Finite Group Databasebeta

← #11863941

Subgroups — #11863941

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
2C3×#5606C211yesmaximal, characteristic, complemented
3C2×#63925C212yesmaximal, complemented
4#10592735C211yesmaximal, characteristic, complemented
5C3×#5036C211yesmaximal, characteristic, complemented
6#10591515C212yesmaximal, complemented
7#10591183C211yesmaximal, characteristic, complemented
8#10591169C211yesmaximal, characteristic, complemented
9#10591154C211yesmaximal, characteristic, complemented
10#10590596C212yesmaximal, complemented
11#10590592C212yesmaximal, complemented
12#82927—31nomaximal
13#80002—31nomaximal
14C23×D32—21no—
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×#237C2211yescharacteristic, 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×#121C2211yescharacteristic, complemented
26C2×#3753C2212yescomplemented
27C3×#938C2211yescharacteristic, complemented
28C3×#937—21no—
29C3×D4×Dic3—21no—
30C2×C3×#213C2212yescomplemented
31C3×#924C2211yescharacteristic, complemented
32C3×#897C2211yescharacteristic, complemented
33C3×#892C2211yescharacteristic, complemented
34C3×#883—21no—
35C3×#67⋊C4—21no—
36#63925—28no—
37C2×#3717C2212yescomplemented
38C2×#3715C2212yescomplemented
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×#911—32no—
52#5606D311yescharacteristic, complemented
53C3×#447—31no—
54#5218—31no—
55#5207—31no—
56#5156—32no—
57#5046—31no—
58#5046—31no—
59#5046—32no—
60#5036—31no—
61#5036—31no—
62#5036—32no—
63#5036—61no—
64#5036D311yescharacteristic, complemented
65#5001—32no—
66#4776—32no—
67#4770—32no—
68#4731—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×D4—21no—
79C2×C32×D4C2311yescharacteristic, complemented
80C22×C32×C4C2311yescharacteristic
81C2×C4⋊(C3⋊D3)—21no—
82C2×C4⋊(C3⋊D3)—24no—
83C2×C4⋊(C3⋊D3)C2312yes—
84C2×C3×#67—21no—
85C2×C3×#67—21no—
86C22×C3×Dic3—21no—
87C22×C3×Dic3D411yescharacteristic
88C3×#237—24no—
89C2×C3×D12—21no—
90C2×C3×D12—24no—
91C2×C3×D12C2312yes—
92C2×C3×C4×D3—24no—
93C2×C3×C4×D3D411yescharacteristic
94C2×C3×C4×D3D411yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic, complemented
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⋊C4C2311yescharacteristic, complemented
108C32×C22⋊C4—21no—
109#3753—24no—
110C2×C3⋊(C3⋊C8)C2312yescomplemented
111C3×#217—21no—
112C3×#217—21no—
113C3×#213—24no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3C2311yescharacteristic, complemented
118C3×Dic3⋊C4—21no—
119C3×C4×Dic3—21no—
120C2×C3×C3⋊C8C2312yescomplemented
121#3717—24no—
122#3715—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×#237C2×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×D8—32no—
149C3×#123—61no—
150C3×C22⋊Q8—31no—
151C3×C22⋊Q8—31no—
152C3×#121—21no—
153C3×#121—31no—
154C3×#121C2×D311yescharacteristic, complemented
155C3×#121C2×D311yescharacteristic, complemented
156C3×#120—61no—
157C3×C4×D4—61no—
158C3×C4×D4—61no—
159C3×#117—31no—
160#949—68no—
161C2×#215—32no—
162C2×#215—32no—
163#938C2×D311yescharacteristic, complemented
164#937—21no—
165D4×Dic3—21no—
166C2×#214—32no—
167C2×#213—32no—
168C2×#213—32no—
169C2×#213—62no—
170C2×#213C2×D312yescomplemented
171#924C2×D311yescharacteristic, complemented
172C2×#208—32no—
173#911—68no—
174C2×#204—32no—
175C2×ΓL(1,𝔽25)—32no—
176#897C2×D311yescharacteristic, complemented
177#892C2×D311yescharacteristic, complemented
178#883—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×C32—21no—
197C23×C32C2×D411yescharacteristic
198C22×C3⋊D3—24no—
199C22×C3⋊D3—22no—
