Finite Group Databasebeta

← #10826930

Subgroups — #10826930

Order 768.

2252 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×D3×#121C211yesmaximal, characteristic
3C2×#5170C211yesmaximal, characteristic, complemented
4C2×#5169C211yesmaximal, characteristic, complemented
5C2×#4806C211yesmaximal, characteristic, complemented
6C2×#4776C211yesmaximal, characteristic, complemented
7C3×#2000C211yesmaximal, characteristic, complemented
8#71699C211yesmaximal, characteristic, complemented
9#71685C211yesmaximal, characteristic, complemented
10#70268C211yesmaximal, characteristic, complemented
11#70200C211yesmaximal, characteristic, complemented
12#69962C211yesmaximal, characteristic, complemented
13#69955C211yesmaximal, characteristic, complemented
14#68880C211yesmaximal, characteristic, complemented
15#68878C211yesmaximal, characteristic, complemented
16#23919—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic, complemented
18C22×D3×D4—21no—
19C22×D3×D4C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic, complemented
22C2×C3×C22⋊Q8C2211yescharacteristic, complemented
23C2×C3×#121C2211yescharacteristic
24C2×#946C2211yescharacteristic
25C22×#215C2211yescharacteristic, complemented
26C2×#939—21no—
27C2×#938C2211yescharacteristic
28C22×#214C2211yescharacteristic, complemented
29C2×#930C2211yescharacteristic
30C2×#924C2211yescharacteristic, complemented
31C22×#204C2211yescharacteristic, complemented
32D3×C22⋊Q8—24no—
33D3×C22⋊Q8—24no—
34D3×#121—24no—
35D3×#121—24no—
36C2×#897C2211yescharacteristic
37C2×#896—21no—
38C2×#895C2211yescharacteristic
39C2×D3×C4⋊C4—21no—
40C2×D3×C4⋊C4C2211yescharacteristic
41C2×D3×C4⋊C4C2211yescharacteristic, complemented
42C2×#884—21no—
43C2×D3×C22⋊C4—21no—
44C2×D3×C22⋊C4—21no—
45C2×#878—21no—
46C2×C3×#103C2211yescharacteristic, complemented
47C2×C3×#102C2211yescharacteristic, complemented
48C2×C3×C22⋊C8C2211yescharacteristic, complemented
49C2×#835C2211yescharacteristic, complemented
50C2×#832C2211yescharacteristic, complemented
51C2×#830C2211yescharacteristic, complemented
52#5170—24no—
53#5169—24no—
54C2×#821C2211yescharacteristic, complemented
55C2×(C2×D3)⋊C8C2211yescharacteristic
56C2×(C2×D3)⋊C8C2211yescharacteristic
57C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C2×#816C2211yescharacteristic, complemented
60C2×#810C2211yescharacteristic, complemented
61C2×#809C2211yescharacteristic, complemented
62#4806—24no—
63#4776—24no—
64C3×#340C2211yescharacteristic, complemented
65#4551C2211yescharacteristic, complemented
66#4529C2211yescharacteristic, complemented
67#4529C2211yescharacteristic, complemented
68C22×C22⋊Q8—31no—
69C22×#121—31no—
