Finite Group Databasebeta

← C3×#77283 #11808893

Subgroups — C3×#77283 #11808893

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#396C211yesmaximal, characteristic
2C3×#4986C213yesmaximal, complemented
3C3×Dic3×C4⋊C4C213yesmaximal, complemented
4C3×#4953C213yesmaximal
5C3×Dic3×C22⋊C4C213yesmaximal
6C3×C3⋊#401C211yesmaximal, characteristic, complemented
7C3×#4648C211yesmaximal, characteristic, complemented
8C3×#2401—31nomaximal
9#77283C311yesmaximal, characteristic, direct product factor
10C23×C3×Dic3C2211yescharacteristic
11C2×C32×C4⋊C4C2213yes—
12C2×C32×C22⋊C4C2213yes—
13C2×C3×#217C2213yes—
14C2×C3×C4⋊Dic3C2213yes—
15C2×C3×C4×Dic3C2213yes—
16C2×C3×C4×Dic3C2213yes—
17C32×#95C2211yescharacteristic
18C3×C3⋊#95C2213yes—
19C3×C3⋊#95C2213yes—
20C3×C3⋊#95C2213yes—
21C3×C3⋊#95C2213yes—
22C3×C3⋊#95C2213yes—
23C3×#401—31no—
24C3×#400—33no—
25C3×#397—33no—
26C3×#396—21no—
27C3×#396D311yescharacteristic
28C3×#396C2×C311yescharacteristic
29C3×C4×C4⋊C4—33no—
30C3×C4×C22⋊C4—33no—
31C3×#376—31no—
32#4986C2×C313yescomplemented
33Dic3×C4⋊C4C2×C313yescomplemented
34#4953C2×C313yes—
35Dic3×C22⋊C4C2×C313yes—
36C3⋊#401C2×C311yescharacteristic, complemented
37#4648C2×C311yescharacteristic, complemented
38C24×C32C2311yescharacteristic
39C22×C32×C4C2313yes—
40C22×C32×C4C2313yes—
41C22×C3×Dic3—26no—
42C22×C3×Dic3C2313yes—
43C22×C3×Dic3C2313yes—
44C22×C3×Dic3C2311yescharacteristic
45C22×C3×Dic3C2311yescharacteristic
46C32×C4⋊C4—26no—
47C32×C22⋊C4—26no—
48C3×#217—26no—
49C3×C4⋊Dic3—26no—
50C3×C4×Dic3—26no—
51C3×C4×Dic3—26no—
52#2401—31noSylow
53C23×C3×C4—31no—
54C23×Dic3C22×C311yescharacteristic
55C2×C3×C4⋊C4—23no—
56C2×C3×C4⋊C4—33no—
57C2×C3×C4⋊C4C2×D313yes—
58C2×C3×C4⋊C4C22×C313yes—
59C2×C3×C22⋊C4—23no—
60C2×C3×C22⋊C4—33no—
61C2×C3×C22⋊C4C2×D313yes—
62C2×C3×C22⋊C4C22×C313yes—
63C2×C3×C42—33no—
64C2×C3×C42—33no—
65C2×#217C22×C313yes—
66C2×C4⋊Dic3C22×C313yes—
67C2×C4×Dic3C22×C313yes—
68C2×C4×Dic3C22×C313yes—
69C3×#95—21no—
70C3×#95—33no—
71C3×#95—33no—
72C3×#95—33no—
73C3×#95—33no—
74C3×#95—33no—
75C3×#95C2×D311yescharacteristic
76C3×#95C22×C311yescharacteristic
77C3⋊#95C22×C313yes—
78C3⋊#95C22×C313yes—
79C3⋊#95C22×C313yes—
80C3⋊#95C22×C313yes—
81C3⋊#95C22×C313yes—
82C23×C32—23no—
83C23×C32—23no—
84C23×C32#4112yes—
85C23×C32C2411yescharacteristic
86C2×C32×C4—23no—
87C2×C32×C4—23no—
88C2×C32×C4—23no—
89C2×C32×C4—23no—
90C2×C32×C4—23no—
91C2×C32×C4#4116yes—
92C2×C3×Dic3—23no—
93C2×C3×Dic3—23no—
94C2×C3×Dic3—23no—
95C2×C3×Dic3—23no—
96C2×C3×Dic3—23no—
97C2×C3×Dic3—23no—
