Finite Group Databasebeta

← #10826333

Subgroups — #10826333

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
1C2×C3×D42C211yesmaximal, characteristic, complemented
2C22×#932C211yesmaximal, characteristic, complemented
3C2×#5218C211yesmaximal, characteristic, complemented
4C2×#5217C211yesmaximal, characteristic, complemented
5C2×#5037C211yesmaximal, characteristic, complemented
6#82402C211yesmaximal, characteristic, complemented
7#72128C211yesmaximal, characteristic, complemented
8#71768C211yesmaximal, characteristic, complemented
9#71767C211yesmaximal, characteristic, complemented
10#71685C211yesmaximal, characteristic, complemented
11#71684C211yesmaximal, characteristic, complemented
12#71682C211yesmaximal, characteristic, complemented
13#71613C211yesmaximal, characteristic, complemented
14#71612C211yesmaximal, characteristic, complemented
15#71611C211yesmaximal, characteristic, complemented
16#23860—31nomaximal, Sylow
17C23×C3×D4—21no—
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C22×#235C2211yescharacteristic, complemented
21C3×D42—24no—
22C3×D42—24no—
23C2×C3×#127C2211yescharacteristic
24C2×C3×#121—21no—
25C2×C3×#121C2211yescharacteristic
26C2×C3×#121C2211yescharacteristic
27C2×C3×#120—21no—
28C2×C3×#120—21no—
29C2×C3×C4×D4C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C22×#214C2211yescharacteristic
32C22×#214C2211yescharacteristic, complemented
33C22×#214C2211yescharacteristic, complemented
34C2×#932—24no—
35C2×#932—24no—
36C2×#932—24no—
37C22×#213C2211yescharacteristic
38C22×#213C2211yescharacteristic, complemented
39C22×#213C2211yescharacteristic, complemented
40C2×#930C2211yescharacteristic, complemented
41C2×#924C2211yescharacteristic, complemented
42C22×#208C2211yescharacteristic, complemented
43#5223—21no—
44#5218—24no—
45#5217—24no—
46C2×#832C2211yescharacteristic
47C2×#832C2211yescharacteristic
48C2×#832C2211yescharacteristic, complemented
49C2×#832C2211yescharacteristic, complemented
50C2×#832C2211yescharacteristic, complemented
51C2×#832C2211yescharacteristic, complemented
52#5212C2211yescharacteristic, complemented
53C2×#830C2211yescharacteristic, complemented
54C2×#830C2211yescharacteristic, complemented
55C2×#830C2211yescharacteristic, complemented
56#5037—24no—
57#4989—21no—
58C2×#810C2211yescharacteristic, complemented
59C2×#809C2211yescharacteristic, complemented
60#4959—21no—
61#4956—21no—
62#4939C2211yescharacteristic, complemented
63#4929C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66#4524C2211yescharacteristic, complemented
67#4524C2211yescharacteristic, complemented
68C22×AGL(1,ℤ/8)—31no—
69C2×D42D311yescharacteristic, complemented
70C2×#449—31no—
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—
83C25×C3—21no—
84C25×C3—21no—
85C22×C3×D4—22no—
86C22×C3×D4—22no—
87C22×C3×D4—28no—
88C22×C3×D4—21no—
89C22×C3×D4—21no—
90C22×C3×D4—22no—
91C22×C3×D4—22no—
92C22×C3×D4—22no—
93C22×C3×D4—22no—
94C22×C3×D4—21no—
95C22×C3×D4—21no—
96C22×C3×D4—21no—
97C22×C3×D4—22no—
98C22×C3×D4—21no—
99C22×C3×D4—41no—
100C22×C3×D4—41no—
101C22×C3×D4—41no—
102C22×C3×D4—41no—
103C22×C3×D4—44no—
104C22×C3×D4—44no—
