Finite Group Databasebeta

← D3×#3227 #11667223

Subgroups — D3×#3227 #11667223

Order 768.

2286 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#532C211yesmaximal, characteristic
2C2×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
3C3×#3227C211yesmaximal, characteristic, complemented
4#83271C211yesmaximal, characteristic, complemented
5#83216C211yesmaximal, characteristic, complemented
6#81894C212yesmaximal, complemented
7D3×#498C212yesmaximal, complemented
8#81572C212yesmaximal, complemented
9D3×#486C212yesmaximal, complemented
10D3×#481C214yesmaximal, complemented
11#81314C214yesmaximal, complemented
12#81064C214yesmaximal, complemented
13D3×#476C214yesmaximal, complemented
14D3×#431C211yesmaximal, characteristic, complemented
15#79269C211yesmaximal, characteristic, complemented
16C2×#3227—31nomaximal, Sylow
17C2×D3×#41—21no—
18C22×D3×Q8—21no—
19C3×#532C2211yescharacteristic
20C2×C3×C4⋊Q8C2211yescharacteristic, complemented
21#5832—21no—
22C2×#944—21no—
23#5725C2211yescharacteristic
24D3×C4⋊Q8—21no—
25D3×C4⋊Q8—21no—
26D3×C4⋊Q8—21no—
27D3×C4⋊Q8—21no—
28D3×C4⋊Q8C2212yes—
29D3×C4⋊Q8C2212yes—
30D3×C4⋊Q8C2211yescharacteristic
31D3×C4⋊Q8C2212yescomplemented
32D3×C4⋊Q8C2212yescomplemented
33#5716C2211yescharacteristic
34D3×#127C2211yescharacteristic
35D3×#124—21no—
36#5668—21no—
37D3×#121—21no—
38D3×#121C2212yes—
39#5596—21no—
40#5596C2212yes—
41#5548—21no—
42#5548C2212yes—
43C4×D3×D4—21no—
44C4×D3×D4C2212yes—
45C2×D3×C4⋊C4—21no—
46C2×D3×C4⋊C4C2212yes—
47C2×#888—21no—
48C2×#888C2212yescomplemented
49#5477C2211yescharacteristic
50C2×C42×D3C2211yescharacteristic
51C2×#869C2211yescharacteristic, complemented
52C3×#498C2212yescomplemented
53C3×#486C2212yescomplemented
54C3×#481C2214yescomplemented
55C3×#476C2214yescomplemented
56C3×#431C2211yescharacteristic, complemented
57#5088C2212yescomplemented
58#5084C2214yescomplemented
59#5080C2212yescomplemented
60#5080C2212yescomplemented
61#5070C2212yescomplemented
62#5034C2214yescomplemented
63#5008C2214yescomplemented
64#4968C2214yescomplemented
65#4925C2211yescharacteristic, complemented
66#4870C2218yescomplemented
67#4863C2218yescomplemented
68D3×#106C2218yes—
69#4855C2218yescomplemented
70#4842C2214yescomplemented
71#4833C2212yescomplemented
72D3×C4⋊C8C2212yes—
73#4777C2218yescomplemented
74D3×#102C2218yes—
75#4761C2218yescomplemented
76#4760C2218yescomplemented
77#4735C2214yescomplemented
78D3×C22⋊C8C2212yes—
79#4718C2212yescomplemented
80#4694C2212yescomplemented
81#4685C2212yescomplemented
82C4×D3×C8C2212yes—
83#4680C2212yescomplemented
84C2×#532—31no—
85C22×C4⋊Q8—31no—
86#3227—32no—
87#3227—32no—
88#3227—34no—
89#3227—34no—
90#3227—31no—
91#3227—31no—
92#3227—31no—
93#3227D311yescharacteristic, direct product factor
94C2×#498—32no—
95C2×#486—32no—
96C2×#481—34no—
97C2×#476—34no—
