Finite Group Databasebeta

← C2×#20261813 #27158727

Subgroups — C2×#20261813 #27158727

Order 12416.

1460 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20261813C2116yesmaximal, direct product factor
2C2×#15690897C218yesmaximal, complemented
3C2×D97⋊M16C212yesmaximal, complemented
4C22×#13095520C214yesmaximal, complemented
5C22×#13095510C211yesmaximal, characteristic
6#15690897C22164yescomplemented
7C2×#13095521C2214yescomplemented
8D97⋊M16C22116yescomplemented
9C2×#13095520C2214yes—
10C2×#13095520C2218yescomplemented
11C2×#13095520C22132yescomplemented
12C2×#13095519C2214yescomplemented
13C22×#11715897C2218yescomplemented
14C2×#13095510C414yes—
15C2×#13095510C418yes—
16C2×#13095510C2214yes—
17C2×#13095510C2218yes—
18C22×Dic194C411yescharacteristic
19C22×C22⋊D97C412yes—
20C23×Dic97C2212yes—
21C22×C4×D97C2211yescharacteristic
22C22×D4×C97C411yescharacteristic
23#13095521C23116yescomplemented
24#13095520C23116yes—
25#13095520C23132yescomplemented
26#13095519C23116yescomplemented
27C2×#11715897C2318yes—
28C2×#11715897C23132yescomplemented
29C23×D97C2×C411yescharacteristic
30#13095510C2×C4116yes—
31#13095510C2×C4132yes—
32#13095510C23116yes—
33C2×Dic194C2×C414yes—
34C2×Dic194C2×C418yes—
35C2×C22⋊D97C2×C418yes—
36C2×C22⋊D97C2×C4116yes—
37C22×Dic97C2×C412yes—
38C22×Dic97C2×C414yes—
39C22×Dic97C2×C418yes—
40C22×Dic97C2311yescharacteristic
41C22×Dic97C2314yes—
42C22×Dic97C2318yes—
43C2×C4×D97C2×C412yes—
44C2×C4×D97C2×C414yes—
45C2×C4×D97C2312yes—
46C2×C4×D97C2314yes—
47C24×C97C2×C412yes—
48C2×D4×C97C2×C414yes—
49C2×D4×C97C2×C418yes—
50C22×C4×C97C2×C411yescharacteristic
51C23×C97—44no—
52C23×C97C22×C411yescharacteristic
53C23×C97C22×C414yes—
54C23×C97C22×C418yes—
55C22×D97—42no—
56C22×D97C22×C412yes—
57C22×D97C22×C414yes—
58D4×C97C22×C4116yes—
59C2×C4×C97C22×C414yes—
60C2×C4×C97C22×C412yes—
61C22⋊D97C22×C4132yes—
62C2×Dic97C22×C412yes—
63C2×Dic97C22×C411yescharacteristic
64C2×Dic97C22×C418yes—
65C2×Dic97C22×C414yes—
66C2×Dic97C22×C418yes—
67C2×Dic97C22×C4116yes—
68C2×Dic97C2411yescharacteristic
69C2×Dic97C2412yes—
70C2×Dic97C2418yes—
71C4×D97C22×C414yes—
72C4×D97C22×C418yes—
73C4×D97C2414yes—
74Dic194C22×C4116yes—
75#11715897C24116yes—
76C22×C97—22no—
77C22×C97—28no—
78C22×C97—48no—
79C22×C97C23×C412yes—
80C22×C97C23×C418yes—
81C22×C97C23×C411yescharacteristic
82C2×D97—24no—
83C2×D97—44no—
84C2×D97C23×C414yes—
85C4×C97C23×C414yes—
86Dic97C23×C418yes—
87Dic97C23×C411yescharacteristic
88Dic97C23×C412yes—
89Dic97C2511yescharacteristic
90C2×C97—22no—
91C2×C97—28no—
92C2×C97#56812yescomplemented
93C2×C97C24×C411yescharacteristic
94D97—24no—
95C2×#568—971nomaximal, Sylow
96C97C2×#56811yescharacteristic, complemented, Sylow
