Finite Group Databasebeta

← #14674412

Subgroups — #14674412

Order 2816.

334 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C2×#10622157C212yesmaximal, complemented
2#13070702C211yesmaximal, characteristic, complemented
3#13066794C212yesmaximal, complemented
4C22⋊(C11⋊C32)C211yesmaximal, characteristic, complemented
5C22×C11×D16C211yesmaximal, characteristic, complemented
6C22×C11×D8—21no—
7C2×C11×D16—24no—
8C2×C11×D16—21no—
9C2×C11×D16C2212yes—
10C22×C11×C16C2211yescharacteristic
11#10622728—21no—
12C2×D176C2211yescharacteristic, complemented
13#10622157—24no—
14#10622147—21no—
15#10622142C2211yescharacteristic, complemented
16C2×C11⋊C32C2212yescomplemented
17C22×D4×C11—41no—
18C2×C11×D8—24no—
19C2×C11×D8—22no—
20C2×C11×D8—42no—
21C2×C11×D8—41no—
22C22×C8×C11D411yescharacteristic
23#66983—41no—
24C2×D88—21no—
25C11×D16—24no—
26C11×D16—22no—
27C11×D16D414yescomplemented
28C2×C11×C16—22no—
29C2×C11×C16D411yescharacteristic
30C2×C11×C16C2311yescharacteristic
31#66885—41no—
32#66882—21no—
33D176—22no—
34C11⋊C32—22no—
35#13661—111nomaximal, Sylow
36C24×C11—81no—
37C2×D4×C11—44no—
38C2×D4×C11—42no—
39C2×D4×C11—82no—
40C2×D4×C11—81no—
41C22×C4×C11D811yescharacteristic
42C2×C22⋊D11—81no—
43C2×D44—41no—
44C11×D8—24no—
45C11×D8—44no—
46C11×D8—42no—
47C2×C8×C11—21no—
48C2×C8×C11—21no—
49C2×C8×C11D811yescharacteristic
50C2×C8×C11C2×D411yescharacteristic
51(C2×D11)⋊C4—81no—
52C4⋊Dic11—41no—
53D88—41no—
54D88—41no—
55C11×C16—21no—
56C11×C16C2×D412yes—
57C22×D16D1111yescharacteristic, complemented
58C2×D32—112no—
59#2215—111no—
60#1415—112no—
61C22⋊C32—111no—
62C23×C11—84no—
63C23×C11—82no—
64C23×C11—162no—
65C23×C11—162no—
66C23×C11D1611yescharacteristic
67C22×D11—81no—
68D4×C11—44no—
69D4×C11—84no—
70D4×C11—82no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11D1611yescharacteristic
74C2×C4×C11C2×D811yescharacteristic
75C22⋊D11—162no—
76C2×Dic11—81no—
77D44—81no—
78D44—81no—
79C8×C11—21no—
80C8×C11#12011yescharacteristic
81C8×C11AGL(1,ℤ/8)11yescharacteristic
82C22×D8—21no—
83C2×D16—24no—
84C2×D16—21no—
85C2×D16—111no—
86C2×D16C2×D1112yes—
87C22×C16C2×D1111yescharacteristic
88#466—221no—
89D32—224no—
90C2×C32—112no—
91#366—111no—
92#357—221no—
93C22×C11—21no—
94C22×C11—21no—
95C22×C11—84no—
96C22×C11—168no—
97C22×C11—162no—
98C22×C11—162no—
99C22×C11D3212yescomplemented
100C22×C11C2×D1611yescharacteristic
101C2×D11—161no—
102C2×D11—161no—
103C2×D11—161no—
104C4×C11—21no—
105C4×C11#44711yescharacteristic
106C4×C11#50911yescharacteristic
107Dic11—161no—
108C22×D4—41no—
109C2×D8—24no—
110C2×D8—22no—
111C2×D8—42no—
112C2×D8—41no—
113C2×D8—221no—
114C22×C8C22⋊D1111yescharacteristic
115#121—441no—
116D16—24no—
117D16—22no—
118D16—222no—
119D16C22⋊D1114yescomplemented
120C2×C16—22no—
121C2×C16C22⋊D1111yescharacteristic
122C2×C16C22×D1111yescharacteristic
123#107—221no—
124#102—441no—
125C32—222no—
126C2×C11—22no—
127C2×C11—164no—
128C2×C11#218411yescharacteristic
129C2×C11C2×D3211yescharacteristic
130C2×C11#226311yescharacteristic
131D11—321no—
132C24—81no—
133C2×D4—44no—
134C2×D4—42no—
135C2×D4—82no—
136C2×D4—81no—
137C2×D4—441no—
138C2×D4—881no—
139C22×C4#432311yescharacteristic
140D8—24no—
141D8—44no—
142D8—42no—
143D8—441no—
144D8—441no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8#432311yescharacteristic
148C2×C8C2×C22⋊D1111yescharacteristic
149C4⋊C4—441no—
150C22⋊C4—881no—
151C16—21no—
152C16C2×C22⋊D1112yes—
153C11#1366111yescharacteristic, complemented, Sylow
154C23—84no—
155C23—82no—
156C23—162no—
157C23—162no—
158C23—881no—
159C23#6689011yescharacteristic
160D4—44no—
161D4—84no—
162D4—82no—
163D4—881no—
164D4—881no—
165D4—1762no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—881no—
169C2×C4#6689011yescharacteristic
170C2×C4C2×#432311yescharacteristic
171C8—21no—
172C8#6698511yescharacteristic
173C8#6700611yescharacteristic
174C22—21no—
175C22—21no—
176C22—84no—
177C22—168no—
178C22—162no—
179C22—162no—
180C22—1761no—
181C22—1761no—
182C22—1761no—
183C22#1062215712yescomplemented
184C22C2×#6689011yescharacteristic
185C4—21no—
186C4—1761no—
187C4#1062276011yescharacteristic
188C4#1062283011yescharacteristic
189C2—22no—
190C2—164no—
191C2—3521no—
192C2#1307052811yescharacteristic
193C2C2×#1062215711yescharacteristic
194C2#1307092911yescharacteristic
subgroupG/H
centerC22C2×#66890
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
FittingC22×C11×D16C2
socleC22×C11C2×D16
hypercenterC22×D16D11
hypocenterC11#13661
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C22×D16

Complements

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

NH ≅ G/Ntype
1. C2×#10622157C2semidirect
2. #13070702C2semidirect
3. #13066794C2semidirect
4. C22⋊(C11⋊C32)C2semidirect
5. C22×C11×D16C2semidirect
12. C2×D176C22semidirect
15. #10622142C22semidirect
16. C2×C11⋊C32C22semidirect
27. C11×D16D4semidirect
57. C22×D16D11semidirect
99. C22×C11D32semidirect
119. D16C22⋊D11semidirect
153. C11#13661semidirect
183. C22#10622157semidirect

Maximal subgroups

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

subgroupindex
C2×#106221572
#130707022
#130667942
C22⋊(C11⋊C32)2
C22×C11×D162
#1366111