Finite Group Databasebeta

← #10826943

Subgroups — #10826943

Order 768.

2272 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic, complemented
2C2×#5791C211yesmaximal, characteristic, complemented
3C2×#5218C211yesmaximal, characteristic, complemented
4C2×#5217C211yesmaximal, characteristic, complemented
5C2×#5037C212yesmaximal, complemented
6#72126C211yesmaximal, characteristic, complemented
7#71685C212yesmaximal, complemented
8#71684C212yesmaximal, complemented
9#71678C212yesmaximal, complemented
10#71560C211yesmaximal, characteristic, complemented
11#71559C211yesmaximal, characteristic, complemented
12#23920—31nomaximal, Sylow
13C23×C3×D4—21no—
14C23×C3×D4C2211yescharacteristic
15C24×C3×C4C2211yescharacteristic
16C22×#235C2211yescharacteristic, complemented
17C2×C3×#121—21no—
18C2×C3×#121—21no—
19C2×C3×#121—28no—
20C2×C3×#121C2212yes—
21C2×C3×#121C2212yes—
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4—21no—
24C2×#953—21no—
25C22×#214C2212yescomplemented
26C22×#213C2212yescomplemented
27#5791—24no—
28#5791—24no—
29C2×#930C2211yescharacteristic
30C2×#930C2211yescharacteristic, complemented
31C2×#929—21no—
32C2×C4×#67—21no—
33C2×C4×#67—21no—
34C2×#926C2211yescharacteristic, complemented
35C2×#924C2211yescharacteristic
36C2×#924C2211yescharacteristic, complemented
37#5218—24no—
38#5217—24no—
39C2×#832C2212yescomplemented
40C2×#832C2212yescomplemented
41C2×#830C2211yescharacteristic
42C2×#830C2211yescharacteristic
43C2×#830C2212yescomplemented
44C2×#830C2212yescomplemented
45#5037—28no—
46C2×#810C2212yescomplemented
47C2×#809C2212yescomplemented
48#4529C2212yescomplemented
49#4529C2212yescomplemented
50C2×#525—31no—
51C22×#121D311yescharacteristic, complemented
52C2×#449—32no—
53C2×#450—31no—
54C2×#447—31no—
55#2000—32no—
56#1999—32no—
57#1875—32no—
58#1874—31no—
59#1872—31no—
60#1779—31no—
61C25×C3—21no—
62C25×C3D411yescharacteristic
63C22×C3×D4—28no—
64C22×C3×D4—22no—
65C22×C3×D4—22no—
66C22×C3×D4—24no—
67C22×C3×D4—21no—
68C22×C3×D4—22no—
69C22×C3×D4—22no—
70C22×C3×D4—42no—
71C22×C3×D4—44no—
72C22×C3×D4—44no—
73C22×C3×D4C2312yes—
74C23×C3×C4—21no—
75C23×C3×C4—22no—
76C23×C3×C4—22no—
77C23×C3×C4—24no—
78C23×C3×C4—42no—
79C23×C3×C4D411yescharacteristic
80C23×C3×C4D411yescharacteristic
81C23×C3×C4D411yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C22×#67—21no—
86C22×#67—21no—
87C22×#67—21no—
88C2×#235—22no—
89C2×#235—24no—
90C2×#235—22no—
91C2×#235—42no—
92C22×D12C2311yescharacteristic
93C22×C4×D3—21no—
94C22×Dic6C2311yescharacteristic
95C3×#121—28no—
96C3×#121—28no—
97C3×#121—24no—
98C3×#121—24no—
99C3×#121—24no—
100C3×#121D418yescomplemented
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4—24no—
103C2×C3×C4⋊C4C2312yes—
104C2×C3×C22⋊C4—28no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107#953—28no—
108C2×#217—21no—
109C2×#217—21no—
110C2×#217—21no—
111C2×#214—24no—
112C2×#214—24no—
113C2×#214—42no—
114C2×#213—24no—
115C2×#213—24no—
116C2×#213—42no—
117#930—22no—
118#930—22no—
119#930—22no—
120#930D414yescomplemented
