Finite Group Databasebeta

← D3×#4819 #11865565

Subgroups — D3×#4819 #11865565

Order 1152.

1190 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#947C211yesmaximal, characteristic, complemented
2C2×D3×#215C211yesmaximal, characteristic, complemented
3C2×D3×D24C211yesmaximal, characteristic
4D3×#893C211yesmaximal, characteristic, complemented
5#10592518C211yesmaximal, characteristic, complemented
6C3×#4819C211yesmaximal, characteristic, complemented
7C3×D3×#103C211yesmaximal, characteristic, complemented
8#10591570C211yesmaximal, characteristic, complemented
9#10591568C211yesmaximal, characteristic, complemented
10#10590770C211yesmaximal, characteristic, complemented
11#10590751C211yesmaximal, characteristic, complemented
12D3×Dic3⋊C8C211yesmaximal, characteristic, complemented
13D3×#809C211yesmaximal, characteristic, complemented
14#10590540C211yesmaximal, characteristic, complemented
15#10590534C211yesmaximal, characteristic, complemented
16D3×#463—31nomaximal
17C2×#4819—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×C4×D32—21no—
22#64156C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic, complemented
24C2×#3745C2211yescharacteristic
25#64102C2211yescharacteristic, complemented
26C3×#947C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C2×C3×D24C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic
30C3×#893C2211yescharacteristic, complemented
31C3×D3×C4⋊C4C2211yescharacteristic
32D3×#215—24no—
33D3×(C2×D3)⋊C4—21no—
34D3×(C2×D3)⋊C4—21no—
35D3×(C2×D3)⋊C4—21no—
36#63907—21no—
37#63907—21no—
38#63904—21no—
39#63898C2211yescharacteristic, complemented
40#63894C2211yescharacteristic, complemented
41#63881—21no—
42C4×D3×Dic3C2211yescharacteristic
43#63864C2211yescharacteristic, complemented
44#63863C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic, complemented
47C2×#3714C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×D3×C3⋊C8C2211yescharacteristic
50D3×D24—24no—
51C32×#103C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53#63636C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63572C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×#947—31no—
64C22×#215—31no—
65C2×D3×SD16—31no—
66C2×D3×D8—31no—
67C22×D24—31no—
68D3×#124—31no—
69C4×D3×D4—31no—
70C2×#893—31no—
71C3×#463—31no—
72C2×C3×#103—31no—
73#5165—31no—
74#5153—31no—
75C2×Dic3⋊C8—31no—
76#5057—31no—
77#5016—31no—
78C2×#809—31no—
79#4844—31no—
80D3×C4⋊C8—31no—
81#4819—31no—
82#4819—31no—
83#4819—31no—
84#4819—31no—
85#4819—31no—
86#4819—31no—
87#4819—31no—
88#4819—31no—
89#4819—61no—
90#4819D311yescharacteristic, direct product factor
91D3×#103D311yescharacteristic, complemented
92#4787—31no—
93D3×#102—31no—
94C22×D32—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C3×D3×Q8—22no—
101C3×D3×Q8—22no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109C2×C3×Dic6C2311yescharacteristic
110C2×#626—21no—
111C2×#626—21no—
112C2×#624—21no—
113C2×D3×Dic3—21no—
114C2×D3×Dic3D411yescharacteristic
115C2×D3×Dic3D411yescharacteristic
