Finite Group Databasebeta

← C3×#68979 #11794279

Subgroups — C3×#68979 #11794279

Order 1152.

509 conjugacy classes of subgroups.

The subgroup lattice has 307 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5500C211yesmaximal, characteristic
2C3×#5121C212yesmaximal
3C3×#4977C211yesmaximal, characteristic
4C32×#343C211yesmaximal, characteristic
5C3×#4555C212yesmaximal
6C3×#2061—31nomaximal
7#68979C311yesmaximal, characteristic, direct product factor
8C2×C32×M16C2212yes—
9C2×C32×C4⋊C4C2211yescharacteristic
10C3×#926C2212yes—
11C2×C3×C4⋊Dic3C2211yescharacteristic
12C3×#924—22no—
13C2×C3×C4×Dic3C2211yescharacteristic
14C3×#890—22no—
15C3×#888—22no—
16C3×C3⋊#95—22no—
17C3×#818—22no—
18C3×#817—22no—
19C3×#544—31no—
20#5500C2×C311yescharacteristic
21C3×#428—32no—
22C3×#382—31no—
23#5121C2×C312yes—
24#4977C2×C311yescharacteristic
25C3×#343—21no—
26C3×#343D311yescharacteristic
27C3×#343C2×C311yescharacteristic
28C3×#339—32no—
29#4555C2×C312yes—
30C22×C32×C4D412yes—
31C22×C32×C4C2311yescharacteristic
32C22×C3×Dic3—21no—
33C22×C3×Dic3—21no—
34C2×C3×Dic6—22no—
35C32×M16—22no—
36C32×M16Q814yescomplemented
37C2×C32×C8—22no—
38C32×C4⋊C4—22no—
39C3×#217—22no—
40C3×C4⋊Dic3—22no—
41C3×C4⋊Dic3—22no—
42C3×C4⋊Dic3D412yes—
43C3×C4⋊Dic3D412yes—
44C3×Dic3⋊C4—24no—
45C3×C4×Dic3—22no—
46C3×C4×Dic3—21no—
47C3×C4×Dic3Q812yescomplemented
48#2061—31noSylow
49C2×C3×M16—22no—
50C2×C3×M16C2×D312yes—
51C2×C3×M16C22×C312yes—
52C3×C4⋊Q8—62no—
53C3×#125—62no—
54C3×C22⋊Q8—62no—
55C3×#117—32no—
56C2×C3×C4⋊C4—21no—
57C2×C3×C4⋊C4—31no—
58C2×C3×C4⋊C4C2×D311yescharacteristic
59C2×C3×C4⋊C4C22×C311yescharacteristic
60C2×C3×C42—31no—
61#926C22×C312yes—
62C2×C4⋊Dic3C22×C311yescharacteristic
63#924—22no—
64C2×C4×Dic3C22×C311yescharacteristic
65#890—22no—
66#888—22no—
67C3×#107—62no—
68C3×#106—62no—
69C3×#95—62no—
70C3⋊#95—22no—
71#818—22no—
72#817—22no—
73C23×C32C2×D411yescharacteristic
74C2×C32×C4—22no—
75C2×C32×C4—42no—
76C2×C32×C4C2×D412yes—
77C2×C32×C4C2×Q812yes—
78C2×C32×C4C2×Q811yescharacteristic
79C2×C32×C4#4111yescharacteristic
80C2×C3×Dic3—22no—
81C2×C3×Dic3—22no—
82C2×C3×Dic3—22no—
83C2×C3×Dic3—41no—
84C2×C3×Dic3—41no—
85C2×C3×Dic3—42no—
86C2×C3×Dic3—41no—
87C3×Dic6—82no—
88C32×C8—24no—
89#544—31no—
90#428—32no—
91#382—31no—
92#343C3×D311yescharacteristic
93#339—32no—
94C2×C3×Q8—62no—
95C22×C3×C4—22no—
96C22×C3×C4—21no—
97C22×C3×C4—61no—
98C22×C3×C4—61no—
99C22×C3×C4D1212yes—
100C22×C3×C4C3×D412yes—
101C22×C3×C4C22×D311yescharacteristic
102C22×C3×C4C23×C311yescharacteristic
103C22×Dic3—21no—
104C22×Dic3—21no—
105C2×Dic6—22no—
106C3×M16—22no—
107C3×M16—22no—
108C3×M16—24no—
109C3×M16—42no—
110C3×M16Dic614yescomplemented
111C3×M16C3×Q814yescomplemented
112C2×C3×C8—22no—
113C2×C3×C8—22no—
114C2×C3×C8—42no—
115C3×C4⋊C4—22no—
116C3×C4⋊C4—22no—
117C3×C4⋊C4—32no—
118C3×C4⋊C4—32no—
119C3×C4⋊C4—42no—
120C3×C4⋊C4—64no—
121C3×C4⋊C4—62no—
122C3×C4⋊C4—62no—
123C3×C22⋊C4—62no—
124C3×C42—32no—
125C3×C42—62no—
126C3×C42—61no—
127#217—22no—
128C4⋊Dic3—22no—
129C4⋊Dic3—22no—
130C4⋊Dic3C3×D412yes—
131C4⋊Dic3C3×D412yes—
132Dic3⋊C4—24no—
133C4×Dic3—22no—
134C4×Dic3—21no—
135C4×Dic3C3×Q812yescomplemented
136C22×C32—21no—
137C22×C32—21no—
138C22×C32#12011yescharacteristic
139C22×C32C22⋊Q811yescharacteristic
140C22×C32C4⋊Q811yescharacteristic
141C32×C4—42no—
142C32×C4C22⋊Q812yes—
143C32×C4C4⋊Q812yes—
144C3×Dic3—42no—
145C3×Dic3—42no—
146C3×Dic3—42no—
147C3×Dic3—81no—
148C2×M16C2×C3×D312yes—
149C4⋊Q8—62no—
150#125—62no—
151C22⋊Q8—62no—
152#117—32no—
153C2×C4⋊C4—31no—
154C2×C4⋊C4C2×C3×D311yescharacteristic
155C2×C42—31no—
156#107—62no—
157#106—62no—
158#95—62no—
159C23×C3—21no—
160C23×C3C2×D1211yescharacteristic
