Finite Group Databasebeta

← #10826947

Subgroups — #10826947

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×#5524C211yesmaximal, characteristic, complemented
3C2×#5037C211yesmaximal, characteristic, complemented
4C2×#4776C211yesmaximal, characteristic, complemented
5C2×#4773C211yesmaximal, characteristic, complemented
6C2×#4734C211yesmaximal, characteristic, complemented
7C3×#1875C211yesmaximal, characteristic, complemented
8#71586C211yesmaximal, characteristic, complemented
9#70205C211yesmaximal, characteristic, complemented
10#70204C211yesmaximal, characteristic, complemented
11#69955C211yesmaximal, characteristic, complemented
12#68887C211yesmaximal, characteristic, complemented
13#68886C211yesmaximal, characteristic, complemented
14#68880C211yesmaximal, characteristic, complemented
15#68878C211yesmaximal, characteristic, complemented
16#23920—31nomaximal, Sylow
17C22×D3×D4—21no—
18C22×D3×D4C2211yescharacteristic
19C22×#235C2211yescharacteristic, complemented
20C23×C4×D3C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×C3×#117C2211yescharacteristic, complemented
23C2×#939—21no—
24C2×#938C2211yescharacteristic
25C22×#214C2211yescharacteristic, complemented
26C22×#213C2211yescharacteristic, complemented
27C2×#930C2211yescharacteristic
28C22×D24C2211yescharacteristic, complemented
29C22×#204C2211yescharacteristic, complemented
30D3×#121—24no—
31D3×#121—24no—
32#5524—24no—
33#5524—24no—
34C2×#897C2211yescharacteristic
35C2×#897C2211yescharacteristic, complemented
36C2×#895C2211yescharacteristic
37C2×#895C2211yescharacteristic
38C2×#895C2211yescharacteristic, complemented
39C2×D3×C4⋊C4C2211yescharacteristic
40C2×#886—21no—
41C2×#884—21no—
42C2×#882—21no—
43C2×D3×C22⋊C4—21no—
44C2×C4×D12—21no—
45C2×C4×D12—21no—
46C2×C3×#102C2211yescharacteristic, complemented
47C2×C3×#102C2211yescharacteristic, complemented
48C2×C3×C22⋊C8C2211yescharacteristic, complemented
49C2×#830C2211yescharacteristic, complemented
50C2×#821C2211yescharacteristic, complemented
51C2×(C2×D3)⋊C8C2211yescharacteristic
52C2×(C2×D3)⋊C8C2211yescharacteristic
53C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
54C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
55C2×#816C2211yescharacteristic, complemented
56#5037—24no—
57C2×#810C2211yescharacteristic, complemented
58C2×#809C2211yescharacteristic, complemented
59C2×#809C2211yescharacteristic, complemented
60C2×#809C2211yescharacteristic, complemented
61#4776—24no—
62#4773—24no—
63#4734—24no—
64C3×#340C2211yescharacteristic, complemented
65C3×#340C2211yescharacteristic, 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#1999—31no—
78#1875—31no—
79#1875D311yescharacteristic, complemented
80#1874—31no—
81#1872—31no—
82#1779—31no—
83C24×D3—21no—
84C24×D3D411yescharacteristic
85C22×C3×D4—21no—
86C22×C3×D4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C22×#67—21no—
89C22×#67—21no—
90C22×#67—21no—
91C22×#67—21no—
92C23×Dic3D411yescharacteristic
93C2×D3×D4—28no—
94C2×D3×D4—22no—
95C2×D3×D4—22no—
96C2×D3×D4—22no—
97C2×D3×D4—22no—
98C2×D3×D4—41no—
99C2×D3×D4—41no—
100C2×D3×D4—44no—
101C2×D3×D4—44no—
102C2×#235—22no—
103C2×#235—22no—
104C2×#235—22no—
105C2×#235—22no—
106C2×#235—41no—
107C2×#235—41no—
108C22×D12—21no—
109C22×D12—21no—
110C22×D12—21no—
111C22×D12C2311yescharacteristic
112C22×D12C2311yescharacteristic
113C22×C4×D3—21no—
114C22×C4×D3—22no—
115C22×C4×D3—22no—
116C22×C4×D3—21no—
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
126C22×C3×C8C2311yescharacteristic
127C22×C3×C8C2311yescharacteristic
128C3×#121—22no—
129C3×#121D414yescomplemented
130C3×#117—22no—
131C3×#117—22no—
