Finite Group Databasebeta

← #13070631

Subgroups — #13070631

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
2#10622674C211yesmaximal, characteristic
3#10622355C212yesmaximal
4C11×#354C211yesmaximal, characteristic, complemented
5#10622110C212yesmaximal, complemented
6#67037C2211yescharacteristic
7C11×#124C2211yescharacteristic
8#66997—21no—
9#66995—21no—
10#66988C2212yes—
11#66939—22no—
12#66932—22no—
13#66931—22no—
14#66923—21no—
15C11×#99C2212yes—
16#66897C2211yescharacteristic
17#66870—22no—
18#66869—21no—
19C2×Q8×C11D411yescharacteristic
20C2×D4×C11C2311yescharacteristic
21C2×C22⋊D11—22no—
22C22×Dic11D412yes—
23#4341—41no—
24D4×D11—41no—
25#4339—21no—
26C2×Dic22—21no—
27C11×C22⋊C4—22no—
28C11×C22⋊C4—22no—
29C42×C11D411yescharacteristic
30C22⋊Dic11—22no—
31C22⋊Dic11D412yes—
32#4326—41no—
33#4325—41no—
34(C2×D11)⋊C4—42no—
35C4⋊Dic11—21no—
36C4⋊Dic11—21no—
37C4⋊Dic11—42no—
38Dic11⋊C4—22no—
39Dic11⋊C4—22no—
40Dic11⋊C4—22no—
41C4×Dic11—21no—
42#4318—21no—
43#2201—111nomaximal, Sylow
44C23×C11C2×D412yes—
45C22×D11—22no—
46Q8×C11—41no—
47D4×C11—41no—
48C2×C4×C11—21no—
49C2×C4×C11—21no—
50C2×C4×C11—42no—
51C2×C4×C11C2×D411yescharacteristic
52C22⋊D11—42no—
53C22⋊D11—41no—
54C2×Dic11—22no—
55C2×Dic11—22no—
56C2×Dic11—22no—
57C2×Dic11—42no—
58D44—21no—
59C4×D11—41no—
60Dic22—21no—
61Dic22—81no—
62C11⋊C8—41no—
63#563—111no—
64#458—112no—
65#455—111no—
66#354D1111yescharacteristic, complemented
67#352—112no—
68C22×C11—22no—
69C22×C11—42no—
70C22×C11#12011yescharacteristic
71C2×D11—41no—
72C2×D11—82no—
73C4×C11—21no—
74C4×C11—41no—
75C4×C11—41no—
76C4×C11—82no—
77Dic11—42no—
78Dic11—41no—
79Dic11—42no—
80H(5,𝔽2)—111no—
81#137—221no—
82C4⋊Q8—221no—
83#126—222no—
84#125—221no—
85#124C2×D1111yescharacteristic
86#123—112no—
87#123—222no—
88C22⋊Q8—222no—
89#104—221no—
90#100—111no—
91#99—222no—
92#99C2×D1112yes—
93C2×C11—21no—
94C2×C11—42no—
95C2×C11B(4,𝔽2)11yescharacteristic
96D11—81no—
97#41—221no—
98#41—441no—
99C2×Q8—221no—
100C2×Q8D4411yescharacteristic
101C2×D4—222no—
102C2×D4—441no—
103C2×D4C22×D1111yescharacteristic
104C22×C4—112no—
105Q16—441no—
106SD16—441no—
107M16—221no—
108C4⋊C4—221no—
109C4⋊C4—222no—
110C4⋊C4—222no—
111C4⋊C4—221no—
112C4⋊C4—222no—
113C4⋊C4—442no—
114C22⋊C4—22no—
115C22⋊C4—22no—
116C22⋊C4—112no—
117C22⋊C4—222no—
118C22⋊C4—442no—
119C42—221no—
120C42D4411yescharacteristic
121C11#220111yescharacteristic, complemented, Sylow
122C23—222no—
123C23D4×D1112yes—
124Q8—41no—
125Q8—221no—
126Q8—881no—
127D4—41no—
128D4—221no—
129D4—442no—
130D4—441no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—42no—
134C2×C4—222no—
135C2×C4—222no—
136C2×C4—222no—
137C2×C4—441no—
138C2×C4—442no—
139C2×C4C2×D4411yescharacteristic
140C8—441no—
141C22—22no—
142C22—42no—
143C22—441no—
144C22—882no—
145C22#6693511yescharacteristic
146C4—21no—
147C4—41no—
148C4—41no—
149C4—82no—
150C4—442no—
151C4—441no—
152C4—442no—
153C2—21no—
154C2—42no—
155C2—881no—
156C2#1062235411yescharacteristic
subgroupG/H
centerC2#10622354
commutator, cosocleC2×D4×C11C23
FrattiniC2×D4C22×D11
FittingC11×#354C2
socleC2×C11B(4,𝔽2)
prime radical#67037C22
hypercenter#354D11
hypocenterC11#2201
LCSG ▷ C2×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
1. #10623203C2semidirect
4. C11×#354C2semidirect
5. #10622110C2semidirect
66. #354D11semidirect
121. C11#2201semidirect

Maximal subgroups

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

subgroupindex
#106232032
#106226742
#106223552
C11×#3542
#106221102
#220111