70C2×#448—31no—
71C2×#448—31no—
72C2×#450—31no—
73C2×#450—31no—
74#2000—31no—
75#2000—31no—
76#2000—31no—
77#2000D311yescharacteristic, complemented
78#1874—31no—
79#1874—31no—
80#1872—31no—
81#1872—31no—
82#1779—31no—
83C24×D3—21no—
84C24×D3D411yescharacteristic
85C22×C3×Q8C2311yescharacteristic
86C22×C3×D4—21no—
87C22×C3×D4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C22×#67—21no—
90C22×#67—21no—
91C22×#67—21no—
92C23×Dic3D411yescharacteristic
93C2×D3×Q8—22no—
94C2×D3×Q8—22no—
95C2×D3×Q8—22no—
96C2×D3×Q8—22no—
97C2×D3×Q8—41no—
98C2×D3×Q8—41no—
99C2×D3×D4—28no—
100C2×D3×D4—22no—
101C2×D3×D4—22no—
102C2×D3×D4—22no—
103C2×D3×D4—22no—
104C2×D3×D4—41no—
105C2×D3×D4—41no—
106C2×D3×D4—44no—
107C2×D3×D4—44no—
108C22×D12—21no—
109C22×D12C2311yescharacteristic
110C22×C4×D3—21no—
111C22×C4×D3—21no—
112C22×C4×D3—21no—
113C22×C4×D3—22no—
114C22×C4×D3—22no—
115C22×C4×D3—22no—
116C22×C4×D3—22no—
117C22×C4×D3—41no—
118C22×C4×D3—41no—
119C22×C4×D3D411yescharacteristic
120C22×C4×D3D411yescharacteristic
121C22×C4×D3C2311yescharacteristic
122C22×C4×D3C2311yescharacteristic
123C22×Dic6—21no—
124C22×Dic6C2311yescharacteristic
125C2×C3×SD16—22no—
126C2×C3×SD16—22no—
127C2×C3×SD16—41no—
128C22×C3×C8C2311yescharacteristic
129C22×C3×C8C2311yescharacteristic
130C3×C22⋊Q8—22no—
131C3×C22⋊Q8—22no—
132C3×#121—22no—
133C3×#121—22no—
134C2×C3×C4⋊C4—21no—
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—21no—
139C2×#217—21no—
140C2×#217—21no—
141#946—22no—
142#946D414yescomplemented
143C2×#215—22no—
144C2×#215—22no—
145C2×#215—41no—
146#939—28no—
147#938—22no—
148#938D414yes—
149C2×#214—22no—
150C2×#214—22no—
151C2×#214—41no—
152#930—22no—
153#930—22no—
154C2×(C2×D3)⋊C4—21no—
155C2×(C2×D3)⋊C4—21no—
156C2×(C2×D3)⋊C4—21no—
157C2×(C2×D3)⋊C4—21no—
158C2×C4⋊Dic3—21no—
159C2×C4⋊Dic3C2311yescharacteristic
160C2×C4⋊Dic3C2311yescharacteristic
161#924—22no—
162#924—22no—
163C2×Dic3⋊C4—21no—
164C2×Dic3⋊C4—21no—
165C2×Dic3⋊C4—21no—
166C2×Dic3⋊C4—21no—
167C22×C3⋊C8C2311yescharacteristic
168C22×C3⋊C8C2311yescharacteristic
169C2×#204—22no—
170C2×#204—22no—
171C2×#204—41no—
172#897—22no—
173#897D414yescomplemented
174#896—28no—
175#895—22no—
176#895D414yes—
177D3×C4⋊C4—28no—
178D3×C4⋊C4—22no—
179D3×C4⋊C4—22no—
180D3×C4⋊C4—22no—
181D3×C4⋊C4—22no—
182#884—28no—
183D3×C22⋊C4—28no—
184D3×C22⋊C4—28no—
185#878—28no—
186C3×#103—22no—
187C3×#102—22no—
188C3×C22⋊C8—41no—
189#835—22no—
190#832—22no—
191#830—41no—
192#821—22no—
193(C2×D3)⋊C8—22no—
194(C2×D3)⋊C8—22no—
195(C2×D3)⋊C8—22no—
196(C2×D3)⋊C8—22no—
197#816—22no—
198#810—22no—
199#809—22no—
200C23×Q8—31no—
201C23×D4—31no—
202C23×D4—61no—
203C24×C4—31no—
204C22×SD16—31no—