105C22×C3×D4D411yescharacteristic
106C22×C3×D4D414yescomplemented
107C22×C3×D4C2311yescharacteristic
108C22×C3×D4C2311yescharacteristic
109C22×C3×D4C2311yescharacteristic
110C23×C3×C4—21no—
111C23×C3×C4C2311yescharacteristic
112C23×C3×C4C2311yescharacteristic
113C22×#67—21no—
114C22×#67—21no—
115C2×#235—22no—
116C2×#235—22no—
117C2×#235—22no—
118C2×#235—22no—
119C2×#235—41no—
120C2×#235—41no—
121C22×D12C2311yescharacteristic
122C22×C4×D3—21no—
123C22×Dic6C2311yescharacteristic
124C3×#127—22no—
125C3×#127—22no—
126C3×#121—28no—
127C3×#121—22no—
128C3×#121—22no—
129C3×#121—22no—
130C3×#121D414yescomplemented
131C3×#120—28no—
132C3×#120—28no—
133C3×C4×D4—22no—
134C3×C4×D4—22no—
135C3×C4×D4—22no—
136C3×C4×D4—22no—
137C2×C3×C4⋊C4D411yescharacteristic
138C2×C3×C4⋊C4C2311yescharacteristic
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4D411yescharacteristic
143C2×C3×C22⋊C4D411yescharacteristic
144C2×C3×C42C2311yescharacteristic
145C2×#217—21no—
146C2×#217—21no—
147C2×#214—22no—
148C2×#214—22no—
149C2×#214—22no—
150C2×#214—22no—
151C2×#214—22no—
152C2×#214—22no—
153C2×#214—22no—
154C2×#214—41no—
155C2×#214D414yescomplemented
156#932—232no—
157C2×#213—22no—
158C2×#213—22no—
159C2×#213—22no—
160C2×#213—22no—
161C2×#213—22no—
162C2×#213—22no—
163C2×#213—22no—
164C2×#213—41no—
165C2×#213D414yescomplemented
166#930—22no—
167#930—41no—
168C2×(C2×D3)⋊C4—21no—
169C2×(C2×D3)⋊C4—21no—
170C2×(C2×D3)⋊C4—21no—
171C2×C4⋊Dic3C2311yescharacteristic
172C2×C4⋊Dic3C2311yescharacteristic
173#924—22no—
174#924—41no—
175C2×Dic3⋊C4—21no—
176C2×#208—22no—
177C2×#208—22no—
178C2×#208—22no—
179C22×C3⋊C8C2311yescharacteristic
180C22×C3⋊C8C2311yescharacteristic
181C22×C3⋊C8C2311yescharacteristic
182C22×C3⋊C8C2311yescharacteristic
183#832—22no—
184#832—22no—
185#832—22no—
186#832—22no—
187#832—41no—
188#832—41no—
189C3⋊#95—21no—
190C3⋊#95—21no—
191C3⋊#95—21no—
192#830—22no—
193#830—22no—
194#830—22no—
195#810—22no—
196#809—22no—
197C22×#41—31no—
198C23×D4—21no—
199C23×D4C2×D311yescharacteristic
200C23×D4C2×D311yescharacteristic
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—24no—
212D42—24no—
213C2×#127C2×D311yescharacteristic
214C2×C22⋊Q8—31no—
215C2×#121—21no—
216C2×#121—31no—
217C2×#121C2×D311yescharacteristic
218C2×#121C2×D311yescharacteristic
219C2×#120—21no—
220C2×#120—21no—
221C2×C4×D4C2×D311yescharacteristic
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—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—24no—
250C24×C3—21no—
251C24×C3—21no—
252C24×C3—24no—
253C24×C3—42no—
254C24×C3—42no—
255C24×C3—42no—
256C24×C3—42no—
257C24×C3—42no—
258C24×C3—42no—
259C24×C3—42no—
260C24×C3—42no—
261C24×C3—81no—
262C24×C3—81no—
263C24×C3—81no—
264C24×C3—81no—
265C24×C3C2×D411yescharacteristic
266C24×C3C2×D411yescharacteristic
267C23×D3—21no—
268C2×C3×D4—22no—
269C2×C3×D4—22no—
270C2×C3×D4—28no—
271C2×C3×D4—24no—
272C2×C3×D4—24no—
273C2×C3×D4—24no—
274C2×C3×D4—24no—
275C2×C3×D4—24no—
276C2×C3×D4—24no—
277C2×C3×D4—22no—
278C2×C3×D4—21no—
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—21no—
290C2×C3×D4—21no—
291C2×C3×D4—44no—
292C2×C3×D4—44no—
293C2×C3×D4—44no—
294C2×C3×D4—42no—
