Finite Group Databasebeta

← #10826933

Subgroups — #10826933

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
1C22×#946C211yesmaximal, characteristic, complemented
2C2×D3×#121C211yesmaximal, characteristic
3C2×C3×#448C211yesmaximal, characteristic, complemented
4C2×#5227C211yesmaximal, characteristic, complemented
5C2×#5169C212yesmaximal, complemented
6#72054C212yesmaximal, complemented
7#71677C211yesmaximal, characteristic, complemented
8#70272C212yesmaximal, complemented
9#70268C212yesmaximal, complemented
10#69955C211yesmaximal, characteristic, complemented
11#69932C211yesmaximal, characteristic, complemented
12#23919—31nomaximal, Sylow
13C23×C3×Q8C2211yescharacteristic, complemented
14C22×D3×D4—21no—
15C22×D3×D4C2211yescharacteristic
16C23×C4×D3C2211yescharacteristic
17C22×C3×SD16C2212yescomplemented
18C2×C3×#121C2211yescharacteristic
19C2×#946—21no—
20C2×#946—21no—
21C2×#946—28no—
22C2×#946C2212yes—
23C2×#946C2212yescomplemented
24C22×#215C2212yescomplemented
25C2×#939—21no—
26C2×#938C2211yescharacteristic
27C2×#930C2211yescharacteristic
28C22×(C2×D3)⋊C4—21no—
29C22×C4⋊Dic3C2211yescharacteristic, complemented
30C22×Dic3⋊C4—21no—
31D3×#121—24no—
32D3×#121—24no—
33C2×#895C2211yescharacteristic
34C2×D3×C4⋊C4C2211yescharacteristic
35C2×#884—21no—
36C2×D3×C22⋊C4—21no—
37C3×#448—24no—
38C2×C3×#103C2212yescomplemented
39C2×C3×C22⋊C8C2211yescharacteristic, complemented
40#5227—24no—
41C2×#835C2212yescomplemented
42C2×#832C2212yescomplemented
43C2×#830C2211yescharacteristic, complemented
44#5169—28no—
45C2×#821C2212yescomplemented
46C2×(C2×D3)⋊C8C2212yes—
47C2×(C2×D3)⋊C8C2212yescomplemented
48#4551C2212yescomplemented
49#4529C2212yescomplemented
50C22×C22⋊Q8—31no—
51C22×#121—31no—
52C2×#448—31no—
53C2×#448D311yescharacteristic, complemented
54C2×#450—32no—
55#2000—32no—
56#2000—32no—
57#1874—31no—
58#1874—31no—
59#1872—32no—
60#1779—31no—
61C24×D3—21no—
62C24×D3D411yescharacteristic
63C22×C3×Q8—24no—
64C22×C3×Q8—21no—
65C22×C3×Q8—22no—
66C22×C3×Q8—22no—
67C22×C3×Q8—42no—
68C22×C3×Q8C2312yes—
69C22×C3×D4—21no—
70C22×C3×D4C2311yescharacteristic
71C23×C3×C4—21no—
72C23×C3×C4C2311yescharacteristic
73C22×#67—21no—
74C22×#67—21no—
75C22×#67—21no—
76C23×Dic3—21no—
77C23×Dic3D411yescharacteristic
78C2×D3×D4—28no—
79C2×D3×D4—22no—
80C2×D3×D4—22no—
81C2×D3×D4—24no—
82C2×D3×D4—42no—
83C2×D3×D4—44no—
84C2×D3×D4—44no—
85C22×D12—21no—
86C22×D12C2311yescharacteristic
87C22×C4×D3—21no—
88C22×C4×D3—22no—
89C22×C4×D3—22no—
90C22×C4×D3—24no—
91C22×C4×D3—42no—
92C22×C4×D3D411yescharacteristic
93C22×C4×D3D411yescharacteristic
94C22×C4×D3C2311yescharacteristic
95C22×C4×D3C2311yescharacteristic
96C2×C3×SD16—24no—
97C2×C3×SD16—24no—
98C2×C3×SD16—42no—
99C22×C3×C8C2312yes—
100C3×#121—22no—
101C3×#121D414yes—
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C22⋊C4—21no—
104C2×#217—21no—
105#946—28no—
106#946—28no—
107#946—24no—
108#946—24no—
109#946—24no—
110#946D418yescomplemented
111C2×#215—24no—
112C2×#215—24no—
