Finite Group Databasebeta

← #11863948

Subgroups — #11863948

Order 1152.

2082 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×D3×D12C211yesmaximal, characteristic, complemented
2#10594892C211yesmaximal, characteristic, complemented
3C2×#63795C212yesmaximal, complemented
4#10592430C211yesmaximal, characteristic, complemented
5C3×#4732C211yesmaximal, characteristic, complemented
6C3×#4726C211yesmaximal, characteristic, complemented
7#10591172C211yesmaximal, characteristic, complemented
8#10591168C211yesmaximal, characteristic, complemented
9#10590946C212yesmaximal, complemented
10#10590944C212yesmaximal, complemented
11#10590939C212yesmaximal, complemented
12#80002—31nomaximal
13#78637—31nomaximal
14C23×D32—21no—
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×#626—21no—
19C2×D3×D12—21no—
20C2×D3×D12—21no—
21C2×D3×D12—28no—
22C2×D3×D12C2212yes—
23C2×D3×D12C2212yes—
24C2×#3795C2211yescharacteristic, complemented
25#64133C2211yescharacteristic, complemented
26C2×#3744C2212yescomplemented
27C3×#930C2211yescharacteristic, complemented
28C2×C3×D24C2212yescomplemented
29C2×C3×ΓL(1,𝔽25)C2212yescomplemented
30#63976—21no—
31Dic3×#67—21no—
32#63908C2211yescharacteristic, complemented
33#63905—21no—
34#63879—21no—
35#63857C2211yescharacteristic, complemented
36#63841C2211yescharacteristic, complemented
37C2×#3716C2212yescomplemented
38C2×#3714C2212yescomplemented
39#63795—28no—
40C32×C22⋊C8C2211yescharacteristic, complemented
41#63648C2212yescomplemented
42C3×#830C2211yescharacteristic, complemented
43C3×#821C2212yescomplemented
44C3×(C2×D3)⋊C8C2212yescomplemented
45#63564C2212yescomplemented
46#63563C2212yescomplemented
47C22×D3×D4—31no—
48C23×D12—31no—
49#5791—31no—
50C2×#911—32no—
51C2×#908—32no—
52#5606—31no—
53C3×#447—31no—
54C3×#407—31no—
55#5218—31no—
56#5156—32no—
57#5131—32no—
58#5036—31no—
59#4776—32no—
60#4770—32no—
61#4732—31no—
62#4732—32no—
63#4732D311yescharacteristic, complemented
64#4731—31no—
65#4731—31no—
66#4731—31no—
67#4731—32no—
68#4731—61no—
69#4726D311yescharacteristic, complemented
70C23×C3⋊D3—21no—
71C23×C3×D3—21no—
72C23×C3×D3D411yescharacteristic
73C22×D32—28no—
74C22×D32—22no—
75C22×D32—22no—
76C22×D32—44no—
77C22×D32—44no—
78C22×C32×C4C2311yescharacteristic
79C2×C4⋊(C3⋊D3)—21no—
80C2×C4⋊(C3⋊D3)—24no—
81C2×C4⋊(C3⋊D3)C2312yes—
82C2×#634C2311yescharacteristic, complemented
83C2×C3×#67—21no—
84C22×C3×Dic3D411yescharacteristic
85C2×C3×D12—21no—
86C2×C3×D12—24no—
87C2×C3×D12C2312yes—
88C2×C3×D12C2311yescharacteristic, complemented
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3D411yescharacteristic
91C2×C3×C4×D3D411yescharacteristic
92C2×C3×C4×D3C2311yescharacteristic
93C2×C3×C4×D3C2311yescharacteristic
94C2×#626—28no—
95C2×#626—22no—
96C2×#626—22no—
97C2×#625—21no—
98C2×#625—21no—
99C2×D3×Dic3—21no—
100D3×D12—28no—
101D3×D12—28no—
102D3×D12—24no—
103D3×D12—24no—
104D3×D12—24no—
105D3×D12D418yescomplemented
