Finite Group Databasebeta

← #11863949

Subgroups — #11863949

Order 1152.

2082 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D12C211yesmaximal, characteristic, complemented
2C3×#5627C211yesmaximal, characteristic, complemented
3C2×#63939C212yesmaximal, complemented
4#10592745C211yesmaximal, characteristic, complemented
5C3×#5046C211yesmaximal, characteristic, complemented
6#10591651C212yesmaximal, complemented
7#10591168C211yesmaximal, characteristic, complemented
8#10591160C211yesmaximal, characteristic, complemented
9#10591154C211yesmaximal, characteristic, complemented
10#10590595C212yesmaximal, complemented
11#10590592C212yesmaximal, complemented
12#82927—31nomaximal
13#80146—31nomaximal
14C23×D32—21no—
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×#239C2211yescharacteristic, complemented
17C22×C3×D12C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic
19C22×#626—21no—
20C2×D3×D12—21no—
21C2×D3×D12—21no—
22C2×D3×D12—28no—
23C2×D3×D12C2212yes—
24C2×D3×D12C2212yes—
25C32×C22⋊Q8C2211yescharacteristic, complemented
26C2×#3755C2212yescomplemented
27C3×#946C2211yescharacteristic, complemented
28C2×C3×#215C2212yescomplemented
29C3×#930C2211yescharacteristic, complemented
30C3×#895C2211yescharacteristic, complemented
31C3×#894—21no—
32C3×#893—21no—
33C3×#892C2211yescharacteristic, complemented
34C3×#882—21no—
35C3×#67⋊C4—21no—
36#63939—28no—
37C2×#3714C2212yescomplemented
38C2×#3713C2212yescomplemented
39C2×#3711C2212yescomplemented
40#63657C2211yescharacteristic, complemented
41#63636C2212yescomplemented
42C3×#830C2211yescharacteristic, complemented
43C3×#809C2212yescomplemented
44#63564C2212yescomplemented
45#63562C2212yescomplemented
46(C2×D3)⋊(C3⋊C8)C2212yescomplemented
47C22×D3×D4—31no—
48C23×D12—31no—
49C3×#525—31no—
50C2×#949—32no—
51C2×#914—32no—
52#5627D311yescharacteristic, complemented
53C3×#450—31no—
54#5217—31no—
55#5207—31no—
56#5169—32no—
57#5046—31no—
58#5046—31no—
59#5046—32no—
60#5046—61no—
61#5046D311yescharacteristic, complemented
62#5036—31no—
63#5036—31no—
64#5036—32no—
65#5001—32no—
66#4773—32no—
67#4770—32no—
68#4732—31no—
69#4726—31no—
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—
78C2×C32×Q8C2311yescharacteristic, complemented
79C22×C32×C4C2311yescharacteristic
80C2×C4⋊(C3⋊D3)—21no—
81C2×C4⋊(C3⋊D3)—24no—
82C2×C4⋊(C3⋊D3)C2312yes—
83C2×C3×#67—21no—
84C22×C3×Dic3D411yescharacteristic
85C3×#239—24no—
86C2×C3×D12—21no—
87C2×C3×D12—24no—
88C2×C3×D12—21no—
89C2×C3×D12—21no—
90C2×C3×D12C2312yes—
91C2×C3×D12C2311yescharacteristic, complemented
92C2×C3×C4×D3—24no—
93C2×C3×C4×D3—21no—
94C2×C3×C4×D3D411yescharacteristic
95C2×C3×C4×D3D411yescharacteristic
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×C4×D3C2311yescharacteristic
98C2×#626—28no—
99C2×#626—22no—
100C2×#626—22no—
101D3×D12—28no—
102D3×D12—28no—
103D3×D12—24no—
104D3×D12—24no—
105D3×D12—24no—
106D3×D12D418yescomplemented
107C32×C4⋊C4—21no—
108C32×C4⋊C4C2311yescharacteristic, complemented
109C32×C22⋊C4—21no—
110#3755—24no—
111C2×C3⋊(C3⋊C8)C2312yescomplemented
112C3×#215—24no—
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3C2311yescharacteristic, complemented
118C3×Dic3⋊C4—21no—
119C3×C4×Dic3—21no—
120C2×C3×C3⋊C8C2312yescomplemented
121#3714—24no—
122#3713—24no—
123#3711—24no—
124#3003—91noSylow
125C24×D3—61no—
126C24×D3—61no—
