Finite Group Databasebeta

← #10826938

Subgroups — #10826938

Order 768.

2272 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#121C211yesmaximal, characteristic, complemented
2C2×#5606C211yesmaximal, characteristic, complemented
3C2×#5158C211yesmaximal, characteristic, complemented
4C2×#5156C211yesmaximal, characteristic, complemented
5C2×#4781C211yesmaximal, characteristic, complemented
6C2×#4776C211yesmaximal, characteristic, complemented
7C3×#1999C211yesmaximal, characteristic, complemented
8#71685C211yesmaximal, characteristic, complemented
9#71684C211yesmaximal, characteristic, complemented
10#70201C211yesmaximal, characteristic, complemented
11#70200C211yesmaximal, characteristic, complemented
12#69962C211yesmaximal, characteristic, complemented
13#69955C211yesmaximal, characteristic, complemented
14#68881C211yesmaximal, characteristic, complemented
15#68878C211yesmaximal, characteristic, complemented
16#23920—31nomaximal, Sylow
17C22×#237C2211yescharacteristic, complemented
18C22×D3×D4—21no—
19C22×D3×D4C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C22×C3×D8C2211yescharacteristic, complemented
22C2×C3×#121C2211yescharacteristic
23C2×C3×#121C2211yescharacteristic, complemented
24C2×#939—21no—
25C2×#938C2211yescharacteristic
26C2×#938C2211yescharacteristic
27C2×#937—21no—
28C2×D4×Dic3—21no—
29C22×#214C2211yescharacteristic, complemented
30C22×#213C2211yescharacteristic, complemented
31C2×#930C2211yescharacteristic
32C2×#924C2211yescharacteristic, complemented
33C22×#204C2211yescharacteristic, complemented
34#5606—24no—
35#5606—24no—
36D3×#121—24no—
37D3×#121—24no—
38C2×#897C2211yescharacteristic
39C2×#895C2211yescharacteristic
40C2×#892C2211yescharacteristic, complemented
41C2×D3×C4⋊C4C2211yescharacteristic
42C2×#884—21no—
43C2×#883—21no—
44C2×#67⋊C4—21no—
45C2×D3×C22⋊C4—21no—
46C2×C3×#102C2211yescharacteristic, complemented
47C2×C3×#102C2211yescharacteristic, complemented
48C2×C3×C22⋊C8C2211yescharacteristic, complemented
49C2×#832C2211yescharacteristic, complemented
50C2×#832C2211yescharacteristic, complemented
51C2×#830C2211yescharacteristic, complemented
52#5158—24no—
53#5156—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#4781—24no—
63#4776—24no—
64C3×#340C2211yescharacteristic, complemented
65#4551C2211yescharacteristic, complemented
66#4529C2211yescharacteristic, complemented
67#4529C2211yescharacteristic, complemented
68C2×#525—31no—
69C22×#121—31no—
70C2×#449—31no—
71C2×#449—31no—
72C2×#450—31no—
73C2×#447—31no—
74#2000—31no—
75#2000—31no—
76#1999—31no—
77#1999D311yescharacteristic, complemented
78#1875—31no—
79#1875—31no—
80#1874—31no—
81#1872—31no—
82#1779—31no—
83C24×D3—21no—
84C24×D3D411yescharacteristic
85C22×C3×D4—21no—
86C22×C3×D4—21no—
87C22×C3×D4C2311yescharacteristic
88C22×C3×D4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C22×#67—21no—
91C22×#67—21no—
92C22×#67—21no—
93C22×#67—21no—
94C22×#67—21no—
95C23×Dic3—21no—
96C23×Dic3D411yescharacteristic
