Finite Group Databasebeta

← D3×#5009 #11868345

Subgroups — D3×#5009 #11868345

Order 1152.

947 conjugacy classes of subgroups.

The subgroup lattice has 751 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×D4C211yesmaximal, characteristic
2D3×#870C211yesmaximal, characteristic, complemented
3#10592708C211yesmaximal, characteristic, complemented
4C3×#5009C211yesmaximal, characteristic, complemented
5D3×#832C211yesmaximal, characteristic
6D3×#832C211yesmaximal, characteristic
7#10591411C211yesmaximal, characteristic, complemented
8#10591409C211yesmaximal, characteristic, complemented
9D3×#808C211yesmaximal, characteristic, complemented
10D3×#807C211yesmaximal, characteristic, complemented
11#10590545C211yesmaximal, characteristic, complemented
12#10590542C211yesmaximal, characteristic, complemented
13D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
14#10590271C211yesmaximal, characteristic, complemented
15#10590270C211yesmaximal, characteristic, complemented
16C2×#5009—31nomaximal
17D3×#478—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C22×C3×C4×D3—21no—
20C32×C4×D4C2211yescharacteristic
21#64079C2211yescharacteristic, complemented
22C3×D4×Dic3C2211yescharacteristic
23C3×C4×#67—21no—
24C3×#893C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×#67⋊C4—21no—
27C3×D3×C22⋊C4—21no—
28C3×C4×D12C2211yescharacteristic
29C3×C42×D3C2211yescharacteristic
30C3×#870C2211yescharacteristic, complemented
31D3×C4⋊Dic3C2211yescharacteristic
32D3×C4⋊Dic3C2211yescharacteristic
33D3×Dic3⋊C4—21no—
34D3×Dic3⋊C4—21no—
35#63869C2211yescharacteristic, complemented
36#63869C2211yescharacteristic, complemented
37#63867—21no—
38#63867—21no—
39C2×D3×C3⋊C8C2211yescharacteristic
40C2×D3×C3⋊C8C2211yescharacteristic
41#63659C2211yescharacteristic
42#63659C2211yescharacteristic
43#63635C2211yescharacteristic, complemented
44#63634C2211yescharacteristic, complemented
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#808C2211yescharacteristic, complemented
49C3×#807C2211yescharacteristic, complemented
50C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61C2×C3×C4×D4—31no—
62D3×#125—31no—
63C4×D3×D4D311yescharacteristic
64C2×#870—31no—
65C3×#478—31no—
66C2×#832—31no—
67C2×#832—31no—
68#5066—31no—
69#5009—31no—
70#5009—31no—
71#5009—31no—
72#5009—31no—
73#5009—31no—
74#5009—31no—
75#5009—31no—
76#5009—31no—
77#5009—61no—
78#5009D311yescharacteristic, direct product factor
79C2×#808—31no—
80C2×#807—31no—
81C2×C4⋊(C3⋊C8)—31no—
82#4891—31no—
83D3×#107—31no—
84#4871—31no—
85D3×#106—31no—
86#4847—31no—
87D3×C4⋊C8—31no—
88D3×#102—31no—
89D3×#102—31no—
90#4766—31no—
91#4763—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C3×D3×D4—22no—
98C3×D3×D4Q814yes—
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—44no—
104C2×C3×C4×D3D411yescharacteristic
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111C32×C42C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3D411yescharacteristic
128C3×C4×Dic3D411yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132#3724—21no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138D3×C3⋊C8—22no—