113C2×#215—42no—
114#939—28no—
115#938—22no—
116#938—22no—
117#930—22no—
118#930D414yes—
119C2×(C2×D3)⋊C4—28no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×C4⋊Dic3—21no—
125C2×C4⋊Dic3—24no—
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2312yes—
128C2×Dic3⋊C4—28no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—22no—
131C2×Dic3⋊C4—22no—
132C22×C3⋊C8C2312yes—
133#895—22no—
134#895—22no—
135D3×C4⋊C4—22no—
136D3×C4⋊C4—22no—
137#884—28no—
138D3×C22⋊C4—28no—
139C3×#103—24no—
140C3×C22⋊C8—22no—
141#835—24no—
142#832—24no—
143#830—22no—
144#821—24no—
145(C2×D3)⋊C8—24no—
146(C2×D3)⋊C8—42no—
147C23×Q8C2×D311yescharacteristic, complemented
148C23×D4—31no—
149C23×D4—61no—
150C24×C4—31no—
151C22×SD16—32no—
152C22×SD16C2×D312yescomplemented
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—31no—
168C22×C4⋊C4—61no—
169C22×C22⋊C4—61no—
170C22×C22⋊C4—61no—
171#450—68no—
172#448—24no—
173#448—64no—
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, complemented
182#340—32no—
183#340—32no—
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×Q8—24no—
204C2×C3×Q8—22no—
205C2×C3×Q8—22no—
206C2×C3×Q8—22no—
207C2×C3×Q8—22no—
208C2×C3×Q8—22no—
209C2×C3×Q8—48no—
210C2×C3×Q8—48no—
211C2×C3×Q8—42no—
212C2×C3×Q8—42no—
213C2×C3×Q8C2×D414yescomplemented
214C2×C3×D4—24no—
215C2×C3×D4—22no—
216C2×C3×D4—21no—
217C2×C3×D4—22no—
218C2×C3×D4—42no—
219C2×C3×D4—42no—
220C2×C3×D4C2×D412yes—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—24no—
224C22×C3×C4—22no—
225C22×C3×C4—21no—
226C22×C3×C4—42no—
227C22×C3×C4—42no—
228C22×C3×C4C2×D411yescharacteristic
229C22×C3×C4C2×D412yes—
230C22×C3×C4C2×D412yes—
231C22×C3×C4C2411yescharacteristic
232C2×#67—24no—
233C2×#67—24no—
234C2×#67—24no—
235C2×#67—42no—
236C2×#67—42no—
237C2×#67—42no—
238C2×#67—42no—
239C2×#67—42no—
240C2×#67—42no—
241C22×Dic3—24no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—21no—
245C22×Dic3—22no—
246C22×Dic3—41no—
247C22×Dic3—42no—
248C22×Dic3—42no—
249C22×Dic3C2×D411yescharacteristic
250C22×Dic3C2×D411yescharacteristic
251D3×D4—48no—
252D3×D4—48no—
253D3×D4—432no—
254C2×D12—22no—
255C2×D12—22no—
256C2×D12—24no—
257C2×D12—21no—
258C2×D12—42no—
259C2×D12—42no—
260C2×D12C2×D412yes—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—22no—
264C2×C4×D3—24no—
265C2×C4×D3—22no—
266C2×C4×D3—22no—
267C2×C4×D3—22no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—22no—
271C2×C4×D3—22no—
272C2×C4×D3—22no—
273C2×C4×D3—48no—
274C2×C4×D3—48no—
275C2×C4×D3—41no—
276C2×C4×D3—41no—
277C2×C4×D3—42no—
278C2×C4×D3—42no—
279C2×C4×D3C2×D414yes—
280C3×SD16—48no—
281C2×C3×C8—22no—
282C2×C3×C8—22no—
283C2×C3×C8—22no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4C2×D412yes—
286C3×C22⋊C4—24no—
287#217—24no—
288#215—48no—
289(C2×D3)⋊C4—24no—
290(C2×D3)⋊C4—28no—
291(C2×D3)⋊C4—28no—
292(C2×D3)⋊C4—24no—
293C4⋊Dic3—24no—
294C4⋊Dic3—21no—
295C4⋊Dic3—22no—
296C4⋊Dic3C2×D412yes—
297C4⋊Dic3C2×D414yescomplemented
298Dic3⋊C4—24no—
299Dic3⋊C4—28no—
