115#940—22no—
116#940—22no—
117#939—44no—
118#939—44no—
119C2×#214—22no—
120C2×#214—22no—
121C2×#214—41no—
122#930—41no—
123#930—41no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×C4⋊Dic3—21no—
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130#924—22no—
131#924—22no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×C4×Dic3—21no—
140C2×C4×Dic3—21no—
141C2×C4×Dic3—22no—
142C2×C4×Dic3—22no—
143C2×C4×Dic3D411yescharacteristic
144C2×C4×Dic3D411yescharacteristic
145C2×C4×Dic3C2311yescharacteristic
146C2×C4×Dic3C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148C22×C3⋊C8C2311yescharacteristic
149C2×#204—22no—
150C2×#204—22no—
151C2×#204—41no—
152#889—28no—
153#888—22no—
154#888D414yescomplemented
155#887—28no—
156#887—22no—
157#887—22no—
158#878—28no—
159#877—28no—
160C3×#103—41no—
161C3×#102—22no—
162C3×C22⋊C8—22no—
163#835—41no—
164#832—22no—
165#830—22no—
166#821—22no—
167#816—41no—
168C8×Dic3—22no—
169C8×Dic3—22no—
170#810—41no—
171#809—22no—
172C22×SD16—31no—
173C22×SD16—31no—
174C22×SD16—31no—
175C22×SD16C2×D311yescharacteristic
176#533—64no—
177#533—64no—
178C2×C4⋊Q8—31no—
179C2×C4⋊Q8—31no—
180C2×#127—31no—
181C2×#125—61no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8—61no—
184C2×C22⋊Q8C2×D311yescharacteristic
185C2×#121—31no—
186C2×#121—61no—
187C2×#121—61no—
188C2×#121C2×D311yescharacteristic
189C2×C4×Q8—31no—
190C2×C4×Q8—31no—
191C2×C4×Q8—61no—
192C2×#117—61no—
193C22×C42—31no—
194#492—64no—
195#486—64no—
196C2×#103—31no—
197C2×#103—31no—
198C2×#103—31no—
199C2×#103C2×D311yescharacteristic
200C2×#102—31no—
201C2×#102—31no—
202C2×#102—31no—
203C2×#102C2×D311yescharacteristic
204C2×C22⋊C8—31no—
205C2×C22⋊C8C2×D311yescharacteristic
206C2×C4×C8—31no—
207C2×C4×C8—31no—
208#390—31no—
209#390—31no—
210#390—61no—
211#390—61no—
212#384—31no—
213#340—31no—
214#340—31no—
215#340—31no—
216#340C2×D311yescharacteristic
217#336—31no—
218#336—31no—
219C24×C3—21no—
220C24×C3C2×D411yescharacteristic
221C23×D3—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8C2×D412yes—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2411yescharacteristic
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—42no—
252C2×#67—42no—
253C2×#67—42no—
254C2×#67—42no—
255C2×#67—42no—
256C2×#67—42no—
257C22×Dic3—22no—
258C22×Dic3—22no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—22no—
262C22×Dic3—22no—
263C22×Dic3—22no—
264C22×Dic3—21no—
265C22×Dic3SD1614yescomplemented
266C22×Dic3C2×D411yescharacteristic
267C22×Dic3C2×D411yescharacteristic
268C22×Dic3C2×D411yescharacteristic
269C22×Dic3C2×D411yescharacteristic
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6—21no—
279C2×Dic6—21no—
280C2×Dic6—21no—
281C2×Dic6—24no—
282C2×Dic6—42no—
283C2×Dic6—42no—
284C2×Dic6C2×D412yes—
285C3×SD16—44no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8#4112yes—
292C3×C4⋊C4—24no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4C2×D412yes—
297C3×C22⋊C4—24no—
298C3×C22⋊C4—42no—
299#217—24no—
300#217—42no—
301#217—42no—
302#215—44no—
303#214—44no—
304(C2×D3)⋊C4—42no—
305(C2×D3)⋊C4—42no—
306(C2×D3)⋊C4—42no—
307C4⋊Dic3—24no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3C2×D412yes—
312Dic3⋊C4—24no—
313Dic3⋊C4—24no—
314Dic3⋊C4—24no—
315Dic3⋊C4—24no—
316Dic3⋊C4—24no—
317Dic3⋊C4—42no—
318Dic3⋊C4—42no—
319C4×Dic3—24no—
320C4×Dic3—24no—
321C4×Dic3—21no—
322C4×Dic3—21no—
323C4×Dic3—22no—
324C4×Dic3—22no—
325C4×Dic3C2×D412yes—
326C4×Dic3C2×D412yes—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8#4112yes—
333#204—44no—
334C22×Q8—31no—
335C22×Q8—61no—
336C22×Q8C22×D311yescharacteristic
337C22×D4—21no—
338C22×D4—31no—
339C22×D4—61no—
340C22×D4—61no—
341C22×D4—61no—
342C22×D4C22×D311yescharacteristic
343C23×C4—31no—
344C23×C4—31no—
345C23×C4C22×D311yescharacteristic
346C2×SD16—22no—
347C2×SD16—22no—
348C2×SD16—41no—
349C2×SD16—62no—
350C2×SD16—62no—
351C2×SD16—62no—
352C2×SD16—62no—
353C2×SD16—62no—
354C2×SD16—62no—
