Finite Group Databasebeta

← #10826934

Subgroups — #10826934

Order 768.

2252 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×#895C211yesmaximal, characteristic
3C2×#5046C211yesmaximal, characteristic, complemented
4C2×#4806C212yesmaximal, complemented
5C2×#4731C211yesmaximal, characteristic, complemented
6C3×#1872C211yesmaximal, characteristic, complemented
7#71559C211yesmaximal, characteristic, complemented
8#70272C212yesmaximal, complemented
9#69955C211yesmaximal, characteristic, complemented
10#68887C212yesmaximal, complemented
11#68880C212yesmaximal, complemented
12#23919—31nomaximal, Sylow
13C22×D3×Q8C2211yescharacteristic, complemented
14C23×D12—21no—
15C23×D12C2211yescharacteristic
16C23×C4×D3C2211yescharacteristic
17C2×C3×C22⋊Q8C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C2×#946C2211yescharacteristic, complemented
20C22×#215C2212yescomplemented
21C22×(C2×D3)⋊C4—21no—
22C2×#924C2211yescharacteristic
23C22×#204C2212yescomplemented
24D3×C22⋊Q8—24no—
25D3×C22⋊Q8—24no—
26C2×#897C2211yescharacteristic, complemented
27C2×#896—21no—
28C2×#895—21no—
29C2×#895—21no—
30C2×#895—28no—
31C2×#895C2212yes—
32C2×#895C2212yes—
33C2×D3×C4⋊C4—21no—
34C2×D3×C4⋊C4C2211yescharacteristic, complemented
35C2×D3×C22⋊C4—21no—
36C2×#878—21no—
37C2×C3×#103C2212yescomplemented
38C2×C3×C22⋊C8C2211yescharacteristic
39C2×#830C2211yescharacteristic
40C2×#821C2212yescomplemented
41C2×(C2×D3)⋊C8C2212yescomplemented
42C2×(C2×D3)⋊C8C2212yescomplemented
43#5046—24no—
44C2×#810C2212yescomplemented
45C2×#809C2212yescomplemented
46#4806—28no—
47#4731—24no—
48C3×#340C2212yescomplemented
49#4529C2212yescomplemented
50C22×C22⋊Q8—31no—
51C22×#121—31no—
52C2×#448—32no—
53C2×#450—31no—
54C2×#450—31no—
55#2000—32no—
56#2000—32no—
57#1874—32no—
58#1872—31no—
59#1872D311yescharacteristic, complemented
60#1779—31no—
61C24×D3—21no—
62C24×D3D411yescharacteristic
63C22×C3×Q8C2311yescharacteristic
64C23×C3×C4—21no—
65C23×C3×C4C2311yescharacteristic
66C23×Dic3D411yescharacteristic
67C2×D3×Q8—22no—
68C2×D3×Q8—22no—
69C2×D3×Q8—24no—
70C2×D3×Q8—42no—
71C22×D12—28no—
72C22×D12—22no—
73C22×D12—22no—
74C22×D12—21no—
75C22×D12—24no—
76C22×D12—22no—
77C22×D12—22no—
78C22×D12—42no—
79C22×D12—44no—
80C22×D12—44no—
81C22×D12C2312yes—
82C22×C4×D3—21no—
83C22×C4×D3—21no—
84C22×C4×D3—22no—
85C22×C4×D3—22no—
86C22×C4×D3—24no—
87C22×C4×D3—42no—
88C22×C4×D3D411yescharacteristic
89C22×C4×D3D411yescharacteristic
90C22×C4×D3C2311yescharacteristic
91C22×C4×D3C2311yescharacteristic
92C22×Dic6—21no—
93C22×Dic6C2311yescharacteristic
94C22×C3×C8C2312yes—
95C3×C22⋊Q8—22no—
96C3×C22⋊Q8D414yescomplemented
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4—21no—
99C2×C3×C4⋊C4—24no—
100C2×C3×C4⋊C4C2312yes—
