Finite Group Databasebeta

← D3×#5227 #11863615

Subgroups — D3×#5227 #11863615

Order 1152.

1663 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Q8C211yesmaximal, characteristic, complemented
2C2×D3×#215C212yesmaximal, complemented
3D3×#930C211yesmaximal, characteristic
4#10592926C211yesmaximal, characteristic, complemented
5C3×#5227C211yesmaximal, characteristic, complemented
6#10591584C212yesmaximal, complemented
7#10591583C212yesmaximal, complemented
8D3×#835C212yesmaximal, complemented
9#10591174C211yesmaximal, characteristic, complemented
10#10591171C211yesmaximal, characteristic, complemented
11D3×#830C211yesmaximal, characteristic, complemented
12C2×#5227—31nomaximal
13D3×#448—31nomaximal
14C22×C32×Q8C2211yescharacteristic, complemented
15C2×C3×D3×Q8—28no—
16C2×C3×D3×Q8—21no—
17C2×C3×D3×Q8—21no—
18C2×C3×D3×Q8C2212yes—
19C2×C3×D3×Q8C2212yescomplemented
20C22×C3×C4×D3—21no—
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×Dic6—21no—
23C22×C3×Dic6C2211yescharacteristic, complemented
24C2×D3×#67—21no—
25C2×D3×D12C2211yescharacteristic
26C2×#3755C2212yescomplemented
27#64139C2211yescharacteristic
28C2×C3×#215C2212yescomplemented
29C3×#930C2211yescharacteristic
30#63978—21no—
31D3×#215—28no—
32D3×(C2×D3)⋊C4—21no—
33#63909C2211yescharacteristic
34#63908C2211yescharacteristic
35#63906—21no—
36D3×C4⋊Dic3C2211yescharacteristic
37C2×#3717C2212yescomplemented
38C2×#3715C2212yescomplemented
39C2×D3×C3⋊C8C2212yes—
40#63662C2212yescomplemented
41#63657C2211yescharacteristic, complemented
42C3×#835C2212yescomplemented
43C3×#830C2211yescharacteristic, complemented
44#63566C2212yescomplemented
45#63565C2212yescomplemented
46(C2×D3)⋊(C3⋊C8)C2212yescomplemented
47C23×C3×Q8—31no—
48C22×D3×Q8D311yescharacteristic, complemented
49C22×#215—32no—
50C2×#930—31no—
51C2×D3×SD16—32no—
52D3×#121—31no—
53C3×#448—31no—
54#5227—31no—
55#5227—31no—
56#5227—32no—
57#5227—31no—
58#5227—32no—
59#5227—31no—
60#5227—61no—
61#5227D311yescharacteristic, direct product factor
62C2×#835—32no—
63C2×#830—31no—
64#5170—32no—
65#5040—31no—
66#4806—32no—
67D3×#103—32no—
68#4738—31no—
69D3×C22⋊C8—31no—
70C23×C3×D3D411yescharacteristic
71C22×D32—21no—
72C2×C32×Q8—24no—
73C2×C32×Q8—21no—
74C2×C32×Q8C2312yes—
75C22×C32×C4—21no—
76C22×C32×C4C2311yescharacteristic
77C2×#638—21no—
78C2×C4⋊(C3⋊D3)C2311yescharacteristic
79C2×C3×#67—21no—
80C22×C3×Dic3—21no—
81C22×C3×Dic3D411yescharacteristic
82C3×D3×Q8—28no—
83C3×D3×Q8—28no—
84C3×D3×Q8—24no—
85C3×D3×Q8—24no—
86C3×D3×Q8—24no—
87C3×D3×Q8D418yescomplemented
88C2×C3×D12C2311yescharacteristic
89C2×C3×C4×D3—28no—
90C2×C3×C4×D3—22no—
91C2×C3×C4×D3—22no—
92C2×C3×C4×D3—24no—
93C2×C3×C4×D3D411yescharacteristic
94C2×C3×C4×D3D411yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×Dic6—28no—
98C2×C3×Dic6—21no—
99C2×C3×Dic6—22no—
