Finite Group Databasebeta

← D3×#4787 #11865563

Subgroups — D3×#4787 #11865563

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×#936C211yesmaximal, characteristic, complemented
2C2×D3×#213C211yesmaximal, characteristic
3C2×D3×#204C211yesmaximal, characteristic, complemented
4D3×#893C211yesmaximal, characteristic, complemented
5#10592486C211yesmaximal, characteristic, complemented
6C3×#4787C211yesmaximal, characteristic, complemented
7C3×D3×#102C211yesmaximal, characteristic, complemented
8#10591434C211yesmaximal, characteristic, complemented
9#10591432C211yesmaximal, characteristic, complemented
10#10590860C211yesmaximal, characteristic, complemented
11#10590750C211yesmaximal, characteristic, complemented
12D3×Dic3⋊C8C211yesmaximal, characteristic, complemented
13D3×#810C211yesmaximal, characteristic, complemented
14#10590540C211yesmaximal, characteristic, complemented
15#10590530C211yesmaximal, characteristic, complemented
16D3×#463—31nomaximal
17C2×#4787—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×C4×D32—21no—
21C2×D3×Dic6C2211yescharacteristic
22#64145C2211yescharacteristic, complemented
23C2×#3753C2211yescharacteristic
24C2×#3744C2211yescharacteristic, complemented
25#64102C2211yescharacteristic, complemented
26C3×#936C2211yescharacteristic, complemented
27C2×C3×#213C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic, complemented
29C2×C3×D3×C8C2211yescharacteristic
30C3×#893C2211yescharacteristic, complemented
31C3×D3×C4⋊C4C2211yescharacteristic
32D3×#217—21no—
33D3×#217—21no—
34#63959—21no—
35#63959—21no—
36D3×#213—24no—
37D3×(C2×D3)⋊C4—21no—
38#63904—21no—
39#63898C2211yescharacteristic, complemented
40#63894C2211yescharacteristic, complemented
41#63881—21no—
42C4×D3×Dic3C2211yescharacteristic
43#63863C2211yescharacteristic, complemented
44#63860C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic, complemented
46C2×#3716C2211yescharacteristic, complemented
47C2×#3714C2211yescharacteristic
48C2×#3713C2211yescharacteristic
49C2×D3×C3⋊C8C2211yescharacteristic
50D3×#204—24no—
51C32×#102C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63572C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63565C2211yescharacteristic, complemented
63C2×#936—31no—
64C22×#213—31no—
65C2×D3×SD16—31no—
66C2×D3×D8—31no—
67C22×#204—31no—
68D3×#124—31no—
69C4×D3×D4—31no—
70C2×#893—31no—
71C3×#463—31no—
72C2×C3×#102—31no—
73#5165—31no—
74#5153—31no—
75C2×Dic3⋊C8—31no—
76#5057—31no—
77#5016—31no—
78C2×#810—31no—
79#4844—31no—
80D3×C4⋊C8—31no—
81#4819—31no—
82D3×#103—31no—
83#4787—31no—
84#4787—31no—
85#4787—31no—
86#4787—31no—
87#4787—31no—
88#4787—31no—
89#4787—31no—
90#4787—31no—
91#4787—61no—
92#4787D311yescharacteristic, direct product factor
93D3×#102D311yescharacteristic, complemented
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C3×D3×D4—22no—
102C3×D3×D4—22no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110C2×#626—21no—
111C2×#624—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114C2×D3×Dic3D411yescharacteristic
115C2×D3×Dic3D411yescharacteristic
116D3×D12—22no—
117D3×D12D414yes—
118C4×D32—44no—
119D3×Dic6—22no—
120D3×Dic6—22no—
121C2×C32×C8C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3757—21no—
124#3757—21no—
125#3753—22no—
126#3752—21no—
127C4×C3⋊Dic3C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129#3744—22no—
130C3×#217—21no—
131C3×#217—21no—
132C3×#213—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×#204—22no—
140C3×D3×C8—22no—
141#3722—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147Dic32D411yescharacteristic
148Dic32D411yescharacteristic
149#3717—22no—
150#3716—22no—
151#3714—22no—
152#3713—22no—
153D3×C3⋊C8—22no—
154C2×#463—91noSylow
155C22×C3×D4—31no—
156C2×D3×Q8—31no—
157C2×D3×D4—31no—
158C2×D3×D4C2×D311yescharacteristic
159C22×D12—31no—
160C22×C4×D3—61no—
161C22×C4×D3—61no—
162C22×Dic6—31no—
163C2×C3×SD16—31no—
164C2×C3×D8—31no—
