Finite Group Databasebeta

← #13070628

Subgroups — #13070628

Order 1408.

226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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#10623203C211yesmaximal, characteristic, complemented
2C11×#455C211yesmaximal, characteristic
3#10622856C212yesmaximal
4#10622179C211yesmaximal, characteristic, complemented
5#10622114C212yesmaximal, complemented
6C11×H(5,𝔽2)C2211yescharacteristic
7C11×#137—21no—
8C11×#124C2211yescharacteristic
9#66997—21no—
10#66988—22no—
11#66988C2212yes—
12#66932—22no—
13#66931—22no—
14#66923—21no—
15C11×#104—21no—
16C11×#100C2211yescharacteristic
17#66898—22no—
18#66898C2212yes—
19C11×#41—21no—
20C11×#41—41no—
21C2×Q8×C11D411yescharacteristic
22C2×D4×C11—22no—
23C2×D4×C11—41no—
24C2×D4×C11C2311yescharacteristic
25C22×Dic11D412yes—
26C2×Dic22—21no—
27C11×Q16—41no—
28C11×SD16—41no—
29C11×M16—21no—
30C11×C22⋊C4—22no—
31C42×C11D411yescharacteristic
32C22⋊Dic11—22no—
33C22⋊Dic11—22no—
34C22⋊Dic11—42no—
35C22⋊Dic11D412yes—
36C4⋊Dic11—21no—
37C4⋊Dic11—21no—
38Dic11⋊C4—22no—
39Dic11⋊C4—22no—
40Dic11⋊C4—22no—
41Dic11⋊C4—42no—
42C4×Dic11—21no—
43#2201—111nomaximal, Sylow
44C23×C11—22no—
45C23×C11C2×D412yes—
46Q8×C11—21no—
47Q8×C11—41no—
48D4×C11—21no—
49D4×C11—41no—
50D4×C11—42no—
51D4×C11—41no—
52C2×C4×C11—22no—
53C2×C4×C11—21no—
54C2×C4×C11—21no—
55C2×C4×C11—41no—
56C2×C4×C11C2×D411yescharacteristic
57C2×Dic11—22no—
58C2×Dic11—22no—
59C2×Dic11—42no—
60C2×Dic11—42no—
61Dic22—81no—
62C8×C11—41no—
63#563—111no—
64#458—112no—
65#455D1111yescharacteristic
66#354—111no—
67#352—112no—
68C22×C11—22no—
69C22×C11—42no—
70C22×C11—41no—
71C22×C11—82no—
72C22×C11#12011yescharacteristic
73C4×C11—21no—
74C4×C11—41no—
75C4×C11—41no—
76C4×C11—41no—
77Dic11—42no—
78Dic11—42no—
79Dic11—82no—
80H(5,𝔽2)C2×D1111yescharacteristic
81#137—21no—
82C4⋊Q8—221no—
83#126—222no—
84#125—221no—
85#124C2×D1111yescharacteristic
86#123—112no—
87#123—222no—
88C22⋊Q8—222no—
89#104—21no—
90#100C2×D1111yescharacteristic
91#99—112no—
92#99—222no—
93C2×C11—21no—
94C2×C11—42no—
95C2×C11—81no—
96C2×C11B(4,𝔽2)11yescharacteristic
97#41—21no—
98#41—41no—
99C2×Q8—221no—
100C2×Q8C22⋊D1111yescharacteristic
101C2×D4—22no—
102C2×D4—41no—
103C2×D4C22×D1111yescharacteristic
104C22×C4—112no—
105Q16—41no—
106SD16—41no—
107M16—21no—
108C4⋊C4—221no—
109C4⋊C4—222no—
110C4⋊C4—222no—
111C4⋊C4—221no—
112C4⋊C4—222no—
113C4⋊C4—442no—
114C22⋊C4—22no—
115C22⋊C4—112no—
116C22⋊C4—222no—
117C22⋊C4—222no—
118C22⋊C4—442no—
119C42—221no—
120C42C22⋊D1111yescharacteristic
121C11#220111yescharacteristic, complemented, Sylow
122C23—22no—
123C23D4×D1112yes—
124Q8—21no—
125Q8—41no—
126Q8—881no—
127D4—21no—
128D4—41no—
129D4—42no—
130D4—41no—
131C2×C4—22no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—41no—
135C2×C4—222no—
136C2×C4—222no—
137C2×C4—442no—
138C2×C4—442no—
139C2×C4C2×C22⋊D1111yescharacteristic
140C8—41no—
141C22—22no—
142C22—42no—
143C22—41no—
144C22—82no—
145C22#6699011yescharacteristic
146C4—21no—
147C4—41no—
148C4—41no—
149C4—41no—
150C4—442no—
151C4—442no—
152C4—882no—
153C2—21no—
154C2—42no—
155C2—81no—
156C2#1062264511yescharacteristic
subgroupG/H
centerC2#10622645
commutator, cosocleC2×D4×C11C23
FrattiniC2×D4C22×D11
FittingC11×#455C2
socleC2×C11B(4,𝔽2)
prime radicalC11×H(5,𝔽2)C22
hypercenter#455D11
hypocenterC11#2201
LCSG ▷ C2×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #10623203C2semidirect
4. #10622179C2semidirect
5. #10622114C2semidirect
121. C11#2201semidirect

Maximal subgroups

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

subgroupindex
#106232032
C11×#4552
#106228562
#106221792
#106221142
#220111