127C2×C3×#41—31no—
128C22×C3×D4—31no—
129C23×C3×C4—31no—
130C22×#67—61no—
131C2×#239C2×D311yescharacteristic, complemented
132C2×D3×D4—32no—
133C2×D3×D4—32no—
134C2×D3×D4—68no—
135C2×D3×D4—61no—
136C2×D3×D4—61no—
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—
149C3×#123—61no—
150C3×C22⋊Q8—21no—
151C3×C22⋊Q8—31no—
152C3×C22⋊Q8C2×D311yescharacteristic, complemented
153C3×C22⋊Q8C2×D311yescharacteristic, complemented
154C3×#121—31no—
155C3×#121—31no—
156C3×#120—61no—
157C3×C4×D4—61no—
158C3×C4×D4—61no—
159C3×#117—31no—
160#949—68no—
161#946C2×D311yescharacteristic, complemented
162C2×#215—32no—
163C2×#215—32no—
164C2×#215—62no—
165C2×#215C2×D312yescomplemented
166C2×#213—32no—
167C2×#213—32no—
168C2×#213—32no—
169#930C2×D311yescharacteristic, complemented
170C2×#208—32no—
171#914—68no—
172C2×D24—32no—
173C2×ΓL(1,𝔽25)—32no—
174#895C2×D311yescharacteristic, complemented
175#894—21no—
176#893—21no—
177#892C2×D311yescharacteristic, complemented
178#882—21no—
179#67⋊C4—21no—
180C3×#102—32no—
181C3×C22⋊C8—31no—
182#832—32no—
183#830—31no—
184#830—31no—
185#830—32no—
186#830—61no—
187#830C2×D311yescharacteristic, complemented
188#821—32no—
189(C2×D3)⋊C8—32no—
190#809—32no—
191#809—32no—
192#809—32no—
193#809—32no—
194#809—62no—
195#809C2×D312yescomplemented
196C23×C32C2×D411yescharacteristic
197C22×C3⋊D3—24no—
198C22×C3⋊D3—22no—
199C22×C3⋊D3—42no—
200C22×C3⋊D3—42no—
201C22×C3×D3—22no—
202C22×C3×D3—22no—
203C22×C3×D3—22no—
204C22×C3×D3—24no—
205C22×C3×D3—22no—
206C22×C3×D3—21no—
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—
218C32×Q8—22no—
219C2×C32×C4—22no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4C2×D411yescharacteristic
223C2×C32×C4C2411yescharacteristic
224C4⋊(C3⋊D3)—24no—
225C4⋊(C3⋊D3)—22no—
226C4⋊(C3⋊D3)C2×D414yes—
227C3×#67—42no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3C2×D411yescharacteristic
231C2×C3×Dic3C2×D411yescharacteristic
232C3×D12—24no—
233C3×D12—22no—
234C3×D12—22no—
235C3×D12—42no—
236C3×D12—42no—
237C3×D12C2×D414yes—
238C3×C4×D3—22no—
239C3×C4×D3—22no—
240C3×C4×D3—22no—
241C3×C4×D3—42no—
242C3×C4×D3C2×D414yes—
243#626—28no—
244#626—28no—
245C3⋊(C3⋊C8)—22no—
246C3×C3⋊C8—22no—
247C23×D4—91no—
248C2×AGL(1,ℤ/8)—92no—
249#525—31no—
250#450—31no—
251#450—92no—
252#450—91no—
253#447—91no—
254#447—92no—
255#447—91no—
256#418—92no—
257#407—91no—
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×D3#6711yescharacteristic
275C3×#41—64no—
276C2×C3×Q8—21no—
277C2×C3×Q8C22×D311yescharacteristic, complemented
278C2×C3×Q8C22×D311yescharacteristic, complemented
279C2×C3×D4—32no—
280C2×C3×D4—31no—
281C2×C3×D4—64no—
282C2×C3×D4—61no—
283C2×C3×D4—61no—
284C2×C3×D4—61no—
285C2×C3×D4—61no—
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—64no—
293C22×C3×C4—61no—
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C2×#67—21no—
297C2×#67—68no—
298C2×#67—62no—
299C2×#67—62no—
300C22×Dic3#6711yescharacteristic
301#239—24no—
302D3×D4—38no—
303D3×D4—64no—
304D3×D4—64no—
305D3×D4—68no—
306D3×D4—68no—
307D3×D4—64no—
308C2×D12—21no—
309C2×D12—24no—
310C2×D12—21no—
311C2×D12—21no—
312C2×D12—32no—
313C2×D12—32no—
314C2×D12—38no—
315C2×D12—62no—
316C2×D12—64no—
317C2×D12—64no—
318C2×D12—68no—
319C2×D12—68no—
320C2×D12—64no—
321C2×D12—64no—
322C2×D12—62no—
323C2×D12—62no—
324C2×D12—68no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12—64no—