165C22×C3×C8—31no—
166C3×#124—31no—
167C3×C4×D4—31no—
168C2×C3×C4⋊C4—31no—
169C2×#217—61no—
170C2×#217—61no—
171#947—31no—
172C2×#215—31no—
173#936—31no—
174#936—31no—
175#936—31no—
176#936—31no—
177#936—61no—
178#936—61no—
179#936—61no—
180#936C2×D311yescharacteristic, complemented
181D4×Dic3—31no—
182C2×#214—31no—
183C2×#213—31no—
184C2×#213—31no—
185C2×#213—31no—
186C2×#213—31no—
187C2×#213—31no—
188C2×#213—61no—
189C2×#213—64no—
190C2×#213C2×D311yescharacteristic
191C4×#67—61no—
192C2×(C2×D3)⋊C4—61no—
193C2×C4×Dic3—31no—
194C22×C3⋊C8—31no—
195D3×SD16—64no—
196D3×D8—64no—
197C2×D24—31no—
198C2×#204—31no—
199C2×#204—31no—
200C2×#204—31no—
201C2×#204—31no—
202C2×#204—61no—
203C2×#204—64no—
204C2×#204C2×D311yescharacteristic, complemented
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—31no—
227C3×#102—21no—
228C3×#102—31no—
229C3×#102—31no—
230C3×#102—31no—
231C3×#102C2×D311yescharacteristic, complemented
232C3×#102C2×D311yescharacteristic, complemented
233#835—31no—
234#832C2×D311yescharacteristic, complemented
235#821C2×D311yescharacteristic, complemented
236#816—31no—
237Dic3⋊C8—31no—
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—61no—
243Dic3⋊C8C2×D311yescharacteristic, complemented
244#810—31no—
245#810—31no—
246#810—31no—
247#810—31no—
248#810—61no—
249#810C2×D311yescharacteristic, complemented
250#809C2×D311yescharacteristic, complemented
251C4⋊(C3⋊C8)—31no—
252C23×C32—21no—
253C22×C3⋊D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—42no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—24no—
261C2×D32—42no—
262C2×D32—42no—
263C32×D4—21no—
264C32×D4—21no—
265C2×C32×C4—21no—
266C2×C32×C4C2411yescharacteristic
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3C2×D411yescharacteristic
269C2×C3⋊Dic3C2×D411yescharacteristic
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)C2×D412yes—
272C4×C3⋊D3—42no—
273#634—21no—
274#634—21no—
275C3×#67—42no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12C2×D412yes—
285C3×C4×D3—42no—
286C3×C4×D3—42no—
287C3×C4×D3C2×D412yes—
288C3×C4×D3#4112yes—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#627—42no—
292#626—24no—
293#624—42no—
294D3×Dic3—22no—
295D3×Dic3—22no—
296D3×Dic3—42no—
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—91no—
316C2×#102—31no—
317C24×C3—61no—
318C23×D3—21no—
319C23×D3—61no—
320C23×D3—61no—
321C2×C3×Q8—31no—
322C2×C3×D4—21no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—62no—
326C2×C3×D4—62no—
327C2×C3×D4—61no—
328C2×C3×D4C22×D311yescharacteristic
329C2×C3×D4C22×D311yescharacteristic
330C22×C3×C4—31no—
331C22×C3×C4—61no—
332C22×C3×C4—61no—
333C2×#67—21no—
334C2×#67—61no—
335C22×Dic3—31no—
336C22×Dic3—31no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339D3×Q8—62no—
340D3×Q8—62no—
341D3×D4—22no—
342D3×D4—22no—
343D3×D4—34no—
344D3×D4—62no—
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—34no—
348C2×D12—61no—
349C2×D12—62no—
350C2×D12—61no—
351C2×D12C22×D311yescharacteristic
352C2×D12C22×D311yescharacteristic
353C2×C4×D3—21no—
354C2×C4×D3—21no—
355C2×C4×D3—31no—
356C2×C4×D3—31no—
357C2×C4×D3—61no—
358C2×C4×D3—61no—
359C2×C4×D3—61no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—121no—
364C2×C4×D3—124no—
365C2×C4×D3—124no—
366C2×C4×D3C22×D311yescharacteristic
367C2×Dic6—31no—
368C2×Dic6—31no—
369C2×Dic6—61no—
370C2×Dic6—62no—
371C2×Dic6—62no—
372C2×Dic6—61no—
373C2×Dic6—61no—
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—21no—
393#217—21no—
394#217—61no—
395#217—61no—
396#217—61no—
397#217—61no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—121no—
404#217—121no—
405#215—62no—
406#214—62no—
407#213—22no—
408#213—62no—
409#213—62no—
410#213—62no—
411#213—62no—
412#213—62no—
413#213—122no—
414(C2×D3)⋊C4—21no—
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—61no—
423(C2×D3)⋊C4—61no—
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—62no—
442#204—22no—
