Finite Group Databasebeta

← #14657267

Subgroups — #14657267

Order 2816.

386 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 91 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#13076684C211yesmaximal, characteristic
2#13069584C212yesmaximal
3C2×#10622103C212yesmaximal
4#13066497C211yesmaximal, characteristic
5C11×#1836C211yesmaximal, characteristic
6C2×#66923C2212yes—
7C2×C11×#97C2211yescharacteristic
8C11×#384C2211yescharacteristic
9C11×#382C2211yescharacteristic
10#10622596—22no—
11C2×#66867C2212yes—
12#10622274—22no—
13#10622272—22no—
14C11×#340—22no—
15#10622167—22no—
16#10622167—22no—
17#10622103—24no—
18C22×C8×C11—21no—
19C2×C11×C4⋊C4—21no—
20C2×C11×C4⋊C4—22no—
21C2×C11×C4⋊C4D412yes—
22C2×C42×C11C2311yescharacteristic
23C2×C4⋊Dic11—22no—
24C2×C4⋊Dic11D412yes—
25C2×C4⋊Dic11D412yes—
26C2×Dic11⋊C4—22no—
27C2×Dic11⋊C4—22no—
28C22×C11⋊C8—22no—
29#66923—22no—
30#66923—22no—
31#66923—22no—
32#66923—22no—
33C11×#97—21no—
34C11×#97D412yes—
35C11×#95—22no—
36C11⋊#95—22no—
37C11⋊#95—24no—
38#66867—22no—
39#66867—22no—
40#10428—111nomaximal, Sylow
41C22×C4×C11—22no—
42C22×C4×C11—41no—
43C22×C4×C11C2×D412yes—
44C22×C4×C11C2×D411yescharacteristic
45C22×Dic11—22no—
46C22×Dic11—22no—
47C2×C8×C11—22no—
48C2×C8×C11—41no—
49C2×C8×C11—41no—
50C11×C4⋊C4—42no—
51C11×C4⋊C4—44no—
52C11×C4⋊C4—42no—
53C42×C11C2×D411yescharacteristic
54C42×C11#4111yescharacteristic
55C42×C11#4112yes—
56C4⋊Dic11—22no—
57C4⋊Dic11—22no—
58C4⋊Dic11—22no—
59C4⋊Dic11—22no—
60C4⋊Dic11—82no—
61Dic11⋊C4—42no—
62Dic11⋊C4—42no—
63Dic11⋊C4—42no—
64Dic11⋊C4—42no—
65C2×C11⋊C8—24no—
66C2×C11⋊C8—42no—
67C2×C11⋊C8—42no—
68#2822—111no—
69#1992—112no—
70#1836D1111yescharacteristic
71C2×#330—112no—
72#1295—111no—
73C23×C11#12011yescharacteristic
74C2×C4×C11—22no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—22no—
78C2×C4×C11—42no—
79C2×C4×C11—42no—
80C2×C4×C11—42no—
81C2×C4×C11—82no—
82C2×C4×C11—81no—
83C2×C4×C11#12112yes—
84C2×C4×C11#12111yescharacteristic
85C2×C4×C11#12312yes—
86C2×C4×C11#12411yescharacteristic
87C2×Dic11—42no—
88C2×Dic11—42no—
89C2×Dic11—42no—
90C2×Dic11—42no—
91C2×Dic11—42no—
92C2×Dic11—42no—
93C8×C11—42no—
94C11⋊C8—44no—
95C2×#125—112no—
96C2×#97—112no—
97C2×#97C2×D1111yescharacteristic
98#400—222no—
99#398—222no—
100#398—222no—
101#384C2×D1111yescharacteristic
102#382C2×D1111yescharacteristic
103#340—22no—
104#340—222no—
105#340—222no—
106#330—224no—
107C22×C11#39411yescharacteristic
108C22×C11#45412yes—
109C22×C11#45411yescharacteristic
110C22×C11#45511yescharacteristic
111C22×C11#45612yes—
112C4×C11—22no—
113C4×C11—22no—
114C4×C11—21no—
115C4×C11—21no—
116C4×C11—82no—
117C4×C11—161no—
118Dic11—82no—
119Dic11—82no—
120C22×C8—21no—
121C22×C8—222no—
122#125—222no—
123#125—222no—
124#125—222no—
125#125—222no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—112no—
129C2×C4⋊C4—112no—
130C2×C4⋊C4—222no—
131C2×C4⋊C4—222no—
132C2×C4⋊C4—222no—
133C2×C4⋊C4C22⋊D1112yes—
134C2×C42C22×D1111yescharacteristic
135#97—21no—
136#97—222no—
137#97—222no—
138#97D4412yes—
139#95—22no—
140#95—224no—
141#95—222no—
142C2×C11#165811yescharacteristic
143C2×C11#166311yescharacteristic
144C2×C11#166412yes—
145C2×C11#203812yes—
146C2×C11#204011yescharacteristic
147C22×C4—22no—
148C22×C4—41no—
149C22×C4—222no—
150C22×C4—222no—
151C22×C4D4×D1112yes—
152C22×C4C2×C22⋊D1111yescharacteristic
153C2×C8—22no—
154C2×C8—41no—
155C2×C8—41no—
156C2×C8—224no—
157C2×C8—442no—
158C2×C8—442no—
159C4⋊C4—42no—
160C4⋊C4—44no—
161C4⋊C4—42no—
162C4⋊C4—222no—
163C4⋊C4—222no—
164C4⋊C4—222no—
165C4⋊C4—222no—
166C4⋊C4—442no—
167C4⋊C4—442no—
168C4⋊C4—442no—
169C4⋊C4—442no—
170C4⋊C4—882no—
171C42C2×D4411yescharacteristic
172C42#433911yescharacteristic
173C42#434312yes—
174C11#1042811yescharacteristic, complemented, Sylow
175C23#6699011yescharacteristic
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—82no—
184C2×C4—81no—
185C2×C4—442no—
186C2×C4—442no—
187C2×C4—442no—
188C2×C4—442no—
189C2×C4—442no—
190C2×C4—442no—
191C2×C4#6694712yes—
192C2×C4#6694812yes—
193C2×C4#6698311yescharacteristic
194C2×C4#6700011yescharacteristic
195C8—42no—
196C8—444no—
197C22#1062260411yescharacteristic
198C22#1062267411yescharacteristic
199C22#1062267511yescharacteristic
200C22#1062281412yes—
201C22#1062281812yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—161no—
208C4—882no—
209C4—882no—
210C2#1306791711yescharacteristic
211C2#1306794211yescharacteristic
212C2#1306794912yes—
213C2#1306983512yes—
214C2#1306984511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1836C2
socle, prime radicalC23×C11#120
hypercenter#1836D11
hypocenterC11#10428
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
174. C11#10428semidirect

Maximal subgroups

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

subgroupindex
#130766842
#130695842
C2×#106221032
#130664972
C11×#18362
#1042811