Finite Group Databasebeta

← D3×#5218 #11863569

Subgroups — D3×#5218 #11863569

Order 1152.

2086 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic
2C2×D3×#214C212yesmaximal, complemented
3D3×#924C211yesmaximal, characteristic, complemented
4#10592917C211yesmaximal, characteristic, complemented
5C3×#5218C211yesmaximal, characteristic, complemented
6#10591459C212yesmaximal, complemented
7#10591458C212yesmaximal, complemented
8D3×#832C212yesmaximal, complemented
9#10591172C211yesmaximal, characteristic, complemented
10#10591169C211yesmaximal, characteristic, complemented
11D3×#830C211yesmaximal, characteristic, complemented
12C2×#5218—31nomaximal
13D3×#450—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×D3×Dic6C2211yescharacteristic, complemented
25C2×#3754C2212yescomplemented
26#64133C2211yescharacteristic, complemented
27C2×C3×#214C2212yescomplemented
28C3×#924C2211yescharacteristic, complemented
29D3×#217—21no—
30#63964—21no—
31D3×#214—28no—
32D3×C4⋊Dic3C2211yescharacteristic, complemented
33D3×Dic3⋊C4—21no—
34#63857C2211yescharacteristic, complemented
35#63856C2211yescharacteristic, complemented
36#63851—21no—
37C2×#3716C2212yescomplemented
38C2×#3715C2212yescomplemented
39C2×D3×C3⋊C8C2212yescomplemented
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
49C22×#214—32no—
50C2×#924—31no—
51C2×D3×SD16—32no—
52D3×C22⋊Q8—31no—
53C3×#450—31no—
54#5218—31no—
55#5218—31no—
56#5218—32no—
57#5218—31no—
58#5218—32no—
59#5218—31no—
60#5218—61no—
61#5218D311yescharacteristic, direct product factor
62C2×#832—32no—
63C2×#830—31no—
64#5169—32no—
65#5046—31no—
66#4776—32no—
67D3×#102—32no—
68#4731—31no—
69D3×C22⋊C8—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×#634C2311yescharacteristic, complemented
83C2×C3×#67—28no—
84C2×C3×#67—22no—
85C2×C3×#67—22no—
86C22×C3×Dic3D411yescharacteristic
87C3×D3×D4—28no—
88C3×D3×D4—28no—
89C3×D3×D4—24no—
90C3×D3×D4—24no—
91C3×D3×D4—24no—
92C3×D3×D4D418yes—
93C2×C3×D12—21no—
94C2×C3×D12—24no—
95C2×C3×D12C2312yes—
96C2×C3×C4×D3—24no—
97C2×C3×C4×D3D411yescharacteristic
98C2×C3×C4×D3D411yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic, complemented
102C2×#627—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105D3×Dic6—24no—
106#3757—21no—
107#3754—24no—
108C4⋊(C3⋊Dic3)C2311yescharacteristic, complemented
109#3750—21no—
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—
117Dic3⋊Dic3—21no—
118Dic3⋊Dic3—21no—
119(C2×D3)⋊Dic3—21no—
120(C2×D3)⋊Dic3—21no—
121#3716—24no—
122#3715—24no—
123D3×C3⋊C8—24no—
124C2×#450—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×D3×Q8—31no—
140C2×D3×D4—28no—
141C2×D3×D4—21no—
142C2×D3×D4—21no—
143C2×D3×D4C2×D312yes—
144C2×D3×D4C2×D312yes—
145C22×D12C2×D311yescharacteristic
146C22×C4×D3C2×D311yescharacteristic
147C22×Dic6—31no—
148C2×C3×SD16—32no—
149C3×C22⋊Q8—31no—
150C2×#217—61no—
151#946—31no—
152C2×#215—32no—
153C2×#214—32no—
154C2×#214—32no—
155C2×#214—32no—
156C2×#214—32no—
157C2×#214—62no—
158C2×#214—68no—
159C2×#214C2×D312yescomplemented
160C2×C4⋊Dic3—31no—
161#924—31no—
162#924—31no—
163#924—31no—
164#924—31no—
165#924—61no—
166#924—61no—
167#924—61no—
168#924C2×D311yescharacteristic, complemented
