Finite Group Databasebeta

← #10826932

Subgroups — #10826932

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
1C22×#938C211yesmaximal, characteristic
2C2×D3×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C3×#450C211yesmaximal, characteristic, complemented
4C2×#5218C211yesmaximal, characteristic, complemented
5C2×#5170C212yesmaximal, complemented
6#72054C212yesmaximal, complemented
7#71692C211yesmaximal, characteristic, complemented
8#70205C212yesmaximal, complemented
9#70200C212yesmaximal, complemented
10#69955C211yesmaximal, characteristic, complemented
11#69930C211yesmaximal, characteristic, complemented
12#23919—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×#67—21no—
15C22×D3×Q8C2211yescharacteristic, complemented
16C23×C4×D3C2211yescharacteristic
17C22×C3×SD16C2212yescomplemented
18C2×C3×C22⋊Q8C2211yescharacteristic
19C22×#217—21no—
20C2×#946C2211yescharacteristic, complemented
21C2×#938—21no—
22C2×#938—21no—
23C2×#938—28no—
24C2×#938C2212yes—
25C2×#938C2212yes—
26C22×#214C2212yescomplemented
27C22×C4⋊Dic3C2211yescharacteristic
28C2×#924C2211yescharacteristic
29D3×C22⋊Q8—24no—
30D3×C22⋊Q8—24no—
31C2×#897C2211yescharacteristic, complemented
32C2×#896—21no—
33C2×D3×C4⋊C4—21no—
34C2×D3×C4⋊C4C2211yescharacteristic, complemented
35C2×D3×C22⋊C4—21no—
36C2×#878—21no—
37C3×#450—24no—
38C2×C3×#102C2212yescomplemented
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×#835C2212yescomplemented
41#5218—24no—
42C2×#832C2212yescomplemented
43C2×#830C2211yescharacteristic
44#5170—28no—
45C2×(C2×D3)⋊C8C2212yescomplemented
46C2×(C2×D3)⋊C8C2212yescomplemented
47C2×#816C2212yescomplemented
48#4551C2212yescomplemented
49#4529C2212yescomplemented
50C22×C22⋊Q8—31no—
51C22×#121—31no—
52C2×#448—32no—
53C2×#450—31no—
54C2×#450D311yescharacteristic, complemented
55#2000—32no—
56#2000—32no—
57#1874—32no—
58#1872—31no—
59#1872—31no—
60#1779—31no—
61C25×C3—21no—
62C24×D3D411yescharacteristic
63C22×C3×Q8C2311yescharacteristic
64C22×C3×D4—24no—
65C22×C3×D4—21no—
66C22×C3×D4—22no—
67C22×C3×D4—22no—
68C22×C3×D4—42no—
69C22×C3×D4C2312yes—
70C23×C3×C4C2311yescharacteristic
71C22×#67—28no—
72C22×#67—22no—
73C22×#67—22no—
74C22×#67—44no—
75C22×#67—44no—
76C23×Dic3—21no—
77C23×Dic3D411yescharacteristic
78C2×D3×Q8—22no—
79C2×D3×Q8—22no—
80C2×D3×Q8—24no—
81C2×D3×Q8—42no—
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
94C2×C3×SD16—24no—
95C2×C3×SD16—24no—
96C2×C3×SD16—42no—
97C22×C3×C8C2312yes—
98C3×C22⋊Q8—22no—
99C3×C22⋊Q8D414yescomplemented
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C22⋊C4—21no—
103C2×#217—28no—
104C2×#217—21no—
105C2×#217—22no—
106C2×#217—22no—
107#946—22no—
108#946—22no—
109#938—28no—
110#938—28no—
111#938—24no—
112#938—24no—
113#938—24no—
114#938D418yes—
115C2×#214—24no—
116C2×#214—24no—
117C2×#214—42no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3—24no—
123C2×C4⋊Dic3C2312yes—
124C2×C4⋊Dic3C2311yescharacteristic
125#924—22no—
126#924D414yescomplemented
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C22×C3⋊C8C2312yes—
131#897—22no—
132#897—22no—
133#896—28no—
134D3×C4⋊C4—28no—
135D3×C4⋊C4—22no—
136D3×C4⋊C4—22no—
137D3×C22⋊C4—28no—
138#878—28no—
139C3×#102—24no—
140C3×C22⋊C8—22no—
141#835—24no—
142#832—24no—
143#830—22no—
144(C2×D3)⋊C8—24no—
145(C2×D3)⋊C8—42no—
146#816—24no—
147C23×Q8—31no—
148C23×D4—61no—
149C23×D4C2×D311yescharacteristic
150C24×C4—31no—
151C22×SD16—32no—
152C22×SD16C2×D312yescomplemented
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—31no—
168C22×C4⋊C4—61no—
169C22×C22⋊C4—61no—
170C22×C22⋊C4—61no—
171#450—24no—
172#450—64no—
173#448—68no—
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
182#340—32no—
183#340—32no—
