Finite Group Databasebeta

← #11864138

Subgroups — #11864138

Order 1152.

1691 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic, complemented
2C2×#63939C212yesmaximal, complemented
3D3×#930C211yesmaximal, characteristic, complemented
4#10592926C211yesmaximal, characteristic, complemented
5C3×#5227C211yesmaximal, characteristic, complemented
6#10591588C212yesmaximal, complemented
7#10591586C212yesmaximal, complemented
8#10591550C212yesmaximal, complemented
9#10591162C211yesmaximal, characteristic, complemented
10#10591160C211yesmaximal, characteristic, complemented
11#10591154C211yesmaximal, characteristic, complemented
12#84082—31nomaximal
13#80040—31nomaximal
14C22×C32×Q8C2211yescharacteristic, complemented
15C2×C3×#239—28no—
16C2×C3×#239—21no—
17C2×C3×#239—21no—
18C2×C3×#239C2212yes—
19C2×C3×#239C2212yescomplemented
20C22×C3×D12—21no—
21C22×C3×D12C2211yescharacteristic, complemented
22C22×C3×C4×D3—21no—
23C22×C3×C4×D3C2211yescharacteristic
24C2×D3×#67—21no—
25C2×D3×D12C2211yescharacteristic, complemented
26C2×#3755C2212yescomplemented
27#64139C2211yescharacteristic
28C2×C3×#215C2212yescomplemented
29C3×#930C2211yescharacteristic
30#63978—21no—
31#63939—28no—
32D3×(C2×D3)⋊C4—21no—
33#63909C2211yescharacteristic, complemented
34#63908C2211yescharacteristic, complemented
35#63906—21no—
36D3×C4⋊Dic3C2211yescharacteristic, complemented
37C2×#3714C2212yescomplemented
38C2×#3713C2212yescomplemented
39C2×#3711C2212yescomplemented
40#63662C2212yescomplemented
41#63657C2211yescharacteristic, complemented
42C3×#835C2212yescomplemented
43C3×#830C2211yescharacteristic, complemented
44#63563C2212yescomplemented
45#63562C2212yescomplemented
46(C2×D3)⋊(C3⋊C8)C2212yescomplemented
47C22×C3×#41—31no—
48C22×#239D311yescharacteristic, complemented
49C2×#949—32no—
50C2×#930—31no—
51C2×#914—32no—
52D3×#121—31no—
53C3×#448—31no—
54#5238—32no—
55#5238—32no—
56#5232—32no—
57#5227—31no—
58#5227—31no—
59#5227—61no—
60#5227D311yescharacteristic, complemented
61#5217—31no—
62#5217—31no—
63#5207—31no—
64#5172—32no—
65#5036—31no—
66#4810—32no—
67#4803—32no—
68#4732—31no—
69#4726—31no—
70C23×C3×D3—21no—
71C23×C3×D3D411yescharacteristic
72C22×D32—21no—
73C2×C32×Q8—24no—
74C2×C32×Q8—21no—
75C2×C32×Q8C2312yes—
76C22×C32×C4—21no—
77C22×C32×C4C2311yescharacteristic
78C2×#638—21no—
79C2×C4⋊(C3⋊D3)C2311yescharacteristic
80C2×C3×#67—21no—
81C22×C3×Dic3D411yescharacteristic
82C3×#239—28no—
83C3×#239—28no—
84C3×#239—24no—
85C3×#239—24no—
86C3×#239—24no—
87C3×#239D418yescomplemented
88C2×C3×D12—28no—
89C2×C3×D12—22no—
90C2×C3×D12—22no—
91C2×C3×D12—21no—
92C2×C3×D12—24no—
93C2×C3×D12C2311yescharacteristic
94C2×C3×D12C2312yes—
95C2×C3×C4×D3—28no—
96C2×C3×C4×D3—22no—
97C2×C3×C4×D3—22no—
98C2×C3×C4×D3—24no—
99C2×C3×C4×D3D411yescharacteristic
100C2×C3×C4×D3D411yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103D3×#67—44no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×D3×Dic3—21no—
108D3×D12—24no—
109#3755—24no—
110#3752—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3⋊(C3⋊C8)C2312yes—
113C3×#215—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#3714—24no—