205C22×SD16—31no—
206C22×SD16—31no—
207C22×SD16C2×D311yescharacteristic, complemented
208C2×C22⋊Q8—31no—
209C2×C22⋊Q8—31no—
210C2×C22⋊Q8—31no—
211C2×C22⋊Q8—61no—
212C2×C22⋊Q8—61no—
213C2×C22⋊Q8—64no—
214C2×C22⋊Q8—64no—
215C2×C22⋊Q8C2×D311yescharacteristic, complemented
216C2×#121—31no—
217C2×#121—31no—
218C2×#121—31no—
219C2×#121—61no—
220C2×#121—64no—
221C2×#121—64no—
222C2×#121—61no—
223C2×#121C2×D311yescharacteristic
224C22×C4⋊C4—31no—
225C22×C4⋊C4—31no—
226C22×C4⋊C4—61no—
227C22×C22⋊C4—61no—
228C22×C22⋊C4—61no—
229#450—64no—
230#450—64no—
231#448—64no—
232#448—64no—
233C2×#103—31no—
234C2×#103—31no—
235C2×#103—31no—
236C2×#103C2×D311yescharacteristic, complemented
237C2×#102—31no—
238C2×#102—31no—
239C2×#102—31no—
240C2×#102C2×D311yescharacteristic, complemented
241C2×C22⋊C8—31no—
242C2×C22⋊C8—31no—
243C2×C22⋊C8—31no—
244C2×C22⋊C8—31no—
245C2×C22⋊C8—31no—
246C2×C22⋊C8C2×D311yescharacteristic, complemented
247#340—31no—
248#340—31no—
249#340—31no—
250#340C2×D311yescharacteristic, complemented
251C24×C3—21no—
252C24×C3C2×D411yescharacteristic
253C23×D3—22no—
254C23×D3—22no—
255C23×D3—22no—
256C23×D3—22no—
257C23×D3—24no—
258C23×D3—21no—
259C23×D3—41no—
260C23×D3—41no—
261C23×D3—42no—
262C23×D3—42no—
263C23×D3—42no—
264C23×D3—42no—
265C23×D3—42no—
266C23×D3—42no—
267C23×D3SD1614yescomplemented
268C23×D3C2×D411yescharacteristic
269C23×D3C2×D411yescharacteristic
270C2×C3×Q8—21no—
271C2×C3×Q8—21no—
272C2×C3×Q8—21no—
273C2×C3×Q8—21no—
274C2×C3×Q8—21no—
275C2×C3×Q8C2×D412yescomplemented
276C2×C3×D4—24no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4—42no—
283C2×C3×D4—42no—
284C2×C3×D4C2×D412yes—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4C2×D411yescharacteristic
295C22×C3×C4C2411yescharacteristic
296C2×#67—24no—
297C2×#67—24no—
298C2×#67—24no—
299C2×#67—42no—
300C2×#67—42no—
301C2×#67—42no—
302C2×#67—42no—
303C2×#67—42no—
304C2×#67—42no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—22no—
309C22×Dic3—22no—
310C22×Dic3—41no—
311C22×Dic3C2×D411yescharacteristic
312C22×Dic3C2×D411yescharacteristic
313D3×Q8—44no—
314D3×Q8—44no—
315D3×Q8—44no—
316D3×Q8—44no—
317D3×D4—44no—
318D3×D4—44no—
319D3×D4—44no—
320D3×D4—44no—
321D3×D4—432no—
322C2×D12—21no—
323C2×D12—21no—
324C2×D12—21no—
325C2×D12—21no—
326C2×D12—24no—
327C2×D12—21no—
328C2×D12—42no—
329C2×D12—42no—
330C2×D12C2×D412yes—
331C2×C4×D3—21no—
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3—21no—
335C2×C4×D3—21no—
336C2×C4×D3—21no—
337C2×C4×D3—21no—
338C2×C4×D3—21no—
339C2×C4×D3—24no—
340C2×C4×D3—24no—
341C2×C4×D3—24no—
342C2×C4×D3—22no—
343C2×C4×D3—22no—
344C2×C4×D3—22no—
345C2×C4×D3—22no—
346C2×C4×D3—44no—