328C2×D12—124no—
329C2×D12—121no—
330C2×D12C22×D312yes—
331C2×D12C22×D311yescharacteristic, complemented
332C2×C4×D3—24no—
333C2×C4×D3—21no—
334C2×C4×D3#6711yescharacteristic
335C2×C4×D3#6711yescharacteristic
336C2×C4×D3C22×D311yescharacteristic
337C2×C4×D3C22×D311yescharacteristic
338C3×SD16—64no—
339C2×C3×C8—32no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—41no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic, complemented
347C3×C4⋊C4C22×D311yescharacteristic, complemented
348C3×C22⋊C4—21no—
349C3×C22⋊C4—21no—
350C3×C22⋊C4—41no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C42—61no—
356#215—24no—
357#215—64no—
358#215—64no—
359#215—124no—
360#213—64no—
361#213—64no—
362#213—64no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367C4⋊Dic3C22×D311yescharacteristic, complemented
368Dic3⋊C4—21no—
369C4×Dic3—21no—
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×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—28no—
386C2×C3×D3—21no—
387C2×C3×D3—21no—
388C2×C3×D3—21no—
389C2×C3×D3—21no—
390C2×C3×D3—24no—
391C2×C3×D3—48no—
392C2×C3×D3—42no—
393C2×C3×D3—42no—
394C2×C3×D3—41no—
395C2×C3×D3—41no—
396C2×C3×D3—41no—
397C2×C3×D3#12012yes—
398C2×C3×D3AGL(1,ℤ/8)12yescomplemented
399D32—416no—
400D32—416no—
401C32×C4—21no—
402C32×C4—41no—
403C32×C4—41no—
404C32×C4C22×D412yes—
405C3×Dic3—21no—
406C3×Dic3—41no—
407C3×Dic3#12012yes—
408C25—181no—
409C2×#41—31no—
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—92no—
425#123—61no—
426C22⋊Q8—31no—
427C22⋊Q8D3211yescharacteristic, complemented
428#121—31no—
429#121—31no—
430#120—61no—
431C4×D4—61no—
432C4×D4—61no—
433#117—31no—
434#102—32no—
435#102—92no—
436#102—92no—
437#102—92no—
438C22⋊C8—31no—
439C22⋊C8—92no—
440C22⋊C8—91no—
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—61no—
450C23×C3—122no—
451C23×C3—122no—
452C23×C3D3×D411yescharacteristic
453C23×C3C2×#6711yescharacteristic
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—24no—
458C22×D3—22no—
459C22×D3—21no—
460C22×D3—42no—
461C22×D3—42no—
462C22×D3—68no—
463C22×D3—68no—
464C22×D3—68no—
465C22×D3—64no—
466C22×D3—64no—
467C22×D3—62no—
468C22×D3—62no—
469C22×D3—68no—
470C22×D3—122no—
471C22×D3—124no—
472C22×D3—1232no—
473C22×D3—124no—
474C22×D3—124no—
475C22×D3—124no—
476C22×D3—124no—
477C22×D3—1232no—
478C22×D3—124no—
479C22×D3—124no—
480C22×D3—124no—
481C22×D3—122no—
482C22×D3—122no—
483C22×D3—122no—
484C22×D3—122no—
485C22×D3—124no—
486C22×D3—242no—
487C22×D3—242no—
488C22×D3C2×#6711yescharacteristic
489C22×D3C2×#6711yescharacteristic
490C3×Q8—22no—
491C3×Q8—22no—
492C3×Q8—42no—
493C3×D4—34no—
494C3×D4—64no—
495C3×D4—62no—
496C3×D4—62no—
497C3×D4—122no—
498C3×D4—122no—
499C3×D4—122no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—34no—
510C2×C3×C4—31no—
511C2×C3×C4—42no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—62no—
515C2×C3×C4—62no—
516C2×C3×C4—62no—
517C2×C3×C4—62no—
518C2×C3×C4—61no—
519C2×C3×C4—122no—
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4C2×#6711yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524#67—42no—
525#67—68no—
526#67—68no—
527C2×Dic3—22no—
528C2×Dic3—21no—
529C2×Dic3C2×#6711yescharacteristic
530C2×Dic3C2×#6711yescharacteristic
531D12—24no—
532D12—22no—
533D12—22no—
534D12—34no—
535D12—34no—
536D12—42no—
537D12—42no—
538D12—64no—
