Finite Group Databasebeta

← #10826332

Subgroups — #10826332

Order 768.

2240 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#949C211yesmaximal, characteristic, complemented
2C2×#5609C211yesmaximal, characteristic, complemented
3C2×C3×#449C211yesmaximal, characteristic, complemented
4#84097C211yesmaximal, characteristic, complemented
5C2×#5169C211yesmaximal, characteristic, complemented
6C2×#5156C211yesmaximal, characteristic, complemented
7#72056C211yesmaximal, characteristic, complemented
8#72044C211yesmaximal, characteristic, complemented
9#71682C211yesmaximal, characteristic, complemented
10#70276C211yesmaximal, characteristic, complemented
11#70272C211yesmaximal, characteristic, complemented
12#70208C211yesmaximal, characteristic, complemented
13#70204C211yesmaximal, characteristic, complemented
14#69959C211yesmaximal, characteristic, complemented
15#69953C211yesmaximal, characteristic, complemented
16#23860—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic, complemented
18C22×D3×D4—21no—
19C22×D3×D4C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic, complemented
22C22×C3×D8C2211yescharacteristic, complemented
23C2×C3×#121C2211yescharacteristic
24C2×#949—24no—
25C2×#949—24no—
26C2×#949—24no—
27C2×#946C2211yescharacteristic, complemented
28C22×#215C2211yescharacteristic
29C22×#215C2211yescharacteristic, complemented
30C2×#940C2211yescharacteristic
31C2×#938C2211yescharacteristic, complemented
32C2×#937—21no—
33C22×#213C2211yescharacteristic
34C22×#213C2211yescharacteristic, complemented
35C2×C4×#67C2211yescharacteristic
36C22×#208C2211yescharacteristic, complemented
37#5609—24no—
38#5609—24no—
39C2×#895C2211yescharacteristic
40C2×#893C2211yescharacteristic
41C2×#884—21no—
42C2×#882—21no—
43C3×#449—24no—
44C2×C3×#103C2211yescharacteristic, complemented
45C2×C3×#102C2211yescharacteristic, complemented
46C2×C3×C22⋊C8C2211yescharacteristic, complemented
47#5229C2211yescharacteristic, complemented
48#5223—21no—
49#5222—21no—
50#5221C2211yescharacteristic, complemented
51C2×#832C2211yescharacteristic, complemented
52C2×#832C2211yescharacteristic, complemented
53#5213—21no—
54#5212C2211yescharacteristic, complemented
55#5210—21no—
56#5169—24no—
57#5156—24no—
58C2×#821C2211yescharacteristic
59C2×#821C2211yescharacteristic
60C2×#821C2211yescharacteristic, complemented
61C2×#821C2211yescharacteristic, complemented
62C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
63C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
64#4550C2211yescharacteristic, complemented
65#4550C2211yescharacteristic, complemented
66#4529C2211yescharacteristic, complemented
67#4529C2211yescharacteristic, complemented
68C22×AGL(1,ℤ/8)—31no—
69C2×D42—31no—
70C2×#449D311yescharacteristic, complemented
71C2×#450—31no—
72C2×#447—31no—
73#2407—31no—
74#2014—31no—
75#2011—31no—
76#2000—31no—
77#1999—31no—
78#1895—31no—
79#1879—31no—
80#1877—31no—
81#1870—31no—
82#1786—31no—
83C24×D3—21no—
84C24×D3—21no—
85C2×C3×#41—22no—
86C2×C3×#41—22no—
87C2×C3×#41—22no—
88C2×C3×#41—22no—
89C2×C3×#41—41no—
90C2×C3×#41—41no—
