Finite Group Databasebeta

← C2×#20261814 #27158729

Subgroups — C2×#20261814 #27158729

Order 12416.

1460 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20261814C2116yesmaximal, direct product factor
2C2×#15690898C212yesmaximal, complemented
3C2×#15690897C216yesmaximal, complemented
4C22×#13095521C213yesmaximal, complemented
5C2×D97⋊M16C213yesmaximal, complemented
6C2×#41×D97C211yesmaximal, characteristic
7#15690898C22116yescomplemented
8#15690897C22148yescomplemented
9C2×#13095521C2211yescharacteristic
10C2×#13095521C2213yes—
11C2×#13095521C2216yescomplemented
12C2×#13095521C22124yescomplemented
13D97⋊M16C22124yescomplemented
14C2×#13095520C2216yescomplemented
15C2×#13095519C2216yescomplemented
16C22×#11715897C2216yescomplemented
17C2×#13095512C2211yescharacteristic
18C2×#13095511C413yes—
19C2×#13095510C2213yes—
20#41×D97C418yes—
21#41×D97C2218yes—
22C2×Q8×D97C411yescharacteristic
23C2×D4×D97C413yes—
24C22×C4×D97C2213yes—
25C2×#41×C97C411yescharacteristic
26#13095521C2314yes—
27#13095521C23112yes—
28#13095521C23124yescomplemented
29#13095520C23124yescomplemented
30#13095519C23124yescomplemented
31C2×#11715897C2316yes—
32C2×#11715897C2312yes—
33C2×#11715897C23124yescomplemented
34C23×D97C2×C413yes—
35#13095512C2×C414yes—
36#13095512C2314yes—
37#13095511C2×C4124yes—
38#13095510C2×C4112yes—
39#13095510C23112yes—
40C2×Dic194C2×C413yes—
41Q8×D97C2×C418yes—
42C2×D388C2×C413yes—
43C2×C22⋊D97C2×C416yes—
44D4×D97C2×C4124yes—
45C22×Dic97C2313yes—
46C2×C4×D97C2×C413yes—
47C2×C4×D97C2×C4112yes—
48C2×C4×D97C2×C413yes—
49C2×C4×D97C2311yescharacteristic
50C2×C4×D97C23112yes—
51C2×C4×D97C2313yes—
52#41×C97C2×C418yes—
53C2×Q8×C97C2×C411yescharacteristic
54C2×D4×C97C2×C413yes—
55C22×C4×C97C2×C413yes—
56C23×C97C22×C413yes—
57C22×D97—46no—
58C22×D97C22×C411yescharacteristic
59C22×D97C22×C413yes—
60C22×D97C22×C4112yes—
61Q8×C97C22×C414yes—
62D4×C97C22×C4112yes—
63C2×C4×C97C22×C411yescharacteristic
64C2×C4×C97C22×C413yes—
65C2×C4×C97C22×C4112yes—
66C22⋊D97C22×C4124yes—
67C2×Dic97C22×C413yes—
68C2×Dic97C22×C416yes—
69C2×Dic97C2411yescharacteristic
70C2×Dic97C2416yes—
71D388C22×C4112yes—
72C4×D97C22×C412yes—
73C4×D97C22×C4112yes—
74C4×D97C22×C416yes—
75C4×D97C22×C4112yes—
76C4×D97C2412yes—
77C4×D97C2416yes—
78Dic194C22×C4112yes—
79#11715897C24112yes—
80#11715897C2414yes—
81C22×C97—26no—
82C22×C97C23×C416yes—
83C22×C97C23×C411yescharacteristic
84C2×D97—22no—
85C2×D97—26no—
86C2×D97—412no—
87C2×D97C23×C412yes—
88C2×D97C23×C416yes—
89C4×C97C23×C416yes—
90C4×C97C23×C412yes—
91Dic97C23×C416yes—
92Dic97C23×C411yescharacteristic
93Dic97C2511yescharacteristic
94C2×C97—26no—
95C2×C97#56812yescomplemented
96C2×C97C24×C411yescharacteristic
97D97—22no—
98D97—26no—
99C2×#568—971nomaximal, Sylow
100C97C2×#56811yescharacteristic, complemented, Sylow
