Finite Group Databasebeta

← #14658284

Subgroups — #14658284

Order 2816.

350 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 97 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#13068750C212yesmaximal
3#13068749C211yesmaximal, characteristic
4#13066498C212yesmaximal
5C11×#1295C211yesmaximal, characteristic
6C2×C11×#97C2212yes—
7C11×#382C2211yescharacteristic
8#10622597—22no—
9#10622549C2212yes—
10#10622548C2211yescharacteristic
11C2×#66867C2211yescharacteristic
12#10622274—22no—
13#10622270—22no—
14#10622189—22no—
15#10622189—22no—
16#10622167—22no—
17C22×C8×C11—22no—
18C2×C11×C4⋊C4D412yes—
19C2×C42×C11C2311yescharacteristic
20C2×C4⋊Dic11—21no—
21C2×C4⋊Dic11—22no—
22C2×C4⋊Dic11—22no—
23C2×C4⋊Dic11D412yes—
24C2×C4⋊Dic11D412yes—
25C2×Dic11⋊C4—22no—
26C2×Dic11⋊C4—22no—
27C22×C11⋊C8—21no—
28C11×#97—22no—
29C11×#97Q814yes—
30C11×#95—22no—
31C11⋊#95—22no—
32C11⋊#95—22no—
33C11⋊#95—22no—
34#66867—21no—
35#66867Q812yes—
36#10586—111nomaximal, Sylow
37C22×C4×C11—22no—
38C22×C4×C11C2×D411yescharacteristic
39C22×C4×C11C2×D412yes—
40C22×Dic11—22no—
41C22×Dic11—22no—
42C22×Dic11—41no—
43C2×C8×C11—24no—
44C2×C8×C11—42no—
45C2×C8×C11—42no—
46C11×C4⋊C4—42no—
47C42×C11C2×Q812yes—
48C42×C11C2×Q811yescharacteristic
49C42×C11#4111yescharacteristic
50C4⋊Dic11—42no—
51C4⋊Dic11—42no—
52C4⋊Dic11—42no—
53C4⋊Dic11—44no—
54C4⋊Dic11—82no—
55Dic11⋊C4—82no—
56Dic11⋊C4—82no—
57C2×C11⋊C8—22no—
58C2×C11⋊C8—41no—
59C2×C11⋊C8—41no—
60#2845—111no—
61#1836—112no—
62#1836—111no—
63#1295—112no—
64#1295D1111yescharacteristic
65C23×C11#12011yescharacteristic
66C2×C4×C11—21no—
67C2×C4×C11—22no—
68C2×C4×C11—21no—
69C2×C4×C11—22no—
70C2×C4×C11—42no—
71C2×C4×C11—42no—
72C2×C4×C11—42no—
73C2×C4×C11C22⋊Q812yes—
74C2×C4×C11C22⋊Q811yescharacteristic
75C2×C4×C11C4⋊Q811yescharacteristic
76C2×C4×C11C4⋊Q812yes—
77C2×Dic11—42no—
78C2×Dic11—42no—
79C2×Dic11—42no—
80C2×Dic11—42no—
81C2×Dic11—42no—
82C2×Dic11—42no—
83C2×Dic11—81no—
84C2×Dic11—82no—
85C8×C11—44no—
86C11⋊C8—42no—
87C2×#97—111no—
88C2×#97C2×D1112yes—
89#398—222no—
90#398—222no—
91#398—222no—
92#384—111no—
93#382—112no—
94#382C2×D1111yescharacteristic
95#340—222no—
96#340—222no—
97#340—222no—
98C22×C11#39511yescharacteristic
99C22×C11#45411yescharacteristic
100C22×C11#45412yes—
101C22×C11#45511yescharacteristic
102C22×C11#45512yes—
103C4×C11—21no—
104C4×C11—22no—
105C4×C11—22no—
106C4×C11—21no—
107C4×C11—82no—
108Dic11—82no—
109Dic11—82no—
110Dic11—161no—
111C22×C8—22no—
112C22×C8—221no—
113C2×C4⋊C4—112no—
114C2×C4⋊C4—112no—
115C2×C4⋊C4—221no—
116C2×C4⋊C4—222no—
117C2×C4⋊C4—222no—
118C2×C4⋊C4—222no—
119C2×C4⋊C4—222no—
120C2×C4⋊C4D4412yes—
121C2×C42C22×D1111yescharacteristic
122#97—22no—
123#97—112no—
124#97—221no—
125#97Dic2214yes—
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—222no—
137C22×C4—222no—
138C22×C4—441no—
139C22×C4C2×D4411yescharacteristic
140C22×C4D4×D1112yes—
141C2×C8—24no—
142C2×C8—42no—
143C2×C8—42no—
144C2×C8—222no—
145C2×C8—441no—
146C2×C8—441no—
147C4⋊C4—42no—
148C4⋊C4—442no—
149C4⋊C4—442no—
150C4⋊C4—442no—
151C4⋊C4—444no—
152C4⋊C4—882no—
153C4⋊C4—882no—
154C4⋊C4—882no—
155C42C2×Dic2212yes—
156C42#434111yescharacteristic
157C42Q8×D1111yescharacteristic
158C11#1058611yescharacteristic, complemented, Sylow
159C23#6693511yescharacteristic
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—442no—
168C2×C4—442no—
169C2×C4—442no—
170C2×C4—442no—
171C2×C4—442no—
172C2×C4—442no—
173C2×C4—881no—
174C2×C4—882no—
175C2×C4#6692211yescharacteristic
176C2×C4#6693112yes—
177C2×C4#6694112yes—
178C2×C4#6695011yescharacteristic
179C8—44no—
180C8—442no—
181C22#1062226911yescharacteristic
182C22#1062235911yescharacteristic
183C22#1062236611yescharacteristic
184C22#1062243812yes—
185C22#1062244012yes—
186C4—22no—
187C4—22no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—882no—
192C4—882no—
193C4—1761no—
194C2#1306791911yescharacteristic
195C2#1306794011yescharacteristic
196C2#1306794112yes—
197C2#1306996512yes—
198C2#1306996711yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socle, prime radicalC23×C11#120
hypercenter#1295D11
hypocenterC11#10586
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

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
#130687502
#130687492
#130664982
C11×#12952
#1058611