91C22×C3×Q8C2311yescharacteristic
92C22×C3×D4—21no—
93C22×C3×D4—21no—
94C22×C3×D4C2311yescharacteristic
95C22×C3×D4C2311yescharacteristic
96C23×C3×C4—21no—
97C23×C3×C4C2311yescharacteristic
98C22×#67—21no—
99C22×#67—21no—
100C22×#67—21no—
101C22×#67—21no—
102C22×#67D411yescharacteristic
103C2×D3×D4—28no—
104C2×D3×D4—22no—
105C2×D3×D4—22no—
106C2×D3×D4—22no—
107C2×D3×D4—22no—
108C2×D3×D4—41no—
109C2×D3×D4—41no—
110C2×D3×D4—44no—
111C2×D3×D4—44no—
112C22×D12—22no—
113C22×D12—22no—
114C22×D12—21no—
115C22×D12—21no—
116C22×D12—22no—
117C22×D12—41no—
118C22×D12—41no—
119C22×D12D414yescomplemented
120C22×D12C2311yescharacteristic
121C22×D12C2311yescharacteristic
122C22×C4×D3—21no—
123C22×C4×D3C2311yescharacteristic
124C2×C3×SD16—22no—
125C2×C3×SD16—22no—
126C2×C3×SD16—41no—
127C2×C3×D8—22no—
128C2×C3×D8—22no—
129C2×C3×D8—41no—
130C22×C3×C8C2311yescharacteristic
131C22×C3×C8C2311yescharacteristic
132C3×#121—22no—
133C3×#121D414yescomplemented
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C22⋊C4—21no—
136C2×#217—21no—
137C2×#217—21no—
138C2×#217—21no—
139C2×#217—21no—
140C2×#217D411yescharacteristic
141#949—232no—
142#946—22no—
143#946—41no—
144C2×#215—22no—
145C2×#215—22no—
146C2×#215—22no—
147C2×#215—22no—
148C2×#215—22no—
149C2×#215D414yescomplemented
150#940—22no—
151#940—22no—
152#938—22no—
153#938—41no—
154#937—28no—
155C2×#213—22no—
156C2×#213—22no—
157C2×#213—22no—
158C2×#213—22no—
159C2×#213—22no—
160C2×#213D414yescomplemented
161C4×#67—22no—
162C4×#67—22no—
163C2×(C2×D3)⋊C4—21no—
164C2×(C2×D3)⋊C4—21no—
165C2×(C2×D3)⋊C4—21no—
166C2×(C2×D3)⋊C4D411yescharacteristic
167C2×C4⋊Dic3C2311yescharacteristic
168C2×C4⋊Dic3C2311yescharacteristic
169C2×Dic3⋊C4—21no—
170C2×Dic3⋊C4D411yescharacteristic
171C2×C4×Dic3C2311yescharacteristic
172C2×#208—22no—
173C2×#208—22no—
174C2×#208—22no—
175C22×C3⋊C8C2311yescharacteristic
176C22×C3⋊C8C2311yescharacteristic
177#895—22no—
178#895—22no—
179#893—22no—
180#893—22no—
181#884—28no—
182#882—28no—
183C3×#103—22no—
184C3×#102—22no—
185C3×C22⋊C8—22no—
186#832—22no—
187#832—22no—
188C3⋊#95—21no—
189C3⋊#95—21no—
190C3⋊#95—21no—
191#821—22no—
192#821—22no—
193#821—41no—
194#821—41no—
195(C2×D3)⋊C8—22no—
196(C2×D3)⋊C8—22no—
197C22×#41C2×D311yescharacteristic, complemented
198C23×D4—31no—
199C23×D4—31no—
200C23×D4—61no—
201C2×AGL(1,ℤ/8)—64no—
202C2×AGL(1,ℤ/8)—64no—
203C2×AGL(1,ℤ/8)—64no—
204C22×SD16—31no—
205C22×SD16—31no—
206C22×SD16C2×D311yescharacteristic, complemented
207C22×D8—31no—
208C22×D8—31no—
209C22×D8C2×D311yescharacteristic, complemented
210C22×M16—31no—
211D42—64no—
212D42—64no—
213C2×#127—31no—
214C2×C22⋊Q8—31no—
215C2×#121—31no—
216C2×#121—31no—
217C2×#121—61no—
218C2×#121C2×D311yescharacteristic
219C2×#120—61no—
220C2×#120—61no—
221C2×C4×D4—31no—
222C2×C4×D4—31no—
223#450—64no—
224#449—24no—
225#447—64no—
226C2×#103C2×D311yescharacteristic, complemented
227C2×#102—31no—
228C2×#102—31no—
229C2×#102—31no—
230C2×#102—31no—
231C2×#102—31no—
232C2×#102—31no—
233C2×#102C2×D311yescharacteristic, complemented
234C2×C22⋊C8—31no—
235C2×C22⋊C8—31no—
