Finite Group Databasebeta

← C2×#13076656 #14960330

Subgroups — C2×#13076656 #14960330

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
2#13076656C2116yesmaximal, direct product factor
3C2×#10622604C216yesmaximal, complemented
4C2×#10622573C216yesmaximal, complemented
5C2×#10622550C211yesmaximal, characteristic, complemented
6C22×C11×#126C211yesmaximal, characteristic, complemented
7C23×C22⋊D11C2214yes—
8C23×D44C2216yes—
9C2×C11×#126—28no—
10C2×C11×#126C2218yescomplemented
11C22×C11×C4⋊C4C2213yes—
12C22×C11×C22⋊C4C2213yes—
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4C22112yes—
15C2×#66927—28no—
16C2×#66927C2218yescomplemented
17C2×C11⋊#95C2216yes—
18#10622604C22148yescomplemented
19#10622573C22148yescomplemented
20#10622550C2218yescomplemented
21C25×C11C2311yescharacteristic
22C24×D11C2314yes—
23C23×C4×C11C2313yes—
24C23×C4×C11C2313yes—
25C22×C22⋊D11—424no—
26C22×C22⋊D11C23116yes—
27C23×Dic11C2314yes—
28C22×D44—224no—
29C22×D44—424no—
30C22×D44C23124yes—
31C11×#126—232no—
32C2×C11×C4⋊C4—212no—
33C2×C11×C4⋊C4C23112yes—
34C2×C11×C22⋊C4—212no—
35C2×C11×C22⋊C4C23112yes—
36C2×C42×C11D418yescomplemented
37C2×C42×C11C2314yes—
38C2×(C2×D11)⋊C4—424no—
39C2×(C2×D11)⋊C4C23148yes—
40#66927—232no—
41C11⋊#95C23124yes—
42C2×#2818—111nomaximal, Sylow
43C24×C11—22no—
44C24×C11—212no—
45C24×C11C2412yes—
46C24×C11C2411yescharacteristic
47C23×D11—28no—
48C23×D11—224no—
49C23×D11—224no—
50C23×D11C2418yes—
51C22×C4×C11—212no—
52C22×C4×C11—26no—
53C22×C4×C11—212no—
54C22×C4×C11C2×D4112yes—
55C22×C4×C11C2416yes—
56C22×C4×C11C2416yes—
57C2×C22⋊D11—448no—
58C2×C22⋊D11—464no—
59C22×Dic11—224no—
60C22×Dic11C2418yes—
61C2×D44—248no—
62C2×D44—448no—
63C2×D44—496no—
64C11×C4⋊C4—224no—
65C11×C22⋊C4—224no—
66C42×C11C2×D4116yescomplemented
67(C2×D11)⋊C4—448no—
68C22×#127—111no—
69C22×#126D1111yescharacteristic, complemented
70#2818—1116no—
71C2×#394—116no—
72C2×#392—116no—
73C2×#383—111no—
74C23×C11—22no—
75C23×C11—212no—
76C23×C11—412no—
77C23×C11—416no—
78C23×C11C22×D412yes—
79C23×C11H(5,𝔽2)112yes—
80C23×C11C2511yescharacteristic
81C22×D11—28no—
82C22×D11—224no—
83C22×D11—224no—
84C22×D11—448no—
85C22×D11—416no—
86C22×D11—448no—
87C2×C4×C11—224no—
88C2×C4×C11—212no—
89C2×C4×C11—26no—
90C2×C4×C11—212no—
91C2×C4×C11—412no—
92C2×C4×C11C22×D4112yes—
93C22⋊D11—464no—
94C2×Dic11—224no—
95C2×Dic11—416no—
96D44—496no—
97C23×D4—114no—
98C23×D4—116no—
99C2×#127—118no—
100C2×#127—228no—
101C2×#126—28no—
102C2×#126C2×D1118yescomplemented
103C22×C4⋊C4C2×D1113yes—
104C22×C22⋊C4—1112no—
105C22×C22⋊C4C2×D1113yes—
106C22×C42C2×D1111yescharacteristic
107#394—1148no—
108#392—1148no—
109#383—118no—
110C2×#95—116no—
111C22×C11—46no—
112C22×C11—48no—
113C22×C11—88no—
114C22×C11#535112yes—
115C22×C11#560116yes—
116C22×C11C23×D411yescharacteristic
117C22×C11C2×H(5,𝔽2)16yes—
