Finite Group Databasebeta

← C3×#83227 #11803809

Subgroups — C3×#83227 #11803809

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 303 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4⋊Q8C211yesmaximal, characteristic
2C2×C3×Q8×Dic3C212yesmaximal
3C3×#5229C212yesmaximal
4C3×#4980C218yesmaximal
5C3×#4936C211yesmaximal, characteristic
6C3×#4932C211yesmaximal, characteristic
7C3×#2327—31nomaximal
8#83227C311yesmaximal, characteristic, direct product factor
9C22×C32×Q8C2212yes—
10C32×C4⋊Q8C418yescomplemented
11C2×C32×C4⋊C4C2214yes—
12C2×C32×C42C2211yescharacteristic
13C3×Q8×Dic3—28no—
14C2×C3×C4⋊Dic3C2212yes—
15C2×C3×C4⋊Dic3C2214yes—
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×C4×Dic3C2214yes—
18C2×C3×C4×Dic3C2211yescharacteristic
19C3×C3⋊#95C2214yes—
20C3×C3⋊#95C2214yes—
21C3×C3⋊#95C2218yes—
22C2×C3×C4⋊Q8—21no—
23C2×C3×C4⋊Q8D311yescharacteristic
24C2×C3×C4⋊Q8C2×C311yescharacteristic
25C2×C3×C4×Q8—32no—
26C2×Q8×Dic3C2×C312yes—
27C3×#391—32no—
28C3×#387—38no—
29C3×#382—31no—
30C3×#376—31no—
31#5229C2×C312yes—
32#4980C2×C318yes—
33#4936C2×C311yescharacteristic
34#4932C2×C311yescharacteristic
35C2×C32×Q8—24no—
36C2×C32×Q8—24no—
37C2×C32×Q8C2×C418yes—
38C22×C32×C4C2314yes—
39C22×C32×C4C2312yes—
40C22×C32×C4C2311yescharacteristic
41C22×C3×Dic3C2314yes—
42C22×C3×Dic3C2312yes—
43C22×C3×Dic3C2312yes—
44C32×C4⋊C4C2×C4116yes—
45C32×C42C2×C414yes—
46C3×C4⋊Dic3—24no—
47C3×C4⋊Dic3—28no—
48C3×C4×Dic3—22no—
49C3×C4×Dic3—28no—
50C3×C4×Dic3D414yes—
51#2327—31noSylow
52C22×C3×Q8—22no—
53C22×C3×Q8C2×D312yes—
54C22×C3×Q8C22×C312yes—
55C3×C4⋊Q8—28no—
56C3×C4⋊Q8Dic318yescomplemented
57C3×C4⋊Q8C3×C418yescomplemented
58C3×C4×Q8—68no—
59C2×C3×C4⋊C4—24no—
60C2×C3×C4⋊C4—32no—
61C2×C3×C4⋊C4—34no—
62C2×C3×C4⋊C4C2×D314yes—
63C2×C3×C4⋊C4C22×C314yes—
64C2×C3×C42—21no—
65C2×C3×C42—31no—
66C2×C3×C42—31no—
67C2×C3×C42—34no—
68C2×C3×C42C2×D311yescharacteristic
69C2×C3×C42C22×C311yescharacteristic
70Q8×Dic3—28no—
71C2×C4⋊Dic3C22×C312yes—
72C2×C4⋊Dic3C22×C314yes—
73C2×C4×Dic3C22×C311yescharacteristic
74C2×C4×Dic3C22×C314yes—
75C2×C4×Dic3C22×C311yescharacteristic
76C3×#95—34no—
77C3×#95—34no—
78C3×#95—38no—
79C3⋊#95C22×C314yes—
80C3⋊#95C22×C314yes—
81C3⋊#95C22×C318yes—
82C23×C32C2411yescharacteristic
83C32×Q8—216no—
84C2×C32×C4—24no—
85C2×C32×C4—24no—
86C2×C32×C4—24no—
87C2×C32×C4C22×C414yes—
88C2×C32×C4C22×C418yes—
89C2×C32×C4C22×C412yes—
90C2×C32×C4C2×D412yes—
91C2×C32×C4#4112yes—
92C2×C3×Dic3—24no—
93C2×C3×Dic3—24no—
94C2×C3×Dic3—22no—
95C2×C3×Dic3—28no—
96C2×C3×Dic3—24no—
