Finite Group Databasebeta

← #14666856

Subgroups — #14666856

Order 2816.

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

normal subgroups only

This group has 330 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#13076888C211yesmaximal, characteristic
2#13067658C212yesmaximal
3#13066642C212yesmaximal
4#13066560C211yesmaximal, characteristic
5C11×#2061C211yesmaximal, characteristic
6C11×#544C2211yescharacteristic
7C11×#428—21no—
8C11×#382C2211yescharacteristic
9#10622657—22no—
10#10622599C2212yes—
11#10622592—21no—
12#10622549—21no—
13#10622273—22no—
14#10622269—22no—
15C11×#343C2211yescharacteristic
16C11×#339—21no—
17#10622176—22no—
18#10622166C2212yes—
19C22×Dic22—21no—
20C2×C11×M16—21no—
21C11×C4⋊Q8—41no—
22C11×#125—41no—
23C11×C22⋊Q8—22no—
24C11×#117—21no—
25C2×C11×C4⋊C4D411yescharacteristic
26C2×C11×C4⋊C4C2311yescharacteristic
27C2×C42×C11D411yescharacteristic
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11D412yes—
31C2×Dic11⋊C4—22no—
32C11×#107—41no—
33C11×#106—41no—
34C11×#95—22no—
35#66899—42no—
36C11⋊#95—22no—
37C11⋊#95—21no—
38C11⋊#95—22no—
39C11⋊#95—22no—
40C11⋊#95D412yes—
41C22⋊(C11⋊C8)—22no—
42#66871—42no—
43#12261—111nomaximal, Sylow
44C2×Q8×C11—22no—
45C22×C4×C11—21no—
46C22×C4×C11—21no—
47C22×C4×C11C2×D411yescharacteristic
48C22×C4×C11C2×D412yes—
49C22×Dic11—22no—
50C22×Dic11—22no—
51C2×Dic22—82no—
52C2×Dic22—81no—
53C11×M16—22no—
54C11×M16—41no—
55C2×C8×C11—41no—
56C11×C4⋊C4—22no—
57C11×C4⋊C4—21no—
58C11×C4⋊C4—21no—
59C11×C4⋊C4—41no—
60C11×C4⋊C4—42no—
61C11×C4⋊C4—41no—
62C11×C22⋊C4—41no—
63C42×C11—21no—
64C42×C11—41no—
65C42×C11Q1612yes—
66C4⋊Dic11—42no—
67C4⋊Dic11—81no—
68C4⋊Dic11—81no—
69Dic11⋊C4—82no—
70C2×C11⋊C8—42no—
71#2844—111no—
72#2061D1111yescharacteristic
73#1617—112no—
74#1353—112no—
75#1324—111no—
76C23×C11#12011yescharacteristic
77Q8×C11—82no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—41no—
83C2×C4×C11—41no—
84C2×C4×C11—42no—
85C2×C4×C11—42no—
86C2×C4×C11—41no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11C2×Q1611yescharacteristic
90C2×C4×C11#13711yescharacteristic
91C2×Dic11—42no—
92C2×Dic11—42no—
93C2×Dic11—42no—
94C2×Dic11—42no—
95C2×Dic11—42no—
96C2×Dic11—42no—
97Dic22—84no—
98C8×C11—42no—
99C11⋊C8—82no—
100#544C2×D1111yescharacteristic
101#484—222no—
102#428—21no—
103#400—112no—
104#400—222no—
105#395—222no—
106#395—221no—
107#382—221no—
108#382C2×D1111yescharacteristic
109#343C2×D1111yescharacteristic
110#339—21no—
111#328—222no—
112#324—112no—
113C22×C11—21no—
114C22×C11—21no—
115C22×C11#45111yescharacteristic
116C22×C11#45611yescharacteristic
117C22×C11B(4,𝔽2)11yescharacteristic
118C4×C11—21no—
119C4×C11—21no—
120C4×C11—42no—
121C4×C11—42no—
122C4×C11—81no—
123C4×C11—81no—
124C4×C11—81no—
125Dic11—82no—
126Dic11—82no—
127C22×Q8—221no—
128C2×M16—21no—
129C4⋊Q8—41no—
130#125—41no—
131C22⋊Q8—22no—
132#117—21no—
133C2×C4⋊C4—112no—
134C2×C4⋊C4—221no—
135C2×C4⋊C4—221no—
136C2×C4⋊C4—222no—
137C2×C4⋊C4C22⋊D1111yescharacteristic
138C2×C4⋊C4C22×D1111yescharacteristic
139C2×C42C22⋊D1111yescharacteristic
140#107—41no—
141#107—442no—
142#106—41no—
143#103—442no—
144C22⋊C8—222no—
145#95—22no—
146#95—112no—
147#95—222no—
148#95—221no—
149#95—222no—
150#95—222no—
151C2×C11—21no—
152C2×C11—21no—
153C2×C11#160511yescharacteristic
154C2×C11#220111yescharacteristic
155C2×C11#220211yescharacteristic
156C2×Q8—22no—
157C2×Q8—882no—
158C2×Q8—881no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—222no—
162C22×C4—222no—
163C22×C4D4×D1112yes—
164C22×C4C2×C22⋊D1111yescharacteristic
165M16—22no—
166M16—41no—
167C2×C8—41no—
168C2×C8—442no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—22no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—42no—
175C4⋊C4—442no—
176C4⋊C4—882no—
177C4⋊C4—881no—
178C4⋊C4—881no—
179C22⋊C4—41no—
180C42—21no—
181C42—41no—
182C42#432612yes—
183C11#1226111yescharacteristic, complemented, Sylow
184C23#6699011yescharacteristic
185Q8—82no—
186Q8—884no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—442no—
199C2×C4—442no—
200C2×C4—442no—
201C2×C4—442no—
202C2×C4—442no—
203C2×C4—442no—
204C2×C4C2×#432611yescharacteristic
205C2×C4#6700411yescharacteristic
206C8—42no—
207C8—882no—
208C22—21no—
209C22—21no—
210C22#1062264511yescharacteristic
211C22#1062266311yescharacteristic
212C22#1062270811yescharacteristic
213C4—21no—
214C4—21no—
215C4—42no—
216C4—42no—
217C4—81no—
218C4—81no—
219C4—81no—
220C4—882no—
221C4—882no—
222C2—21no—
223C2—21no—
224C2#1306758911yescharacteristic
225C2#1307062811yescharacteristic
226C2#1307063211yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2061C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#2061D11
hypocenterC11#12261
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2061

Complements

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

NH ≅ G/Ntype
183. C11#12261semidirect

Maximal subgroups

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

subgroupindex
#130768882
#130676582
#130666422
#130665602
C11×#20612
#1226111