Finite Group Databasebeta

← D3×#5046 #11863567

Subgroups — D3×#5046 #11863567

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×D3×D12C211yesmaximal, characteristic
2C3×D3×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×D3×#215C212yesmaximal, complemented
4#10592745C211yesmaximal, characteristic, complemented
5C3×#5046C211yesmaximal, characteristic, complemented
6#10591651C212yesmaximal, complemented
7#10591183C211yesmaximal, characteristic, complemented
8#10591169C211yesmaximal, characteristic, complemented
9D3×#830C211yesmaximal, characteristic, complemented
10#10590596C212yesmaximal, complemented
11D3×#809C212yesmaximal, complemented
12C2×#5046—31nomaximal
13D3×#450—31nomaximal
14C23×D32—21no—
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×D3×Q8C2211yescharacteristic, 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×#924C2211yescharacteristic, complemented
30C3×#897C2211yescharacteristic, complemented
31C3×#896—21no—
32C3×D3×C4⋊C4—21no—
33C3×D3×C4⋊C4C2211yescharacteristic, complemented
34C3×D3×C22⋊C4—21no—
35C3×#878—21no—
36D3×#215—28no—
37C2×#3717C2212yescomplemented
38C2×#3715C2212yescomplemented
39C2×D3×C3⋊C8C2212yescomplemented
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—
49C2×C3×C22⋊Q8—31no—
50C22×#215—32no—
51C2×D3×SD16—32no—
52D3×C22⋊Q8D311yescharacteristic, complemented
53C3×#450—31no—
54#5218—31no—
55C2×#830—31no—
56#5169—32no—
57#5046—31no—
58#5046—31no—
59#5046—31no—
60#5046—32no—
61#5046—31no—
62#5046—32no—
63#5046—61no—
64#5046D311yescharacteristic, direct product factor
65C2×#809—32no—
66#4776—32no—
67D3×#102—32no—
68#4731—31no—
69D3×C22⋊C8—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—
83C22×C3×Dic3D411yescharacteristic
84C3×D3×Q8—24no—
85C2×C3×D12—21no—
86C2×C3×D12—24no—
87C2×C3×D12C2312yes—
88C2×C3×C4×D3—24no—
89C2×C3×C4×D3—21no—
90C2×C3×C4×D3—21no—
91C2×C3×C4×D3D411yescharacteristic
92C2×C3×C4×D3D411yescharacteristic
93C2×C3×C4×D3C2311yescharacteristic
94C2×C3×C4×D3C2311yescharacteristic
95C2×C3×Dic6—21no—
96C2×C3×Dic6C2311yescharacteristic, complemented
97C2×#626—28no—
98C2×#626—22no—
99C2×#626—22no—
100D3×D12—28no—
101D3×D12—28no—
102D3×D12—24no—
103D3×D12—24no—
104D3×D12—24no—
105D3×D12D418yes—
106C32×C4⋊C4—21no—
107C32×C4⋊C4C2311yescharacteristic, complemented
108C32×C22⋊C4—21no—
109#3755—24no—
110C2×C3⋊(C3⋊C8)C2312yescomplemented
111C3×#217—21no—
112C3×#215—24no—
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3C2311yescharacteristic, complemented
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C2×C3×C3⋊C8C2312yescomplemented
121#3717—24no—
122#3715—24no—
123D3×C3⋊C8—24no—
124C2×#450—91noSylow
125C24×D3—61no—
126C24×D3—61no—
127C22×C3×Q8—31no—
128C22×C3×D4—31no—
129C23×C3×C4—31no—
130C22×#67—61no—
131C2×D3×Q8C2×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×C22⋊Q8—21no—
150C3×C22⋊Q8—31no—
151C3×C22⋊Q8—31no—
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8—61no—
154C3×C22⋊Q8—61no—
155C3×C22⋊Q8C2×D311yescharacteristic, complemented
156C3×C22⋊Q8C2×D311yescharacteristic, complemented
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4—61no—
159C2×C3×C22⋊C4—61no—
160#946C2×D311yescharacteristic, complemented
161C2×#215—32no—