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—
218C32×D4—22no—
219C32×D4—42no—
220C2×C32×C4—22no—
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—
228C3×#67—42no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—21no—
231C2×C3×Dic3—21no—
232C2×C3×Dic3—42no—
233C2×C3×Dic3C2×D411yescharacteristic
234C2×C3×Dic3C2×D411yescharacteristic
235C3×D12—24no—
236C3×D12—22no—
237C3×D12C2×D414yes—
238C3×C4×D3—22no—
239C3×C4×D3—22no—
240C3×C4×D3—22no—
241C3×C4×D3C2×D414yes—
242C3×Dic6—22no—
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—91no—
251#450—92no—
252#450—91no—
253#447—31no—
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—31no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—32no—
281C2×C3×D4—41no—
282C2×C3×D4—64no—
283C2×C3×D4—61no—
284C2×C3×D4—61no—
285C2×C3×D4—61no—
286C2×C3×D4C22×D311yescharacteristic, complemented
287C2×C3×D4C22×D311yescharacteristic, complemented
288C22×C3×C4—21no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—64no—
295C22×C3×C4—61no—
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C2×#67—21no—
299C2×#67—21no—
300C2×#67—68no—
301C2×#67—62no—
302C2×#67—62no—
303C22×Dic3—21no—
304C22×Dic3#6711yescharacteristic
305#237—24no—
306D3×D4—38no—
307D3×D4—64no—
308D3×D4—64no—
309D3×D4—68no—
310D3×D4—68no—
311D3×D4—64no—
312C2×D12—21no—
313C2×D12—24no—
314C2×D12—32no—
315C2×D12—32no—
316C2×D12—38no—
317C2×D12—62no—
318C2×D12—64no—
319C2×D12—64no—
320C2×D12—68no—
321C2×D12—68no—
322C2×D12—64no—
323C2×D12—64no—
324C2×D12—62no—
325C2×D12—62no—
326C2×D12—68no—
327C2×D12—61no—
328C2×D12—61no—
329C2×D12—64no—
330C2×D12—124no—
331C2×D12—121no—
332C2×D12C22×D312yes—
333C2×C4×D3—24no—
334C2×C4×D3#6711yescharacteristic
335C2×C4×D3#6711yescharacteristic
336C2×C4×D3C22×D311yescharacteristic
337C2×C4×D3C22×D311yescharacteristic
338C2×Dic6C22×D311yescharacteristic, complemented
339C3×D8—64no—
340C2×C3×C8—32no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4C22×D311yescharacteristic, complemented
346C3×C4⋊C4C22×D311yescharacteristic, complemented
347C3×C22⋊C4—21no—
348C3×C22⋊C4—21no—
349C3×C22⋊C4—41no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—61no—
355#217—21no—
356#217—21no—
357#215—64no—
358#215—64no—
359#214—64no—
360#213—24no—
361#213—64no—
362#213—64no—
363#213—124no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366C4⋊Dic3—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
375#204—64no—
376ΓL(1,𝔽25)—64no—
377C22×C32—21no—
378C22×C32—21no—
379C22×C32—41no—
380C22×C32—41no—
381C22×C32—41no—
382C22×C32AGL(1,ℤ/8)12yescomplemented
383C22×C32C22×D411yescharacteristic
384C2×C3⋊D3—24no—
385C2×C3⋊D3—48no—
386C2×C3⋊D3—42no—
387C2×C3⋊D3—42no—
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×C4—41no—
403C32×C4C22×D412yes—
404C3×Dic3—21no—
405C3×Dic3—41no—
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—92no—
421C2×SD16—92no—
422C2×D8—32no—
423C2×D8—92no—
424C2×M16—92no—
425#123—61no—
426C22⋊Q8—31no—
427C22⋊Q8—31no—
428#121—31no—
429#121D3211yescharacteristic, complemented
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—21no—
443C23×C3—21no—
444C23×C3—31no—
445C23×C3—31no—
446C23×C3—41no—
447C23×C3—62no—
448C23×C3—62no—
449C23×C3—64no—
450C23×C3—62no—
451C23×C3—62no—
452C23×C3—122no—
453C23×C3—122no—
454C23×C3D3×D411yescharacteristic
455C23×C3C2×#6711yescharacteristic
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—24no—
460C22×D3—22no—
461C22×D3—42no—
462C22×D3—42no—
463C22×D3—68no—
464C22×D3—68no—
465C22×D3—68no—
466C22×D3—64no—
467C22×D3—64no—
468C22×D3—62no—
469C22×D3—62no—
