Finite Group Databasebeta

← C3×#67495 #11771832

Subgroups — C3×#67495 #11771832

Order 1152.

297 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 297 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C3×#4981C211yesmaximal, characteristic
2C32×#343C211yesmaximal, characteristic
3C3×#4528C211yesmaximal, characteristic
4C3×#1346—31nomaximal
5#67495C311yesmaximal, characteristic, direct product factor
6C2×C32×M16—21no—
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×C3×C4⋊Dic3C411yescharacteristic
9C2×C3×Dic3⋊C4—21no—
10C3×C3⋊#95—21no—
11C3×C3⋊#95C411yescharacteristic
12C3×#830—21no—
13C3×#398—31no—
14#4981C2×C311yescharacteristic
15C3×#343—21no—
16C3×#343D311yescharacteristic
17C3×#343C2×C311yescharacteristic
18C3×#324—31no—
19#4528C2×C311yescharacteristic
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4D411yescharacteristic
22C22×C32×C4D411yescharacteristic
23C22×C3×Dic3—21no—
24C22×C3×Dic3—21no—
25C32×M16—22no—
26C32×M16—41no—
27C2×C32×C8—41no—
28C32×C4⋊C4—41no—
29C3×C4⋊Dic3—41no—
30C3×Dic3⋊C4—41no—
31C3×Dic3⋊C4—41no—
32C2×C3×C3⋊C8—41no—
33#1346—31noSylow
34C2×C3×M16—22no—
35C2×C3×M16—21no—
36C2×C3×M16—21no—
37C2×C3×C4⋊C4—21no—
38C2×C3×C4⋊C4—31no—
39C2×C3×C4⋊C4—61no—
40C2×C3×C4⋊C4C2×D311yescharacteristic
41C2×C3×C4⋊C4C22×C311yescharacteristic
42C2×C4⋊Dic3C3×C411yescharacteristic
43C2×Dic3⋊C4—21no—
44C3×C22⋊C8—61no—
45C3×#95—31no—
46C3×#95—61no—
47C3⋊#95—21no—
48C3⋊#95C3×C411yescharacteristic
49#830—21no—
50C23×C32C22⋊C411yescharacteristic
51C2×C32×C4—21no—
52C2×C32×C4—21no—
53C2×C32×C4—21no—
54C2×C32×C4—21no—
55C2×C32×C4—41no—
56C2×C32×C4—41no—
57C2×C32×C4D811yescharacteristic
58C2×C32×C4SD1611yescharacteristic
59C2×C3×Dic3—22no—
60C2×C3×Dic3—41no—
61C2×C3×Dic3—41no—
62C2×C3×Dic3—41no—
63C2×C3×Dic3—41no—
64C2×C3×Dic3—41no—
65C32×C8—42no—
66C3×C3⋊C8—81no—
67#398—31no—
68#343C3×D311yescharacteristic
69#324—31no—
70C22×C3×C4—21no—
71C22×C3×C4—21no—
72C22×C3×C4—21no—
73C22×C3×C4—61no—
74C22×C3×C4—61no—
75C22×C3×C4C4×D311yescharacteristic
76C22×C3×C4D1211yescharacteristic
77C22×C3×C4#6711yescharacteristic
78C22×C3×C4C2×C3×C411yescharacteristic
79C22×C3×C4C3×D411yescharacteristic
80C22×C3×C4C3×D411yescharacteristic
81C22×Dic3—21no—
82C22×Dic3—21no—
83C3×M16—24no—
84C3×M16—22no—
85C3×M16—22no—
86C3×M16—42no—
87C3×M16—41no—
88C3×M16—41no—
89C2×C3×C8—42no—
90C2×C3×C8—41no—
91C2×C3×C8—41no—
92C2×C3×C8—121no—
93C3×C4⋊C4—41no—
94C3×C4⋊C4—41no—
95C3×C4⋊C4—42no—
96C3×C4⋊C4—121no—
97C3×C4⋊C4—121no—
98C3×C4⋊C4—121no—
99C4⋊Dic3—41no—
100Dic3⋊C4—41no—
101Dic3⋊C4—41no—
102C2×C3⋊C8—41no—
103C22×C32—21no—
104C22×C32—21no—
105C22×C32#9911yescharacteristic
106C22×C32#10211yescharacteristic
107C22×C32#10411yescharacteristic
108C32×C4—21no—
109C32×C4—21no—
110C32×C4—41no—
111C32×C4—41no—
112C3×Dic3—42no—
113C3×Dic3—81no—
114C2×M16—21no—
115C2×C4⋊C4—31no—
116C2×C4⋊C4—61no—
117C2×C4⋊C4C2×C3×D311yescharacteristic
118C22⋊C8—61no—
119#95—31no—
120#95—61no—
121C23×C3—21no—
122C23×C3(C2×D3)⋊C411yescharacteristic
123C23×C3C3×C22⋊C411yescharacteristic
124C2×C3×C4—22no—
125C2×C3×C4—22no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—41no—
137C2×C3×C4—41no—
138C2×C3×C4—41no—
139C2×C3×C4—41no—
140C2×C3×C4—41no—