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C22⋊C4—21no—
103C2×#217—21no—
104#946—22no—
105#946—22no—
106C2×#215—24no—
107C2×#215—24no—
108C2×#215—42no—
109C2×(C2×D3)⋊C4—28no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—22no—
113C2×(C2×D3)⋊C4—22no—
114C2×C4⋊Dic3—21no—
115C2×C4⋊Dic3C2311yescharacteristic
116#924—22no—
117#924D414yescomplemented
118C2×Dic3⋊C4—21no—
119C2×Dic3⋊C4—21no—
120C2×Dic3⋊C4—21no—
121C22×C3⋊C8C2312yes—
122C2×#204—24no—
123C2×#204—24no—
124C2×#204—42no—
125#897—22no—
126#897—22no—
127#896—28no—
128#895—28no—
129#895—28no—
130#895—24no—
131#895—24no—
132#895—24no—
133#895D418yes—
134D3×C4⋊C4—28no—
135D3×C4⋊C4—22no—
136D3×C4⋊C4—22no—
137D3×C22⋊C4—28no—
138#878—28no—
139C3×#103—24no—
140C3×C22⋊C8—22no—
141#830—22no—
142#821—24no—
143(C2×D3)⋊C8—24no—
144(C2×D3)⋊C8—42no—
145#810—24no—
146#809—24no—
147C23×Q8—31no—
148C23×D4—31no—
149C23×D4—61no—
150C24×C4—31no—
151C22×SD16—32no—
152C22×SD16—32no—
153C2×C22⋊Q8—31no—
154C2×C22⋊Q8—31no—
155C2×C22⋊Q8—31no—
156C2×C22⋊Q8—61no—
157C2×C22⋊Q8—61no—
158C2×C22⋊Q8—64no—
159C2×C22⋊Q8—64no—
160C2×C22⋊Q8C2×D311yescharacteristic
161C2×#121—32no—
162C2×#121—32no—
163C2×#121—68no—
164C2×#121—61no—
165C2×#121—61no—
166C22×C4⋊C4—31no—
167C22×C4⋊C4—61no—
168C22×C4⋊C4C2×D311yescharacteristic
169C22×C22⋊C4—61no—
170C22×C22⋊C4—61no—
171#450—64no—
172#450—64no—
173#448—68no—
174C2×#103—32no—
175C2×#103C2×D312yescomplemented
176C2×#102—32no—
177C2×#102—32no—
178C2×C22⋊C8—31no—
179C2×C22⋊C8—32no—
180C2×C22⋊C8—32no—
181C2×C22⋊C8C2×D311yescharacteristic
182#340—32no—
183#340C2×D312yescomplemented
184C24×C3C2×D411yescharacteristic
185C23×D3—22no—
186C23×D3—22no—
187C23×D3—22no—
188C23×D3—22no—
189C23×D3—24no—
190C23×D3—22no—
191C23×D3—41no—
192C23×D3—41no—
193C23×D3—42no—
194C23×D3—42no—
195C23×D3—42no—
196C23×D3—42no—
197C23×D3—42no—
198C23×D3—42no—
199C23×D3SD1614yescomplemented
200C23×D3C2×D411yescharacteristic
201C23×D3C2×D411yescharacteristic
202C2×C3×Q8—21no—
203C2×C3×Q8—22no—
204C2×C3×Q8—22no—
205C2×C3×Q8C2×D412yescomplemented
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—24no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—22no—
212C22×C3×C4—42no—
213C22×C3×C4—42no—
214C22×C3×C4C2×D412yes—
215C22×C3×C4C2×D411yescharacteristic
216C22×C3×C4C2×D412yes—
217C22×C3×C4C2411yescharacteristic
218C22×Dic3—22no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—22no—
222C22×Dic3—41no—
223C22×Dic3C2×D411yescharacteristic
224C22×Dic3C2×D411yescharacteristic
225D3×Q8—48no—
226D3×Q8—48no—
227C2×D12—22no—
228C2×D12—22no—
229C2×D12—22no—
230C2×D12—22no—
231C2×D12—24no—
232C2×D12—28no—
233C2×D12—28no—
234C2×D12—22no—
235C2×D12—48no—
236C2×D12—48no—
237C2×D12—42no—
238C2×D12—44no—
239C2×D12—432no—
240C2×D12—44no—
241C2×D12—44no—
