Finite Group Databasebeta

← C3×#71829 #11776240

Subgroups — C3×#71829 #11776240

Order 1152.

515 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 515 conjugacy classes of subgroups — too many to draw. Only its 170 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×#533C211yesmaximal, characteristic
2C3×#4925C212yesmaximal
3C3×#4547C214yesmaximal, complemented
4C3×#1544—31nomaximal
5#71829C311yesmaximal, characteristic, direct product factor
6C32×C4⋊Q8C2212yes—
7C32×#125C412yes—
8C32×C22⋊Q8—22no—
9C32×C4×Q8—22no—
10C32×#117C412yes—
11C2×C32×C42C2211yescharacteristic
12C3×#830—22no—
13C3×C4⋊(C3⋊C8)C2214yes—
14C3×C4×C3⋊C8—22no—
15C3×#533—21no—
16C3×#533D311yescharacteristic
17C3×#533C2×C311yescharacteristic
18C3×#431—32no—
19#4925C2×C312yes—
20C3×#332—34no—
21#4547C2×C314yescomplemented
22C2×C32×Q8—22no—
23C22×C32×C4C2×C411yescharacteristic
24C22×C32×C4D412yes—
25C32×C4⋊C4—24no—
26C32×C4⋊C4—22no—
27C32×C4⋊C4C2×C414yes—
28C32×C22⋊C4—22no—
29C32×C42—22no—
30C32×C42C2×C411yescharacteristic
31C32×C42D412yes—
32C32×C42C2311yescharacteristic
33C2×C3×C3⋊C8—24no—
34#1544—31noSylow
35C3×C4⋊Q8—22no—
36C3×C4⋊Q8C2×D312yes—
37C3×C4⋊Q8C22×C312yes—
38C3×#125—22no—
39C3×#125Dic312yes—
40C3×#125C3×C412yes—
41C3×C22⋊Q8—24no—
42C3×C22⋊Q8—22no—
43C3×C22⋊Q8—22no—
44C3×C4×Q8—24no—
45C3×C4×Q8—22no—
46C3×C4×Q8—22no—
47C3×#117—22no—
48C3×#117Dic312yes—
49C3×#117C3×C412yes—
50C2×C3×C42—21no—
51C2×C3×C42C2×D311yescharacteristic
52C2×C3×C42C22×C311yescharacteristic
53C3×C4⋊C8—34no—
54C3×C22⋊C8—62no—
55C3×C4×C8—62no—
56#830—22no—
57C4⋊(C3⋊C8)C22×C314yes—
58C4×C3⋊C8—22no—
59C23×C32C22⋊C411yescharacteristic
60C32×Q8—44no—
61C2×C32×C4—22no—
62C2×C32×C4—24no—
63C2×C32×C4—24no—
64C2×C32×C4C22⋊C412yes—
65C2×C32×C4C22⋊C411yescharacteristic
66C2×C32×C4C22×C411yescharacteristic
67C2×C32×C4C2×D412yes—
68C3×C3⋊C8—44no—
69#533C3×D311yescharacteristic
70#431—32no—
71#332—34no—
72C2×C3×Q8—24no—
73C2×C3×Q8—22no—
74C2×C3×Q8—22no—
75C22×C3×C4—21no—
76C22×C3×C4—22no—
77C22×C3×C4C2×Dic311yescharacteristic
78C22×C3×C4#6712yes—
79C22×C3×C4C2×C3×C411yescharacteristic
80C22×C3×C4C3×D412yes—
81C2×C3×C8—64no—
82C3×C4⋊C4—28no—
83C3×C4⋊C4—24no—
84C3×C4⋊C4—24no—
85C3×C4⋊C4—24no—
86C3×C4⋊C4—22no—
87C3×C4⋊C4—22no—
88C3×C4⋊C4—24no—
89C3×C4⋊C4C2×Dic314yes—
90C3×C4⋊C4C2×C3×C414yes—
91C3×C22⋊C4—24no—
92C3×C22⋊C4—22no—
93C3×C22⋊C4—22no—
94C3×C42—24no—
95C3×C42—22no—
96C3×C42—22no—
97C3×C42—21no—
98C3×C42—22no—
99C3×C42—21no—
100C3×C42C2×Dic311yescharacteristic
101C3×C42#6712yes—
102C3×C42C2×C3×C411yescharacteristic
103C3×C42C3×D412yes—
104C3×C42C22×D311yescharacteristic
105C3×C42C23×C311yescharacteristic
106C2×C3⋊C8—24no—
107C22×C32—21no—
108C22×C32—22no—
109C22×C32C2×C22⋊C411yescharacteristic
110C32×C4—21no—
111C32×C4—22no—
112C32×C4—44no—
113C32×C4#10112yes—
114C32×C4#13514yes—
115C4⋊Q8C2×C3×D312yes—
116#125C3×Dic312yes—
117C22⋊Q8—22no—
118C4×Q8—22no—
119#117C3×Dic312yes—
120C2×C42C2×C3×D311yescharacteristic
