Finite Group Databasebeta

← #14667163

Subgroups — #14667163

Order 2816.

280 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 53 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#13080018C211yesmaximal, characteristic
2#13070833C211yesmaximal, characteristic, complemented
3#13070831C211yesmaximal, characteristic
4#13070192C211yesmaximal, characteristic, complemented
5#13066600C211yesmaximal, characteristic
6#13066566C211yesmaximal, characteristic, complemented
7C11×#1340C211yesmaximal, characteristic, complemented
8#10623155—21no—
9C11×#470C2211yescharacteristic
10#10622798—21no—
11#10622748C2211yescharacteristic
12#10622738C2211yescharacteristic
13#10622731C2211yescharacteristic
14#10622662—21no—
15#10622484—21no—
16#10622432—21no—
17#10622412—21no—
18C11×#349C2211yescharacteristic
19C11×H(3,ℤ/4)C2211yescharacteristic
20#10622203—21no—
21#10622191C2211yescharacteristic
22#10622171—21no—
23#10622170—21no—
24#10622154—21no—
25#10622151—21no—
26#10622125—21no—
27C2×C11×Q16D411yescharacteristic
28C2×C11×M16C2311yescharacteristic
29C11×C22⋊Q8—21no—
30C11×#117—21no—
31#67000—21no—
32Q8×Dic11—21no—
33C2×#4325—21no—
34#66983—21no—
35C2×C4×Dic11D411yescharacteristic
36C2×#4318—21no—
37C2×#4318D411yescharacteristic
38C2×D88D411yescharacteristic
39#66951—41no—
40#66946—21no—
41#66945—41no—
42#66943—21no—
43#66939—41no—
44(C22⋊D11)⋊C4—41no—
45C11×M32—21no—
46C11×#106D411yescharacteristic
47C11×#103—21no—
48#66899—21no—
49#66885—21no—
50#66883—21no—
51#66883—21no—
52#66881D411yescharacteristic
53Dic11⋊C8—21no—
54Dic11⋊C8—21no—
55#66876—21no—
56#66873—21no—
57#66871—21no—
58#12309—111nomaximal, Sylow
59C2×Q8×C11—21no—
60C22×C4×C11C2×D411yescharacteristic
61C2×C22⋊D11—41no—
62C22×Dic11—21no—
63C2×D44—21no—
64C2×C4×D11—41no—
65C11×Q16—41no—
66C11×M16—41no—
67C2×C8×C11C2×D411yescharacteristic
68C2×C8×C11C2×D411yescharacteristic
69C11×C4⋊C4—21no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C11×C22⋊C4—41no—
73C11×C22⋊C4—41no—
74C42×C11—41no—
75#4325—81no—
76(C2×D11)⋊C4—41no—
77(C2×D11)⋊C4—41no—
78(C2×D11)⋊C4—41no—
79(C2×D11)⋊C4—41no—
80C4⋊Dic11—21no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83Dic11⋊C4—41no—
84C4×Dic11—21no—
85C4×Dic11—41no—
86C4×Dic11SD1611yescharacteristic
87C4×Dic11SD1611yescharacteristic
88#4318—41no—
89#4318—41no—
90#4318—41no—
91C2×C11⋊C8—21no—
92C2×C11⋊C8—41no—
93D88—41no—
94C11×C16—41no—
95C11⋊C16—41no—
96#3256—111no—
97#2239—111no—
98#2238—111no—
99#2102—111no—
100#1340D1111yescharacteristic, complemented
101#1339—111no—
102#1327—111no—
103C23×C11AGL(1,ℤ/8)11yescharacteristic
104C22×D11—41no—
105Q8×C11—41no—
106Q8×C11—41no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—81no—
112C2×C4×C11#12011yescharacteristic
113C2×C4×C11C2×SD1611yescharacteristic
114C22⋊D11—82no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11—41no—
118C2×Dic11—81no—
119D44—41no—
120D44—41no—
121C4×D11—82no—
122C8×C11—21no—
123C8×C11—21no—
124C11⋊C8—41no—
125C11⋊C8—81no—
126#529—221no—
127#479—221no—
128#478—221no—
129#470C2×D1111yescharacteristic
130#469—111no—
131#468—221no—
132#464—221no—
133#463—221no—
134#430—111no—
135#423—111no—
136#365—221no—