98C2×#431—31no—
99C2×C3×#41—21no—
100C22×C3×Q8—21no—
101D3×#41—48no—
102C2×#239—21no—
103C2×D3×Q8—21no—
104C2×D3×Q8—22no—
105C2×D3×Q8—22no—
106C2×D3×Q8—22no—
107C2×D3×Q8—22no—
108C2×D3×Q8—48no—
109C2×#237—22no—
110C2×#237—21no—
111C2×D3×D4—22no—
112C2×D3×D4—21no—
113C2×D3×D4—21no—
114C2×D3×D4C2312yes—
115C2×#235—21no—
116C2×#235—22no—
117C22×C4×D3—22no—
118C22×C4×D3—22no—
119C22×C4×D3D411yescharacteristic
120C22×C4×D3D411yescharacteristic
121C22×C4×D3C2311yescharacteristic
122C22×Dic6—21no—
123C22×Dic6—22no—
124C3×C4⋊Q8—21no—
125C3×C4⋊Q8—21no—
126C3×C4⋊Q8C2312yes—
127C3×C4⋊Q8C2312yes—
128C3×C4⋊Q8C2311yescharacteristic
129C3×#127C2311yescharacteristic
130C3×#124—21no—
131C3×#121—21no—
132C3×#121C2312yes—
133C3×C4×D4—21no—
134C3×C4×D4C2312yes—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4C2312yes—
137C2×C3×C42C2311yescharacteristic
138#947—21no—
139#944—21no—
140#944—22no—
141#944—22no—
142#944—22no—
143#944—22no—
144#940—21no—
145#940—21no—
146#940C2312yes—
147#939—22no—
148#939—22no—
149#938—21no—
150#938C2312yes—
151#936—21no—
152D4×Dic3—21no—
153D4×Dic3C2312yes—
154#930—21no—
155#930C2312yes—
156C4×#67—22no—
157C4×#67—22no—
158C2×C4⋊Dic3—21no—
159C2×C4⋊Dic3C2312yes—
160C2×Dic3⋊C4—22no—
161C2×Dic3⋊C4—22no—
162C2×C4×Dic3D411yescharacteristic
163C2×C4×Dic3D411yescharacteristic
164C2×C4×Dic3C2311yescharacteristic
165C2×D3×C8C2314yes—
166#895—21no—
167#895C2312yes—
168#893—21no—
169#893C2312yes—
170D3×C4⋊C4—22no—
171D3×C4⋊C4—22no—
172D3×C4⋊C4—22no—
173D3×C4⋊C4—22no—
174D3×C4⋊C4—22no—
175D3×C4⋊C4—22no—
176D3×C4⋊C4—21no—
177D3×C4⋊C4C2314yes—
178D3×C4⋊C4C2312yes—
179D3×C4⋊C4C2314yes—
180#888—22no—
181#888—22no—
182#888—22no—
183#888—22no—
184#888—22no—
185#888—22no—
186#888—21no—
187#888C2314yes—
188#888C2314yes—
189#888C2312yes—
190#885—22no—
191#885—22no—
192#884—22no—
193#884—22no—
194#67⋊C4—22no—
195#67⋊C4—22no—
196D3×C22⋊C4—22no—
197D3×C22⋊C4—22no—
198#875—21no—
199#874C2311yescharacteristic
200C4×D12—21no—
201C4×D12C2312yes—
202C42×D3D411yescharacteristic
203C42×D3D411yescharacteristic
204C42×D3D411yescharacteristic
205C42×D3D411yescharacteristic
206C42×D3C2311yescharacteristic
207C42×D3C2311yescharacteristic
208C42×D3C2311yescharacteristic
209C42×D3C2311yescharacteristic
210#869—21no—
211#869—21no—
212#869C2311yescharacteristic
213#869C2312yes—
214#869C2312yes—
215C3×#106C2318yes—
216C3×C4⋊C8C2312yes—
217C3×#102C2318yes—
218C3×C22⋊C8C2312yes—
219C3×C4×C8C2312yes—
220#832C2318yes—
221#830C2312yes—
222#821C2318yes—
223(C2×D3)⋊C8C2314yes—
224#817C2318yes—
225Dic3⋊C8C2314yes—
226C8×Dic3C2314yes—
227#809C2318yes—
228#808C2318yes—
229#808C2318yes—
230C4⋊(C3⋊C8)C2312yes—
231C4×C3⋊C8C2312yes—
232C22×#41—61no—
233C23×Q8—61no—
234#532—31no—
235#532—31no—
236#532—32no—
237#532—32no—
238#532—31no—
239#532—61no—
240#532—61no—
241#532—61no—
