Finite Group Databasebeta

← #10826330

Subgroups — #10826330

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×D4×D12C211yesmaximal, characteristic, complemented
3C3×#2407C211yesmaximal, characteristic, complemented
4C2×#5238C211yesmaximal, characteristic, complemented
5C2×#5046C211yesmaximal, characteristic, complemented
6C2×#5036C211yesmaximal, characteristic, complemented
7#71699C211yesmaximal, characteristic, complemented
8#71684C211yesmaximal, characteristic, complemented
9#71611C211yesmaximal, characteristic, complemented
10#69688C211yesmaximal, characteristic, complemented
11#69687C211yesmaximal, characteristic, complemented
12#69658C211yesmaximal, characteristic, complemented
13#69657C211yesmaximal, characteristic, complemented
14#69521C211yesmaximal, characteristic, complemented
15#69517C211yesmaximal, characteristic, complemented
16#23860—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic, complemented
18C22×D3×D4—21no—
19C23×D12C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic, complemented
22C2×C3×#121C2211yescharacteristic, complemented
23C2×C3×C4×D4C2211yescharacteristic
24C2×#949—24no—
25C2×#949—24no—
26C2×#949—24no—
27C22×#215C2211yescharacteristic
28C22×#215C2211yescharacteristic, complemented
29C22×#215C2211yescharacteristic, complemented
30C22×#213C2211yescharacteristic
31C22×#213C2211yescharacteristic, complemented
32C22×#213C2211yescharacteristic, complemented
33C2×#930C2211yescharacteristic
34C2×#930C2211yescharacteristic
35C22×#208C2211yescharacteristic, complemented
36D4×D12—24no—
37D4×D12—24no—
38C2×#895—21no—
39C2×#882—21no—
40C2×#882—21no—
41C2×#874C2211yescharacteristic
42C2×C4×D12C2211yescharacteristic
43C3×#394—21no—
44C3×#392—21no—
45C3×#391C2211yescharacteristic, complemented
46C3×#390C2211yescharacteristic, complemented
47C3×#386—21no—
48C3×#385—21no—
49C3×#380C2211yescharacteristic, complemented
50#5238—24no—
51C2×#835C2211yescharacteristic, complemented
52C2×#832C2211yescharacteristic, complemented
53C2×#830C2211yescharacteristic, complemented
54C2×#830C2211yescharacteristic, complemented
55C2×#830C2211yescharacteristic, complemented
56#5046—24no—
57#5036—24no—
58C2×#809C2211yescharacteristic
59C2×#809C2211yescharacteristic
60C2×#809C2211yescharacteristic, complemented
61C2×#809C2211yescharacteristic, complemented
62C2×#809C2211yescharacteristic, complemented
63C2×#809C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66#4524C2211yescharacteristic, complemented
67#4524C2211yescharacteristic, complemented
68C22×AGL(1,ℤ/8)—31no—
69C2×D42—31no—
70C2×#449—31no—
71C2×#450—31no—
72C2×#447—31no—
73#2407D311yescharacteristic, complemented
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×D4D411yescharacteristic
95C22×C3×D4C2311yescharacteristic
96C23×C3×C4—21no—
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C22×#67—21no—
100C22×#67—21no—
101C2×D3×D4—28no—
102C2×D3×D4—44no—
103C2×D3×D4—44no—
104C22×D12—22no—
105C22×D12—22no—
106C22×D12—21no—
107C22×D12—21no—
108C22×D12—22no—
109C22×D12—21no—
110C22×D12—21no—
111C22×D12—22no—
112C22×D12—22no—
113C22×D12—22no—
114C22×D12—22no—
115C22×D12—41no—
116C22×D12—41no—
117C22×D12—41no—
118C22×D12—41no—
119C22×D12D414yescomplemented