295C2×C3×D4—42no—
296C2×C3×D4—42no—
297C2×C3×D4—42no—
298C2×C3×D4—42no—
299C2×C3×D4—44no—
300C2×C3×D4—44no—
301C2×C3×D4—432no—
302C2×C3×D4—44no—
303C2×C3×D4—42no—
304C2×C3×D4—42no—
305C2×C3×D4—42no—
306C2×C3×D4—42no—
307C2×C3×D4—44no—
308C2×C3×D4—42no—
309C2×C3×D4—81no—
310C2×C3×D4—81no—
311C2×C3×D4C2×D412yes—
312C2×C3×D4C2×D412yes—
313C2×C3×D4C2×D412yes—
314C2×C3×D4C2×D412yes—
315C2×C3×D4C2×D412yes—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—24no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—42no—
329C22×C3×C4—42no—
330C22×C3×C4C2×D411yescharacteristic
331C22×C3×C4C2×D411yescharacteristic
332C22×C3×C4C2×D411yescharacteristic
333C22×C3×C4C2×D412yes—
334C22×C3×C4C2×D412yes—
335C22×C3×C4C2×D411yescharacteristic
336C22×C3×C4C2411yescharacteristic
337C2×#67—42no—
338C2×#67—42no—
339C2×#67—42no—
340C2×#67—42no—
341C2×#67—42no—
342C2×#67—81no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346#235—28no—
347#235—44no—
348#235—44no—
349#235—44no—
350C2×D12—21no—
351C2×D12—21no—
352C2×D12—21no—
353C2×D12—21no—
354C2×D12—21no—
355C2×D12C2×D412yescomplemented
356C2×C4×D3—42no—
357C2×C4×D3—42no—
358C2×C4×D3—42no—
359C2×Dic6—21no—
360C2×Dic6—21no—
361C2×Dic6—21no—
362C2×Dic6—21no—
363C2×Dic6—21no—
364C2×Dic6C2×D412yescomplemented
365C3×C4⋊C4—22no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4C2×D412yes—
368C3×C22⋊C4—24no—
369C3×C22⋊C4—24no—
370C3×C22⋊C4—22no—
371C3×C22⋊C4—24no—
372C3×C22⋊C4—22no—
373C3×C42—21no—
374C3×C42—21no—
375#217—42no—
376#217—81no—
377#214—28no—
378#214—28no—
379#214—44no—
380#213—28no—
381#213—28no—
382#213—44no—
383(C2×D3)⋊C4—42no—
384(C2×D3)⋊C4—42no—
385(C2×D3)⋊C4—81no—
386C4⋊Dic3—21no—
387C4⋊Dic3—21no—
388C4⋊Dic3—21no—
389C4⋊Dic3—21no—
390Dic3⋊C4—42no—
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—21no—
405C25—21no—
406C2×#41—62no—
407C2×#41—62no—
408C2×#41—62no—
409C2×#41—62no—
410C2×#41—121no—
411C2×#41—121no—
412C22×Q8—31no—
413C22×D4—22no—
414C22×D4—22no—
415C22×D4—28no—
416C22×D4—21no—
417C22×D4—21no—
418C22×D4—22no—
419C22×D4—22no—
420C22×D4—22no—
421C22×D4—22no—
422C22×D4—21no—
423C22×D4—21no—
424C22×D4—21no—
425C22×D4—22no—
426C22×D4—21no—
427C22×D4—31no—
428C22×D4—41no—
429C22×D4—41no—
430C22×D4—41no—
431C22×D4—41no—
432C22×D4—44no—
433C22×D4—44no—
434C22×D4—61no—
435C22×D4—61no—
436C22×D4#6711yescharacteristic
437C22×D4#6714yescomplemented
438C22×D4C22×D311yescharacteristic
439C22×D4C22×D311yescharacteristic
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—22no—
472#127—22no—
473C22⋊Q8—62no—
474C22⋊Q8—121no—
475#121—28no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—62no—
480#121—121no—
481#121#6714yescomplemented
482#120—28no—
483#120—28no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—22no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—61no—
491C2×C4⋊C4#6711yescharacteristic
492C2×C4⋊C4C22×D311yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—61no—
497C2×C22⋊C4—61no—
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—61no—
516#95—61no—
517#95—61no—
518C23×C3—21no—
519C23×C3—22no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—22no—
534C23×C3—22no—