242#532—61no—
243#532C2×D311yescharacteristic
244C2×C4⋊Q8—32no—
245C2×C4⋊Q8—31no—
246C2×C4⋊Q8—32no—
247C2×C4⋊Q8—32no—
248C2×C4⋊Q8—32no—
249C2×C4⋊Q8—32no—
250C2×C4⋊Q8—31no—
251C2×C4⋊Q8—61no—
252C2×C4⋊Q8—61no—
253C2×C4⋊Q8—61no—
254C2×C4⋊Q8—61no—
255C2×C4⋊Q8—61no—
256C2×C4⋊Q8—61no—
257C2×C4⋊Q8C2×D311yescharacteristic, complemented
258C2×#127—31no—
259C2×#124—61no—
260C2×#121—32no—
261C2×#121—61no—
262C2×C4×D4—32no—
263C2×C4×D4—61no—
264C22×C4⋊C4—32no—
265C22×C4⋊C4—61no—
266C22×C42—31no—
267#498—32no—
268#498—32no—
269#498—38no—
270#498—32no—
271#498C2×D312yescomplemented
272#486—32no—
273#486—32no—
274#486—38no—
275#486—32no—
276#486C2×D312yescomplemented
277#481—34no—
278#481—34no—
279#481—38no—
280#481—38no—
281#481—34no—
282#481C2×D314yescomplemented
283#476—34no—
284#476—34no—
285#476—38no—
286#476—34no—
287#476—38no—
288#476C2×D314yescomplemented
289#431—31no—
290#431—32no—
291#431—32no—
292#431—32no—
293#431C2×D311yescharacteristic, complemented
294C2×#106—38no—
295C2×C4⋊C8—32no—
296C2×#102—38no—
297C2×C22⋊C8—32no—
298C2×C4×C8—32no—
299C23×D3—22no—
300C23×D3C2×D411yescharacteristic
301C3×#41—44no—
302C2×C3×Q8—22no—
303C2×C3×Q8—22no—
304C2×C3×Q8—21no—
305C2×C3×Q8—44no—
306C2×C3×D4—22no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4C2412yes—
310C22×C3×C4—22no—
311C22×C3×C4—22no—
312C22×C3×C4C2×D411yescharacteristic
313C22×C3×C4C2×D411yescharacteristic
314C22×C3×C4C2411yescharacteristic
315C2×#67—22no—
316C2×#67—22no—
317C2×#67—22no—
318C2×#67—22no—
319C2×#67—22no—
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3C2×D411yescharacteristic
323C22×Dic3C2×D411yescharacteristic
324C22×Dic3C2×D411yescharacteristic
325#239—44no—
326D3×Q8—48no—
327D3×Q8—48no—
328D3×Q8—48no—
329D3×Q8—44no—
330D3×Q8—48no—
331#237—48no—
332#237—44no—
333D3×D4—28no—
334D3×D4—48no—
335D3×D4—44no—
336D3×D4—44no—
337#235—44no—
338#235—48no—
339C2×D12—22no—
340C2×D12—21no—
341C2×D12—21no—
342C2×D12C2412yes—
343C2×C4×D3—24no—
344C2×C4×D3—24no—
345C2×C4×D3—22no—
346C2×C4×D3—24no—
347C2×C4×D3—24no—
348C2×C4×D3—22no—
349C2×C4×D3—22no—
350C2×C4×D3—48no—
351C2×C4×D3—48no—
352C2×C4×D3SD1618yes—
353C2×C4×D3C2×D411yescharacteristic
354C2×C4×D3C2×D411yescharacteristic
355C2×C4×D3C2×D411yescharacteristic
356C2×C4×D3C2×D411yescharacteristic
357C2×C4×D3C2×D411yescharacteristic
358C2×C4×D3C2×D411yescharacteristic
359C2×C4×D3C2×D411yescharacteristic
360C2×C4×D3C2×D411yescharacteristic
361C2×C4×D3C2×D411yescharacteristic
362C2×C4×D3C2×D411yescharacteristic
363C2×C4×D3C2411yescharacteristic
364C2×C4×D3C2411yescharacteristic
365C2×Dic6—22no—
366C2×Dic6—22no—
367C2×Dic6—21no—
368C2×Dic6—22no—
369C2×Dic6—24no—
370C2×Dic6—24no—
371C2×Dic6—48no—
372C2×Dic6—44no—
373C2×C3×C8C2414yes—
374C3×C4⋊C4—22no—
375C3×C4⋊C4—22no—
376C3×C4⋊C4—22no—
377C3×C4⋊C4—21no—
378C3×C4⋊C4C2412yes—
