Finite Group Databasebeta

← #11863946

Subgroups — #11863946

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×D3×D12C211yesmaximal, characteristic, complemented
2#10595005C211yesmaximal, characteristic, complemented
3C2×#63794C212yesmaximal, complemented
4#10592431C211yesmaximal, characteristic, complemented
5C3×#4731C211yesmaximal, characteristic, complemented
6C3×#4726C211yesmaximal, characteristic, complemented
7#10591183C211yesmaximal, characteristic, complemented
8#10591162C211yesmaximal, characteristic, complemented
9#10590947C212yesmaximal, complemented
10#10590942C212yesmaximal, complemented
11#10590939C212yesmaximal, complemented
12#80146—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×#3799C2211yescharacteristic, complemented
25#64139C2211yescharacteristic, complemented
26C2×#3745C2212yescomplemented
27C3×#924C2211yescharacteristic, complemented
28C2×C3×#204C2212yescomplemented
29C2×C3×ΓL(1,𝔽25)C2212yescomplemented
30#63977—21no—
31#63952—21no—
32#63909C2211yescharacteristic, complemented
33#63904—21no—
34#63856C2211yescharacteristic, complemented
35#63850—21no—
36#63841C2211yescharacteristic, complemented
37C2×#3717C2212yescomplemented
38C2×#3714C2212yescomplemented
39#63794—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×#914—32no—
51C2×#908—32no—
52#5627—31no—
53C3×#450—31no—
54C3×#407—31no—
55#5217—31no—
56#5169—32no—
57#5131—32no—
58#5046—31no—
59#4773—32no—
60#4770—32no—
61#4732—31no—
62#4732—31no—
63#4732—31no—
64#4732—32no—
65#4732—61no—
66#4731—31no—
67#4731—32no—
68#4731D311yescharacteristic, complemented
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×#638—21no—
80C2×C4⋊(C3⋊D3)—21no—
81C2×C4⋊(C3⋊D3)—24no—
82C2×C4⋊(C3⋊D3)C2312yes—
83C2×C4⋊(C3⋊D3)C2311yescharacteristic, complemented
84C22×C3×Dic3D411yescharacteristic
85C2×C3×D12—21no—
86C2×C3×D12—24no—
87C2×C3×D12C2312yes—
88C2×C3×C4×D3—24no—
89C2×C3×C4×D3D411yescharacteristic
90C2×C3×C4×D3D411yescharacteristic
91C2×C3×C4×D3C2311yescharacteristic
92C2×C3×C4×D3C2311yescharacteristic
93C2×C3×Dic6C2311yescharacteristic, complemented
94C2×#626—28no—
95C2×#626—22no—
96C2×#626—22no—
97C2×#626—21no—
98C2×#626—21no—
99C2×#624—21no—
100D3×D12—28no—
101D3×D12—28no—
102D3×D12—24no—
103D3×D12—24no—
104D3×D12—24no—
105D3×D12D418yescomplemented
106#3799—24no—
107C2×C32×C8C2312yescomplemented
108#3752—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic, complemented
110#3745—24no—
111C3×#217—21no—
112C3×C4⋊Dic3C2311yescharacteristic, complemented
113C3×Dic3⋊C4—21no—
114C2×C3×C3⋊C8C2312yescomplemented
115C3×#204—24no—
116C3×ΓL(1,𝔽25)—24no—
117#3724—21no—
118#3722—21no—
119(C2×D3)⋊Dic3—21no—
120(C2×D3)⋊Dic3—21no—
121Dic32—21no—
122#3717—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×#239—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×SD16—32no—
149C2×C3×M16—32no—
150C3×C22⋊Q8—31no—
151#953—61no—
152#946—31no—
153C2×#215—32no—
154C2×#213—32no—
155#930—31no—
156#930—31no—
157#930—31no—
158#930—61no—
159#929—61no—
160C4×#67—61no—
161C4×#67—61no—
162#926—31no—
163#924—31no—
164#924C2×D311yescharacteristic, complemented
165#914—68no—
166#908—68no—
167C2×D24—32no—
168C2×D24—32no—
169C2×D24—32no—
170C2×D24—62no—
171C2×#204—32no—
172C2×#204C2×D312yescomplemented
173C2×ΓL(1,𝔽25)C2×D312yescomplemented
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—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—21no—
