Finite Group Databasebeta

← D3×#4853 #11860132

Subgroups — D3×#4853 #11860132

Order 1152.

1014 conjugacy classes of subgroups.

The subgroup lattice has 475 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Dic12C211yesmaximal, characteristic
2D3×#887C212yesmaximal
3#10592552C211yesmaximal, characteristic, complemented
4C3×D3×#106C211yesmaximal, characteristic
5C3×#4853C211yesmaximal, characteristic, complemented
6#10590819C211yesmaximal, characteristic, complemented
7#10590810C211yesmaximal, characteristic, complemented
8D3×#815C211yesmaximal, characteristic
9D3×#810C212yesmaximal
10#10590485C212yesmaximal, complemented
11#10590480C212yesmaximal, complemented
12D3×#441—31nomaximal
13C2×#4853—31nomaximal
14C2×D3×Dic6C2212yes—
15C2×#3746C2211yescharacteristic
16#64096C2212yes—
17C2×C3×Dic12C2211yescharacteristic
18C2×C3×D3×C8C2211yescharacteristic
19C3×D3×C4⋊C4C2212yes—
20C3×#887C2212yes—
21D3×Dic3⋊C4—22no—
22C4×D3×Dic3—22no—
23C4×D3×Dic3C2211yescharacteristic
24#63844C2212yes—
25#63843C2212yes—
26#63838—22no—
27#63837—22no—
28C2×#3719C2212yes—
29C2×D3×C3⋊C8C2211yescharacteristic
30D3×Dic12C418yescomplemented
31C32×#106C2211yescharacteristic
32#63642C2211yescharacteristic
33#63637C2212yes—
34C3×#817C2211yescharacteristic
35C3×#815C2211yescharacteristic
36C3×#810C2212yes—
37C3×#808C2212yes—
38#63567C2212yes—
39#63565C2212yes—
40#63555C2211yescharacteristic
41#63554C2211yescharacteristic
42C2×D3×Q16—31no—
43C22×Dic12—31no—
44C4×D3×Q8—32no—
45C2×#887—32no—
46C3×#441—31no—
47C2×C3×#106—31no—
48#5184—31no—
49C2×#815—31no—
50#5030—32no—
51C2×#810—32no—
52D3×#106D311yescharacteristic
53#4853—31no—
54#4853—32no—
55#4853—31no—
56#4853—31no—
57#4853—31no—
58#4853—32no—
59#4853—61no—
60#4853D311yescharacteristic, direct product factor
61D3×#103—32no—
62#4789—32no—
63#4716—31no—
64D3×#97—31no—
65C2×#634C2312yes—
66C2×C3×C4×D3—22no—
67C2×C3×C4×D3C2311yescharacteristic
68C2×C3×Dic6C2312yes—
69C2×#627—22no—
70C2×D3×Dic3—22no—
71C2×D3×Dic3D412yes—
72D3×Dic6—24no—
73D3×Dic6C2×C418yes—
74C2×C32×C8C2311yescharacteristic
75C32×C4⋊C4C2312yes—
76#3750—22no—
77C4×C3⋊Dic3—22no—
78C4×C3⋊Dic3C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80#3746C2×C414yescomplemented
81C3×C4⋊Dic3C2312yes—
82C3×Dic3⋊C4—22no—
83C3×Dic3⋊C4—22no—
84C3×C4×Dic3—22no—
85C3×C4×Dic3C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C3×Dic12C2×C414yescomplemented
89C3×D3×C8C2×C414yes—
90#3724—22no—
91Dic3⋊Dic3—22no—
92Dic32—22no—
93Dic32—22no—
94Dic32D412yes—
95#3719C2×C418yescomplemented
96D3×C3⋊C8—22no—
97C2×#441—91noSylow
98C2×D3×Q8—32no—
99C22×Dic6—32no—
100C2×C3×Q16—31no—
101C22×C3×C8—31no—
