Finite Group Databasebeta

← C3×Dic3×#125 #11802477

Subgroups — C3×Dic3×#125 #11802477

Order 1152.

1081 conjugacy classes of subgroups.

The subgroup lattice has 343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#125C211yesmaximal, characteristic
2C3×#4984C212yesmaximal
3C3×#4980C214yesmaximal
4C3×Dic3×C4⋊C4C214yesmaximal
5C3×Dic3×C4⋊C4C212yesmaximal
6C3×#4936C211yesmaximal, characteristic
7C3×C42×Dic3C211yesmaximal, characteristic
8C3×C4×#125—31nomaximal
9Dic3×#125C311yesmaximal, characteristic, direct product factor
10C32×#125C418yescomplemented
11C2×C32×C4⋊C4C2214yes—
12C2×C32×C4⋊C4C2212yes—
13C2×C32×C42C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C2×C3×C4⋊Dic3C2214yes—
16C2×C3×C4×Dic3C2212yes—
17C2×C3×C4×Dic3C2212yes—
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2214yes—
20C2×C3×C4×Dic3C2211yescharacteristic
21C3×C3⋊#95C2214yes—
22C3×C3⋊#95C2214yes—
23C3×C3⋊#95C2214yes—
24C2×C3×#125—21no—
25C2×C3×#125D311yescharacteristic
26C2×C3×#125C2×C311yescharacteristic
27C3×#389—32no—
28C3×#387—34no—
29C3×#382—31no—
30C3×C4×C4⋊C4—34no—
31C3×C4×C4⋊C4—32no—
32C3×C43—31no—
33#4984C2×C312yes—
34#4980C2×C314yes—
35Dic3×C4⋊C4C2×C314yes—
36Dic3×C4⋊C4C2×C312yes—
37#4936C2×C311yescharacteristic
38C42×Dic3C2×C311yescharacteristic
39C22×C32×C4C2312yes—
40C22×C32×C4C2314yes—
41C22×C32×C4C2311yescharacteristic
42C22×C3×Dic3C2314yes—
43C22×C3×Dic3C2311yescharacteristic
44C22×C3×Dic3C2312yes—
45C22×C3×Dic3C2311yescharacteristic
46C32×C4⋊C4C2×C4116yes—
47C32×C4⋊C4C2×C418yes—
48C32×C42C2×C414yes—
49C3×C4⋊Dic3—24no—
50C3×C4⋊Dic3—28no—
51C3×C4×Dic3—22no—
52C3×C4×Dic3—24no—
53C3×C4×Dic3—24no—
54C3×C4×Dic3—28no—
55C3×C4×Dic3Q814yes—
56C4×#125—31noSylow
57C3×#125—28no—
58C3×#125Dic318yesdirect product factor
59C3×#125C3×C418yescomplemented
60C2×C3×C4⋊C4—24no—
61C2×C3×C4⋊C4—22no—
62C2×C3×C4⋊C4—32no—
63C2×C3×C4⋊C4—34no—
64C2×C3×C4⋊C4C2×D314yes—
65C2×C3×C4⋊C4C2×D312yes—
66C2×C3×C4⋊C4C22×C314yes—
67C2×C3×C4⋊C4C22×C312yes—
68C2×C3×C42—21no—
69C2×C3×C42—31no—
70C2×C3×C42—32no—
71C2×C3×C42—32no—
72C2×C3×C42—31no—
73C2×C3×C42—34no—
74C2×C3×C42C2×D311yescharacteristic
75C2×C3×C42C22×C311yescharacteristic
76C2×C4⋊Dic3C22×C312yes—
77C2×C4⋊Dic3C22×C314yes—
78C2×C4×Dic3C22×C312yes—
79C2×C4×Dic3C22×C312yes—
80C2×C4×Dic3C22×C311yescharacteristic
81C2×C4×Dic3C22×C314yes—
82C2×C4×Dic3C22×C311yescharacteristic
83C3×#95—34no—
84C3×#95—34no—
85C3×#95—34no—
86C3⋊#95C22×C314yes—
87C3⋊#95C22×C314yes—
88C3⋊#95C22×C314yes—
89C23×C32C2411yescharacteristic
90C2×C32×C4—22no—
91C2×C32×C4—24no—
92C2×C32×C4—22no—
93C2×C32×C4—24no—
94C2×C32×C4C22×C414yes—
95C2×C32×C4C22×C418yes—
96C2×C32×C4C22×C412yes—
97C2×C32×C4C2×Q812yes—
98C2×C32×C4#4112yes—
99C2×C3×Dic3—22no—
100C2×C3×Dic3—22no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—24no—
103C2×C3×Dic3—24no—
104C2×C3×Dic3—24no—
105C2×C3×Dic3C2×Q812yes—
106C2×C3×Dic3C2×Q812yes—
107C2×C3×Dic3#4114yes—
108C2×C3×Dic3#4114yes—