200C22×C3⋊D3—42no—
201C22×C3⋊D3—42no—
202C22×C3×D3—22no—
203C22×C3×D3—22no—
204C22×C3×D3—22no—
205C22×C3×D3—24no—
206C22×C3×D3—22no—
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
221#638—42no—
222C2×C3⋊Dic3—21no—
223C4⋊(C3⋊D3)—24no—
224C4⋊(C3⋊D3)—22no—
225C4⋊(C3⋊D3)—22no—
226C4⋊(C3⋊D3)C2×D414yes—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3C2×D411yescharacteristic
231C2×C3×Dic3C2×D411yescharacteristic
232C3×D12—24no—
233C3×D12—22no—
234C3×D12C2×D414yes—
235C3×C4×D3—22no—
236C3×C4×D3—22no—
237C3×C4×D3—22no—
238C3×C4×D3C2×D414yes—
239C3×Dic6—22no—
240#626—28no—
241#626—28no—
242#626—42no—
243#626—42no—
244#624—42no—
245C32×C8—22no—
246C3×C3⋊C8—22no—
247C23×D4—91no—
248C2×AGL(1,ℤ/8)—92no—
249#525—91no—
250#450—31no—
251#450—91no—
252#450—92no—
253#447—92no—
254#447—91no—
255#447—91no—
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×Q8—31no—
276C2×C3×D4—32no—
277C2×C3×D4—64no—
278C2×C3×D4—61no—
279C22×C3×C4—21no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—64no—
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C2×#67—68no—
289C2×#67—61no—
290C2×#67—61no—
291C2×#67—61no—
292C2×#67—61no—
293C2×#67—62no—
294C2×#67—62no—
295C2×#67—121no—
296C22×Dic3D1211yescharacteristic
297#239—64no—
298D3×D4—38no—
299D3×D4—64no—
300D3×D4—64no—
301D3×D4—68no—
302D3×D4—68no—
303D3×D4—64no—
304#235—64no—
305C2×D12—21no—
306C2×D12—24no—
307C2×D12—32no—
308C2×D12—32no—
309C2×D12—38no—
310C2×D12—31no—
311C2×D12—31no—
312C2×D12—62no—
313C2×D12—61no—
314C2×D12—64no—
315C2×D12—64no—
316C2×D12—68no—
317C2×D12—68no—
318C2×D12—64no—
319C2×D12—64no—
320C2×D12—62no—
321C2×D12—62no—
322C2×D12—68no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—64no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12—124no—
329C2×D12—121no—
330C2×D12C22×D312yes—
331C2×C4×D3—24no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3D1211yescharacteristic
335C2×C4×D3D1211yescharacteristic
336C2×C4×D3C22×D311yescharacteristic
337C2×C4×D3C22×D311yescharacteristic
338C2×Dic6C22×D311yescharacteristic, complemented
339C3×SD16—64no—
340C3×M16—64no—
341C2×C3×C8—22no—
342C2×C3×C8—32no—
343C2×C3×C8C22×D312yescomplemented
344C2×C3×C8C22×D312yescomplemented
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C22⋊C4—61no—
348#217—21no—
349#217—61no—
350#217—61no—
351#215—64no—
352#213—64no—
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—61no—
359(C2×D3)⋊C4—121no—
360C4⋊Dic3—31no—
361C4⋊Dic3—31no—
362C4⋊Dic3—61no—
363C4⋊Dic3C22×D311yescharacteristic, complemented
364Dic3⋊C4—21no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C2×C3⋊C8C22×D312yescomplemented
370D24—64no—
371D24—64no—
372D24—64no—
373D24—124no—
374#204—24no—
375#204—64no—
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—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—48no—
395C2×C3×D3—42no—
396C2×C3×D3—42no—
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—21no—
405C3×Dic3—41no—
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—32no—
421C2×SD16—92no—
422C2×D8—92no—
423C2×D8—92no—
424C2×M16—32no—
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—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—122no—
450C23×C3—122no—
451C23×C3C2×D1211yescharacteristic
452C23×C3D3×D411yescharacteristic
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—24no—
457C22×D3—22no—
458C22×D3—42no—
459C22×D3—42no—
460C22×D3—68no—
