Finite Group Databasebeta

← #14657264

Subgroups — #14657264

Order 2816.

386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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#13069586C212yesmaximal
2#13068749C211yesmaximal, characteristic
3C2×#10622181C212yesmaximal
4#13066497C211yesmaximal, characteristic
5C11×#2822C211yesmaximal, characteristic
6C2×C11×#125C2212yes—
7C11×#400—22no—
8C11×#398—22no—
9C11×#398—22no—
10C11×#382C2211yescharacteristic
11#10622548C2211yescharacteristic
12C2×#66867C2212yes—
13C2×#66867C2211yescharacteristic
14#10622181—24no—
15#10622167—22no—
16#10622167—22no—
17#10622167—22no—
18C11×#125—22no—
19C11×#125—22no—
20C11×#125—22no—
21C11×#125—22no—
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4—22no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4D412yes—
26C2×C11×C4⋊C4D412yes—
27C2×C11×C4⋊C4D412yes—
28C2×C42×C11C2311yescharacteristic
29C2×C4⋊Dic11—22no—
30C2×C4⋊Dic11—21no—
31C22×C11⋊C8—22no—
32C22×C11⋊C8—21no—
33C11×#95—24no—
34C11×#95—22no—
35C11×#95—22no—
36#66867—21no—
37#66867—22no—
38#66867—22no—
39#66867D412yes—
40#10428—111nomaximal, Sylow
41C22×C4×C11—22no—
42C22×C4×C11—22no—
43C22×C4×C11—22no—
44C22×C4×C11C2×D412yes—
45C22×C4×C11C2×D411yescharacteristic
46C22×Dic11—41no—
47C11×C4⋊C4—22no—
48C11×C4⋊C4—22no—
49C11×C4⋊C4—22no—
50C11×C4⋊C4—22no—
51C11×C4⋊C4—42no—
52C11×C4⋊C4—42no—
53C11×C4⋊C4—42no—
54C11×C4⋊C4—42no—
55C11×C4⋊C4—42no—
56C11×C4⋊C4—82no—
57C42×C11C2×D411yescharacteristic
58C42×C11#4111yescharacteristic
59C42×C11#4112yes—
60C4⋊Dic11—44no—
61C4⋊Dic11—42no—
62C2×C11⋊C8—24no—
63C2×C11⋊C8—22no—
64C2×C11⋊C8—42no—
65C2×C11⋊C8—41no—
66C2×C11⋊C8—41no—
67C2×C11⋊C8—42no—
68#2822D1111yescharacteristic
69#1992—112no—
70#1836—111no—
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—42no—
82C2×C4×C11—42no—
83C2×C4×C11—42no—
84C2×C4×C11—42no—
85C2×C4×C11—42no—
86C2×C4×C11—42no—
87C2×C4×C11#12111yescharacteristic
88C2×C4×C11#12112yes—
89C2×C4×C11#12312yes—
90C2×C4×C11#12411yescharacteristic
91C2×Dic11—81no—
92C2×Dic11—82no—
93C11⋊C8—44no—
94C11⋊C8—42no—
95C2×#125C2×D1112yes—
96C2×#97—111no—
97C2×#97—112no—
98#400—22no—
99#398—22no—
100#398—22no—
101#384—111no—
102#382C2×D1111yescharacteristic
103#340—222no—
104#340—222no—
105#340—222no—
106#330—224no—
107C22×C11#39411yescharacteristic
108C22×C11#45411yescharacteristic
109C22×C11#45412yes—
110C22×C11#45511yescharacteristic
111C22×C11#45612yes—
112C4×C11—22no—
113C4×C11—22no—
114C4×C11—21no—
115C4×C11—21no—
116C4×C11—82no—
117C4×C11—82no—
118C4×C11—82no—
119Dic11—161no—
120C22×C8—222no—
121C22×C8—221no—
122#125—22no—
123#125—22no—
124#125—22no—
125#125—22no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—222no—
130C2×C4⋊C4—221no—
131C2×C4⋊C4C22⋊D1112yes—
132C2×C4⋊C4C22⋊D1112yes—
133C2×C4⋊C4C22⋊D1112yes—
134C2×C42C22×D1111yescharacteristic
135#97—112no—
136#97—222no—
137#97—221no—
138#97—222no—
139#95—24no—
140#95—22no—
141#95—22no—
142C2×C11#165811yescharacteristic
143C2×C11#166311yescharacteristic
144C2×C11#166412yes—
145C2×C11#203812yes—
146C2×C11#204011yescharacteristic
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—441no—
151C22×C4C2×C22⋊D1112yes—
152C22×C4C2×C22⋊D1111yescharacteristic
153C2×C8—224no—
154C2×C8—222no—
155C2×C8—441no—
156C2×C8—442no—
157C2×C8—441no—
158C2×C8—442no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—42no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—82no—
169C4⋊C4—444no—
170C4⋊C4—442no—
171C42D4×D1111yescharacteristic
172C42#434111yescharacteristic
173C42#434112yes—
174C11#1042811yescharacteristic, complemented, Sylow
175C23#6700611yescharacteristic
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—882no—
190C2×C4—881no—
191C2×C4#6698812yes—
192C2×C4#6698911yescharacteristic
193C2×C4#6699111yescharacteristic
194C2×C4#6699212yes—
195C8—444no—
196C8—442no—
197C22#1062283511yescharacteristic
198C22#1062285511yescharacteristic
199C22#1062285812yes—
200C22#1062285811yescharacteristic
201C22#1062285912yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—82no—
208C4—82no—
209C4—1761no—
210C2#1306791811yescharacteristic
211C2#1306794411yescharacteristic
212C2#1306795012yes—
213C2#1306983012yes—
214C2#1306984211yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2822C2
socle, prime radicalC23×C11#120
hypercenter#2822D11
hypocenterC11#10428
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

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
#130695862
#130687492
C2×#106221812
#130664972
C11×#28222
#1042811