118C2×D11—424no—
119C2×D11—424no—
120C2×D11—48no—
121C2×D11—832no—
122C4×C11—212no—
123C4×C11—46no—
124Dic11—48no—
125C25—114no—
126C25C22×D1111yescharacteristic
127C22×D4—1116no—
128C22×D4—1124no—
129C22×D4—2224no—
130C22×D4—4424no—
131C22×D4—4424no—
132C23×C4—114no—
133C23×C4C22×D1113yes—
134C23×C4C22×D1113yes—
135#127—2232no—
136#126—232no—
137C2×C4⋊C4—212no—
138C2×C4⋊C4C22×D11112yes—
139C2×C22⋊C4—212no—
140C2×C22⋊C4—1148no—
141C2×C22⋊C4—4424no—
142C2×C22⋊C4C22×D11112yes—
143C2×C42C22⋊D1118yescomplemented
144C2×C42C22×D1114yes—
145#95—1124no—
146C2×C11—82no—
147C2×C11#281818yescomplemented
148C2×C11C2×#53513yes—
149C2×C11C2×#56014yes—
150D11—88no—
151C24—212no—
152C24—22no—
153C24—118no—
154C24—2224no—
155C24—2224no—
156C24—228no—
157C24C23×D1112yes—
158C24C23×D1111yescharacteristic
159C2×D4—2248no—
160C2×D4—4448no—
161C2×D4—4496no—
162C2×D4—4448no—
163C2×D4—4464no—
164C22×C4—212no—
165C22×C4—212no—
166C22×C4—26no—
167C22×C4—118no—
168C22×C4—2224no—
169C22×C4C2×C22⋊D11112yes—
170C22×C4C23×D1116yes—
171C22×C4C23×D1116yes—
172C4⋊C4—224no—
173C22⋊C4—224no—
174C22⋊C4—4448no—
175C42C2×C22⋊D11116yescomplemented
176C11C2×#281811yescharacteristic, complemented, Sylow
177C23—212no—
178C23—22no—
179C23—416no—
180C23—412no—
181C23—2224no—
182C23—2224no—
183C23—228no—
184C23—4416no—
185C23—4448no—
186C23—4448no—
187C23#67042112yes—
188C23C22×C22⋊D1112yes—
189C23C24×D1111yescharacteristic
190D4—4496no—
191D4—4464no—
192C2×C4—224no—
193C2×C4—212no—
194C2×C4—212no—
195C2×C4—26no—
196C2×C4—412no—
197C2×C4—2224no—
198C2×C4—4416no—
199C2×C4C22×C22⋊D11112yes—
200C22—46no—
201C22—48no—
202C22—88no—
203C22—4424no—
204C22—448no—
205C22—4424no—
206C22—8832no—
207C22#10623242116yes—
208C22#10623361112yes—
209C22C2×#6704216yes—
210C22C23×C22⋊D1111yescharacteristic
211C4—212no—
212C4—46no—
213C4—448no—
214C2—82no—
215C2—888no—
216C2#1307665618yesdirect product factor
217C2C2×#1062336113yes—
218C2C2×#1062324214yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#126C2
socleC24×C11C24
hypercenterC22×#126D11
hypocenterC11C2×#2818
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. C22×#66927C2semidirect
2. #13076656C2direct (N × H)
3. C2×#10622604C2semidirect
4. C2×#10622573C2semidirect
5. C2×#10622550C2semidirect
6. C22×C11×#126C2semidirect
10. C2×C11×#126C22semidirect
16. C2×#66927C22semidirect
18. #10622604C22semidirect
19. #10622573C22semidirect
20. #10622550C22semidirect
36. C2×C42×C11D4semidirect
66. C42×C11C2×D4semidirect
69. C22×#126D11semidirect
102. C2×#126C2×D11semidirect
143. C2×C42C22⋊D11semidirect
147. C2×C11#2818semidirect
175. C42C2×C22⋊D11semidirect
176. C11C2×#2818semidirect
216. C2#13076656direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669272
#130766562
C2×#106226042
C2×#106225732
C2×#106225502
C22×C11×#1262
C2×#281811