Finite Group Databasebeta

← #14667122

Subgroups — #14667122

Order 2816.

310 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 55 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#13079511C211yesmaximal, characteristic
2#13070836C212yesmaximal, complemented
3#13070169C211yesmaximal, characteristic
4#13066605C212yesmaximal, complemented
5C11×#1321C211yesmaximal, characteristic
6#10623356—21no—
7C11×#408C2211yescharacteristic
8#10622849—21no—
9#10622750C2212yes—
10#10622738C2211yescharacteristic
11#10622729—21no—
12#10622715—21no—
13#10622352—22no—
14#10622336—22no—
15C11×#349C2212yes—
16#10622195C2211yescharacteristic
17#10622155—22no—
18#10622151—22no—
19C2×C11×#41D411yescharacteristic
20C22×Dic22—21no—
21C2×C11×M16C2311yescharacteristic
22C22×C8×C11D411yescharacteristic
23#66997—41no—
24#66989—41no—
25#66988—41no—
26#66988—41no—
27#66979—21no—
28#66979—21no—
29#66977—22no—
30#66977—22no—
31C2×#4318—21no—
32C2×Dic44—21no—
33C2×Dic44D412yes—
34C11×M32—22no—
35C11×C22⋊C8—22no—
36#66901—42no—
37#66883—22no—
38#66882—21no—
39#66881D412yes—
40#66880—22no—
41#66880—22no—
42Dic11⋊C8—42no—
43#12302—111nomaximal, Sylow
44C11×#41—41no—
45C11×#41—41no—
46C2×Q8×C11SD1611yescharacteristic
47C2×D4×C11—21no—
48C2×D4×C11SD1611yescharacteristic
49C22×C4×C11—21no—
50C22×C4×C11C2×D411yescharacteristic
51C22×Dic11—41no—
52C2×Dic22—22no—
53C2×Dic22—41no—
54C2×Dic22—81no—
55C2×Dic22—81no—
56C11×M16—41no—
57C2×C8×C11—21no—
58C2×C8×C11—41no—
59C2×C8×C11C2×D412yes—
60C22⋊Dic11—42no—
61C22⋊Dic11—41no—
62C22⋊Dic11—42no—
63C22⋊Dic11—41no—
64C4⋊Dic11—22no—
65C4⋊Dic11—41no—
66Dic11⋊C4—42no—
67Dic11⋊C4—42no—
68C4×Dic11—22no—
69C4×Dic11—41no—
70#4318—41no—
71#4318—41no—
72C2×C11⋊C8—41no—
73Dic44—42no—
74Dic44—81no—
75C11×C16—42no—
76#3202—111no—
77#2239—112no—
78#2098—111no—
79#1340—112no—
80#1321D1111yescharacteristic
81C23×C11—21no—
82C23×C11AGL(1,ℤ/8)11yescharacteristic
83Q8×C11—41no—
84D4×C11—41no—
85D4×C11—81no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11#12011yescharacteristic
92C2×C4×C11C2×SD1611yescharacteristic
93C2×Dic11—42no—
94C2×Dic11—42no—
95C2×Dic11—42no—
96C2×Dic11—82no—
97Dic22—42no—
98Dic22—42no—
99Dic22—82no—
100C8×C11—22no—
101C8×C11—41no—
102C11⋊C8—81no—
103#536—221no—
104#485—222no—
105#470—112no—
106#467—221no—
107#451—222no—
108#430—111no—
109#424—221no—
110#421—221no—
111#408C2×D1111yescharacteristic
112#365—222no—
113#362—222no—
114#349C2×D1112yes—
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#45311yescharacteristic
124C4×C11#45811yescharacteristic
125Dic11—82no—
126Dic11—82no—
127Dic11—82no—
128C2×#41D4411yescharacteristic
129C22×Q8—221no—
130C2×Q16—112no—
131C2×Q16—221no—
132C2×M16—221no—
133C2×M16C22×D1111yescharacteristic
134C22×C8D4411yescharacteristic
135C4⋊Q8—441no—
136#124—441no—
137#123—441no—
138#123—441no—
139C22⋊Q8—222no—
140C22⋊Q8—222no—
141#117—221no—
142#117—221no—
143M32—22no—
144#108—222no—
145#107—221no—
146#106—112no—
147C4⋊C8—442no—
148#104—442no—
149#103—222no—
150#103—222no—
151C22⋊C8—22no—
152C2×C11—21no—
153C2×C11—41no—
154C2×C11—81no—
155C2×C11#161311yescharacteristic
156#41—41no—
157#41—41no—
158C2×Q8—222no—
159C2×Q8—441no—
160C2×Q8—881no—
161C2×Q8—881no—
162C2×Q8#431411yescharacteristic
163C2×D4—21no—
164C2×D4#431411yescharacteristic
165C22×C4—21no—
166C22×C4—441no—
167C22×C4C2×D4411yescharacteristic
168Q16—442no—
169Q16—881no—
170M16—41no—
171M16—441no—
172M16—441no—
173C2×C8—21no—
174C2×C8—41no—
175C2×C8—441no—
176C2×C8D4×D1112yes—
177C4⋊C4—222no—
178C4⋊C4—441no—
179C4⋊C4—442no—
180C4⋊C4—442no—
181C22⋊C4—441no—
182C22⋊C4—442no—
183C22⋊C4—441no—
184C22⋊C4—442no—
185C42—222no—
186C42—441no—
187C16—42no—
188C11#1230211yescharacteristic, complemented, Sylow
189C23—21no—
190C23#6696111yescharacteristic
191Q8—41no—
192Q8—442no—
193Q8—442no—
194Q8—882no—
195D4—41no—
196D4—81no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—442no—
203C2×C4—442no—
204C2×C4—442no—
205C2×C4—882no—
206C2×C4#6693511yescharacteristic
207C2×C4C2×#431411yescharacteristic
208C8—22no—
209C8—41no—
210C8—881no—
211C22—21no—
212C22—41no—
213C22—42no—
214C22—41no—
215C22#1062234411yescharacteristic
216C4—21no—
217C4—41no—
218C4—882no—
219C4—882no—
220C4—882no—
221C4#1062235511yescharacteristic
222C4#1062236011yescharacteristic
223C2—21no—
224C2—41no—
225C2—81no—
226C2#1306763811yescharacteristic
subgroupG/H
centerC2#13067638
commutator, cosocleC2×C11×M16C23
FrattiniC2×M16C22×D11
FittingC11×#1321C2
socleC2×C11#1613
prime radicalC2×C11×#41D4
hypercenter#1321D11
hypocenterC11#12302
LCSG ▷ C2×C11×M16 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1321

Complements

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

NH ≅ G/Ntype
2. #13070836C2semidirect
4. #13066605C2semidirect
188. C11#12302semidirect

Maximal subgroups

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

subgroupindex
#130795112
#130708362
#130701692
#130666052
C11×#13212
#1230211