242C2×D12—44no—
243C2×D12—42no—
244C2×D12C2×D414yes—
245C2×C4×D3—21no—
246C2×C4×D3—21no—
247C2×C4×D3—22no—
248C2×C4×D3—24no—
249C2×C4×D3—24no—
250C2×C4×D3—22no—
251C2×C4×D3—22no—
252C2×C4×D3—22no—
253C2×C4×D3—22no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—22no—
257C2×C4×D3—22no—
258C2×C4×D3—48no—
259C2×C4×D3—48no—
260C2×C4×D3—41no—
261C2×C4×D3—41no—
262C2×C4×D3—42no—
263C2×C4×D3—42no—
264C2×C4×D3—42no—
265C2×C4×D3—42no—
266C2×C4×D3C2×D414yes—
267C2×Dic6—22no—
268C2×Dic6—22no—
269C2×Dic6—24no—
270C2×Dic6—21no—
271C2×Dic6—42no—
272C2×Dic6—42no—
273C2×Dic6C2×D412yescomplemented
274C2×C3×C8—22no—
275C2×C3×C8—22no—
276C2×C3×C8—22no—
277C3×C4⋊C4—24no—
278C3×C4⋊C4—24no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—22no—
281C3×C4⋊C4C2×D414yes—
282C3×C4⋊C4C2×D412yescomplemented
283C3×C22⋊C4—24no—
284#217—24no—
285#215—48no—
286(C2×D3)⋊C4—24no—
287(C2×D3)⋊C4—24no—
288(C2×D3)⋊C4—28no—
289(C2×D3)⋊C4—28no—
290C4⋊Dic3—24no—
291C4⋊Dic3—21no—
292C4⋊Dic3C2×D412yescomplemented
293Dic3⋊C4—24no—
294Dic3⋊C4—24no—
295Dic3⋊C4—24no—
296C2×C3⋊C8—22no—
297C2×C3⋊C8—22no—
298C2×C3⋊C8—22no—
299#204—48no—
300C25—31no—
301C25—61no—
302C22×Q8—31no—
303C22×Q8—61no—
304C22×Q8—64no—
305C22×Q8—62no—
306C22×Q8—62no—
307C22×Q8—122no—
308C22×Q8C22×D311yescharacteristic
309C22×D4—32no—
310C22×D4—64no—
311C22×D4—62no—
312C22×D4—62no—
313C22×D4—68no—
314C22×D4—62no—
315C22×D4—61no—
316C22×D4—62no—
317C22×D4—122no—
318C22×D4—124no—
319C22×D4—124no—
320C23×C4—21no—
321C23×C4—31no—
322C23×C4—31no—
323C23×C4—31no—
324C23×C4—31no—
325C23×C4—31no—
326C23×C4—64no—
327C23×C4—61no—
328C23×C4—61no—
329C23×C4—62no—
330C23×C4—62no—
331C23×C4—122no—
332C23×C4C22×D311yescharacteristic
333C2×SD16—64no—
334C2×SD16—64no—
335C2×SD16—64no—
336C2×SD16—64no—
337C2×SD16—122no—
338C2×SD16—122no—
339C22×C8—32no—
340C22×C8C22×D312yes—
341C22⋊Q8—22no—
342C22⋊Q8—34no—
343C22⋊Q8—68no—
344C22⋊Q8—62no—
345C22⋊Q8—68no—
346C22⋊Q8—62no—
347C22⋊Q8—62no—
348C22⋊Q8—62no—
349C22⋊Q8—62no—
350C22⋊Q8D1214yescomplemented
351#121—38no—
352#121—64no—
353#121—64no—
354#121—68no—
355#121—68no—
356#121—64no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—62no—
362C2×C4⋊C4—68no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4—62no—
368C2×C4⋊C4C22×D311yescharacteristic
369C2×C4⋊C4C22×D312yes—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—68no—
372C2×C22⋊C4—62no—
373C2×C22⋊C4—62no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—68no—
377C2×C22⋊C4—61no—
378#103—24no—
379#103—64no—
380#102—64no—
381#102—64no—
382C22⋊C8—22no—
383C22⋊C8—64no—
384C22⋊C8—62no—
385C22⋊C8—122no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3#12012yes—
391C23×C3C2×SD1612yes—
392C23×C3#13712yes—
393C23×C3C22×D411yescharacteristic
394C22×D3—21no—
