Finite Group Databasebeta

← #13069166

Subgroups — #13069166

Order 1408.

308 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 85 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#10623356C211yesmaximal, characteristic
2#10623350C211yesmaximal, characteristic
3C11×#413C211yesmaximal, characteristic
4C2×#66888C212yesmaximal, complemented
5#10622194C212yesmaximal, complemented
6C2×C11×#41C2211yescharacteristic
7C22×Dic22C2211yescharacteristic
8C2×C11×M16C2212yes—
9#67001—24no—
10#66997—21no—
11#66989—21no—
12#66988C414yes—
13#66979C2211yescharacteristic
14#66977—22no—
15C2×#4318—22no—
16C2×#4318C2212yes—
17C11×#101—21no—
18C11×#100—21no—
19#66888—24no—
20C11×#41—22no—
21C11×#41—22no—
22C2×Q8×C11D411yescharacteristic
23C2×D4×C11C2×C412yes—
24C2×D4×C11D411yescharacteristic
25C22×C4×C11D412yes—
26C22×C4×C11C2311yescharacteristic
27C22×Dic11C2×C412yes—
28C2×Dic22—22no—
29C2×Dic22—21no—
30C2×Dic22—21no—
31C2×Dic22—22no—
32C11×M16—22no—
33C11×M16—22no—
34C2×C8×C11—22no—
35C22⋊Dic11—24no—
36C22⋊Dic11C2×C412yes—
37C4⋊Dic11—21no—
38Dic11⋊C4—24no—
39C4×Dic11—21no—
40#4318—24no—
41#4318—22no—
42#4318D414yes—
43C2×C11⋊C8—24no—
44C2×C11⋊C8—22no—
45#1915—111nomaximal, Sylow
46C23×C11C22⋊C412yes—
47C23×C11C22×C411yescharacteristic
48Q8×C11—22no—
49D4×C11—24no—
50D4×C11—22no—
51C2×C4×C11—22no—
52C2×C4×C11—22no—
53C2×C4×C11C22⋊C412yes—
54C2×C4×C11C2×D411yescharacteristic
55C2×C4×C11C2×D412yes—
56C2×C4×C11C2×D411yescharacteristic
57C2×C4×C11#4112yes—
58C2×Dic11—22no—
59C2×Dic11—22no—
60C2×Dic11—24no—
61Dic22—41no—
62Dic22—42no—
63Dic22—41no—
64C8×C11—42no—
65C11⋊C8—24no—
66#568—111no—
67#536—111no—
68#413D1111yescharacteristic
69C2×#101—112no—
70#344—112no—
71C22×C11—22no—
72C22×C11—41no—
73C22×C11—42no—
74C22×C11C2×C22⋊C411yescharacteristic
75C22×C11C4×D412yes—
76C4×C11—22no—
77C4×C11#12011yescharacteristic
78C4×C11#12112yes—
79C4×C11#12311yescharacteristic
80Dic11—42no—
81Dic11—42no—
82C2×#41C2×D1111yescharacteristic
83C22×Q8—111no—
84#131—224no—
85C2×M16—112no—
86C2×M16—222no—
87C2×M16C2×D1112yes—
88C4⋊Q8—221no—
89#124—221no—
90#123—114no—
91C22⋊Q8—222no—
92#117—111no—
93#101—21no—
94#101—224no—
95#100—21no—
96C2×C11—21no—
97C2×C11—22no—
98C2×C11—42no—
99C2×C11#38611yescharacteristic
100#41—22no—
101#41—22no—
102C2×Q8—221no—
103C2×Q8—222no—
104C2×Q8—222no—
105C2×Q8—221no—
106C2×Q8C22⋊D1111yescharacteristic
107C2×D4C4×D1112yes—
108C2×D4C22⋊D1111yescharacteristic
109C22×C4—112no—
110C22×C4D4412yes—
111C22×C4C22×D1111yescharacteristic
112M16—22no—
113M16—22no—
114M16—114no—
115M16—224no—
116M16—222no—
117C2×C8—22no—
118C2×C8—224no—
119C2×C8—222no—
120C4⋊C4—224no—
121C4⋊C4—221no—
122C22⋊C4—112no—
123C22⋊C4—224no—
124C42—221no—
125C11#191511yescharacteristic, complemented, Sylow
126C23(C2×D11)⋊C412yes—
127C23C2×C4×D1111yescharacteristic
128Q8—22no—
129Q8—441no—
130Q8—441no—
131Q8—442no—
132D4—24no—
133D4—22no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—224no—
137C2×C4—222no—
138C2×C4—222no—
139C2×C4(C2×D11)⋊C412yes—
140C2×C4C2×D4411yescharacteristic
141C2×C4D4×D1112yes—
142C2×C4#434112yes—
143C2×C4C2×C22⋊D1111yescharacteristic
144C8—42no—
145C8—224no—
146C22—22no—
147C22—41no—
148C22—42no—
149C22(C22⋊D11)⋊C412yes—
150C22C2×(C2×D11)⋊C411yescharacteristic
151C4—22no—
152C4—442no—
153C4—442no—
154C4#6693511yescharacteristic
155C4#6693911yescharacteristic
156C4#6699212yes—
157C2—21no—
158C2—22no—
159C2—42no—
160C2#1062257111yescharacteristic
subgroupG/H
centerC2#10622571
commutatorC23×C11C22×C4
FrattiniC22×C4C22×D11
FittingC11×#413C2
socleC2×C11#386
prime radicalC2×C11×#41C22
cosocleC22×C4×C11C23
hypercenter#413D11
hypocenterC11#1915
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
4. C2×#66888C2semidirect
5. #10622194C2semidirect
125. C11#1915semidirect

Maximal subgroups

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

subgroupindex
#106233562
#106233502
C11×#4132
C2×#668882
#106221942
#191511