Finite Group Databasebeta

← Dic3×#870 #11802485

Subgroups — Dic3×#870 #11802485

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 341 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#870C211yesmaximal, characteristic
2#10592635C211yesmaximal, characteristic
3C3×C42×Dic3C211yesmaximal, characteristic
4#10591352C212yesmaximal
5Dic3×C4⋊Dic3C212yesmaximal
6Dic3×Dic3⋊C4C214yesmaximal
7#10591201C214yesmaximal
8Dic3×#125—31nomaximal
9C4×#870—31nomaximal
10C2×C32×C42C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2212yes—
12C2×C3×C4⋊Dic3C2212yes—
13C2×C3×Dic3⋊C4C2214yes—
14C2×C3×C4×Dic3C2212yes—
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2212yes—
17C2×C3×C4×Dic3C2211yescharacteristic
18C3×#870C418yescomplemented
19C2×Dic3⋊Dic3C2214yes—
20C2×Dic32C2214yes—
21#63658C2214yes—
22#63579C2214yes—
23#63579C2214yes—
24C2×C3×#125—31no—
25C2×#870D311yescharacteristic
26C3×C43—31no—
27#4984—32no—
28#4980—34no—
29Dic3×C4⋊C4—34no—
30Dic3×C4⋊C4—32no—
31#4936—31no—
32#4936—31no—
33#4936—61no—
34C4×C4⋊Dic3—32no—
35#4933—34no—
36C4×Dic3⋊C4—34no—
37C42×Dic3D311yescharacteristic
38#4928—32no—
39C22×C32×C4C2312yes—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3C2314yes—
42C22×C3×Dic3C2314yes—
43C22×C3×Dic3C2311yescharacteristic
44C22×C3×Dic3C2312yes—
45C22×C3×Dic3C2311yescharacteristic
46C32×C42C2×C414yes—
47C4⋊(C3⋊Dic3)—24no—
48C3×C4⋊Dic3C2×C418yes—
49C3×Dic3⋊C4C2×C4116yes—
50C3×C4×Dic3—22no—
51C3×C4×Dic3—24no—
52C3×C4×Dic3—24no—
53C3×C4×Dic3Q814yes—
54Dic3⋊Dic3—28no—
55Dic32—28no—
56C4×#125—91noSylow
57C3×#125—38no—
58C2×C3×C4⋊C4—34no—
59C2×C3×C4⋊C4—32no—
60C2×C3×C42—21no—
61C2×C3×C42—31no—
62C2×C3×C42—31no—
63C2×C3×C42—32no—
64C2×C3×C42—32no—
65C2×C3×C42C2×D311yescharacteristic
66C2×C3×C42C2×D311yescharacteristic
67C2×C4⋊Dic3—32no—
68C2×C4⋊Dic3—32no—
69C2×C4⋊Dic3—34no—
70C2×C4⋊Dic3—62no—
71C2×C4⋊Dic3C2×D312yes—
72C2×Dic3⋊C4—34no—
73C2×Dic3⋊C4C2×D314yes—
74C2×C4×Dic3—34no—
75C2×C4×Dic3—34no—
76C2×C4×Dic3C2×D312yes—
77C2×C4×Dic3C2×D312yes—
78C2×C4×Dic3C2×D311yescharacteristic
79C2×C4×Dic3C2×D311yescharacteristic
80#870Dic318yesdirect product factor
81C3⋊#95—34no—
82C3⋊#95—34no—
83C3⋊#95—34no—
84C3⋊#95—34no—
85C3⋊#95—34no—
86C3⋊#95—34no—
87C3⋊#95—64no—
88C23×C32C2411yescharacteristic
89C2×C32×C4—22no—
90C2×C32×C4—22no—
91C2×C32×C4C22×C414yes—
92C2×C32×C4C22×C412yes—
93C2×C32×C4C2×Q812yes—
94C2×C32×C4#4112yes—
95C2×C3⋊Dic3—24no—
96C2×C3⋊Dic3—24no—
97C2×C3⋊Dic3—24no—
98C2×C3×Dic3—24no—
99C2×C3×Dic3—24no—
100C2×C3×Dic3—22no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—22no—
103C2×C3×Dic3C22×C418yes—
104C2×C3×Dic3C2×Q812yes—
105C2×C3×Dic3C2×Q812yes—
106C2×C3×Dic3#4114yes—
107C2×C3×Dic3#4114yes—
