Finite Group Databasebeta

← #11863943

Subgroups — #11863943

Order 1152.

2087 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic, complemented
2C2×#63934C212yesmaximal, complemented
3#10595005C211yesmaximal, characteristic, complemented
4#10592916C211yesmaximal, characteristic, complemented
5C3×#5218C211yesmaximal, characteristic, complemented
6#10591458C212yesmaximal, complemented
7#10591448C212yesmaximal, complemented
8#10591421C212yesmaximal, complemented
9#10591169C211yesmaximal, characteristic, complemented
10#10591162C211yesmaximal, characteristic, complemented
11#10591154C211yesmaximal, characteristic, complemented
12#84038—31nomaximal
13#80146—31nomaximal
14C24×C3×D3—21no—
15C22×C32×D4C2211yescharacteristic
16C22×C3×#67—21no—
17C2×C3×D3×D4—28no—
18C2×C3×D3×D4—21no—
19C2×C3×D3×D4—21no—
20C2×C3×D3×D4C2212yes—
21C2×C3×D3×D4C2212yes—
22C22×C3×D12C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C2×#3799C2211yescharacteristic, complemented
25C2×#3753C2212yescomplemented
26#64139C2211yescharacteristic, complemented
27C2×C3×#214C2212yescomplemented
28C3×#924C2211yescharacteristic, complemented
29#63977—21no—
30#63952—21no—
31#63934—28no—
32#63909C2211yescharacteristic, complemented
33#63904—21no—
34#63856C2211yescharacteristic, complemented
35#63850—21no—
36#63841C2211yescharacteristic, complemented
37C2×#3715C2212yescomplemented
38C2×#3714C2212yescomplemented
39C2×#3711C2212yescomplemented
40#63659C2212yescomplemented
41#63657C2211yescharacteristic, complemented
42C3×#832C2212yescomplemented
43C3×#830C2211yescharacteristic, complemented
44#63563C2212yescomplemented
45#63562C2212yescomplemented
46(C2×D3)⋊(C3⋊C8)C2212yescomplemented
47C23×C3×D4—31no—
48C22×D3×D4D311yescharacteristic, complemented
49C2×#932—32no—
50#5791—31no—
51C2×#914—32no—
52#5627—31no—
53C3×#450—31no—
54#5218—32no—
55#5218—31no—
56#5218D311yescharacteristic, complemented
57#5217—31no—
58#5217—31no—
59#5217—32no—
60#5217—31no—
61#5217—61no—
62#5215—32no—
63#5207—31no—
64#5169—32no—
65#5046—31no—
66#4773—32no—
67#4770—32no—
68#4732—31no—
69#4726—31no—
70C24×C32—21no—
71C23×C3×D3—28no—
72C23×C3×D3—21no—
73C23×C3×D3—22no—
74C23×C3×D3—22no—
75C23×C3×D3—44no—
76C23×C3×D3—44no—
77C23×C3×D3D411yescharacteristic
78C2×C32×D4—24no—
79C2×C32×D4—21no—
80C2×C32×D4C2312yes—
81C22×C32×C4C2311yescharacteristic
82C2×#638—21no—
83C2×C4⋊(C3⋊D3)C2311yescharacteristic, complemented
84C2×C3×#67—28no—
85C2×C3×#67—22no—
86C2×C3×#67—22no—
87C22×C3×Dic3D411yescharacteristic
88C3×D3×D4—28no—
89C3×D3×D4—28no—
90C3×D3×D4—24no—
91C3×D3×D4—24no—
92C3×D3×D4—24no—
93C3×D3×D4D418yescomplemented
94C2×C3×D12—21no—
95C2×C3×D12—24no—
96C2×C3×D12C2312yes—
97C2×C3×C4×D3—24no—
98C2×C3×C4×D3D411yescharacteristic
99C2×C3×C4×D3D411yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic, complemented
103C2×#626—21no—