121#929—28no—
122C4×#67—28no—
123C4×#67—28no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126#926—22no—
127#926—22no—
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130#924—22no—
131#924—22no—
132#924—22no—
133#924D414yescomplemented
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×C4×Dic3—21no—
137C22×C3⋊C8C2312yes—
138C22×C3⋊C8C2312yes—
139#832—24no—
140#832—24no—
141#830—22no—
142#830—22no—
143#830—24no—
144#830—42no—
145#810—24no—
146#809—24no—
147C22×#41—31no—
148C23×D4—21no—
149C23×D4C2×D311yescharacteristic
150C24×C4C2×D311yescharacteristic
151C22×SD16—32no—
152C22×D8—32no—
153#525—64no—
154#525—64no—
155C2×#123—61no—
156C2×C22⋊Q8—31no—
157C2×C22⋊Q8—31no—
158C2×#121—21no—
159C2×#121—21no—
160C2×#121—28no—
161C2×#121—31no—
162C2×#121—31no—
163C2×#121C2×D312yes—
164C2×#121C2×D312yes—
165C2×#120—61no—
166C2×C4×D4—61no—
167C2×C4×D4—61no—
168C2×#117—31no—
169C22×C4⋊C4C2×D311yescharacteristic
170C22×C22⋊C4—21no—
171#450—64no—
172#449—68no—
173#447—64no—
174C2×#103—32no—
175C2×#102—32no—
176C2×#102—32no—
177C2×#102—32no—
178C2×C22⋊C8—31no—
179C2×C22⋊C8—31no—
180C2×C22⋊C8—32no—
181C2×C22⋊C8—32no—
182#340—32no—
183#340—32no—
184C24×C3—22no—
185C24×C3—22no—
186C24×C3—22no—
187C24×C3—24no—
188C24×C3—22no—
189C24×C3—22no—
190C24×C3—22no—
191C24×C3—41no—
192C24×C3—41no—
193C24×C3—42no—
194C24×C3—42no—
195C24×C3—42no—
196C24×C3—42no—
197C24×C3—42no—
198C24×C3—42no—
199C24×C3C2×D411yescharacteristic
200C24×C3C2×D411yescharacteristic
201C24×C3C2×D411yescharacteristic
202C23×D3—21no—
203C2×C3×D4—24no—
204C2×C3×D4—28no—
205C2×C3×D4—28no—
206C2×C3×D4—22no—
207C2×C3×D4—22no—
208C2×C3×D4—22no—
209C2×C3×D4—22no—
210C2×C3×D4—22no—
211C2×C3×D4—48no—
212C2×C3×D4—48no—
213C2×C3×D4—42no—
214C2×C3×D4—432no—
215C2×C3×D4—44no—
216C2×C3×D4—44no—
217C2×C3×D4—44no—
218C2×C3×D4—44no—
219C2×C3×D4—42no—
220C2×C3×D4C2×D414yes—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—24no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—41no—
239C22×C3×C4—41no—
240C22×C3×C4—41no—
241C22×C3×C4—48no—
242C22×C3×C4—48no—
243C22×C3×C4—42no—
244C22×C3×C4—42no—
245C22×C3×C4C2×D412yes—
246C22×C3×C4C2×D412yes—
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D414yes—
251C22×C3×C4C2411yescharacteristic
252C2×#67—24no—
253C2×#67—24no—
254C2×#67—24no—
255C2×#67—42no—
256C2×#67—42no—
257C2×#67—42no—
258C2×#67—42no—
259C2×#67—42no—
260C2×#67—42no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264#235—48no—
265#235—48no—
266C2×D12—22no—
267C2×D12—22no—
268C2×D12—21no—
269C2×D12C2×D412yescomplemented
270C2×C4×D3—24no—
271C2×C4×D3—42no—
272C2×C4×D3—42no—
273C2×Dic6—22no—
274C2×Dic6—22no—
275C2×Dic6—21no—
276C2×Dic6C2×D412yescomplemented
277C3×C4⋊C4—24no—
278C3×C4⋊C4—22no—
279C3×C4⋊C4C2×D414yes—
280C3×C22⋊C4—28no—
281C3×C22⋊C4—28no—
282#217—24no—
283#217—24no—
284#217—24no—
285#214—48no—
286#213—48no—
287(C2×D3)⋊C4—24no—
288(C2×D3)⋊C4—24no—
289C4⋊Dic3—21no—
290C4⋊Dic3—21no—
291C4⋊Dic3C2×D412yescomplemented
292C4⋊Dic3C2×D412yescomplemented
293Dic3⋊C4—24no—