443#204—62no—
444#204—62no—
445#204—62no—
446#204—62no—
447#204—122no—
448D3×C8—22no—
449D3×C8—62no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32C22×D411yescharacteristic
454C2×C3⋊D3—22no—
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—84no—
464C2×C3×D3#12112yes—
465C2×C3×D3#13512yes—
466C2×C3×D3AGL(1,ℤ/8)12yes—
467D32—48no—
468C32×C4—41no—
469C32×C4C22×D411yescharacteristic
470C32×C4C2×#4111yescharacteristic
471C3⋊Dic3—21no—
472C3⋊Dic3—21no—
473C3⋊Dic3—41no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3#12112yes—
479C22×Q8—91no—
480C22×D4—31no—
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—91no—
518#103—91no—
519#103—91no—
520#102—31no—
521#102—31no—
522#102—31no—
523#102D3211yescharacteristic, complemented
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—31no—
527C23×C3—41no—
528C23×C3—61no—
529C23×C3—61no—
530C23×C3—122no—
531C23×C3—122no—
532C23×C3—122no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—42no—
536C22×D3—42no—
537C22×D3—42no—
538C22×D3—64no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—64no—
542C22×D3—121no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3D3×D411yescharacteristic
548C3×Q8—61no—
549C3×Q8—61no—
550C3×D4—21no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—32no—
555C3×D4—41no—
556C3×D4—41no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—122no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—31no—
565C2×C3×C4—32no—
566C2×C3×C4—32no—
567C2×C3×C4—31no—
568C2×C3×C4—31no—
569C2×C3×C4—41no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—122no—
573C2×C3×C4—122no—
574C2×C3×C4C23×D311yescharacteristic
575C2×C3×C4C23×D311yescharacteristic
576#67—42no—
577#67—64no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—31no—
581C2×Dic3—31no—
582C2×Dic3—31no—
583C2×Dic3—31no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—62no—
587C2×Dic3—62no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—121no—
591C2×Dic3—122no—
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—121no—
606D12D3×D412yes—
607C4×D3—42no—
608C4×D3—42no—
609C4×D3—62no—
610C4×D3—62no—
611C4×D3—122no—
612C4×D3—122no—
613C4×D3—122no—
614C4×D3—122no—
615C4×D3—122no—
616C4×D3—122no—
617C4×D3—242no—
618C4×D3#23512yes—
619C4×D3D3×D412yes—
620Dic6—21no—
621Dic6—21no—
622Dic6—61no—
623Dic6—61no—
624Dic6—61no—
625Dic6—61no—
626Dic6—121no—
627Dic6—121no—
628Dic6—122no—
629Dic6—122no—
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×C32—81no—
641C2×C32C2×#12111yescharacteristic
642C2×C32C2×#13511yescharacteristic
643C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
644C3⋊D3—42no—
645C3×D3—42no—
646C3×D3—81no—
647C3×D3#46314yescomplemented
648C24—61no—
649C24—181no—
650C2×Q8—31no—
651C2×Q8—91no—
652C2×Q8—181no—
653C2×Q8—182no—
654C2×Q8—182no—
655C2×D4—31no—
656C2×D4—31no—
657C2×D4—62no—
658C2×D4—62no—
659C2×D4—61no—
660C2×D4—94no—
661C2×D4—91no—
662C2×D4—182no—
663C2×D4—181no—
664C2×D4C2×D3211yescharacteristic
665C22×C4—31no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—91no—
669C22×C4—91no—
670C22×C4—181no—
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—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—62no—
719C22×C3—81no—
720C22×C3—81no—
721C22×C3—81no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—244no—
728C22×C3C2×D3×D411yescharacteristic
729C22×C3C2×D3×D411yescharacteristic
730C2×D3—22no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—62no—
737C2×D3—62no—
738C2×D3—84no—
739C2×D3—122no—
740C2×D3—128no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—128no—
746C2×D3—241no—
747C2×D3—241no—
748C2×D3#88412yes—
749C2×D3#91112yes—
750C2×D3#91612yes—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—32no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4—61no—
757C3×C4—61no—
758C3×C4—81no—
759C3×C4—121no—
760C3×C4—121no—
761C3×C4C2×#23511yescharacteristic
762C3×C4C2×D3×D411yescharacteristic
