Finite Group Databasebeta

← C4×D3×Dic12 #11859940

Subgroups — C4×D3×Dic12 #11859940

Order 1152.

1031 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Dic12C211yesmaximal, characteristic
2C4×D3×Dic6C212yesmaximal
3C4×#3746C211yesmaximal, characteristic, complemented
4C3×C4×Dic12C211yesmaximal, characteristic, complemented
5C3×C4×D3×C8C211yesmaximal, characteristic
6#10590807C211yesmaximal, characteristic, complemented
7Dic3×Dic12C211yesmaximal, characteristic, complemented
8#10590793C212yesmaximal, complemented
9D3×#818C211yesmaximal, characteristic
10D3×#816C212yesmaximal
11C4×#3719C212yesmaximal, complemented
12C4×D3×Q16—31nomaximal
13C2×C4×Dic12—31nomaximal
14C2×D3×Dic6C2212yes—
15C2×#3746C2211yescharacteristic
16C4×#634C2212yes—
17C2×C3×Dic12C2211yescharacteristic
18C2×C3×D3×C8C2211yescharacteristic
19C2×C3×D3×C8C2211yescharacteristic
20C3×C42×D3C2211yescharacteristic
21C3×C4×Dic6C2212yes—
22C4×#627—22no—
23D3×C4⋊Dic3C2212yes—
24D3×Dic3⋊C4—22no—
25C4×D3×Dic3—22no—
26#63844C2212yes—
27Dic3×Dic6C2212yes—
28#63837—22no—
29C2×#3719C2212yes—
30D3×Dic12C418yesdirect product factor
31C32×C4×C8C2211yescharacteristic
32#63645C2211yescharacteristic
33#63643C2212yes—
34C3×#818C2211yescharacteristic
35C3×#816C2212yes—
36C3×C8×Dic3C2211yescharacteristic
37C3×C8×Dic3C2211yescharacteristic
38C3×C4×C3⋊C8C2211yescharacteristic
39#63575C2212yes—
40#63567C2212yes—
41#63566C2212yes—
42C2×D3×Q16—31no—
43C22×Dic12—31no—
44C4×D3×Q8—32no—
45C2×C4×Dic6—32no—
46C3×C4×Q16—31no—
47C2×C3×C4×C8—31no—
48Dic3×Q16—31no—
49C2×#818—31no—
50C2×#816—32no—
51C4×#216—32no—
52D3×#107—31no—
53#4873—31no—
54D3×#103—32no—
55#4790—32no—
56C4×Dic12—31no—
57C4×Dic12—32no—
58C4×Dic12—31no—
59C4×Dic12—31no—
60C4×Dic12—31no—
61C4×Dic12—32no—
62C4×Dic12—61no—
63C4×Dic12D311yescharacteristic, direct product factor
64C4×D3×C8D311yescharacteristic
65C2×#634C2312yes—
66C2×C3×C4×D3D411yescharacteristic
67C2×C3×C4×D3D411yescharacteristic
68C2×C3×C4×D3C2311yescharacteristic
69C2×C3×Dic6C2312yes—
70C2×#627—22no—
71C2×D3×Dic3—22no—
72C2×D3×Dic3—22no—
73D3×Dic6—24no—
74D3×Dic6C2×C418yes—
75C2×C32×C8C2311yescharacteristic
76C2×C32×C8C2311yescharacteristic
77C32×C42C2311yescharacteristic
78C4⋊(C3⋊Dic3)C2312yes—
79#3750—22no—
80C4×C3⋊Dic3—22no—
81#3746C2×C414yescomplemented
82C3×C4⋊Dic3C2312yes—
83C3×Dic3⋊C4—22no—
84C3×C4×Dic3—22no—
85C3×C4×Dic3D411yescharacteristic
86C3×C4×Dic3D411yescharacteristic
87C3×C4×Dic3C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90C3×Dic12C2×C414yescomplemented
91C3×D3×C8—22no—
92C3×D3×C8C2×C414yes—
93#3724—22no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96Dic32—22no—
97Dic32—22no—
98#3719C2×C418yescomplemented
99C2×C4×Q16—91noSylow
100C2×D3×Q8—32no—
101C22×Dic6—32no—
102C2×C3×Q16—31no—
103C22×C3×C8—31no—
104C22×C3×C8—31no—
105C3×C4×Q8—32no—
106C2×C3×C42—31no—
107Q8×Dic3—32no—
108C2×#216—32no—
109C2×C4⋊Dic3—32no—
110C2×Dic3⋊C4—62no—
111C2×C4×Dic3—62no—
112D3×Q16—38no—
113C2×Dic12—32no—
114C2×Dic12—31no—
115C2×Dic12—31no—
116C2×Dic12—38no—
117C2×Dic12—61no—
