Finite Group Databasebeta

← #13074719

Subgroups — #13074719

Order 1408.

804 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 153 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×#66948C213yesmaximal, complemented
2C2×#66937C213yesmaximal, complemented
3C11×#399C211yesmaximal, characteristic, complemented
4#10622605C213yesmaximal, complemented
5#10622573C213yesmaximal, complemented
6#10622284C211yesmaximal, characteristic, complemented
7D11×#95C211yesmaximal, characteristic, complemented
8C22×C22⋊D11C2211yescharacteristic
9C22×C22⋊D11C2213yes—
10C22×D44C2213yes—
11C22×D44C2213yes—
12C22×C4×D11C2213yes—
13C2×C11×C4⋊C4C2213yes—
14C2×C11×C22⋊C4C2213yes—
15C2×(C2×D11)⋊C4C2213yes—
16C2×(C2×D11)⋊C4C2216yes—
17C2×Dic11⋊C4C2213yes—
18#66948—212no—
19#66937—212no—
20C11×#95C2211yescharacteristic
21C11⋊#95C2213yes—
22C24×C11C2311yescharacteristic
23C23×D11C2313yes—
24C23×D11C2311yescharacteristic
25C22×C4×C11C2313yes—
26C22×C4×C11C2313yes—
27C2×C22⋊D11—26no—
28C2×C22⋊D11—26no—
29C2×C22⋊D11—46no—
30C22×Dic11C2311yescharacteristic
31C22×Dic11C2313yes—
32C2×D44—26no—
33C2×D44—212no—
34C2×D44—26no—
35C2×D44—46no—
36C2×C4×D11—46no—
37C2×C4×D11D4112yescomplemented
38C11×C4⋊C4—26no—
39C11×C22⋊C4—26no—
40(C2×D11)⋊C4—212no—
41(C2×D11)⋊C4—26no—
42Dic11⋊C4—26no—
43#2656—111nomaximal, Sylow
44C23×C11—23no—
45C23×C11—23no—
46C23×C11—21no—
47C23×C11C2411yescharacteristic
48C22×D11—23no—
49C22×D11—21no—
50C22×D11—26no—
51C22×D11—23no—
52C22×D11—23no—
53C22×D11—26no—
54C22×D11—23no—
55C22×D11C2×D416yes—
56C2×C4×C11—26no—
57C2×C4×C11—23no—
58C2×C4×C11—26no—
59C2×C4×C11C2×D416yes—
60C22⋊D11—412no—
61C22⋊D11—44no—
62C2×Dic11—26no—
63C2×Dic11—23no—
64C2×Dic11C2×D416yes—
65D44—412no—
66D44—412no—
67C4×D11—412no—
68C2×#121—113no—
69C2×#121—113no—
70#399—113no—
71#399D1111yescharacteristic, complemented
72#392—113no—
73#392—111no—
74C2×#95—111no—
75C22×C11—41no—
76C22×C11—43no—
77C22×C11—43no—
78C22×C11C22×D413yes—
79C22×C11H(5,𝔽2)13yes—
80C22×C112−1+411yescharacteristic
81C2×D11—26no—
82C2×D11—26no—
83C2×D11—43no—
84C2×D11—46no—
85C2×D11—43no—
86C2×D11—46no—
87C2×D11—43no—
88C2×D11#12714yes—
89C4×C11—26no—
90C4×C11—43no—
91Dic11—26no—
92Dic11—41no—
93C22×D4—111no—
94C22×D4—113no—
95C22×D4—113no—
96C22×D4—113no—
97C23×C4—113no—
98#121—2212no—
99#121—2212no—
100C2×C4⋊C4—113no—
101C2×C4⋊C4C2×D1113yes—
102C2×C22⋊C4—116no—
103C2×C22⋊C4—113no—
104C2×C22⋊C4C2×D1113yes—
105#95—113no—
106#95C2×D1111yescharacteristic
107C2×C11—81no—
108C2×C11C2×#12711yescharacteristic
109C2×C11#53413yes—
110C2×C11#53713yes—
111D11—24no—
112D11—83no—
113C24—111no—
114C24—113no—
115C24C22×D1111yescharacteristic
116C2×D4—226no—
117C2×D4—2212no—
118C2×D4—226no—
119C2×D4—226no—
120C2×D4—226no—
121C2×D4—446no—
122C2×D4—446no—
123C22×C4—113no—
124C22×C4—1112no—
125C22×C4—111no—
126C22×C4—446no—
127C22×C4C22×D1113yes—
128C22×C4C22×D1113yes—
129C4⋊C4—26no—
130C4⋊C4—226no—
131C22⋊C4—26no—
132C22⋊C4—2212no—
133C22⋊C4—226no—
134C11#265611yescharacteristic, complemented, Sylow
135C23—23no—
136C23—21no—
137C23—23no—
138C23—116no—
139C23—221no—
140C23—223no—
141C23—226no—
142C23—223no—
143C23—223no—
144C23—223no—
145C23—226no—
146C23C23×D1111yescharacteristic
147D4—4412no—
148D4—4412no—
149D4—4412no—
150D4—444no—
151C2×C4—26no—
152C2×C4—23no—
153C2×C4—26no—
154C2×C4—116no—
155C2×C4—226no—
156C2×C4—223no—
157C2×C4—4412no—
158C2×C4D4×D1116yes—
159C22—41no—
160C22—43no—
161C22—43no—
162C22—114no—
163C22—226no—
164C22—226no—
165C22—443no—
166C22—446no—
167C22—443no—
168C22—446no—
169C22—443no—
170C22C2×D4×D1113yes—
171C22#6704011yescharacteristic
172C22#6704213yes—
173C4—26no—
174C4—43no—
175C4—226no—
176C4—441no—
177C2—81no—
178C2—224no—
179C2—883no—
180C2#1062316013yes—
181C2#1062318413yes—
182C2D11×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#399C2
hypercenter#399D11
hypocenterC11#2656
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#66948C2semidirect
2. C2×#66937C2semidirect
3. C11×#399C2semidirect
4. #10622605C2semidirect
5. #10622573C2semidirect
6. #10622284C2semidirect
7. D11×#95C2semidirect
37. C2×C4×D11D4semidirect
71. #399D11semidirect
134. C11#2656semidirect

Maximal subgroups

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

subgroupindex
C2×#669482
C2×#669372
C11×#3992
#106226052
#106225732
#106222842
D11×#952
#265611