139D3×C3⋊C8—22no—
140C2×#478—91noSylow
141C22×C3×D4—31no—
142C23×C3×C4—61no—
143C2×D3×D4C2×D311yescharacteristic
144C22×C4×D3—21no—
145C3×#125—31no—
146C3×C4×D4—21no—
147C3×C4×D4—31no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150C3×C4×D4—61no—
151C3×C4×D4—61no—
152C3×C4×D4C2×D311yescharacteristic
153C3×C4×D4C2×D311yescharacteristic
154C2×C3×C4⋊C4—31no—
155C2×C3×C22⋊C4—61no—
156C2×C3×C42—31no—
157D4×Dic3C2×D311yescharacteristic
158C4×#67—21no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—31no—
161C2×Dic3⋊C4—61no—
162C2×Dic3⋊C4—61no—
163C22×C3⋊C8—31no—
164C22×C3⋊C8—31no—
165C2×D3×C8—31no—
166C2×D3×C8—31no—
167#893C2×D311yescharacteristic
168D3×C4⋊C4—31no—
169D3×C4⋊C4—31no—
170D3×C4⋊C4—61no—
171D3×C4⋊C4—61no—
172D3×C4⋊C4C2×D311yescharacteristic
173#890—31no—
174#890—31no—
175#889—61no—
176#889—61no—
177#67⋊C4—21no—
178D3×C22⋊C4—21no—
179C4×D12C2×D311yescharacteristic
180C42×D3C2×D311yescharacteristic
181#870—31no—
182#870—31no—
183#870—31no—
184#870—31no—
185#870—61no—
186#870—61no—
187#870—61no—
188#870C2×D311yescharacteristic, complemented
189C3×#107—31no—
190C3×#106—31no—
191C3×C4⋊C8—31no—
192C3×#102—31no—
193C3×#102—31no—
194#832—31no—
195#832—31no—
196#832—31no—
197#832—31no—
198#832—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—61no—
203#832—61no—
204#832C2×D311yescharacteristic
205#832C2×D311yescharacteristic
206#821—31no—
207#821—31no—
208#818—31no—
209#817—31no—
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212#809—31no—
213#809—31no—
214#808—31no—
215#808—31no—
216#808—31no—
217#808—31no—
218#808—31no—
219#808—61no—
220#808C2×D311yescharacteristic, complemented
221#807—31no—
222#807—31no—
223#807—31no—
224#807—31no—
225#807—31no—
226#807—61no—
227#807C2×D311yescharacteristic, complemented
228C4⋊(C3⋊C8)—31no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—61no—
233C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
234C23×C32—21no—
235C22×C3×D3—21no—
236C22×C3×D3—24no—
237C22×C3×D3—42no—
238C22×C3×D3—42no—
239C22×C3×D3C2×D411yescharacteristic
240C32×D4—21no—
241C32×D4C2×Q812yes—
242C2×C32×C4—21no—
243C2×C32×C4—42no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C3×#67—24no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—42no—
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—21no—
258C3×D12C2×Q812yes—
259C3×C4×D3—22no—
260C3×C4×D3—22no—
261C3×C4×D3—42no—
262C3×C4×D3—42no—
263C3×C4×D3—42no—
264C3×C4×D3C2×Q812yes—
265C3×C4×D3#4112yes—
266D3×Dic3—42no—
267D3×Dic3—42no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272C2×#125—91no—
273C2×C4×D4—31no—
274#478—31no—
275#478—91no—
276#478—91no—
277#478—91no—
278#478—91no—
279#478—91no—
280#478—91no—
281#478—91no—
282C2×#107—91no—
283C2×#106—91no—
284C2×C4⋊C8—91no—
285C2×#102—91no—
286C2×#102—91no—
287C24×C3—61no—
288C23×D3—21no—
289C2×C3×D4—21no—
290C2×C3×D4—34no—
291C2×C3×D4—31no—
292C2×C3×D4—62no—
293C2×C3×D4—61no—
294C2×C3×D4C22×D311yescharacteristic
295C2×C3×D4C22×D311yescharacteristic
