Finite Group Databasebeta

← C2×#13076659 #14960328

Subgroups — C2×#13076659 #14960328

Order 2816.

3666 conjugacy classes of subgroups; only the 667 normal subgroups are shown.

normal subgroups only

This group has 3666 conjugacy classes of subgroups — too many to draw. Only its 667 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
1C22×#66927C211yesmaximal, characteristic, complemented
2C22×#66929C211yesmaximal, characteristic, complemented
3#13076659C2116yesmaximal, direct product factor
4C2×#10622285C216yesmaximal, complemented
5C2×#10622284C216yesmaximal, complemented
6C2×C11×#383C211yesmaximal, characteristic, complemented
7C23×D44C2216yes—
8C23×D44C2214yes—
9C22×C42×C11C2211yescharacteristic
10C22×(C2×D11)⋊C4C2213yes—
11C22×(C2×D11)⋊C4C22112yes—
12C22×Dic11⋊C4C2213yes—
13C2×#66929—28no—
14C2×#66929C2218yescomplemented
15C2×#66927—28no—
16C2×#66927C2218yescomplemented
17C11×#383C2218yescomplemented
18C2×C11×#95C2216yes—
19#10622285C22148yescomplemented
20#10622284C22148yescomplemented
21C24×D11C2311yescharacteristic
22C24×D11C2314yes—
23C23×C4×C11C2314yes—
24C23×C4×C11C2313yes—
25C23×Dic11C2313yes—
26C22×D44—224no—
27C22×D44—424no—
28C22×D44—424no—
29C22×D44C23124yes—
30C22×D44C23116yes—
31C2×C42×C11D418yescomplemented
32C2×C42×C11C2314yes—
33C2×(C2×D11)⋊C4—212no—
34C2×(C2×D11)⋊C4—424no—
35C2×(C2×D11)⋊C4C23112yes—
36C2×(C2×D11)⋊C4C23148yes—
37C2×Dic11⋊C4—212no—
38C2×Dic11⋊C4C23112yes—
39#66929—232no—
40#66927—232no—
41C11×#95C23124yes—
42C2×#2818—111nomaximal, Sylow
43C24×C11C2411yescharacteristic
44C23×D11—22no—
45C23×D11—28no—
46C23×D11—224no—
47C23×D11—224no—
48C23×D11—212no—
49C23×D11C2412yes—
50C23×D11C2418yes—
51C22×C4×C11—212no—
52C22×C4×C11—224no—
53C22×C4×C11C2×D4112yes—
54C22×C4×C11C2418yes—
55C22×C4×C11C2416yes—
56C22×Dic11—26no—
57C22×Dic11—212no—
58C22×Dic11C2416yes—
59C2×D44—248no—
60C2×D44—448no—
61C2×D44—448no—
62C2×D44—496no—
63C2×D44—464no—
64C42×C11C2×D4116yescomplemented
65(C2×D11)⋊C4—224no—
66(C2×D11)⋊C4—448no—
67Dic11⋊C4—224no—
68C22×#127—111no—
69C22×#126—111no—
70#2818—1116no—
71C2×#394—116no—
72C2×#392—116no—
73C2×#383D1111yescharacteristic, complemented
74C23×C11C22×D412yes—
75C23×C11H(5,𝔽2)112yes—
76C23×C11C2511yescharacteristic
77C22×D11—22no—
78C22×D11—28no—
79C22×D11—224no—
80C22×D11—212no—
81C22×D11—224no—
82C22×D11—448no—
83C22×D11—412no—
84C22×D11—416no—
85C22×D11—416no—
86C22×D11—448no—
87C2×C4×C11—224no—
88C2×C4×C11—212no—
89C2×C4×C11—224no—
90C2×C4×C11—416no—
91C2×C4×C11C22×D4112yes—
92C2×Dic11—26no—
93C2×Dic11—212no—
94C2×Dic11—412no—
95D44—496no—
96D44—464no—
97C23×D4—116no—
98C23×D4—114no—
99C2×#127—118no—
100C2×#127—228no—
101C2×#126—118no—
102C2×#126—228no—
103C22×C4⋊C4—113no—
104C22×C22⋊C4—113no—
105C22×C22⋊C4—1112no—
106C22×C42C2×D1111yescharacteristic
107#394—1148no—
108#392—1148no—
109#383C2×D1118yescomplemented
110C2×#95C2×D1116yes—
111C22×C11#535112yes—
