Finite Group Databasebeta

← #11864132

Subgroups — #11864132

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×#3795C211yesmaximal, characteristic, complemented
2C3×D3×#121C211yesmaximal, characteristic, complemented
3C2×#63932C212yesmaximal, complemented
4#10592739C211yesmaximal, characteristic, complemented
5C3×#5036C211yesmaximal, characteristic, complemented
6#10591519C212yesmaximal, complemented
7#10591181C211yesmaximal, characteristic, complemented
8#10591160C211yesmaximal, characteristic, complemented
9#10591154C211yesmaximal, characteristic, complemented
10#10590613C212yesmaximal, complemented
11#10590607C212yesmaximal, complemented
12#82624—31nomaximal
13#80003—31nomaximal
14C22×#634C2211yescharacteristic, complemented
15C2×C3×D3×D4—21no—
16C2×C3×D3×D4C2211yescharacteristic, complemented
17C22×C3×D12C2211yescharacteristic, complemented
18C22×C3×C4×D3C2211yescharacteristic
19C22×#625—21no—
20C22×D3×Dic3—21no—
21C2×#3795—21no—
22C2×#3795—21no—
23C2×#3795—28no—
24C2×#3795C2212yes—
25C2×#3795C2212yescomplemented
26C32×#121C2211yescharacteristic
27C2×#3754C2212yescomplemented
28C3×#939—21no—
29C3×#938C2211yescharacteristic, complemented
30C2×C3×#213C2212yescomplemented
31C3×#930C2211yescharacteristic
32C3×#895C2211yescharacteristic, complemented
33C3×D3×C4⋊C4C2211yescharacteristic, complemented
34C3×#884—21no—
35C3×D3×C22⋊C4—21no—
36#63932—28no—
37C2×#3716C2212yescomplemented
38C2×#3713C2212yescomplemented
39C2×#3711C2212yescomplemented
40#63657C2211yescharacteristic, complemented
41#63637C2212yescomplemented
42C3×#830C2211yescharacteristic, complemented
43C3×#809C2212yescomplemented
44#63567C2212yescomplemented
45#63562C2212yescomplemented
46(C2×D3)⋊(C3⋊C8)C2212yescomplemented
47C22×#237—31no—
48C22×#235—31no—
49C2×C3×#121—31no—
50C2×#932—32no—
51C2×#911—32no—
52D3×#121D311yescharacteristic, complemented
53C3×#447—31no—
54#5217—31no—
55#5207—31no—
56#5158—32no—
57#5040—31no—
58#5040—31no—
59#5040—31no—
60#5040—61no—
61#5037—32no—
62#5037—32no—
63#5036—31no—
64#5036D311yescharacteristic, complemented
65#4966—32no—
66#4781—32no—
67#4771—32no—
68#4738—31no—
69#4726—31no—
70C23×C3×D3—21no—
71C23×C3×D3—21no—
72C23×C3×D3D411yescharacteristic
73C2×C32×D4—21no—
74C2×C32×D4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C3⋊Dic3—21no—
77C2×#634—21no—
78C2×#634—24no—
79C2×#634C2312yes—
80C2×C3×#67—21no—
81C2×C3×#67—21no—
82C2×C3×#67—21no—
83C22×C3×Dic3D411yescharacteristic
84C3×D3×D4—24no—
85C3×D3×D4—44no—
86C2×C3×D12—21no—
87C2×C3×D12—24no—
88C2×C3×D12—21no—
89C2×C3×D12C2311yescharacteristic
90C2×C3×D12C2312yes—
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3—21no—
93C2×C3×C4×D3D411yescharacteristic
94C2×C3×C4×D3D411yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×C4×D3C2311yescharacteristic
97C2×#625—28no—
98C2×#625—22no—
99C2×#625—22no—
100C2×D3×Dic3—28no—
101C2×D3×Dic3—22no—
102C2×D3×Dic3—22no—
103#3795—28no—
104#3795—28no—
105#3795—24no—
106#3795—24no—
107#3795—24no—
108#3795D418yescomplemented
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111#3754—24no—
112C2×C3⋊(C3⋊C8)C2312yes—
113C3×#217—21no—
114C3×#213—24no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4—21no—
119C2×C3×C3⋊C8C2312yes—
120#3716—24no—
