Finite Group Databasebeta

← C3×#67459 #11771957

Subgroups — C3×#67459 #11771957

Order 1152.

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

normal subgroups only

This group has 271 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×#4986C211yesmaximal, characteristic
2C32×#324C211yesmaximal, characteristic
3C3×#4530C211yesmaximal, characteristic
4C3×#1353—31nomaximal
5#67459C311yesmaximal, characteristic, direct product factor
6C2×C32×C4⋊C4C2211yescharacteristic
7C2×C3×C4⋊Dic3C411yescharacteristic
8C2×C3×#208—21no—
9C32×C22⋊C8—21no—
10C3×C3⋊#95—21no—
11C3×C3⋊#95—21no—
12C3×C3⋊#95C411yescharacteristic
13C3×#400—31no—
14#4986C2×C311yescharacteristic
15C3×#343—31no—
16C3×#324—21no—
17C3×#324D311yescharacteristic
18C3×#324C2×C311yescharacteristic
19#4530C2×C311yescharacteristic
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4D411yescharacteristic
22C22×C32×C4D411yescharacteristic
23C22×C3×Dic3—21no—
24C22×C3×Dic3—21no—
25C2×C32×C8—41no—
26C32×C4⋊C4—41no—
27C3×C4⋊Dic3—41no—
28C3×#208—22no—
29C3×#208—41no—
30C2×C3×C3⋊C8—41no—
31#1353—31noSylow
32C2×C3×M16—61no—
33C2×C3×C4⋊C4—21no—
34C2×C3×C4⋊C4—31no—
35C2×C3×C4⋊C4C2×D311yescharacteristic
36C2×C3×C4⋊C4C22×C311yescharacteristic
37C2×C4⋊Dic3C3×C411yescharacteristic
38C2×#208—21no—
39C3×C22⋊C8—22no—
40C3×C22⋊C8—21no—
41C3×C22⋊C8—21no—
42C3×#95—31no—
43C3×#95—61no—
44C3×#95—61no—
45C3⋊#95—21no—
46C3⋊#95—21no—
47C3⋊#95C3×C411yescharacteristic
48C23×C32C22⋊C411yescharacteristic
49C2×C32×C4—21no—
50C2×C32×C4—21no—
51C2×C32×C4—21no—
52C2×C32×C4—21no—
53C2×C32×C4—41no—
54C2×C32×C4—41no—
55C2×C32×C4SD1611yescharacteristic
56C2×C32×C4Q1611yescharacteristic
57C2×C3×Dic3—41no—
58C2×C3×Dic3—41no—
59C2×C3×Dic3—42no—
60C2×C3×Dic3—41no—
61C2×C3×Dic3—41no—
62C32×C8—81no—
63C3×C3⋊C8—42no—
64#400—31no—
65#343—31no—
66#324C3×D311yescharacteristic
67C22×C3×C4—21no—
68C22×C3×C4—21no—
69C22×C3×C4—21no—
70C22×C3×C4—61no—
71C22×C3×C4—61no—
72C22×C3×C4C4×D311yescharacteristic
73C22×C3×C4D1211yescharacteristic
74C22×C3×C4#6711yescharacteristic
75C22×C3×C4C2×C3×C411yescharacteristic
76C22×C3×C4C3×D411yescharacteristic
77C22×C3×C4C3×D411yescharacteristic
78C22×Dic3—21no—
79C22×Dic3—21no—
80C3×M16—62no—
81C3×M16—121no—
82C2×C3×C8—42no—
83C2×C3×C8—41no—
84C2×C3×C8—41no—
85C2×C3×C8—121no—
86C3×C4⋊C4—41no—
87C3×C4⋊C4—41no—
88C3×C4⋊C4—42no—
89C3×C4⋊C4—121no—
90C4⋊Dic3—41no—
91#208—22no—
92#208—41no—
93C2×C3⋊C8—41no—
94C22×C32—21no—
95C22×C32—21no—
96C22×C32#9911yescharacteristic
97C22×C32#10311yescharacteristic
98C22×C32#10411yescharacteristic
99C32×C4—21no—
100C32×C4—21no—
101C32×C4—41no—
102C32×C4—41no—
103C3×Dic3—81no—
104C3×Dic3—81no—
105C2×M16—61no—
106C2×C4⋊C4—31no—
107C2×C4⋊C4C2×C3×D311yescharacteristic
108C22⋊C8—21no—
109#95—31no—
110#95—61no—
111#95—61no—
112C23×C3—21no—
113C23×C3(C2×D3)⋊C411yescharacteristic
114C23×C3C3×C22⋊C411yescharacteristic
115C2×C3×C4—21no—
116C2×C3×C4—21no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—22no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—21no—
126C2×C3×C4—41no—
127C2×C3×C4—41no—
128C2×C3×C4—41no—
129C2×C3×C4—41no—
130C2×C3×C4—41no—
131C2×C3×C4—41no—