116D3×D12—22no—
117D3×D12—22no—
118D3×D12—22no—
119D3×D12D414yes—
120C4×D32—44no—
121C2×C32×C8C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3755—22no—
124#3752—21no—
125#3752—21no—
126#3752—21no—
127C4×C3⋊Dic3C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129#3745—22no—
130C3×#215—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×D24—22no—
140C3×D3×C8—22no—
141#3722—21no—
142#3722—21no—
143#3722—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147Dic32D411yescharacteristic
148Dic32D411yescharacteristic
149#3717—22no—
150#3715—22no—
151#3714—22no—
152#3714—22no—
153D3×C3⋊C8—22no—
154C2×#463—91noSylow
155C22×C3×Q8—31no—
156C2×D3×Q8C2×D311yescharacteristic
157C2×D3×D4—31no—
158C2×D3×D4—31no—
159C22×D12—31no—
160C22×D12—31no—
161C22×C4×D3—61no—
162C22×C4×D3—61no—
163C2×C3×SD16—31no—
164C2×C3×D8—31no—
165C22×C3×C8—31no—
166C3×#124—31no—
167C3×C4×D4—31no—
168C2×C3×C4⋊C4—31no—
169#947—31no—
170#947—31no—
171#947—31no—
172#947—31no—
173#947—61no—
174#947—61no—
175#947—61no—
176#947C2×D311yescharacteristic, complemented
177C2×#215—31no—
178C2×#215—31no—
179C2×#215—31no—
180C2×#215—31no—
181C2×#215—61no—
182C2×#215—64no—
183C2×#215C2×D311yescharacteristic, complemented
184#936—31no—
185D4×Dic3—31no—
186C2×#214—31no—
187C2×#213—31no—
188C2×#213—31no—
189C4×#67—61no—
190C2×(C2×D3)⋊C4—61no—
191C2×(C2×D3)⋊C4—61no—
192C2×(C2×D3)⋊C4—61no—
193C2×C4×Dic3—31no—
194C22×C3⋊C8—31no—
195D3×SD16—64no—
196D3×D8—64no—
197C2×D24—31no—
198C2×D24—31no—
199C2×D24—31no—
200C2×D24—31no—
201C2×D24—61no—
202C2×D24—64no—
203C2×D24C2×D311yescharacteristic
204C2×#204—31no—
205C2×D3×C8—31no—
206C2×D3×C8C2×D311yescharacteristic
207#893—31no—
208#893—31no—
209#893—31no—
210#893—31no—
211#893—61no—
212#893—61no—
213#893—61no—
214#893C2×D311yescharacteristic, complemented
215D3×C4⋊C4C2×D311yescharacteristic
216#885—61no—
217#885—61no—
218#67⋊C4—61no—
219D3×C22⋊C4—61no—
220D3×C22⋊C4—61no—
221D3×C22⋊C4—61no—
222#875—31no—
223C4×D12—31no—
224C42×D3—31no—
225C3×C4⋊C8—31no—
226C3×#103—21no—
227C3×#103—31no—
228C3×#103—31no—
229C3×#103—31no—
230C3×#103C2×D311yescharacteristic, complemented
231C3×#103C2×D311yescharacteristic, complemented
232C3×#102—31no—
233#835C2×D311yescharacteristic, complemented
234#832—31no—
235#821—31no—
236#816C2×D311yescharacteristic, complemented
237Dic3⋊C8—31no—
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—61no—
243Dic3⋊C8C2×D311yescharacteristic, complemented
244#810C2×D311yescharacteristic, complemented
245#809—31no—
246#809—31no—
247#809—31no—
248#809—31no—
249#809—61no—
250#809C2×D311yescharacteristic, complemented
251C4⋊(C3⋊C8)—31no—
252C22×C3⋊D3—21no—
253C22×C3⋊D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C2×D32—24no—
258C2×D32—42no—
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—42no—
263C32×Q8—21no—
264C32×Q8—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268C2×C3⋊Dic3C2×D411yescharacteristic
269C2×C3⋊Dic3C2×D411yescharacteristic
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)C2×D412yes—
