Finite Group Databasebeta

← Dic6×C4⋊Dic3 #11805566

Subgroups — Dic6×C4⋊Dic3 #11805566

Order 1152.

1229 conjugacy classes of subgroups.

The subgroup lattice has 445 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C211yesmaximal, characteristic
2C2×Dic3×Dic6C212yesmaximal
3#10592634C211yesmaximal, characteristic
4C3×C4×C4⋊Dic3C211yesmaximal, characteristic
5#10591352C212yesmaximal
6#10591349C212yesmaximal
7#10591268C214yesmaximal
8Dic3×C4⋊Dic3C212yesmaximal
9Q8×C4⋊Dic3—31nomaximal
10C4⋊C4×Dic6—31nomaximal
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2212yes—
14C2×C4⋊(C3⋊Dic3)C2212yes—
15C2×C4⋊(C3⋊Dic3)C2212yes—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×C3×C4×Dic3C2212yes—
22C3×C4×Dic6C418yescomplemented
23C2×Dic3⋊Dic3C2214yes—
24C2×Dic3⋊Dic3C2214yes—
25C2×Dic32C2214yes—
26Dic3×Dic6—28no—
27C3×C3⋊#95C2212yes—
28#63579C2214yes—
29C2×C3×C4×Q8—31no—
30C2×Q8×Dic3—32no—
31C2×C4×Dic6—32no—
32C2×C4×Dic6D311yescharacteristic
33C3×C4×C4⋊C4—31no—
34#4984—32no—
35#4984—34no—
36#4975—32no—
37Dic3×C4⋊C4—32no—
38#4935—31no—
39#4935—31no—
40#4935—32no—
41#4935—61no—
42C4×C4⋊Dic3—32no—
43C4×C4⋊Dic3D311yescharacteristic
44#4928—32no—
45#4647—34no—
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3C2314yes—
50C22×C3×Dic3C2312yes—
51C22×C3×Dic3C2312yes—
52C22×C3×Dic3C2312yes—
53C22×C3×Dic3C2312yes—
54C2×C3×Dic6C2×C414yes—
55C2×C3×Dic6D414yes—
56C2×C3×Dic6Q814yes—
57C32×C42C2×C414yes—
58C4⋊(C3⋊Dic3)—24no—
59C4⋊(C3⋊Dic3)—24no—
60C4⋊(C3⋊Dic3)—42no—
61C3×C4⋊Dic3—22no—
62C3×C4⋊Dic3C2×C414yes—
63C3×C4⋊Dic3Q814yescomplemented
64C3×Dic3⋊C4C2×C418yes—
65C3×C4×Dic3—24no—
66C3×C4×Dic3C2×C418yes—
67Dic3⋊Dic3—28no—
68Dic3⋊Dic3—44no—
69Dic32—28no—
70Q8×C4⋊C4—91noSylow
71C22×C3×Q8—31no—
72C22×Dic6C2×D311yescharacteristic
73C3×C4×Q8—38no—
74C2×C3×C4⋊C4—32no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4—31no—
77C2×C3×C4⋊C4—31no—
78C2×C3×C42—21no—
79C2×C3×C42—32no—
80C2×C3×C42—32no—
81C2×C3×C42C2×D311yescharacteristic
82C2×C3×C42C2×D311yescharacteristic
83Q8×Dic3—68no—
84C2×C4⋊Dic3—32no—
85C2×C4⋊Dic3—32no—
86C2×C4⋊Dic3—32no—
87C2×C4⋊Dic3—32no—
88C2×C4⋊Dic3—34no—
89C2×C4⋊Dic3—32no—
90C2×C4⋊Dic3—32no—
91C2×C4⋊Dic3—34no—
92C2×C4⋊Dic3—62no—
93C2×C4⋊Dic3—62no—
94C2×C4⋊Dic3—62no—
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×Dic3⋊C4—34no—
99C2×Dic3⋊C4—34no—
100C2×Dic3⋊C4C2×D312yes—
101C2×C4×Dic3—34no—
102C2×C4×Dic3—34no—
103C2×C4×Dic3C2×D312yes—
104C2×C4×Dic3C2×D312yes—
105C4×Dic6—68no—
106C4×Dic6Dic318yescomplemented
107C3×#95—32no—
108C3⋊#95—34no—
109C3⋊#95—34no—