162C2×#215—32no—
163C2×#215—32no—
164C2×#215—32no—
165C2×#215—62no—
166C2×#215—68no—
167C2×#215C2×D312yescomplemented
168C2×#214—32no—
169#924C2×D311yescharacteristic, complemented
170C22×C3⋊C8—32no—
171D3×SD16—68no—
172C2×#204—32no—
173C2×D3×C8—32no—
174#897C2×D311yescharacteristic, complemented
175#896—21no—
176D3×C4⋊C4—21no—
177D3×C4⋊C4C2×D311yescharacteristic, complemented
178D3×C22⋊C4—21no—
179#878—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—24no—
204C22×C3×D3—22no—
205C22×C3×D3—42no—
206C22×C3×D3—42no—
207C22×C3×D3SD1614yescomplemented
208C22×C3×D3C2×D411yescharacteristic
209C22×C3×D3C2×D411yescharacteristic
210C2×D32—28no—
211C2×D32—28no—
212C2×D32—44no—
213C2×D32—432no—
214C2×D32—44no—
215C2×D32—44no—
216C2×D32—44no—
217C32×Q8—22no—
218C2×C32×C4—22no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4C2×D411yescharacteristic
222C2×C32×C4C2411yescharacteristic
223C4⋊(C3⋊D3)—24no—
224C4⋊(C3⋊D3)—22no—
225C4⋊(C3⋊D3)C2×D414yes—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3C2×D411yescharacteristic
230C2×C3×Dic3C2×D411yescharacteristic
231C3×D12—24no—
232C3×D12—22no—
233C3×D12C2×D414yes—
234C3×C4×D3—22no—
235C3×C4×D3—22no—
236C3×C4×D3—22no—
237C3×C4×D3—42no—
238C3×C4×D3—42no—
239C3×C4×D3C2×D414yes—
240C3×Dic6—22no—
241C3×Dic6—42no—
242#626—28no—
243#626—28no—
244C3⋊(C3⋊C8)—22no—
245C3×C3⋊C8—22no—
246C23×D4—91no—
247C22×SD16—92no—
248C2×C22⋊Q8—31no—
249#450—31no—
250#450—91no—
251#450—92no—
252#450—92no—
253#450—91no—
254#450—91no—
255C2×#102—92no—
256C2×C22⋊C8—91no—
257C24×C3—31no—
258C24×C3—61no—
259C23×D3—21no—
260C23×D3—62no—
261C23×D3—62no—
262C23×D3—68no—
263C23×D3—68no—
264C23×D3—61no—
265C23×D3—61no—
266C23×D3—62no—
267C23×D3—62no—
268C23×D3—121no—
269C23×D3—124no—
270C23×D3—124no—
271C23×D3—124no—
272C23×D3—124no—
273C23×D3#6711yescharacteristic
274C2×C3×Q8—21no—
275C2×C3×Q8—31no—
276C2×C3×Q8—61no—
277C2×C3×Q8—64no—
278C2×C3×Q8C22×D311yescharacteristic, complemented
279C2×C3×Q8C22×D311yescharacteristic, complemented
280C2×C3×D4—32no—
281C2×C3×D4—64no—
282C2×C3×D4—61no—
283C22×C3×C4—21no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—64no—
290C22×C3×C4—61no—
291C22×C3×C4—61no—
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C2×#67—68no—
295C2×#67—62no—
296C2×#67—62no—
297C22×Dic3#6711yescharacteristic
298D3×Q8—24no—
299D3×D4—38no—
300D3×D4—64no—
301D3×D4—64no—
302D3×D4—68no—
303D3×D4—68no—
304D3×D4—64no—
305C2×D12—21no—
306C2×D12—24no—
307C2×D12—32no—
308C2×D12—32no—
309C2×D12—38no—
310C2×D12—62no—
311C2×D12—64no—
312C2×D12—64no—
313C2×D12—68no—
314C2×D12—68no—
315C2×D12—64no—
316C2×D12—64no—
317C2×D12—62no—
318C2×D12—62no—
319C2×D12—68no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—64no—
323C2×D12—124no—
324C2×D12—121no—
325C2×D12C22×D312yes—
326C2×C4×D3—24no—
327C2×C4×D3—21no—
328C2×C4×D3—21no—
329C2×C4×D3#6711yescharacteristic
330C2×C4×D3#6711yescharacteristic
331C2×C4×D3C22×D311yescharacteristic
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—21no—
334C2×Dic6C22×D311yescharacteristic, complemented
335C3×SD16—64no—
336C2×C3×C8—32no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—41no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
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—
