Finite Group Databasebeta

← #14674434

Subgroups — #14674434

Order 2816.

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

normal subgroups only

This group has 284 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×#10622160C212yesmaximal, complemented
2#13070707C211yesmaximal, characteristic
3#13066797C212yesmaximal, complemented
4C22⋊(C11⋊C32)C211yesmaximal, characteristic
5C22×C11×Q32C211yesmaximal, characteristic
6C22×C11×Q16—21no—
7C2×C11×Q32—24no—
8C2×C11×Q32—21no—
9C2×C11×Q32C2212yes—
10C22×C11×C16C2211yescharacteristic
11#10622729—21no—
12C2×Dic88C2211yescharacteristic
13#10622160—24no—
14#10622142C2211yescharacteristic
15#10622141—21no—
16C2×C11⋊C32C2212yes—
17C22×Q8×C11—41no—
18C2×C11×Q16—24no—
19C2×C11×Q16—22no—
20C2×C11×Q16—42no—
21C2×C11×Q16—41no—
22C22×C8×C11D411yescharacteristic
23#66977—41no—
24C2×Dic44—21no—
25C11×Q32—24no—
26C11×Q32—22no—
27C11×Q32D414yes—
28C2×C11×C16—22no—
29C2×C11×C16D411yescharacteristic
30C2×C11×C16C2311yescharacteristic
31#66882—21no—
32#66880—41no—
33Dic88—22no—
34C11⋊C32—22no—
35#13665—111nomaximal, Sylow
36C2×Q8×C11—44no—
37C2×Q8×C11—42no—
38C2×Q8×C11—82no—
39C2×Q8×C11—81no—
40C22×C4×C11—81no—
41C22×C4×C11D811yescharacteristic
42C2×Dic22—41no—
43C11×Q16—24no—
44C11×Q16—44no—
45C11×Q16—42no—
46C2×C8×C11—21no—
47C2×C8×C11—21no—
48C2×C8×C11D811yescharacteristic
49C2×C8×C11C2×D411yescharacteristic
50C22⋊Dic11—81no—
51C4⋊Dic11—41no—
52Dic11⋊C4—81no—
53Dic44—41no—
54Dic44—41no—
55C11×C16—21no—
56C11×C16C2×D412yes—
57C22×Q32D1111yescharacteristic
58C2×Q64—112no—
59#2216—111no—
60#1416—112no—
61C22⋊C32—111no—
62C23×C11D1611yescharacteristic
63Q8×C11—44no—
64Q8×C11—84no—
65Q8×C11—82no—
66C2×C4×C11—21no—
67C2×C4×C11—21no—
68C2×C4×C11—84no—
69C2×C4×C11—82no—
70C2×C4×C11D1611yescharacteristic
71C2×C4×C11C2×D811yescharacteristic
72C2×Dic11—81no—
73C2×Dic11—81no—
74Dic22—81no—
75Dic22—81no—
76C8×C11—21no—
77C8×C11#12011yescharacteristic
78C8×C11AGL(1,ℤ/8)11yescharacteristic
79C22×Q16—21no—
80C2×Q32—24no—
81C2×Q32—21no—
82C2×Q32—111no—
83C2×Q32C2×D1112yes—
84C22×C16C2×D1111yescharacteristic
85#467—221no—
86Q64—224no—
87C2×C32—112no—
88#366—111no—
89#358—221no—
90C22×C11—21no—
91C22×C11—21no—
92C22×C11Q6412yescomplemented
93C22×C11C2×D1611yescharacteristic
94C4×C11—21no—
95C4×C11—84no—
96C4×C11#44711yescharacteristic
97C4×C11#50911yescharacteristic
98Dic11—161no—
99Dic11—161no—
100C22×Q8—41no—
101C2×Q16—24no—
102C2×Q16—22no—
103C2×Q16—42no—
104C2×Q16—41no—
105C2×Q16—221no—
106C22×C8C22⋊D1111yescharacteristic
107C22⋊Q8—441no—
108Q32—24no—
109Q32—22no—
110Q32—222no—
111Q32C22⋊D1114yes—
112C2×C16—22no—
113C2×C16C22⋊D1111yescharacteristic
114C2×C16C22×D1111yescharacteristic
115#107—221no—
116#103—441no—
117C32—222no—
118C2×C11—22no—
119C2×C11#218411yescharacteristic
120C2×C11C2×Q6411yescharacteristic
121C2×C11#226411yescharacteristic
122C2×Q8—44no—
123C2×Q8—42no—
124C2×Q8—82no—
125C2×Q8—81no—
126C2×Q8—441no—
127C22×C4—81no—
128C22×C4#432311yescharacteristic
129Q16—24no—
130Q16—44no—
131Q16—42no—
132Q16—441no—
133Q16—441no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8#432311yescharacteristic
137C2×C8C2×C22⋊D1111yescharacteristic
138C4⋊C4—441no—
139C4⋊C4—881no—
140C22⋊C4—881no—
141C16—21no—
142C16C2×C22⋊D1112yes—
143C11#1366511yescharacteristic, complemented, Sylow
144C23#6689011yescharacteristic
145Q8—44no—
146Q8—84no—
147Q8—82no—
148Q8—881no—
149Q8—881no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—84no—
153C2×C4—82no—
154C2×C4—881no—
155C2×C4—881no—
156C2×C4#6689011yescharacteristic
157C2×C4C2×#432311yescharacteristic
158C8—21no—
159C8#6698511yescharacteristic
160C8#6700611yescharacteristic
161C22—21no—
162C22—21no—
163C22#1062216012yescomplemented
164C22C2×#6689011yescharacteristic
165C4—21no—
166C4—84no—
167C4—1761no—
168C4—1761no—
169C4#1062276011yescharacteristic
170C4#1062283011yescharacteristic
171C2—22no—
172C2#1307052811yescharacteristic
173C2C2×#1062216011yescharacteristic
174C2#1307093411yescharacteristic
subgroupG/H
centerC22C2×#66890
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
FittingC22×C11×Q32C2
socleC22×C11C2×D16
prime radicalC23×C11D16
hypercenterC22×Q32D11
hypocenterC11#13665
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C22×Q32

Complements

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

NH ≅ G/Ntype
1. C2×#10622160C2semidirect
3. #13066797C2semidirect
92. C22×C11Q64semidirect
143. C11#13665semidirect
163. C22#10622160semidirect

Maximal subgroups

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

subgroupindex
C2×#106221602
#130707072
#130667972
C22⋊(C11⋊C32)2
C22×C11×Q322
#1366511