110C3⋊#95C2×D312yes—
111C23×C32C2411yescharacteristic
112C2×C32×C4—21no—
113C2×C32×C4—21no—
114C2×C32×C4C22×C412yes—
115C2×C32×C4C22×C412yes—
116C2×C32×C4C22×C412yes—
117C2×C32×C4C2×D412yes—
118C2×C32×C4C2×Q812yes—
119C2×C32×C4C2×Q812yes—
120C2×C32×C4#4112yes—
121C2×C3⋊Dic3—24no—
122C2×C3⋊Dic3—24no—
123C2×C3⋊Dic3—24no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3C22×C414yes—
132C2×C3×Dic3C22×C414yes—
133C2×C3×Dic3C2×D414yes—
134C2×C3×Dic3C2×Q814yes—
135C2×C3×Dic3C2×Q814yes—
136C3×Dic6C4⋊C4116yescomplemented
137C2×C4×Q8—31no—
138C2×C4×Q8—92no—
139#389—94no—
140#389—92no—
141#384—92no—
142#384—91no—
143C4×C4⋊C4—31no—
144C4×C4⋊C4—92no—
145C2×C3×Q8—34no—
146C2×C3×Q8—34no—
147C2×C3×Q8—34no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—32no—
152C22×C3×C4—32no—
153C22×C3×C4—32no—
154C22×C3×C4—32no—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×Dic3—34no—
162C22×Dic3—34no—
163C22×Dic3—64no—
164C22×Dic3C22×D312yes—
165C22×Dic3C22×D312yes—
166C22×Dic3C22×D312yes—
167C22×Dic3C22×D312yes—
168C2×Dic6Dic614yes—
169C2×Dic6D1214yes—
170C2×Dic6C2×Dic314yes—
171C3×C4⋊C4—38no—
172C3×C4⋊C4—34no—
173C3×C4⋊C4—34no—
174C3×C4⋊C4—62no—
175C3×C42—24no—
176C3×C42—38no—
177C3×C42—64no—
178C3×C42C4×D314yes—
179C3×C42C2×Dic314yes—
180C4⋊Dic3—22no—
181C4⋊Dic3—68no—
182C4⋊Dic3—64no—
183C4⋊Dic3—64no—
184C4⋊Dic3—64no—
185C4⋊Dic3—64no—
186C4⋊Dic3—124no—
187C4⋊Dic3—124no—
188C4⋊Dic3—124no—
189C4⋊Dic3—122no—
190C4⋊Dic3—122no—
191C4⋊Dic3—124no—
192C4⋊Dic3Dic614yesdirect product factor
193C4⋊Dic3C2×Dic314yes—
194Dic3⋊C4—68no—
195Dic3⋊C4—124no—
196Dic3⋊C4C2×Dic318yes—
197C4×Dic3—24no—
198C4×Dic3—68no—
199C4×Dic3—68no—
200C4×Dic3C2×Dic318yes—
201C22×C32C23×C411yescharacteristic
202C22×C32C22×D411yescharacteristic
203C22×C32C22×Q811yescharacteristic
204C22×C32C22×Q811yescharacteristic
205C22×C32C2×#4111yescharacteristic
206C22×C32H(5,𝔽2)11yescharacteristic
207C22×C322−1+411yescharacteristic
208C32×C4—22no—
209C32×C4C2×C4⋊C414yes—
210C32×C4C4×Q814yescomplemented
211C3⋊Dic3—44no—
212C3×Dic3—24no—
213C3×Dic3—24no—
214C3×Dic3—42no—
215C3×Dic3C2×C4⋊C418yes—
216C22×Q8—31no—
217C4×Q8—38no—
218C4×Q8—188no—
219C2×C4⋊C4—32no—
220C2×C4⋊C4—31no—
221C2×C4⋊C4—31no—
222C2×C4⋊C4—31no—
223C2×C4⋊C4—94no—
224C2×C4⋊C4—92no—
225C2×C4⋊C4—92no—
226C2×C4⋊C4—94no—
227C2×C4⋊C4—92no—
228C2×C42—32no—
229C2×C42—32no—
230C2×C42—94no—
231C2×C42D3211yescharacteristic
232#95—32no—
233#95—94no—
234C23×C3—21no—
235C23×C3C23×D311yescharacteristic
236C23×C3C23×D311yescharacteristic