120C22×D12C2311yescharacteristic
121C22×D12C2311yescharacteristic
122C22×D12C2311yescharacteristic
123C22×C4×D3—21no—
124C3×C22⋊Q8—22no—
125C3×C22⋊Q8—41no—
126C3×#121—22no—
127C3×#121—41no—
128C3×C4×D4—22no—
129C3×C4×D4—22no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4D411yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4D411yescharacteristic
140C2×C3×C22⋊C4D411yescharacteristic
141C2×C3×C42C2311yescharacteristic
142#949—232no—
143C2×#215—22no—
144C2×#215—22no—
145C2×#215—22no—
146C2×#215—22no—
147C2×#215—22no—
148C2×#215—22no—
149C2×#215—22no—
150C2×#215—41no—
151C2×#215D414yescomplemented
152C2×#213—22no—
153C2×#213—22no—
154C2×#213—22no—
155C2×#213—22no—
156C2×#213—22no—
157C2×#213—22no—
158C2×#213—22no—
159C2×#213—41no—
160C2×#213D414yescomplemented
161#930—22no—
162#930—22no—
163#930—22no—
164#930D414yescomplemented
165C2×(C2×D3)⋊C4—21no—
166C2×(C2×D3)⋊C4—21no—
167C2×(C2×D3)⋊C4—21no—
168C2×C4⋊Dic3C2311yescharacteristic
169C2×#208—22no—
170C2×#208—22no—
171C2×#208—22no—
172C22×C3⋊C8C2311yescharacteristic
173C22×C3⋊C8C2311yescharacteristic
174C22×C3⋊C8C2311yescharacteristic
175C22×C3⋊C8C2311yescharacteristic
176#895—28no—
177#882—28no—
178#882—28no—
179#874—22no—
180#874—22no—
181C4×D12—22no—
182C4×D12—22no—
183C3×#95—21no—
184C3×#95—21no—
185C3×#95—21no—
186#835—22no—
187#832—22no—
188#830—22no—
189#830—22no—
190#830—22no—
191#809—22no—
192#809—22no—
193#809—22no—
194#809—22no—
195#809—41no—
196#809—41no—
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×SD16—31no—
207C22×D8—31no—
208C22×D8—31no—
209C22×D8—31no—
210C22×M16—31no—
211D42—64no—
212D42—64no—
213C2×#127—31no—
214C2×C22⋊Q8C2×D311yescharacteristic, complemented
215C2×#121—31no—
216C2×#121—31no—
217C2×#121—61no—
218C2×#121C2×D311yescharacteristic, complemented
219C2×#120—61no—
220C2×#120—61no—
221C2×C4×D4—31no—
222C2×C4×D4C2×D311yescharacteristic
223#450—64no—
224#449—64no—
225#447—64no—
226C2×#103—31no—
227C2×#102—31no—
228C2×#102—31no—
229C2×#102—31no—
230C2×#102—31no—
231C2×#102—31no—
232C2×#102—31no—
233C2×#102—31no—
234C2×C22⋊C8—31no—
235C2×C22⋊C8—31no—
236C2×C22⋊C8—31no—
237#394—21no—
238#392—21no—
239#391C2×D311yescharacteristic, complemented
240#390C2×D311yescharacteristic, complemented
241#386—21no—
242#385—21no—
243#380C2×D311yescharacteristic, complemented
244#340—31no—
245#340—31no—
246#336—31no—
247#336—31no—
248C24×C3—21no—
249C24×C3C2×D411yescharacteristic
250C24×C3C2×D411yescharacteristic
251C23×D3—21no—
252C23×D3—21no—
253C23×D3—21no—
254C23×D3—24no—
255C23×D3—24no—
256C23×D3—42no—
257C23×D3—42no—
258C23×D3—42no—
259C23×D3—42no—
260C23×D3—42no—
261C23×D3—42no—
262C23×D3—42no—
263C23×D3—42no—
264C23×D3—81no—
265C23×D3—81no—
266C23×D3—81no—
267C23×D3—81no—
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—22no—
279C2×C3×D4—22no—
280C2×C3×D4—22no—
281C2×C3×D4—21no—
282C2×C3×D4—21no—
283C2×C3×D4—21no—
284C2×C3×D4—21no—
285C2×C3×D4—21no—
286C2×C3×D4—42no—
287C2×C3×D4—42no—
288C2×C3×D4—42no—
289C2×C3×D4—42no—
290C2×C3×D4—42no—
291C2×C3×D4—81no—
292C2×C3×D4C2×D412yescomplemented
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
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—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—42no—
307C22×C3×C4—42no—
