Finite Group Databasebeta

← #10826937

Subgroups — #10826937

Order 768.

2252 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#121C211yesmaximal, characteristic
2C22×#897C211yesmaximal, characteristic, complemented
3C2×#5040C211yesmaximal, characteristic, complemented
4C2×#4776C212yesmaximal, complemented
5C2×#4738C211yesmaximal, characteristic, complemented
6C3×#1874C211yesmaximal, characteristic, complemented
7#71560C211yesmaximal, characteristic, complemented
8#70205C212yesmaximal, complemented
9#69955C211yesmaximal, characteristic, complemented
10#68887C212yesmaximal, complemented
11#68878C212yesmaximal, complemented
12#23919—31nomaximal, Sylow
13C22×D3×D4—21no—
14C22×D3×D4C2211yescharacteristic
15C23×C4×D3C2211yescharacteristic
16C23×Dic6C2211yescharacteristic, complemented
17C2×C3×#121C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic, complemented
19C2×#939—21no—
20C2×#938C2211yescharacteristic
21C22×#214C2212yescomplemented
22C2×#930C2211yescharacteristic
23C22×(C2×D3)⋊C4—21no—
24C22×C4⋊Dic3—21no—
25C22×#204C2212yescomplemented
26D3×#121—24no—
27D3×#121—24no—
28C2×#897—21no—
29C2×#897—21no—
30C2×#897—28no—
31C2×#897C2212yes—
32C2×#897C2212yescomplemented
33C2×#895C2211yescharacteristic
34C2×D3×C4⋊C4C2211yescharacteristic
35C2×#884—21no—
36C2×D3×C22⋊C4—21no—
37C2×C3×#102C2212yescomplemented
38C2×C3×C22⋊C8C2211yescharacteristic, complemented
39C2×#830C2211yescharacteristic, complemented
40C2×(C2×D3)⋊C8C2212yes—
41C2×(C2×D3)⋊C8C2212yescomplemented
42C2×#816C2212yescomplemented
43#5040—24no—
44C2×#810C2212yescomplemented
45C2×#809C2212yescomplemented
46#4776—28no—
47#4738—24no—
48C3×#340C2212yescomplemented
49#4529C2212yescomplemented
50C22×C22⋊Q8—31no—
51C22×#121—31no—
52C2×#448—31no—
53C2×#448—31no—
54C2×#450—32no—
55#2000—32no—
56#2000—32no—
57#1874—31no—
58#1874D311yescharacteristic, complemented
59#1872—32no—
60#1779—31no—
61C24×D3—21no—
62C24×D3D411yescharacteristic
63C22×C3×D4—21no—
64C22×C3×D4C2311yescharacteristic
65C23×C3×C4—21no—
66C23×C3×C4C2311yescharacteristic
67C22×#67—21no—
68C22×#67—21no—
69C22×#67—21no—
70C23×Dic3—21no—
71C23×Dic3D411yescharacteristic
72C2×D3×D4—28no—
73C2×D3×D4—22no—
74C2×D3×D4—22no—
75C2×D3×D4—24no—
76C2×D3×D4—42no—
77C2×D3×D4—44no—
78C2×D3×D4—44no—
79C22×D12—21no—
80C22×D12C2311yescharacteristic
81C22×C4×D3—21no—
82C22×C4×D3—22no—
83C22×C4×D3—22no—
84C22×C4×D3—24no—
85C22×C4×D3—42no—
86C22×C4×D3D411yescharacteristic
87C22×C4×D3D411yescharacteristic
88C22×C4×D3C2311yescharacteristic
89C22×C4×D3C2311yescharacteristic
90C22×Dic6—21no—
91C22×Dic6—24no—
92C22×Dic6—22no—
93C22×Dic6—22no—
94C22×Dic6—42no—
95C22×Dic6C2312yes—
96C22×C3×C8C2312yes—
97C3×#121—22no—
98C3×#121D414yes—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—24no—
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C4⋊C4C2312yes—
