Finite Group Databasebeta

← #14666833

Subgroups — #14666833

Order 2816.

342 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 63 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#13069961C211yesmaximal, characteristic
2#13067657C212yesmaximal
3#13066643C212yesmaximal
4#13066562C211yesmaximal, characteristic
5C11×#2571C211yesmaximal, characteristic
6#10623031C2211yescharacteristic
7C11×#400—21no—
8C11×#400C2212yes—
9C11×#389—22no—
10C11×#384C2211yescharacteristic
11C11×#382—22no—
12C4×C11×C4⋊C4—21no—
13#10622583—22no—
14#10622577—21no—
15#10622168C2211yescharacteristic
16#10622166C2212yes—
17#10622161—21no—
18#10622090—22no—
19C2×C11×C4⋊C4—21no—
20C2×C11×C4⋊C4—21no—
21C2×C11×C4⋊C4—22no—
22C2×C11×C4⋊C4—21no—
23C2×C11×C4⋊C4D411yescharacteristic
24C2×C11×C4⋊C4D412yes—
25C2×C11×C4⋊C4C2311yescharacteristic
26C2×C42×C11—22no—
27C2×C42×C11D411yescharacteristic
28#66979—21no—
29#66977—22no—
30C2×#4318—21no—
31#66943—41no—
32#66941—41no—
33C11×#95—21no—
34C11×#95—22no—
35C11×#95—22no—
36C11×#95—22no—
37C11×#95D412yes—
38C22⋊(C11⋊C8)—22no—
39#66874—42no—
40#66872—41no—
41#66871—41no—
42#66871—42no—
43#12257—111nomaximal, Sylow
44C22×C4×C11—21no—
45C22×C4×C11—22no—
46C22×C4×C11—22no—
47C22×C4×C11—21no—
48C22×C4×C11C2×D411yescharacteristic
49C22×C4×C11C2×D412yes—
50C2×Dic22—22no—
51C11×C4⋊C4—41no—
52C11×C4⋊C4—42no—
53C11×C4⋊C4—44no—
54C11×C4⋊C4—42no—
55C11×C4⋊C4—41no—
56C11×C4⋊C4—42no—
57C11×C4⋊C4—81no—
58C42×C11—21no—
59C42×C11—44no—
60C42×C11Q1612yes—
61C22⋊Dic11—41no—
62C4⋊Dic11—21no—
63C4⋊Dic11—22no—
64C4⋊Dic11—21no—
65Dic11⋊C4—42no—
66C4×Dic11—41no—
67#4318—22no—
68#4318—41no—
69C2×C11⋊C8—41no—
70C2×C11⋊C8—42no—
71#2571D1111yescharacteristic
72#2060—111no—
73#1617—112no—
74#1353—112no—
75#1325—111no—
76C23×C11#12011yescharacteristic
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—22no—
83C2×C4×C11—42no—
84C2×C4×C11—42no—
85C2×C4×C11—42no—
86C2×C4×C11—42no—
87C2×C4×C11—42no—
88C2×C4×C11—42no—
89C2×C4×C11—42no—
90C2×C4×C11—41no—
91C2×C4×C11—42no—
92C2×C4×C11C2×Q1611yescharacteristic
93C2×C4×C11#13711yescharacteristic
94C2×Dic11—41no—
95C2×Dic11—41no—
96Dic22—82no—
97C11⋊C8—42no—
98C11⋊C8—82no—
99#544—111no—
100#484—222no—
101#428—221no—
102#400—21no—
103#400C2×D1112yes—
104#389—22no—
105#384C2×D1111yescharacteristic
106#382—22no—
107C4×C4⋊C4—21no—
108#343—111no—
109#339—221no—
110#328—222no—
111#324—112no—
112C22×C11—21no—
113C22×C11—21no—
114C22×C11#45111yescharacteristic
115C22×C11#45611yescharacteristic
116C22×C11B(4,𝔽2)11yescharacteristic
117C4×C11—24no—
118C4×C11—21no—
119C4×C11—21no—
120C4×C11—42no—
121C4×C11—82no—
122C4×C11—81no—
123C4×C11—82no—
124Dic11—81no—
125Dic11—81no—
126C2×M16—221no—
127C4⋊Q8—441no—
128#125—441no—
129C22⋊Q8—222no—
130#117—221no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4C22⋊D1111yescharacteristic
136C2×C4⋊C4C22⋊D1112yes—
137C2×C4⋊C4C22×D1111yescharacteristic
138C2×C42—22no—
139C2×C42C22⋊D1111yescharacteristic
140#107—441no—
141#107—442no—
142#106—441no—
143#103—442no—
144C22⋊C8—222no—
145#95—21no—
146#95—22no—
147#95—22no—
148#95—22no—
149#95C22⋊D1112yes—
150C2×C11—21no—
151C2×C11—21no—
152C2×C11#160511yescharacteristic
153C2×C11#219811yescharacteristic
154C2×C11#220411yescharacteristic
155C2×Q8—222no—
156C22×C4—21no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—21no—
160C22×C4C2×C22⋊D1111yescharacteristic
161C22×C4C2×C22⋊D1112yes—
162M16—222no—
163M16—441no—
164C2×C8—441no—
165C2×C8—442no—
166C4⋊C4—41no—
167C4⋊C4—42no—
168C4⋊C4—41no—
169C4⋊C4—42no—
170C4⋊C4—44no—
171C4⋊C4—42no—
172C4⋊C4—81no—
173C4⋊C4—221no—
174C4⋊C4—221no—
175C4⋊C4—222no—
176C4⋊C4—442no—
177C22⋊C4—441no—
178C42—21no—
179C42—44no—
180C42—441no—
181C42#432612yes—
182C11#1225711yescharacteristic, complemented, Sylow
183C23#6700611yescharacteristic
184Q8—882no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—441no—
201C2×C4—441no—
202C2×C4#6699511yescharacteristic
203C2×C4C2×#432611yescharacteristic
204C8—442no—
205C8—882no—
206C22—21no—
207C22—21no—
208C22#1062284111yescharacteristic
209C22#1062285711yescharacteristic
210C22#1062285911yescharacteristic
211C4—24no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—82no—
216C4—81no—
217C4—82no—
218C4—881no—
219C4—881no—
220C2—21no—
221C2—21no—
222C2#1306759011yescharacteristic
223C2#1307061211yescharacteristic
224C2#1307064211yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2571C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#2571D11
hypocenterC11#12257
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2571

Complements

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

NH ≅ G/Ntype
182. C11#12257semidirect

Maximal subgroups

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

subgroupindex
#130699612
#130676572
#130666432
#130665622
C11×#25712
#1225711