Finite Group Databasebeta

← D3×#3230 #11667231

Subgroups — D3×#3230 #11667231

Order 768.

2006 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#533C211yesmaximal, characteristic
2C2×D3×C4⋊Q8C211yesmaximal, characteristic
3C3×#3230C211yesmaximal, characteristic, complemented
4#83324C211yesmaximal, characteristic, complemented
5#83224C211yesmaximal, characteristic, complemented
6#81943C212yesmaximal, complemented
7D3×#500C212yesmaximal, complemented
8#81608C212yesmaximal, complemented
9D3×#487C212yesmaximal, complemented
10D3×#484C214yesmaximal
11#81458C214yesmaximal, complemented
12#81112C214yesmaximal, complemented
13D3×#477C214yesmaximal, complemented
14D3×#431C211yesmaximal, characteristic
15#79272C211yesmaximal, characteristic, complemented
16C2×#3230—31nomaximal, Sylow
17C22×D3×Q8—21no—
18C3×#533C2211yescharacteristic
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×#944—21no—
21#5728C2211yescharacteristic
22#5728C2211yescharacteristic
23D3×C4⋊Q8—21no—
24D3×C4⋊Q8—21no—
25D3×C4⋊Q8—21no—
26D3×C4⋊Q8—21no—
27D3×C4⋊Q8C2211yescharacteristic
28D3×C4⋊Q8C2211yescharacteristic
29D3×C4⋊Q8C2212yes—
30D3×C4⋊Q8C2212yes—
31D3×C4⋊Q8C2212yes—
32D3×C4⋊Q8C2212yes—
33#5688—21no—
34D3×#125—21no—
35D3×C22⋊Q8—21no—
36D3×C22⋊Q8C2212yes—
37#5622—21no—
38#5622C2212yes—
39#5578—21no—
40#5578C2212yes—
41C4×D3×Q8—21no—
42C4×D3×Q8C2212yes—
43D3×#117—21no—
44#5517—21no—
45C2×D3×C4⋊C4—21no—
46C2×D3×C4⋊C4C2212yes—
47C2×#888—21no—
48C2×#888C2212yes—
49C2×C42×D3C2211yescharacteristic
50#5470C2211yescharacteristic
51C2×#869C2211yescharacteristic
52C3×#500C2212yescomplemented
53C3×#487C2212yescomplemented
54C3×#484C2214yes—
55C3×#477C2214yescomplemented
56C3×#431C2211yescharacteristic
57#5093C2212yescomplemented
58#5091C2214yescomplemented
59#5079C2212yescomplemented
60#5078C2212yescomplemented
61#5078C2212yescomplemented
62#5044C2214yes—
63#5021C2214yescomplemented
64#4970C2214yes—
65#4925C2211yescharacteristic
66#4884C2218yes—
67D3×#107C2218yes—
68#4875C2218yescomplemented
69#4874C2218yescomplemented
70#4850C2214yescomplemented
71#4833C2212yes—
72D3×C4⋊C8C2212yes—
73#4811C2218yes—
74D3×#103C2218yes—
75#4793C2218yescomplemented
76#4792C2218yescomplemented
77D3×C22⋊C8C2212yes—
78#4722C2214yes—
79#4718C2212yes—
80#4685C2212yes—
81C4×D3×C8C2212yes—
82#4682C2212yescomplemented
83#4681C2212yescomplemented
84C2×#533—31no—
85C22×C4⋊Q8—31no—
86#3230—32no—
87#3230—32no—
88#3230—34no—
89#3230—34no—
90#3230—31no—
91#3230—31no—
92#3230—31no—
93#3230D311yescharacteristic, direct product factor
