Finite Group Databasebeta

← D3×#5000 #11858788

Subgroups — D3×#5000 #11858788

Order 1152.

872 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#117C211yesmaximal, characteristic
2#10592699C211yesmaximal, characteristic, complemented
3C3×#5000C211yesmaximal, characteristic, complemented
4D3×#830C212yesmaximal
5#10591056C212yesmaximal, complemented
6D3×C4⋊(C3⋊C8)C212yesmaximal, complemented
7D3×#803C211yesmaximal, characteristic, complemented
8C4×D3×C3⋊C8C211yesmaximal, characteristic, complemented
9#10590265C211yesmaximal, characteristic, complemented
10#10590264C211yesmaximal, characteristic, complemented
11#10590253C212yesmaximal, complemented
12C2×#5000—31nomaximal
13D3×#433—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C3×#926C2211yescharacteristic
17C3×#892C412yes—
18C3×D3×C4⋊C4C412yes—
19C3×D3×C22⋊C4C412yes—
20C3×#877C412yes—
21C3×#872C2211yescharacteristic
22C3×#872C2211yescharacteristic
23C3×C42×D3C2211yescharacteristic
24C3×C42×D3C2211yescharacteristic
25C2×D3×C3⋊C8C2212yes—
26C2×D3×C3⋊C8C2212yes—
27#63657C2212yes—
28C4⋊(C3⋊(C3⋊C8))C2212yescomplemented
29#63630C2211yescharacteristic, complemented
30C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
31C3×#830C2212yes—
32C3×C4⋊(C3⋊C8)C2212yescomplemented
33C3×#803C2211yescharacteristic, complemented
34C3×C4×C3⋊C8C2211yescharacteristic, complemented
35Dic3⋊(C3⋊C8)C2212yescomplemented
36Dic3⋊(C3⋊C8)C2212yescomplemented
37(C2×D3)⋊(C3⋊C8)C2212yes—
38(C2×D3)⋊(C3⋊C8)C2212yes—
39#63554C2212yescomplemented
40Dic3×C3⋊C8C2212yescomplemented
41C2×C3×#117—31no—
42D3×#117D311yescharacteristic
43C3×#433—31no—
44C2×#830—32no—
45#5000—31no—
46#5000—31no—
47#5000—32no—
48#5000—32no—
49#5000—31no—
50#5000—31no—
51#5000—61no—
52#5000D311yescharacteristic, direct product factor
53C2×C4⋊(C3⋊C8)—32no—
54C2×#803—31no—
55C2×C4×C3⋊C8—31no—
56#4840—32no—
57D3×C4⋊C8—32no—
58D3×C22⋊C8—32no—
59#4720—32no—
60#4709—31no—
61D3×#97—31no—
62#4690—31no—
63C4×D3×C8—31no—
64C23×C3×D3C2×C411yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3×Dic3C2×C411yescharacteristic
67C2×C3×C4×D3—24no—
68C2×C3×C4×D3C2×C412yes—
69C2×C3×C4×D3C2×C412yes—
70C2×C3×C4×D3C2×C411yescharacteristic
71C2×C3×C4×D3C2×C411yescharacteristic
72C2×C3×C4×D3C2311yescharacteristic
73C2×C3×C4×D3C2311yescharacteristic
74C32×C4⋊C4C2×C412yes—
75C32×C22⋊C4C2×C412yes—
76C32×C42C2311yescharacteristic
77C32×C42C2311yescharacteristic
78C2×C3⋊(C3⋊C8)C2312yes—