379C3×C4⋊C4C2414yes—
380C3×C22⋊C4—22no—
381C3×C22⋊C4—22no—
382C3×C42C2×D411yescharacteristic
383C3×C42C2×D411yescharacteristic
384C3×C42C2411yescharacteristic
385C3×C42C2411yescharacteristic
386#217—22no—
387#217—22no—
388(C2×D3)⋊C4—22no—
389(C2×D3)⋊C4—22no—
390(C2×D3)⋊C4—22no—
391(C2×D3)⋊C4—22no—
392C4⋊Dic3—22no—
393C4⋊Dic3—22no—
394C4⋊Dic3—22no—
395C4⋊Dic3—21no—
396C4⋊Dic3C2412yes—
397C4⋊Dic3C2414yes—
398Dic3⋊C4—22no—
399Dic3⋊C4—22no—
400Dic3⋊C4—24no—
401Dic3⋊C4—24no—
402Dic3⋊C4—24no—
403Dic3⋊C4—24no—
404C4×Dic3C2×D411yescharacteristic
405C4×Dic3C2×D411yescharacteristic
406C4×Dic3C2×D411yescharacteristic
407C4×Dic3C2×D411yescharacteristic
408C4×Dic3C2×D411yescharacteristic
409C4×Dic3C2×D411yescharacteristic
410C4×Dic3C2×D411yescharacteristic
411C4×Dic3C2×D411yescharacteristic
412C4×Dic3C2×D411yescharacteristic
413C4×Dic3C2×D411yescharacteristic
414C4×Dic3C2411yescharacteristic
415C4×Dic3C2411yescharacteristic
416C2×C3⋊C8C2414yes—
417D3×C8—28no—
418C2×#41—21no—
419C2×#41—62no—
420C2×#41—62no—
421C2×#41—61no—
422C2×#41—61no—
423C2×#41—61no—
424C2×#41—128no—
425C22×Q8—21no—
426C22×Q8—62no—
427C22×Q8—61no—
428C22×Q8—62no—
429C22×Q8—62no—
430C22×Q8—62no—
431C22×Q8—62no—
432C22×Q8—61no—
433C22×Q8—128no—
434C22×D4—32no—
435C22×D4—61no—
436C22×D4—61no—
437C22×D4—62no—
438C23×C4—31no—
439C23×C4—31no—
440C23×C4—31no—
441C23×C4—62no—
442C23×C4—62no—
443C22×C8—34no—
444C4⋊Q8—21no—
445C4⋊Q8—21no—
446C4⋊Q8—34no—
447C4⋊Q8—34no—
448C4⋊Q8—32no—
449C4⋊Q8—32no—
450C4⋊Q8—32no—
451C4⋊Q8—31no—
452C4⋊Q8—62no—
453C4⋊Q8—62no—
454C4⋊Q8—62no—
455C4⋊Q8—62no—
456C4⋊Q8—62no—
457C4⋊Q8—62no—
458C4⋊Q8—61no—
459C4⋊Q8—62no—
460C4⋊Q8—62no—
461C4⋊Q8—62no—
462C4⋊Q8—62no—
463C4⋊Q8—61no—
464C4⋊Q8—61no—
465C4⋊Q8—61no—
466C4⋊Q8C22×D312yes—
467C4⋊Q8C22×D312yes—
468C4⋊Q8C22×D311yescharacteristic
469#127—32no—
470#127—31no—
471#127—61no—
472#127—61no—
473#127C22×D311yescharacteristic
474#124—21no—
475#124—62no—
476#124—62no—
477#124—61no—
478#124—61no—
479#124—61no—
480#121—21no—
481#121—32no—
482#121—32no—
483#121—32no—
484#121—62no—
485#121—62no—
486#121—61no—
487#121—62no—
488#121—61no—
489#121—62no—
490#121—61no—
491#121C22×D312yes—
492C4×D4—21no—
493C4×D4—32no—
494C4×D4—32no—
495C4×D4—32no—
496C4×D4—62no—
497C4×D4—62no—
498C4×D4—61no—
499C4×D4—62no—
500C4×D4—62no—
501C4×D4—61no—
502C4×D4—61no—
503C4×D4C22×D312yes—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—32no—
506C2×C4⋊C4—34no—
507C2×C4⋊C4—34no—
508C2×C4⋊C4—32no—
509C2×C4⋊C4—62no—
510C2×C4⋊C4—62no—
511C2×C4⋊C4—62no—
512C2×C4⋊C4—62no—
513C2×C4⋊C4—62no—
514C2×C4⋊C4—62no—
515C2×C4⋊C4—61no—
516C2×C4⋊C4—62no—
517C2×C4⋊C4—62no—
518C2×C4⋊C4—61no—
519C2×C4⋊C4C22×D312yes—
520C2×C22⋊C4—62no—
521C2×C22⋊C4—62no—
522C2×C42—31no—
523C2×C42—31no—
524C2×C42—31no—
525C2×C42—31no—
526C2×C42—31no—
527C2×C42—31no—
528C2×C42—31no—
529C2×C42—31no—