461C22×D3—68no—
462C22×D3—68no—
463C22×D3—64no—
464C22×D3—64no—
465C22×D3—62no—
466C22×D3—62no—
467C22×D3—68no—
468C22×D3—61no—
469C22×D3—61no—
470C22×D3—122no—
471C22×D3—124no—
472C22×D3—121no—
473C22×D3—1232no—
474C22×D3—124no—
475C22×D3—124no—
476C22×D3—124no—
477C22×D3—124no—
478C22×D3—1232no—
479C22×D3—124no—
480C22×D3—124no—
481C22×D3—124no—
482C22×D3—122no—
483C22×D3—122no—
484C22×D3—122no—
485C22×D3—122no—
486C22×D3—124no—
487C22×D3—242no—
488C22×D3—242no—
489C22×D3C2×D1211yescharacteristic
490C22×D3C2×D1211yescharacteristic
491C3×Q8—62no—
492C3×D4—34no—
493C3×D4—64no—
494C3×D4—62no—
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×C4—61no—
509C2×C3×C4C2×D1211yescharacteristic
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513#67—68no—
514#67—68no—
515#67—122no—
516#67—122no—
517#67—122no—
518#67—122no—
519#67—242no—
520C2×Dic3—22no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—121no—
526C2×Dic3C2×D1211yescharacteristic
527C2×Dic3C2×D1211yescharacteristic
528D12—24no—
529D12—22no—
530D12—34no—
531D12—34no—
532D12—64no—
533D12—64no—
534D12—64no—
535D12—68no—
536D12—68no—
537D12—62no—
538D12—62no—
539D12—62no—
540D12—62no—
541D12—122no—
542D12—122no—
543D12—124no—
544D12—122no—
545D12—122no—
546D12D3×D414yes—
547C4×D3—22no—
548C4×D3—22no—
549C4×D3—22no—
550C4×D3—122no—
551C4×D3—122no—
552C4×D3D3×D414yes—
553Dic6—22no—
554C3×C8—22no—
555C3×C8—22no—
556C3×C8—42no—
557C3×C8—62no—
558C3⋊C8—22no—
559C2×C32—22no—
560C2×C32C2×#12011yescharacteristic
561C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
562C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
563C3⋊D3—44no—
564C3⋊D3—81no—
565C3×D3—22no—
566C3×D3—22no—
567C3×D3—44no—
568C24—31no—
569C24—61no—
570C24—182no—
571C24—182no—
572C24—188no—
573C24—181no—
574C24—364no—
575C24—364no—
576#41—184no—
577C2×Q8—31no—
578C2×D4—32no—
579C2×D4—64no—
580C2×D4—61no—
581C2×D4—98no—
582C2×D4—92no—
583C2×D4—91no—
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—
596C2×D4—181no—
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—64no—
610C2×C8—32no—
611C2×C8C2×D3212yescomplemented
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—21no—
627C22×C3—22no—
628C22×C3—32no—
629C22×C3—32no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—68no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—64no—
638C22×C3—128no—
639C22×C3—122no—
640C22×C3—122no—
641C22×C3#90812yescomplemented
642C22×C3#91412yescomplemented
643C22×C3C22×D1211yescharacteristic
644C22×C3C2×D3×D411yescharacteristic
645C2×D3—28no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—24no—
651C2×D3—48no—
652C2×D3—42no—
653C2×D3—42no—
654C2×D3—64no—
655C2×D3—64no—
656C2×D3—124no—
657C2×D3—1216no—
658C2×D3—1216no—
659C2×D3—1216no—
660C2×D3—1216no—
661C2×D3—128no—
662C2×D3—128no—
663C2×D3—122no—
664C2×D3—122no—
665C2×D3—122no—
666C2×D3—122no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—242no—
674C2×D3—242no—
675C2×D3—248no—
676C2×D3—241no—
677C2×D3—241no—
678C2×D3—241no—
679C2×D3#88212yes—
680C2×D3#90812yescomplemented
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×C4C2×D3×D412yes—
691Dic3—21no—
692Dic3—41no—
693Dic3—41no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697Dic3#88212yes—
698C32#300311yescharacteristic, complemented, Sylow
699C23—31no—
700C23—31no—
701C23—62no—
702C23—62no—
703C23—64no—
704C23—62no—
705C23—62no—
706C23—122no—
