Finite Group Databasebeta

← C11×#2201 #13065039

Subgroups — C11×#2201 #13065039

Order 1408.

226 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 56 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
2C11×#458C212yesmaximal
3C11×#455C211yesmaximal, characteristic
4C11×#354C211yesmaximal, characteristic, complemented
5C11×#352C212yesmaximal, complemented
6C11×H(5,𝔽2)C2211yescharacteristic
7C11×#137—21no—
8C11×C4⋊Q8—21no—
9C11×#126—22no—
10C11×#125—21no—
11C11×#124C2211yescharacteristic
12C11×#123—22no—
13C11×#123C2212yes—
14C11×C22⋊Q8—22no—
15C11×#104—21no—
16C11×#100C2211yescharacteristic
17C11×#99—22no—
18C11×#99C2212yes—
19C11×#41—21no—
20C11×#41—41no—
21C2×Q8×C11—21no—
22C2×Q8×C11D411yescharacteristic
23C2×D4×C11—22no—
24C2×D4×C11—41no—
25C2×D4×C11C2311yescharacteristic
26C22×C4×C11D412yes—
27C11×Q16—41no—
28C11×SD16—41no—
29C11×M16—21no—
30C11×C4⋊C4—21no—
31C11×C4⋊C4—22no—
32C11×C4⋊C4—22no—
33C11×C4⋊C4—21no—
34C11×C4⋊C4—22no—
35C11×C4⋊C4—42no—
36C11×C22⋊C4—22no—
37C11×C22⋊C4—22no—
38C11×C22⋊C4—22no—
39C11×C22⋊C4—42no—
40C11×C22⋊C4D412yes—
41C42×C11—21no—
42C42×C11D411yescharacteristic
43#2201C1111yesmaximal, characteristic, direct product factor, Sylow
44C23×C11—22no—
45C23×C11C2×D412yes—
46Q8×C11—21no—
47Q8×C11—41no—
48Q8×C11—81no—
49D4×C11—21no—
50D4×C11—41no—
51D4×C11—42no—
52D4×C11—41no—
53C2×C4×C11—22no—
54C2×C4×C11—21no—
55C2×C4×C11—22no—
56C2×C4×C11—21no—
57C2×C4×C11—22no—
58C2×C4×C11—41no—
59C2×C4×C11—42no—
60C2×C4×C11—42no—
61C2×C4×C11C2×D411yescharacteristic
62C8×C11—41no—
63#563C2×C1111yescharacteristic, complemented
64#458C2×C1112yes—
65#455C2×C1111yescharacteristic
66#354C2×C1111yescharacteristic, complemented
67#352C2×C1112yescomplemented
68C22×C11—22no—
69C22×C11—42no—
70C22×C11—41no—
71C22×C11—82no—
72C22×C11#12011yescharacteristic
73C4×C11—21no—
74C4×C11—42no—
75C4×C11—41no—
76C4×C11—41no—
77C4×C11—42no—
78C4×C11—41no—
79C4×C11—82no—
80H(5,𝔽2)C22×C1111yescharacteristic
81#137—21no—
82C4⋊Q8—21no—
83#126—22no—
84#125—21no—
85#124C22×C1111yescharacteristic
86#123—22no—
87#123C22×C1112yes—
88C22⋊Q8—22no—
89#104—21no—
90#100C22×C1111yescharacteristic
91#99—22no—
92#99C22×C1112yes—
93C2×C11—21no—
94C2×C11—42no—
95C2×C11—81no—
96C2×C11B(4,𝔽2)11yescharacteristic
97#41—21no—
98#41—41no—
99C2×Q8—21no—
100C2×Q8D4×C1111yescharacteristic
101C2×D4—22no—
102C2×D4—41no—
103C2×D4C23×C1111yescharacteristic
104C22×C4D4×C1112yes—
105Q16—41no—
106SD16—41no—
107M16—21no—
108C4⋊C4—21no—
109C4⋊C4—22no—
110C4⋊C4—22no—
111C4⋊C4—21no—
112C4⋊C4—22no—
113C4⋊C4—42no—
114C22⋊C4—22no—
115C22⋊C4—22no—
116C22⋊C4—22no—
117C22⋊C4—42no—
118C22⋊C4D4×C1112yes—
119C42—21no—
120C42D4×C1111yescharacteristic
121C11#220111yescharacteristic, direct product factor, Sylow
122C23—22no—
123C23C2×D4×C1112yes—
124Q8—21no—
125Q8—41no—
126Q8—81no—
127D4—21no—
128D4—41no—
129D4—42no—
130D4—41no—
131C2×C4—22no—
132C2×C4—21no—
133C2×C4—22no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—42no—
139C2×C4C2×D4×C1111yescharacteristic
140C8—41no—
141C22—22no—
142C22—42no—
143C22—41no—
144C22—82no—
145C22C11×#12011yescharacteristic
146C4—21no—
147C4—42no—
148C4—41no—
149C4—41no—
150C4—42no—
151C4—41no—
152C4—82no—
153C2—21no—
154C2—42no—
155C2—81no—
156C2C11×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C23×C11
prime radicalC11×H(5,𝔽2)C22
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C22×C11 ◁ C2×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#563C2semidirect
4. C11×#354C2semidirect
5. C11×#352C2semidirect
43. #2201C11direct (N × H)
63. #563C2×C11semidirect
66. #354C2×C11semidirect
67. #352C2×C11semidirect
121. C11#2201direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#5632
C11×#4582
C11×#4552
C11×#3542
C11×#3522
#220111