347C2×C4×D3—44no—
348C2×C4×D3—44no—
349C2×C4×D3—44no—
350C2×C4×D3—41no—
351C2×C4×D3—41no—
352C2×C4×D3—42no—
353C2×C4×D3—42no—
354C2×C4×D3—42no—
355C2×C4×D3—42no—
356C2×C4×D3—42no—
357C2×C4×D3—42no—
358C2×C4×D3C2×D412yes—
359C2×C4×D3C2×D412yes—
360C2×C4×D3C2×D412yes—
361C2×C4×D3C2×D412yes—
362C2×Dic6—21no—
363C2×Dic6—21no—
364C2×Dic6—21no—
365C2×Dic6—21no—
366C2×Dic6—24no—
367C2×Dic6—21no—
368C2×Dic6—42no—
369C2×Dic6—42no—
370C2×Dic6C2×D412yescomplemented
371C3×SD16—44no—
372C2×C3×C8—21no—
373C2×C3×C8—21no—
374C2×C3×C8—21no—
375C2×C3×C8—21no—
376C2×C3×C8—21no—
377C2×C3×C8—21no—
378C3×C4⋊C4—24no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—21no—
381C3×C4⋊C4C2×D412yes—
382C3×C4⋊C4C2×D412yescomplemented
383C3×C22⋊C4—24no—
384C3×C22⋊C4—24no—
385#217—24no—
386#217—24no—
387#215—44no—
388#214—44no—
389(C2×D3)⋊C4—24no—
390(C2×D3)⋊C4—24no—
391(C2×D3)⋊C4—24no—
392(C2×D3)⋊C4—24no—
393C4⋊Dic3—21no—
394C4⋊Dic3—21no—
395C4⋊Dic3—24no—
396C4⋊Dic3C2×D412yes—
397C4⋊Dic3C2×D412yescomplemented
398Dic3⋊C4—24no—
399Dic3⋊C4—24no—
400Dic3⋊C4—24no—
401Dic3⋊C4—24no—
402C2×C3⋊C8—21no—
403C2×C3⋊C8—21no—
404C2×C3⋊C8—21no—
405C2×C3⋊C8—21no—
406C2×C3⋊C8—21no—
407C2×C3⋊C8—21no—
408#204—44no—
409C25—31no—
410C25—61no—
411C22×Q8—31no—
412C22×Q8—61no—
413C22×Q8—62no—
414C22×Q8—62no—
415C22×Q8—62no—
416C22×Q8—62no—
417C22×Q8—121no—
418C22×Q8—121no—
419C22×Q8C22×D311yescharacteristic
420C22×D4—21no—
421C22×D4—31no—
422C22×D4—61no—
423C22×D4—62no—
424C22×D4—62no—
425C22×D4—61no—
426C22×D4—62no—
427C22×D4—68no—
428C22×D4—61no—
429C22×D4—61no—
430C22×D4—62no—
431C22×D4—121no—
432C22×D4—121no—
433C22×D4—124no—
434C22×D4—124no—
435C22×D4C22×D311yescharacteristic
436C23×C4—31no—
437C23×C4—31no—
438C23×C4—31no—
439C23×C4—31no—
440C23×C4—31no—
441C23×C4—62no—
442C23×C4—62no—
443C23×C4—62no—
444C23×C4—62no—
445C23×C4—61no—
446C23×C4—61no—
447C23×C4—61no—
448C23×C4—121no—
449C23×C4—121no—
450C23×C4C22×D311yescharacteristic
451C2×SD16—22no—
452C2×SD16—22no—
453C2×SD16—41no—
454C2×SD16—62no—
455C2×SD16—62no—
456C2×SD16—62no—
457C2×SD16—62no—
458C2×SD16—62no—
459C2×SD16—62no—
460C2×SD16—121no—
461C2×SD16—121no—
462C2×SD16—121no—
463C22×C8—31no—
464C22×C8—31no—
465C22×C8C22×D311yescharacteristic
466C22×C8C22×D311yescharacteristic
467C22⋊Q8—22no—
468C22⋊Q8—22no—
469C22⋊Q8—34no—
470C22⋊Q8—34no—
471C22⋊Q8—68no—
472C22⋊Q8—62no—
473C22⋊Q8—68no—
474C22⋊Q8—62no—
475C22⋊Q8—62no—
476C22⋊Q8—62no—
477#121—22no—
478#121—22no—
479#121—34no—
480#121—34no—
481#121—68no—
482#121—62no—
483#121—62no—
484#121—62no—
485#121—62no—
486#121—68no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—62no—
491C2×C4⋊C4—62no—
492C2×C4⋊C4—68no—
