Finite Group Databasebeta

← #14647299

Subgroups — #14647299

Order 2816.

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

normal subgroups only

This group has 398 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#13071219C211yesmaximal, characteristic
2#13068696C211yesmaximal, characteristic
3#13066525C214yesmaximal
4C11×#1821C211yesmaximal, characteristic
5C22×C11×C4⋊C4C2211yescharacteristic
6C11×#407C2212yes—
7#10622825C412yes—
8#10622824C2212yes—
9C4×C22⋊Dic11C412yes—
10#10622820C2212yes—
11#10622594—22no—
12#10622594—22no—
13C11×#343—22no—
14#10622168—22no—
15C23×C4×C11C2×C411yescharacteristic
16C23×C4×C11C2×C411yescharacteristic
17C23×C4×C11C2311yescharacteristic
18C2×C11×M16—22no—
19C2×C11×C4⋊C4—24no—
20C2×C11×C4⋊C4D412yes—
21C2×C11×C4⋊C4D412yes—
22C2×C22⋊Dic11C2×C414yes—
23C2×C4⋊Dic11—22no—
24C2×C4×Dic11—22no—
25C2×#4318—22no—
26C11×C22⋊C8—24no—
27C11⋊#95—22no—
28C11⋊#95—22no—
29C11⋊#95—22no—
30C11⋊#95—22no—
31C22⋊(C11⋊C8)—24no—
32#8755—111nomaximal, Sylow
33C24×C11C22×C411yescharacteristic
34C22×C4×C11—22no—
35C22×C4×C11—22no—
36C22×C4×C11—42no—
37C22×C4×C11—81no—
38C22×C4×C11—81no—
39C22×C4×C11C22⋊C412yes—
40C22×C4×C11C22⋊C412yes—
41C22×C4×C11C2×D411yescharacteristic
42C22×C4×C11C2×D411yescharacteristic
43C22×C4×C11#4114yes—
44C22×Dic11—24no—
45C11×M16—44no—
46C2×C8×C11—42no—
47C11×C4⋊C4—24no—
48C11×C4⋊C4—24no—
49C22⋊Dic11—44no—
50C4⋊Dic11—82no—
51C4×Dic11—82no—
52#4318—44no—
53C2×C11⋊C8—42no—
54#2313—111no—
55#1821—111no—
56#1821D1111yescharacteristic
57#1306—114no—
58C23×C11—22no—
59C23×C11—41no—
60C23×C11—41no—
61C23×C11C2×C22⋊C411yescharacteristic
62C23×C11#11712yes—
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—44no—
68C2×C4×C11—42no—
69C2×C4×C11—42no—
70C2×C4×C11—82no—
71C2×C4×C11—82no—
72C2×C4×C11#12312yes—
73C2×C4×C11#12312yes—
74C2×Dic11—44no—
75C2×Dic11—44no—
76C2×Dic11—44no—
77C8×C11—82no—
78C11⋊C8—82no—
79C22×C4⋊C4C2×D1111yescharacteristic
80#407—112no—
81#407C2×D1112yes—
82#387—222no—
83#387—222no—
84#381—112no—
85#380—112no—
86C4×C22⋊C4—112no—
87#343—22no—
88#343—222no—
89C22×C11—21no—
90C22×C11—21no—
91C22×C11—22no—
92C22×C11—22no—
93C22×C11—22no—
94C22×C11—44no—
95C22×C11#38111yescharacteristic
96C22×C11#41012yes—
97C4×C11—22no—
98C4×C11—22no—
99C4×C11—42no—
100C4×C11—42no—
101Dic11—84no—
102C23×C4C4×D1111yescharacteristic
103C23×C4C4×D1111yescharacteristic
104C23×C4C22×D1111yescharacteristic
105C2×M16—22no—
106C2×M16—222no—
107C2×C4⋊C4—24no—
108C2×C4⋊C4—222no—
109C2×C4⋊C4D4412yes—
110C2×C4⋊C4C22⋊D1112yes—
111C2×C22⋊C4—114no—
112C2×C42—222no—
113C22⋊C8—24no—
114C22⋊C8—224no—
115#95—222no—
116#95—222no—
117#95—222no—
118#95—222no—
119C2×C11—22no—
120C2×C11—42no—
121C2×C11#182011yescharacteristic
122C2×C11#182911yescharacteristic
123C2×C11#183011yescharacteristic
124C24C2×C4×D1111yescharacteristic
125C22×C4—22no—
126C22×C4—22no—
127C22×C4—42no—
128C22×C4—81no—
129C22×C4—81no—
130C22×C4—224no—
131C22×C4(C2×D11)⋊C412yes—
132C22×C4(C2×D11)⋊C412yes—
133C22×C4C2×D4411yescharacteristic
134C22×C4#434114yes—
135C22×C4C2×C22⋊D1111yescharacteristic
136M16—44no—
137M16—444no—
138C2×C8—42no—
139C2×C8—442no—
140C4⋊C4—24no—
141C4⋊C4—24no—
142C4⋊C4—882no—
143C22⋊C4—444no—
144C42—882no—
145C11#875511yescharacteristic, complemented, Sylow
146C23—22no—
147C23—41no—
148C23—41no—
149C23#6693012yes—
150C23C2×(C2×D11)⋊C411yescharacteristic
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—44no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—82no—
159C2×C4—82no—
160C2×C4—444no—
161C2×C4—444no—
162C2×C4—444no—
163C2×C4#6693912yes—
164C2×C4#6698812yes—
165C8—82no—
166C8—882no—
167C22—21no—
168C22—21no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—44no—
173C22#1062255611yescharacteristic
174C22#1062261912yes—
175C4—22no—
176C4—22no—
177C4—42no—
178C4—42no—
179C4—884no—
180C2—22no—
181C2—42no—
182C2#1306869111yescharacteristic
183C2#1306872511yescharacteristic
184C2#1306872811yescharacteristic
subgroupG/H
centerC22#10622556
commutator, prime radicalC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1821C2
socleC22×C11#381
cosocleC23×C4×C11C23
hypercenter#1821D11
hypocenterC11#8755
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
145. C11#8755semidirect

Maximal subgroups

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

subgroupindex
#130712192
#130686962
#130665252
C11×#18212
#875511