94C2×#500—32no—
95C2×#487—32no—
96C2×#484—34no—
97C2×#477—34no—
98C2×#431—31no—
99C22×C3×Q8—21no—
100C2×D3×Q8—22no—
101C2×D3×Q8—22no—
102C2×D3×Q8—22no—
103C2×D3×Q8—22no—
104C2×D3×Q8—21no—
105C2×D3×Q8—48no—
106C2×D3×Q8C2312yes—
107C22×C4×D3—22no—
108C22×C4×D3D411yescharacteristic
109C22×C4×D3D411yescharacteristic
110C22×C4×D3C2311yescharacteristic
111C22×Dic6—21no—
112C22×Dic6—22no—
113C3×C4⋊Q8—21no—
114C3×C4⋊Q8—21no—
115C3×C4⋊Q8C2311yescharacteristic
116C3×C4⋊Q8C2312yes—
117C3×C4⋊Q8C2312yes—
118C3×C4⋊Q8C2311yescharacteristic
119C3×#125—21no—
120C3×C22⋊Q8—21no—
121C3×C22⋊Q8C2312yes—
122C3×C4×Q8—21no—
123C3×C4×Q8C2312yes—
124C3×#117—21no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4C2312yes—
127C2×C3×C42C2311yescharacteristic
128#946—21no—
129#946C2312yes—
130Q8×Dic3—21no—
131Q8×Dic3C2312yes—
132#944—22no—
133#944—22no—
134#944—22no—
135#944—22no—
136#944—21no—
137#944C2312yes—
138#926—21no—
139C2×C4⋊Dic3—21no—
140C2×C4⋊Dic3C2312yes—
141#924—21no—
142#924C2312yes—
143C2×Dic3⋊C4—22no—
144C2×Dic3⋊C4—22no—
145C2×C4×Dic3D411yescharacteristic
146C2×C4×Dic3D411yescharacteristic
147C2×C4×Dic3C2311yescharacteristic
148C2×D3×C8C2314yes—
149#897—21no—
150#897C2312yes—
151#896—22no—
152#896—22no—
153#892—21no—
154#892—21no—
155D3×C4⋊C4—21no—
156D3×C4⋊C4—21no—
157D3×C4⋊C4—22no—
158D3×C4⋊C4—22no—
159D3×C4⋊C4—22no—
160D3×C4⋊C4—22no—
161D3×C4⋊C4—22no—
162D3×C4⋊C4—22no—
163D3×C4⋊C4—22no—
164D3×C4⋊C4—22no—
165D3×C4⋊C4—21no—
166D3×C4⋊C4C2312yes—
167D3×C4⋊C4C2314yes—
168D3×C4⋊C4C2314yes—
169#890—21no—
170#890—21no—
171#889—22no—
172#889—22no—
173#888—21no—
174#888—21no—
175#888—22no—
176#888—22no—
177#888—22no—
178#888—22no—
179#888—22no—
180#888—22no—
181#888—21no—
182#888C2312yes—
183#888C2314yes—
184#888C2314yes—
185#887—22no—
186#887—22no—
187#887—21no—
188#887C2312yes—
189D3×C22⋊C4—22no—
190#878—22no—
191#878—22no—
192#877—22no—
193#872—22no—
194C42×D3—22no—
195C42×D3D411yescharacteristic
196C42×D3D411yescharacteristic
197C42×D3D411yescharacteristic
198C42×D3D411yescharacteristic
199C42×D3C2311yescharacteristic
200C42×D3C2311yescharacteristic
201C42×D3C2311yescharacteristic
202C42×D3C2311yescharacteristic
203#870—21no—
204#869—21no—
205#869—21no—
206#869C2311yescharacteristic
207#869C2312yes—
208#869C2311yescharacteristic
209#869C2312yes—
210C4×Dic6—21no—
211C4×Dic6—22no—
212C4×Dic6—22no—
213C4×Dic6C2312yes—
214C3×#107C2318yes—
215C3×C4⋊C8C2312yes—
216C3×#103C2318yes—
217C3×C22⋊C8C2312yes—
218C3×C4×C8C2312yes—
219#835C2318yes—
220#830C2312yes—