274C4×C3⋊D3—42no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12C2×D412yes—
284C3×C4×D3—42no—
285C3×C4×D3—42no—
286C3×C4×D3—42no—
287C3×C4×D3C2×D412yes—
288C3×C4×D3#4112yes—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—42no—
292#626—24no—
293#626—42no—
294#624—42no—
295D3×Dic3—22no—
296D3×Dic3—22no—
297D3×Dic3—42no—
298C32×C8—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C22×SD16—91no—
303C22×D8—91no—
304C2×#124—91no—
305C2×C4×D4—91no—
306#463—31no—
307#463—91no—
308#463—91no—
309#463—91no—
310#463—91no—
311#463—91no—
312#463—91no—
313#463—91no—
314C2×C4⋊C8—91no—
315C2×#103—31no—
316C2×#102—91no—
317C23×D3—61no—
318C23×D3—61no—
319C23×D3—61no—
320C23×D3—61no—
321C2×C3×Q8—21no—
322C2×C3×Q8—31no—
323C2×C3×Q8—61no—
324C2×C3×Q8—62no—
325C2×C3×Q8—62no—
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—61no—
332C22×C3×C4—61no—
333C22×C3×C4—61no—
334C2×#67—61no—
335C2×#67—61no—
336C22×Dic3—31no—
337C22×Dic3—31no—
338C22×Dic3—61no—
339D3×Q8—22no—
340D3×Q8—22no—
341D3×D4—34no—
342D3×D4—62no—
343D3×D4—62no—
344D3×D4—62no—
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—34no—
348C2×D12—31no—
349C2×D12—31no—
350C2×D12—61no—
351C2×D12—61no—
352C2×D12—62no—
353C2×D12—62no—
354C2×D12—62no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12C22×D311yescharacteristic
358C2×D12C22×D311yescharacteristic
359C2×C4×D3—21no—
360C2×C4×D3—21no—
361C2×C4×D3—21no—
362C2×C4×D3—31no—
363C2×C4×D3—31no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—121no—
370C2×C4×D3—124no—
371C2×C4×D3—124no—
372C2×C4×D3C22×D311yescharacteristic
373C2×Dic6—21no—
374C2×Dic6C22×D311yescharacteristic
375C3×SD16—62no—
376C3×D8—62no—
377C2×C3×C8—21no—
378C2×C3×C8—31no—
379C2×C3×C8—31no—
380C2×C3×C8—62no—
381C2×C3×C8C22×D311yescharacteristic
382C2×C3×C8C22×D311yescharacteristic
383C3×C4⋊C4—21no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4—61no—
386C3×C4⋊C4C22×D311yescharacteristic
387C3×C4⋊C4C22×D311yescharacteristic
388C3×C22⋊C4—61no—
389C3×C22⋊C4—61no—
390C3×C22⋊C4—61no—
391C3×C42—31no—
392#217—61no—
393#217—61no—
394#217—61no—
395#215—22no—
396#215—62no—
397#215—62no—
398#215—62no—
399#215—62no—
400#215—122no—
401#214—62no—
402#213—62no—
403#213—62no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4—61no—
408(C2×D3)⋊C4—61no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—121no—
423(C2×D3)⋊C4—121no—
424(C2×D3)⋊C4—121no—
425C4⋊Dic3C22×D311yescharacteristic
426Dic3⋊C4—21no—
427C4×Dic3—31no—
428C4×Dic3—31no—
429C4×Dic3—31no—
430C4×Dic3—31no—
431C4×Dic3—31no—
432C4×Dic3—31no—
433C4×Dic3—61no—
434C4×Dic3C22×D311yescharacteristic
435C2×C3⋊C8—31no—
436C2×C3⋊C8—31no—
437C2×C3⋊C8—61no—
438C2×C3⋊C8—62no—
439C2×C3⋊C8C22×D311yescharacteristic
440C2×C3⋊C8C22×D311yescharacteristic
441D24—22no—
442D24—62no—
443D24—62no—
444D24—62no—
445D24—62no—
446D24—122no—
447#204—62no—
448D3×C8—22no—
449D3×C8—62no—
450C22×C32C22×D411yescharacteristic
451C2×C3⋊D3—22no—