294Dic3⋊C4—24no—
295C4×Dic3—24no—
296C2×C3⋊C8—22no—
297C2×C3⋊C8—22no—
298C2×C3⋊C8—22no—
299C2×C3⋊C8—22no—
300C2×C3⋊C8—22no—
301C2×C3⋊C8—22no—
302C25—21no—
303C25#6711yescharacteristic
304C2×#41—62no—
305C2×#41—62no—
306C2×#41—64no—
307C2×#41—122no—
308C22×Q8—31no—
309C22×D4—28no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—24no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—21no—
316C22×D4—31no—
317C22×D4—42no—
318C22×D4—44no—
319C22×D4—44no—
320C22×D4—61no—
321C22×D4—61no—
322C22×D4—61no—
323C22×D4C22×D312yes—
324C23×C4—21no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—24no—
328C23×C4—42no—
329C23×C4—61no—
330C23×C4#6711yescharacteristic
331C23×C4#6711yescharacteristic
332C23×C4#6711yescharacteristic
333C23×C4C22×D311yescharacteristic
334C23×C4C22×D311yescharacteristic
335C23×C4C22×D311yescharacteristic
336C2×SD16—64no—
337C2×SD16—64no—
338C2×SD16—122no—
339C2×D8—64no—
340C2×D8—64no—
341C2×D8—122no—
342C22×C8—32no—
343C22×C8—32no—
344#123—68no—
345C22⋊Q8—34no—
346C22⋊Q8—62no—
347C22⋊Q8—62no—
348C22⋊Q8—62no—
349#121—28no—
350#121—28no—
351#121—24no—
352#121—24no—
353#121—24no—
354#121—34no—
355#121—62no—
356#121—62no—
357#121—62no—
358#121#6718yescomplemented
359#120—68no—
360C4×D4—68no—
361C4×D4—68no—
362#117—62no—
363#117—62no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4—61no—
370C2×C4⋊C4C22×D312yes—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C42—61no—
380#103—64no—
381#102—64no—
382#102—64no—
383#102—64no—
384C22⋊C8—62no—
385C22⋊C8—62no—
386C22⋊C8—64no—
387C22⋊C8—122no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—28no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—24no—
406C23×C3—44no—
407C23×C3—44no—
408C23×C3—44no—
409C23×C3—44no—
410C23×C3—44no—
411C23×C3—48no—
412C23×C3—48no—
413C23×C3—48no—
414C23×C3—44no—
415C23×C3—42no—
416C23×C3—42no—
417C23×C3—42no—
418C23×C3—42no—
419C23×C3—42no—
420C23×C3—42no—
421C23×C3—84no—
422C23×C3—84no—
423C23×C3—84no—
424C23×C3—84no—
425C23×C3#12012yes—
426C23×C3#12012yes—
427C23×C3#13512yes—
428C23×C3AGL(1,ℤ/8)12yes—
429C23×C3AGL(1,ℤ/8)12yes—
430C23×C3C22×D411yescharacteristic
431C22×D3—22no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C3×D4—24no—
439C3×D4—24no—
440C3×D4—48no—
441C3×D4—416no—
442C3×D4—416no—
443C3×D4—42no—
444C3×D4—42no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—24no—
450C2×C3×C4—24no—
451C2×C3×C4—24no—
452C2×C3×C4—24no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—24no—
456C2×C3×C4—21no—
457C2×C3×C4—44no—
458C2×C3×C4—44no—
459C2×C3×C4—44no—
460C2×C3×C4—48no—
461C2×C3×C4—42no—
462C2×C3×C4—42no—
463C2×C3×C4—42no—
464C2×C3×C4—42no—
465C2×C3×C4#12012yes—
466C2×C3×C4#12012yes—
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4C22×D411yescharacteristic
469C2×C3×C4C22×D412yes—
470C2×C3×C4H(5,𝔽2)12yes—
471#67—48no—
472#67—48no—
473#67—48no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483D12—24no—
484D12—42no—
485C4×D3—48no—
486Dic6—24no—
487Dic6—42no—
488C3⋊C8—42no—