493C2×C4⋊C4—61no—
494C2×C4⋊C4—61no—
495C2×C4⋊C4—61no—
496C2×C4⋊C4—61no—
497C2×C4⋊C4—61no—
498C2×C4⋊C4—62no—
499C2×C4⋊C4—62no—
500C2×C4⋊C4C22×D311yescharacteristic
501C2×C4⋊C4C22×D311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—68no—
505C2×C22⋊C4—68no—
506C2×C22⋊C4—61no—
507C2×C22⋊C4—61no—
508C2×C22⋊C4—61no—
509C2×C22⋊C4—61no—
510C2×C22⋊C4—61no—
511C2×C22⋊C4—61no—
512#103—22no—
513#103—62no—
514#103—62no—
515#103—62no—
516#102—22no—
517#102—62no—
518#102—62no—
519#102—62no—
520C22⋊C8—41no—
521C22⋊C8—62no—
522C22⋊C8—62no—
523C22⋊C8—62no—
524C22⋊C8—62no—
525C22⋊C8—121no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—22no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3C2×SD1612yes—
540C23×C3C22×D411yescharacteristic
541C22×D3—21no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—28no—
550C22×D3—28no—
551C22×D3—22no—
552C22×D3—44no—
553C22×D3—44no—
554C22×D3—44no—
555C22×D3—44no—
556C22×D3—44no—
557C22×D3—48no—
558C22×D3—48no—
559C22×D3—48no—
560C22×D3—41no—
561C22×D3—41no—
562C22×D3—41no—
563C22×D3—41no—
564C22×D3—41no—
565C22×D3—41no—
566C22×D3—84no—
567C22×D3—84no—
568C22×D3—84no—
569C22×D3—84no—
570C22×D3#12012yes—
571C22×D3#12012yes—
572C22×D3C2×SD1612yes—
573C22×D3C2×SD1612yes—
574C22×D3AGL(1,ℤ/8)12yes—
575C22×D3#13712yes—
576C3×Q8—22no—
577C3×Q8—22no—
578C3×Q8—41no—
579C3×Q8—41no—
580C3×D4—22no—
581C3×D4—22no—
582C3×D4—48no—
583C3×D4—41no—
584C3×D4—41no—
585C2×C3×C4—21no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4C22×D411yescharacteristic
602C2×C3×C4C22×D411yescharacteristic
603C2×C3×C4C22×D411yescharacteristic
604C2×C3×C4C22×D411yescharacteristic
605C2×C3×C4H(5,𝔽2)11yescharacteristic
606C2×C3×C4H(5,𝔽2)11yescharacteristic
607#67—48no—
608#67—48no—
609#67—48no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—44no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3#12012yes—
625C2×Dic3#12012yes—
626D12—22no—
627D12—22no—
628D12—48no—
629D12—41no—
630D12—41no—
631C4×D3—22no—
632C4×D3—22no—
633C4×D3—22no—
634C4×D3—22no—
635C4×D3—22no—
636C4×D3—22no—
637C4×D3—22no—
638C4×D3—22no—
639C4×D3—44no—
640C4×D3—44no—
641C4×D3—48no—
642C4×D3—48no—
643C4×D3—48no—
644Dic6—22no—
645Dic6—22no—
646Dic6—48no—
647Dic6—41no—
648Dic6—41no—
649C3×C8—41no—
650C3×C8—41no—
651C3⋊C8—41no—
652C3⋊C8—41no—
653C24—21no—
654C24—31no—
655C24—31no—
656C24—34no—
657C24—62no—
658C24—62no—
659C24—62no—
660C24—62no—
661C24—64no—
662C24—61no—
663C24—121no—
664C24—121no—
665C24—122no—
666C24—122no—
667C24—122no—
668C24—122no—
669C24—122no—
670C24—122no—
671C24D3×D411yescharacteristic
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—32no—
678C2×Q8—64no—
679C2×Q8—61no—
