Finite Group Databasebeta

← #14658551

Subgroups — #14658551

Order 2816.

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

normal subgroups only

This group has 310 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#13068736C211yesmaximal, characteristic, complemented
2#13067265C212yesmaximal
3#13066511C212yesmaximal, complemented
4#13066445C211yesmaximal, characteristic, complemented
5C11×#1963C211yesmaximal, characteristic
6C11×#532C2211yescharacteristic
7C11×#423C2211yescharacteristic
8C2×C11×#104—22no—
9C11×#376C2211yescharacteristic
10#10622538C2212yes—
11C2×C4⋊(C11⋊C8)C2212yes—
12#10622185—22no—
13#10622182—22no—
14#10622162—22no—
15C2×C11×#41—21no—
16C2×C11×M16—21no—
17C11×C4⋊Q8D411yescharacteristic
18C11×#127D411yescharacteristic
19C11×#124—21no—
20C11×#121—22no—
21C4×D4×C11—22no—
22C2×C42×C11D412yes—
23C2×C42×C11C2311yescharacteristic
24C22×C11⋊C8—22no—
25C11×C4⋊C8—22no—
26C11×#104—44no—
27C11×#95—22no—
28C22⋊(C11⋊C8)—22no—
29C4⋊(C11⋊C8)—22no—
30C4⋊(C11⋊C8)—22no—
31C4⋊(C11⋊C8)—22no—
32C4×C11⋊C8—22no—
33#10629—111nomaximal, Sylow
34C11×#41—42no—
35C11×#41—42no—
36C2×Q8×C11—21no—
37C2×D4×C11—21no—
38C2×D4×C11—22no—
39C2×D4×C11—41no—
40C22×C4×C11—22no—
41C22×C4×C11—41no—
42C22×C4×C11C2×D411yescharacteristic
43C22×C4×C11#4112yes—
44C11×M16—42no—
45C2×C8×C11—41no—
46C11×C4⋊C4—22no—
47C11×C22⋊C4—42no—
48C42×C11—22no—
49C42×C11—22no—
50C42×C11C2×D411yescharacteristic
51C42×C11#4111yescharacteristic
52C42×C11#4112yes—
53C2×C11⋊C8—42no—
54C2×C11⋊C8—42no—
55C2×C11⋊C8—42no—
56C2×C11⋊C8—42no—
57#1963D1111yescharacteristic
58#1832—111no—
59#1540—112no—
60#1301—112no—
61#1274—111no—
62C23×C11—41no—
63C23×C11#12311yescharacteristic
64Q8×C11—42no—
65D4×C11—42no—
66D4×C11—82no—
67D4×C11—82no—
68C2×C4×C11—42no—
69C2×C4×C11—44no—
70C2×C4×C11—41no—
71C2×C4×C11—42no—
72C2×C4×C11—81no—
73C2×C4×C11—81no—
74C2×C4×C11#12111yescharacteristic
75C2×C4×C11#12312yes—
76C2×C4×C11#12411yescharacteristic
77C2×C4×C11#12612yes—
78C2×C4×C11#13512yes—
79C2×C4×C11AGL(1,ℤ/8)12yes—
80C8×C11—81no—
81C11⋊C8—82no—
82C11⋊C8—82no—
83#532C2×D1111yescharacteristic
84#431—112no—
85#423C2×D1111yescharacteristic
86C2×C4⋊C8—112no—
87C2×#104—22no—
88#376C2×D1111yescharacteristic
89#336—222no—
90#332—222no—
91#331—222no—
92C22×C11—22no—
93C22×C11—81no—
94C22×C11—82no—
95C22×C11#39711yescharacteristic
96C22×C11#48212yes—
97C4×C11—22no—
98C4×C11—22no—
99C4×C11—82no—
100C4×C11—81no—
101C4×C11#46312yes—
102C4×C11#48811yescharacteristic
103C4×C11#49011yescharacteristic
104C2×#41—21no—
105C2×M16—21no—
106C22×C8—222no—
107C4⋊Q8D4411yescharacteristic
108#127D4411yescharacteristic
109#124—21no—
110#121—22no—
111C4×D4—22no—
112C2×C42C22⋊D1112yes—
113C2×C42C22×D1111yescharacteristic
114C4⋊C8—22no—
115C4⋊C8—222no—
116C4⋊C8—222no—
117C4⋊C8—222no—
118#104—44no—
119C22⋊C8—222no—
120C4×C8—222no—
121#95—22no—
122C2×C11—22no—
123C2×C11—161no—
124C2×C11#207311yescharacteristic
125C2×C11#208012yes—
126#41—42no—
127#41—42no—
128C2×Q8—21no—
129C2×D4—22no—
130C2×D4—21no—
131C2×D4—41no—
132C22×C4—22no—
133C22×C4—41no—
134C22×C4#434112yes—
135C22×C4C2×C22⋊D1111yescharacteristic
136M16—42no—
137C2×C8—41no—
138C2×C8—442no—
139C2×C8—442no—
140C2×C8—442no—
141C2×C8—442no—
142C4⋊C4—22no—
143C22⋊C4—42no—
144C42—22no—
145C42—22no—
146C42C2×D4411yescharacteristic
147C42#433911yescharacteristic
148C42#434112yes—
149C11#1062911yescharacteristic, complemented, Sylow
150C23—41no—
151C23#6698811yescharacteristic
152Q8—42no—
153D4—42no—
154D4—82no—
155D4—82no—
156C2×C4—42no—
157C2×C4—44no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—81no—
161C2×C4—81no—
162C2×C4#6693212yes—
163C2×C4#6693912yes—
164C2×C4#6698311yescharacteristic
165C2×C4#6698512yes—
166C2×C4#6698911yescharacteristic
167C2×C4#6700312yes—
168C8—81no—
169C8—882no—
170C8—882no—
171C22—22no—
172C22—81no—
173C22—82no—
174C22#1062256611yescharacteristic
175C22#1062264812yes—
176C4—22no—
177C4—22no—
178C4—82no—
179C4—81no—
180C4#1062262912yes—
181C4#1062266911yescharacteristic
182C4#1062268411yescharacteristic
183C2—22no—
184C2—161no—
185C2#1307002911yescharacteristic
186C2#1307006612yes—
subgroupG/H
centerC2×C4#66989
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1963C2
socleC22×C11#397
prime radicalC11×#532C22
hypercenter#1963D11
hypocenterC11#10629
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
1. #13068736C2semidirect
3. #13066511C2semidirect
4. #13066445C2semidirect
149. C11#10629semidirect

Maximal subgroups

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

subgroupindex
#130687362
#130672652
#130665112
#130664452
C11×#19632
#1062911