236C2×C22⋊C8C2×D311yescharacteristic, complemented
237#394—61no—
238#392—61no—
239#391—31no—
240#390—31no—
241#386—61no—
242#385—61no—
243#380—31no—
244#340—31no—
245#340—31no—
246#336—31no—
247#336—31no—
248C24×C3—21no—
249C24×C3—21no—
250C24×C3C2×D411yescharacteristic
251C23×D3—21no—
252C23×D3—21no—
253C23×D3—24no—
254C23×D3—24no—
255C23×D3—42no—
256C23×D3—42no—
257C23×D3—42no—
258C23×D3—42no—
259C23×D3—42no—
260C23×D3—42no—
261C23×D3—42no—
262C23×D3—42no—
263C23×D3—81no—
264C23×D3—81no—
265C23×D3—81no—
266C23×D3—81no—
267C23×D3C2×D411yescharacteristic
268C3×#41—28no—
269C3×#41—44no—
270C3×#41—44no—
271C3×#41—44no—
272C2×C3×Q8—21no—
273C2×C3×Q8—21no—
274C2×C3×Q8—21no—
275C2×C3×Q8—21no—
276C2×C3×Q8—21no—
277C2×C3×Q8C2×D412yescomplemented
278C2×C3×D4—24no—
279C2×C3×D4—21no—
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4—21no—
283C2×C3×D4—21no—
284C2×C3×D4—21no—
285C2×C3×D4—21no—
286C2×C3×D4—21no—
287C2×C3×D4—21no—
288C2×C3×D4—21no—
289C2×C3×D4—42no—
290C2×C3×D4—42no—
291C2×C3×D4—42no—
292C2×C3×D4—42no—
293C2×C3×D4—42no—
294C2×C3×D4C2×D412yes—
295C2×C3×D4C2×D412yescomplemented
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—42no—
303C22×C3×C4—42no—
304C22×C3×C4—42no—
305C22×C3×C4C2×D411yescharacteristic
306C22×C3×C4C2×D412yes—
307C22×C3×C4C2×D412yes—
308C22×C3×C4C2411yescharacteristic
309C2×#67—22no—
310C2×#67—22no—
311C2×#67—24no—
312C2×#67—24no—
313C2×#67—24no—
314C2×#67—22no—
315C2×#67—42no—
316C2×#67—42no—
317C2×#67—42no—
318C2×#67—42no—
319C2×#67—42no—
320C2×#67—42no—
321C2×#67—81no—
322C2×#67—81no—
323C2×#67—81no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3C2×D411yescharacteristic
327C22×Dic3C2×D411yescharacteristic
328C22×Dic3C2×D411yescharacteristic
329D3×D4—44no—
330D3×D4—44no—
331D3×D4—44no—
332D3×D4—432no—
333D3×D4—44no—
334C2×D12—21no—
335C2×D12—21no—
336C2×D12—21no—
337C2×D12—21no—
338C2×D12—21no—
339C2×D12—21no—
340C2×D12—21no—
341C2×D12—28no—
342C2×D12—24no—
343C2×D12—24no—
344C2×D12—21no—
345C2×D12—44no—
346C2×D12—44no—
347C2×D12—44no—
348C2×D12—42no—
349C2×D12—42no—
350C2×D12—42no—
351C2×D12—42no—
352C2×D12C2×D412yes—
353C2×D12C2×D412yes—
354C2×D12C2×D412yes—
355C2×D12C2×D412yes—
356C2×C4×D3—24no—
357C2×C4×D3—21no—
358C2×C4×D3—21no—
359C2×C4×D3—21no—
360C2×C4×D3—21no—
361C2×C4×D3—21no—
362C2×C4×D3—21no—
363C2×C4×D3—42no—
364C2×C4×D3—42no—
365C3×SD16—44no—
366C3×D8—44no—
367C2×C3×C8—21no—
368C2×C3×C8—21no—
369C2×C3×C8—21no—
370C2×C3×C8—21no—
371C2×C3×C8—21no—
372C2×C3×C8—21no—
373C3×C4⋊C4—21no—
374C3×C4⋊C4C2×D412yes—
375C3×C22⋊C4—24no—
376#217—22no—
377#217—42no—
378#217—42no—
379#217—81no—
380#217—81no—
381#215—28no—
382#215—28no—
383#213—28no—
384#213—28no—
385(C2×D3)⋊C4—24no—
386(C2×D3)⋊C4—24no—
387(C2×D3)⋊C4—22no—
388(C2×D3)⋊C4—42no—
389C4⋊Dic3—21no—
390C4⋊Dic3—21no—
391C4⋊Dic3—21no—
392C4⋊Dic3—21no—
393Dic3⋊C4—22no—
394Dic3⋊C4—42no—
395C4×Dic3—21no—
396C4×Dic3—21no—
397#208—28no—
398C2×C3⋊C8—21no—
399C2×C3⋊C8—21no—
400C2×C3⋊C8—21no—
401C2×C3⋊C8—21no—
402C2×C3⋊C8C2×D412yescomplemented
403C2×C3⋊C8C2×D412yescomplemented
404C25—61no—
405C25—61no—
406C2×#41—22no—
407C2×#41—22no—
408C2×#41—22no—