104C2×#626—21no—
105C2×#624—21no—
106#3799—24no—
107#3753—24no—
108#3752—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic, complemented
110C2×C3⋊(C3⋊C8)C2312yescomplemented
111C3×#217—21no—
112C3×#214—24no—
113C3×C4⋊Dic3C2311yescharacteristic, complemented
114C3×Dic3⋊C4—21no—
115C2×C3×C3⋊C8C2312yescomplemented
116#3724—21no—
117#3722—21no—
118(C2×D3)⋊Dic3—21no—
119(C2×D3)⋊Dic3—21no—
120Dic32—21no—
121#3715—24no—
122#3714—24no—
123#3711—24no—
124#3003—91noSylow
125C25×C3—61no—
126C24×D3—21no—
127C22×C3×D4—21no—
128C22×C3×D4—32no—
129C22×C3×D4—32no—
130C22×C3×D4—31no—
131C22×C3×D4—61no—
132C22×C3×D4—61no—
133C22×C3×D4—61no—
134C22×C3×D4—68no—
135C22×C3×D4C2×D311yescharacteristic
136C22×C3×D4C2×D311yescharacteristic
137C23×C3×C4—31no—
138C22×#67—21no—
139C2×#239—31no—
140C2×D3×D4—28no—
141C2×D3×D4—21no—
142C2×D3×D4—21no—
143C2×D3×D4C2×D312yes—
144C2×D3×D4C2×D312yes—
145C2×#235—31no—
146C22×D12C2×D311yescharacteristic
147C22×C4×D3C2×D311yescharacteristic
148C2×C3×SD16—32no—
149C3×C22⋊Q8—31no—
150#953—61no—
151#946—31no—
152C2×#215—32no—
153C2×#214—32no—
154C2×#214C2×D312yescomplemented
155#932—68no—
156C2×#213—32no—
157C2×#213—32no—
158C2×#213—32no—
159C2×#213—62no—
160#930—31no—
161#930—31no—
162#930—31no—
163#930—61no—
164#929—61no—
165C4×#67—61no—
166C4×#67—61no—
167#926—31no—
168#924—31no—
169#924C2×D311yescharacteristic, complemented
170C2×#208—32no—
171#914—68no—
172C2×D24—32no—
173C2×ΓL(1,𝔽25)—32no—
174#895—31no—
175#894—61no—
176#893—61no—
177#892—31no—
178#882—61no—
179#67⋊C4—61no—
180C3×#102—32no—
181C3×C22⋊C8—31no—
182#832—32no—
183#832—32no—
184#832—32no—
185#832—32no—
186#832—62no—
187#832C2×D312yescomplemented
188#830—31no—
189#830—31no—
190#830—32no—
191#830—61no—
192#830C2×D311yescharacteristic, complemented
193#821—32no—
194(C2×D3)⋊C8—32no—
195#809—32no—
196C23×C32—24no—
197C23×C32—22no—
198C23×C32—42no—
199C23×C32—42no—
200C23×C32C2×D411yescharacteristic
201C22×C3⋊D3—21no—
202C22×C3×D3—22no—
203C22×C3×D3—22no—
204C22×C3×D3—22no—
205C22×C3×D3—24no—
206C22×C3×D3—28no—
207C22×C3×D3—22no—
208C22×C3×D3—28no—
209C22×C3×D3—432no—
210C22×C3×D3—44no—
211C22×C3×D3—44no—
212C22×C3×D3—44no—
213C22×C3×D3—42no—
214C22×C3×D3—42no—
215C22×C3×D3—44no—
216C22×C3×D3C2×D411yescharacteristic
217C22×C3×D3C2×D411yescharacteristic
218C32×D4—24no—
219C32×D4—22no—
220C32×D4C2×D414yes—
221C2×C32×C4—22no—
222C2×C32×C4C2×D411yescharacteristic
223C2×C32×C4C2411yescharacteristic
224#638—42no—
225C2×C3⋊Dic3—21no—
226C4⋊(C3⋊D3)—22no—
227C3×#67—28no—
228C3×#67—28no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—21no—
231C2×C3×Dic3—21no—
232C2×C3×Dic3C2×D411yescharacteristic
233C2×C3×Dic3C2×D411yescharacteristic
234C3×D12—24no—
235C3×D12—22no—
236C3×D12C2×D414yes—
237C3×C4×D3—22no—
238C3×C4×D3—22no—
239C3×C4×D3—22no—
240C3×C4×D3C2×D414yes—
241C3×Dic6—22no—
242#626—42no—