539D12—64no—
540D12—64no—
541D12—68no—
542D12—68no—
543D12—62no—
544D12—62no—
545D12—122no—
546D12—124no—
547D12D3×D414yes—
548C4×D3—22no—
549C4×D3—22no—
550C4×D3—22no—
551C4×D3—42no—
552C4×D3D3×D414yes—
553C3×C8—62no—
554C3⋊C8—22no—
555C3⋊C8—62no—
556C3⋊C8—62no—
557C3⋊C8—122no—
558C2×C32—22no—
559C2×C32C2×#12011yescharacteristic
560C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
561C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
562C3⋊D3—44no—
563C3×D3—22no—
564C3×D3—22no—
565C3×D3—44no—
566C3×D3—81no—
567C24—31no—
568C24—61no—
569C24—182no—
570C24—182no—
571C24—188no—
572C24—181no—
573C24—364no—
574C24—364no—
575#41—64no—
576C2×Q8C2×D3211yescharacteristic, complemented
577C2×D4—32no—
578C2×D4—31no—
579C2×D4—64no—
580C2×D4—61no—
581C2×D4—61no—
582C2×D4—61no—
583C2×D4—61no—
584C2×D4—98no—
585C2×D4—92no—
586C2×D4—184no—
587C2×D4—184no—
588C2×D4—182no—
589C2×D4—182no—
590C2×D4—184no—
591C2×D4—184no—
592C2×D4—188no—
593C2×D4—188no—
594C2×D4—188no—
595C2×D4—181no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—64no—
602C22×C4—61no—
603C22×C4C2×D3211yescharacteristic
604SD16—64no—
605SD16—184no—
606D8—184no—
607D8—184no—
608M16—184no—
609C2×C8—32no—
610C2×C8—92no—
611C4⋊C4—21no—
612C4⋊C4—31no—
613C4⋊C4—61no—
614C4⋊C4C2×D3211yescharacteristic, complemented
615C22⋊C4—21no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C42—61no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—22no—
627C22×C3—32no—
628C22×C3—32no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—68no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—64no—
637C22×C3—128no—
638C22×C3—122no—
639C22×C3—122no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3#91412yescomplemented
644C22×C3#94912yescomplemented
645C22×C3C2×D3×D411yescharacteristic
646C22×C3C22×#6711yescharacteristic
647C2×D3—28no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—24no—
653C2×D3—48no—
654C2×D3—42no—
655C2×D3—42no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—64no—
660C2×D3—64no—
661C2×D3—124no—
662C2×D3—1216no—
663C2×D3—1216no—
664C2×D3—1216no—
665C2×D3—1216no—
666C2×D3—128no—
667C2×D3—128no—
668C2×D3—122no—
669C2×D3—122no—
670C2×D3—122no—
671C2×D3—122no—
672C2×D3—242no—
673C2×D3—242no—
674C2×D3—248no—
675C2×D3#93712yes—
676C2×D3#94912yescomplemented
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—22no—
680C3×C4—32no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—61no—
687C3×C4—81no—
688C3×C4—81no—
689C3×C4—121no—
690C3×C4C2×D3×D412yes—
691C3×C4C2×D3×D412yes—
692Dic3—21no—
693Dic3—41no—
694Dic3#93712yes—
695C32#300311yescharacteristic, complemented, Sylow
696C23—31no—
697C23—31no—
698C23—62no—
699C23—62no—
700C23—64no—
701C23—62no—
702C23—62no—
703C23—61no—
704C23—122no—
705C23—122no—
706C23—184no—
707C23—188no—
708C23—188no—
709C23—182no—
710C23—362no—
711C23—364no—
712C23—3632no—
713C23—364no—
714C23—364no—
715C23—364no—
716C23—362no—
717C23D3×#6711yescharacteristic
718Q8—22no—
719D4—34no—
720D4—64no—
721D4—62no—
722D4—62no—
723D4—94no—
724D4—122no—
725D4—122no—
726D4—122no—
727D4—184no—
728D4—188no—
729D4—188no—
730D4—182no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—31no—
735C2×C4—34no—
736C2×C4—31no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—61no—
742C2×C4—122no—
743C2×C4D3×#6711yescharacteristic
744C2×C4C22×D3211yescharacteristic