300Dic3⋊C4—28no—
301C2×C3⋊C8—22no—
302C2×C3⋊C8—22no—
303C2×C3⋊C8—22no—
304C25—31no—
305C25—61no—
306C22×Q8—24no—
307C22×Q8—21no—
308C22×Q8—22no—
309C22×Q8—22no—
310C22×Q8—42no—
311C22×Q8C22×D312yes—
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—24no—
340C2×SD16—24no—
341C2×SD16—42no—
342C2×SD16—64no—
343C2×SD16—64no—
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#121#6714yes—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—32no—
365C2×C4⋊C4—62no—
366C2×C4⋊C4—64no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4—62no—
369C2×C4⋊C4—62no—
370C2×C4⋊C4—68no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—62no—
373C2×C4⋊C4C22×D311yescharacteristic
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—24no—
383#103—64no—
384#102—64no—
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×Q8—24no—
441C3×Q8—24no—
442C3×Q8—48no—
443C3×Q8—42no—
444C3×Q8—42no—
445C3×D4—24no—
446C3×D4—48no—
447C3×D4—42no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—24no—
451C2×C3×C4—24no—
452C2×C3×C4—24no—
453C2×C3×C4—22no—
454C2×C3×C4—48no—
455C2×C3×C4—42no—
456C2×C3×C4—42no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4#12012yes—
460C2×C3×C4C22×D411yescharacteristic
461C2×C3×C4C22×D412yes—
462C2×C3×C4C22×D411yescharacteristic
463C2×C3×C4H(5,𝔽2)12yes—
464#67—48no—
465#67—48no—
466#67—48no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—24no—
471C2×Dic3—22no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—44no—
475C2×Dic3—48no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—42no—
479C2×Dic3—42no—
480C2×Dic3#12012yes—
481D12—24no—
482D12—48no—
483D12—42no—
484C4×D3—24no—
485C4×D3—24no—
486C4×D3—44no—
487C4×D3—44no—
488C4×D3—48no—
489C4×D3—42no—
490C4×D3—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—24no—
513C2×Q8—22no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—48no—
519C2×Q8—48no—
520C2×Q8—42no—
521C2×Q8—42no—
522C2×Q8D3×D414yescomplemented
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—62no—
535C2×D4—62no—
536C2×D4—61no—
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×#6712yes—
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—62no—
565C22×C4—61no—
566C22×C4—64no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—61no—
570C22×C4—62no—
571C22×C4—62no—
572C22×C4—61no—
573C22×C4—62no—
574C22×C4—62no—
575C22×C4—61no—
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×C4D3×D411yescharacteristic
586C22×C4D3×D412yes—
587C22×C4C2×#6712yes—
588C22×C4C23×D311yescharacteristic
589SD16—48no—
590SD16—128no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—62no—
595C2×C8—62no—
596C2×C8—62no—
597C4⋊C4—21no—
598C4⋊C4—34no—
599C4⋊C4—32no—
600C4⋊C4—68no—
601C4⋊C4—64no—
602C4⋊C4—68no—
603C4⋊C4—64no—
604C4⋊C4—62no—
605C4⋊C4—61no—
606C4⋊C4C2×#6712yes—
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—44no—
659C3×C4—42no—
660C3×C4D4212yes—
661C3×C4D4212yes—
662Dic3—22no—
663Dic3—41no—
664Dic3—42no—
665Dic3—44no—