395C22×D3—21no—
396C22×D3—21no—
397C22×D3—21no—
398C22×D3—21no—
399C22×D3—21no—
400C22×D3—21no—
401C22×D3—21no—
402C22×D3—21no—
403C22×D3—21no—
404C22×D3—28no—
405C22×D3—28no—
406C22×D3—24no—
407C22×D3—44no—
408C22×D3—44no—
409C22×D3—44no—
410C22×D3—44no—
411C22×D3—44no—
412C22×D3—48no—
413C22×D3—48no—
414C22×D3—48no—
415C22×D3—42no—
416C22×D3—42no—
417C22×D3—42no—
418C22×D3—42no—
419C22×D3—42no—
420C22×D3—42no—
421C22×D3—84no—
422C22×D3—84no—
423C22×D3—84no—
424C22×D3—84no—
425C22×D3#12012yes—
426C22×D3C2×SD1612yes—
427C22×D3C2×SD1612yes—
428C22×D3AGL(1,ℤ/8)12yes—
429C3×Q8—24no—
430C3×Q8—42no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—24no—
434C2×C3×C4—24no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—24no—
438C2×C3×C4—48no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—42no—
442C2×C3×C4—41no—
443C2×C3×C4—42no—
444C2×C3×C4—41no—
445C2×C3×C4#12012yes—
446C2×C3×C4C22×D411yescharacteristic
447C2×C3×C4C22×D412yes—
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4H(5,𝔽2)12yes—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—22no—
453C2×Dic3—21no—
454C2×Dic3—22no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—44no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3#12012yes—
463D12—24no—
464D12—24no—
465D12—48no—
466D12—416no—
467D12—416no—
468D12—42no—
469D12—42no—
470C4×D3—24no—
471C4×D3—24no—
472C4×D3—44no—
473C4×D3—44no—
474C4×D3—48no—
475C4×D3—48no—
476C4×D3—42no—
477C4×D3—42no—
478Dic6—24no—
479Dic6—48no—
480Dic6—42no—
481C3×C8—42no—
482C3⋊C8—42no—
483C24—31no—
484C24—31no—
485C24—34no—
486C24—62no—
487C24—62no—
488C24—64no—
489C24—62no—
490C24—62no—
491C24—62no—
492C24—121no—
493C24—121no—
494C24—122no—
495C24—122no—
496C24—122no—
497C24—122no—
498C24—122no—
499C24—122no—
500C24D3×D411yescharacteristic
501C2×Q8—21no—
502C2×Q8—22no—
503C2×Q8—22no—
504C2×Q8—32no—
505C2×Q8—64no—
506C2×Q8—61no—
507C2×Q8—62no—
508C2×Q8—62no—
509C2×Q8—122no—
510C2×Q8—122no—
511C2×Q8—128no—
512C2×Q8—128no—
513C2×Q8C2×D1212yescomplemented
514C2×D4—34no—
515C2×D4—68no—
516C2×D4—64no—
517C2×D4—68no—
518C2×D4—62no—
519C2×D4—62no—
520C2×D4—62no—
521C2×D4—62no—
522C2×D4—62no—
523C2×D4—128no—
524C2×D4—128no—
525C2×D4—122no—
526C2×D4—124no—
527C2×D4—124no—
528C2×D4—124no—
529C2×D4—1232no—
530C2×D4—124no—
531C2×D4—122no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—31no—
539C22×C4—34no—
540C22×C4—31no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—64no—
546C22×C4—64no—
547C22×C4—62no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—61no—
557C22×C4—62no—
558C22×C4—61no—
559C22×C4—62no—
560C22×C4—121no—
561C22×C4—121no—
562C22×C4—128no—
563C22×C4—128no—
564C22×C4—122no—
565C22×C4—122no—
566C22×C4—122no—
567C22×C4—122no—
568C22×C4—121no—
569C22×C4C2×D1212yes—
