Finite Group Databasebeta

← #14658766

Subgroups — #14658766

Order 2816.

320 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 99 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#13067386C212yesmaximal
3#13067045C212yesmaximal
4#13066447C211yesmaximal, characteristic
5C11×#1985C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×C11×C4⋊C8C2211yescharacteristic
8C2×C11×#97C2211yescharacteristic
9C2×#66883—22no—
10#10622538C2212yes—
11#10622537C2212yes—
12C11×#336—22no—
13Q8⋊(C11⋊C8)—24no—
14#10622118—24no—
15C22×Q8×C11Q811yescharacteristic
16C22×C8×C11—21no—
17C22×C8×C11D412yes—
18C4×Q8×C11—22no—
19C4×Q8×C11—22no—
20C2×C11×C4⋊C4—21no—
21C2×C11×C4⋊C4Q811yescharacteristic
22C2×C42×C11—21no—
23C2×C42×C11C2311yescharacteristic
24C2×#4318—22no—
25C11×C4⋊C8—22no—
26C11×#97—22no—
27C22⋊(C11⋊C8)—22no—
28#66883—44no—
29C4⋊(C11⋊C8)—22no—
30C4⋊(C11⋊C8)—22no—
31C4⋊(C11⋊C8)—22no—
32C4×C11⋊C8D414yes—
33#10663—111nomaximal, Sylow
34C2×Q8×C11—22no—
35C2×Q8×C11—42no—
36C22×C4×C11—21no—
37C22×C4×C11—21no—
38C22×C4×C11C2×D411yescharacteristic
39C22×C4×C11C2×Q811yescharacteristic
40C22×C4×C11#4111yescharacteristic
41C2×C8×C11—22no—
42C2×C8×C11—22no—
43C2×C8×C11—41no—
44C2×C8×C11—42no—
45C2×C8×C11SD1614yes—
46C11×C4⋊C4—22no—
47C11×C4⋊C4—42no—
48C42×C11—41no—
49C42×C11—41no—
50C42×C11C2×D412yes—
51C42×C11#4112yes—
52#4318—44no—
53C2×C11⋊C8—24no—
54C2×C11⋊C8—42no—
55#1985D1111yescharacteristic
56#1849—111no—
57#1570—112no—
58#1487—112no—
59#1275—111no—
60C23×C11C22⋊Q811yescharacteristic
61Q8×C11—24no—
62Q8×C11—42no—
63C2×C4×C11—22no—
64C2×C4×C11—41no—
65C2×C4×C11—41no—
66C2×C4×C11—41no—
67C2×C4×C11—41no—
68C2×C4×C11—42no—
69C2×C4×C11—41no—
70C2×C4×C11C22⋊Q812yes—
71C2×C4×C11#12312yes—
72C2×C4×C11#12311yescharacteristic
73C2×C4×C11#12711yescharacteristic
74C2×C4×C11C2×SD1612yes—
75C2×C4×C11#13712yes—
76C8×C11—24no—
77C8×C11—81no—
78C11⋊C8—44no—
79C11⋊C8—82no—
80C2×C4×Q8C2×D1111yescharacteristic
81#431—112no—
82C2×#108—222no—
83#423—112no—
84C2×C4⋊C8C2×D1111yescharacteristic
85C2×#97C2×D1111yescharacteristic
86#336—22no—
87#334—224no—
88Q8⋊C8—224no—
89C22×C11—21no—
90C22×C11—21no—
91C22×C11#39911yescharacteristic
92C22×C11#47512yes—
93C4×C11—22no—
94C4×C11—22no—
95C4×C11—42no—
96C4×C11—81no—
97C4×C11#48312yes—
98C4×C11#49211yescharacteristic
99C4×C11#49711yescharacteristic
100C22×Q8Dic2211yescharacteristic
101C2×M16—222no—
102C22×C8—21no—
103C22×C8C22⋊D1112yes—
104C4×Q8—22no—
105C4×Q8—22no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4Dic2211yescharacteristic
108C2×C42—21no—
109C2×C42C22×D1111yescharacteristic
110#108—444no—
111C4⋊C8—22no—
112C4⋊C8—222no—
113C4⋊C8—222no—
114C4⋊C8—222no—
115C22⋊C8—222no—
116#97—22no—
117C4×C8—114no—
118C2×C11—22no—
119C2×C11#209111yescharacteristic
120C2×C11#209611yescharacteristic
121C2×C11#209811yescharacteristic
122C2×Q8—22no—
123C2×Q8—42no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4C2×Dic2211yescharacteristic
127C22×C4#433911yescharacteristic
128C22×C4C2×C22⋊D1111yescharacteristic
129M16—444no—
130C2×C8—22no—
131C2×C8—22no—
132C2×C8—41no—
133C2×C8—42no—
134C2×C8—224no—
135C2×C8—442no—
136C2×C8#432514yes—
137C4⋊C4—22no—
138C4⋊C4—42no—
139C42—41no—
140C42—41no—
141C42D4×D1112yes—
142C42#434112yes—
143C11#1066311yescharacteristic, complemented, Sylow
144C23#6697711yescharacteristic
145Q8—24no—
146Q8—42no—
147C2×C4—22no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—42no—
153C2×C4—41no—
154C2×C4#6693112yes—
155C2×C4#6693612yes—
156C2×C4#6698811yescharacteristic
157C2×C4#6699311yescharacteristic
158C2×C4C2×#432512yes—
159C2×C4#6700412yes—
160C8—24no—
161C8—81no—
162C8—444no—
163C8—882no—
164C22—21no—
165C22—21no—
166C22#1062256211yescharacteristic
167C22#1062263312yes—
168C4—22no—
169C4—22no—
170C4—42no—
171C4—81no—
172C4#1062265612yes—
173C4#1062267311yescharacteristic
174C4#1062269811yescharacteristic
175C2—22no—
176C2#1307013211yescharacteristic
177C2#1307015911yescharacteristic
178C2#1307016911yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1985C2
socleC22×C11#399
prime radicalC23×C11C22⋊Q8
hypercenter#1985D11
hypocenterC11#10663
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
143. C11#10663semidirect

Maximal subgroups

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

subgroupindex
#130687912
#130673862
#130670452
#130664472
C11×#19852
#1066311