184C24×C3—24no—
185C24×C3—22no—
186C24×C3—42no—
187C24×C3—42no—
188C24×C3—42no—
189C24×C3—42no—
190C24×C3—42no—
191C24×C3—42no—
192C24×C3C2×D411yescharacteristic
193C23×D3—22no—
194C23×D3—22no—
195C23×D3—22no—
196C23×D3—22no—
197C23×D3—41no—
198C23×D3—41no—
199C23×D3SD1614yescomplemented
200C23×D3C2×D411yescharacteristic
201C23×D3C2×D411yescharacteristic
202C2×C3×Q8—21no—
203C2×C3×Q8—22no—
204C2×C3×Q8—22no—
205C2×C3×Q8C2×D412yescomplemented
206C2×C3×D4—24no—
207C2×C3×D4—22no—
208C2×C3×D4—22no—
209C2×C3×D4—22no—
210C2×C3×D4—22no—
211C2×C3×D4—22no—
212C2×C3×D4—48no—
213C2×C3×D4—48no—
214C2×C3×D4—42no—
215C2×C3×D4—42no—
216C2×C3×D4C2×D414yes—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4C2×D411yescharacteristic
222C22×C3×C4C2×D412yes—
223C22×C3×C4C2×D412yes—
224C22×C3×C4C2411yescharacteristic
225C2×#67—28no—
226C2×#67—28no—
227C2×#67—432no—
228C2×#67—44no—
229C2×#67—44no—
230C2×#67—44no—
231C2×#67—44no—
232C22×Dic3—24no—
233C22×Dic3—22no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—41no—
239C22×Dic3—42no—
240C22×Dic3—42no—
241C22×Dic3C2×D411yescharacteristic
242C22×Dic3C2×D411yescharacteristic
243D3×Q8—48no—
244D3×Q8—48no—
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—21no—
254C2×C4×D3—21no—
255C2×C4×D3—22no—
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
274C3×SD16—48no—
275C2×C3×C8—22no—
276C2×C3×C8—22no—
277C2×C3×C8—22no—
278C3×C4⋊C4—24no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4C2×D412yescomplemented
281C3×C22⋊C4—24no—
282#217—28no—
283#217—24no—
284#217—28no—
285#214—48no—
286(C2×D3)⋊C4—24no—
287(C2×D3)⋊C4—24no—
288C4⋊Dic3—24no—
289C4⋊Dic3—24no—
290C4⋊Dic3—21no—
291C4⋊Dic3—22no—
292C4⋊Dic3C2×D414yes—
293C4⋊Dic3C2×D412yescomplemented
294Dic3⋊C4—24no—
295Dic3⋊C4—24no—
296Dic3⋊C4—24no—
297C2×C3⋊C8—22no—
298C2×C3⋊C8—22no—
299C2×C3⋊C8—22no—
300C25—21no—
301C25—31no—
302C22×Q8—31no—
303C22×Q8—61no—
304C22×Q8—64no—
305C22×Q8—62no—
306C22×Q8—62no—
307C22×Q8—122no—
308C22×Q8C22×D311yescharacteristic
309C22×D4—24no—
310C22×D4—21no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—42no—
314C22×D4—62no—
315C22×D4—62no—
316C22×D4—68no—
317C22×D4—124no—
318C22×D4—124no—
319C22×D4C22×D312yes—
320C23×C4—31no—
321C23×C4—31no—
322C23×C4—31no—
323C23×C4—31no—
324C23×C4—31no—
325C23×C4—64no—
326C23×C4—61no—
327C23×C4—61no—
328C23×C4—61no—
329C23×C4—62no—
330C23×C4—62no—
331C23×C4—122no—
332C23×C4C22×D311yescharacteristic
333C2×SD16—24no—
334C2×SD16—24no—
335C2×SD16—42no—
336C2×SD16—64no—
337C2×SD16—64no—
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⋊Q8#6714yescomplemented
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—32no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—62no—
361C2×C4⋊C4—68no—
362C2×C4⋊C4—64no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4—62no—
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—68no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—62no—
375C2×C22⋊C4—62no—
376C2×C22⋊C4—68no—
377C2×C22⋊C4—61no—
378#103—64no—
379#103—64no—
380#102—24no—
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—24no—
391C23×C3—48no—
392C23×C3—48no—
393C23×C3—48no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—84no—
401C23×C3—84no—
402C23×C3—84no—
403C23×C3—84no—
404C23×C3#12012yes—
405C23×C3C2×SD1612yes—
406C23×C3#13712yes—
407C23×C3C22×D411yescharacteristic
408C22×D3—21no—
409C22×D3—21no—
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—21no—
416C22×D3—21no—
417C22×D3—21no—
418C22×D3—28no—
419C22×D3—28no—
420C22×D3—44no—
421C22×D3—44no—
422C22×D3—44no—
423C22×D3—44no—
424C22×D3—44no—
425C22×D3#12012yes—
426C22×D3C2×SD1612yes—
427C22×D3C2×SD1612yes—
428C22×D3AGL(1,ℤ/8)12yes—
429C3×Q8—24no—
430C3×Q8—42no—