97C2×#237—22no—
98C2×#237—22no—
99C2×#237—22no—
100C2×#237—22no—
101C2×#237—41no—
102C2×#237—41no—
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—21no—
113C22×D12C2311yescharacteristic
114C22×C4×D3—21no—
115C22×C4×D3—22no—
116C22×C4×D3—22no—
117C22×C4×D3—22no—
118C22×C4×D3—22no—
119C22×C4×D3—41no—
120C22×C4×D3—41no—
121C22×C4×D3D411yescharacteristic
122C22×C4×D3D411yescharacteristic
123C22×C4×D3C2311yescharacteristic
124C22×C4×D3C2311yescharacteristic
125C22×Dic6C2311yescharacteristic
126C2×C3×D8—22no—
127C2×C3×D8—22no—
128C2×C3×D8—41no—
129C22×C3×C8C2311yescharacteristic
130C22×C3×C8C2311yescharacteristic
131C3×#121—22no—
132C3×#121—22no—
133C3×#121—22no—
134C3×#121—22no—
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—21no—
139C2×#217—21no—
140C2×#217—21no—
141C2×#217—21no—
142#939—28no—
143#938—22no—
144#938—22no—
145#938D414yescomplemented
146#938D414yescomplemented
147#937—28no—
148D4×Dic3—28no—
149C2×#214—22no—
150C2×#214—22no—
151C2×#214—41no—
152C2×#213—22no—
153C2×#213—22no—
154C2×#213—41no—
155#930—22no—
156#930—22no—
157C2×(C2×D3)⋊C4—21no—
158C2×(C2×D3)⋊C4—21no—
159C2×(C2×D3)⋊C4—21no—
160C2×(C2×D3)⋊C4—21no—
161C2×C4⋊Dic3—21no—
162C2×C4⋊Dic3C2311yescharacteristic
163C2×C4⋊Dic3C2311yescharacteristic
164#924—22no—
165#924—22no—
166C2×Dic3⋊C4—21no—
167C2×Dic3⋊C4—21no—
168C2×C4×Dic3—21no—
169C22×C3⋊C8C2311yescharacteristic
170C22×C3⋊C8C2311yescharacteristic
171C2×#204—22no—
172C2×#204—22no—
173C2×#204—41no—
174#897—22no—
175#897D414yescomplemented
176#895—22no—
177#895D414yescomplemented
178#892—22no—
179#892—22no—
180D3×C4⋊C4—22no—
181D3×C4⋊C4—22no—
182#884—28no—
183#883—28no—
184#67⋊C4—28no—
185D3×C22⋊C4—28no—
186C3×#102—22no—
187C3×#102—22no—
188C3×C22⋊C8—41no—
189#832—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—
200C22×#41—31no—
201C23×D4—31no—
202C23×D4—61no—
203C24×C4—31no—
204C22×SD16—31no—
205C22×SD16—31no—
206C22×D8—31no—
207C22×D8C2×D311yescharacteristic, complemented
208#525—64no—
209#525—64no—
210C2×#123—61no—
211C2×C22⋊Q8—31no—
212C2×C22⋊Q8—31no—
213C2×#121—31no—
214C2×#121—31no—
215C2×#121—31no—
216C2×#121—31no—
217C2×#121—61no—
218C2×#121—64no—
219C2×#121—64no—
220C2×#121—61no—
221C2×#121C2×D311yescharacteristic
222C2×#121C2×D311yescharacteristic, complemented
223C2×#120—61no—
224C2×C4×D4—61no—
225C2×C4×D4—61no—
226C2×#117—31no—
227C22×C4⋊C4—31no—
228C22×C22⋊C4—61no—
229#450—64no—
230#449—64no—
231#449—64no—
232#447—64no—
233C2×#103—31no—
234C2×#103—31no—
235C2×#102—31no—
236C2×#102—31no—
237C2×#102—31no—
238C2×#102—31no—
239C2×#102C2×D311yescharacteristic, complemented
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×C3—21no—
253C24×C3C2×D411yescharacteristic
254C23×D3—22no—
255C23×D3—22no—
256C23×D3—22no—
257C23×D3—24no—
258C23×D3—21no—
259C23×D3—22no—
260C23×D3—22no—
261C23×D3—41no—
262C23×D3—41no—
263C23×D3—42no—
264C23×D3—42no—
265C23×D3—42no—
266C23×D3—42no—
267C23×D3—42no—
268C23×D3—42no—
269C23×D3C2×D411yescharacteristic