535C23×C3—48no—
536C23×C3—48no—
537C23×C3—48no—
538C23×C3—48no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—84no—
556C23×C3—84no—
557C23×C3—84no—
558C23×C3—84no—
559C23×C3—84no—
560C23×C3—84no—
561C23×C3—84no—
562C23×C3—84no—
563C23×C3—84no—
564C23×C3—84no—
565C23×C3#12012yes—
566C23×C3AGL(1,ℤ/8)12yescomplemented
567C23×C3C22×D411yescharacteristic
568C22×D3—22no—
569C22×D3—41no—
570C22×D3—41no—
571C22×D3—41no—
572C22×D3—41no—
573C22×D3—41no—
574C22×D3—41no—
575C3×D4—28no—
576C3×D4—22no—
577C3×D4—22no—
578C3×D4—22no—
579C3×D4—22no—
580C3×D4—22no—
581C3×D4—22no—
582C3×D4—22no—
583C3×D4—48no—
584C3×D4—48no—
585C3×D4—48no—
586C3×D4—48no—
587C3×D4—48no—
588C3×D4—41no—
589C3×D4—41no—
590C3×D4—41no—
591C3×D4—41no—
592C3×D4—84no—
593C3×D4#12014yes—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—22no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—48no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4#12012yes—
617C2×C3×C4AGL(1,ℤ/8)12yescomplemented
618C2×C3×C4C22×D411yescharacteristic
619C2×C3×C4C22×D411yescharacteristic
620C2×C3×C4C22×D411yescharacteristic
621C2×C3×C4C22×D411yescharacteristic
622C2×C3×C4H(5,𝔽2)11yescharacteristic
623C2×C3×C4H(5,𝔽2)11yescharacteristic
624#67—48no—
625#67—84no—
626C2×Dic3—22no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635D12—22no—
636D12—22no—
637D12—41no—
638D12—41no—
639C4×D3—48no—
640Dic6—22no—
641Dic6—22no—
642Dic6—41no—
643Dic6—41no—
644C3⋊C8—22no—
645C3⋊C8—22no—
646C3⋊C8—41no—
647C3⋊C8—41no—
648C24—21no—
649C24—24no—
650C24—21no—
651C24—21no—
652C24—24no—
653C24—42no—
654C24—42no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—42no—
659C24—42no—
660C24—42no—
661C24—61no—
662C24—81no—
663C24—81no—
664C24—81no—
665C24—81no—
666C24C2×#6711yescharacteristic
667C24C2×#6711yescharacteristic
668#41—68no—
669#41—124no—
670#41—124no—
671#41—124no—
672C2×Q8—32no—
673C2×Q8—61no—
674C2×Q8—61no—
675C2×Q8—61no—
676C2×Q8—61no—
677C2×Q8—61no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—28no—
681C2×D4—24no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—24no—
686C2×D4—22no—
687C2×D4—24no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—32no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—42no—
706C2×D4—42no—
707C2×D4—42no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—44no—
711C2×D4—44no—
712C2×D4—432no—
713C2×D4—44no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—44no—
719C2×D4—42no—
720C2×D4—61no—
721C2×D4—61no—
722C2×D4—61no—
723C2×D4—61no—
724C2×D4—61no—
725C2×D4—81no—
726C2×D4—81no—
727C2×D4—122no—
728C2×D4—122no—
729C2×D4—122no—
730C2×D4—122no—
731C2×D4—122no—
732C2×D4—241no—
733C2×D4D3×D412yes—
734C2×D4D3×D412yes—
735C2×D4C2×#6712yes—
736C2×D4C2×#6712yes—
737C2×D4C2×#6712yes—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—24no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—122no—
756C22×C4—122no—
757C22×C4—122no—
758C22×C4C2×#6711yescharacteristic
759C22×C4C2×#6711yescharacteristic
760C22×C4C2×#6711yescharacteristic
761C22×C4C2×#6711yescharacteristic
762C22×C4C2×#6712yes—
763C22×C4C2×#6712yes—
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—61no—
