Finite Group Databasebeta

← #14658912

Subgroups — #14658912

Order 2816.

248 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 83 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#13069337C211yesmaximal, characteristic
2#13068756C211yesmaximal, characteristic
3#13066518C211yesmaximal, characteristic
4#13066517C211yesmaximal, characteristic
5#13066513C211yesmaximal, characteristic
6#13066446C211yesmaximal, characteristic
7C11×#1301C211yesmaximal, characteristic
8C11×#431C2211yescharacteristic
9C11×#423C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×Dic11⋊C8—21no—
12C4×C4⋊Dic11C2211yescharacteristic
13#10622538C2211yescharacteristic
14#10622537C2211yescharacteristic
15C2×#66867C2211yescharacteristic
16#10622196—21no—
17#10622196—21no—
18#10622188—21no—
19C2×C11×M16—21no—
20C22×C8×C11—21no—
21C2×C42×C11C2311yescharacteristic
22C2×C4⋊Dic11—21no—
23C2×C4×Dic11—21no—
24C2×#4318—21no—
25C22×C11⋊C8D411yescharacteristic
26C22×C11⋊C8D411yescharacteristic
27C11×C4⋊C8—21no—
28C11×C4⋊C8—21no—
29C11×C4⋊C8—21no—
30C11×C4⋊C8—21no—
31C11×C4⋊C8—21no—
32C11×C22⋊C8—21no—
33C4×C8×C11—21no—
34C11⋊#95Q811yescharacteristic
35C11⋊#95Q811yescharacteristic
36C22⋊(C11⋊C8)—21no—
37Dic11⋊C8—42no—
38C4⋊(C11⋊C8)—21no—
39C4⋊(C11⋊C8)—21no—
40C4⋊(C11⋊C8)—21no—
41#66867—21no—
42#66867—21no—
43C4×C11⋊C8—21no—
44#10689—111nomaximal, Sylow
45C22×C4×C11C2×D411yescharacteristic
46C22×C4×C11C2×Q811yescharacteristic
47C22×C4×C11#4111yescharacteristic
48C22×Dic11—21no—
49C22×Dic11—21no—
50C11×M16—41no—
51C11×M16—41no—
52C2×C8×C11—41no—
53C2×C8×C11—41no—
54C2×C8×C11—41no—
55C2×C8×C11—41no—
56C2×C8×C11—41no—
57C42×C11#4111yescharacteristic
58C42×C11#4111yescharacteristic
59C42×C11#4111yescharacteristic
60C42×C11#4111yescharacteristic
61C4⋊Dic11—42no—
62C4×Dic11—41no—
63C4×Dic11—41no—
64#4318—41no—
65#4318—41no—
66C2×C11⋊C8—21no—
67C2×C11⋊C8—21no—
68C2×C11⋊C8—21no—
69C2×C11⋊C8—21no—
70C2×C11⋊C8—21no—
71C2×C11⋊C8—21no—
72C2×C11⋊C8—41no—
73C2×C11⋊C8—41no—
74#1940—111no—
75#1838—111no—
76#1303—111no—
77#1303—111no—
78#1301—111no—
79#1301D1111yescharacteristic
80#1275—111no—
81C23×C11C22⋊Q811yescharacteristic
82C2×C4×C11—41no—
83C2×C4×C11—41no—
84C2×C4×C11#12311yescharacteristic
85C2×C4×C11#12411yescharacteristic
86C2×C4×C11#12511yescharacteristic
87C2×C4×C11#12511yescharacteristic
88C2×C4×C11#12611yescharacteristic
89C2×C4×C11#12611yescharacteristic
90C2×C4×C11#13511yescharacteristic
91C2×C4×C11#13511yescharacteristic
92C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
93C2×C4×C11#13711yescharacteristic
94C2×Dic11—22no—
95C2×Dic11—41no—
96C2×Dic11—41no—
97C2×Dic11—41no—
98C2×Dic11—41no—
99C2×Dic11—41no—
100C8×C11—81no—
101C8×C11—81no—
102C8×C11—81no—
103C11⋊C8—41no—
104C11⋊C8—41no—
105C11⋊C8—81no—
106C11⋊C8—81no—
107#431—111no—
108#431C2×D1111yescharacteristic
109#423—111no—
110#423C2×D1111yescharacteristic
111C2×C4⋊C8—221no—
112C2×C4⋊C8C2×D1111yescharacteristic
113C2×#97—111no—
114C4×C4⋊C4—111no—
115#341—221no—
116#341—221no—
117#336—221no—
118C22×C11—21no—