489C3⋊C8—42no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—24no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—41no—
498C24—41no—
499C24—42no—
500C24—42no—
501C24—42no—
502C24—42no—
503C24—42no—
504C24—42no—
505C24—61no—
506C24C2×#6711yescharacteristic
507C24C2×#6711yescharacteristic
508C24C2×#6711yescharacteristic
509#41—128no—
510#41—128no—
511C2×Q8—32no—
512C2×Q8—61no—
513C2×Q8—62no—
514C2×Q8—62no—
515C2×D4—24no—
516C2×D4—28no—
517C2×D4—28no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—32no—
524C2×D4—48no—
525C2×D4—48no—
526C2×D4—42no—
527C2×D4—432no—
528C2×D4—44no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—42no—
533C2×D4—64no—
534C2×D4—64no—
535C2×D4—64no—
536C2×D4—61no—
537C2×D4—62no—
538C2×D4—62no—
539C2×D4—122no—
540C2×D4—122no—
541C2×D4—122no—
542C2×D4—122no—
543C2×D4—122no—
544C2×D4—122no—
545C2×D4C2×#6714yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—64no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—122no—
575C22×C4—122no—
576C22×C4D3×D412yes—
577C22×C4D3×D412yes—
578C22×C4C2×#6711yescharacteristic
579C22×C4C2×#6711yescharacteristic
580C22×C4C2×#6711yescharacteristic
581C22×C4C2×#6714yes—
582C22×C4C23×D311yescharacteristic
583SD16—128no—
584D8—128no—
585C2×C8—62no—
586C2×C8—62no—
587C2×C8—62no—
588C2×C8—62no—
589C2×C8—62no—
590C2×C8—62no—
591C4⋊C4—24no—
592C4⋊C4—22no—
593C4⋊C4—32no—
594C4⋊C4—32no—
595C4⋊C4—64no—
596C4⋊C4—64no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4C2×#6714yes—
600C22⋊C4—28no—
601C22⋊C4—28no—
602C22⋊C4—64no—
603C22⋊C4—64no—
604C22⋊C4—64no—
605C22⋊C4—64no—
606C22⋊C4—64no—
607C42—64no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—416no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—44no—
630C22×C3—44no—
631C22×C3—44no—
632C22×C3—816no—
633C22×C3—82no—
634C22×C3—82no—
635C22×C3—82no—
636C22×C3—82no—
637C22×C3#44914yescomplemented
638C22×C3C2×#12011yescharacteristic
639C22×C3C2×#12011yescharacteristic
640C22×C3#53411yescharacteristic
641C22×C3C2×#13511yescharacteristic
642C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
643C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
644C22×C3#57511yescharacteristic
645C2×D3—42no—
646C2×D3—42no—
647C2×D3—42no—
648C2×D3—81no—
649C2×D3—81no—
650C2×D3—81no—
651C2×D3—81no—
652C3×C4—22no—
653C3×C4—22no—
654C3×C4—41no—
655C3×C4—44no—
656C3×C4D4212yes—
657C3×C4D4212yes—
658Dic3—42no—
659Dic3—42no—
660Dic3—42no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—28no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—24no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—48no—
685C23—48no—
686C23—48no—
687C23—44no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—62no—
695C23—84no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—121no—
700C23—121no—
701C23—121no—
702C23—121no—
703C23—121no—
704C23—121no—
705C23#93212yes—
706C23#93212yes—
707C23#93712yes—
708C23#95012yes—
709C23#95312yes—
710C23C22×#6711yescharacteristic
711Q8—64no—
712Q8—122no—
713D4—24no—
714D4—24no—
715D4—48no—
716D4—416no—
717D4—416no—
718D4—42no—
719D4—42no—
