Finite Group Databasebeta

← #14642972

Subgroups — #14642972

Order 2816.

398 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 87 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#13076609C211yesmaximal, characteristic
2#13070159C211yesmaximal, characteristic
3#13070026C212yesmaximal
4#13066441C212yesmaximal
5C11×#1272C211yesmaximal, characteristic
6C11×#391C2211yescharacteristic
7#10622843—21no—
8C2×#66899—21no—
9C2×#66880—22no—
10#10622592—21no—
11C2×#66872—21no—
12#10622548C2211yescharacteristic
13#10622542C2212yes—
14#10622269—22no—
15#10622259—22no—
16C11×#336C2212yes—
17#10622189—22no—
18#10622162C2211yescharacteristic
19C22×Q8×C11D411yescharacteristic
20C22×Dic22—21no—
21C22×Dic22D412yes—
22C22×C8×C11—22no—
23C2×C11×C4⋊C4D411yescharacteristic
24C2×C42×C11C2311yescharacteristic
25C2×C4⋊Dic11—21no—
26C2×C4⋊Dic11—22no—
27C2×C4⋊Dic11—21no—
28C2×C4⋊Dic11D412yes—
29C2×Dic11⋊C4—22no—
30C2×C4×Dic11—21no—
31C22×C11⋊C8—21no—
32C11×#95—22no—
33#66899—42no—
34C11⋊#95—21no—
35C11⋊#95—22no—
36C11⋊#95—22no—
37C11⋊#95—22no—
38#66880—44no—
39#66872—42no—
40#7812—111nomaximal, Sylow
41C2×Q8×C11—21no—
42C2×Q8×C11—41no—
43C2×Q8×C11—41no—
44C2×Q8×C11Q1612yes—
45C22×C4×C11—21no—
46C22×C4×C11—21no—
47C22×C4×C11C2×D412yes—
48C22×C4×C11C2×D411yescharacteristic
49C22×Dic11—22no—
50C22×Dic11—22no—
51C22×Dic11—41no—
52C2×Dic22—22no—
53C2×Dic22—42no—
54C2×Dic22—42no—
55C2×Dic22—81no—
56C2×Dic22—82no—
57C2×Dic22SD1614yes—
58C2×C8×C11—42no—
59C2×C8×C11—42no—
60C2×C8×C11—42no—
61C11×C4⋊C4—41no—
62C42×C11—41no—
63C4⋊Dic11—42no—
64C4⋊Dic11—41no—
65C4⋊Dic11—41no—
66C4⋊Dic11—42no—
67C4⋊Dic11—42no—
68C4⋊Dic11—81no—
69Dic11⋊C4—82no—
70C4×Dic11—81no—
71C2×C11⋊C8—22no—
72C2×C11⋊C8—41no—
73C2×C11⋊C8—41no—
74#2811—111no—
75#2096—111no—
76#2072—112no—
77#1272—112no—
78#1272D1111yescharacteristic
79C23×C11#12011yescharacteristic
80Q8×C11—42no—
81Q8×C11—81no—
82C2×C4×C11—21no—
83C2×C4×C11—22no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11—41no—
90C2×C4×C11—42no—
91C2×C4×C11C2×SD1612yes—
92C2×C4×C11C2×Q1611yescharacteristic
93C2×C4×C11#13711yescharacteristic
94C2×C4×C11#13712yes—
95C2×Dic11—24no—
96C2×Dic11—42no—
97C2×Dic11—42no—
98C2×Dic11—42no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—82no—
102C2×Dic11—81no—
103Dic22—44no—
104Dic22—82no—
105Dic22—84no—
106C8×C11—82no—
107C11⋊C8—42no—
108C2×#106—221no—
109C2×#103—222no—
110C2×#103—221no—
111#395—222no—
112#395—221no—
113#391—112no—
114#391—222no—
115#391—221no—
116#391C2×D1111yescharacteristic
117#384—111no—
118#340—222no—
119#336—111no—
120#336C2×D1112yes—
121C22×C11#44812yes—
122C22×C11#45111yescharacteristic
123C22×C11#45311yescharacteristic
124C22×C11#45512yes—
125C22×C11#45811yescharacteristic
126C4×C11—22no—
127C4×C11—22no—
128C4×C11—21no—
129C4×C11—21no—
130C4×C11—42no—
131C4×C11—81no—
132Dic11—44no—
133Dic11—82no—
134Dic11—161no—
135C22×Q8—112no—
136C22×Q8—221no—
137C22×Q8D4411yescharacteristic
138C22×C8—22no—
139C22×C8—221no—
140C2×C4⋊C4—112no—
141C2×C4⋊C4—221no—
142C2×C4⋊C4—222no—
143C2×C4⋊C4—222no—
144C2×C4⋊C4—221no—
145C2×C4⋊C4D4411yescharacteristic
146C2×C42—221no—
147C2×C42C22×D1111yescharacteristic
148#106—442no—
149#103—444no—
150#103—442no—
151#95—22no—
152#95—222no—
153#95—221no—
154#95—222no—
155#95—222no—
156C2×C11#160812yes—
157C2×C11#161411yescharacteristic
158C2×C11#162311yescharacteristic
159C2×C11#164512yes—
160C2×C11#165911yescharacteristic
161C2×Q8—21no—
162C2×Q8—41no—
163C2×Q8—41no—
164C2×Q8—114no—
165C2×Q8—222no—
166C2×Q8—442no—
167C2×Q8—442no—
168C2×Q8—881no—
169C2×Q8—882no—
170C2×Q8Dic4412yes—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—222no—
174C22×C4—222no—
175C22×C4—441no—
176C22×C4C2×D4411yescharacteristic
177C22×C4D4×D1112yes—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—222no—
182C2×C8—441no—
183C2×C8—441no—
184C4⋊C4—41no—
185C4⋊C4—442no—
186C4⋊C4—441no—
187C4⋊C4—441no—
188C4⋊C4—442no—
189C4⋊C4—442no—
190C4⋊C4—882no—
191C4⋊C4—881no—
192C42—41no—
193C42—881no—
194C11#781211yescharacteristic, complemented, Sylow
195C23#6693511yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—444no—
199Q8—882no—
200Q8—884no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—224no—
211C2×C4—442no—
212C2×C4—442no—
213C2×C4—442no—
214C2×C4—442no—
215C2×C4—442no—
216C2×C4—881no—
217C2×C4—882no—
218C2×C4C2×Dic4411yescharacteristic
219C2×C4#6696211yescharacteristic
220C2×C4SD16×D1112yes—
221C2×C4#6697112yes—
222C8—82no—
223C8—442no—
224C22#1062235211yescharacteristic
225C22#1062235511yescharacteristic
226C22#1062236011yescharacteristic
227C22#1062241912yes—
228C22#1062243812yes—
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—42no—
234C4—81no—
235C4—444no—
236C4—882no—
237C4—1761no—
238C2#1306760812yes—
239C2#1306764311yescharacteristic
240C2#1306769511yescharacteristic
241C2#1306784012yes—
242C2#1306792311yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1272C2
socle, prime radicalC23×C11#120
hypercenter#1272D11
hypocenterC11#7812
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
194. C11#7812semidirect

Maximal subgroups

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

subgroupindex
#130766092
#130701592
#130700262
#130664412
C11×#12722
#781211