97C22×#41—971no—
98#568—9716no—
99C2×#131—978no—
100C22×M16—974no—
101C22×M16—972no—
102C2×#41—974no—
103C2×#41—978no—
104C2×#41—978no—
105C2×#41—974no—
106C22×Q8—971no—
107C22×D4—972no—
108C22×D4#8760411yescharacteristic
109C23×C4—972no—
110C23×C4—971no—
111#131—9764no—
112C2×M16—974no—
113C2×M16—978no—
114C2×M16—974no—
115C2×M16—9732no—
116C2×M16—9716no—
117C22×C8—978no—
118C22×C8—974no—
119C24—971no—
120C24C2×#8760412yes—
121#41—9716no—
122#41—9732no—
123#41—9716no—
124C2×Q8—978no—
125C2×Q8—974no—
126C2×D4—9716no—
127C2×D4—978no—
128C2×D4C2×#8760418yes—
129C2×D4C2×#8760414yes—
130C22×C4—972no—
131C22×C4—978no—
132C22×C4—974no—
133C22×C4—974no—
134C22×C4—971no—
135C22×C4—978no—
136C22×C4—974no—
137C22×C4—972no—
138C22×C4—972no—
139C22×C4—974no—
140C22×C4C2×#8760411yescharacteristic
141M16—9716no—
142M16—9732no—
143M16—9716no—
144C2×C8—978no—
145C2×C8—9732no—
146C2×C8—9716no—
147C23—44no—
148C23—974no—
149C23—972no—
150C23—3882no—
151C23C22×#8760411yescharacteristic
152C23C22×#8760414yes—
153C23C22×#8760418yes—
154Q8—9716no—
155D4—9732no—
156D4C22×#87604116yes—
157C2×C4—978no—
158C2×C4—972no—
159C2×C4—972no—
160C2×C4—978no—
161C2×C4—978no—
162C2×C4—9716no—
163C2×C4—971no—
164C2×C4—971no—
165C2×C4—974no—
166C2×C4—974no—
167C2×C4—974no—
168C2×C4—978no—
169C2×C4C22×#8760414yes—
170C2×C4C22×#8760412yes—
171C8—9716no—
172C22—22no—
173C22—28no—
174C22—48no—
175C22—974no—
176C22—3884no—
177C22—1944no—
178C22C23×#8760412yes—
179C22C23×#8760418yes—
180C22C23×#8760411yescharacteristic
181C4—971no—
182C4—972no—
183C4—971no—
184C4—978no—
185C4C23×#8760414yes—
186C2—22no—
187C2—28no—
188C2—1944no—
189C2#2026181312yesdirect product factor
190C2C24×#8760411yescharacteristic
subgroupG/H
centerC22C23×#87604
commutatorC2×C97C24×C4
FrattiniC2C24×#87604
FittingC22×D4×C97C4
socleC22×C97C23×C4
prime radicalC22×#13095510C2
cosocleDic97C25
hypercenterC22×D4#87604
hypocenterC97C2×#568
LCSG ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #20261813C2direct (N × H)
2. C2×#15690897C2semidirect
3. C2×D97⋊M16C2semidirect
4. C22×#13095520C2semidirect
6. #15690897C22semidirect
7. C2×#13095521C22semidirect
8. D97⋊M16C22semidirect
10. C2×#13095520C22semidirect
11. C2×#13095520C22semidirect
12. C2×#13095519C22semidirect
13. C22×#11715897C22semidirect
23. #13095521C23semidirect
25. #13095520C23semidirect
26. #13095519C23semidirect
28. C2×#11715897C23semidirect
92. C2×C97#568semidirect
96. C97C2×#568semidirect
189. C2#20261813direct (N × H)

Maximal subgroups

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

subgroupindex
#202618132
C2×#156908972
C2×D97⋊M162
C22×#130955202
C22×#130955102
C2×#56897