243#626—42no—
244#624—42no—
245C3⋊(C3⋊C8)—22no—
246C3×C3⋊C8—22no—
247C23×D4—31no—
248C2×AGL(1,ℤ/8)—92no—
249#525—91no—
250#450—31no—
251#450—91no—
252#450—92no—
253#447—91no—
254#447—92no—
255#447—91no—
256#418—92no—
257#407—91no—
258C24×C3—21no—
259C24×C3—21no—
260C24×C3—31no—
261C24×C3—41no—
262C24×C3—62no—
263C24×C3—62no—
264C24×C3—68no—
265C24×C3—61no—
266C24×C3—124no—
267C24×C3—124no—
268C23×D3—28no—
269C23×D3—21no—
270C23×D3—22no—
271C23×D3—22no—
272C23×D3—44no—
273C23×D3—44no—
274C23×D3#6711yescharacteristic
275C2×C3×Q8—31no—
276C2×C3×D4—24no—
277C2×C3×D4—24no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—22no—
281C2×C3×D4—38no—
282C2×C3×D4—32no—
283C2×C3×D4—41no—
284C2×C3×D4—44no—
285C2×C3×D4—64no—
286C2×C3×D4—64no—
287C2×C3×D4—62no—
288C2×C3×D4—62no—
289C2×C3×D4—64no—
290C2×C3×D4—68no—
291C2×C3×D4—68no—
292C2×C3×D4—68no—
293C2×C3×D4—64no—
294C2×C3×D4—61no—
295C2×C3×D4C22×D312yes—
296C2×C3×D4C22×D312yes—
297C22×C3×C4—21no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—64no—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C2×#67—28no—
307C2×#67—22no—
308C2×#67—22no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—121no—
314C22×Dic3#6711yescharacteristic
315#239—64no—
316D3×D4—28no—
317D3×D4—28no—
318D3×D4—24no—
319D3×D4—24no—
320D3×D4—24no—
321D3×D4#6718yescomplemented
322#235—64no—
323C2×D12—21no—
324C2×D12—24no—
325C2×D12—31no—
326C2×D12—31no—
327C2×D12—61no—
328C2×D12—61no—
329C2×D12—61no—
330C2×D12C22×D312yes—
331C2×C4×D3—24no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3#6711yescharacteristic
335C2×C4×D3#6711yescharacteristic
336C2×C4×D3C22×D311yescharacteristic
337C2×C4×D3C22×D311yescharacteristic
338C2×Dic6C22×D311yescharacteristic, complemented
339C3×SD16—64no—
340C2×C3×C8—32no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C22⋊C4—61no—
344#217—21no—
345#217—61no—
346#217—61no—
347#215—64no—
348#214—24no—
349#214—64no—
350#213—64no—
351#213—64no—
352#213—64no—
353#213—124no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—121no—
361C4⋊Dic3—31no—
362C4⋊Dic3—31no—
363C4⋊Dic3—61no—
364C4⋊Dic3C22×D311yescharacteristic, complemented
365Dic3⋊C4—21no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370#208—64no—
371C2×C3⋊C8—32no—
372C2×C3⋊C8—32no—
373C2×C3⋊C8—62no—
374C2×C3⋊C8C22×D312yescomplemented
375D24—64no—
376ΓL(1,𝔽25)—64no—
377C22×C32—21no—
378C22×C32—21no—
379C22×C32—24no—
380C22×C32—48no—
381C22×C32—42no—
382C22×C32—42no—
383C22×C32AGL(1,ℤ/8)12yescomplemented
384C22×C32C22×D411yescharacteristic
385C2×C3⋊D3—41no—
386C2×C3⋊D3—41no—
387C2×C3⋊D3—41no—
388C2×C3×D3—28no—
389C2×C3×D3—21no—
390C2×C3×D3—21no—
391C2×C3×D3—21no—
392C2×C3×D3—21no—
393C2×C3×D3—24no—
394C2×C3×D3—416no—
395C2×C3×D3—416no—
396C2×C3×D3—48no—
397C2×C3×D3—42no—
398C2×C3×D3—42no—
399C2×C3×D3#12012yes—
400C2×C3×D3AGL(1,ℤ/8)12yescomplemented