221(C2×D3)⋊C8C2314yes—
222#818C2318yes—
223#816C2318yes—
224Dic3⋊C8C2314yes—
225C8×Dic3C2314yes—
226#810C2318yes—
227#807C2318yes—
228#807C2318yes—
229C4⋊(C3⋊C8)C2312yes—
230C4×C3⋊C8C2312yes—
231C23×Q8—61no—
232#533—31no—
233#533—31no—
234#533—32no—
235#533—32no—
236#533—31no—
237#533—61no—
238#533—61no—
239#533—61no—
240#533—61no—
241#533C2×D311yescharacteristic
242C2×C4⋊Q8—32no—
243C2×C4⋊Q8—32no—
244C2×C4⋊Q8—31no—
245C2×C4⋊Q8—32no—
246C2×C4⋊Q8—32no—
247C2×C4⋊Q8—32no—
248C2×C4⋊Q8—31no—
249C2×C4⋊Q8—31no—
250C2×C4⋊Q8—61no—
251C2×C4⋊Q8—61no—
252C2×C4⋊Q8—61no—
253C2×C4⋊Q8—61no—
254C2×C4⋊Q8—61no—
255C2×C4⋊Q8—61no—
256C2×C4⋊Q8C2×D311yescharacteristic
257C2×#125—61no—
258C2×C22⋊Q8—32no—
259C2×C22⋊Q8—61no—
260C2×C4×Q8—32no—
261C2×C4×Q8—61no—
262C2×#117—61no—
263C22×C4⋊C4—32no—
264C22×C4⋊C4—61no—
265C22×C42—31no—
266#500—32no—
267#500—32no—
268#500—38no—
269#500—32no—
270#500C2×D312yescomplemented
271#487—32no—
272#487—32no—
273#487—38no—
274#487—32no—
275#487C2×D312yescomplemented
276#484—34no—
277#484—34no—
278#484—38no—
279#484—38no—
280#484—34no—
281#484C2×D314yes—
282#477—34no—
283#477—34no—
284#477—38no—
285#477—34no—
286#477—38no—
287#477C2×D314yescomplemented
288#431—31no—
289#431—32no—
290#431—32no—
291#431—32no—
292#431C2×D311yescharacteristic
293C2×#107—38no—
294C2×C4⋊C8—32no—
295C2×#103—38no—
296C2×C22⋊C8—32no—
297C2×C4×C8—32no—
298C23×D3C2×D411yescharacteristic
299C2×C3×Q8—22no—
300C2×C3×Q8—22no—
301C2×C3×Q8—21no—
302C2×C3×Q8—44no—
303C2×C3×Q8C2412yes—
304C22×C3×C4—22no—
305C22×C3×C4C2×D411yescharacteristic
306C22×C3×C4C2×D411yescharacteristic
307C22×C3×C4C2411yescharacteristic
308C22×Dic3—22no—
309C22×Dic3C2×D411yescharacteristic
310C22×Dic3C2×D411yescharacteristic
311C22×Dic3C2×D411yescharacteristic
312D3×Q8—28no—
313D3×Q8—48no—
314D3×Q8—48no—
315D3×Q8—48no—
316D3×Q8—44no—
317D3×Q8—48no—
318C2×C4×D3—24no—
319C2×C4×D3—24no—
320C2×C4×D3—22no—
321C2×C4×D3—22no—
322C2×C4×D3—24no—
323C2×C4×D3—24no—
324C2×C4×D3—48no—
325C2×C4×D3Q1618yes—
326C2×C4×D3C2×D411yescharacteristic
327C2×C4×D3C2×D411yescharacteristic
328C2×C4×D3C2×D411yescharacteristic
329C2×C4×D3C2×D411yescharacteristic
330C2×C4×D3C2×D411yescharacteristic
331C2×C4×D3C2×D411yescharacteristic
332C2×C4×D3C2×D411yescharacteristic
333C2×C4×D3C2×D411yescharacteristic
334C2×C4×D3C2×D411yescharacteristic
335C2×C4×D3C2×D411yescharacteristic
336C2×C4×D3C2411yescharacteristic
337C2×C4×D3C2411yescharacteristic
338C2×Dic6—21no—
339C2×Dic6—22no—
340C2×Dic6—22no—
341C2×Dic6—22no—
342C2×Dic6—22no—
