Finite Group Databasebeta

← #14667057

Subgroups — #14667057

Order 2816.

310 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 67 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#13079961C211yesmaximal, characteristic
2#13070818C212yesmaximal
3#13066627C212yesmaximal
4#13066556C211yesmaximal, characteristic
5C11×#2087C211yesmaximal, characteristic
6#10623001—21no—
7C2×C11×#107C2211yescharacteristic
8C2×C11×C4⋊C8C2211yescharacteristic
9C11×#389—21no—
10#10622729—21no—
11#10622729C2212yes—
12#10622463—22no—
13#10622462—22no—
14C11×#340—21no—
15C11×#340C2211yescharacteristic
16C22⋊(C11⋊C16)C2212yes—
17#10622130—22no—
18#10622127—22no—
19C22×C8×C11D411yescharacteristic
20C22×C8×C11C2311yescharacteristic
21C2×C11×C4⋊C4—21no—
22C2×C11×C4⋊C4—21no—
23C2×C11×C4⋊C4—41no—
24C2×C42×C11D411yescharacteristic
25#66979—41no—
26#66977—22no—
27#66977—41no—
28C2×Dic44—21no—
29C2×Dic44D412yes—
30#66923—41no—
31#66922—21no—
32#66922—21no—
33C4×Dic22—22no—
34C4×Dic22—41no—
35C11×#107—22no—
36C11×C4⋊C8—22no—
37C11×#95—41no—
38#66882—21no—
39#66882D412yes—
40#66880—22no—
41#66880—22no—
42C2×C11⋊C16—22no—
43#12292—111nomaximal, Sylow
44C22×C4×C11—41no—
45C22×C4×C11—41no—
46C22×C4×C11D811yescharacteristic
47C22×C4×C11D811yescharacteristic
48C22×C4×C11C2×D411yescharacteristic
49C2×Dic22—22no—
50C2×Dic22—41no—
51C2×C8×C11—21no—
52C2×C8×C11—41no—
53C2×C8×C11—41no—
54C2×C8×C11C2×D412yes—
55C11×C4⋊C4—22no—
56C11×C4⋊C4—41no—
57C11×C4⋊C4—41no—
58C11×C4⋊C4—41no—
59C11×C4⋊C4—82no—
60C42×C11—21no—
61C42×C11—21no—
62C22⋊Dic11—42no—
63C4⋊Dic11—22no—
64C4⋊Dic11—41no—
65C4⋊Dic11—41no—
66C4⋊Dic11—41no—
67Dic11⋊C4—42no—
68Dic11⋊C4—42no—
69C4×Dic11—42no—
70Dic44—42no—
71Dic44—81no—
72C11⋊C16—42no—
73#3249—111no—
74#2236—112no—
75#2087D1111yescharacteristic
76#1348—112no—
77#1322—111no—
78C23×C11C2×D811yescharacteristic
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—41no—
85C2×C4×C11—42no—
86C2×C4×C11—81no—
87C2×C4×C11—81no—
88C2×C4×C11—81no—
89C2×C4×C11—81no—
90C2×C4×C11—81no—
91C2×C4×C11Q3212yes—
92C2×C4×C11#12011yescharacteristic
93C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
94C2×Dic11—42no—
95C2×Dic11—42no—
96Dic22—42no—
97Dic22—42no—
98Dic22—82no—
99C8×C11—22no—
100C8×C11—41no—
101#533—221no—
102#477—222no—
103#467—112no—
104#467—221no—
105#462—222no—
106C2×#107C2×D1111yescharacteristic
107C2×C4⋊C8C2×D1111yescharacteristic
108#389—21no—
109#366—222no—
110#358—222no—
111C22⋊C16—112no—
112#340—21no—
113#340C2×D1111yescharacteristic
114C22×C11—21no—
115C22×C11—21no—
116C22×C11#44711yescharacteristic
117C22×C11C2×Q3211yescharacteristic
118C22×C11#51011yescharacteristic
119C4×C11—21no—
120C4×C11—22no—
121C4×C11—41no—
122C4×C11—82no—
123C4×C11—161no—
124C4×C11#45611yescharacteristic
125C4×C11#45811yescharacteristic
126Dic11—82no—
127Dic11—82no—
128C2×Q16—112no—
129C2×Q16—221no—
130C22×C8C22⋊D1111yescharacteristic
131C22×C8C22×D1111yescharacteristic
132C4⋊Q8—221no—
133C4⋊Q8—221no—
134#125—441no—
135C22⋊Q8—222no—
136C22⋊Q8—441no—
137C4×Q8—222no—
138C4×Q8—441no—
139#117—441no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—41no—
143C2×C42C22⋊D1111yescharacteristic
144C2×C16—222no—
145#107—22no—
146#107—112no—
147#107—221no—
148C4⋊C8—22no—
149#103—222no—
150#103—222no—
151#95—41no—
152C2×C11—21no—
153C2×C11—21no—
154C2×C11#161011yescharacteristic
155C2×C11#218811yescharacteristic
156C2×C11#219011yescharacteristic
157C2×Q8—222no—
158C2×Q8—441no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4#432311yescharacteristic
162C22×C4#432311yescharacteristic
163C22×C4C2×C22⋊D1111yescharacteristic
164Q16—442no—
165Q16—881no—
166C2×C8—21no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8D4×D1112yes—
170C4⋊C4—22no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—82no—
175C4⋊C4—222no—
176C4⋊C4—441no—
177C4⋊C4—441no—
178C4⋊C4—442no—
179C4⋊C4—441no—
180C4⋊C4—442no—
181C22⋊C4—442no—
182C42—21no—
183C42—21no—
184C42—442no—
185C16—442no—
186C11#1229211yescharacteristic, complemented, Sylow
187C23C2×#432311yescharacteristic
188Q8—442no—
189Q8—442no—
190Q8—882no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—81no—
199C2×C4—81no—
200C2×C4—81no—
201C2×C4—81no—
202C2×C4—81no—
203C2×C4—442no—
204C2×C4—442no—
205C2×C4#6689312yes—
206C2×C4#6699011yescharacteristic
207C2×C4#6700211yescharacteristic
208C8—22no—
209C8—41no—
210C22—21no—
211C22—21no—
212C22#1062264911yescharacteristic
213C22C2×#6689311yescharacteristic
214C22#1062280811yescharacteristic
215C4—21no—
216C4—22no—
217C4—41no—
218C4—82no—
219C4—161no—
220C4—882no—
221C4—882no—
222C4#1062266611yescharacteristic
223C4#1062270811yescharacteristic
224C2—21no—
225C2—21no—
226C2#1306761811yescharacteristic
227C2#1307054911yescharacteristic
228C2#1307056111yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#2087C2
socleC22×C11#447
prime radicalC23×C11C2×D8
hypercenter#2087D11
hypocenterC11#12292
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #2087

Complements

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

NH ≅ G/Ntype
186. C11#12292semidirect

Maximal subgroups

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

subgroupindex
#130799612
#130708182
#130666272
#130665562
C11×#20872
#1229211