Finite Group Databasebeta

← #14668046

Subgroups — #14668046

Order 2816.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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#13070865C211yesmaximal, characteristic
2#13070521C211yesmaximal, characteristic, complemented
3#13067977C211yesmaximal, characteristic, complemented
4#13067973C211yesmaximal, characteristic, complemented
5#13066689C211yesmaximal, characteristic, complemented
6#13066663C211yesmaximal, characteristic, complemented
7C11×#1361C211yesmaximal, characteristic, complemented
8C11×#493C2211yescharacteristic
9C2×#66890—21no—
10C2×#66890—21no—
11#10622688—21no—
12#10622461—21no—
13#10622308C2211yescharacteristic
14C8×Dic22C2211yescharacteristic
15C11×C4⋊C16C2211yescharacteristic
16C11×#335C2211yescharacteristic
17#10622182—21no—
18#10622140—21no—
19Dic11⋊C16—21no—
20#10622123—21no—
21C4×C11⋊C16C2211yescharacteristic
22#10622096C2211yescharacteristic
23C2×C11×D8—21no—
24C2×C11×D8—21no—
25C11×#127—21no—
26C2×#4324—41no—
27C2×D88—21no—
28C2×D88—21no—
29C2×#4314—41no—
30#66927—21no—
31C4×Dic22D411yescharacteristic
32C2×C11×C16—21no—
33C11×C4⋊C8—21no—
34C4×C8×C11C2311yescharacteristic
35#66896—41no—
36#66890—42no—
37#66890—42no—
38#66885—41no—
39Dic11⋊C8—21no—
40C8×Dic11—21no—
41C2×C11⋊C16D411yescharacteristic
42C2×C11⋊C16D411yescharacteristic
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)D411yescharacteristic
45#12442—111nomaximal, Sylow
46C2×D4×C11—41no—
47C2×D4×C11—41no—
48C2×D4×C11—41no—
49C2×D44—41no—
50C2×D44—41no—
51C2×D44—41no—
52C2×Dic22D811yescharacteristic
53C11×D8—41no—
54C11×D8—41no—
55C11×D8—81no—
56C2×C8×C11—41no—
57C2×C8×C11C2×D411yescharacteristic
58C2×C8×C11#4111yescharacteristic
59C42×C11C2×D411yescharacteristic
60#4324—82no—
61C4⋊Dic11D811yescharacteristic
62Dic11⋊C4—21no—
63C4×Dic11—21no—
64C2×C11⋊C8—21no—
65C2×C11⋊C8—41no—
66D88—41no—
67D88—41no—
68D88—81no—
69#4314—82no—
70C11×C16—41no—
71C11⋊C16—21no—
72C11⋊C16SD1612yescomplemented
73#2246—111no—
74#2183—111no—
75#1668—111no—
76#1668—111no—
77#1372—111no—
78#1361—111no—
79#1361D1111yescharacteristic, complemented
80C23×C11—81no—
81C22×D11—81no—
82D4×C11—81no—
83D4×C11—81no—
84D4×C11—81no—
85D4×C11—81no—
86D4×C11—161no—
87C2×C4×C11#12111yescharacteristic
88C2×C4×C11C2×D811yescharacteristic
89C2×C4×C11#13511yescharacteristic
90C2×Dic11—21no—
91C2×Dic11—21no—
92D44—81no—
93D44—81no—
94D44—81no—
95D44—81no—
96D44—161no—
97Dic22—21no—
98Dic22—21no—
99C8×C11—21no—
100C8×C11—81no—
101C8×C11C2×SD1611yescharacteristic
102C8×C11AGL(1,ℤ/8)11yescharacteristic
103C11⋊C8—41no—
104C11⋊C8—81no—
105C2×D16—221no—
106C2×D16—221no—
107#493—111no—
108#493C2×D1111yescharacteristic
109#460—221no—
110#460—221no—
111C8×Q8—111no—
112C4⋊C16—221no—
113C4⋊C16C2×D1111yescharacteristic
114#346—221no—
115C4×C16—111no—
116#335—111no—
117#335C2×D1111yescharacteristic
