Finite Group Databasebeta

← #13067835

Subgroups — #13067835

Order 1408.

200 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 59 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
1Q8×Dic22C211yesmaximal, characteristic
2C11×#462C211yesmaximal, characteristic
3#10622707C211yesmaximal, characteristic
4#10622706C211yesmaximal, characteristic
5Q8⋊(C11⋊C8)C211yesmaximal, characteristic
6#10622122C211yesmaximal, characteristic
7#10622119C211yesmaximal, characteristic
8C2×C11×Q16—21no—
9C11×C4⋊Q8C2211yescharacteristic
10C4×Q8×C11C2211yescharacteristic
11Q8×Dic11—21no—
12#66941—22no—
13#66941—21no—
14#66922—21no—
15#66922C2211yescharacteristic
16C4×Dic22—21no—
17C4×Dic22C2211yescharacteristic
18C11×C4⋊C8C2211yescharacteristic
19C11×#103—21no—
20#66874—22no—
21#66874—21no—
22#66872—21no—
23C4⋊(C11⋊C8)C2211yescharacteristic
24C4×C11⋊C8C2211yescharacteristic
25C2×Q8×C11—21no—
26C2×Q8×C11D411yescharacteristic
27C2×Dic22—22no—
28C2×Dic22D411yescharacteristic
29C2×Dic22D412yes—
30C11×Q16—42no—
31C2×C8×C11—21no—
32C11×C4⋊C4—21no—
33C11×C4⋊C4—21no—
34C11×C4⋊C4—21no—
35C11×C4⋊C4D411yescharacteristic
36C42×C11—21no—
37C42×C11C2311yescharacteristic
38C4⋊Dic11—22no—
39C4⋊Dic11—21no—
40C4⋊Dic11—21no—
41C4⋊Dic11D411yescharacteristic
42Dic11⋊C4—22no—
43Dic11⋊C4—21no—
44C4×Dic11—22no—
45C4×Dic11—21no—
46C2×C11⋊C8—21no—
47C2×C11⋊C8—21no—
48#1645—111nomaximal, Sylow
49Q8×C11—21no—
50Q8×C11—41no—
51Q8×C11—41no—
52Q8×C11SD1612yes—
53C2×C4×C11—21no—
54C2×C4×C11—21no—
55C2×C4×C11—41no—
56C2×C4×C11C2×D411yescharacteristic
57C2×C4×C11C2×D411yescharacteristic
58C2×C4×C11C2×D411yescharacteristic
59C2×Dic11—21no—
60C2×Dic11—22no—
61C2×Dic11—21no—
62Dic22—21no—
63Dic22—42no—
64Dic22—82no—
65Dic22Q1612yescomplemented
66C8×C11—41no—
67C11⋊C8—41no—
68C11⋊C8—41no—
69Q82—111no—
70#487—111no—
71#475—111no—
72#462D1111yescharacteristic
73#333—111no—
74Q8⋊C8—111no—
75Q8⋊C8—111no—
76C22×C11#12011yescharacteristic
77C4×C11—22no—
78C4×C11—21no—
79C4×C11—41no—
80C4×C11—81no—
81C4×C11C2×SD1611yescharacteristic
82C4×C11C2×Q1611yescharacteristic
83C4×C11#13711yescharacteristic
84C4×C11#13711yescharacteristic
85Dic11—22no—
86Dic11—42no—
87Dic11—41no—
88C2×Q16—21no—
89C4⋊Q8—111no—
90C4⋊Q8—221no—
91C4⋊Q8—222no—
92C4⋊Q8—221no—
93C4⋊Q8C2×D1111yescharacteristic
94C4×Q8—111no—
95C4×Q8—221no—
96C4×Q8—221no—
97C4×Q8C2×D1111yescharacteristic
98#106—221no—
99C4⋊C8—111no—
100C4⋊C8C2×D1111yescharacteristic
101#103—21no—
102#103—221no—
103#103—222no—
104C4×C8—111no—
105C2×C11#44811yescharacteristic
106C2×C11#45111yescharacteristic
107C2×C11#45511yescharacteristic
108C2×Q8—21no—
109C2×Q8—111no—
110C2×Q8—112no—
111C2×Q8—222no—
112C2×Q8C22⋊D1111yescharacteristic
113Q16—42no—
114C2×C8—21no—
115C2×C8—221no—
116C2×C8—221no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—111no—
121C4⋊C4—222no—
122C4⋊C4—222no—
123C4⋊C4—221no—
124C4⋊C4—221no—
125C4⋊C4—221no—
126C4⋊C4C22⋊D1111yescharacteristic
127C42—21no—
128C42—222no—
129C42—221no—
130C42C22×D1111yescharacteristic
131C11#164511yescharacteristic, complemented, Sylow
132Q8—21no—
133Q8—41no—
134Q8—41no—
135Q8—112no—
136Q8—221no—
137Q8—442no—
138Q8—882no—
139Q8#432412yes—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—221no—
144C2×C4—221no—
145C2×C4—222no—
146C2×C4D4×D1111yescharacteristic
147C2×C4D4×D1111yescharacteristic
148C2×C4C2×C22⋊D1111yescharacteristic
149C8—41no—
150C8—441no—
151C8—441no—
152C22#6699011yescharacteristic
153C4—21no—
154C4—22no—
155C4—41no—
156C4—81no—
157C4—222no—
158C4—442no—
159C4—441no—
160C4Q16×D1111yescharacteristic
161C4#6697111yescharacteristic
162C4C2×#432411yescharacteristic
163C4#6700411yescharacteristic
164C2#1062265311yescharacteristic
165C2#1062279911yescharacteristic
166C2#1062281511yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC42×C11C23
FrattiniC42C22×D11
FittingC11×#462C2
socle, prime radicalC22×C11#120
hypercenter#462D11
hypocenterC11#1645
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
65. Dic22Q16semidirect
131. C11#1645semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic222
C11×#4622
#106227072
#106227062
Q8⋊(C11⋊C8)2
#106221222
#106221192
#164511