169C2×Dic3⋊C4—61no—
170C22×C3⋊C8—32no—
171D3×SD16—68no—
172C2×#204—32no—
173C2×D3×C8—32no—
174#897—31no—
175#896—61no—
176D3×C4⋊C4—31no—
177D3×C4⋊C4—61no—
178D3×C22⋊C4—61no—
179#878—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—22no—
202C22×C3×D3—22no—
203C22×C3×D3—24no—
204C22×C3×D3—28no—
205C22×C3×D3—22no—
206C22×C3×D3—28no—
207C22×C3×D3—44no—
208C22×C3×D3—432no—
209C22×C3×D3—42no—
210C22×C3×D3—42no—
211C22×C3×D3—44no—
212C22×C3×D3—44no—
213C22×C3×D3—44no—
214C22×C3×D3SD1614yescomplemented
215C22×C3×D3C2×D411yescharacteristic
216C22×C3×D3C2×D411yescharacteristic
217C32×D4—24no—
218C32×D4—22no—
219C32×D4C2×D414yes—
220C2×C32×C4—22no—
221C2×C32×C4C2×D411yescharacteristic
222C2×C32×C4C2411yescharacteristic
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225#634—22no—
226C3×#67—28no—
227C3×#67—28no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3—21no—
231C2×C3×Dic3C2×D411yescharacteristic
232C2×C3×Dic3C2×D411yescharacteristic
233C3×D12—24no—
234C3×D12—22no—
235C3×D12C2×D414yes—
236C3×C4×D3—22no—
237C3×C4×D3—22no—
238C3×C4×D3—22no—
239C3×C4×D3C2×D414yes—
240C3×Dic6—22no—
241#627—42no—
242D3×Dic3—42no—
243D3×Dic3—42no—
244C3⋊(C3⋊C8)—22no—
245C3×C3⋊C8—22no—
246C23×D4—31no—
247C22×SD16—92no—
248C2×C22⋊Q8—91no—
249#450—31no—
250#450—91no—
251#450—92no—
252#450—91no—
253#450—92no—
254#450—91no—
255C2×#102—92no—
256C2×C22⋊C8—91no—
257C24×C3—21no—
258C24×C3—21no—
259C24×C3—31no—
260C24×C3—41no—
261C24×C3—62no—
262C24×C3—62no—
263C24×C3—68no—
264C24×C3—61no—
265C24×C3—124no—
266C24×C3—124no—
267C23×D3—28no—
268C23×D3—21no—
269C23×D3—22no—
270C23×D3—22no—
271C23×D3—44no—
272C23×D3—44no—
273C23×D3#6711yescharacteristic
274C2×C3×Q8—31no—
275C2×C3×D4—24no—
276C2×C3×D4—24no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—22no—
280C2×C3×D4—38no—
281C2×C3×D4—32no—
282C2×C3×D4—41no—
283C2×C3×D4—44no—
284C2×C3×D4—64no—
285C2×C3×D4—64no—
286C2×C3×D4—62no—
287C2×C3×D4—62no—
288C2×C3×D4—64no—
289C2×C3×D4—68no—
290C2×C3×D4—68no—
291C2×C3×D4—68no—
292C2×C3×D4—64no—
293C2×C3×D4—61no—
294C2×C3×D4C22×D312yes—
295C2×C3×D4C22×D312yes—
296C22×C3×C4—21no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—64no—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C2×#67—28no—
306C2×#67—22no—
307C2×#67—22no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3#6711yescharacteristic
311D3×Q8—64no—
312D3×D4—28no—
313D3×D4—28no—
314D3×D4—24no—
315D3×D4—24no—
316D3×D4—24no—
317D3×D4#6718yes—
318C2×D12—21no—
319C2×D12—24no—
320C2×D12C22×D312yes—
321C2×C4×D3—24no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3#6711yescharacteristic
325C2×C4×D3#6711yescharacteristic
326C2×C4×D3C22×D311yescharacteristic
327C2×C4×D3C22×D311yescharacteristic
328C2×Dic6—31no—
329C2×Dic6—31no—
330C2×Dic6—61no—
331C2×Dic6—64no—
332C2×Dic6—61no—
333C2×Dic6—61no—
334C2×Dic6C22×D311yescharacteristic, complemented
335C3×SD16—64no—
336C2×C3×C8—32no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—61no—
339C3×C22⋊C4—61no—
340#217—21no—
341#217—61no—
342#217—61no—
343#217—61no—
344#217—61no—
345#217—121no—
346#215—64no—
347#214—24no—
348#214—64no—
349#214—64no—
350#214—64no—
351#214—64no—
