Finite Group Databasebeta

← #14673670

Subgroups — #14673670

Order 2816.

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

normal subgroups only

This group has 276 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#13070411C211yesmaximal, characteristic, complemented
2#13070231C211yesmaximal, characteristic
3#13068667C212yesmaximal
4#13066711C212yesmaximal, complemented
5C11×#1384C211yesmaximal, characteristic, complemented
6C2×#66954C2211yescharacteristic
7C2×C11×M32C2211yescharacteristic
8C11×#427C2212yes—
9C2×#66883C2212yes—
10C22×C11⋊C16C2211yescharacteristic
11#10622618—22no—
12#10622171—22no—
13(C2×D11)⋊C16—22no—
14#10622144—22no—
15C2×#4339D411yescharacteristic
16C22×C8×C11C2311yescharacteristic
17C11×#117—22no—
18C2×#4318—22no—
19C2×#4318D411yescharacteristic
20#66954—22no—
21#66954—22no—
22C2×#4313—21no—
23C2×C8×D11—21no—
24C11×M32—22no—
25C2×C11×C16D412yes—
26C11×#107—22no—
27C11×#106—22no—
28#66883—22no—
29#66883—22no—
30C2×C11⋊C16—21no—
31C2×C11⋊C16—22no—
32#66869—44no—
33#13499—111nomaximal, Sylow
34C22×C4×C11C2×D411yescharacteristic
35C2×C22⋊D11—21no—
36#4339—22no—
37#4339—22no—
38C2×D44Q1611yescharacteristic
39C2×C4×D11—21no—
40C2×Dic22Q1611yescharacteristic
41C2×C8×C11C2×D411yescharacteristic
42C2×C8×C11#4111yescharacteristic
43C2×C8×C11#4112yes—
44C2×C8×C11#4112yes—
45C11×C4⋊C4—42no—
46C11×C22⋊C4—42no—
47C42×C11—42no—
48#4318—22no—
49#4318—42no—
50#4318—42no—
51C2×C11⋊C8—21no—
52C2×C11⋊C8—42no—
53#4313—42no—
54C8×D11—41no—
55C8×D11—41no—
56C11×C16—22no—
57C11⋊C16—41no—
58#2161—111no—
59#2113—111no—
60#1814—112no—
61#1384D1111yescharacteristic, complemented
62#1382—112no—
63C23×C11#13511yescharacteristic
64C22×D11—21no—
65C2×C4×C11—82no—
66C2×C4×C11#12111yescharacteristic
67C2×C4×C11#12312yes—
68C2×C4×C11C2×Q1611yescharacteristic
69C2×C4×C11AGL(1,ℤ/8)12yes—
70C22⋊D11—42no—
71C2×Dic11—21no—
72D44—22no—
73C4×D11—41no—
74C4×D11—41no—
75Dic22—22no—
76C8×C11#12311yescharacteristic
77C8×C11#12411yescharacteristic
78C8×C11#12612yes—
79C11⋊C8—41no—
80C11⋊C8—82no—
81C2×#131—111no—
82C2×M32C2×D1111yescharacteristic
83C22×C16—111no—
84C2×#108—112no—
85#427C2×D1112yes—
86#421—222no—
87#368—222no—
88C22⋊C16—222no—
89#344—222no—
90C22×C11—41no—
91C22×C11#46711yescharacteristic
92C22×C11#48212yes—
93C2×D11—42no—
94C2×D11—41no—
95C4×C11—162no—
96C4×C11#39711yescharacteristic
97C4×C11#46911yescharacteristic
98C4×C11#48412yes—
99Dic11—41no—
100C2×#41—111no—
101#131—222no—
102#131—222no—
103C2×M16—111no—
104C2×M16—221no—
105C2×M16—222no—
106C22×C8—221no—
107C22×C8C22×D1111yescharacteristic
108#117—22no—
109M32—22no—
110C2×C16—221no—
111C2×C16—222no—
112C2×C16D4412yes—
113#108—222no—
114#108—222no—
115#107—22no—
116#106—22no—
117#104—444no—
118C2×C11—22no—
119C2×C11—21no—
120C2×C11#207611yescharacteristic
121D11—81no—
122#41—222no—
123#41—222no—
124C2×Q8—111no—
125C2×D4—111no—
126C2×D4—221no—
127C22×C4—221no—
128C22×C4D4×D1111yescharacteristic
129M16—222no—
130M16—442no—
131M16—442no—
132M16—442no—
133C2×C8—221no—
134C2×C8—441no—
135C2×C8—441no—
136C2×C8—442no—
137C2×C8C2×D4411yescharacteristic
138C2×C8#433912yes—
139C2×C8#434112yes—
140C2×C8#434311yescharacteristic
141C4⋊C4—42no—
142C22⋊C4—42no—
143C42—42no—
144C16—22no—
145C16—441no—
146C11#1349911yescharacteristic, complemented, Sylow
147C23—221no—
148C23#6696511yescharacteristic
149Q8—222no—
150D4—222no—
151D4—442no—
152C2×C4—82no—
153C2×C4—221no—
154C2×C4—441no—
155C2×C4—441no—
156C2×C4#6693612yes—
157C2×C4#6694811yescharacteristic
158C2×C4#6696712yes—
159C2×C4Q16×D1111yescharacteristic
160C8—441no—
161C8—882no—
162C8#6692811yescharacteristic
163C8#6693911yescharacteristic
164C8#6695112yes—
165C22—41no—
166C22—442no—
167C22—441no—
168C22#1062239712yes—
169C22#1062250011yescharacteristic
170C4—162no—
171C4—441no—
172C4#1062228711yescharacteristic
173C4#1062242212yes—
174C4#1062247811yescharacteristic
175C2—22no—
176C2—21no—
177C2—881no—
178C2#1307004611yescharacteristic
subgroupG/H
centerC4#10622478
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1384C2
socleC2×C11#2076
prime radicalC2×#4339D4
hypercenter#1384D11
hypocenterC11#13499
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #1384

Complements

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

NH ≅ G/Ntype
1. #13070411C2semidirect
4. #13066711C2semidirect
5. C11×#1384C2semidirect
61. #1384D11semidirect
146. C11#13499semidirect

Maximal subgroups

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

subgroupindex
#130704112
#130702312
#130686672
#130667112
C11×#13842
#1349911