Finite Group Databasebeta

← C3×#67640 #11771389

Subgroups — C3×#67640 #11771389

Order 1152.

469 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 469 conjugacy classes of subgroups — too many to draw. Only its 82 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×#390C211yesmaximal, characteristic
2C3×#4528C212yesmaximal, complemented
3C3×#1318—31nomaximal
4#67640C311yesmaximal, characteristic, direct product factor
5C22×C32×D4C411yescharacteristic
6C2×C32×C4⋊C4C2211yescharacteristic
7C2×C32×C22⋊C4—22no—
8C2×C32×C42C411yescharacteristic
9C3×#830—22no—
10C3×#390—21no—
11C3×#390D311yescharacteristic
12C3×#390C2×C311yescharacteristic
13C3×#324—32no—
14#4528C2×C312yescomplemented
15C24×C32—21no—
16C2×C32×D4—21no—
17C2×C32×D4—41no—
18C2×C32×D4—41no—
19C2×C32×D4C812yescomplemented
20C22×C32×C4—21no—
21C22×C32×C4C2×C411yescharacteristic
22C22×C32×C4D412yes—
23C32×C4⋊C4—41no—
24C32×C22⋊C4—44no—
25C32×C42—41no—
26C2×C3×C3⋊C8—42no—
27#1318—31noSylow
28C22×C3×D4—21no—
29C22×C3×D4Dic311yescharacteristic
30C22×C3×D4C3×C411yescharacteristic
31C2×C3×C4⋊C4—21no—
32C2×C3×C4⋊C4C2×D311yescharacteristic
33C2×C3×C4⋊C4C22×C311yescharacteristic
34C2×C3×C22⋊C4—24no—
35C2×C3×C22⋊C4—22no—
36C2×C3×C22⋊C4—22no—
37C2×C3×C42—21no—
38C2×C3×C42Dic311yescharacteristic
39C2×C3×C42C3×C411yescharacteristic
40C3×C22⋊C8—62no—
41#830—22no—
42C23×C32—22no—
43C23×C32—42no—
44C23×C32—42no—
45C23×C32—41no—
46C23×C32—41no—
47C23×C32C22⋊C411yescharacteristic
48C32×D4—42no—
49C32×D4—42no—
50C2×C32×C4—21no—
51C2×C32×C4—21no—
52C2×C32×C4—22no—
53C2×C32×C4—22no—
54C2×C32×C4—41no—
55C2×C32×C4—41no—
56C2×C32×C4—42no—
57C2×C32×C4C2×C811yescharacteristic
58C2×C32×C4M1611yescharacteristic
59C3×C3⋊C8—82no—
60#390C3×D311yescharacteristic
61#324—32no—
62C24×C3—22no—
63C24×C3—21no—
64C24×C3—21no—
65C2×C3×D4—22no—
66C2×C3×D4—21no—
67C2×C3×D4—21no—
68C2×C3×D4—22no—
69C2×C3×D4—41no—
70C2×C3×D4—41no—
71C2×C3×D4—41no—
72C2×C3×D4—41no—
73C2×C3×D4—42no—
74C2×C3×D4—42no—
75C2×C3×D4C3⋊C812yescomplemented
76C2×C3×D4C3×C812yescomplemented
77C22×C3×C4—22no—
78C22×C3×C4—21no—
79C22×C3×C4—21no—
80C22×C3×C4—21no—
81C22×C3×C4—22no—
82C22×C3×C4C2×Dic311yescharacteristic
83C22×C3×C4#6712yes—
84C22×C3×C4C2×C3×C411yescharacteristic
85C22×C3×C4C3×D412yes—
86C2×C3×C8—122no—
87C3×C4⋊C4—41no—
88C3×C4⋊C4—41no—
89C3×C4⋊C4—42no—
90C3×C22⋊C4—44no—
91C3×C22⋊C4—44no—
92C3×C22⋊C4—48no—
93C3×C42—41no—
94C3×C42—41no—
95C3×C42—42no—
96C2×C3⋊C8—42no—
97C22×C32—21no—
98C22×C32—21no—
99C22×C32—44no—
100C22×C32—42no—
101C22×C32—82no—
102C22×C32—81no—
103C22×C32—81no—
104C22×C32C22⋊C811yescharacteristic
105C22×C32#9911yescharacteristic
106C22×C32#10011yescharacteristic
107C32×C4—21no—
108C32×C4—21no—
109C32×C4—42no—
110C32×C4—42no—
111C22×D4C3×Dic311yescharacteristic
112C2×C4⋊C4C2×C3×D311yescharacteristic
113C2×C22⋊C4—22no—
114C2×C42C3×Dic311yescharacteristic
115C22⋊C8—62no—
116C23×C3—24no—
117C23×C3—22no—
118C23×C3—22no—
119C23×C3—21no—
120C23×C3—44no—
121C23×C3—42no—
122C23×C3—42no—
123C23×C3—42no—
124C23×C3—42no—
125C23×C3—44no—
126C23×C3—42no—
127C23×C3—42no—
128C23×C3—41no—
129C23×C3—41no—
130C23×C3—41no—
131C23×C3—41no—
132C23×C3#21711yescharacteristic
133C23×C3C3×C22⋊C411yescharacteristic
134C3×D4—42no—
135C3×D4—42no—
136C3×D4—44no—
137C3×D4—44no—
138C3×D4—42no—
139C3×D4—42no—
140C2×C3×C4—22no—
141C2×C3×C4—22no—
142C2×C3×C4—21no—
143C2×C3×C4—21no—
144C2×C3×C4—21no—
145C2×C3×C4—21no—
146C2×C3×C4—24no—
147C2×C3×C4—22no—
148C2×C3×C4—22no—
149C2×C3×C4—22no—
