Finite Group Databasebeta

← C3⋊C8×(C2×D3)⋊C4 #11783647

Subgroups — C3⋊C8×(C2×D3)⋊C4 #11783647

Order 1152.

827 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C3⋊C8C211yesmaximal, characteristic
2C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×C3×C4×C3⋊C8C211yesmaximal, characteristic, complemented
4C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
5C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
6#10589390C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8C8×(C2×D3)⋊C4—31nomaximal
9C22⋊C4×C3⋊C8—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4C412yes—
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×D3×C3⋊C8—22no—
19C2×D3×C3⋊C8—22no—
20C2×D3×C3⋊C8C414yescomplemented
21C3×C3⋊#95C412yes—
22C3×C4×C3⋊C8—22no—
23(C2×D3)⋊(C3⋊C8)C414yescomplemented
24Dic3×C3⋊C8—22no—
25C23×C3⋊C8—31no—
26C22×D3×C8—31no—
27C2×C3×C4×C8—31no—
28C3×C4×C22⋊C4—31no—
29C2×#830—31no—
30C2×(C2×D3)⋊C8—31no—
31C2×C8×Dic3—31no—
32C4×(C2×D3)⋊C4D311yescharacteristic
33C2×C4×C3⋊C8—31no—
34C2×C4×C3⋊C8D311yescharacteristic, complemented
35#4550—31no—
36#4524—31no—
37#4524—31no—
38#4524—31no—
39#4524—61no—
40C23×C3×D3C2×C411yescharacteristic
41C22×C32×C4C2×C412yes—
42C22×C32×C4C2311yescharacteristic
43C22×C3×Dic3C2×C411yescharacteristic
44C22×C3×Dic3C2×C412yes—
45C2×C3×C4×D3—21no—
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3—21no—
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3C2×C412yes—
50C2×C3×C4×D3C2×C412yes—
51C32×C42—21no—
52C32×C42—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)C2×C412yes—
58C2×C3⋊(C3⋊C8)C2×C412yes—
59C3×(C2×D3)⋊C4C818yescomplemented
60C3×C4×Dic3—21no—
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8C2×C412yes—
65C2×C3×C3⋊C8C2×C412yes—
66C2×C3×C3⋊C8D412yes—
67C2×C3×C3⋊C8D412yes—
68D3×C3⋊C8—28no—
69C8×C22⋊C4—91noSylow
70C23×C3×C4—31no—
71C22×C4×D3C2×D311yescharacteristic
72C22×C3×C8—31no—
73C22×C3×C8—31no—
74C2×C3×C22⋊C4—32no—
75C2×C3×C42—21no—
76C2×C3×C42—31no—
77C2×C3×C42C2×D311yescharacteristic
78C2×C3×C42C2×D311yescharacteristic
79C2×(C2×D3)⋊C4Dic312yes—
80C2×C4×Dic3C2×D311yescharacteristic
81C22×C3⋊C8—31no—
82C22×C3⋊C8—31no—
83C22×C3⋊C8—31no—
84C22×C3⋊C8—31no—
85C22×C3⋊C8—34no—
86C22×C3⋊C8—61no—
87C22×C3⋊C8—61no—
88C22×C3⋊C8—62no—
89C22×C3⋊C8—62no—
90C22×C3⋊C8C2×D311yescharacteristic
91C22×C3⋊C8C2×D311yescharacteristic
92C2×D3×C8—34no—
93C2×D3×C8—62no—
94C2×D3×C8—62no—
95C3×C4×C8—62no—
96C3×#95—32no—
97C3⋊#95Dic312yes—
98#830—34no—
99(C2×D3)⋊C8—34no—
100C8×Dic3—62no—
101C4×C3⋊C8—22no—
102C4×C3⋊C8—62no—
103C23×C32C22×C411yescharacteristic
104C22×C3×D3—21no—
105C22×C3×D3—21no—
106C22×C3×D3—22no—
107C22×C3×D3C4212yes—
108C22×C3×D3C2×C814yes—
109C2×C32×C4—22no—
110C2×C32×C4—22no—
111C2×C32×C4C2×C814yescomplemented
112C2×C32×C4C22×C411yescharacteristic