570C22×C4D3×D411yescharacteristic
571C22×C4D3×D412yes—
572C22×C4C23×D311yescharacteristic
573SD16—128no—
574SD16—128no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—62no—
579C2×C8—62no—
580C2×C8—62no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—22no—
584C4⋊C4—21no—
585C4⋊C4—32no—
586C4⋊C4—64no—
587C4⋊C4—64no—
588C4⋊C4—64no—
589C4⋊C4—64no—
590C4⋊C4—61no—
591C4⋊C4C2×D1212yescomplemented
592C4⋊C4D3×D414yes—
593C22⋊C4—24no—
594C22⋊C4—68no—
595C22⋊C4—68no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4—64no—
599C22×C3—22no—
600C22×C3—22no—
601C22×C3—22no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3#44814yescomplemented
606C22×C3C2×#12011yescharacteristic
607C22×C3C2×#12011yescharacteristic
608C22×C3#53411yescharacteristic
609C22×C3C22×SD1611yescharacteristic
610C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
611C22×C3C2×#13711yescharacteristic
612C22×C3#57511yescharacteristic
613C2×D3—22no—
614C2×D3—22no—
615C2×D3—22no—
616C2×D3—22no—
617C2×D3—22no—
618C2×D3—22no—
619C2×D3—22no—
620C2×D3—22no—
621C2×D3—22no—
622C2×D3—416no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—41no—
626C2×D3—41no—
627C2×D3—44no—
628C2×D3—44no—
629C2×D3—44no—
630C2×D3—816no—
631C2×D3—82no—
632C2×D3—82no—
633C2×D3—82no—
634C2×D3—82no—
635C2×D3#45014yescomplemented
636C3×C4—22no—
637C3×C4—42no—
638C3×C4—44no—
639C3×C4—42no—
640C3×C4D4212yes—
641C3×C4D4212yes—
642Dic3—22no—
643Dic3—42no—
644Dic3—41no—
645Dic3—42no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—32no—
651C23—32no—
652C23—32no—
653C23—32no—
654C23—68no—
655C23—61no—
656C23—61no—
657C23—61no—
658C23—61no—
659C23—61no—
660C23—61no—
661C23—61no—
662C23—61no—
663C23—61no—
664C23—68no—
665C23—61no—
666C23—64no—
667C23—124no—
668C23—124no—
669C23—124no—
670C23—124no—
671C23—124no—
672C23—128no—
673C23—128no—
674C23—128no—
675C23—122no—
676C23—122no—
677C23—122no—
678C23—122no—
679C23—122no—
680C23—122no—
681C23—244no—
682C23—244no—
683C23—244no—
684C23—244no—
685C23#88212yes—
686C23D3×SD1612yes—
687C23#91812yes—
688C23C2×D3×D411yescharacteristic
689Q8—24no—
690Q8—42no—
691Q8—64no—
692Q8—128no—
693Q8—122no—
694D4—64no—
695D4—64no—
696D4—128no—
697D4—1216no—
698D4—1216no—
699D4—122no—
700D4—122no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—32no—
709C2×C4—48no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—64no—
719C2×C4—64no—
720C2×C4—61no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—124no—
726C2×C4—124no—
727C2×C4—128no—
728C2×C4—128no—
729C2×C4—124no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—122no—
735C2×C4—122no—
736C2×C4#88212yes—
737C2×C4C22×D1211yescharacteristic
738C2×C4C2×D3×D412yes—
739C2×C4C2×D3×D411yescharacteristic
740C2×C4#100912yes—
741C8—42no—