118#331—221no—
119#331—221no—
120C22×C11—161no—
121C22×C11—161no—
122C22×C11—161no—
123C22×C11#46611yescharacteristic
124C2×D11—161no—
125C2×D11—161no—
126C2×D11—161no—
127C4×C11—21no—
128C4×C11#46011yescharacteristic
129C4×C11#47211yescharacteristic
130C4×C11#50911yescharacteristic
131C4×C11#50911yescharacteristic
132Dic11—41no—
133Dic11—41no—
134C2×SD16—441no—
135C2×SD16—441no—
136C2×D8—21no—
137C2×D8—21no—
138C2×D8—221no—
139C2×D8—221no—
140#127—21no—
141#127—221no—
142C4×Q8—111no—
143D16—442no—
144D16—442no—
145C2×C16—21no—
146C2×C16—111no—
147C2×C16—111no—
148C4⋊C8—21no—
149C4⋊C8—111no—
150C4⋊C8—221no—
151C4⋊C8—221no—
152#102—441no—
153#102—441no—
154C4×C8—221no—
155C4×C8C22×D1111yescharacteristic
156C2×C11—321no—
157C2×C11#166811yescharacteristic
158C2×C11#221811yescharacteristic
159C2×C11#222111yescharacteristic
160D11—321no—
161C2×Q8—111no—
162C2×D4—41no—
163C2×D4—41no—
164C2×D4—41no—
165C2×D4—441no—
166C2×D4—441no—
167C2×D4—441no—
168SD16—882no—
169SD16—882no—
170D8—41no—
171D8—41no—
172D8—81no—
173D8—441no—
174D8—441no—
175D8—881no—
176C2×C8—41no—
177C2×C8—221no—
178C2×C8—441no—
179C2×C8#433911yescharacteristic
180C2×C8D4×D1111yescharacteristic
181C4⋊C4—111no—
182C4⋊C4—221no—
183C42—221no—
184C42D4×D1111yescharacteristic
185C16—41no—
186C16—112no—
187C16—221no—
188C11#1244211yescharacteristic, complemented, Sylow
189C23—81no—
190C23—881no—
191Q8—221no—
192Q8—221no—
193D4—81no—
194D4—81no—
195D4—81no—
196D4—81no—
197D4—161no—
198D4—881no—
199D4—881no—
200D4—881no—
201D4—881no—
202D4—1761no—
203C2×C4—221no—
204C2×C4—221no—
205C2×C4#6693711yescharacteristic
206C2×C4D8×D1111yescharacteristic
207C2×C4#6696911yescharacteristic
208C8—21no—
209C8—81no—
210C8—441no—
211C8—881no—
212C8#6696411yescharacteristic
213C8SD16×D1111yescharacteristic
214C22—161no—
215C22—161no—
216C22—161no—
217C22—1761no—
218C22—1761no—
219C22—1761no—
220C22#1062238811yescharacteristic
221C4—21no—
222C4—441no—
223C4—441no—
224C4#1062236211yescharacteristic
225C4#1062237511yescharacteristic
226C4#1062252411yescharacteristic
227C4#1062252711yescharacteristic
228C2—321no—
229C2—3521no—
230C2#1306797511yescharacteristic
231C2#1307071811yescharacteristic
232C2#1307073511yescharacteristic
subgroupG/H
centerC22#10622388
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1361C2
socleC22×C11#466
prime radical#13070865C2
hypercenter#1361D11
hypocenterC11#12442
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
2. #13070521C2semidirect
3. #13067977C2semidirect
4. #13067973C2semidirect
5. #13066689C2semidirect
6. #13066663C2semidirect
7. C11×#1361C2semidirect
72. C11⋊C16SD16semidirect
79. #1361D11semidirect
188. C11#12442semidirect

Maximal subgroups

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

subgroupindex
#130708652
#130705212
#130679772
#130679732
#130666892
#130666632
C11×#13612
#1244211