308C22×C3×C4—42no—
309C22×C3×C4C2×D412yes—
310C22×C3×C4C2×D412yes—
311C22×C3×C4C2×D411yescharacteristic
312C22×C3×C4C2×D411yescharacteristic
313C22×C3×C4C2×D411yescharacteristic
314C22×C3×C4C2×D411yescharacteristic
315C22×C3×C4C2411yescharacteristic
316C2×#67—24no—
317C2×#67—24no—
318C2×#67—42no—
319C2×#67—42no—
320C2×#67—42no—
321C2×#67—42no—
322C22×Dic3—21no—
323D3×D4—432no—
324C2×D12—21no—
325C2×D12—21no—
326C2×D12—21no—
327C2×D12—21no—
328C2×D12—21no—
329C2×D12—21no—
330C2×D12—21no—
331C2×D12—21no—
332C2×D12—21no—
333C2×D12—21no—
334C2×D12—21no—
335C2×D12—28no—
336C2×D12—24no—
337C2×D12—24no—
338C2×D12—24no—
339C2×D12—21no—
340C2×D12—21no—
341C2×D12—24no—
342C2×D12—44no—
343C2×D12—44no—
344C2×D12—44no—
345C2×D12—44no—
346C2×D12—44no—
347C2×D12—44no—
348C2×D12—42no—
349C2×D12—42no—
350C2×D12—42no—
351C2×D12—42no—
352C2×D12—42no—
353C2×D12—42no—
354C2×D12—44no—
355C2×D12—81no—
356C2×D12—81no—
357C2×D12C2×D412yes—
358C2×D12C2×D412yes—
359C2×D12C2×D412yes—
360C2×D12C2×D412yes—
361C2×D12C2×D412yes—
362C2×C4×D3—24no—
363C2×C4×D3—42no—
364C2×C4×D3—42no—
365C3×C4⋊C4—22no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—42no—
371C3×C22⋊C4—22no—
372C3×C22⋊C4—22no—
373C3×C22⋊C4—42no—
374C3×C22⋊C4—42no—
375C3×C22⋊C4—42no—
376C3×C22⋊C4—81no—
377C3×C22⋊C4—81no—
378C3×C42—21no—
379C3×C42—21no—
380#215—28no—
381#215—28no—
382#215—44no—
383#213—28no—
384#213—28no—
385#213—44no—
386(C2×D3)⋊C4—24no—
387(C2×D3)⋊C4—24no—
388(C2×D3)⋊C4—24no—
389C4⋊Dic3—21no—
390C4⋊Dic3C2×D412yes—
391#208—28no—
392C2×C3⋊C8—21no—
393C2×C3⋊C8—21no—
394C2×C3⋊C8—21no—
395C2×C3⋊C8—21no—
396C2×C3⋊C8—21no—
397C2×C3⋊C8—21no—
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—34no—
416C22×D4—31no—
417C22×D4—31no—
418C22×D4—31no—
419C22×D4—62no—
420C22×D4—62no—
421C22×D4—62no—
422C22×D4—62no—
423C22×D4—62no—
424C22×D4—62no—
425C22×D4—68no—
426C22×D4—61no—
427C22×D4—61no—
428C22×D4—62no—
429C22×D4—61no—
430C22×D4—61no—
431C22×D4—61no—
432C22×D4—61no—
433C22×D4—121no—
434C22×D4—121no—
435C22×D4—121no—
436C22×D4—121no—
437C22×D4—124no—
438C22×D4—124no—
439C22×D4#6711yescharacteristic
440C22×D4C22×D311yescharacteristic
441C23×C4—21no—
442C23×C4—61no—
443C23×C4C22×D311yescharacteristic
444C23×C4C22×D311yescharacteristic
445AGL(1,ℤ/8)—632no—
446C2×SD16—34no—
447C2×SD16—62no—
448C2×SD16—62no—
449C2×SD16—62no—
450C2×SD16—62no—
451C2×SD16—62no—
452C2×SD16—62no—
453C2×SD16—62no—
454C2×SD16—121no—
455C2×D8—34no—
456C2×D8—62no—
457C2×D8—62no—
458C2×D8—62no—
459C2×D8—62no—
460C2×D8—62no—
461C2×D8—62no—
462C2×D8—62no—
463C2×D8—121no—
464C2×M16—62no—
465C2×M16—62no—
466C2×M16—62no—
467C22×C8—31no—
468C22×C8—31no—
469C22×C8—31no—
470C22×C8—31no—
471#127—62no—
472#127—62no—
473C22⋊Q8—22no—
474C22⋊Q8—41no—
475#121—22no—
476#121—34no—
477#121—41no—
478#121—68no—
479#121—62no—
480#121—62no—
481#121—62no—
482#120—68no—
483#120—68no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—62no—
487C4×D4—62no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4#6711yescharacteristic
491C2×C4⋊C4C22×D311yescharacteristic
492C2×C4⋊C4C22×D311yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—61no—
499C2×C22⋊C4—61no—
500C2×C22⋊C4—61no—
501C2×C22⋊C4#6711yescharacteristic
502C2×C22⋊C4#6711yescharacteristic
