Finite Group Databasebeta

← C3×#67686 #11771246

Subgroups — C3×#67686 #11771246

Order 1152.

479 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#407C211yesmaximal, characteristic
2C3×#5211C211yesmaximal, characteristic
3C3×#5207C211yesmaximal, characteristic
4C3×#1306—31nomaximal
5#67686C311yesmaximal, characteristic, direct product factor
6C23×C32×C4C2211yescharacteristic
7C2×C32×M16—21no—
8C2×C3×#217C412yes—
9C2×C3×#208—21no—
10C32×C22⋊C8—21no—
11C32×C22⋊C8C412yescomplemented
12C3×C3⋊#95—21no—
13C3×C3⋊#95—21no—
14C3×#830—21no—
15C3×#830C412yescomplemented
16C3×#407—21no—
17C3×#407—31no—
18C3×#407D311yescharacteristic
19C3×#407C2×C311yescharacteristic
20C3×#381—31no—
21#5211C2×C311yescharacteristic
22#5207C2×C311yescharacteristic
23C24×C32C2×C411yescharacteristic
24C22×C32×C4—42no—
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4D411yescharacteristic
28C22×C32×C4D411yescharacteristic
29C22×C32×C4D411yescharacteristic
30C22×C32×C4Q811yescharacteristic
31C22×C3×Dic3—22no—
32C32×M16—42no—
33C2×C32×C8—22no—
34C3×#217—42no—
35C3×#208—42no—
36C2×C3×C3⋊C8—22no—
37#1306—31noSylow
38C23×C3×C4—21no—
39C23×C3×C4C2×D311yescharacteristic
40C23×C3×C4C22×C311yescharacteristic
41C2×C3×M16—22no—
42C2×C3×M16—21no—
43C2×C3×M16—21no—
44C2×C3×M16—61no—
45C2×C3×C22⋊C4—32no—
46C2×#217C3×C412yes—
47C2×#208—21no—
48C3×C22⋊C8—22no—
49C3×C22⋊C8—21no—
50C3×C22⋊C8—21no—
51C3×C22⋊C8—22no—
52C3×C22⋊C8—32no—
53C3×C22⋊C8—61no—
54C3×C22⋊C8Dic312yescomplemented
55C3×C22⋊C8C3×C412yescomplemented
56C3×#95—61no—
57C3×#95—61no—
58C3⋊#95—21no—
59C3⋊#95—21no—
60#830—21no—
61#830C3×C412yescomplemented
62C23×C32—22no—
63C23×C32—41no—
64C23×C32—41no—
65C23×C32C4211yescharacteristic
66C23×C32C22⋊C411yescharacteristic
67C23×C32C4⋊C411yescharacteristic
68C2×C32×C4—22no—
69C2×C32×C4—22no—
70C2×C32×C4—41no—
71C2×C32×C4—41no—
72C2×C32×C4—41no—
73C2×C32×C4—41no—
74C2×C32×C4C22⋊C411yescharacteristic
75C2×C32×C4C22⋊C411yescharacteristic
76C2×C32×C4C4⋊C411yescharacteristic
77C2×C32×C4C4⋊C411yescharacteristic
78C2×C3×Dic3—42no—
79C2×C3×Dic3—42no—
80C2×C3×Dic3—42no—
81C32×C8—42no—
82C3×C3⋊C8—42no—
83#407—31no—
84#407C3×D311yescharacteristic
85#381—31no—
86C24×C3—21no—
87C24×C3C4×D311yescharacteristic
88C24×C3C2×C3×C411yescharacteristic
89C22×C3×C4—21no—
90C22×C3×C4—21no—
91C22×C3×C4—21no—
92C22×C3×C4—21no—
93C22×C3×C4—21no—
94C22×C3×C4—21no—
95C22×C3×C4—42no—
96C22×C3×C4—42no—
97C22×C3×C4—44no—
98C22×C3×C4—62no—
99C22×C3×C4Dic611yescharacteristic
100C22×C3×C4C4×D311yescharacteristic
101C22×C3×C4D1211yescharacteristic
102C22×C3×C4C2×Dic311yescharacteristic
103C22×C3×C4#6711yescharacteristic
