Finite Group Databasebeta

← #14658908

Subgroups — #14658908

Order 2816.

248 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 87 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#13068757C211yesmaximal, characteristic
2#13066519C211yesmaximal, characteristic
3#13066519C211yesmaximal, characteristic
4#13066513C211yesmaximal, characteristic
5#13066513C211yesmaximal, characteristic
6#13066447C211yesmaximal, characteristic
7C11×#1940C211yesmaximal, characteristic
8C2×C11×C4⋊C8—21no—
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×#97C2211yescharacteristic
11C4×C11×C4⋊C4C2211yescharacteristic
12#10622538C2211yescharacteristic
13#10622538C2211yescharacteristic
14#10622537C2211yescharacteristic
15#10622537C2211yescharacteristic
16C11×#336—21no—
17#10622190—21no—
18#10622190—21no—
19C22×C8×C11—21no—
20C22×C8×C11D411yescharacteristic
21C22×C8×C11D411yescharacteristic
22C2×C11×C4⋊C4—21no—
23C2×C42×C11—21no—
24C2×C42×C11C2311yescharacteristic
25C2×#4318—21no—
26C2×#4318—21no—
27C11×C4⋊C8—21no—
28C11×C4⋊C8—21no—
29C11×C4⋊C8—42no—
30C11×#97—21no—
31C11×#97—21no—
32C11×#95Q811yescharacteristic
33C11×#95Q811yescharacteristic
34C22⋊(C11⋊C8)—21no—
35C22⋊(C11⋊C8)—21no—
36C4⋊(C11⋊C8)—21no—
37C4⋊(C11⋊C8)—21no—
38C4⋊(C11⋊C8)—21no—
39C4⋊(C11⋊C8)—21no—
40C4⋊(C11⋊C8)—21no—
41C4⋊(C11⋊C8)—21no—
42C4×C11⋊C8—21no—
43C4×C11⋊C8—21no—
44#10689—111nomaximal, Sylow
45C22×C4×C11—21no—
46C22×C4×C11—21no—
47C22×C4×C11C2×D411yescharacteristic
48C22×C4×C11C2×Q811yescharacteristic
49C22×C4×C11#4111yescharacteristic
50C2×C8×C11—21no—
51C2×C8×C11—21no—
52C2×C8×C11—21no—
53C2×C8×C11—21no—
54C2×C8×C11—21no—
55C2×C8×C11—21no—
56C2×C8×C11—41no—
57C2×C8×C11—41no—
58C2×C8×C11—41no—
59C11×C4⋊C4—42no—
60C42×C11—41no—
61C42×C11—41no—
62C42×C11#4111yescharacteristic
63C42×C11#4111yescharacteristic
64C42×C11#4111yescharacteristic
65C42×C11#4111yescharacteristic
66#4318—41no—
67#4318—41no—
68#4318—41no—
69#4318—41no—
70C2×C11⋊C8—41no—
71C2×C11⋊C8—41no—
72C2×C11⋊C8—41no—
73C2×C11⋊C8—41no—
74#1940D1111yescharacteristic
75#1838—111no—
76#1303—111no—
77#1303—111no—
78#1301—111no—
79#1301—111no—
80#1275—111no—
81C23×C11C22⋊Q811yescharacteristic
82C2×C4×C11—22no—
83C2×C4×C11—41no—
84C2×C4×C11—41no—
85C2×C4×C11—41no—
86C2×C4×C11—41no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11—41no—
90C2×C4×C11#12311yescharacteristic
91C2×C4×C11#12411yescharacteristic
92C2×C4×C11#12511yescharacteristic
93C2×C4×C11#12511yescharacteristic
94C2×C4×C11#12611yescharacteristic
95C2×C4×C11#12611yescharacteristic
96C2×C4×C11#13511yescharacteristic
97C2×C4×C11#13511yescharacteristic
98C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
99C2×C4×C11#13711yescharacteristic
100C8×C11—41no—
101C8×C11—41no—
102C8×C11—81no—
103C11⋊C8—81no—
104C11⋊C8—81no—
105C11⋊C8—81no—
106C11⋊C8—81no—
107#431—111no—
108#431—111no—
109#423—111no—
110#423—111no—
111C2×C4⋊C8—21no—