270C23×D3C2×D411yescharacteristic
271C2×C3×D4—24no—
272C2×C3×D4—24no—
273C2×C3×D4—21no—
274C2×C3×D4—21no—
275C2×C3×D4—21no—
276C2×C3×D4—21no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4—21no—
283C2×C3×D4—42no—
284C2×C3×D4—42no—
285C2×C3×D4—42no—
286C2×C3×D4—42no—
287C2×C3×D4C2×D412yes—
288C2×C3×D4C2×D412yescomplemented
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4C2×D411yescharacteristic
298C22×C3×C4C2411yescharacteristic
299C2×#67—24no—
300C2×#67—24no—
301C2×#67—24no—
302C2×#67—24no—
303C2×#67—24no—
304C2×#67—42no—
305C2×#67—42no—
306C2×#67—42no—
307C2×#67—42no—
308C2×#67—42no—
309C2×#67—42no—
310C2×#67—42no—
311C2×#67—42no—
312C2×#67—42no—
313C2×#67—42no—
314C22×Dic3—24no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—22no—
319C22×Dic3—22no—
320C22×Dic3—41no—
321C22×Dic3—42no—
322C22×Dic3—42no—
323C22×Dic3C2×D411yescharacteristic
324C22×Dic3C2×D411yescharacteristic
325#237—44no—
326#237—44no—
327#237—44no—
328#237—44no—
329D3×D4—44no—
330D3×D4—44no—
331D3×D4—44no—
332D3×D4—44no—
333D3×D4—432no—
334C2×D12—21no—
335C2×D12—21no—
336C2×D12—21no—
337C2×D12—21no—
338C2×D12—24no—
339C2×D12—21no—
340C2×D12—42no—
341C2×D12—42no—
342C2×D12C2×D412yes—
343C2×C4×D3—21no—
344C2×C4×D3—21no—
345C2×C4×D3—21no—
346C2×C4×D3—21no—
347C2×C4×D3—21no—
348C2×C4×D3—21no—
349C2×C4×D3—21no—
350C2×C4×D3—21no—
351C2×C4×D3—24no—
352C2×C4×D3—22no—
353C2×C4×D3—22no—
354C2×C4×D3—22no—
355C2×C4×D3—22no—
356C2×C4×D3—44no—
357C2×C4×D3—44no—
358C2×C4×D3—44no—
359C2×C4×D3—44no—
360C2×C4×D3—41no—
361C2×C4×D3—41no—
362C2×C4×D3—42no—
363C2×C4×D3—42no—
364C2×C4×D3C2×D412yes—
365C2×C4×D3C2×D412yes—
366C2×C4×D3C2×D412yes—
367C2×C4×D3C2×D412yes—
368C2×Dic6—21no—
369C2×Dic6—21no—
370C2×Dic6—21no—
371C2×Dic6—21no—
372C2×Dic6—21no—
373C2×Dic6C2×D412yescomplemented
374C3×D8—44no—
375C2×C3×C8—21no—
376C2×C3×C8—21no—
377C2×C3×C8—21no—
378C2×C3×C8—21no—
379C2×C3×C8—21no—
380C2×C3×C8—21no—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4C2×D412yes—
384C3×C4⋊C4C2×D412yescomplemented
385C3×C22⋊C4—24no—
386C3×C22⋊C4—24no—
387#217—24no—
388#217—24no—
389#217—24no—
390#214—44no—
391#213—44no—
392(C2×D3)⋊C4—24no—
393(C2×D3)⋊C4—24no—
394(C2×D3)⋊C4—24no—
395(C2×D3)⋊C4—24no—
396C4⋊Dic3—21no—
397C4⋊Dic3—21no—
398C4⋊Dic3—24no—
399C4⋊Dic3C2×D412yes—
400C4⋊Dic3C2×D412yescomplemented
401Dic3⋊C4—24no—
402Dic3⋊C4—24no—
403C4×Dic3—24no—
404C2×C3⋊C8—21no—
405C2×C3⋊C8—21no—
406C2×C3⋊C8—21no—
407C2×C3⋊C8—21no—
408C2×C3⋊C8—21no—
409C2×C3⋊C8—21no—
410#204—44no—
411C25—31no—
412C25—61no—
413C2×#41—62no—
414C2×#41—62no—
415C2×#41—62no—
416C2×#41—62no—
417C2×#41—121no—
418C2×#41—121no—
419C22×Q8—31no—
420C22×D4—21no—
421C22×D4—21no—
422C22×D4—31no—
423C22×D4—61no—
424C22×D4—62no—
425C22×D4—62no—
426C22×D4—61no—
427C22×D4—62no—
428C22×D4—68no—
429C22×D4—61no—
430C22×D4—61no—
431C22×D4—61no—
432C22×D4—61no—
433C22×D4—62no—
434C22×D4—121no—
435C22×D4—121no—
436C22×D4—124no—
437C22×D4—124no—
438C22×D4C22×D311yescharacteristic
439C22×D4C22×D311yescharacteristic