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C42—21no—
138C2×#217—21no—
139#939—28no—
140#938—22no—
141#938—22no—
142C2×#214—22no—
143C2×#214—22no—
144C2×#214—41no—
145C2×#213—22no—
146C2×#213—22no—
147C2×#213—41no—
148#930—22no—
149#930D414yescomplemented
150C2×(C2×D3)⋊C4—21no—
151C2×(C2×D3)⋊C4—21no—
152C2×(C2×D3)⋊C4—21no—
153C2×(C2×D3)⋊C4—21no—
154C2×(C2×D3)⋊C4—21no—
155C2×(C2×D3)⋊C4—21no—
156C2×C4⋊Dic3—21no—
157C2×C4⋊Dic3—21no—
158C2×C4⋊Dic3C2311yescharacteristic
159C2×Dic3⋊C4—21no—
160C22×C3⋊C8C2311yescharacteristic
161C22×C3⋊C8C2311yescharacteristic
162C2×D24—22no—
163C2×D24—22no—
164C2×D24—41no—
165C2×#204—22no—
166C2×#204—22no—
167C2×#204—41no—
168#897—22no—
169#897—22no—
170#897—22no—
171#897D414yescomplemented
172#895—22no—
173#895—22no—
174#895—22no—
175#895—22no—
176#895—22no—
177#895D414yescomplemented
178D3×C4⋊C4—22no—
179D3×C4⋊C4—22no—
180#886—28no—
181#884—28no—
182#882—28no—
183D3×C22⋊C4—28no—
184C4×D12—28no—
185C4×D12—28no—
186C3×#102—22no—
187C3×#102—22no—
188C3×C22⋊C8—22no—
189#830—22no—
190#821—22no—
191(C2×D3)⋊C8—22no—
192(C2×D3)⋊C8—22no—
193(C2×D3)⋊C8—41no—
194(C2×D3)⋊C8—41no—
195#816—22no—
196#810—22no—
197#809—22no—
198#809—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×D8—31no—
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—31no—
218C2×#121—61no—
219C2×#121—64no—
220C2×#121—61no—
221C2×#121—64no—
222C2×#121C2×D311yescharacteristic
223C2×#120—61no—
224C2×C4×D4—61no—
225C2×C4×D4—61no—
226C2×#117C2×D311yescharacteristic, complemented
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#340C2×D311yescharacteristic, complemented
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×D4—24no—
272C2×C3×D4—21no—
273C2×C3×D4—21no—
274C2×C3×D4—21no—
275C2×C3×D4—21no—
276C2×C3×D4—21no—
277C2×C3×D4—42no—
278C2×C3×D4—42no—
279C2×C3×D4C2×D412yes—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4C2×D412yes—
288C22×C3×C4C2×D411yescharacteristic
289C22×C3×C4C2×D412yes—
290C22×C3×C4C2411yescharacteristic
291C2×#67—24no—
292C2×#67—24no—
293C2×#67—24no—
294C2×#67—24no—
295C2×#67—42no—
296C2×#67—42no—
297C2×#67—42no—
298C2×#67—42no—
299C2×#67—42no—
300C2×#67—42no—
301C2×#67—42no—
302C2×#67—42no—
303C22×Dic3—22no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—22no—
307C22×Dic3—41no—
308C22×Dic3C2×D411yescharacteristic
309C22×Dic3C2×D411yescharacteristic
310D3×D4—44no—
311D3×D4—44no—
312D3×D4—44no—
313D3×D4—44no—
314D3×D4—432no—
315#235—44no—
316#235—44no—
317#235—44no—
318#235—44no—
319C2×D12—21no—
320C2×D12—21no—
321C2×D12—21no—
322C2×D12—21no—
323C2×D12—21no—
324C2×D12—21no—
325C2×D12—21no—
326C2×D12—21no—
327C2×D12—24no—
328C2×D12—24no—
329C2×D12—24no—
330C2×D12—21no—
331C2×D12—21no—
332C2×D12—42no—
333C2×D12—42no—
334C2×D12—42no—
335C2×D12—42no—
336C2×D12—42no—
337C2×D12—42no—
338C2×D12C2×D412yes—
339C2×D12C2×D412yescomplemented
340C2×C4×D3—21no—
341C2×C4×D3—21no—
342C2×C4×D3—21no—
343C2×C4×D3—21no—
344C2×C4×D3—24no—
345C2×C4×D3—24no—
346C2×C4×D3—22no—
347C2×C4×D3—22no—
348C2×C4×D3—22no—
349C2×C4×D3—21no—
350C2×C4×D3—21no—
351C2×C4×D3—21no—
352C2×C4×D3—21no—
353C2×C4×D3—21no—
354C2×C4×D3—21no—
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×D3—42no—
365C2×C4×D3—42no—
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
374C2×C3×C8—21no—
375C2×C3×C8—21no—
376C2×C3×C8—21no—
377C2×C3×C8—21no—
378C2×C3×C8—21no—
379C2×C3×C8—21no—
380C3×C4⋊C4—21no—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4C2×D412yes—
384C3×C4⋊C4C2×D412yescomplemented
385C3×C4⋊C4C2×D412yescomplemented
386C3×C22⋊C4—24no—
387C3×C22⋊C4—24no—
388C3×C42—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—
396(C2×D3)⋊C4—24no—
397(C2×D3)⋊C4—24no—
398C4⋊Dic3—24no—