401C32×C4—21no—
402C32×C4C22×D412yes—
403C3⋊Dic3—41no—
404C3×Dic3—21no—
405C3×Dic3—41no—
406C3×Dic3—41no—
407C3×Dic3#12012yes—
408C25—61no—
409C2×#41—91no—
410C22×D4—32no—
411C22×D4—32no—
412C22×D4—31no—
413C22×D4—61no—
414C22×D4—61no—
415C22×D4—61no—
416C22×D4—68no—
417C22×D4D3211yescharacteristic
418C23×C4—31no—
419AGL(1,ℤ/8)—188no—
420C2×SD16—32no—
421C2×SD16—92no—
422C2×D8—92no—
423C2×D8—92no—
424C2×M16—92no—
425#123—181no—
426C22⋊Q8—31no—
427C22⋊Q8—91no—
428#121—91no—
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—92no—
440C22⋊C8—91no—
441C23×C3—24no—
442C23×C3—24no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—21no—
446C23×C3—31no—
447C23×C3—31no—
448C23×C3—42no—
449C23×C3—44no—
450C23×C3—42no—
451C23×C3—42no—
452C23×C3—42no—
453C23×C3—42no—
454C23×C3—62no—
455C23×C3—62no—
456C23×C3—68no—
457C23×C3—64no—
458C23×C3—68no—
459C23×C3—62no—
460C23×C3—62no—
461C23×C3—82no—
462C23×C3—82no—
463C23×C3—122no—
464C23×C3—124no—
465C23×C3—1232no—
466C23×C3—124no—
467C23×C3—124no—
468C23×C3—124no—
469C23×C3—122no—
470C23×C3D3×D411yescharacteristic
471C23×C3C2×#6711yescharacteristic
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—24no—
476C22×D3—28no—
477C22×D3—22no—
478C22×D3—28no—
479C22×D3—432no—
480C22×D3—44no—
481C22×D3—44no—
482C22×D3—44no—
483C22×D3—42no—
484C22×D3—42no—
485C22×D3—44no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—121no—
489C22×D3C2×#6711yescharacteristic
490C22×D3C2×#6711yescharacteristic
491C3×Q8—62no—
492C3×D4—24no—
493C3×D4—24no—
494C3×D4—22no—
495C3×D4—22no—
496C3×D4—24no—
497C3×D4—34no—
498C3×D4—42no—
499C3×D4—44no—
500C3×D4—64no—
501C3×D4—68no—
502C3×D4—68no—
503C3×D4—62no—
504C3×D4D3×D414yes—
505C3×D4C2×#6714yes—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—34no—
512C2×C3×C4—31no—
513C2×C3×C4—42no—
514C2×C3×C4—62no—
515C2×C3×C4—62no—
516C2×C3×C4—62no—
517C2×C3×C4—62no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4C2×#6711yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524#67—28no—
525#67—28no—
526#67—122no—
527#67—122no—
528#67—122no—
529#67—122no—
530#67—242no—
531C2×Dic3—22no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—121no—
537C2×Dic3C2×#6711yescharacteristic
538C2×Dic3C2×#6711yescharacteristic
539D12—24no—
540D12—22no—
541D12—62no—
542D12—62no—
543D12—122no—
544D12—122no—
545D12—122no—
546D12C2×#6714yes—
547C4×D3—22no—
548C4×D3—22no—
549C4×D3—22no—
550C4×D3—122no—
551C4×D3—122no—
552C4×D3C2×#6714yes—
553Dic6—22no—
554C3×C8—62no—
555C3⋊C8—22no—
556C3⋊C8—62no—
557C3⋊C8—62no—
558C3⋊C8—122no—
559C2×C32—22no—
560C2×C32—44no—
561C2×C32C2×#12011yescharacteristic
562C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
563C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
564C3⋊D3—81no—
565C3×D3—22no—
566C3×D3—22no—
567C3×D3—44no—
568C24—21no—
569C24—31no—
570C24—62no—
571C24—62no—
572C24—68no—