121#3713—24no—
122#3711—24no—
123#3006—91noSylow
124C22×C3×D4—31no—
125C22×C3×D4—31no—
126C22×C3×D4—61no—
127C23×C3×C4—31no—
128C22×#67—61no—
129C22×#67—61no—
130C23×Dic3—61no—
131C2×#237—32no—
132C2×#237—32no—
133C2×#237—68no—
134C2×#237—61no—
135C2×#237—61no—
136C2×D3×D4—21no—
137C2×D3×D4C2×D311yescharacteristic, complemented
138C2×#235—32no—
139C2×#235—32no—
140C2×#235—68no—
141C2×#235—61no—
142C2×#235—61no—
143C22×D12C2×D311yescharacteristic, complemented
144C22×C4×D3—61no—
145C22×C4×D3C2×D311yescharacteristic
146C22×Dic6—31no—
147C22×Dic6—31no—
148C22×Dic6—61no—
149C2×C3×D8—32no—
150C3×#121—21no—
151C3×#121—31no—
152C3×#121—31no—
153C3×#121—31no—
154C3×#121—61no—
155C3×#121—61no—
156C3×#121C2×D311yescharacteristic
157C3×#121C2×D311yescharacteristic
158C2×C3×C4⋊C4—31no—
159C2×C3×C22⋊C4—61no—
160#939—21no—
161#938C2×D311yescharacteristic, complemented
162C2×#214—32no—
163C2×#214—32no—
164C2×#214—32no—
165C2×#214—62no—
166#932—68no—
167C2×#213—32no—
168C2×#213—32no—
169C2×#213C2×D312yescomplemented
170#930C2×D311yescharacteristic
171C2×#208—32no—
172#911—68no—
173C2×#204—32no—
174C2×ΓL(1,𝔽25)—32no—
175#895C2×D311yescharacteristic, complemented
176D3×C4⋊C4C2×D311yescharacteristic, complemented
177#884—21no—
178D3×C22⋊C4—21no—
179C3×#102—32no—
180C3×C22⋊C8—31no—
181#832—32no—
182#830—31no—
183#830—31no—
184#830—32no—
185#830—61no—
186#830C2×D311yescharacteristic, complemented
187(C2×D3)⋊C8—32no—
188#816—32no—
189#810—32no—
190#810—32no—
191#810—32no—
192#810—62no—
193#809—32no—
194#809C2×D312yescomplemented
195C23×C32—21no—
196C23×C32C2×D411yescharacteristic
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×D3—42no—
206C22×C3×D3—42no—
207C22×C3×D3—42no—
208C22×C3×D3C2×D411yescharacteristic
209C22×C3×D3C2×D411yescharacteristic
210C32×D4—22no—
211C32×D4—42no—
212C2×C32×C4—22no—
213C2×C32×C4—21no—
214C2×C32×C4C2×D411yescharacteristic
215C2×C32×C4C2411yescharacteristic
216C2×C3⋊Dic3—24no—
217C2×C3⋊Dic3—22no—
218#634—24no—
219#634—22no—
220#634C2×D414yescomplemented
221C3×#67—42no—
222C3×#67—42no—
223C3×#67—42no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—21no—
226C2×C3×Dic3C2×D411yescharacteristic
227C2×C3×Dic3C2×D411yescharacteristic
228C3×D12—24no—
229C3×D12—22no—
230C3×D12—22no—
231C3×D12—42no—
232C3×D12C2×D414yescomplemented
233C3×C4×D3—22no—
234C3×C4×D3—22no—
235C3×C4×D3—22no—
236C3×C4×D3—42no—
237C3×C4×D3C2×D414yes—
238#625—28no—
239#625—28no—
240D3×Dic3—28no—
241D3×Dic3—28no—
242C3⋊(C3⋊C8)—22no—
243C3×C3⋊C8—22no—
244C22×#41—91no—
245C2×AGL(1,ℤ/8)—92no—
246C2×#121—31no—
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—31no—
256C24×C3—61no—
257C24×C3—61no—
258C23×D3—21no—
259C23×D3—21no—
260C23×D3#6711yescharacteristic
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—32no—
265C2×C3×D4—31no—
266C2×C3×D4—41no—
267C2×C3×D4—64no—
268C2×C3×D4—61no—
269C2×C3×D4—64no—
270C2×C3×D4—61no—
271C2×C3×D4—61no—
272C2×C3×D4—61no—
273C2×C3×D4—61no—
274C2×C3×D4—124no—
275C2×C3×D4C22×D311yescharacteristic
276C2×C3×D4C22×D311yescharacteristic
277C22×C3×C4—21no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—64no—
284C22×C3×C4—61no—
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C2×#67—21no—
288C2×#67—21no—
289C2×#67—21no—
