Finite Group Databasebeta

← #14651313

Subgroups — #14651313

Order 2816.

422 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 95 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#13078996C211yesmaximal, characteristic
2#13071797C211yesmaximal, characteristic
3#13067168C212yesmaximal
4#13066482C212yesmaximal
5C11×#1558C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7#10623001C2211yescharacteristic
8C11×#432C2212yes—
9#10622843—22no—
10#10622838—22no—
11#10622695—22no—
12#10622694C414yescomplemented
13#10622594—24no—
14#10622550C2212yes—
15C4×#4318C2211yescharacteristic
16C11×#333—22no—
17#10622105—24no—
18C22×Q8×C11D412yes—
19C11×C4⋊Q8—22no—
20C11×C4⋊Q8C2×C412yes—
21C11×C4⋊Q8D412yes—
22C2×C11×C4⋊C4—22no—
23C2×C42×C11C2311yescharacteristic
24#66979—21no—
25C2×C4⋊Dic11—22no—
26#66977—22no—
27C2×C4×Dic11—22no—
28C2×#4318—21no—
29#66923—21no—
30#66922C2×C412yes—
31C4×Dic22—22no—
32C11×C4⋊C8—22no—
33C11×C22⋊C8—22no—
34C11×#97—22no—
35#66899—28no—
36C11⋊#95—24no—
37C11⋊#95—22no—
38C11⋊#95—22no—
39C11⋊#95D414yes—
40#66867—21no—
41C4×C11⋊C8C2×C412yes—
42#9426—111nomaximal, Sylow
43C2×Q8×C11—22no—
44C2×Q8×C11—42no—
45C2×Q8×C11—42no—
46C2×Q8×C11C22⋊C414yes—
47C22×C4×C11—22no—
48C22×C4×C11C2×D411yescharacteristic
49C22×C4×C11C2×D412yes—
50C22×Dic11—24no—
51C2×Dic22—22no—
52C2×C8×C11—42no—
53C11×C4⋊C4—24no—
54C11×C4⋊C4—24no—
55C42×C11C22×C411yescharacteristic
56C42×C11C2×D411yescharacteristic
57C42×C11#4112yes—
58C22⋊Dic11—41no—
59C4⋊Dic11—22no—
60C4⋊Dic11—22no—
61C4⋊Dic11—82no—
62Dic11⋊C4—42no—
63C4×Dic11—41no—
64C4×Dic11—82no—
65#4318—42no—
66C2×C11⋊C8—22no—
67#3139—111no—
68#2381—111no—
69#1558D1111yescharacteristic
70#1515—112no—
71#1288—112no—
72C23×C11#12011yescharacteristic
73Q8×C11—44no—
74Q8×C11—82no—
75C2×C4×C11—22no—
76C2×C4×C11—24no—
77C2×C4×C11—42no—
78C2×C4×C11—42no—
79C2×C4×C11—42no—
80C2×C4×C11C2×C22⋊C411yescharacteristic
81C2×C4×C11C4×D412yes—
82C2×C4×C11#12112yes—
83C2×C4×C11#12311yescharacteristic
84C2×Dic11—48no—
85C2×Dic11—42no—
86C2×Dic11—44no—
87Dic22—82no—
88C8×C11—82no—
89C11⋊C8—42no—
90#533—111no—
91C2×C4⋊Q8C2×D1111yescharacteristic
92#491—222no—
93#487—114no—
94#432C2×D1112yes—
95#419—222no—
96C4×M16—111no—
97#391—222no—
98#387—224no—
99#383—112no—
100#333—22no—
101#328—224no—
102C22×C11—22no—
103C22×C11#38611yescharacteristic
104C22×C11#45512yes—
105C4×C11—21no—
106C4×C11—21no—
107C4×C11—22no—
108C4×C11—22no—
109C4×C11—44no—
110Dic11—84no—
111Dic11—82no—
112C22×Q8D4412yes—
113C2×M16—221no—
114C4⋊Q8—22no—
115C4⋊Q8—112no—
116C4⋊Q8C4×D1112yes—
117C4⋊Q8C22⋊D1112yes—
118#125—221no—
119C22⋊Q8—222no—
120C4×Q8—222no—
121#117—221no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—222no—
124C2×C42—222no—
125C2×C42C22×D1111yescharacteristic
126C4⋊C8—22no—
127#103—228no—
128C22⋊C8—22no—
129#97—22no—
130#97—221no—
131C4×C8—112no—
132#95—114no—
133#95—224no—
134#95—222no—
135#95—222no—
136C2×C11—22no—
137C2×C11#188511yescharacteristic
138C2×C11#190512yes—
139C2×Q8—22no—
140C2×Q8—42no—
141C2×Q8—42no—
142C2×Q8—222no—
143C2×Q8(C2×D11)⋊C414yes—
144C22×C4—22no—
145C22×C4—224no—
146C22×C4C2×D4411yescharacteristic
147C22×C4D4×D1112yes—
148M16—442no—
149C2×C8—42no—
150C2×C8—222no—
151C4⋊C4—24no—
152C4⋊C4—24no—
153C4⋊C4—222no—
154C4⋊C4—222no—
155C4⋊C4—442no—
156C4⋊C4—882no—
157C22⋊C4—441no—
158C42—441no—
159C42—882no—
160C42C2×C4×D1111yescharacteristic
161C42#434112yes—
162C42C2×C22⋊D1111yescharacteristic
163C11#942611yescharacteristic, complemented, Sylow
164C23#6693511yescharacteristic
165Q8—44no—
166Q8—82no—
167Q8—882no—
168C2×C4—22no—
169C2×C4—24no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—448no—
174C2×C4—442no—
175C2×C4—444no—
176C2×C4(C22⋊D11)⋊C412yes—
177C2×C4#6693911yescharacteristic
178C2×C4C2×(C2×D11)⋊C411yescharacteristic
179C2×C4#6699212yes—
180C8—82no—
181C8—442no—
182C22—22no—
183C22#1062235912yes—
184C22#1062257111yescharacteristic
185C4—22no—
186C4—22no—
187C4—21no—
188C4—21no—
189C4—44no—
190C4—884no—
191C4—882no—
192C2—22no—
193C2#1306900211yescharacteristic
194C2#1306910812yes—
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1558C2
socleC22×C11#386
prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#1558D11
hypocenterC11#9426
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1558

Complements

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

NH ≅ G/Ntype
12. #10622694C4semidirect
163. C11#9426semidirect

Maximal subgroups

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

subgroupindex
#130789962
#130717972
#130671682
#130664822
C11×#15582
#942611