Finite Group Databasebeta

← D3×#1548 #10763525

Subgroups — D3×#1548 #10763525

Order 768.

1246 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊Q8C211yesmaximal, characteristic
2D3×#431C211yesmaximal, characteristic
3D3×#423C211yesmaximal, characteristic
4C3×#1548C211yesmaximal, characteristic, complemented
5#71774C211yesmaximal, characteristic, complemented
6#70779C211yesmaximal, characteristic, complemented
7#70507C211yesmaximal, characteristic, complemented
8#68483C214yesmaximal, complemented
9D3×#333C214yesmaximal, complemented
10C2×#1548—31nomaximal, Sylow
11C22×D3×Q8C412yes—
12C2×C3×C4⋊Q8C2211yescharacteristic
13C2×#944C412yes—
14C2×D3×M16—21no—
15D3×C4⋊Q8—21no—
16D3×C4⋊Q8—21no—
17D3×C4⋊Q8—21no—
18D3×C4⋊Q8—21no—
19D3×C4⋊Q8C412yes—
20D3×C4⋊Q8C412yes—
21D3×C4⋊Q8C2212yes—
22D3×C4⋊Q8C2212yes—
23C2×D3×C4⋊C4—21no—
24C2×D3×C4⋊C4—21no—
25C2×#888—21no—
26C2×#888—21no—
27C2×C42×D3C2211yescharacteristic
28C2×#869C2211yescharacteristic
29C3×#431C2211yescharacteristic
30C3×#423C2211yescharacteristic
31#5118—21no—
32#4925C2211yescharacteristic
33#4924C2211yescharacteristic
34#4837—21no—
35#4837C2212yes—
36#4833C2212yes—
37D3×C4⋊C8—21no—
38D3×C4⋊C8C2212yes—
39D3×C4⋊C8C2212yes—
40D3×C22⋊C8—21no—
41#4718—21no—
42#4685—21no—
43C4×D3×C8—21no—
44C3×#333C2214yescomplemented
45#4546C2214yescomplemented
46#4481C2214yescomplemented
47#4481C2214yescomplemented
48C22×C4⋊Q8—31no—
49C2×#431—31no—
50C2×#423—31no—
51#1548—31no—
52#1548—31no—
53#1548—34no—
54#1548—31no—
55#1548D311yescharacteristic, direct product factor
56C2×#333—34no—
57C22×C3×Q8C2×C412yes—
58C2×D3×Q8—22no—
59C2×D3×Q8—22no—
60C2×D3×Q8—48no—
61C2×D3×Q8C2×C414yes—
62C2×D3×Q8C2×C414yes—
63C22×C4×D3—22no—
64C22×C4×D3C2×C411yescharacteristic
65C22×C4×D3D411yescharacteristic
66C22×C4×D3D411yescharacteristic
67C22×Dic6—22no—
68C22×Dic6C2×C412yes—
69C2×C3×M16—21no—
70C3×C4⋊Q8—21no—
71C3×C4⋊Q8—21no—
72C3×C4⋊Q8C2×C412yes—
73C3×C4⋊Q8C2312yes—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4—21no—
76C2×C3×C42C2311yescharacteristic
77#944—22no—
78#944—22no—
79#944C2×C414yes—
80#944C2×C414yes—
81C2×C4⋊Dic3—21no—
82C2×C4⋊Dic3—21no—
83C2×Dic3⋊C4—22no—
84C2×Dic3⋊C4—22no—
85C2×C4×Dic3C2×C411yescharacteristic
86C2×C4×Dic3D411yescharacteristic
87C2×C4×Dic3D411yescharacteristic
88C2×#208—21no—
89D3×M16—44no—
90C2×ΓL(1,𝔽25)—22no—
91C2×D3×C8—22no—
92C2×D3×C8—22no—
93D3×C4⋊C4—22no—
94D3×C4⋊C4—22no—
95D3×C4⋊C4—22no—
96D3×C4⋊C4—22no—
97D3×C4⋊C4—22no—
98D3×C4⋊C4—22no—
99D3×C4⋊C4—22no—
100D3×C4⋊C4—22no—
101#888—22no—
102#888—22no—
103#888—22no—
104#888—22no—
105#888—22no—