109C2×#125C3×D311yescharacteristic
110#389—32no—
111#387—34no—
112#382—31no—
113C4×C4⋊C4—34no—
114C4×C4⋊C4—32no—
115C43—31no—
116C22×C3×C4—21no—
117C22×C3×C4—22no—
118C22×C3×C4—24no—
119C22×C3×C4—31no—
120C22×C3×C4—31no—
121C22×C3×C4—32no—
122C22×C3×C4—34no—
123C22×C3×C4C22×D312yes—
124C22×C3×C4C22×D314yes—
125C22×C3×C4C22×D311yescharacteristic
126C22×C3×C4C23×C312yes—
127C22×C3×C4C23×C314yes—
128C22×C3×C4C23×C311yescharacteristic
129C22×Dic3C23×C314yes—
130C22×Dic3C23×C311yescharacteristic
131C22×Dic3C23×C312yes—
132C22×Dic3C23×C311yescharacteristic
133C3×C4⋊C4—28no—
134C3×C4⋊C4—216no—
135C3×C4⋊C4—68no—
136C3×C4⋊C4—64no—
137C3×C4⋊C4C2×Dic3116yes—
138C3×C4⋊C4C2×Dic318yes—
139C3×C4⋊C4C2×C3×C4116yes—
140C3×C4⋊C4C2×C3×C418yes—
141C3×C42—24no—
142C3×C42—34no—
143C3×C42—64no—
144C3×C42—68no—
145C3×C42—64no—
146C3×C42—62no—
147C3×C42C2×Dic314yes—
148C3×C42C2×C3×C414yes—
149C4⋊Dic3—24no—
150C4⋊Dic3—28no—
151C4×Dic3—22no—
152C4×Dic3—24no—
153C4×Dic3—24no—
154C4×Dic3—28no—
155C4×Dic3C3×Q814yes—
156C22×C32C23×C411yescharacteristic
157C22×C32C22×Q811yescharacteristic
158C22×C32C2×#4111yescharacteristic
159C22×C32C2×#4112yes—
160C22×C32C2×#4112yes—
161C32×C4—24no—
162C32×C4—28no—
163C32×C4C4×Q814yes—
164C3×Dic3—24no—
165C3×Dic3—22no—
166C3×Dic3—44no—
167C3×Dic3#12514yesdirect product factor
168#125C3×Dic318yesdirect product factor
169C2×C4⋊C4—32no—
170C2×C4⋊C4—34no—
171C2×C4⋊C4C2×C3×D314yes—
172C2×C4⋊C4C2×C3×D312yes—
173C2×C42—31no—
174C2×C42—32no—
175C2×C42—32no—
176C2×C42—31no—
177C2×C42—34no—
178C2×C42C2×C3×D311yescharacteristic
179#95—34no—
180#95—34no—
181#95—34no—
182C23×C3—21no—
183C23×C3C23×D311yescharacteristic
184C23×C3C24×C311yescharacteristic
185C2×C3×C4—22no—
186C2×C3×C4—24no—
187C2×C3×C4—22no—
188C2×C3×C4—24no—
189C2×C3×C4—22no—
190C2×C3×C4—24no—
191C2×C3×C4—22no—
192C2×C3×C4—24no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—24no—
197C2×C3×C4—28no—
198C2×C3×C4—32no—
199C2×C3×C4—34no—
200C2×C3×C4—32no—
201C2×C3×C4—34no—
202C2×C3×C4—42no—
203C2×C3×C4—42no—
204C2×C3×C4—44no—
205C2×C3×C4—44no—
206C2×C3×C4—62no—
207C2×C3×C4—62no—
208C2×C3×C4—62no—
209C2×C3×C4—64no—
210C2×C3×C4—64no—
211C2×C3×C4—64no—
212C2×C3×C4D3×Q812yes—
213C2×C3×C4#23912yes—
214C2×C3×C4C22×Dic314yes—
215C2×C3×C4C22×Dic318yes—
216C2×C3×C4C22×Dic312yes—
217C2×C3×C4C22×C3×C414yes—
218C2×C3×C4C22×C3×C418yes—
219C2×C3×C4C22×C3×C412yes—
220C2×C3×C4C2×C3×Q812yes—
221C2×C3×C4C3×#4112yes—
222C2×Dic3—22no—
223C2×Dic3—22no—
224C2×Dic3—22no—
225C2×Dic3—24no—
226C2×Dic3—24no—
227C2×Dic3—24no—
228C2×Dic3C2×C3×Q812yes—
229C2×Dic3C2×C3×Q812yes—
230C2×Dic3C3×#4114yes—
231C2×Dic3C3×#4114yes—
232C2×C32C2×C4×Q811yescharacteristic
233C2×C32C4×#4112yes—
234C2×C32C2×#12511yescharacteristic
235C2×C32#52912yes—
236C2×C32#53311yescharacteristic
237C22×C4—31no—
238C22×C4—31no—
239C22×C4—32no—
240C22×C4—34no—
241C22×C4C22×C3×D312yes—
242C22×C4C22×C3×D314yes—
243C22×C4C22×C3×D311yescharacteristic
244C4⋊C4—68no—