119C22×C11—21no—
120C22×C11#40011yescharacteristic
121C22×C11#47811yescharacteristic
122C22×C11#47911yescharacteristic
123C4×C11—21no—
124C4×C11—21no—
125C4×C11—21no—
126C4×C11—21no—
127C4×C11#48211yescharacteristic
128C4×C11#48511yescharacteristic
129C4×C11#48811yescharacteristic
130C4×C11#48911yescharacteristic
131Dic11—42no—
132Dic11—81no—
133C2×M16—21no—
134C2×M16—221no—
135C22×C8—21no—
136C22×C8—111no—
137C22×C8—111no—
138C2×C4⋊C4—221no—
139C2×C42—221no—
140C2×C42C22×D1111yescharacteristic
141C4⋊C8—21no—
142C4⋊C8—21no—
143C4⋊C8—21no—
144C4⋊C8—21no—
145C4⋊C8—21no—
146C4⋊C8—221no—
147C4⋊C8—221no—
148C4⋊C8—221no—
149C4⋊C8—442no—
150C22⋊C8—21no—
151C22⋊C8—221no—
152#97—221no—
153#97—221no—
154C4×C8—21no—
155C4×C8—221no—
156#95—111no—
157#95—111no—
158C2×C11—21no—
159C2×C11—21no—
160C2×C11#210111yescharacteristic
161C2×C11#210211yescharacteristic
162C2×C11#210311yescharacteristic
163C22×C4—221no—
164C22×C4—221no—
165C22×C4#433911yescharacteristic
166C22×C4D4×D1111yescharacteristic
167C22×C4Q8×D1111yescharacteristic
168M16—41no—
169M16—41no—
170M16—441no—
171M16—441no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—221no—
178C2×C8—221no—
179C2×C8—221no—
180C2×C8—221no—
181C2×C8—221no—
182C2×C8—221no—
183C2×C8—441no—
184C2×C8—441no—
185C4⋊C4—442no—
186C42—441no—
187C42—441no—
188C42#433911yescharacteristic
189C42#433911yescharacteristic
190C42#434111yescharacteristic
191C42#434111yescharacteristic
192C11#1068911yescharacteristic, complemented, Sylow
193C23#6694911yescharacteristic
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—222no—
197C2×C4—441no—
198C2×C4—441no—
199C2×C4—441no—
200C2×C4—441no—
201C2×C4—441no—
202C2×C4#6692911yescharacteristic
203C2×C4#6693211yescharacteristic
204C2×C4#6693611yescharacteristic
205C2×C4#6693811yescharacteristic
206C2×C4#6694211yescharacteristic
207C2×C4#6694211yescharacteristic
208C2×C4#6696411yescharacteristic
209C2×C4#6696811yescharacteristic
210C2×C4#6696911yescharacteristic
211C2×C4#6697211yescharacteristic
212C8—81no—
213C8—81no—
214C8—81no—
215C8—441no—
216C8—441no—
217C8—881no—
218C8—881no—
219C22—21no—
220C22—21no—
221C22#1062227111yescharacteristic
222C22#1062247011yescharacteristic
223C22#1062250411yescharacteristic
224C4—21no—
225C4—21no—
226C4—21no—
227C4—21no—
228C4—442no—
229C4—881no—
230C4#1062237811yescharacteristic
231C4#1062239211yescharacteristic
232C4#1062241311yescharacteristic
233C4#1062242711yescharacteristic
234C2—21no—
235C2—21no—
236C2#1307018811yescharacteristic
237C2#1307019311yescharacteristic
238C2#1307019811yescharacteristic
subgroupG/H
centerC2×C4#66938
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1301C2
socleC22×C11#400
prime radicalC23×C11C22⋊Q8
hypercenter#1301D11
hypocenterC11#10689
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
192. C11#10689semidirect

Maximal subgroups

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

subgroupindex
#130693372
#130687562
#130665182
#130665172
#130665132
#130664462
C11×#13012
#1068911