106#3795—24no—
107C2×C32×C8C2312yescomplemented
108#3757—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic, complemented
110#3750—21no—
111#3744—24no—
112C3×(C2×D3)⋊C4—21no—
113C3×C4⋊Dic3C2311yescharacteristic, complemented
114C2×C3×C3⋊C8C2312yescomplemented
115C3×D24—24no—
116C3×ΓL(1,𝔽25)—24no—
117Dic3⋊Dic3—21no—
118(C2×D3)⋊Dic3—21no—
119(C2×D3)⋊Dic3—21no—
120(C2×D3)⋊Dic3—21no—
121Dic32—21no—
122#3716—24no—
123#3714—24no—
124#3003—91noSylow
125C24×D3—61no—
126C24×D3—61no—
127C22×C3×D4—31no—
128C23×C3×C4—31no—
129C22×#67—61no—
130C2×#237—31no—
131C2×D3×D4—32no—
132C2×D3×D4—32no—
133C2×D3×D4—68no—
134C2×D3×D4—61no—
135C2×D3×D4—61no—
136C2×#235—31no—
137C22×D12—32no—
138C22×D12—31no—
139C22×D12—31no—
140C22×D12—32no—
141C22×D12—61no—
142C22×D12—68no—
143C22×D12—61no—
144C22×D12—61no—
145C22×D12—61no—
146C22×D12C2×D311yescharacteristic
147C22×C4×D3C2×D311yescharacteristic
148C2×C3×D8—32no—
149C2×C3×M16—32no—
150C3×#121—31no—
151#953—61no—
152#938—31no—
153#937—61no—
154D4×Dic3—61no—
155C2×#214—32no—
156C2×#213—32no—
157#930—31no—
158#930C2×D311yescharacteristic, complemented
159#929—61no—
160C4×#67—61no—
161C4×#67—61no—
162#926—31no—
163#924—31no—
164#924—31no—
165#924—31no—
166#924—61no—
167#911—68no—
168#908—68no—
169C2×D24—32no—
170C2×D24C2×D312yescomplemented
171C2×#204—32no—
172C2×#204—32no—
173C2×#204—32no—
174C2×#204—62no—
175C2×ΓL(1,𝔽25)C2×D312yescomplemented
176#897—31no—
177#892—31no—
178#883—61no—
179#67⋊C4—61no—
180C3×#102—32no—
181C3×C22⋊C8—21no—
182C3×C22⋊C8—31no—
183C3×C22⋊C8—32no—
184C3×C22⋊C8C2×D311yescharacteristic, complemented
185C3×C22⋊C8C2×D311yescharacteristic, complemented
186#832—32no—
187#830C2×D311yescharacteristic, complemented
188#821—32no—
189#821—32no—
190#821—32no—
191#821—32no—
192#821—62no—
193#821C2×D312yescomplemented
194(C2×D3)⋊C8C2×D312yescomplemented
195#809—32no—
196C23×C32C2×D411yescharacteristic
197C22×C3⋊D3—24no—
198C22×C3⋊D3—22no—
199C22×C3⋊D3—42no—
200C22×C3⋊D3—42no—
201C22×C3×D3—22no—
202C22×C3×D3—22no—
203C22×C3×D3—22no—
204C22×C3×D3—24no—
205C22×C3×D3—22no—
206C22×C3×D3—21no—
207C22×C3×D3—42no—
208C22×C3×D3—42no—
209C22×C3×D3C2×D411yescharacteristic
210C22×C3×D3C2×D411yescharacteristic
211C2×D32—28no—
212C2×D32—28no—
213C2×D32—432no—
214C2×D32—44no—
215C2×D32—44no—
216C2×D32—44no—
217C2×D32—44no—
218C2×C32×C4—22no—
219C2×C32×C4C2×D411yescharacteristic
220C2×C32×C4C2411yescharacteristic
221C2×C3⋊Dic3—21no—
222C2×C3⋊Dic3—21no—
223C4⋊(C3⋊D3)—24no—
224C4⋊(C3⋊D3)—22no—
225C4⋊(C3⋊D3)C2×D414yes—
226#634—22no—
227C3×#67—42no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3C2×D411yescharacteristic
231C2×C3×Dic3C2×D411yescharacteristic
232C3×D12—24no—
233C3×D12—22no—
234C3×D12—22no—
235C3×D12C2×D414yes—
236C3×C4×D3—22no—
237C3×C4×D3—22no—
238C3×C4×D3—22no—
239C3×C4×D3C2×D414yes—
240#626—28no—
241#626—28no—
242#625—42no—
243#625—42no—
244D3×Dic3—42no—
245C32×C8—22no—
246C3×C3⋊C8—22no—
247C23×D4—91no—
