Finite Group Databasebeta

← C3×#67536 #11771736

Subgroups — C3×#67536 #11771736

Order 1152.

237 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 237 conjugacy classes of subgroups — too many to draw. Only its 62 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×#5137C211yesmaximal, characteristic
2C32×#349C211yesmaximal, characteristic
3C3×#4557C211yesmaximal, characteristic
4C3×#1340—31nomaximal
5#67536C311yesmaximal, characteristic, direct product factor
6C2×C32×M16C2211yescharacteristic
7C3×#926—21no—
8C3×#924—21no—
9C2×C3×Dic12C411yescharacteristic, complemented
10C32×M32—21no—
11C3×#817C411yescharacteristic, complemented
12C3×#816—21no—
13C3×#470—31no—
14#5137C2×C311yescharacteristic
15C3×#349—21no—
16C3×#349D311yescharacteristic
17C3×#349C2×C311yescharacteristic
18C3×H(3,ℤ/4)—31no—
19#4557C2×C311yescharacteristic
20C22×C32×C4D411yescharacteristic
21C2×C3×Dic6—21no—
22C32×M16—41no—
23C2×C32×C8C2×C411yescharacteristic
24C2×C32×C8D411yescharacteristic
25C3×#217—41no—
26C3×#217—41no—
27C3×C4⋊Dic3—21no—
28C3×C4⋊Dic3—41no—
29C3×Dic3⋊C4—41no—
30C3×C4×Dic3—22no—
31C3×Dic12—41no—
32C32×C16—41no—
33#1340—31noSylow
34C2×C3×Q16—31no—
35C2×C3×M16—21no—
36C2×C3×M16C2×D311yescharacteristic
37C2×C3×M16C22×C311yescharacteristic
38C3×C22⋊Q8—61no—
39C3×#117—61no—
40#926—21no—
41#924—21no—
42C2×Dic12C3×C411yescharacteristic, complemented
43C3×M32—22no—
44C3×M32—21no—
45C3×M32—21no—
46C3×#106—31no—
47C3×#103—61no—
48#817C3×C411yescharacteristic, complemented
49#816—21no—
50C23×C32D811yescharacteristic
51C2×C32×C4—21no—
52C2×C32×C4—21no—
53C2×C32×C4C22⋊C411yescharacteristic
54C2×C32×C4SD1611yescharacteristic
55C2×C3×Dic3—42no—
56C2×C3×Dic3—41no—
57C2×C3×Dic3—41no—
58C3×Dic6—41no—
59C3×Dic6—41no—
60C32×C8—21no—
61C32×C8—21no—
62#470—31no—
63#349C3×D311yescharacteristic
64H(3,ℤ/4)—31no—
65C2×C3×Q8—61no—
66C22×C3×C4—21no—
67C22×C3×C4D1211yescharacteristic
68C22×C3×C4C3×D411yescharacteristic
69C2×Dic6—21no—
70C3×Q16—121no—
71C3×M16—41no—
72C3×M16—41no—
73C3×M16—42no—
74C2×C3×C8—21no—
75C2×C3×C8—21no—
76C2×C3×C8C4×D311yescharacteristic
77C2×C3×C8#6711yescharacteristic
78C2×C3×C8C2×C3×C411yescharacteristic
79C2×C3×C8C3×D411yescharacteristic
80C3×C4⋊C4—61no—
81C3×C4⋊C4—121no—
82C3×C4⋊C4—121no—
83C3×C22⋊C4—121no—
84C3×C22⋊C4—121no—
85C3×C42—62no—
86#217—41no—
87#217—41no—
88C4⋊Dic3—21no—
89C4⋊Dic3—41no—
90Dic3⋊C4—41no—
91C4×Dic3—22no—
92Dic12—41no—
93C3×C16—42no—
94C3×C16—41no—
95C3×C16—41no—
96C22×C32—21no—
97C22×C32—41no—
98C22×C32#10211yescharacteristic
99C32×C4—21no—
100C32×C4#9911yescharacteristic
101C32×C4#10411yescharacteristic
102C3×Dic3—81no—
103C3×Dic3—82no—
104C3×Dic3—81no—
105C2×Q16—31no—
106C2×M16C2×C3×D311yescharacteristic
107C22⋊Q8—61no—
108#117—61no—
109M32—21no—
110#106—31no—
111#103—61no—
112C23×C3—21no—
113C23×C3D2411yescharacteristic
114C23×C3C3×D811yescharacteristic
115C3×Q8—121no—