354#217—21no—
355#215—24no—
356#215—64no—
357#215—64no—
358#215—64no—
359#215—64no—
360#215—124no—
361#214—64no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364C4⋊Dic3—21no—
365C4⋊Dic3C22×D311yescharacteristic, complemented
366Dic3⋊C4—21no—
367Dic3⋊C4—21no—
368Dic3⋊C4—21no—
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×C32C2×SD1612yescomplemented
379C22×C32C22×D411yescharacteristic
380C2×C3⋊D3—24no—
381C2×C3⋊D3—48no—
382C2×C3⋊D3—42no—
383C2×C3⋊D3—42no—
384C2×C3×D3—21no—
385C2×C3×D3—21no—
386C2×C3×D3—28no—
387C2×C3×D3—24no—
388C2×C3×D3—48no—
389C2×C3×D3—42no—
390C2×C3×D3—42no—
391C2×C3×D3#12012yes—
392C2×C3×D3C2×SD1612yes—
393C2×C3×D3C2×SD1612yescomplemented
394C2×C3×D3AGL(1,ℤ/8)12yes—
395D32—416no—
396D32—416no—
397C32×C4—21no—
398C32×C4—41no—
399C32×C4—41no—
400C32×C4C22×D412yes—
401C3×Dic3—21no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3#12012yes—
405C25—181no—
406C22×Q8—31no—
407C22×D4—31no—
408C22×D4—92no—
409C22×D4—92no—
410C22×D4—91no—
411C22×D4—181no—
412C22×D4—181no—
413C22×D4—181no—
414C22×D4—188no—
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—31no—
424C22⋊Q8—31no—
425C22⋊Q8—61no—
426C22⋊Q8—61no—
427C22⋊Q8D3211yescharacteristic, complemented
428C2×C4⋊C4—31no—
429C2×C4⋊C4—61no—
430C2×C22⋊C4—61no—
431#102—32no—
432#102—92no—
433#102—92no—
434#102—92no—
435C22⋊C8—31no—
436C22⋊C8—92no—
437C22⋊C8—91no—
438C23×C3—21no—
439C23×C3—31no—
440C23×C3—34no—
441C23×C3—31no—
442C23×C3—62no—
443C23×C3—62no—
444C23×C3—64no—
445C23×C3—62no—
446C23×C3—122no—
447C23×C3—122no—
448C23×C3D3×D411yescharacteristic
449C23×C3C2×#6711yescharacteristic
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—24no—
453C22×D3—22no—
454C22×D3—42no—
455C22×D3—42no—
456C22×D3—68no—
457C22×D3—68no—
458C22×D3—68no—
459C22×D3—64no—
460C22×D3—64no—
461C22×D3—62no—
462C22×D3—62no—
463C22×D3—68no—
464C22×D3—122no—
465C22×D3—124no—
466C22×D3—124no—
467C22×D3—1232no—
468C22×D3—124no—
469C22×D3—124no—
470C22×D3—124no—
471C22×D3—1232no—
472C22×D3—124no—
473C22×D3—122no—
474C22×D3—122no—
475C22×D3—122no—
476C22×D3—122no—
477C22×D3—124no—
478C22×D3—124no—
479C22×D3—124no—
480C22×D3—242no—
481C22×D3—242no—
482C22×D3#21514yescomplemented
483C22×D3C2×#6711yescharacteristic
484C22×D3C2×#6711yescharacteristic
485C3×Q8—22no—
486C3×Q8—22no—
487C3×Q8—42no—
488C3×Q8—62no—
489C3×Q8—122no—
490C3×D4—34no—
491C3×D4—64no—
492C3×D4—62no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—31no—
502C2×C3×C4—34no—
503C2×C3×C4—31no—
504C2×C3×C4—42no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—62no—
508C2×C3×C4—62no—
509C2×C3×C4—62no—
510C2×C3×C4—62no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—122no—
514C2×C3×C4—122no—
515C2×C3×C4D3×D411yescharacteristic
516C2×C3×C4C2×#6711yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519#67—68no—
520#67—68no—
521C2×Dic3—22no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3C2×#6711yescharacteristic
525C2×Dic3C2×#6711yescharacteristic
526D12—24no—
527D12—22no—
528D12—34no—
529D12—34no—
530D12—64no—
531D12—64no—
532D12—64no—
533D12—68no—
534D12—68no—
535D12—62no—
536D12—62no—
537D12—122no—
538D12—124no—
539D12D3×D414yes—
540C4×D3—22no—
541C4×D3—22no—
542C4×D3—22no—