121#3713—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—21no—
130C22×C3×Q8C2×D311yescharacteristic, complemented
131C22×C3×Q8C2×D311yescharacteristic, complemented
132C22×C3×D4—31no—
133C22×C3×D4—61no—
134C23×C3×C4—31no—
135C23×C3×C4—61no—
136C22×#67—61no—
137C2×#239—28no—
138C2×#239—21no—
139C2×#239—21no—
140C2×#239C2×D312yes—
141C2×#239C2×D312yescomplemented
142C2×D3×D4—31no—
143C2×D3×D4—61no—
144C22×D12—21no—
145C22×D12—31no—
146C22×D12C2×D311yescharacteristic, complemented
147C22×C4×D3—21no—
148C22×C4×D3C2×D311yescharacteristic
149C2×C3×SD16—32no—
150C3×#121—31no—
151#949—68no—
152C2×#215—32no—
153C2×#215—32no—
154C2×#215—62no—
155C2×#215C2×D312yescomplemented
156#939—61no—
157#938—31no—
158C2×#213—32no—
159C2×#213—32no—
160C2×#213—32no—
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#914—68no—
173C2×D24—32no—
174C2×ΓL(1,𝔽25)—32no—
175#895—31no—
176D3×C4⋊C4—31no—
177#884—61no—
178D3×C22⋊C4—61no—
179C3×#103—32no—
180C3×C22⋊C8—31no—
181#835—32no—
182#835—32no—
183#835—62no—
184#835C2×D312yescomplemented
185#832—32no—
186#832—32no—
187#830—31no—
188#830—31no—
189#830—32no—
190#830—61no—
191#830C2×D311yescharacteristic, complemented
192#821—32no—
193(C2×D3)⋊C8—32no—
194#809—32no—
195C23×C32C2×D411yescharacteristic
196C22×C3⋊D3—21no—
197C22×C3×D3—24no—
198C22×C3×D3—22no—
199C22×C3×D3—22no—
200C22×C3×D3—22no—
201C22×C3×D3—21no—
202C22×C3×D3—41no—
203C22×C3×D3—42no—
204C22×C3×D3—42no—
205C22×C3×D3C2×D411yescharacteristic
206C22×C3×D3C2×D411yescharacteristic
207C2×D32—42no—
208C2×D32—42no—
209C2×D32—42no—
210C32×Q8—24no—
211C32×Q8—22no—
212C32×Q8C2×D414yescomplemented
213C2×C32×C4—24no—
214C2×C32×C4—22no—
215C2×C32×C4—22no—
216C2×C32×C4C2×D411yescharacteristic
217C2×C32×C4C2411yescharacteristic
218#638—42no—
219C2×C3⋊Dic3—21no—
220C4⋊(C3⋊D3)—22no—
221C3×#67—42no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3—21no—
224C2×C3×Dic3C2×D411yescharacteristic
225C2×C3×Dic3C2×D411yescharacteristic
226C3×D12—28no—
227C3×D12—24no—
228C3×D12—28no—
229C3×D12—22no—
230C3×D12—22no—
231C3×D12C2×D414yescomplemented
232C3×C4×D3—28no—
233C3×C4×D3—22no—
234C3×C4×D3—22no—
235C3×C4×D3—28no—
236C3×C4×D3—22no—
237C3×C4×D3C2×D414yes—
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—31no—
250#448—91no—
251#447—91no—
252#447—91no—
253#417—92no—
254#407—91no—
255C24×C3—31no—
256C24×C3—61no—
257C23×D3—21no—
258C23×D3—61no—
259C23×D3—61no—
260C23×D3#6711yescharacteristic
261C3×#41—38no—
262C3×#41—64no—
263C3×#41—64no—
264C3×#41—68no—
265C3×#41—68no—
266C3×#41—64no—
267C2×C3×Q8—24no—
268C2×C3×Q8—24no—
269C2×C3×Q8—21no—
270C2×C3×Q8—21no—
271C2×C3×Q8—22no—
272C2×C3×Q8—41no—
273C2×C3×Q8—44no—
274C2×C3×Q8C22×D312yes—
275C2×C3×Q8C22×D312yes—
276C2×C3×D4—32no—
277C2×C3×D4—31no—
278C2×C3×D4—64no—
279C2×C3×D4—62no—
280C2×C3×D4—62no—
281C2×C3×D4—68no—
282C2×C3×D4—61no—
283C2×C3×D4—61no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—41no—
293C22×C3×C4—64no—
294C22×C3×C4—62no—
295C22×C3×C4—62no—
296C22×C3×C4—68no—
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C2×#67—21no—
300C2×#67—61no—
301C2×#67—61no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—121no—
