Finite Group Databasebeta

← C3×#83027 #11807988

Subgroups — C3×#83027 #11807988

Order 1152.

929 conjugacy classes of subgroups.

The subgroup lattice has 283 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#125C211yesmaximal, characteristic
2C3×#4984C214yesmaximal
3C3×#4980C214yesmaximal
4C3×#4980C214yesmaximal
5C3×#4936C212yesmaximal
6C3×#2382—31nomaximal
7#83027C311yesmaximal, characteristic, direct product factor
8C32×#125C418yescomplemented
9C2×C32×C4⋊C4C2212yes—
10C2×C32×C4⋊C4C2214yes—
11C2×C32×C42C2211yescharacteristic
12C2×C3×C4⋊Dic3C2212yes—
13C2×C3×C4⋊Dic3C2212yes—
14C2×C3×C4⋊Dic3C2214yes—
15C2×C3×C4×Dic3C2214yes—
16C3×C3⋊#95C2214yes—
17C3×C3⋊#95C2214yes—
18C3×C3⋊#95C2214yes—
19C3×C3⋊#95C2214yes—
20C2×C3×#125—21no—
21C2×C3×#125D311yescharacteristic
22C2×C3×#125C2×C311yescharacteristic
23C3×#389—34no—
24C3×#387—34no—
25C3×#387—34no—
26C3×#382—32no—
27#4984C2×C314yes—
28#4980C2×C314yes—
29#4980C2×C314yes—
30#4936C2×C312yes—
31C22×C32×C4C2314yes—
32C22×C32×C4C2312yes—
33C22×C32×C4C2311yescharacteristic
34C22×C3×Dic3C2314yes—
35C22×C3×Dic3C2314yes—
36C32×C4⋊C4C2×C418yes—
37C32×C4⋊C4C2×C4116yes—
38C32×C42C2×C414yes—
39C3×C4⋊Dic3—42no—
40C3×C4⋊Dic3—44no—
41C3×C4⋊Dic3—42no—
42C3×C4×Dic3—44no—
43#2382—31noSylow
44C3×#125—28no—
45C3×#125Dic318yescomplemented
46C3×#125C3×C418yescomplemented
47C2×C3×C4⋊C4—22no—
48C2×C3×C4⋊C4—24no—
49C2×C3×C4⋊C4—32no—
50C2×C3×C4⋊C4—32no—
51C2×C3×C4⋊C4—34no—
52C2×C3×C4⋊C4C2×D312yes—
53C2×C3×C4⋊C4C2×D314yes—
54C2×C3×C4⋊C4C22×C312yes—
55C2×C3×C4⋊C4C22×C314yes—
56C2×C3×C42—21no—
57C2×C3×C42—34no—
58C2×C3×C42C2×D311yescharacteristic
59C2×C3×C42C22×C311yescharacteristic
60C2×C4⋊Dic3C22×C312yes—
61C2×C4⋊Dic3C22×C312yes—
62C2×C4⋊Dic3C22×C314yes—
63C2×C4×Dic3C22×C314yes—
64C3×#95—34no—
65C3×#95—34no—
66C3×#95—34no—
67C3×#95—34no—
68C3⋊#95C22×C314yes—
69C3⋊#95C22×C314yes—
70C3⋊#95C22×C314yes—
71C3⋊#95C22×C314yes—
72C23×C32C2411yescharacteristic
73C2×C32×C4—21no—
74C2×C32×C4—21no—
75C2×C32×C4—24no—
76C2×C32×C4—22no—
77C2×C32×C4—24no—
78C2×C32×C4—22no—
79C2×C32×C4C22×C412yes—
80C2×C32×C4C22×C414yes—
81C2×C32×C4C22×C418yes—
82C2×C3×Dic3—24no—
83C2×C3×Dic3—24no—
84C2×C3×Dic3—24no—
85C2×C3×Dic3—24no—
86C2×C3×Dic3—24no—
87C2×C3×Dic3—24no—
88C2×#125C3×D311yescharacteristic
89#389—34no—
90#387—34no—
91#387—34no—
92#382—32no—
93C22×C3×C4—21no—
94C22×C3×C4—22no—
95C22×C3×C4—24no—
96C22×C3×C4—34no—
97C22×C3×C4—34no—
98C22×C3×C4C22×D311yescharacteristic
99C22×C3×C4C22×D314yes—
100C22×C3×C4C22×D312yes—
101C22×C3×C4C23×C311yescharacteristic
102C22×C3×C4C23×C314yes—
103C22×C3×C4C23×C312yes—
104C22×Dic3C23×C314yes—
105C22×Dic3C23×C314yes—
106C3×C4⋊C4—28no—
107C3×C4⋊C4—216no—
108C3×C4⋊C4—124no—
109C3×C4⋊C4—122no—
110C3×C4⋊C4—122no—
111C3×C4⋊C4C2×Dic318yes—
112C3×C4⋊C4C2×Dic3116yes—
113C3×C4⋊C4C2×C3×C418yes—
114C3×C4⋊C4C2×C3×C4116yes—
115C3×C42—24no—
116C3×C42—124no—
117C3×C42C2×Dic314yes—
118C3×C42C2×C3×C414yes—
119C4⋊Dic3—42no—
120C4⋊Dic3—44no—
121C4⋊Dic3—42no—
122C4×Dic3—44no—
123C22×C32C23×C411yescharacteristic
124C22×C32H(5,𝔽2)12yes—
125C22×C322−1+411yescharacteristic
126C22×C322−1+411yescharacteristic
127C22×C322−1+412yes—
128C32×C4—22no—
129C32×C4—28no—
130C32×C4—24no—
131C3×Dic3—44no—
132C3×Dic3—44no—
133#125C3×Dic318yescomplemented
134C2×C4⋊C4—32no—
135C2×C4⋊C4—32no—
136C2×C4⋊C4—34no—
137C2×C4⋊C4C2×C3×D312yes—
138C2×C4⋊C4C2×C3×D314yes—
139C2×C42—34no—
140C2×C42C2×C3×D311yescharacteristic
141#95—34no—
142#95—34no—
143#95—34no—
144#95—34no—
145C23×C3—21no—
146C23×C3C23×D311yescharacteristic
