Finite Group Databasebeta

← #13069919

Subgroups — #13069919

Order 1408.

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

normal subgroups only

This group has 264 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
1C11×#575C211yesmaximal, characteristic
2#10622853C212yesmaximal, complemented
3#10622846C212yesmaximal, complemented
4#10622732C211yesmaximal, characteristic, complemented
5#10622195C211yesmaximal, characteristic, complemented
6C2×C11×#41C2212yes—
7C11×#137—22no—
8C11×AGL(1,ℤ/8)—22no—
9C11×#135—22no—
10C2×C11×M16C2211yescharacteristic
11#66979C2212yes—
12#66979C2211yescharacteristic
13C22×C11⋊C8C2211yescharacteristic
14#66899—22no—
15#66898—24no—
16#66896—22no—
17Dic11⋊C8—22no—
18C11×#41—22no—
19C11×#41—22no—
20C11×#41—22no—
21C11×#41—22no—
22C2×Q8×C11D412yes—
23C2×D4×C11—22no—
24C2×D4×C11D412yes—
25C22×C4×C11—22no—
26C22×C4×C11C2311yescharacteristic
27C11×Q16—22no—
28C11×SD16—24no—
29C11×D8—22no—
30C11×M16—22no—
31C2×C8×C11D412yes—
32C22⋊Dic11—22no—
33C22⋊Dic11D412yes—
34C4⋊Dic11—22no—
35C4⋊Dic11—21no—
36C4×Dic11—21no—
37C4×Dic11—22no—
38C2×C11⋊C8—21no—
39C2×C11⋊C8—22no—
40#2053—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—
49C2×C4×C11—22no—
50C2×C4×C11—42no—
51C2×C4×C11—42no—
52C2×C4×C11C2×D412yes—
53C2×C4×C11C2×D411yescharacteristic
54C2×C4×C11#4111yescharacteristic
55C2×C4×C11#4112yes—
56C2×Dic11—22no—
57C2×Dic11—42no—
58C8×C11—22no—
59C11⋊C8—41no—
60#575D1111yescharacteristic
61#424—111no—
62#416—112no—
63#410—112no—
64H(3,ℤ/4)—111no—
65C22×C11—41no—
66C22×C11—42no—
67C22×C11—82no—
68C22×C11#12111yescharacteristic
69C22×C11#12112yes—
70C4×C11—42no—
71C4×C11#12011yescharacteristic
72C4×C11#12312yes—
73C4×C11#12411yescharacteristic
74Dic11—42no—
75Dic11—82no—
76C2×#41C2×D1112yes—
77#137—22no—
78AGL(1,ℤ/8)—22no—
79#135—22no—
80C2×M16C2×D1111yescharacteristic
81C22×C8—111no—
82#117—111no—
83#117—112no—
84C4⋊C8—222no—
85#103—222no—
86#102—222no—
87#99—224no—
88C2×C11—21no—
89C2×C11—22no—
90C2×C11—82no—
91C2×C11#39411yescharacteristic
92#41—22no—
93#41—22no—
94#41—22no—
95#41—22no—
96C2×Q8C22⋊D1112yes—
97C2×D4—22no—
98C2×D4C22⋊D1112yes—
99C22×C4—22no—
100C22×C4C22×D1111yescharacteristic
101Q16—22no—
102SD16—24no—
103D8—22no—
104M16—22no—
105C2×C8—222no—
106C2×C8—221no—
107C2×C8C22⋊D1112yes—
108C4⋊C4—221no—
109C4⋊C4—222no—
110C22⋊C4—112no—
111C22⋊C4—222no—
112C42—221no—
113C42—222no—
114C11#205311yescharacteristic, complemented, Sylow
115C23—22no—
116C23D4×D1111yescharacteristic
117Q8—22no—
118Q8—22no—
119D4—22no—
120D4—22no—
121D4—42no—
122D4—42no—
123C2×C4—22no—
124C2×C4—42no—
125C2×C4—42no—
126C2×C4—222no—
127C2×C4—442no—
128C2×C4#434111yescharacteristic
129C2×C4#434112yes—
130C2×C4C2×C22⋊D1112yes—
131C2×C4C2×C22⋊D1111yescharacteristic
132C8—22no—
133C8—441no—
134C22—41no—
135C22—42no—
136C22—82no—
137C22#6699111yescharacteristic
138C22#6699212yes—
139C4—42no—
140C4—442no—
141C4—882no—
142C4#6698812yes—
143C4#6698911yescharacteristic
144C4#6700611yescharacteristic
145C2—21no—
146C2—22no—
147C2—82no—
148C2#1062283511yescharacteristic
subgroupG/H
centerC4#66989
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
Fitting, prime radicalC11×#575C2
socleC2×C11#394
hypercenter#575D11
hypocenterC11#2053
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
2. #10622853C2semidirect
3. #10622846C2semidirect
4. #10622732C2semidirect
5. #10622195C2semidirect
114. C11#2053semidirect

Maximal subgroups

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

subgroupindex
C11×#5752
#106228532
#106228462
#106227322
#106221952
#205311