Finite Group Databasebeta

← C2×#10620861 #13059434

Subgroups — C2×#10620861 #13059434

Order 1344.

596 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 160 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×C7×D12C211yesmaximal, characteristic, complemented
2C2×C3×#1157C211yesmaximal, characteristic, complemented
3C2×#66627C211yesmaximal, characteristic, complemented
4C2×#66564C212yesmaximal, complemented
5#10620861C218yesmaximal, direct product factor
6C2×#66560C212yesmaximal, complemented
7C2×#6495—31nomaximal, Hall
8C23×D3×C7—21no—
9C22×C3×C4×C7C2211yescharacteristic
10C2×C7×D12—22no—
11C2×C7×D12—21no—
12C2×C7×D12C2212yes—
13C2×C7×D12C2214yescomplemented
14C2×C3×C22⋊D7—21no—
15C3×#1157—22no—
16C3×#1157C2214yescomplemented
17C2×C3×D28C2211yescharacteristic, complemented
18C2×C3×C4×D7—21no—
19C2×C3×Dic14C2211yescharacteristic, complemented
20#66627C2214yescomplemented
21C2×C3⋊(C7⋊C8)C2212yescomplemented
22#66564C2218yescomplemented
23#66560C2218yescomplemented
24C22×C7×D4—31no—
25C2×#1157D311yescharacteristic, complemented
26C2×#1142—32no—
27#6495—38no—
28C2×#1141—32no—
29C2×#1136—31no—
30C2×#949—71nomaximal, Hall
31C23×C3×C7D411yescharacteristic
32C22×D3×C7—22no—
33C22×D3×C7—24no—
34C22×D3×C7—44no—
35C22×C3×D7—21no—
36C2×C3×C4×C7D411yescharacteristic
37C2×C3×C4×C7D412yes—
38C2×C3×C4×C7C2311yescharacteristic
39C2×C3×C4×C7C2312yes—
40C7×D12—22no—
41C7×D12—24no—
42C7×D12C2314yes—
43C3×C22⋊D7—24no—
44C2×C3×Dic7—21no—
45C3×D28—21no—
46C3×D28C2312yescomplemented
47C3×C4×D7—24no—
48C3×Dic14—21no—
49C3×Dic14C2312yescomplemented
50C3⋊(C7⋊C8)C2314yescomplemented
51C24×C7—61no—
52C2×C7×D4—32no—
53C2×C7×D4—34no—
54C2×C7×D4—61no—
55C2×C7×D4—62no—
56C22×C4×C7C2×D311yescharacteristic
57C2×C22⋊D7—21no—
58#1157—22no—
59#1157C2×D314yescomplemented
60C2×D28C2×D311yescharacteristic, complemented
61C2×C4×D7—21no—
62C2×Dic14C2×D311yescharacteristic, complemented
63#1142—38no—
64#1141—38no—
65#1136—34no—
66C2×C7⋊C8—32no—
67C2×C3×#41—71no—
68C22×D12D711yescharacteristic, complemented
69#949—78no—
70C2×#215—72no—
71C2×#213—72no—
72C2×#208—71no—
73C22×C3×C7—22no—
74C22×C3×C7C2×D412yes—
75C22×C3×C7C2×D411yescharacteristic
76C2×D3×C7—24no—
77C2×D3×C7—48no—
78C2×D3×C7—44no—
79C2×C3×D7—22no—
80C2×C3×D7—42no—
81C3×C4×C7C2×D411yescharacteristic
82C3×C4×C7C2×D412yes—
83C3×C4×C7C2411yescharacteristic
84C3×Dic7—22no—
85C2×AGL(1,ℤ/8)—211noSylow
86C23×C7—64no—
87C23×C7—62no—
88C23×C7—124no—
89C23×C7#6711yescharacteristic
90C22×D7—21no—
91C7×D4—34no—
92C7×D4—62no—
93C7×D4—64no—
94C2×C4×C7#6711yescharacteristic
95C2×C4×C7#6712yes—
96C2×C4×C7C22×D311yescharacteristic
97C2×C4×C7C22×D312yes—
98C22⋊D7—24no—
99C2×Dic7—21no—
100D28—21no—
101D28C22×D312yescomplemented
102C4×D7—24no—
103Dic14—21no—
104Dic14C22×D312yescomplemented
105C7⋊C8—34no—
106C23×D3—21no—
107C3×#41—74no—
108C3×#41—142no—
109C2×C3×Q8—71no—
110C2×C3×D4—71no—
111C2×C3×D4—141no—
112C22×C3×C4—141no—
113C22×C3×C4C2×D711yescharacteristic
114C2×D12—22no—
115C2×D12—21no—
116C2×D12C2×D712yes—
117C2×D12C2×D714yescomplemented
118#215—78no—
119#213—78no—
120#208—74no—
121C2×C3⋊C8—72no—
122C2×C3×C7—22no—
123C2×C3×C7AGL(1,ℤ/8)12yescomplemented
124C2×C3×C7C22×D411yescharacteristic
125C3×D7—42no—
126D3×C7—44no—
127C2×#41—71no—
128C22×D4—31no—
129AGL(1,ℤ/8)—218no—
130C2×SD16—212no—
131C2×D8—212no—
132C2×M16—211no—
133C22×C7—22no—
134C22×C7—64no—
135C22×C7—128no—
136C22×C7—124no—