245C4⋊C4—64no—
246C4⋊C4C2×C3×Dic3116yes—
247C4⋊C4C2×C3×Dic318yes—
248C42—34no—
249C42—64no—
250C42—68no—
251C42—64no—
252C42—62no—
253C42C2×C3×Dic314yes—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—22no—
257C22×C3—22no—
258C22×C3—21no—
259C22×C3C2×D3×Q811yescharacteristic
260C22×C3C2×#23911yescharacteristic
261C22×C3D3×#4112yes—
262C22×C3D3×#4112yes—
263C22×C3C23×Dic311yescharacteristic
264C22×C3C23×C3×C411yescharacteristic
265C22×C3C22×C3×Q811yescharacteristic
266C22×C3C2×C3×#4111yescharacteristic
267C22×C3C2×C3×#4112yes—
268C22×C3C2×C3×#4112yes—
269C3×C4—24no—
270C3×C4—28no—
271C3×C4—24no—
272C3×C4—28no—
273C3×C4—24no—
274C3×C4—34no—
275C3×C4—44no—
276C3×C4—48no—
277C3×C4—62no—
278C3×C4—64no—
279C3×C4—124no—
280C3×C4Q8×Dic314yes—
281C3×C4C3×C4×Q814yes—
282Dic3—24no—
283Dic3—22no—
284Dic3—44no—
285Dic3C3×#12514yesdirect product factor
286C32C4×#12511yescharacteristic, complemented, Sylow
287C23C23×C3×D311yescharacteristic
288C2×C4—22no—
289C2×C4—24no—
290C2×C4—22no—
291C2×C4—24no—
292C2×C4—32no—
293C2×C4—34no—
294C2×C4—32no—
295C2×C4—34no—
296C2×C4—62no—
297C2×C4—62no—
298C2×C4—62no—
299C2×C4—64no—
300C2×C4—64no—
301C2×C4—64no—
302C2×C4C3×D3×Q812yes—
303C2×C4C3×#23912yes—
304C2×C4C22×C3×Dic314yes—
305C2×C4C22×C3×Dic318yes—
306C2×C4C22×C3×Dic312yes—
307C2×C3—21no—
308C2×C3—22no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—22no—
312C2×C3D3×#12511yescharacteristic
313C2×C3#568811yescharacteristic
314C2×C3#569112yes—
315C2×C3C2×Q8×Dic311yescharacteristic
316C2×C3Dic3×#4112yes—
317C2×C3C2×C3×C4×Q811yescharacteristic
318C2×C3C3×C4×#4112yes—
319C2×C3C2×C3×#12511yescharacteristic
320C2×C3C3×#52912yes—
321C2×C3C3×#53311yescharacteristic
322C22C2×C3×D3×Q811yescharacteristic
323C22C2×C3×#23911yescharacteristic
324C22C3×D3×#4112yes—
325C22C3×D3×#4112yes—
326C22C23×C3×Dic311yescharacteristic
327C4—24no—
328C4—28no—
329C4—34no—
330C4—62no—
331C4—64no—
332C4—124no—
333C4C3×Q8×Dic314yes—
334C3—21no—
335C3Dic3×#12511yescharacteristic, direct product factor
336C3C3×C4×#12511yescharacteristic, complemented
337C2C3×D3×#12511yescharacteristic
338C2C3×#568811yescharacteristic
339C2C3×#569112yes—
340C2C2×C3×Q8×Dic311yescharacteristic
341C2C3×Dic3×#4112yes—
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×#125C2
socle, prime radicalC23×C32C24
cosocleC23×C3C24×C3
hypercenterC2×C3×#125D3
hypocenterC3C3×C4×#125
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#125

Complements

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

NH ≅ G/Ntype
9. Dic3×#125C3direct (N × H)
10. C32×#125C4semidirect
58. C3×#125Dic3direct (N × H)
59. C3×#125C3×C4semidirect
167. C3×Dic3#125direct (N × H)
168. #125C3×Dic3direct (N × H)
285. Dic3C3×#125direct (N × H)
286. C32C4×#125semidirect
335. C3Dic3×#125direct (N × H)
336. C3C3×C4×#125semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1252
C3×#49842
C3×#49802
C3×Dic3×C4⋊C42
C3×#49362
C3×C42×Dic32
C3×C4×#1253
Dic3×#1253