Finite Group Databasebeta

← #13076611

Subgroups — #13076611

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×C11×#120C211yesmaximal, characteristic, complemented
2C2×#67006C211yesmaximal, characteristic, complemented
3#10622860C211yesmaximal, characteristic, complemented
4#10622836C213yesmaximal, complemented
5#10622835C213yesmaximal, complemented
6#10622572C213yesmaximal, complemented
7#10622565C213yesmaximal, complemented
8C25×C11C2211yescharacteristic
9C22×D4×C11C2213yes—
10C22×C22⋊D11C2213yes—
11C22×C22⋊D11C2211yescharacteristic, complemented
12C11×#120—24no—
13C2×C11×C22⋊C4C2213yes—
14#67006—24no—
15C2×C22⋊Dic11C2213yes—
16C2×C22⋊Dic11C2213yes—
17C2×C22⋊Dic11C2213yes—
18C2×C22⋊Dic11C2213yescomplemented
19C2×(C2×D11)⋊C4C2213yescomplemented
20C2×Dic11⋊C4C2213yescomplemented
21C11⋊#95C2213yescomplemented
22C11⋊#95C2213yescomplemented
23C24×C11—43no—
24C24×C11—43no—
25C24×C11D414yescomplemented
26C24×C11C2311yescharacteristic
27C24×C11C2313yes—
28C23×D11C2311yescharacteristic
29C2×D4×C11—26no—
30C2×D4×C11—43no—
31C2×D4×C11—43no—
32C22×C4×C11C2313yes—
33C2×C22⋊D11—26no—
34C2×C22⋊D11—43no—
35C2×C22⋊D11—43no—
36C2×C22⋊D11—43no—
37C22×Dic11C2311yescharacteristic
38C22×Dic11C2313yes—
39C22×Dic11C2313yes—
40C11×C22⋊C4—26no—
41C22⋊Dic11—26no—
42C22⋊Dic11—43no—
43C22⋊Dic11—43no—
44C22⋊Dic11—43no—
45(C2×D11)⋊C4—43no—
46Dic11⋊C4—43no—
47#2812—111nomaximal, Sylow
48C23×C11—23no—
49C23×C11—23no—
50C23×C11—23no—
51C23×C11—23no—
52C23×C11—23no—
53C23×C11—23no—
54C23×C11—21no—
55C23×C11—23no—
56C23×C11—23no—
57C23×C11—412no—
58C23×C11—412no—
59C23×C11—44no—
60C23×C11C2×D416yes—
61C23×C11C2411yescharacteristic
62C22×D11—21no—
63C22×D11—23no—
64C22×D11—23no—
65D4×C11—412no—
66C2×C4×C11—23no—
67C2×C4×C11—23no—
68C2×C4×C11—23no—
69C22⋊D11—412no—
70C22⋊D11—44no—
71C2×Dic11—23no—
72C2×Dic11—23no—
73C2×Dic11—23no—
74C2×Dic11—23no—
75C2×Dic11—23no—
76C2×Dic11—23no—
77C2×Dic11—23no—
78C2×#120—111no—
79C2×#120D1111yescharacteristic, complemented
80#397—113no—
81#394—113no—
82#394—113no—
83#392—113no—
84#379—111no—
85C22×C11—26no—
86C22×C11—26no—
87C22×C11—26no—
88C22×C11—416no—
89C22×C11—43no—
90C22×C11—43no—
91C22×C11—43no—
92C22×C11—43no—
93C22×C11—43no—
94C22×C11—43no—
95C22×C11—41no—
96C22×C11C22×D411yescharacteristic
97C22×C11H(5,𝔽2)13yes—
98C22×C11H(5,𝔽2)13yes—
99C2×D11—43no—
100C2×D11—43no—
101C2×D11—41no—
102C4×C11—43no—
103Dic11—43no—
104Dic11—43no—
105Dic11—41no—
106C25C2×D1111yescharacteristic
107C22×D4—113no—
108C22×D4—111no—
109C22×D4C2×D1113yes—
110#120—24no—
111#120—224no—
112C2×C4⋊C4—113no—
113C2×C22⋊C4—113no—
114C2×C22⋊C4—113no—
115C2×C22⋊C4—113no—
116C2×C22⋊C4—113no—
117C2×C22⋊C4—113no—
118C2×C22⋊C4C2×D1113yes—
119#95—113no—
120#95—113no—
121C2×C11—46no—
122C2×C11—81no—
123C2×C11#53413yes—
124C2×C11#56013yes—
125C2×C11H(3,𝔽4)11yescharacteristic
126D11—81no—
127C24—43no—
128C24—43no—
129C24—111no—
130C24C22⋊D1114yescomplemented
131C24C22×D1111yescharacteristic
132C24C22×D1113yes—
133C2×D4—26no—
134C2×D4—43no—
135C2×D4—43no—
136C2×D4—226no—
137C2×D4—443no—
138C2×D4—443no—
139C2×D4—443no—
140C22×C4—111no—
141C22×C4—113no—
142C22×C4—113no—
143C22×C4C22×D1113yes—
144C4⋊C4—443no—
145C22⋊C4—26no—
146C22⋊C4—226no—
147C22⋊C4—443no—
148C22⋊C4—443no—
149C22⋊C4—443no—
150C22⋊C4—443no—
151C11#281211yescharacteristic, complemented, Sylow
152C23—23no—
153C23—23no—
154C23—23no—
155C23—23no—
156C23—23no—
157C23—23no—
158C23—23no—
159C23—23no—
160C23—21no—
161C23—412no—
162C23—44no—
163C23—412no—
164C23—223no—
165C23—223no—
166C23—221no—
167C23C2×C22⋊D1116yes—
168C23C23×D1111yescharacteristic
169D4—412no—
170D4—4412no—
171D4—444no—
172C2×C4—23no—
173C2×C4—23no—
174C2×C4—23no—
175C2×C4—223no—
176C2×C4—223no—
177C2×C4—223no—
178C2×C4—223no—
179C2×C4—223no—
180C2×C4—223no—
181C2×C4—223no—
182C22—26no—
183C22—26no—
184C22—26no—
185C22—416no—
186C22—43no—
187C22—43no—
188C22—43no—
189C22—43no—
190C22—43no—
191C22—41no—
192C22—43no—
193C22—443no—
194C22—441no—
195C22—443no—
196C22#6703713yes—
197C22#6703713yes—
198C22C22×C22⋊D1111yescharacteristic
199C4—43no—
200C4—443no—
201C4—441no—
202C4—443no—
203C2—46no—
204C2—81no—
205C2—881no—
206C2#1062312511yescharacteristic
207C2#1062312613yes—
208C2#1062333513yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#120C2
hypercenterC2×#120D11
hypocenterC11#2812
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×C11×#120C2semidirect
2. C2×#67006C2semidirect
3. #10622860C2semidirect
4. #10622836C2semidirect
5. #10622835C2semidirect
6. #10622572C2semidirect
7. #10622565C2semidirect
11. C22×C22⋊D11C22semidirect
18. C2×C22⋊Dic11C22semidirect
19. C2×(C2×D11)⋊C4C22semidirect
20. C2×Dic11⋊C4C22semidirect
21. C11⋊#95C22semidirect
22. C11⋊#95C22semidirect
25. C24×C11D4semidirect
79. C2×#120D11semidirect
130. C24C22⋊D11semidirect
151. C11#2812semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1202
C2×#670062
#106228602
#106228362
#106228352
#106225722
#106225652
#281211