307C2×#67—124no—
308C22×Dic3—61no—
309C22×Dic3#6711yescharacteristic
310#239—28no—
311#239—28no—
312#239—24no—
313#239—24no—
314#239—24no—
315#239#6718yescomplemented
316D3×D4—64no—
317D3×D4—124no—
318C2×D12—28no—
319C2×D12—22no—
320C2×D12—22no—
321C2×D12—21no—
322C2×D12—24no—
323C2×D12—31no—
324C2×D12—31no—
325C2×D12—61no—
326C2×D12—64no—
327C2×D12—61no—
328C2×D12—61no—
329C2×D12C22×D311yescharacteristic
330C2×D12C22×D312yes—
331C2×C4×D3—28no—
332C2×C4×D3—22no—
333C2×C4×D3—22no—
334C2×C4×D3—24no—
335C2×C4×D3—61no—
336C2×C4×D3#6711yescharacteristic
337C2×C4×D3#6711yescharacteristic
338C2×C4×D3C22×D311yescharacteristic
339C2×C4×D3C22×D311yescharacteristic
340C3×SD16—64no—
341C2×C3×C8—32no—
342C3×C4⋊C4—31no—
343C3×C22⋊C4—61no—
344#217—61no—
345#215—24no—
346#215—64no—
347#215—64no—
348#215—124no—
349#213—64no—
350#213—64no—
351#213—64no—
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—
370D24—64no—
371ΓL(1,𝔽25)—64no—
372C22×C32—21no—
373C22×C32—21no—
374C22×C32AGL(1,ℤ/8)12yescomplemented
375C22×C32C22×D411yescharacteristic
376C2×C3⋊D3—41no—
377C2×C3⋊D3—41no—
378C2×C3⋊D3—41no—
379C2×C3×D3—21no—
380C2×C3×D3—21no—
381C2×C3×D3—21no—
382C2×C3×D3—24no—
383C2×C3×D3—21no—
384C2×C3×D3—21no—
385C2×C3×D3—44no—
386C2×C3×D3—48no—
387C2×C3×D3—42no—
388C2×C3×D3—42no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C2×C3×D3#12012yes—
393D32—84no—
394C32×C4—24no—
395C32×C4—21no—
396C32×C4C22×D412yes—
397C3⋊Dic3—41no—
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×Q8D3211yescharacteristic, complemented
407C22×D4—31no—
408C22×D4—61no—
409C22×D4—91no—
410C22×D4—181no—
411C23×C4—31no—
412C23×C4—61no—
413AGL(1,ℤ/8)—188no—
414C2×SD16—32no—
415C2×SD16—92no—
416C2×D8—92no—
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—32no—
428#103—92no—
429#102—92no—
430#102—92no—
431C22⋊C8—31no—
432C22⋊C8—92no—
433C22⋊C8—91no—
434C23×C3—21no—
435C23×C3—31no—
436C23×C3—31no—
437C23×C3—62no—
438C23×C3—64no—
439C23×C3—62no—
440C23×C3—62no—
441C23×C3—61no—
442C23×C3—121no—
443C23×C3—122no—
444C23×C3—122no—
445C23×C3D3×D411yescharacteristic
446C23×C3C2×#6711yescharacteristic
447C22×D3—24no—
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—21no—
452C22×D3—41no—
453C22×D3—42no—
454C22×D3—42no—
455C22×D3—61no—
456C22×D3—61no—
457C22×D3—121no—
458C22×D3—122no—
459C22×D3—122no—
460C22×D3—122no—
461C22×D3—122no—
462C22×D3—122no—
463C22×D3—122no—
464C22×D3C2×#6711yescharacteristic
465C22×D3C2×#6711yescharacteristic
466C3×Q8—24no—
467C3×Q8—24no—
468C3×Q8—22no—
469C3×Q8—22no—
470C3×Q8—24no—
471C3×Q8—42no—
472C3×Q8—44no—
473C3×Q8D3×D414yescomplemented
474C3×Q8C2×#6714yescomplemented
475C3×D4—34no—
476C3×D4—68no—
477C3×D4—68no—
478C3×D4—64no—
479C3×D4—62no—
480C3×D4—62no—
481C3×D4—122no—
482C2×C3×C4—24no—
483C2×C3×C4—24no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
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—42no—
495C2×C3×C4—44no—
496C2×C3×C4—62no—
497C2×C3×C4—68no—
498C2×C3×C4—62no—
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—42no—
508#67—122no—
509#67—122no—
510#67—122no—
511#67—122no—
512#67—122no—
513#67—122no—
514#67—242no—