440C23×C4—31no—
441C23×C4—31no—
442C23×C4—31no—
443C23×C4—31no—
444C23×C4—31no—
445C23×C4—62no—
446C23×C4—62no—
447C23×C4—62no—
448C23×C4—62no—
449C23×C4—61no—
450C23×C4—61no—
451C23×C4—121no—
452C23×C4—121no—
453C23×C4C22×D311yescharacteristic
454C2×SD16—62no—
455C2×SD16—62no—
456C2×SD16—62no—
457C2×SD16—62no—
458C2×SD16—121no—
459C2×SD16—121no—
460C2×D8—22no—
461C2×D8—22no—
462C2×D8—41no—
463C2×D8—62no—
464C2×D8—62no—
465C2×D8—121no—
466C22×C8—31no—
467C22×C8—31no—
468C22×C8C22×D311yescharacteristic
469C22×C8C22×D311yescharacteristic
470#123—68no—
471C22⋊Q8—34no—
472C22⋊Q8—62no—
473C22⋊Q8—62no—
474C22⋊Q8—62no—
475#121—22no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—34no—
480#121—34no—
481#121—34no—
482#121—68no—
483#121—62no—
484#121—62no—
485#121—62no—
486#121—62no—
487#121—62no—
488#121—68no—
489#120—68no—
490C4×D4—68no—
491C4×D4—68no—
492#117—62no—
493#117—62no—
494C2×C4⋊C4—31no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—62no—
497C2×C4⋊C4—61no—
498C2×C4⋊C4—61no—
499C2×C4⋊C4—61no—
500C2×C4⋊C4—62no—
501C2×C4⋊C4C22×D311yescharacteristic
502C2×C4⋊C4C22×D311yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
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—
512C2×C22⋊C4—61no—
513C2×C42—61no—
514#103—62no—
515#103—62no—
516#102—22no—
517#102—22no—
518#102—62no—
519#102—62no—
520#102—62no—
521#102—62no—
522C22⋊C8—41no—
523C22⋊C8—62no—
524C22⋊C8—62no—
525C22⋊C8—62no—
526C22⋊C8—62no—
527C22⋊C8—121no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—22no—
535C23×C3—22no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
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×C3AGL(1,ℤ/8)12yes—
549C23×C3C22×D411yescharacteristic
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—28no—
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—21no—
560C22×D3—21no—
561C22×D3—22no—
562C22×D3—44no—
563C22×D3—44no—
564C22×D3—44no—
565C22×D3—44no—
566C22×D3—44no—
567C22×D3—48no—
568C22×D3—48no—
569C22×D3—48no—
570C22×D3—44no—
571C22×D3—41no—
572C22×D3—41no—
573C22×D3—41no—
574C22×D3—41no—
575C22×D3—41no—
576C22×D3—41no—
577C22×D3—84no—
578C22×D3—84no—
579C22×D3—84no—
580C22×D3—84no—
581C22×D3#12012yes—
582C22×D3#12012yes—
583C22×D3#13512yes—
584C22×D3AGL(1,ℤ/8)12yes—
585C3×D4—22no—
586C3×D4—22no—
587C3×D4—22no—
588C3×D4—22no—
589C3×D4—48no—
590C3×D4—48no—
591C3×D4—41no—
592C3×D4—41no—
593C3×D4—41no—
594C3×D4—41no—
595C2×C3×C4—22no—
596C2×C3×C4—21no—
597C2×C3×C4—22no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
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×C4C22×D411yescharacteristic
609C2×C3×C4C22×D411yescharacteristic
610C2×C3×C4C22×D411yescharacteristic
611C2×C3×C4C22×D411yescharacteristic
612C2×C3×C4H(5,𝔽2)11yescharacteristic
613C2×C3×C4H(5,𝔽2)11yescharacteristic
614#67—48no—
615#67—48no—
616#67—48no—
617#67—48no—
618#67—48no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—44no—
627C2×Dic3—48no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3#12012yes—