452C2×C3⋊D3—41no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3×D3—22no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3#12112yes—
464C2×C3×D3#13512yes—
465C2×C3×D3AGL(1,ℤ/8)12yes—
466D32—48no—
467D32—84no—
468C32×C4—41no—
469C32×C4—41no—
470C32×C4C22×D411yescharacteristic
471C32×C4C2×#4111yescharacteristic
472C3⋊Dic3—21no—
473C3⋊Dic3—21no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3#12112yes—
479C22×Q8—31no—
480C22×D4—91no—
481C22×D4—91no—
482C23×C4—181no—
483C2×SD16—31no—
484C2×SD16—91no—
485C2×SD16—91no—
486C2×SD16—91no—
487C2×SD16—184no—
488C2×D8—31no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—91no—
492C2×D8—184no—
493C22×C8—31no—
494C22×C8—91no—
495#124—31no—
496#124—91no—
497#124—91no—
498#124—91no—
499#124—181no—
500#124—181no—
501C4×D4—31no—
502C4×D4—91no—
503C4×D4—91no—
504C4×D4—91no—
505C4×D4—181no—
506C4×D4—181no—
507C2×C4⋊C4—31no—
508C2×C22⋊C4—181no—
509C2×C22⋊C4—181no—
510C2×C22⋊C4—181no—
511C2×C42—91no—
512C4⋊C8—31no—
513C4⋊C8—91no—
514C4⋊C8—91no—
515C4⋊C8—91no—
516#103—31no—
517#103—31no—
518#103—31no—
519#103D3211yescharacteristic, complemented
520#102—31no—
521#102—91no—
522#102—91no—
523#102—91no—
524C23×C3—31no—
525C23×C3—61no—
526C23×C3—61no—
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—64no—
530C22×D3—61no—
531C22×D3—61no—
532C22×D3—64no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—121no—
536C22×D3—121no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3D3×D411yescharacteristic
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—41no—
553C3×Q8—41no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×Q8—122no—
557C3×D4—32no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—61no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—31no—
567C2×C3×C4—32no—
568C2×C3×C4—32no—
569C2×C3×C4—31no—
570C2×C3×C4—31no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—122no—
576C2×C3×C4—122no—
577C2×C3×C4—122no—
578C2×C3×C4C23×D311yescharacteristic
579C2×C3×C4C23×D311yescharacteristic
580#67—64no—
581#67—122no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—31no—
585C2×Dic3—31no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—62no—
591C2×Dic3—62no—
592C2×Dic3—122no—
593C2×Dic3D3×D411yescharacteristic
594C2×Dic3D3×D411yescharacteristic
595C2×Dic3D3×D411yescharacteristic
596D12—21no—
597D12—21no—
598D12—21no—
599D12—32no—
600D12—32no—
601D12—62no—
602D12—64no—
603D12—61no—
604D12—61no—
605D12—61no—
606D12—61no—
607D12—61no—
608D12—61no—
609D12—121no—
610D12—121no—
611D12—121no—
612D12—122no—
613D12D3×D412yes—
614C4×D3—42no—
615C4×D3—42no—
616C4×D3—42no—
617C4×D3—62no—
618C4×D3—62no—
619C4×D3—122no—
620C4×D3—122no—
621C4×D3—122no—
622C4×D3—122no—
623C4×D3—122no—
624C4×D3—242no—
625C4×D3#23512yes—
626C4×D3D3×D412yes—
627Dic6—21no—
628Dic6—21no—
629Dic6—42no—
630C3×C8—21no—
631C3×C8—21no—
632C3×C8—41no—
633C3×C8—61no—
634C3×C8—61no—
635C3⋊C8—21no—
636C3⋊C8—21no—
637C3⋊C8—61no—
638C3⋊C8—61no—
639C3⋊C8—121no—
640C2×C32C2×#12111yescharacteristic
641C2×C32C2×#13511yescharacteristic
