Finite Group Databasebeta

← #14658283

Subgroups — #14658283

Order 2816.

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

normal subgroups only

This group has 350 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#13076891C211yesmaximal, characteristic
2#13068751C212yesmaximal
3#13066498C212yesmaximal
4#13066497C211yesmaximal, characteristic
5C11×#1836C211yesmaximal, characteristic
6C2×C11×#97C2211yescharacteristic
7C11×#384C2211yescharacteristic
8C11×#382C2211yescharacteristic
9#10622597—22no—
10#10622549C2212yes—
11C2×#66867C2212yes—
12#10622274—22no—
13#10622270—22no—
14C11×#340—22no—
15#10622167—22no—
16#10622167—22no—
17C22×C8×C11—21no—
18C2×C11×C4⋊C4—21no—
19C2×C11×C4⋊C4—22no—
20C2×C11×C4⋊C4D412yes—
21C2×C42×C11C2311yescharacteristic
22C2×C4⋊Dic11—22no—
23C2×C4⋊Dic11D412yes—
24C2×C4⋊Dic11D412yes—
25C2×Dic11⋊C4—22no—
26C2×Dic11⋊C4—22no—
27C22×C11⋊C8—22no—
28C11×#97—21no—
29C11×#97Q812yes—
30C11×#95—22no—
31C11⋊#95—22no—
32C11⋊#95—22no—
33C11⋊#95—22no—
34#66867—22no—
35#66867Q814yes—
36#10586—111nomaximal, Sylow
37C22×C4×C11—22no—
38C22×C4×C11—41no—
39C22×C4×C11C2×D412yes—
40C22×C4×C11C2×D411yescharacteristic
41C22×Dic11—22no—
42C22×Dic11—22no—
43C2×C8×C11—22no—
44C2×C8×C11—41no—
45C2×C8×C11—41no—
46C11×C4⋊C4—42no—
47C11×C4⋊C4—44no—
48C11×C4⋊C4—42no—
49C42×C11C2×Q811yescharacteristic
50C42×C11C2×Q812yes—
51C42×C11#4111yescharacteristic
52C4⋊Dic11—42no—
53C4⋊Dic11—42no—
54C4⋊Dic11—82no—
55Dic11⋊C4—82no—
56Dic11⋊C4—82no—
57C2×C11⋊C8—24no—
58C2×C11⋊C8—42no—
59C2×C11⋊C8—42no—
60#2845—111no—
61#1836—112no—
62#1836D1111yescharacteristic
63#1295—112no—
64#1295—111no—
65C23×C11#12011yescharacteristic
66C2×C4×C11—22no—
67C2×C4×C11—21no—
68C2×C4×C11—22no—
69C2×C4×C11—21no—
70C2×C4×C11—42no—
71C2×C4×C11—42no—
72C2×C4×C11—42no—
73C2×C4×C11—82no—
74C2×C4×C11—81no—
75C2×C4×C11C22⋊Q812yes—
76C2×C4×C11C22⋊Q811yescharacteristic
77C2×C4×C11C4⋊Q812yes—
78C2×C4×C11C4⋊Q811yescharacteristic
79C2×Dic11—42no—
80C2×Dic11—42no—
81C2×Dic11—42no—
82C2×Dic11—42no—
83C2×Dic11—42no—
84C2×Dic11—42no—
85C8×C11—42no—
86C11⋊C8—44no—
87C2×#97—112no—
88C2×#97C2×D1111yescharacteristic
89#398—222no—
90#398—222no—
91#398—222no—
92#384C2×D1111yescharacteristic
93#382—112no—
94#382C2×D1111yescharacteristic
95#340—22no—
96#340—222no—
97#340—222no—
98C22×C11#39511yescharacteristic
99C22×C11#45412yes—
100C22×C11#45411yescharacteristic
101C22×C11#45512yes—
102C22×C11#45511yescharacteristic
103C4×C11—22no—
104C4×C11—21no—
105C4×C11—22no—
106C4×C11—21no—
107C4×C11—82no—
108C4×C11—161no—
109Dic11—82no—
110Dic11—82no—
111C22×C8—21no—
112C22×C8—222no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—112no—
116C2×C4⋊C4—112no—
117C2×C4⋊C4—222no—
118C2×C4⋊C4—222no—
119C2×C4⋊C4—222no—
120C2×C4⋊C4C22⋊D1112yes—
121C2×C42C22×D1111yescharacteristic
122#97—21no—
123#97—114no—
124#97—222no—
125#97Dic2212yes—
126#95—22no—
127#95—222no—
128#95—222no—
129#95—222no—
130C2×C11#165811yescharacteristic
131C2×C11#166211yescharacteristic
132C2×C11#166212yes—
133C2×C11#206112yes—
134C2×C11#206111yescharacteristic
135C22×C4—22no—
136C22×C4—41no—
137C22×C4—222no—
138C22×C4—222no—
139C22×C4D4×D1112yes—
140C22×C4C2×C22⋊D1111yescharacteristic
141C2×C8—22no—
142C2×C8—41no—
143C2×C8—41no—
144C2×C8—224no—
145C2×C8—442no—
146C2×C8—442no—
147C4⋊C4—42no—
148C4⋊C4—44no—
149C4⋊C4—42no—
150C4⋊C4—442no—
151C4⋊C4—442no—
152C4⋊C4—882no—
153C4⋊C4—882no—
154C4⋊C4—882no—
155C42C2×Dic2211yescharacteristic
156C42#433911yescharacteristic
157C42Q8×D1112yes—
158C11#1058611yescharacteristic, complemented, Sylow
159C23#6699011yescharacteristic
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—82no—
168C2×C4—81no—
169C2×C4—442no—
170C2×C4—442no—
171C2×C4—442no—
172C2×C4—442no—
173C2×C4—442no—
174C2×C4—442no—
175C2×C4#6694112yes—
176C2×C4#6694912yes—
177C2×C4#6697711yescharacteristic
178C2×C4#6699711yescharacteristic
179C8—42no—
180C8—444no—
181C22#1062259211yescharacteristic
182C22#1062267411yescharacteristic
183C22#1062267511yescharacteristic
184C22#1062281412yes—
185C22#1062281512yes—
186C4—22no—
187C4—22no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—161no—
192C4—882no—
193C4—882no—
194C2#1306791711yescharacteristic
195C2#1306793711yescharacteristic
196C2#1306793812yes—
197C2#1306996412yes—
198C2#1306996611yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1836C2
socle, prime radicalC23×C11#120
hypercenter#1836D11
hypocenterC11#10586
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
158. C11#10586semidirect

Maximal subgroups

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

subgroupindex
#130768912
#130687512
#130664982
#130664972
C11×#18362
#1058611