Finite Group Databasebeta

← #14674153

Subgroups — #14674153

Order 2816.

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

normal subgroups only

This group has 322 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#13079016C211yesmaximal, characteristic
2#13070301C211yesmaximal, characteristic
3#13066790C214yesmaximal, complemented
4C11×#2126C211yesmaximal, characteristic
5C11×#532C2211yescharacteristic
6C2×#66923C411yescharacteristic, complemented
7C11×#410—21no—
8#10622850—21no—
9#10622845—21no—
10#10622845—21no—
11#10622695—21no—
12#10622684—21no—
13#10622669C412yescomplemented
14#10622669C2212yes—
15C4×#4318C411yescharacteristic, complemented
16C11×#354C2212yes—
17C11×#353—21no—
18#10622186—21no—
19#10622180C2212yes—
20C2×C11×#41D411yescharacteristic
21C2×C11×#41D411yescharacteristic
22C11×C4⋊Q8D411yescharacteristic
23C11×#127D411yescharacteristic
24C11×#124C2×C411yescharacteristic
25C11×#124C2311yescharacteristic
26C11×#121—41no—
27C4×D4×C11—41no—
28C11×#117—41no—
29C2×C42×C11C2×C411yescharacteristic
30C2×C4⋊Dic11—21no—
31C2×Dic11⋊C4—41no—
32C2×#4318—21no—
33C2×#4318—41no—
34#66923—21no—
35#66923—41no—
36#66923C2×C412yes—
37C11×#99—22no—
38C11×#99—41no—
39#66900—22no—
40#66899—22no—
41#66899—22no—
42#66897—41no—
43#66896—22no—
44#66896—22no—
45#66867—21no—
46C4×C11⋊C8C2×C412yes—
47#13604—111nomaximal, Sylow
48C11×#41—41no—
49C11×#41—41no—
50C11×#41—41no—
51C11×#41—41no—
52C2×Q8×C11C22⋊C411yescharacteristic
53C2×Q8×C11C2×D411yescharacteristic
54C2×D4×C11—21no—
55C2×D4×C11—21no—
56C2×D4×C11—41no—
57C2×D4×C11C22⋊C411yescharacteristic
58C2×D4×C11C2×D411yescharacteristic
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11C22⋊C411yescharacteristic
63C22×Dic11—41no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—81no—
66C11×C22⋊C4—41no—
67C11×C22⋊C4—41no—
68C11×C22⋊C4—42no—
69C42×C11—21no—
70C42×C11—81no—
71C42×C11C22⋊C411yescharacteristic
72C42×C11C22×C411yescharacteristic
73C4⋊Dic11—22no—
74C4⋊Dic11—41no—
75Dic11⋊C4—42no—
76Dic11⋊C4—42no—
77#4318—41no—
78#4318—41no—
79#4318—42no—
80#4318—81no—
81C2×C11⋊C8—22no—
82C2×C11⋊C8—81no—
83#3142—111no—
84#2132—111no—
85#2126D1111yescharacteristic
86#1414—114no—
87C23×C11—21no—
88C23×C11—21no—
89C23×C11#9911yescharacteristic
90Q8×C11—41no—
91Q8×C11—41no—
92D4×C11—41no—
93D4×C11—41no—
94D4×C11—81no—
95D4×C11—81no—
96D4×C11—82no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—81no—
108C2×C4×C11—82no—
109C2×C4×C11#9911yescharacteristic
110C2×C4×C11C2×C22⋊C411yescharacteristic
111C2×Dic11—42no—
112C2×Dic11—82no—
113C11⋊C8—42no—
114C11⋊C8—82no—
115#532C2×D1111yescharacteristic
116C2×#125—111no—
117#491—221no—
118#490—221no—
119#488—112no—
120#488—112no—
121#417—221no—
122#417—221no—
123#413—221no—
124#410—21no—
125C4×M16—111no—
126#356—221no—
127#355—112no—
128#354C2×D1112yes—
129#353—21no—
130C22×C11—21no—
131C22×C11—41no—
132C22×C11—41no—
133C22×C11—41no—
134C22×C11—81no—
135C22×C11—81no—