352#214—124no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355C4⋊Dic3—31no—
356C4⋊Dic3—31no—
357C4⋊Dic3—61no—
358C4⋊Dic3—61no—
359C4⋊Dic3—61no—
360C4⋊Dic3C22×D311yescharacteristic, complemented
361Dic3⋊C4—21no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—121no—
369C2×C3⋊C8—32no—
370C2×C3⋊C8—32no—
371C2×C3⋊C8—62no—
372C2×C3⋊C8—64no—
373C2×C3⋊C8C22×D312yescomplemented
374#204—64no—
375D3×C8—64no—
376C22×C32—21no—
377C22×C32—21no—
378C22×C32—24no—
379C22×C32—48no—
380C22×C32—42no—
381C22×C32—42no—
382C22×C32C2×SD1612yescomplemented
383C22×C32C22×D411yescharacteristic
384C2×C3×D3—21no—
385C2×C3×D3—21no—
386C2×C3×D3—28no—
387C2×C3×D3—24no—
388C2×C3×D3—416no—
389C2×C3×D3—48no—
390C2×C3×D3—42no—
391C2×C3×D3—42no—
392C2×C3×D3—416no—
393C2×C3×D3#12012yes—
394C2×C3×D3C2×SD1612yes—
395C2×C3×D3C2×SD1612yescomplemented
396C2×C3×D3AGL(1,ℤ/8)12yes—
397C32×C4—21no—
398C32×C4C22×D412yes—
399C3⋊Dic3—41no—
400C3⋊Dic3—41no—
401C3×Dic3—21no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3#12012yes—
405C25—61no—
406C22×Q8—91no—
407C22×D4—32no—
408C22×D4—32no—
409C22×D4—31no—
410C22×D4—61no—
411C22×D4—61no—
412C22×D4—61no—
413C22×D4—68no—
414C22×D4D3211yescharacteristic
415C23×C4—31no—
416C2×SD16—32no—
417C2×SD16—92no—
418C2×SD16—92no—
419C2×SD16—92no—
420C2×SD16—188no—
421C22×C8—92no—
422C22⋊Q8—31no—
423C22⋊Q8—91no—
424C22⋊Q8—91no—
425C22⋊Q8—91no—
426C22⋊Q8—181no—
427C22⋊Q8—181no—
428C2×C4⋊C4—91no—
429C2×C4⋊C4—181no—
430C2×C22⋊C4—181no—
431#102—32no—
432#102—92no—
433#102—92no—
434#102—92no—
435C22⋊C8—31no—
436C22⋊C8—92no—
437C22⋊C8—91no—
438C23×C3—24no—
439C23×C3—24no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—21no—
443C23×C3—31no—
444C23×C3—34no—
445C23×C3—31no—
446C23×C3—42no—
447C23×C3—44no—
448C23×C3—42no—
449C23×C3—42no—
450C23×C3—42no—
451C23×C3—42no—
452C23×C3—62no—
453C23×C3—62no—
454C23×C3—68no—
455C23×C3—64no—
456C23×C3—68no—
457C23×C3—62no—
458C23×C3—82no—
459C23×C3—82no—
460C23×C3—122no—
461C23×C3—124no—
462C23×C3—124no—
463C23×C3—124no—
464C23×C3—1232no—
465C23×C3—124no—
466C23×C3—122no—
467C23×C3D3×D411yescharacteristic
468C23×C3C2×#6711yescharacteristic
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—24no—
472C22×D3—28no—
473C22×D3—22no—
474C22×D3—28no—
475C22×D3—44no—
476C22×D3—432no—
477C22×D3—42no—
478C22×D3—42no—
479C22×D3—44no—
480C22×D3—44no—
481C22×D3—44no—
482C22×D3#21414yescomplemented
483C22×D3C2×#6711yescharacteristic
484C22×D3C2×#6711yescharacteristic
485C3×Q8—62no—
486C3×D4—24no—
487C3×D4—24no—
488C3×D4—22no—
489C3×D4—22no—
490C3×D4—24no—
491C3×D4—34no—
492C3×D4—42no—
493C3×D4—44no—
494C3×D4—64no—
495C3×D4—68no—
496C3×D4—68no—
497C3×D4—62no—
498C3×D4D3×D414yes—
499C3×D4C2×#6714yes—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—34no—
506C2×C3×C4—31no—
507C2×C3×C4—42no—
508C2×C3×C4—62no—
509C2×C3×C4—62no—
510C2×C3×C4—62no—
511C2×C3×C4—62no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4C2×#6711yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—28no—
519#67—28no—
520C2×Dic3—22no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—121no—
528C2×Dic3—121no—
529C2×Dic3—122no—
530C2×Dic3—122no—
531C2×Dic3C2×#6711yescharacteristic
