Finite Group Databasebeta

← #13069842

Subgroups — #13069842

Order 1408.

290 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C11×#537C211yesmaximal, characteristic
2C2×#66901C212yesmaximal, complemented
3#10622845C212yesmaximal, complemented
4#10622590C211yesmaximal, characteristic, complemented
5#10622168C211yesmaximal, characteristic, complemented
6C2×C11×#41C2212yes—
7C11×C22⋊Q8—22no—
8C11×#121—22no—
9C11×#121—22no—
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C4⋊Dic11C2211yescharacteristic
12C2×C4×Dic11C2211yescharacteristic
13C2×#4318C2212yes—
14#66901—24no—
15#66899—22no—
16#66896—22no—
17C11⋊#95—22no—
18C11×#41—22no—
19C11×#41—22no—
20C11×#41—22no—
21C11×#41—22no—
22C2×Q8×C11D412yes—
23C2×D4×C11—22no—
24C2×D4×C11—22no—
25C2×D4×C11D412yes—
26C22×C4×C11—22no—
27C22×C4×C11D412yes—
28C22×C4×C11C2311yescharacteristic
29C22×Dic11—21no—
30C22×Dic11—21no—
31C11×C4⋊C4—22no—
32C11×C4⋊C4—22no—
33C11×C22⋊C4—24no—
34C4⋊Dic11—22no—
35C4×Dic11—21no—
36C4×Dic11D412yescomplemented
37#4318—22no—
38#4318—22no—
39C2×C11⋊C8—22no—
40#2040—111nomaximal, Sylow
41C23×C11—22no—
42C23×C11C2×D411yescharacteristic
43Q8×C11—22no—
44Q8×C11—22no—
45D4×C11—22no—
46D4×C11—22no—
47D4×C11—42no—
48D4×C11—42no—
49D4×C11—82no—
50C2×C4×C11—22no—
51C2×C4×C11—22no—
52C2×C4×C11—42no—
53C2×C4×C11—42no—
54C2×C4×C11—42no—
55C2×C4×C11C2×D411yescharacteristic
56C2×C4×C11C2×D412yes—
57C2×C4×C11#4112yes—
58C2×C4×C11#4111yescharacteristic
59C2×Dic11—22no—
60C2×Dic11—41no—
61C2×Dic11—41no—
62C2×Dic11—42no—
63C2×Dic11—41no—
64C11⋊C8—42no—
65#537D1111yescharacteristic
66C2×#104—112no—
67#417—112no—
68#382—111no—
69#343—111no—
70C22×C11—21no—
71C22×C11—21no—
72C22×C11—42no—
73C22×C11—42no—
74C22×C11—42no—
75C22×C11#12011yescharacteristic
76C22×C11#12111yescharacteristic
77C22×C11#12411yescharacteristic
78C4×C11—42no—
79C4×C11—42no—
80C4×C11#12112yes—
81C4×C11#12312yes—
82Dic11—42no—
83Dic11—81no—
84C2×#41C2×D1112yes—
85C2×M16—112no—
86C22⋊Q8—22no—
87#121—22no—
88#121—22no—
89C2×C4⋊C4—111no—
90C2×C4⋊C4C2×D1111yescharacteristic
91C2×C42—111no—
92#104—224no—
93#103—222no—
94#102—222no—
95#95—222no—
96C2×C11—21no—
97C2×C11—21no—
98C2×C11—82no—
99C2×C11#39411yescharacteristic
100C2×C11#45411yescharacteristic
101C2×C11#45511yescharacteristic
102#41—22no—
103#41—22no—
104#41—22no—
105#41—22no—
106C2×Q8C22⋊D1112yes—
107C2×D4—22no—
108C2×D4—22no—
109C2×D4C22⋊D1112yes—
110C22×C4—22no—
111C22×C4—221no—
112C22×C4—221no—
113C22×C4C22⋊D1112yes—
114C22×C4C22×D1111yescharacteristic
115M16—222no—
116M16—222no—
117C2×C8—222no—
118C4⋊C4—22no—
119C4⋊C4—22no—
120C4⋊C4—222no—
121C22⋊C4—24no—
122C42—112no—
123C42—221no—
124C11#204011yescharacteristic, complemented, Sylow
125C23—22no—
126C23C2×C22⋊D1111yescharacteristic
127Q8—22no—
128Q8—22no—
129D4—22no—
130D4—22no—
131D4—42no—
132D4—42no—
133D4—82no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—42no—
137C2×C4—42no—
138C2×C4—42no—
139C2×C4—222no—
140C2×C4—441no—
141C2×C4—441no—
142C2×C4—442no—
143C2×C4—441no—
144C2×C4D4×D1111yescharacteristic
145C2×C4#434111yescharacteristic
146C2×C4#434112yes—
147C2×C4C2×C22⋊D1112yes—
148C8—442no—
149C22—21no—
150C22—21no—
151C22—42no—
152C22—42no—
153C22—42no—
154C22#6698911yescharacteristic
155C22#6699111yescharacteristic
156C22#6700611yescharacteristic
157C4—42no—
158C4—42no—
159C4—442no—
160C4—881no—
161C4#6698812yes—
162C4#6699212yes—
163C2—21no—
164C2—21no—
165C2—82no—
166C2#1062283511yescharacteristic
167C2#1062285511yescharacteristic
168C2#1062285811yescharacteristic
subgroupG/H
centerC22#67006
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
Fitting, prime radicalC11×#537C2
socleC22×C11#120
hypercenter#537D11
hypocenterC11#2040
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
2. C2×#66901C2semidirect
3. #10622845C2semidirect
4. #10622590C2semidirect
5. #10622168C2semidirect
36. C4×Dic11D4semidirect
124. C11#2040semidirect

Maximal subgroups

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

subgroupindex
C11×#5372
C2×#669012
#106228452
#106225902
#106221682
#204011