248C2×AGL(1,ℤ/8)—92no—
249#525—91no—
250#450—92no—
251#450—91no—
252#450—91no—
253#447—31no—
254#447—91no—
255#447—92no—
256#418—92no—
257#407—31no—
258C24×C3—31no—
259C24×C3—61no—
260C23×D3—21no—
261C23×D3—62no—
262C23×D3—62no—
263C23×D3—68no—
264C23×D3—68no—
265C23×D3—61no—
266C23×D3—61no—
267C23×D3—62no—
268C23×D3—62no—
269C23×D3—121no—
270C23×D3—124no—
271C23×D3—124no—
272C23×D3—124no—
273C23×D3—124no—
274C23×D3D1211yescharacteristic
275C2×C3×D4—32no—
276C2×C3×D4—31no—
277C2×C3×D4—64no—
278C2×C3×D4—61no—
279C2×C3×D4—61no—
280C22×C3×C4—21no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—64no—
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C2×#67—21no—
290C2×#67—68no—
291C2×#67—61no—
292C2×#67—61no—
293C2×#67—61no—
294C2×#67—61no—
295C2×#67—62no—
296C2×#67—62no—
297C22×Dic3—61no—
298C22×Dic3D1211yescharacteristic
299#237—64no—
300D3×D4—38no—
301D3×D4—64no—
302D3×D4—64no—
303D3×D4—68no—
304D3×D4—68no—
305D3×D4—64no—
306#235—64no—
307C2×D12—21no—
308C2×D12—24no—
309C2×D12—32no—
310C2×D12—32no—
311C2×D12—38no—
312C2×D12—62no—
313C2×D12—64no—
314C2×D12—64no—
315C2×D12—68no—
316C2×D12—68no—
317C2×D12—64no—
318C2×D12—64no—
319C2×D12—62no—
320C2×D12—62no—
321C2×D12—68no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—64no—
325C2×D12—124no—
326C2×D12—121no—
327C2×D12C22×D312yes—
328C2×D12C22×D311yescharacteristic, complemented
329C2×C4×D3—24no—
330C2×C4×D3—61no—
331C2×C4×D3D1211yescharacteristic
332C2×C4×D3D1211yescharacteristic
333C2×C4×D3C22×D311yescharacteristic
334C2×C4×D3C22×D311yescharacteristic
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—61no—
338C3×D8—64no—
339C3×M16—64no—
340C2×C3×C8—22no—
341C2×C3×C8—32no—
342C2×C3×C8C22×D312yescomplemented
343C2×C3×C8C22×D312yescomplemented
344C3×C4⋊C4—31no—
345C3×C22⋊C4—61no—
346#217—61no—
347#217—61no—
348#217—61no—
349#217—61no—
350#217—61no—
351#217—121no—
352#214—64no—
353#213—64no—
354(C2×D3)⋊C4—21no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358C4⋊Dic3—31no—
359C4⋊Dic3—31no—
360C4⋊Dic3—61no—
361C4⋊Dic3—61no—
362C4⋊Dic3C22×D311yescharacteristic, complemented
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—121no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C2×C3⋊C8C22×D312yescomplemented
370D24—24no—
371D24—64no—
372#204—64no—
373#204—64no—
374#204—64no—
375#204—124no—
376ΓL(1,𝔽25)—24no—
377C22×C32—21no—
378C22×C32—21no—
379C22×C32AGL(1,ℤ/8)12yescomplemented
380C22×C32C22×D411yescharacteristic
381C2×C3⋊D3—24no—
382C2×C3⋊D3—48no—
383C2×C3⋊D3—42no—
384C2×C3⋊D3—42no—
385C2×C3×D3—28no—
386C2×C3×D3—21no—
387C2×C3×D3—21no—
388C2×C3×D3—21no—
389C2×C3×D3—21no—
390C2×C3×D3—24no—
391C2×C3×D3—48no—
392C2×C3×D3—42no—
393C2×C3×D3—42no—
394C2×C3×D3—41no—
395C2×C3×D3—41no—
396C2×C3×D3—41no—
397C2×C3×D3#12012yes—
398C2×C3×D3AGL(1,ℤ/8)12yescomplemented
399D32—416no—
400D32—416no—
401C32×C4—21no—
402C32×C4C22×D412yes—
403C3⋊Dic3—41no—
404C3⋊Dic3—41no—
405C3×Dic3—21no—
