Finite Group Databasebeta

← #10826944

Subgroups — #10826944

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×#5627C211yesmaximal, characteristic, complemented
2C2×D3×#121C211yesmaximal, characteristic, complemented
3C2×#5172C211yesmaximal, characteristic, complemented
4C2×#5169C211yesmaximal, characteristic, complemented
5C2×#4810C211yesmaximal, characteristic, complemented
6C2×#4773C211yesmaximal, characteristic, complemented
7C3×#2000C211yesmaximal, characteristic, complemented
8#71699C211yesmaximal, characteristic, complemented
9#71684C211yesmaximal, characteristic, complemented
10#70268C211yesmaximal, characteristic, complemented
11#70201C211yesmaximal, characteristic, complemented
12#69961C211yesmaximal, characteristic, complemented
13#69955C211yesmaximal, characteristic, complemented
14#68881C211yesmaximal, characteristic, complemented
15#68880C211yesmaximal, characteristic, complemented
16#23920—31nomaximal, Sylow
17C22×#239C2211yescharacteristic, 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×#213C2211yescharacteristic, complemented
29C2×#930C2211yescharacteristic
30C2×#930C2211yescharacteristic, complemented
31C22×D24C2211yescharacteristic, complemented
32#5627—24no—
33#5627—24no—
34D3×#121—24no—
35D3×#121—24no—
36C2×#895C2211yescharacteristic
37C2×#895C2211yescharacteristic
38C2×#894—21no—
39C2×#893—21no—
40C2×#892C2211yescharacteristic, complemented
41C2×D3×C4⋊C4C2211yescharacteristic
42C2×#884—21no—
43C2×#882—21no—
44C2×#67⋊C4—21no—
45C2×D3×C22⋊C4—21no—
46C2×C3×#103C2211yescharacteristic, complemented
47C2×C3×#102C2211yescharacteristic, complemented
48C2×C3×C22⋊C8C2211yescharacteristic, complemented
49C2×#835C2211yescharacteristic, complemented
50C2×#832C2211yescharacteristic, complemented
51C2×#830C2211yescharacteristic, complemented
52#5172—24no—
53#5169—24no—
54C2×#821C2211yescharacteristic, complemented
55C2×#821C2211yescharacteristic, complemented
56C2×(C2×D3)⋊C8C2211yescharacteristic
57C2×(C2×D3)⋊C8C2211yescharacteristic
58C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
60C2×#809C2211yescharacteristic, complemented
61C2×#809C2211yescharacteristic, complemented
62#4810—24no—
63#4773—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#2000D311yescharacteristic, complemented
76#1999—31no—
77#1999—31no—
78#1875—31no—
79#1875—31no—
80#1874—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—
92C22×#67—21no—
93C23×Dic3D411yescharacteristic
94C2×#239—22no—
95C2×#239—22no—
96C2×#239—22no—
97C2×#239—22no—
98C2×#239—41no—
99C2×#239—41no—
100C2×D3×D4—28no—
101C2×D3×D4—22no—
102C2×D3×D4—22no—
103C2×D3×D4—22no—
104C2×D3×D4—22no—
105C2×D3×D4—41no—
106C2×D3×D4—41no—
107C2×D3×D4—44no—
108C2×D3×D4—44no—
109C22×D12—21no—
110C22×D12—21no—
111C22×D12—21no—
112C22×D12C2311yescharacteristic
113C22×D12C2311yescharacteristic
114C22×C4×D3—21no—
115C22×C4×D3—21no—
116C22×C4×D3—22no—
117C22×C4×D3—22no—
118C22×C4×D3—22no—
119C22×C4×D3—22no—
120C22×C4×D3—41no—
121C22×C4×D3—41no—