680C2×Q8—61no—
681C2×Q8—61no—
682C2×Q8—61no—
683C2×Q8—61no—
684C2×Q8—122no—
685C2×Q8—122no—
686C2×Q8—124no—
687C2×Q8—124no—
688C2×Q8—124no—
689C2×Q8—124no—
690C2×Q8D3×D412yescomplemented
691C2×D4—24no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—32no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—64no—
701C2×D4—64no—
702C2×D4—64no—
703C2×D4—64no—
704C2×D4—61no—
705C2×D4—61no—
706C2×D4—61no—
707C2×D4—61no—
708C2×D4—61no—
709C2×D4—122no—
710C2×D4—122no—
711C2×D4—122no—
712C2×D4—124no—
713C2×D4—124no—
714C2×D4—124no—
715C2×D4—124no—
716C2×D4—122no—
717C2×D4—1232no—
718C2×D4—122no—
719C2×D4—122no—
720C2×D4—122no—
721C2×D4—122no—
722C2×D4D3×D412yes—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—31no—
733C22×C4—31no—
734C22×C4—32no—
735C22×C4—32no—
736C22×C4—32no—
737C22×C4—32no—
738C22×C4—62no—
739C22×C4—62no—
740C22×C4—62no—
741C22×C4—62no—
742C22×C4—64no—
743C22×C4—64no—
744C22×C4—64no—
745C22×C4—62no—
746C22×C4—62no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—121no—
759C22×C4—121no—
760C22×C4—124no—
761C22×C4—124no—
762C22×C4—124no—
763C22×C4—124no—
764C22×C4—122no—
765C22×C4—122no—
766C22×C4—122no—
767C22×C4—122no—
768C22×C4—122no—
769C22×C4—122no—
770C22×C4—121no—
771C22×C4D3×D411yescharacteristic
772C22×C4C23×D311yescharacteristic
773SD16—44no—
774SD16—124no—
775SD16—124no—
776SD16—124no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—61no—
784C2×C8—61no—
785C2×C8—61no—
786C2×C8—61no—
787C2×C8—61no—
788C2×C8—61no—
789C4⋊C4—24no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—32no—
793C4⋊C4—32no—
794C4⋊C4—64no—
795C4⋊C4—64no—
796C4⋊C4—64no—
797C4⋊C4—64no—
798C4⋊C4—64no—
799C4⋊C4—61no—
800C4⋊C4—61no—
801C4⋊C4D3×D412yes—
802C4⋊C4D3×D412yescomplemented
803C22⋊C4—24no—
804C22⋊C4—24no—
805C22⋊C4—64no—
806C22⋊C4—64no—
807C22⋊C4—64no—
808C22⋊C4—64no—
809C22⋊C4—64no—
810C22⋊C4—64no—
811C22×C3—22no—
812C22×C3—22no—
813C22×C3—22no—
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×C3C2×#12011yescharacteristic
827C22×C3#53411yescharacteristic
828C22×C3C22×SD1611yescharacteristic
829C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
830C22×C3C2×#13711yescharacteristic
831C22×C3#57511yescharacteristic
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—22no—
843C2×D3—22no—
844C2×D3—416no—
845C2×D3—42no—
846C2×D3—42no—
847C2×D3—42no—
848C2×D3—816no—
849C2×D3—81no—
850C2×D3—81no—
851C2×D3—81no—
852C2×D3—81no—
853C2×D3#44814yescomplemented
854C2×D3#45014yescomplemented
855C3×C4—42no—
856C3×C4—41no—
857C3×C4—42no—
858C3×C4—42no—
859C3×C4D4211yescharacteristic
860C3×C4D4211yescharacteristic
861C3×C4D4211yescharacteristic
862C3×C4D4211yescharacteristic
