Finite Group Databasebeta

← C3×#74150 #11802459

Subgroups — C3×#74150 #11802459

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 341 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#870C211yesmaximal, characteristic
2C32×#382C211yesmaximal, characteristic
3C3×Dic3×C4⋊C4C212yesmaximal
4C3×#4972C212yesmaximal
5C3×C42×Dic3C211yesmaximal, characteristic
6C3×#4652C214yesmaximal
7C3×#4649C214yesmaximal
8C3×C4×#125—31nomaximal
9#74150C311yesmaximal, characteristic, direct product factor
10C2×C32×C4⋊C4C2212yes—
11C2×C32×C42C2211yescharacteristic
12C2×C3×C4⋊Dic3C2212yes—
13C2×C3×Dic3⋊C4C2214yes—
14C2×C3×Dic3⋊C4C2214yes—
15C2×C3×C4×Dic3C2212yes—
16C2×C3×C4×Dic3C2214yes—
17C2×C3×C4×Dic3C2212yes—
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C3×#870C418yescomplemented
21C32×#95C2214yes—
22C3×C3⋊#95C2214yes—
23C3×C3⋊#95C2214yes—
24C2×C3×#125—31no—
25C2×#870C2×C311yescharacteristic
26C3×#389—32no—
27C3×#387—34no—
28C3×#382—21no—
29C3×#382D311yescharacteristic
30C3×#382C2×C311yescharacteristic
31C3×C4×C4⋊C4—32no—
32C3×C4×C4⋊C4—34no—
33C3×C43—31no—
34Dic3×C4⋊C4C2×C312yes—
35#4972C2×C312yes—
36C42×Dic3C2×C311yescharacteristic
37#4652C2×C314yes—
38#4649C2×C314yes—
39C22×C32×C4C2314yes—
40C22×C32×C4C2312yes—
41C22×C32×C4C2311yescharacteristic
42C22×C3×Dic3C2314yes—
43C22×C3×Dic3C2311yescharacteristic
44C22×C3×Dic3C2312yes—
45C22×C3×Dic3C2311yescharacteristic
46C32×C4⋊C4—24no—
47C32×C42C2×C414yes—
48C3×C4⋊Dic3C2×C418yes—
49C3×Dic3⋊C4—28no—
50C3×Dic3⋊C4C2×C4116yes—
51C3×C4×Dic3—22no—
52C3×C4×Dic3—24no—
53C3×C4×Dic3—24no—
54C3×C4×Dic3—28no—
55C3×C4×Dic3Q814yes—
56C4×#125—31noSylow
57C3×#125—38no—
58C2×C3×C4⋊C4—22no—
59C2×C3×C4⋊C4—34no—
60C2×C3×C4⋊C4—32no—
61C2×C3×C4⋊C4—34no—
62C2×C3×C4⋊C4C2×D312yes—
63C2×C3×C4⋊C4C22×C312yes—
64C2×C3×C42—21no—
65C2×C3×C42—31no—
66C2×C3×C42—32no—
67C2×C3×C42—32no—
68C2×C3×C42—31no—
69C2×C3×C42—34no—
70C2×C3×C42C2×D311yescharacteristic
71C2×C3×C42C22×C311yescharacteristic
72C2×C4⋊Dic3C22×C312yes—
73C2×Dic3⋊C4C22×C314yes—
74C2×Dic3⋊C4C22×C314yes—
75C2×C4×Dic3C22×C312yes—
76C2×C4×Dic3C22×C314yes—
77C2×C4×Dic3C22×C312yes—
78C2×C4×Dic3C22×C311yescharacteristic
79C2×C4×Dic3C22×C311yescharacteristic
80#870C3×C418yescomplemented
81C3×#95—24no—
82C3×#95—34no—
83C3×#95—34no—
84C3×#95C2×D314yes—
85C3×#95C22×C314yes—
86C3⋊#95C22×C314yes—
87C3⋊#95C22×C314yes—
88C23×C32C2411yescharacteristic
89C2×C32×C4—22no—
90C2×C32×C4—22no—
91C2×C32×C4—24no—
92C2×C32×C4—24no—
93C2×C32×C4—24no—
94C2×C32×C4C22×C414yes—
95C2×C32×C4C22×C412yes—
96C2×C32×C4C2×Q812yes—
97C2×C32×C4#4112yes—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—24no—
100C2×C3×Dic3—22no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—24no—
103C2×C3×Dic3C22×C418yes—
104C2×C3×Dic3C2×Q812yes—
105C2×C3×Dic3C2×Q812yes—
106C2×C3×Dic3#4114yes—
