Finite Group Databasebeta

← C2×#10620931 #13059384

Subgroups — C2×#10620931 #13059384

Order 1344.

644 conjugacy classes of subgroups; only the 208 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 208 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×C4×D3×C7C211yesmaximal, characteristic
2C22×C3×Dic14C211yesmaximal, characteristic, complemented
3C2×C4⋊Dic21C211yesmaximal, characteristic, complemented
4C2×#66577C212yesmaximal, complemented
5C2×(C2×D3)⋊Dic7C212yesmaximal
6#10620931C218yesmaximal, direct product factor
7C2×#6487—31nomaximal, Hall
8C23×D3×C7C2211yescharacteristic
9C22×C3×C4×C7C2211yescharacteristic
10C22×Dic21C2212yes—
11C22×C7×Dic3C2211yescharacteristic
12C2×C4×D3×C7—24no—
13C2×C4×D3×C7C2214yes—
14C22×C3×Dic7C2212yes—
15C2×C3×Dic14—24no—
16C2×C3×Dic14C2214yescomplemented
17C4⋊Dic21C2214yescomplemented
18#66577C2218yescomplemented
19(C2×D3)⋊Dic7C2218yes—
20C23×C4×C7—31no—
21C22×Dic14D311yescharacteristic, complemented
22C2×C22⋊Dic7—32no—
23C2×C4⋊Dic7—31no—
24#6487—38no—
25C2×Dic7⋊C4—32no—
26C2×#946—71nomaximal, Hall
27C23×C3×C7C2311yescharacteristic
28C22×D3×C7—22no—
29C22×D3×C7—22no—
30C22×D3×C7Q814yescomplemented
31C22×D3×C7C2312yes—
32C2×C3×C4×C7D414yes—
33C2×C3×C4×C7C2312yes—
34C2×Dic21—24no—
35C2×Dic21C2314yes—
36C2×C7×Dic3—22no—
37C2×C7×Dic3C2312yes—
38C4×D3×C7—28no—
39C2×C3×Dic7—24no—
40C2×C3×Dic7C2314yes—
41C3×Dic14—28no—
42C24×C7—31no—
43C22×C4×C7—31no—
44C22×C4×C7—34no—
45C22×C4×C7—64no—
46C22×C4×C7C2×D311yescharacteristic
47C22×Dic7—32no—
48C22×Dic7C2×D312yes—
49C2×Dic14—24no—
50C2×Dic14C2×D314yescomplemented
51C22⋊Dic7—38no—
52C4⋊Dic7—34no—
53Dic7⋊C4—38no—
54C22×C3×Q8—71no—
55C22×C4×D3D711yescharacteristic
56#946—78no—
57C2×(C2×D3)⋊C4—72no—
58C2×C4⋊Dic3—71no—
59C2×Dic3⋊C4—72no—
60C22×C3×C7C2×D412yes—
61C22×C3×C7C2×Q812yes—
62C22×C3×C7#4112yes—
63C22×C3×C7C2411yescharacteristic
64C2×D3×C7—28no—
65C2×D3×C7—22no—
66C2×D3×C7—22no—
67C2×D3×C7C2×Q814yescomplemented
68C3×C4×C7C2×D414yes—
69Dic21—24no—
70C3×Dic7—24no—
71C7×Dic3—22no—
72C2×C22⋊Q8—211noSylow
73C23×C7—34no—
74C23×C7—32no—
75C23×C7—62no—
76C23×C7—62no—
77C23×C7C22×D311yescharacteristic
78C2×C4×C7—32no—
79C2×C4×C7—62no—
80C2×C4×C7—68no—
81C2×C4×C7#6714yes—
82C2×C4×C7C22×D312yes—
83C2×Dic7—24no—
84C2×Dic7—34no—
85C2×Dic7—64no—
86C2×Dic7C22×D314yes—
87Dic14—28no—
88C23×D3C2×D711yescharacteristic
89C2×C3×Q8—74no—
90C2×C3×Q8—144no—
91C22×C3×C4—72no—
92C22×C3×C4C2×D711yescharacteristic
93C22×Dic3—72no—
94C22×Dic3C2×D711yescharacteristic
95C2×C4×D3—24no—
96C2×C4×D3C2×D714yes—
97(C2×D3)⋊C4—78no—
98C4⋊Dic3—74no—
99Dic3⋊C4—78no—
100C2×C3×C7C22⋊Q814yescomplemented
101C2×C3×C7C22×D411yescharacteristic
102C2×C3×C7C22×Q811yescharacteristic
103C2×C3×C7C2×#4111yescharacteristic
104D3×C7—24no—
105C22×Q8—71no—
106C23×C4—31no—
107C22⋊Q8—218no—
108C2×C4⋊C4—212no—
109C2×C4⋊C4—211no—
110C2×C22⋊C4—212no—
111C22×C7—34no—
112C22×C7—68no—
113C22×C7—62no—
114C22×C7—62no—
115C22×C7D3×Q812yes—
