Finite Group Databasebeta

← C3×#69543 #11794276

Subgroups — C3×#69543 #11794276

Order 1152.

537 conjugacy classes of subgroups.

The subgroup lattice has 317 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5500C211yesmaximal, characteristic
2C32×#382C211yesmaximal, characteristic
3C3×#4964C212yesmaximal
4C3×#4530C211yesmaximal, characteristic
5C3×#4523C212yesmaximal
6C3×#2061—31nomaximal
7#69543C311yesmaximal, characteristic, direct product factor
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×C32×C42C2211yescharacteristic
11C3×#926C2212yes—
12C3×#924—22no—
13C2×C3×#208C2212yes—
14C3×#890—22no—
15C3×#888—22no—
16C32×#95—22no—
17C3×#808—22no—
18C3×#807—22no—
19C3×#544—31no—
20#5500C2×C311yescharacteristic
21C3×#428—32no—
22C3×#382—21no—
23C3×#382D311yescharacteristic
24C3×#382C2×C311yescharacteristic
25#4964C2×C312yes—
26C3×#343—31no—
27C3×#339—32no—
28#4530C2×C311yescharacteristic
29#4523C2×C312yes—
30C22×C32×C4—21no—
31C22×C32×C4—21no—
32C22×C32×C4D412yes—
33C22×C32×C4C2311yescharacteristic
34C2×C3×Dic6—22no—
35C32×C4⋊C4—22no—
36C32×C4⋊C4—22no—
37C32×C42—21no—
38C32×C42Q812yescomplemented
39C3×#217—22no—
40C3×C4⋊Dic3—22no—
41C3×C4⋊Dic3D412yes—
42C3×C4⋊Dic3D412yes—
43C3×Dic3⋊C4—24no—
44C3×C4×Dic3—22no—
45C3×#208—22no—
46C3×#208Q814yescomplemented
47C2×C3×C3⋊C8—22no—
48#2061—31noSylow
49C2×C3×M16—32no—
50C3×C4⋊Q8—62no—
51C3×#125—62no—
52C3×C22⋊Q8—62no—
53C3×#117—32no—
54C2×C3×C4⋊C4—21no—
55C2×C3×C4⋊C4—21no—
56C2×C3×C4⋊C4C2×D311yescharacteristic
57C2×C3×C4⋊C4C2×D311yescharacteristic
58C2×C3×C4⋊C4C22×C311yescharacteristic
59C2×C3×C4⋊C4C22×C311yescharacteristic
60C2×C3×C42—21no—
61C2×C3×C42C2×D311yescharacteristic
62C2×C3×C42C22×C311yescharacteristic
63#926C22×C312yes—
64#924—22no—
65C2×#208C22×C312yes—
66#890—22no—
67#888—22no—
68C3×#107—62no—
69C3×#106—62no—
70C3×#95—24no—
71C3×#95—22no—
72C3×#95—22no—
73#808—22no—
74#807—22no—
75C23×C32C2×D411yescharacteristic
76C2×C32×C4—22no—
77C2×C32×C4—22no—
78C2×C32×C4—41no—
79C2×C32×C4—41no—
80C2×C32×C4—42no—
81C2×C32×C4—42no—
82C2×C32×C4—41no—
83C2×C32×C4C2×D412yes—
84C2×C32×C4C2×Q811yescharacteristic
85C2×C32×C4C2×Q812yes—
86C2×C32×C4#4111yescharacteristic
87C2×C3×Dic3—22no—
88C2×C3×Dic3—22no—
89C3×Dic6—82no—
90C3×C3⋊C8—24no—
91#544—31no—
92#428—32no—
93#382C3×D311yescharacteristic
94#343—31no—
95#339—32no—
96C2×C3×Q8—62no—
97C22×C3×C4—22no—
98C22×C3×C4—21no—
99C22×C3×C4—21no—
100C22×C3×C4—22no—
101C22×C3×C4—21no—
102C22×C3×C4—21no—
103C22×C3×C4—22no—
104C22×C3×C4—21no—
105C22×C3×C4#6712yes—
106C22×C3×C4C3×D412yes—
107C22×C3×C4C22×D311yescharacteristic
108C22×C3×C4C23×C311yescharacteristic
109C2×Dic6—22no—
110C3×M16—34no—
111C3×M16—62no—
112C2×C3×C8—62no—
113C3×C4⋊C4—22no—
114C3×C4⋊C4—22no—
115C3×C4⋊C4—22no—
116C3×C4⋊C4—22no—
117C3×C4⋊C4—32no—
118C3×C4⋊C4—32no—
119C3×C4⋊C4—42no—
120C3×C4⋊C4—42no—
121C3×C4⋊C4—64no—
122C3×C4⋊C4—62no—
123C3×C22⋊C4—62no—
124C3×C42—22no—
125C3×C42—21no—
126C3×C42—21no—
127C3×C42—22no—
128C3×C42—62no—
129C3×C42Dic612yescomplemented
130C3×C42C3×Q812yescomplemented
131#217—22no—
132C4⋊Dic3—22no—
133C4⋊Dic3C3×D412yes—
134C4⋊Dic3C3×D412yes—
135Dic3⋊C4—24no—
136C4×Dic3—22no—
137#208—22no—
138#208C3×Q814yescomplemented
139C2×C3⋊C8—22no—
140C22×C32—21no—
141C22×C32—21no—
142C22×C32#12011yescharacteristic
143C22×C32C22⋊Q811yescharacteristic
144C22×C32C4⋊Q811yescharacteristic
145C32×C4—42no—
146C32×C4—42no—
147C32×C4—81no—
148C32×C4C22⋊Q812yes—
149C32×C4C4⋊Q812yes—
150C3×Dic3—42no—
151C3×Dic3—42no—
152C2×M16—32no—
153C4⋊Q8—62no—
154#125—62no—
155C22⋊Q8—62no—
156#117—32no—
157C2×C4⋊C4C2×C3×D311yescharacteristic
158C2×C4⋊C4C2×C3×D311yescharacteristic
159C2×C42C2×C3×D311yescharacteristic
160#107—62no—
161#106—62no—