113C2×C32×C4C22×C411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C3×Dic3—22no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3C4212yes—
123C2×C3×Dic3C2×C814yescomplemented
124C3×C4×D3—22no—
125C3×C4×D3—22no—
126C3×C4×D3—22no—
127C3×C4×D3—22no—
128C3⋊(C3⋊C8)—22no—
129C3⋊(C3⋊C8)—22no—
130C3×C3⋊C8—22no—
131C3×C3⋊C8C22⋊C414yescomplemented
132C23×C8—91no—
133C2×C22⋊C8—91no—
134C2×C4×C8—31no—
135C2×C4×C8—91no—
136C4×C22⋊C4—31no—
137#336—91no—
138#336—91no—
139C24×C3—31no—
140C23×D3C2×Dic311yescharacteristic
141C22×C3×C4—22no—
142C22×C3×C4—21no—
143C22×C3×C4—31no—
144C22×C3×C4—32no—
145C22×C3×C4—32no—
146C22×C3×C4—32no—
147C22×C3×C4—61no—
148C22×C3×C4—61no—
149C22×C3×C4—61no—
150C22×C3×C4—61no—
151C22×C3×C4C4×D312yes—
152C22×C3×C4C2×Dic312yes—
153C22×C3×C4C22×D311yescharacteristic
154C22×C3×C4C22×D311yescharacteristic
155C22×Dic3C2×Dic312yes—
156C22×Dic3C2×Dic311yescharacteristic
157C2×C4×D3—21no—
158C2×C4×D3—21no—
159C2×C4×D3—21no—
160C2×C4×D3—21no—
161C2×C4×D3C4×D312yes—
162C2×C4×D3C4×D312yes—
163C2×C3×C8—32no—
164C2×C3×C8—32no—
165C2×C3×C8—32no—
166C2×C3×C8—32no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C3×C22⋊C4—38no—
170C3×C42—21no—
171C3×C42—21no—
172C3×C42—21no—
173C3×C42—21no—
174C3×C42—41no—
175C3×C42—41no—
176C3×C42—61no—
177C3×C42—61no—
178(C2×D3)⋊C4C3⋊C818yesdirect product factor
179C4×Dic3—21no—
180C4×Dic3—21no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—32no—
184C2×C3⋊C8—32no—
185C2×C3⋊C8—32no—
186C2×C3⋊C8—32no—
187C2×C3⋊C8—62no—
188C2×C3⋊C8—62no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—68no—
198C2×C3⋊C8—121no—
199C2×C3⋊C8—121no—
200C2×C3⋊C8—121no—
201C2×C3⋊C8—121no—
202C2×C3⋊C8C4×D312yes—
203C2×C3⋊C8C4×D312yes—
204C2×C3⋊C8D1212yes—
205C2×C3⋊C8#6712yes—
206D3×C8—68no—
207C22×C32C2×C4211yescharacteristic
208C22×C32C4×D411yescharacteristic
209C22×C32C4×D411yescharacteristic
210C22×C32C22×C812yes—
211C22×C32#13112yes—
212C2×C3×D3—22no—
213C2×C3×D3—22no—
214C2×C3×D3—24no—
215C2×C3×D3—24no—
216C2×C3×D3C4×C814yescomplemented
217C32×C4—24no—
218C32×C4C2×C22⋊C411yescharacteristic
219C32×C4#11711yescharacteristic
220C32×C4C4×D411yescharacteristic
221C32×C4C4×D411yescharacteristic
222C3×Dic3—22no—
223C3×Dic3—24no—
224C23×C4—31no—
225C22×C8—31no—
226C22×C8—31no—
227C22×C8—94no—
228C22×C8—91no—
229C22×C8—91no—
230C22×C8—182no—
231C22×C8—182no—
232C2×C22⋊C4—32no—
233C2×C42—31no—
234C2×C42D3211yescharacteristic
235C22⋊C8—94no—
236C4×C8—62no—
237C4×C8—182no—
238#95—32no—
239C23×C3—21no—
240C23×C3—32no—
241C23×C3—34no—
242C23×C3—61no—
243C23×C3—62no—
244C23×C3—61no—
245C23×C3C2×C4×D311yescharacteristic
246C23×C3C22×Dic311yescharacteristic
247C22×D3—21no—
248C22×D3—21no—
249C22×D3—22no—
250C22×D3C2×C3⋊C814yes—
251C22×D3C4×Dic312yes—