635C2×Dic3#12012yes—
636D12—22no—
637D12—22no—
638D12—48no—
639D12—41no—
640D12—41no—
641C4×D3—22no—
642C4×D3—22no—
643C4×D3—22no—
644C4×D3—22no—
645C4×D3—22no—
646C4×D3—22no—
647C4×D3—22no—
648C4×D3—22no—
649C4×D3—44no—
650C4×D3—44no—
651C4×D3—48no—
652Dic6—22no—
653Dic6—22no—
654Dic6—41no—
655Dic6—41no—
656C3×C8—41no—
657C3×C8—41no—
658C3⋊C8—41no—
659C3⋊C8—41no—
660C24—21no—
661C24—21no—
662C24—31no—
663C24—31no—
664C24—62no—
665C24—62no—
666C24—62no—
667C24—62no—
668C24—64no—
669C24—62no—
670C24—61no—
671C24—121no—
672C24—121no—
673C24—122no—
674C24—122no—
675C24—122no—
676C24—122no—
677C24—122no—
678C24—122no—
679C24D3×D411yescharacteristic
680#41—124no—
681#41—124no—
682#41—124no—
683#41—124no—
684C2×Q8—32no—
685C2×Q8—61no—
686C2×Q8—61no—
687C2×Q8—61no—
688C2×Q8—61no—
689C2×Q8—61no—
690C2×D4—24no—
691C2×D4—24no—
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—21no—
702C2×D4—32no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—42no—
707C2×D4—64no—
708C2×D4—64no—
709C2×D4—64no—
710C2×D4—64no—
711C2×D4—64no—
712C2×D4—64no—
713C2×D4—61no—
714C2×D4—61no—
715C2×D4—61no—
716C2×D4—61no—
717C2×D4—61no—
718C2×D4—122no—
719C2×D4—122no—
720C2×D4—122no—
721C2×D4—124no—
722C2×D4—124no—
723C2×D4—124no—
724C2×D4—124no—
725C2×D4—122no—
726C2×D4—1232no—
727C2×D4—122no—
728C2×D4—122no—
729C2×D4—122no—
730C2×D4—122no—
731C2×D4—122no—
732C2×D4—122no—
733C2×D4—122no—
734C2×D4—122no—
735C2×D4D3×D412yes—
736C2×D4D3×D412yescomplemented
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—31no—
746C22×C4—31no—
747C22×C4—32no—
748C22×C4—32no—
749C22×C4—32no—
750C22×C4—32no—
751C22×C4—62no—
752C22×C4—62no—
753C22×C4—62no—
754C22×C4—62no—
755C22×C4—64no—
756C22×C4—62no—
757C22×C4—62no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—64no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—121no—
771C22×C4—121no—
772C22×C4—122no—
773C22×C4—124no—
774C22×C4—124no—
775C22×C4—124no—
776C22×C4—124no—
777C22×C4—122no—
778C22×C4—122no—
779C22×C4—121no—
780C22×C4—122no—
781C22×C4D3×D411yescharacteristic
782C22×C4C23×D311yescharacteristic
783SD16—124no—
784SD16—124no—
785D8—44no—
786D8—124no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—61no—
794C2×C8—61no—
795C2×C8—61no—
796C2×C8—61no—
797C2×C8—61no—
798C2×C8—61no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—32no—
802C4⋊C4—32no—
803C4⋊C4—64no—
804C4⋊C4—64no—
805C4⋊C4—64no—
806C4⋊C4—61no—
807C4⋊C4—61no—
808C4⋊C4D3×D412yes—
809C4⋊C4D3×D412yescomplemented
810C22⋊C4—24no—
811C22⋊C4—24no—
812C22⋊C4—64no—
813C22⋊C4—64no—
814C22⋊C4—64no—
815C22⋊C4—64no—
816C22⋊C4—64no—
817C22⋊C4—64no—
818C22⋊C4—64no—
819C42—64no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—22no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—42no—
828C22×C3—42no—
829C22×C3—42no—
830C22×C3—42no—
831C22×C3—42no—
832C22×C3—42no—
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×C3C2×#12011yescharacteristic
843C22×C3#53411yescharacteristic
844C22×C3C2×#13511yescharacteristic
