Finite Group Databasebeta

← #11864133

Subgroups — #11864133

Order 1152.

1711 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic, complemented
2C2×#63925C212yesmaximal, complemented
3D3×#930C211yesmaximal, characteristic, complemented
4#10592916C211yesmaximal, characteristic, complemented
5C3×#5217C211yesmaximal, characteristic, complemented
6#10591452C212yesmaximal, complemented
7#10591450C212yesmaximal, complemented
8#10591414C212yesmaximal, complemented
9#10591174C211yesmaximal, characteristic, complemented
10#10591171C211yesmaximal, characteristic, complemented
11#10591154C211yesmaximal, characteristic, complemented
12#84082—31nomaximal
13#80003—31nomaximal
14C22×C32×D4C2211yescharacteristic, complemented
15C22×C3×#67—21no—
16C23×C3×Dic3—21no—
17C2×C3×#237—28no—
18C2×C3×#237—21no—
19C2×C3×#237—21no—
20C2×C3×#237C2212yes—
21C2×C3×#237C2212yescomplemented
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic, complemented
24C2×D3×#67—21no—
25C2×D3×D12C2211yescharacteristic, complemented
26C2×#3753C2212yescomplemented
27#64139C2211yescharacteristic
28C2×C3×#213C2212yescomplemented
29C3×#930C2211yescharacteristic
30#63978—21no—
31#63925—28no—
32D3×(C2×D3)⋊C4—21no—
33#63909C2211yescharacteristic, complemented
34#63908C2211yescharacteristic, complemented
35#63906—21no—
36D3×C4⋊Dic3C2211yescharacteristic, complemented
37C2×#3717C2212yescomplemented
38C2×#3715C2212yescomplemented
39C2×#3711C2212yescomplemented
40#63659C2212yescomplemented
41#63657C2211yescharacteristic, complemented
42C3×#832C2212yescomplemented
43C3×#830C2211yescharacteristic, complemented
44#63566C2212yescomplemented
45#63565C2212yescomplemented
46(C2×D3)⋊(C3⋊C8)C2212yescomplemented
47C22×C3×#41—31no—
48C22×#237D311yescharacteristic, complemented
49C2×#949—32no—
50C2×#930—31no—
51C2×#911—32no—
52D3×#121—31no—
53C3×#447—31no—
54#5238—32no—
55#5238—32no—
56#5232—32no—
57#5227—31no—
58#5227—31no—
59#5217—31no—
60#5217—31no—
61#5217—61no—
62#5217D311yescharacteristic, complemented
63#5207—31no—
64#5158—32no—
65#5040—31no—
66#4781—32no—
67#4771—32no—
68#4738—31no—
69#4726—31no—
70C24×C32—21no—
71C23×C3×D3D411yescharacteristic
72C22×D32—21no—
73C2×C32×D4—24no—
74C2×C32×D4—21no—
75C2×C32×D4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C2×#638—21no—
78C2×C4⋊(C3⋊D3)C2311yescharacteristic
79C2×C3×#67—28no—
80C2×C3×#67—22no—
81C2×C3×#67—22no—
82C2×C3×#67—21no—
83C22×C3×Dic3—28no—
84C22×C3×Dic3—21no—
85C22×C3×Dic3—22no—
86C22×C3×Dic3—22no—
87C22×C3×Dic3D411yescharacteristic
88C3×#237—28no—
89C3×#237—28no—
90C3×#237—24no—
91C3×#237—24no—
92C3×#237—24no—
93C3×#237D418yescomplemented
94C2×C3×D12C2311yescharacteristic
95C2×C3×C4×D3—24no—
96C2×C3×C4×D3D411yescharacteristic
97C2×C3×C4×D3D411yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6—21no—
