Finite Group Databasebeta

← C11×#7442 #14584635

Subgroups — C11×#7442 #14584635

Order 2816.

194 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 46 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×#2061C211yesmaximal, characteristic
2C11×#1324C211yesmaximal, characteristic
3C11×#1295C211yesmaximal, characteristic
4C11×#544C411yescharacteristic
5C11×#428—21no—
6C2×C11×#97—21no—
7C11×#382C2211yescharacteristic
8C11×#343C411yescharacteristic
9C11×#339—21no—
10C11×#324—21no—
11C2×C11×M16—21no—
12C22×C8×C11—41no—
13C11×C4⋊Q8—41no—
14C11×#125—41no—
15C11×C22⋊Q8—41no—
16C11×#117—21no—
17C2×C11×C4⋊C4C2×C411yescharacteristic
18C2×C11×C4⋊C4D411yescharacteristic
19C2×C42×C11D411yescharacteristic
20C11×#107—41no—
21C11×#106—41no—
22C11×C22⋊C8—41no—
23C11×#97—22no—
24C11×#97—41no—
25C11×#95—41no—
26#7442C1111yesmaximal, characteristic, direct product factor, Sylow
27C2×Q8×C11—41no—
28C22×C4×C11—21no—
29C22×C4×C11—21no—
30C22×C4×C11—21no—
31C22×C4×C11C22⋊C411yescharacteristic
32C11×M16—22no—
33C11×M16—41no—
34C2×C8×C11—42no—
35C2×C8×C11—41no—
36C2×C8×C11—42no—
37C2×C8×C11—42no—
38C2×C8×C11—81no—
39C11×C4⋊C4—21no—
40C11×C4⋊C4—21no—
41C11×C4⋊C4—41no—
42C11×C4⋊C4—41no—
43C11×C4⋊C4—42no—
44C11×C4⋊C4—41no—
45C11×C22⋊C4—41no—
46C42×C11—21no—
47C42×C11—41no—
48C42×C11SD1611yescharacteristic
49C42×C11Q1611yescharacteristic
50#2061C2×C1111yescharacteristic
51#1324C2×C1111yescharacteristic
52#1295C2×C1111yescharacteristic
53C23×C11#9911yescharacteristic
54Q8×C11—161no—
55C2×C4×C11—21no—
56C2×C4×C11—21no—
57C2×C4×C11—21no—
58C2×C4×C11—21no—
59C2×C4×C11—41no—
60C2×C4×C11—41no—
61C2×C4×C11—41no—
62C2×C4×C11—41no—
63C2×C4×C11—41no—
64C2×C4×C11—41no—
65C2×C4×C11—81no—
66C2×C4×C11—81no—
67C2×C4×C11#10311yescharacteristic
68C2×C4×C11#10411yescharacteristic
69C8×C11—42no—
70C8×C11—44no—
71C8×C11—161no—
72#544C4×C1111yescharacteristic
73#428—21no—
74C2×#97—21no—
75#382C22×C1111yescharacteristic
76#343C4×C1111yescharacteristic
77#339—21no—
78#324—21no—
79C22×C11—21no—
80C22×C11—21no—
81C22×C11#32811yescharacteristic
82C22×C11AΣL(1,𝔽16)11yescharacteristic
83C22×C11#35611yescharacteristic
84C4×C11—21no—
85C4×C11—21no—
86C4×C11—41no—
87C4×C11—41no—
88C4×C11—81no—
89C4×C11—81no—
90C4×C11—81no—
91C4×C11—81no—
92C2×M16—21no—
93C22×C8—41no—
94C4⋊Q8—41no—
95#125—41no—
96C22⋊Q8—41no—
97#117—21no—
98C2×C4⋊C4C2×C4×C1111yescharacteristic
99C2×C4⋊C4D4×C1111yescharacteristic
100C2×C42D4×C1111yescharacteristic
101#107—41no—
102#106—41no—
103C22⋊C8—41no—
104#97—22no—
105#97—41no—
106#95—41no—
107C2×C11—21no—
108C2×C11—21no—
109C2×C11#135411yescharacteristic
110C2×C11#140311yescharacteristic
111C2×C11#140411yescharacteristic
112C2×Q8—41no—
113C22×C4—21no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4C11×C22⋊C411yescharacteristic
117M16—22no—
118M16—41no—
119C2×C8—42no—
120C2×C8—41no—
121C2×C8—42no—
122C2×C8—42no—
123C2×C8—81no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—41no—
127C4⋊C4—41no—
128C4⋊C4—41no—
129C4⋊C4—42no—
130C22⋊C4—41no—
131C42—21no—
132C42—41no—
133C42C11×SD1611yescharacteristic
134C42C11×Q1611yescharacteristic
135C11#744211yescharacteristic, direct product factor, Sylow
136C23C11×#9911yescharacteristic
137Q8—161no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—81no—
149C2×C4—81no—
150C2×C4C11×#10311yescharacteristic
151C2×C4C11×#10411yescharacteristic
152C8—42no—
153C8—44no—
154C8—161no—
155C22—21no—
156C22—21no—
157C22C11×#32811yescharacteristic
158C22C11×AΣL(1,𝔽16)11yescharacteristic
159C22C11×#35611yescharacteristic
160C4—21no—
161C4—21no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—81no—
166C4—81no—
167C4—81no—
168C2—21no—
169C2—21no—
170C2C11×#135411yescharacteristic
171C2C11×#140311yescharacteristic
172C2C11×#140411yescharacteristic
subgroupG/H
center, socleC22×C11AΣL(1,𝔽16)
commutatorC2×C4⋊C4C2×C4×C11
Frattini, cosocle#382C22×C11
prime radicalC23×C11#99
LCSG ▷ C2×C4⋊C4 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C22×C4×C11 ◁ C11×#382 ◁ G

Complements

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

NH ≅ G/Ntype
26. #7442C11direct (N × H)
135. C11#7442direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#20612
C11×#13242
C11×#12952
#744211