Finite Group Databasebeta

← #23782201

Subgroups — #23782201

Order 10432.

234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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
1#19104730C212yesmaximal, complemented
2#19104726C211yesmaximal, characteristic, complemented
3#19104724C211yesmaximal, characteristic, complemented
4#19104719C212yesmaximal, complemented
5#19104709C211yesmaximal, characteristic
6Q8×Dic163C211yesmaximal, characteristic, complemented
7#19104697C211yesmaximal, characteristic, complemented
8(C22⋊D163)⋊C4C212yesmaximal, complemented
9#19104693C212yesmaximal, complemented
10C2×C4×Dic163C211yesmaximal, characteristic, complemented
11C22⋊Q8×C163C211yesmaximal, characteristic, complemented
12C2×D652C2211yescharacteristic
13C2×C22⋊D163C2212yes—
14C22×Dic163C2211yescharacteristic
15C22×Dic163C2211yescharacteristic
16C2×C4×D163C2212yes—
17C4⋊Dic163C2212yes—
18C4⋊Dic163C2211yescharacteristic
19C4⋊Dic163C2212yes—
20Dic163⋊C4C2212yes—
21(C2×D163)⋊C4C2212yes—
22(C2×D163)⋊C4C2212yes—
23(C2×D163)⋊C4C2212yes—
24(C2×D163)⋊C4C2212yes—
25C4×Dic163C2211yescharacteristic
26C4×Dic163C2211yescharacteristic
27C4×Dic163C2211yescharacteristic
28C4×Dic163C2211yescharacteristic
29C4×Dic163C2212yes—
30C2×Q8×C163C2211yescharacteristic
31C22×C4×C163C2211yescharacteristic
32C4⋊C4×C163C2212yes—
33C4⋊C4×C163C2211yescharacteristic
34C22⋊C4×C163C2212yes—
35C22×D163C2312yes—
36D652—22no—
37C22⋊D163—24no—
38C2×Dic163—22no—
39C2×Dic163—22no—
40C2×Dic163C2311yescharacteristic
41C2×Dic163C2311yescharacteristic
42C2×Dic163C2311yescharacteristic
43C2×Dic163C2312yes—
44C2×Dic163C2311yescharacteristic
45C4×D163—24no—
46C23×C163C2311yescharacteristic
47Q8×C163—22no—
48C2×C4×C163—22no—
49C2×C4×C163C2312yes—
50C2×C4×C163C2312yes—
51C2×C4×C163C2311yescharacteristic
52C2×C4×C163C2311yescharacteristic
53C22×C163—21no—
54C22×C163—21no—
55C22×C163#4112yes—
56C22×C163C2411yescharacteristic
57C2×D163—22no—
58C2×D163—22no—
59C2×D163—22no—
60C4×C163—21no—
61C4×C163—22no—
62C4×C163—22no—
63C4×C163#4112yes—
64Dic163—21no—
65Dic163—21no—
66Dic163—21no—
67Dic163—22no—
68Dic163#4112yes—
69C2×C163—22no—
70C2×C163C2×#4111yescharacteristic
71C2×C163C2×#4111yescharacteristic
72C2×C163C2×#4111yescharacteristic
73D163—42no—
74C163#52911yescharacteristic, complemented, Sylow
75#529—1631nomaximal, Sylow
76#126—1632no—
77#125—1631no—
78#124—1631no—
79#123—1632no—
80C22⋊Q8D16311yescharacteristic, complemented
81#121—1631no—
82C4×Q8—1631no—
83C4×D4—1631no—
84C4×D4—1632no—
85#117—1632no—
86C2×C42—1631no—
87C2×Q8C2×D16311yescharacteristic
88C2×D4—1632no—
89C2×D4—1631no—
90C22×C4—1631no—
91C22×C4—1631no—
92C22×C4—1632no—
93C22×C4C2×D16311yescharacteristic
94C4⋊C4—1632no—
95C4⋊C4—1632no—
96C4⋊C4—1631no—
97C4⋊C4—1632no—
98C4⋊C4C2×D16312yes—
99C4⋊C4C2×D16311yescharacteristic
100C22⋊C4—1632no—
101C22⋊C4—1632no—
102C22⋊C4—1632no—
103C22⋊C4—1632no—
104C22⋊C4C2×D16312yes—
105C42—1631no—
106C42—1631no—
107C42—1631no—
108C42—1631no—
109C42—1632no—
110C23—1632no—
111C23C22×D16311yescharacteristic
112Q8—22no—
113D4—3264no—
114D4—3262no—
115C2×C4—22no—
116C2×C4—3264no—
117C2×C4—3262no—
118C2×C4—3262no—
119C2×C4—1631no—
120C2×C4—1631no—
121C2×C4—1631no—
122C2×C4—1632no—
123C2×C4—1631no—
124C2×C4C22×D16311yescharacteristic
125C2×C4C22×D16312yes—
126C2×C4C22×D16312yes—
127C2×C4C22×D16311yescharacteristic
128C22—21no—
129C22—21no—
130C22—3262no—
131C22—3262no—
132C22—3262no—
133C22#1457970012yes—
134C22C23×D16311yescharacteristic
135C4—22no—
136C4—21no—
137C4—22no—
138C4—3261no—
139C4—3261no—
140C4—3261no—
141C4—3262no—
142C4—1632no—
143C4#1457969812yes—
144C2—22no—
145C2—6522no—
146C2#41×D16311yescharacteristic
147C2C2×#1457969811yescharacteristic
148C2C2×#1457970011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D163
commutator, socle, cosocleC22×C163C24
FittingC22⋊Q8×C163C2
prime radical#19104709C2
hypercenterC22⋊Q8D163
hypocenterC163#529
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #19104730C2semidirect
2. #19104726C2semidirect
3. #19104724C2semidirect
4. #19104719C2semidirect
6. Q8×Dic163C2semidirect
7. #19104697C2semidirect
8. (C22⋊D163)⋊C4C2semidirect
9. #19104693C2semidirect
10. C2×C4×Dic163C2semidirect
11. C22⋊Q8×C163C2semidirect
74. C163#529semidirect
80. C22⋊Q8D163semidirect