118C2×Dic12C2×D311yescharacteristic
119C2×D3×C8C2×D311yescharacteristic
120C2×D3×C8C2×D311yescharacteristic
121D3×C4⋊C4—32no—
122D3×C4⋊C4—62no—
123#887—32no—
124#887—62no—
125C42×D3—62no—
126C42×D3C2×D311yescharacteristic
127C4×Dic6—32no—
128C4×Dic6—32no—
129C4×Dic6—32no—
130C4×Dic6—32no—
131C4×Dic6—62no—
132C4×Dic6—62no—
133C4×Dic6—62no—
134C4×Dic6—62no—
135C4×Dic6C2×D312yes—
136C3×#107—31no—
137C3×#103—32no—
138C3×C4×C8—21no—
139C3×C4×C8—31no—
140C3×C4×C8—31no—
141C3×C4×C8—31no—
142C3×C4×C8C2×D311yescharacteristic
143C3×C4×C8C2×D311yescharacteristic
144#835—32no—
145#818—31no—
146#818—31no—
147#818—32no—
148#818—61no—
149#818C2×D311yescharacteristic
150#816—32no—
151#816—32no—
152#816—32no—
153#816—32no—
154#816—62no—
155#816C2×D312yes—
156C8×Dic3C2×D311yescharacteristic
157C8×Dic3C2×D311yescharacteristic
158#810—32no—
159#807—32no—
160C4×C3⋊C8C2×D311yescharacteristic
161C22×C3×D3C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2411yescharacteristic
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167#634—22no—
168#634C22×C414yes—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3C2×D411yescharacteristic
172C2×C3×Dic3C2×D411yescharacteristic
173C2×C3×Dic3C2×D411yescharacteristic
174C3×C4×D3—22no—
175C3×C4×D3Q1614yescomplemented
176C3×C4×D3C22×C412yes—
177C3×C4×D3#4112yes—
178C3×Dic6—22no—
179C3×Dic6C22×C414yes—
180#627—28no—
181D3×Dic3—28no—
182D3×Dic3—44no—
183C32×C8—21no—
184C32×C8C22×C412yes—
185C3×C3⋊C8—21no—
186C3×C3⋊C8C22×C412yes—
187C22×Q16—91no—
188C2×C4×Q8—92no—
189C4×Q16—31no—
190C4×Q16—92no—
191C4×Q16—91no—
192C4×Q16—92no—
193C4×Q16—91no—
194C4×Q16—91no—
195C2×#107—91no—
196C2×#103—92no—
197C2×C4×C8—31no—
198C2×C3×Q8—32no—
199C22×C3×C4—31no—
200C22×C3×C4—31no—
201C22×C3×C4—31no—
202C22×Dic3—62no—
203C22×Dic3—62no—
204D3×Q8—38no—
205D3×Q8—64no—
206C2×C4×D3—62no—
207C2×C4×D3—62no—
208C2×C4×D3D1211yescharacteristic
209C2×C4×D3D1211yescharacteristic
210C2×C4×D3C22×D311yescharacteristic
211C2×Dic6—32no—
212C2×Dic6—32no—
213C2×Dic6—38no—
214C2×Dic6—62no—
215C2×Dic6—64no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6C22×D312yes—
219C3×Q16—34no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8—31no—
223C2×C3×C8—34no—
224C2×C3×C8—31no—
225C2×C3×C8—62no—
226C2×C3×C8C22×D311yescharacteristic
227C2×C3×C8C22×D311yescharacteristic
228C2×C3×C8C22×D311yescharacteristic
229C2×C3×C8C22×D311yescharacteristic
230C3×C4⋊C4—32no—
231C3×C4⋊C4—62no—
232C3×C42—21no—
233C3×C42—31no—
234C3×C42—31no—
235C3×C42—31no—
236C3×C42—62no—
237C3×C42C22×D311yescharacteristic
238C3×C42C22×D311yescharacteristic
239#216—38no—
240C4⋊Dic3—32no—
241C4⋊Dic3—32no—
242C4⋊Dic3—62no—
243C4⋊Dic3—62no—
244C4⋊Dic3—62no—
245C4⋊Dic3C22×D312yes—
246Dic3⋊C4—22no—
247Dic3⋊C4—62no—
248Dic3⋊C4—62no—
249Dic3⋊C4—62no—
250Dic3⋊C4—62no—
251Dic3⋊C4—62no—
252Dic3⋊C4—62no—
253Dic3⋊C4—122no—
254C4×Dic3—22no—
255C4×Dic3—62no—
256C4×Dic3—62no—
257C4×Dic3—62no—
258C4×Dic3—62no—
259C4×Dic3—62no—
260C4×Dic3—62no—
261C4×Dic3—122no—
262C4×Dic3D1211yescharacteristic