343C2×Dic6—24no—
344C2×Dic6—24no—
345C2×Dic6—48no—
346C2×Dic6—44no—
347C2×Dic6C2412yes—
348C2×C3×C8C2414yes—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—22no—
351C3×C4⋊C4—22no—
352C3×C4⋊C4—22no—
353C3×C4⋊C4—22no—
354C3×C4⋊C4—22no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4C2412yes—
358C3×C4⋊C4C2414yes—
359C3×C22⋊C4—22no—
360C3×C42—22no—
361C3×C42C2×D411yescharacteristic
362C3×C42C2×D411yescharacteristic
363C3×C42C2411yescharacteristic
364C3×C42C2411yescharacteristic
365#217—22no—
366(C2×D3)⋊C4—22no—
367(C2×D3)⋊C4—22no—
368C4⋊Dic3—21no—
369C4⋊Dic3—22no—
370C4⋊Dic3—22no—
371C4⋊Dic3—22no—
372C4⋊Dic3—21no—
373C4⋊Dic3—21no—
374C4⋊Dic3—22no—
375C4⋊Dic3—22no—
376C4⋊Dic3C2412yes—
377C4⋊Dic3C2414yes—
378Dic3⋊C4—22no—
379Dic3⋊C4—22no—
380Dic3⋊C4—22no—
381Dic3⋊C4—22no—
382Dic3⋊C4—22no—
383Dic3⋊C4—22no—
384Dic3⋊C4—22no—
385Dic3⋊C4—22no—
386Dic3⋊C4—24no—
387Dic3⋊C4—24no—
388Dic3⋊C4—24no—
389Dic3⋊C4—24no—
390C4×Dic3—22no—
391C4×Dic3—22no—
392C4×Dic3—22no—
393C4×Dic3C2×D411yescharacteristic
394C4×Dic3C2×D411yescharacteristic
395C4×Dic3C2×D411yescharacteristic
396C4×Dic3C2×D411yescharacteristic
397C4×Dic3C2×D411yescharacteristic
398C4×Dic3C2×D411yescharacteristic
399C4×Dic3C2×D411yescharacteristic
400C4×Dic3C2×D411yescharacteristic
401C4×Dic3C2×D411yescharacteristic
402C4×Dic3C2×D411yescharacteristic
403C4×Dic3C2411yescharacteristic
404C4×Dic3C2411yescharacteristic
405C2×C3⋊C8C2414yes—
406D3×C8—28no—
407C22×Q8—21no—
408C22×Q8—32no—
409C22×Q8—62no—
410C22×Q8—61no—
411C22×Q8—62no—
412C22×Q8—62no—
413C22×Q8—62no—
414C22×Q8—62no—
415C22×Q8—61no—
416C22×Q8—128no—
417C23×C4—31no—
418C23×C4—31no—
419C23×C4—31no—
420C23×C4—62no—
421C22×C8—34no—
422C4⋊Q8—21no—
423C4⋊Q8—21no—
424C4⋊Q8—34no—
425C4⋊Q8—34no—
426C4⋊Q8—32no—
427C4⋊Q8—32no—
428C4⋊Q8—32no—
429C4⋊Q8—32no—
430C4⋊Q8—31no—
431C4⋊Q8—31no—
432C4⋊Q8—62no—
433C4⋊Q8—62no—
434C4⋊Q8—62no—
435C4⋊Q8—62no—
436C4⋊Q8—62no—
437C4⋊Q8—62no—
438C4⋊Q8—61no—
439C4⋊Q8—61no—
440C4⋊Q8—61no—
441C4⋊Q8—62no—
442C4⋊Q8—62no—
443C4⋊Q8—62no—
444C4⋊Q8—62no—
445C4⋊Q8—61no—
446C4⋊Q8—61no—
447C4⋊Q8—61no—
448C4⋊Q8C22×D311yescharacteristic
449C4⋊Q8C22×D312yes—
450C4⋊Q8C22×D312yes—
451C4⋊Q8C22×D311yescharacteristic
452#125—21no—
453#125—62no—
454#125—62no—
455#125—61no—
456#125—61no—
457#125—61no—
458C22⋊Q8—21no—
459C22⋊Q8—32no—
460C22⋊Q8—32no—
461C22⋊Q8—32no—
462C22⋊Q8—62no—
463C22⋊Q8—62no—
464C22⋊Q8—62no—
465C22⋊Q8—62no—
466C22⋊Q8—61no—
467C22⋊Q8—61no—
468C22⋊Q8—61no—
469C22⋊Q8C22×D312yes—
470C4×Q8—21no—
471C4×Q8—32no—
472C4×Q8—32no—
