Finite Group Databasebeta

← C11×#11383 #14588576

Subgroups — C11×#11383 #14588576

Order 2816.

926 conjugacy classes of subgroups; only the 270 normal subgroups are shown.

normal subgroups only

This group has 926 conjugacy classes of subgroups — too many to draw. Only its 270 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
1C22×C11×#125C211yesmaximal, characteristic
2C2×C11×#343C214yesmaximal
3C11×#1728C212yesmaximal
4C22×C11×M16C2214yes—
5C2×C11×#125—28no—
6C2×C11×#125—24no—
7C22×C11×C4⋊C4C414yes—
8C22×C11×C4⋊C4C2212yes—
9C22×C42×C11C2211yescharacteristic
10C11×#343—28no—
11C11×#336—24no—
12C23×C4×C11C2×C412yes—
13C23×C4×C11C2×C414yes—
14C23×C4×C11C2311yescharacteristic
15C2×C11×M16—24no—
16C2×C11×M16—28no—
17C2×C11×M16—28no—
18C2×C11×M16Q818yes—
19C22×C8×C11—24no—
20C11×#125—232no—
21C2×C11×C4⋊C4—28no—
22C2×C11×C4⋊C4—28no—
23C2×C11×C4⋊C4—28no—
24C2×C11×C4⋊C4—24no—
25C2×C11×C4⋊C4—24no—
26C2×C11×C4⋊C4D418yes—
27C2×C42×C11—24no—
28C2×C42×C11D414yes—
29#11383C1111yesmaximal, characteristic, direct product factor, Sylow
30C24×C11C22×C411yescharacteristic
31C22×C4×C11—22no—
32C22×C4×C11—22no—
33C22×C4×C11—24no—
34C22×C4×C11—24no—
35C22×C4×C11—44no—
36C22×C4×C11—48no—
37C22×C4×C11C22⋊C414yes—
38C22×C4×C11C22⋊C418yes—
39C22×C4×C11C2×D414yes—
40C22×C4×C11C2×D412yes—
41C22×C4×C11C2×Q814yes—
42C22×C4×C11#4114yes—
43C11×M16—216no—
44C11×M16—48no—
45C2×C8×C11—28no—
46C2×C8×C11—44no—
47C2×C8×C11—44no—
48C11×C4⋊C4—232no—
49C11×C4⋊C4—216no—
50C42×C11—28no—
51C22×#125C2×C1111yescharacteristic
52C2×#343C2×C1114yes—
53#1728C2×C1112yes—
54C23×C11—24no—
55C23×C11C2×C22⋊C412yes—
56C23×C11C2×C22⋊C411yescharacteristic
57C23×C11C4×Q814yes—
58C2×C4×C11—24no—
59C2×C4×C11—28no—
60C2×C4×C11—28no—
61C2×C4×C11—44no—
62C2×C4×C11—44no—
63C2×C4×C11—48no—
64C2×C4×C11—48no—
65C2×C4×C11—48no—
66C2×C4×C11#12014yes—
67C2×C4×C11C22⋊Q814yes—
68C2×C4×C11C22⋊Q818yes—
69C2×C4×C11#12412yes—
70C2×C4×C11#12414yes—
71C2×C4×C11C4⋊Q814yes—
72C2×C4×C11C4⋊Q812yes—
73C8×C11—48no—
74C22×M16C22×C1114yes—
75C2×#125—28no—
76C2×#125—24no—
77C22×C4⋊C4C4×C1114yes—
78C22×C4⋊C4C22×C1112yes—
79C22×C42C22×C1111yescharacteristic
80#343—28no—
81#336—24no—
82C22×C11—28no—
83C22×C11—22no—
84C22×C11—22no—
85C22×C11#37911yescharacteristic
86C22×C11#39114yes—
87C22×C11#39112yes—
88C22×C11#41314yes—
89C4×C11—44no—
90C4×C11—48no—
91C4×C11#39314yes—
92C4×C11#39514yes—
93C23×C4C2×C4×C1114yes—
94C23×C4C2×C4×C1112yes—
95C23×C4C23×C1111yescharacteristic
96C2×M16—24no—
97C2×M16—28no—
98C2×M16—28no—
99C2×M16Q8×C1118yes—
100C22×C8—24no—
101#125—232no—
102C2×C4⋊C4—28no—
103C2×C4⋊C4—28no—
104C2×C4⋊C4—28no—
105C2×C4⋊C4—24no—
106C2×C4⋊C4—24no—
107C2×C4⋊C4D4×C1118yes—
108C2×C42—24no—
109C2×C42D4×C1114yes—
110C2×C11—24no—
111C2×C11#144611yescharacteristic
112C2×C11#178512yes—
113C2×C11#199814yes—
114C24C22×C4×C1111yescharacteristic
115C22×C4—22no—
116C22×C4—22no—
117C22×C4—24no—
118C22×C4—24no—
119C22×C4—44no—
120C22×C4—48no—
121C22×C4C11×C22⋊C414yes—
122C22×C4C11×C22⋊C418yes—
123C22×C4C2×D4×C1114yes—
124C22×C4C2×D4×C1112yes—
125C22×C4C2×Q8×C1114yes—
126C22×C4C11×#4114yes—
127M16—216no—
128M16—48no—
129C2×C8—28no—
130C2×C8—44no—
131C2×C8—44no—
132C4⋊C4—232no—
133C4⋊C4—216no—
134C42—28no—
135C11#1138311yescharacteristic, direct product factor, Sylow
136C23—24no—
137C23C2×C11×C22⋊C412yes—
138C23C2×C11×C22⋊C411yescharacteristic
139C23C4×Q8×C1114yes—
140C2×C4—24no—
141C2×C4—28no—
142C2×C4—28no—
143C2×C4—44no—
144C2×C4—44no—
145C2×C4—48no—
146C2×C4—48no—
147C2×C4—48no—
148C2×C4C11×#12014yes—
149C2×C4C11×C22⋊Q814yes—
150C2×C4C11×C22⋊Q818yes—
151C2×C4C11×#12412yes—
152C2×C4C11×#12414yes—
153C2×C4C11×C4⋊Q814yes—
154C2×C4C11×C4⋊Q812yes—
155C8—48no—
156C22—28no—
157C22—22no—
158C22—22no—
159C22C11×#37911yescharacteristic
160C22C11×#39114yes—
161C22C11×#39112yes—
162C22C11×#41314yes—
163C4—44no—
164C4—48no—
165C4C11×#39314yes—
166C4C11×#39514yes—
167C2—24no—
168C2C11×#144611yescharacteristic
169C2C11×#178512yes—
170C2C11×#199814yes—
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC24C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11C22×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
29. #11383C11direct (N × H)
135. C11#11383direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1252
C2×C11×#3432
C11×#17282
#1138311