106#888—22no—
107#888—22no—
108#888—22no—
109C42×D3C2×C411yescharacteristic
110C42×D3C2×C411yescharacteristic
111C42×D3D411yescharacteristic
112C42×D3D411yescharacteristic
113C42×D3D411yescharacteristic
114C42×D3D411yescharacteristic
115C42×D3C2311yescharacteristic
116C42×D3C2311yescharacteristic
117#869—21no—
118#869—21no—
119#869C2×C412yes—
120#869C2312yes—
121C3×C4⋊C8—21no—
122C3×C4⋊C8C2312yes—
123C3×C4⋊C8C2312yes—
124C3×C22⋊C8—21no—
125C3×C4×C8—21no—
126#830—21no—
127(C2×D3)⋊C8—22no—
128Dic3⋊C8—22no—
129Dic3⋊C8—22no—
130Dic3⋊C8—22no—
131C8×Dic3—22no—
132C4⋊(C3⋊C8)—21no—
133C4⋊(C3⋊C8)C2312yes—
134C4⋊(C3⋊C8)C2312yes—
135C4×C3⋊C8—21no—
136C23×Q8—32no—
137C22×M16—61no—
138C2×C4⋊Q8—32no—
139C2×C4⋊Q8—32no—
140C2×C4⋊Q8—32no—
141C2×C4⋊Q8—32no—
142C2×C4⋊Q8—32no—
143C2×C4⋊Q8—31no—
144C2×C4⋊Q8—61no—
145C2×C4⋊Q8—61no—
146C2×C4⋊Q8—61no—
147C2×C4⋊Q8—61no—
148C2×C4⋊Q8—61no—
149C2×C4⋊Q8—61no—
150C2×C4⋊Q8C2×D311yescharacteristic
151C22×C4⋊C4—61no—
152C22×C4⋊C4—61no—
153C22×C42—31no—
154#431—31no—
155#431—32no—
156#431—61no—
157#431—61no—
158#431C2×D311yescharacteristic
159#423—31no—
160#423—32no—
161#423—61no—
162#423—61no—
163#423C2×D311yescharacteristic
164C2×C4⋊C8—32no—
165C2×C4⋊C8—32no—
166C2×C4⋊C8—61no—
167C2×C22⋊C8—61no—
168C2×C4×C8—61no—
169#333—34no—
170#333—34no—
171#333—34no—
172#333C2×D314yescomplemented
173C23×D3C22⋊C411yescharacteristic
174C2×C3×Q8—22no—
175C2×C3×Q8—44no—
176C2×C3×Q8C22×C414yes—
177C22×C3×C4—22no—
178C22×C3×C4C22×C411yescharacteristic
179C22×C3×C4C2×D411yescharacteristic
180C22×C3×C4C2×D411yescharacteristic
181C22×Dic3—22no—
182C22×Dic3C22⋊C411yescharacteristic
183C22×Dic3C22⋊C411yescharacteristic
184C22×Dic3C22⋊C411yescharacteristic
185D3×Q8—48no—
186D3×Q8—48no—
187D3×Q8—48no—
188D3×Q8—48no—
189C2×C4×D3—24no—
190C2×C4×D3—24no—
191C2×C4×D3—24no—
192C2×C4×D3—24no—
193C2×C4×D3—48no—
194C2×C4×D3C22⋊C411yescharacteristic
195C2×C4×D3C22⋊C411yescharacteristic
196C2×C4×D3C22⋊C411yescharacteristic
197C2×C4×D3C22⋊C411yescharacteristic
198C2×C4×D3C22⋊C411yescharacteristic
199C2×C4×D3C22⋊C411yescharacteristic
200C2×C4×D3SD1614yes—
201C2×C4×D3Q1614yes—
202C2×C4×D3C22×C411yescharacteristic
203C2×C4×D3C22×C411yescharacteristic
204C2×C4×D3C2×D411yescharacteristic
205C2×C4×D3C2×D411yescharacteristic
206C2×C4×D3C2×D411yescharacteristic
207C2×C4×D3C2×D411yescharacteristic
208C2×Dic6—22no—
209C2×Dic6—24no—
210C2×Dic6—24no—
211C2×Dic6—48no—
212C2×Dic6—44no—
213C2×Dic6C22×C414yes—
214C3×M16—42no—
215C2×C3×C8—22no—
216C2×C3×C8—22no—
217C3×C4⋊C4—22no—
218C3×C4⋊C4—22no—
219C3×C4⋊C4—22no—
220C3×C4⋊C4—22no—
