Finite Group Databasebeta

← #14666859

Subgroups — #14666859

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#13069966C211yesmaximal, characteristic
3#13067660C212yesmaximal
4#13066644C212yesmaximal
5C11×#1324C211yesmaximal, characteristic
6#10623031C2211yescharacteristic
7C11×#382C2211yescharacteristic
8#10622599C2212yes—
9#10622592—21no—
10#10622577—21no—
11#10622549—21no—
12#10622335—22no—
13#10622273—22no—
14#10622269—22no—
15C11×#324C2212yes—
16#10622168C2211yescharacteristic
17#10622161—21no—
18#10622105—22no—
19C22×Dic22—21no—
20C2×C11×C4⋊C4D411yescharacteristic
21C2×C11×C4⋊C4C2311yescharacteristic
22C2×C42×C11D411yescharacteristic
23#66979—21no—
24C2×C4⋊Dic11—21no—
25C2×C4⋊Dic11—21no—
26C2×C4⋊Dic11D412yes—
27#66977—22no—
28C2×Dic11⋊C4—22no—
29C2×#4318—21no—
30#66943—41no—
31#66941—41no—
32C11×C22⋊C8—22no—
33C11×#95—22no—
34C11⋊#95—22no—
35C11⋊#95—21no—
36C11⋊#95—22no—
37C11⋊#95—22no—
38C11⋊#95D412yes—
39#66882—42no—
40#66880—42no—
41#66872—41no—
42#66871—41no—
43#12261—111nomaximal, Sylow
44C22×C4×C11—21no—
45C22×C4×C11—21no—
46C22×C4×C11C2×D411yescharacteristic
47C22×C4×C11C2×D412yes—
48C22×Dic11—22no—
49C22×Dic11—22no—
50C2×Dic22—22no—
51C2×Dic22—82no—
52C2×Dic22—81no—
53C2×C8×C11—42no—
54C11×C4⋊C4—41no—
55C11×C4⋊C4—41no—
56C42×C11—21no—
57C42×C11Q1612yes—
58C22⋊Dic11—41no—
59C4⋊Dic11—21no—
60C4⋊Dic11—21no—
61C4⋊Dic11—22no—
62C4⋊Dic11—42no—
63C4⋊Dic11—81no—
64C4⋊Dic11—81no—
65Dic11⋊C4—42no—
66Dic11⋊C4—82no—
67C4×Dic11—41no—
68#4318—22no—
69#4318—41no—
70C2×C11⋊C8—41no—
71#2844—111no—
72#2061—111no—
73#1617—112no—
74#1353—112no—
75#1324D1111yescharacteristic
76C23×C11#12011yescharacteristic
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—41no—
82C2×C4×C11—41no—
83C2×C4×C11—42no—
84C2×C4×C11—42no—
85C2×C4×C11—41no—
86C2×C4×C11C2×Q1611yescharacteristic
87C2×C4×C11#13711yescharacteristic
88C2×Dic11—42no—
89C2×Dic11—42no—
90C2×Dic11—42no—
91C2×Dic11—42no—
92C2×Dic11—42no—
93C2×Dic11—41no—
94C2×Dic11—41no—
95C2×Dic11—42no—
96Dic22—84no—
97Dic22—82no—
98C8×C11—82no—
99C11⋊C8—42no—
100#544—111no—
101#484—222no—
102#428—221no—
103#400—112no—
104#400—222no—
105#395—222no—
106#395—221no—
107#382—221no—
108#382C2×D1111yescharacteristic
109#343—111no—
110#339—221no—
111#328—222no—
112#324C2×D1112yes—
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—
123Dic11—82no—
124Dic11—81no—
125Dic11—82no—
126Dic11—81no—
127C22×Q8—221no—
128C2×M16—221no—
129C4⋊Q8—441no—
130#125—441no—
131C22⋊Q8—222no—
132#117—221no—
133C2×C4⋊C4—112no—
134C2×C4⋊C4—221no—
135C2×C4⋊C4—221no—
136C2×C4⋊C4—222no—
137C2×C4⋊C4D4411yescharacteristic
138C2×C4⋊C4C22×D1111yescharacteristic
139C2×C42D4411yescharacteristic
140#107—441no—
141#107—442no—
142#106—441no—
143#103—442no—
144C22⋊C8—22no—
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—222no—
157C2×Q8—882no—
158C2×Q8—881no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—222no—
162C22×C4—222no—
163C22×C4C2×D4411yescharacteristic
164C22×C4D4×D1112yes—
165M16—222no—
166M16—441no—
167C2×C8—42no—
168C2×C8—441no—
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—221no—
172C4⋊C4—221no—
173C4⋊C4—222no—
174C4⋊C4—442no—
175C4⋊C4—442no—
176C4⋊C4—882no—
177C4⋊C4—881no—
178C4⋊C4—881no—
179C22⋊C4—441no—
180C42—21no—
181C42—441no—
182C42Dic4412yes—
183C11#1226111yescharacteristic, complemented, Sylow
184C23#6693511yescharacteristic
185Q8—882no—
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—442no—
197C2×C4—442no—
198C2×C4—442no—
199C2×C4—442no—
200C2×C4—441no—
201C2×C4—441no—
202C2×C4—442no—
203C2×C4—442no—
204C2×C4C2×Dic4411yescharacteristic
205C2×C4#6696211yescharacteristic
206C8—82no—
207C8—442no—
208C22—21no—
209C22—21no—
210C22#1062235211yescharacteristic
211C22#1062235411yescharacteristic
212C22#1062236511yescharacteristic
213C4—21no—
214C4—21no—
215C4—42no—
216C4—42no—
217C4—81no—
218C4—882no—
219C4—881no—
220C4—882no—
221C4—881no—
222C2—21no—
223C2—21no—
224C2#1306759211yescharacteristic
225C2#1307063111yescharacteristic
226C2#1307063411yescharacteristic
subgroupG/H
centerC22#10622354
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1324C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#1324D11
hypocenterC11#12261
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

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
#130699662
#130676602
#130666442
C11×#13242
#1226111