Finite Group Databasebeta

← C3×#67644 #11772614

Subgroups — C3×#67644 #11772614

Order 1152.

437 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 437 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#391C211yesmaximal, characteristic
2C2×C3×#836C212yesmaximal
3C3×#1394—31nomaximal
4#67644C311yesmaximal, characteristic, direct product factor
5C22×C32×Q8C2211yescharacteristic
6C2×C32×C4⋊C4C411yescharacteristic
7C2×C32×C42C411yescharacteristic
8C2×C3×#208—22no—
9C32×#95—22no—
10C3×#836—22no—
11C3×#836C414yescomplemented
12C2×C3×#101—32no—
13C3×#391—21no—
14C3×#391D311yescharacteristic
15C3×#391C2×C311yescharacteristic
16C2×#836C2×C312yes—
17C2×C32×Q8—41no—
18C2×C32×Q8—41no—
19C2×C32×Q8C2×C412yes—
20C2×C32×Q8D411yescharacteristic
21C2×C32×Q8Q811yescharacteristic
22C22×C32×C4—21no—
23C22×C32×C4—21no—
24C22×C32×C4C2×C411yescharacteristic
25C22×C32×C4D412yes—
26C32×C4⋊C4—41no—
27C32×C42—41no—
28C3×#208—24no—
29C3×#208—42no—
30C2×C3×C3⋊C8—42no—
31#1394—31noSylow
32C22×C3×Q8—21no—
33C22×C3×Q8C2×D311yescharacteristic
34C22×C3×Q8C22×C311yescharacteristic
35C2×C3×M16—62no—
36C2×C3×C4⋊C4—21no—
37C2×C3×C4⋊C4Dic311yescharacteristic
38C2×C3×C4⋊C4C3×C411yescharacteristic
39C2×C3×C42—21no—
40C2×C3×C42Dic311yescharacteristic
41C2×C3×C42C3×C411yescharacteristic
42C2×#208—22no—
43C3×#101—34no—
44C3×#101—62no—
45C3×#95—24no—
46C3×#95—22no—
47C3×#95—22no—
48#836—22no—
49#836C3×C414yescomplemented
50C23×C32C22⋊C411yescharacteristic
51C32×Q8—42no—
52C32×Q8—41no—
53C32×Q8—41no—
54C2×C32×C4—21no—
55C2×C32×C4—21no—
56C2×C32×C4—22no—
57C2×C32×C4—22no—
58C2×C32×C4—22no—
59C2×C32×C4—41no—
60C2×C32×C4—41no—
61C2×C32×C4—42no—
62C2×C32×C4—41no—
63C2×C32×C4C4211yescharacteristic
64C2×C32×C4C22⋊C412yes—
65C2×C32×C4C4⋊C412yes—
66C2×C32×C4C4⋊C411yescharacteristic
67C3×C3⋊C8—44no—
68C2×#101—32no—
69#391C3×D311yescharacteristic
70C2×C3×Q8—21no—
71C2×C3×Q8—22no—
72C2×C3×Q8—21no—
73C2×C3×Q8—41no—
74C2×C3×Q8—41no—
75C2×C3×Q8—41no—
76C2×C3×Q8—41no—
77C2×C3×Q8—42no—
78C2×C3×Q8—42no—
79C2×C3×Q8Dic611yescharacteristic
80C2×C3×Q8C4×D312yes—
81C2×C3×Q8D1211yescharacteristic
82C2×C3×Q8C2×C3×C412yes—
83C2×C3×Q8C3×D411yescharacteristic
84C2×C3×Q8C3×Q811yescharacteristic
85C22×C3×C4—22no—
86C22×C3×C4—21no—
87C22×C3×C4—21no—
88C22×C3×C4—22no—
89C22×C3×C4—21no—
90C22×C3×C4—21no—
91C22×C3×C4—21no—
92C22×C3×C4—22no—
93C22×C3×C4C2×Dic311yescharacteristic
94C22×C3×C4#6712yes—
95C22×C3×C4C2×C3×C411yescharacteristic
96C22×C3×C4C3×D412yes—
97C3×M16—64no—
98C3×M16—122no—
99C2×C3×C8—122no—
100C3×C4⋊C4—41no—
101C3×C4⋊C4—41no—
102C3×C4⋊C4—42no—
103C3×C42—41no—
104C3×C42—41no—
105C3×C42—42no—
106#208—24no—
107#208—42no—
108C2×C3⋊C8—42no—
109C22×C32—21no—
110C22×C32—21no—
111C22×C32#9511yescharacteristic
112C22×C32#9911yescharacteristic
113C22×C32#9911yescharacteristic
114C32×C4—21no—
115C32×C4—21no—
116C32×C4—22no—
117C32×C4—22no—
118C32×C4—42no—
119C32×C4—81no—
120C22×Q8C2×C3×D311yescharacteristic
121C2×M16—62no—
122C2×C4⋊C4C3×Dic311yescharacteristic
123C2×C42C3×Dic311yescharacteristic
124#101—34no—
125#101—62no—
126#95—22no—
127C23×C3—21no—
128C23×C3#21711yescharacteristic
129C23×C3C3×C22⋊C411yescharacteristic
130C3×Q8—41no—
131C3×Q8—42no—
132C3×Q8—41no—
133C3×Q8—42no—
134C3×Q8—41no—
135C3×Q8—41no—
136C3×Q8—42no—
137C3×Q8—44no—
138C3×Q8—42no—
139C2×C3×C4—22no—
140C2×C3×C4—22no—
141C2×C3×C4—21no—
142C2×C3×C4—22no—
143C2×C3×C4—21no—
144C2×C3×C4—22no—
145C2×C3×C4—22no—
146C2×C3×C4—22no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—24no—
