Finite Group Databasebeta

← #13067337

Subgroups — #13067337

Order 1408.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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
1#10623256C211yesmaximal, characteristic
2#10622450C211yesmaximal, characteristic, complemented
3#10622448C211yesmaximal, characteristic, complemented
4C11×#332C211yesmaximal, characteristic, complemented
5#10622185C211yesmaximal, characteristic, complemented
6#10622123C211yesmaximal, characteristic, complemented
7#10622123C211yesmaximal, characteristic, complemented
8C2×#4343—21no—
9C11×C4⋊Q8C2211yescharacteristic
10#67000—21no—
11C2×#4313—21no—
12#66948—21no—
13#66948C412yes—
14#66946—21no—
15#66946C412yes—
16#66927C2211yescharacteristic
17C42×D11C2211yescharacteristic
18C11×C4⋊C8C2211yescharacteristic
19C11×C4⋊C8C2211yescharacteristic
20(C2×D11)⋊C8—21no—
21#66879—21no—
22Dic11⋊C8—21no—
23C4⋊(C11⋊C8)C2211yescharacteristic
24C4⋊(C11⋊C8)C2211yescharacteristic
25C2×Q8×C11—21no—
26#4343—42no—
27#4343—42no—
28C2×D44—22no—
29C2×D44—21no—
30C2×D44—21no—
31C2×D44C2×C412yes—
32C2×C4×D11—22no—
33C2×C4×D11C2×C411yescharacteristic
34C2×C4×D11D411yescharacteristic
35C2×C4×D11D411yescharacteristic
36C2×C8×C11—21no—
37C2×C8×C11—21no—
38C11×C4⋊C4—21no—
39C11×C4⋊C4C2×C412yes—
40C42×C11C2311yescharacteristic
41(C2×D11)⋊C4—22no—
42(C2×D11)⋊C4—22no—
43C4×Dic11C2×C411yescharacteristic
44C4×Dic11D411yescharacteristic
45C4×Dic11D411yescharacteristic
46C2×C11⋊C8—21no—
47C2×C11⋊C8—21no—
48#4313—42no—
49#1557—111nomaximal, Sylow
50C22×D11—22no—
51C22×D11C22⋊C411yescharacteristic
52Q8×C11—41no—
53Q8×C11—41no—
54C2×C4×C11—22no—
55C2×C4×C11C22×C411yescharacteristic
56C2×C4×C11C2×D411yescharacteristic
57C2×C4×C11C2×D411yescharacteristic
58C2×Dic11C22⋊C411yescharacteristic
59C2×Dic11C22⋊C411yescharacteristic
60C2×Dic11C22⋊C411yescharacteristic
61D44—42no—
62D44—44no—
63D44—41no—
64D44—41no—
65D44—41no—
66D44—41no—
67C4×D11—21no—
68C4×D11—21no—
69C4×D11—21no—
70C4×D11—21no—
71C4×D11—41no—
72C4×D11—44no—
73C8×C11—41no—
74C8×C11—41no—
75C11⋊C8—41no—
76C11⋊C8—41no—
77#532—111no—
78#432—111no—
79#423—111no—
80#332—111no—
81#332D1111yescharacteristic, complemented
82#331—111no—
83#331—111no—
84C22×C11C2×C22⋊C411yescharacteristic
85C2×D11—21no—
86C2×D11—21no—
87C2×D11—21no—
88C2×D11—42no—
89C2×D11—42no—
90C2×D11—42no—
91C4×C11—21no—
92C4×C11—42no—
93C4×C11AGL(1,ℤ/8)11yescharacteristic
94C4×C11AGL(1,ℤ/8)11yescharacteristic
95C4×C11AGL(1,ℤ/8)11yescharacteristic
96C4×C11#13711yescharacteristic
97Dic11—21no—
98Dic11—21no—
99Dic11—21no—
100C2×#41—221no—
101C2×M16—221no—
102C4⋊Q8C2×D1111yescharacteristic
103#127—111no—
104#124—221no—
105#121—112no—
106#121—221no—
107C4×D4—112no—
108C4×D4—221no—
109C2×C42—111no—
110C4⋊C8—111no—
111C4⋊C8—111no—
112C4⋊C8—221no—
113C4⋊C8C2×D1111yescharacteristic
114C4⋊C8C2×D1111yescharacteristic
115C22⋊C8—221no—
116#97—221no—
117C2×C11#41311yescharacteristic
118C2×C11#41711yescharacteristic
119C2×C11#41811yescharacteristic
120D11—41no—
121D11—82no—
122#41—442no—
123#41—442no—
124C2×Q8—21no—
125C2×D4—112no—
126C2×D4—222no—
127C2×D4—221no—
128C2×D4—221no—
129C22×C4—111no—
130C22×C4—111no—
131C22×C4—111no—
132C22×C4—222no—
133M16—442no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—221no—
137C2×C8—221no—
138C4⋊C4—21no—
139C4⋊C4C4×D1112yes—
140C22⋊C4—222no—
141C22⋊C4—222no—
142C42—111no—
143C42—111no—
144C42—111no—
145C42C22×D1111yescharacteristic
146C11#155711yescharacteristic, complemented, Sylow
147C23—111no—
148C23—222no—
149Q8—41no—
150Q8—41no—
151D4—442no—
152D4—444no—
153D4—441no—
154D4—441no—
155D4—441no—
156D4—441no—
157C2×C4—22no—
158C2×C4—111no—
159C2×C4—111no—
160C2×C4—111no—
161C2×C4—221no—
162C2×C4—221no—
163C2×C4—221no—
164C2×C4—221no—
165C2×C4—441no—
166C2×C4—444no—
167C2×C4C2×C4×D1111yescharacteristic
168C2×C4D4×D1111yescharacteristic
169C2×C4D4×D1111yescharacteristic
170C8—41no—
171C8—41no—
172C8—441no—
173C8—441no—
174C22—221no—
175C22—221no—
176C22—221no—
177C22—442no—
178C22—442no—
179C22—442no—
180C22C22⋊C4×D1111yescharacteristic
181C4—21no—
182C4—42no—
183C4—221no—
184C4—221no—
185C4—221no—
186C4#6696411yescharacteristic
187C4#6696711yescharacteristic
188C4#6696711yescharacteristic
189C4#6697111yescharacteristic
190C2—441no—
191C2—882no—
192C2#1062236411yescharacteristic
193C2#1062238311yescharacteristic
194C2#1062241611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D11
commutatorC2×C4×C11C22×C4
FrattiniC42C22×D11
FittingC11×#332C2
socleC22×C11C2×C22⋊C4
prime radical#10623256C2
cosocleC42×C11C23
hypercenter#332D11
hypocenterC11#1557
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #10622450C2semidirect
3. #10622448C2semidirect
4. C11×#332C2semidirect
5. #10622185C2semidirect
6. #10622123C2semidirect
7. #10622123C2semidirect
81. #332D11semidirect
146. C11#1557semidirect

Maximal subgroups

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

subgroupindex
#106232562
#106224502
#106224482
C11×#3322
#106221852
#106221232
#155711