150C2×C3×C4—22no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—42no—
154C2×C3×C4—42no—
155C2×C3×C4—42no—
156C2×C3×C4—41no—
157C2×C3×C4—41no—
158C2×C3×C4—41no—
159C2×C3×C4—41no—
160C2×C3×C4—42no—
161C2×C3×C4—42no—
162C2×C3×C4—44no—
163C2×C3×C4C2×C3⋊C811yescharacteristic
164C2×C3×C4#20811yescharacteristic
165C2×C3×C4C2×C3×C811yescharacteristic
166C2×C3×C4C3×M1611yescharacteristic
167C3×C8—242no—
168C3⋊C8—82no—
169C2×C32—21no—
170C2×C32—21no—
171C2×C32—82no—
172C2×C32#32311yescharacteristic
173C2×C32#35311yescharacteristic
174C2×C32#35511yescharacteristic
175C24—21no—
176C2×D4—21no—
177C2×D4—41no—
178C2×D4—41no—
179C2×D4C3×C3⋊C812yescomplemented
180C22×C4—21no—
181C22×C4C2×C3×Dic311yescharacteristic
182C22×C4C3×#6712yes—
183C2×C8—122no—
184C4⋊C4—41no—
185C22⋊C4—44no—
186C42—41no—
187C22×C3—22no—
188C22×C3—22no—
189C22×C3—21no—
190C22×C3—21no—
191C22×C3—21no—
192C22×C3—21no—
193C22×C3—21no—
194C22×C3—21no—
195C22×C3—21no—
196C22×C3—44no—
197C22×C3—48no—
198C22×C3—44no—
199C22×C3—44no—
200C22×C3—42no—
201C22×C3—42no—
202C22×C3—84no—
203C22×C3—82no—
204C22×C3—82no—
205C22×C3—82no—
206C22×C3—82no—
207C22×C3—81no—
208C22×C3—81no—
209C22×C3—81no—
210C22×C3—81no—
211C22×C3#83011yescharacteristic
212C22×C3#83311yescharacteristic
213C22×C3#83411yescharacteristic
214C22×C3C3×C22⋊C811yescharacteristic
215C22×C3C3×#9911yescharacteristic
216C22×C3C3×#10011yescharacteristic
217C3×C4—22no—
218C3×C4—22no—
219C3×C4—21no—
220C3×C4—21no—
221C3×C4—21no—
222C3×C4—21no—
223C3×C4—44no—
224C3×C4—42no—
225C3×C4—42no—
226C3×C4—42no—
227C3×C4—42no—
228C3×C4—82no—
229C32#131811yescharacteristic, complemented, Sylow
230C23—22no—
231C23—42no—
232C23—42no—
233C23—41no—
234C23—41no—
235C23C3×#21711yescharacteristic
236D4—42no—
237D4—42no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4C2×C3×C3⋊C811yescharacteristic
246C2×C4C3×#20811yescharacteristic
247C8—242no—
248C2×C3—22no—
249C2×C3—22no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3—21no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—21no—
257C2×C3—84no—
258C2×C3—82no—
259C2×C3—82no—
260C2×C3#452511yescharacteristic
261C2×C3#454211yescharacteristic
262C2×C3#454511yescharacteristic
263C2×C3C3×#32311yescharacteristic
264C2×C3C3×#35311yescharacteristic
265C2×C3C3×#35511yescharacteristic
266C22—21no—
267C22—21no—
268C22—44no—
269C22—42no—
270C22—82no—
271C22—81no—
272C22—81no—
273C22C3×#83011yescharacteristic
274C22C3×#83311yescharacteristic
275C22C3×#83411yescharacteristic
276C4—21no—
277C4—21no—
278C4—42no—
279C4—42no—
280C3—21no—
281C3#6764011yescharacteristic, direct product factor
282C3C3×#131811yescharacteristic, complemented
283C2—21no—
284C2—21no—
285C2—82no—
286C2C3×#452511yescharacteristic
287C2C3×#454211yescharacteristic
288C2C3×#454511yescharacteristic
subgroupG/H
centerC22×C3#834
commutatorC2×C3×C4C2×C3×C8
FrattiniC2×C4⋊C4C2×C3×D3
FittingC32×#390C2
socleC22×C32#99
prime radicalC22×C32×D4C4
cosocleC2×C3×C4⋊C4C22×C3
hypercenterC3×#390D3
hypocenterC3C3×#1318
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C2×C3×C4⋊C4 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
2. C3×#4528C2semidirect
4. #67640C3direct (N × H)
14. #4528C2×C3semidirect
19. C2×C32×D4C8semidirect
75. C2×C3×D4C3⋊C8semidirect
76. C2×C3×D4C3×C8semidirect
179. C2×D4C3×C3⋊C8semidirect
229. C32#1318semidirect
281. C3#67640direct (N × H)
282. C3C3×#1318semidirect

Maximal subgroups

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

subgroupindex
C32×#3902
C3×#45282
C3×#13183
#676403