290C2×#67—62no—
291C2×#67—62no—
292C2×#67—68no—
293C2×#67—68no—
294C2×#67—62no—
295C2×#67—62no—
296C22×Dic3—68no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299C22×Dic3—62no—
300C22×Dic3—62no—
301C22×Dic3—121no—
302C22×Dic3#6711yescharacteristic
303#237—38no—
304#237—64no—
305#237—64no—
306#237—68no—
307#237—68no—
308#237—64no—
309D3×D4—24no—
310D3×D4—44no—
311#235—38no—
312#235—64no—
313#235—64no—
314#235—68no—
315#235—68no—
316#235—64no—
317C2×D12—21no—
318C2×D12—24no—
319C2×D12—21no—
320C2×D12C22×D311yescharacteristic
321C2×D12C22×D312yes—
322C2×C4×D3—24no—
323C2×C4×D3—21no—
324C2×C4×D3—62no—
325C2×C4×D3—62no—
326C2×C4×D3—68no—
327C2×C4×D3#6711yescharacteristic
328C2×C4×D3#6711yescharacteristic
329C2×C4×D3C22×D311yescharacteristic
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—32no—
332C2×Dic6—32no—
333C2×Dic6—62no—
334C2×Dic6—64no—
335C2×Dic6—64no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6—124no—
339C2×Dic6—121no—
340C3×D8—64no—
341C2×C3×C8—32no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C22⋊C4—21no—
348C3×C22⋊C4—21no—
349C3×C22⋊C4—41no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353#217—21no—
354#214—64no—
355#214—64no—
356#214—64no—
357#214—124no—
358#213—24no—
359#213—64no—
360#213—64no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363C4⋊Dic3C22×D311yescharacteristic
364Dic3⋊C4—21no—
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—41no—
375C22×C32—41no—
376C22×C32—41no—
377C22×C32AGL(1,ℤ/8)12yescomplemented
378C22×C32C22×D411yescharacteristic
379C2×C3×D3—21no—
380C2×C3×D3—21no—
381C2×C3×D3—24no—
382C2×C3×D3—21no—
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—84no—
393C2×C3×D3#12012yes—
394C32×C4—21no—
395C32×C4—41no—
396C32×C4C22×D412yes—
397C3⋊Dic3—24no—
398C3×Dic3—21no—
399C3×Dic3—41no—
400C3×Dic3#12012yes—
401C2×#41—92no—
402C2×#41—92no—
403C2×#41—181no—
404C2×#41—181no—
405C2×#41—188no—
406C22×Q8—91no—
407C22×D4—31no—
408C22×D4—31no—
409C22×D4—61no—
410C22×D4—181no—
411C23×C4—31no—
412C23×C4—181no—
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—31no—
421#121—31no—
422#121—61no—
423#121—61no—
424#121D3211yescharacteristic
425C2×C4⋊C4—31no—
426C2×C22⋊C4—61no—
427#103—92no—
428#103—92no—
429#102—32no—
430#102—92no—
431C22⋊C8—31no—
432C22⋊C8—92no—
433C22⋊C8—91no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—31no—
438C23×C3—31no—
439C23×C3—41no—
440C23×C3—62no—
441C23×C3—64no—
442C23×C3—62no—
443C23×C3—62no—
444C23×C3—61no—
445C23×C3—121no—
446C23×C3—122no—
447C23×C3—122no—
448C23×C3—122no—
449C23×C3—122no—
450C23×C3—122no—
451C23×C3D3×D411yescharacteristic
452C23×C3C2×#6711yescharacteristic
453C22×D3—24no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—21no—
458C22×D3—41no—
459C22×D3—42no—
460C22×D3—42no—
461C22×D3—42no—
462C22×D3—42no—
463C22×D3—42no—
464C22×D3C2×#6711yescharacteristic
465C22×D3C2×#6711yescharacteristic
466C3×D4—22no—
467C3×D4—22no—
468C3×D4—34no—
469C3×D4—42no—
470C3×D4—42no—
471C3×D4—42no—
472C3×D4—64no—
473C3×D4—62no—
474C3×D4—62no—
475C3×D4—82no—
476C3×D4—122no—
477C3×D4—122no—
478C3×D4—122no—
479C3×D4—122no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—31no—
487C2×C3×C4—34no—
488C2×C3×C4—31no—
489C2×C3×C4—42no—
