Finite Group Databasebeta

← #13070083

Subgroups — #13070083

Order 1408.

184 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 59 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
1C2×C11×#101C211yesmaximal, characteristic
2#10622838C211yesmaximal, characteristic
3#10622838C211yesmaximal, characteristic
4#10622737C211yesmaximal, characteristic
5#10622197C211yesmaximal, characteristic
6#10622195C211yesmaximal, characteristic
7#10622194C211yesmaximal, characteristic
8C22×Q8×C11C2211yescharacteristic
9C2×C11×M16C2211yescharacteristic
10C2×C11×M16C2211yescharacteristic
11#66979C2211yescharacteristic
12#66979C2211yescharacteristic
13C2×#4318C2211yescharacteristic
14C2×#4318C2211yescharacteristic
15C11×#101—22no—
16#66899—22no—
17#66899—22no—
18#66886—22no—
19C2×Q8×C11—21no—
20C2×Q8×C11—21no—
21C2×Q8×C11—21no—
22C2×Q8×C11—21no—
23C2×Q8×C11—21no—
24C2×Q8×C11D412yes—
25C22×C4×C11—21no—
26C22×C4×C11C2311yescharacteristic
27C11×M16—21no—
28C11×M16—21no—
29C11×M16—21no—
30C11×M16—21no—
31C2×C8×C11—21no—
32C2×C8×C11—21no—
33C22⋊Dic11—21no—
34C22⋊Dic11—21no—
35C4⋊Dic11—21no—
36C4⋊Dic11—21no—
37C4×Dic11—21no—
38C4×Dic11—21no—
39#4318—21no—
40#4318—21no—
41#4318—21no—
42#4318—21no—
43C2×C11⋊C8—21no—
44C2×C11⋊C8D412yes—
45#2082—111nomaximal, Sylow
46C23×C11#4111yescharacteristic
47Q8×C11—22no—
48Q8×C11—22no—
49Q8×C11—41no—
50Q8×C11—41no—
51C2×C4×C11—22no—
52C2×C4×C11—41no—
53C2×C4×C11—41no—
54C2×C4×C11C2×D411yescharacteristic
55C2×C4×C11C2×D411yescharacteristic
56C2×C4×C11#4111yescharacteristic
57C2×C4×C11#4111yescharacteristic
58C2×C4×C11#4111yescharacteristic
59C2×C4×C11#4111yescharacteristic
60C2×Dic11—41no—
61C2×Dic11—41no—
62C8×C11—41no—
63C8×C11—41no—
64C11⋊C8—22no—
65C11⋊C8—41no—
66#430—111no—
67#419—111no—
68#419—111no—
69C2×#101D1111yescharacteristic
70#344—111no—
71#344—111no—
72H(3,ℤ/4)—111no—
73C22×C11—41no—
74C22×C11#12311yescharacteristic
75C22×C11#12411yescharacteristic
76C22×C11#12611yescharacteristic
77C4×C11—42no—
78C4×C11#12111yescharacteristic
79C4×C11#12311yescharacteristic
80C4×C11#12311yescharacteristic
81C4×C11#12611yescharacteristic
82Dic11—81no—
83Dic11—81no—
84C22×Q8C2×D1111yescharacteristic
85C2×M16—111no—
86C2×M16—111no—
87C2×M16C2×D1111yescharacteristic
88C2×M16C2×D1111yescharacteristic
89#117—111no—
90#117—111no—
91#108—222no—
92#103—222no—
93#103—222no—
94#101—22no—
95C2×C11—21no—
96C2×C11—21no—
97C2×C11—21no—
98C2×C11#39711yescharacteristic
99C2×Q8—21no—
100C2×Q8—21no—
101C2×Q8—21no—
102C2×Q8—21no—
103C2×Q8—21no—
104C2×Q8C22⋊D1112yes—
105C22×C4—21no—
106C22×C4C22×D1111yescharacteristic
107M16—21no—
108M16—21no—
109M16—21no—
110M16—21no—
111M16—221no—
112M16—221no—
113M16—221no—
114M16—221no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—112no—
118C2×C8—221no—
119C4⋊C4—221no—
120C4⋊C4—221no—
121C22⋊C4—221no—
122C22⋊C4—221no—
123C42—221no—
124C42—221no—
125C11#208211yescharacteristic, complemented, Sylow
126C23#433911yescharacteristic
127Q8—22no—
128Q8—22no—
129Q8—41no—
130Q8—41no—
131C2×C4—22no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—441no—
135C2×C4—441no—
136C2×C4#433911yescharacteristic
137C2×C4D4×D1111yescharacteristic
138C2×C4#434111yescharacteristic
139C2×C4#434111yescharacteristic
140C2×C4#434111yescharacteristic
141C2×C4C2×C22⋊D1111yescharacteristic
142C8—41no—
143C8—41no—
144C8—222no—
145C8—441no—
146C22—41no—
147C22#6693211yescharacteristic
148C22#6693811yescharacteristic
149C22#6698211yescharacteristic
150C4—42no—
151C4—881no—
152C4—881no—
153C4#6693211yescharacteristic
154C4#6693611yescharacteristic
155C4#6698811yescharacteristic
156C4#6699211yescharacteristic
157C2—21no—
158C2—21no—
159C2—21no—
160C2#1062256511yescharacteristic
subgroupG/H
centerC2#10622565
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#101C2
socleC2×C11#397
prime radicalC23×C11#41
hypercenterC2×#101D11
hypocenterC11#2082
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
125. C11#2082semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1012
#106228382
#106227372
#106221972
#106221952
#106221942
#208211