355C2×SD16—121no—
356C2×SD16—121no—
357C2×SD16—121no—
358C22×C8—31no—
359C22×C8—31no—
360C22×C8C22×D311yescharacteristic
361C22×C8C22×D311yescharacteristic
362C4⋊Q8—34no—
363C4⋊Q8—34no—
364C4⋊Q8—62no—
365C4⋊Q8—62no—
366#127—62no—
367#127—62no—
368#125—68no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—68no—
372C22⋊Q8—62no—
373C22⋊Q8—62no—
374#121—41no—
375#121—41no—
376#121—121no—
377#121—121no—
378#121—124no—
379#121—124no—
380C4×Q8—62no—
381C4×Q8—68no—
382C4×Q8—62no—
383C4×Q8—62no—
384C4×Q8—62no—
385#117—68no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—61no—
390C2×C4⋊C4—61no—
391C2×C4⋊C4—61no—
392C2×C4⋊C4—61no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4—61no—
396C2×C4⋊C4—61no—
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C4⋊C4C22×D311yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—61no—
402C2×C22⋊C4—61no—
403C2×C22⋊C4—61no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C42—31no—
408C2×C42—31no—
409C2×C42—31no—
410C2×C42—31no—
411C2×C42—62no—
412C2×C42—62no—
413C2×C42—61no—
414C2×C42—61no—
415#103—41no—
416#103—121no—
417#103—121no—
418#103—121no—
419#102—22no—
420#102—62no—
421#102—62no—
422#102—62no—
423C22⋊C8—22no—
424C22⋊C8—62no—
425C4×C8—62no—
426C4×C8—62no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3C2×SD1612yes—
441C23×C3C22×D411yescharacteristic
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—41no—
446C22×D3—41no—
447C22×D3—41no—
448C22×D3—41no—
449C3×Q8—22no—
450C3×Q8—22no—
451C3×Q8—41no—
452C3×Q8—41no—
453C3×D4—41no—
454C3×D4—41no—
455C3×D4—41no—
456C3×D4—41no—
457C3×D4—84no—
458C2×C3×C4—21no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C22×D411yescharacteristic
476C2×C3×C4C2×#4111yescharacteristic
477C2×C3×C4C2×#4111yescharacteristic
478C2×C3×C4H(5,𝔽2)11yescharacteristic
479C2×C3×C4H(5,𝔽2)11yescharacteristic
480#67—84no—
481#67—84no—
482#67—84no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—28no—
486C2×Dic3—21no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—44no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3#12012yes—
500C2×Dic3#12012yes—
501C2×Dic3C2×SD1612yes—
502C2×Dic3C2×SD1612yes—
503C2×Dic3#13512yes—
504C2×Dic3AGL(1,ℤ/8)12yes—
505C2×Dic3#13712yes—
506D12—41no—
507D12—41no—
508D12—41no—
509D12—41no—
510Dic6—22no—
511Dic6—22no—
512Dic6—41no—
513Dic6—41no—
514Dic6—48no—
515C3×C8—22no—
516C3×C8—41no—
517C3⋊C8—22no—
518C3⋊C8—41no—
519C24—21no—
520C24—61no—
521C24D3×D411yescharacteristic
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—32no—
528C2×Q8—64no—
529C2×Q8—61no—
530C2×Q8—61no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—61no—
534C2×Q8—122no—
535C2×Q8—122no—
536C2×Q8D3×D412yes—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—61no—
547C2×D4—61no—
548C2×D4—61no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—122no—
553C2×D4—122no—
554C2×D4—122no—
555C2×D4—122no—
556C2×D4—122no—
557C2×D4—122no—
558C2×D4—122no—
559C2×D4—122no—
560C2×D4—122no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—34no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—62no—
576C22×C4—62no—
577C22×C4—62no—
578C22×C4—62no—
579C22×C4—62no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4D3×D411yescharacteristic
584C22×C4C23×D311yescharacteristic
585SD16—44no—
586SD16—124no—
587SD16—124no—
588SD16—124no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—32no—
595C2×C8—61no—
596C2×C8—61no—
597C2×C8—61no—
598C2×C8—61no—
599C2×C8—61no—
600C2×C8#23712yes—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—32no—
606C4⋊C4—64no—
607C4⋊C4—64no—
608C4⋊C4—64no—
609C4⋊C4—64no—
610C4⋊C4—64no—
611C4⋊C4—64no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—122no—
616C4⋊C4—122no—
617C4⋊C4D3×D412yes—
618C22⋊C4—24no—
619C22⋊C4—42no—
620C22⋊C4—64no—
621C22⋊C4—122no—
622C22⋊C4—122no—
623C22⋊C4—122no—
624C22⋊C4—122no—
625C22⋊C4—122no—
626C42—32no—
627C42—32no—
628C42—62no—
629C42—62no—
630C42—64no—
631C42—64no—
632C42—61no—