116C22×C7#23912yes—
117C22×C7C2×#6712yes—
118C22×C7C23×D311yescharacteristic
119C4×C7—62no—
120C4×C7C2×#6714yes—
121Dic7—24no—
122Dic7—64no—
123C23×C3C22×D711yescharacteristic
124C22×D3—22no—
125C22×D3—22no—
126C22×D3Dic1414yescomplemented
127C22×D3C22×D712yes—
128C3×Q8—148no—
129C2×C3×C4—74no—
130C2×C3×C4—144no—
131C2×C3×C4C22⋊D714yes—
132C2×C3×C4C22×D712yes—
133C2×Dic3—22no—
134C2×Dic3—74no—
135C2×Dic3—144no—
136C2×Dic3C22×D712yes—
137C4×D3—28no—
138C3×C7C2×C22⋊Q811yescharacteristic, complemented, Hall
139C24—31no—
140C2×Q8—74no—
141C2×Q8—144no—
142C22×C4—31no—
143C22×C4—34no—
144C22×C4—64no—
145C22×C4—72no—
146C22×C4—212no—
147C22×C4D3×D711yescharacteristic
148C4⋊C4—218no—
149C4⋊C4—214no—
150C22⋊C4—218no—
151C2×C7—64no—
152C2×C7#94614yescomplemented
153C2×C7C2×D3×Q811yescharacteristic
154C2×C7C2×#23911yescharacteristic
155C2×C7C22×#6711yescharacteristic
156C22×C3C2×Dic1412yes—
157C22×C3#115712yes—
158C22×C3C2×C22⋊D712yes—
159C22×C3C23×D711yescharacteristic
160C2×D3—28no—
161C2×D3—22no—
162C2×D3—22no—
163C2×D3C2×Dic1414yescomplemented
164C3×C4—144no—
165C3×C4C2×C22⋊D714yes—
166Dic3—22no—
167Dic3—144no—
168C23—34no—
169C23—32no—
170C23—62no—
171C23—62no—
172C23C2×D3×D711yescharacteristic
173Q8—148no—
174C2×C4—32no—
175C2×C4—62no—
176C2×C4—68no—
177C2×C4—74no—
178C2×C4—144no—
179C2×C4—214no—
180C2×C4—424no—
181C2×C4#424514yes—
182C2×C4C2×D3×D712yes—
183C7C2×#94611yescharacteristic, complemented, Sylow
184C2×C3#648714yescomplemented
185C2×C3C22×Dic1411yescharacteristic
186C2×C3C2×#115711yescharacteristic
187C2×C3C22×C22⋊D711yescharacteristic
188D3—24no—
189C22—34no—
190C22—68no—
191C22—62no—
192C22—62no—
193C22D3×Dic1412yes—
194C22#6667312yes—
195C22C2×#424512yes—
196C22C22×D3×D711yescharacteristic
197C4—62no—
198C4—144no—
199C4—424no—
200C4C2×#424514yes—
201C3C2×#648711yescharacteristic, complemented, Sylow
202C2—64no—
203C2#1062093114yesdirect product factor
204C2C2×D3×Dic1411yescharacteristic
205C2C2×#6667311yescharacteristic
206C2C22×#424511yescharacteristic
subgroupG/H
centerC23C2×D3×D7
commutator, cosocleC22×C3×C7C24
FrattiniC22C22×D3×D7
FittingC22×C3×C4×C7C22
socleC23×C3×C7C23
prime radicalC23×D3×C7C22
hypercenterC22×C4D3×D7
hypocenterC3×C7C2×C22⋊Q8
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×Dic14C2semidirect
3. C2×C4⋊Dic21C2semidirect
4. C2×#66577C2semidirect
6. #10620931C2direct (N × H)
16. C2×C3×Dic14C22semidirect
17. C4⋊Dic21C22semidirect
18. #66577C22semidirect
21. C22×Dic14D3semidirect
30. C22×D3×C7Q8semidirect
50. C2×Dic14C2×D3semidirect
67. C2×D3×C7C2×Q8semidirect
100. C2×C3×C7C22⋊Q8semidirect
126. C22×D3Dic14semidirect
138. C3×C7C2×C22⋊Q8semidirect
152. C2×C7#946semidirect
163. C2×D3C2×Dic14semidirect
183. C7C2×#946semidirect
184. C2×C3#6487semidirect
201. C3C2×#6487semidirect
203. C2#10620931direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D3×C72
C22×C3×Dic142
C2×C4⋊Dic212
C2×#665772
C2×(C2×D3)⋊Dic72
#106209312
C2×#64873
C2×#9467