221C3×C42C22×C411yescharacteristic
222C3×C42C2×D411yescharacteristic
223C3×C42C2×D411yescharacteristic
224C3×C42C2411yescharacteristic
225C4⋊Dic3—22no—
226C4⋊Dic3—22no—
227C4⋊Dic3—22no—
228C4⋊Dic3—22no—
229Dic3⋊C4—24no—
230Dic3⋊C4—24no—
231Dic3⋊C4—24no—
232Dic3⋊C4—24no—
233C4×Dic3C22⋊C411yescharacteristic
234C4×Dic3C22⋊C411yescharacteristic
235C4×Dic3C22⋊C411yescharacteristic
236C4×Dic3C22⋊C411yescharacteristic
237C4×Dic3C22⋊C411yescharacteristic
238C4×Dic3C22⋊C411yescharacteristic
239C4×Dic3C22×C411yescharacteristic
240C4×Dic3C22×C411yescharacteristic
241C4×Dic3C2×D411yescharacteristic
242C4×Dic3C2×D411yescharacteristic
243C4×Dic3C2×D411yescharacteristic
244C4×Dic3C2×D411yescharacteristic
245#208—42no—
246C2×C3⋊C8—22no—
247C2×C3⋊C8—22no—
248ΓL(1,𝔽25)—44no—
249D3×C8—44no—
250D3×C8—44no—
251C22×Q8—34no—
252C22×Q8—34no—
253C22×Q8—32no—
254C22×Q8—62no—
255C22×Q8—62no—
256C22×Q8—62no—
257C22×Q8—128no—
258C22×Q8C4×D312yes—
259C23×C4—31no—
260C23×C4—31no—
261C23×C4—31no—
262C23×C4—62no—
263C2×M16—21no—
264C2×M16—62no—
265C2×M16—61no—
266C2×M16—124no—
267C22×C8—62no—
268C22×C8—62no—
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271C4⋊Q8—34no—
272C4⋊Q8—34no—
273C4⋊Q8—32no—
274C4⋊Q8—32no—
275C4⋊Q8—62no—
276C4⋊Q8—62no—
277C4⋊Q8—62no—
278C4⋊Q8—62no—
279C4⋊Q8—62no—
280C4⋊Q8—62no—
281C4⋊Q8—62no—
282C4⋊Q8—62no—
283C4⋊Q8—62no—
284C4⋊Q8—62no—
285C4⋊Q8—61no—
286C4⋊Q8—61no—
287C4⋊Q8C4×D312yes—
288C4⋊Q8C22×D312yes—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—62no—
292C2×C4⋊C4—62no—
293C2×C4⋊C4—62no—
294C2×C4⋊C4—62no—
295C2×C4⋊C4—62no—
296C2×C4⋊C4—62no—
297C2×C4⋊C4—62no—
298C2×C4⋊C4—62no—
299C2×C4⋊C4—62no—
300C2×C4⋊C4—62no—
301C2×C4⋊C4—61no—
302C2×C4⋊C4—61no—
303C2×C42—31no—
304C2×C42—31no—
305C2×C42—31no—
306C2×C42—31no—
307C2×C42—31no—
308C2×C42—31no—
309C2×C42—31no—
310C2×C42—31no—
311C2×C42—31no—
312C2×C42—31no—
313C2×C42—31no—
314C2×C42C22×D311yescharacteristic
315C4⋊C8—21no—
316C4⋊C8—32no—
317C4⋊C8—32no—
318C4⋊C8—62no—
319C4⋊C8—62no—
320C4⋊C8—62no—
321C4⋊C8—61no—
322C4⋊C8C22×D312yes—
323C4⋊C8C22×D312yes—
324C22⋊C8—21no—
325C22⋊C8—62no—
326C22⋊C8—61no—
327C4×C8—21no—
328C4×C8—62no—
329C4×C8—61no—
330C23×C3C2×C22⋊C411yescharacteristic
331C22×D3—22no—
332C22×D3—22no—
333C22×D3#10314yes—
334C22×D3C2×C22⋊C411yescharacteristic
335C22×D3C2×C22⋊C411yescharacteristic
336C3×Q8—44no—
337C3×Q8—44no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—24no—
341C2×C3×C4—44no—
342C2×C3×C4C2×C22⋊C411yescharacteristic
343C2×C3×C4C2×C22⋊C411yescharacteristic
344C2×C3×C4C2×C22⋊C411yescharacteristic
345C2×C3×C4C2×SD1612yes—