102C3×C4×Q8—32no—
103C2×C3×C4⋊C4—32no—
104Q8×Dic3—32no—
105C2×#216—32no—
106C2×Dic3⋊C4—62no—
107C2×C4×Dic3—31no—
108C2×C4×Dic3—62no—
109C22×C3⋊C8—31no—
110D3×Q16—38no—
111C2×Dic12—32no—
112C2×Dic12—31no—
113C2×Dic12—31no—
114C2×Dic12—38no—
115C2×Dic12—61no—
116C2×Dic12C2×D311yescharacteristic
117C2×D3×C8—31no—
118C2×D3×C8C2×D311yescharacteristic
119D3×C4⋊C4—62no—
120D3×C4⋊C4C2×D312yes—
121#887—32no—
122#887—32no—
123#887—32no—
124#887—32no—
125#887—62no—
126#887—62no—
127#887—62no—
128#887—62no—
129#887C2×D312yes—
130C42×D3—31no—
131C42×D3—62no—
132C4×Dic6—32no—
133C4×Dic6—62no—
134C3×#106—21no—
135C3×#106—31no—
136C3×#106—32no—
137C3×#106C2×D311yescharacteristic
138C3×#106C2×D311yescharacteristic
139C3×#103—32no—
140C3×#97—31no—
141#835—32no—
142#817C2×D311yescharacteristic
143#816—32no—
144#815—31no—
145#815—31no—
146#815—31no—
147#815—31no—
148#815—31no—
149#815—61no—
150#815C2×D311yescharacteristic
151#810—32no—
152#810—32no—
153#810—32no—
154#810—32no—
155#810—62no—
156#810C2×D312yes—
157#808C2×D312yes—
158#803—31no—
159C22×C3×D3C2×D411yescharacteristic
160C2×C32×C4—22no—
161C2×C32×C4C2411yescharacteristic
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3C2×D412yes—
164#634—22no—
165#634C22×C414yes—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3C2×D412yes—
169C2×C3×Dic3C2×D411yescharacteristic
170C3×C4×D3—44no—
171C3×C4×D3C22×C412yes—
172C3×C4×D3#4112yes—
173C3×Dic6—22no—
174C3×Dic6C22×C414yes—
175#627—28no—
176D3×Dic3—28no—
177D3×Dic3—24no—
178C32×C8C22×C412yes—
179C3⋊(C3⋊C8)—21no—
180C3×C3⋊C8—21no—
181C3×C3⋊C8C22×C412yes—
182C22×Q16—91no—
183C2×C4×Q8—92no—
184#441—31no—
185#441—91no—
186#441—92no—
187#441—92no—
188#441—91no—
189#441—91no—
190C2×#106—31no—
191C2×#103—92no—
192C2×#97—91no—
193C2×C3×Q8—32no—
194C22×C3×C4—31no—
195C22×C3×C4—62no—
196C22×Dic3—32no—
197C22×Dic3—62no—
198D3×Q8—38no—
199D3×Q8—64no—
200C2×C4×D3—22no—
201C2×C4×D3—32no—
202C2×C4×D3—62no—
203C2×C4×D3C22×D311yescharacteristic
204C2×Dic6—32no—
205C2×Dic6—32no—
206C2×Dic6—38no—
207C2×Dic6—62no—
208C2×Dic6—64no—
209C2×Dic6—62no—
210C2×Dic6—62no—
211C2×Dic6C22×D312yes—
212C3×Q16—34no—
213C2×C3×C8—21no—
214C2×C3×C8—31no—
215C2×C3×C8—34no—
216C2×C3×C8—31no—
217C2×C3×C8C22×D311yescharacteristic
218C2×C3×C8C22×D311yescharacteristic
219C3×C4⋊C4—22no—
220C3×C4⋊C4—32no—
221C3×C4⋊C4—62no—
222C3×C4⋊C4—62no—
223C3×C4⋊C4C22×D312yes—
224C3×C4⋊C4C22×D312yes—
225C3×C42—31no—
226C3×C42—62no—
227#216—38no—
228C4⋊Dic3—62no—
229C4⋊Dic3C22×D312yes—
230Dic3⋊C4—22no—
231Dic3⋊C4—22no—
232Dic3⋊C4—62no—
233Dic3⋊C4—62no—
234Dic3⋊C4—62no—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237Dic3⋊C4—122no—
