Finite Group Databasebeta

← #23782238

Subgroups — #23782238

Order 10432.

270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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×#14579699C211yesmaximal, characteristic
2C2×Q8×D163C211yesmaximal, characteristic, complemented
3#19104734C212yesmaximal, complemented
4#19104721C212yesmaximal, complemented
5#19104720C212yesmaximal, complemented
6#19104717C212yesmaximal, complemented
7#19104715C211yesmaximal, characteristic, complemented
8#19104714C211yesmaximal, characteristic, complemented
9#19104711C211yesmaximal, characteristic, complemented
10#19104693C211yesmaximal, characteristic, complemented
11C22⋊Q8×C163C211yesmaximal, characteristic, complemented
12#14579699—24no—
13C2×Dic326C2211yescharacteristic
14C2×Dic326C2212yes—
15C2×Dic326C2211yescharacteristic
16Q8×D163—24no—
17C2×D652C2211yescharacteristic
18C2×C22⋊D163C2211yescharacteristic
19C2×C22⋊D163C2211yescharacteristic
20C2×C4×D163C2212yes—
21C2×C4×D163C2211yescharacteristic
22C2×C4×D163C2211yescharacteristic
23C4⋊Dic163C2211yescharacteristic
24C4⋊Dic163C2212yes—
25Dic163⋊C4C2212yes—
26Dic163⋊C4C2212yes—
27C22⋊Dic163C2212yes—
28(C2×D163)⋊C4C2212yes—
29(C2×D163)⋊C4C2212yes—
30(C2×D163)⋊C4C2212yes—
31C4×Dic163C2212yes—
32C2×Q8×C163C2211yescharacteristic
33C22×C4×C163C2211yescharacteristic
34C4⋊C4×C163C2211yescharacteristic
35C4⋊C4×C163C2212yes—
36C22⋊C4×C163C2212yes—
37C22×D163C2311yescharacteristic
38C22×D163C2311yescharacteristic
39Dic326—22no—
40Dic326—24no—
41Dic326—22no—
42D652—22no—
43C22⋊D163—22no—
44C22⋊D163—22no—
45C2×Dic163C2312yes—
46C2×Dic163C2312yes—
47C2×Dic163C2311yescharacteristic
48C2×Dic163C2311yescharacteristic
49C4×D163—24no—
50C4×D163—22no—
51C4×D163D414yes—
52C23×C163C2311yescharacteristic
53Q8×C163—22no—
54C2×C4×C163—22no—
55C2×C4×C163C2312yes—
56C2×C4×C163C2312yes—
57C2×C4×C163C2311yescharacteristic
58C2×C4×C163C2311yescharacteristic
59C22×C163—21no—
60C22×C163—21no—
61C22×C163—21no—
62C22×C163C2411yescharacteristic
63C2×D163—21no—
64C2×D163—21no—
65C2×D163—21no—
66C2×D163—21no—
67C2×D163—21no—
68C2×D163C2×D412yes—
69C4×C163—21no—
70C4×C163—22no—
71C4×C163—22no—
72C4×C163C2×D412yes—
73Dic163—21no—
74Dic163—22no—
75Dic163—22no—
76Dic163C2×D412yes—
77C2×C163—41no—
78C2×C163C22×D411yescharacteristic
79C2×C1632−1+411yescharacteristic
80C2×C1632−1+411yescharacteristic
81D163—22no—
82D163—41no—
83C163#53611yescharacteristic, complemented, Sylow
84#536—1631nomaximal, Sylow
85C2×#41—1631no—
86C22×Q8—1631no—
87C4⋊Q8—1632no—
88#124—1632no—
89#123—1632no—
90#123—1632no—
91C22⋊Q8—1631no—
92C22⋊Q8—1631no—
93C22⋊Q8—1631no—
94C22⋊Q8D16311yescharacteristic, complemented
95#117—1631no—
96#41—3264no—
97C2×Q8—3264no—
98C2×Q8—1631no—
99C2×Q8—1632no—
100C2×Q8—1631no—
101C2×Q8C2×D16311yescharacteristic
102C2×D4—1631no—
103C2×D4—1631no—
104C2×D4—1631no—
105C22×C4—1631no—
106C22×C4—1632no—
107C22×C4—1631no—
108C22×C4C2×D16311yescharacteristic
109C4⋊C4—1631no—
110C4⋊C4—1632no—
111C4⋊C4—1632no—
112C4⋊C4—1632no—
113C4⋊C4C2×D16311yescharacteristic
114C4⋊C4C2×D16312yes—
115C22⋊C4—1632no—
116C22⋊C4—1632no—
117C22⋊C4—1632no—
118C22⋊C4—1632no—
119C22⋊C4C2×D16312yes—
120C42—1632no—
121C23—1631no—
122C23—1631no—
123C23C22×D16311yescharacteristic
124Q8—22no—
125Q8—3264no—
126Q8—3262no—
127Q8—3262no—
128D4—3262no—
129D4—3262no—
130D4—3262no—
131C2×C4—22no—
132C2×C4—3264no—
133C2×C4—3262no—
134C2×C4—1632no—
135C2×C4—1632no—
136C2×C4—1631no—
137C2×C4—1631no—
138C2×C4—1634no—
139C2×C4C22×D16312yes—
140C2×C4C22×D16312yes—
141C2×C4C22×D16311yescharacteristic
142C2×C4C22×D16311yescharacteristic
143C22—21no—
144C22—21no—
145C22—21no—
146C22—3261no—
147C22—3261no—
148C22—3261no—
149C22—3261no—
150C22—3261no—
151C22—1632no—
152C22C23×D16311yescharacteristic
153C4—21no—
154C4—22no—
155C4—22no—
156C4—3261no—
157C4—3262no—
158C4—3262no—
159C4—1632no—
160C4D4×D16312yes—
161C2—41no—
162C2—3262no—
163C2—6521no—
164C2C2×D4×D16311yescharacteristic
165C2#1910478211yescharacteristic
166C2#1910478311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D163
commutator, socle, cosocleC22×C163C24
FittingC22⋊Q8×C163C2
prime radicalC2×#14579699C2
hypercenterC22⋊Q8D163
hypocenterC163#536
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×Q8×D163C2semidirect
3. #19104734C2semidirect
4. #19104721C2semidirect
5. #19104720C2semidirect
6. #19104717C2semidirect
7. #19104715C2semidirect
8. #19104714C2semidirect
9. #19104711C2semidirect
10. #19104693C2semidirect
11. C22⋊Q8×C163C2semidirect
83. C163#536semidirect
94. C22⋊Q8D163semidirect