108C2×#125—31no—
109#389—92no—
110#387—94no—
111#382—91no—
112C4×C4⋊C4—94no—
113C4×C4⋊C4—92no—
114C43—31no—
115C22×C3×C4—21no—
116C22×C3×C4—22no—
117C22×C3×C4—31no—
118C22×C3×C4—31no—
119C22×C3×C4—34no—
120C22×C3×C4—32no—
121C22×C3×C4C22×D312yes—
122C22×C3×C4C22×D312yes—
123C22×C3×C4C22×D311yescharacteristic
124C22×C3×C4C22×D311yescharacteristic
125C22×Dic3—34no—
126C22×Dic3—34no—
127C22×Dic3—64no—
128C22×Dic3C22×D311yescharacteristic
129C22×Dic3C22×D312yes—
130C22×Dic3C22×D314yes—
131C22×Dic3C22×D311yescharacteristic
132C3×C4⋊C4—316no—
133C3×C4⋊C4—38no—
134C3×C42—24no—
135C3×C42—34no—
136C3×C42—64no—
137C3×C42—64no—
138C3×C42—62no—
139C3×C42C4×D314yes—
140C3×C42C2×Dic314yes—
141C4⋊Dic3—64no—
142C4⋊Dic3—64no—
143C4⋊Dic3—68no—
144C4⋊Dic3—124no—
145C4⋊Dic3C2×Dic318yes—
146Dic3⋊C4—68no—
147Dic3⋊C4C2×Dic3116yes—
148C4×Dic3—22no—
149C4×Dic3—24no—
150C4×Dic3—24no—
151C4×Dic3—68no—
152C4×Dic3—68no—
153C4×Dic3Dic614yes—
154C22×C32C23×C411yescharacteristic
155C22×C32C22×Q811yescharacteristic
156C22×C32C2×#4111yescharacteristic
157C22×C32C2×#4112yes—
158C22×C32C2×#4112yes—
159C32×C4—24no—
160C32×C4C4×Q814yes—
161C3⋊Dic3—44no—
162C3×Dic3—28no—
163C3×Dic3—24no—
164C3×Dic3—22no—
165C3×Dic3#12514yescomplemented
166#125—38no—
167C2×C4⋊C4—34no—
168C2×C4⋊C4—32no—
169C2×C4⋊C4—94no—
170C2×C4⋊C4—92no—
171C2×C42—31no—
172C2×C42—32no—
173C2×C42—32no—
174C2×C42—31no—
175C2×C42—94no—
176C2×C42D3211yescharacteristic
177#95—94no—
178#95—94no—
179#95—94no—
180C23×C3—21no—
181C23×C3C23×D311yescharacteristic
182C23×C3C23×D311yescharacteristic
183C2×C3×C4—22no—
184C2×C3×C4—22no—
185C2×C3×C4—22no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—22no—
189C2×C3×C4—22no—
190C2×C3×C4—24no—
191C2×C3×C4—32no—
192C2×C3×C4—34no—
193C2×C3×C4—38no—
194C2×C3×C4—32no—
195C2×C3×C4—34no—
196C2×C3×C4—42no—
197C2×C3×C4—42no—
198C2×C3×C4—64no—
199C2×C3×C4—64no—
200C2×C3×C4—62no—
201C2×C3×C4—62no—
202C2×C3×C4—62no—
203C2×C3×C4C2×Dic612yes—
204C2×C3×C4C2×C4×D314yes—
205C2×C3×C4C2×C4×D312yes—
206C2×C3×C4#23512yes—
207C2×C3×C4D3×Q812yes—
208C2×C3×C4#23912yes—
209C2×C3×C4C22×Dic314yes—
210C2×C3×C4C22×Dic312yes—
211C2×Dic3—22no—
212C2×Dic3—22no—
213C2×Dic3—22no—
214C2×Dic3—24no—
215C2×Dic3—24no—
216C2×Dic3—64no—
217C2×Dic3—64no—
218C2×Dic3—64no—
219C2×Dic3—64no—
220C2×Dic3—64no—
221C2×Dic3—64no—
222C2×Dic3—124no—
223C2×Dic3—124no—
224C2×Dic3—124no—
225C2×Dic3C2×Dic612yes—
226C2×Dic3C2×Dic612yes—
227C2×Dic3#23514yes—
228C2×Dic3#23514yes—
229C2×Dic3C22×Dic318yes—
230C2×C32C2×C4×Q811yescharacteristic
231C2×C32C4×#4112yes—
232C2×C32C2×#12511yescharacteristic
233C2×C32#52912yes—
234C2×C32#53311yescharacteristic
235C22×C4—31no—
236C22×C4—31no—
237C22×C4—32no—