263C4×Dic3D1211yescharacteristic
264C4×Dic3C22×D311yescharacteristic
265C2×C3⋊C8C22×D311yescharacteristic
266C2×C3⋊C8C22×D311yescharacteristic
267Dic12—38no—
268Dic12—34no—
269Dic12—34no—
270Dic12—64no—
271Dic12C4×D314yesdirect product factor
272D3×C8—22no—
273D3×C8C4×D314yes—
274C22×C32C22×D411yescharacteristic
275C2×C3×D3C4×D412yes—
276C2×C3×D3C2×Q1612yes—
277C2×C3×D3#13512yes—
278C32×C4—21no—
279C32×C4C2×Q1612yescomplemented
280C32×C4C23×C411yescharacteristic
281C32×C4C2×#4111yescharacteristic
282C3⋊Dic3—24no—
283C3⋊Dic3—42no—
284C3×Dic3—24no—
285C3×Dic3—21no—
286C3×Dic3—42no—
287C3×Dic3C4×D412yes—
288C3×Dic3C2×Q1612yescomplemented
289C22×Q8—92no—
290C2×Q16—31no—
291C2×Q16—98no—
292C2×Q16—92no—
293C2×Q16—91no—
294C22×C8—31no—
295C22×C8—31no—
296C4×Q8—32no—
297C4×Q8—92no—
298C4×Q8—92no—
299C4×Q8—92no—
300C4×Q8—182no—
301C4×Q8—182no—
302C2×C4⋊C4—92no—
303C2×C4⋊C4—182no—
304C2×C42—31no—
305C2×C42—182no—
306#107—31no—
307#107—92no—
308#107—91no—
309#103—32no—
310#103—92no—
311#103—92no—
312#103—92no—
313C4×C8—31no—
314C4×C8—31no—
315C4×C8—31no—
316C4×C8D3211yescharacteristic
317C23×C3—31no—
318C22×D3C2×D1211yescharacteristic
319C3×Q8—34no—
320C3×Q8—62no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—31no—
325C2×C3×C4—31no—
326C2×C3×C4—34no—
327C2×C3×C4—32no—
328C2×C3×C4—32no—
329C2×C3×C4—31no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4C2×D1211yescharacteristic
334C2×C3×C4C2×D1211yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4C23×D311yescharacteristic
338C2×C3×C4C23×D311yescharacteristic
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—68no—
342C2×Dic3—62no—
343C2×Dic3—62no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—122no—
347C2×Dic3—122no—
348C2×Dic3—124no—
349C2×Dic3C2×D1211yescharacteristic
350C2×Dic3C2×D1211yescharacteristic
351C2×Dic3C2×D1211yescharacteristic
352C4×D3—22no—
353C4×D3—68no—
354C4×D3—124no—
355C4×D3Dic1214yesdirect product factor
356C4×D3C2×C4×D312yes—
357C4×D3#23512yes—
358Dic6—22no—
359Dic6—34no—
360Dic6—34no—
361Dic6—64no—
362Dic6—68no—
363Dic6—62no—
364Dic6—62no—
365Dic6—68no—
366Dic6—122no—
367Dic6C2×C4×D314yes—
368C3×C8—21no—
369C3×C8—21no—
370C3×C8—22no—
371C3×C8—32no—
372C3×C8—41no—
373C3×C8—61no—
374C3×C8C2×C4×D312yes—
375C3×C8C2×C4×D312yes—
376C3⋊C8—21no—
377C3⋊C8C2×C4×D312yes—
378C2×C32C2×C4×D411yescharacteristic
379C2×C32C22×Q1611yescharacteristic
380C2×C32C2×#13511yescharacteristic
381C3×D3C4×Q1614yescomplemented
382C2×Q8—32no—
383C2×Q8—98no—
384C2×Q8—92no—
385C2×Q8—182no—
386C2×Q8—184no—
387C22×C4—31no—
388C22×C4—31no—
389C22×C4—31no—
390C22×C4—182no—
391C22×C4—182no—
392Q16—34no—
393Q16—98no—
394Q16—94no—
395C2×C8—31no—
396C2×C8—34no—
397C2×C8—31no—
398C2×C8—62no—
399C2×C8C2×D3211yescharacteristic
400C2×C8C2×D3211yescharacteristic
401C4⋊C4—32no—
402C4⋊C4—62no—
403C4⋊C4—92no—
404C4⋊C4—182no—
405C4⋊C4—182no—
406C4⋊C4—182no—
407C4⋊C4—182no—
408C42—31no—
409C42—31no—
410C42—31no—
411C42—62no—
412C42—182no—
413C42—182no—
414C42—182no—
415C42C2×D3211yescharacteristic
416C22×C3—21no—