122C22×C4×D3D411yescharacteristic
123C22×C4×D3D411yescharacteristic
124C22×C4×D3C2311yescharacteristic
125C22×C4×D3C2311yescharacteristic
126C2×C3×SD16—22no—
127C2×C3×SD16—22no—
128C2×C3×SD16—41no—
129C22×C3×C8C2311yescharacteristic
130C22×C3×C8C2311yescharacteristic
131C3×C22⋊Q8—22no—
132C3×C22⋊Q8—22no—
133C3×#121—22no—
134C3×#121—22no—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C4⋊C4C2311yescharacteristic
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—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#938D414yescomplemented
149C2×#213—22no—
150C2×#213—22no—
151C2×#213—41no—
152#930—22no—
153#930—22no—
154#930—22no—
155#930—22no—
156C2×(C2×D3)⋊C4—21no—
157C2×(C2×D3)⋊C4—21no—
158C2×(C2×D3)⋊C4—21no—
159C2×(C2×D3)⋊C4—21no—
160C2×(C2×D3)⋊C4—21no—
161C2×(C2×D3)⋊C4—21no—
162C2×C4⋊Dic3C2311yescharacteristic
163C2×C4⋊Dic3C2311yescharacteristic
164C2×Dic3⋊C4—21no—
165C2×Dic3⋊C4—21no—
166C2×C4×Dic3—21no—
167C22×C3⋊C8C2311yescharacteristic
168C22×C3⋊C8C2311yescharacteristic
169C2×D24—22no—
170C2×D24—22no—
171C2×D24—41no—
172#895—22no—
173#895—22no—
174#895D414yescomplemented
175#895D414yescomplemented
176#894—28no—
177#893—28no—
178#892—22no—
179#892—22no—
180D3×C4⋊C4—22no—
181D3×C4⋊C4—22no—
182#884—28no—
183#882—28no—
184#67⋊C4—28no—
185D3×C22⋊C4—28no—
186C3×#103—22no—
187C3×#102—22no—
188C3×C22⋊C8—41no—
189#835—22no—
190#832—22no—
191#830—41no—
192#821—22no—
193#821—22no—
194(C2×D3)⋊C8—22no—
195(C2×D3)⋊C8—22no—
196(C2×D3)⋊C8—22no—
197(C2×D3)⋊C8—22no—
198#809—22no—
199#809—22no—
200C22×#41—31no—
201C23×D4—31no—
202C23×D4—61no—
203C24×C4—31no—
204C22×SD16—31no—
205C22×SD16C2×D311yescharacteristic, complemented
206C22×D8—31no—
207C22×D8—31no—
208#525—64no—
209#525—64no—
210C2×#123—61no—
211C2×C22⋊Q8—31no—
212C2×C22⋊Q8C2×D311yescharacteristic, complemented
213C2×#121—31no—
214C2×#121—31no—
215C2×#121—31no—
216C2×#121—31no—
217C2×#121—31no—
218C2×#121—61no—
219C2×#121—64no—
220C2×#121—64no—
221C2×#121—61no—
222C2×#121C2×D311yescharacteristic
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×#103C2×D311yescharacteristic, complemented
235C2×#102—31no—
236C2×#102—31no—
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—24no—
257C23×D3—21no—
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×Q8—21no—
272C2×C3×Q8—21no—
273C2×C3×Q8—21no—
274C2×C3×Q8—21no—
275C2×C3×Q8—21no—
276C2×C3×Q8C2×D412yescomplemented
277C2×C3×D4—24no—
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×D4C2×D412yes—
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×C4—21no—
295C22×C3×C4C2×D411yescharacteristic
296C22×C3×C4C2411yescharacteristic
297C2×#67—24no—
298C2×#67—24no—
299C2×#67—24no—
300C2×#67—24no—
301C2×#67—42no—
302C2×#67—42no—
303C2×#67—42no—
304C2×#67—42no—
305C2×#67—42no—
306C2×#67—42no—
307C2×#67—42no—
308C2×#67—42no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—22no—
312C22×Dic3—22no—
313C22×Dic3—41no—
314C22×Dic3C2×D411yescharacteristic
315C22×Dic3C2×D411yescharacteristic
316#239—44no—
317#239—44no—
