Finite Group Databasebeta

← #14673663

Subgroups — #14673663

Order 2816.

292 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 87 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#13070411C211yesmaximal, characteristic, complemented
2#13068654C212yesmaximal
3#13066728C212yesmaximal, complemented
4#13066720C211yesmaximal, characteristic, complemented
5C11×#2112C211yesmaximal, characteristic
6C23×C8×C11C2211yescharacteristic
7C2×C11×M32C2211yescharacteristic
8C2×C11×M32C2211yescharacteristic
9#10622820—22no—
10C2×#66883C2212yes—
11C2×#66883C2212yes—
12C11×C22⋊C16—22no—
13#10622190—22no—
14#10622144—22no—
15C23×C4×C11D411yescharacteristic
16C22×C8×C11—21no—
17C22×C8×C11—21no—
18C22×C8×C11—22no—
19C22×C8×C11—22no—
20C22×C8×C11D411yescharacteristic
21C22×C8×C11C2311yescharacteristic
22C2×#4318—22no—
23C2×#4318—22no—
24C11×M32—22no—
25C11×M32—22no—
26C2×C11×C16—21no—
27C2×C11×C16D412yes—
28C22⋊(C11⋊C8)—44no—
29#66883—22no—
30#66883—22no—
31#66883—22no—
32#66883—22no—
33#13498—111nomaximal, Sylow
34C24×C11Q1611yescharacteristic
35C22×C4×C11—21no—
36C22×C4×C11—22no—
37C22×C4×C11—21no—
38C22×C4×C11—22no—
39C22×C4×C11Q1611yescharacteristic
40C22×C4×C11C2×D411yescharacteristic
41C2×C8×C11—21no—
42C2×C8×C11—22no—
43C2×C8×C11—41no—
44C2×C8×C11—41no—
45C2×C8×C11—42no—
46C2×C8×C11C2×D411yescharacteristic
47C2×C8×C11#4111yescharacteristic
48C2×C8×C11#4112yes—
49C2×C8×C11#4112yes—
50#4318—42no—
51#4318—42no—
52#4318—42no—
53#4318—42no—
54C2×C11⋊C8—42no—
55C2×C11⋊C8—42no—
56C11×C16—22no—
57C11×C16—41no—
58#2161—111no—
59#2112D1111yescharacteristic
60#1810—112no—
61#1388—112no—
62#1385—111no—
63C23×C11—21no—
64C23×C11—22no—
65C23×C11—42no—
66C23×C11C2×Q1611yescharacteristic
67C2×C4×C11—21no—
68C2×C4×C11—22no—
69C2×C4×C11—41no—
70C2×C4×C11—41no—
71C2×C4×C11—42no—
72C2×C4×C11#12111yescharacteristic
73C2×C4×C11#12312yes—
74C2×C4×C11#13511yescharacteristic
75C2×C4×C11AGL(1,ℤ/8)12yes—
76C8×C11—41no—
77C8×C11#12311yescharacteristic
78C8×C11#12411yescharacteristic
79C8×C11#12612yes—
80C11⋊C8—82no—
81C11⋊C8—82no—
82C23×C8C2×D1111yescharacteristic
83C2×M32C2×D1111yescharacteristic
84C2×M32C2×D1111yescharacteristic
85C2×#108—112no—
86C2×#108—112no—
87#407—222no—
88#368—222no—
89C22⋊C16—22no—
90#341—222no—
91C22×C11—22no—
92C22×C11—24no—
93C22×C11—41no—
94C22×C11—41no—
95C22×C11—42no—
96C22×C11—41no—
97C22×C11#46711yescharacteristic
98C22×C11#48412yes—
99C4×C11—41no—
100C4×C11#39711yescharacteristic
101C4×C11#46911yescharacteristic
102C4×C11#48212yes—
103C23×C4D4411yescharacteristic
104C2×M16—222no—
105C2×M16—222no—
106C22×C8—21no—
107C22×C8—22no—
108C22×C8—22no—
109C22×C8—21no—
110C22×C8D4411yescharacteristic
111C22×C8C22×D1111yescharacteristic
112M32—22no—
113M32—22no—
114C2×C16—21no—
115C2×C16C22⋊D1112yes—
116#108—222no—
117#108—222no—
118#108—222no—
119#108—222no—
120C22⋊C8—444no—
121C2×C11—21no—
122C2×C11—22no—
123C2×C11—42no—
124C2×C11#207611yescharacteristic
125C24Dic4411yescharacteristic
126C22×C4—22no—
127C22×C4—21no—
128C22×C4—22no—
129C22×C4—21no—
130C22×C4Dic4411yescharacteristic
131C22×C4C2×D4411yescharacteristic
132M16—442no—
133M16—442no—
134M16—442no—
135M16—442no—
136C2×C8—22no—
137C2×C8—21no—
138C2×C8—42no—
139C2×C8—41no—
140C2×C8—41no—
141C2×C8—442no—
142C2×C8—442no—
143C2×C8#433911yescharacteristic
144C2×C8#434112yes—
145C2×C8#434112yes—
146C2×C8C2×C22⋊D1111yescharacteristic
147C16—22no—
148C16—41no—
149C11#1349811yescharacteristic, complemented, Sylow
150C23—21no—
151C23—22no—
152C23—42no—
153C23C2×Dic4411yescharacteristic
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4#6693912yes—
160C2×C4#6695711yescharacteristic
161C2×C4#6696112yes—
162C2×C4#6698311yescharacteristic
163C8—41no—
164C8—882no—
165C8—882no—
166C8#6693212yes—
167C8#6698811yescharacteristic
168C8#6698911yescharacteristic
169C22—22no—
170C22—24no—
171C22—41no—
172C22—41no—
173C22—42no—
174C22—41no—
175C22#1062233512yes—
176C22#1062272911yescharacteristic
177C4—41no—
178C4#1062235012yes—
179C4#1062256611yescharacteristic
180C4#1062274811yescharacteristic
181C2—21no—
182C2—22no—
183C2—42no—
184C2#1307004411yescharacteristic
subgroupG/H
centerC4#10622748
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#2112C2
socleC2×C11#2076
prime radicalC24×C11Q16
hypercenter#2112D11
hypocenterC11#13498
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C23×C8 ◁ #2112

Complements

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

NH ≅ G/Ntype
1. #13070411C2semidirect
3. #13066728C2semidirect
4. #13066720C2semidirect
149. C11#13498semidirect

Maximal subgroups

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

subgroupindex
#130704112
#130686542
#130667282
#130667202
C11×#21122
#1349811