238C4×Dic3—22no—
239C4×Dic3—31no—
240C4×Dic3—31no—
241C4×Dic3—32no—
242C4×Dic3—32no—
243C4×Dic3—61no—
244C4×Dic3—62no—
245C4×Dic3—62no—
246C4×Dic3—62no—
247C4×Dic3—62no—
248C4×Dic3—62no—
249C4×Dic3—62no—
250C4×Dic3—122no—
251C4×Dic3C22×D311yescharacteristic
252C2×C3⋊C8—31no—
253C2×C3⋊C8—31no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—62no—
256C2×C3⋊C8C22×D311yescharacteristic
257C2×C3⋊C8C22×D311yescharacteristic
258Dic12—38no—
259Dic12—34no—
260Dic12—34no—
261Dic12—64no—
262Dic12C4×D314yescomplemented
263D3×C8—62no—
264D3×C8C4×D314yes—
265C22×C32C22×D411yescharacteristic
266C2×C3×D3C4×D412yes—
267C2×C3×D3#13714yes—
268C32×C4—42no—
269C32×C4C23×C411yescharacteristic
270C32×C4C2×#4111yescharacteristic
271C3⋊Dic3—24no—
272C3⋊Dic3—22no—
273C3×Dic3—24no—
274C3×Dic3—22no—
275C3×Dic3—42no—
276C3×Dic3C4×D412yes—
277C22×Q8—92no—
278C2×Q16—31no—
279C2×Q16—98no—
280C2×Q16—92no—
281C2×Q16—91no—
282C22×C8—31no—
283C22×C8—91no—
284C4×Q8—32no—
285C4×Q8—92no—
286C4×Q8—92no—
287C4×Q8—92no—
288C4×Q8—182no—
289C4×Q8—182no—
290C2×C4⋊C4—32no—
291C2×C4⋊C4—182no—
292C2×C42—91no—
293C2×C42—182no—
294#106—31no—
295#106—32no—
296#106D3211yescharacteristic
297#103—32no—
298#103—92no—
299#103—92no—
300#103—92no—
301#97—31no—
302#97—91no—
303#97—91no—
304#97—91no—
305C23×C3—31no—
306C22×D3D3×D411yescharacteristic
307C3×Q8—34no—
308C3×Q8—62no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—21no—
312C2×C3×C4—31no—
313C2×C3×C4—32no—
314C2×C3×C4—32no—
315C2×C3×C4—32no—
316C2×C3×C4—42no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—124no—
320C2×C3×C4C23×D311yescharacteristic
321C2×C3×C4C23×D311yescharacteristic
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—32no—
325C2×Dic3—32no—
326C2×Dic3—62no—
327C2×Dic3—68no—
328C2×Dic3—64no—
329C2×Dic3—62no—
330C2×Dic3—62no—
331C2×Dic3—122no—
332C2×Dic3D3×D412yes—
333C2×Dic3D3×D411yescharacteristic
334C4×D3—44no—
335C4×D3—68no—
336C4×D3—64no—
337C4×D3C2×C4×D312yes—
338C4×D3#23912yes—
339Dic6—22no—
340Dic6—34no—
341Dic6—34no—
342Dic6—64no—
343Dic6—68no—
344Dic6—62no—
345Dic6—62no—
346Dic6—68no—
347Dic6—122no—
348Dic6C2×C4×D314yes—
349C3×C8—22no—
350C3×C8—32no—
351C3×C8—61no—
352C3×C8C2×C4×D312yes—
353C3×C8C2×C4×D312yes—
354C3⋊C8—21no—
355C3⋊C8—61no—
356C3⋊C8—61no—
357C3⋊C8—121no—
358C3⋊C8C2×C4×D312yes—
359C2×C32C2×C4×D411yescharacteristic
360C2×C32C2×#13712yes—
361C3×D3#44114yescomplemented
362C2×Q8—32no—
363C2×Q8—98no—
364C2×Q8—92no—
365C2×Q8—182no—
366C2×Q8—184no—
367C22×C4—31no—
368C22×C4—62no—
369C22×C4—92no—
370C22×C4—182no—
371Q16—34no—
372Q16—98no—
373Q16—94no—
374C2×C8—31no—
375C2×C8—34no—