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—68no—
687C23—61no—
688C23—61no—
689C23—61no—
690C23—61no—
691C23—61no—
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—
712C23D3×SD1612yes—
713C23#91412yes—
714C23#93712yes—
715C23C2×D3×D411yescharacteristic
716Q8—24no—
717Q8—24no—
718Q8—48no—
719Q8—42no—
720Q8—42no—
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—41no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—64no—
745C2×C4—64no—
746C2×C4—61no—
747C2×C4—62no—
748C2×C4—64no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—124no—
752C2×C4—124no—
753C2×C4—128no—
754C2×C4—124no—
755C2×C4—128no—
756C2×C4—121no—
757C2×C4—121no—
758C2×C4—122no—
759C2×C4—122no—
760C2×C4—122no—
761C2×C4—122no—
762C2×C4#93712yes—
763C2×C4C2×D3×D412yes—
764C2×C4C2×D3×D411yescharacteristic
765C2×C4#100412yes—
766C2×C4C22×#6711yescharacteristic
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#516914yescomplemented
818C22D3×#12011yescharacteristic
819C22#558911yescharacteristic
820C22C2×D3×SD1611yescharacteristic
821C22C2×#91411yescharacteristic
822C22D3×#13711yescharacteristic
823C22#577711yescharacteristic
824C22C2×#93711yescharacteristic
825C4—22no—
826C4—42no—
827C4—44no—
828C4—62no—
829C4—122no—
830C4—124no—
831C4—121no—
832C4#559012yes—
833C4D4×#6712yes—
834C3#2391911yescharacteristic, complemented, Sylow
835C2—24no—
836C2—64no—
837C2—82no—
838C2—122no—
839C2—242no—
840C2D3×#44811yescharacteristic
841C2#8004011yescharacteristic
842C2#8004311yescharacteristic
843C2#8004511yescharacteristic
844C2#8260411yescharacteristic
845C2C2×#516911yescharacteristic
846C2#8398111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#448C2
socleC23×C3C22×D4
prime radicalC2×D3×#121C2
hypercenterC2×#448D3
hypocenterC3#23919
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C22×#946C2semidirect
3. C2×C3×#448C2semidirect
4. C2×#5227C2semidirect
5. C2×#5169C2semidirect
6. #72054C2semidirect
7. #71677C2semidirect
8. #70272C2semidirect
9. #70268C2semidirect
10. #69955C2semidirect
11. #69932C2semidirect
13. C23×C3×Q8C22semidirect
17. C22×C3×SD16C22semidirect
23. C2×#946C22semidirect
24. C22×#215C22semidirect
29. C22×C4⋊Dic3C22semidirect
38. C2×C3×#103C22semidirect
39. C2×C3×C22⋊C8C22semidirect
41. C2×#835C22semidirect
42. C2×#832C22semidirect
43. C2×#830C22semidirect
45. C2×#821C22semidirect
47. C2×(C2×D3)⋊C8C22semidirect
48. #4551C22semidirect
49. #4529C22semidirect
53. C2×#448D3semidirect
110. #946D4semidirect
147. C23×Q8C2×D3semidirect
152. C22×SD16C2×D3semidirect
175. C2×#103C2×D3semidirect
181. C2×C22⋊C8C2×D3semidirect
200. C23×D3SD16semidirect
213. C2×C3×Q8C2×D4semidirect
297. C4⋊Dic3C2×D4semidirect
522. C2×Q8D3×D4semidirect
626. C22×C3#450semidirect
656. C2×D3#448semidirect
817. C22#5169semidirect
834. C3#23919semidirect

Maximal subgroups

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

subgroupindex
C22×#9462
C2×D3×#1212
C2×C3×#4482
C2×#52272
C2×#51692
#720542
#716772
#702722
#702682
#699552
#699322
#239193