161C23×C3C2×C3×D411yescharacteristic
162C3×Q8—242no—
163C2×C3×C4—22no—
164C2×C3×C4—22no—
165C2×C3×C4—22no—
166C2×C3×C4—22no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—42no—
170C2×C3×C4—42no—
171C2×C3×C4—42no—
172C2×C3×C4—62no—
173C2×C3×C4—62no—
174C2×C3×C4—62no—
175C2×C3×C4—82no—
176C2×C3×C4—121no—
177C2×C3×C4—121no—
178C2×C3×C4—122no—
179C2×C3×C4—121no—
180C2×C3×C4C2×Dic612yes—
181C2×C3×C4D3×D412yes—
182C2×C3×C4#23711yescharacteristic
183C2×C3×C4D3×Q811yescharacteristic
184C2×C3×C4C2×C3×D412yes—
185C2×C3×C4C2×C3×Q812yes—
186C2×C3×C4C2×C3×Q811yescharacteristic
187C2×C3×C4C3×#4111yescharacteristic
188C2×Dic3—22no—
189C2×Dic3—22no—
190C2×Dic3—22no—
191C2×Dic3—41no—
192C2×Dic3—41no—
193C2×Dic3—42no—
194C2×Dic3—41no—
195Dic6—82no—
196C3×C8—24no—
197C3×C8—24no—
198C3×C8—44no—
199C2×C32—21no—
200C2×C32—21no—
201C2×C32#39511yescharacteristic
202C2×C32#45411yescharacteristic
203C2×C32#45511yescharacteristic
204C2×Q8—62no—
205C22×C4—61no—
206C22×C4—61no—
207C22×C4C3×D1212yes—
208C22×C4C22×C3×D311yescharacteristic
209M16—22no—
210M16C3×Dic614yescomplemented
211C2×C8—22no—
212C4⋊C4—22no—
213C4⋊C4—32no—
214C4⋊C4—32no—
215C4⋊C4—62no—
216C4⋊C4—64no—
217C4⋊C4—62no—
218C22⋊C4—62no—
219C42—32no—
220C42—62no—
221C42—61no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3—21no—
227C22×C3—21no—
228C22×C3—21no—
229C22×C3—41no—
230C22×C3—41no—
231C22×C3#86911yescharacteristic
232C22×C3#88211yescharacteristic
233C22×C3#89711yescharacteristic
234C22×C3C3×#12011yescharacteristic
235C22×C3C3×C22⋊Q811yescharacteristic
236C22×C3C3×C4⋊Q811yescharacteristic
237C3×C4—22no—
238C3×C4—22no—
239C3×C4—42no—
240C3×C4—42no—
241C3×C4—82no—
242C3×C4—122no—
243C3×C4—122no—
244C3×C4—122no—
245C3×C4—241no—
246C3×C4#87812yes—
247C3×C4#88812yes—
248C3×C4C3×C22⋊Q812yes—
249C3×C4C3×C4⋊Q812yes—
250Dic3—42no—
251Dic3—42no—
252Dic3—42no—
253Dic3—81no—
254C32#206111yescharacteristic, complemented, Sylow
255C23C2×C3×D1211yescharacteristic
256Q8—242no—
257C2×C4—22no—
258C2×C4—42no—
259C2×C4—62no—
260C2×C4—62no—
261C2×C4—62no—
262C2×C4—121no—
263C2×C4—121no—
264C2×C4—122no—
265C2×C4—121no—
266C2×C4C2×C3×Dic612yes—
267C2×C4C3×D3×D412yes—
268C2×C4C3×#23711yescharacteristic
269C2×C4C3×D3×Q811yescharacteristic
270C8—24no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—41no—
279C2×C3—41no—
280C2×C3#465611yescharacteristic
281C2×C3#474611yescharacteristic
282C2×C3#475311yescharacteristic
283C2×C3C3×#39511yescharacteristic
284C2×C3C3×#45411yescharacteristic
285C2×C3C3×#45511yescharacteristic
286C22—21no—
287C22—21no—
288C22C3×#86911yescharacteristic
289C22C3×#88211yescharacteristic
290C22C3×#89711yescharacteristic
291C4—42no—
292C4—122no—
293C4—122no—
294C4—122no—
295C4—241no—
296C4C3×#87812yes—
297C4C3×#88812yes—
298C3—21no—
299C3#6897911yescharacteristic, direct product factor
300C3C3×#206111yescharacteristic, complemented
301C2—21no—
302C2—21no—
303C2C3×#465611yescharacteristic
304C2C3×#474611yescharacteristic
305C2C3×#475311yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#343C2
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC3×#343D3
hypocenterC3C3×#2061
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#343

Complements

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

NH ≅ G/Ntype
7. #68979C3direct (N × H)
36. C32×M16Q8semidirect
47. C3×C4×Dic3Q8semidirect
110. C3×M16Dic6semidirect
111. C3×M16C3×Q8semidirect
135. C4×Dic3C3×Q8semidirect
210. M16C3×Dic6semidirect
254. C32#2061semidirect
299. C3#68979direct (N × H)
300. C3C3×#2061semidirect

Maximal subgroups

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

subgroupindex
C3×#55002
C3×#51212
C3×#49772
C32×#3432
C3×#45552
C3×#20613
#689793