101C2×C3×Dic6—24no—
102C2×C3×Dic6C2312yes—
103D3×#67—44no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×D3×Dic3—21no—
108D3×D12—24no—
109#3753—24no—
110#3752—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3⋊(C3⋊C8)C2312yes—
113C3×#213—24no—
114C3×(C2×D3)⋊C4—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊C8C2312yes—
117Dic3⋊Dic3—21no—
118#3722—21no—
119(C2×D3)⋊Dic3—21no—
120#3717—24no—
121#3715—24no—
122#3711—24no—
123#3006—91noSylow
124C2×C3×#41—32no—
125C2×C3×#41—32no—
126C2×C3×#41—61no—
127C2×C3×#41—61no—
128C2×C3×#41—68no—
129C22×C3×Q8—31no—
130C22×C3×D4—21no—
131C22×C3×D4—61no—
132C22×C3×D4C2×D311yescharacteristic, complemented
133C22×C3×D4C2×D311yescharacteristic, complemented
134C23×C3×C4—31no—
135C23×C3×C4—61no—
136C22×#67—21no—
137C22×#67—61no—
138C23×Dic3—21no—
139C2×#237—28no—
140C2×#237—21no—
141C2×#237—21no—
142C2×#237C2×D312yes—
143C2×#237C2×D312yescomplemented
144C2×D3×D4—31no—
145C2×D3×D4—61no—
146C22×D12—31no—
147C22×C4×D3C2×D311yescharacteristic
148C22×Dic6C2×D311yescharacteristic, complemented
149C2×C3×D8—32no—
150C3×#121—31no—
151#949—68no—
152C2×#215—32no—
153C2×#215—32no—
154#939—61no—
155#938—31no—
156C2×#214—32no—
157C2×#213—32no—
158C2×#213—32no—
159C2×#213—62no—
160C2×#213C2×D312yescomplemented
161#930—31no—
162#930—31no—
163#930—31no—
164#930—31no—
165#930—61no—
166#930—61no—
167#930—61no—
168#930C2×D311yescharacteristic
169C2×(C2×D3)⋊C4—61no—
170C2×C4⋊Dic3—31no—
171C2×#208—32no—
172#911—68no—
173C2×#204—32no—
174C2×ΓL(1,𝔽25)—32no—
175#895—31no—
176D3×C4⋊C4—31no—
177#884—61no—
178D3×C22⋊C4—61no—
179C3×#102—32no—
180C3×C22⋊C8—31no—
181#835—32no—
182#835—32no—
183#832—32no—
184#832—32no—
185#832—62no—
186#832C2×D312yescomplemented
187#830—31no—
188#830—31no—
189#830—32no—
190#830—61no—
191#830C2×D311yescharacteristic, complemented
192(C2×D3)⋊C8—32no—
193#816—32no—
194#810—32no—
195C23×C32—24no—
196C23×C32—22no—
197C23×C32—42no—
198C23×C32—42no—
199C23×C32C2×D411yescharacteristic
200C22×C3⋊D3—21no—
201C22×C3×D3—22no—
202C22×C3×D3—22no—
203C22×C3×D3—21no—
204C22×C3×D3—41no—
205C22×C3×D3C2×D411yescharacteristic
206C22×C3×D3C2×D411yescharacteristic
207C2×D32—42no—
208C2×D32—42no—
209C2×D32—42no—
210C32×D4—24no—
211C32×D4—22no—
212C32×D4C2×D414yescomplemented
213C2×C32×C4—22no—
214C2×C32×C4C2×D411yescharacteristic
215C2×C32×C4C2411yescharacteristic
216#638—42no—
217C2×C3⋊Dic3—21no—
218C4⋊(C3⋊D3)—22no—
219C3×#67—28no—
220C3×#67—28no—
221C3×#67—42no—
222C2×C3×Dic3—24no—
223C2×C3×Dic3—28no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—28no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3C2×D411yescharacteristic
229C2×C3×Dic3C2×D411yescharacteristic
230C3×D12—22no—
231C3×C4×D3—22no—
232C3×C4×D3—22no—
233C3×C4×D3—22no—
234C3×C4×D3C2×D414yes—
235C3×Dic6—24no—
236C3×Dic6—22no—
