Finite Group Databasebeta

← C2×#19128031 #24917340

Subgroups — C2×#19128031 #24917340

Order 10624.

460 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C2×#14581771C211yesmaximal, characteristic
2#19128031C218yesmaximal, direct product factor
3C2×#14581723C212yesmaximal, complemented
4C2×#14581715C212yesmaximal, complemented
5C2×C22⋊(C83⋊C8)C211yesmaximal, characteristic
6C22×C4⋊C4×C83C211yesmaximal, characteristic
7C22×Dic166C2211yescharacteristic
8C22×C83⋊C8C2212yes—
9#14581771—22no—
10#14581771C2214yes—
11C2×C4⋊Dic83C2211yescharacteristic
12C2×Dic83⋊C4—21no—
13C2×C22⋊Dic83—21no—
14#14581723C2218yescomplemented
15#14581715C2218yescomplemented
16C22⋊(C83⋊C8)C2214yes—
17C23×C4×C83—21no—
18C23×C4×C83C2211yescharacteristic
19C2×C4⋊C4×C83—22no—
20C2×C4⋊C4×C83—21no—
21C2×C4⋊C4×C83C2212yes—
22C2×C4⋊C4×C83C2214yes—
23C2×Dic166—24no—
24C2×Dic166—21no—
25C2×Dic166C2312yes—
26C22×Dic83—21no—
27C22×Dic83—21no—
28C2×C83⋊C8—24no—
29C2×C83⋊C8C2314yes—
30C4⋊Dic83—21no—
31C4⋊Dic83C2312yes—
32Dic83⋊C4—24no—
33C22⋊Dic83—24no—
34C24×C83D411yescharacteristic
35C22×C4×C83—24no—
36C22×C4×C83—24no—
37C22×C4×C83—22no—
38C22×C4×C83—44no—
39C22×C4×C83D412yes—
40C22×C4×C83D411yescharacteristic
41C22×C4×C83C2312yes—
42C22×C4×C83C2311yescharacteristic
43C4⋊C4×C83—24no—
44C4⋊C4×C83—22no—
45C4⋊C4×C83C2314yes—
46C23×C83—22no—
47C23×C83—22no—
48C23×C83SD1614yes—
49C23×C83C2×D412yes—
50C23×C83C2×D411yescharacteristic
51C2×C4×C83—22no—
52C2×C4×C83—24no—
53C2×C4×C83—24no—
54C2×C4×C83—24no—
55C2×C4×C83—48no—
56C2×C4×C83—44no—
57C2×C4×C83C2×D412yes—
58C2×C4×C83C2×D411yescharacteristic
59C2×C4×C83#4114yes—
60C2×C4×C83C2411yescharacteristic
61C2×Dic83—22no—
62C2×Dic83—22no—
63C2×Dic83—42no—
64C2×Dic83—42no—
65Dic166—24no—
66Dic166—42no—
67C83⋊C8—24no—
68C22×C83—22no—
69C22×C83—22no—
70C22×C83—28no—
71C22×C83#12312yes—
72C22×C83C2×SD1614yes—
73C22×C83C2×SD1612yes—
74C22×C83#13712yes—
75C22×C83C22×D411yescharacteristic
76C4×C83—22no—
77C4×C83—44no—
78C4×C83#12312yes—
79C4×C83C2×#4112yes—
80Dic83—42no—
81Dic83—42no—
82C2×C83—24no—
83C2×C83#48314yescomplemented
84C2×C83C2×#12311yescharacteristic
85C2×C83C22×SD1611yescharacteristic
86C2×C83C2×#13711yescharacteristic
87C2×#483—831nomaximal, Sylow
88C83C2×#48311yescharacteristic, complemented, Sylow
89C2×C22⋊Q8—831no—
90C22×C4⋊C4D8311yescharacteristic
91#483—838no—
92C2×#106—832no—
93C2×#103—832no—
94C2×C22⋊C8—831no—
95C22×Q8—831no—
96C23×C4—21no—
97C23×C4C2×D8311yescharacteristic
98C22×C8—832no—
99C22⋊Q8—834no—
100C22⋊Q8—1662no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—831no—
104C2×C4⋊C4—1661no—
105C2×C4⋊C4C2×D8312yes—
106C2×C4⋊C4C2×D8314yes—
107C2×C22⋊C4—1661no—
108#106—838no—
109#103—838no—
110C22⋊C8—834no—
111C24C22⋊D8311yescharacteristic
112C2×Q8—832no—
113C2×Q8—1664no—
114C2×Q8—1661no—
115C22×C4—24no—
116C22×C4—24no—
117C22×C4—22no—
118C22×C4—44no—
119C22×C4—1661no—
120C22×C4—1661no—
121C22×C4C22⋊D8312yes—
122C22×C4C22⋊D8311yescharacteristic
123C22×C4C22×D8312yes—
124C22×C4C22×D8311yescharacteristic
125C2×C8—834no—
126C2×C8—1664no—
127C4⋊C4—24no—
128C4⋊C4—22no—
129C4⋊C4—832no—
130C4⋊C4—1661no—
131C4⋊C4—1664no—
132C4⋊C4C22×D8314yes—
133C22⋊C4—1664no—
134C23—22no—
135C23—22no—
136C23#1305057814yes—
137C23C2×C22⋊D8312yes—
138C23C2×C22⋊D8311yescharacteristic
139Q8—3322no—
140Q8—1664no—
141C2×C4—22no—
142C2×C4—24no—
143C2×C4—24no—
144C2×C4—24no—
145C2×C4—48no—
146C2×C4—44no—
147C2×C4—3322no—
148C2×C4—3322no—
149C2×C4—1662no—
150C2×C4—1662no—
151C2×C4C2×C22⋊D8312yes—
152C2×C4C2×C22⋊D8311yescharacteristic
153C2×C4#1305059014yes—
154C2×C4C23×D8311yescharacteristic
155C8—1664no—
156C22—22no—
157C22—22no—
158C22—28no—
159C22#1458177512yes—
160C22C2×#1305057814yes—
161C22C2×#1305057812yes—
162C22#1458182312yes—
163C22C22×C22⋊D8311yescharacteristic
164C4—22no—
165C4—44no—
166C4—3322no—
167C4—3322no—
168C4#1458177512yes—
169C4C2×#1305059012yes—
170C2—24no—
171C2#1912803114yesdirect product factor
172C2C2×#1458177511yescharacteristic
173C2C22×#1305057811yescharacteristic
174C2C2×#1458182311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC22×C4⋊C4×C83C2
socleC23×C83C2×D4
prime radicalC24×C83D4
hypercenterC22×C4⋊C4D83
hypocenterC83C2×#483
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #19128031C2direct (N × H)
3. C2×#14581723C2semidirect
4. C2×#14581715C2semidirect
14. #14581723C22semidirect
15. #14581715C22semidirect
83. C2×C83#483semidirect
88. C83C2×#483semidirect
171. C2#19128031direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145817712
#191280312
C2×#145817232
C2×#145817152
C2×C22⋊(C83⋊C8)2
C22×C4⋊C4×C832
C2×#48383