845C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
846C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
847C22×C3#57511yescharacteristic
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—22no—
852C2×D3—22no—
853C2×D3—22no—
854C2×D3—22no—
855C2×D3—22no—
856C2×D3—22no—
857C2×D3—416no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—41no—
861C2×D3—41no—
862C2×D3—42no—
863C2×D3—42no—
864C2×D3—42no—
865C2×D3—816no—
866C2×D3—81no—
867C2×D3—81no—
868C2×D3—81no—
869C2×D3—81no—
870C2×D3#44914yescomplemented
871C3×C4—41no—
872C3×C4—42no—
873C3×C4—42no—
874C3×C4D4211yescharacteristic
875C3×C4D4211yescharacteristic
876C3×C4D4211yescharacteristic
877C3×C4D4211yescharacteristic
878Dic3—22no—
879Dic3—22no—
880Dic3—42no—
881Dic3—42no—
882Dic3—42no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—21no—
889C23—22no—
890C23—22no—
891C23—32no—
892C23—32no—
893C23—32no—
894C23—32no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—68no—
908C23—61no—
909C23—61no—
910C23—61no—
911C23—61no—
912C23—61no—
913C23—61no—
914C23—61no—
915C23—61no—
916C23—61no—
917C23—61no—
918C23—62no—
919C23—124no—
920C23—124no—
921C23—124no—
922C23—124no—
923C23—124no—
924C23—124no—
925C23—128no—
926C23—128no—
927C23—128no—
928C23—121no—
929C23—121no—
930C23—121no—
931C23—121no—
932C23—121no—
933C23—121no—
934C23—244no—
935C23—244no—
936C23—244no—
937C23—244no—
938C23#91112yes—
939C23C2×D3×D411yescharacteristic
940Q8—62no—
941Q8—62no—
942Q8—121no—
943Q8—121no—
944D4—22no—
945D4—22no—
946D4—22no—
947D4—22no—
948D4—48no—
949D4—48no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—41no—
954D4—62no—
955D4—62no—
956D4—128no—
957D4—128no—
958D4—128no—
959D4—128no—
960D4—128no—
961D4—128no—
962D4—121no—
963D4—121no—
964C2×C4—22no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—21no—
969C2×C4—32no—
970C2×C4—32no—
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—61no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—62no—
984C2×C4—62no—
985C2×C4—62no—
986C2×C4—62no—
987C2×C4—62no—
988C2×C4—62no—
989C2×C4—62no—
990C2×C4—62no—
991C2×C4—62no—
992C2×C4—62no—
993C2×C4—62no—
994C2×C4—124no—
995C2×C4—124no—
996C2×C4—128no—
997C2×C4—124no—
998C2×C4—128no—
999C2×C4—121no—
1000C2×C4—121no—
1001C2×C4—121no—
1002C2×C4—121no—
1003C2×C4—121no—
1004C2×C4—121no—
1005C2×C4C2×D3×D411yescharacteristic
1006C2×C4C2×D3×D411yescharacteristic
1007C2×C4C2×D3×D411yescharacteristic
1008C2×C4C2×D3×D411yescharacteristic
1009C2×C4#100411yescharacteristic
1010C2×C4#100911yescharacteristic
1011C8—41no—
1012C8—41no—
1013C8—121no—
1014C8—121no—
1015C2×C3—42no—
1016C2×C3—82no—
1017C2×C3—82no—
1018C2×C3#240311yescharacteristic
1019C2×C3C2×#44911yescharacteristic
1020C2×C3#300211yescharacteristic
1021C2×C3#300311yescharacteristic
1022C2×C3#300611yescharacteristic
1023C2×C3#318811yescharacteristic
1024C2×C3#319411yescharacteristic
1025D3—24no—
1026D3—42no—
1027D3—82no—
1028C22—22no—
1029C22—22no—
1030C22—22no—
1031C22—34no—
1032C22—41no—
