Finite Group Databasebeta

← C3×#71648 #11785922

Subgroups — C3×#71648 #11785922

Order 1152.

713 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 713 conjugacy classes of subgroups — too many to draw. Only its 178 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×#518C211yesmaximal, characteristic
2C2×C3×#833C212yesmaximal
3C3×#4533C214yesmaximal, complemented
4C3×#1829—31nomaximal
5#71648C311yesmaximal, characteristic, direct product factor
6C22×C32×D4C2211yescharacteristic
7C32×C4×D4—24no—
8C32×#117C2212yes—
9C2×C32×C22⋊C4C414yes—
10C2×C3×#208C2214yes—
11C3×#833—24no—
12C3×#518—21no—
13C3×#518D311yescharacteristic
14C3×#518C2×C311yescharacteristic
15C2×C3×#100—32no—
16C2×#833C2×C312yes—
17C3×#344—34no—
18#4533C2×C314yescomplemented
19C24×C32C2×C412yes—
20C2×C32×D4—24no—
21C2×C32×D4D414yes—
22C22×C32×C4—24no—
23C22×C32×C4C2311yescharacteristic
24C32×C4⋊C4—22no—
25C32×C22⋊C4—24no—
26C32×C22⋊C4C2×C414yes—
27C32×C42—22no—
28C3×#208—24no—
29C3×#208—24no—
30C2×C3×C3⋊C8—24no—
31#1829—31noSylow
32C22×C3×D4—21no—
33C22×C3×D4C2×D311yescharacteristic
34C22×C3×D4C22×C311yescharacteristic
35C2×C3×M16—34no—
36C3×C4×D4—28no—
37C3×C4×D4—24no—
38C3×C4×D4—24no—
39C3×#117—22no—
40C3×#117C2×D312yes—
41C3×#117C22×C312yes—
42C2×C3×C22⋊C4—24no—
43C2×C3×C22⋊C4Dic314yes—
44C2×C3×C22⋊C4C3×C414yes—
45C2×#208C22×C314yes—
46C3×#100—64no—
47#833—24no—
48C23×C32—24no—
49C23×C32—82no—
50C23×C32C22⋊C414yes—
51C23×C32C22×C411yescharacteristic
52C32×D4—28no—
53C2×C32×C4—24no—
54C2×C32×C4—84no—
55C2×C32×C4C2×D412yes—
56C2×C32×C4#4114yes—
57C3×C3⋊C8—44no—
58#518C3×D311yescharacteristic
59C2×#100—32no—
60#344—34no—
61C24×C3—22no—
62C24×C3C2×Dic312yes—
63C24×C3C2×C3×C412yes—
64C2×C3×D4—28no—
65C2×C3×D4—24no—
66C2×C3×D4—24no—
67C2×C3×D4—24no—
68C2×C3×D4#6714yes—
69C2×C3×D4C3×D414yes—
70C22×C3×C4—28no—
71C22×C3×C4—24no—
72C22×C3×C4—24no—
73C22×C3×C4—21no—
74C22×C3×C4C22×D311yescharacteristic
75C22×C3×C4C23×C311yescharacteristic
76C3×M16—64no—
77C3×M16—64no—
78C2×C3×C8—64no—
79C3×C4⋊C4—24no—
80C3×C4⋊C4—22no—
81C3×C4⋊C4—22no—
82C3×C22⋊C4—28no—
83C3×C22⋊C4—24no—
84C3×C22⋊C4—24no—
85C3×C22⋊C4—24no—
86C3×C22⋊C4C2×Dic314yes—
87C3×C22⋊C4C2×C3×C414yes—
88C3×C42—24no—
89C3×C42—22no—
90C3×C42—22no—
91#208—24no—
92#208—24no—
93C2×C3⋊C8—24no—
94C22×C32—24no—
95C22×C32—41no—
96C22×C32—44no—
97C22×C32—84no—
98C22×C32C2×C22⋊C411yescharacteristic
99C22×C32#11712yes—
100C32×C4—44no—
101C32×C4#12314yes—
102C22×D4C2×C3×D311yescharacteristic
103C2×M16—34no—
104C4×D4—24no—
105#117C2×C3×D312yes—
106C2×C22⋊C4C3×Dic314yes—
107#100—64no—
108C23×C3—28no—
109C23×C3—24no—
110C23×C3—24no—
111C23×C3—24no—
112C23×C3—21no—
113C23×C3—82no—