409C2×#41—22no—
410C2×#41—41no—
411C2×#41—41no—
412C22×Q8C22×D311yescharacteristic
413C22×D4—21no—
414C22×D4—21no—
415C22×D4—31no—
416C22×D4—34no—
417C22×D4—31no—
418C22×D4—31no—
419C22×D4—62no—
420C22×D4—62no—
421C22×D4—61no—
422C22×D4—61no—
423C22×D4—61no—
424C22×D4—61no—
425C22×D4—62no—
426C22×D4—62no—
427C22×D4—62no—
428C22×D4—68no—
429C22×D4—62no—
430C22×D4—61no—
431C22×D4—61no—
432C22×D4—62no—
433C22×D4—121no—
434C22×D4—121no—
435C22×D4—121no—
436C22×D4—121no—
437C22×D4—124no—
438C22×D4—124no—
439C22×D4C22×D311yescharacteristic
440C22×D4C22×D311yescharacteristic
441C23×C4—21no—
442C23×C4—31no—
443C23×C4—61no—
444C23×C4C22×D311yescharacteristic
445AGL(1,ℤ/8)—632no—
446C2×SD16—22no—
447C2×SD16—22no—
448C2×SD16—34no—
449C2×SD16—41no—
450C2×SD16—62no—
451C2×SD16—62no—
452C2×SD16—62no—
453C2×SD16—62no—
454C2×SD16—62no—
455C2×D8—22no—
456C2×D8—22no—
457C2×D8—34no—
458C2×D8—41no—
459C2×D8—62no—
460C2×D8—62no—
461C2×D8—62no—
462C2×D8—62no—
463C2×D8—62no—
464C2×M16—62no—
465C2×M16—62no—
466C2×M16—62no—
467C22×C8—31no—
468C22×C8—31no—
469C22×C8C22×D311yescharacteristic
470C22×C8C22×D311yescharacteristic
471#127—62no—
472#127—62no—
473C22⋊Q8—62no—
474C22⋊Q8—121no—
475#121—22no—
476#121—68no—
477#121—62no—
478#121—62no—
479#121—62no—
480#121—121no—
481#121#6714yescomplemented
482#120—68no—
483#120—68no—
484C4×D4—62no—
485C4×D4—62no—
486C4×D4—62no—
487C4×D4—62no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—31no—
491C2×C4⋊C4—61no—
492C2×C4⋊C4C22×D311yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—31no—
495C2×C22⋊C4—31no—
496C2×C22⋊C4—61no—
497C2×C22⋊C4—61no—
498C2×C22⋊C4—61no—
499C2×C22⋊C4—61no—
500C2×C22⋊C4—61no—
501C2×C22⋊C4—61no—
502C2×C22⋊C4—61no—
503C2×C42—31no—
504#103—22no—
505#102—22no—
506#102—62no—
507#102—62no—
508#102—62no—
509#102—62no—
510#102—121no—
511#102—121no—
512C22⋊C8—22no—
513C22⋊C8—62no—
514C22⋊C8—62no—
515#95—61no—
516#95—61no—
517#95—61no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3#12012yes—
539C23×C3C22×D411yescharacteristic
540C22×D3—21no—
541C22×D3—22no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—22no—
545C22×D3—22no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—22no—
550C22×D3—48no—
551C22×D3—48no—
552C22×D3—48no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3—41no—
556C22×D3—41no—
557C22×D3—48no—
558C22×D3—41no—
559C22×D3—41no—
560C22×D3—41no—
561C22×D3—41no—
562C22×D3—41no—
563C22×D3—41no—
564C22×D3—84no—
565C22×D3—84no—
566C22×D3—84no—
567C22×D3—84no—
568C22×D3—84no—
569C22×D3—84no—
570C22×D3—84no—
571C22×D3—84no—
572C22×D3—84no—
573C22×D3—84no—
574C22×D3AGL(1,ℤ/8)12yescomplemented
575C3×Q8—22no—
576C3×Q8—22no—
577C3×Q8—41no—
578C3×Q8—41no—
579C3×D4—22no—
580C3×D4—22no—
581C3×D4—22no—
582C3×D4—22no—
583C3×D4—48no—
584C3×D4—48no—
585C3×D4—41no—
586C3×D4—41no—
587C3×D4—41no—
588C3×D4—41no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—48no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4#12012yes—
603C2×C3×C4C22×D411yescharacteristic
604C2×C3×C4C22×D411yescharacteristic
605C2×C3×C4C22×D411yescharacteristic