79C2×C3⋊(C3⋊C8)C2312yes—
80C3×#217C2×C412yes—
81C3×(C2×D3)⋊C4C2×C412yes—
82C3×(C2×D3)⋊C4C2×C412yes—
83C3×C4⋊Dic3C2×C412yes—
84C3×Dic3⋊C4C2×C412yes—
85C3×Dic3⋊C4C2×C412yes—
86C3×C4×Dic3C2×C412yes—
87C3×C4×Dic3C2×C412yes—
88C3×C4×Dic3C2311yescharacteristic
89C3×C4×Dic3C2311yescharacteristic
90C2×C3×C3⋊C8C2312yes—
91C2×C3×C3⋊C8C2312yes—
92D3×C3⋊C8—24no—
93D3×C3⋊C8—24no—
94C2×#433—91noSylow
95C23×C3×C4—31no—
96C22×C4×D3C2×D311yescharacteristic
97C3×#117—21no—
98C3×#117—31no—
99C3×#117—32no—
100C3×#117—32no—
101C3×#117—31no—
102C3×#117—31no—
103C3×#117C2×D311yescharacteristic
104C3×#117C2×D311yescharacteristic
105C2×C3×C4⋊C4—32no—
106C2×C3×C22⋊C4—32no—
107C2×C3×C42—31no—
108C2×C3×C42—31no—
109#926C2×D311yescharacteristic
110C22×C3⋊C8—32no—
111C22×C3⋊C8—32no—
112C2×D3×C8—32no—
113C2×D3×C8—32no—
114#892Dic312yes—
115D3×C4⋊C4Dic312yes—
116D3×C22⋊C4Dic312yes—
117#877Dic312yes—
118#872C2×D311yescharacteristic
119#872C2×D311yescharacteristic
120C42×D3C2×D311yescharacteristic
121C42×D3C2×D311yescharacteristic
122C3×C4⋊C8—32no—
123C3×C22⋊C8—32no—
124C3×#97—31no—
125C3×C4×C8—31no—
126#830—32no—
127#830—32no—
128#830—32no—
129#830—32no—
130#830—62no—
131#830C2×D312yes—
132(C2×D3)⋊C8—32no—
133(C2×D3)⋊C8—32no—
134#815—32no—
135Dic3⋊C8—32no—
136Dic3⋊C8—32no—
137C8×Dic3—32no—
138C4⋊(C3⋊C8)—32no—
139C4⋊(C3⋊C8)—32no—
140C4⋊(C3⋊C8)—32no—
141C4⋊(C3⋊C8)—32no—
142C4⋊(C3⋊C8)—62no—
143C4⋊(C3⋊C8)C2×D312yescomplemented
144#803—31no—
145#803—31no—
146#803—32no—
147#803—61no—
148#803C2×D311yescharacteristic, complemented
149C4×C3⋊C8—31no—
150C4×C3⋊C8—31no—
151C4×C3⋊C8—32no—
152C4×C3⋊C8—61no—
153C4×C3⋊C8C2×D311yescharacteristic, complemented
154C23×C32C22×C411yescharacteristic
155C22×C3×D3—22no—
156C22×C3×D3—24no—
157C22×C3×D3C22×C411yescharacteristic
158C22×C3×D3C22×C411yescharacteristic
159C2×C32×C4—22no—
160C2×C32×C4C22×C412yes—
161C2×C32×C4C22×C412yes—
162C2×C32×C4C22×C411yescharacteristic
163C2×C32×C4C2411yescharacteristic
164C2×C3×Dic3—22no—
165C2×C3×Dic3C22×C412yes—
166C2×C3×Dic3C22×C412yes—
167C2×C3×Dic3C22×C411yescharacteristic
168C2×C3×Dic3C22×C411yescharacteristic
169C3×C4×D3—22no—
170C3×C4×D3—24no—
171C3×C4×D3—24no—
172C3×C4×D3—22no—
173C3×C4×D3—22no—
174C3×C4×D3#4114yes—
175C3⋊(C3⋊C8)—22no—
176C3⋊(C3⋊C8)—22no—
177C3×C3⋊C8—22no—
178C3×C3⋊C8—22no—
179C2×#117—31no—
180#433—31no—
181#433—91no—
182#433—91no—
183#433—92no—
184#433—92no—
185#433—91no—
186C2×C4⋊C8—92no—