503C2×C42C22×D311yescharacteristic
504#103—62no—
505#102—62no—
506#102—62no—
507#102—62no—
508#102—62no—
509#102—62no—
510#102—121no—
511#102—121no—
512C22⋊C8—62no—
513C22⋊C8—62no—
514C22⋊C8—62no—
515#95—21no—
516#95—21no—
517#95—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—22no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3#12012yes—
538C23×C3AGL(1,ℤ/8)12yescomplemented
539C23×C3C22×D411yescharacteristic
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—22no—
545C22×D3—48no—
546C22×D3—48no—
547C22×D3—41no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—48no—
552C22×D3—48no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3—41no—
556C22×D3—41no—
557C22×D3—41no—
558C22×D3—41no—
559C22×D3—41no—
560C22×D3—41no—
561C22×D3—41no—
562C22×D3—41no—
563C22×D3—41no—
564C22×D3—41no—
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×D3—84no—
575C3×Q8—22no—
576C3×Q8—22no—
577C3×Q8—41no—
578C3×Q8—41no—
579C3×D4—28no—
580C3×D4—22no—
581C3×D4—22no—
582C3×D4—48no—
583C3×D4—41no—
584C3×D4—41no—
585C3×D4—84no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—22no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—48no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4#12012yes—
615C2×C3×C4AGL(1,ℤ/8)12yescomplemented
616C2×C3×C4C22×D411yescharacteristic
617C2×C3×C4C22×D411yescharacteristic
618C2×C3×C4C22×D411yescharacteristic
619C2×C3×C4C22×D411yescharacteristic
620C2×C3×C4H(5,𝔽2)11yescharacteristic
621C2×C3×C4H(5,𝔽2)11yescharacteristic
622#67—48no—
623#67—48no—
624C2×Dic3—22no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627D12—22no—
628D12—22no—
629D12—22no—
630D12—22no—
631D12—22no—
632D12—22no—
633D12—22no—
634D12—48no—
635D12—48no—
636D12—48no—
637D12—41no—
638D12—41no—
639D12—41no—
640D12—41no—
641D12—84no—
642D12#12014yes—
643C4×D3—48no—
644C3⋊C8—22no—
645C3⋊C8—22no—
646C3⋊C8—41no—
647C3⋊C8—41no—
648C24—21no—
649C24—64no—
650C24—61no—
651C24—61no—
652C24—61no—
653C24—64no—
654C24—122no—
655C24—122no—
656C24—122no—
657C24—122no—
658C24—122no—
659C24—122no—
660C24—122no—
661C24—122no—
662C24—241no—
663C24—241no—
664C24—241no—
665C24—241no—
666C24C2×#6711yescharacteristic
667C24C2×#6711yescharacteristic
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—22no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—32no—
687C2×D4—32no—
688C2×D4—32no—
689C2×D4—32no—
690C2×D4—32no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—68no—
697C2×D4—64no—
698C2×D4—64no—
699C2×D4—64no—
700C2×D4—64no—
701C2×D4—64no—
702C2×D4—64no—
703C2×D4—61no—
704C2×D4—61no—
705C2×D4—61no—
706C2×D4—61no—
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—61no—
716C2×D4—81no—
717C2×D4—124no—
718C2×D4—124no—
719C2×D4—124no—
720C2×D4—122no—
721C2×D4—122no—
722C2×D4—122no—
723C2×D4—122no—
724C2×D4—122no—
725C2×D4—124no—
726C2×D4—124no—
727C2×D4—124no—
728C2×D4—124no—
729C2×D4—1232no—
730C2×D4—122no—
731C2×D4—122no—
732C2×D4—122no—
733C2×D4—122no—
734C2×D4—122no—
735C2×D4—241no—
736C2×D4—241no—
737C2×D4D3×D412yescomplemented
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4—64no—
755C22×C4—61no—
756C22×C4—122no—
757C22×C4—122no—
758C22×C4D3×D412yes—
759C22×C4D3×D412yes—
760C22×C4C2×#6711yescharacteristic
761C22×C4C2×#6711yescharacteristic