147C23×C3C24×C311yescharacteristic
148C2×C3×C4—22no—
149C2×C3×C4—22no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—24no—
153C2×C3×C4—22no—
154C2×C3×C4—24no—
155C2×C3×C4—22no—
156C2×C3×C4—24no—
157C2×C3×C4—22no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—24no—
161C2×C3×C4—22no—
162C2×C3×C4—22no—
163C2×C3×C4—24no—
164C2×C3×C4—28no—
165C2×C3×C4—44no—
166C2×C3×C4—42no—
167C2×C3×C4—42no—
168C2×C3×C4—44no—
169C2×C3×C4—64no—
170C2×C3×C4—64no—
171C2×C3×C4—64no—
172C2×C3×C4—64no—
173C2×C3×C4—64no—
174C2×C3×C4—64no—
175C2×C3×C4C22×Dic312yes—
176C2×C3×C4C22×Dic314yes—
177C2×C3×C4C22×Dic318yes—
178C2×C3×C4C22×C3×C412yes—
179C2×C3×C4C22×C3×C414yes—
180C2×C3×C4C22×C3×C418yes—
181C2×Dic3—24no—
182C2×Dic3—24no—
183C2×Dic3—24no—
184C2×Dic3—24no—
185C2×Dic3—24no—
186C2×Dic3—24no—
187C2×C32#51911yescharacteristic
188C2×C32#52012yes—
189C2×C32#56211yescharacteristic
190C2×C32#56312yes—
191C2×C32#56411yescharacteristic
192C22×C4—34no—
193C22×C4—34no—
194C22×C4C22×C3×D311yescharacteristic
195C22×C4C22×C3×D314yes—
196C22×C4C22×C3×D312yes—
197C4⋊C4—124no—
198C4⋊C4—122no—
199C4⋊C4—122no—
200C4⋊C4C2×C3×Dic318yes—
201C4⋊C4C2×C3×Dic3116yes—
202C42—124no—
203C42C2×C3×Dic314yes—
204C22×C3—21no—
205C22×C3—21no—
206C22×C3—22no—
207C22×C3—22no—
208C22×C3—21no—
209C22×C3#100711yescharacteristic
210C22×C3#100711yescharacteristic
211C22×C3#100912yes—
212C22×C3#101012yes—
213C22×C3C23×Dic311yescharacteristic
214C22×C3C23×C3×C411yescharacteristic
215C22×C3C3×H(5,𝔽2)12yes—
216C22×C3C3×2−1+411yescharacteristic
217C22×C3C3×2−1+411yescharacteristic
218C22×C3C3×2−1+412yes—
219C3×C4—24no—
220C3×C4—22no—
221C3×C4—28no—
222C3×C4—24no—
223C3×C4—22no—
224C3×C4—28no—
225C3×C4—24no—
226C3×C4—44no—
227C3×C4—48no—
228C3×C4—124no—
229C3×C4—124no—
230Dic3—44no—
231Dic3—44no—
232C32#238211yescharacteristic, complemented, Sylow
233C23C23×C3×D311yescharacteristic
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—24no—
237C2×C4—22no—
238C2×C4—24no—
239C2×C4—22no—
240C2×C4—64no—
241C2×C4—64no—
242C2×C4—64no—
243C2×C4—64no—
244C2×C4—64no—
245C2×C4—64no—
246C2×C4C22×C3×Dic312yes—
247C2×C4C22×C3×Dic314yes—
248C2×C4C22×C3×Dic318yes—
249C2×C3—21no—
250C2×C3—22no—
251C2×C3—21no—
252C2×C3—22no—
253C2×C3—21no—
254C2×C3C3⋊#56411yescharacteristic
255C2×C3#569912yes—
256C2×C3#570011yescharacteristic
257C2×C3#581211yescharacteristic
258C2×C3#582712yes—
259C2×C3C3×#51911yescharacteristic
260C2×C3C3×#52012yes—
261C2×C3C3×#56211yescharacteristic
262C2×C3C3×#56312yes—
263C2×C3C3×#56411yescharacteristic
264C22C3×#100711yescharacteristic
265C22C3×#100711yescharacteristic
266C22C3×#100912yes—
267C22C3×#101012yes—
268C22C23×C3×Dic311yescharacteristic
269C4—22no—
270C4—28no—
271C4—24no—
272C4—124no—
273C4—124no—
274C3—21no—
275C3#8302711yescharacteristic, direct product factor
276C3C3×#238211yescharacteristic, complemented
277C2C3×C3⋊#56411yescharacteristic
278C2C3×#569912yes—
279C2C3×#570011yescharacteristic
280C2C3×#581211yescharacteristic
281C2C3×#582712yes—
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×#2382
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#125

Complements

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

NH ≅ G/Ntype
7. #83027C3direct (N × H)
8. C32×#125C4semidirect
45. C3×#125Dic3semidirect
46. C3×#125C3×C4semidirect
133. #125C3×Dic3semidirect
232. C32#2382semidirect
275. C3#83027direct (N × H)
276. C3C3×#2382semidirect

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×#49362
C3×#23823
#830273