Finite Group Databasebeta

← #13069841

Subgroups — #13069841

Order 1408.

306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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#10623041C211yesmaximal, characteristic
2C2×#66889C212yesmaximal, complemented
3#10622746C212yesmaximal, complemented
4#10622589C211yesmaximal, characteristic, complemented
5C11×#343C211yesmaximal, characteristic, complemented
6C2×#4339C2212yes—
7C2×C11×M16C2212yes—
8C2×C11×C4⋊C4C2211yescharacteristic
9#66983—22no—
10C2×C4⋊Dic11C2211yescharacteristic
11C2×Dic11⋊C4—22no—
12C2×C4×Dic11C2211yescharacteristic
13#66950—22no—
14#66948—22no—
15#66889—24no—
16#66885—22no—
17#66880—22no—
18C22×C4×C11D412yes—
19C22×C4×C11C2311yescharacteristic
20C2×C22⋊D11—22no—
21C22×Dic11—21no—
22C22×Dic11—21no—
23#4339—22no—
24#4339—22no—
25#4339—22no—
26#4339—22no—
27C2×D44—22no—
28C2×D44D412yes—
29C2×C4×D11—22no—
30C2×Dic22D412yes—
31C11×M16—22no—
32C11×M16—22no—
33C2×C8×C11—22no—
34C11×C4⋊C4—22no—
35(C2×D11)⋊C4—24no—
36C4⋊Dic11—22no—
37C4⋊Dic11—22no—
38Dic11⋊C4—44no—
39C4×Dic11—21no—
40C4×Dic11D412yescomplemented
41#2039—111nomaximal, Sylow
42C23×C11C2×D411yescharacteristic
43C22×D11—22no—
44C2×C4×C11—22no—
45C2×C4×C11—42no—
46C2×C4×C11C2×D411yescharacteristic
47C2×C4×C11C2×D412yes—
48C2×C4×C11#4112yes—
49C2×C4×C11#4111yescharacteristic
50C22⋊D11—42no—
51C22⋊D11—42no—
52C2×Dic11—22no—
53C2×Dic11—22no—
54C2×Dic11—22no—
55C2×Dic11—22no—
56C2×Dic11—42no—
57C2×Dic11—41no—
58D44—22no—
59D44—22no—
60D44—82no—
61C4×D11—42no—
62C4×D11—42no—
63Dic22—22no—
64Dic22—22no—
65C8×C11—42no—
66#537—111no—
67C2×#104—112no—
68#417—112no—
69#384—111no—
70#343D1111yescharacteristic, complemented
71C22×C11—21no—
72C22×C11—21no—
73C22×C11#12011yescharacteristic
74C22×C11#12111yescharacteristic
75C22×C11#12411yescharacteristic
76C2×D11—42no—
77C2×D11—42no—
78C2×D11—42no—
79C4×C11—42no—
80C4×C11#12112yes—
81C4×C11#12312yes—
82Dic11—24no—
83Dic11—42no—
84Dic11—81no—
85C2×#41—112no—
86C2×M16C2×D1112yes—
87C22⋊Q8—222no—
88#121—222no—
89#121—222no—
90C2×C4⋊C4—111no—
91C2×C4⋊C4—222no—
92C2×C4⋊C4C2×D1111yescharacteristic
93C2×C42—111no—
94#104—224no—
95#103—222no—
96#102—222no—
97C2×C11—21no—
98C2×C11—21no—
99C2×C11#39411yescharacteristic
100C2×C11#45311yescharacteristic
101C2×C11#45611yescharacteristic
102D11—82no—
103#41—222no—
104#41—222no—
105#41—222no—
106#41—222no—
107C2×Q8—112no—
108C2×D4—112no—
109C2×D4—222no—
110C2×D4—222no—
111C22×C4—221no—
112C22×C4—222no—
113C22×C4—221no—
114C22×C4D4412yes—
115C22×C4C22×D1111yescharacteristic
116M16—22no—
117M16—22no—
118C2×C8—22no—
119C4⋊C4—22no—
120C4⋊C4—222no—
121C4⋊C4—222no—
122C4⋊C4—444no—
123C22⋊C4—224no—
124C42—112no—
125C42—221no—
126C11#203911yescharacteristic, complemented, Sylow
127C23—222no—
128C23C2×D4411yescharacteristic
129Q8—222no—
130Q8—222no—
131D4—222no—
132D4—222no—
133D4—442no—
134D4—442no—
135D4—882no—
136C2×C4—22no—
137C2×C4—42no—
138C2×C4—222no—
139C2×C4—222no—
140C2×C4—222no—
141C2×C4—222no—
142C2×C4—442no—
143C2×C4—442no—
144C2×C4—442no—
145C2×C4—441no—
146C2×C4#433912yes—
147C2×C4D4×D1111yescharacteristic
148C2×C4D4×D1112yes—
149C2×C4#434311yescharacteristic
150C8—42no—
151C22—21no—
152C22—21no—
153C22—442no—
154C22—442no—
155C22—442no—
156C22#6692811yescharacteristic
157C22#6693511yescharacteristic
158C22#6694811yescharacteristic
159C4—42no—
160C4—224no—
161C4—442no—
162C4—881no—
163C4#6693712yes—
164C4#6694712yes—
165C2—21no—
166C2—21no—
167C2—882no—
168C2#1062228511yescharacteristic
169C2#1062236011yescharacteristic
170C2#1062236511yescharacteristic
subgroupG/H
centerC22#66935
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#343C2
socleC22×C11#120
prime radical#10623041C2
hypercenter#343D11
hypocenterC11#2039
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
2. C2×#66889C2semidirect
3. #10622746C2semidirect
4. #10622589C2semidirect
5. C11×#343C2semidirect
40. C4×Dic11D4semidirect
70. #343D11semidirect
126. C11#2039semidirect

Maximal subgroups

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

subgroupindex
#106230412
C2×#668892
#106227462
#106225892
C11×#3432
#203911