417C22×C3—32no—
418C22×C3—32no—
419C22×C3—32no—
420C22×C3C22×D1211yescharacteristic
421C22×C3C2×D3×D411yescharacteristic
422C2×D3C4×D1212yes—
423C2×D3#90412yes—
424C2×D3C2×Dic1212yes—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—22no—
430C3×C4—32no—
431C3×C4—32no—
432C3×C4—41no—
433C3×C4—64no—
434C3×C4—61no—
435C3×C4—122no—
436C3×C4C2×Dic1212yescomplemented
437C3×C4D3×Q1612yescomplemented
438C3×C4C22×C4×D311yescharacteristic
439C3×C4C22×C4×D311yescharacteristic
440C3×C4C2×#23511yescharacteristic
441C3×C4D3×#4111yescharacteristic
442Dic3—21no—
443Dic3—24no—
444Dic3—42no—
445Dic3—64no—
446Dic3—64no—
447Dic3—124no—
448Dic3—122no—
449Dic3—122no—
450Dic3—242no—
451Dic3C4×D1212yes—
452Dic3C2×Dic1212yescomplemented
453C32C2×C4×Q1611yescharacteristic, complemented, Sylow
454C23—31no—
455Q8—34no—
456Q8—62no—
457Q8—94no—
458Q8—188no—
459Q8—182no—
460C2×C4—31no—
461C2×C4—31no—
462C2×C4—32no—
463C2×C4—32no—
464C2×C4—34no—
465C2×C4—31no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—188no—
470C2×C4—182no—
471C2×C4—182no—
472C2×C4—364no—
473C2×C4D3×D1211yescharacteristic
474C2×C4D3×D1211yescharacteristic
475C2×C4C22×D3211yescharacteristic
476C8—21no—
477C8—32no—
478C8—61no—
479C8C4×D3212yes—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—34no—
484C2×C3C2×C4×D1211yescharacteristic
485C2×C3C4×D3×D411yescharacteristic
486C2×C3C2×#90411yescharacteristic
487C2×C3C22×Dic1211yescharacteristic
488C2×C3C2×D3×Q1611yescharacteristic
489C2×C3D3×#13511yescharacteristic
490D3C4×Dic1214yesdirect product factor
491C22—32no—
492C22—32no—
493C22—32no—
494C22C2×D3×D1211yescharacteristic
495C4—21no—
496C4—32no—
497C4—32no—
498C4—61no—
499C4—64no—
500C4—122no—
501C4—184no—
502C4—362no—
503C4D3×Dic1212yesdirect product factor
504C4C2×C4×D3211yescharacteristic
505C4D3×#23511yescharacteristic
506C3—21no—
507C3C2×C4×Dic1211yescharacteristic, complemented
508C3C4×D3×Q1611yescharacteristic, complemented
509C2—34no—
510C2C4×D3×D1211yescharacteristic
511C2D3×#90411yescharacteristic
512C2C2×D3×Dic1211yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32C2×C4×Q16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
3. C4×#3746C2semidirect
4. C3×C4×Dic12C2semidirect
6. #10590807C2semidirect
7. Dic3×Dic12C2semidirect
8. #10590793C2semidirect
11. C4×#3719C2semidirect
30. D3×Dic12C4direct (N × H)
63. C4×Dic12D3direct (N × H)
81. #3746C2×C4semidirect
90. C3×Dic12C2×C4semidirect
98. #3719C2×C4semidirect
175. C3×C4×D3Q16semidirect
271. Dic12C4×D3direct (N × H)
279. C32×C4C2×Q16semidirect
288. C3×Dic3C2×Q16semidirect
355. C4×D3Dic12direct (N × H)
381. C3×D3C4×Q16semidirect
436. C3×C4C2×Dic12semidirect
437. C3×C4D3×Q16semidirect
452. Dic3C2×Dic12semidirect
453. C32C2×C4×Q16semidirect
490. D3C4×Dic12direct (N × H)
503. C4D3×Dic12direct (N × H)
507. C3C2×C4×Dic12semidirect
508. C3C4×D3×Q16semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic122
C4×D3×Dic62
C4×#37462
C3×C4×Dic122
C3×C4×D3×C82
#105908072
Dic3×Dic122
#105907932
D3×#8182
D3×#8162
C4×#37192
C4×D3×Q163
C2×C4×Dic123