112C2×C4⋊C8C2×D1111yescharacteristic
113C2×#97C2×D1111yescharacteristic
114C4×C4⋊C4C2×D1111yescharacteristic
115#341—221no—
116#341—221no—
117#336—21no—
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—42no—
128C4×C11—81no—
129C4×C11#48211yescharacteristic
130C4×C11#48511yescharacteristic
131C4×C11#48811yescharacteristic
132C4×C11#48911yescharacteristic
133C2×M16—221no—
134C2×M16—221no—
135C22×C8—21no—
136C22×C8C22⋊D1111yescharacteristic
137C22×C8C22⋊D1111yescharacteristic
138C2×C4⋊C4—21no—
139C2×C42—21no—
140C2×C42C22×D1111yescharacteristic
141C4⋊C8—21no—
142C4⋊C8—21no—
143C4⋊C8—42no—
144C4⋊C8—221no—
145C4⋊C8—221no—
146C4⋊C8—221no—
147C4⋊C8—221no—
148C4⋊C8—221no—
149C4⋊C8—221no—
150C22⋊C8—221no—
151C22⋊C8—221no—
152#97—21no—
153#97—21no—
154C4×C8—221no—
155C4×C8—221no—
156#95Dic2211yescharacteristic
157#95Dic2211yescharacteristic
158C2×C11—21no—
159C2×C11—21no—
160C2×C11#210111yescharacteristic
161C2×C11#210211yescharacteristic
162C2×C11#210311yescharacteristic
163C22×C4—21no—
164C22×C4—21no—
165C22×C4C2×Dic2211yescharacteristic
166C22×C4#433911yescharacteristic
167C22×C4C2×C22⋊D1111yescharacteristic
168M16—441no—
169M16—441no—
170M16—441no—
171M16—441no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—441no—
182C2×C8—441no—
183C2×C8—441no—
184C2×C8—441no—
185C4⋊C4—42no—
186C42—41no—
187C42—41no—
188C42#434111yescharacteristic
189C42#434111yescharacteristic
190C42#434311yescharacteristic
191C42#434311yescharacteristic
192C11#1068911yescharacteristic, complemented, Sylow
193C23#6697711yescharacteristic
194C2×C4—22no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4#6694311yescharacteristic
203C2×C4#6694311yescharacteristic
204C2×C4#6695111yescharacteristic
205C2×C4#6695111yescharacteristic
206C2×C4#6698511yescharacteristic
207C2×C4#6698811yescharacteristic
208C2×C4#6699511yescharacteristic
209C2×C4#6700011yescharacteristic
210C2×C4#6700311yescharacteristic
211C2×C4#6700311yescharacteristic
212C8—41no—
213C8—41no—
214C8—81no—
215C8—881no—
216C8—881no—
217C8—881no—
218C8—881no—
219C22—21no—
220C22—21no—
221C22#1062259911yescharacteristic
222C22#1062262211yescharacteristic
223C22#1062263511yescharacteristic
224C4—21no—
225C4—21no—
226C4—21no—
227C4—21no—
228C4—42no—
229C4—81no—
230C4#1062264811yescharacteristic
231C4#1062265811yescharacteristic
232C4#1062268111yescharacteristic
233C4#1062270211yescharacteristic
234C2—21no—
235C2—21no—
236C2#1307018411yescharacteristic
237C2#1307019111yescharacteristic
238C2#1307019611yescharacteristic
subgroupG/H
centerC2×C4#67000
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1940C2
socleC22×C11#400
prime radicalC23×C11C22⋊Q8
hypercenter#1940D11
hypocenterC11#10689
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1940

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
#130687572
#130665192
#130665132
#130664472
C11×#19402
#1068911