Finite Group Databasebeta

← #14667120

Subgroups — #14667120

Order 2816.

310 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 59 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
1#13070833C212yesmaximal, complemented
2#13070169C211yesmaximal, characteristic
3#13066604C212yesmaximal, complemented
4#13066554C211yesmaximal, characteristic
5C11×#3202C211yesmaximal, characteristic
6C11×#536—21no—
7C11×#485—22no—
8C11×#470C2212yes—
9C11×#467—21no—
10C11×#451—22no—
11C11×#408C2211yescharacteristic
12#10622849—21no—
13#10622738C2211yescharacteristic
14#10622715—21no—
15#10622203—22no—
16#10622195C2211yescharacteristic
17#10622191C2212yes—
18#10622125—22no—
19C2×C11×#41D411yescharacteristic
20C22×Q8×C11—21no—
21C2×C11×Q16—21no—
22C2×C11×Q16D412yes—
23C2×C11×M16C2311yescharacteristic
24C22×C8×C11D411yescharacteristic
25C11×C4⋊Q8—41no—
26C11×#124—41no—
27C11×#123—41no—
28C11×#123—41no—
29C11×C22⋊Q8—22no—
30C11×C22⋊Q8—22no—
31C11×#117—21no—
32#66979—21no—
33C2×#4318—21no—
34C11×#107—21no—
35C11×#106D412yes—
36C11×#103—22no—
37C11×#103—22no—
38C11×C22⋊C8—22no—
39#66901—42no—
40#66883—22no—
41Dic11⋊C8—42no—
42#66876—22no—
43#12302—111nomaximal, Sylow
44C11×#41—41no—
45C11×#41—41no—
46C2×Q8×C11—22no—
47C2×Q8×C11—41no—
48C2×Q8×C11—81no—
49C2×Q8×C11—81no—
50C2×Q8×C11SD1611yescharacteristic
51C2×D4×C11—21no—
52C2×D4×C11SD1611yescharacteristic
53C22×C4×C11—21no—
54C22×C4×C11—41no—
55C22×C4×C11C2×D411yescharacteristic
56C11×Q16—42no—
57C11×Q16—81no—
58C11×M16—41no—
59C2×C8×C11—21no—
60C2×C8×C11—41no—
61C2×C8×C11C2×D412yes—
62C11×C4⋊C4—22no—
63C11×C4⋊C4—42no—
64C11×C4⋊C4—42no—
65C11×C22⋊C4—41no—
66C11×C22⋊C4—42no—
67C11×C22⋊C4—42no—
68C42×C11—41no—
69C22⋊Dic11—41no—
70C4⋊Dic11—41no—
71C4×Dic11—22no—
72#4318—41no—
73#4318—41no—
74C2×C11⋊C8—41no—
75C11⋊C16—42no—
76#3202D1111yescharacteristic
77#2239—112no—
78#2098—111no—
79#1340—112no—
80#1321—111no—
81C23×C11—21no—
82C23×C11AGL(1,ℤ/8)11yescharacteristic
83Q8×C11—41no—
84Q8×C11—42no—
85Q8×C11—42no—
86Q8×C11—82no—
87D4×C11—41no—
88D4×C11—81no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—41no—
93C2×C4×C11—41no—
94C2×C4×C11—42no—
95C2×C4×C11—42no—
96C2×C4×C11—82no—
97C2×C4×C11#12011yescharacteristic
98C2×C4×C11C2×SD1611yescharacteristic
99C2×Dic11—42no—
100C8×C11—22no—
101C8×C11—41no—
102C11⋊C8—81no—
103#536—21no—
104#485—22no—
105#470C2×D1112yes—
106#467—21no—
107#451—22no—
108#430—111no—
109#424—221no—
110#421—221no—
111#408C2×D1111yescharacteristic
112#365—222no—
113#362—222no—
114#349—112no—
115H(3,ℤ/4)—111no—
116C22×C11—21no—
117C22×C11—41no—
118C22×C11—42no—
119C22×C11—41no—
120C22×C11#45011yescharacteristic
121C4×C11—21no—
122C4×C11—41no—
123C4×C11—82no—
124C4×C11—82no—
125C4×C11#45311yescharacteristic
126C4×C11#45811yescharacteristic
127Dic11—82no—
128C2×#41C22⋊D1111yescharacteristic
129C22×Q8—21no—
130C2×Q16—21no—
131C2×Q16C22⋊D1112yes—
132C2×M16—221no—
133C2×M16C22×D1111yescharacteristic
134C22×C8C22⋊D1111yescharacteristic
135C4⋊Q8—41no—
136#124—41no—
137#123—41no—
138#123—41no—
139C22⋊Q8—22no—
140C22⋊Q8—22no—
141#117—21no—
142#117—221no—
143M32—222no—
144#108—222no—
145#107—21no—
146#106C22⋊D1112yes—
147C4⋊C8—442no—
148#104—442no—
149#103—22no—
150#103—22no—
151C22⋊C8—22no—
152C2×C11—21no—
153C2×C11—41no—
154C2×C11—81no—
155C2×C11#161311yescharacteristic
156#41—41no—
157#41—41no—
158C2×Q8—22no—
159C2×Q8—41no—
160C2×Q8—81no—
161C2×Q8—81no—
162C2×Q8#432411yescharacteristic
163C2×D4—21no—
164C2×D4#432411yescharacteristic
165C22×C4—21no—
166C22×C4—41no—
167C22×C4C2×C22⋊D1111yescharacteristic
168Q16—42no—
169Q16—81no—
170M16—41no—
171M16—441no—
172M16—441no—
173C2×C8—21no—
174C2×C8—41no—
175C2×C8—441no—
176C2×C8C2×C22⋊D1112yes—
177C4⋊C4—22no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—441no—
181C22⋊C4—41no—
182C22⋊C4—42no—
183C22⋊C4—42no—
184C22⋊C4—441no—
185C42—41no—
186C42—222no—
187C16—442no—
188C11#1230211yescharacteristic, complemented, Sylow
189C23—21no—
190C23#6698511yescharacteristic
191Q8—41no—
192Q8—42no—
193Q8—42no—
194Q8—82no—
195D4—41no—
196D4—81no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—82no—
205C2×C4—442no—
206C2×C4C2×#432411yescharacteristic
207C2×C4#6700611yescharacteristic
208C8—22no—
209C8—41no—
210C8—881no—
211C22—21no—
212C22—41no—
213C22—42no—
214C22—41no—
215C22#1062283111yescharacteristic
216C4—21no—
217C4—41no—
218C4—82no—
219C4—82no—
220C4—882no—
221C4#1062285411yescharacteristic
222C4#1062285611yescharacteristic
223C2—21no—
224C2—41no—
225C2—81no—
226C2#1306763611yescharacteristic
subgroupG/H
centerC2#13067636
commutator, cosocleC2×C11×M16C23
FrattiniC2×M16C22×D11
FittingC11×#3202C2
socleC2×C11#1613
prime radicalC2×C11×#41D4
hypercenter#3202D11
hypocenterC11#12302
LCSG ▷ C2×C11×M16 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3202

Complements

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

NH ≅ G/Ntype
1. #13070833C2semidirect
3. #13066604C2semidirect
188. C11#12302semidirect

Maximal subgroups

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

subgroupindex
#130708332
#130701692
#130666042
#130665542
C11×#32022
#1230211