863Dic3—22no—
864Dic3—22no—
865Dic3—42no—
866Dic3—42no—
867Dic3—42no—
868C23—21no—
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—22no—
875C23—32no—
876C23—32no—
877C23—32no—
878C23—32no—
879C23—32no—
880C23—32no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—68no—
888C23—68no—
889C23—61no—
890C23—61no—
891C23—61no—
892C23—61no—
893C23—61no—
894C23—61no—
895C23—61no—
896C23—61no—
897C23—62no—
898C23—124no—
899C23—124no—
900C23—124no—
901C23—124no—
902C23—124no—
903C23—128no—
904C23—128no—
905C23—128no—
906C23—121no—
907C23—121no—
908C23—121no—
909C23—121no—
910C23—121no—
911C23—121no—
912C23—244no—
913C23—244no—
914C23—244no—
915C23—244no—
916C23D3×SD1612yes—
917C23C2×D3×D411yescharacteristic
918Q8—22no—
919Q8—22no—
920Q8—41no—
921Q8—41no—
922Q8—62no—
923Q8—62no—
924Q8—128no—
925Q8—121no—
926Q8—121no—
927D4—22no—
928D4—22no—
929D4—48no—
930D4—41no—
931D4—41no—
932D4—62no—
933D4—62no—
934D4—128no—
935D4—128no—
936D4—128no—
937D4—128no—
938D4—121no—
939D4—121no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—32no—
947C2×C4—32no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—61no—
959C2×C4—61no—
960C2×C4—61no—
961C2×C4—61no—
962C2×C4—62no—
963C2×C4—62no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—62no—
967C2×C4—62no—
968C2×C4—62no—
969C2×C4—62no—
970C2×C4—62no—
971C2×C4—62no—
972C2×C4—62no—
973C2×C4—124no—
974C2×C4—124no—
975C2×C4—128no—
976C2×C4—128no—
977C2×C4—128no—
978C2×C4—124no—
979C2×C4—121no—
980C2×C4—121no—
981C2×C4—121no—
982C2×C4—121no—
983C2×C4—121no—
984C2×C4—121no—
985C2×C4C2×D3×D411yescharacteristic
986C2×C4C2×D3×D411yescharacteristic
987C2×C4C2×D3×D411yescharacteristic
988C2×C4C2×D3×D411yescharacteristic
989C2×C4#100411yescharacteristic
990C2×C4#100911yescharacteristic
991C8—41no—
992C8—41no—
993C8—121no—
994C8—121no—
995C2×C3—42no—
996C2×C3—82no—
997C2×C3#240311yescharacteristic
998C2×C3C2×#45011yescharacteristic
999C2×C3C2×#44811yescharacteristic
1000C2×C3#300611yescharacteristic
1001C2×C3#300711yescharacteristic
1002C2×C3#318711yescharacteristic
1003C2×C3#319311yescharacteristic
1004D3—24no—
1005D3—24no—
1006D3—82no—
1007C22—22no—
1008C22—22no—
1009C22—22no—
1010C22—34no—
1011C22—34no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—42no—
1017C22—42no—
1018C22—42no—
1019C22—62no—
1020C22—62no—
1021C22—62no—
1022C22—62no—
1023C22—62no—
1024C22—62no—
1025C22—62no—
1026C22—62no—
1027C22—62no—
1028C22—62no—
1029C22—62no—
1030C22—62no—
1031C22—81no—
1032C22—81no—
1033C22—81no—
1034C22—81no—
1035C22—1216no—
1036C22—122no—
1037C22—122no—
1038C22—122no—
1039C22—2416no—
1040C22—241no—
1041C22—241no—
1042C22—241no—
1043C22—241no—