98C2×C3×Dic3—23no—
99C2×C3×Dic3—44no—
100C2×C3×Dic3#4116yes—
101#401—31no—
102#400—33no—
103#397—33no—
104#396C3×D311yescharacteristic
105C4×C4⋊C4—33no—
106C4×C22⋊C4—33no—
107#376—31no—
108C24×C3—21no—
109C24×C3C22×D311yescharacteristic
110C24×C3C23×C311yescharacteristic
111C22×C3×C4—23no—
112C22×C3×C4—23no—
113C22×C3×C4—31no—
114C22×C3×C4—31no—
115C22×C3×C4—33no—
116C22×C3×C4—33no—
117C22×C3×C4—66no—
118C22×C3×C4C22×D313yes—
119C22×C3×C4C22×D313yes—
120C22×C3×C4C23×C313yes—
121C22×C3×C4C23×C313yes—
122C22×Dic3—26no—
123C22×Dic3C23×C311yescharacteristic
124C22×Dic3C23×C313yes—
125C22×Dic3C23×C313yes—
126C22×Dic3C23×C311yescharacteristic
127C3×C4⋊C4—26no—
128C3×C4⋊C4—26no—
129C3×C4⋊C4—46no—
130C3×C4⋊C4—66no—
131C3×C22⋊C4—26no—
132C3×C22⋊C4—26no—
133C3×C22⋊C4—46no—
134C3×C22⋊C4—66no—
135C3×C42—66no—
136C3×C42—66no—
137#217—26no—
138C4⋊Dic3—26no—
139C4×Dic3—26no—
140C4×Dic3—26no—
141C22×C32—26no—
142C22×C32—41no—
143C22×C32—43no—
144C22×C32C2×#4113yes—
145C22×C32C2×#4111yescharacteristic
146C22×C32C2×#4113yes—
147C32×C4—26no—
148C32×C4—43no—
149C3×Dic3—41no—
150C3×Dic3—43no—
151C3×Dic3—43no—
152C3×Dic3#12614yes—
153C23×C4—31no—
154C2×C4⋊C4—33no—
155C2×C4⋊C4C2×C3×D313yes—
156C2×C22⋊C4—33no—
157C2×C22⋊C4C2×C3×D313yes—
158C2×C42—33no—
159C2×C42—33no—
160#95—33no—
161#95—33no—
162#95—33no—
163#95—33no—
164#95—33no—
165#95C2×C3×D311yescharacteristic
166C23×C3—23no—
167C23×C3—23no—
168C23×C3—23no—
169C23×C3—23no—
170C23×C3—21no—
171C23×C3—22no—
172C23×C3—43no—
173C23×C3—43no—
174C23×C3#23912yes—
175C23×C3C3×#4112yes—
176C23×C3C23×D311yescharacteristic
177C23×C3C24×C311yescharacteristic
178C2×C3×C4—23no—
179C2×C3×C4—23no—
180C2×C3×C4—23no—
181C2×C3×C4—23no—
182C2×C3×C4—23no—
183C2×C3×C4—23no—
184C2×C3×C4—23no—
185C2×C3×C4—23no—
186C2×C3×C4—23no—
187C2×C3×C4—23no—
188C2×C3×C4—26no—
189C2×C3×C4—36no—
190C2×C3×C4—43no—
191C2×C3×C4—43no—
192C2×C3×C4—43no—
193C2×C3×C4—43no—
194C2×C3×C4—43no—
195C2×C3×C4—63no—
196C2×C3×C4—63no—
197C2×C3×C4—63no—
198C2×C3×C4—63no—
199C2×C3×C4—63no—
200C2×C3×C4—63no—
201C2×C3×C4—63no—
202C2×C3×C4—124no—
203C2×C3×C4#23716yes—
204C2×C3×C4C3×#4116yes—
205C2×Dic3—23no—
206C2×Dic3—23no—
207C2×Dic3—23no—
208C2×Dic3—23no—
209C2×Dic3—23no—
210C2×Dic3—23no—
211C2×Dic3—23no—
212C2×Dic3—44no—
213C2×Dic3C3×#4116yes—
214C2×C32—42no—
215C2×C32C2×#12611yescharacteristic
216C2×C32#52913yes—
217C2×C32#52913yes—
218C24C22×C3×D311yescharacteristic
219C22×C4—31no—
220C22×C4—31no—
221C22×C4—33no—
222C22×C4—33no—
223C22×C4—66no—