720D4—64no—
721D4—128no—
722D4—128no—
723D4—128no—
724D4—122no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—24no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—48no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—128no—
749C2×C4—121no—
750C2×C4—121no—
751C2×C4—121no—
752C2×C4—121no—
753C2×C4—121no—
754C2×C4—121no—
755C2×C4#93712yes—
756C2×C4#95312yes—
757C2×C4C2×D3×D411yescharacteristic
758C2×C4C2×D3×D411yescharacteristic
759C2×C4#100412yes—
760C2×C4C22×#6712yes—
761C8—122no—
762C8—122no—
763C2×C3—24no—
764C2×C3—42no—
765C2×C3—42no—
766C2×C3—84no—
767C2×C3#240311yescharacteristic
768C2×C3C2×#44911yescharacteristic
769C2×C3#300211yescharacteristic
770C2×C3#300311yescharacteristic
771C2×C3#300611yescharacteristic
772C2×C3#318811yescharacteristic
773C2×C3#319411yescharacteristic
774D3—82no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—416no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—816no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—122no—
805C22—122no—
806C22—122no—
807C22—241no—
808C22—241no—
809C22—241no—
810C22—241no—
811C22#503714yescomplemented
812C22C2×#93211yescharacteristic
813C22C2×#93211yescharacteristic
814C22C2×#93711yescharacteristic
815C22#580411yescharacteristic
816C22C2×#95011yescharacteristic
817C22#582211yescharacteristic
818C22C2×#95311yescharacteristic
819C4—22no—
820C4—22no—
821C4—44no—
822C4—41no—
823C4—122no—
824C4—122no—
825C4—122no—
826C4D4×#6712yes—
827C4D4×#6712yes—
828C3#2392011yescharacteristic, complemented, Sylow
829C2—24no—
830C2—42no—
831C2—42no—
832C2—84no—
833C2—242no—
834C2C2×#503711yescharacteristic
835C2#8262411yescharacteristic
836C2#8262611yescharacteristic
837C2#8262811yescharacteristic
838C2#8403811yescharacteristic
839C2#8405211yescharacteristic
840C2#8408011yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC22×C3×#121C2
socleC23×C3C22×D4
hypercenterC22×#121D3
hypocenterC3#23920
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×C3×#121C2semidirect
2. C2×#5791C2semidirect
3. C2×#5218C2semidirect
4. C2×#5217C2semidirect
5. C2×#5037C2semidirect
6. #72126C2semidirect
7. #71685C2semidirect
8. #71684C2semidirect
9. #71678C2semidirect
10. #71560C2semidirect
11. #71559C2semidirect
16. C22×#235C22semidirect
25. C22×#214C22semidirect
26. C22×#213C22semidirect
30. C2×#930C22semidirect
34. C2×#926C22semidirect
36. C2×#924C22semidirect
39. C2×#832C22semidirect
40. C2×#832C22semidirect
43. C2×#830C22semidirect
44. C2×#830C22semidirect
46. C2×#810C22semidirect
47. C2×#809C22semidirect
48. #4529C22semidirect
49. #4529C22semidirect
51. C22×#121D3semidirect
100. C3×#121D4semidirect
120. #930D4semidirect
133. #924D4semidirect
269. C2×D12C2×D4semidirect
276. C2×Dic6C2×D4semidirect
291. C4⋊Dic3C2×D4semidirect
292. C4⋊Dic3C2×D4semidirect
358. #121#67semidirect
637. C22×C3#449semidirect
811. C22#5037semidirect
828. C3#23920semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1212
C2×#57912
C2×#52182
C2×#52172
C2×#50372
#721262
#716852
#716842
#716782
#715602
#715592
#239203