318#239—44no—
319#239—44no—
320D3×D4—44no—
321D3×D4—44no—
322D3×D4—44no—
323D3×D4—44no—
324D3×D4—432no—
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—24no—
334C2×D12—24no—
335C2×D12—24no—
336C2×D12—21no—
337C2×D12—21no—
338C2×D12—42no—
339C2×D12—42no—
340C2×D12—42no—
341C2×D12—42no—
342C2×D12—42no—
343C2×D12—42no—
344C2×D12C2×D412yes—
345C2×D12C2×D412yescomplemented
346C2×C4×D3—21no—
347C2×C4×D3—21no—
348C2×C4×D3—21no—
349C2×C4×D3—21no—
350C2×C4×D3—21no—
351C2×C4×D3—21no—
352C2×C4×D3—21no—
353C2×C4×D3—21no—
354C2×C4×D3—24no—
355C2×C4×D3—24no—
356C2×C4×D3—22no—
357C2×C4×D3—22no—
358C2×C4×D3—22no—
359C2×C4×D3—22no—
360C2×C4×D3—44no—
361C2×C4×D3—44no—
362C2×C4×D3—44no—
363C2×C4×D3—44no—
364C2×C4×D3—41no—
365C2×C4×D3—41no—
366C2×C4×D3—42no—
367C2×C4×D3—42no—
368C2×C4×D3—42no—
369C2×C4×D3—42no—
370C2×C4×D3C2×D412yes—
371C2×C4×D3C2×D412yes—
372C2×C4×D3C2×D412yes—
373C2×C4×D3C2×D412yes—
374C3×SD16—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—24no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—21no—
384C3×C4⋊C4C2×D412yes—
385C3×C4⋊C4C2×D412yescomplemented
386C3×C22⋊C4—24no—
387C3×C22⋊C4—24no—
388#217—24no—
389#215—44no—
390#213—44no—
391(C2×D3)⋊C4—24no—
392(C2×D3)⋊C4—24no—
393(C2×D3)⋊C4—24no—
394(C2×D3)⋊C4—24no—
395(C2×D3)⋊C4—24no—
396(C2×D3)⋊C4—24no—
397C4⋊Dic3—21no—
398C4⋊Dic3—21no—
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—
410D24—44no—
411C25—31no—
412C25—61no—
413C2×#41—62no—
414C2×#41—62no—
415C2×#41—62no—
416C2×#41—62no—
417C2×#41—121no—
418C2×#41—121no—
419C22×Q8C22×D311yescharacteristic
420C22×D4—21no—
421C22×D4—31no—
422C22×D4—31no—
423C22×D4—61no—
424C22×D4—61no—
425C22×D4—61no—
426C22×D4—62no—
427C22×D4—62no—
428C22×D4—61no—
429C22×D4—62no—
430C22×D4—68no—
431C22×D4—61no—
432C22×D4—61no—
433C22×D4—61no—
434C22×D4—62no—
435C22×D4—121no—
436C22×D4—121no—
437C22×D4—124no—
438C22×D4—124no—
439C22×D4C22×D311yescharacteristic
440C23×C4—31no—
441C23×C4—31no—
442C23×C4—31no—
443C23×C4—31no—
444C23×C4—31no—
445C23×C4—61no—
446C23×C4—62no—
447C23×C4—62no—
448C23×C4—62no—
449C23×C4—62no—
450C23×C4—61no—
451C23×C4—121no—
452C23×C4—121no—
453C23×C4C22×D311yescharacteristic
454C2×SD16—22no—
455C2×SD16—22no—
456C2×SD16—41no—
457C2×SD16—62no—
458C2×SD16—62no—
459C2×SD16—121no—
460C2×D8—62no—
461C2×D8—62no—
462C2×D8—62no—
463C2×D8—62no—
464C2×D8—121no—
465C2×D8—121no—
466C22×C8—31no—
467C22×C8—31no—
468C22×C8C22×D311yescharacteristic
469C22×C8C22×D311yescharacteristic
470#123—68no—
471C22⋊Q8—22no—
472C22⋊Q8—22no—
473C22⋊Q8—34no—
474C22⋊Q8—62no—
475#121—22no—
476#121—22no—
477#121—34no—
478#121—34no—
479#121—34no—
480#121—68no—
481#121—62no—
482#121—62no—
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—21no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—62no—
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—22no—
515#103—62no—
516#102—22no—
517#102—62no—
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—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3AGL(1,ℤ/8)12yes—
