Finite Group Databasebeta

← #13070629

Subgroups — #13070629

Order 1408.

226 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 45 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×#563C211yesmaximal, characteristic, complemented
2#10622674C211yesmaximal, characteristic
3#10622666C212yesmaximal
4#10622179C211yesmaximal, characteristic, complemented
5#10622177C212yesmaximal, complemented
6#67037C2211yescharacteristic
7C11×C4⋊Q8—21no—
8C11×#126—22no—
9C11×#125—21no—
10C11×#124C2211yescharacteristic
11C11×#123C2212yes—
12C11×C22⋊Q8—22no—
13#66995—21no—
14#66982—22no—
15#66898C2212yes—
16#66897C2211yescharacteristic
17#66870—22no—
18#66869—21no—
19C2×Q8×C11—21no—
20C2×Q8×C11D411yescharacteristic
21C2×D4×C11C2311yescharacteristic
22C22×C4×C11D412yes—
23C2×C22⋊D11—22no—
24#4341—41no—
25D4×D11—41no—
26#4339—21no—
27C11×C4⋊C4—21no—
28C11×C4⋊C4—22no—
29C11×C4⋊C4—22no—
30C11×C4⋊C4—21no—
31C11×C4⋊C4—22no—
32C11×C22⋊C4—22no—
33C11×C22⋊C4—22no—
34C11×C22⋊C4D412yes—
35C42×C11—21no—
36C42×C11D411yescharacteristic
37C22⋊Dic11—22no—
38#4326—41no—
39#4325—41no—
40(C2×D11)⋊C4—42no—
41Dic11⋊C4—42no—
42#4318—21no—
43#2201—111nomaximal, Sylow
44C23×C11C2×D412yes—
45C22×D11—22no—
46Q8×C11—41no—
47Q8×C11—81no—
48D4×C11—41no—
49C2×C4×C11—21no—
50C2×C4×C11—22no—
51C2×C4×C11—21no—
52C2×C4×C11—22no—
53C2×C4×C11—42no—
54C2×C4×C11C2×D411yescharacteristic
55C22⋊D11—42no—
56C22⋊D11—41no—
57C2×Dic11—22no—
58C2×Dic11—42no—
59D44—21no—
60C4×D11—41no—
61Dic22—21no—
62C11⋊C8—41no—
63#563D1111yescharacteristic, complemented
64#458—112no—
65#455—111no—
66#354—111no—
67#352—112no—
68C22×C11—22no—
69C22×C11—42no—
70C22×C11#12011yescharacteristic
71C2×D11—41no—
72C2×D11—82no—
73C4×C11—21no—
74C4×C11—42no—
75C4×C11—41no—
76C4×C11—42no—
77C4×C11—41no—
78Dic11—41no—
79Dic11—82no—
80H(5,𝔽2)—111no—
81#137—221no—
82C4⋊Q8—21no—
83#126—22no—
84#125—21no—
85#124C2×D1111yescharacteristic
86#123—222no—
87#123C2×D1112yes—
88C22⋊Q8—22no—
89#104—221no—
90#100—111no—
91#99—112no—
92#99—222no—
93C2×C11—21no—
94C2×C11—42no—
95C2×C11B(4,𝔽2)11yescharacteristic
96D11—81no—
97#41—221no—
98#41—441no—
99C2×Q8—21no—
100C2×Q8C22⋊D1111yescharacteristic
101C2×D4—222no—
102C2×D4—441no—
103C2×D4C22×D1111yescharacteristic
104C22×C4C22⋊D1112yes—
105Q16—441no—
106SD16—441no—
107M16—221no—
108C4⋊C4—21no—
109C4⋊C4—22no—
110C4⋊C4—22no—
111C4⋊C4—21no—
112C4⋊C4—22no—
113C4⋊C4—442no—
114C22⋊C4—22no—
115C22⋊C4—22no—
116C22⋊C4—222no—
117C22⋊C4—442no—
118C22⋊C4C22⋊D1112yes—
119C42—21no—
120C42C22⋊D1111yescharacteristic
121C11#220111yescharacteristic, complemented, Sylow
122C23—222no—
123C23C2×C22⋊D1112yes—
124Q8—41no—
125Q8—81no—
126Q8—221no—
127D4—41no—
128D4—221no—
129D4—442no—
130D4—441no—
131C2×C4—21no—
132C2×C4—22no—
133C2×C4—21no—
134C2×C4—22no—
135C2×C4—42no—
136C2×C4—222no—
137C2×C4—441no—
138C2×C4—442no—
139C2×C4C2×C22⋊D1111yescharacteristic
140C8—441no—
141C22—22no—
142C22—42no—
143C22—441no—
144C22—882no—
145C22#6700611yescharacteristic
146C4—21no—
147C4—42no—
148C4—41no—
149C4—42no—
150C4—41no—
151C4—441no—
152C4—882no—
153C2—21no—
154C2—42no—
155C2—881no—
156C2#1062285711yescharacteristic
subgroupG/H
centerC2#10622857
commutator, cosocleC2×D4×C11C23
FrattiniC2×D4C22×D11
FittingC11×#563C2
socleC2×C11B(4,𝔽2)
prime radical#67037C22
hypercenter#563D11
hypocenterC11#2201
LCSG ▷ C2×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #563

Complements

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

NH ≅ G/Ntype
1. C11×#563C2semidirect
4. #10622179C2semidirect
5. #10622177C2semidirect
63. #563D11semidirect
121. C11#2201semidirect

Maximal subgroups

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

subgroupindex
C11×#5632
#106226742
#106226662
#106221792
#106221772
#220111