406C3×Dic3—41no—
407C3×Dic3#12012yes—
408C25—181no—
409C2×#41—91no—
410C22×D4—31no—
411C22×D4—92no—
412C22×D4—92no—
413C22×D4—91no—
414C22×D4—181no—
415C22×D4—181no—
416C22×D4—181no—
417C22×D4—188no—
418C23×C4—31no—
419AGL(1,ℤ/8)—188no—
420C2×SD16—92no—
421C2×SD16—92no—
422C2×D8—32no—
423C2×D8—92no—
424C2×M16—32no—
425#123—181no—
426C22⋊Q8—91no—
427C22⋊Q8—91no—
428#121—31no—
429#121—91no—
430#120—181no—
431C4×D4—181no—
432C4×D4—181no—
433#117—91no—
434#102—32no—
435#102—92no—
436#102—92no—
437#102—92no—
438C22⋊C8—31no—
439C22⋊C8—32no—
440C22⋊C8D3211yescharacteristic, complemented
441C23×C3—21no—
442C23×C3—31no—
443C23×C3—31no—
444C23×C3—62no—
445C23×C3—62no—
446C23×C3—64no—
447C23×C3—62no—
448C23×C3—62no—
449C23×C3—61no—
450C23×C3—122no—
451C23×C3—122no—
452C23×C3C2×D1211yescharacteristic
453C23×C3D3×D411yescharacteristic
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—24no—
458C22×D3—22no—
459C22×D3—21no—
460C22×D3—42no—
461C22×D3—42no—
462C22×D3—68no—
463C22×D3—68no—
464C22×D3—68no—
465C22×D3—64no—
466C22×D3—64no—
467C22×D3—62no—
468C22×D3—62no—
469C22×D3—68no—
470C22×D3—122no—
471C22×D3—124no—
472C22×D3—1232no—
473C22×D3—124no—
474C22×D3—124no—
475C22×D3—124no—
476C22×D3—124no—
477C22×D3—1232no—
478C22×D3—124no—
479C22×D3—124no—
480C22×D3—124no—
481C22×D3—122no—
482C22×D3—122no—
483C22×D3—122no—
484C22×D3—122no—
485C22×D3—124no—
486C22×D3—242no—
487C22×D3—242no—
488C22×D3C2×D1211yescharacteristic
489C22×D3C2×D1211yescharacteristic
490C3×D4—34no—
491C3×D4—64no—
492C3×D4—62no—
493C3×D4—62no—
494C3×D4—122no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—31no—
500C2×C3×C4—34no—
501C2×C3×C4—31no—
502C2×C3×C4—42no—
503C2×C3×C4—62no—
504C2×C3×C4—62no—
505C2×C3×C4—62no—
506C2×C3×C4—62no—
507C2×C3×C4—61no—
508C2×C3×C4C2×D1211yescharacteristic
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—42no—
513#67—68no—
514#67—68no—
515#67—122no—
516#67—122no—
517#67—122no—
518#67—122no—
519C2×Dic3—22no—
520C2×Dic3—21no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—121no—
526C2×Dic3—121no—
527C2×Dic3—122no—
528C2×Dic3C2×D1211yescharacteristic
529C2×Dic3C2×D1211yescharacteristic
530D12—24no—
531D12—22no—
532D12—22no—
533D12—34no—
534D12—34no—
535D12—64no—
536D12—64no—
537D12—64no—
538D12—68no—
539D12—68no—
540D12—62no—
541D12—62no—
542D12—122no—
543D12—124no—
544D12D3×D414yes—
545C4×D3—22no—
546C4×D3—22no—
547C4×D3—22no—
548C4×D3—122no—
549C4×D3D3×D414yes—
550Dic6—62no—
551Dic6—62no—
552Dic6—122no—
553C3×C8—22no—
554C3×C8—22no—
555C3×C8—42no—
556C3×C8—62no—
557C3⋊C8—22no—
558C2×C32—22no—
559C2×C32C2×#12011yescharacteristic
560C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
561C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
562C3⋊D3—44no—
563C3×D3—22no—
564C3×D3—22no—
565C3×D3—44no—
566C3×D3—81no—
567C24—31no—
568C24—61no—
569C24—182no—
570C24—182no—
571C24—188no—
572C24—181no—
573C24—364no—
574C24—364no—
575#41—184no—
576C2×Q8—91no—