141C2×C3×C4—41no—
142C2×C3×C4—62no—
143C2×C3×C4—81no—
144C2×C3×C4—81no—
145C2×C3×C4—121no—
146C2×C3×C4—121no—
147C2×C3×C4—121no—
148C2×C3×C4—121no—
149C2×C3×C4—121no—
150C2×C3×C4#21311yescharacteristic
151C2×C3×C4#21511yescharacteristic
152C2×C3×C4C3×D811yescharacteristic
153C2×C3×C4C3×SD1611yescharacteristic
154C2×Dic3—22no—
155C2×Dic3—41no—
156C2×Dic3—41no—
157C2×Dic3—41no—
158C2×Dic3—41no—
159C2×Dic3—41no—
160C3×C8—44no—
161C3×C8—42no—
162C3×C8—42no—
163C3×C8—241no—
164C3⋊C8—81no—
165C2×C32—21no—
166C2×C32—21no—
167C2×C32#32711yescharacteristic
168C2×C32#35211yescharacteristic
169C2×C32#35611yescharacteristic
170C22×C4—61no—
171C22×C4—61no—
172C22×C4C3×C4×D311yescharacteristic
173C22×C4C3×D1211yescharacteristic
174C22×C4C3×#6711yescharacteristic
175M16—22no—
176M16—41no—
177C2×C8—41no—
178C2×C8—121no—
179C4⋊C4—41no—
180C4⋊C4—121no—
181C4⋊C4—121no—
182C4⋊C4—121no—
183C22×C3—21no—
184C22×C3—21no—
185C22×C3—21no—
186C22×C3—21no—
187C22×C3—21no—
188C22×C3—21no—
189C22×C3—21no—
190C22×C3—41no—
191C22×C3—41no—
192C22×C3#80511yescharacteristic
193C22×C3#80611yescharacteristic
194C22×C3#80911yescharacteristic
195C22×C3C3×#9911yescharacteristic
196C22×C3C3×#10211yescharacteristic
197C22×C3C3×#10411yescharacteristic
198C3×C4—22no—
199C3×C4—22no—
200C3×C4—21no—
201C3×C4—21no—
202C3×C4—21no—
203C3×C4—21no—
204C3×C4—41no—
205C3×C4—41no—
206C3×C4—41no—
207C3×C4—41no—
208C3×C4—81no—
209C3×C4—81no—
210C3×C4—122no—
211C3×C4—241no—
212Dic3—42no—
213Dic3—81no—
214C32#134611yescharacteristic, complemented, Sylow
215C23C3×(C2×D3)⋊C411yescharacteristic
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—62no—
223C2×C4—121no—
224C2×C4—121no—
225C2×C4—121no—
226C2×C4—121no—
227C2×C4—121no—
228C2×C4C3×#21311yescharacteristic
229C2×C4C3×#21511yescharacteristic
230C8—42no—
231C8—241no—
232C2×C3—21no—
233C2×C3—21no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—21no—
238C2×C3—21no—
239C2×C3—41no—
240C2×C3—41no—
241C2×C3#445111yescharacteristic
242C2×C3#447611yescharacteristic
243C2×C3#447811yescharacteristic
244C2×C3C3×#32711yescharacteristic
245C2×C3C3×#35211yescharacteristic
246C2×C3C3×#35611yescharacteristic
247C22—21no—
248C22—21no—
249C22C3×#80511yescharacteristic
250C22C3×#80611yescharacteristic
251C22C3×#80911yescharacteristic
252C4—21no—
253C4—21no—
254C4—41no—
255C4—41no—
256C4—122no—
257C4—241no—
258C3—21no—
259C3#6749511yescharacteristic, direct product factor
260C3C3×#134611yescharacteristic, complemented
261C2—21no—
262C2—21no—
263C2C3×#445111yescharacteristic
264C2C3×#447611yescharacteristic
265C2C3×#447811yescharacteristic
subgroupG/H
centerC22×C3#806
commutatorC22×C3×C4C2×C3×C4
FrattiniC2×C4⋊C4C2×C3×D3
FittingC32×#343C2
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×C3×C4⋊C4C22×C3
hypercenterC3×#343D3
hypocenterC3C3×#1346
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C2×C3×C4⋊C4 ◁ C3×#343

Complements

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

NH ≅ G/Ntype
5. #67495C3direct (N × H)
214. C32#1346semidirect
259. C3#67495direct (N × H)
260. C3C3×#1346semidirect

Maximal subgroups

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

subgroupindex
C3×#49812
C32×#3432
C3×#45282
C3×#13463
#674953