490C2×C3×C4—41no—
491C2×C3×C4—62no—
492C2×C3×C4—62no—
493C2×C3×C4—62no—
494C2×C3×C4—62no—
495C2×C3×C4—61no—
496C2×C3×C4—122no—
497C2×C3×C4D3×D411yescharacteristic
498C2×C3×C4C2×#6711yescharacteristic
499C2×C3×C4C23×D311yescharacteristic
500C2×C3×C4C23×D311yescharacteristic
501#67—42no—
502#67—42no—
503#67—42no—
504#67—68no—
505#67—68no—
506#67—68no—
507#67—68no—
508C2×Dic3—22no—
509C2×Dic3—21no—
510C2×Dic3—68no—
511C2×Dic3—64no—
512C2×Dic3—64no—
513C2×Dic3—62no—
514C2×Dic3—62no—
515C2×Dic3—68no—
516C2×Dic3—122no—
517C2×Dic3—124no—
518C2×Dic3C2×#6711yescharacteristic
519C2×Dic3C2×#6711yescharacteristic
520D12—24no—
521D12—22no—
522D12—22no—
523D12—42no—
524D12D3×D414yescomplemented
525C4×D3—22no—
526C4×D3—22no—
527C4×D3—22no—
528C4×D3—42no—
529C4×D3—68no—
530C4×D3—68no—
531C4×D3D3×D414yes—
532Dic6—34no—
533Dic6—34no—
534Dic6—64no—
535Dic6—64no—
536Dic6—64no—
537Dic6—62no—
538Dic6—62no—
539Dic6—122no—
540Dic6—124no—
541C3×C8—62no—
542C3⋊C8—22no—
543C3⋊C8—62no—
544C3⋊C8—62no—
545C3⋊C8—122no—
546C2×C32—22no—
547C2×C32—81no—
548C2×C32C2×#12011yescharacteristic
549C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
550C2×C32#57511yescharacteristic
551C3×D3—22no—
552C3×D3—41no—
553C3×D3—44no—
554C3×D3—81no—
555C24—31no—
556C24—61no—
557C24—61no—
558#41—98no—
559#41—184no—
560#41—184no—
561#41—184no—
562#41—188no—
563#41—188no—
564C2×Q8—92no—
565C2×Q8—184no—
566C2×Q8—181no—
567C2×D4—21no—
568C2×D4—32no—
569C2×D4—31no—
570C2×D4—64no—
571C2×D4—61no—
572C2×D4—64no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—124no—
578C2×D4—182no—
579C2×D4—182no—
580C2×D4—188no—
581C2×D4C2×D3211yescharacteristic
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—64no—
588C22×C4—61no—
589C22×C4—182no—
590C22×C4—182no—
591C22×C4—188no—
592C22×C4—181no—
593C22×C4C2×D3211yescharacteristic
594SD16—184no—
595SD16—184no—
596D8—64no—
597D8—184no—
598M16—184no—
599C2×C8—32no—
600C2×C8—92no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4C2×D3211yescharacteristic
604C22⋊C4—21no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
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—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—64no—
628C22×C3—61no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—124no—
633C22×C3—128no—
634C22×C3—122no—
635C22×C3—122no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—244no—
640C22×C3#91112yescomplemented
641C22×C3#93212yescomplemented
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C22×#6711yescharacteristic
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—24no—
650C2×D3—44no—
651C2×D3—48no—
652C2×D3—42no—
653C2×D3—42no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—84no—
658C2×D3#93712yes—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—22no—
662C3×C4—32no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—61no—
667C3×C4—81no—
668C3×C4—121no—
669C3×C4C2×D3×D412yes—
670C3×C4C2×D3×D412yes—
671Dic3—21no—
672Dic3—41no—
673Dic3—64no—
674Dic3—64no—
675Dic3—124no—
676Dic3#93712yes—
677C32#300611yescharacteristic, complemented, Sylow
678C23—21no—
679C23—31no—
680C23—31no—
681C23—62no—
682C23—64no—
683C23—62no—
684C23—62no—
685C23—61no—
686C23—121no—
687C23—122no—
688C23—122no—
689C23—122no—
690C23—122no—