104C22×C3×C4#6711yescharacteristic
105C22×C3×C4C2×C3×C411yescharacteristic
106C22×C3×C4C2×C3×C411yescharacteristic
107C22×C3×C4C3×D411yescharacteristic
108C22×C3×C4C3×D411yescharacteristic
109C22×C3×C4C3×D411yescharacteristic
110C22×C3×C4C3×Q811yescharacteristic
111C22×Dic3—22no—
112C3×M16—44no—
113C3×M16—42no—
114C3×M16—42no—
115C3×M16—122no—
116C2×C3×C8—24no—
117C2×C3×C8—22no—
118C2×C3×C8—22no—
119C2×C3×C8—62no—
120C3×C22⋊C4—122no—
121#217—42no—
122#208—42no—
123C2×C3⋊C8—22no—
124C22×C32—21no—
125C22×C32—21no—
126C22×C32—21no—
127C22×C32—21no—
128C22×C32—21no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32—21no—
132C22×C32—44no—
133C22×C32#9511yescharacteristic
134C22×C32#9912yes—
135C32×C4—21no—
136C32×C4—21no—
137C32×C4—21no—
138C32×C4—21no—
139C3×Dic3—82no—
140C23×C4C2×C3×D311yescharacteristic
141C2×M16—21no—
142C2×M16—61no—
143C2×C22⋊C4—32no—
144C22⋊C8—21no—
145C22⋊C8—32no—
146C22⋊C8—61no—
147C22⋊C8C3×Dic312yescomplemented
148#95—61no—
149#95—61no—
150C23×C3—22no—
151C23×C3—22no—
152C23×C3—21no—
153C23×C3—21no—
154C23×C3—21no—
155C23×C3—42no—
156C23×C3—41no—
157C23×C3—41no—
158C23×C3—41no—
159C23×C3—41no—
160C23×C3—42no—
161C23×C3—42no—
162C23×C3C4×Dic311yescharacteristic
163C23×C3Dic3⋊C411yescharacteristic
164C23×C3(C2×D3)⋊C411yescharacteristic
165C23×C3C3×C4211yescharacteristic
166C23×C3C3×C22⋊C411yescharacteristic
167C23×C3C3×C4⋊C411yescharacteristic
168C2×C3×C4—24no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×C3×C4—22no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—42no—
178C2×C3×C4—41no—
179C2×C3×C4—41no—
180C2×C3×C4—41no—
181C2×C3×C4—41no—
182C2×C3×C4—41no—
183C2×C3×C4—41no—
184C2×C3×C4—41no—
185C2×C3×C4—41no—
186C2×C3×C4—42no—
187C2×C3×C4—42no—
188C2×C3×C4—42no—
189C2×C3×C4—42no—
190C2×C3×C4—122no—
191C2×C3×C4—122no—
192C2×C3×C4—122no—
193C2×C3×C4Dic3⋊C411yescharacteristic
194C2×C3×C4C4⋊Dic311yescharacteristic
195C2×C3×C4(C2×D3)⋊C411yescharacteristic
196C2×C3×C4#21711yescharacteristic
197C2×C3×C4C3×C22⋊C411yescharacteristic
198C2×C3×C4C3×C22⋊C411yescharacteristic
199C2×C3×C4C3×C4⋊C411yescharacteristic
200C2×C3×C4C3×C4⋊C411yescharacteristic
201C2×Dic3—42no—
202C2×Dic3—42no—
203C2×Dic3—42no—
204C3×C8—44no—
205C3×C8—42no—
206C3×C8—42no—
207C3×C8—122no—
208C3⋊C8—42no—
209C2×C32—22no—
210C2×C32—41no—
211C2×C32—41no—
212C2×C32#34211yescharacteristic
213C2×C32#34411yescharacteristic
214C2×C32#34411yescharacteristic
215C24C3×C4×D311yescharacteristic
216C22×C4—42no—
217C22×C4—62no—
218C22×C4C3×Dic611yescharacteristic
219C22×C4C3×C4×D311yescharacteristic
220C22×C4C3×D1211yescharacteristic
221C22×C4C2×C3×Dic311yescharacteristic
