Finite Group Databasebeta

← #14658913

Subgroups — #14658913

Order 2816.

248 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 85 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#13069340C211yesmaximal, characteristic
2#13068756C211yesmaximal, characteristic
3#13066519C211yesmaximal, characteristic
4#13066512C211yesmaximal, characteristic
5#13066511C211yesmaximal, characteristic
6#13066446C211yesmaximal, characteristic
7C11×#1303C211yesmaximal, characteristic
8C11×#431C2211yescharacteristic
9C11×#423C2211yescharacteristic
10C4×C11×C4⋊C4C2211yescharacteristic
11#10622538C2211yescharacteristic
12#10622537C2211yescharacteristic
13C2×C4⋊(C11⋊C8)—21no—
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15C2×#66867C2211yescharacteristic
16#10622196—21no—
17#10622196—21no—
18#10622162—21no—
19C2×C11×M16—21no—
20C2×C11×C4⋊C4—21no—
21C2×C42×C11—21no—
22C2×C42×C11C2311yescharacteristic
23C2×#4318—21no—
24C22×C11⋊C8—21no—
25C22×C11⋊C8D411yescharacteristic
26C22×C11⋊C8D411yescharacteristic
27C11×C4⋊C8—21no—
28C11×C4⋊C8—21no—
29C11×C4⋊C8—21no—
30C11×C22⋊C8—21no—
31C4×C8×C11—21no—
32C11×#95Q811yescharacteristic
33C11×#95Q811yescharacteristic
34C22⋊(C11⋊C8)—21no—
35C4⋊(C11⋊C8)—21no—
36C4⋊(C11⋊C8)—21no—
37C4⋊(C11⋊C8)—21no—
38C4⋊(C11⋊C8)—21no—
39C4⋊(C11⋊C8)—21no—
40C4⋊(C11⋊C8)—42no—
41#66867—21no—
42#66867—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
50C11×M16—41no—
51C11×M16—41no—
52C2×C8×C11—41no—
53C2×C8×C11—41no—
54C11×C4⋊C4—42no—
55C42×C11—41no—
56C42×C11—41no—
57C42×C11#4111yescharacteristic
58C42×C11#4111yescharacteristic
59C42×C11#4111yescharacteristic
60C42×C11#4111yescharacteristic
61#4318—41no—
62#4318—41no—
63C2×C11⋊C8—21no—
64C2×C11⋊C8—21no—
65C2×C11⋊C8—21no—
66C2×C11⋊C8—21no—
67C2×C11⋊C8—21no—
68C2×C11⋊C8—21no—
69C2×C11⋊C8—41no—
70C2×C11⋊C8—41no—
71C2×C11⋊C8—41no—
72C2×C11⋊C8—41no—
73C2×C11⋊C8—41no—
74#1940—111no—
75#1838—111no—
76#1303—111no—
77#1303D1111yescharacteristic
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—81no—
101C8×C11—81no—
102C11⋊C8—41no—
103C11⋊C8—41no—
104C11⋊C8—81no—
105C11⋊C8—81no—
106C11⋊C8—81no—
107#431—111no—
108#431C2×D1111yescharacteristic
109#423—111no—
110#423C2×D1111yescharacteristic
111C2×C4⋊C8—111no—
112C2×C4⋊C8—221no—
113C2×#97—111no—
114C4×C4⋊C4C2×D1111yescharacteristic
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—42no—
128C4×C11—81no—
129C4×C11#48211yescharacteristic
130C4×C11#48511yescharacteristic
131C4×C11#48811yescharacteristic
132C4×C11#48911yescharacteristic
133C2×M16—21no—
134C2×M16—221no—
135C22×C8—111no—
136C22×C8—111no—
137C22×C8—221no—
138C2×C4⋊C4—21no—
139C2×C42—21no—
140C2×C42C22×D1111yescharacteristic
141C4⋊C8—21no—
142C4⋊C8—21no—
143C4⋊C8—21no—
144C4⋊C8—221no—
145C4⋊C8—221no—
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#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×C4D4×D1111yescharacteristic
167C22×C4#434111yescharacteristic
168M16—41no—
169M16—41no—
170M16—441no—
171M16—441no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—221no—
175C2×C8—221no—
176C2×C8—221no—
177C2×C8—221no—
178C2×C8—221no—
179C2×C8—221no—
180C2×C8—441no—
181C2×C8—441no—
182C2×C8—441no—
183C2×C8—441no—
184C2×C8—441no—
185C4⋊C4—42no—
186C42—41no—
187C42—41no—
188C42#433911yescharacteristic
189C42#433911yescharacteristic
190C42#434111yescharacteristic
191C42#434311yescharacteristic
192C11#1068911yescharacteristic, complemented, Sylow
193C23#6693111yescharacteristic
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#6692311yescharacteristic
203C2×C4#6693211yescharacteristic
204C2×C4#6693811yescharacteristic
205C2×C4#6694311yescharacteristic
206C2×C4#6694711yescharacteristic
207C2×C4#6695111yescharacteristic
208C2×C4#6696411yescharacteristic
209C2×C4#6696811yescharacteristic
210C2×C4#6696911yescharacteristic
211C2×C4#6697211yescharacteristic
212C8—81no—
213C8—81no—
214C8—441no—
215C8—441no—
216C8—881no—
217C8—881no—
218C8—881no—
219C22—21no—
220C22—21no—
221C22#1062227311yescharacteristic
222C22#1062237611yescharacteristic
223C22#1062240911yescharacteristic
224C4—21no—
225C4—21no—
226C4—21no—
227C4—21no—
228C4—42no—
229C4—81no—
230C4#1062237811yescharacteristic
231C4#1062241311yescharacteristic
232C4#1062248011yescharacteristic
233C4#1062249811yescharacteristic
234C2—21no—
235C2—21no—
236C2#1307018911yescharacteristic
237C2#1307019411yescharacteristic
238C2#1307019911yescharacteristic
subgroupG/H
centerC2×C4#66938
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1303C2
socleC22×C11#400
prime radicalC23×C11C22⋊Q8
hypercenter#1303D11
hypocenterC11#10689
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

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
#130693402
#130687562
#130665192
#130665122
#130665112
#130664462
C11×#13032
#1068911