114C23×C3—82no—
115C23×C3—84no—
116C23×C3#21714yes—
117C23×C3C3×C22⋊C414yes—
118C23×C3C22×Dic311yescharacteristic
119C23×C3C22×C3×C411yescharacteristic
120C3×D4—216no—
121C3×D4—28no—
122C3×D4—28no—
123C2×C3×C4—28no—
124C2×C3×C4—24no—
125C2×C3×C4—24no—
126C2×C3×C4—24no—
127C2×C3×C4—22no—
128C2×C3×C4—84no—
129C2×C3×C4—84no—
130C2×C3×C4—88no—
131C2×C3×C4#23514yes—
132C2×C3×C4C2×#6712yes—
133C2×C3×C4C2×C3×D412yes—
134C2×C3×C4C3×#4114yes—
135C3×C8—124no—
136C3⋊C8—44no—
137C2×C32—21no—
138C2×C32—22no—
139C2×C32—44no—
140C2×C32#38111yescharacteristic
141C24C2×C3×Dic312yes—
142C2×D4—24no—
143C2×D4C3×#6714yes—
144C22×C4—24no—
145C22×C4C22×C3×D311yescharacteristic
146M16—64no—
147M16—64no—
148C2×C8—64no—
149C4⋊C4—22no—
150C22⋊C4—24no—
151C22⋊C4C2×C3×Dic314yes—
152C42—22no—
153C22×C3—28no—
154C22×C3—24no—
155C22×C3—24no—
156C22×C3—22no—
157C22×C3—21no—
158C22×C3—41no—
159C22×C3—41no—
160C22×C3—44no—
161C22×C3—44no—
162C22×C3—48no—
163C22×C3—42no—
164C22×C3—84no—
165C22×C3—84no—
166C22×C3—88no—
167C22×C3#92612yes—
168C22×C3C2×#21711yescharacteristic
169C22×C3C2×C3×C22⋊C411yescharacteristic
170C22×C3C3×#11712yes—
171C3×C4—24no—
172C3×C4—48no—
173C3×C4—44no—
174C3×C4—44no—
175C3×C4#92914yes—
176C3×C4C3×#12314yes—
177C32#182911yescharacteristic, complemented, Sylow
178C23—24no—
179C23—82no—
180C23C3×#21714yes—
181C23C22×C3×Dic311yescharacteristic
182D4—28no—
183C2×C4—24no—
184C2×C4—84no—
185C2×C4C3×#23514yes—
186C2×C4C2×C3×#6712yes—
187C8—124no—
188C2×C3—22no—
189C2×C3—21no—
190C2×C3—22no—
191C2×C3—21no—
192C2×C3—22no—
193C2×C3—21no—
194C2×C3—42no—
195C2×C3—48no—
196C2×C3—44no—
197C2×C3—44no—
198C2×C3#521111yescharacteristic
199C2×C3C3×#38111yescharacteristic
200C22—24no—
201C22—41no—
202C22—44no—
203C22—84no—
204C22C3×#92612yes—
205C22C2×C3×#21711yescharacteristic
206C4—44no—
207C4C3×#92914yes—
208C3—21no—
209C3#7164811yescharacteristic, direct product factor
210C3C3×#182911yescharacteristic, complemented
211C2—21no—
212C2—22no—
213C2—44no—
214C2C3×#521111yescharacteristic
subgroupG/H
centerC2×C3#5211
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#518C2
socleC2×C32#381
prime radicalC22×C32×D4C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#518D3
hypocenterC3C3×#1829
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#518

Complements

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

NH ≅ G/Ntype
3. C3×#4533C2semidirect
5. #71648C3direct (N × H)
18. #4533C2×C3semidirect
177. C32#1829semidirect
209. C3#71648direct (N × H)
210. C3C3×#1829semidirect

Maximal subgroups

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

subgroupindex
C32×#5182
C2×C3×#8332
C3×#45332
C3×#18293
#716483