Finite Group Databasebeta

← #14648149

Subgroups — #14648149

Order 2816.

428 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 119 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#13071802C211yesmaximal, characteristic
2#13069586C211yesmaximal, characteristic
3#13068784C212yesmaximal
4#13066498C212yesmaximal
5C2×C11×#330C211yesmaximal, characteristic
6C2×C11×#125C2211yescharacteristic
7C2×C11×#97C2212yes—
8C2×#66882—22no—
9C2×#66881—22no—
10#10622598—22no—
11#10622594—22no—
12#10622594—22no—
13#10622549C2212yes—
14#10622548C2211yescharacteristic
15C2×#66867C2211yescharacteristic
16C11×#330C414yescomplemented
17#10622167—22no—
18C22×C8×C11—22no—
19C11×#125—22no—
20C11×#125C2×C412yes—
21C11×#125Q812yes—
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4D412yes—
24C2×C42×C11C2311yescharacteristic
25C2×C4⋊Dic11—21no—
26C2×C4⋊Dic11—22no—
27C2×C4⋊Dic11—22no—
28C2×C4⋊Dic11D412yes—
29C2×C4⋊Dic11D412yes—
30C2×C4×Dic11—22no—
31C22×C11⋊C8—21no—
32C11×#97—22no—
33C11×#97C2×C414yes—
34C11⋊#95—22no—
35C11⋊#95—22no—
36C11⋊#95—22no—
37C11⋊#95—22no—
38#66882—44no—
39#66881—44no—
40#66867—22no—
41#8913—111nomaximal, Sylow
42C22×C4×C11—22no—
43C22×C4×C11C2×D411yescharacteristic
44C22×C4×C11C2×D412yes—
45C22×Dic11—22no—
46C22×Dic11—22no—
47C22×Dic11—41no—
48C2×C8×C11—24no—
49C2×C8×C11—24no—
50C2×C8×C11—24no—
51C11×C4⋊C4—24no—
52C11×C4⋊C4—24no—
53C11×C4⋊C4—22no—
54C11×C4⋊C4C4⋊C414yes—
55C42×C11C22×C411yescharacteristic
56C42×C11C2×Q811yescharacteristic
57C42×C11#4112yes—
58C4⋊Dic11—42no—
59C4⋊Dic11—42no—
60C4⋊Dic11—42no—
61C4⋊Dic11—42no—
62C4⋊Dic11—42no—
63C4⋊Dic11—82no—
64C4×Dic11—82no—
65C2×C11⋊C8—22no—
66C2×C11⋊C8—41no—
67C2×C11⋊C8—41no—
68#2382—111no—
69#1992—111no—
70#1847—112no—
71C2×#330D1111yescharacteristic
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×C11C2×C4⋊C411yescharacteristic
82C2×C4×C11C4×D412yes—
83C2×C4×C11C22⋊Q812yes—
84C2×C4×C11#12311yescharacteristic
85C2×Dic11—42no—
86C2×Dic11—42no—
87C2×Dic11—42no—
88C2×Dic11—42no—
89C2×Dic11—42no—
90C2×Dic11—42no—
91C2×Dic11—82no—
92C2×Dic11—81no—
93C8×C11—28no—
94C11⋊C8—42no—
95C2×#125C2×D1111yescharacteristic
96C2×#107—222no—
97C2×#106—222no—
98C2×#97—111no—
99C2×#97C2×D1112yes—
100#389—222no—
101#387—222no—
102#387—222no—
103#384—111no—
104#382—112no—
105#340—222no—
106#330Dic1114yescomplemented
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—
117Dic11—82no—
118Dic11—82no—
119Dic11—161no—
120C22×C8—22no—
121C22×C8—221no—
122#125—22no—
123#125Dic2212yes—
124#125C2×Dic1112yes—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—112no—
127C2×C4⋊C4—112no—
128C2×C4⋊C4—221no—
129C2×C4⋊C4—222no—
130C2×C4⋊C4—222no—
131C2×C4⋊C4D4412yes—
132C2×C42—222no—
133C2×C42C22×D1111yescharacteristic
134#107—444no—
135#106—444no—
136#97—22no—
137#97—222no—
138#97C2×Dic1114yes—
139#95—222no—
140#95—222no—
141#95—222no—
142#95—222no—
143C2×C11#165611yescharacteristic
144C2×C11#166012yes—
145C2×C11#166311yescharacteristic
146C2×C11#185711yescharacteristic
147C2×C11#185912yes—
148C22×C4—22no—
149C22×C4—222no—
150C22×C4—222no—
151C22×C4—441no—
152C22×C4C2×D4411yescharacteristic
153C22×C4D4×D1112yes—
154C2×C8—24no—
155C2×C8—24no—
156C2×C8—24no—
157C2×C8—222no—
158C2×C8—441no—
159C2×C8—441no—
160C4⋊C4—24no—
161C4⋊C4—22no—
162C4⋊C4—24no—
163C4⋊C4—442no—
164C4⋊C4—442no—
165C4⋊C4—442no—
166C4⋊C4—442no—
167C4⋊C4—442no—
168C4⋊C4—882no—
169C4⋊C4C4⋊Dic1114yes—
170C42—882no—
171C42C2×Dic2211yescharacteristic
172C42#434112yes—
173C42C22×Dic1111yescharacteristic
174C11#891311yescharacteristic, complemented, Sylow
175C23#6693511yescharacteristic
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—442no—
184C2×C4—442no—
185C2×C4—442no—
186C2×C4—442no—
187C2×C4—442no—
188C2×C4—442no—
189C2×C4—881no—
190C2×C4—882no—
191C2×C4#6693112yes—
192C2×C4#6693911yescharacteristic
193C2×C4C2×C4⋊Dic1111yescharacteristic
194C2×C4D4×Dic1112yes—
195C8—28no—
196C8—442no—
197C22#1062236511yescharacteristic
198C22#1062236611yescharacteristic
199C22#1062243512yes—
200C22#1062243912yes—
201C22#1062256311yescharacteristic
202C4—21no—
203C4—21no—
204C4—22no—
205C4—22no—
206C4—44no—
207C4—882no—
208C4—882no—
209C4—1761no—
210C2#1306791111yescharacteristic
211C2#1306792912yes—
212C2#1306794511yescharacteristic
213C2#1306883311yescharacteristic
214C2#1306884412yes—
subgroupG/H
centerC23#66935
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#330C2
socle, prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenterC2×#330D11
hypocenterC11#8913
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
16. C11×#330C4semidirect
106. #330Dic11semidirect
174. C11#8913semidirect

Maximal subgroups

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

subgroupindex
#130718022
#130695862
#130687842
#130664982
C2×C11×#3302
#891311