542C23×C3C22×D411yescharacteristic
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—28no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—44no—
557C22×D3—44no—
558C22×D3—44no—
559C22×D3—44no—
560C22×D3—44no—
561C22×D3—48no—
562C22×D3—48no—
563C22×D3—48no—
564C22×D3—44no—
565C22×D3—41no—
566C22×D3—41no—
567C22×D3—41no—
568C22×D3—41no—
569C22×D3—41no—
570C22×D3—41no—
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×Q8—22no—
586C3×Q8—22no—
587C3×Q8—41no—
588C3×Q8—41no—
589C3×D4—22no—
590C3×D4—22no—
591C3×D4—48no—
592C3×D4—41no—
593C3×D4—41no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—21no—
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×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4C22×D411yescharacteristic
611C2×C3×C4C22×D411yescharacteristic
612C2×C3×C4C22×D411yescharacteristic
613C2×C3×C4C22×D411yescharacteristic
614C2×C3×C4H(5,𝔽2)11yescharacteristic
615C2×C3×C4H(5,𝔽2)11yescharacteristic
616#67—48no—
617#67—48no—
618#67—48no—
619#67—48no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—44no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3#12012yes—
632C2×Dic3#12012yes—
633D12—22no—
634D12—22no—
635D12—22no—
636D12—22no—
637D12—48no—
638D12—48no—
639D12—48no—
640D12—41no—
641D12—41no—
642D12—41no—
643D12—41no—
644C4×D3—22no—
645C4×D3—22no—
646C4×D3—22no—
647C4×D3—22no—
648C4×D3—22no—
649C4×D3—22no—
650C4×D3—22no—
651C4×D3—22no—
652C4×D3—44no—
653C4×D3—44no—
654C4×D3—48no—
655C4×D3—48no—
656C3×C8—41no—
657C3×C8—41no—
658C3⋊C8—41no—
659C3⋊C8—41no—
660C24—21no—
661C24—31no—
662C24—31no—
663C24—62no—
664C24—62no—
665C24—62no—
666C24—62no—
667C24—64no—
668C24—62no—
669C24—61no—
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—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8D3×D412yescomplemented
690C2×D4—24no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—32no—
697C2×D4—32no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—64no—
701C2×D4—64no—
702C2×D4—64no—
703C2×D4—64no—
704C2×D4—64no—
705C2×D4—64no—
706C2×D4—64no—
707C2×D4—61no—
708C2×D4—61no—
709C2×D4—61no—
710C2×D4—61no—
711C2×D4—61no—
712C2×D4—61no—
713C2×D4—61no—
714C2×D4—61no—
715C2×D4—61no—
716C2×D4—61no—
717C2×D4—122no—
718C2×D4—122no—
719C2×D4—122no—
720C2×D4—122no—
721C2×D4—122no—
722C2×D4—122no—
723C2×D4—122no—
724C2×D4—124no—
725C2×D4—124no—
726C2×D4—124no—
727C2×D4—124no—
728C2×D4—122no—
729C2×D4—1232no—
730C2×D4—122no—
731C2×D4—122no—
732C2×D4—122no—
733C2×D4—122no—
734C2×D4—122no—
735C2×D4—122no—
736C2×D4D3×D412yes—
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—21no—
746C22×C4—31no—
747C22×C4—31no—
748C22×C4—32no—
749C22×C4—32no—
750C22×C4—32no—
751C22×C4—32no—
752C22×C4—62no—
753C22×C4—62no—
754C22×C4—62no—
755C22×C4—62no—
756C22×C4—64no—
757C22×C4—64no—
758C22×C4—62no—
759C22×C4—62no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
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—122no—
780C22×C4—121no—
781C22×C4D3×D411yescharacteristic