745C8—62no—
746C8—182no—
747C2×C3—22no—
748C2×C3—22no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—42no—
753C2×C3—62no—
754C2×C3—62no—
755C2×C3—124no—
756C2×C3—241no—
757C2×C3D3×#12011yescharacteristic
758C2×C3C2×#91411yescharacteristic
759C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
760C2×C3C2×#93711yescharacteristic
761C2×C3C2×#94911yescharacteristic
762C2×C3C2×#94911yescharacteristic
763D3—22no—
764D3—22no—
765D3—44no—
766D3—81no—
767D3—124no—
768D3—124no—
769D3—244no—
770C22—21no—
771C22—21no—
772C22—32no—
773C22—32no—
774C22—68no—
775C22—61no—
776C22—61no—
777C22—61no—
778C22—61no—
779C22—64no—
780C22—128no—
781C22—122no—
782C22—122no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—184no—
787C22—368no—
788C22—3616no—
789C22—3616no—
790C22—362no—
791C22—362no—
792C22#6393912yescomplemented
793C22C2×D3×#6711yescharacteristic
794C4—21no—
795C4—32no—
796C4—41no—
797C4—41no—
798C4—61no—
799C4—121no—
800C4D32×D412yes—
801C3—21no—
802C3#8014611yescharacteristic, complemented
803C3#8292711yescharacteristic, complemented
804C2—22no—
805C2—62no—
806C2—62no—
807C2—124no—
808C2—241no—
809C2—364no—
810C2D3×#93711yescharacteristic
811C2C2×#6393911yescharacteristic
812C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
hypercenterC22⋊Q8D32
hypocenterC32#3003
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×D3×D12C2semidirect
2. C3×#5627C2semidirect
3. C2×#63939C2semidirect
4. #10592745C2semidirect
5. C3×#5046C2semidirect
6. #10591651C2semidirect
7. #10591168C2semidirect
8. #10591160C2semidirect
9. #10591154C2semidirect
10. #10590595C2semidirect
11. #10590592C2semidirect
16. C2×C3×#239C22semidirect
25. C32×C22⋊Q8C22semidirect
26. C2×#3755C22semidirect
27. C3×#946C22semidirect
28. C2×C3×#215C22semidirect
29. C3×#930C22semidirect
30. C3×#895C22semidirect
33. C3×#892C22semidirect
37. C2×#3714C22semidirect
38. C2×#3713C22semidirect
39. C2×#3711C22semidirect
40. #63657C22semidirect
41. #63636C22semidirect
42. C3×#830C22semidirect
43. C3×#809C22semidirect
44. #63564C22semidirect
45. #63562C22semidirect
46. (C2×D3)⋊(C3⋊C8)C22semidirect
52. #5627D3semidirect
61. #5046D3semidirect
78. C2×C32×Q8C23semidirect
91. C2×C3×D12C23semidirect
106. D3×D12D4semidirect
108. C32×C4⋊C4C23semidirect
111. C2×C3⋊(C3⋊C8)C23semidirect
117. C3×C4⋊Dic3C23semidirect
120. C2×C3×C3⋊C8C23semidirect
131. C2×#239C2×D3semidirect
152. C3×C22⋊Q8C2×D3semidirect
153. C3×C22⋊Q8C2×D3semidirect
161. #946C2×D3semidirect
165. C2×#215C2×D3semidirect
169. #930C2×D3semidirect
174. #895C2×D3semidirect
177. #892C2×D3semidirect
187. #830C2×D3semidirect
195. #809C2×D3semidirect
277. C2×C3×Q8C22×D3semidirect
278. C2×C3×Q8C22×D3semidirect
331. C2×D12C22×D3semidirect
346. C3×C4⋊C4C22×D3semidirect
347. C3×C4⋊C4C22×D3semidirect
367. C4⋊Dic3C22×D3semidirect
374. C2×C3⋊C8C22×D3semidirect
379. C22×C32AGL(1,ℤ/8)semidirect
398. C2×C3×D3AGL(1,ℤ/8)semidirect
427. C22⋊Q8D32semidirect
576. C2×Q8C2×D32semidirect
614. C4⋊C4C2×D32semidirect
643. C22×C3#914semidirect
644. C22×C3#949semidirect
676. C2×D3#949semidirect
695. C32#3003semidirect
792. C22#63939semidirect
802. C3#80146semidirect
803. C3#82927semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D122
C3×#56272
C2×#639392
#105927452
C3×#50462
#105916512
#105911682
#105911602
#105911542
#105905952
#105905922
#829273
#801463