530C2×C42—31no—
531C2×C42—31no—
532C2×C42—31no—
533C2×C42C22×D311yescharacteristic
534#106—38no—
535#106—38no—
536#106—38no—
537#106C22×D318yes—
538C4⋊C8—34no—
539C4⋊C8—32no—
540C4⋊C8C22×D312yes—
541#102—38no—
542#102—38no—
543#102—38no—
544#102C22×D318yes—
545C22⋊C8—32no—
546C22⋊C8—34no—
547C22⋊C8C22×D312yes—
548C4×C8—34no—
549C4×C8—32no—
550C4×C8C22×D312yes—
551C23×C3—22no—
552C23×C3C22×D411yescharacteristic
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—44no—
557C22×D3—44no—
558C22×D3—44no—
559C22×D3C2×SD1614yes—
560C22×D3C22×D411yescharacteristic
561C22×D3C22×D411yescharacteristic
562C3×Q8—44no—
563C3×Q8—42no—
564C3×Q8—44no—
565C3×D4—24no—
566C3×D4—44no—
567C3×D4—42no—
568C3×D4—42no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—24no—
572C2×C3×C4—22no—
573C2×C3×C4—44no—
574C2×C3×C4—44no—
575C2×C3×C4C2×SD1614yes—
576C2×C3×C4C22×D411yescharacteristic
577C2×C3×C4C22×D411yescharacteristic
578C2×C3×C4C22×D411yescharacteristic
579C2×C3×C4C22×D411yescharacteristic
580C2×C3×C4C22×D411yescharacteristic
581C2×C3×C4C2511yescharacteristic
582#67—44no—
583#67—44no—
584#67—44no—
585#67—44no—
586#67—44no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—24no—
590C2×Dic3—22no—
591C2×Dic3—44no—
592C2×Dic3—44no—
593C2×Dic3C2×SD1614yes—
594C2×Dic3C22×D411yescharacteristic
595C2×Dic3C22×D411yescharacteristic
596C2×Dic3C22×D411yescharacteristic
597C2×Dic3C22×D411yescharacteristic
598C2×Dic3C22×D411yescharacteristic
599C2×Dic3C22×D411yescharacteristic
600D12—24no—
601D12—44no—
602D12—42no—
603D12—42no—
604C4×D3—22no—
605C4×D3—22no—
606C4×D3—22no—
607C4×D3—22no—
608C4×D3—22no—
609C4×D3—22no—
610C4×D3—48no—
611C4×D3—44no—
612C4×D3—48no—
613C4×D3—44no—
614C4×D3—44no—
615C4×D3C2×SD1614yes—
616C4×D3C2×SD1614yes—
617C4×D3C2×SD1614yes—
618C4×D3C2×SD1614yes—
619C4×D3AGL(1,ℤ/8)14yes—
620C4×D32−1+414yes—
621Dic6—48no—
622Dic6—44no—
623Dic6—42no—
624Dic6—44no—
625Dic6—44no—
626Dic6—48no—
627C3×C8—24no—
628C3⋊C8—24no—
629C24—31no—
630C24—62no—
631#41—44no—
632#41—128no—
633#41—128no—
634#41—124no—
635#41—124no—
636#41—124no—
637C2×Q8—21no—
638C2×Q8—22no—
639C2×Q8—22no—
640C2×Q8—44no—
641C2×Q8—62no—
642C2×Q8—64no—
643C2×Q8—64no—
644C2×Q8—61no—
645C2×Q8—62no—
646C2×Q8—62no—
647C2×Q8—124no—
648C2×Q8—128no—
649C2×Q8—124no—
650C2×Q8—128no—
651C2×Q8—128no—
652C2×Q8—128no—
653C2×Q8—128no—
654C2×D4—22no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—32no—
658C2×D4—62no—
659C2×D4—68no—
660C2×D4—62no—
661C2×D4—62no—
662C2×D4—62no—
663C2×D4—62no—
664C2×D4—62no—
665C2×D4—61no—
666C2×D4—61no—
667C2×D4—124no—
668C2×D4—124no—
669C2×D4—128no—
670C2×D4C23×D312yes—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—31no—
674C22×C4—38no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—31no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—64no—