573C24—61no—
574C24—124no—
575C24—124no—
576#41—184no—
577C2×Q8—31no—
578C2×D4—24no—
579C2×D4—21no—
580C2×D4—38no—
581C2×D4—32no—
582C2×D4—64no—
583C2×D4—64no—
584C2×D4—62no—
585C2×D4—62no—
586C2×D4—64no—
587C2×D4—68no—
588C2×D4—68no—
589C2×D4—68no—
590C2×D4—64no—
591C2×D4—61no—
592C2×D4—91no—
593C2×D4—181no—
594C2×D4—181no—
595C2×D4—181no—
596C2×D4C2×D3212yes—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—64no—
603C22×C4—181no—
604C22×C4C2×D3211yescharacteristic
605SD16—64no—
606SD16—184no—
607D8—184no—
608D8—184no—
609M16—184no—
610C2×C8—32no—
611C2×C8—92no—
612C4⋊C4—31no—
613C4⋊C4—61no—
614C4⋊C4—91no—
615C4⋊C4—181no—
616C22⋊C4—61no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C42—181no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—24no—
627C22×C3—24no—
628C22×C3—21no—
629C22×C3—22no—
630C22×C3—32no—
631C22×C3—32no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—44no—
635C22×C3—48no—
636C22×C3—48no—
637C22×C3—42no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3—68no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—64no—
647C22×C3—82no—
648C22×C3—82no—
649C22×C3—88no—
650C22×C3—128no—
651C22×C3—1216no—
652C22×C3—1216no—
653C22×C3—122no—
654C22×C3—122no—
655C22×C3#91412yescomplemented
656C22×C3#93212yescomplemented
657C22×C3C2×D3×D411yescharacteristic
658C22×C3C22×#6711yescharacteristic
659C2×D3—28no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—24no—
665C2×D3—416no—
666C2×D3—416no—
667C2×D3—48no—
668C2×D3—42no—
669C2×D3—42no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—241no—
677C2×D3—241no—
678C2×D3—241no—
679C2×D3#93212yescomplemented
680C2×D3#95312yes—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—22no—
684C3×C4—32no—
685C3×C4—41no—
686C3×C4—61no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4C2×D3×D412yes—
690C3×C4C22×#6712yes—
691Dic3—21no—
692Dic3—41no—
693Dic3—41no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697Dic3#95312yes—
698C32#300311yescharacteristic, complemented, Sylow
699C23—24no—
700C23—22no—
701C23—31no—
702C23—31no—
703C23—42no—
704C23—42no—
705C23—62no—
706C23—62no—
707C23—68no—
708C23—64no—
709C23—68no—
710C23—62no—
711C23—62no—
712C23—122no—
713C23—124no—
714C23—1232no—
715C23—124no—
716C23—124no—
717C23—124no—
718C23—122no—
719C23—181no—
720C23D3×#6711yescharacteristic
721Q8—62no—
722D4—24no—
723D4—22no—
724D4—34no—
725D4—64no—
726D4—68no—
727D4—68no—
728D4—62no—
729D4—182no—
730D4—362no—
731D4—362no—
732D4—362no—
733D4D3×#6714yes—
734C2×C4—22no—
735C2×C4—31no—
736C2×C4—34no—
737C2×C4—31no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—181no—
745C2×C4—362no—
746C2×C4D3×#6711yescharacteristic
747C2×C4C22×D3211yescharacteristic
748C8—62no—
749C8—182no—
750C2×C3—22no—
751C2×C3—22no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—42no—
756C2×C3—44no—