577C2×D4—32no—
578C2×D4—31no—
579C2×D4—64no—
580C2×D4—61no—
581C2×D4—61no—
582C2×D4—98no—
583C2×D4—92no—
584C2×D4—184no—
585C2×D4—184no—
586C2×D4—182no—
587C2×D4—182no—
588C2×D4—184no—
589C2×D4—184no—
590C2×D4—188no—
591C2×D4—188no—
592C2×D4—188no—
593C2×D4—181no—
594C2×D4—181no—
595C2×D4—181no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—64no—
602C22×C4—181no—
603C22×C4C2×D3211yescharacteristic
604SD16—184no—
605SD16—184no—
606D8—64no—
607D8—184no—
608M16—64no—
609C2×C8—32no—
610C2×C8C2×D3212yescomplemented
611C4⋊C4—31no—
612C4⋊C4—91no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C22⋊C4—61no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C42—181no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—22no—
627C22×C3—32no—
628C22×C3—32no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—68no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—64no—
637C22×C3—128no—
638C22×C3—122no—
639C22×C3—122no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3#90812yescomplemented
644C22×C3#91112yescomplemented
645C22×C3C22×D1211yescharacteristic
646C22×C3C2×D3×D411yescharacteristic
647C2×D3—28no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—24no—
653C2×D3—48no—
654C2×D3—42no—
655C2×D3—42no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—64no—
660C2×D3—64no—
661C2×D3—124no—
662C2×D3—1216no—
663C2×D3—1216no—
664C2×D3—1216no—
665C2×D3—1216no—
666C2×D3—128no—
667C2×D3—128no—
668C2×D3—122no—
669C2×D3—122no—
670C2×D3—122no—
671C2×D3—122no—
672C2×D3—242no—
673C2×D3—242no—
674C2×D3—248no—
675C2×D3#88212yes—
676C2×D3#90812yescomplemented
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—22no—
680C3×C4—32no—
681C3×C4—41no—
682C3×C4—61no—
683C3×C4—121no—
684C3×C4C2×D3×D412yes—
685C3×C4C2×D3×D412yes—
686Dic3—21no—
687Dic3—41no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—241no—
693Dic3—241no—
694Dic3#88212yes—
695C32#300311yescharacteristic, complemented, Sylow
696C23—31no—
697C23—31no—
698C23—62no—
699C23—62no—
700C23—64no—
701C23—62no—
702C23—62no—
703C23—61no—
704C23—122no—
705C23—122no—
706C23—184no—
707C23—188no—
708C23—188no—
709C23—182no—
710C23—362no—
711C23—364no—
712C23—3632no—
713C23—364no—
714C23—364no—
715C23—364no—
716C23—362no—
717C23D3×D1211yescharacteristic
718Q8—182no—
719D4—34no—
720D4—64no—
721D4—62no—
722D4—62no—
723D4—94no—
724D4—122no—
725D4—184no—
726D4—188no—
727D4—188no—
728D4—182no—
729D4—362no—
730D4—362no—
731C2×C4—22no—
732C2×C4—31no—
733C2×C4—34no—
734C2×C4—31no—
735C2×C4—62no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—61no—
740C2×C4—181no—
741C2×C4—181no—
742C2×C4—362no—
743C2×C4D3×D1211yescharacteristic
744C2×C4C22×D3211yescharacteristic
745C8—22no—
746C8—62no—
747C2×C3—22no—
748C2×C3—22no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—42no—
753C2×C3—62no—
754C2×C3—62no—
755C2×C3—124no—
756C2×C3—241no—
757C2×C3C2×#88211yescharacteristic
758C2×C3D3×#12011yescharacteristic