532C2×Dic3C2×#6711yescharacteristic
533D12—24no—
534D12—22no—
535D12C2×#6714yes—
536C4×D3—22no—
537C4×D3—22no—
538C4×D3—22no—
539C4×D3—122no—
540C4×D3—122no—
541C4×D3C2×#6714yes—
542Dic6—22no—
543Dic6—62no—
544Dic6—62no—
545Dic6—122no—
546Dic6—122no—
547Dic6—122no—
548C3×C8—62no—
549C3⋊C8—22no—
550C3⋊C8—62no—
551C3⋊C8—62no—
552C3⋊C8—122no—
553C2×C32—22no—
554C2×C32—44no—
555C2×C32C2×#12011yescharacteristic
556C2×C32C22×SD1611yescharacteristic
557C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
558C3×D3—22no—
559C3×D3—44no—
560C3×D3#45014yescomplemented
561C24—21no—
562C24—31no—
563C24—62no—
564C24—62no—
565C24—68no—
566C24—61no—
567C24—124no—
568C24—124no—
569C2×Q8—31no—
570C2×Q8—91no—
571C2×Q8—181no—
572C2×Q8—184no—
573C2×D4—24no—
574C2×D4—21no—
575C2×D4—38no—
576C2×D4—32no—
577C2×D4—64no—
578C2×D4—64no—
579C2×D4—62no—
580C2×D4—62no—
581C2×D4—64no—
582C2×D4—68no—
583C2×D4—68no—
584C2×D4—68no—
585C2×D4—64no—
586C2×D4—61no—
587C2×D4C2×D3212yes—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—64no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4C2×D3211yescharacteristic
597SD16—64no—
598SD16—184no—
599SD16—184no—
600SD16—184no—
601C2×C8—32no—
602C2×C8—92no—
603C2×C8—184no—
604C4⋊C4—31no—
605C4⋊C4—61no—
606C4⋊C4—91no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C22⋊C4—61no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—24no—
620C22×C3—24no—
621C22×C3—21no—
622C22×C3—22no—
623C22×C3—32no—
624C22×C3—32no—
625C22×C3—32no—
626C22×C3—32no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—44no—
630C22×C3—48no—
631C22×C3—48no—
632C22×C3—42no—
633C22×C3—42no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3—68no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—64no—
640C22×C3—82no—
641C22×C3—82no—
642C22×C3—88no—
643C22×C3—128no—
644C22×C3—1216no—
645C22×C3—1216no—
646C22×C3—122no—
647C22×C3—122no—
648C22×C3D3×SD1612yescomplemented
649C22×C3C2×#21412yescomplemented
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C22×#6711yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—28no—
655C2×D3—24no—
656C2×D3—416no—
657C2×D3—48no—
658C2×D3—42no—
659C2×D3—42no—
660C2×D3—416no—
661C2×D3#93212yes—
662C2×D3C2×#21412yes—
663C2×D3C2×#21412yescomplemented
664C2×D3#95312yes—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—22no—
668C3×C4—32no—
669C3×C4—41no—
670C3×C4—61no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4C2×D3×D412yes—
674C3×C4C22×#6712yes—
675Dic3—21no—
676Dic3—41no—
677Dic3—41no—
678Dic3—121no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682Dic3—241no—
683Dic3—241no—
684Dic3#95312yes—
685C32C2×#45011yescharacteristic, complemented, Sylow
686C23—24no—
687C23—22no—
688C23—31no—
689C23—31no—
690C23—34no—
691C23—42no—
692C23—42no—
693C23—62no—
694C23—62no—
695C23—68no—
696C23—64no—
697C23—68no—
698C23—62no—
699C23—122no—
700C23—124no—
701C23—124no—
702C23—124no—
703C23—1232no—
704C23—124no—
705C23—122no—
706C23D3×#6711yescharacteristic
707Q8—62no—
708Q8—182no—
709Q8—362no—
710D4—24no—
711D4—22no—
712D4—34no—
713D4—64no—
714D4—68no—
715D4—68no—
716D4—62no—
717D4D3×#6714yes—
718C2×C4—22no—
719C2×C4—31no—
720C2×C4—34no—