431C3×D4—24no—
432C3×D4—24no—
433C3×D4—48no—
434C3×D4—42no—
435C3×D4—42no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—24no—
439C2×C3×C4—24no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4#12012yes—
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C22×D412yes—
449C2×C3×C4C22×D411yescharacteristic
450C2×C3×C4H(5,𝔽2)12yes—
451#67—416no—
452#67—416no—
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—22no—
456C2×Dic3—21no—
457C2×Dic3—22no—
458C2×Dic3—24no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—44no—
462C2×Dic3—48no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—42no—
466C2×Dic3—41no—
467C2×Dic3—42no—
468C2×Dic3—41no—
469C2×Dic3#12012yes—
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—24no—
484C24—22no—
485C24—31no—
486C24—31no—
487C24—34no—
488C24—42no—
489C24—42no—
490C24—42no—
491C24—42no—
492C24—42no—
493C24—42no—
494C24—62no—
495C24—62no—
496C24—62no—
497C24—62no—
498C24—121no—
499C24—121no—
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×#6712yescomplemented
514C2×D4—24no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—48no—
521C2×D4—48no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—68no—
525C2×D4—68no—
526C2×D4—124no—
527C2×D4—124no—
528C2×D4—124no—
529C2×D4—1232no—
530C2×D4—124no—
531C2×D4D3×D414yes—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—31no—
537C22×C4—34no—
538C22×C4—31no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—64no—
542C22×C4—64no—
543C22×C4—62no—
544C22×C4—61no—
545C22×C4—62no—
546C22×C4—61no—
547C22×C4—64no—
548C22×C4—62no—
549C22×C4—61no—
550C22×C4—62no—
551C22×C4—61no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—61no—
556C22×C4—62no—
557C22×C4—61no—
558C22×C4—121no—
559C22×C4—121no—
560C22×C4—128no—
561C22×C4—128no—
562C22×C4—122no—
563C22×C4—122no—
564C22×C4—122no—
565C22×C4—122no—
566C22×C4—121no—
567C22×C4—122no—
568C22×C4—122no—
569C22×C4D3×D411yescharacteristic
570C22×C4D3×D412yes—
571C22×C4C2×#6712yes—
572C22×C4C23×D311yescharacteristic
573SD16—48no—
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—21no—
583C4⋊C4—32no—
584C4⋊C4—34no—
585C4⋊C4—64no—
586C4⋊C4—64no—
587C4⋊C4—64no—
588C4⋊C4—64no—
589C4⋊C4—64no—
590C4⋊C4—62no—
591C4⋊C4—61no—
592C4⋊C4C2×#6712yescomplemented
593C22⋊C4—24no—
594C22⋊C4—64no—
595C22⋊C4—64no—
596C22⋊C4—68no—
597C22⋊C4—68no—
598C22⋊C4—64no—
599C22×C3—22no—
600C22×C3—22no—
601C22×C3—22no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—44no—
606C22×C3—44no—
607C22×C3—44no—
608C22×C3—816no—
609C22×C3—82no—
610C22×C3—82no—
611C22×C3—82no—
612C22×C3—82no—
613C22×C3#44814yescomplemented
614C22×C3C2×#12011yescharacteristic
615C22×C3C2×#12011yescharacteristic
616C22×C3#53411yescharacteristic
617C22×C3C22×SD1611yescharacteristic
618C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
619C22×C3C2×#13711yescharacteristic
620C22×C3#57511yescharacteristic
621C2×D3—22no—
622C2×D3—22no—
623C2×D3—22no—
624C2×D3—22no—
625C2×D3—22no—
626C2×D3—22no—
627C2×D3—22no—
628C2×D3—22no—
629C2×D3—22no—
630C2×D3—416no—
631C2×D3—41no—
632C2×D3—41no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3#45014yescomplemented
636C3×C4—22no—
637C3×C4—42no—
638C3×C4—42no—
639C3×C4D4212yes—
640C3×C4D4212yes—
641Dic3—22no—
642Dic3—42no—
643Dic3—41no—
644Dic3—44no—
645Dic3—42no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—32no—
652C23—32no—
653C23—32no—
654C23—32no—
655C23—48no—
656C23—48no—
657C23—48no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—68no—
665C23—61no—
666C23—61no—
667C23—61no—
668C23—61no—
669C23—68no—
670C23—61no—
671C23—61no—
672C23—61no—
673C23—61no—
674C23—61no—
675C23—61no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—124no—