137#365—221no—
138#362—221no—
139#361—221no—
140#349—111no—
141#349C2×D1111yescharacteristic
142#344—221no—
143#339—221no—
144H(3,ℤ/4)C2×D1111yescharacteristic
145C22×C11—21no—
146C22×C11—41no—
147C22×C11#45011yescharacteristic
148C2×D11—81no—
149C2×D11—81no—
150C2×D11—81no—
151C4×C11—21no—
152C4×C11—81no—
153C4×C11—81no—
154C4×C11—161no—
155C4×C11#45411yescharacteristic
156C4×C11#45811yescharacteristic
157Dic11—41no—
158Dic11—41no—
159Dic11—81no—
160C2×Q16D4411yescharacteristic
161C2×SD16—221no—
162C2×D8—111no—
163C2×M16—111no—
164C2×M16—221no—
165C2×M16C22×D1111yescharacteristic
166#126—441no—
167#125—221no—
168#124—221no—
169#123—441no—
170C22⋊Q8—21no—
171#121—221no—
172C4×Q8—221no—
173C4×D4—221no—
174C4×D4—441no—
175#117—21no—
176#117—441no—
177C2×C42—111no—
178M32—21no—
179M32—221no—
180#108—221no—
181#108—221no—
182#107—221no—
183#106—111no—
184#106D4411yescharacteristic
185C4⋊C8—221no—
186C4⋊C8—221no—
187#103—21no—
188#103—221no—
189#102—221no—
190#102—221no—
191C2×C11—21no—
192C2×C11—41no—
193C2×C11#161611yescharacteristic
194D11—161no—
195C2×Q8—21no—
196C2×D4—221no—
197C2×D4—441no—
198C22×C4—221no—
199C22×C4—441no—
200C22×C4D4×D1111yescharacteristic
201Q16—41no—
202SD16—881no—
203D8—441no—
204M16—41no—
205M16—441no—
206M16—441no—
207M16—441no—
208C2×C8—221no—
209C2×C8—441no—
210C2×C8C2×D4411yescharacteristic
211C2×C8D4×D1111yescharacteristic
212C4⋊C4—21no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—221no—
216C4⋊C4—441no—
217C4⋊C4—441no—
218C4⋊C4—441no—
219C22⋊C4—41no—
220C22⋊C4—41no—
221C22⋊C4—441no—
222C22⋊C4—441no—
223C22⋊C4—441no—
224C22⋊C4—441no—
225C42—41no—
226C42—111no—
227C42—111no—
228C42—221no—
229C42—441no—
230C16—41no—
231C16—441no—
232C11#1230911yescharacteristic, complemented, Sylow
233C23—441no—
234C23#6696411yescharacteristic
235Q8—41no—
236Q8—41no—
237D4—441no—
238D4—441no—
239D4—882no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—81no—
245C2×C4—221no—
246C2×C4—221no—
247C2×C4—441no—
248C2×C4—882no—
249C2×C4—881no—
250C2×C4#6693511yescharacteristic
251C2×C4SD16×D1111yescharacteristic
252C8—21no—
253C8—21no—
254C8—441no—
255C8—881no—
256C22—21no—
257C22—41no—
258C22—881no—
259C22—881no—
260C22—881no—
261C22#1062238911yescharacteristic
262C4—21no—
263C4—81no—
264C4—81no—
265C4—161no—
266C4—441no—
267C4—441no—
268C4—881no—
269C4#1062235511yescharacteristic
270C4#1062244011yescharacteristic
271C2—21no—
272C2—41no—
273C2—1761no—
274C2#1306765411yescharacteristic
subgroupG/H
centerC2#13067654
commutator, cosocleC2×C11×M16C23
FrattiniC2×M16C22×D11
FittingC11×#1340C2
socleC2×C11#1616
prime radical#10622748C22
hypercenter#1340D11
hypocenterC11#12309
LCSG ▷ C2×C11×M16 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1340

Complements

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

NH ≅ G/Ntype
2. #13070833C2semidirect
4. #13070192C2semidirect
6. #13066566C2semidirect
7. C11×#1340C2semidirect
100. #1340D11semidirect
232. C11#12309semidirect

Maximal subgroups

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

subgroupindex
#130800182
#130708332
#130708312
#130701922
#130666002
#130665662
C11×#13402
#1230911