252C2×C3×C4—22no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—24no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—32no—
264C2×C3×C4—34no—
265C2×C3×C4—42no—
266C2×C3×C4—42no—
267C2×C3×C4—62no—
268C2×C3×C4—61no—
269C2×C3×C4—62no—
270C2×C3×C4—61no—
271C2×C3×C4—62no—
272C2×C3×C4—62no—
273C2×C3×C4—62no—
274C2×C3×C4—62no—
275C2×C3×C4D3×C814yescomplemented
276C2×C3×C4C2×C3⋊C814yescomplemented
277C2×C3×C4C2×C4×D311yescharacteristic
278C2×C3×C4C2×C4×D311yescharacteristic
279C2×C3×C4C2×C4×D311yescharacteristic
280C2×C3×C4C2×C4×D311yescharacteristic
281C2×C3×C4C2×D1211yescharacteristic
282C2×C3×C4#23511yescharacteristic
283C2×C3×C4#23511yescharacteristic
284C2×C3×C4D3×D411yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4#23711yescharacteristic
287C2×C3×C4#23711yescharacteristic
288C2×C3×C4C2×#6711yescharacteristic
289C2×Dic3—22no—
290C2×Dic3—21no—
291C2×Dic3—21no—
292C2×Dic3—22no—
293C2×Dic3C2×C3⋊C814yescomplemented
294C2×Dic3C4×Dic312yes—
295C4×D3—22no—
296C4×D3—22no—
297C4×D3—22no—
298C4×D3—22no—
299C3×C8—34no—
300C3×C8—62no—
301C3⋊C8—22no—
302C3⋊C8—62no—
303C3⋊C8—62no—
304C3⋊C8—62no—
305C3⋊C8—62no—
306C3⋊C8—122no—
307C3⋊C8—122no—
308C3⋊C8(C2×D3)⋊C414yesdirect product factor
309C2×C32C4×C22⋊C411yescharacteristic
310C2×C32C2×C4×C811yescharacteristic
311C2×C32#40511yescharacteristic
312C2×C32C8×D412yes—
313C2×C32C8×D412yes—
314C3×D3—24no—
315C24—31no—
316C22×C4—31no—
317C22×C4—32no—
318C22×C4—32no—
319C22×C4—32no—
320C22×C4—61no—
321C22×C4—61no—
322C22×C4—61no—
323C22×C4—61no—
324C22×C4D3×Dic312yes—
325C22×C4C2×D3211yescharacteristic
326C2×C8—32no—
327C2×C8—32no—
328C2×C8—32no—
329C2×C8—32no—
330C2×C8—61no—
331C2×C8—61no—
332C2×C8—92no—
333C2×C8—92no—
334C2×C8—188no—
335C2×C8—181no—
336C2×C8—181no—
337C2×C8—181no—
338C2×C8—181no—
339C22⋊C4—38no—
340C42—21no—
341C42—21no—
342C42—61no—
343C42—61no—
344C22×C3—22no—
345C22×C3—22no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—34no—
350C22×C3—62no—
351C22×C3—64no—
352C22×C3—62no—
353C22×C3—64no—
354C22×C3C42×D311yescharacteristic
355C22×C3C4×D1211yescharacteristic
356C22×C3C2×D3×C812yes—
357C22×C3#90112yes—
358C22×C3C22×C3⋊C812yes—
359C22×C3C2×C4×Dic311yescharacteristic
360C22×C3C4×#6711yescharacteristic
361C22×C3D4×Dic311yescharacteristic
362C22×C3D4×Dic311yescharacteristic
363C22×C3#94812yes—
364C2×D3—22no—
365C2×D3—22no—
366C2×D3—24no—
367C2×D3—24no—
368C2×D3C4×C3⋊C814yescomplemented
369C3×C4—24no—
370C3×C4—24no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—44no—
376C3×C4—62no—
377C3×C4—64no—
378C3×C4#87211yescharacteristic
379C3×C4C4×D1211yescharacteristic
380C3×C4#87711yescharacteristic
381C3×C4D3×C22⋊C411yescharacteristic
382C3×C4#67⋊C411yescharacteristic
383C3×C4#67⋊C411yescharacteristic
384C3×C4C2×(C2×D3)⋊C411yescharacteristic
385C3×C4C4×#6711yescharacteristic