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—41no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4—124no—
307C2×#67—21no—
308C22×Dic3—21no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311D3×D4—22no—
312D3×D4Dic614yes—
313C2×D12C22×D311yescharacteristic
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—44no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3#6711yescharacteristic
321C2×C4×D3#6711yescharacteristic
322C2×C4×D3C22×D311yescharacteristic
323C2×C3×C8—31no—
324C2×C3×C8—31no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4C22×D311yescharacteristic
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C22⋊C4—21no—
335C3×C22⋊C4—21no—
336C3×C22⋊C4—41no—
337C3×C22⋊C4—61no—
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C42—21no—
341C3×C42—31no—
342C3×C42—31no—
343C3×C42—31no—
344C3×C42C22×D311yescharacteristic
345C3×C42C22×D311yescharacteristic
346#217—21no—
347(C2×D3)⋊C4—21no—
348(C2×D3)⋊C4—21no—
349C4⋊Dic3—31no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3—61no—
357C4⋊Dic3—61no—
358C4⋊Dic3—61no—
359C4⋊Dic3C22×D311yescharacteristic
360C4⋊Dic3C22×D311yescharacteristic
361C4⋊Dic3C22×D311yescharacteristic
362Dic3⋊C4—21no—
363Dic3⋊C4—21no—
364Dic3⋊C4—21no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—121no—
378Dic3⋊C4—121no—
379C4×Dic3#6711yescharacteristic
380C4×Dic3#6711yescharacteristic
381C4×Dic3C22×D311yescharacteristic
382C2×C3⋊C8—31no—
383C2×C3⋊C8—31no—
384C2×C3⋊C8—31no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—61no—
387C2×C3⋊C8—61no—
388C2×C3⋊C8—62no—
389C2×C3⋊C8—62no—
390C2×C3⋊C8C22×D311yescharacteristic
391C2×C3⋊C8C22×D311yescharacteristic
392D3×C8—62no—
393D3×C8—62no—
394C22×C32—22no—
395C22×C32—41no—
396C22×C32—41no—
397C22×C32C22×D411yescharacteristic
398C2×C3×D3—22no—
399C2×C3×D3—41no—
400C2×C3×D3—41no—
401C2×C3×D3—48no—
402C2×C3×D3C22⋊Q812yes—
403C2×C3×D3#13512yes—
404C2×C3×D3AGL(1,ℤ/8)12yes—
405C32×C4—21no—
406C32×C4—21no—
407C32×C4—41no—
408C32×C4C22×Q811yescharacteristic
409C32×C4C2×#4111yescharacteristic
410C3⋊Dic3—41no—
411C3⋊Dic3—41no—
412C3×Dic3—21no—
413C3×Dic3—21no—
414C3×Dic3—41no—
415C3×Dic3—41no—
416C3×Dic3—41no—
417C3×Dic3C22⋊Q812yes—
418C22×D4—31no—
419C23×C4—61no—
420C22×C8—91no—
421C22×C8—91no—
422#125—31no—
423#125—91no—
424#125—91no—
425#125—91no—
426#125—181no—
427#125—181no—
428C4×D4—31no—
429C4×D4—31no—
430C4×D4—31no—
431C4×D4—61no—
432C4×D4—61no—
433C4×D4D3211yescharacteristic
434C2×C4⋊C4—31no—
435C2×C4⋊C4—91no—
436C2×C4⋊C4—91no—
437C2×C4⋊C4—181no—
438C2×C4⋊C4—181no—
439C2×C22⋊C4—61no—
440C2×C42—31no—
441#107—31no—
442#107—91no—
443#107—91no—
444#107—91no—
445#106—31no—
446#106—91no—
447#106—91no—
448#106—91no—
449C4⋊C8—31no—
450C4⋊C8—91no—
451C4⋊C8—91no—
452C4⋊C8—91no—
453#102—31no—
454#102—31no—
455#102—91no—
456#102—91no—
457#102—91no—
458#102—91no—
459#102—91no—
460#102—91no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—31no—
464C23×C3—41no—
465C23×C3—64no—
466C23×C3—61no—
467C23×C3—122no—
468C23×C3—122no—
469C22×D3—21no—
470C22×D3—24no—
471C22×D3—42no—
472C22×D3—42no—
473C22×D3C2×#6711yescharacteristic
474C3×D4—21no—
475C3×D4—21no—