606C2×C3×C4C22×D411yescharacteristic
607C2×C3×C4H(5,𝔽2)11yescharacteristic
608C2×C3×C4H(5,𝔽2)11yescharacteristic
609#67—28no—
610#67—48no—
611#67—48no—
612#67—84no—
613#67—84no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—41no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3AGL(1,ℤ/8)12yescomplemented
629D12—22no—
630D12—22no—
631D12—22no—
632D12—22no—
633D12—22no—
634D12—48no—
635D12—48no—
636D12—41no—
637D12—41no—
638D12#12014yes—
639C4×D3—48no—
640C4×D3—41no—
641C4×D3—41no—
642C4×D3—41no—
643C4×D3—41no—
644C3×C8—41no—
645C3×C8—41no—
646C3⋊C8—22no—
647C3⋊C8—22no—
648C24—21no—
649C24—21no—
650C24—31no—
651C24—64no—
652C24—61no—
653C24—61no—
654C24—64no—
655C24—122no—
656C24—122no—
657C24—122no—
658C24—122no—
659C24—122no—
660C24—122no—
661C24—122no—
662C24—122no—
663C24—241no—
664C24—241no—
665C24—241no—
666C24—241no—
667C24D3×D411yescharacteristic
668#41—28no—
669#41—44no—
670#41—44no—
671#41—44no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8D3×D412yescomplemented
678C2×D4—24no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—32no—
690C2×D4—32no—
691C2×D4—32no—
692C2×D4—32no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—68no—
699C2×D4—64no—
700C2×D4—62no—
701C2×D4—62no—
702C2×D4—62no—
703C2×D4—64no—
704C2×D4—64no—
705C2×D4—64no—
706C2×D4—64no—
707C2×D4—61no—
708C2×D4—61no—
709C2×D4—61no—
710C2×D4—61no—
711C2×D4—61no—
712C2×D4—61no—
713C2×D4—61no—
714C2×D4—61no—
715C2×D4—124no—
716C2×D4—124no—
717C2×D4—124no—
718C2×D4—122no—
719C2×D4—122no—
720C2×D4—122no—
721C2×D4—122no—
722C2×D4—122no—
723C2×D4—122no—
724C2×D4—122no—
725C2×D4—122no—
726C2×D4—124no—
727C2×D4—124no—
728C2×D4—124no—
729C2×D4—1232no—
730C2×D4—124no—
731C2×D4—122no—
732C2×D4—122no—
733C2×D4—241no—
734C2×D4—241no—
735C2×D4—241no—
736C2×D4D3×D412yescomplemented
737C2×D4C2×#6712yes—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—31no—
745C22×C4—31no—
746C22×C4—31no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—64no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—122no—
760C22×C4—122no—
761C22×C4D3×D411yescharacteristic
762C22×C4D3×D412yes—
763C22×C4C2×#6712yes—
764C22×C4C23×D311yescharacteristic
765SD16—44no—
766SD16—68no—
767SD16—68no—
768D8—44no—
769D8—68no—
770D8—68no—
771M16—68no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—32no—
779C2×C8—32no—
780C2×C8—61no—
781C2×C8—61no—
782C2×C8—61no—
783C2×C8—61no—
784C4⋊C4—21no—
785C4⋊C4—62no—
786C4⋊C4—61no—
787C4⋊C4—61no—
788C4⋊C4—61no—
789C4⋊C4—61no—
790C4⋊C4—122no—
791C4⋊C4C2×#6712yes—
792C22⋊C4—24no—
793C22⋊C4—64no—
794C22⋊C4—64no—
795C22⋊C4—62no—
796C22⋊C4—62no—
797C22⋊C4—122no—
798C22⋊C4—122no—
799C22⋊C4—122no—
800C22⋊C4—241no—
801C22⋊C4—241no—
802C42—61no—
803C42—61no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—41no—
808C22×C3—41no—
809C22×C3—41no—
810C22×C3—41no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—42no—
816C22×C3—42no—
817C22×C3—81no—
818C22×C3—81no—
819C22×C3—81no—
820C22×C3—81no—
821C22×C3—81no—
822C22×C3—81no—
823C22×C3—81no—
824C22×C3—81no—
825C22×C3C2×#12011yescharacteristic
826C22×C3D4211yescharacteristic