100C2×C3×Dic6—22no—
101C2×C3×Dic6—24no—
102C2×C3×Dic6C2312yes—
103D3×#67—44no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×D3×Dic3—21no—
108D3×D12—24no—
109#3755—24no—
110#3752—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3⋊(C3⋊C8)C2312yes—
113C3×#215—24no—
114C3×(C2×D3)⋊C4—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊C8C2312yes—
117Dic3⋊Dic3—21no—
118#3722—21no—
119(C2×D3)⋊Dic3—21no—
120#3717—24no—
121#3715—24no—
122D3×C3⋊C8—24no—
123C2×#448—91noSylow
124C22×C3×Q8—21no—
125C22×C3×Q8—32no—
126C22×C3×Q8—32no—
127C22×C3×Q8—31no—
128C22×C3×Q8—61no—
129C22×C3×Q8—61no—
130C22×C3×Q8—61no—
131C22×C3×Q8—68no—
132C22×C3×Q8C2×D311yescharacteristic, complemented
133C22×C3×Q8C2×D311yescharacteristic, complemented
134C23×C3×C4—31no—
135C23×C3×C4—61no—
136C22×#67—61no—
137C2×D3×Q8—28no—
138C2×D3×Q8—21no—
139C2×D3×Q8—21no—
140C2×D3×Q8C2×D312yes—
141C2×D3×Q8C2×D312yescomplemented
142C2×D3×D4—31no—
143C2×D3×D4—61no—
144C22×D12—31no—
145C22×C4×D3—21no—
146C22×C4×D3C2×D311yescharacteristic
147C22×Dic6—21no—
148C22×Dic6C2×D311yescharacteristic, complemented
149C2×C3×SD16—32no—
150C3×#121—31no—
151C2×#215—32no—
152C2×#215—32no—
153C2×#215—32no—
154C2×#215—32no—
155C2×#215—62no—
156C2×#215—68no—
157C2×#215C2×D312yescomplemented
158#939—61no—
159#938—31no—
160C2×#214—32no—
161#930—31no—
162#930—31no—
163#930—31no—
164#930—31no—
165#930—61no—
166#930—61no—
167#930—61no—
168#930C2×D311yescharacteristic
169C2×(C2×D3)⋊C4—61no—
170C2×C4⋊Dic3—31no—
171C22×C3⋊C8—32no—
172D3×SD16—68no—
173C2×#204—32no—
174C2×D3×C8—32no—
175#895—31no—
176D3×C4⋊C4—31no—
177#884—61no—
178D3×C22⋊C4—61no—
179C3×#103—32no—
180C3×C22⋊C8—31no—
181#835—32no—
182#835—32no—
183#835—32no—
184#835—32no—
185#835—62no—
186#835C2×D312yescomplemented
187#830—31no—
188#830—31no—
189#830—32no—
190#830—61no—
191#830C2×D311yescharacteristic, complemented
192(C2×D3)⋊C8—32no—
193#816—32no—
194#810—32no—
195C23×C32C2×D411yescharacteristic
196C22×C3⋊D3—21no—
197C22×C3×D3—22no—
198C22×C3×D3—22no—
199C22×C3×D3—21no—
200C22×C3×D3SD1614yescomplemented
201C22×C3×D3C2×D411yescharacteristic
202C22×C3×D3C2×D411yescharacteristic
203C2×D32—42no—
204C2×D32—42no—
205C2×D32—42no—
206C32×Q8—24no—
207C32×Q8—22no—
208C32×Q8C2×D414yescomplemented
209C2×C32×C4—24no—
210C2×C32×C4—22no—
211C2×C32×C4—22no—
212C2×C32×C4C2×D411yescharacteristic
213C2×C32×C4C2411yescharacteristic
214#638—42no—
215C2×C3⋊Dic3—21no—
216C4⋊(C3⋊D3)—22no—
217C3×#67—42no—
218C2×C3×Dic3—24no—
219C2×C3×Dic3—22no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—21no—
222C2×C3×Dic3C2×D411yescharacteristic
223C2×C3×Dic3C2×D411yescharacteristic
224C3×D12—22no—
225C3×C4×D3—28no—
226C3×C4×D3—28no—
227C3×C4×D3—22no—
228C3×C4×D3—22no—
229C3×C4×D3—22no—
230C3×C4×D3C2×D414yes—
231C3×Dic6—28no—
232C3×Dic6—24no—
233C3×Dic6—22no—
234C3×Dic6—28no—