150C2×C3×C4—22no—
151C2×C3×C4—22no—
152C2×C3×C4—21no—
153C2×C3×C4—22no—
154C2×C3×C4—21no—
155C2×C3×C4—22no—
156C2×C3×C4—42no—
157C2×C3×C4—42no—
158C2×C3×C4—42no—
159C2×C3×C4—42no—
160C2×C3×C4—41no—
161C2×C3×C4—41no—
162C2×C3×C4—41no—
163C2×C3×C4—41no—
164C2×C3×C4—42no—
165C2×C3×C4—44no—
166C2×C3×C4—42no—
167C2×C3×C4—42no—
168C2×C3×C4—41no—
169C2×C3×C4—41no—
170C2×C3×C4C4×Dic311yescharacteristic
171C2×C3×C4Dic3⋊C412yes—
172C2×C3×C4C4⋊Dic311yescharacteristic
173C2×C3×C4(C2×D3)⋊C412yes—
174C2×C3×C4C3×C4211yescharacteristic
175C2×C3×C4C3×C22⋊C412yes—
176C2×C3×C4C3×C4⋊C412yes—
177C2×C3×C4C3×C4⋊C411yescharacteristic
178C3×C8—124no—
179C3⋊C8—44no—
180C2×C32—21no—
181C2×C32—21no—
182C2×C32#34211yescharacteristic
183C2×C32#35511yescharacteristic
184C2×C32#35611yescharacteristic
185C2×Q8—41no—
186C2×Q8—41no—
187C2×Q8C3×Dic611yescharacteristic
188C2×Q8C3×C4×D312yes—
189C2×Q8C3×D1211yescharacteristic
190C22×C4—21no—
191C22×C4—21no—
192C22×C4C2×C3×Dic311yescharacteristic
193C22×C4C3×#6712yes—
194M16—64no—
195M16—122no—
196C2×C8—122no—
197C4⋊C4—41no—
198C42—41no—
199C22×C3—22no—
200C22×C3—22no—
201C22×C3—21no—
202C22×C3—21no—
203C22×C3—21no—
204C22×C3—21no—
205C22×C3—21no—
206C22×C3—21no—
207C22×C3—21no—
208C22×C3C3⋊#9511yescharacteristic
209C22×C3#83411yescharacteristic
210C22×C3#83411yescharacteristic
211C22×C3C3×#9511yescharacteristic
212C22×C3C3×#9911yescharacteristic
213C22×C3C3×#9911yescharacteristic
214C3×C4—22no—
215C3×C4—22no—
216C3×C4—22no—
217C3×C4—21no—
218C3×C4—22no—
219C3×C4—21no—
220C3×C4—22no—
221C3×C4—21no—
222C3×C4—22no—
223C3×C4—21no—
224C3×C4—42no—
225C3×C4—42no—
226C3×C4—44no—
227C3×C4—42no—
228C3×C4—42no—
229C3×C4—82no—
230C3×C4—81no—
231C3×C4—81no—
232C32#139411yescharacteristic, complemented, Sylow
233C23C3×#21711yescharacteristic
234Q8—41no—
235Q8—42no—
236Q8—41no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4C3×C4×Dic311yescharacteristic
247C2×C4C3×Dic3⋊C412yes—
248C2×C4C3×C4⋊Dic311yescharacteristic
249C2×C4C3×(C2×D3)⋊C412yes—
250C8—124no—
251C2×C3—22no—
252C2×C3—22no—
253C2×C3—21no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—21no—
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—21no—
260C2×C3#452611yescharacteristic
261C2×C3#454211yescharacteristic
262C2×C3#454811yescharacteristic
263C2×C3C3×#34211yescharacteristic
264C2×C3C3×#35511yescharacteristic
265C2×C3C3×#35611yescharacteristic
266C22—21no—
267C22—21no—
268C22C3×C3⋊#9511yescharacteristic
269C22C3×#83411yescharacteristic
270C22C3×#83411yescharacteristic
271C4—22no—
272C4—21no—
273C4—22no—
274C4—21no—
275C4—42no—
276C4—81no—
277C3—21no—
278C3#6764411yescharacteristic, direct product factor
279C3C3×#139411yescharacteristic, complemented
280C2—21no—
281C2—21no—
282C2C3×#452611yescharacteristic
283C2C3×#454211yescharacteristic
284C2C3×#454811yescharacteristic
subgroupG/H
centerC22×C3#834
commutatorC2×C3×C4C3×C42
FrattiniC22×Q8C2×C3×D3
FittingC32×#391C2
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC22×C3×Q8C22×C3
hypercenterC3×#391D3
hypocenterC3C3×#1394
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C22×C3×Q8 ◁ C3×#391

Complements

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

NH ≅ G/Ntype
4. #67644C3direct (N × H)
11. C3×#836C4semidirect
49. #836C3×C4semidirect
232. C32#1394semidirect
278. C3#67644direct (N × H)
279. C3C3×#1394semidirect

Maximal subgroups

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

subgroupindex
C32×#3912
C2×C3×#8362
C3×#13943
#676443