515C2×Dic3—22no—
516C2×Dic3—21no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—121no—
520C2×Dic3—122no—
521C2×Dic3C2×#6711yescharacteristic
522C2×Dic3C2×#6711yescharacteristic
523D12—28no—
524D12—24no—
525D12—28no—
526D12—22no—
527D12—22no—
528D12—62no—
529D12—62no—
530D12—122no—
531D12—122no—
532D12—122no—
533D12C2×#6714yescomplemented
534C4×D3—28no—
535C4×D3—22no—
536C4×D3—22no—
537C4×D3—28no—
538C4×D3—22no—
539C4×D3—122no—
540C4×D3C2×#6714yes—
541C3×C8—62no—
542C3⋊C8—22no—
543C3⋊C8—62no—
544C3⋊C8—62no—
545C3⋊C8—122no—
546C2×C32—22no—
547C2×C32C2×#12011yescharacteristic
548C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
549C2×C32#57511yescharacteristic
550C3⋊D3—81no—
551C3×D3—22no—
552C3×D3—41no—
553C3×D3—44no—
554C3×D3—81no—
555C24—31no—
556C24—61no—
557C24—181no—
558#41—38no—
559#41—64no—
560#41—64no—
561#41—68no—
562#41—68no—
563#41—64no—
564C2×Q8—24no—
565C2×Q8—21no—
566C2×Q8C2×D3212yes—
567C2×D4—32no—
568C2×D4—31no—
569C2×D4—64no—
570C2×D4—62no—
571C2×D4—62no—
572C2×D4—68no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—91no—
576C2×D4—184no—
577C2×D4—181no—
578C2×D4—181no—
579C2×D4—181no—
580C2×D4—181no—
581C2×D4—364no—
582C22×C4—21no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—64no—
589C22×C4—62no—
590C22×C4—62no—
591C22×C4—68no—
592C22×C4—181no—
593C22×C4C2×D3211yescharacteristic
594SD16—64no—
595SD16—184no—
596D8—184no—
597D8—184no—
598M16—184no—
599C2×C8—32no—
600C2×C8—92no—
601C4⋊C4—31no—
602C4⋊C4—91no—
603C4⋊C4—181no—
604C22⋊C4—61no—
605C22⋊C4—181no—
606C22⋊C4—181no—
607C22⋊C4—181no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—22no—
614C22×C3—32no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3—64no—
622C22×C3—61no—
623C22×C3—124no—
624C22×C3—128no—
625C22×C3—122no—
626C22×C3—122no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3—121no—
630C22×C3#91412yescomplemented
631C22×C3#94912yescomplemented
632C22×C3C2×D3×D411yescharacteristic
633C22×C3C22×#6711yescharacteristic
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—24no—
640C2×D3—44no—
641C2×D3—48no—
642C2×D3—42no—
643C2×D3—42no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—241no—
654C2×D3—241no—
655C2×D3—241no—
656C2×D3—244no—
657C2×D3—244no—
658C2×D3#95312yes—
659C3×C4—24no—
660C3×C4—21no—
661C3×C4—24no—
662C3×C4—21no—
663C3×C4—22no—
664C3×C4—32no—
665C3×C4—41no—
666C3×C4—44no—
667C3×C4—61no—
668C3×C4—121no—
669C3×C4C2×D3×D412yes—
670C3×C4C22×#6712yes—
671Dic3—21no—
672Dic3—41no—
673Dic3—121no—
674Dic3—121no—
675Dic3—241no—
676Dic3#95312yes—
677C32#300611yescharacteristic, complemented, Sylow
678C23—31no—
679C23—31no—
680C23—62no—
681C23—64no—
682C23—62no—
683C23—62no—
684C23—61no—
685C23—121no—
686C23—122no—
687C23—122no—
688C23—181no—
689C23—362no—
690C23—362no—
691C23—362no—
692C23D3×#6711yescharacteristic
693Q8—24no—
694Q8—22no—
695Q8D3×#6714yescomplemented
696D4—34no—
697D4—68no—
698D4—68no—
699D4—64no—
700D4—62no—
701D4—62no—
702D4—122no—
703D4—182no—
704D4—362no—
705D4—362no—
706D4—362no—
707D4—362no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—31no—
712C2×C4—34no—
713C2×C4—31no—
714C2×C4—62no—