107C2×C3×Dic3#4114yes—
108C2×#125—31no—
109#389—32no—
110#387—34no—
111#382C3×D311yescharacteristic
112C4×C4⋊C4—32no—
113C4×C4⋊C4—34no—
114C43—31no—
115C22×C3×C4—21no—
116C22×C3×C4—22no—
117C22×C3×C4—24no—
118C22×C3×C4—31no—
119C22×C3×C4—31no—
120C22×C3×C4—32no—
121C22×C3×C4—34no—
122C22×C3×C4C22×D314yes—
123C22×C3×C4C22×D312yes—
124C22×C3×C4C22×D311yescharacteristic
125C22×C3×C4C23×C314yes—
126C22×C3×C4C23×C312yes—
127C22×C3×C4C23×C311yescharacteristic
128C22×Dic3C23×C314yes—
129C22×Dic3C23×C311yescharacteristic
130C22×Dic3C23×C312yes—
131C22×Dic3C23×C311yescharacteristic
132C3×C4⋊C4—24no—
133C3×C4⋊C4—24no—
134C3×C4⋊C4—316no—
135C3×C4⋊C4—38no—
136C3×C4⋊C4—44no—
137C3×C4⋊C4—68no—
138C3×C42—24no—
139C3×C42—34no—
140C3×C42—64no—
141C3×C42—64no—
142C3×C42—68no—
143C3×C42—62no—
144C3×C42C4×D314yes—
145C3×C42C2×C3×C414yes—
146C4⋊Dic3C2×C3×C418yes—
147Dic3⋊C4—28no—
148Dic3⋊C4C2×C3×C4116yes—
149C4×Dic3—22no—
150C4×Dic3—24no—
151C4×Dic3—24no—
152C4×Dic3—28no—
153C4×Dic3C3×Q814yes—
154C22×C32C23×C411yescharacteristic
155C22×C32C22×Q811yescharacteristic
156C22×C32C2×#4111yescharacteristic
157C22×C32C2×#4112yes—
158C22×C32C2×#4112yes—
159C32×C4—24no—
160C32×C4—44no—
161C32×C4C4×Q814yes—
162C3×Dic3—28no—
163C3×Dic3—24no—
164C3×Dic3—22no—
165C3×Dic3#12514yescomplemented
166#125—38no—
167C2×C4⋊C4—34no—
168C2×C4⋊C4—32no—
169C2×C4⋊C4—34no—
170C2×C4⋊C4C2×C3×D312yes—
171C2×C42—31no—
172C2×C42—32no—
173C2×C42—32no—
174C2×C42—31no—
175C2×C42—34no—
176C2×C42C2×C3×D311yescharacteristic
177#95—34no—
178#95—34no—
179#95C2×C3×D314yes—
180C23×C3—21no—
181C23×C3C23×D311yescharacteristic
182C23×C3C24×C311yescharacteristic
183C2×C3×C4—22no—
184C2×C3×C4—22no—
185C2×C3×C4—22no—
186C2×C3×C4—22no—
187C2×C3×C4—24no—
188C2×C3×C4—24no—
189C2×C3×C4—24no—
190C2×C3×C4—24no—
191C2×C3×C4—24no—
192C2×C3×C4—24no—
193C2×C3×C4—22no—
194C2×C3×C4—24no—
195C2×C3×C4—22no—
196C2×C3×C4—22no—
197C2×C3×C4—32no—
198C2×C3×C4—34no—
199C2×C3×C4—38no—
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—44no—
207C2×C3×C4—62no—
208C2×C3×C4—62no—
209C2×C3×C4—62no—
210C2×C3×C4—64no—
211C2×C3×C4—64no—
212C2×C3×C4C2×C4×D314yes—
213C2×C3×C4C2×C4×D312yes—
214C2×C3×C4#23712yes—
215C2×C3×C4D3×Q812yes—
216C2×C3×C4C22×C3×C414yes—
217C2×C3×C4C22×C3×C412yes—
218C2×C3×C4C2×C3×Q812yes—
219C2×C3×C4C3×#4112yes—
220C2×Dic3—22no—
221C2×Dic3—24no—
222C2×Dic3—22no—
223C2×Dic3—22no—
224C2×Dic3—24no—
225C2×Dic3C22×C3×C418yes—
226C2×Dic3C2×C3×Q812yes—
227C2×Dic3C2×C3×Q812yes—
228C2×Dic3C3×#4114yes—
229C2×Dic3C3×#4114yes—
230C2×C32C2×C4×Q811yescharacteristic
231C2×C32C4×#4112yes—
232C2×C32C2×#12511yescharacteristic
233C2×C32#52912yes—
234C2×C32#53311yescharacteristic
235C22×C4—31no—
236C22×C4—31no—
237C22×C4—32no—
238C22×C4—34no—
239C22×C4C22×C3×D314yes—
240C22×C4C22×C3×D312yes—
