Finite Group Databasebeta

← #14648147

Subgroups — #14648147

Order 2816.

428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 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#13069586C211yesmaximal, characteristic
2#13068785C212yesmaximal
3C2×#10622181C211yesmaximal, characteristic
4#13066497C212yesmaximal
5C11×#2382C211yesmaximal, characteristic
6C2×C11×#125C2211yescharacteristic
7C11×#389—22no—
8C11×#387—22no—
9C11×#387—22no—
10C11×#382C2212yes—
11C2×#66872—22no—
12C2×#66871—22no—
13#10622548C2211yescharacteristic
14C2×#66867C2211yescharacteristic
15C2×#66867C2212yes—
16#10622181C414yescomplemented
17#10622167—22no—
18C11×#125—22no—
19C11×#125C2×C412yes—
20C11×#125Q812yes—
21C2×C11×C4⋊C4—22no—
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4D412yes—
24C2×C11×C4⋊C4D412yes—
25C2×C11×C4⋊C4D412yes—
26C2×C42×C11—22no—
27C2×C42×C11C2311yescharacteristic
28C2×C4⋊Dic11—22no—
29C2×C4⋊Dic11—21no—
30C22×C11⋊C8—22no—
31C22×C11⋊C8—21no—
32C11×#95—22no—
33C11×#95—22no—
34C11×#95—22no—
35C11×#95—22no—
36#66872—44no—
37#66871—44no—
38#66867—22no—
39#66867—22no—
40#66867C2×C414yes—
41#8913—111nomaximal, Sylow
42C22×C4×C11—22no—
43C22×C4×C11—22no—
44C22×C4×C11—22no—
45C22×C4×C11C2×D411yescharacteristic
46C22×C4×C11C2×D412yes—
47C22×Dic11—41no—
48C11×C4⋊C4—24no—
49C11×C4⋊C4—24no—
50C11×C4⋊C4—22no—
51C11×C4⋊C4—42no—
52C11×C4⋊C4—42no—
53C11×C4⋊C4—82no—
54C11×C4⋊C4C4⋊C414yes—
55C42×C11—82no—
56C42×C11C22×C411yescharacteristic
57C42×C11C2×Q811yescharacteristic
58C42×C11#4112yes—
59C4⋊Dic11—42no—
60C4⋊Dic11—42no—
61C4⋊Dic11—42no—
62C2×C11⋊C8—24no—
63C2×C11⋊C8—24no—
64C2×C11⋊C8—22no—
65C2×C11⋊C8—24no—
66C2×C11⋊C8—41no—
67C2×C11⋊C8—41no—
68#2382D1111yescharacteristic
69#1992—111no—
70#1847—112no—
71C2×#330—111no—
72#1295—112no—
73C23×C11#12011yescharacteristic
74C2×C4×C11—22no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—22no—
78C2×C4×C11—24no—
79C2×C4×C11—42no—
80C2×C4×C11—42no—
81C2×C4×C11—42no—
82C2×C4×C11—42no—
83C2×C4×C11—42no—
84C2×C4×C11—42no—
85C2×C4×C11—42no—
86C2×C4×C11—42no—
87C2×C4×C11C2×C4⋊C411yescharacteristic
88C2×C4×C11C4×D412yes—
89C2×C4×C11C22⋊Q812yes—
90C2×C4×C11#12311yescharacteristic
91C2×Dic11—82no—
92C2×Dic11—81no—
93C11⋊C8—28no—
94C11⋊C8—42no—
95C2×#125C2×D1111yescharacteristic
96C2×#107—222no—
97C2×#106—222no—
98C2×#97—112no—
99C2×#97—111no—
100#389—22no—
101#387—22no—
102#387—22no—
103#384—111no—
104#382C2×D1112yes—
105#340—222no—
106#330—114no—
107C22×C11#38511yescharacteristic
108C22×C11#45312yes—
109C22×C11#45411yescharacteristic
110C22×C11#45611yescharacteristic
111C22×C11#45612yes—
112C4×C11—21no—
113C4×C11—21no—
114C4×C11—22no—
115C4×C11—22no—
116C4×C11—44no—
117C4×C11—82no—
118C4×C11—82no—
119Dic11—161no—
120C22×C8—222no—
121C22×C8—221no—
122#125—22no—
123#125Dic2212yes—
124#125C4×D1112yes—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—221no—
128C2×C4⋊C4—222no—
129C2×C4⋊C4C22⋊D1112yes—
130C2×C4⋊C4C22⋊D1112yes—
131C2×C4⋊C4C22⋊D1112yes—
132C2×C42—22no—
133C2×C42C22×D1111yescharacteristic
134#107—444no—
135#106—444no—
136#97—114no—
137#97—222no—
138#97—222no—
139#95—22no—
140#95—22no—
141#95—22no—
142#95—22no—
143C2×C11#165611yescharacteristic
144C2×C11#166012yes—
145C2×C11#166311yescharacteristic
146C2×C11#185711yescharacteristic
147C2×C11#185912yes—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—441no—
152C22×C4C2×C22⋊D1111yescharacteristic
153C22×C4C2×C22⋊D1112yes—
154C2×C8—224no—
155C2×C8—224no—
156C2×C8—224no—
157C2×C8—222no—
158C2×C8—441no—
159C2×C8—441no—
160C4⋊C4—24no—
161C4⋊C4—24no—
162C4⋊C4—22no—
163C4⋊C4—42no—
164C4⋊C4—42no—
165C4⋊C4—82no—
166C4⋊C4—442no—
167C4⋊C4—442no—
168C4⋊C4—442no—
169C4⋊C4Dic11⋊C414yes—
170C42—82no—
171C42C2×Dic2211yescharacteristic
172C42C2×C4×D1111yescharacteristic
173C42#433912yes—
174C11#891311yescharacteristic, complemented, Sylow
175C23#6700611yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—882no—
190C2×C4—881no—
191C2×C4C2×Dic11⋊C411yescharacteristic
192C2×C4#6697712yes—
193C2×C4C4×C22⋊D1112yes—
194C2×C4#6698211yescharacteristic
195C8—228no—
196C8—442no—
197C22#1062282311yescharacteristic
198C22#1062285412yes—
199C22#1062285811yescharacteristic
200C22#1062285911yescharacteristic
201C22#1062285912yes—
202C4—21no—
203C4—21no—
204C4—22no—
205C4—22no—
206C4—44no—
207C4—82no—
208C4—82no—
209C4—1761no—
210C2#1306790911yescharacteristic
211C2#1306792712yes—
212C2#1306794411yescharacteristic
213C2#1306883111yescharacteristic
214C2#1306884212yes—
subgroupG/H
centerC23#67006
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2382C2
socle, prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#2382D11
hypocenterC11#8913
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2382

Complements

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

NH ≅ G/Ntype
16. #10622181C4semidirect
174. C11#8913semidirect

Maximal subgroups

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

subgroupindex
#130695862
#130687852
C2×#106221812
#130664972
C11×#23822
#891311