237C3×Dic6C2×D414yescomplemented
238#626—42no—
239#626—42no—
240#625—42no—
241D3×Dic3—42no—
242C3⋊(C3⋊C8)—22no—
243C3×C3⋊C8—22no—
244C22×#41—31no—
245C2×AGL(1,ℤ/8)—92no—
246C2×#121—91no—
247#449—92no—
248#449—92no—
249#448—91no—
250#448—91no—
251#447—31no—
252#447—91no—
253#417—92no—
254#407—91no—
255C24×C3—21no—
256C24×C3—21no—
257C24×C3—31no—
258C24×C3—41no—
259C23×D3—61no—
260C23×D3—61no—
261C23×D3#6711yescharacteristic
262C3×#41—38no—
263C3×#41—64no—
264C3×#41—64no—
265C3×#41—68no—
266C3×#41—68no—
267C3×#41—64no—
268C2×C3×Q8—32no—
269C2×C3×Q8—64no—
270C2×C3×Q8—61no—
271C2×C3×D4—24no—
272C2×C3×D4—24no—
273C2×C3×D4—21no—
274C2×C3×D4—21no—
275C2×C3×D4—22no—
276C2×C3×D4—31no—
277C2×C3×D4—41no—
278C2×C3×D4—44no—
279C2×C3×D4—62no—
280C2×C3×D4—62no—
281C2×C3×D4—68no—
282C2×C3×D4—61no—
283C2×C3×D4C22×D312yes—
284C2×C3×D4C22×D312yes—
285C22×C3×C4—21no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—64no—
292C22×C3×C4—62no—
293C22×C3×C4—62no—
294C22×C3×C4—68no—
295C22×C3×C4—61no—
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C2×#67—28no—
299C2×#67—22no—
300C2×#67—22no—
301C2×#67—21no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—121no—
309C2×#67—124no—
310C22×Dic3—28no—
311C22×Dic3—21no—
312C22×Dic3—22no—
313C22×Dic3—22no—
314C22×Dic3—61no—
315C22×Dic3#6711yescharacteristic
316#237—28no—
317#237—28no—
318#237—24no—
319#237—24no—
320#237—24no—
321#237#6718yescomplemented
322D3×D4—64no—
323D3×D4—124no—
324C2×D12—31no—
325C2×D12—31no—
326C2×D12—61no—
327C2×D12—64no—
328C2×D12—61no—
329C2×D12—61no—
330C2×D12C22×D311yescharacteristic
331C2×C4×D3—24no—
332C2×C4×D3—61no—
333C2×C4×D3#6711yescharacteristic
334C2×C4×D3#6711yescharacteristic
335C2×C4×D3C22×D311yescharacteristic
336C2×C4×D3C22×D311yescharacteristic
337C2×Dic6—21no—
338C2×Dic6—24no—
339C2×Dic6C22×D312yes—
340C3×D8—64no—
341C2×C3×C8—32no—
342C3×C4⋊C4—31no—
343C3×C22⋊C4—61no—
344#217—61no—
345#215—64no—
346#215—64no—
347#214—64no—
348#213—24no—
349#213—64no—
350#213—64no—
351#213—124no—
352(C2×D3)⋊C4—21no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—121no—
359C4⋊Dic3—31no—
360C4⋊Dic3—31no—
361C4⋊Dic3—61no—
362C4⋊Dic3—61no—
363C4⋊Dic3C22×D311yescharacteristic
364Dic3⋊C4—61no—
365#208—64no—
366C2×C3⋊C8—32no—
367C2×C3⋊C8—32no—
368C2×C3⋊C8—62no—
369C2×C3⋊C8C22×D312yes—
370#204—64no—
371ΓL(1,𝔽25)—64no—
372C22×C32—21no—
373C22×C32—21no—
374C22×C32—24no—
375C22×C32—48no—
376C22×C32—42no—
377C22×C32—42no—
378C22×C32AGL(1,ℤ/8)12yescomplemented
379C22×C32C22×D411yescharacteristic
380C2×C3⋊D3—41no—
381C2×C3⋊D3—41no—
382C2×C3⋊D3—41no—
383C2×C3×D3—21no—
384C2×C3×D3—21no—
385C2×C3×D3—21no—
386C2×C3×D3—21no—
387C2×C3×D3—21no—
388C2×C3×D3—44no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C2×C3×D3#12012yes—
393D32—84no—
394C32×C4—21no—
395C32×C4C22×D412yes—
396C3⋊Dic3—41no—