241C22×C4C22×C3×D311yescharacteristic
242C4⋊C4—24no—
243C4⋊C4—316no—
244C4⋊C4—38no—
245C4⋊C4—68no—
246C42—34no—
247C42—64no—
248C42—64no—
249C42—68no—
250C42—62no—
251C42C3×C4×D314yes—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—22no—
256C22×C3—22no—
257C22×C3C22×C4×D311yescharacteristic
258C22×C3C2×#23711yescharacteristic
259C22×C3C2×D3×Q811yescharacteristic
260C22×C3D3×#4112yes—
261C22×C3D3×#4112yes—
262C22×C3C23×C3×C411yescharacteristic
263C22×C3C22×C3×Q811yescharacteristic
264C22×C3C2×C3×#4111yescharacteristic
265C22×C3C2×C3×#4112yes—
266C22×C3C2×C3×#4112yes—
267C3×C4—24no—
268C3×C4—24no—
269C3×C4—24no—
270C3×C4—34no—
271C3×C4—44no—
272C3×C4—44no—
273C3×C4—44no—
274C3×C4—64no—
275C3×C4—62no—
276C3×C4—68no—
277C3×C4—84no—
278C3×C4#88714yes—
279C3×C4C3×C4×Q814yes—
280Dic3—28no—
281Dic3—24no—
282Dic3—22no—
283Dic3C3×#12514yescomplemented
284C32C4×#12511yescharacteristic, complemented, Sylow
285C23C23×C3×D311yescharacteristic
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—24no—
291C2×C4—32no—
292C2×C4—34no—
293C2×C4—38no—
294C2×C4—32no—
295C2×C4—34no—
296C2×C4—62no—
297C2×C4—64no—
298C2×C4—62no—
299C2×C4—62no—
300C2×C4—64no—
301C2×C4C2×C3×C4×D314yes—
302C2×C4C2×C3×C4×D312yes—
303C2×C4C3×#23712yes—
304C2×C4C3×D3×Q812yes—
305C2×C3—21no—
306C2×C3—22no—
307C2×C3—22no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3C2×#88711yescharacteristic
311C2×C3#552212yes—
312C2×C3#568012yes—
313C2×C3D3×#12511yescharacteristic
314C2×C3#568811yescharacteristic
315C2×C3C2×C3×C4×Q811yescharacteristic
316C2×C3C3×C4×#4112yes—
317C2×C3C2×C3×#12511yescharacteristic
318C2×C3C3×#52912yes—
319C2×C3C3×#53311yescharacteristic
320C22C22×C3×C4×D311yescharacteristic
321C22C2×C3×#23711yescharacteristic
322C22C2×C3×D3×Q811yescharacteristic
323C22C3×D3×#4112yes—
324C22C3×D3×#4112yes—
325C4—24no—
326C4—34no—
327C4—44no—
328C4—68no—
329C4—64no—
330C4—62no—
331C4C3×#88714yes—
332C3—21no—
333C3#7415011yescharacteristic, direct product factor
334C3C3×C4×#12511yescharacteristic, complemented
335C2C2×C3×#88711yescharacteristic
336C2C3×#552212yes—
337C2C3×#568012yes—
338C2C3×D3×#12511yescharacteristic
339C2C3×#568811yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#382C2
socle, prime radicalC23×C32C24
cosocleC23×C3C24×C3
hypercenterC3×#382D3
hypocenterC3C3×C4×#125
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#382

Complements

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

NH ≅ G/Ntype
9. #74150C3direct (N × H)
20. C3×#870C4semidirect
80. #870C3×C4semidirect
165. C3×Dic3#125semidirect
283. Dic3C3×#125semidirect
284. C32C4×#125semidirect
333. C3#74150direct (N × H)
334. C3C3×C4×#125semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8702
C32×#3822
C3×Dic3×C4⋊C42
C3×#49722
C3×C42×Dic32
C3×#46522
C3×#46492
C3×C4×#1253
#741503