237C3×Q8—316no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—34no—
252C2×C3×C4—34no—
253C2×C3×C4—34no—
254C2×C3×C4—34no—
255C2×C3×C4—34no—
256C2×C3×C4—62no—
257C2×C3×C4—62no—
258C2×C3×C4—62no—
259C2×C3×C4—62no—
260C2×C3×C4—62no—
261C2×C3×C4—62no—
262C2×C3×C4—62no—
263C2×C3×C4C2×Dic612yes—
264C2×C3×C4C2×Dic612yes—
265C2×C3×C4C2×C4×D312yes—
266C2×C3×C4C2×C4×D312yes—
267C2×C3×C4C2×C4×D312yes—
268C2×C3×C4C2×D1212yes—
269C2×C3×C4#23512yes—
270C2×C3×C4D3×D412yes—
271C2×C3×C4D3×Q812yes—
272C2×C3×C4D3×Q812yes—
273C2×C3×C4#23912yes—
274C2×C3×C4C22×Dic312yes—
275C2×C3×C4C22×Dic312yes—
276C2×C3×C4C22×Dic312yes—
277C2×Dic3—22no—
278C2×Dic3—22no—
279C2×Dic3—22no—
280C2×Dic3—22no—
281C2×Dic3—22no—
282C2×Dic3—22no—
283C2×Dic3—22no—
284C2×Dic3—64no—
285C2×Dic3—64no—
286C2×Dic3—64no—
287C2×Dic3—64no—
288C2×Dic3—64no—
289C2×Dic3—64no—
290C2×Dic3—124no—
291C2×Dic3—124no—
292C2×Dic3—124no—
293C2×Dic3C2×Dic614yes—
294C2×Dic3C2×Dic614yes—
295C2×Dic3C2×D1214yes—
296C2×Dic3C22×Dic314yes—
297C2×Dic3C22×Dic314yes—
298Dic6C4⋊Dic3116yesdirect product factor
299C2×C32C22×C4⋊C411yescharacteristic
300C2×C32C2×C4×Q811yescharacteristic
301C2×C32#52011yescharacteristic
302C2×C32D4×Q811yescharacteristic
303C2×C32#55011yescharacteristic
304C2×C32#55711yescharacteristic
305C2×C32Q8211yescharacteristic
306C2×Q8—34no—
307C2×Q8—34no—
308C2×Q8—34no—
309C22×C4—32no—
310C22×C4—32no—
311C22×C4—32no—
312C22×C4—32no—
313C22×C4—94no—
314C22×C4C2×D3211yescharacteristic
315C22×C4C2×D3211yescharacteristic
316C22×C4C2×D3211yescharacteristic
317C4⋊C4—34no—
318C4⋊C4—38no—
319C4⋊C4—34no—
320C4⋊C4—62no—
321C4⋊C4—188no—
322C4⋊C4—184no—
323C4⋊C4—184no—
324C4⋊C4—362no—
325C4⋊C4—364no—
326C42—38no—
327C42—64no—
328C42—188no—
329C42D3×Dic314yes—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3C22×Dic611yescharacteristic
338C22×C3C22×Dic611yescharacteristic
339C22×C3C22×C4×D311yescharacteristic
340C22×C3C22×D1211yescharacteristic
341C22×C3C2×#23511yescharacteristic
342C22×C3C2×D3×D411yescharacteristic
343C22×C3C2×D3×Q811yescharacteristic
344C22×C3C2×D3×Q811yescharacteristic
345C22×C3C2×#23911yescharacteristic
346C22×C3#100911yescharacteristic
347C22×C3#100911yescharacteristic
348C22×C3#101011yescharacteristic
349C22×C3#101011yescharacteristic
350C22×C3C23×Dic311yescharacteristic
351C3×C4—24no—
352C3×C4—22no—
353C3×C4—22no—
354C3×C4—24no—
355C3×C4—24no—
356C3×C4—38no—
357C3×C4—64no—
358C3×C4—64no—
359C3×C4—122no—
360C3×C4C4×Dic614yescomplemented
361C3×C4D3×C4⋊C414yes—
362C3×C4C2×C4⋊Dic314yes—
363C3×C4Q8×Dic314yescomplemented
364Dic3—24no—