103C2×C3×C22⋊C4—21no—
104C2×#217—21no—
105#939—28no—
106#938—22no—
107#938—22no—
108C2×#214—24no—
109C2×#214—24no—
110C2×#214—42no—
111#930—22no—
112#930D414yes—
113C2×(C2×D3)⋊C4—28no—
114C2×(C2×D3)⋊C4—22no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×C4⋊Dic3—28no—
119C2×C4⋊Dic3—22no—
120C2×C4⋊Dic3—22no—
121C2×C4⋊Dic3C2311yescharacteristic
122C2×Dic3⋊C4—21no—
123C22×C3⋊C8C2312yes—
124C2×#204—24no—
125C2×#204—24no—
126C2×#204—42no—
127#897—28no—
128#897—28no—
129#897—24no—
130#897—24no—
131#897—24no—
132#897D418yescomplemented
133#895—22no—
134#895—22no—
135D3×C4⋊C4—22no—
136D3×C4⋊C4—22no—
137#884—28no—
138D3×C22⋊C4—28no—
139C3×#102—24no—
140C3×C22⋊C8—22no—
141#830—22no—
142(C2×D3)⋊C8—24no—
143(C2×D3)⋊C8—42no—
144#816—24no—
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—32no—
154C2×C22⋊Q8—32no—
155C2×C22⋊Q8—68no—
156C2×C22⋊Q8—61no—
157C2×C22⋊Q8—61no—
158C2×#121—31no—
159C2×#121—31no—
160C2×#121—31no—
161C2×#121—61no—
162C2×#121—64no—
163C2×#121—61no—
164C2×#121—64no—
165C2×#121C2×D311yescharacteristic
166C22×C4⋊C4—31no—
167C22×C4⋊C4—61no—
168C22×C4⋊C4C2×D311yescharacteristic, complemented
169C22×C22⋊C4—61no—
170C22×C22⋊C4—61no—
171#450—68no—
172#448—64no—
173#448—64no—
174C2×#103—32no—
175C2×#103—32no—
176C2×#102—32no—
177C2×#102C2×D312yescomplemented
178C2×C22⋊C8—31no—
179C2×C22⋊C8—32no—
180C2×C22⋊C8—32no—
181C2×C22⋊C8C2×D311yescharacteristic, complemented
182#340—32no—
183#340C2×D312yescomplemented
184C24×C3—21no—
185C24×C3C2×D411yescharacteristic
186C23×D3—22no—
187C23×D3—22no—
188C23×D3—22no—
189C23×D3—22no—
190C23×D3—24no—
191C23×D3—21no—
192C23×D3—41no—
193C23×D3—41no—
194C23×D3—42no—
195C23×D3—42no—
196C23×D3—42no—
197C23×D3—42no—
198C23×D3—42no—
199C23×D3—42no—
200C23×D3SD1614yescomplemented
201C23×D3C2×D411yescharacteristic
202C23×D3C2×D411yescharacteristic
203C2×C3×D4—24no—
204C2×C3×D4—22no—
205C2×C3×D4—21no—
206C2×C3×D4—22no—
207C2×C3×D4—42no—
208C2×C3×D4—42no—
209C2×C3×D4C2×D412yes—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—24no—
213C22×C3×C4—21no—
214C22×C3×C4—22no—
215C22×C3×C4—42no—
216C22×C3×C4—42no—
217C22×C3×C4C2×D412yes—
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2×D412yes—
220C22×C3×C4C2411yescharacteristic
221C2×#67—24no—
222C2×#67—24no—
223C2×#67—24no—
224C2×#67—42no—
225C2×#67—42no—
226C2×#67—42no—
227C2×#67—42no—
228C2×#67—42no—
229C2×#67—42no—
230C22×Dic3—24no—
231C22×Dic3—22no—
232C22×Dic3—21no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—41no—
236C22×Dic3—42no—
237C22×Dic3—42no—
238C22×Dic3C2×D411yescharacteristic
239C22×Dic3C2×D411yescharacteristic
240D3×D4—48no—
241D3×D4—48no—
242D3×D4—432no—
243C2×D12—22no—
244C2×D12—22no—
245C2×D12—24no—
246C2×D12—21no—
247C2×D12—42no—
248C2×D12—42no—
249C2×D12C2×D412yes—
250C2×C4×D3—21no—