721C2×C4—31no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—362no—
731C2×C4—362no—
732C2×C4D3×#6711yescharacteristic
733C2×C4C22×D3211yescharacteristic
734C8—62no—
735C8—182no—
736C2×C3—22no—
737C2×C3—22no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—34no—
742C2×C3—42no—
743C2×C3—44no—
744C2×C3—44no—
745C2×C3—62no—
746C2×C3—84no—
747C2×C3—124no—
748C2×C3D3×#12011yescharacteristic
749C2×C3C2×D3×SD1611yescharacteristic
750C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
751C2×C3C2×#93211yescharacteristic
752C2×C3C22×#21411yescharacteristic
753C2×C3C2×#95311yescharacteristic
754D3—22no—
755D3—44no—
756D3#521814yesdirect product factor
757C22—21no—
758C22—21no—
759C22—24no—
760C22—32no—
761C22—32no—
762C22—32no—
763C22—32no—
764C22—48no—
765C22—42no—
766C22—42no—
767C22—68no—
768C22—61no—
769C22—61no—
770C22—64no—
771C22—128no—
772C22—1216no—
773C22—1216no—
774C22—122no—
775C22—122no—
776C22D3×#21412yescomplemented
777C22C2×D3×#6711yescharacteristic
778C4—21no—
779C4—32no—
780C4—61no—
781C4—121no—
782C4—121no—
783C4—361no—
784C4—361no—
785C4C2×D3×#6712yes—
786C3—21no—
787C3D3×#45011yescharacteristic, complemented
788C3C2×#521811yescharacteristic, complemented
789C2—22no—
790C2—34no—
791C2—44no—
792C2—62no—
793C2—124no—
794C2D3×#93211yescharacteristic
795C2C2×D3×#21411yescharacteristic
796C2D3×#95311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC22×C3×D3×D4C2
hypercenterC22×D4D32
hypocenterC32C2×#450
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
2. C2×D3×#214C2semidirect
3. D3×#924C2semidirect
4. #10592917C2semidirect
5. C3×#5218C2semidirect
6. #10591459C2semidirect
7. #10591458C2semidirect
8. D3×#832C2semidirect
9. #10591172C2semidirect
10. #10591169C2semidirect
11. D3×#830C2semidirect
24. C2×D3×Dic6C22semidirect
25. C2×#3754C22semidirect
26. #64133C22semidirect
27. C2×C3×#214C22semidirect
28. C3×#924C22semidirect
32. D3×C4⋊Dic3C22semidirect
34. #63857C22semidirect
35. #63856C22semidirect
37. C2×#3716C22semidirect
38. C2×#3715C22semidirect
39. C2×D3×C3⋊C8C22semidirect
40. #63659C22semidirect
41. #63657C22semidirect
42. C3×#832C22semidirect
43. C3×#830C22semidirect
44. #63563C22semidirect
45. #63562C22semidirect
46. (C2×D3)⋊(C3⋊C8)C22semidirect
61. #5218D3direct (N × H)
82. C2×#634C23semidirect
101. C2×C3×Dic6C23semidirect
108. C4⋊(C3⋊Dic3)C23semidirect
110. C2×C3⋊(C3⋊C8)C23semidirect
113. C3×C4⋊Dic3C23semidirect
115. C2×C3×C3⋊C8C23semidirect
159. C2×#214C2×D3semidirect
168. #924C2×D3semidirect
187. #832C2×D3semidirect
192. #830C2×D3semidirect
214. C22×C3×D3SD16semidirect
334. C2×Dic6C22×D3semidirect
360. C4⋊Dic3C22×D3semidirect
373. C2×C3⋊C8C22×D3semidirect
382. C22×C32C2×SD16semidirect
395. C2×C3×D3C2×SD16semidirect
482. C22×D3#214semidirect
560. C3×D3#450semidirect
648. C22×C3D3×SD16semidirect
649. C22×C3C2×#214semidirect
663. C2×D3C2×#214semidirect
685. C32C2×#450semidirect
756. D3#5218direct (N × H)
776. C22D3×#214semidirect
787. C3D3×#450semidirect
788. C3C2×#5218semidirect

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×D3×#2142
D3×#9242
#105929172
C3×#52182
#105914592
#105914582
D3×#8322
#105911722
#105911692
D3×#8302
C2×#52183
D3×#4503