Finite Group Databasebeta

← #14651398

Subgroups — #14651398

Order 2816.

434 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 103 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#13071722C211yesmaximal, characteristic
2#13067243C211yesmaximal, characteristic
3#13067128C212yesmaximal
4#13066510C212yesmaximal
5C11×#3166C211yesmaximal, characteristic
6C11×#533C2211yescharacteristic
7C2×C11×#125C2211yescharacteristic
8C11×#501C414yescomplemented
9C11×#499—22no—
10C11×#428—22no—
11C4×C11×M16C2211yescharacteristic
12#10622594—22no—
13#10622594—22no—
14C4⋊C4×Dic11—22no—
15#10622545C2212yes—
16#10622539C2212yes—
17#10622181—22no—
18#10622176—22no—
19#10622176—22no—
20C2×C11×M16—21no—
21C11×C4⋊Q8C2×C412yes—
22C11×#125—21no—
23C11×#125—22no—
24C11×#125C2×C412yes—
25C11×#125D412yes—
26C11×C22⋊Q8—22no—
27C4×Q8×C11—22no—
28C11×#117—21no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4D412yes—
31C2×C42×C11C2311yescharacteristic
32C2×C4⋊Dic11—22no—
33C2×C4×Dic11—22no—
34C2×C4×Dic11—22no—
35C11×#107—24no—
36C11×#106—24no—
37C11×#97C2×C412yes—
38C4×C8×C11—21no—
39C11⋊#95—22no—
40C11⋊#95—22no—
41C11⋊#95—22no—
42C11⋊#95D412yes—
43C11⋊#95D412yes—
44C22⋊(C11⋊C8)—22no—
45C4⋊(C11⋊C8)—22no—
46#66867—22no—
47#9440—111nomaximal, Sylow
48C2×Q8×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11C2×D411yescharacteristic
51C22×C4×C11C2×D412yes—
52C22×Dic11—22no—
53C22×Dic11—22no—
54C11×M16—24no—
55C2×C8×C11—22no—
56C11×C4⋊C4—24no—
57C11×C4⋊C4—24no—
58C11×C4⋊C4—22no—
59C11×C4⋊C4—22no—
60C11×C4⋊C4—22no—
61C11×C4⋊C4—42no—
62C11×C4⋊C4C22⋊C414yes—
63C11×C22⋊C4—41no—
64C42×C11—41no—
65C42×C11C22×C411yescharacteristic
66C42×C11C2×D411yescharacteristic
67C42×C11#4112yes—
68C4⋊Dic11—44no—
69C4×Dic11—44no—
70C4×Dic11—44no—
71C2×C11⋊C8—42no—
72#3166D1111yescharacteristic
73#2371—111no—
74#1534—111no—
75#1506—112no—
76#1300—112no—
77C23×C11#12011yescharacteristic
78Q8×C11—82no—
79C2×C4×C11—22no—
80C2×C4×C11—24no—
81C2×C4×C11—42no—
82C2×C4×C11—42no—
83C2×C4×C11—42no—
84C2×C4×C11—42no—
85C2×C4×C11C2×C22⋊C411yescharacteristic
86C2×C4×C11C4×D412yes—
87C2×C4×C11#12112yes—
88C2×C4×C11#12311yescharacteristic
89C2×Dic11—24no—
90C2×Dic11—42no—
91C2×Dic11—42no—
92C2×Dic11—42no—
93C2×Dic11—42no—
94C2×Dic11—42no—
95C8×C11—24no—
96C11⋊C8—82no—
97#533C2×D1111yescharacteristic
98C2×#125C2×D1111yescharacteristic
99#501Dic1114yescomplemented
100#499—22no—
101#432—112no—
102#428—22no—
103C4×M16C2×D1111yescharacteristic
104#387—222no—
105#387—222no—
106C4×C4⋊C4—222no—
107#376—112no—
108#330—222no—
109#328—222no—
110#328—222no—
111C22×C11—22no—
112C22×C11#38611yescharacteristic
113C22×C11#45612yes—
114C4×C11—21no—
115C4×C11—21no—
116C4×C11—22no—
117C4×C11—22no—
118C4×C11—44no—
119C4×C11—82no—
120Dic11—44no—
121Dic11—82no—
122C2×M16—21no—
123C4⋊Q8C2×Dic1112yes—
124#125—22no—
125#125—21no—
126#125C2×Dic1112yes—
127#125C22⋊D1112yes—
128C22⋊Q8—22no—
129C4×Q8—22no—
130#117—21no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—222no—
133C2×C4⋊C4C22⋊D1112yes—
134C2×C42—222no—
135C2×C42—222no—
136C2×C42C22×D1111yescharacteristic
137#107—24no—
138#106—24no—
139C4⋊C8—222no—
140C22⋊C8—222no—
141#97—222no—
142#97C2×Dic1112yes—
143C4×C8—21no—
144#95—112no—
145#95—112no—
146#95—222no—
147#95—222no—
148#95—222no—
149C2×C11—22no—
150C2×C11#188611yescharacteristic
151C2×C11#190612yes—
152C2×Q8—22no—
153C22×C4—22no—
154C22×C4—222no—
155C22×C4—222no—
156C22×C4D4×D1112yes—
157C22×C4C2×C22⋊D1111yescharacteristic
158M16—24no—
159C2×C8—22no—
160C2×C8—442no—
161C4⋊C4—24no—
162C4⋊C4—22no—
163C4⋊C4—24no—
164C4⋊C4—22no—
165C4⋊C4—22no—
166C4⋊C4—42no—
167C4⋊C4—444no—
168C4⋊C4C22⋊Dic1114yes—
169C22⋊C4—41no—
170C42—41no—
171C42—444no—
172C42—444no—
173C42#434112yes—
174C42C22×Dic1111yescharacteristic
175C42C2×C22⋊D1111yescharacteristic
176C11#944011yescharacteristic, complemented, Sylow
177C23#6699011yescharacteristic
178Q8—82no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—224no—
186C2×C4—442no—
187C2×C4—442no—
188C2×C4—442no—
189C2×C4—442no—
190C2×C4—442no—
191C2×C4D4×Dic1112yes—
192C2×C4#6698811yescharacteristic
193C2×C4#6699212yes—
194C2×C4C2×C22⋊Dic1111yescharacteristic
195C8—24no—
196C8—882no—
197C22—22no—
198C22#1062270812yes—
199C22#1062283311yescharacteristic
200C4—22no—
201C4—22no—
202C4—21no—
203C4—21no—
204C4—44no—
205C4—82no—
206C4—444no—
207C4—882no—
208C2—22no—
209C2#1306901011yescharacteristic
210C2#1306911912yes—
subgroupG/H
centerC22#10622833
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3166C2
socleC22×C11#386
prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#3166D11
hypocenterC11#9440
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3166

Complements

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

NH ≅ G/Ntype
8. C11×#501C4semidirect
99. #501Dic11semidirect
176. C11#9440semidirect

Maximal subgroups

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

subgroupindex
#130717222
#130672432
#130671282
#130665102
C11×#31662
#944011