251C2×C4×D3—21no—
252C2×C4×D3—22no—
253C2×C4×D3—24no—
254C2×C4×D3—22no—
255C2×C4×D3—22no—
256C2×C4×D3—22no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—22no—
260C2×C4×D3—22no—
261C2×C4×D3—22no—
262C2×C4×D3—48no—
263C2×C4×D3—48no—
264C2×C4×D3—41no—
265C2×C4×D3—41no—
266C2×C4×D3—42no—
267C2×C4×D3—42no—
268C2×C4×D3C2×D414yes—
269C2×Dic6—22no—
270C2×Dic6—22no—
271C2×Dic6—22no—
272C2×Dic6—22no—
273C2×Dic6—24no—
274C2×Dic6—22no—
275C2×Dic6—48no—
276C2×Dic6—48no—
277C2×Dic6—42no—
278C2×Dic6—42no—
279C2×Dic6C2×D414yescomplemented
280C2×C3×C8—22no—
281C2×C3×C8—22no—
282C2×C3×C8—22no—
283C3×C4⋊C4—24no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—22no—
286C3×C4⋊C4C2×D412yes—
287C3×C4⋊C4C2×D414yescomplemented
288C3×C22⋊C4—24no—
289#217—24no—
290#214—48no—
291(C2×D3)⋊C4—24no—
292(C2×D3)⋊C4—28no—
293(C2×D3)⋊C4—28no—
294(C2×D3)⋊C4—24no—
295C4⋊Dic3—28no—
296C4⋊Dic3—21no—
297C4⋊Dic3—28no—
298C4⋊Dic3C2×D412yes—
299Dic3⋊C4—24no—
300C2×C3⋊C8—22no—
301C2×C3⋊C8—22no—
302C2×C3⋊C8—22no—
303#204—48no—
304C25—31no—
305C25—61no—
306C22×Q8—32no—
307C22×Q8—64no—
308C22×Q8—61no—
309C22×Q8—62no—
310C22×Q8—62no—
311C22×Q8—122no—
312C22×D4—21no—
313C22×D4—31no—
314C22×D4—61no—
315C22×D4—64no—
316C22×D4—61no—
317C22×D4—62no—
318C22×D4—68no—
319C22×D4—61no—
320C22×D4—61no—
321C22×D4—62no—
322C22×D4—122no—
323C22×D4—124no—
324C22×D4—124no—
325C22×D4C22×D311yescharacteristic
326C23×C4—21no—
327C23×C4—31no—
328C23×C4—31no—
329C23×C4—31no—
330C23×C4—31no—
331C23×C4—31no—
332C23×C4—64no—
333C23×C4—61no—
334C23×C4—61no—
335C23×C4—62no—
336C23×C4—62no—
337C23×C4—122no—
338C23×C4C22×D311yescharacteristic
339C2×SD16—64no—
340C2×SD16—64no—
341C2×SD16—64no—
342C2×SD16—64no—
343C2×SD16—122no—
344C2×SD16—122no—
345C22×C8—32no—
346C22×C8C22×D312yes—
347C22⋊Q8—38no—
348C22⋊Q8—64no—
349C22⋊Q8—64no—
350C22⋊Q8—68no—
351C22⋊Q8—68no—
352C22⋊Q8—64no—
353#121—22no—
354#121—34no—
355#121—68no—
356#121—62no—
357#121—62no—
358#121—68no—
359#121—62no—
360#121—62no—
361#121—62no—
362#121D1214yes—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—62no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4—62no—
369C2×C4⋊C4—62no—
370C2×C4⋊C4—68no—
371C2×C4⋊C4—62no—
372C2×C4⋊C4C22×D311yescharacteristic
373C2×C4⋊C4C22×D312yes—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—68no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—62no—
378C2×C22⋊C4—62no—
379C2×C22⋊C4—68no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382#103—64no—
383#103—64no—
384#102—24no—
385#102—64no—
386C22⋊C8—22no—
387C22⋊C8—64no—
388C22⋊C8—62no—
389C22⋊C8—122no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—22no—
395C23×C3—41no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3#12012yes—
402C23×C3C2×SD1612yes—
403C23×C3AGL(1,ℤ/8)12yes—
404C23×C3C22×D411yescharacteristic
