Finite Group Databasebeta

← C2×#10621376 #13061594

Subgroups — C2×#10621376 #13061594

Order 1344.

852 conjugacy classes of subgroups; only the 251 normal subgroups are shown.

normal subgroups only

This group has 852 conjugacy classes of subgroups — too many to draw. Only its 251 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×D84C211yesmaximal, characteristic
2C22×C4×D21C212yesmaximal, complemented
3C2×C3×C7×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×#66631C212yesmaximal, complemented
5C2×C4×Dic21C211yesmaximal, characteristic, complemented
6#10621376C218yesmaximal, direct product factor
7C2×#6456—31nomaximal, Hall
8C23×D21C2212yes—
9C22×C3×C4×C7C2212yes—
10C22×C3×C4×C7C2211yescharacteristic
11C22×Dic21C2211yescharacteristic
12C22×Dic21C2211yescharacteristic
13C2×D84C418yescomplemented
14C2×D84C2214yes—
15C2×C4×D21—28no—
16C2×C4×D21C2218yescomplemented
17C3×C7×C4⋊C4C2214yescomplemented
18#66631C2218yescomplemented
19C4×Dic21C2214yescomplemented
20C22×D28—31no—
21C22×C4×D7—32no—
22C2×C7×C4⋊C4D311yescharacteristic, complemented
23C2×(C2×D7)⋊C4—32no—
24C2×C4×Dic7—31no—
25#6456—38no—
26C2×#893—71nomaximal, Hall
27C23×C3×C7C2311yescharacteristic
28C22×D21—24no—
29C22×D21—24no—
30C22×D21C2×C418yescomplemented
31C22×D21C2314yes—
32C2×C3×C4×C7—24no—
33C2×C3×C4×C7C2×C414yescomplemented
34C2×C3×C4×C7C2314yes—
35C2×C3×C4×C7C2312yes—
36C2×Dic21—22no—
37C2×Dic21D414yescomplemented
38C2×Dic21C2312yes—
39C2×Dic21C2312yes—
40D84C2×C4116yescomplemented
41C4×D21—216no—
42C23×D7—32no—
43C22×C4×C7C2×D312yes—
44C22×C4×C7C2×D311yescharacteristic
45C22×Dic7—31no—
46C22×Dic7—31no—
47C2×D28—38no—
48C2×D28—34no—
49C2×C4×D7—38no—
50C2×C4×D7—68no—
51C7×C4⋊C4C2×D314yescomplemented
52(C2×D7)⋊C4—38no—
53C4×Dic7—34no—
54C22×D12—71no—
55C22×C4×D3—72no—
56C2×C3×C4⋊C4D711yescharacteristic, complemented
57C2×(C2×D3)⋊C4—72no—
58C2×C4×Dic3—71no—
59#893—78no—
60C22×C3×C7C22×C412yes—
61C22×C3×C7C2×D412yes—
62C22×C3×C7#4112yes—
63C22×C3×C7C2411yescharacteristic
64C2×D21—216no—
65C2×D21—24no—
66C2×D21—24no—
67C2×D21C22×C418yescomplemented
68C3×C4×C7—24no—
69C3×C4×C7C22×C414yescomplemented
70Dic21—22no—
71Dic21C2×D414yescomplemented
72C2×C4×D4—211noSylow
73C23×C7C22×D311yescharacteristic
74C22×D7—38no—
75C22×D7—34no—
76C22×D7—64no—
77C22×D7—64no—
78C2×C4×C7—24no—
79C2×C4×C7C4×D314yescomplemented
80C2×C4×C7C22×D314yes—
81C2×C4×C7C22×D312yes—
82C2×Dic7—34no—
83C2×Dic7—32no—
84C2×Dic7—32no—
85C2×Dic7—62no—
86D28—316no—
87C4×D7—616no—
88C23×D3—72no—
89C22×C3×C4C2×D712yes—
90C22×C3×C4C2×D711yescharacteristic
91C22×Dic3—71no—
92C22×Dic3—71no—
93C2×D12—78no—
94C2×D12—74no—
95C2×C4×D3—78no—
96C2×C4×D3—148no—
97C3×C4⋊C4C2×D714yescomplemented
98(C2×D3)⋊C4—78no—
99C4×Dic3—74no—
100C2×C3×C7C4×D414yescomplemented
101C2×C3×C7C23×C411yescharacteristic
102C2×C3×C7C22×D411yescharacteristic
103C2×C3×C7C2×#4111yescharacteristic
104D21—28no—
105C22×D4—211no—
106C23×C4—212no—
107C4×D4—218no—
108C2×C4⋊C4D2111yescharacteristic, complemented
109C2×C22⋊C4—212no—
110C2×C42—211no—
111C22×C7C2×C4×D312yes—
112C22×C7D3×D412yes—
113C22×C7#23912yes—
114C22×C7C23×D311yescharacteristic
115C2×D7—38no—
116C2×D7—616no—
117C2×D7—64no—
118C2×D7—64no—
119C4×C7—24no—
120C4×C7C2×C4×D314yescomplemented
121Dic7—34no—
122Dic7—62no—