476C3×D4—22no—
477C3×D4—32no—
478C3×D4—41no—
479C3×D4—64no—
480C3×D4—61no—
481C3×D4C2×Dic612yes—
482C3×D4D3×Q812yes—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—31no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—41no—
494C2×C3×C4—42no—
495C2×C3×C4—42no—
496C2×C3×C4—62no—
497C2×C3×C4—62no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—82no—
502C2×C3×C4—122no—
503C2×C3×C4—122no—
504C2×C3×C4—122no—
505C2×C3×C4—122no—
506C2×C3×C4D3×D411yescharacteristic
507C2×C3×C4D3×D411yescharacteristic
508C2×C3×C4C2×#6711yescharacteristic
509C2×C3×C4C2×#6711yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—24no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—42no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—121no—
522C2×Dic3—121no—
523C2×Dic3—122no—
524C2×Dic3—122no—
525C2×Dic3C2×#6711yescharacteristic
526C2×Dic3C2×#6711yescharacteristic
527C2×Dic3C2×#6711yescharacteristic
528D12—21no—
529D12C2×Dic612yes—
530C4×D3—22no—
531C4×D3—22no—
532C4×D3—42no—
533C4×D3—42no—
534C4×D3—42no—
535C4×D3—122no—
536C4×D3—122no—
537C4×D3C2×Dic612yes—
538C4×D3#23512yes—
539C3×C8—61no—
540C3×C8—61no—
541C3⋊C8—21no—
542C3⋊C8—21no—
543C3⋊C8—61no—
544C3⋊C8—61no—
545C3⋊C8—61no—
546C3⋊C8—61no—
547C3⋊C8—121no—
548C3⋊C8—121no—
549C2×C32—42no—
550C2×C32C2×C22⋊Q811yescharacteristic
551C2×C32C2×#13511yescharacteristic
552C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
553C3×D3—42no—
554C3×D3#47814yescomplemented
555C24—61no—
556C2×D4—34no—
557C2×D4—31no—
558C2×D4—62no—
559C2×D4—61no—
560C2×D4C2×D3211yescharacteristic
561C22×C4—21no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—124no—
570C22×C4—181no—
571C22×C4—181no—
572C2×C8—31no—
573C2×C8—31no—
574C2×C8—91no—
575C2×C8—91no—
576C2×C8—182no—
577C2×C8—182no—
578C4⋊C4—31no—
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—91no—
585C4⋊C4—91no—
586C4⋊C4—181no—
587C4⋊C4—181no—
588C4⋊C4—181no—
589C4⋊C4—181no—
590C4⋊C4—181no—
591C4⋊C4—181no—
592C4⋊C4—181no—
593C4⋊C4—181no—
594C4⋊C4C2×D3211yescharacteristic
595C22⋊C4—21no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C22⋊C4—61no—
599C42—31no—
600C42—31no—
601C42—31no—
602C42C2×D3211yescharacteristic
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—21no—
606C22×C3—32no—
607C22×C3—32no—
608C22×C3—32no—
609C22×C3—42no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—62no—
615C22×C3—81no—
616C22×C3—81no—
617C22×C3—128no—
618C22×C3—121no—
619C22×C3—121no—
620C22×C3C2×D3×D411yescharacteristic
621C22×C3C22×#6711yescharacteristic
622C2×D3—22no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—48no—
626C2×D3#92412yes—
627C2×D3#93212yes—
628C2×D3#95012yes—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—32no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—61no—
641C3×C4—61no—
642C3×C4—81no—
643C3×C4—121no—
644C3×C4—121no—
645C3×C4—121no—
646C3×C4C22×Dic611yescharacteristic
647C3×C4C2×#23511yescharacteristic
648C3×C4C2×D3×Q811yescharacteristic
649C3×C4D3×#4111yescharacteristic
650Dic3—21no—
651Dic3—21no—
652Dic3—41no—
653Dic3—41no—
654Dic3—41no—
655Dic3—121no—
656Dic3—121no—
