Finite Group Databasebeta

← C11×#10983 #14588176

Subgroups — C11×#10983 #14588176

Order 2816.

1318 conjugacy classes of subgroups; only the 286 normal subgroups are shown.

normal subgroups only

This group has 1318 conjugacy classes of subgroups — too many to draw. Only its 286 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×C4⋊Q8C211yesmaximal, characteristic
2C22×C11×#101C214yesmaximal
3C11×#1728C212yesmaximal
4C23×Q8×C11C2212yes—
5C22×C11×M16C2214yes—
6C2×C11×C4⋊Q8—28no—
7C2×C11×C4⋊Q8—24no—
8C22×C11×C4⋊C4C414yes—
9C22×C42×C11C2211yescharacteristic
10C2×C11×#101—28no—
11C2×C11×#101—216no—
12C11×#336—24no—
13C22×Q8×C11—24no—
14C22×Q8×C11—24no—
15C22×Q8×C11—28no—
16C22×Q8×C11—28no—
17C22×Q8×C11D418yes—
18C23×C4×C11C2×C412yes—
19C23×C4×C11C2×C414yes—
20C23×C4×C11C2311yescharacteristic
21C2×C11×M16—24no—
22C2×C11×M16—28no—
23C2×C11×M16—28no—
24C2×C11×M16D418yes—
25C22×C8×C11—24no—
26C11×C4⋊Q8—232no—
27C2×C11×C4⋊C4—216no—
28C2×C11×C4⋊C4—28no—
29C2×C42×C11—24no—
30C2×C42×C11D414yes—
31C11×#101—232no—
32#10983C1111yesmaximal, characteristic, direct product factor, Sylow
33C24×C11C22×C411yescharacteristic
34C2×Q8×C11—28no—
35C2×Q8×C11—216no—
36C2×Q8×C11—216no—
37C2×Q8×C11—28no—
38C2×Q8×C11—44no—
39C2×Q8×C11—48no—
40C2×Q8×C11—48no—
41C2×Q8×C11—44no—
42C2×Q8×C11—44no—
43C2×Q8×C11—44no—
44C22×C4×C11—24no—
45C22×C4×C11—28no—
46C22×C4×C11—24no—
47C22×C4×C11—24no—
48C22×C4×C11—216no—
49C22×C4×C11C22⋊C418yes—
50C22×C4×C11C22⋊C414yes—
51C22×C4×C11C2×D414yes—
52C22×C4×C11C2×D414yes—
53C22×C4×C11C2×D412yes—
54C22×C4×C11#4114yes—
55C11×M16—216no—
56C11×M16—48no—
57C2×C8×C11—28no—
58C2×C8×C11—44no—
59C2×C8×C11—44no—
60C11×C4⋊C4—232no—
61C42×C11—28no—
62C22×C4⋊Q8C2×C1111yescharacteristic
63C22×#101C2×C1114yes—
64#1728C2×C1112yes—
65C23×C11—24no—
66C23×C11C2×C22⋊C412yes—
67C23×C11C2×C22⋊C411yescharacteristic
68C23×C11C4×D414yes—
69Q8×C11—416no—
70Q8×C11—416no—
71C2×C4×C11—216no—
72C2×C4×C11—24no—
73C2×C4×C11—24no—
74C2×C4×C11—28no—
75C2×C4×C11—216no—
76C2×C4×C11—48no—
77C2×C4×C11—48no—
78C2×C4×C11#10118yescomplemented
79C2×C4×C11#12014yes—
80C2×C4×C11#12014yes—
81C2×C4×C11#12118yes—
82C2×C4×C11#12114yes—
83C2×C4×C11#12314yes—
84C2×C4×C11#12412yes—
85C2×C4×C11#12712yes—
86C8×C11—48no—
87C23×Q8C22×C1112yes—
88C22×M16C22×C1114yes—
89C2×C4⋊Q8—28no—
90C2×C4⋊Q8—24no—
91C22×C4⋊C4C4×C1114yes—
92C22×C42C22×C1111yescharacteristic
93C2×#101—28no—
94C2×#101—216no—
95#336—24no—
96C22×C11—28no—
97C22×C11—24no—
98C22×C11#37911yescharacteristic
99C22×C11#38614yes—
100C22×C11#39012yes—
101C22×C11C2×#10114yes—
102C4×C11—28no—
103C4×C11—48no—
104C4×C11#39214yes—
105C4×C11#39414yes—
106C22×Q8—24no—
107C22×Q8—24no—
108C22×Q8—28no—
109C22×Q8—28no—
110C22×Q8D4×C1118yes—
111C23×C4C2×C4×C1114yes—
112C23×C4C2×C4×C1112yes—
113C23×C4C23×C1111yescharacteristic
114C2×M16—24no—
115C2×M16—28no—
116C2×M16—28no—
117C2×M16D4×C1118yes—
118C22×C8—24no—
119C4⋊Q8—232no—
120C2×C4⋊C4—216no—
121C2×C4⋊C4—28no—
122C2×C42—24no—
123C2×C42D4×C1114yes—
124#101—232no—
125C2×C11—24no—
126C2×C11#143811yescharacteristic
127C2×C11#178412yes—
128C2×C11#196614yes—
129C24C22×C4×C1111yescharacteristic
130C2×Q8—28no—
131C2×Q8—216no—
132C2×Q8—216no—
133C2×Q8—28no—
134C2×Q8—44no—
135C2×Q8—48no—
136C2×Q8—48no—
137C2×Q8—44no—
138C2×Q8—44no—
139C2×Q8—44no—
140C22×C4—24no—
141C22×C4—28no—
142C22×C4—24no—
143C22×C4—24no—
144C22×C4—216no—
145C22×C4C11×C22⋊C418yes—
146C22×C4C11×C22⋊C414yes—
147C22×C4C2×D4×C1114yes—
148C22×C4C2×D4×C1114yes—
149C22×C4C2×D4×C1112yes—
150C22×C4C11×#4114yes—
151M16—216no—
152M16—48no—
153C2×C8—28no—
154C2×C8—44no—
155C2×C8—44no—
156C4⋊C4—232no—
157C42—28no—
158C11#1098311yescharacteristic, direct product factor, Sylow
159C23—24no—
160C23C2×C11×C22⋊C412yes—
161C23C2×C11×C22⋊C411yescharacteristic
162C23C4×D4×C1114yes—
163Q8—416no—
164Q8—416no—
165C2×C4—216no—
166C2×C4—24no—
167C2×C4—24no—
168C2×C4—28no—
169C2×C4—216no—
170C2×C4—48no—
171C2×C4—48no—
172C2×C4C11×#10118yescomplemented
173C2×C4C11×#12014yes—
174C2×C4C11×#12014yes—
175C2×C4C11×#12118yes—
176C2×C4C11×#12114yes—
177C2×C4C11×#12314yes—
178C2×C4C11×#12412yes—
179C2×C4C11×#12712yes—
180C8—48no—
181C22—28no—
182C22—24no—
183C22C11×#37911yescharacteristic
184C22C11×#38614yes—
185C22C11×#39012yes—
186C22C2×C11×#10114yes—
187C4—28no—
188C4—48no—
189C4C11×#39214yes—
190C4C11×#39414yes—
191C2—24no—
192C2C11×#143811yescharacteristic
193C2C11×#178412yes—
194C2C11×#196614yes—
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
32. #10983C11direct (N × H)
78. C2×C4×C11#101semidirect
158. C11#10983direct (N × H)
172. C2×C4C11×#101semidirect

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊Q82
C22×C11×#1012
C11×#17282
#1098311