762C22×C4C2×#6711yescharacteristic
763C22×C4C2×#6711yescharacteristic
764C22×C4C23×D311yescharacteristic
765SD16—68no—
766SD16—68no—
767SD16—124no—
768D8—68no—
769D8—68no—
770D8—124no—
771M16—68no—
772C2×C8—32no—
773C2×C8—32no—
774C2×C8—61no—
775C2×C8—61no—
776C2×C8—61no—
777C2×C8—61no—
778C2×C8—61no—
779C2×C8—61no—
780C2×C8—61no—
781C2×C8—61no—
782C2×C8—61no—
783C2×C8—61no—
784C4⋊C4—22no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—32no—
790C4⋊C4—42no—
791C4⋊C4—61no—
792C22⋊C4—22no—
793C22⋊C4—22no—
794C22⋊C4—42no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—64no—
798C22⋊C4—64no—
799C22⋊C4—64no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—41no—
811C22×C3—41no—
812C22×C3—41no—
813C22×C3—41no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—42no—
819C22×C3—42no—
820C22×C3—42no—
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—42no—
834C2×D3—42no—
835C2×D3—42no—
836C2×D3—42no—
837C2×D3—42no—
838C2×D3—42no—
839C2×D3—42no—
840C2×D3—42no—
841C2×D3—42no—
842C2×D3—42no—
843C2×D3—42no—
844C2×D3—42no—
845C2×D3—816no—
846C2×D3—816no—
847C2×D3—81no—
848C2×D3—81no—
849C2×D3—81no—
850C2×D3—81no—
851C2×D3—81no—
852C2×D3—81no—
853C2×D3—81no—
854C2×D3—81no—
855C3×C4—22no—
856C3×C4—22no—
857C3×C4—41no—
858C3×C4—42no—
859C3×C4—41no—
860C3×C4—81no—
861C3×C4—81no—
862C3×C4C2×#12011yescharacteristic
863C3×C4#53411yescharacteristic
864C3×C4D4211yescharacteristic
865C3×C4D4211yescharacteristic
866Dic3—42no—
867C23—21no—
868C23—21no—
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—21no—
875C23—21no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—22no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—128no—
892C23—128no—
893C23—128no—
894C23—128no—
895C23—121no—
896C23—121no—
897C23—121no—
898C23—121no—
899C23—121no—
900C23—121no—
901C23—121no—
902C23—121no—
903C23—121no—
904C23—121no—
905C23—121no—
906C23—121no—
907C23—121no—
908C23—121no—
909C23—121no—
910C23—121no—
911C23—244no—
912C23—244no—
913C23—244no—
914C23—244no—
915C23—244no—
916C23—244no—
917C23—244no—
918C23—244no—
919C23—244no—
920C23—244no—
921C23#93712yes—
922C23#94912yescomplemented
923C23C22×#6711yescharacteristic
924Q8—22no—
925Q8—22no—
926Q8—41no—
927Q8—41no—
928D4—28no—
929D4—22no—
930D4—22no—
931D4—34no—
932D4—48no—
933D4—41no—
934D4—41no—
935D4—62no—
936D4—62no—
937D4—62no—
938D4—62no—
939D4—62no—
940D4—62no—
941D4—62no—
942D4—84no—
943D4—128no—
944D4—128no—
945D4—128no—
946D4—128no—
947D4—128no—
948D4—121no—
949D4—121no—
950D4—121no—
951D4—121no—
952D4—244no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—22no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—48no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—62no—
982C2×C4—128no—
983C2×C4—121no—
984C2×C4—121no—
985C2×C4#93712yes—
986C2×C4#94912yescomplemented
987C2×C4C2×D3×D411yescharacteristic
988C2×C4C2×D3×D411yescharacteristic
989C2×C4C2×D3×D411yescharacteristic
990C2×C4C2×D3×D411yescharacteristic
991C2×C4#100411yescharacteristic
992C2×C4#100411yescharacteristic
993C8—62no—
994C8—62no—
995C8—121no—
996C8—121no—
997C2×C3—42no—
998C2×C3—42no—
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—44no—
1008D3—82no—
1009D3—82no—
1010C22—22no—
1011C22—22no—