112C22×C11#560116yes—
113C22×C11C23×D411yescharacteristic
114C22×C11C2×H(5,𝔽2)16yes—
115C2×D11—46no—
116C2×D11—424no—
117C2×D11—424no—
118C2×D11—48no—
119C2×D11—48no—
120C2×D11—832no—
121C2×D11—88no—
122C4×C11—212no—
123C4×C11—48no—
124Dic11—46no—
125C25—111no—
126C25—114no—
127C22×D4—1124no—
128C22×D4—1116no—
129C22×D4—2224no—
130C22×D4—4424no—
131C22×D4—4424no—
132C23×C4—113no—
133C23×C4C22×D1114yes—
134C23×C4C22×D1113yes—
135#127—2232no—
136#126—2232no—
137C2×C4⋊C4—1112no—
138C2×C4⋊C4—2212no—
139C2×C22⋊C4—1112no—
140C2×C22⋊C4—1148no—
141C2×C22⋊C4—2212no—
142C2×C22⋊C4—4424no—
143C2×C42D4418yescomplemented
144C2×C42C22×D1114yes—
145#95C22×D11124yes—
146C2×C11#281818yescomplemented
147C2×C11C2×#53513yes—
148C2×C11C2×#56014yes—
149D11—82no—
150D11—88no—
151C24—112no—
152C24—118no—
153C24—222no—
154C24—228no—
155C24—2224no—
156C24—2212no—
157C24—2224no—
158C24C23×D1111yescharacteristic
159C2×D4—2248no—
160C2×D4—4448no—
161C2×D4—4448no—
162C2×D4—4496no—
163C2×D4—4464no—
164C22×C4—212no—
165C22×C4—224no—
166C22×C4—116no—
167C22×C4—226no—
168C22×C4—2212no—
169C22×C4C2×D44112yes—
170C22×C4C23×D1118yes—
171C22×C4C23×D1116yes—
172C4⋊C4—2224no—
173C22⋊C4—2224no—
174C22⋊C4—4448no—
175C42C2×D44116yescomplemented
176C11C2×#281811yescharacteristic, complemented, Sylow
177C23—222no—
178C23—228no—
179C23—2224no—
180C23—2224no—
181C23—2212no—
182C23—4416no—
183C23—4416no—
184C23—4448no—
185C23—4448no—
186C23—4412no—
187C23C22×D4412yes—
188C23#67042112yes—
189C23C24×D1111yescharacteristic
190D4—4496no—
191D4—4464no—
192C2×C4—224no—
193C2×C4—212no—
194C2×C4—224no—
195C2×C4—416no—
196C2×C4—226no—
197C2×C4—2212no—
198C2×C4—4412no—
199C2×C4C22×D44112yes—
200C22—4424no—
201C22—446no—
202C22—448no—
203C22—448no—
204C22—4424no—
205C22—888no—
206C22—8832no—
207C22#10623056112yes—
208C22#10623242116yes—
209C22C23×D4411yescharacteristic
210C22C2×#6704216yes—
211C4—212no—
212C4—48no—
213C4—446no—
214C2—888no—
215C2—882no—
216C2#1307665918yesdirect product factor
217C2C2×#1062305613yes—
218C2C2×#1062324214yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#383C2
socleC24×C11C24
hypercenterC2×#383D11
hypocenterC11C2×#2818
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
1. C22×#66927C2semidirect
2. C22×#66929C2semidirect
3. #13076659C2direct (N × H)
4. C2×#10622285C2semidirect
5. C2×#10622284C2semidirect
6. C2×C11×#383C2semidirect
14. C2×#66929C22semidirect
16. C2×#66927C22semidirect
17. C11×#383C22semidirect
19. #10622285C22semidirect
20. #10622284C22semidirect
31. C2×C42×C11D4semidirect
64. C42×C11C2×D4semidirect
73. C2×#383D11semidirect
109. #383C2×D11semidirect
143. C2×C42D44semidirect
146. C2×C11#2818semidirect
175. C42C2×D44semidirect
176. C11C2×#2818semidirect
216. C2#13076659direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669272
C22×#669292
#130766592
C2×#106222852
C2×#106222842
C2×C11×#3832
C2×#281811