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—21no—
408C22×D3—21no—
409C22×D3—21no—
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—28no—
416C22×D3—28no—
417C22×D3—22no—
418C22×D3—44no—
419C22×D3—44no—
420C22×D3—44no—
421C22×D3—44no—
422C22×D3—44no—
423C22×D3—48no—
424C22×D3—48no—
425C22×D3—48no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—84no—
433C22×D3—84no—
434C22×D3—84no—
435C22×D3—84no—
436C22×D3#12012yes—
437C22×D3C2×SD1612yes—
438C22×D3C2×SD1612yes—
439C22×D3#13712yes—
440C3×D4—24no—
441C3×D4—48no—
442C3×D4—42no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—24no—
446C2×C3×C4—24no—
447C2×C3×C4—22no—
448C2×C3×C4—24no—
449C2×C3×C4—48no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—42no—
453C2×C3×C4—42no—
454C2×C3×C4#12012yes—
455C2×C3×C4C22×D411yescharacteristic
456C2×C3×C4C22×D412yes—
457C2×C3×C4C22×D411yescharacteristic
458C2×C3×C4H(5,𝔽2)12yes—
459#67—48no—
460#67—48no—
461#67—48no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—22no—
465C2×Dic3—21no—
466C2×Dic3—24no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—44no—
470C2×Dic3—48no—
471C2×Dic3—42no—
472C2×Dic3—42no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3#12012yes—
476D12—24no—
477D12—48no—
478D12—42no—
479C4×D3—24no—
480C4×D3—24no—
481C4×D3—44no—
482C4×D3—44no—
483C4×D3—48no—
484C4×D3—42no—
485C4×D3—42no—
486Dic6—24no—
487Dic6—24no—
488Dic6—48no—
489Dic6—42no—
490Dic6—42no—
491C3×C8—42no—
492C3⋊C8—42no—
493C24—21no—
494C24—31no—
495C24—31no—
496C24—34no—
497C24—62no—
498C24—62no—
499C24—64no—
500C24—62no—
501C24—62no—
502C24—61no—
503C24—121no—
504C24—121no—
505C24—122no—
506C24—122no—
507C24—122no—
508C24—122no—
509C24—122no—
510C24—122no—
511C24D3×D411yescharacteristic
512C2×Q8—34no—
513C2×Q8—64no—
514C2×Q8—62no—
515C2×Q8—62no—
516C2×Q8—62no—
517C2×Q8—62no—
518C2×Q8—62no—
519C2×Q8—128no—
520C2×Q8—128no—
521C2×Q8—122no—
522C2×Q8—122no—
523C2×D4—24no—
524C2×D4—22no—
525C2×D4—21no—
526C2×D4—22no—
527C2×D4—32no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—64no—
531C2×D4—64no—
532C2×D4—64no—
533C2×D4—64no—
534C2×D4—61no—
535C2×D4—62no—
536C2×D4—62no—
537C2×D4—122no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—128no—
541C2×D4—128no—
542C2×D4—122no—
543C2×D4—1232no—
544C2×D4—122no—
545C2×D4—122no—
546C2×D4—122no—
547C2×D4—122no—
548C2×D4C2×D1212yes—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—31no—
555C22×C4—34no—
556C22×C4—31no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—64no—
562C22×C4—62no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—62no—
566C22×C4—64no—
567C22×C4—62no—
568C22×C4—61no—
569C22×C4—62no—
570C22×C4—62no—
571C22×C4—62no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—62no—
575C22×C4—62no—
576C22×C4—121no—
577C22×C4—121no—
578C22×C4—128no—
579C22×C4—128no—
580C22×C4—122no—
