Finite Group Databasebeta

← C11×#2075 #13064913

Subgroups — C11×#2075 #13064913

Order 1408.

256 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 96 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×#107C211yesmaximal, characteristic, complemented
2C2×C11×C22⋊C8C211yesmaximal, characteristic
3C11×#380C212yesmaximal
4C11×#340C211yesmaximal, characteristic, complemented
5C11×#340C212yesmaximal, complemented
6C23×C4×C11C2211yescharacteristic
7C22×C8×C11C2211yescharacteristic
8C22×C8×C11C2211yescharacteristic
9C2×C11×C4⋊C4C2212yes—
10C2×C11×C4⋊C4C2212yes—
11C2×C11×C22⋊C4—22no—
12C11×#107—22no—
13C11×C22⋊C8—22no—
14C11×#95—22no—
15C24×C11D411yescharacteristic
16C22×C4×C11—21no—
17C22×C4×C11—21no—
18C22×C4×C11—22no—
19C22×C4×C11—22no—
20C22×C4×C11—22no—
21C22×C4×C11—22no—
22C22×C4×C11D411yescharacteristic
23C22×C4×C11C2311yescharacteristic
24C2×C8×C11—21no—
25C2×C8×C11—22no—
26C2×C8×C11—22no—
27C2×C8×C11D412yes—
28C11×C4⋊C4—22no—
29C11×C4⋊C4—22no—
30C11×C4⋊C4—22no—
31C11×C4⋊C4—22no—
32C11×C22⋊C4—44no—
33#2075C1111yesmaximal, characteristic, direct product factor, Sylow
34C23×C11—21no—
35C23×C11—22no—
36C23×C11—21no—
37C23×C11—22no—
38C23×C11D812yes—
39C23×C11C2×D411yescharacteristic
40C2×C4×C11—21no—
41C2×C4×C11—22no—
42C2×C4×C11—41no—
43C2×C4×C11—41no—
44C2×C4×C11—42no—
45C2×C4×C11—42no—
46C2×C4×C11—42no—
47C2×C4×C11—42no—
48C2×C4×C11—42no—
49C2×C4×C11—42no—
50C2×C4×C11—42no—
51C2×C4×C11C2×D411yescharacteristic
52C2×C4×C11#4112yes—
53C2×C4×C11#4112yes—
54C2×C4×C11#4111yescharacteristic
55C8×C11—22no—
56C8×C11—41no—
57C2×#107C2×C1111yescharacteristic, complemented
58C2×C22⋊C8C2×C1111yescharacteristic
59#380C2×C1112yes—
60#340C2×C1111yescharacteristic, complemented
61#340C2×C1112yescomplemented
62C22×C11—22no—
63C22×C11—24no—
64C22×C11—41no—
65C22×C11—41no—
66C22×C11—42no—
67C22×C11#12111yescharacteristic
68C22×C11#12312yes—
69C22×C11C2×D811yescharacteristic
70C22×C11#13511yescharacteristic
71C22×C11#13712yes—
72C4×C11—41no—
73C4×C11—82no—
74C4×C11—82no—
75C4×C11#12311yescharacteristic
76C4×C11#12411yescharacteristic
77C4×C11#12612yes—
78C23×C4C22×C1111yescharacteristic
79C22×C8C22×C1111yescharacteristic
80C22×C8C22×C1111yescharacteristic
81C2×C4⋊C4C22×C1112yes—
82C2×C4⋊C4C22×C1112yes—
83C2×C22⋊C4—22no—
84#107—22no—
85C22⋊C8—22no—
86#95—22no—
87C2×C11—42no—
88C2×C11#39711yescharacteristic
89C2×C11#46611yescharacteristic
90C2×C11#47011yescharacteristic
91C2×C11#48012yes—
92C2×C11#48512yes—
93C24D4×C1111yescharacteristic
94C22×C4—21no—
95C22×C4—21no—
96C22×C4—22no—
97C22×C4—22no—
98C22×C4—22no—
99C22×C4—22no—
100C22×C4D4×C1111yescharacteristic
101C22×C4C23×C1111yescharacteristic
102C2×C8—22no—
103C2×C8—21no—
104C2×C8—22no—
105C2×C8D4×C1112yes—
106C4⋊C4—22no—
107C4⋊C4—22no—
108C4⋊C4—22no—
109C4⋊C4—22no—
110C22⋊C4—44no—
111C11#207511yescharacteristic, direct product factor, Sylow
112C23—21no—
113C23—22no—
114C23—21no—
115C23—22no—
116C23C11×D812yes—
117C23C2×D4×C1111yescharacteristic
118C2×C4—21no—
119C2×C4—22no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—42no—
123C2×C4—42no—
124C2×C4—42no—
125C2×C4—42no—
126C2×C4—42no—
127C2×C4—42no—
128C2×C4—42no—
129C2×C4C2×D4×C1111yescharacteristic
130C2×C4C11×#4112yes—
131C2×C4C11×#4112yes—
132C2×C4C11×#4111yescharacteristic
133C8—22no—
134C8—41no—
135C22—22no—
136C22—24no—
137C22—41no—
138C22—41no—
139C22—42no—
140C22C11×#12111yescharacteristic
141C22C11×#12312yes—
142C22C2×C11×D811yescharacteristic
143C22C11×#13511yescharacteristic
144C22C11×#13712yes—
145C4—41no—
146C4—82no—
147C4—82no—
148C4C11×#12311yescharacteristic
149C4C11×#12411yescharacteristic
150C4C11×#12612yes—
151C2—42no—
152C2C11×#39711yescharacteristic
153C2C11×#46611yescharacteristic
154C2C11×#47011yescharacteristic
155C2C11×#48012yes—
156C2C11×#48512yes—
subgroupG/H
center, socleC23×C11C2×D4
commutator, Frattini, cosocleC22×C4C23×C11
prime radicalC24×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#107C2semidirect
4. C11×#340C2semidirect
5. C11×#340C2semidirect
33. #2075C11direct (N × H)
57. C2×#107C2×C11semidirect
60. #340C2×C11semidirect
61. #340C2×C11semidirect
111. C11#2075direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1072
C2×C11×C22⋊C82
C11×#3802
C11×#3402
#207511