757C2×C3—44no—
758C2×C3—62no—
759C2×C3—62no—
760C2×C3—84no—
761C2×C3—124no—
762C2×C3D3×#12011yescharacteristic
763C2×C3C2×#91411yescharacteristic
764C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
765C2×C3C2×#93211yescharacteristic
766C2×C3C2×#93211yescharacteristic
767C2×C3C2×#95311yescharacteristic
768D3—22no—
769D3—22no—
770D3—44no—
771D3—241no—
772D3—241no—
773D3—481no—
774C22—21no—
775C22—21no—
776C22—24no—
777C22—32no—
778C22—32no—
779C22—48no—
780C22—42no—
781C22—42no—
782C22—68no—
783C22—61no—
784C22—61no—
785C22—61no—
786C22—61no—
787C22—64no—
788C22—128no—
789C22—1216no—
790C22—1216no—
791C22—122no—
792C22—122no—
793C22—361no—
794C22—361no—
795C22—361no—
796C22#6393412yescomplemented
797C22C2×D3×#6711yescharacteristic
798C4—21no—
799C4—32no—
800C4—61no—
801C4—121no—
802C4—121no—
803C4—361no—
804C4C2×D3×#6712yes—
805C3—21no—
806C3#8014611yescharacteristic, complemented
807C3#8403811yescharacteristic, complemented
808C2—22no—
809C2—44no—
810C2—62no—
811C2—62no—
812C2—124no—
813C2—721no—
814C2D3×#93211yescharacteristic
815C2C2×#6393411yescharacteristic
816C2D3×#95311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3003
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×D3×D4C2semidirect
2. C2×#63934C2semidirect
3. #10595005C2semidirect
4. #10592916C2semidirect
5. C3×#5218C2semidirect
6. #10591458C2semidirect
7. #10591448C2semidirect
8. #10591421C2semidirect
9. #10591169C2semidirect
10. #10591162C2semidirect
11. #10591154C2semidirect
24. C2×#3799C22semidirect
25. C2×#3753C22semidirect
26. #64139C22semidirect
27. C2×C3×#214C22semidirect
28. C3×#924C22semidirect
32. #63909C22semidirect
34. #63856C22semidirect
36. #63841C22semidirect
37. C2×#3715C22semidirect
38. C2×#3714C22semidirect
39. C2×#3711C22semidirect
40. #63659C22semidirect
41. #63657C22semidirect
42. C3×#832C22semidirect
43. C3×#830C22semidirect
44. #63563C22semidirect
45. #63562C22semidirect
46. (C2×D3)⋊(C3⋊C8)C22semidirect
48. C22×D3×D4D3semidirect
56. #5218D3semidirect
83. C2×C4⋊(C3⋊D3)C23semidirect
93. C3×D3×D4D4semidirect
102. C2×C3×Dic6C23semidirect
109. C4⋊(C3⋊Dic3)C23semidirect
110. C2×C3⋊(C3⋊C8)C23semidirect
113. C3×C4⋊Dic3C23semidirect
115. C2×C3×C3⋊C8C23semidirect
154. C2×#214C2×D3semidirect
169. #924C2×D3semidirect
187. #832C2×D3semidirect
192. #830C2×D3semidirect
321. D3×D4#67semidirect
338. C2×Dic6C22×D3semidirect
364. C4⋊Dic3C22×D3semidirect
374. C2×C3⋊C8C22×D3semidirect
383. C22×C32AGL(1,ℤ/8)semidirect
400. C2×C3×D3AGL(1,ℤ/8)semidirect
655. C22×C3#914semidirect
656. C22×C3#932semidirect
679. C2×D3#932semidirect
698. C32#3003semidirect
796. C22#63934semidirect
806. C3#80146semidirect
807. C3#84038semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C2×#639342
#105950052
#105929162
C3×#52182
#105914582
#105914482
#105914212
#105911692
#105911622
#105911542
#840383
#801463