Finite Group Databasebeta

← #13076613

Subgroups — #13076613

Order 1408.

712 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 133 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×#67006C212yesmaximal, complemented
2C11×#379C211yesmaximal, characteristic, complemented
3#10622574C216yesmaximal, complemented
4#10622573C213yesmaximal, complemented
5#10622566C213yesmaximal, complemented
6C25×C11C2211yescharacteristic
7C22×C22⋊D11C2216yes—
8C22×D44C2211yescharacteristic, complemented
9C2×C11×C22⋊C4C2213yes—
10C2×C11×C22⋊C4C2213yes—
11#67006—28no—
12C2×C22⋊Dic11C2216yes—
13C2×(C2×D11)⋊C4C2216yescomplemented
14C2×C4⋊Dic11C2213yescomplemented
15C11⋊#95C2213yescomplemented
16C11⋊#95C2213yescomplemented
17C24×C11—43no—
18C24×C11—43no—
19C24×C11D414yescomplemented
20C24×C11C2313yes—
21C23×D11C2312yes—
22C22×C4×C11C2311yescharacteristic
23C22×C4×C11C2313yes—
24C2×C22⋊D11—212no—
25C2×C22⋊D11—46no—
26C2×C22⋊D11—46no—
27C22×Dic11C2316yes—
28C2×D44—43no—
29C11×C22⋊C4—43no—
30C11×C22⋊C4—43no—
31C22⋊Dic11—212no—
32(C2×D11)⋊C4—46no—
33C4⋊Dic11—43no—
34#2812—111nomaximal, Sylow
35C23×C11—23no—
36C23×C11—23no—
37C23×C11—26no—
38C23×C11—26no—
39C23×C11—412no—
40C23×C11—412no—
41C23×C11—44no—
42C23×C11C2×D416yes—
43C23×C11C2411yescharacteristic
44C22×D11—22no—
45C22×D11—26no—
46C22×D11—26no—
47C2×C4×C11—23no—
48C2×C4×C11—26no—
49C2×C4×C11—23no—
50C22⋊D11—424no—
51C2×Dic11—26no—
52C2×Dic11—26no—
53C2×Dic11—26no—
54D44—44no—
55C2×#120—112no—
56#397—113no—
57#394—116no—
58#392—113no—
59#379D1111yescharacteristic, complemented
60C22×C11—26no—
61C22×C11—212no—
62C22×C11—416no—
63C22×C11—46no—
64C22×C11—43no—
65C22×C11—43no—
66C22×C11C22×D411yescharacteristic
67C22×C11H(5,𝔽2)13yes—
68C22×C11H(5,𝔽2)13yes—
69C2×D11—46no—
70C2×D11—46no—
71C2×D11—42no—
72C4×C11—43no—
73C4×C11—41no—
74Dic11—46no—
75C25C2×D1111yescharacteristic
76C22×D4—116no—
77C22×D4—111no—
78#120—228no—
79C2×C4⋊C4—113no—
80C2×C22⋊C4—116no—
81C2×C22⋊C4—116no—
82C2×C22⋊C4C2×D1113yes—
83C2×C22⋊C4C2×D1113yes—
84#95—113no—
85#95—113no—
86C2×C11—46no—
87C2×C11#53413yes—
88C2×C11#56013yes—
89C2×C11H(3,𝔽4)11yescharacteristic
90D11—82no—
91C24—43no—
92C24—43no—
93C24—112no—
94C24D4414yescomplemented
95C24C22×D1113yes—
96C2×D4—2212no—
97C2×D4—443no—
98C2×D4—446no—
99C2×D4—446no—
100C22×C4—116no—
101C22×C4C22×D1111yescharacteristic
102C22×C4C22×D1113yes—
103C4⋊C4—443no—
104C22⋊C4—43no—
105C22⋊C4—43no—
106C22⋊C4—2212no—
107C22⋊C4—446no—
108C11#281211yescharacteristic, complemented, Sylow
109C23—23no—
110C23—23no—
111C23—26no—
112C23—26no—
113C23—412no—
114C23—44no—
115C23—412no—
116C23—222no—
117C23—226no—
118C23—226no—
119C23C2×D4416yes—
120C23C23×D1111yescharacteristic
121D4—444no—
122D4—4424no—
123C2×C4—26no—
124C2×C4—23no—
125C2×C4—23no—
126C2×C4—226no—
127C2×C4—226no—
128C2×C4—226no—
129C22—212no—
130C22—26no—
131C22—416no—
132C22—43no—
133C22—43no—
134C22—46no—
135C22—446no—
136C22—442no—
137C22—446no—
138C22C22×D4411yescharacteristic
139C22#6703713yes—
140C22#6703713yes—
141C4—41no—
142C4—43no—
143C4—446no—
144C2—46no—
145C2—882no—
146C2#1062302413yes—
147C2#1062312511yescharacteristic
148C2#1062312613yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#379C2
hypercenter#379D11
hypocenterC11#2812
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#67006C2semidirect
2. C11×#379C2semidirect
3. #10622574C2semidirect
4. #10622573C2semidirect
5. #10622566C2semidirect
8. C22×D44C22semidirect
13. C2×(C2×D11)⋊C4C22semidirect
14. C2×C4⋊Dic11C22semidirect
15. C11⋊#95C22semidirect
16. C11⋊#95C22semidirect
19. C24×C11D4semidirect
59. #379D11semidirect
94. C24D44semidirect
108. C11#2812semidirect

Maximal subgroups

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

subgroupindex
C2×#670062
C11×#3792
#106225742
#106225732
#106225662
#281211