222C22×C4C3×#6711yescharacteristic
223C22×C4C3×#6711yescharacteristic
224M16—42no—
225M16—122no—
226C2×C8—22no—
227C2×C8—62no—
228C22⋊C4—122no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3—21no—
233C22×C3—22no—
234C22×C3—22no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—22no—
248C22×C3—21no—
249C22×C3—41no—
250C22×C3—41no—
251C22×C3—41no—
252C22×C3—41no—
253C22×C3—41no—
254C22×C3—41no—
255C22×C3—44no—
256C22×C3—44no—
257C22×C3—48no—
258C22×C3#80612yes—
259C22×C3C3⋊#9511yescharacteristic
260C22×C3C3×#9511yescharacteristic
261C22×C3C3×#9912yes—
262C3×C4—22no—
263C3×C4—22no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—41no—
273C3×C4—41no—
274C3×C4—242no—
275Dic3—82no—
276C32#130611yescharacteristic, complemented, Sylow
277C23—22no—
278C23—41no—
279C23—41no—
280C23C3×C4×Dic311yescharacteristic
281C23C3×Dic3⋊C411yescharacteristic
282C23C3×(C2×D3)⋊C411yescharacteristic
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—122no—
290C2×C4—122no—
291C2×C4—122no—
292C2×C4C3×Dic3⋊C411yescharacteristic
293C2×C4C3×C4⋊Dic311yescharacteristic
294C2×C4C3×(C2×D3)⋊C411yescharacteristic
295C2×C4C3×#21711yescharacteristic
296C8—42no—
297C8—122no—
298C2×C3—22no—
299C2×C3—22no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—42no—
304C2×C3—42no—
305C2×C3—42no—
306C2×C3—41no—
307C2×C3—41no—
308C2×C3—41no—
309C2×C3—41no—
310C2×C3#452711yescharacteristic
311C2×C3#455611yescharacteristic
312C2×C3#455911yescharacteristic
313C2×C3C3×#34211yescharacteristic
314C2×C3C3×#34411yescharacteristic
315C2×C3C3×#34411yescharacteristic
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—44no—
325C22C3×#80612yes—
326C22C3×C3⋊#9511yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—242no—
332C3—21no—
333C3#6768611yescharacteristic, direct product factor
334C3C3×#130611yescharacteristic, complemented
335C2—22no—
336C2—41no—
337C2—41no—
338C2C3×#452711yescharacteristic
339C2C3×#455611yescharacteristic
340C2C3×#455911yescharacteristic
subgroupG/H
centerC22×C3C3⋊#95
commutatorC23×C3C3×C42
FrattiniC23×C4C2×C3×D3
FittingC32×#407C2
socleC22×C32#95
prime radicalC24×C32C2×C4
cosocleC23×C3×C4C22×C3
hypercenterC3×#407D3
hypocenterC3C3×#1306
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
5. #67686C3direct (N × H)
11. C32×C22⋊C8C4semidirect
15. C3×#830C4semidirect
54. C3×C22⋊C8Dic3semidirect
55. C3×C22⋊C8C3×C4semidirect
61. #830C3×C4semidirect
147. C22⋊C8C3×Dic3semidirect
276. C32#1306semidirect
333. C3#67686direct (N × H)
334. C3C3×#1306semidirect

Maximal subgroups

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

subgroupindex
C32×#4072
C3×#52112
C3×#52072
C3×#13063
#676863