101C22×#41—971no—
102#568—9716no—
103C2×#131—976no—
104C2×#131—972no—
105C22×M16—973no—
106C22×M16—973no—
107C2×#41—978no—
108C2×#41—978no—
109C2×#41—971no—
110C2×#41—973no—
111C2×#41—973no—
112C2×#41#8760411yescharacteristic
113C22×Q8—971no—
114C22×D4—973no—
115C23×C4—973no—
116#131—9748no—
117#131—9716no—
118C2×M16—971no—
119C2×M16—973no—
120C2×M16—976no—
121C2×M16—976no—
122C2×M16—9724no—
123C2×M16—9724no—
124C22×C8—976no—
125C22×C8—976no—
126C24—973no—
127#41—974no—
128#41—974no—
129#41—9712no—
130#41—9712no—
131#41—9724no—
132#41C2×#8760418yes—
133C2×Q8—978no—
134C2×Q8—973no—
135C2×Q8C2×#8760411yescharacteristic
136C2×D4—976no—
137C2×D4—9724no—
138C2×D4—973no—
139C2×D4C2×#8760413yes—
140C22×C4—973no—
141C22×C4—973no—
142C22×C4—9712no—
143C22×C4—973no—
144C22×C4—973no—
145C22×C4—971no—
146C22×C4—9712no—
147C22×C4C2×#8760413yes—
148M16—9724no—
149M16—974no—
150M16—9712no—
151M16—9724no—
152C2×C8—976no—
153C2×C8—972no—
154C2×C8—9724no—
155C2×C8—9724no—
156C23—9712no—
157C23—971no—
158C23—973no—
159C23—3886no—
160C23C22×#8760413yes—
161Q8—9712no—
162Q8C22×#8760414yes—
163D4—9724no—
164D4—9712no—
165D4C22×#87604112yes—
166C2×C4—976no—
167C2×C4—976no—
168C2×C4—971no—
169C2×C4—973no—
170C2×C4—976no—
171C2×C4—972no—
172C2×C4—972no—
173C2×C4—9712no—
174C2×C4—976no—
175C2×C4—9712no—
176C2×C4C22×#87604112yes—
177C2×C4C22×#8760411yescharacteristic
178C2×C4C22×#8760413yes—
179C8—9712no—
180C8—974no—
181C22—26no—
182C22—972no—
183C22—976no—
184C22—38812no—
185C22—1942no—
186C22—1946no—
187C22C23×#8760416yes—
188C22C23×#8760411yescharacteristic
189C4—971no—
190C4—971no—
191C4—976no—
192C4C23×#8760412yes—
193C4C23×#8760416yes—
194C2—26no—
195C2—1942no—
196C2—1946no—
197C2#2026181412yesdirect product factor
198C2C24×#8760411yescharacteristic
subgroupG/H
centerC22C23×#87604
commutatorC2×C97C24×C4
FrattiniC2C24×#87604
FittingC2×#41×C97C4
socleC22×C97C23×C4
prime radicalC2×#41×D97C2
cosocleDic97C25
hypercenterC2×#41#87604
hypocenterC97C2×#568
LCSG ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #20261814C2direct (N × H)
2. C2×#15690898C2semidirect
3. C2×#15690897C2semidirect
4. C22×#13095521C2semidirect
5. C2×D97⋊M16C2semidirect
7. #15690898C22semidirect
8. #15690897C22semidirect
11. C2×#13095521C22semidirect
12. C2×#13095521C22semidirect
13. D97⋊M16C22semidirect
14. C2×#13095520C22semidirect
15. C2×#13095519C22semidirect
16. C22×#11715897C22semidirect
28. #13095521C23semidirect
29. #13095520C23semidirect
30. #13095519C23semidirect
33. C2×#11715897C23semidirect
95. C2×C97#568semidirect
100. C97C2×#568semidirect
197. C2#20261814direct (N × H)

Maximal subgroups

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

subgroupindex
#202618142
C2×#156908982
C2×#156908972
C22×#130955212
C2×D97⋊M162
C2×#41×D972
C2×#56897