581C22×C4—122no—
582C22×C4—121no—
583C22×C4—122no—
584C22×C4—122no—
585C22×C4C2×D1212yes—
586C22×C4D3×D411yescharacteristic
587C22×C4D3×D412yes—
588C22×C4C23×D311yescharacteristic
589SD16—128no—
590SD16—128no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—62no—
595C2×C8—62no—
596C2×C8—62no—
597C4⋊C4—24no—
598C4⋊C4—22no—
599C4⋊C4—21no—
600C4⋊C4—32no—
601C4⋊C4—68no—
602C4⋊C4—64no—
603C4⋊C4—68no—
604C4⋊C4—61no—
605C4⋊C4C2×D1212yes—
606C4⋊C4D3×D414yescomplemented
607C22⋊C4—24no—
608C22⋊C4—68no—
609C22⋊C4—64no—
610C22⋊C4—68no—
611C22⋊C4—64no—
612C22⋊C4—64no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3#45014yescomplemented
627C22×C3C2×#12011yescharacteristic
628C22×C3C2×#12011yescharacteristic
629C22×C3#53411yescharacteristic
630C22×C3C22×SD1611yescharacteristic
631C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
632C22×C3C2×#13711yescharacteristic
633C22×C3#57511yescharacteristic
634C2×D3—22no—
635C2×D3—22no—
636C2×D3—22no—
637C2×D3—22no—
638C2×D3—22no—
639C2×D3—22no—
640C2×D3—22no—
641C2×D3—22no—
642C2×D3—22no—
643C2×D3—416no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—42no—
649C2×D3—42no—
650C2×D3—42no—
651C2×D3—816no—
652C2×D3—81no—
653C2×D3—81no—
654C2×D3—81no—
655C2×D3—81no—
656C2×D3#44814yescomplemented
657C3×C4—22no—
658C3×C4—42no—
659C3×C4—44no—
660C3×C4D4212yes—
661C3×C4D4212yes—
662Dic3—22no—
663Dic3—44no—
664Dic3—41no—
665Dic3—42no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—32no—
672C23—32no—
673C23—32no—
674C23—32no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—68no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—61no—
686C23—61no—
687C23—61no—
688C23—61no—
689C23—61no—
690C23—61no—
691C23—68no—
692C23—61no—
693C23—62no—
694C23—124no—
695C23—124no—
696C23—124no—
697C23—124no—
698C23—124no—
699C23—128no—
700C23—128no—
701C23—128no—
702C23—121no—
703C23—121no—
704C23—121no—
705C23—121no—
706C23—121no—
707C23—121no—
708C23—244no—
709C23—244no—
710C23—244no—
711C23—244no—
712C23#88212yes—
713C23#91112yes—
714C23D3×SD1612yes—
715C23C2×D3×D411yescharacteristic
716Q8—64no—
717Q8—64no—
718Q8—128no—
719Q8—122no—
720Q8—122no—
721D4—24no—
722D4—48no—
723D4—42no—
724D4—64no—
725D4—128no—
726D4—128no—
727D4—128no—
728D4—128no—
729D4—122no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—32no—
737C2×C4—48no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—64no—
745C2×C4—64no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—62no—
749C2×C4—64no—
750C2×C4—61no—
751C2×C4—124no—
752C2×C4—124no—
753C2×C4—128no—
754C2×C4—124no—
755C2×C4—128no—
756C2×C4—122no—
757C2×C4—122no—
758C2×C4—121no—
759C2×C4—121no—
760C2×C4—122no—
761C2×C4—122no—
762C2×C4#88212yes—
763C2×C4C22×D1211yescharacteristic
764C2×C4C2×D3×D412yes—
765C2×C4C2×D3×D411yescharacteristic
766C2×C4#100912yes—