782C22×C4C23×D311yescharacteristic
783SD16—44no—
784SD16—124no—
785D8—124no—
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—24no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—32no—
803C4⋊C4—32no—
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—81no—
831C22×C3—81no—
832C22×C3—81no—
833C22×C3—81no—
834C22×C3C2×#12011yescharacteristic
835C22×C3C2×#12011yescharacteristic
836C22×C3#53411yescharacteristic
837C22×C3C2×#13511yescharacteristic
838C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
839C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
840C22×C3#57511yescharacteristic
841C2×D3—22no—
842C2×D3—22no—
843C2×D3—22no—
844C2×D3—22no—
845C2×D3—22no—
846C2×D3—22no—
847C2×D3—22no—
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—416no—
851C2×D3—41no—
852C2×D3—41no—
853C2×D3—41no—
854C2×D3—41no—
855C2×D3—42no—
856C2×D3—42no—
857C2×D3—42no—
858C2×D3—42no—
859C2×D3—42no—
860C2×D3—42no—
861C2×D3—816no—
862C2×D3—81no—
863C2×D3—81no—
864C2×D3—81no—
865C2×D3—81no—
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×C4—42no—
875C3×C4D4211yescharacteristic
876C3×C4D4211yescharacteristic
877C3×C4D4211yescharacteristic
878C3×C4D4211yescharacteristic
879Dic3—22no—
880Dic3—22no—
881Dic3—42no—
882Dic3—42no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—21no—
889C23—22no—
890C23—32no—
891C23—32no—
892C23—32no—
893C23—32no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—68no—
901C23—61no—
902C23—61no—
903C23—61no—
904C23—61no—
905C23—61no—
906C23—61no—
907C23—61no—
908C23—61no—
909C23—61no—
910C23—61no—
911C23—62no—
912C23—62no—
913C23—124no—
914C23—124no—
915C23—124no—
916C23—124no—
917C23—124no—
918C23—124no—
919C23—128no—
920C23—128no—
921C23—128no—
922C23—121no—
923C23—121no—
924C23—121no—
925C23—121no—
926C23—121no—
927C23—121no—
928C23—121no—
929C23—121no—
930C23—121no—
931C23—121no—
932C23—121no—
933C23—121no—
934C23—244no—
935C23—244no—
936C23—244no—
937C23—244no—
938C23#91412yes—
939C23C2×D3×D411yescharacteristic
940Q8—22no—
941Q8—22no—
942Q8—41no—
943Q8—41no—
944D4—22no—
945D4—22no—
946D4—48no—
947D4—41no—
948D4—41no—
949D4—62no—
950D4—62no—
951D4—62no—
952D4—62no—
953D4—128no—
954D4—128no—
955D4—128no—
956D4—128no—
957D4—128no—
958D4—128no—
959D4—128no—
960D4—121no—
961D4—121no—
962D4—121no—
963D4—121no—
964C2×C4—22no—
965C2×C4—21no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—32no—
971C2×C4—32no—
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—41no—
982C2×C4—61no—
983C2×C4—61no—
984C2×C4—61no—
985C2×C4—61no—
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—62no—
995C2×C4—62no—
996C2×C4—124no—
997C2×C4—124no—
998C2×C4—128no—
999C2×C4—128no—
1000C2×C4—124no—
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#240311yescharacteristic
1018C2×C3C2×#44911yescharacteristic
1019C2×C3#300211yescharacteristic
1020C2×C3#300311yescharacteristic
1021C2×C3#300611yescharacteristic
1022C2×C3#318811yescharacteristic
1023C2×C3#319411yescharacteristic
1024D3—24no—