137C22×C7C2×#6712yes—
138C22×C7C2×#6711yescharacteristic
139C2×D7—22no—
140C2×D7—42no—
141C4×C7C2×#6711yescharacteristic
142C4×C7C2×#6712yes—
143C4×C7C23×D311yescharacteristic
144Dic7—22no—
145C23×C3—141no—
146C23×C3C22⋊D711yescharacteristic
147C22×D3—22no—
148C22×D3—24no—
149C22×D3—44no—
150C3×Q8—72no—
151C3×Q8—141no—
152C3×D4—72no—
153C3×D4—144no—
154C3×D4—141no—
155C2×C3×C4—141no—
156C2×C3×C4—144no—
157C2×C3×C4C22⋊D711yescharacteristic
158C2×C3×C4C22⋊D712yes—
159C2×C3×C4C22×D711yescharacteristic
160C2×C3×C4C22×D712yes—
161D12—22no—
162D12—24no—
163D12C22×D714yes—
164C3⋊C8—74no—
165C3×C7C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
166C24—61no—
167#41—74no—
168#41—142no—
169C2×Q8—71no—
170C2×D4—32no—
171C2×D4—34no—
172C2×D4—62no—
173C2×D4—61no—
174C2×D4—71no—
175C2×D4—141no—
176C22×C4—141no—
177C22×C4D3×D711yescharacteristic
178SD16—218no—
179D8—218no—
180M16—214no—
181C2×C8—212no—
182C2×C7—22no—
183C2×C7—124no—
184C2×C7#94912yescomplemented
185C2×C7C22×#6711yescharacteristic
186D7—42no—
187C22×C3—22no—
188C22×C3—142no—
189C22×C3—282no—
190C22×C3C2×C22⋊D712yes—
191C22×C3C2×C22⋊D711yescharacteristic
192C2×D3—24no—
193C2×D3—48no—
194C2×D3—44no—
195C3×C4—142no—
196C3×C4C2×C22⋊D712yes—
197C3×C4C2×C22⋊D711yescharacteristic
198C3×C4C23×D711yescharacteristic
199C23—64no—
200C23—62no—
201C23—124no—
202C23—141no—
203C23#424511yescharacteristic
204Q8—72no—
205Q8—141no—
206D4—34no—
207D4—64no—
208D4—62no—
209D4—72no—
210D4—144no—
211D4—141no—
212C2×C4—141no—
213C2×C4—144no—
214C2×C4#424512yes—
215C2×C4#424511yescharacteristic
216C2×C4C2×D3×D712yes—
217C2×C4C2×D3×D711yescharacteristic
218C8—214no—
219C7C2×#94911yescharacteristic, complemented, Sylow
220C2×C3—22no—
221C2×C3—282no—
222C2×C3#649512yescomplemented
223C2×C3C22×C22⋊D711yescharacteristic
224D3—44no—
225C22—22no—
226C22—64no—
227C22—128no—
228C22—124no—
229C22—142no—
230C22—282no—
231C22C2×#424512yes—
232C22C2×#424511yescharacteristic
233C4—142no—
234C4C2×#424512yes—
235C4C2×#424511yescharacteristic
236C4C22×D3×D711yescharacteristic
237C3C2×#649511yescharacteristic, complemented, Sylow
238C2—22no—
239C2—124no—
240C2—282no—
241C2#1062086112yesdirect product factor
242C2C22×#424511yescharacteristic
subgroupG/H
centerC22C2×#4245
commutator, cosocleC3×C4×C7C24
FrattiniC4C22×D3×D7
FittingC22×C3×C4×C7C22
socleC22×C3×C7C2×D4
hypercenterC22×C4D3×D7
hypocenterC3×C7C2×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C7×D12C2semidirect
2. C2×C3×#1157C2semidirect
3. C2×#66627C2semidirect
4. C2×#66564C2semidirect
5. #10620861C2direct (N × H)
6. C2×#66560C2semidirect
13. C2×C7×D12C22semidirect
16. C3×#1157C22semidirect
17. C2×C3×D28C22semidirect
19. C2×C3×Dic14C22semidirect
20. #66627C22semidirect
21. C2×C3⋊(C7⋊C8)C22semidirect
22. #66564C22semidirect
23. #66560C22semidirect
25. C2×#1157D3semidirect
46. C3×D28C23semidirect
49. C3×Dic14C23semidirect
50. C3⋊(C7⋊C8)C23semidirect
59. #1157C2×D3semidirect
60. C2×D28C2×D3semidirect
62. C2×Dic14C2×D3semidirect
68. C22×D12D7semidirect
101. D28C22×D3semidirect
104. Dic14C22×D3semidirect
117. C2×D12C2×D7semidirect
123. C2×C3×C7AGL(1,ℤ/8)semidirect
165. C3×C7C2×AGL(1,ℤ/8)semidirect
184. C2×C7#949semidirect
219. C7C2×#949semidirect
222. C2×C3#6495semidirect
237. C3C2×#6495semidirect
241. C2#10620861direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×D122
C2×C3×#11572
C2×#666272
C2×#665642
#106208612
C2×#665602
C2×#64953
C2×#9497