397C3×Dic3—24no—
398C3×Dic3—21no—
399C3×Dic3—41no—
400C3×Dic3#12012yes—
401C2×#41—32no—
402C2×#41—32no—
403C2×#41—61no—
404C2×#41—61no—
405C2×#41—68no—
406C22×Q8—31no—
407C22×D4—61no—
408C22×D4—91no—
409C22×D4—181no—
410C22×D4D3211yescharacteristic, complemented
411C23×C4—31no—
412C23×C4—61no—
413AGL(1,ℤ/8)—188no—
414C2×SD16—92no—
415C2×SD16—92no—
416C2×D8—32no—
417C2×D8—92no—
418C2×M16—92no—
419#121—31no—
420#121—91no—
421#121—91no—
422#121—91no—
423#121—181no—
424#121—181no—
425C2×C4⋊C4—91no—
426C2×C22⋊C4—181no—
427#103—92no—
428#103—92no—
429#102—32no—
430#102—92no—
431C22⋊C8—31no—
432C22⋊C8—92no—
433C22⋊C8—91no—
434C23×C3—24no—
435C23×C3—24no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—21no—
439C23×C3—31no—
440C23×C3—31no—
441C23×C3—42no—
442C23×C3—44no—
443C23×C3—42no—
444C23×C3—42no—
445C23×C3—42no—
446C23×C3—42no—
447C23×C3—62no—
448C23×C3—62no—
449C23×C3—61no—
450C23×C3—82no—
451C23×C3—82no—
452C23×C3—121no—
453C23×C3D3×D411yescharacteristic
454C23×C3C2×#6711yescharacteristic
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—21no—
458C22×D3—41no—
459C22×D3—61no—
460C22×D3—61no—
461C22×D3—121no—
462C22×D3—122no—
463C22×D3—122no—
464C22×D3—122no—
465C22×D3—122no—
466C22×D3—122no—
467C22×D3—122no—
468C22×D3C2×#6711yescharacteristic
469C22×D3C2×#6711yescharacteristic
470C3×Q8—34no—
471C3×Q8—64no—
472C3×Q8—62no—
473C3×D4—24no—
474C3×D4—24no—
475C3×D4—22no—
476C3×D4—22no—
477C3×D4—24no—
478C3×D4—42no—
479C3×D4—44no—
480C3×D4—68no—
481C3×D4—68no—
482C3×D4—62no—
483C3×D4—122no—
484C3×D4D3×D414yescomplemented
485C3×D4C2×#6714yescomplemented
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—31no—
491C2×C3×C4—34no—
492C2×C3×C4—31no—
493C2×C3×C4—42no—
494C2×C3×C4—62no—
495C2×C3×C4—62no—
496C2×C3×C4—62no—
497C2×C3×C4—68no—
498C2×C3×C4—64no—
499C2×C3×C4—68no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4—61no—
503C2×C3×C4D3×D411yescharacteristic
504C2×C3×C4C2×#6711yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507#67—28no—
508#67—28no—
509#67—42no—
510#67—122no—
511#67—122no—
512#67—122no—
513#67—122no—
514#67—122no—
515#67—122no—
516#67—242no—
517C2×Dic3—24no—
518C2×Dic3—28no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—28no—
522C2×Dic3—21no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—121no—
526C2×Dic3—122no—
527C2×Dic3C2×#6711yescharacteristic
528C2×Dic3C2×#6711yescharacteristic
529D12—22no—
530D12—62no—
531D12—62no—
532D12—122no—
533D12—122no—
534D12—122no—
535C4×D3—22no—
536C4×D3—22no—
537C4×D3—22no—
538C4×D3—122no—
539C4×D3C2×#6714yes—
540Dic6—24no—
541Dic6—22no—
542Dic6C2×#6714yescomplemented
543C3×C8—62no—
544C3⋊C8—22no—
545C3⋊C8—62no—
546C3⋊C8—62no—
547C3⋊C8—122no—
548C2×C32—22no—
549C2×C32—44no—
550C2×C32C2×#12011yescharacteristic
551C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