543C4×D3—42no—
544C4×D3—42no—
545C4×D3D3×D414yes—
546Dic6—22no—
547Dic6—42no—
548C3×C8—62no—
549C3⋊C8—22no—
550C3⋊C8—62no—
551C3⋊C8—62no—
552C3⋊C8—122no—
553C2×C32—22no—
554C2×C32C2×#12011yescharacteristic
555C2×C32C22×SD1611yescharacteristic
556C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
557C3⋊D3—44no—
558C3×D3—22no—
559C3×D3—44no—
560C3×D3#45014yescomplemented
561C24—31no—
562C24—61no—
563C24—182no—
564C24—182no—
565C24—188no—
566C24—181no—
567C24—364no—
568C24—364no—
569C2×Q8—31no—
570C2×Q8—61no—
571C2×Q8—64no—
572C2×Q8C2×D3211yescharacteristic, complemented
573C2×D4—32no—
574C2×D4—64no—
575C2×D4—61no—
576C2×D4—98no—
577C2×D4—92no—
578C2×D4—184no—
579C2×D4—184no—
580C2×D4—182no—
581C2×D4—182no—
582C2×D4—184no—
583C2×D4—184no—
584C2×D4—188no—
585C2×D4—188no—
586C2×D4—188no—
587C2×D4—181no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—64no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4C2×D3211yescharacteristic
597SD16—64no—
598SD16—184no—
599SD16—184no—
600SD16—184no—
601C2×C8—32no—
602C2×C8—92no—
603C2×C8—184no—
604C4⋊C4—21no—
605C4⋊C4—31no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4C2×D3211yescharacteristic, complemented
611C22⋊C4—21no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—22no—
621C22×C3—32no—
622C22×C3—32no—
623C22×C3—32no—
624C22×C3—32no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—68no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—64no—
631C22×C3—128no—
632C22×C3—122no—
633C22×C3—122no—
634C22×C3D3×SD1612yescomplemented
635C22×C3C2×#21512yescomplemented
636C22×C3C2×D3×D411yescharacteristic
637C22×C3C22×#6711yescharacteristic
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—28no—
641C2×D3—24no—
642C2×D3—48no—
643C2×D3—42no—
644C2×D3—42no—
645C2×D3—64no—
646C2×D3—64no—
647C2×D3—124no—
648C2×D3—1216no—
649C2×D3—1216no—
650C2×D3—1216no—
651C2×D3—128no—
652C2×D3—128no—
653C2×D3—122no—
654C2×D3—122no—
655C2×D3—122no—
656C2×D3—122no—
657C2×D3—1216no—
658C2×D3—242no—
659C2×D3—242no—
660C2×D3—248no—
661C2×D3#93712yes—
662C2×D3C2×#21512yes—
663C2×D3C2×#21512yescomplemented
664C2×D3#94912yes—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—22no—
668C3×C4—32no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—61no—
675C3×C4—81no—
676C3×C4—81no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4C2×D3×D412yes—
680C3×C4C2×D3×D412yes—
681Dic3—21no—
682Dic3—41no—
683Dic3—41no—
684Dic3#93712yes—
685C32C2×#45011yescharacteristic, complemented, Sylow
686C23—31no—
687C23—31no—
688C23—34no—
689C23—62no—
690C23—62no—
691C23—64no—
692C23—62no—
693C23—122no—
694C23—122no—
695C23—184no—
696C23—188no—
697C23—188no—
698C23—182no—
699C23—362no—
700C23—364no—
701C23—364no—
702C23—364no—
703C23—3632no—
704C23—364no—
705C23—362no—
706C23D3×#6711yescharacteristic
707Q8—22no—
708Q8—62no—
709Q8—122no—
710D4—34no—
711D4—64no—
712D4—62no—
713D4—94no—
714D4—184no—
715D4—188no—
716D4—188no—
717D4—182no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—31no—
722C2×C4—34no—
723C2×C4—31no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—122no—
731C2×C4—122no—
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—62no—
744C2×C3—124no—
745C2×C3D3×#12011yescharacteristic
