Finite Group Databasebeta

← #13070639

Subgroups — #13070639

Order 1408.

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

normal subgroups only

This group has 216 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#10622675C211yesmaximal, characteristic
3#10622365C212yesmaximal, complemented
4C11×#355C211yesmaximal, characteristic, complemented
5#10622116C212yesmaximal, complemented
6#67040C2211yescharacteristic
7C11×#124C2211yescharacteristic
8#66997C2212yes—
9#66988—21no—
10#66985—21no—
11#66962—22no—
12#66932—22no—
13#66931—22no—
14#66923—21no—
15C11×#101C2212yes—
16#66900C2211yescharacteristic
17#66889—22no—
18#66869—21no—
19C2×Q8×C11C2311yescharacteristic
20C2×D4×C11D411yescharacteristic
21C22×Dic11—21no—
22#4343—41no—
23Q8×D11—41no—
24#4339—21no—
25#4339—22no—
26C2×Dic22D412yes—
27C11×M16—22no—
28C11×C22⋊C4—22no—
29C42×C11D411yescharacteristic
30C22⋊Dic11—22no—
31C22⋊Dic11—21no—
32#4324—41no—
33#4323—41no—
34C4⋊Dic11—21no—
35C4⋊Dic11—21no—
36Dic11⋊C4—22no—
37Dic11⋊C4—22no—
38Dic11⋊C4—22no—
39C4×Dic11D412yes—
40#4318—21no—
41Dic44—42no—
42#4314—42no—
43#2203—111nomaximal, Sylow
44C23×C11—21no—
45Q8×C11—41no—
46D4×C11—41no—
47C2×C4×C11—21no—
48C2×C4×C11C2×D411yescharacteristic
49C2×C4×C11C2×D412yes—
50C22⋊D11—41no—
51C2×Dic11—22no—
52C2×Dic11—22no—
53C2×Dic11—81no—
54D44—22no—
55D44—21no—
56C4×D11—41no—
57C4×D11—42no—
58Dic22—22no—
59Dic22—21no—
60Dic22—42no—
61C8×C11—42no—
62C11⋊C8—41no—
63#563—111no—
64#456—112no—
65#454—111no—
66#356—112no—
67#355D1111yescharacteristic, complemented
68C22×C11—42no—
69C22×C11—41no—
70C22×C11#12011yescharacteristic
71C2×D11—41no—
72C4×C11—21no—
73C4×C11—22no—
74C4×C11—41no—
75Dic11—42no—
76Dic11—41no—
77Dic11—42no—
782−1+4—111no—
79#137—222no—
80AGL(1,ℤ/8)—221no—
81C4⋊Q8—112no—
82#126—222no—
83#125—221no—
84#124C2×D1111yescharacteristic
85#123—221no—
86C22⋊Q8—222no—
87#104—222no—
88#104—221no—
89#101—111no—
90#101C2×D1112yes—
91C2×C11—21no—
92C2×C11—81no—
93C2×C11B(4,𝔽2)11yescharacteristic
94D11—81no—
95#41—221no—
96#41—222no—
97#41—441no—
98C2×Q8—112no—
99C2×Q8—441no—
100C2×Q8C22×D1111yescharacteristic
101C2×D4D4411yescharacteristic
102C22×C4—221no—
103Q16—442no—
104SD16—442no—
105SD16—441no—
106D8—441no—
107M16—22no—
108M16—221no—
109C4⋊C4—221no—
110C4⋊C4—222no—
111C4⋊C4—221no—
112C4⋊C4—222no—
113C4⋊C4—222no—
114C22⋊C4—22no—
115C22⋊C4—222no—
116C22⋊C4—221no—
117C42—112no—
118C42D4411yescharacteristic
119C11#220311yescharacteristic, complemented, Sylow
120C23—21no—
121Q8—41no—
122Q8—221no—
123Q8—222no—
124Q8—442no—
125D4—41no—
126D4—221no—
127D4—222no—
128D4—441no—
129C2×C4—21no—
130C2×C4—222no—
131C2×C4—222no—
132C2×C4—442no—
133C2×C4—441no—
134C2×C4—881no—
135C2×C4C2×D4411yescharacteristic
136C2×C4D4×D1112yes—
137C8—42no—
138C8—441no—
139C22—42no—
140C22—41no—
141C22—441no—
142C22#6693511yescharacteristic
143C4—22no—
144C4—21no—
145C4—41no—
146C4—442no—
147C4—442no—
148C4—441no—
149C2—21no—
150C2—81no—
151C2—881no—
152C2#1062235411yescharacteristic
subgroupG/H
centerC2#10622354
commutator, cosocleC2×Q8×C11C23
FrattiniC2×Q8C22×D11
FittingC11×#355C2
socleC2×C11B(4,𝔽2)
prime radical#10622675C2
hypercenter#355D11
hypocenterC11#2203
LCSG ▷ C2×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
1. #10623203C2semidirect
3. #10622365C2semidirect
4. C11×#355C2semidirect
5. #10622116C2semidirect
67. #355D11semidirect
119. C11#2203semidirect

Maximal subgroups

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

subgroupindex
#106232032
#106226752
#106223652
C11×#3552
#106221162
#220311