365Dic3—24no—
366Dic3—42no—
367Dic3—124no—
368Dic3—124no—
369Dic3—244no—
370Dic3C2×C4⋊Dic318yes—
371C32Q8×C4⋊C411yescharacteristic, complemented, Sylow
372C23C22×D3211yescharacteristic
373Q8—316no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—34no—
377C2×C4—34no—
378C2×C4—34no—
379C2×C4—34no—
380C2×C4—34no—
381C2×C4—62no—
382C2×C4—62no—
383C2×C4—62no—
384C2×C4—62no—
385C2×C4—62no—
386C2×C4—62no—
387C2×C4—62no—
388C2×C4—184no—
389C2×C4—184no—
390C2×C4—184no—
391C2×C4D3×Dic612yes—
392C2×C4D3×Dic612yes—
393C2×C4#379912yes—
394C2×C4D3×D1212yes—
395C2×C4C2×D3×Dic312yes—
396C2×C4C2×D3×Dic312yes—
397C2×C4C2×D3×Dic312yes—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3C2×C4×Dic611yescharacteristic
406C2×C3C2×D3×C4⋊C411yescharacteristic
407C2×C3#552311yescharacteristic
408C2×C3D4×Dic611yescharacteristic
409C2×C3#555311yescharacteristic
410C2×C3Q8×Dic611yescharacteristic
411C2×C3Q8×Dic611yescharacteristic
412C2×C3#556711yescharacteristic
413C2×C3#557011yescharacteristic
414C2×C3Q8×D1211yescharacteristic
415C2×C3#557711yescharacteristic
416C2×C3C22×C4⋊Dic311yescharacteristic
417C2×C3C2×Q8×Dic311yescharacteristic
418C2×C3#582711yescharacteristic
419C22C2×D3×Dic611yescharacteristic
420C22C2×D3×Dic611yescharacteristic
421C22#6429811yescharacteristic
422C22C2×#379911yescharacteristic
423C22C2×D3×D1211yescharacteristic
424C22#6430811yescharacteristic
425C22C22×D3×Dic311yescharacteristic
426C4—22no—
427C4—38no—
428C4—64no—
429C4—64no—
430C4—122no—
431C4—364no—
432C4Dic3×Dic614yescomplemented
433C4D3×C4⋊Dic314yes—
434C3—21no—
435C3C4⋊C4×Dic611yescharacteristic, complemented
436C3Q8×C4⋊Dic311yescharacteristic, complemented
437C2Dic6211yescharacteristic
438C2#1059386011yescharacteristic
439C2Dic6×D1211yescharacteristic
440C2#1059390211yescharacteristic
441C2C2×Dic3×Dic611yescharacteristic
442C2C2×D3×C4⋊Dic311yescharacteristic
443C2#1059499211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32Q8×C4⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
22. C3×C4×Dic6C4semidirect
63. C3×C4⋊Dic3Q8semidirect
106. C4×Dic6Dic3semidirect
136. C3×Dic6C4⋊C4semidirect
192. C4⋊Dic3Dic6direct (N × H)
210. C32×C4C4×Q8semidirect
298. Dic6C4⋊Dic3direct (N × H)
360. C3×C4C4×Dic6semidirect
363. C3×C4Q8×Dic3semidirect
371. C32Q8×C4⋊C4semidirect
432. C4Dic3×Dic6semidirect
435. C3C4⋊C4×Dic6semidirect
436. C3Q8×C4⋊Dic3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×Dic62
C2×Dic3×Dic62
#105926342
C3×C4×C4⋊Dic32
#105913522
#105913492
#105912682
Dic3×C4⋊Dic32
Q8×C4⋊Dic33
C4⋊C4×Dic63