97C2×C3×Dic3C2×D414yes—
98C2×C4⋊Q8C3×D311yescharacteristic
99C2×C4×Q8—32no—
100#391—32no—
101#387—38no—
102#382—31no—
103#376—31no—
104C2×C3×Q8—24no—
105C2×C3×Q8—24no—
106C2×C3×Q8—24no—
107C2×C3×Q8—24no—
108C2×C3×Q8—28no—
109C2×C3×Q8—44no—
110C2×C3×Q8—44no—
111C2×C3×Q8C2×Dic318yes—
112C2×C3×Q8C2×C3×C418yes—
113C22×C3×C4—22no—
114C22×C3×C4—21no—
115C22×C3×C4—24no—
116C22×C3×C4—32no—
117C22×C3×C4—32no—
118C22×C3×C4—34no—
119C22×C3×C4C22×D312yes—
120C22×C3×C4C22×D314yes—
121C22×C3×C4C22×D311yescharacteristic
122C22×C3×C4C23×C312yes—
123C22×C3×C4C23×C314yes—
124C22×C3×C4C23×C311yescharacteristic
125C22×Dic3C23×C312yes—
126C22×Dic3C23×C314yes—
127C22×Dic3C23×C312yes—
128C3×C4⋊C4—216no—
129C3×C4⋊C4—68no—
130C3×C4⋊C4—64no—
131C3×C4⋊C4C2×Dic3116yes—
132C3×C4⋊C4C2×C3×C4116yes—
133C3×C42—24no—
134C3×C42—34no—
135C3×C42—68no—
136C3×C42—62no—
137C3×C42C2×Dic314yes—
138C3×C42C2×C3×C414yes—
139C4⋊Dic3—24no—
140C4⋊Dic3—28no—
141C4×Dic3—22no—
142C4×Dic3—28no—
143C4×Dic3C3×D414yes—
144C22×C32C23×C411yescharacteristic
145C22×C32C22×D411yescharacteristic
146C22×C32C2×#4111yescharacteristic
147C22×C322−1+414yes—
148C32×C4—24no—
149C32×C4—28no—
150C32×C4C4×D414yes—
151C3×Dic3—24no—
152C3×Dic3—44no—
153C3×Dic3—42no—
154C22×Q8C2×C3×D312yes—
155C4⋊Q8C3×Dic318yescomplemented
156C4×Q8—68no—
157C2×C4⋊C4—32no—
158C2×C4⋊C4—34no—
159C2×C4⋊C4C2×C3×D314yes—
160C2×C42—31no—
161C2×C42—34no—
162C2×C42—31no—
163C2×C42C2×C3×D311yescharacteristic
164#95—34no—
165#95—34no—
166#95—38no—
167C23×C3—21no—
168C23×C3C23×D311yescharacteristic
169C23×C3C24×C311yescharacteristic
170C3×Q8—216no—
171C3×Q8—216no—
172C3×Q8—416no—
173C2×C3×C4—28no—
174C2×C3×C4—24no—
175C2×C3×C4—24no—
176C2×C3×C4—24no—
177C2×C3×C4—24no—
178C2×C3×C4—24no—
179C2×C3×C4—24no—
180C2×C3×C4—22no—
181C2×C3×C4—22no—
182C2×C3×C4—24no—
183C2×C3×C4—22no—
184C2×C3×C4—28no—
185C2×C3×C4—34no—
186C2×C3×C4—44no—
187C2×C3×C4—44no—
188C2×C3×C4—64no—
189C2×C3×C4—64no—
190C2×C3×C4—62no—
191C2×C3×C4—68no—
192C2×C3×C4—64no—
193C2×C3×C4D3×D412yes—
194C2×C3×C4#23712yes—
195C2×C3×C4C22×Dic314yes—
196C2×C3×C4C22×Dic318yes—
197C2×C3×C4C22×Dic312yes—
198C2×C3×C4C22×C3×C414yes—
199C2×C3×C4C22×C3×C418yes—
200C2×C3×C4C22×C3×C412yes—
201C2×C3×C4C2×C3×D412yes—
202C2×C3×C4C3×#4112yes—
203C2×Dic3—24no—
204C2×Dic3—24no—
205C2×Dic3—22no—
206C2×Dic3—28no—
207C2×Dic3—24no—
208C2×Dic3C2×C3×D414yes—
209C2×C32C2×C4×D411yescharacteristic
210C2×C32#51912yes—
211C2×C32#53612yes—
212C2×C32#54112yes—
213C2×Q8—24no—
214C2×Q8—24no—
215C2×Q8C2×C3×Dic318yes—
216C22×C4—32no—