473C4×Q8—32no—
474C4×Q8—62no—
475C4×Q8—62no—
476C4×Q8—62no—
477C4×Q8—61no—
478C4×Q8—62no—
479C4×Q8—61no—
480C4×Q8—61no—
481C4×Q8C22×D312yes—
482#117—21no—
483#117—62no—
484#117—62no—
485#117—61no—
486#117—61no—
487#117—61no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—32no—
490C2×C4⋊C4—34no—
491C2×C4⋊C4—34no—
492C2×C4⋊C4—32no—
493C2×C4⋊C4—62no—
494C2×C4⋊C4—62no—
495C2×C4⋊C4—62no—
496C2×C4⋊C4—62no—
497C2×C4⋊C4—62no—
498C2×C4⋊C4—62no—
499C2×C4⋊C4—61no—
500C2×C4⋊C4—61no—
501C2×C4⋊C4—62no—
502C2×C4⋊C4—62no—
503C2×C4⋊C4—61no—
504C2×C4⋊C4—62no—
505C2×C4⋊C4—62no—
506C2×C4⋊C4—61no—
507C2×C4⋊C4C22×D312yes—
508C2×C22⋊C4—62no—
509C2×C42—31no—
510C2×C42—31no—
511C2×C42—31no—
512C2×C42—31no—
513C2×C42—31no—
514C2×C42—31no—
515C2×C42—31no—
516C2×C42—31no—
517C2×C42—31no—
518C2×C42—31no—
519C2×C42—31no—
520C2×C42—62no—
521C2×C42C22×D311yescharacteristic
522#107—38no—
523#107—38no—
524#107—38no—
525#107C22×D318yes—
526C4⋊C8—34no—
527C4⋊C8—32no—
528C4⋊C8C22×D312yes—
529#103—38no—
530#103—38no—
531#103—38no—
532#103C22×D318yes—
533C22⋊C8—32no—
534C22⋊C8—34no—
535C22⋊C8C22×D312yes—
536C4×C8—34no—
537C4×C8—32no—
538C4×C8C22×D312yes—
539C23×C3C22×D411yescharacteristic
540C22×D3—22no—
541C22×D3—22no—
542C22×D3C2×Q1614yes—
543C22×D3C22×D411yescharacteristic
544C22×D3C22×D411yescharacteristic
545C3×Q8—24no—
546C3×Q8—44no—
547C3×Q8—44no—
548C3×Q8—42no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—24no—
554C2×C3×C4—44no—
555C2×C3×C4C2×Q1614yes—
556C2×C3×C4C22×D411yescharacteristic
557C2×C3×C4C22×D411yescharacteristic
558C2×C3×C4C22×D411yescharacteristic
559C2×C3×C4C22×D411yescharacteristic
560C2×C3×C4C22×D411yescharacteristic
561C2×C3×C4C2511yescharacteristic
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—22no—
566C2×Dic3—24no—
567C2×Dic3—44no—
568C2×Dic3C2×Q1614yes—
569C2×Dic3C22×D411yescharacteristic
570C2×Dic3C22×D411yescharacteristic
571C2×Dic3C22×D411yescharacteristic
572C2×Dic3C22×D411yescharacteristic
573C2×Dic3C22×D411yescharacteristic
574C2×Dic3C22×D411yescharacteristic
575C4×D3—22no—
576C4×D3—22no—
577C4×D3—22no—
578C4×D3—22no—
579C4×D3—22no—
580C4×D3—22no—
581C4×D3—48no—
582C4×D3—44no—
583C4×D3—48no—
584C4×D3—44no—
585C4×D3C2×Q1614yes—
586C4×D3C2×Q1614yes—
587C4×D3C2×Q1614yes—
588C4×D3C2×Q1614yes—
589C4×D3AGL(1,ℤ/8)14yes—
590C4×D32−1+414yes—
591Dic6—24no—
592Dic6—48no—
593Dic6—44no—
594Dic6—44no—
595Dic6—42no—
596Dic6—44no—
597Dic6—48no—
598Dic6—44no—
599C3×C8—24no—
600C3⋊C8—24no—
601C24—31no—
602C2×Q8—21no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—32no—