746C2×C3C2×D3×SD1611yescharacteristic
747C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
748C2×C3C2×#93711yescharacteristic
749C2×C3C22×#21511yescharacteristic
750C2×C3C2×#94911yescharacteristic
751D3—22no—
752D3—44no—
753D3—124no—
754D3—124no—
755D3—244no—
756D3#504614yesdirect product factor
757C22—21no—
758C22—21no—
759C22—32no—
760C22—32no—
761C22—32no—
762C22—32no—
763C22—68no—
764C22—61no—
765C22—61no—
766C22—64no—
767C22—128no—
768C22—122no—
769C22—122no—
770C22—184no—
771C22—368no—
772C22—3616no—
773C22—3616no—
774C22—362no—
775C22—362no—
776C22D3×#21512yescomplemented
777C22C2×D3×#6711yescharacteristic
778C4—21no—
779C4—32no—
780C4—41no—
781C4—41no—
782C4—61no—
783C4—121no—
784C4—121no—
785C4D32×D412yes—
786C3—21no—
787C3D3×#45011yescharacteristic, complemented
788C3C2×#504611yescharacteristic, complemented
789C2—22no—
790C2—34no—
791C2—62no—
792C2—124no—
793C2—364no—
794C2D3×#93711yescharacteristic
795C2C2×D3×#21511yescharacteristic
796C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×D3×D12C2
hypercenterC22⋊Q8D32
hypocenterC32C2×#450
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
2. C3×D3×C22⋊Q8C2semidirect
3. C2×D3×#215C2semidirect
4. #10592745C2semidirect
5. C3×#5046C2semidirect
6. #10591651C2semidirect
7. #10591183C2semidirect
8. #10591169C2semidirect
9. D3×#830C2semidirect
10. #10590596C2semidirect
11. D3×#809C2semidirect
16. C2×C3×D3×Q8C22semidirect
25. C32×C22⋊Q8C22semidirect
26. C2×#3755C22semidirect
27. C3×#946C22semidirect
28. C2×C3×#215C22semidirect
29. C3×#924C22semidirect
30. C3×#897C22semidirect
33. C3×D3×C4⋊C4C22semidirect
37. C2×#3717C22semidirect
38. C2×#3715C22semidirect
39. C2×D3×C3⋊C8C22semidirect
40. #63657C22semidirect
41. #63636C22semidirect
42. C3×#830C22semidirect
43. C3×#809C22semidirect
44. #63564C22semidirect
45. #63562C22semidirect
46. (C2×D3)⋊(C3⋊C8)C22semidirect
52. D3×C22⋊Q8D3semidirect
64. #5046D3direct (N × H)
78. C2×C32×Q8C23semidirect
96. C2×C3×Dic6C23semidirect
107. C32×C4⋊C4C23semidirect
110. C2×C3⋊(C3⋊C8)C23semidirect
116. C3×C4⋊Dic3C23semidirect
120. C2×C3×C3⋊C8C23semidirect
131. C2×D3×Q8C2×D3semidirect
155. C3×C22⋊Q8C2×D3semidirect
156. C3×C22⋊Q8C2×D3semidirect
160. #946C2×D3semidirect
167. C2×#215C2×D3semidirect
169. #924C2×D3semidirect
174. #897C2×D3semidirect
177. D3×C4⋊C4C2×D3semidirect
187. #830C2×D3semidirect
195. #809C2×D3semidirect
207. C22×C3×D3SD16semidirect
278. C2×C3×Q8C22×D3semidirect
279. C2×C3×Q8C22×D3semidirect
334. C2×Dic6C22×D3semidirect
346. C3×C4⋊C4C22×D3semidirect
347. C3×C4⋊C4C22×D3semidirect
365. C4⋊Dic3C22×D3semidirect
373. C2×C3⋊C8C22×D3semidirect
378. C22×C32C2×SD16semidirect
393. C2×C3×D3C2×SD16semidirect
427. C22⋊Q8D32semidirect
482. C22×D3#215semidirect
560. C3×D3#450semidirect
572. C2×Q8C2×D32semidirect
610. C4⋊C4C2×D32semidirect
634. C22×C3D3×SD16semidirect
635. C22×C3C2×#215semidirect
663. C2×D3C2×#215semidirect
685. C32C2×#450semidirect
756. D3#5046direct (N × H)
776. C22D3×#215semidirect
787. C3D3×#450semidirect
788. C3C2×#5046semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D122
C3×D3×C22⋊Q82
C2×D3×#2152
#105927452
C3×#50462
#105916512
#105911832
#105911692
D3×#8302
#105905962
D3×#8092
C2×#50463
D3×#4503