132C2×C3×C4—41no—
133C2×C3×C4—81no—
134C2×C3×C4—81no—
135C2×C3×C4—121no—
136C2×C3×C4—121no—
137C2×C3×C4—122no—
138C2×C3×C4—121no—
139C2×C3×C4—121no—
140C2×C3×C4#20411yescharacteristic
141C2×C3×C4Dic1211yescharacteristic
142C2×C3×C4C3×SD1611yescharacteristic
143C2×C3×C4C3×Q1611yescharacteristic
144C2×Dic3—41no—
145C2×Dic3—41no—
146C2×Dic3—42no—
147C2×Dic3—41no—
148C2×Dic3—41no—
149C3×C8—82no—
150C3×C8—81no—
151C3×C8—81no—
152C3×C8—122no—
153C3⋊C8—42no—
154C2×C32—21no—
155C2×C32—21no—
156C2×C32#32811yescharacteristic
157C2×C32#35211yescharacteristic
158C2×C32#35511yescharacteristic
159C22×C4—61no—
160C22×C4—61no—
161C22×C4C3×C4×D311yescharacteristic
162C22×C4C3×D1211yescharacteristic
163C22×C4C3×#6711yescharacteristic
164M16—62no—
165M16—121no—
166C2×C8—41no—
167C2×C8—121no—
168C4⋊C4—41no—
169C4⋊C4—121no—
170C22×C3—21no—
171C22×C3—21no—
172C22×C3—21no—
173C22×C3—21no—
174C22×C3—21no—
175C22×C3—21no—
176C22×C3—21no—
177C22×C3—41no—
178C22×C3—41no—
179C22×C3#80611yescharacteristic
180C22×C3#81611yescharacteristic
181C22×C3#82511yescharacteristic
182C22×C3C3×#9911yescharacteristic
183C22×C3C3×#10311yescharacteristic
184C22×C3C3×#10411yescharacteristic
185C3×C4—21no—
186C3×C4—21no—
187C3×C4—21no—
188C3×C4—21no—
189C3×C4—41no—
190C3×C4—41no—
191C3×C4—42no—
192C3×C4—41no—
193C3×C4—41no—
194C3×C4—41no—
195C3×C4—41no—
196C3×C4—81no—
197C3×C4—241no—
198C3×C4—241no—
199Dic3—81no—
200Dic3—81no—
201C32#135311yescharacteristic, complemented, Sylow
202C23C3×(C2×D3)⋊C411yescharacteristic
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—121no—
210C2×C4—121no—
211C2×C4—122no—
212C2×C4—121no—
213C2×C4—121no—
214C2×C4C3×#20411yescharacteristic
215C2×C4C3×Dic1211yescharacteristic
216C8—81no—
217C8—122no—
218C2×C3—21no—
219C2×C3—21no—
220C2×C3—21no—
221C2×C3—21no—
222C2×C3—21no—
223C2×C3—21no—
224C2×C3—21no—
225C2×C3—41no—
226C2×C3—41no—
227C2×C3#446711yescharacteristic
228C2×C3#447211yescharacteristic
229C2×C3#447711yescharacteristic
230C2×C3C3×#32811yescharacteristic
231C2×C3C3×#35211yescharacteristic
232C2×C3C3×#35511yescharacteristic
233C22—21no—
234C22—21no—
235C22C3×#80611yescharacteristic
236C22C3×#81611yescharacteristic
237C22C3×#82511yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—41no—
242C4—241no—
243C4—241no—
244C3—21no—
245C3#6745911yescharacteristic, direct product factor
246C3C3×#135311yescharacteristic, complemented
247C2—21no—
248C2—21no—
249C2C3×#446711yescharacteristic
250C2C3×#447211yescharacteristic
251C2C3×#447711yescharacteristic
subgroupG/H
centerC22×C3#806
commutatorC22×C3×C4C2×C3×C4
FrattiniC2×C4⋊C4C2×C3×D3
FittingC32×#324C2
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×C3×C4⋊C4C22×C3
hypercenterC3×#324D3
hypocenterC3C3×#1353
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C2×C3×C4⋊C4 ◁ C3×#324

Complements

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

NH ≅ G/Ntype
5. #67459C3direct (N × H)
201. C32#1353semidirect
245. C3#67459direct (N × H)
246. C3C3×#1353semidirect

Maximal subgroups

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

subgroupindex
C3×#49862
C32×#3242
C3×#45302
C3×#13533
#674593