136C22×C11C2×#9911yescharacteristic
137C4×C11—21no—
138C4×C11—41no—
139C4×C11—41no—
140C4×C11—41no—
141C4×C11—41no—
142C4×C11—162no—
143C4×C11#35411yescharacteristic
144C4×C11#35411yescharacteristic
145Dic11—82no—
146C2×#41D4411yescharacteristic
147C2×#41C22⋊D1111yescharacteristic
148C2×M16—221no—
149C2×M16—441no—
150C4⋊Q8D4411yescharacteristic
151#127C22⋊D1111yescharacteristic
152#125—112no—
153#125—221no—
154#125—441no—
155#124C4×D1111yescharacteristic
156#124C22×D1111yescharacteristic
157#121—41no—
158C4×D4—41no—
159#117—41no—
160C2×C4⋊C4—221no—
161C2×C4⋊C4—441no—
162C2×C42C4×D1111yescharacteristic
163#103—222no—
164#103—222no—
165#102—222no—
166#102—222no—
167#101—222no—
168#100—441no—
169#99—22no—
170#99—41no—
171#97—221no—
172C4×C8—112no—
173C2×C11—21no—
174C2×C11—41no—
175C2×C11—81no—
176C2×C11—81no—
177C2×C11C2×#35411yescharacteristic
178#41—41no—
179#41—41no—
180#41—41no—
181#41—41no—
182C2×Q8(C2×D11)⋊C411yescharacteristic
183C2×Q8C2×D4411yescharacteristic
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—41no—
187C2×D4(C2×D11)⋊C411yescharacteristic
188C2×D4C2×C22⋊D1111yescharacteristic
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—441no—
193C22×C4(C2×D11)⋊C411yescharacteristic
194M16—441no—
195M16—441no—
196M16—442no—
197M16—881no—
198C2×C8—222no—
199C2×C8—881no—
200C4⋊C4—41no—
201C4⋊C4—81no—
202C4⋊C4—222no—
203C4⋊C4—442no—
204C4⋊C4—442no—
205C4⋊C4—441no—
206C22⋊C4—41no—
207C22⋊C4—41no—
208C22⋊C4—42no—
209C42—21no—
210C42—81no—
211C42(C2×D11)⋊C411yescharacteristic
212C42C2×C4×D1111yescharacteristic
213C11#1360411yescharacteristic, complemented, Sylow
214C23—21no—
215C23—21no—
216C23#6687011yescharacteristic
217Q8—41no—
218Q8—41no—
219D4—41no—
220D4—41no—
221D4—81no—
222D4—81no—
223D4—82no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—81no—
235C2×C4—82no—
236C2×C4—442no—
237C2×C4—882no—
238C2×C4#6687011yescharacteristic
239C2×C4C2×(C2×D11)⋊C411yescharacteristic
240C8—442no—
241C8—882no—
242C22—21no—
243C22—41no—
244C22—41no—
245C22—41no—
246C22—81no—
247C22—81no—
248C22C2×#6687011yescharacteristic
249C4—21no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—41no—
254C4—162no—
255C4—882no—
256C4#1062211111yescharacteristic
257C4#1062211111yescharacteristic
258C2—21no—
259C2—41no—
260C2—81no—
261C2—81no—
262C2C2×#1062211111yescharacteristic
subgroupG/H
centerC2C2×#10622111
commutatorC42×C11C22×C4
Frattini#124C22×D11
FittingC11×#2126C2
socleC2×C11C2×#354
prime radicalC11×#532C22
cosocleC11×#124C23
hypercenter#2126D11
hypocenterC11#13604
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #2126

Complements

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

NH ≅ G/Ntype
3. #13066790C2semidirect
6. C2×#66923C4semidirect
13. #10622669C4semidirect
15. C4×#4318C4semidirect
213. C11#13604semidirect

Maximal subgroups

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

subgroupindex
#130790162
#130703012
#130667902
C11×#21262
#1360411