346C2×C3×C4C2×Q1612yes—
347C2×C3×C4C23×C411yescharacteristic
348C2×C3×C4C22×D411yescharacteristic
349C2×C3×C4C22×D411yescharacteristic
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—24no—
353C2×Dic3—44no—
354C2×Dic3#10314yes—
355C2×Dic3C2×C22⋊C411yescharacteristic
356C2×Dic3C2×C22⋊C411yescharacteristic
357C2×Dic3C2×C22⋊C411yescharacteristic
358C2×Dic3C2×C22⋊C411yescharacteristic
359C2×Dic3C2×C22⋊C411yescharacteristic
360C2×Dic3C2×C22⋊C411yescharacteristic
361C4×D3—22no—
362C4×D3—22no—
363C4×D3—22no—
364C4×D3—22no—
365C4×D3—22no—
366C4×D3—22no—
367C4×D3—48no—
368C4×D3—48no—
369C4×D3#10014yes—
370C4×D3#10314yes—
371C4×D3#10314yes—
372C4×D3C2×SD1612yes—
373C4×D3C2×SD1612yes—
374C4×D3C2×Q1612yes—
375C4×D3C2×Q1612yes—
376C4×D3#13714yes—
377Dic6—48no—
378Dic6—44no—
379Dic6—48no—
380Dic6—44no—
381C3×C8—42no—
382C3×C8—42no—
383C3⋊C8—42no—
384C3⋊C8—42no—
385C24—31no—
386C2×Q8—22no—
387C2×Q8—34no—
388C2×Q8—44no—
389C2×Q8—64no—
390C2×Q8—64no—
391C2×Q8—62no—
392C2×Q8—124no—
393C2×Q8—128no—
394C2×Q8—128no—
395C2×Q8—128no—
396C2×Q8—128no—
397C2×Q8—128no—
398C2×Q8C2×C4×D314yes—
399C22×C4—22no—
400C22×C4—31no—
401C22×C4—31no—
402C22×C4—31no—
403C22×C4—31no—
404C22×C4—34no—
405C22×C4—34no—
406C22×C4—31no—
407C22×C4—31no—
408C22×C4—31no—
409C22×C4—31no—
410C22×C4—31no—
411C22×C4—31no—
412C22×C4—31no—
413C22×C4—31no—
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—64no—
418C22×C4—64no—
419C22×C4—64no—
420C22×C4—64no—
421C22×C4—62no—
422C22×C4—128no—
423C22×C4C2×C4×D311yescharacteristic
424C22×C4D3×D411yescharacteristic
425C22×C4D3×D411yescharacteristic
426M16—42no—
427M16—124no—
428M16—122no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—62no—
432C2×C8—62no—
433C2×C8—124no—
434C2×C8—124no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—64no—
440C4⋊C4—64no—
441C4⋊C4—64no—
442C4⋊C4—64no—
443C4⋊C4—62no—
444C4⋊C4—62no—
445C4⋊C4—62no—
446C4⋊C4—62no—
447C42—31no—
448C42—31no—
449C42—31no—
450C42—31no—
451C42—31no—
452C42—31no—
453C42—31no—
454C42—31no—
455C42—31no—
456C42—31no—
457C42—31no—
458C42—31no—
459C42C2×C4×D311yescharacteristic
460C42D3×D411yescharacteristic
461C42D3×D411yescharacteristic
462C42C23×D311yescharacteristic
463C22×C3—21no—
464C22×C3—21no—
465C22×C3C2×#10312yes—
466C22×C3C22×C22⋊C411yescharacteristic
467C2×D3—21no—
468C2×D3—21no—
469C2×D3—28no—
470C2×D3C2×#10012yes—
471C2×D3C2×#10312yes—
472C2×D3C2×#10312yes—
473C2×D3#41912yes—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—44no—
477C3×C4C2×#10012yes—
478C3×C4C2×#10312yes—
479C3×C4C22×SD1611yescharacteristic
