Finite Group Databasebeta

← #13069030

Subgroups — #13069030

Order 1408.

386 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×C11×#123C211yesmaximal, characteristic
2#10623329C211yesmaximal, characteristic
3C2×#66898C211yesmaximal, characteristic
4#10622824C212yesmaximal, complemented
5#10622165C212yesmaximal, complemented
6C22×D4×C11C2211yescharacteristic
7C23×C4×C11C2211yescharacteristic
8C11×#123—22no—
9C11×#123C414yescomplemented
10C2×C11×C4⋊C4—21no—
11C2×C11×C22⋊C4—21no—
12C2×C11×C22⋊C4C2211yescharacteristic
13C2×C22⋊Dic11—21no—
14C2×C22⋊Dic11C2212yes—
15C2×C22⋊Dic11C2212yes—
16D4×Dic11—24no—
17#66979—21no—
18#66898—22no—
19C11⋊#95—24no—
20C24×C11D411yescharacteristic
21C24×C11C2311yescharacteristic
22C2×D4×C11—22no—
23C2×D4×C11—22no—
24C2×D4×C11C2×C412yes—
25C2×D4×C11D412yes—
26C22×C4×C11—22no—
27C22×C4×C11—21no—
28C22×C4×C11—21no—
29C22×C4×C11—21no—
30C22×C4×C11—22no—
31C22×C4×C11C2×C412yescomplemented
32C22×C4×C11D411yescharacteristic
33C22×Dic11—22no—
34C22×Dic11—22no—
35C22×Dic11D414yes—
36C11×C4⋊C4—24no—
37C11×C22⋊C4—24no—
38C11×C22⋊C4—21no—
39C11×C22⋊C4C2×C412yescomplemented
40C22⋊Dic11—22no—
41C22⋊Dic11—22no—
42C22⋊Dic11—22no—
43C22⋊Dic11—22no—
44C22⋊Dic11—22no—
45C4⋊Dic11—22no—
46C4×Dic11—22no—
47#1890—111nomaximal, Sylow
48C23×C11—21no—
49C23×C11—21no—
50C23×C11—42no—
51C23×C11—42no—
52C23×C11C22⋊C412yes—
53C23×C11C22×C411yescharacteristic
54C23×C11C2×D412yes—
55C23×C11C2×D411yescharacteristic
56C23×C11C2×D411yescharacteristic
57C23×C11#4112yes—
58D4×C11—24no—
59D4×C11—24no—
60C2×C4×C11—21no—
61C2×C4×C11—21no—
62C2×C4×C11—22no—
63C2×C4×C11—22no—
64C2×C4×C11—24no—
65C2×C4×C11—42no—
66C2×C4×C11—41no—
67C2×C4×C11—42no—
68C2×C4×C11—41no—
69C2×C4×C11C22⋊C412yes—
70C2×Dic11—24no—
71C2×Dic11—44no—
72C2×Dic11—44no—
73C2×Dic11—42no—
74C2×Dic11—82no—
75C2×#123D1111yescharacteristic
76#518—111no—
77C2×#99—111no—
78#381—112no—
79#342—112no—
80C22×C11—22no—
81C22×C11—24no—
82C22×C11—22no—
83C22×C11—41no—
84C22×C11—41no—
85C22×C11—42no—
86C22×C11—42no—
87C22×C11—42no—
88C22×C11—81no—
89C22×C11C2×C22⋊C411yescharacteristic
90C22×C11C4×D412yes—
91C22×C11#12011yescharacteristic
92C22×C11#12112yes—
93C22×C11#12311yescharacteristic
94C4×C11—22no—
95C4×C11—42no—
96C4×C11—42no—
97Dic11—44no—
98Dic11—82no—
99C22×D4C2×D1111yescharacteristic
100C23×C4C2×D1111yescharacteristic
101#123—22no—
102#123Dic1114yescomplemented
103C4×D4—224no—
104#117—221no—
105C2×C4⋊C4—21no—
106C2×C22⋊C4—21no—
107C2×C22⋊C4—112no—
108C2×C22⋊C4—112no—
109C2×C22⋊C4—221no—
110C2×C22⋊C4C2×D1111yescharacteristic
111#99—222no—
112#95—224no—
113C2×C11—22no—
114C2×C11—21no—
115C2×C11—21no—
116C2×C11—22no—
117C2×C11—42no—
118C2×C11#38611yescharacteristic
119C2×C11#45812yes—
120C24C22⋊D1111yescharacteristic
121C24C22×D1111yescharacteristic
122C2×D4—22no—
123C2×D4—22no—
124C2×D4C2×Dic1112yes—
125C2×D4C22⋊D1112yes—
126C22×C4—22no—
127C22×C4—22no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—114no—
132C22×C4—222no—
133C22×C4—222no—
134C22×C4C2×Dic1112yescomplemented
135C22×C4C22⋊D1111yescharacteristic
136C4⋊C4—24no—
137C4⋊C4—222no—
138C22⋊C4—24no—
139C22⋊C4—21no—
140C22⋊C4—222no—
141C22⋊C4—222no—
142C22⋊C4—222no—
143C22⋊C4—222no—
144C22⋊C4—222no—
145C22⋊C4C2×Dic1112yescomplemented
146C42—222no—
147C11#189011yescharacteristic, complemented, Sylow
148C23—21no—
149C23—21no—
150C23—42no—
151C23—42no—
152C23C22⋊Dic1112yes—
153C23D4×D1112yes—
154C23#434112yes—
155C23C22×Dic1111yescharacteristic
156C23C2×C22⋊D1111yescharacteristic
157C23C2×C22⋊D1111yescharacteristic
158D4—24no—
159D4—24no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—24no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—42no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—224no—
170C2×C4—444no—
171C2×C4—444no—
172C2×C4—442no—
173C2×C4—882no—
174C2×C4C22⋊Dic1112yes—
175C22—22no—
176C22—24no—
177C22—22no—
178C22—42no—
179C22—41no—
180C22—41no—
181C22—42no—
182C22—42no—
183C22—81no—
184C22D4×Dic1112yes—
185C22#6698811yescharacteristic
186C22#6699011yescharacteristic
187C22#6699212yes—
188C22C2×C22⋊Dic1111yescharacteristic
189C4—22no—
190C4—42no—
191C4—42no—
192C4—444no—
193C4—882no—
194C2—21no—
195C2—22no—
196C2—21no—
197C2—22no—
198C2—42no—
199C2#1062266612yes—
200C2#1062283311yescharacteristic
subgroupG/H
centerC22#66990
commutatorC23×C11C22×C4
FrattiniC24C22×D11
FittingC2×C11×#123C2
socleC22×C11#120
prime radicalC22×D4×C11C22
cosocleC24×C11C23
hypercenterC2×#123D11
hypocenterC11#1890
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
4. #10622824C2semidirect
5. #10622165C2semidirect
9. C11×#123C4semidirect
31. C22×C4×C11C2×C4semidirect
39. C11×C22⋊C4C2×C4semidirect
102. #123Dic11semidirect
134. C22×C4C2×Dic11semidirect
145. C22⋊C4C2×Dic11semidirect
147. C11#1890semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1232
#106233292
C2×#668982
#106228242
#106221652
#189011