470C22×D3—68no—
471C22×D3—122no—
472C22×D3—124no—
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×#6711yescharacteristic
490C22×D3C2×#6711yescharacteristic
491C3×Q8—62no—
492C3×D4—22no—
493C3×D4—22no—
494C3×D4—34no—
495C3×D4—42no—
496C3×D4—42no—
497C3×D4—42no—
498C3×D4—64no—
499C3×D4—62no—
500C3×D4—82no—
501C3×D4—122no—
502C3×D4—122no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—34no—
511C2×C3×C4—31no—
512C2×C3×C4—42no—
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—61no—
520C2×C3×C4—122no—
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4C2×#6711yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525#67—42no—
526#67—42no—
527#67—68no—
528#67—68no—
529C2×Dic3—22no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—42no—
533C2×Dic3C2×#6711yescharacteristic
534C2×Dic3C2×#6711yescharacteristic
535D12—24no—
536D12—22no—
537D12—34no—
538D12—34no—
539D12—64no—
540D12—64no—
541D12—64no—
542D12—68no—
543D12—68no—
544D12—62no—
545D12—62no—
546D12—122no—
547D12—124no—
548D12D3×D414yes—
549C4×D3—22no—
550C4×D3—22no—
551C4×D3—22no—
552C4×D3D3×D414yes—
553Dic6—22no—
554C3×C8—62no—
555C3⋊C8—22no—
556C3⋊C8—62no—
557C3⋊C8—62no—
558C3⋊C8—122no—
559C2×C32—22no—
560C2×C32—81no—
561C2×C32C2×#12011yescharacteristic
562C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
563C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
564C3⋊D3—44no—
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—64no—
577C2×Q8—31no—
578C2×D4—21no—
579C2×D4—32no—
580C2×D4—64no—
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—
596C2×D4C2×D3211yescharacteristic, complemented
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—64no—
603C22×C4—61no—
604C22×C4C2×D3211yescharacteristic
605SD16—184no—
606SD16—184no—
607D8—64no—
608D8—184no—
609M16—184no—
610C2×C8—32no—
611C2×C8—92no—
612C4⋊C4—31no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4C2×D3211yescharacteristic, complemented
616C22⋊C4—21no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C42—61no—
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—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—68no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—64no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—81no—
647C22×C3—128no—
648C22×C3—122no—
649C22×C3—122no—
650C22×C3#91112yescomplemented
651C22×C3#94912yescomplemented
652C22×C3C2×D3×D411yescharacteristic
653C22×C3C22×#6711yescharacteristic
654C2×D3—28no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—24no—
660C2×D3—48no—
661C2×D3—42no—
662C2×D3—42no—
663C2×D3—64no—
664C2×D3—64no—
665C2×D3—124no—
666C2×D3—1216no—
667C2×D3—1216no—
668C2×D3—1216no—
669C2×D3—1216no—
670C2×D3—128no—
671C2×D3—128no—
672C2×D3—122no—
673C2×D3—122no—
674C2×D3—122no—
675C2×D3—122no—
676C2×D3—242no—
677C2×D3—242no—
678C2×D3—248no—
679C2×D3#93712yes—
680C2×D3#94912yescomplemented
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—22no—
684C3×C4—32no—
685C3×C4—41no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—61no—
689C3×C4—81no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4C2×D3×D412yes—
693C3×C4C2×D3×D412yes—
694Dic3—21no—
695Dic3—41no—
696Dic3—41no—
697Dic3#93712yes—
698C32#300311yescharacteristic, complemented, Sylow
699C23—21no—
700C23—31no—
701C23—31no—
702C23—62no—
703C23—62no—
704C23—64no—
705C23—62no—
706C23—62no—
707C23—122no—
708C23—122no—
709C23—184no—
710C23—188no—
711C23—188no—
712C23—182no—
713C23—362no—
714C23—364no—
715C23—3632no—
716C23—364no—
717C23—364no—
718C23—364no—
719C23—362no—
720C23D3×#6711yescharacteristic