1033C22—41no—
1034C22—41no—
1035C22—41no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—62no—
1043C22—62no—
1044C22—62no—
1045C22—62no—
1046C22—62no—
1047C22—62no—
1048C22—62no—
1049C22—62no—
1050C22—62no—
1051C22—81no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—81no—
1059C22—1216no—
1060C22—121no—
1061C22—121no—
1062C22—121no—
1063C22—121no—
1064C22—122no—
1065C22—122no—
1066C22—122no—
1067C22—2416no—
1068C22—241no—
1069C22—241no—
1070C22—241no—
1071C22—241no—
1072C22D3×#12011yescharacteristic
1073C22D3×#12011yescharacteristic
1074C22#560511yescharacteristic
1075C22C2×#91111yescharacteristic
1076C22D3×#13511yescharacteristic
1077C22D3×AGL(1,ℤ/8)11yescharacteristic
1078C22#577311yescharacteristic
1079C4—42no—
1080C4—42no—
1081C4—41no—
1082C4—62no—
1083C4—62no—
1084C4—122no—
1085C4—122no—
1086C4—122no—
1087C4#559011yescharacteristic
1088C4#560911yescharacteristic
1089C4#560911yescharacteristic
1090C4#571711yescharacteristic
1091C3#2392011yescharacteristic, complemented, Sylow
1092C2—42no—
1093C2—64no—
1094C2—82no—
1095C2—82no—
1096C2—122no—
1097C2—242no—
1098C2#7675311yescharacteristic
1099C2#8000211yescharacteristic
1100C2#8000311yescharacteristic
1101C2D3×#44911yescharacteristic
1102C2#8008211yescharacteristic
1103C2#8072011yescharacteristic
1104C2#8086911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1999C2
socleC23×C3C22×D4
hypercenter#1999D3
hypocenterC3#23920
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1999

Complements

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

NH ≅ G/Ntype
1. C2×D3×#121C2semidirect
2. C2×#5606C2semidirect
3. C2×#5158C2semidirect
4. C2×#5156C2semidirect
5. C2×#4781C2semidirect
6. C2×#4776C2semidirect
7. C3×#1999C2semidirect
8. #71685C2semidirect
9. #71684C2semidirect
10. #70201C2semidirect
11. #70200C2semidirect
12. #69962C2semidirect
13. #69955C2semidirect
14. #68881C2semidirect
15. #68878C2semidirect
17. C22×#237C22semidirect
21. C22×C3×D8C22semidirect
23. C2×C3×#121C22semidirect
29. C22×#214C22semidirect
30. C22×#213C22semidirect
32. C2×#924C22semidirect
33. C22×#204C22semidirect
40. C2×#892C22semidirect
46. C2×C3×#102C22semidirect
47. C2×C3×#102C22semidirect
48. C2×C3×C22⋊C8C22semidirect
49. C2×#832C22semidirect
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. #1999D3semidirect
145. #938D4semidirect
146. #938D4semidirect
175. #897D4semidirect
177. #895D4semidirect
207. C22×D8C2×D3semidirect
222. C2×#121C2×D3semidirect
239. C2×#102C2×D3semidirect
240. C2×#102C2×D3semidirect
246. C2×C22⋊C8C2×D3semidirect
250. #340C2×D3semidirect
288. C2×C3×D4C2×D4semidirect
373. C2×Dic6C2×D4semidirect
384. C3×C4⋊C4C2×D4semidirect
400. C4⋊Dic3C2×D4semidirect
736. C2×D4D3×D4semidirect
809. C4⋊C4D3×D4semidirect
870. C2×D3#449semidirect
1091. C3#23920semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#1212
C2×#56062
C2×#51582
C2×#51562
C2×#47812
C2×#47762
C3×#19992
#716852
#716842
#702012
#702002
#699622
#699552
#688812
#688782
#239203