Finite Group Databasebeta

← #14666854

Subgroups — #14666854

Order 2816.

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

normal subgroups only

This group has 342 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#13067592C212yesmaximal
4#13066647C212yesmaximal
5C11×#1324C211yesmaximal, characteristic
6#10623031C2211yescharacteristic
7C11×#382C2211yescharacteristic
8#10622599—21no—
9#10622592C2212yes—
10#10622577—21no—
11#10622549—21no—
12#10622352—22no—
13#10622273—22no—
14#10622269—22no—
15C11×#324C2212yes—
16#10622168C2211yescharacteristic
17#10622161—21no—
18#10622105—22no—
19C22×Dic22D412yes—
20C2×C11×C4⋊C4D411yescharacteristic
21C2×C11×C4⋊C4C2311yescharacteristic
22C2×C42×C11D411yescharacteristic
23#66979—21no—
24C2×C4⋊Dic11—21no—
25C2×C4⋊Dic11—21no—
26C2×C4⋊Dic11—21no—
27#66977—22no—
28C2×Dic11⋊C4—22no—
29C2×#4318—21no—
30C2×Dic44—42no—
31#66943—41no—
32#66941—41no—
33C11×C22⋊C8—22no—
34C11×#95—22no—
35C11⋊#95—22no—
36C11⋊#95—22no—
37C11⋊#95—21no—
38C11⋊#95—22no—
39C11⋊#95D412yes—
40#66880—42no—
41#66872—41no—
42#66871—41no—
43#12260—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—42no—
52C2×Dic22—82no—
53C2×C8×C11—42no—
54C11×C4⋊C4—41no—
55C11×C4⋊C4—41no—
56C42×C11—21no—
57C42×C11Q1612yescomplemented
58C22⋊Dic11—41no—
59C4⋊Dic11—21no—
60C4⋊Dic11—21no—
61C4⋊Dic11—22no—
62C4⋊Dic11—81no—
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—
71Dic44—84no—
72#2844—111no—
73#2061—111no—
74#1605—112no—
75#1354—112no—
76#1324D1111yescharacteristic
77C23×C11#12011yescharacteristic
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×C11C2×Q1611yescharacteristic
88C2×C4×C11#13711yescharacteristic
89C2×Dic11—42no—
90C2×Dic11—42no—
91C2×Dic11—42no—
92C2×Dic11—42no—
93C2×Dic11—42no—
94C2×Dic11—41no—
95C2×Dic11—41no—
96C2×Dic11—42no—
97Dic22—44no—
98Dic22—82no—
99Dic22—82no—
100C8×C11—82no—
101C11⋊C8—42no—
102#544—111no—
103#451—222no—
104#428—221no—
105#400—222no—
106#400—221no—
107#395—112no—
108#395—222no—
109#382—221no—
110#382C2×D1111yescharacteristic
111#343—111no—
112#339—221no—
113#328—222no—
114#324C2×D1112yes—
115C22×C11—21no—
116C22×C11—21no—
117C22×C11#45111yescharacteristic
118C22×C11#45611yescharacteristic
119C22×C11B(4,𝔽2)11yescharacteristic
120C4×C11—21no—
121C4×C11—21no—
122C4×C11—42no—
123C4×C11—42no—
124C4×C11—81no—
125Dic11—82no—
126Dic11—82no—
127Dic11—81no—
128Dic11—81no—
129C22×Q8—112no—
130C2×Q16—442no—
131C2×M16—221no—
132C4⋊Q8—441no—
133#125—441no—
134C22⋊Q8—222no—
135#117—221no—
136C2×C4⋊C4—221no—
137C2×C4⋊C4—221no—
138C2×C4⋊C4—221no—
139C2×C4⋊C4—222no—
140C2×C4⋊C4D4411yescharacteristic
141C2×C4⋊C4C22×D1111yescharacteristic
142C2×C42D4411yescharacteristic
143#107—441no—
144#106—441no—
145#103—442no—
146C22⋊C8—22no—
147#95—22no—
148#95—112no—
149#95—222no—
150#95—222no—
151#95—221no—
152#95—222no—
153C2×C11—21no—
154C2×C11—21no—
155C2×C11#160511yescharacteristic
156C2×C11#219911yescharacteristic
157C2×C11#220311yescharacteristic
158C2×Q8—222no—
159C2×Q8—442no—
160C2×Q8—882no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—222no—
164C22×C4—222no—
165C22×C4C2×D4411yescharacteristic
166C22×C4D4×D1112yes—
167Q16—884no—
168M16—222no—
169M16—441no—
170C2×C8—42no—
171C2×C8—441no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—222no—
175C4⋊C4—221no—
176C4⋊C4—221no—
177C4⋊C4—442no—
178C4⋊C4—882no—
179C4⋊C4—881no—
180C4⋊C4—881no—
181C4⋊C4—881no—
182C22⋊C4—441no—
183C42—21no—
184C42—441no—
185C42Dic4412yescomplemented
186C11#1226011yescharacteristic, complemented, Sylow
187C23#6693511yescharacteristic
188Q8—444no—
189Q8—882no—
190Q8—882no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—41no—
200C2×C4—442no—
201C2×C4—442no—
202C2×C4—442no—
203C2×C4—442no—
204C2×C4—441no—
205C2×C4—441no—
206C2×C4—442no—
207C2×C4—442no—
208C2×C4C2×Dic4411yescharacteristic
209C2×C4#6696211yescharacteristic
210C8—82no—
211C8—442no—
212C22—21no—
213C22—21no—
214C22#1062235211yescharacteristic
215C22#1062235411yescharacteristic
216C22#1062236511yescharacteristic
217C4—21no—
218C4—21no—
219C4—42no—
220C4—42no—
221C4—81no—
222C4—882no—
223C4—882no—
224C4—881no—
225C4—881no—
226C2—21no—
227C2—21no—
228C2#1306759211yescharacteristic
229C2#1307061911yescharacteristic
230C2#1307063911yescharacteristic
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#12260
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
57. C42×C11Q16semidirect
185. C42Dic44semidirect
186. C11#12260semidirect

Maximal subgroups

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

subgroupindex
#130768882
#130699662
#130675922
#130666472
C11×#13242
#1226011