123C23×C3C22×D711yescharacteristic
124C22×D3—78no—
125C22×D3—74no—
126C22×D3—144no—
127C22×D3—144no—
128C2×C3×C4—24no—
129C2×C3×C4C4×D714yescomplemented
130C2×C3×C4C22×D714yes—
131C2×C3×C4C22×D712yes—
132C2×Dic3—74no—
133C2×Dic3—72no—
134C2×Dic3—72no—
135C2×Dic3—142no—
136D12—716no—
137C4×D3—1416no—
138C3×C7C2×C4×D411yescharacteristic, complemented, Hall
139C24—212no—
140C2×D4—218no—
141C2×D4—214no—
142C22×C4—211no—
143C22×C4—211no—
144C22×C4—218no—
145C22×C4—428no—
146C22×C4C2×D2112yes—
147C22×C4C2×D2111yescharacteristic
148C4⋊C4C2×D2114yescomplemented
149C22⋊C4—218no—
150C42—214no—
151C2×C7#89314yescomplemented
152C2×C7C22×C4×D311yescharacteristic
153C2×C7C2×D3×D411yescharacteristic
154C2×C7C2×#23911yescharacteristic
155D7—68no—
156C22×C3C2×C4×D712yes—
157C22×C3D4×D712yes—
158C22×C3#116112yes—
159C22×C3C23×D711yescharacteristic
160C2×D3—78no—
161C2×D3—1416no—
162C2×D3—144no—
163C2×D3—144no—
164C3×C4—24no—
165C3×C4C2×C4×D714yescomplemented
166Dic3—74no—
167Dic3—142no—
168C23—218no—
169C23—214no—
170C23—424no—
171C23—424no—
172C23C22×D2111yescharacteristic
173D4—2116no—
174C2×C4—24no—
175C2×C4—214no—
176C2×C4—212no—
177C2×C4—212no—
178C2×C4—4216no—
179C2×C4—422no—
180C2×C4C4×D2114yescomplemented
181C2×C4C22×D2114yes—
182C2×C4C22×D2112yes—
183C7C2×#89311yescharacteristic, complemented, Sylow
184C2×C3#645614yescomplemented
185C2×C3C22×C4×D711yescharacteristic
186C2×C3C2×D4×D711yescharacteristic
187C2×C3C2×#116111yescharacteristic
188D3—148no—
189C22—218no—
190C22—4216no—
191C22—424no—
192C22—424no—
193C22C2×C4×D2112yes—
194C22D4×D2112yes—
195C22#6673212yes—
196C22C23×D2111yescharacteristic
197C4—24no—
198C4—214no—
199C4—422no—
200C4C2×C4×D2114yescomplemented
201C3C2×#645611yescharacteristic, complemented, Sylow
202C2—428no—
203C2#1062137614yesdirect product factor
204C2C22×C4×D2111yescharacteristic
205C2C2×D4×D2111yescharacteristic
206C2C2×#6673211yescharacteristic
subgroupG/H
centerC23C22×D21
commutatorC2×C3×C7C23×C4
FrattiniC22C23×D21
FittingC2×C3×C7×C4⋊C4C2
socleC23×C3×C7C23
prime radicalC22×D84C2
cosocleC22×C3×C7C24
hypercenterC2×C4⋊C4D21
hypocenterC3×C7C2×C4×D4
LCSG ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×D21C2semidirect
3. C2×C3×C7×C4⋊C4C2semidirect
4. C2×#66631C2semidirect
5. C2×C4×Dic21C2semidirect
6. #10621376C2direct (N × H)
13. C2×D84C4semidirect
16. C2×C4×D21C22semidirect
17. C3×C7×C4⋊C4C22semidirect
18. #66631C22semidirect
19. C4×Dic21C22semidirect
22. C2×C7×C4⋊C4D3semidirect
30. C22×D21C2×C4semidirect
33. C2×C3×C4×C7C2×C4semidirect
37. C2×Dic21D4semidirect
40. D84C2×C4semidirect
51. C7×C4⋊C4C2×D3semidirect
56. C2×C3×C4⋊C4D7semidirect
67. C2×D21C22×C4semidirect
69. C3×C4×C7C22×C4semidirect
71. Dic21C2×D4semidirect
79. C2×C4×C7C4×D3semidirect
97. C3×C4⋊C4C2×D7semidirect
100. C2×C3×C7C4×D4semidirect
108. C2×C4⋊C4D21semidirect
120. C4×C7C2×C4×D3semidirect
129. C2×C3×C4C4×D7semidirect
138. C3×C7C2×C4×D4semidirect
148. C4⋊C4C2×D21semidirect
151. C2×C7#893semidirect
165. C3×C4C2×C4×D7semidirect
180. C2×C4C4×D21semidirect
183. C7C2×#893semidirect
184. C2×C3#6456semidirect
200. C4C2×C4×D21semidirect
201. C3C2×#6456semidirect
203. C2#10621376direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D842
C22×C4×D212
C2×C3×C7×C4⋊C42
C2×#666312
C2×C4×Dic212
#106213762
C2×#64563
C2×#8937