767C8—42no—
768C8—122no—
769C2×C3—24no—
770C2×C3—82no—
771C2×C3#240311yescharacteristic
772C2×C3C2×#45011yescharacteristic
773C2×C3C2×#44811yescharacteristic
774C2×C3#300611yescharacteristic
775C2×C3#300711yescharacteristic
776C2×C3#318711yescharacteristic
777C2×C3#319311yescharacteristic
778D3—24no—
779D3—42no—
780D3—82no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—34no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—62no—
792C22—62no—
793C22—62no—
794C22—62no—
795C22—62no—
796C22—62no—
797C22—62no—
798C22—62no—
799C22—62no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—1216no—
805C22—121no—
806C22—121no—
807C22—121no—
808C22—121no—
809C22—122no—
810C22—122no—
811C22—122no—
812C22—2416no—
813C22—241no—
814C22—241no—
815C22—241no—
816C22—241no—
817C22#477614yescomplemented
818C22C2×#88211yescharacteristic
819C22D3×#12011yescharacteristic
820C22#565311yescharacteristic
821C22C2×#91111yescharacteristic
822C22C2×D3×SD1611yescharacteristic
823C22#577311yescharacteristic
824C22D3×#13711yescharacteristic
825C4—22no—
826C4—44no—
827C4—42no—
828C4—62no—
829C4—121no—
830C4—124no—
831C4—122no—
832C4D4×D1212yes—
833C4#560912yes—
834C3#2391911yescharacteristic, complemented, Sylow
835C2—24no—
836C2—64no—
837C2—82no—
838C2—122no—
839C2—242no—
840C2#7488411yescharacteristic
841C2C2×#477611yescharacteristic
842C2#7888511yescharacteristic
843C2#8000311yescharacteristic
844C2D3×#44811yescharacteristic
845C2#8128611yescharacteristic
846C2#8132911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1874C2
socleC23×C3C22×D4
prime radicalC2×D3×#121C2
hypercenter#1874D3
hypocenterC3#23919
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C22×#897C2semidirect
3. C2×#5040C2semidirect
4. C2×#4776C2semidirect
5. C2×#4738C2semidirect
6. C3×#1874C2semidirect
7. #71560C2semidirect
8. #70205C2semidirect
9. #69955C2semidirect
10. #68887C2semidirect
11. #68878C2semidirect
16. C23×Dic6C22semidirect
18. C22×C3×C4⋊C4C22semidirect
21. C22×#214C22semidirect
25. C22×#204C22semidirect
32. C2×#897C22semidirect
37. C2×C3×#102C22semidirect
38. C2×C3×C22⋊C8C22semidirect
39. C2×#830C22semidirect
41. C2×(C2×D3)⋊C8C22semidirect
42. C2×#816C22semidirect
44. C2×#810C22semidirect
45. C2×#809C22semidirect
48. C3×#340C22semidirect
49. #4529C22semidirect
58. #1874D3semidirect
132. #897D4semidirect
168. C22×C4⋊C4C2×D3semidirect
177. C2×#102C2×D3semidirect
181. C2×C22⋊C8C2×D3semidirect
183. #340C2×D3semidirect
200. C23×D3SD16semidirect
279. C2×Dic6C2×D4semidirect
287. C3×C4⋊C4C2×D4semidirect
606. C4⋊C4D3×D4semidirect
626. C22×C3#450semidirect
656. C2×D3#448semidirect
817. C22#4776semidirect
834. C3#23919semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#1212
C22×#8972
C2×#50402
C2×#47762
C2×#47382
C3×#18742
#715602
#702052
#699552
#688872
#688782
#239193