399C4⋊Dic3—21no—
400C4⋊Dic3—24no—
401C4⋊Dic3C2×D412yes—
402Dic3⋊C4—24no—
403C2×C3⋊C8—21no—
404C2×C3⋊C8—21no—
405C2×C3⋊C8—21no—
406C2×C3⋊C8—21no—
407C2×C3⋊C8—21no—
408C2×C3⋊C8—21no—
409D24—44no—
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—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—62no—
446C23×C4—62no—
447C23×C4—61no—
448C23×C4—62no—
449C23×C4—61no—
450C23×C4—62no—
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—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—34no—
472C22⋊Q8—62no—
473C22⋊Q8—62no—
474C22⋊Q8—62no—
475#121—22no—
476#121—34no—
477#121—34no—
478#121—68no—
479#121—62no—
480#121—62no—
481#121—62no—
482#121—62no—
483#121—68no—
484#121—62no—
485#121—62no—
486#121—62no—
487#121—62no—
488#121D1214yescomplemented
489#120—68no—
490C4×D4—68no—
491C4×D4—68no—
492#117—22no—
493#117—22no—
494C2×C4⋊C4—31no—
495C2×C4⋊C4—62no—
496C2×C4⋊C4—61no—
497C2×C4⋊C4—61no—
498C2×C4⋊C4—61no—
499C2×C4⋊C4—62no—
500C2×C4⋊C4C22×D311yescharacteristic
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—21no—
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—22no—
523C22⋊C8—62no—
524C22⋊C8—62no—
525C22⋊C8—62no—
526C22⋊C8—121no—
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×C3#12012yes—
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#13512yes—
583C22×D3AGL(1,ℤ/8)12yes—
584C22×D3AGL(1,ℤ/8)12yes—
585C3×D4—22no—
586C3×D4—22no—
587C3×D4—48no—
588C3×D4—41no—
589C3×D4—41no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4#12012yes—
606C2×C3×C4C22×D411yescharacteristic
607C2×C3×C4C22×D411yescharacteristic
608C2×C3×C4C22×D411yescharacteristic
609C2×C3×C4C22×D411yescharacteristic
610C2×C3×C4H(5,𝔽2)11yescharacteristic
611C2×C3×C4H(5,𝔽2)11yescharacteristic
612#67—48no—
613#67—48no—
614#67—48no—
615#67—48no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—44no—
624C2×Dic3—41no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3#12012yes—
629D12—22no—
630D12—22no—
631D12—22no—
632D12—22no—
633D12—48no—
634D12—48no—
635D12—48no—
636D12—41no—
637D12—41no—
638D12—41no—
639D12—41no—
640C4×D3—22no—
641C4×D3—22no—
642C4×D3—22no—
643C4×D3—22no—
644C4×D3—44no—
645C4×D3—44no—
646C4×D3—48no—
647C4×D3—48no—
648C4×D3—41no—
649C4×D3—41no—
650C4×D3—41no—
651C4×D3—41no—
652Dic6—22no—
653Dic6—22no—
654Dic6—41no—
655Dic6—41no—
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—32no—
685C2×Q8—61no—
686C2×Q8—61no—
687C2×Q8—61no—
688C2×Q8—61no—
689C2×Q8—61no—
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×D4C2×D1212yes—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—31no—
745C22×C4—32no—
746C22×C4—32no—
747C22×C4—31no—
748C22×C4—62no—
749C22×C4—62no—
750C22×C4—64no—
751C22×C4—64no—
752C22×C4—62no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—62no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—62no—
761C22×C4—62no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—121no—
769C22×C4—121no—
770C22×C4—124no—
771C22×C4—124no—
772C22×C4—124no—
773C22×C4—124no—
774C22×C4—122no—
775C22×C4—122no—
776C22×C4—122no—
777C22×C4—121no—
778C22×C4—122no—
779C22×C4C2×D1212yes—
780C22×C4D3×D411yescharacteristic
781C22×C4D3×D412yes—
782C22×C4C23×D311yescharacteristic
783SD16—124no—
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—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—32no—
803C4⋊C4—64no—
804C4⋊C4—64no—
805C4⋊C4—64no—
806C4⋊C4—61no—
807C4⋊C4C2×D1212yes—
808C4⋊C4D3×D412yescomplemented
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—24no—
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—22no—
872C3×C4—42no—
873C3×C4—42no—
874C3×C4—42no—
875C3×C4D4211yescharacteristic
876C3×C4D4211yescharacteristic
