Finite Group Databasebeta

← #14667058

Subgroups — #14667058

Order 2816.

310 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 71 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#13070816C212yesmaximal
2#13070109C211yesmaximal, characteristic
3#13066628C212yesmaximal
4#13066556C211yesmaximal, characteristic
5C11×#3249C211yesmaximal, characteristic
6C11×#533—21no—
7C11×#477—22no—
8C11×#467—21no—
9C11×#467C2212yes—
10C11×#462—22no—
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×#66882C2211yescharacteristic
13#10622541—21no—
14#10622202—22no—
15#10622189—21no—
16#10622189C2211yescharacteristic
17C22⋊(C11⋊C16)C2212yes—
18#10622127—22no—
19C2×C11×Q16—21no—
20C2×C11×Q16D412yes—
21C22×C8×C11D411yescharacteristic
22C22×C8×C11C2311yescharacteristic
23C11×C4⋊Q8—21no—
24C11×C4⋊Q8—21no—
25C11×#125—41no—
26C11×C22⋊Q8—22no—
27C11×C22⋊Q8—41no—
28C4×Q8×C11—22no—
29C4×Q8×C11—41no—
30C11×#117—41no—
31C2×C42×C11D411yescharacteristic
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×Dic11⋊C4—41no—
35C11×#107—21no—
36C11×#107D412yes—
37C11×C4⋊C8—22no—
38C11×#103—22no—
39C11×#103—22no—
40C11⋊#95—41no—
41#66882—22no—
42C2×C11⋊C16—22no—
43#12292—111nomaximal, Sylow
44C2×Q8×C11—22no—
45C2×Q8×C11—41no—
46C22×C4×C11D811yescharacteristic
47C22×C4×C11D811yescharacteristic
48C22×C4×C11C2×D411yescharacteristic
49C22×Dic11—41no—
50C22×Dic11—41no—
51C11×Q16—42no—
52C11×Q16—81no—
53C2×C8×C11—21no—
54C2×C8×C11—41no—
55C2×C8×C11—41no—
56C2×C8×C11C2×D412yes—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—41no—
59C11×C4⋊C4—41no—
60C11×C4⋊C4—42no—
61C11×C4⋊C4—41no—
62C11×C4⋊C4—42no—
63C11×C22⋊C4—42no—
64C42×C11—21no—
65C42×C11—21no—
66C42×C11—42no—
67C4⋊Dic11—22no—
68C4⋊Dic11—41no—
69C4⋊Dic11—41no—
70C4⋊Dic11—41no—
71Dic11⋊C4—82no—
72C11⋊C16—42no—
73#3249D1111yescharacteristic
74#2236—112no—
75#2087—111no—
76#1348—112no—
77#1322—111no—
78C23×C11C2×D811yescharacteristic
79Q8×C11—42no—
80Q8×C11—42no—
81Q8×C11—82no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—41no—
88C2×C4×C11—42no—
89C2×C4×C11—42no—
90C2×C4×C11Q3212yes—
91C2×C4×C11#12011yescharacteristic
92C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
93C2×Dic11—42no—
94C2×Dic11—81no—
95C2×Dic11—81no—
96C2×Dic11—81no—
97C2×Dic11—81no—
98C2×Dic11—81no—
99C8×C11—22no—
100C8×C11—41no—
101#533—21no—
102#477—22no—
103#467—21no—
104#467C2×D1112yes—
105#462—22no—
106C2×#107—111no—
107C2×C4⋊C8C2×D1111yescharacteristic
108#389—221no—
109#366—222no—
110#358—222no—
111C22⋊C16—112no—
112#340—111no—
113#340—221no—
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—82no—
124C4×C11#45611yescharacteristic
125C4×C11#45811yescharacteristic
126Dic11—82no—
127Dic11—161no—
128C2×Q16—21no—
129C2×Q16C22⋊D1112yes—
130C22×C8C22⋊D1111yescharacteristic
131C22×C8C22×D1111yescharacteristic
132C4⋊Q8—21no—
133C4⋊Q8—21no—
134#125—41no—
135C22⋊Q8—22no—
136C22⋊Q8—41no—
137C4×Q8—22no—
138C4×Q8—41no—
139#117—41no—
140C2×C4⋊C4—221no—
141C2×C4⋊C4—221no—
142C2×C4⋊C4—441no—
143C2×C42C22⋊D1111yescharacteristic
144C2×C16—222no—
145#107—21no—
146#107—222no—
147#107C22⋊D1112yes—
148C4⋊C8—22no—
149#103—22no—
150#103—22no—
151#95—441no—
152C2×C11—21no—
153C2×C11—21no—
154C2×C11#161011yescharacteristic
155C2×C11#218811yescharacteristic
156C2×C11#219011yescharacteristic
157C2×Q8—22no—
158C2×Q8—41no—
159C22×C4—441no—
160C22×C4—441no—
161C22×C4#432311yescharacteristic
162C22×C4#432311yescharacteristic
163C22×C4C2×C22⋊D1111yescharacteristic
164Q16—42no—
165Q16—81no—
166C2×C8—21no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8C2×C22⋊D1112yes—
170C4⋊C4—22no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—42no—
174C4⋊C4—41no—
175C4⋊C4—42no—
176C4⋊C4—222no—
177C4⋊C4—441no—
178C4⋊C4—441no—
179C4⋊C4—441no—
180C4⋊C4—882no—
181C22⋊C4—42no—
182C42—21no—
183C42—21no—
184C42—42no—
185C16—442no—
186C11#1229211yescharacteristic, complemented, Sylow
187C23C2×#432311yescharacteristic
188Q8—42no—
189Q8—42no—
190Q8—82no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—442no—
200C2×C4—881no—
201C2×C4—881no—
202C2×C4—881no—
203C2×C4—881no—
204C2×C4—881no—
205C2×C4#6689312yes—
206C2×C4#6698511yescharacteristic
207C2×C4#6700611yescharacteristic
208C8—22no—
209C8—41no—
210C22—21no—
211C22—21no—
212C22#1062279211yescharacteristic
213C22C2×#6689311yescharacteristic
214C22#1062283011yescharacteristic
215C4—21no—
216C4—22no—
217C4—41no—
218C4—82no—
219C4—82no—
220C4—882no—
221C4—1761no—
222C4#1062285611yescharacteristic
223C4#1062285911yescharacteristic
224C2—21no—
225C2—21no—
226C2#1306761911yescharacteristic
227C2#1307055011yescharacteristic
228C2#1307056211yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#3249C2
socleC22×C11#447
prime radicalC23×C11C2×D8
hypercenter#3249D11
hypocenterC11#12292
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #3249

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
#130708162
#130701092
#130666282
#130665562
C11×#32492
#1229211