642C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
643C3⋊D3—42no—
644C3⋊D3—81no—
645C3×D3—42no—
646C3×D3—81no—
647C3×D3#46314yescomplemented
648C24—181no—
649C24—181no—
650C2×Q8—31no—
651C2×Q8—61no—
652C2×Q8—62no—
653C2×Q8—62no—
654C2×Q8C2×D3211yescharacteristic
655C2×D4—31no—
656C2×D4—31no—
657C2×D4—94no—
658C2×D4—91no—
659C2×D4—91no—
660C2×D4—182no—
661C2×D4—182no—
662C2×D4—182no—
663C2×D4—181no—
664C2×D4—181no—
665C22×C4—31no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—91no—
670C22×C4—91no—
671C22×C4—181no—
672C22×C4—181no—
673C22×C4—181no—
674C22×C4—364no—
675SD16—62no—
676SD16—182no—
677SD16—182no—
678SD16—182no—
679D8—62no—
680D8—182no—
681D8—182no—
682D8—182no—
683C2×C8—31no—
684C2×C8—31no—
685C2×C8—62no—
686C2×C8—91no—
687C2×C8—182no—
688C2×C8C2×D3211yescharacteristic
689C4⋊C4—31no—
690C4⋊C4—61no—
691C4⋊C4C2×D3211yescharacteristic
692C22⋊C4—61no—
693C22⋊C4—61no—
694C22⋊C4—61no—
695C22⋊C4—181no—
696C22⋊C4—181no—
697C22⋊C4—181no—
698C22⋊C4—181no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C42—31no—
705C42—91no—
706C42—91no—
707C42—91no—
708C22×C3—21no—
709C22×C3—32no—
710C22×C3—32no—
711C22×C3—32no—
712C22×C3—62no—
713C22×C3—121no—
714C22×C3—121no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3—121no—
718C22×C3C2×D3×D411yescharacteristic
719C22×C3C2×D3×D411yescharacteristic
720C2×D3—22no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—41no—
726C2×D3—62no—
727C2×D3—62no—
728C2×D3—122no—
729C2×D3—128no—
730C2×D3—121no—
731C2×D3—121no—
732C2×D3—121no—
733C2×D3—121no—
734C2×D3—128no—
735C2×D3—121no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—241no—
742C2×D3—241no—
743C2×D3—241no—
744C2×D3—241no—
745C2×D3—241no—
746C2×D3—244no—
747C2×D3—244no—
748C2×D3#88412yes—
749C2×D3#91412yes—
750C2×D3#91912yes—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—32no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—61no—
759C3×C4—61no—
760C3×C4—81no—
761C3×C4—81no—
762C3×C4—121no—
763C3×C4—121no—
764C3×C4C2×#23511yescharacteristic
765C3×C4C2×D3×D411yescharacteristic
766C3×C4C2×D3×D411yescharacteristic
767C3×C4D3×#4111yescharacteristic
768Dic3—21no—
769Dic3—21no—
770Dic3—41no—
771Dic3—41no—
772Dic3—61no—
773Dic3—61no—
774Dic3—61no—
775Dic3—61no—
776Dic3—121no—
777Dic3—121no—
778Dic3#88412yes—
779C32C2×#46311yescharacteristic, complemented, Sylow
780C23—31no—
781C23—61no—
782C23—61no—
783C23—184no—
784C23—181no—
785C23—181no—
786C23—362no—
787C23—362no—
788C23—362no—
789C23—362no—
790C23—362no—
791Q8—21no—
792Q8—21no—
793Q8—61no—
794Q8—61no—
795Q8—122no—
796D4—32no—
797D4—61no—
798D4—61no—
799D4—61no—
800D4—92no—
801D4—184no—
802D4—181no—
803D4—181no—
804D4—181no—
805D4—362no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—31no—
809C2×C4—32no—
810C2×C4—32no—
811C2×C4—31no—
812C2×C4—31no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—91no—
816C2×C4—91no—
817C2×C4—122no—
818C2×C4—122no—
819C2×C4—122no—
820C2×C4—182no—
821C2×C4—182no—
822C2×C4—362no—
823C2×C4—362no—
824C2×C4—362no—
825C2×C4C22×D3211yescharacteristic
