Finite Group Databasebeta

← #13068173

Subgroups — #13068173

Order 1408.

146 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 49 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#10622706C211yesmaximal, characteristic
2#10622703C211yesmaximal, characteristic
3#10622464C211yesmaximal, characteristic
4#10622444C211yesmaximal, characteristic
5C11×#332C211yesmaximal, characteristic
6#10622120C211yesmaximal, characteristic
7#10622117C211yesmaximal, characteristic
8C11×C4⋊Q8C2211yescharacteristic
9C2×#4326—21no—
10#66922C2211yescharacteristic
11C4×Dic22C2211yescharacteristic
12C11×C4⋊C8C2211yescharacteristic
13C11×C4⋊C8C2211yescharacteristic
14#66899—21no—
15#66881—21no—
16#66880—21no—
17#66879—21no—
18Dic11⋊C8—21no—
19#66874—21no—
20#66874—21no—
21C4⋊(C11⋊C8)C2211yescharacteristic
22C4×C11⋊C8C2211yescharacteristic
23C2×Q8×C11—21no—
24C2×Dic22—21no—
25C2×Dic22D411yescharacteristic
26C2×C8×C11—21no—
27C2×C8×C11—21no—
28C11×C4⋊C4—21no—
29C11×C4⋊C4—21no—
30C42×C11C2311yescharacteristic
31#4326—42no—
32C4⋊Dic11—21no—
33C4⋊Dic11—21no—
34C4⋊Dic11D411yescharacteristic
35Dic11⋊C4—21no—
36C4×Dic11—21no—
37C2×C11⋊C8—21no—
38C2×C11⋊C8D411yescharacteristic
39C2×C11⋊C8D411yescharacteristic
40#1700—111nomaximal, Sylow
41Q8×C11—41no—
42Q8×C11—41no—
43C2×C4×C11—41no—
44C2×C4×C11C2×D411yescharacteristic
45C2×C4×C11C2×D411yescharacteristic
46C2×C4×C11#4111yescharacteristic
47C2×Dic11—21no—
48C2×Dic11—21no—
49C2×Dic11—41no—
50Dic22—21no—
51Dic22—21no—
52Dic22—41no—
53Dic22—41no—
54C8×C11—41no—
55C8×C11—41no—
56C11⋊C8—21no—
57C11⋊C8—21no—
58C11⋊C8—41no—
59#487—111no—
60#475—111no—
61#462—111no—
62#446—111no—
63#335—111no—
64#332—111no—
65#332D1111yescharacteristic
66C22×C11#12111yescharacteristic
67C4×C11—21no—
68C4×C11—81no—
69C4×C11#13511yescharacteristic
70C4×C11AGL(1,ℤ/8)11yescharacteristic
71C4×C11#13711yescharacteristic
72C4×C11#13711yescharacteristic
73Dic11—41no—
74Dic11—41no—
75Dic11—81no—
76C2×Q16—221no—
77C4⋊Q8—111no—
78C4⋊Q8C2×D1111yescharacteristic
79C4×Q8—111no—
80#106—221no—
81C4⋊C8—111no—
82C4⋊C8—221no—
83C4⋊C8C2×D1111yescharacteristic
84C4⋊C8C2×D1111yescharacteristic
85#103—221no—
86#103—221no—
87#103—221no—
88#103—221no—
89#97—221no—
90C4×C8—111no—
91C2×C11#46411yescharacteristic
92C2×C11#46811yescharacteristic
93C2×C11#47311yescharacteristic
94C2×Q8—21no—
95C2×Q8—111no—
96C2×Q8—221no—
97Q16—442no—
98C2×C8—21no—
99C2×C8—21no—
100C2×C8—111no—
101C2×C8—111no—
102C2×C8—221no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—111no—
106C4⋊C4—221no—
107C4⋊C4—221no—
108C4⋊C4—221no—
109C42—221no—
110C42C22×D1111yescharacteristic
111C11#170011yescharacteristic, complemented, Sylow
112Q8—41no—
113Q8—41no—
114Q8—221no—
115Q8—221no—
116Q8—441no—
117Q8—441no—
118C2×C4—41no—
119C2×C4—221no—
120C2×C4—221no—
121C2×C4—441no—
122C2×C4#433911yescharacteristic
123C2×C4D4×D1111yescharacteristic
124C2×C4D4×D1111yescharacteristic
125C8—41no—
126C8—41no—
127C8—221no—
128C8—221no—
129C8—441no—
130C22#6693711yescharacteristic
131C4—21no—
132C4—81no—
133C4—441no—
134C4—441no—
135C4—881no—
136C4#6696411yescharacteristic
137C4#6696811yescharacteristic
138C4#6696911yescharacteristic
139C4#6697111yescharacteristic
140C2#1062236811yescharacteristic
141C2#1062239311yescharacteristic
142C2#1062241111yescharacteristic
subgroupG/H
centerC22#66937
commutator, cosocleC42×C11C23
FrattiniC42C22×D11
FittingC11×#332C2
socle, prime radicalC22×C11#121
hypercenter#332D11
hypocenterC11#1700
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
111. C11#1700semidirect

Maximal subgroups

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

subgroupindex
#106227062
#106227032
#106224642
#106224442
C11×#3322
#106221202
#106221172
#170011