606C2×Q8—44no—
607C2×Q8—62no—
608C2×Q8—62no—
609C2×Q8—64no—
610C2×Q8—64no—
611C2×Q8—68no—
612C2×Q8—61no—
613C2×Q8—62no—
614C2×Q8—62no—
615C2×Q8—124no—
616C2×Q8—128no—
617C2×Q8—124no—
618C2×Q8—128no—
619C2×Q8—128no—
620C2×Q8—128no—
621C2×Q8—128no—
622C2×Q8C23×D312yes—
623C22×C4—22no—
624C22×C4—31no—
625C22×C4—38no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—31no—
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—64no—
641C22×C4—64no—
642C22×C4—62no—
643C22×C4—62no—
644C22×C4—64no—
645C22×C4—64no—
646C22×C4—62no—
647C22×C4—128no—
648C22×C4D3×D411yescharacteristic
649C22×C4D3×D411yescharacteristic
650C22×C4C23×D311yescharacteristic
651C2×C8—34no—
652C2×C8—68no—
653C2×C8C23×D314yes—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—34no—
663C4⋊C4—32no—
664C4⋊C4—64no—
665C4⋊C4—64no—
666C4⋊C4—62no—
667C4⋊C4—64no—
668C4⋊C4—64no—
669C4⋊C4—62no—
670C4⋊C4—62no—
671C4⋊C4—62no—
672C4⋊C4—62no—
673C4⋊C4—62no—
674C4⋊C4—62no—
675C4⋊C4—62no—
676C4⋊C4—62no—
677C4⋊C4—62no—
678C4⋊C4—62no—
679C4⋊C4—61no—
680C4⋊C4—61no—
681C4⋊C4—62no—
682C4⋊C4—62no—
683C4⋊C4—61no—
684C4⋊C4C23×D314yes—
685C4⋊C4C23×D312yes—
686C22⋊C4—22no—
687C22⋊C4—62no—
688C22⋊C4—62no—
689C22⋊C4—62no—
690C42—22no—
691C42—31no—
692C42—31no—
693C42—31no—
694C42—31no—
695C42—31no—
696C42—31no—
697C42—31no—
698C42—31no—
699C42—31no—
700C42—31no—
701C42—31no—
702C42—31no—
703C42—62no—
704C42—62no—
705C42—62no—
706C42D3×D411yescharacteristic
707C42D3×D411yescharacteristic
708C42C23×D311yescharacteristic
709C42C23×D311yescharacteristic
710C22×C3—21no—
711C22×C3—21no—
712C22×C3C22×Q1612yes—
713C22×C3C23×D411yescharacteristic
714C2×D3—21no—
715C2×D3—21no—
716C2×D3—28no—
717C2×D3#53612yes—
718C2×D3C22×Q1612yes—
719C2×D3C22×Q1612yes—
720C2×D3C2×AGL(1,ℤ/8)12yes—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—42no—
724C3×C4—44no—
725C3×C4—42no—
726C3×C4C22×Q1612yes—
727C3×C4C22×Q1612yes—
728C3×C4C2×AGL(1,ℤ/8)12yes—
729C3×C4C2×2−1+412yes—
730Dic3—21no—
731Dic3—21no—
732Dic3—42no—
733Dic3—44no—
734Dic3—42no—
735Dic3#53612yes—
736Dic3C22×Q1612yes—
737Dic3C22×Q1612yes—
738Dic3C2×AGL(1,ℤ/8)12yes—
739C23—31no—
740C23—31no—
741C23—34no—
742C23—62no—
743C23—62no—
744C23C2×D3×D411yescharacteristic
745Q8—24no—
746Q8—44no—
747Q8—44no—
748Q8—42no—
749Q8—64no—
750Q8—124no—
751Q8—124no—
752Q8—128no—
753Q8—124no—
754Q8—128no—
755Q8—124no—
756Q8—122no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—31no—
763C2×C4—31no—
764C2×C4—31no—
765C2×C4—31no—
766C2×C4—34no—
767C2×C4—34no—