715C2×C4—68no—
716C2×C4—62no—
717C2×C4—68no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—61no—
721C2×C4—181no—
722C2×C4—362no—
723C2×C4D3×#6711yescharacteristic
724C2×C4C22×D3211yescharacteristic
725C8—62no—
726C8—182no—
727C2×C3—22no—
728C2×C3—22no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—42no—
733C2×C3—62no—
734C2×C3—121no—
735C2×C3—124no—
736C2×C3—241no—
737C2×C3D3×#12011yescharacteristic
738C2×C3C2×#91411yescharacteristic
739C2×C3#577711yescharacteristic
740C2×C3C2×#94911yescharacteristic
741C2×C3#582211yescharacteristic
742C2×C3C2×#95311yescharacteristic
743D3—22no—
744D3—41no—
745D3—44no—
746D3—81no—
747D3—241no—
748D3—241no—
749D3—481no—
750C22—21no—
751C22—21no—
752C22—32no—
753C22—61no—
754C22—61no—
755C22—64no—
756C22—61no—
757C22—61no—
758C22—61no—
759C22—124no—
760C22—128no—
761C22—122no—
762C22—122no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—361no—
767C22—361no—
768C22—361no—
769C22—724no—
770C22#6393912yescomplemented
771C22C2×D3×#6711yescharacteristic
772C4—24no—
773C4—21no—
774C4—32no—
775C4—61no—
776C4—121no—
777C4—361no—
778C4C2×D3×#6712yes—
779C3—21no—
780C3#8004011yescharacteristic, complemented
781C3#8408211yescharacteristic, complemented
782C2—22no—
783C2—62no—
784C2—121no—
785C2—124no—
786C2—241no—
787C2—721no—
788C2C2×#6393911yescharacteristic
789C2#1059531711yescharacteristic
790C2D3×#95311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
hypercenterC22×Q8D32
hypocenterC32#3006
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#239C2semidirect
2. C2×#63939C2semidirect
3. D3×#930C2semidirect
4. #10592926C2semidirect
5. C3×#5227C2semidirect
6. #10591588C2semidirect
7. #10591586C2semidirect
8. #10591550C2semidirect
9. #10591162C2semidirect
10. #10591160C2semidirect
11. #10591154C2semidirect
14. C22×C32×Q8C22semidirect
19. C2×C3×#239C22semidirect
21. C22×C3×D12C22semidirect
25. C2×D3×D12C22semidirect
26. C2×#3755C22semidirect
28. C2×C3×#215C22semidirect
33. #63909C22semidirect
34. #63908C22semidirect
36. D3×C4⋊Dic3C22semidirect
37. C2×#3714C22semidirect
38. C2×#3713C22semidirect
39. C2×#3711C22semidirect
40. #63662C22semidirect
41. #63657C22semidirect
42. C3×#835C22semidirect
43. C3×#830C22semidirect
44. #63563C22semidirect
45. #63562C22semidirect
46. (C2×D3)⋊(C3⋊C8)C22semidirect
48. C22×#239D3semidirect
60. #5227D3semidirect
87. C3×#239D4semidirect
130. C22×C3×Q8C2×D3semidirect
131. C22×C3×Q8C2×D3semidirect
141. C2×#239C2×D3semidirect
146. C22×D12C2×D3semidirect
155. C2×#215C2×D3semidirect
184. #835C2×D3semidirect
191. #830C2×D3semidirect
212. C32×Q8C2×D4semidirect
231. C3×D12C2×D4semidirect
315. #239#67semidirect
374. C22×C32AGL(1,ℤ/8)semidirect
406. C22×Q8D32semidirect
473. C3×Q8D3×D4semidirect
474. C3×Q8C2×#67semidirect
533. D12C2×#67semidirect
630. C22×C3#914semidirect
631. C22×C3#949semidirect
677. C32#3006semidirect
695. Q8D3×#67semidirect
770. C22#63939semidirect
780. C3#80040semidirect
781. C3#84082semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C2×#639392
D3×#9302
#105929262
C3×#52272
#105915882
#105915862
#105915502
#105911622
#105911602
#105911542
#840823
#800403