690C22×C4—64no—
691C22×C4—62no—
692C22×C4—62no—
693C22×C4—64no—
694C22×C4—64no—
695C22×C4—62no—
696C22×C4—62no—
697C22×C4—62no—
698C22×C4—128no—
699C22×C4—128no—
700C22×C4D3×D411yescharacteristic
701C22×C4D3×D411yescharacteristic
702C22×C4C23×D311yescharacteristic
703C2×C8—34no—
704C2×C8—68no—
705C2×C8C23×D314yes—
706C4⋊C4—22no—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—21no—
710C4⋊C4—34no—
711C4⋊C4—32no—
712C4⋊C4—64no—
713C4⋊C4—64no—
714C4⋊C4—62no—
715C4⋊C4—64no—
716C4⋊C4—64no—
717C4⋊C4—62no—
718C4⋊C4—62no—
719C4⋊C4—62no—
720C4⋊C4—62no—
721C4⋊C4—61no—
722C4⋊C4C23×D314yes—
723C4⋊C4C23×D312yes—
724C22⋊C4—22no—
725C22⋊C4—22no—
726C22⋊C4—62no—
727C22⋊C4—62no—
728C22⋊C4—62no—
729C22⋊C4—62no—
730C22⋊C4—62no—
731C22⋊C4—62no—
732C42—31no—
733C42—31no—
734C42—31no—
735C42—31no—
736C42—31no—
737C42—31no—
738C42—31no—
739C42—31no—
740C42—31no—
741C42—31no—
742C42—31no—
743C42—31no—
744C42D3×D411yescharacteristic
745C42D3×D411yescharacteristic
746C42C23×D311yescharacteristic
747C42C23×D311yescharacteristic
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—42no—
751C22×C3—42no—
752C22×C3—42no—
753C22×C3C22×SD1612yes—
754C22×C3C23×D411yescharacteristic
755C2×D3—21no—
756C2×D3—21no—
757C2×D3—28no—
758C2×D3—42no—
759C2×D3—42no—
760C2×D3—42no—
761C2×D3—88no—
762C2×D3#53612yes—
763C2×D3C22×SD1612yes—
764C2×D3C22×SD1612yes—
765C2×D3C2×AGL(1,ℤ/8)12yes—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—42no—
769C3×C4—44no—
770C3×C4C22×SD1612yes—
771C3×C4C22×SD1612yes—
772C3×C4C2×AGL(1,ℤ/8)12yes—
773C3×C4C2×2−1+412yes—
774Dic3—21no—
775Dic3—21no—
776Dic3—42no—
777Dic3—44no—
778Dic3#53612yes—
779Dic3C22×SD1612yes—
780Dic3C22×SD1612yes—
781Dic3C2×AGL(1,ℤ/8)12yes—
782C23—22no—
783C23—31no—
784C23—31no—
785C23—34no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—124no—
790C23—124no—
791C23—124no—
792C23C2×D3×D411yescharacteristic
793Q8—44no—
794Q8—42no—
795Q8—44no—
796Q8—124no—
797Q8—128no—
798Q8—124no—
799Q8—128no—
800Q8—122no—
801Q8—124no—
802D4—24no—
803D4—44no—
804D4—42no—
805D4—42no—
806D4—64no—
807D4—124no—
808D4—124no—
809D4—124no—
810D4—124no—
811D4—124no—
812D4—124no—
813D4—122no—
814D4—122no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—24no—
819C2×C4—31no—
820C2×C4—31no—
821C2×C4—31no—
822C2×C4—31no—
823C2×C4—34no—
824C2×C4—34no—
825C2×C4—34no—
826C2×C4—34no—
827C2×C4—34no—
828C2×C4—34no—
829C2×C4—34no—
830C2×C4—31no—
831C2×C4—31no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—62no—
837C2×C4—62no—
838C2×C4—62no—
839C2×C4—62no—
840C2×C4—62no—
841C2×C4—62no—
842C2×C4—62no—
843C2×C4—64no—
844C2×C4—124no—
845C2×C4—124no—
846C2×C4—124no—
847C2×C4—128no—
848C2×C4—128no—
849C2×C4—124no—
850C2×C4—124no—
851C2×C4D3×SD1614yes—
852C2×C4C2×D3×D411yescharacteristic
853C2×C4C2×D3×D411yescharacteristic
854C2×C4C2×D3×D411yescharacteristic