1012C22—22no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—64no—
1028C22—81no—
1029C22—81no—
1030C22—81no—
1031C22—81no—
1032C22—122no—
1033C22—122no—
1034C22—122no—
1035C22—122no—
1036C22—122no—
1037C22—122no—
1038C22—122no—
1039C22—122no—
1040C22—122no—
1041C22—122no—
1042C22—122no—
1043C22—122no—
1044C22—2416no—
1045C22—2416no—
1046C22—241no—
1047C22—241no—
1048C22—241no—
1049C22—241no—
1050C22—241no—
1051C22—241no—
1052C22—241no—
1053C22—241no—
1054C22C2×#93711yescharacteristic
1055C22D4×#6711yescharacteristic
1056C22D4×#6711yescharacteristic
1057C22C2×#94911yescharacteristic
1058C22C2×#94911yescharacteristic
1059C22#583511yescharacteristic
1060C22#583711yescharacteristic
1061C4—22no—
1062C4—22no—
1063C4—41no—
1064C4—42no—
1065C4—41no—
1066C4—81no—
1067C4—81no—
1068C4—122no—
1069C4D3×#12011yescharacteristic
1070C4#558911yescharacteristic
1071C4#559011yescharacteristic
1072C4#559011yescharacteristic
1073C3#2386011yescharacteristic, complemented, Sylow
1074C2—42no—
1075C2—42no—
1076C2—82no—
1077C2—124no—
1078C2—242no—
1079C2—242no—
1080C2#8260411yescharacteristic
1081C2#8292711yescharacteristic
1082C2#8342411yescharacteristic
1083C2#8350211yescharacteristic
1084C2#8352311yescharacteristic
1085C2#8354211yescharacteristic
1086C2#8357811yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2407C2
socleC23×C3C22×D4
hypercenter#2407D3
hypocenterC3#23860
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2407

Complements

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

NH ≅ G/Ntype
1. C22×#949C2semidirect
2. C2×D4×D12C2semidirect
3. C3×#2407C2semidirect
4. C2×#5238C2semidirect
5. C2×#5046C2semidirect
6. C2×#5036C2semidirect
7. #71699C2semidirect
8. #71684C2semidirect
9. #71611C2semidirect
10. #69688C2semidirect
11. #69687C2semidirect
12. #69658C2semidirect
13. #69657C2semidirect
14. #69521C2semidirect
15. #69517C2semidirect
17. C22×C3×#41C22semidirect
21. C2×C3×C22⋊Q8C22semidirect
22. C2×C3×#121C22semidirect
28. C22×#215C22semidirect
29. C22×#215C22semidirect
31. C22×#213C22semidirect
32. C22×#213C22semidirect
35. C22×#208C22semidirect
45. C3×#391C22semidirect
46. C3×#390C22semidirect
49. C3×#380C22semidirect
51. C2×#835C22semidirect
52. C2×#832C22semidirect
53. C2×#830C22semidirect
54. C2×#830C22semidirect
55. C2×#830C22semidirect
60. C2×#809C22semidirect
61. C2×#809C22semidirect
62. C2×#809C22semidirect
63. C2×#809C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
66. #4524C22semidirect
67. #4524C22semidirect
73. #2407D3semidirect
119. C22×D12D4semidirect
151. C2×#215D4semidirect
160. C2×#213D4semidirect
164. #930D4semidirect
197. C22×#41C2×D3semidirect
214. C2×C22⋊Q8C2×D3semidirect
218. C2×#121C2×D3semidirect
239. #391C2×D3semidirect
240. #390C2×D3semidirect
243. #380C2×D3semidirect
277. C2×C3×Q8C2×D4semidirect
292. C2×C3×D4C2×D4semidirect
402. C2×C3⋊C8C2×D4semidirect
403. C2×C3⋊C8C2×D4semidirect
538. C23×C3AGL(1,ℤ/8)semidirect
615. C2×C3×C4AGL(1,ℤ/8)semidirect
677. C2×Q8D3×D4semidirect
737. C2×D4D3×D4semidirect
922. C23#949semidirect
986. C2×C4#949semidirect
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×D4×D122
C3×#24072
C2×#52382
C2×#50462
C2×#50362
#716992
#716842
#716112
#696882
#696872
#696582
#696572
#695212
#695172
#238603