235C3×Dic6C2×D414yescomplemented
236#626—42no—
237#626—42no—
238#625—42no—
239D3×Dic3—42no—
240C3⋊(C3⋊C8)—22no—
241C3×C3⋊C8—22no—
242C23×Q8—31no—
243C22×SD16—92no—
244C2×#121—91no—
245#448—31no—
246#448—91no—
247#448—92no—
248#448—91no—
249#448—92no—
250#448—91no—
251C2×#103—92no—
252C2×C22⋊C8—91no—
253C24×C3—31no—
254C23×D3—61no—
255C23×D3—61no—
256C23×D3#6711yescharacteristic
257C2×C3×Q8—24no—
258C2×C3×Q8—24no—
259C2×C3×Q8—21no—
260C2×C3×Q8—21no—
261C2×C3×Q8—22no—
262C2×C3×Q8—38no—
263C2×C3×Q8—32no—
264C2×C3×Q8—41no—
265C2×C3×Q8—44no—
266C2×C3×Q8—62no—
267C2×C3×Q8—62no—
268C2×C3×Q8—64no—
269C2×C3×Q8—68no—
270C2×C3×Q8—64no—
271C2×C3×Q8—64no—
272C2×C3×Q8—68no—
273C2×C3×Q8—68no—
274C2×C3×Q8—64no—
275C2×C3×Q8—61no—
276C2×C3×Q8C22×D312yes—
277C2×C3×Q8C22×D312yes—
278C2×C3×D4—31no—
279C2×C3×D4—61no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—41no—
289C22×C3×C4—64no—
290C22×C3×C4—62no—
291C22×C3×C4—62no—
292C22×C3×C4—68no—
293C22×C3×C4—61no—
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C2×#67—21no—
297C2×#67—61no—
298C2×#67—61no—
299C2×#67—61no—
300C2×#67—61no—
301C2×#67—61no—
302C2×#67—61no—
303C2×#67—121no—
304C2×#67—124no—
305C22×Dic3—21no—
306C22×Dic3—61no—
307C22×Dic3#6711yescharacteristic
308D3×Q8—28no—
309D3×Q8—28no—
310D3×Q8—24no—
311D3×Q8—24no—
312D3×Q8—24no—
313D3×Q8#6718yescomplemented
314D3×D4—64no—
315D3×D4—124no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—61no—
319C2×D12—64no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—28no—
324C2×C4×D3—22no—
325C2×C4×D3—22no—
326C2×C4×D3—24no—
327C2×C4×D3—61no—
328C2×C4×D3#6711yescharacteristic
329C2×C4×D3#6711yescharacteristic
330C2×C4×D3C22×D311yescharacteristic
331C2×C4×D3C22×D311yescharacteristic
332C2×Dic6—28no—
333C2×Dic6—21no—
334C2×Dic6—22no—
335C2×Dic6—22no—
336C2×Dic6—24no—
337C2×Dic6C22×D312yes—
338C3×SD16—64no—
339C2×C3×C8—32no—
340C3×C4⋊C4—31no—
341C3×C22⋊C4—61no—
342#217—61no—
343#215—24no—
344#215—64no—
345#215—64no—
346#215—64no—
347#215—64no—
348#215—124no—
349#214—64no—
350(C2×D3)⋊C4—21no—
351(C2×D3)⋊C4—61no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—121no—
357C4⋊Dic3—31no—
358C4⋊Dic3—31no—
359C4⋊Dic3—61no—
360C4⋊Dic3—61no—
361C4⋊Dic3C22×D311yescharacteristic
362Dic3⋊C4—61no—
363C2×C3⋊C8—32no—
364C2×C3⋊C8—32no—
365C2×C3⋊C8—62no—
366C2×C3⋊C8—64no—
367C2×C3⋊C8C22×D312yes—
368#204—64no—
369D3×C8—64no—
370C22×C32—21no—
371C22×C32—21no—
372C22×C32C2×SD1612yescomplemented
373C22×C32C22×D411yescharacteristic
374C2×C3⋊D3—41no—
375C2×C3⋊D3—41no—
376C2×C3⋊D3—41no—
377C2×C3×D3—21no—
378C2×C3×D3—21no—
379C2×C3×D3—28no—
380C2×C3×D3—41no—
381C2×C3×D3—41no—
382C2×C3×D3—41no—
383C2×C3×D3#12012yes—
384C2×C3×D3C2×SD1612yes—
385C2×C3×D3C2×SD1612yescomplemented
386C2×C3×D3#13712yes—
387D32—84no—
388C32×C4—24no—
389C32×C4—21no—
390C32×C4C22×D412yes—