691C23—122no—
692C23D3×#6711yescharacteristic
693Q8—94no—
694Q8—184no—
695Q8—182no—
696D4—22no—
697D4—34no—
698D4—42no—
699D4—64no—
700D4—62no—
701D4—62no—
702D4—122no—
703D4—122no—
704D4—122no—
705D4—122no—
706D4—188no—
707D4—188no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—31no—
711C2×C4—34no—
712C2×C4—31no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—61no—
718C2×C4—122no—
719C2×C4—188no—
720C2×C4—188no—
721C2×C4—184no—
722C2×C4—182no—
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—81no—
735C2×C3—81no—
736C2×C3—121no—
737C2×C3—124no—
738C2×C3—161no—
739C2×C3—241no—
740C2×C3D3×#12011yescharacteristic
741C2×C3C2×#91111yescharacteristic
742C2×C3#577311yescharacteristic
743C2×C3C2×#93211yescharacteristic
744C2×C3C2×#93711yescharacteristic
745C2×C3#582211yescharacteristic
746D3—22no—
747D3—44no—
748D3—41no—
749D3—81no—
750C22—21no—
751C22—21no—
752C22—32no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—61no—
757C22—61no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—64no—
762C22—124no—
763C22—128no—
764C22—122no—
765C22—122no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—244no—
770C22#6393212yescomplemented
771C22C2×D3×#6711yescharacteristic
772C4—21no—
773C4—32no—
774C4—41no—
775C4—61no—
776C4—121no—
777C4—184no—
778C4D32×D412yes—
779C3—21no—
780C3#8000311yescharacteristic, complemented
781C3#8262411yescharacteristic, complemented
782C2—22no—
783C2—62no—
784C2—81no—
785C2—121no—
786C2—124no—
787C2—241no—
788C2C2×#6393211yescharacteristic
789C2D3×#93711yescharacteristic
790C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3006
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C22×#3795C2semidirect
2. C3×D3×#121C2semidirect
3. C2×#63932C2semidirect
4. #10592739C2semidirect
5. C3×#5036C2semidirect
6. #10591519C2semidirect
7. #10591181C2semidirect
8. #10591160C2semidirect
9. #10591154C2semidirect
10. #10590613C2semidirect
11. #10590607C2semidirect
14. C22×#634C22semidirect
16. C2×C3×D3×D4C22semidirect
17. C22×C3×D12C22semidirect
25. C2×#3795C22semidirect
27. C2×#3754C22semidirect
29. C3×#938C22semidirect
30. C2×C3×#213C22semidirect
32. C3×#895C22semidirect
33. C3×D3×C4⋊C4C22semidirect
37. C2×#3716C22semidirect
38. C2×#3713C22semidirect
39. C2×#3711C22semidirect
40. #63657C22semidirect
41. #63637C22semidirect
42. C3×#830C22semidirect
43. C3×#809C22semidirect
44. #63567C22semidirect
45. #63562C22semidirect
46. (C2×D3)⋊(C3⋊C8)C22semidirect
52. D3×#121D3semidirect
64. #5036D3semidirect
108. #3795D4semidirect
137. C2×D3×D4C2×D3semidirect
143. C22×D12C2×D3semidirect
161. #938C2×D3semidirect
169. C2×#213C2×D3semidirect
175. #895C2×D3semidirect
176. D3×C4⋊C4C2×D3semidirect
186. #830C2×D3semidirect
194. #809C2×D3semidirect
220. #634C2×D4semidirect
232. C3×D12C2×D4semidirect
377. C22×C32AGL(1,ℤ/8)semidirect
524. D12D3×D4semidirect
640. C22×C3#911semidirect
641. C22×C3#932semidirect
677. C32#3006semidirect
770. C22#63932semidirect
780. C3#80003semidirect
781. C3#82624semidirect

Maximal subgroups

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

subgroupindex
C22×#37952
C3×D3×#1212
C2×#639322
#105927392
C3×#50362
#105915192
#105911812
#105911602
#105911542
#105906132
#105906072
#826243
#800033