Finite Group Databasebeta

← C3×#71562 #11785721

Subgroups — C3×#71562 #11785721

Order 1152.

841 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
1C22×C32×C4⋊C4C211yesmaximal, characteristic
2C3×#5207C212yesmaximal
3C3×#4530C214yesmaximal, complemented
4C3×#1821—31nomaximal
5#71562C311yesmaximal, characteristic, direct product factor
6C23×C32×C4C412yes—
7C23×C32×C4C2211yescharacteristic
8C2×C32×C4⋊C4—22no—
9C2×C32×C4⋊C4—22no—
10C2×C32×C4⋊C4C412yes—
11C2×C32×C4⋊C4C2212yes—
12C2×C3×#208C2214yes—
13C3×#830—22no—
14C3×#830—22no—
15C22×C3×C4⋊C4—21no—
16C22×C3×C4⋊C4D311yescharacteristic
17C22×C3×C4⋊C4C2×C311yescharacteristic
18C3×#407—32no—
19#5207C2×C312yes—
20C3×#343—34no—
21#4530C2×C314yescomplemented
22C24×C32C2×C411yescharacteristic
23C22×C32×C4—24no—
24C22×C32×C4—22no—
25C22×C32×C4—22no—
26C22×C32×C4—44no—
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4C2×C414yes—
29C22×C32×C4D412yes—
30C22×C32×C4D412yes—
31C22×C32×C4C2311yescharacteristic
32C32×C4⋊C4—24no—
33C32×C4⋊C4—24no—
34C3×#208—28no—
35C2×C3×C3⋊C8—24no—
36#1821—31noSylow
37C23×C3×C4—22no—
38C23×C3×C4—21no—
39C23×C3×C4Dic312yes—
40C23×C3×C4C3×C412yes—
41C23×C3×C4C2×D311yescharacteristic
42C23×C3×C4C22×C311yescharacteristic
43C2×C3×M16—34no—
44C2×C3×C4⋊C4—24no—
45C2×C3×C4⋊C4—24no—
46C2×C3×C4⋊C4—22no—
47C2×C3×C4⋊C4—22no—
48C2×C3×C4⋊C4—22no—
49C2×C3×C4⋊C4—22no—
50C2×C3×C4⋊C4—22no—
51C2×C3×C4⋊C4—22no—
52C2×C3×C4⋊C4Dic312yes—
53C2×C3×C4⋊C4C3×C412yes—
54C2×C3×C4⋊C4C2×D312yes—
55C2×C3×C4⋊C4C22×C312yes—
56C2×#208C22×C314yes—
57C3×C22⋊C8—62no—
58C3×C22⋊C8—62no—
59#830—22no—
60#830—22no—
61C23×C32—22no—
62C23×C32—22no—
63C23×C32—22no—
64C23×C32C22⋊C411yescharacteristic
65C23×C32C22⋊C411yescharacteristic
66C23×C32C22×C411yescharacteristic
67C2×C32×C4—22no—
68C2×C32×C4—24no—
69C2×C32×C4—24no—
70C2×C32×C4—24no—
71C2×C32×C4—44no—
72C2×C32×C4—44no—
73C2×C32×C4—44no—
74C2×C32×C4C22⋊C412yes—
75C2×C32×C4C2×D412yes—
76C2×C32×C4#4114yes—
77C3×C3⋊C8—44no—
78C22×C4⋊C4C3×D311yescharacteristic
79#407—32no—
80#343—34no—
81C24×C3—21no—
82C24×C3C2×Dic311yescharacteristic
83C24×C3C2×C3×C411yescharacteristic
84C22×C3×C4—28no—
85C22×C3×C4—24no—
86C22×C3×C4—24no—
87C22×C3×C4—24no—
88C22×C3×C4—24no—
89C22×C3×C4—22no—
90C22×C3×C4—22no—
91C22×C3×C4—22no—
92C22×C3×C4—22no—
93C22×C3×C4—21no—
94C22×C3×C4—24no—
95C22×C3×C4—22no—
96C22×C3×C4—22no—
97C22×C3×C4—21no—
98C22×C3×C4—48no—
99C22×C3×C4—44no—
100C22×C3×C4—44no—
101C22×C3×C4C2×Dic311yescharacteristic
102C22×C3×C4C2×Dic314yes—
103C22×C3×C4#6712yes—
104C22×C3×C4#6712yes—
105C22×C3×C4C2×C3×C411yescharacteristic
106C22×C3×C4C2×C3×C414yes—
107C22×C3×C4C3×D412yes—
108C22×C3×C4C3×D412yes—
109C22×C3×C4C22×D311yescharacteristic
110C22×C3×C4C23×C311yescharacteristic
111C3×M16—68no—
112C2×C3×C8—64no—
113C3×C4⋊C4—28no—
114C3×C4⋊C4—28no—
115C3×C4⋊C4—24no—
116C3×C4⋊C4—24no—
117C3×C4⋊C4—24no—
118C3×C4⋊C4—24no—
119#208—28no—
120C2×C3⋊C8—24no—
121C22×C32—28no—
122C22×C32—21no—
123C22×C32—21no—
124C22×C32—21no—
125C22×C32—21no—
126C22×C32—21no—
127C22×C32—21no—
128C22×C32#10012yes—
129C22×C32#10112yes—
130C22×C32C2×C22⋊C411yescharacteristic
131C22×C32#11712yes—
132C32×C4—22no—
133C32×C4—44no—
134C32×C4#12314yes—
135C23×C4C3×Dic312yes—
136C23×C4C2×C3×D311yescharacteristic
137C2×M16—34no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4C3×Dic312yes—
141C2×C4⋊C4C2×C3×D312yes—
142C22⋊C8—62no—
143C22⋊C8—62no—
144C23×C3—24no—
145C23×C3—24no—
146C23×C3—24no—
147C23×C3—22no—
148C23×C3—22no—
149C23×C3—22no—
150C23×C3—22no—
151C23×C3—22no—
152C23×C3—22no—
153C23×C3—21no—
154C23×C3—21no—
155C23×C3—21no—
156C23×C3#21711yescharacteristic
157C23×C3#21711yescharacteristic
158C23×C3C3×C22⋊C411yescharacteristic
159C23×C3C3×C22⋊C411yescharacteristic