552C2×C32#57511yescharacteristic
553C3⋊D3—81no—
554C3×D3—22no—
555C3×D3—41no—
556C3×D3—81no—
557C24—21no—
558C24—31no—
559C24—181no—
560#41—38no—
561#41—64no—
562#41—64no—
563#41—68no—
564#41—68no—
565#41—64no—
566C2×Q8—32no—
567C2×Q8—64no—
568C2×Q8—61no—
569C2×D4—24no—
570C2×D4—21no—
571C2×D4—31no—
572C2×D4—62no—
573C2×D4—62no—
574C2×D4—68no—
575C2×D4—61no—
576C2×D4—91no—
577C2×D4—184no—
578C2×D4—181no—
579C2×D4—181no—
580C2×D4—181no—
581C2×D4—181no—
582C2×D4—364no—
583C2×D4C2×D3212yes—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—64no—
590C22×C4—62no—
591C22×C4—62no—
592C22×C4—68no—
593C22×C4—61no—
594C22×C4—181no—
595C22×C4C2×D3211yescharacteristic
596SD16—184no—
597SD16—184no—
598D8—64no—
599D8—184no—
600M16—184no—
601C2×C8—32no—
602C2×C8—92no—
603C4⋊C4—31no—
604C4⋊C4—91no—
605C4⋊C4—181no—
606C22⋊C4—61no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—24no—
615C22×C3—24no—
616C22×C3—21no—
617C22×C3—22no—
618C22×C3—32no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—44no—
622C22×C3—48no—
623C22×C3—48no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—42no—
627C22×C3—42no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—82no—
634C22×C3—82no—
635C22×C3—88no—
636C22×C3—124no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3#91112yescomplemented
641C22×C3#94912yescomplemented
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C22×#6711yescharacteristic
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—44no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—241no—
660C2×D3—241no—
661C2×D3—241no—
662C2×D3—244no—
663C2×D3—244no—
664C2×D3#95312yes—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—22no—
668C3×C4—32no—
669C3×C4—41no—
670C3×C4—61no—
671C3×C4—64no—
672C3×C4—121no—
673C3×C4C2×D3×D412yes—
674C3×C4C22×#6712yes—
675Dic3—24no—
676Dic3—21no—
677Dic3—41no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681Dic3#95312yes—
682C32#300611yescharacteristic, complemented, Sylow
683C23—24no—
684C23—22no—
685C23—31no—
686C23—31no—
687C23—42no—
688C23—42no—
689C23—62no—
690C23—62no—
691C23—61no—
692C23—121no—
693C23—181no—
694C23—362no—
695C23—362no—
696C23—362no—
697C23D3×#6711yescharacteristic
698Q8—34no—
699Q8—64no—
700Q8—62no—
701D4—24no—
702D4—22no—
703D4—68no—
704D4—68no—
705D4—62no—
706D4—122no—
707D4—182no—
708D4—362no—
709D4—362no—
710D4—362no—
711D4—362no—
712D4D3×#6714yescomplemented
713C2×C4—22no—
714C2×C4—31no—
715C2×C4—34no—
716C2×C4—31no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—68no—
721C2×C4—64no—
722C2×C4—68no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—61no—
726C2×C4—181no—
727C2×C4—362no—
728C2×C4D3×#6711yescharacteristic
729C2×C4C22×D3211yescharacteristic
730C8—62no—
731C8—182no—
732C2×C3—22no—