116C3×Q8—121no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—21no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—21no—
123C2×C3×C4—41no—
124C2×C3×C4—41no—
125C2×C3×C4—122no—
126C2×C3×C4—121no—
127C2×C3×C4—121no—
128C2×C3×C4#20411yescharacteristic
129C2×C3×C4(C2×D3)⋊C411yescharacteristic
130C2×C3×C4C3×C22⋊C411yescharacteristic
131C2×C3×C4C3×SD1611yescharacteristic
132C2×Dic3—42no—
133C2×Dic3—41no—
134C2×Dic3—41no—
135Dic6—41no—
136Dic6—41no—
137C3×C8—22no—
138C3×C8—21no—
139C3×C8—21no—
140C3×C8—21no—
141C3×C8—21no—
142C3×C8—41no—
143C2×C32—21no—
144C2×C32—41no—
145C2×C32#32711yescharacteristic
146C2×Q8—61no—
147C22×C4C3×D1211yescharacteristic
148Q16—121no—
149M16—41no—
150C2×C8C3×C4×D311yescharacteristic
151C2×C8C3×#6711yescharacteristic
152C4⋊C4—61no—
153C4⋊C4—121no—
154C4⋊C4—121no—
155C22⋊C4—121no—
156C22⋊C4—121no—
157C42—62no—
158C16—41no—
159C22×C3—21no—
160C22×C3—21no—
161C22×C3—21no—
162C22×C3—41no—
163C22×C3—41no—
164C22×C3—41no—
165C22×C3—81no—
166C22×C3#82111yescharacteristic
167C22×C3C3×#10211yescharacteristic
168C3×C4—21no—
169C3×C4—21no—
170C3×C4—21no—
171C3×C4—21no—
172C3×C4—41no—
173C3×C4—241no—
174C3×C4—242no—
175C3×C4—241no—
176C3×C4#80611yescharacteristic
177C3×C4#82511yescharacteristic
178C3×C4C3×#9911yescharacteristic
179C3×C4C3×#10411yescharacteristic
180Dic3—81no—
181Dic3—82no—
182Dic3—81no—
183C32#134011yescharacteristic, complemented, Sylow
184C23C3×D2411yescharacteristic
185Q8—121no—
186Q8—121no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—122no—
190C2×C4—121no—
191C2×C4—121no—
192C2×C4C3×#20411yescharacteristic
193C2×C4C3×(C2×D3)⋊C411yescharacteristic
194C8—21no—
195C8—21no—
196C2×C3—21no—
197C2×C3—21no—
198C2×C3—21no—
199C2×C3—41no—
200C2×C3—41no—
201C2×C3—41no—
202C2×C3—81no—
203C2×C3#447011yescharacteristic
204C2×C3C3×#32711yescharacteristic
205C22—21no—
206C22—41no—
207C22C3×#82111yescharacteristic
208C4—21no—
209C4—241no—
210C4—242no—
211C4—241no—
212C4C3×#80611yescharacteristic
213C4C3×#82511yescharacteristic
214C3—21no—
215C3#6753611yescharacteristic, direct product factor
216C3C3×#134011yescharacteristic, complemented
217C2—21no—
218C2—41no—
219C2C3×#447011yescharacteristic
subgroupG/H
centerC2×C3#4470
commutatorC2×C3×C8C2×C3×C4
FrattiniC2×M16C2×C3×D3
FittingC32×#349C2
socleC2×C32#327
prime radicalC23×C32D8
cosocleC2×C3×M16C22×C3
hypercenterC3×#349D3
hypocenterC3C3×#1340
LCSG ▷ C2×C3×C8 ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×M16 ◁ C3×#349

Complements

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

NH ≅ G/Ntype
5. #67536C3direct (N × H)
9. C2×C3×Dic12C4semidirect
11. C3×#817C4semidirect
42. C2×Dic12C3×C4semidirect
48. #817C3×C4semidirect
183. C32#1340semidirect
215. C3#67536direct (N × H)
216. C3C3×#1340semidirect

Maximal subgroups

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

subgroupindex
C3×#51372
C32×#3492
C3×#45572
C3×#13403
#675363