1044C22D3×#12011yescharacteristic
1045C22D3×#12011yescharacteristic
1046C22#560511yescharacteristic
1047C22C2×D3×SD1611yescharacteristic
1048C22#576811yescharacteristic
1049C22D3×AGL(1,ℤ/8)11yescharacteristic
1050C22D3×#13711yescharacteristic
1051C4—42no—
1052C4—41no—
1053C4—42no—
1054C4—42no—
1055C4—62no—
1056C4—62no—
1057C4—122no—
1058C4—122no—
1059C4—122no—
1060C4#559011yescharacteristic
1061C4#560911yescharacteristic
1062C4#560911yescharacteristic
1063C4#571711yescharacteristic
1064C3#2391911yescharacteristic, complemented, Sylow
1065C2—42no—
1066C2—64no—
1067C2—64no—
1068C2—82no—
1069C2—242no—
1070C2#7675311yescharacteristic
1071C2D3×#44811yescharacteristic
1072C2#8008411yescharacteristic
1073C2D3×#45011yescharacteristic
1074C2#8022811yescharacteristic
1075C2#8066311yescharacteristic
1076C2#8081111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
prime radicalC2×D3×#121C2
hypercenter#2000D3
hypocenterC3#23919
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×D3×C22⋊Q8C2semidirect
3. C2×#5170C2semidirect
4. C2×#5169C2semidirect
5. C2×#4806C2semidirect
6. C2×#4776C2semidirect
7. C3×#2000C2semidirect
8. #71699C2semidirect
9. #71685C2semidirect
10. #70268C2semidirect
11. #70200C2semidirect
12. #69962C2semidirect
13. #69955C2semidirect
14. #68880C2semidirect
15. #68878C2semidirect
17. C22×D3×Q8C22semidirect
21. C22×C3×SD16C22semidirect
22. C2×C3×C22⋊Q8C22semidirect
25. C22×#215C22semidirect
28. C22×#214C22semidirect
30. C2×#924C22semidirect
31. C22×#204C22semidirect
41. C2×D3×C4⋊C4C22semidirect
46. C2×C3×#103C22semidirect
47. C2×C3×#102C22semidirect
48. C2×C3×C22⋊C8C22semidirect
49. C2×#835C22semidirect
50. C2×#832C22semidirect
51. C2×#830C22semidirect
54. C2×#821C22semidirect
57. C2×(C2×D3)⋊C8C22semidirect
58. C2×(C2×D3)⋊C8C22semidirect
59. C2×#816C22semidirect
60. C2×#810C22semidirect
61. C2×#809C22semidirect
64. C3×#340C22semidirect
65. #4551C22semidirect
66. #4529C22semidirect
67. #4529C22semidirect
77. #2000D3semidirect
142. #946D4semidirect
173. #897D4semidirect
207. C22×SD16C2×D3semidirect
215. C2×C22⋊Q8C2×D3semidirect
236. C2×#103C2×D3semidirect
240. C2×#102C2×D3semidirect
246. C2×C22⋊C8C2×D3semidirect
250. #340C2×D3semidirect
267. C23×D3SD16semidirect
275. C2×C3×Q8C2×D4semidirect
370. C2×Dic6C2×D4semidirect
382. C3×C4⋊C4C2×D4semidirect
397. C4⋊Dic3C2×D4semidirect
690. C2×Q8D3×D4semidirect
802. C4⋊C4D3×D4semidirect
853. C2×D3#448semidirect
854. C2×D3#450semidirect
1064. C3#23919semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C22⋊Q82
C2×D3×#1212
C2×#51702
C2×#51692
C2×#48062
C2×#47762
C3×#20002
#716992
#716852
#702682
#702002
#699622
#699552
#688802
#688782
#239193