707C23—122no—
708C23—184no—
709C23—188no—
710C23—188no—
711C23—182no—
712C23—181no—
713C23—362no—
714C23—364no—
715C23—3632no—
716C23—364no—
717C23—364no—
718C23—364no—
719C23—362no—
720C23D3×D1211yescharacteristic
721Q8—62no—
722D4—34no—
723D4—64no—
724D4—62no—
725D4—94no—
726D4—184no—
727D4—188no—
728D4—188no—
729D4—182no—
730D4—182no—
731D4—362no—
732D4—362no—
733D4—362no—
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×D1211yescharacteristic
747C2×C4C22×D3211yescharacteristic
748C8—22no—
749C8—62no—
750C2×C3—22no—
751C2×C3—22no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—42no—
756C2×C3—62no—
757C2×C3—62no—
758C2×C3—124no—
759C2×C3C2×#88211yescharacteristic
760C2×C3D3×#12011yescharacteristic
761C2×C3C2×#90811yescharacteristic
762C2×C3C2×#90811yescharacteristic
763C2×C3C2×#91411yescharacteristic
764C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
765D3—22no—
766D3—22no—
767D3—44no—
768D3—124no—
769D3—124no—
770D3—244no—
771D3—241no—
772D3—241no—
773D3—481no—
774C22—21no—
775C22—21no—
776C22—32no—
777C22—32no—
778C22—68no—
779C22—61no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—64no—
784C22—128no—
785C22—122no—
786C22—122no—
787C22—184no—
788C22—368no—
789C22—3616no—
790C22—3616no—
791C22—362no—
792C22—362no—
793C22—361no—
794C22—361no—
795C22—361no—
796C22#6379412yescomplemented
797C22C2×D3×D1211yescharacteristic
798C4—21no—
799C4—32no—
800C4—61no—
801C4—121no—
802C4—121no—
803C4—361no—
804C4D32×D412yes—
805C3—21no—
806C3#7863711yescharacteristic, complemented
807C3#8014611yescharacteristic, complemented
808C2—22no—
809C2—62no—
810C2—62no—
811C2—124no—
812C2—364no—
813C2—721no—
814C2D3×#88211yescharacteristic
815C2C2×#6379411yescharacteristic
816C2D3×#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. #10595005C2semidirect
3. C2×#63794C2semidirect
4. #10592431C2semidirect
5. C3×#4731C2semidirect
6. C3×#4726C2semidirect
7. #10591183C2semidirect
8. #10591162C2semidirect
9. #10590947C2semidirect
10. #10590942C2semidirect
11. #10590939C2semidirect
24. C2×#3799C22semidirect
25. #64139C22semidirect
26. C2×#3745C22semidirect
27. C3×#924C22semidirect
28. C2×C3×#204C22semidirect
29. C2×C3×ΓL(1,𝔽25)C22semidirect
32. #63909C22semidirect
34. #63856C22semidirect
36. #63841C22semidirect
37. C2×#3717C22semidirect
38. C2×#3714C22semidirect
40. C32×C22⋊C8C22semidirect
41. #63648C22semidirect
42. C3×#830C22semidirect
43. C3×#821C22semidirect
44. C3×(C2×D3)⋊C8C22semidirect
45. #63564C22semidirect
46. #63563C22semidirect
68. #4731D3semidirect
69. #4726D3semidirect
83. C2×C4⋊(C3⋊D3)C23semidirect
93. C2×C3×Dic6C23semidirect
105. D3×D12D4semidirect
107. C2×C32×C8C23semidirect
109. C4⋊(C3⋊Dic3)C23semidirect
112. C3×C4⋊Dic3C23semidirect
114. C2×C3×C3⋊C8C23semidirect
164. #924C2×D3semidirect
172. C2×#204C2×D3semidirect
173. 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
338. C2×Dic6C22×D3semidirect
343. C2×C3×C8C22×D3semidirect
344. C2×C3×C8C22×D3semidirect
363. 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
611. C2×C8C2×D32semidirect
641. C22×C3#908semidirect
642. C22×C3#914semidirect
680. C2×D3#908semidirect
698. C32#3003semidirect
796. C22#63794semidirect
806. C3#78637semidirect
807. C3#80146semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D122
#105950052
C2×#637942
#105924312
C3×#47312
C3×#47262
#105911832
#105911622
#105909472
#105909422
#105909392
#801463
#786373