Finite Group Databasebeta

← #14656917

Subgroups — #14656917

Order 2816.

364 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 89 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#13071921C211yesmaximal, characteristic
2#13069597C211yesmaximal, characteristic
3#13067116C212yesmaximal
4#13066518C212yesmaximal
5C11×#1274C211yesmaximal, characteristic
6#10623001C2211yescharacteristic
7C11×#431C2212yes—
8C11×#376C2211yescharacteristic
9C4×C4⋊Dic11C2212yes—
10C4×Dic11⋊C4—22no—
11#10622537C2211yescharacteristic
12#10622273—22no—
13#10622270—22no—
14#10622161—22no—
15#10622105—22no—
16#10622105—22no—
17C2×C42×C11D412yes—
18C2×C42×C11C2311yescharacteristic
19#66979—21no—
20C2×C4⋊Dic11—22no—
21#66977—22no—
22C2×Dic11⋊C4—22no—
23C2×Dic11⋊C4—22no—
24C2×C4×Dic11—22no—
25C2×#4318—21no—
26#66923—21no—
27#66922Q812yes—
28C4×Dic22—22no—
29C11×C4⋊C8—22no—
30C11×C22⋊C8—22no—
31C4×C8×C11—22no—
32C11×#95—22no—
33C11⋊#95—22no—
34C11⋊#95—22no—
35C11⋊#95D412yes—
36C11⋊#95D412yes—
37C4⋊(C11⋊C8)—22no—
38#10373—111nomaximal, Sylow
39C22×C4×C11—22no—
40C22×C4×C11C2×D412yes—
41C22×C4×C11C2×D411yescharacteristic
42C22×Dic11—22no—
43C22×Dic11—22no—
44C2×Dic22—22no—
45C2×C8×C11—42no—
46C42×C11—22no—
47C42×C11—22no—
48C42×C11C2×Q811yescharacteristic
49C42×C11#4112yes—
50C42×C11#4111yescharacteristic
51C22⋊Dic11—41no—
52C4⋊Dic11—22no—
53C4⋊Dic11—22no—
54C4⋊Dic11—44no—
55Dic11⋊C4—44no—
56Dic11⋊C4—44no—
57Dic11⋊C4—42no—
58C4×Dic11—41no—
59C4×Dic11—42no—
60C4×Dic11—42no—
61#4318—42no—
62C2×C11⋊C8—41no—
63#2402—111no—
64#1995—111no—
65#1503—112no—
66#1303—112no—
67#1274D1111yescharacteristic
68C23×C11#12011yescharacteristic
69C2×C4×C11—42no—
70C2×C4×C11—42no—
71C2×C4×C11—42no—
72C2×C4×C11—42no—
73C2×C4×C11C22⋊Q812yes—
74C2×C4×C11C22⋊Q811yescharacteristic
75C2×C4×C11#12411yescharacteristic
76C2×C4×C11#12412yes—
77C2×C4×C11#13512yes—
78C2×C4×C11#13712yes—
79C2×Dic11—24no—
80C2×Dic11—42no—
81C2×Dic11—42no—
82C2×Dic11—42no—
83C2×Dic11—42no—
84C2×Dic11—42no—
85C2×Dic11—42no—
86Dic22—82no—
87C8×C11—82no—
88C11⋊C8—81no—
89#533—111no—
90#431C2×D1112yes—
91#423—111no—
92#400—222no—
93#398—222no—
94C4×C4⋊C4—112no—
95C4×C4⋊C4—222no—
96#376C2×D1111yescharacteristic
97#339—222no—
98#328—222no—
99#328—222no—
100C22×C11—22no—
101C22×C11#39311yescharacteristic
102C22×C11#45212yes—
103C4×C11—22no—
104C4×C11—22no—
105C4×C11—82no—
106C4×C11#47912yes—
107C4×C11#48811yescharacteristic
108C4×C11#49111yescharacteristic
109Dic11—44no—
110Dic11—82no—
111Dic11—82no—
112C2×M16—221no—
113C4⋊Q8—112no—
114#125—221no—
115C22⋊Q8—222no—
116C4×Q8—222no—
117#117—221no—
118C2×C4⋊C4—222no—
119C2×C4⋊C4—222no—
120C2×C4⋊C4—222no—
121C2×C42—222no—
122C2×C42D4412yes—
123C2×C42C22×D1111yescharacteristic
124C4⋊C8—22no—
125C4⋊C8—222no—
126C22⋊C8—22no—
127C4×C8—22no—
128#95—22no—
129#95—112no—
130#95—112no—
131#95—222no—
132#95—222no—
133C2×C11—22no—
134C2×C11#202611yescharacteristic
135C2×C11#203112yes—
136C2×Q8—222no—
137C22×C4—22no—
138C22×C4—222no—
139C22×C4—222no—
140C22×C4C2×D4411yescharacteristic
141C22×C4D4×D1112yes—
142M16—442no—
143C2×C8—42no—
144C2×C8—441no—
145C4⋊C4—222no—
146C4⋊C4—222no—
147C4⋊C4—444no—
148C4⋊C4—444no—
149C4⋊C4—444no—
150C4⋊C4—442no—
151C22⋊C4—441no—
152C42—22no—
153C42—22no—
154C42—441no—
155C42—442no—
156C42—442no—
157C42#433912yes—
158C42#434111yescharacteristic
159C42Q8×D1111yescharacteristic
160C11#1037311yescharacteristic, complemented, Sylow
161C23#6693511yescharacteristic
162Q8—882no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—224no—
168C2×C4—442no—
169C2×C4—442no—
170C2×C4—442no—
171C2×C4—442no—
172C2×C4—442no—
173C2×C4—442no—
174C2×C4#6692811yescharacteristic
175C2×C4#6693812yes—
176C2×C4#6694912yes—
177C2×C4#6695011yescharacteristic
178C2×C4#6695712yes—
179C2×C4#6696212yes—
180C8—82no—
181C8—881no—
182C22—22no—
183C22#1062228611yescharacteristic
184C22#1062234612yes—
185C4—22no—
186C4—22no—
187C4—82no—
188C4—444no—
189C4—882no—
190C4—882no—
191C4#1062231011yescharacteristic
192C4#1062231611yescharacteristic
193C4#1062244212yes—
194C2—22no—
195C2#1306976811yescharacteristic
196C2#1306978712yes—
subgroupG/H
centerC2×C4#66928
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1274C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1274D11
hypocenterC11#10373
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
160. C11#10373semidirect

Maximal subgroups

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

subgroupindex
#130719212
#130695972
#130671162
#130665182
C11×#12742
#1037311