391C3⋊Dic3—41no—
392C3×Dic3—21no—
393C3×Dic3—24no—
394C3×Dic3—41no—
395C3×Dic3#12012yes—
396C22×Q8—32no—
397C22×Q8—32no—
398C22×Q8—31no—
399C22×Q8—61no—
400C22×Q8—61no—
401C22×Q8—61no—
402C22×Q8—68no—
403C22×Q8D3211yescharacteristic, complemented
404C22×D4—91no—
405C22×D4—181no—
406C23×C4—31no—
407C23×C4—61no—
408C2×SD16—32no—
409C2×SD16—92no—
410C2×SD16—92no—
411C2×SD16—92no—
412C2×SD16—188no—
413C22×C8—92no—
414#121—31no—
415#121—91no—
416#121—91no—
417#121—91no—
418#121—181no—
419#121—181no—
420C2×C4⋊C4—91no—
421C2×C22⋊C4—181no—
422#103—32no—
423#103—92no—
424#103—92no—
425#103—92no—
426C22⋊C8—31no—
427C22⋊C8—92no—
428C22⋊C8—91no—
429C23×C3—21no—
430C23×C3—31no—
431C23×C3—34no—
432C23×C3—31no—
433C23×C3—62no—
434C23×C3—62no—
435C23×C3—61no—
436C23×C3D3×D411yescharacteristic
437C23×C3C2×#6711yescharacteristic
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—21no—
441C22×D3—61no—
442C22×D3—61no—
443C22×D3—121no—
444C22×D3—122no—
445C22×D3—122no—
446C22×D3—122no—
447C22×D3—122no—
448C22×D3—122no—
449C22×D3—122no—
450C22×D3#21514yescomplemented
451C22×D3C2×#6711yescharacteristic
452C22×D3C2×#6711yescharacteristic
453C3×Q8—24no—
454C3×Q8—24no—
455C3×Q8—22no—
456C3×Q8—22no—
457C3×Q8—24no—
458C3×Q8—34no—
459C3×Q8—42no—
460C3×Q8—44no—
461C3×Q8—68no—
462C3×Q8—68no—
463C3×Q8—64no—
464C3×Q8—62no—
465C3×Q8D3×D414yescomplemented
466C3×Q8C2×#6714yescomplemented
467C3×D4—62no—
468C3×D4—122no—
469C2×C3×C4—24no—
470C2×C3×C4—24no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—31no—
478C2×C3×C4—34no—
479C2×C3×C4—31no—
480C2×C3×C4—42no—
481C2×C3×C4—42no—
482C2×C3×C4—44no—
483C2×C3×C4—62no—
484C2×C3×C4—62no—
485C2×C3×C4—68no—
486C2×C3×C4—68no—
487C2×C3×C4—62no—
488C2×C3×C4—64no—
489C2×C3×C4—62no—
490C2×C3×C4—62no—
491C2×C3×C4—61no—
492C2×C3×C4D3×D411yescharacteristic
493C2×C3×C4C2×#6711yescharacteristic
494C2×C3×C4C23×D311yescharacteristic
495C2×C3×C4C23×D311yescharacteristic
496#67—42no—
497#67—122no—
498#67—122no—
499#67—122no—
500#67—122no—
501#67—122no—
502#67—122no—
503#67—242no—
504C2×Dic3—24no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—21no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—121no—
511C2×Dic3—122no—
512C2×Dic3C2×#6711yescharacteristic
513C2×Dic3C2×#6711yescharacteristic
514D12—22no—
515D12—62no—
516D12—62no—
517D12—122no—
518D12—122no—
519D12—122no—
520C4×D3—28no—
521C4×D3—28no—
522C4×D3—22no—
523C4×D3—22no—
524C4×D3—22no—
525C4×D3—122no—
526C4×D3C2×#6714yes—
527Dic6—28no—
528Dic6—24no—
529Dic6—22no—
530Dic6—28no—
531Dic6C2×#6714yescomplemented
532C3×C8—62no—
533C3⋊C8—22no—
534C3⋊C8—62no—
535C3⋊C8—62no—
536C3⋊C8—122no—
537C2×C32—22no—
538C2×C32C2×#12011yescharacteristic
539C2×C32C22×SD1611yescharacteristic
540C2×C32C2×#13711yescharacteristic
541C3⋊D3—81no—
542C3×D3—22no—
543C3×D3—81no—
544C3×D3#44814yescomplemented