827C22×C3D4211yescharacteristic
828C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
829C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
830C22×C3#57611yescharacteristic
831C22×C3#57711yescharacteristic
832C2×D3—24no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—41no—
837C2×D3—42no—
838C2×D3—42no—
839C2×D3—42no—
840C2×D3—41no—
841C2×D3—42no—
842C2×D3—41no—
843C2×D3—42no—
844C2×D3—41no—
845C2×D3—42no—
846C2×D3—42no—
847C2×D3—42no—
848C2×D3—42no—
849C2×D3—816no—
850C2×D3—816no—
851C2×D3—81no—
852C2×D3—81no—
853C2×D3—81no—
854C2×D3—81no—
855C3×C4—22no—
856C3×C4—42no—
857C3×C4—42no—
858C3×C4C2×#12011yescharacteristic
859C3×C4#53411yescharacteristic
860C3×C4D4211yescharacteristic
861C3×C4D4211yescharacteristic
862Dic3—22no—
863Dic3—41no—
864Dic3—41no—
865Dic3—81no—
866Dic3—81no—
867C23—21no—
868C23—21no—
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—22no—
874C23—22no—
875C23—32no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—61no—
889C23—61no—
890C23—61no—
891C23—62no—
892C23—61no—
893C23—61no—
894C23—61no—
895C23—62no—
896C23—62no—
897C23—62no—
898C23—128no—
899C23—128no—
900C23—128no—
901C23—128no—
902C23—121no—
903C23—121no—
904C23—121no—
905C23—121no—
906C23—121no—
907C23—121no—
908C23—121no—
909C23—121no—
910C23—121no—
911C23—121no—
912C23—244no—
913C23—244no—
914C23—244no—
915C23—244no—
916C23—244no—
917C23—244no—
918C23—244no—
919C23—244no—
920C23—244no—
921C23—244no—
922C23#93712yes—
923C23C2×D3×D411yescharacteristic
924Q8—22no—
925Q8—22no—
926Q8—41no—
927Q8—41no—
928D4—22no—
929D4—22no—
930D4—22no—
931D4—22no—
932D4—34no—
933D4—48no—
934D4—48no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—68no—
940D4—62no—
941D4—62no—
942D4—62no—
943D4—62no—
944D4—62no—
945D4—128no—
946D4—128no—
947D4—128no—
948D4—128no—
949D4—121no—
950D4—121no—
951D4—244no—
952D4—244no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—32no—
962C2×C4—48no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—61no—
975C2×C4—128no—
976C2×C4—121no—
977C2×C4—121no—
978C2×C4—121no—
979C2×C4—121no—
980C2×C4—121no—
981C2×C4—121no—
982C2×C4—121no—
983C2×C4—121no—
984C2×C4—121no—
985C2×C4—121no—
986C2×C4#93712yes—
987C2×C4C2×D3×D411yescharacteristic
988C2×C4C2×D3×D411yescharacteristic
989C2×C4C2×D3×D411yescharacteristic
990C2×C4#100411yescharacteristic
991C2×C4#100411yescharacteristic
992C2×C4C22×#6711yescharacteristic
993C8—41no—
994C8—41no—
995C8—62no—
996C8—62no—
997C2×C3—42no—
998C2×C3—82no—
999C2×C3—82no—
1000C2×C3#240311yescharacteristic
1001C2×C3#300311yescharacteristic
1002C2×C3#301211yescharacteristic
1003C2×C3#326411yescharacteristic
1004C2×C3#326511yescharacteristic
1005C2×C3#327211yescharacteristic
1006C2×C3#327411yescharacteristic
1007D3—42no—
1008D3—44no—
1009D3—82no—
1010C22—22no—
1011C22—22no—
1012C22—22no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—42no—
1018C22—42no—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—42no—
1023C22—64no—
1024C22—62no—
1025C22—62no—
1026C22—62no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—81no—
1031C22—81no—
1032C22—81no—
1033C22—81no—