1025D3—42no—
1026D3—82no—
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—62no—
1040C22—62no—
1041C22—62no—
1042C22—62no—
1043C22—62no—
1044C22—62no—
1045C22—62no—
1046C22—62no—
1047C22—62no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—81no—
1052C22—1216no—
1053C22—121no—
1054C22—121no—
1055C22—121no—
1056C22—121no—
1057C22—122no—
1058C22—122no—
1059C22—122no—
1060C22—122no—
1061C22—122no—
1062C22—122no—
1063C22—2416no—
1064C22—241no—
1065C22—241no—
1066C22—241no—
1067C22—241no—
1068C22—241no—
1069C22—241no—
1070C22—241no—
1071C22—241no—
1072C22D3×#12011yescharacteristic
1073C22D3×#12011yescharacteristic
1074C22#560511yescharacteristic
1075C22C2×#91411yescharacteristic
1076C22D3×#13511yescharacteristic
1077C22D3×AGL(1,ℤ/8)11yescharacteristic
1078C22#577711yescharacteristic
1079C4—42no—
1080C4—41no—
1081C4—42no—
1082C4—42no—
1083C4—62no—
1084C4—62no—
1085C4—122no—
1086C4—122no—
1087C4#559011yescharacteristic
1088C4#560911yescharacteristic
1089C4#560911yescharacteristic
1090C4#571711yescharacteristic
1091C3#2392011yescharacteristic, complemented, Sylow
1092C2—42no—
1093C2—64no—
1094C2—82no—
1095C2—122no—
1096C2—242no—
1097C2—242no—
1098C2#7675311yescharacteristic
1099C2#8004011yescharacteristic
1100C2D3×#44911yescharacteristic
1101C2#8014611yescharacteristic
1102C2#8022611yescharacteristic
1103C2#8066411yescharacteristic
1104C2#8081211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
hypercenter#2000D3
hypocenterC3#23920
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×#5627C2semidirect
2. C2×D3×#121C2semidirect
3. C2×#5172C2semidirect
4. C2×#5169C2semidirect
5. C2×#4810C2semidirect
6. C2×#4773C2semidirect
7. C3×#2000C2semidirect
8. #71699C2semidirect
9. #71684C2semidirect
10. #70268C2semidirect
11. #70201C2semidirect
12. #69961C2semidirect
13. #69955C2semidirect
14. #68881C2semidirect
15. #68880C2semidirect
17. C22×#239C22semidirect
21. C22×C3×SD16C22semidirect
22. C2×C3×C22⋊Q8C22semidirect
25. C22×#215C22semidirect
28. C22×#213C22semidirect
30. C2×#930C22semidirect
31. C22×D24C22semidirect
40. C2×#892C22semidirect
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
55. C2×#821C22semidirect
58. C2×(C2×D3)⋊C8C22semidirect
59. C2×(C2×D3)⋊C8C22semidirect
60. C2×#809C22semidirect
61. C2×#809C22semidirect
64. C3×#340C22semidirect
65. #4551C22semidirect
66. #4529C22semidirect
67. #4529C22semidirect
75. #2000D3semidirect
142. #946D4semidirect
148. #938D4semidirect
174. #895D4semidirect
175. #895D4semidirect
205. C22×SD16C2×D3semidirect
212. C2×C22⋊Q8C2×D3semidirect
234. C2×#103C2×D3semidirect
240. C2×#102C2×D3semidirect
246. C2×C22⋊C8C2×D3semidirect
250. #340C2×D3semidirect
276. C2×C3×Q8C2×D4semidirect
345. C2×D12C2×D4semidirect
385. C3×C4⋊C4C2×D4semidirect
400. C4⋊Dic3C2×D4semidirect
689. C2×Q8D3×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×#56272
C2×D3×#1212
C2×#51722
C2×#51692
C2×#48102
C2×#47732
C3×#20002
#716992
#716842
#702682
#702012
#699612
#699552
#688812
#688802
#239203