217C22×C4—32no—
218C22×C4—34no—
219C22×C4C22×C3×D312yes—
220C22×C4C22×C3×D314yes—
221C22×C4C22×C3×D311yescharacteristic
222C4⋊C4—68no—
223C4⋊C4—64no—
224C4⋊C4C2×C3×Dic3116yes—
225C42—34no—
226C42—68no—
227C42—62no—
228C42C2×C3×Dic314yes—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—24no—
232C22×C3—21no—
233C22×C3C2×D3×D411yescharacteristic
234C22×C3C2×#23711yescharacteristic
235C22×C3#100714yes—
236C22×C3C23×Dic311yescharacteristic
237C22×C3C23×C3×C411yescharacteristic
238C22×C3C22×C3×D411yescharacteristic
239C22×C3C2×C3×#4111yescharacteristic
240C22×C3C3×2−1+414yes—
241C3×C4—28no—
242C3×C4—28no—
243C3×C4—24no—
244C3×C4—28no—
245C3×C4—24no—
246C3×C4—24no—
247C3×C4—48no—
248C3×C4—64no—
249C3×C4—124no—
250C3×C4—122no—
251C3×C4D4×Dic314yes—
252C3×C4C3×C4×D414yes—
253Dic3—24no—
254Dic3—44no—
255Dic3—42no—
256C32#232711yescharacteristic, complemented, Sylow
257C23C23×C3×D311yescharacteristic
258Q8—216no—
259C2×C4—24no—
260C2×C4—24no—
261C2×C4—24no—
262C2×C4—34no—
263C2×C4—64no—
264C2×C4—64no—
265C2×C4—62no—
266C2×C4—68no—
267C2×C4—64no—
268C2×C4C3×D3×D412yes—
269C2×C4C3×#23712yes—
270C2×C4C22×C3×Dic314yes—
271C2×C4C22×C3×Dic318yes—
272C2×C4C22×C3×Dic312yes—
273C2×C3—21no—
274C2×C3—22no—
275C2×C3—22no—
276C2×C3—22no—
277C2×C3#572412yes—
278C2×C3#573112yes—
279C2×C3C2×D4×Dic311yescharacteristic
280C2×C3#581212yes—
281C2×C3C2×C3×C4×D411yescharacteristic
282C2×C3C3×#51912yes—
283C2×C3C3×#53612yes—
284C2×C3C3×#54112yes—
285C22C2×C3×D3×D411yescharacteristic
286C22C2×C3×#23711yescharacteristic
287C22C3×#100714yes—
288C22C23×C3×Dic311yescharacteristic
289C4—28no—
290C4—24no—
291C4—64no—
292C4—124no—
293C4—122no—
294C4C3×D4×Dic314yes—
295C3—21no—
296C3#8322711yescharacteristic, direct product factor
297C3C3×#232711yescharacteristic, complemented
298C2C3×#572412yes—
299C2C3×#573112yes—
300C2C2×C3×D4×Dic311yescharacteristic
301C2C3×#581212yes—
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×C4⋊Q8C2
socle, prime radicalC23×C32C24
cosocleC23×C3C24×C3
hypercenterC2×C3×C4⋊Q8D3
hypocenterC3C3×#2327
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4⋊Q8

Complements

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

NH ≅ G/Ntype
8. #83227C3direct (N × H)
10. C32×C4⋊Q8C4semidirect
56. C3×C4⋊Q8Dic3semidirect
57. C3×C4⋊Q8C3×C4semidirect
155. C4⋊Q8C3×Dic3semidirect
256. C32#2327semidirect
296. C3#83227direct (N × H)
297. C3C3×#2327semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4⋊Q82
C2×C3×Q8×Dic32
C3×#52292
C3×#49802
C3×#49362
C3×#49322
C3×#23273
#832273