763C3×C4C2×D3×D411yescharacteristic
764C3×C4D3×#4111yescharacteristic
765Dic3—21no—
766Dic3—21no—
767Dic3—41no—
768Dic3—41no—
769Dic3—61no—
770Dic3—61no—
771Dic3—61no—
772Dic3—61no—
773Dic3—121no—
774Dic3—121no—
775Dic3—121no—
776Dic3—121no—
777Dic3—241no—
778Dic3#88412yes—
779C32C2×#46311yescharacteristic, complemented, Sylow
780C23—21no—
781C23—31no—
782C23—61no—
783C23—61no—
784C23—122no—
785C23—122no—
786C23—122no—
787C23—184no—
788C23—181no—
789C23—362no—
790C23—362no—
791Q8—61no—
792Q8—61no—
793Q8—181no—
794Q8—181no—
795Q8—362no—
796D4—21no—
797D4—21no—
798D4—32no—
799D4—61no—
800D4—61no—
801D4—61no—
802D4—92no—
803D4—122no—
804D4—184no—
805D4—181no—
806C2×C4—21no—
807C2×C4—31no—
808C2×C4—32no—
809C2×C4—32no—
810C2×C4—31no—
811C2×C4—31no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—91no—
815C2×C4—91no—
816C2×C4—122no—
817C2×C4—122no—
818C2×C4—182no—
819C2×C4—182no—
820C2×C4—181no—
821C2×C4—362no—
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—81no—
835C2×C3—81no—
836C2×C3—122no—
837C2×C3—161no—
838C2×C3—241no—
839C2×C3C2×#88411yescharacteristic
840C2×C3D3×#12111yescharacteristic
841C2×C3C2×#91111yescharacteristic
842C2×C3C2×#91611yescharacteristic
843C2×C3D3×#13511yescharacteristic
844C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
845D3—42no—
846D3—81no—
847D3—122no—
848D3—122no—
849D3—242no—
850D3#478714yesdirect product factor
851C22—32no—
852C22—32no—
853C22—32no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—62no—
858C22—121no—
859C22—121no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—182no—
864C22—244no—
865C22—368no—
866C22—361no—
867C22—361no—
868C22D32×D411yescharacteristic
869C4—32no—
870C4—41no—
871C4—61no—
872C4—61no—
873C4—121no—
874C4—121no—
875C4—181no—
876C4—181no—
877C4—361no—
878C4D3×#23511yescharacteristic
879C4D32×D411yescharacteristic
880C3—21no—
881C3C2×#478711yescharacteristic, complemented
882C3D3×#46311yescharacteristic, complemented
883C2—34no—
884C2—81no—
885C2—122no—
886C2—241no—
887C2—362no—
888C2D3×#88411yescharacteristic
889C2D3×#91111yescharacteristic
890C2D3×#91611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×D3×#213C2
hypercenter#102D32
hypocenterC32C2×#463
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. D3×#936C2semidirect
3. C2×D3×#204C2semidirect
4. D3×#893C2semidirect
5. #10592486C2semidirect
6. C3×#4787C2semidirect
7. C3×D3×#102C2semidirect
8. #10591434C2semidirect
9. #10591432C2semidirect
10. #10590860C2semidirect
11. #10590750C2semidirect
12. D3×Dic3⋊C8C2semidirect
13. D3×#810C2semidirect
14. #10590540C2semidirect
15. #10590530C2semidirect
22. #64145C22semidirect
24. C2×#3744C22semidirect
25. #64102C22semidirect
26. C3×#936C22semidirect
28. C2×C3×#204C22semidirect
30. C3×#893C22semidirect
39. #63898C22semidirect
40. #63894C22semidirect
43. #63863C22semidirect
44. #63860C22semidirect
45. C2×#3717C22semidirect
46. C2×#3716C22semidirect
51. C32×#102C22semidirect
52. #63641C22semidirect
53. #63637C22semidirect
54. C3×#832C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#809C22semidirect
59. #63572C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63567C22semidirect
62. #63565C22semidirect
92. #4787D3direct (N × H)
93. D3×#102D3semidirect
180. #936C2×D3semidirect
204. C2×#204C2×D3semidirect
214. #893C2×D3semidirect
231. C3×#102C2×D3semidirect
232. C3×#102C2×D3semidirect
234. #832C2×D3semidirect
235. #821C2×D3semidirect
243. Dic3⋊C8C2×D3semidirect
249. #810C2×D3semidirect
250. #809C2×D3semidirect
523. #102D32semidirect
647. C3×D3#463semidirect
779. C32C2×#463semidirect
850. D3#4787direct (N × H)
881. C3C2×#4787semidirect
882. C3D3×#463semidirect

Maximal subgroups

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

subgroupindex
D3×#9362
C2×D3×#2132
C2×D3×#2042
D3×#8932
#105924862
C3×#47872
C3×D3×#1022
#105914342
#105914322
#105908602
#105907502
D3×Dic3⋊C82
D3×#8102
#105905402
#105905302
D3×#4633
C2×#47873