Finite Group Databasebeta

← #13070169

Subgroups — #13070169

Order 1408.

210 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 65 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
1C11×#408C211yesmaximal, characteristic
2#10622849C212yesmaximal
3#10622738C211yesmaximal, characteristic, complemented
4#10622715C212yesmaximal, complemented
5#10622195C211yesmaximal, characteristic, complemented
6C2×C11×#41C2211yescharacteristic
7C2×C11×M16C2211yescharacteristic
8C22×C8×C11C2211yescharacteristic
9#66979C2212yes—
10C2×#4318C2212yes—
11C11×C22⋊C8—22no—
12#66901—24no—
13#66883—22no—
14Dic11⋊C8—24no—
15C11×#41—22no—
16C11×#41—22no—
17C2×Q8×C11Q811yescharacteristic
18C2×D4×C11—21no—
19C2×D4×C11Q811yescharacteristic
20C22×C4×C11—21no—
21C22×C4×C11C2311yescharacteristic
22C11×M16—22no—
23C2×C8×C11—22no—
24C2×C8×C11—21no—
25C2×C8×C11D412yes—
26C22⋊Dic11—22no—
27C4⋊Dic11—22no—
28C4×Dic11D414yes—
29#4318—22no—
30#4318—22no—
31C2×C11⋊C8—22no—
32#2098—111nomaximal, Sylow
33C23×C11—21no—
34C23×C11#4111yescharacteristic
35Q8×C11—22no—
36D4×C11—22no—
37D4×C11—42no—
38C2×C4×C11—21no—
39C2×C4×C11—41no—
40C2×C4×C11—41no—
41C2×C4×C11C2×D412yes—
42C2×C4×C11C2×D411yescharacteristic
43C2×C4×C11C2×Q811yescharacteristic
44C2×C4×C11#4112yes—
45C2×Dic11—24no—
46C8×C11—22no—
47C8×C11—41no—
48C11⋊C8—42no—
49#430—111no—
50#424—112no—
51#421—112no—
52#408D1111yescharacteristic
53H(3,ℤ/4)—111no—
54C22×C11—41no—
55C22×C11—42no—
56C22×C11—41no—
57C22×C11C22⋊Q811yescharacteristic
58C22×C11#12312yes—
59C4×C11—41no—
60C4×C11C22⋊Q812yes—
61C4×C11#12311yescharacteristic
62C4×C11#12711yescharacteristic
63Dic11—44no—
64C2×#41C2×D1111yescharacteristic
65C2×M16—112no—
66C2×M16C2×D1111yescharacteristic
67C22×C8C2×D1111yescharacteristic
68#117—112no—
69#108—222no—
70C4⋊C8—224no—
71#104—224no—
72C22⋊C8—22no—
73C2×C11—22no—
74C2×C11—21no—
75C2×C11—81no—
76C2×C11#39911yescharacteristic
77#41—22no—
78#41—22no—
79C2×Q8Dic2211yescharacteristic
80C2×D4—21no—
81C2×D4Dic2211yescharacteristic
82C22×C4—21no—
83C22×C4C22×D1111yescharacteristic
84M16—22no—
85M16—222no—
86M16—222no—
87C2×C8—22no—
88C2×C8—21no—
89C2×C8—222no—
90C2×C8C22⋊D1112yes—
91C4⋊C4—222no—
92C22⋊C4—222no—
93C42—114no—
94C11#209811yescharacteristic, complemented, Sylow
95C23—21no—
96C23#433911yescharacteristic
97Q8—22no—
98D4—22no—
99D4—42no—
100C2×C4—21no—
101C2×C4—41no—
102C2×C4—41no—
103C2×C4—224no—
104C2×C4C2×Dic2211yescharacteristic
105C2×C4D4×D1112yes—
106C2×C4#434112yes—
107C2×C4C2×C22⋊D1111yescharacteristic
108C8—22no—
109C8—41no—
110C8—442no—
111C22—41no—
112C22—42no—
113C22—41no—
114C22#6693612yes—
115C22#6697711yescharacteristic
116C4—41no—
117C4—444no—
118C4#6693112yes—
119C4#6698811yescharacteristic
120C4#6699311yescharacteristic
121C2—22no—
122C2—21no—
123C2—81no—
124C2#1062256211yescharacteristic
subgroupG/H
centerC4#66993
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#408C2
socleC2×C11#399
prime radicalC2×C11×#41C22
hypercenter#408D11
hypocenterC11#2098
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
3. #10622738C2semidirect
4. #10622715C2semidirect
5. #10622195C2semidirect
94. C11#2098semidirect

Maximal subgroups

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

subgroupindex
C11×#4082
#106228492
#106227382
#106227152
#106221952
#209811