733C2×C3—22no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3—44no—
739C2×C3—44no—
740C2×C3—62no—
741C2×C3—84no—
742C2×C3—121no—
743C2×C3—241no—
744C2×C3D3×#12011yescharacteristic
745C2×C3C2×#91111yescharacteristic
746C2×C3#577311yescharacteristic
747C2×C3C2×#94911yescharacteristic
748C2×C3#582211yescharacteristic
749C2×C3C2×#95311yescharacteristic
750D3—22no—
751D3—41no—
752D3—81no—
753D3—241no—
754D3—241no—
755D3—481no—
756C22—21no—
757C22—21no—
758C22—24no—
759C22—32no—
760C22—48no—
761C22—42no—
762C22—42no—
763C22—61no—
764C22—61no—
765C22—61no—
766C22—61no—
767C22—61no—
768C22—124no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—361no—
773C22—361no—
774C22—361no—
775C22—724no—
776C22#6392512yescomplemented
777C22C2×D3×#6711yescharacteristic
778C4—21no—
779C4—32no—
780C4—61no—
781C4—64no—
782C4—121no—
783C4—361no—
784C4C2×D3×#6712yes—
785C3—21no—
786C3#8000311yescharacteristic, complemented
787C3#8408211yescharacteristic, complemented
788C2—22no—
789C2—44no—
790C2—62no—
791C2—121no—
792C2—241no—
793C2—721no—
794C2C2×#6392511yescharacteristic
795C2#1059509511yescharacteristic
796C2D3×#95311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3006
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C2×#63925C2semidirect
3. D3×#930C2semidirect
4. #10592916C2semidirect
5. C3×#5217C2semidirect
6. #10591452C2semidirect
7. #10591450C2semidirect
8. #10591414C2semidirect
9. #10591174C2semidirect
10. #10591171C2semidirect
11. #10591154C2semidirect
14. C22×C32×D4C22semidirect
21. C2×C3×#237C22semidirect
23. C22×C3×Dic6C22semidirect
25. C2×D3×D12C22semidirect
26. C2×#3753C22semidirect
28. C2×C3×#213C22semidirect
33. #63909C22semidirect
34. #63908C22semidirect
36. D3×C4⋊Dic3C22semidirect
37. C2×#3717C22semidirect
38. C2×#3715C22semidirect
39. C2×#3711C22semidirect
40. #63659C22semidirect
41. #63657C22semidirect
42. C3×#832C22semidirect
43. C3×#830C22semidirect
44. #63566C22semidirect
45. #63565C22semidirect
46. (C2×D3)⋊(C3⋊C8)C22semidirect
48. C22×#237D3semidirect
62. #5217D3semidirect
93. C3×#237D4semidirect
132. C22×C3×D4C2×D3semidirect
133. C22×C3×D4C2×D3semidirect
143. C2×#237C2×D3semidirect
148. C22×Dic6C2×D3semidirect
160. C2×#213C2×D3semidirect
186. #832C2×D3semidirect
191. #830C2×D3semidirect
212. C32×D4C2×D4semidirect
237. C3×Dic6C2×D4semidirect
321. #237#67semidirect
378. C22×C32AGL(1,ℤ/8)semidirect
410. C22×D4D32semidirect
484. C3×D4D3×D4semidirect
485. C3×D4C2×#67semidirect
542. Dic6C2×#67semidirect
640. C22×C3#911semidirect
641. C22×C3#949semidirect
682. C32#3006semidirect
712. D4D3×#67semidirect
776. C22#63925semidirect
786. C3#80003semidirect
787. C3#84082semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C2×#639252
D3×#9302
#105929162
C3×#52172
#105914522
#105914502
#105914142
#105911742
#105911712
#105911542
#840823
#800033