545C24—31no—
546C24—181no—
547C2×Q8—24no—
548C2×Q8—21no—
549C2×Q8—38no—
550C2×Q8—32no—
551C2×Q8—62no—
552C2×Q8—62no—
553C2×Q8—64no—
554C2×Q8—68no—
555C2×Q8—64no—
556C2×Q8—64no—
557C2×Q8—68no—
558C2×Q8—68no—
559C2×Q8—64no—
560C2×Q8—61no—
561C2×Q8C2×D3212yes—
562C2×D4—31no—
563C2×D4—61no—
564C2×D4—91no—
565C2×D4—184no—
566C2×D4—181no—
567C2×D4—181no—
568C2×D4—181no—
569C2×D4—181no—
570C2×D4—364no—
571C22×C4—21no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—31no—
577C22×C4—64no—
578C22×C4—62no—
579C22×C4—62no—
580C22×C4—68no—
581C22×C4—61no—
582C22×C4—181no—
583C22×C4C2×D3211yescharacteristic
584SD16—64no—
585SD16—184no—
586SD16—184no—
587SD16—184no—
588C2×C8—32no—
589C2×C8—92no—
590C2×C8—184no—
591C4⋊C4—31no—
592C4⋊C4—91no—
593C4⋊C4—181no—
594C22⋊C4—61no—
595C22⋊C4—181no—
596C22⋊C4—181no—
597C22⋊C4—181no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—22no—
604C22×C3—32no—
605C22×C3—32no—
606C22×C3—32no—
607C22×C3—32no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—68no—
611C22×C3—61no—
612C22×C3—61no—
613C22×C3—121no—
614C22×C3—121no—
615C22×C3—121no—
616C22×C3D3×SD1612yescomplemented
617C22×C3C2×#21512yescomplemented
618C22×C3C2×D3×D411yescharacteristic
619C22×C3C22×#6711yescharacteristic
620C2×D3—21no—
621C2×D3—21no—
622C2×D3—28no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—41no—
626C2×D3—121no—
627C2×D3—121no—
628C2×D3—121no—
629C2×D3—121no—
630C2×D3—121no—
631C2×D3—121no—
632C2×D3—241no—
633C2×D3—241no—
634C2×D3—241no—
635C2×D3—244no—
636C2×D3—244no—
637C2×D3C2×#21512yes—
638C2×D3C2×#21512yescomplemented
639C2×D3#94212yes—
640C2×D3#95312yes—
641C3×C4—24no—
642C3×C4—21no—
643C3×C4—24no—
644C3×C4—21no—
645C3×C4—22no—
646C3×C4—32no—
647C3×C4—41no—
648C3×C4—44no—
649C3×C4—61no—
650C3×C4—64no—
651C3×C4—121no—
652C3×C4C2×D3×D412yes—
653C3×C4C22×#6712yes—
654Dic3—21no—
655Dic3—24no—
656Dic3—41no—
657Dic3—121no—
658Dic3—121no—
659Dic3—241no—
660Dic3#95312yes—
661C32C2×#44811yescharacteristic, complemented, Sylow
662C23—31no—
663C23—31no—
664C23—34no—
665C23—62no—
666C23—62no—
667C23—61no—
668C23—181no—
669C23—362no—
670C23—362no—
671C23—362no—
672C23D3×#6711yescharacteristic
673Q8—24no—
674Q8—22no—
675Q8—34no—
676Q8—68no—
677Q8—68no—
678Q8—64no—
679Q8—62no—
680Q8D3×#6714yescomplemented
681D4—62no—
682D4—122no—
683D4—182no—
684D4—362no—
685D4—362no—
686D4—362no—
687D4—362no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—31no—
692C2×C4—34no—
693C2×C4—31no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—68no—
697C2×C4—68no—
698C2×C4—62no—
699C2×C4—64no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—61no—
703C2×C4—181no—
704C2×C4—362no—
705C2×C4D3×#6711yescharacteristic
706C2×C4C22×D3211yescharacteristic
707C8—62no—
708C8—182no—
709C2×C3—22no—
710C2×C3—22no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—34no—
