Finite Group Databasebeta

← #14658902

Subgroups — #14658902

Order 2816.

264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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#13069339C211yesmaximal, characteristic
2#13066517C212yesmaximal
3#13066511C212yesmaximal
4#13066447C211yesmaximal, characteristic
5C11×#1849C211yesmaximal, characteristic
6C2×C11×#108—21no—
7C2×C11×#108—21no—
8C11×#423C2212yes—
9C2×C11×#97C2211yescharacteristic
10C2×Dic11⋊C8—21no—
11C4×C4⋊Dic11C2211yescharacteristic
12#10622538C2212yes—
13C2×C4⋊(C11⋊C8)C2211yescharacteristic
14#10622188—21no—
15C2×C11×M16—22no—
16C22×C8×C11D411yescharacteristic
17C22×C8×C11D411yescharacteristic
18C2×C42×C11C2311yescharacteristic
19C2×C4⋊Dic11—21no—
20C2×C4×Dic11—21no—
21C22×C11⋊C8—21no—
22C11×#108—42no—
23C11×#108—42no—
24C11×C4⋊C8—24no—
25C11×#97—22no—
26C11⋊#95Q811yescharacteristic
27C11⋊#95Q811yescharacteristic
28C22⋊(C11⋊C8)—22no—
29Dic11⋊C8—42no—
30C4⋊(C11⋊C8)—22no—
31C4⋊(C11⋊C8)—22no—
32C4×C11⋊C8—22no—
33#10688—111nomaximal, Sylow
34C22×C4×C11C2×D411yescharacteristic
35C22×C4×C11C2×Q811yescharacteristic
36C22×C4×C11#4111yescharacteristic
37C22×Dic11—21no—
38C22×Dic11—21no—
39C11×M16—42no—
40C11×M16—42no—
41C2×C8×C11—21no—
42C2×C8×C11—21no—
43C2×C8×C11—21no—
44C2×C8×C11—21no—
45C2×C8×C11—42no—
46C2×C8×C11SD1612yes—
47C2×C8×C11Q1612yes—
48C42×C11#4112yes—
49C42×C11#4112yes—
50C4⋊Dic11—42no—
51C4×Dic11—41no—
52C4×Dic11—41no—
53C2×C11⋊C8—41no—
54C2×C11⋊C8—42no—
55C2×C11⋊C8—41no—
56C2×C11⋊C8—41no—
57#1940—111no—
58#1849D1111yescharacteristic
59#1303—112no—
60#1301—112no—
61#1275—111no—
62C23×C11C22⋊Q811yescharacteristic
63C2×C4×C11—41no—
64C2×C4×C11—41no—
65C2×C4×C11#12311yescharacteristic
66C2×C4×C11#12411yescharacteristic
67C2×C4×C11#12512yes—
68C2×C4×C11#12612yes—
69C2×C4×C11C2×SD1611yescharacteristic
70C2×C4×C11C2×Q1611yescharacteristic
71C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
72C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
73C2×Dic11—22no—
74C2×Dic11—41no—
75C2×Dic11—41no—
76C2×Dic11—41no—
77C2×Dic11—41no—
78C2×Dic11—41no—
79C8×C11—22no—
80C8×C11—22no—
81C8×C11—82no—
82C11⋊C8—82no—
83C11⋊C8—81no—
84#431—112no—
85C2×#108—21no—
86C2×#108—21no—
87#423C2×D1112yes—
88C2×C4⋊C8—111no—
89C2×C4⋊C8—221no—
90C2×#97C2×D1111yescharacteristic
91C4×C4⋊C4—111no—
92#336—221no—
93C22×C11—21no—
94C22×C11—21no—
95C22×C11#40011yescharacteristic
96C22×C11#47611yescharacteristic
97C22×C11#47711yescharacteristic
98C4×C11—22no—
99C4×C11—22no—
100C4×C11#48111yescharacteristic
101C4×C11#48411yescharacteristic
102C4×C11#48711yescharacteristic
103C4×C11#49011yescharacteristic
104Dic11—42no—
105Dic11—81no—
106C2×M16—22no—
107C22×C8—221no—
108C22×C8C22⋊D1111yescharacteristic
109C22×C8C22⋊D1111yescharacteristic
110C2×C4⋊C4—221no—
111C2×C42—221no—
112C2×C42C22×D1111yescharacteristic
113#108—42no—
114#108—42no—
115C4⋊C8—24no—
116C4⋊C8—222no—
117C4⋊C8—222no—
118C4⋊C8—442no—
119C22⋊C8—222no—
120#97—22no—
121C4×C8—222no—
122#95—111no—
123#95—111no—
124C2×C11—21no—
125C2×C11—21no—
126C2×C11#210011yescharacteristic
127C2×C11#210211yescharacteristic
128C2×C11#210311yescharacteristic
129C22×C4—221no—
130C22×C4—221no—
131C22×C4Q8×D1111yescharacteristic
132C22×C4#434311yescharacteristic
133C22×C4C2×C22⋊D1111yescharacteristic
134M16—42no—
135M16—42no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—42no—
141C2×C8—442no—
142C2×C8—441no—
143C2×C8—441no—
144C2×C8—441no—
145C2×C8#432512yes—
146C2×C8#432612yes—
147C4⋊C4—442no—
148C42—441no—
149C42—441no—
150C42#433912yes—
151C42#434112yes—
152C11#1068811yescharacteristic, complemented, Sylow
153C23#6699911yescharacteristic
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—222no—
157C2×C4—441no—
158C2×C4—441no—
159C2×C4—441no—
160C2×C4—441no—
161C2×C4—441no—
162C2×C4#6694212yes—
163C2×C4#6695112yes—
164C2×C4#6698211yescharacteristic
165C2×C4#6698511yescharacteristic
166C2×C4#6698511yescharacteristic
167C2×C4#6698911yescharacteristic
168C2×C4C2×#432511yescharacteristic
169C2×C4C2×#432611yescharacteristic
170C8—22no—
171C8—22no—
172C8—82no—
173C8—882no—
174C8—881no—
175C22—21no—
176C22—21no—
177C22#1062259511yescharacteristic
178C22#1062269711yescharacteristic
179C22#1062270411yescharacteristic
180C4—22no—
181C4—22no—
182C4—442no—
183C4—881no—
184C4#1062258111yescharacteristic
185C4#1062258311yescharacteristic
186C4#1062268411yescharacteristic
187C4#1062269411yescharacteristic
188C2—21no—
189C2—21no—
190C2#1307017811yescharacteristic
191C2#1307019011yescharacteristic
192C2#1307019511yescharacteristic
subgroupG/H
centerC2×C4#66989
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1849C2
socleC22×C11#400
prime radicalC23×C11C22⋊Q8
hypercenter#1849D11
hypocenterC11#10688
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1849

Complements

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

NH ≅ G/Ntype
152. C11#10688semidirect

Maximal subgroups

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

subgroupindex
#130693392
#130665172
#130665112
#130664472
C11×#18492
#1068811