Finite Group Databasebeta

← #14642970

Subgroups — #14642970

Order 2816.

398 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 95 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#13070159C211yesmaximal, characteristic
2#13070024C212yesmaximal
3#13066442C211yesmaximal, characteristic
4#13066442C212yesmaximal
5C11×#2811C211yesmaximal, characteristic
6C11×#395—21no—
7C11×#395—22no—
8C11×#391—22no—
9C11×#391—21no—
10C11×#391C2211yescharacteristic
11C11×#391C2212yes—
12C2×#66899—21no—
13C2×#66899—22no—
14C2×#66872—21no—
15#10622548C2211yescharacteristic
16#10622167—22no—
17#10622162C2211yescharacteristic
18#10622162C2212yes—
19C22×Q8×C11—21no—
20C22×Q8×C11D412yes—
21C22×Q8×C11D411yescharacteristic
22C2×C11×C4⋊C4—21no—
23C2×C11×C4⋊C4—22no—
24C2×C11×C4⋊C4D411yescharacteristic
25C2×C11×C4⋊C4D412yes—
26C2×C42×C11—21no—
27C2×C42×C11C2311yescharacteristic
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11—22no—
30C22×C11⋊C8—21no—
31C22×C11⋊C8—22no—
32C11×#95—21no—
33C11×#95—22no—
34C11×#95—22no—
35C11×#95—22no—
36C11×#95—22no—
37#66899—42no—
38#66899—44no—
39#66872—42no—
40#7812—111nomaximal, Sylow
41C2×Q8×C11—22no—
42C2×Q8×C11—21no—
43C2×Q8×C11—41no—
44C2×Q8×C11—42no—
45C2×Q8×C11—42no—
46C2×Q8×C11—41no—
47C2×Q8×C11—81no—
48C2×Q8×C11—82no—
49C2×Q8×C11SD1614yes—
50C2×Q8×C11Q1612yes—
51C22×C4×C11—22no—
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11—22no—
55C22×C4×C11C2×D412yes—
56C22×C4×C11C2×D411yescharacteristic
57C22×Dic11—41no—
58C11×C4⋊C4—41no—
59C11×C4⋊C4—42no—
60C11×C4⋊C4—81no—
61C11×C4⋊C4—82no—
62C42×C11—41no—
63C42×C11—81no—
64C4⋊Dic11—41no—
65C4⋊Dic11—41no—
66C4⋊Dic11—42no—
67C4⋊Dic11—42no—
68C2×C11⋊C8—22no—
69C2×C11⋊C8—41no—
70C2×C11⋊C8—42no—
71C2×C11⋊C8—42no—
72C2×C11⋊C8—42no—
73C2×C11⋊C8—41no—
74#2811D1111yescharacteristic
75#2096—111no—
76#2072—112no—
77#1272—111no—
78#1272—112no—
79C23×C11#12011yescharacteristic
80Q8×C11—44no—
81Q8×C11—42no—
82Q8×C11—82no—
83Q8×C11—81no—
84Q8×C11—84no—
85C2×C4×C11—21no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—24no—
90C2×C4×C11—22no—
91C2×C4×C11—41no—
92C2×C4×C11—42no—
93C2×C4×C11—42no—
94C2×C4×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11C2×SD1612yes—
101C2×C4×C11C2×Q1611yescharacteristic
102C2×C4×C11#13712yes—
103C2×C4×C11#13711yescharacteristic
104C2×Dic11—82no—
105C2×Dic11—81no—
106C11⋊C8—42no—
107C11⋊C8—82no—
108C2×#106—221no—
109C2×#103—222no—
110C2×#103—221no—
111#395—22no—
112#395—21no—
113#391—22no—
114#391—21no—
115#391C2×D1112yes—
116#391C2×D1111yescharacteristic
117#384—111no—
118#340—222no—
119#336—112no—
120#336—111no—
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—44no—
131C4×C11—42no—
132C4×C11—81no—
133C4×C11—82no—
134Dic11—161no—
135C22×Q8—21no—
136C22×Q8C22⋊D1112yes—
137C22×Q8C22⋊D1111yescharacteristic
138C22×C8—221no—
139C22×C8—222no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—222no—
143C2×C4⋊C4—221no—
144C2×C4⋊C4C22⋊D1112yes—
145C2×C4⋊C4C22⋊D1111yescharacteristic
146C2×C42—21no—
147C2×C42C22×D1111yescharacteristic
148#106—442no—
149#103—442no—
150#103—444no—
151#95—21no—
152#95—22no—
153#95—22no—
154#95—22no—
155#95—22no—
156C2×C11#160812yes—
157C2×C11#161411yescharacteristic
158C2×C11#162311yescharacteristic
159C2×C11#164512yes—
160C2×C11#165911yescharacteristic
161C2×Q8—22no—
162C2×Q8—21no—
163C2×Q8—41no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8—41no—
167C2×Q8—81no—
168C2×Q8—82no—
169C2×Q8#432514yes—
170C2×Q8#432612yes—
171C22×C4—22no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—22no—
175C22×C4—441no—
176C22×C4C2×C22⋊D1112yes—
177C22×C4C2×C22⋊D1111yescharacteristic
178C2×C8—222no—
179C2×C8—441no—
180C2×C8—441no—
181C2×C8—442no—
182C2×C8—442no—
183C2×C8—442no—
184C4⋊C4—41no—
185C4⋊C4—42no—
186C4⋊C4—81no—
187C4⋊C4—82no—
188C4⋊C4—441no—
189C4⋊C4—441no—
190C4⋊C4—442no—
191C4⋊C4—442no—
192C42—41no—
193C42—81no—
194C11#781211yescharacteristic, complemented, Sylow
195C23#6700611yescharacteristic
196Q8—44no—
197Q8—42no—
198Q8—82no—
199Q8—81no—
200Q8—84no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—24no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—882no—
217C2×C4—881no—
218C2×C4C2×#432512yes—
219C2×C4#6699512yes—
220C2×C4#6699511yescharacteristic
221C2×C4C2×#432611yescharacteristic
222C8—442no—
223C8—882no—
224C22#1062284012yes—
225C22#1062284111yescharacteristic
226C22#1062285411yescharacteristic
227C22#1062285512yes—
228C22#1062285611yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—44no—
234C4—42no—
235C4—81no—
236C4—82no—
237C4—1761no—
238C2#1306760712yes—
239C2#1306764111yescharacteristic
240C2#1306769411yescharacteristic
241C2#1306783712yes—
242C2#1306792211yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2811C2
socle, prime radicalC23×C11#120
hypercenter#2811D11
hypocenterC11#7812
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2811

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
#130701592
#130700242
#130664422
C11×#28112
#781211