742C8—122no—
743C2×C3—24no—
744C2×C3#240311yescharacteristic
745C2×C3C2×#45011yescharacteristic
746C2×C3C2×#44811yescharacteristic
747C2×C3#300611yescharacteristic
748C2×C3#300711yescharacteristic
749C2×C3#318711yescharacteristic
750C2×C3#319311yescharacteristic
751D3—24no—
752D3—42no—
753D3—84no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—34no—
761C22—62no—
762C22—62no—
763C22—62no—
764C22—62no—
765C22—62no—
766C22—62no—
767C22—62no—
768C22—62no—
769C22—62no—
770C22—1216no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—124no—
776C22—124no—
777C22—124no—
778C22—2416no—
779C22—242no—
780C22—242no—
781C22—242no—
782C22—242no—
783C22#480614yescomplemented
784C22C2×#88211yescharacteristic
785C22D3×#12011yescharacteristic
786C22#565311yescharacteristic
787C22C2×D3×SD1611yescharacteristic
788C22C2×#91811yescharacteristic
789C22D3×AGL(1,ℤ/8)11yescharacteristic
790C22#577711yescharacteristic
791C4—22no—
792C4—44no—
793C4—42no—
794C4—42no—
795C4—62no—
796C4—122no—
797C4—121no—
798C4—122no—
799C4D4×D1212yes—
800C4#560912yes—
801C3#2391911yescharacteristic, complemented, Sylow
802C2—24no—
803C2—64no—
804C2—122no—
805C2—244no—
806C2#7488411yescharacteristic
807C2C2×#480611yescharacteristic
808C2#7888411yescharacteristic
809C2D3×#45011yescharacteristic
810C2#8018411yescharacteristic
811C2#8144211yescharacteristic
812C2#8148311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1872C2
socleC23×C3C22×D4
prime radicalC22×#895C2
hypercenter#1872D3
hypocenterC3#23919
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
1. C2×D3×C22⋊Q8C2semidirect
3. C2×#5046C2semidirect
4. C2×#4806C2semidirect
5. C2×#4731C2semidirect
6. C3×#1872C2semidirect
7. #71559C2semidirect
8. #70272C2semidirect
9. #69955C2semidirect
10. #68887C2semidirect
11. #68880C2semidirect
13. C22×D3×Q8C22semidirect
19. C2×#946C22semidirect
20. C22×#215C22semidirect
23. C22×#204C22semidirect
26. C2×#897C22semidirect
34. C2×D3×C4⋊C4C22semidirect
37. C2×C3×#103C22semidirect
40. C2×#821C22semidirect
41. C2×(C2×D3)⋊C8C22semidirect
42. C2×(C2×D3)⋊C8C22semidirect
44. C2×#810C22semidirect
45. C2×#809C22semidirect
48. C3×#340C22semidirect
49. #4529C22semidirect
59. #1872D3semidirect
96. C3×C22⋊Q8D4semidirect
117. #924D4semidirect
175. C2×#103C2×D3semidirect
183. #340C2×D3semidirect
199. C23×D3SD16semidirect
205. C2×C3×Q8C2×D4semidirect
273. C2×Dic6C2×D4semidirect
282. C3×C4⋊C4C2×D4semidirect
292. C4⋊Dic3C2×D4semidirect
350. C22⋊Q8D12semidirect
513. C2×Q8C2×D12semidirect
591. C4⋊C4C2×D12semidirect
605. C22×C3#448semidirect
635. C2×D3#450semidirect
783. C22#4806semidirect
801. 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
C22×#8952
C2×#50462
C2×#48062
C2×#47312
C3×#18722
#715592
#702722
#699552
#688872
#688802
#239193