787C4⋊C4—61no—
788C4⋊C4—61no—
789C4⋊C4—61no—
790C4⋊C4—122no—
791C4⋊C4C2×#6712yes—
792C22⋊C4—24no—
793C22⋊C4—24no—
794C22⋊C4—22no—
795C22⋊C4—24no—
796C22⋊C4—22no—
797C22⋊C4—122no—
798C22⋊C4—122no—
799C22⋊C4—122no—
800C22⋊C4—241no—
801C22⋊C4—241no—
802C42—21no—
803C42—21no—
804C22×C3—22no—
805C22×C3—24no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—22no—
811C22×C3—41no—
812C22×C3—42no—
813C22×C3—41no—
814C22×C3—42no—
815C22×C3—41no—
816C22×C3—42no—
817C22×C3—41no—
818C22×C3—42no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—42no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—42no—
828C22×C3—42no—
829C22×C3—42no—
830C22×C3—42no—
831C22×C3—816no—
832C22×C3—816no—
833C22×C3—81no—
834C22×C3—81no—
835C22×C3—81no—
836C22×C3—81no—
837C22×C3—81no—
838C22×C3—81no—
839C22×C3—81no—
840C22×C3—81no—
841C22×C3C2×#12011yescharacteristic
842C22×C3D4211yescharacteristic
843C22×C3D4211yescharacteristic
844C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
845C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
846C22×C3#57611yescharacteristic
847C22×C3#57711yescharacteristic
848C2×D3—42no—
849C2×D3—42no—
850C2×D3—42no—
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×C4C2×#12011yescharacteristic
861C3×C4#53411yescharacteristic
862C3×C4D4211yescharacteristic
863C3×C4D4211yescharacteristic
864Dic3—42no—
865Dic3—81no—
866Dic3—81no—
867C23—21no—
868C23—21no—
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—22no—
875C23—22no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—48no—
885C23—48no—
886C23—48no—
887C23—48no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—62no—
905C23—84no—
906C23—84no—
907C23—84no—
908C23—84no—
909C23—84no—
910C23—84no—
911C23—84no—
912C23—84no—
913C23—84no—
914C23—84no—
915C23—121no—
916C23—121no—
917C23—121no—
918C23—121no—
919C23—121no—
920C23—121no—
921C23#93212yescomplemented
922C23#95312yes—
923C23C22×#6711yescharacteristic
924Q8—62no—
925Q8—62no—
926Q8—121no—
927Q8—121no—
928D4—28no—
929D4—22no—
930D4—22no—
931D4—22no—
932D4—22no—
933D4—22no—
934D4—22no—
935D4—22no—
936D4—48no—
937D4—48no—
938D4—48no—
939D4—48no—
940D4—48no—
941D4—41no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—62no—
946D4—62no—
947D4—84no—
948D4—128no—
949D4—121no—
950D4—121no—
951D4—244no—
952D4#93714yes—
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—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—48no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—62no—
976C2×C4—128no—
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#93212yescomplemented
986C2×C4#95312yes—
987C2×C4C2×D3×D411yescharacteristic
988C2×C4C2×D3×D411yescharacteristic
989C2×C4#100411yescharacteristic
990C2×C4#100411yescharacteristic
991C2×C4C22×#6711yescharacteristic
992C2×C4C22×#6711yescharacteristic
993C8—62no—
994C8—62no—
995C8—121no—
996C8—121no—
997C2×C3—42no—
998C2×C3—42no—
999C2×C3—44no—
1000C2×C3—82no—
1001C2×C3—82no—
1002C2×C3#240311yescharacteristic
1003C2×C3#300311yescharacteristic
1004C2×C3#301211yescharacteristic
1005C2×C3#326411yescharacteristic
1006C2×C3#326511yescharacteristic
1007C2×C3#327211yescharacteristic