376C2×C8—31no—
377C2×C8—91no—
378C2×C8—182no—
379C2×C8C2×D3211yescharacteristic
380C4⋊C4—32no—
381C4⋊C4—62no—
382C4⋊C4—62no—
383C4⋊C4—182no—
384C4⋊C4—182no—
385C4⋊C4—182no—
386C4⋊C4C2×D3212yes—
387C42—31no—
388C42—62no—
389C42—92no—
390C42—91no—
391C42—182no—
392C42—182no—
393C42—182no—
394C22×C3—21no—
395C22×C3—34no—
396C22×C3—32no—
397C22×C3C2×D3×D411yescharacteristic
398C22×C3C2×D3×D411yescharacteristic
399C2×D3#89312yes—
400C2×D3#91514yes—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—32no—
404C3×C4—42no—
405C3×C4—42no—
406C3×C4—64no—
407C3×C4—62no—
408C3×C4—82no—
409C3×C4—122no—
410C3×C4C22×C4×D311yescharacteristic
411C3×C4C22×C4×D311yescharacteristic
412C3×C4C2×#23911yescharacteristic
413C3×C4D3×#4111yescharacteristic
414Dic3—22no—
415Dic3—24no—
416Dic3—42no—
417Dic3—64no—
418Dic3—62no—
419Dic3—62no—
420Dic3—64no—
421Dic3—124no—
422Dic3—122no—
423Dic3#89312yes—
424C32C2×#44111yescharacteristic, complemented, Sylow
425C23—31no—
426Q8—34no—
427Q8—62no—
428Q8—94no—
429Q8—188no—
430Q8—182no—
431C2×C4—22no—
432C2×C4—31no—
433C2×C4—32no—
434C2×C4—32no—
435C2×C4—32no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—92no—
439C2×C4—124no—
440C2×C4—184no—
441C2×C4—188no—
442C2×C4—182no—
443C2×C4C22×D3211yescharacteristic
444C8—32no—
445C8—61no—
446C8—181no—
447C8C4×D3212yes—
448C2×C3—21no—
449C2×C3—22no—
450C2×C3—34no—
451C2×C3C2×#89311yescharacteristic
452C2×C3C4×D3×D411yescharacteristic
453C2×C3C2×#91512yes—
454C2×C3D3×#13712yes—
455D3#485314yesdirect product factor
456C22—32no—
457C22—34no—
458C22D32×D411yescharacteristic
459C4—32no—
460C4—42no—
461C4—64no—
462C4—62no—
463C4—122no—
464C4—184no—
465C4—182no—
466C4C2×C4×D3211yescharacteristic
467C4D3×#23911yescharacteristic
468C3—21no—
469C3C2×#485311yescharacteristic, complemented
470C3D3×#44111yescharacteristic, complemented
471C2—34no—
472C2D3×#89311yescharacteristic
473C2D3×#91512yes—
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32C2×#441
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. #10592552C2semidirect
5. C3×#4853C2semidirect
6. #10590819C2semidirect
7. #10590810C2semidirect
10. #10590485C2semidirect
11. #10590480C2semidirect
30. D3×Dic12C4semidirect
60. #4853D3direct (N × H)
80. #3746C2×C4semidirect
88. C3×Dic12C2×C4semidirect
95. #3719C2×C4semidirect
262. Dic12C4×D3semidirect
361. C3×D3#441semidirect
424. C32C2×#441semidirect
455. D3#4853direct (N × H)
469. C3C2×#4853semidirect
470. C3D3×#441semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic122
D3×#8872
#105925522
C3×D3×#1062
C3×#48532
#105908192
#105908102
D3×#8152
D3×#8102
#105904852
#105904802
D3×#4413
C2×#48533