162#95—22no—
163C23×C3—21no—
164C23×C3C2×#6711yescharacteristic
165C23×C3C2×C3×D411yescharacteristic
166C3×Q8—242no—
167C2×C3×C4—24no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—22no—
175C2×C3×C4—22no—
176C2×C3×C4—42no—
177C2×C3×C4—42no—
178C2×C3×C4—42no—
179C2×C3×C4—41no—
180C2×C3×C4—41no—
181C2×C3×C4—41no—
182C2×C3×C4—41no—
183C2×C3×C4—42no—
184C2×C3×C4—42no—
185C2×C3×C4—42no—
186C2×C3×C4—44no—
187C2×C3×C4—44no—
188C2×C3×C4—42no—
189C2×C3×C4—42no—
190C2×C3×C4—41no—
191C2×C3×C4—41no—
192C2×C3×C4—62no—
193C2×C3×C4—62no—
194C2×C3×C4C2×Dic611yescharacteristic
195C2×C3×C4#23511yescharacteristic
196C2×C3×C4D3×D412yes—
197C2×C3×C4D3×Q812yes—
198C2×C3×C4C2×C3×D412yes—
199C2×C3×C4C2×C3×Q811yescharacteristic
200C2×C3×C4C2×C3×Q812yes—
201C2×C3×C4C3×#4111yescharacteristic
202C2×Dic3—22no—
203C2×Dic3—22no—
204Dic6—82no—
205C3×C8—64no—
206C3⋊C8—24no—
207C2×C32—21no—
208C2×C32—21no—
209C2×C32#39511yescharacteristic
210C2×C32#45411yescharacteristic
211C2×C32#45511yescharacteristic
212C2×Q8—62no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4C3×#6712yes—
216C22×C4C22×C3×D311yescharacteristic
217M16—34no—
218M16—62no—
219C2×C8—62no—
220C4⋊C4—22no—
221C4⋊C4—22no—
222C4⋊C4—32no—
223C4⋊C4—32no—
224C4⋊C4—62no—
225C4⋊C4—64no—
226C22⋊C4—62no—
227C42—21no—
228C42—62no—
229C42C3×Dic612yescomplemented
230C22×C3—22no—
231C22×C3—22no—
232C22×C3—21no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3#92411yescharacteristic
240C22×C3#93711yescharacteristic
241C22×C3#94411yescharacteristic
242C22×C3C3×#12011yescharacteristic
243C22×C3C3×C22⋊Q811yescharacteristic
244C22×C3C3×C4⋊Q811yescharacteristic
245C3×C4—22no—
246C3×C4—22no—
247C3×C4—44no—
248C3×C4—42no—
249C3×C4—42no—
250C3×C4—42no—
251C3×C4—42no—
252C3×C4—82no—
253C3×C4—82no—
254C3×C4—81no—
255C3×C4—81no—
256C3×C4—122no—
257C3×C4—122no—
258C3×C4#88812yes—
259C3×C4#89612yes—
260C3×C4C3×C22⋊Q812yes—
261C3×C4C3×C4⋊Q812yes—
262Dic3—42no—
263Dic3—42no—
264C32#206111yescharacteristic, complemented, Sylow
265C23C2×C3×#6711yescharacteristic
266Q8—242no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—62no—
275C2×C4—62no—
276C2×C4C2×C3×Dic611yescharacteristic
277C2×C4C3×#23511yescharacteristic
278C2×C4C3×D3×D412yes—
279C2×C4C3×D3×Q812yes—
280C8—64no—
281C2×C3—22no—
282C2×C3—22no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3#497911yescharacteristic
291C2×C3#506111yescharacteristic
292C2×C3#506211yescharacteristic
293C2×C3C3×#39511yescharacteristic
294C2×C3C3×#45411yescharacteristic
295C2×C3C3×#45511yescharacteristic
296C22—21no—
297C22—21no—
298C22C3×#92411yescharacteristic
299C22C3×#93711yescharacteristic
300C22C3×#94411yescharacteristic
301C4—42no—
302C4—42no—
303C4—81no—
304C4—122no—
305C4—122no—
306C4C3×#88812yes—
307C4C3×#89612yes—
308C3—21no—
309C3#6954311yescharacteristic, direct product factor
310C3C3×#206111yescharacteristic, complemented
311C2—21no—
312C2—21no—
313C2C3×#497911yescharacteristic
314C2C3×#506111yescharacteristic
315C2C3×#506211yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#382C2
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC3×#382D3
hypocenterC3C3×#2061
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#382

Complements

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

NH ≅ G/Ntype
7. #69543C3direct (N × H)
38. C32×C42Q8semidirect
46. C3×#208Q8semidirect
129. C3×C42Dic6semidirect
130. C3×C42C3×Q8semidirect
138. #208C3×Q8semidirect
229. C42C3×Dic6semidirect
264. C32#2061semidirect
309. C3#69543direct (N × H)
310. C3C3×#2061semidirect

Maximal subgroups

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

subgroupindex
C3×#55002
C32×#3822
C3×#49642
C3×#45302
C3×#45232
C3×#20613
#695433