657Dic3—121no—
658Dic3—121no—
659Dic3—241no—
660Dic3—241no—
661Dic3#92412yes—
662C32C2×#47811yescharacteristic, complemented, Sylow
663C23—21no—
664C23—31no—
665C23—64no—
666C23—61no—
667C23—122no—
668C23—122no—
669D4—21no—
670D4—32no—
671D4—64no—
672D4—61no—
673D4D3×Dic612yes—
674C2×C4—21no—
675C2×C4—31no—
676C2×C4—32no—
677C2×C4—32no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—42no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—122no—
687C2×C4—122no—
688C2×C4—122no—
689C2×C4—122no—
690C2×C4—181no—
691C2×C4—181no—
692C2×C4—362no—
693C2×C4—362no—
694C2×C4D3×#6711yescharacteristic
695C2×C4D3×#6711yescharacteristic
696C2×C4C22×D3211yescharacteristic
697C8—61no—
698C8—61no—
699C8—181no—
700C8—181no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—34no—
705C2×C3—42no—
706C2×C3—42no—
707C2×C3—82no—
708C2×C3—122no—
709C2×C3D3×C22⋊Q811yescharacteristic
710C2×C3D3×#13511yescharacteristic
711C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
712C2×C3C2×#92411yescharacteristic
713C2×C3C2×#93211yescharacteristic
714C2×C3C2×#95011yescharacteristic
715D3—42no—
716D3#500914yesdirect product factor
717C22—22no—
718C22—32no—
719C22—32no—
720C22—32no—
721C22—41no—
722C22—41no—
723C22—62no—
724C22—128no—
725C22—121no—
726C22—121no—
727C22C2×D3×#6711yescharacteristic
728C4—21no—
729C4—21no—
730C4—32no—
731C4—41no—
732C4—61no—
733C4—61no—
734C4—121no—
735C4—121no—
736C4—121no—
737C4—361no—
738C4—361no—
739C4C2×D3×Dic611yescharacteristic
740C4D3×#23511yescharacteristic
741C3—21no—
742C3D3×#47811yescharacteristic, complemented
743C3C2×#500911yescharacteristic, complemented
744C2—34no—
745C2—42no—
746C2—122no—
747C2D3×#92411yescharacteristic
748C2D3×#93211yescharacteristic
749C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenterC4×D4D32
hypocenterC32C2×#478
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. D3×#870C2semidirect
3. #10592708C2semidirect
4. C3×#5009C2semidirect
7. #10591411C2semidirect
8. #10591409C2semidirect
9. D3×#808C2semidirect
10. D3×#807C2semidirect
11. #10590545C2semidirect
12. #10590542C2semidirect
13. D3×C4⋊(C3⋊C8)C2semidirect
14. #10590271C2semidirect
15. #10590270C2semidirect
21. #64079C22semidirect
30. C3×#870C22semidirect
35. #63869C22semidirect
36. #63869C22semidirect
43. #63635C22semidirect
44. #63634C22semidirect
45. C4⋊(C3⋊(C3⋊C8))C22semidirect
48. C3×#808C22semidirect
49. C3×#807C22semidirect
50. C3×C4⋊(C3⋊C8)C22semidirect
51. #63576C22semidirect
52. #63575C22semidirect
53. #63574C22semidirect
54. #63573C22semidirect
55. Dic3⋊(C3⋊C8)C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
78. #5009D3direct (N × H)
188. #870C2×D3semidirect
220. #808C2×D3semidirect
227. #807C2×D3semidirect
233. C4⋊(C3⋊C8)C2×D3semidirect
554. C3×D3#478semidirect
662. C32C2×#478semidirect
716. D3#5009direct (N × H)
742. C3D3×#478semidirect
743. C3C2×#5009semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×D42
D3×#8702
#105927082
C3×#50092
D3×#8322
#105914112
#105914092
D3×#8082
D3×#8072
#105905452
#105905422
D3×C4⋊(C3⋊C8)2
#105902712
#105902702
C2×#50093
D3×#4783