768C2×C4—34no—
769C2×C4—34no—
770C2×C4—34no—
771C2×C4—34no—
772C2×C4—34no—
773C2×C4—31no—
774C2×C4—31no—
775C2×C4—44no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—64no—
787C2×C4—128no—
788C2×C4—124no—
789C2×C4—124no—
790C2×C4—128no—
791C2×C4—124no—
792C2×C4D3×Q1614yes—
793C2×C4C2×D3×D411yescharacteristic
794C2×C4C2×D3×D411yescharacteristic
795C2×C4C2×D3×D411yescharacteristic
796C2×C4C2×D3×D411yescharacteristic
797C2×C4C2×D3×D411yescharacteristic
798C2×C4C24×D311yescharacteristic
799C8—24no—
800C8—64no—
801C2×C3—22no—
802C2×C3C2×#53611yescharacteristic
803C2×C3C23×Q1611yescharacteristic
804C2×C3C22×AGL(1,ℤ/8)11yescharacteristic
805D3—22no—
806D3#323014yesdirect product factor
807C22—21no—
808C22—21no—
809C22—32no—
810C22—32no—
811C22—32no—
812C22—32no—
813C22—68no—
814C22—61no—
815C22—61no—
816C22C2×D3×Q1612yes—
817C22C22×D3×D411yescharacteristic
818C4—21no—
819C4—21no—
820C4—32no—
821C4—32no—
822C4—32no—
823C4—32no—
824C4—42no—
825C4—44no—
826C4—42no—
827C4—61no—
828C4—61no—
829C4—122no—
830C4—124no—
831C4—122no—
832C4C2×D3×Q1612yes—
833C4C2×D3×Q1612yes—
834C4D3×AGL(1,ℤ/8)12yes—
835C4D3×2−1+412yes—
836C3C2×#323011yescharacteristic, complemented, Sylow
837C2—22no—
838C2—34no—
839C2—62no—
840C2D3×#53611yescharacteristic
841C2C22×D3×Q1611yescharacteristic
842C2C2×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3230C2
socleC22×C3C23×D4
prime radicalC23×D3C2×D4
hypercenter#3230D3
hypocenterC3C2×#3230
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C3×#3230C2semidirect
4. #83324C2semidirect
5. #83224C2semidirect
6. #81943C2semidirect
7. D3×#500C2semidirect
8. #81608C2semidirect
9. D3×#487C2semidirect
11. #81458C2semidirect
12. #81112C2semidirect
13. D3×#477C2semidirect
15. #79272C2semidirect
52. C3×#500C22semidirect
53. C3×#487C22semidirect
55. C3×#477C22semidirect
57. #5093C22semidirect
58. #5091C22semidirect
59. #5079C22semidirect
60. #5078C22semidirect
61. #5078C22semidirect
63. #5021C22semidirect
68. #4875C22semidirect
69. #4874C22semidirect
70. #4850C22semidirect
75. #4793C22semidirect
76. #4792C22semidirect
82. #4682C22semidirect
83. #4681C22semidirect
93. #3230D3direct (N × H)
270. #500C2×D3semidirect
275. #487C2×D3semidirect
287. #477C2×D3semidirect
806. D3#3230direct (N × H)
836. C3C2×#3230semidirect

Maximal subgroups

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

subgroupindex
D3×#5332
C2×D3×C4⋊Q82
C3×#32302
#833242
#832242
#819432
D3×#5002
#816082
D3×#4872
D3×#4842
#814582
#811122
D3×#4772
D3×#4312
#792722
C2×#32303