187C2×C22⋊C8—92no—
188C2×#97—91no—
189C2×C4×C8—91no—
190C24×C3—31no—
191C23×D3C2×Dic311yescharacteristic
192C22×C3×C4—21no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—32no—
196C22×C3×C4—32no—
197C22×C3×C4—31no—
198C22×C3×C4—31no—
199C22×C3×C4—31no—
200C22×C3×C4—64no—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×Dic3C2×Dic311yescharacteristic
204C2×C4×D3—24no—
205C2×C4×D3C2×Dic312yes—
206C2×C4×D3C2×Dic312yes—
207C2×C4×D3C2×Dic311yescharacteristic
208C2×C4×D3C2×Dic311yescharacteristic
209C2×C4×D3C22×D311yescharacteristic
210C2×C4×D3C22×D311yescharacteristic
211C2×C3×C8—32no—
212C2×C3×C8—32no—
213C3×C4⋊C4—22no—
214C3×C4⋊C4—32no—
215C3×C4⋊C4—32no—
216C3×C4⋊C4—32no—
217C3×C4⋊C4C4×D312yes—
218C3×C4⋊C4C2×Dic312yes—
219C3×C22⋊C4—22no—
220C3×C22⋊C4—32no—
221C3×C22⋊C4—32no—
222C3×C22⋊C4—32no—
223C3×C22⋊C4C4×D312yes—
224C3×C22⋊C4C2×Dic312yes—
225C3×C42—21no—
226C3×C42—21no—
227C3×C42—32no—
228C3×C42—32no—
229C3×C42—31no—
230C3×C42—31no—
231C3×C42C22×D311yescharacteristic
232C3×C42C22×D311yescharacteristic
233C3×C42C22×D311yescharacteristic
234C3×C42C22×D311yescharacteristic
235#217C2×Dic312yes—
236(C2×D3)⋊C4C2×Dic312yes—
237(C2×D3)⋊C4C2×Dic312yes—
238C4⋊Dic3C2×Dic312yes—
239Dic3⋊C4C2×Dic312yes—
240Dic3⋊C4C2×Dic312yes—
241C4×Dic3C2×Dic312yes—
242C4×Dic3C2×Dic312yes—
243C4×Dic3C22×D311yescharacteristic
244C4×Dic3C22×D311yescharacteristic
245C2×C3⋊C8—32no—
246C2×C3⋊C8—32no—
247C2×C3⋊C8—32no—
248C2×C3⋊C8—32no—
249C2×C3⋊C8—62no—
250C2×C3⋊C8—62no—
251C2×C3⋊C8—64no—
252C2×C3⋊C8—64no—
253C2×C3⋊C8C22×D312yes—
254C2×C3⋊C8C22×D312yes—
255D3×C8—64no—
256D3×C8—64no—
257C22×C32—21no—
258C22×C32—22no—
259C22×C32C23×C411yescharacteristic
260C2×C3×D3—21no—
261C2×C3×D3—22no—
262C2×C3×D3—44no—
263C2×C3×D3#11712yes—
264C2×C3×D3#13114yes—
265C32×C4—21no—
266C32×C4—22no—
267C32×C4—22no—
268C32×C4C2×#4112yes—
269C3×Dic3—21no—
270C3×Dic3—22no—
271C3×Dic3—22no—
272C3×Dic3#11712yes—
273C23×C4—31no—
274C22×C8—92no—
275C22×C8—92no—
276#117—31no—
277#117—32no—
278#117—32no—
279#117—31no—
280#117—31no—
281#117D3211yescharacteristic
282C2×C4⋊C4—32no—
283C2×C22⋊C4—32no—
284C2×C42—31no—
285C2×C42—31no—
286C4⋊C8—32no—
287C4⋊C8—92no—
288C4⋊C8—92no—
289C4⋊C8—92no—
290C22⋊C8—32no—
291C22⋊C8—92no—
292C22⋊C8—92no—
293C22⋊C8—92no—
294#97—31no—
295#97—92no—
296#97—91no—
297C4×C8—31no—
298C4×C8—92no—
299C4×C8—91no—
300C23×C3—21no—
301C23×C3—31no—
302C23×C3—31no—
303C23×C3—62no—