121C4⋊C8—34no—
122C22⋊C8—62no—
123C4×C8—62no—
124C23×C3—21no—
125C23×C3#21711yescharacteristic
126C23×C3C3×C22⋊C411yescharacteristic
127C3×Q8—48no—
128C3×Q8—44no—
129C3×Q8—44no—
130C2×C3×C4—24no—
131C2×C3×C4—22no—
132C2×C3×C4—22no—
133C2×C3×C4—24no—
134C2×C3×C4—24no—
135C2×C3×C4—28no—
136C2×C3×C4—24no—
137C2×C3×C4—24no—
138C2×C3×C4—21no—
139C2×C3×C4—22no—
140C2×C3×C4—21no—
141C2×C3×C4—22no—
142C2×C3×C4—44no—
143C2×C3×C4#21712yes—
144C2×C3×C4#21711yescharacteristic
145C2×C3×C4C3×C22⋊C412yes—
146C2×C3×C4C3×C22⋊C411yescharacteristic
147C2×C3×C4C22×Dic311yescharacteristic
148C2×C3×C4C2×#6712yes—
149C2×C3×C4C22×C3×C411yescharacteristic
150C2×C3×C4C2×C3×D412yes—
151C3×C8—124no—
152C3⋊C8—44no—
153C2×C32—41no—
154C2×C32C2×#10111yescharacteristic
155C2×C32#41612yes—
156C2×Q8—22no—
157C22×C4C2×C3×Dic311yescharacteristic
158C22×C4C3×#6712yes—
159C2×C8—64no—
160C4⋊C4—24no—
161C4⋊C4—22no—
162C4⋊C4C2×C3×Dic314yes—
163C22⋊C4—22no—
164C42—22no—
165C42C2×C3×Dic311yescharacteristic
166C42C3×#6712yes—
167C42C22×C3×D311yescharacteristic
168C22×C3—22no—
169C22×C3—21no—
170C22×C3—22no—
171C22×C3—21no—
172C22×C3—22no—
173C22×C3—21no—
174C22×C3—42no—
175C22×C3C2×#21711yescharacteristic
176C22×C3C2×C3×C22⋊C411yescharacteristic
177C3×C4—22no—
178C3×C4—21no—
179C3×C4—22no—
180C3×C4—21no—
181C3×C4—22no—
182C3×C4—24no—
183C3×C4—22no—
184C3×C4—42no—
185C3×C4—48no—
186C3×C4—44no—
187C3×C4—44no—
188C3×C4#83612yes—
189C3×C4C3×#10112yes—
190C3×C4#95014yes—
191C3×C4C3×#13514yes—
192C32#154411yescharacteristic, complemented, Sylow
193C23C3×#21711yescharacteristic
194Q8—44no—
195C2×C4—24no—
196C2×C4—22no—
197C2×C4—24no—
198C2×C4C3×#21712yes—
199C2×C4C3×#21711yescharacteristic
200C2×C4C22×C3×Dic311yescharacteristic
201C2×C4C2×C3×#6712yes—
202C8—124no—
203C2×C3—21no—
204C2×C3—22no—
205C2×C3—42no—
206C2×C3—41no—
207C2×C3—41no—
208C2×C3C2×#83611yescharacteristic
209C2×C3#523312yes—
210C2×C3C2×C3×#10111yescharacteristic
211C2×C3C3×#41612yes—
212C22—21no—
213C22—22no—
214C22C2×C3×#21711yescharacteristic
215C4—21no—
216C4—22no—
217C4—44no—
218C4C3×#83612yes—
219C4C3×#95014yes—
220C3—21no—
221C3#7182911yescharacteristic, direct product factor
222C3C3×#154411yescharacteristic, complemented
223C2—41no—
224C2C2×C3×#83611yescharacteristic
225C2C3×#523312yes—
subgroupG/H
centerC2×C3×C4#217
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×#533C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC3×C42C23×C3
hypercenterC3×#533D3
hypocenterC3C3×#1544
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×#533

Complements

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

NH ≅ G/Ntype
3. C3×#4547C2semidirect
5. #71829C3direct (N × H)
21. #4547C2×C3semidirect
192. C32#1544semidirect
221. C3#71829direct (N × H)
222. C3C3×#1544semidirect

Maximal subgroups

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

subgroupindex
C32×#5332
C3×#49252
C3×#45472
C3×#15443
#718293