Finite Group Databasebeta

← #14674154

Subgroups — #14674154

Order 2816.

322 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 79 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#13070301C211yesmaximal, characteristic
2#13070281C211yesmaximal, characteristic
3#13066791C214yesmaximal, complemented
4C11×#3142C211yesmaximal, characteristic
5C11×#532C2211yescharacteristic
6C2×C11×#125C411yescharacteristic, complemented
7C11×#491—21no—
8C11×#490—21no—
9C11×#488C412yescomplemented
10C11×#488C2212yes—
11C11×#417—21no—
12C11×#417—21no—
13C4×C11×M16C411yescharacteristic, complemented
14#10622853—21no—
15#10622850—21no—
16#10622186—21no—
17#10622183—21no—
18#10622180C2212yes—
19#10622179C2212yes—
20C2×C11×#41D411yescharacteristic
21C2×C11×#41D411yescharacteristic
22C2×C11×M16—21no—
23C11×C4⋊Q8D411yescharacteristic
24C11×#127D411yescharacteristic
25C11×#125—21no—
26C11×#125—41no—
27C11×#125C2×C412yes—
28C11×#124C2×C411yescharacteristic
29C11×#124C2311yescharacteristic
30C11×#121—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—41no—
34C2×C42×C11C2×C411yescharacteristic
35#66979—41no—
36C2×#4318—41no—
37C11×#103—22no—
38C11×#103—22no—
39C11×#102—22no—
40C11×#102—22no—
41C11×#97—21no—
42C4×C8×C11C2×C412yes—
43#66900—22no—
44#66898—22no—
45#66898—41no—
46#66897—41no—
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×C11—41no—
63C22×C4×C11C22⋊C411yescharacteristic
64C11×M16—41no—
65C11×M16—41no—
66C2×C8×C11—22no—
67C11×C4⋊C4—22no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—41no—
72C11×C22⋊C4—41no—
73C11×C22⋊C4—41no—
74C42×C11—21no—
75C42×C11C22⋊C411yescharacteristic
76C42×C11C22×C411yescharacteristic
77C22⋊Dic11—42no—
78C4⋊Dic11—81no—
79C4×Dic11—81no—
80#4318—42no—
81#4318—81no—
82C2×C11⋊C8—81no—
83#3142D1111yescharacteristic
84#2132—111no—
85#2126—111no—
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—42no—
108C2×C4×C11—81no—
109C2×C4×C11—82no—
110C2×C4×C11#9911yescharacteristic
111C2×C4×C11C2×C22⋊C411yescharacteristic
112C2×Dic11—82no—
113C8×C11—42no—
114C11⋊C8—82no—
115#532C2×D1111yescharacteristic
116C2×#125Dic1111yescharacteristic, complemented
117#491—21no—
118#490—21no—
119#488Dic1112yescomplemented
120#488C2×D1112yes—
121#417—21no—
122#417—21no—
123#413—221no—
124#410—221no—
125C4×M16Dic1111yescharacteristic, complemented
126#356—221no—
127#355—112no—
128#354—112no—
129#353—221no—
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—82no—
143C4×C11#35411yescharacteristic
144C4×C11#35411yescharacteristic
145Dic11—162no—
146C2×#41C22⋊D1111yescharacteristic
147C2×#41C22⋊D1111yescharacteristic
148C2×M16—21no—
149C2×M16—441no—
150C4⋊Q8C22⋊D1111yescharacteristic
151#127C22⋊D1111yescharacteristic
152#125—21no—
153#125—41no—
154#125C2×Dic1112yes—
155#124C2×Dic1111yescharacteristic
156#124C22×D1111yescharacteristic
157#121—41no—
158C4×D4—41no—
159#117—441no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—41no—
162C2×C42C2×Dic1111yescharacteristic
163#103—22no—
164#103—22no—
165#102—22no—
166#102—22no—
167#101—222no—
168#100—441no—
169#99—222no—
170#99—441no—
171#97—21no—
172C4×C8C2×Dic1112yes—
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×Q8C22⋊Dic1111yescharacteristic
183C2×Q8C2×C22⋊D1111yescharacteristic
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—41no—
187C2×D4C22⋊Dic1111yescharacteristic
188C2×D4C2×C22⋊D1111yescharacteristic
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—41no—
193C22×C4C22⋊Dic1111yescharacteristic
194M16—41no—
195M16—41no—
196M16—442no—
197M16—881no—
198C2×C8—22no—
199C2×C8—881no—
200C4⋊C4—22no—
201C4⋊C4—41no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—41no—
205C4⋊C4—881no—
206C22⋊C4—41no—
207C22⋊C4—41no—
208C22⋊C4—442no—
209C42—21no—
210C42—881no—
211C42C22⋊Dic1111yescharacteristic
212C42C22×Dic1111yescharacteristic
213C11#1360411yescharacteristic, complemented, Sylow
214C23—21no—
215C23—21no—
216C23#6689811yescharacteristic
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—42no—
235C2×C4—81no—
236C2×C4—82no—
237C2×C4—882no—
238C2×C4#6689811yescharacteristic
239C2×C4C2×C22⋊Dic1111yescharacteristic
240C8—42no—
241C8—882no—
242C22—21no—
243C22—41no—
244C22—41no—
245C22—41no—
246C22—81no—
247C22—81no—
248C22C2×#6689811yescharacteristic
249C4—21no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—41no—
254C4—82no—
255C4—1762no—
256C4#1062217911yescharacteristic
257C4#1062217911yescharacteristic
258C2—21no—
259C2—41no—
260C2—81no—
261C2—81no—
262C2C2×#1062217911yescharacteristic
subgroupG/H
centerC2C2×#10622179
commutatorC42×C11C22×C4
Frattini#124C22×D11
FittingC11×#3142C2
socleC2×C11C2×#354
prime radicalC11×#532C22
cosocleC11×#124C23
hypercenter#3142D11
hypocenterC11#13604
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #3142

Complements

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

NH ≅ G/Ntype
3. #13066791C2semidirect
6. C2×C11×#125C4semidirect
9. C11×#488C4semidirect
13. C4×C11×M16C4semidirect
116. C2×#125Dic11semidirect
119. #488Dic11semidirect
125. C4×M16Dic11semidirect
213. C11#13604semidirect

Maximal subgroups

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

subgroupindex
#130703012
#130702812
#130667912
C11×#31422
#1360411