304C23×C3—64no—
305C23×C3C2×C4×D311yescharacteristic
306C23×C3C22×Dic311yescharacteristic
307C22×D3—22no—
308C22×D3—24no—
309C22×D3C22×Dic311yescharacteristic
310C22×D3C22×Dic311yescharacteristic
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—21no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—21no—
317C2×C3×C4—31no—
318C2×C3×C4—34no—
319C2×C3×C4—32no—
320C2×C3×C4—32no—
321C2×C3×C4—31no—
322C2×C3×C4—42no—
323C2×C3×C4—62no—
324C2×C3×C4—64no—
325C2×C3×C4—64no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4C2×C4×D312yes—
330C2×C3×C4C2×C4×D312yes—
331C2×C3×C4C2×C4×D311yescharacteristic
332C2×C3×C4C22×Dic312yes—
333C2×C3×C4C22×Dic312yes—
334C2×C3×C4C22×Dic311yescharacteristic
335C2×C3×C4C23×D311yescharacteristic
336C2×C3×C4C23×D311yescharacteristic
337C2×Dic3—22no—
338C2×Dic3C22×Dic312yes—
339C2×Dic3C22×Dic312yes—
340C2×Dic3C22×Dic311yescharacteristic
341C2×Dic3C22×Dic311yescharacteristic
342C4×D3—22no—
343C4×D3—24no—
344C4×D3—24no—
345C4×D3—22no—
346C4×D3—22no—
347C4×D3#23514yes—
348C3×C8—62no—
349C3×C8—62no—
350C3⋊C8—22no—
351C3⋊C8—22no—
352C3⋊C8—62no—
353C3⋊C8—62no—
354C3⋊C8—62no—
355C3⋊C8—62no—
356C3⋊C8—122no—
357C3⋊C8—122no—
358C2×C32—41no—
359C2×C32C2×#11711yescharacteristic
360C2×C32C2×#13112yes—
361C3×D3—41no—
362C3×D3#43314yescomplemented
363C24—31no—
364C22×C4—31no—
365C22×C4—31no—
366C22×C4—31no—
367C22×C4—32no—
368C22×C4—32no—
369C22×C4—31no—
370C22×C4—31no—
371C22×C4—64no—
372C22×C4C2×D3211yescharacteristic
373C2×C8—32no—
374C2×C8—32no—
375C2×C8—92no—
376C2×C8—92no—
377C2×C8—184no—
378C2×C8—184no—
379C4⋊C4—32no—
380C4⋊C4—32no—
381C4⋊C4—32no—
382C4⋊C4D3×Dic312yes—
383C22⋊C4—32no—
384C22⋊C4—32no—
385C22⋊C4—32no—
386C22⋊C4D3×Dic312yes—
387C42—31no—
388C42—31no—
389C42—32no—
390C42—32no—
391C42C2×D3211yescharacteristic
392C42C2×D3211yescharacteristic
393C22×C3—22no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—22no—
397C22×C3—21no—
398C22×C3—34no—
399C22×C3—32no—
400C22×C3—41no—
401C22×C3—42no—
402C22×C3—62no—
403C22×C3—61no—
404C22×C3—124no—
405C22×C3C22×C4×D311yescharacteristic
406C22×C3C23×Dic311yescharacteristic
407C2×D3—21no—
408C2×D3—22no—
409C2×D3—44no—
410C2×D3#92612yes—
411C2×D3#94814yes—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—22no—
417C3×C4—22no—
418C3×C4—22no—
419C3×C4—32no—
420C3×C4—41no—
421C3×C4—42no—
422C3×C4—42no—
423C3×C4—62no—
424C3×C4—62no—
425C3×C4—61no—
426C3×C4C2×#23512yes—
427C3×C4D3×#4112yes—
