Finite Group Databasebeta

← #13074909

Subgroups — #13074909

Order 1408.

804 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 149 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×#396C211yesmaximal, characteristic, complemented
4#10622602C213yesmaximal, complemented
5#10622573C213yesmaximal, complemented
6#10622289C211yesmaximal, characteristic, complemented
7#10622284C211yesmaximal, characteristic, complemented
8C22×C22⋊D11C2213yes—
9C22×C22⋊D11C2211yescharacteristic
10C22×D44C2213yes—
11C22×D44C2213yes—
12C22×C4×D11C2213yes—
13C2×C11×C4⋊C4C2213yes—
14C2×C11×C22⋊C4C2213yes—
15C2×(C2×D11)⋊C4C2213yes—
16C2×(C2×D11)⋊C4C2213yes—
17C2×(C2×D11)⋊C4C2213yes—
18C2×Dic11⋊C4C2213yes—
19#66948—212no—
20#66937—212no—
21C11×#95C2211yescharacteristic
22C11⋊#95C2213yes—
23C24×C11C2311yescharacteristic
24C23×D11C2311yescharacteristic
25C23×D11C2313yes—
26C22×C4×C11C2313yes—
27C22×C4×C11C2313yes—
28C2×C22⋊D11—26no—
29C2×C22⋊D11—26no—
30C2×C22⋊D11—43no—
31C2×C22⋊D11—43no—
32C22×Dic11C2311yescharacteristic
33C22×Dic11C2313yes—
34C2×D44—26no—
35C2×D44—26no—
36C2×D44—26no—
37C2×D44—26no—
38C2×D44—43no—
39C2×D44—43no—
40C2×C4×D11—26no—
41C2×C4×D11—26no—
42C2×C4×D11—43no—
43C11×C4⋊C4—26no—
44C11×C22⋊C4—26no—
45(C2×D11)⋊C4—26no—
46(C2×D11)⋊C4—43no—
47(C2×D11)⋊C4D4112yescomplemented
48Dic11⋊C4—26no—
49#2675—111nomaximal, Sylow
50C23×C11—23no—
51C23×C11—23no—
52C23×C11—21no—
53C23×C11C2411yescharacteristic
54C22×D11—23no—
55C22×D11—23no—
56C22×D11—23no—
57C22×D11—23no—
58C22×D11—23no—
59C22×D11—23no—
60C22×D11—23no—
61C22×D11—23no—
62C22×D11—21no—
63C22×D11C2×D416yes—
64C2×C4×C11—23no—
65C2×C4×C11—23no—
66C2×C4×C11—23no—
67C2×C4×C11—23no—
68C2×C4×C11—23no—
69C2×C4×C11C2×D416yes—
70C22⋊D11—412no—
71C22⋊D11—44no—
72C2×Dic11—23no—
73C2×Dic11—23no—
74C2×Dic11—23no—
75C2×Dic11C2×D416yes—
76D44—412no—
77D44—412no—
78C4×D11—412no—
79C2×#121—113no—
80C2×#121—113no—
81#396—111no—
82#396D1111yescharacteristic, complemented
83#392—113no—
84#392—111no—
85#385—113no—
86C22×C11—43no—
87C22×C11—43no—
88C22×C11—41no—
89C22×C11C22×D413yes—
90C22×C11H(5,𝔽2)13yes—
91C22×C112−1+411yescharacteristic
92C2×D11—26no—
93C2×D11—26no—
94C2×D11—26no—
95C2×D11—43no—
96C2×D11—43no—
97C2×D11—43no—
98C2×D11—43no—
99C2×D11—43no—
100C2×D11—43no—
101C2×D11—41no—
102C4×C11—26no—
103C4×C11—43no—
104Dic11—26no—
105Dic11—41no—
106C22×D4—113no—
107C22×D4—111no—
108C22×D4—113no—
109C22×D4—113no—
110C23×C4—113no—
111#121—2212no—
112#121—2212no—
113C2×C4⋊C4—113no—
114C2×C4⋊C4C2×D1113yes—
115C2×C22⋊C4—113no—
116C2×C22⋊C4—113no—
117C2×C22⋊C4—113no—
118C2×C22⋊C4C2×D1113yes—
119#95—113no—
120#95C2×D1111yescharacteristic
121C2×C11—81no—
122C2×C11#53713yes—
123C2×C11D4213yes—
124C2×C11#56011yescharacteristic
125D11—46no—
126D11—81no—
127C24—113no—
128C24—111no—
129C24C22×D1111yescharacteristic
130C2×D4—226no—
131C2×D4—226no—
132C2×D4—226no—
133C2×D4—226no—
134C2×D4—226no—
135C2×D4—226no—
136C2×D4—443no—
137C2×D4—443no—
138C2×D4—443no—
139C2×D4—443no—
140C22×C4—113no—
141C22×C4—111no—
142C22×C4—226no—
143C22×C4—226no—
144C22×C4—443no—
145C22×C4C22×D1113yes—
146C22×C4C22×D1113yes—
147C4⋊C4—26no—
148C4⋊C4—226no—
149C22⋊C4—26no—
150C22⋊C4—1112no—
151C22⋊C4—226no—
152C22⋊C4—443no—
153C11#267511yescharacteristic, complemented, Sylow
154C23—23no—
155C23—21no—
156C23—23no—
157C23—116no—
158C23—223no—
159C23—223no—
160C23—223no—
161C23—223no—
162C23—223no—
163C23—223no—
164C23—223no—
165C23—221no—
166C23—223no—
167C23C23×D1111yescharacteristic
168D4—4412no—
169D4—4412no—
170D4—4412no—
171D4—444no—
172C2×C4—23no—
173C2×C4—23no—
174C2×C4—23no—
175C2×C4—23no—
176C2×C4—23no—
177C2×C4—116no—
178C2×C4—223no—
179C2×C4—223no—
180C2×C4—223no—
181C2×C4—4412no—
182C2×C4D4×D1116yes—
183C22—41no—
184C22—43no—
185C22—43no—
186C22—226no—
187C22—226no—
188C22—226no—
189C22—443no—
190C22—443no—
191C22—443no—
192C22—443no—
193C22—441no—
194C22—443no—
195C22—443no—
196C22C2×D4×D1113yes—
197C22#6704011yescharacteristic
198C22#6704213yes—
199C4—26no—
200C4—43no—
201C4—226no—
202C4—441no—
203C2—81no—
204C2—446no—
205C2—881no—
206C2#1062314013yes—
207C2#1062316013yes—
208C2#1062324211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#396C2
hypercenter#396D11
hypocenterC11#2675
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#66948C2semidirect
2. C2×#66937C2semidirect
3. C11×#396C2semidirect
4. #10622602C2semidirect
5. #10622573C2semidirect
6. #10622289C2semidirect
7. #10622284C2semidirect
47. (C2×D11)⋊C4D4semidirect
82. #396D11semidirect
153. C11#2675semidirect

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×#3962
#106226022
#106225732
#106222892
#106222842
#267511