855C2×C4C2×D3×D411yescharacteristic
856C2×C4C2×D3×D411yescharacteristic
857C2×C4C24×D311yescharacteristic
858C8—24no—
859C8—64no—
860C2×C3—22no—
861C2×C3—82no—
862C2×C3C2×#53611yescharacteristic
863C2×C3C23×SD1611yescharacteristic
864C2×C3C22×AGL(1,ℤ/8)11yescharacteristic
865D3—22no—
866D3—82no—
867D3#322714yesdirect product factor
868C22—21no—
869C22—21no—
870C22—32no—
871C22—32no—
872C22—32no—
873C22—32no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—68no—
878C22—61no—
879C22—61no—
880C22—122no—
881C22—122no—
882C22—122no—
883C22—248no—
884C22C2×D3×SD1612yes—
885C22C22×D3×D411yescharacteristic
886C4—21no—
887C4—21no—
888C4—32no—
889C4—32no—
890C4—32no—
891C4—32no—
892C4—42no—
893C4—44no—
894C4—61no—
895C4—61no—
896C4—122no—
897C4—124no—
898C4C2×D3×SD1612yes—
899C4C2×D3×SD1612yes—
900C4D3×AGL(1,ℤ/8)12yes—
901C4D3×2−1+412yes—
902C3C2×#322711yescharacteristic, complemented, Sylow
903C2—22no—
904C2—34no—
905C2—62no—
906C2—82no—
907C2—242no—
908C2D3×#53611yescharacteristic
909C2C22×D3×SD1611yescharacteristic
910C2C2×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3227C2
socleC22×C3C23×D4
prime radicalD3×#532C2
hypercenter#3227D3
hypocenterC3C2×#3227
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
2. C2×D3×C4⋊Q8C2semidirect
3. C3×#3227C2semidirect
4. #83271C2semidirect
5. #83216C2semidirect
6. #81894C2semidirect
7. D3×#498C2semidirect
8. #81572C2semidirect
9. D3×#486C2semidirect
10. D3×#481C2semidirect
11. #81314C2semidirect
12. #81064C2semidirect
13. D3×#476C2semidirect
14. D3×#431C2semidirect
15. #79269C2semidirect
20. C2×C3×C4⋊Q8C22semidirect
31. D3×C4⋊Q8C22semidirect
32. D3×C4⋊Q8C22semidirect
48. C2×#888C22semidirect
51. C2×#869C22semidirect
52. C3×#498C22semidirect
53. C3×#486C22semidirect
54. C3×#481C22semidirect
55. C3×#476C22semidirect
56. C3×#431C22semidirect
57. #5088C22semidirect
58. #5084C22semidirect
59. #5080C22semidirect
60. #5080C22semidirect
61. #5070C22semidirect
62. #5034C22semidirect
63. #5008C22semidirect
64. #4968C22semidirect
65. #4925C22semidirect
66. #4870C22semidirect
67. #4863C22semidirect
69. #4855C22semidirect
70. #4842C22semidirect
71. #4833C22semidirect
73. #4777C22semidirect
75. #4761C22semidirect
76. #4760C22semidirect
77. #4735C22semidirect
79. #4718C22semidirect
80. #4694C22semidirect
81. #4685C22semidirect
83. #4680C22semidirect
93. #3227D3direct (N × H)
257. C2×C4⋊Q8C2×D3semidirect
271. #498C2×D3semidirect
276. #486C2×D3semidirect
282. #481C2×D3semidirect
288. #476C2×D3semidirect
293. #431C2×D3semidirect
867. D3#3227direct (N × H)
902. C3C2×#3227semidirect

Maximal subgroups

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

subgroupindex
D3×#5322
C2×D3×C4⋊Q82
C3×#32272
#832712
#832162
#818942
D3×#4982
#815722
D3×#4862
D3×#4812
#813142
#810642
D3×#4762
D3×#4312
#792692
C2×#32273