428Dic3—21no—
429Dic3—22no—
430Dic3—22no—
431Dic3#92612yes—
432C32C2×#43311yescharacteristic, complemented, Sylow
433C23—31no—
434C23—31no—
435C23—62no—
436C23—64no—
437C23C2×D3×Dic311yescharacteristic
438C2×C4—22no—
439C2×C4—31no—
440C2×C4—34no—
441C2×C4—32no—
442C2×C4—32no—
443C2×C4—31no—
444C2×C4—62no—
445C2×C4—62no—
446C2×C4—64no—
447C2×C4—64no—
448C2×C4—62no—
449C2×C4—62no—
450C2×C4C2×D3×Dic312yes—
451C2×C4C2×D3×Dic312yes—
452C2×C4C2×D3×Dic311yescharacteristic
453C2×C4C22×D3211yescharacteristic
454C8—62no—
455C8—62no—
456C8—182no—
457C8—182no—
458C2×C3—22no—
459C2×C3—21no—
460C2×C3—34no—
461C2×C3—41no—
462C2×C3—41no—
463C2×C3—81no—
464C2×C3—121no—
465C2×C3D3×#11711yescharacteristic
466C2×C3D3×#13112yes—
467C2×C3C2×#92611yescharacteristic
468C2×C3C2×#94812yes—
469D3—41no—
470D3#500014yesdirect product factor
471C22—22no—
472C22—21no—
473C22—34no—
474C22—32no—
475C22—62no—
476C22—61no—
477C22—124no—
478C22C22×D3×Dic311yescharacteristic
479C4—22no—
480C4—22no—
481C4—21no—
482C4—32no—
483C4—62no—
484C4—62no—
485C4—61no—
486C4D3×#23512yes—
487C3—21no—
488C3D3×#43311yescharacteristic, complemented
489C3C2×#500011yescharacteristic, complemented
490C2—34no—
491C2—41no—
492C2—121no—
493C2D3×#92611yescharacteristic
494C2D3×#94812yes—
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×#117C22
prime radicalC23×C3×D3C2×C4
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32C2×#433
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10592699C2semidirect
3. C3×#5000C2semidirect
5. #10591056C2semidirect
6. D3×C4⋊(C3⋊C8)C2semidirect
7. D3×#803C2semidirect
8. C4×D3×C3⋊C8C2semidirect
9. #10590265C2semidirect
10. #10590264C2semidirect
11. #10590253C2semidirect
28. C4⋊(C3⋊(C3⋊C8))C22semidirect
29. #63630C22semidirect
30. C4×C3⋊(C3⋊C8)C22semidirect
32. C3×C4⋊(C3⋊C8)C22semidirect
33. C3×#803C22semidirect
34. C3×C4×C3⋊C8C22semidirect
35. Dic3⋊(C3⋊C8)C22semidirect
36. Dic3⋊(C3⋊C8)C22semidirect
39. #63554C22semidirect
40. Dic3×C3⋊C8C22semidirect
52. #5000D3direct (N × H)
143. C4⋊(C3⋊C8)C2×D3semidirect
148. #803C2×D3semidirect
153. C4×C3⋊C8C2×D3semidirect
362. C3×D3#433semidirect
432. C32C2×#433semidirect
470. D3#5000direct (N × H)
488. C3D3×#433semidirect
489. C3C2×#5000semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1172
#105926992
C3×#50002
D3×#8302
#105910562
D3×C4⋊(C3⋊C8)2
D3×#8032
C4×D3×C3⋊C82
#105902652
#105902642
#105902532
C2×#50003
D3×#4333