Finite Group Databasebeta

← #14673913

Subgroups — #14673913

Order 2816.

254 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 95 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#13068791C211yesmaximal, characteristic
2#13066724C212yesmaximal
3#13066714C212yesmaximal
4#13066700C211yesmaximal, characteristic
5C11×#1944C211yesmaximal, characteristic
6C2×C11×#107C2211yescharacteristic
7C2×C11×#106C2211yescharacteristic
8C2×C11×#97C2211yescharacteristic
9C11×#389—21no—
10C2×#66883—21no—
11C2×#66883C2212yes—
12C2×#66876C2212yes—
13#10622537—21no—
14C11×#340—21no—
15C22×C8×C11D411yescharacteristic
16C22×C8×C11C2311yescharacteristic
17C2×C11×C4⋊C4—21no—
18C2×C11×C4⋊C4—21no—
19C2×C11×C4⋊C4—41no—
20C2×C42×C11D411yescharacteristic
21C2×#4318—22no—
22C11×#107—22no—
23C11×#106—21no—
24C11×#106Q812yes—
25C11×#97—22no—
26C11×#95—41no—
27#66883—24no—
28#66883—42no—
29#66876—22no—
30#66876—22no—
31C2×C11⋊C16—22no—
32C4⋊(C11⋊C8)—42no—
33#13541—111nomaximal, Sylow
34C22×C4×C11—41no—
35C22×C4×C11—41no—
36C22×C4×C11SD1611yescharacteristic
37C22×C4×C11SD1611yescharacteristic
38C22×C4×C11C2×D411yescharacteristic
39C2×C8×C11—21no—
40C2×C8×C11—21no—
41C2×C8×C11Q1612yes—
42C2×C8×C11C2×Q811yescharacteristic
43C2×C8×C11#4111yescharacteristic
44C2×C8×C11#4112yes—
45C2×C8×C11#4112yes—
46C11×C4⋊C4—22no—
47C11×C4⋊C4—41no—
48C11×C4⋊C4—41no—
49C11×C4⋊C4—41no—
50C11×C4⋊C4—82no—
51C42×C11—21no—
52C42×C11—21no—
53#4318—42no—
54#4318—42no—
55C2×C11⋊C8—42no—
56C11⋊C16—42no—
57#1944D1111yescharacteristic
58#1849—111no—
59#1387—112no—
60#1383—112no—
61#1377—111no—
62C23×C11C2×SD1611yescharacteristic
63C2×C4×C11—21no—
64C2×C4×C11—21no—
65C2×C4×C11—41no—
66C2×C4×C11—41no—
67C2×C4×C11—42no—
68C2×C4×C11—81no—
69C2×C4×C11—81no—
70C2×C4×C11—81no—
71C2×C4×C11—81no—
72C2×C4×C11—81no—
73C2×C4×C11C22⋊Q811yescharacteristic
74C2×C4×C11#12311yescharacteristic
75C2×C4×C11#12411yescharacteristic
76C2×C4×C11C2×Q1611yescharacteristic
77C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
78C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
79C8×C11—22no—
80C8×C11#12512yes—
81C8×C11#12612yes—
82C11⋊C8—82no—
83C2×M32—112no—
84C2×#108—112no—
85C2×#108—221no—
86C2×#107C2×D1111yescharacteristic
87C2×#106C2×D1111yescharacteristic
88#423—221no—
89C2×#97C2×D1111yescharacteristic
90#389—21no—
91#340—21no—
92C22×C11—21no—
93C22×C11—21no—
94C22×C11#47611yescharacteristic
95C22×C11#48111yescharacteristic
96C22×C11#48711yescharacteristic
97C4×C11—41no—
98C4×C11—41no—
99C4×C11—82no—
100C4×C11—161no—
101C4×C11#40011yescharacteristic
102C4×C11#47711yescharacteristic
103C4×C11#48411yescharacteristic
104C4×C11#49011yescharacteristic
105C2×M16—222no—
106C22×C8C22⋊D1111yescharacteristic
107C22×C8C22×D1111yescharacteristic
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—41no—
111C2×C42C22⋊D1111yescharacteristic
112M32—222no—
113M32—222no—
114C2×C16—222no—
115#108—224no—
116#108—442no—
117#107—22no—
118#106—21no—
119#106Dic2212yes—
120C4⋊C8—442no—
121#97—22no—
122#95—41no—
123C2×C11—21no—
124C2×C11—21no—
125C2×C11#210011yescharacteristic
126C2×C11#223811yescharacteristic
127C2×C11#223911yescharacteristic
128C22×C4—41no—
129C22×C4—41no—
130C22×C4#432411yescharacteristic
131C22×C4#432411yescharacteristic
132C22×C4C2×C22⋊D1111yescharacteristic
133M16—442no—
134M16—442no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—442no—
138C2×C8#432612yes—
139C2×C8C2×Dic2211yescharacteristic
140C2×C8#433911yescharacteristic
141C2×C8#434112yes—
142C2×C8#434312yes—
143C4⋊C4—22no—
144C4⋊C4—41no—
145C4⋊C4—41no—
146C4⋊C4—41no—
147C4⋊C4—82no—
148C42—21no—
149C42—21no—
150C16—442no—
151C11#1354111yescharacteristic, complemented, Sylow
152C23C2×#432411yescharacteristic
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—42no—
158C2×C4—81no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—81no—
162C2×C4—81no—
163C2×C4#6697711yescharacteristic
164C2×C4#6698811yescharacteristic
165C2×C4C2×#432611yescharacteristic
166C2×C4#6700011yescharacteristic
167C2×C4#6700211yescharacteristic
168C2×C4#6700211yescharacteristic
169C8—22no—
170C8—882no—
171C8#6694312yes—
172C8#6695112yes—
173C22—21no—
174C22—21no—
175C22#1062262111yescharacteristic
176C22#1062264711yescharacteristic
177C22#1062270611yescharacteristic
178C4—41no—
179C4—41no—
180C4—82no—
181C4—161no—
182C4#1062259911yescharacteristic
183C4#1062263411yescharacteristic
184C4#1062265711yescharacteristic
185C4#1062268011yescharacteristic
186C2—21no—
187C2—21no—
188C2#1307017911yescharacteristic
189C2#1307082811yescharacteristic
190C2#1307083311yescharacteristic
subgroupG/H
centerC22#10622647
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1944C2
socleC22×C11#481
prime radicalC23×C11C2×SD16
hypercenter#1944D11
hypocenterC11#13541
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ #1944

Complements

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

NH ≅ G/Ntype
151. C11#13541semidirect

Maximal subgroups

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

subgroupindex
#130687912
#130667242
#130667142
#130667002
C11×#19442
#1354111