633C42—61no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—22no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—81no—
647C22×C3—81no—
648C22×C3C2×#12011yescharacteristic
649C22×C3#53211yescharacteristic
650C22×C3#53511yescharacteristic
651C22×C3C22×SD1611yescharacteristic
652C22×C3C2×#13511yescharacteristic
653C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
654C22×C3C2×#13711yescharacteristic
655C2×D3—81no—
656C2×D3—81no—
657C2×D3—81no—
658C2×D3—81no—
659C2×D3—81no—
660C2×D3—81no—
661C2×D3—81no—
662C3×C4—41no—
663C3×C4—42no—
664C3×C4—42no—
665C3×C4—81no—
666C3×C4#54611yescharacteristic
667C3×C4#54611yescharacteristic
668C3×C4#55011yescharacteristic
669C3×C4#55011yescharacteristic
670Dic3—22no—
671Dic3—42no—
672Dic3—42no—
673Dic3—41no—
674Dic3—81no—
675Dic3#44814yes—
676Dic3#44914yes—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23—121no—
694C23—121no—
695C23—121no—
696C23—121no—
697C23D3×SD1612yes—
698C23C2×D3×D411yescharacteristic
699Q8—22no—
700Q8—22no—
701Q8—41no—
702Q8—41no—
703Q8—62no—
704Q8—62no—
705Q8—128no—
706Q8—121no—
707Q8—121no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—84no—
713D4—121no—
714D4—121no—
715D4—121no—
716D4—121no—
717D4—244no—
718D4—244no—
719D4—244no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—32no—
726C2×C4—32no—
727C2×C4—32no—
728C2×C4—32no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—68no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—62no—
750C2×C4—62no—
751C2×C4—124no—
752C2×C4—121no—
753C2×C4—121no—
754C2×C4—121no—
755C2×C4—121no—
756C2×C4—121no—
757C2×C4—121no—
758C2×C4—121no—
759C2×C4C2×D3×D411yescharacteristic
760C2×C4C2×D3×D411yescharacteristic
761C2×C4C2×#23711yescharacteristic
762C2×C4#100411yescharacteristic
763C2×C4#100411yescharacteristic
764C2×C4D3×#4111yescharacteristic
765C8—22no—
766C8—41no—
767C8—62no—
768C8—121no—
769C2×C3—42no—
770C2×C3—161no—
771C2×C3#243111yescharacteristic
772C2×C3C2×#44811yescharacteristic
773C2×C3C2×#44911yescharacteristic
774C2×C3#316711yescharacteristic
775C2×C3#318211yescharacteristic
776C2×C3#320811yescharacteristic
777C2×C3#321011yescharacteristic
778D3—161no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—241no—
794C22—241no—
795C22—241no—
796C22—241no—
797C22—241no—
798C22—241no—
799C22—241no—
800C22D3×#12011yescharacteristic
801C22#559211yescharacteristic
802C22#559611yescharacteristic
803C22C2×D3×SD1611yescharacteristic
804C22D3×#13511yescharacteristic
805C22D3×AGL(1,ℤ/8)11yescharacteristic
806C22D3×#13711yescharacteristic
807C4—34no—
808C4—34no—
809C4—41no—
810C4—42no—
811C4—42no—
812C4—62no—
813C4—81no—
814C4—122no—
815C4—121no—
816C4—122no—
817C4—241no—
818C4#559111yescharacteristic
819C4#559911yescharacteristic
820C4#561011yescharacteristic
821C4#571811yescharacteristic
822C3#2559811yescharacteristic, complemented, Sylow
823C2—42no—
824C2—161no—
825C2—481no—
826C2#7667211yescharacteristic
827C2D3×#44811yescharacteristic
828C2D3×#44911yescharacteristic
829C2#8013811yescharacteristic
830C2#8022011yescharacteristic
831C2#8063211yescharacteristic
832C2#8079011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
prime radical#82700C2
hypercenter#2000D3
hypocenterC3#25598
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
1. C2×#5622C2semidirect
2. C2×#5175C2semidirect
4. C2×#4760C2semidirect
5. C3×#2000C2semidirect
6. #72048C2semidirect
7. #71699C2semidirect
8. #71685C2semidirect
9. #70240C2semidirect
10. #70225C2semidirect
11. #70213C2semidirect
12. #69962C2semidirect
13. Dic3×C22⋊C8C2semidirect
14. #68909C2semidirect
15. #68803C2semidirect
71. #2000D3semidirect
111. #944D4semidirect
154. #888D4semidirect
265. C22×Dic3SD16semidirect
822. C3#25598semidirect

Maximal subgroups

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

subgroupindex
C2×#56222
C2×#51752
#827002
C2×#47602
C3×#20002
#720482
#716992
#716852
#702402
#702252
#702132
#699622
Dic3×C22⋊C82
#689092
#688032
#255983