681C23—124no—
682C23—124no—
683C23—124no—
684C23—124no—
685C23D3×SD1612yes—
686C23#91512yes—
687C23#93712yes—
688C23C2×D3×D411yescharacteristic
689Q8—24no—
690Q8—42no—
691Q8—64no—
692Q8—128no—
693Q8—122no—
694D4—24no—
695D4—24no—
696D4—48no—
697D4—42no—
698D4—42no—
699D4—1216no—
700D4—1216no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—32no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—64no—
715C2×C4—64no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—64no—
721C2×C4—61no—
722C2×C4—124no—
723C2×C4—124no—
724C2×C4—128no—
725C2×C4—128no—
726C2×C4—124no—
727C2×C4—128no—
728C2×C4—122no—
729C2×C4—122no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—122no—
735C2×C4—122no—
736C2×C4#93712yes—
737C2×C4C2×D3×D412yes—
738C2×C4C2×D3×D411yescharacteristic
739C2×C4#100412yes—
740C2×C4C22×#6711yescharacteristic
741C8—42no—
742C8—122no—
743C2×C3—24no—
744C2×C3—84no—
745C2×C3#240311yescharacteristic
746C2×C3C2×#45011yescharacteristic
747C2×C3C2×#44811yescharacteristic
748C2×C3#300611yescharacteristic
749C2×C3#300711yescharacteristic
750C2×C3#318711yescharacteristic
751C2×C3#319311yescharacteristic
752D3—24no—
753D3—42no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—34no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—62no—
765C22—62no—
766C22—62no—
767C22—62no—
768C22—62no—
769C22—62no—
770C22—62no—
771C22—62no—
772C22—62no—
773C22—816no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—1216no—
779C22—121no—
780C22—121no—
781C22—121no—
782C22—121no—
783C22#517014yescomplemented
784C22D3×#12011yescharacteristic
785C22#558911yescharacteristic
786C22C2×D3×SD1611yescharacteristic
787C22C2×#91511yescharacteristic
788C22D3×AGL(1,ℤ/8)11yescharacteristic
789C22#577311yescharacteristic
790C22C2×#93711yescharacteristic
791C4—22no—
792C4—42no—
793C4—42no—
794C4—62no—
795C4—124no—
796C4—121no—
797C4—122no—
798C4—122no—
799C4#559012yes—
800C4D4×#6712yes—
801C3#2391911yescharacteristic, complemented, Sylow
802C2—24no—
803C2—64no—
804C2—84no—
805C2—122no—
806C2D3×#45011yescharacteristic
807C2#8014711yescharacteristic
808C2#8015011yescharacteristic
809C2#8015211yescharacteristic
810C2#8260411yescharacteristic
811C2C2×#517011yescharacteristic
812C2#8394611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#450C2
socleC23×C3C22×D4
prime radicalC22×#938C2
hypercenterC2×#450D3
hypocenterC3#23919
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
2. C2×D3×C22⋊Q8C2semidirect
3. C2×C3×#450C2semidirect
4. C2×#5218C2semidirect
5. C2×#5170C2semidirect
6. #72054C2semidirect
7. #71692C2semidirect
8. #70205C2semidirect
9. #70200C2semidirect
10. #69955C2semidirect
11. #69930C2semidirect
15. C22×D3×Q8C22semidirect
17. C22×C3×SD16C22semidirect
20. C2×#946C22semidirect
26. C22×#214C22semidirect
31. C2×#897C22semidirect
34. C2×D3×C4⋊C4C22semidirect
38. C2×C3×#102C22semidirect
40. C2×#835C22semidirect
42. C2×#832C22semidirect
45. C2×(C2×D3)⋊C8C22semidirect
46. C2×(C2×D3)⋊C8C22semidirect
47. C2×#816C22semidirect
48. #4551C22semidirect
49. #4529C22semidirect
54. C2×#450D3semidirect
99. C3×C22⋊Q8D4semidirect
126. #924D4semidirect
152. C22×SD16C2×D3semidirect
177. C2×#102C2×D3semidirect
199. C23×D3SD16semidirect
205. C2×C3×Q8C2×D4semidirect
273. C2×Dic6C2×D4semidirect
280. C3×C4⋊C4C2×D4semidirect
293. C4⋊Dic3C2×D4semidirect
350. C22⋊Q8#67semidirect
513. C2×Q8C2×#67semidirect
592. C4⋊C4C2×#67semidirect
613. C22×C3#448semidirect
635. C2×D3#450semidirect
783. C22#5170semidirect
801. C3#23919semidirect

Maximal subgroups

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

subgroupindex
C22×#9382
C2×D3×C22⋊Q82
C2×C3×#4502
C2×#52182
C2×#51702
#720542
#716922
#702052
#702002
#699552
#699302
#239193