715C2×C3—42no—
716C2×C3—62no—
717C2×C3—241no—
718C2×C3D3×#12011yescharacteristic
719C2×C3C2×D3×SD1611yescharacteristic
720C2×C3D3×#13711yescharacteristic
721C2×C3C22×#21511yescharacteristic
722C2×C3C2×#94211yescharacteristic
723C2×C3C2×#95311yescharacteristic
724D3—22no—
725D3—81no—
726D3—241no—
727D3—241no—
728D3—481no—
729D3#522714yesdirect product factor
730C22—21no—
731C22—21no—
732C22—32no—
733C22—32no—
734C22—32no—
735C22—32no—
736C22—68no—
737C22—61no—
738C22—61no—
739C22—121no—
740C22—121no—
741C22—121no—
742C22—361no—
743C22—361no—
744C22—361no—
745C22—724no—
746C22D3×#21512yescomplemented
747C22C2×D3×#6711yescharacteristic
748C4—24no—
749C4—21no—
750C4—32no—
751C4—61no—
752C4—64no—
753C4—121no—
754C4—361no—
755C4C2×D3×#6712yes—
756C3—21no—
757C3D3×#44811yescharacteristic, complemented
758C3C2×#522711yescharacteristic, complemented
759C2—22no—
760C2—34no—
761C2—62no—
762C2—241no—
763C2—721no—
764C2C2×D3×#21511yescharacteristic
765C2D3×#94211yescharacteristic
766C2D3×#95311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalD3×#930C2
hypercenterC22×Q8D32
hypocenterC32C2×#448
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×C3×D3×Q8C2semidirect
2. C2×D3×#215C2semidirect
4. #10592926C2semidirect
5. C3×#5227C2semidirect
6. #10591584C2semidirect
7. #10591583C2semidirect
8. D3×#835C2semidirect
9. #10591174C2semidirect
10. #10591171C2semidirect
11. D3×#830C2semidirect
14. C22×C32×Q8C22semidirect
19. C2×C3×D3×Q8C22semidirect
23. C22×C3×Dic6C22semidirect
26. C2×#3755C22semidirect
28. C2×C3×#215C22semidirect
37. C2×#3717C22semidirect
38. C2×#3715C22semidirect
40. #63662C22semidirect
41. #63657C22semidirect
42. C3×#835C22semidirect
43. C3×#830C22semidirect
44. #63566C22semidirect
45. #63565C22semidirect
46. (C2×D3)⋊(C3⋊C8)C22semidirect
48. C22×D3×Q8D3semidirect
61. #5227D3direct (N × H)
87. C3×D3×Q8D4semidirect
132. C22×C3×Q8C2×D3semidirect
133. C22×C3×Q8C2×D3semidirect
141. C2×D3×Q8C2×D3semidirect
148. C22×Dic6C2×D3semidirect
157. C2×#215C2×D3semidirect
186. #835C2×D3semidirect
191. #830C2×D3semidirect
200. C22×C3×D3SD16semidirect
208. C32×Q8C2×D4semidirect
235. C3×Dic6C2×D4semidirect
313. D3×Q8#67semidirect
372. C22×C32C2×SD16semidirect
385. C2×C3×D3C2×SD16semidirect
403. C22×Q8D32semidirect
450. C22×D3#215semidirect
465. C3×Q8D3×D4semidirect
466. C3×Q8C2×#67semidirect
531. Dic6C2×#67semidirect
544. C3×D3#448semidirect
616. C22×C3D3×SD16semidirect
617. C22×C3C2×#215semidirect
638. C2×D3C2×#215semidirect
661. C32C2×#448semidirect
680. Q8D3×#67semidirect
729. D3#5227direct (N × H)
746. C22D3×#215semidirect
757. C3D3×#448semidirect
758. C3C2×#5227semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C2×D3×#2152
D3×#9302
#105929262
C3×#52272
#105915842
#105915832
D3×#8352
#105911742
#105911712
D3×#8302
C2×#52273
D3×#4483