1034C22—81no—
1035C22—121no—
1036C22—121no—
1037C22—122no—
1038C22—122no—
1039C22—122no—
1040C22—122no—
1041C22—121no—
1042C22—122no—
1043C22—121no—
1044C22—122no—
1045C22—122no—
1046C22—122no—
1047C22—122no—
1048C22—2416no—
1049C22—2416no—
1050C22—241no—
1051C22—241no—
1052C22—241no—
1053C22—241no—
1054C22#559011yescharacteristic
1055C22#559011yescharacteristic
1056C22#576911yescharacteristic
1057C22#577011yescharacteristic
1058C22D3×AGL(1,ℤ/8)11yescharacteristic
1059C22D3×AGL(1,ℤ/8)11yescharacteristic
1060C22C2×#93711yescharacteristic
1061C4—22no—
1062C4—42no—
1063C4—42no—
1064C4—62no—
1065C4—121no—
1066C4—121no—
1067C4—241no—
1068C4—241no—
1069C4D3×#12011yescharacteristic
1070C4#558911yescharacteristic
1071C4D4×#6711yescharacteristic
1072C4D4×#6711yescharacteristic
1073C3#2386011yescharacteristic, complemented, Sylow
1074C2—42no—
1075C2—82no—
1076C2—82no—
1077C2—122no—
1078C2—124no—
1079C2—242no—
1080C2#8012011yescharacteristic
1081C2#8012111yescharacteristic
1082C2#8012411yescharacteristic
1083C2#8012511yescharacteristic
1084C2#8260411yescharacteristic
1085C2#8391211yescharacteristic
1086C2#8394411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#449C2
socleC23×C3C22×D4
hypercenterC2×#449D3
hypocenterC3#23860
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C22×#949C2semidirect
2. C2×#5609C2semidirect
3. C2×C3×#449C2semidirect
4. #84097C2semidirect
5. C2×#5169C2semidirect
6. C2×#5156C2semidirect
7. #72056C2semidirect
8. #72044C2semidirect
9. #71682C2semidirect
10. #70276C2semidirect
11. #70272C2semidirect
12. #70208C2semidirect
13. #70204C2semidirect
14. #69959C2semidirect
15. #69953C2semidirect
17. C22×C3×#41C22semidirect
21. C22×C3×SD16C22semidirect
22. C22×C3×D8C22semidirect
27. C2×#946C22semidirect
29. C22×#215C22semidirect
31. C2×#938C22semidirect
34. C22×#213C22semidirect
36. C22×#208C22semidirect
44. C2×C3×#103C22semidirect
45. C2×C3×#102C22semidirect
46. C2×C3×C22⋊C8C22semidirect
47. #5229C22semidirect
50. #5221C22semidirect
51. C2×#832C22semidirect
52. C2×#832C22semidirect
54. #5212C22semidirect
60. C2×#821C22semidirect
61. C2×#821C22semidirect
62. C2×(C2×D3)⋊C8C22semidirect
63. C2×(C2×D3)⋊C8C22semidirect
64. #4550C22semidirect
65. #4550C22semidirect
66. #4529C22semidirect
67. #4529C22semidirect
70. C2×#449D3semidirect
119. C22×D12D4semidirect
133. C3×#121D4semidirect
149. C2×#215D4semidirect
160. C2×#213D4semidirect
197. C22×#41C2×D3semidirect
206. C22×SD16C2×D3semidirect
209. C22×D8C2×D3semidirect
226. C2×#103C2×D3semidirect
233. C2×#102C2×D3semidirect
236. C2×C22⋊C8C2×D3semidirect
277. C2×C3×Q8C2×D4semidirect
295. C2×C3×D4C2×D4semidirect
402. C2×C3⋊C8C2×D4semidirect
403. C2×C3⋊C8C2×D4semidirect
481. #121#67semidirect
574. C22×D3AGL(1,ℤ/8)semidirect
628. C2×Dic3AGL(1,ℤ/8)semidirect
677. C2×Q8D3×D4semidirect
736. C2×D4D3×D4semidirect
1073. C3#23860semidirect

Maximal subgroups

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

subgroupindex
C22×#9492
C2×#56092
C2×C3×#4492
#840972
C2×#51692
C2×#51562
#720562
#720442
#716822
#702762
#702722
#702082
#702042
#699592
#699532
#238603