721Q8—62no—
722D4—22no—
723D4—34no—
724D4—42no—
725D4—64no—
726D4—62no—
727D4—94no—
728D4—122no—
729D4—122no—
730D4—184no—
731D4—188no—
732D4—188no—
733D4—182no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—31no—
737C2×C4—34no—
738C2×C4—31no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—122no—
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—62no—
757C2×C3—62no—
758C2×C3—81no—
759C2×C3—81no—
760C2×C3—124no—
761C2×C3—161no—
762C2×C3D3×#12011yescharacteristic
763C2×C3C2×#91111yescharacteristic
764C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
765C2×C3C2×#93711yescharacteristic
766C2×C3C2×#94911yescharacteristic
767C2×C3C2×#94911yescharacteristic
768D3—22no—
769D3—22no—
770D3—44no—
771D3—124no—
772D3—124no—
773D3—244no—
774C22—21no—
775C22—21no—
776C22—32no—
777C22—32no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—68no—
782C22—61no—
783C22—61no—
784C22—61no—
785C22—61no—
786C22—64no—
787C22—128no—
788C22—122no—
789C22—122no—
790C22—184no—
791C22—368no—
792C22—3616no—
793C22—3616no—
794C22—362no—
795C22—362no—
796C22#6392512yescomplemented
797C22C2×D3×#6711yescharacteristic
798C4—21no—
799C4—32no—
800C4—41no—
801C4—61no—
802C4—121no—
803C4—121no—
804C4D32×D412yes—
805C3—21no—
806C3#8000211yescharacteristic, complemented
807C3#8292711yescharacteristic, complemented
808C2—22no—
809C2—62no—
810C2—62no—
811C2—81no—
812C2—124no—
813C2—364no—
814C2C2×#6392511yescharacteristic
815C2D3×#93711yescharacteristic
816C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3003
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×D3×D12C2semidirect
2. C3×#5606C2semidirect
3. C2×#63925C2semidirect
4. #10592735C2semidirect
5. C3×#5036C2semidirect
6. #10591515C2semidirect
7. #10591183C2semidirect
8. #10591169C2semidirect
9. #10591154C2semidirect
10. #10590596C2semidirect
11. #10590592C2semidirect
16. C2×C3×#237C22semidirect
25. C32×#121C22semidirect
26. C2×#3753C22semidirect
27. C3×#938C22semidirect
30. C2×C3×#213C22semidirect
31. C3×#924C22semidirect
32. C3×#897C22semidirect
33. C3×#892C22semidirect
37. C2×#3717C22semidirect
38. C2×#3715C22semidirect
39. C2×#3711C22semidirect
40. #63657C22semidirect
41. #63636C22semidirect
42. C3×#830C22semidirect
43. C3×#809C22semidirect
44. #63564C22semidirect
45. #63562C22semidirect
46. (C2×D3)⋊(C3⋊C8)C22semidirect
52. #5606D3semidirect
64. #5036D3semidirect
79. C2×C32×D4C23semidirect
97. C2×C3×Dic6C23semidirect
106. D3×D12D4semidirect
107. C32×C4⋊C4C23semidirect
110. C2×C3⋊(C3⋊C8)C23semidirect
117. C3×C4⋊Dic3C23semidirect
120. C2×C3×C3⋊C8C23semidirect
131. C2×#237C2×D3semidirect
154. C3×#121C2×D3semidirect
155. C3×#121C2×D3semidirect
163. #938C2×D3semidirect
170. C2×#213C2×D3semidirect
171. #924C2×D3semidirect
176. #897C2×D3semidirect
177. #892C2×D3semidirect
187. #830C2×D3semidirect
195. #809C2×D3semidirect
286. C2×C3×D4C22×D3semidirect
287. C2×C3×D4C22×D3semidirect
338. C2×Dic6C22×D3semidirect
345. C3×C4⋊C4C22×D3semidirect
346. C3×C4⋊C4C22×D3semidirect
367. C4⋊Dic3C22×D3semidirect
374. C2×C3⋊C8C22×D3semidirect
382. C22×C32AGL(1,ℤ/8)semidirect
398. C2×C3×D3AGL(1,ℤ/8)semidirect
429. #121D32semidirect
596. C2×D4C2×D32semidirect
615. C4⋊C4C2×D32semidirect
650. C22×C3#911semidirect
651. C22×C3#949semidirect
680. C2×D3#949semidirect
698. C32#3003semidirect
796. C22#63925semidirect
806. C3#80002semidirect
807. 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×#56062
C2×#639252
#105927352
C3×#50362
#105915152
#105911832
#105911692
#105911542
#105905962
#105905922
#829273
#800023