224C22×C4C22×C3×D313yes—
225C22×C4C22×C3×D313yes—
226C4⋊C4—26no—
227C4⋊C4—66no—
228C22⋊C4—26no—
229C22⋊C4—66no—
230C42—66no—
231C42—66no—
232C22×C3—26no—
233C22×C3—26no—
234C22×C3—23no—
235C22×C3—21no—
236C22×C3—23no—
237C22×C3—46no—
238C22×C3—41no—
239C22×C3—43no—
240C22×C3—41no—
241C22×C3—43no—
242C22×C3—83no—
243C22×C3—81no—
244C22×C3C2×#23713yes—
245C22×C3C2×#23911yescharacteristic
246C22×C3D3×#4113yes—
247C22×C3C2×C3×#4113yes—
248C22×C3C2×C3×#4111yescharacteristic
249C22×C3C2×C3×#4113yes—
250C3×C4—26no—
251C3×C4—26no—
252C3×C4—34no—
253C3×C4—46no—
254C3×C4—43no—
255C3×C4—43no—
256C3×C4—83no—
257C3×C4—121no—
258C3×C4—123no—
259C3×C4—123no—
260Dic3—41no—
261Dic3—43no—
262Dic3—43no—
263Dic3C3×#12614yes—
264C32#240111yescharacteristic, complemented, Sylow
265C23—23no—
266C23—23no—
267C23C3×#23912yes—
268C23C23×C3×D311yescharacteristic
269C2×C4—23no—
270C2×C4—23no—
271C2×C4—23no—
272C2×C4—23no—
273C2×C4—23no—
274C2×C4—36no—
275C2×C4—63no—
276C2×C4—63no—
277C2×C4—63no—
278C2×C4—63no—
279C2×C4—63no—
280C2×C4—63no—
281C2×C4—63no—
282C2×C4—124no—
283C2×C4C3×#23716yes—
284C2×C3—23no—
285C2×C3—23no—
286C2×C3—21no—
287C2×C3—42no—
288C2×C3—42no—
289C2×C3—82no—
290C2×C3#560013yes—
291C2×C3#562413yes—
292C2×C3D3×#12611yescharacteristic
293C2×C3C2×C3×#12611yescharacteristic
294C2×C3C3×#52913yes—
295C2×C3C3×#52913yes—
296C22—26no—
297C22—43no—
298C22—41no—
299C22C2×C3×#23713yes—
300C22C2×C3×#23911yescharacteristic
301C22C3×D3×#4113yes—
302C4—26no—
303C4—34no—
304C4—43no—
305C4—123no—
306C4—123no—
307C4—121no—
308C3—21no—
309C3#7728311yescharacteristic, direct product factor
310C3C3×#240111yescharacteristic, complemented
311C2—42no—
312C2C3×#560013yes—
313C2C3×#562413yes—
314C2C3×D3×#12611yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#396C2
socleC23×C32C24
prime radicalC24×C32C23
hypercenterC3×#396D3
hypocenterC3C3×#2401
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#396

Complements

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

NH ≅ G/Ntype
2. C3×#4986C2semidirect
3. C3×Dic3×C4⋊C4C2semidirect
6. C3×C3⋊#401C2semidirect
7. C3×#4648C2semidirect
9. #77283C3direct (N × H)
32. #4986C2×C3semidirect
33. Dic3×C4⋊C4C2×C3semidirect
36. C3⋊#401C2×C3semidirect
37. #4648C2×C3semidirect
264. C32#2401semidirect
309. C3#77283direct (N × H)
310. C3C3×#2401semidirect

Maximal subgroups

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

subgroupindex
C32×#3962
C3×#49862
C3×Dic3×C4⋊C42
C3×#49532
C3×Dic3×C22⋊C42
C3×C3⋊#4012
C3×#46482
C3×#24013
#772833