160C23×C3C22×Dic311yescharacteristic
161C23×C3C22×C3×C411yescharacteristic
162C2×C3×C4—24no—
163C2×C3×C4—28no—
164C2×C3×C4—28no—
165C2×C3×C4—22no—
166C2×C3×C4—22no—
167C2×C3×C4—24no—
168C2×C3×C4—24no—
169C2×C3×C4—24no—
170C2×C3×C4—24no—
171C2×C3×C4—28no—
172C2×C3×C4—24no—
173C2×C3×C4—24no—
174C2×C3×C4—22no—
175C2×C3×C4—24no—
176C2×C3×C4—22no—
177C2×C3×C4—48no—
178C2×C3×C4—44no—
179C2×C3×C4—44no—
180C2×C3×C4—48no—
181C2×C3×C4—48no—
182C2×C3×C4—44no—
183C2×C3×C4—44no—
184C2×C3×C4—44no—
185C2×C3×C4—44no—
186C2×C3×C4#21712yes—
187C2×C3×C4C3×C22⋊C412yes—
188C2×C3×C4#23514yes—
189C2×C3×C4C2×#6712yes—
190C2×C3×C4C2×C3×D412yes—
191C2×C3×C4C3×#4114yes—
192C3×C8—124no—
193C3⋊C8—44no—
194C2×C32—22no—
195C2×C32—22no—
196C2×C32—22no—
197C2×C32#38111yescharacteristic
198C2×C32C2×#10011yescharacteristic
199C2×C32C2×#10111yescharacteristic
200C24C2×C3×Dic311yescharacteristic
201C22×C4—24no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—44no—
205C22×C4C2×C3×Dic311yescharacteristic
206C22×C4C2×C3×Dic314yes—
207C22×C4C3×#6712yes—
208C22×C4C3×#6712yes—
209C22×C4C22×C3×D311yescharacteristic
210M16—68no—
211C2×C8—64no—
212C4⋊C4—24no—
213C4⋊C4—24no—
214C22×C3—22no—
215C22×C3—22no—
216C22×C3—22no—
217C22×C3—22no—
218C22×C3—216no—
219C22×C3—28no—
220C22×C3—28no—
221C22×C3—22no—
222C22×C3—22no—
223C22×C3—21no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3—21no—
227C22×C3—21no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3—21no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—22no—
236C22×C3—21no—
237C22×C3—22no—
238C22×C3—22no—
239C22×C3#83312yes—
240C22×C3#83612yes—
241C22×C3C3×#10012yes—
242C22×C3C3×#10112yes—
243C22×C3#92612yes—
244C22×C3C2×#21711yescharacteristic
245C22×C3C2×C3×C22⋊C411yescharacteristic
246C22×C3C3×#11712yes—
247C3×C4—24no—
248C3×C4—22no—
249C3×C4—22no—
250C3×C4—24no—
251C3×C4—48no—
252C3×C4—44no—
253C3×C4—44no—
254C3×C4#92914yes—
255C3×C4C3×#12314yes—
256C32#182111yescharacteristic, complemented, Sylow
257C23—22no—
258C23—22no—
259C23—22no—
260C23C3×#21711yescharacteristic
261C23C3×#21711yescharacteristic
262C23C22×C3×Dic311yescharacteristic
263C2×C4—22no—
264C2×C4—24no—
265C2×C4—24no—
266C2×C4—24no—
267C2×C4—44no—
268C2×C4—44no—
269C2×C4—44no—
270C2×C4C3×#21712yes—
271C2×C4C3×#23514yes—
272C2×C4C2×C3×#6712yes—
273C8—124no—
274C2×C3—24no—
275C2×C3—24no—
276C2×C3—24no—
277C2×C3—22no—
278C2×C3—22no—
279C2×C3—22no—
280C2×C3—22no—
281C2×C3—22no—
282C2×C3—22no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3#521111yescharacteristic
287C2×C3C2×#83311yescharacteristic
288C2×C3C2×#83611yescharacteristic
289C2×C3C3×#38111yescharacteristic
290C2×C3C2×C3×#10011yescharacteristic
291C2×C3C2×C3×#10111yescharacteristic
292C22—28no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22C3×#83312yes—
300C22C3×#83612yes—
301C22C3×#92612yes—
302C22C2×C3×#21711yescharacteristic
303C4—22no—
304C4—44no—
305C4C3×#92914yes—
306C3—21no—
307C3#7156211yescharacteristic, direct product factor
308C3C3×#182111yescharacteristic, complemented
309C2—22no—
310C2—22no—
311C2—22no—
312C2C3×#521111yescharacteristic
313C2C2×C3×#83311yescharacteristic
314C2C2×C3×#83611yescharacteristic
subgroupG/H
centerC22×C3C2×#217
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC22×C32×C4⋊C4C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC22×C3×C4⋊C4D3
hypocenterC3C3×#1821
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C22×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4530C2semidirect
5. #71562C3direct (N × H)
21. #4530C2×C3semidirect
256. C32#1821semidirect
307. C3#71562direct (N × H)
308. C3C3×#1821semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
C3×#52072
C3×#45302
C3×#18213
#715623