877C3×C4D4211yescharacteristic
878C3×C4D4211yescharacteristic
879Dic3—22no—
880Dic3—42no—
881Dic3—41no—
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#88212yes—
939C23C2×D3×D411yescharacteristic
940Q8—62no—
941Q8—62no—
942Q8—121no—
943Q8—121no—
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—21no—
965C2×C4—21no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—32no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—62no—
983C2×C4—62no—
984C2×C4—62no—
985C2×C4—62no—
986C2×C4—61no—
987C2×C4—61no—
988C2×C4—62no—
989C2×C4—61no—
990C2×C4—62no—
991C2×C4—124no—
992C2×C4—124no—
993C2×C4—128no—
994C2×C4—128no—
995C2×C4—124no—
996C2×C4—121no—
997C2×C4—121no—
998C2×C4—121no—
999C2×C4—121no—
1000C2×C4—121no—
1001C2×C4—121no—
1002C2×C4—121no—
1003C2×C4—121no—
1004C2×C4#88212yes—
1005C2×C4C22×D1211yescharacteristic
1006C2×C4C2×D3×D411yescharacteristic
1007C2×C4C2×D3×D411yescharacteristic
1008C2×C4C2×D3×D411yescharacteristic
1009C2×C4#100911yescharacteristic
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—
1072C22C2×#88211yescharacteristic
1073C22D3×#12011yescharacteristic
1074C22#565311yescharacteristic
1075C22D3×#13511yescharacteristic
1076C22#576811yescharacteristic
1077C22D3×AGL(1,ℤ/8)11yescharacteristic
1078C22D3×AGL(1,ℤ/8)11yescharacteristic
1079C4—22no—
1080C4—42no—
1081C4—42no—
1082C4—42no—
1083C4—62no—
1084C4—122no—
1085C4—121no—
1086C4—122no—
1087C4D4×D1211yescharacteristic
1088C4D4×D1211yescharacteristic
1089C4#560911yescharacteristic
1090C4#560911yescharacteristic
1091C3#2392011yescharacteristic, complemented, Sylow
1092C2—42no—
1093C2—64no—
1094C2—82no—
1095C2—122no—
1096C2—242no—
1097C2—242no—
1098C2#7488411yescharacteristic
1099C2#7883311yescharacteristic
1100C2#7892611yescharacteristic
1101C2D3×#44911yescharacteristic
1102C2#8008411yescharacteristic
1103C2#8137811yescharacteristic
1104C2#8137911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1875C2
socleC23×C3C22×D4
hypercenter#1875D3
hypocenterC3#23920
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
1. C2×D3×#121C2semidirect
2. C2×#5524C2semidirect
3. C2×#5037C2semidirect
4. C2×#4776C2semidirect
5. C2×#4773C2semidirect
6. C2×#4734C2semidirect
7. C3×#1875C2semidirect
8. #71586C2semidirect
9. #70205C2semidirect
10. #70204C2semidirect
11. #69955C2semidirect
12. #68887C2semidirect
13. #68886C2semidirect
14. #68880C2semidirect
15. #68878C2semidirect
19. C22×#235C22semidirect
22. C2×C3×#117C22semidirect
25. C22×#214C22semidirect
26. C22×#213C22semidirect
28. C22×D24C22semidirect
29. C22×#204C22semidirect
35. C2×#897C22semidirect
38. C2×#895C22semidirect
46. C2×C3×#102C22semidirect
47. C2×C3×#102C22semidirect
48. C2×C3×C22⋊C8C22semidirect
49. C2×#830C22semidirect
50. C2×#821C22semidirect
53. C2×(C2×D3)⋊C8C22semidirect
54. C2×(C2×D3)⋊C8C22semidirect
55. C2×#816C22semidirect
57. C2×#810C22semidirect
58. C2×#809C22semidirect
59. C2×#809C22semidirect
60. C2×#809C22semidirect
64. C3×#340C22semidirect
65. C3×#340C22semidirect
66. #4529C22semidirect
67. #4529C22semidirect
79. #1875D3semidirect
129. C3×#121D4semidirect
149. #930D4semidirect
171. #897D4semidirect
177. #895D4semidirect
226. C2×#117C2×D3semidirect
239. C2×#102C2×D3semidirect
240. C2×#102C2×D3semidirect
246. C2×C22⋊C8C2×D3semidirect
249. #340C2×D3semidirect
250. #340C2×D3semidirect
339. C2×D12C2×D4semidirect
373. C2×Dic6C2×D4semidirect
384. C3×C4⋊C4C2×D4semidirect
385. C3×C4⋊C4C2×D4semidirect
488. #121D12semidirect
808. C4⋊C4D3×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×#55242
C2×#50372
C2×#47762
C2×#47732
C2×#47342
C3×#18752
#715862
#702052
#702042
#699552
#688872
#688862
#688802
#688782
#239203