1008C2×C3#327411yescharacteristic
1009D3—82no—
1010C22—22no—
1011C22—22no—
1012C22—22no—
1013C22—22no—
1014C22—22no—
1015C22—24no—
1016C22—22no—
1017C22—41no—
1018C22—42no—
1019C22—41no—
1020C22—41no—
1021C22—42no—
1022C22—41no—
1023C22—42no—
1024C22—41no—
1025C22—41no—
1026C22—42no—
1027C22—42no—
1028C22—41no—
1029C22—41no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—816no—
1038C22—816no—
1039C22—81no—
1040C22—81no—
1041C22—81no—
1042C22—81no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—122no—
1048C22—122no—
1049C22—122no—
1050C22—241no—
1051C22—241no—
1052C22—241no—
1053C22—241no—
1054C22C2×#93211yescharacteristic
1055C22C2×#93211yescharacteristic
1056C22D4×#6711yescharacteristic
1057C22D4×#6711yescharacteristic
1058C22#583511yescharacteristic
1059C22#583611yescharacteristic
1060C22C2×#95311yescharacteristic
1061C4—22no—
1062C4—22no—
1063C4—42no—
1064C4—41no—
1065C4—41no—
1066C4—122no—
1067C4—241no—
1068C4—241no—
1069C4C2×#93711yescharacteristic
1070C4D4×#6711yescharacteristic
1071C4D4×#6711yescharacteristic
1072C4#580411yescharacteristic
1073C3#2386011yescharacteristic, complemented, Sylow
1074C2—42no—
1075C2—42no—
1076C2—44no—
1077C2—82no—
1078C2—82no—
1079C2—242no—
1080C2#8348811yescharacteristic
1081C2#8348911yescharacteristic
1082C2#8349111yescharacteristic
1083C2#8349211yescharacteristic
1084C2#8403811yescharacteristic
1085C2#8405211yescharacteristic
1086C2#8410211yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×D42C2
socleC23×C3C22×D4
hypercenterC2×D42D3
hypocenterC3#23860
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C2×C3×D42C2semidirect
2. C22×#932C2semidirect
3. C2×#5218C2semidirect
4. C2×#5217C2semidirect
5. C2×#5037C2semidirect
6. #82402C2semidirect
7. #72128C2semidirect
8. #71768C2semidirect
9. #71767C2semidirect
10. #71685C2semidirect
11. #71684C2semidirect
12. #71682C2semidirect
13. #71613C2semidirect
14. #71612C2semidirect
15. #71611C2semidirect
20. C22×#235C22semidirect
32. C22×#214C22semidirect
33. C22×#214C22semidirect
38. C22×#213C22semidirect
39. C22×#213C22semidirect
40. C2×#930C22semidirect
41. C2×#924C22semidirect
42. C22×#208C22semidirect
48. C2×#832C22semidirect
49. C2×#832C22semidirect
50. C2×#832C22semidirect
51. C2×#832C22semidirect
52. #5212C22semidirect
53. C2×#830C22semidirect
54. C2×#830C22semidirect
55. C2×#830C22semidirect
58. C2×#810C22semidirect
59. C2×#809C22semidirect
62. #4939C22semidirect
63. #4929C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
66. #4524C22semidirect
67. #4524C22semidirect
69. C2×D42D3semidirect
106. C22×C3×D4D4semidirect
130. C3×#121D4semidirect
155. C2×#214D4semidirect
165. C2×#213D4semidirect
355. C2×D12C2×D4semidirect
364. C2×Dic6C2×D4semidirect
402. C2×C3⋊C8C2×D4semidirect
403. C2×C3⋊C8C2×D4semidirect
437. C22×D4#67semidirect
481. #121#67semidirect
566. C23×C3AGL(1,ℤ/8)semidirect
617. C2×C3×C4AGL(1,ℤ/8)semidirect
921. C23#932semidirect
985. C2×C4#932semidirect
1073. C3#23860semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D422
C22×#9322
C2×#52182
C2×#52172
C2×#50372
#824022
#721282
#717682
#717672
#716852
#716842
#716822
#716132
#716122
#716112
#238603