386Dic3—22no—
387Dic3—24no—
388C32C8×C22⋊C411yescharacteristic, complemented, Sylow
389C23—34no—
390C23—32no—
391C23—62no—
392C23—61no—
393C23—61no—
394C23C2×D3×Dic311yescharacteristic
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—34no—
398C2×C4—32no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—62no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—62no—
407C2×C4D3×C3⋊C814yescomplemented
408C2×C4#379511yescharacteristic
409C2×C4C4×D3211yescharacteristic
410C2×C4C4×D3211yescharacteristic
411C2×C4D3×D1211yescharacteristic
412C2×C4#380411yescharacteristic
413C2×C4D3×#6711yescharacteristic
414C8—34no—
415C8—62no—
416C8—182no—
417C8—182no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—22no—
421C2×C3—21no—
422C2×C3—22no—
423C2×C3—64no—
424C2×C3C4×D3×C811yescharacteristic
425C2×C3C8×D1212yes—
426C2×C3#468911yescharacteristic
427C2×C3C2×C4×C3⋊C811yescharacteristic
428C2×C3C4×(C2×D3)⋊C411yescharacteristic
429C2×C3Dic3×C22⋊C411yescharacteristic
430C2×C3#499711yescharacteristic
431C2×C3D4×C3⋊C812yes—
432C2×C3D4×C3⋊C812yes—
433C2×C3C8×#6712yes—
434D3—24no—
435C22—34no—
436C22—62no—
437C22—64no—
438C22—62no—
439C22—64no—
440C22C2×D3×C3⋊C812yes—
441C22#6381412yes—
442C22C4×D3×Dic311yescharacteristic
443C22Dic3×D1211yescharacteristic
444C22Dic3×#6711yescharacteristic
445C4—24no—
446C4—64no—
447C4—62no—
448C4#6387711yescharacteristic
449C4#6387911yescharacteristic
450C4#6388011yescharacteristic
451C4D3×(C2×D3)⋊C411yescharacteristic
452C3—21no—
453C3C22⋊C4×C3⋊C811yescharacteristic, complemented
454C3C8×(C2×D3)⋊C411yescharacteristic, complemented
455C2—64no—
456C2C4×D3×C3⋊C811yescharacteristic
457C2#1059031811yescharacteristic
458C2C3⋊C8×D1212yes—
459C2C3⋊C8×#6712yes—
460C2Dic3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC2×C32C2×C4×C8
FittingC2×C32×C42C22
socleC23×C32C22×C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32C8×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C2×C3×C4×C3⋊C8C2semidirect
5. C2×Dic3×C3⋊C8C2semidirect
6. #10589390C2semidirect
7. #10589155C2semidirect
20. C2×D3×C3⋊C8C4semidirect
23. (C2×D3)⋊(C3⋊C8)C4semidirect
34. C2×C4×C3⋊C8D3semidirect
59. C3×(C2×D3)⋊C4C8semidirect
111. C2×C32×C4C2×C8semidirect
123. C2×C3×Dic3C2×C8semidirect
131. C3×C3⋊C8C22⋊C4semidirect
178. (C2×D3)⋊C4C3⋊C8direct (N × H)
216. C2×C3×D3C4×C8semidirect
275. C2×C3×C4D3×C8semidirect
276. C2×C3×C4C2×C3⋊C8semidirect
293. C2×Dic3C2×C3⋊C8semidirect
308. C3⋊C8(C2×D3)⋊C4direct (N × H)
368. C2×D3C4×C3⋊C8semidirect
388. C32C8×C22⋊C4semidirect
407. C2×C4D3×C3⋊C8semidirect
453. C3C22⋊C4×C3⋊C8semidirect
454. C3C8×(C2×D3)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×D3×C3⋊C82
C3×C4×(C2×D3)⋊C42
C2×C3×C4×C3⋊C82
C2×(C2×D3)⋊(C3⋊C8)2
C2×Dic3×C3⋊C82
#105893902
#105891552
C8×(C2×D3)⋊C43
C22⋊C4×C3⋊C83