238C22×C4—34no—
239C22×C4—94no—
240C22×C4C2×D3212yes—
241C22×C4C2×D3211yescharacteristic
242C4⋊C4—316no—
243C4⋊C4—38no—
244C4⋊C4—188no—
245C4⋊C4—184no—
246C42—34no—
247C42—64no—
248C42—64no—
249C42—62no—
250C42—188no—
251C42D3×Dic314yes—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—22no—
255C22×C3—22no—
256C22×C3—21no—
257C22×C3C22×Dic611yescharacteristic
258C22×C3C22×C4×D311yescharacteristic
259C22×C3C2×#23511yescharacteristic
260C22×C3C2×#23512yes—
261C22×C3C2×#23512yes—
262C22×C3C2×D3×Q811yescharacteristic
263C22×C3C2×#23911yescharacteristic
264C22×C3D3×#4112yes—
265C22×C3D3×#4112yes—
266C22×C3C23×Dic311yescharacteristic
267C3×C4—24no—
268C3×C4—24no—
269C3×C4—24no—
270C3×C4—34no—
271C3×C4—44no—
272C3×C4—62no—
273C3×C4—64no—
274C3×C4—68no—
275C3×C4C4×Dic614yes—
276C3×C4Q8×Dic314yes—
277Dic3—22no—
278Dic3—24no—
279Dic3—28no—
280Dic3—124no—
281Dic3—124no—
282Dic3—244no—
283Dic3#87014yesdirect product factor
284C32C4×#12511yescharacteristic, complemented, Sylow
285C23C22×D3211yescharacteristic
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—32no—
289C2×C4—34no—
290C2×C4—32no—
291C2×C4—34no—
292C2×C4—38no—
293C2×C4—62no—
294C2×C4—62no—
295C2×C4—62no—
296C2×C4—64no—
297C2×C4—64no—
298C2×C4—184no—
299C2×C4—184no—
300C2×C4—184no—
301C2×C4D3×Dic612yes—
302C2×C4#379912yes—
303C2×C4C2×D3×Dic314yes—
304C2×C4C2×D3×Dic312yes—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—22no—
309C2×C3—22no—
310C2×C3C2×C4×Dic611yescharacteristic
311C2×C3C2×#87011yescharacteristic
312C2×C3#547011yescharacteristic
313C2×C3C4×#23512yes—
314C2×C3#547912yes—
315C2×C3D3×#12511yescharacteristic
316C2×C3#568811yescharacteristic
317C2×C3#569112yes—
318C2×C3C2×Q8×Dic311yescharacteristic
319C2×C3Dic3×#4112yes—
320C22C2×D3×Dic611yescharacteristic
321C22C2×#379911yescharacteristic
322C22D3×#23512yes—
323C22D3×#23512yes—
324C22C22×D3×Dic311yescharacteristic
325C4—24no—
326C4—34no—
327C4—62no—
328C4—68no—
329C4—64no—
330C4—364no—
331C4Dic3×Dic614yes—
332C3—21no—
333C3C4×#87011yescharacteristic, complemented
334C3Dic3×#12511yescharacteristic, complemented
335C2#1059387411yescharacteristic
336C2D3×#87011yescharacteristic
337C2#1059397612yes—
338C2C2×Dic3×Dic611yescharacteristic
339C2Dic3×#23512yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C4×#125
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
18. C3×#870C4semidirect
80. #870Dic3direct (N × H)
165. C3×Dic3#125semidirect
283. Dic3#870direct (N × H)
284. C32C4×#125semidirect
333. C3C4×#870semidirect
334. C3Dic3×#125semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8702
#105926352
C3×C42×Dic32
#105913522
Dic3×C4⋊Dic32
Dic3×Dic3⋊C42
#105912012
Dic3×#1253
C4×#8703