759C2×C3C2×#90811yescharacteristic
760C2×C3C2×#90811yescharacteristic
761C2×C3C2×#91111yescharacteristic
762C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
763D3—22no—
764D3—22no—
765D3—44no—
766D3—81no—
767D3—124no—
768D3—124no—
769D3—244no—
770C22—21no—
771C22—21no—
772C22—32no—
773C22—32no—
774C22—68no—
775C22—61no—
776C22—61no—
777C22—61no—
778C22—61no—
779C22—64no—
780C22—128no—
781C22—122no—
782C22—122no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—184no—
787C22—368no—
788C22—3616no—
789C22—3616no—
790C22—362no—
791C22—362no—
792C22#6379512yescomplemented
793C22C2×D3×D1211yescharacteristic
794C4—21no—
795C4—32no—
796C4—61no—
797C4—121no—
798C4—361no—
799C4—361no—
800C4D32×D412yes—
801C3—21no—
802C3#7863711yescharacteristic, complemented
803C3#8000211yescharacteristic, complemented
804C2—22no—
805C2—62no—
806C2—62no—
807C2—124no—
808C2—241no—
809C2—364no—
810C2D3×#88211yescharacteristic
811C2C2×#6379511yescharacteristic
812C2D3×#90811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3003
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C22×D3×D12C2semidirect
2. #10594892C2semidirect
3. C2×#63795C2semidirect
4. #10592430C2semidirect
5. C3×#4732C2semidirect
6. C3×#4726C2semidirect
7. #10591172C2semidirect
8. #10591168C2semidirect
9. #10590946C2semidirect
10. #10590944C2semidirect
11. #10590939C2semidirect
24. C2×#3795C22semidirect
25. #64133C22semidirect
26. C2×#3744C22semidirect
27. C3×#930C22semidirect
28. C2×C3×D24C22semidirect
29. C2×C3×ΓL(1,𝔽25)C22semidirect
32. #63908C22semidirect
35. #63857C22semidirect
36. #63841C22semidirect
37. C2×#3716C22semidirect
38. C2×#3714C22semidirect
40. C32×C22⋊C8C22semidirect
41. #63648C22semidirect
42. C3×#830C22semidirect
43. C3×#821C22semidirect
44. C3×(C2×D3)⋊C8C22semidirect
45. #63564C22semidirect
46. #63563C22semidirect
63. #4732D3semidirect
69. #4726D3semidirect
82. C2×#634C23semidirect
88. C2×C3×D12C23semidirect
105. D3×D12D4semidirect
107. C2×C32×C8C23semidirect
109. C4⋊(C3⋊Dic3)C23semidirect
113. C3×C4⋊Dic3C23semidirect
114. C2×C3×C3⋊C8C23semidirect
158. #930C2×D3semidirect
170. C2×D24C2×D3semidirect
175. C2×ΓL(1,𝔽25)C2×D3semidirect
184. C3×C22⋊C8C2×D3semidirect
185. C3×C22⋊C8C2×D3semidirect
187. #830C2×D3semidirect
193. #821C2×D3semidirect
194. (C2×D3)⋊C8C2×D3semidirect
328. C2×D12C22×D3semidirect
342. C2×C3×C8C22×D3semidirect
343. C2×C3×C8C22×D3semidirect
362. C4⋊Dic3C22×D3semidirect
369. C2×C3⋊C8C22×D3semidirect
379. C22×C32AGL(1,ℤ/8)semidirect
398. C2×C3×D3AGL(1,ℤ/8)semidirect
440. C22⋊C8D32semidirect
610. C2×C8C2×D32semidirect
643. C22×C3#908semidirect
644. C22×C3#911semidirect
676. C2×D3#908semidirect
695. C32#3003semidirect
792. C22#63795semidirect
802. C3#78637semidirect
803. C3#80002semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D122
#105948922
C2×#637952
#105924302
C3×#47322
C3×#47262
#105911722
#105911682
#105909462
#105909442
#105909392
#800023
#786373