826C8—21no—
827C8—61no—
828C8—61no—
829C8—181no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—34no—
834C2×C3—122no—
835C2×C3—241no—
836C2×C3C2×#88411yescharacteristic
837C2×C3D3×#12111yescharacteristic
838C2×C3C2×#91411yescharacteristic
839C2×C3C2×#91911yescharacteristic
840C2×C3D3×#13511yescharacteristic
841C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
842D3—42no—
843D3—81no—
844D3—122no—
845D3—122no—
846D3—242no—
847D3—241no—
848D3—241no—
849D3—481no—
850D3#481914yesdirect product factor
851C22—32no—
852C22—32no—
853C22—32no—
854C22—62no—
855C22—121no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—182no—
861C22—368no—
862C22—361no—
863C22—361no—
864C22—361no—
865C22—361no—
866C22—361no—
867C22—724no—
868C22D32×D411yescharacteristic
869C4—32no—
870C4—41no—
871C4—41no—
872C4—61no—
873C4—61no—
874C4—121no—
875C4—121no—
876C4—181no—
877C4—181no—
878C4D3×#23511yescharacteristic
879C4D32×D411yescharacteristic
880C3—21no—
881C3C2×#481911yescharacteristic, complemented
882C3D3×#46311yescharacteristic, complemented
883C2—34no—
884C2—122no—
885C2—241no—
886C2—362no—
887C2—721no—
888C2D3×#88411yescharacteristic
889C2D3×#91411yescharacteristic
890C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×D3×D24C2
hypercenter#103D32
hypocenterC32C2×#463
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. D3×#947C2semidirect
2. C2×D3×#215C2semidirect
4. D3×#893C2semidirect
5. #10592518C2semidirect
6. C3×#4819C2semidirect
7. C3×D3×#103C2semidirect
8. #10591570C2semidirect
9. #10591568C2semidirect
10. #10590770C2semidirect
11. #10590751C2semidirect
12. D3×Dic3⋊C8C2semidirect
13. D3×#809C2semidirect
14. #10590540C2semidirect
15. #10590534C2semidirect
22. #64156C22semidirect
23. C2×#3755C22semidirect
25. #64102C22semidirect
26. C3×#947C22semidirect
27. C2×C3×#215C22semidirect
30. C3×#893C22semidirect
39. #63898C22semidirect
40. #63894C22semidirect
43. #63864C22semidirect
44. #63863C22semidirect
45. C2×#3717C22semidirect
46. C2×#3715C22semidirect
51. C32×#103C22semidirect
52. #63641C22semidirect
53. #63636C22semidirect
54. C3×#835C22semidirect
55. C3×#816C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#809C22semidirect
59. #63572C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
90. #4819D3direct (N × H)
91. D3×#103D3semidirect
176. #947C2×D3semidirect
183. C2×#215C2×D3semidirect
214. #893C2×D3semidirect
230. C3×#103C2×D3semidirect
231. C3×#103C2×D3semidirect
233. #835C2×D3semidirect
236. #816C2×D3semidirect
243. Dic3⋊C8C2×D3semidirect
244. #810C2×D3semidirect
250. #809C2×D3semidirect
519. #103D32semidirect
647. C3×D3#463semidirect
779. C32C2×#463semidirect
850. D3#4819direct (N × H)
881. C3C2×#4819semidirect
882. C3D3×#463semidirect

Maximal subgroups

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

subgroupindex
D3×#9472
C2×D3×#2152
C2×D3×D242
D3×#8932
#105925182
C3×#48192
C3×D3×#1032
#105915702
#105915682
#105907702
#105907512
D3×Dic3⋊C82
D3×#8092
#105905402
#105905342
D3×#4633
C2×#48193