480C3×C4C22×Q1611yescharacteristic
481C3×C4C2×#13712yes—
482Dic3—21no—
483Dic3—21no—
484Dic3—44no—
485Dic3C2×#10012yes—
486Dic3C2×#10312yes—
487Dic3C2×#10312yes—
488Dic3#41912yes—
489C23—31no—
490C23—31no—
491C23—34no—
492C23—62no—
493C23—62no—
494C23D3×C22⋊C411yescharacteristic
495Q8—44no—
496Q8—44no—
497Q8—124no—
498Q8—128no—
499Q8—128no—
500Q8—124no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—31no—
505C2×C4—31no—
506C2×C4—31no—
507C2×C4—31no—
508C2×C4—34no—
509C2×C4—32no—
510C2×C4—32no—
511C2×C4—32no—
512C2×C4—32no—
513C2×C4—34no—
514C2×C4—34no—
515C2×C4—34no—
516C2×C4—34no—
517C2×C4—31no—
518C2×C4—31no—
519C2×C4—44no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—64no—
529C2×C4—128no—
530C2×C4—128no—
531C2×C4—124no—
532C2×C4D3×C22⋊C411yescharacteristic
533C2×C4D3×C22⋊C411yescharacteristic
534C2×C4D3×C22⋊C411yescharacteristic
535C2×C4D3×SD1612yes—
536C2×C4D3×Q1612yes—
537C2×C4C22×C4×D311yescharacteristic
538C2×C4C2×D3×D411yescharacteristic
539C2×C4C2×D3×D411yescharacteristic
540C8—42no—
541C8—42no—
542C8—122no—
543C8—122no—
544C2×C3—22no—
545C2×C3C22×#10011yescharacteristic
546C2×C3C22×#10311yescharacteristic
547C2×C3C2×#41911yescharacteristic
548D3—22no—
549D3#154814yesdirect product factor
550C22—21no—
551C22—21no—
552C22—32no—
553C22—32no—
554C22—32no—
555C22—32no—
556C22—68no—
557C22—61no—
558C22—61no—
559C22D3×#10312yes—
560C22C2×D3×C22⋊C411yescharacteristic
561C4—21no—
562C4—21no—
563C4—32no—
564C4—32no—
565C4—32no—
566C4—32no—
567C4—44no—
568C4—61no—
569C4—61no—
570C4—124no—
571C4D3×#10012yes—
572C4D3×#10312yes—
573C4C2×D3×SD1611yescharacteristic
574C4C2×D3×Q1611yescharacteristic
575C4D3×#13712yes—
576C3C2×#154811yescharacteristic, complemented, Sylow
577C2—22no—
578C2—34no—
579C2—62no—
580C2C2×D3×#10011yescharacteristic
581C2C2×D3×#10311yescharacteristic
582C2D3×#41911yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC2×C3×C4C23×C4
FrattiniC42C23×D3
FittingC3×#1548C2
socleC22×C3C22×C22⋊C4
prime radicalC23×D3C22⋊C4
cosocleC3×C42C24
hypercenter#1548D3
hypocenterC3C2×#1548
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
4. C3×#1548C2semidirect
5. #71774C2semidirect
6. #70779C2semidirect
7. #70507C2semidirect
8. #68483C2semidirect
9. D3×#333C2semidirect
44. C3×#333C22semidirect
45. #4546C22semidirect
46. #4481C22semidirect
47. #4481C22semidirect
55. #1548D3direct (N × H)
172. #333C2×D3semidirect
549. D3#1548direct (N × H)
576. C3C2×#1548semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊Q82
D3×#4312
D3×#4232
C3×#15482
#717742
#707792
#705072
#684832
D3×#3332
C2×#15483