Finite Group Databasebeta

← #14673664

Subgroups — #14673664

Order 2816.

292 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 83 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#13070226C211yesmaximal, characteristic
2#13068651C212yesmaximal
3#13066727C212yesmaximal, complemented
4#13066720C211yesmaximal, characteristic, complemented
5C11×#2161C211yesmaximal, characteristic, complemented
6C22×C8×D11C2211yescharacteristic
7C2×C11×M32C2211yescharacteristic
8C2×C11×#108C2212yes—
9#10622739—22no—
10C2×#66883C2212yes—
11C2×#66876C2211yescharacteristic
12C11×#368—22no—
13#10622196—22no—
14(C2×D11)⋊C16—22no—
15C22×C4×D11D411yescharacteristic
16C2×C11×M16—22no—
17C22×C8×C11C2311yescharacteristic
18C2×#4318—22no—
19C22×C11⋊C8D411yescharacteristic
20C2×C8×D11—21no—
21C2×C8×D11—22no—
22C2×C8×D11—21no—
23C2×C8×D11—22no—
24C11×M32—22no—
25C2×C11×C16D412yes—
26C11×#108—22no—
27C11×#108—22no—
28(C2×D11)⋊C8—44no—
29#66883—22no—
30#66883—22no—
31#66876—22no—
32C2×C11⋊C16—21no—
33#13498—111nomaximal, Sylow
34C23×D11Q1611yescharacteristic
35C22×C4×C11C2×D411yescharacteristic
36C22×Dic11Q1611yescharacteristic
37C2×C4×D11—21no—
38C2×C4×D11—22no—
39C2×C4×D11—21no—
40C2×C4×D11—22no—
41C11×M16—42no—
42C11×M16—42no—
43C2×C8×C11—42no—
44C2×C8×C11C2×D411yescharacteristic
45C2×C8×C11#4111yescharacteristic
46C2×C8×C11#4112yes—
47C2×C8×C11#4112yes—
48#4318—42no—
49#4318—42no—
50C2×C11⋊C8—21no—
51C2×C11⋊C8—22no—
52C2×C11⋊C8—42no—
53C8×D11—41no—
54C8×D11—41no—
55C8×D11—42no—
56C11×C16—22no—
57C11⋊C16—41no—
58#2161D1111yescharacteristic, complemented
59#2112—111no—
60#1810—112no—
61#1388—112no—
62#1385—111no—
63C23×C11C2×Q1611yescharacteristic
64C22×D11—21no—
65C22×D11—22no—
66C22×D11—42no—
67C2×C4×C11#12111yescharacteristic
68C2×C4×C11#12312yes—
69C2×C4×C11#13511yescharacteristic
70C2×C4×C11AGL(1,ℤ/8)12yes—
71C2×Dic11—21no—
72C2×Dic11—22no—
73C4×D11—41no—
74C4×D11—41no—
75C4×D11—42no—
76C8×C11—82no—
77C8×C11#12311yescharacteristic
78C8×C11#12411yescharacteristic
79C8×C11#12612yes—
80C11⋊C8—41no—
81C11⋊C8—82no—
82C23×C8—111no—
83C2×M32—111no—
84C2×M32C2×D1111yescharacteristic
85C2×#108—112no—
86C2×#108C2×D1112yes—
87#407—222no—
88#368—22no—
89C22⋊C16—222no—
90#341—222no—
91C22×C11—41no—
92C22×C11#46711yescharacteristic
93C22×C11#48412yes—
94C2×D11—22no—
95C2×D11—24no—
96C2×D11—41no—
97C2×D11—42no—
98C2×D11—41no—
99C4×C11#39711yescharacteristic
100C4×C11#46911yescharacteristic
101C4×C11#48212yes—
102Dic11—41no—
103C23×C4—111no—
104C2×M16—22no—
105C2×M16—222no—
106C22×C8—111no—
107C22×C8—222no—
108C22×C8—221no—
109C22×C8—222no—
110C22×C8—221no—
111C22×C8C22×D1111yescharacteristic
112M32—22no—
113M32—222no—
114C2×C16—221no—
115C2×C16C22⋊D1112yes—
116#108—22no—
117#108—22no—
118#108—222no—
119#108—222no—
120C22⋊C8—444no—
121C2×C11—21no—
122C2×C11—22no—
123C2×C11#207611yescharacteristic
124D11—42no—
125C24—111no—
126C22×C4—111no—
127C22×C4—222no—
128C22×C4—222no—
129C22×C4—221no—
130C22×C4—221no—
131C22×C4D4×D1111yescharacteristic
132M16—42no—
133M16—42no—
134M16—442no—
135M16—442no—
136C2×C8—42no—
137C2×C8—222no—
138C2×C8—221no—
139C2×C8—442no—
140C2×C8—441no—
141C2×C8—441no—
142C2×C8—442no—
143C2×C8#433912yes—
144C2×C8#434111yescharacteristic
145C2×C8#434312yes—
146C2×C8C2×C22⋊D1111yescharacteristic
147C16—22no—
148C16—441no—
149C11#1349811yescharacteristic, complemented, Sylow
150C23—222no—
151C23—221no—
152C23—442no—
153C23Q16×D1111yescharacteristic
154C2×C4—222no—
155C2×C4—221no—
156C2×C4—442no—
157C2×C4—441no—
158C2×C4—441no—
159C2×C4#6694712yes—
160C2×C4#6696412yes—
161C2×C4#6697211yescharacteristic
162C2×C4#6699111yescharacteristic
163C8—82no—
164C8—441no—
165C8—882no—
166C8#6695112yes—
167C8#6698211yescharacteristic
168C8#6700011yescharacteristic
169C22—41no—
170C22—224no—
171C22—222no—
172C22—442no—
173C22—441no—
174C22—441no—
175C22#1062249712yes—
176C22#1062280111yescharacteristic
177C4—441no—
178C4#1062249812yes—
179C4#1062260611yescharacteristic
180C4#1062277211yescharacteristic
181C2—22no—
182C2—21no—
183C2—442no—
184C2#1307004511yescharacteristic
subgroupG/H
centerC4#10622772
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#2161C2
socleC2×C11#2076
prime radicalC23×D11Q16
hypercenter#2161D11
hypocenterC11#13498
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2161

Complements

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

NH ≅ G/Ntype
3. #13066727C2semidirect
4. #13066720C2semidirect
5. C11×#2161C2semidirect
58. #2161D11semidirect
149. C11#13498semidirect

Maximal subgroups

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

subgroupindex
#130702262
#130686512
#130667272
#130667202
C11×#21612
#1349811