Finite Group Databasebeta

← #35213075

Subgroups — #35213075

Order 20864.

222 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 69 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#23782199C211yesmaximal, characteristic
2#23781531C211yesmaximal, characteristic, complemented
3#23781403C212yesmaximal, complemented
4#23781400C212yesmaximal
5#432×C163C211yesmaximal, characteristic, complemented
6#19104729—21no—
7#19104727C411yescharacteristic, complemented
8#19104723C411yescharacteristic, complemented
9#19104718—21no—
10#19104714C2211yescharacteristic
11#19104709C2211yescharacteristic
12C4×Dic326C411yescharacteristic, complemented
13C4×D652C411yescharacteristic, complemented
14C4×C22⋊D163—21no—
15#19104692—21no—
16C2×C4⋊Dic163—21no—
17C163⋊#95—21no—
18C163⋊#95C2212yes—
19C2×C42×C163C2211yescharacteristic
20C4⋊C8×C163—21no—
21C22⋊C8×C163C2212yes—
22#97×C163—21no—
23C2×Dic326C2×C411yescharacteristic
24C2×D652C2×C411yescharacteristic
25C2×C22⋊D163—21no—
26C22×Dic163—22no—
27C2×C4×D163—21no—
28C4⋊Dic163—42no—
29C4⋊Dic163C2×C411yescharacteristic
30C4⋊Dic163C2×C411yescharacteristic
31Dic163⋊C4—21no—
32Dic163⋊C4—21no—
33Dic163⋊C4—21no—
34Dic163⋊C4—21no—
35C22⋊Dic163—21no—
36(C2×D163)⋊C4—21no—
37(C2×D163)⋊C4—21no—
38(C2×D163)⋊C4—21no—
39(C2×D163)⋊C4—21no—
40C4×Dic163—21no—
41C22×C4×C163D411yescharacteristic
42C22×C4×C163D411yescharacteristic
43C22×C4×C163C2311yescharacteristic
44C2×C8×C163—22no—
45C42×C163C2×C411yescharacteristic
46C42×C163C2×C411yescharacteristic
47C42×C163D411yescharacteristic
48C42×C163D411yescharacteristic
49C22×D163—21no—
50Dic326—41no—
51D652—41no—
52C22⋊D163—41no—
53C22⋊D163—41no—
54C2×Dic163—21no—
55C2×Dic163—21no—
56C2×Dic163—21no—
57C2×Dic163—42no—
58C2×Dic163—42no—
59C2×Dic163—42no—
60C4×D163—42no—
61C23×C163C2×D411yescharacteristic
62C2×C4×C163—21no—
63C2×C4×C163—21no—
64C2×C4×C163—41no—
65C2×C4×C163—41no—
66C2×C4×C163C22⋊C411yescharacteristic
67C2×C4×C163C22⋊C411yescharacteristic
68C2×C4×C163C22⋊C411yescharacteristic
69C2×C4×C163C22⋊C411yescharacteristic
70C2×C4×C163C22×C411yescharacteristic
71C2×C4×C163C2×D411yescharacteristic
72C8×C163—42no—
73C22×C163—21no—
74C22×C163—21no—
75C22×C163C2×C22⋊C411yescharacteristic
76C22×C163AGL(1,ℤ/8)11yescharacteristic
77C22×C163#13711yescharacteristic
78C2×D163—41no—
79C2×D163—41no—
80C2×D163—41no—
81C4×C163—21no—
82C4×C163—21no—
83C4×C163—21no—
84C4×C163—21no—
85C4×C163—21no—
86C4×C163—21no—
87Dic163—41no—
88Dic163—41no—
89Dic163—41no—
90Dic163—82no—
91C2×C163—21no—
92C2×C163—21no—
93C2×C163#41011yescharacteristic
94C2×C163#41711yescharacteristic
95C2×C163#42111yescharacteristic
96D163—81no—
97C163#151211yescharacteristic, complemented, Sylow
98#1512—1631nomaximal, Sylow
99#529—1631no—
100#432D16311yescharacteristic, complemented
101#382—1631no—
102#328—1632no—
103#327—1632no—
104#126—3261no—
105#125—1631no—
106#124—1631no—
107#123—3261no—
108C22⋊Q8—1631no—
109#121—1631no—
110C4×Q8—1631no—
111C4×D4—3261no—
112C4×D4—1631no—
113#117—3261no—
114C2×C4⋊C4—3261no—
115C2×C42C2×D16311yescharacteristic
116C4⋊C8—21no—
117C22⋊C8C2×D16312yes—
118#97—21no—
119#95—3261no—
120#95—1632no—
121C2×Q8—1631no—
122C2×D4—3261no—
123C2×D4—1631no—
124C22×C4—3261no—
125C22×C4—3262no—
126C22×C4D65211yescharacteristic
127C22×C4D65211yescharacteristic
128C22×C4C22×D16311yescharacteristic
129C2×C8—22no—
130C4⋊C4—3261no—
131C4⋊C4—3261no—
132C4⋊C4—3261no—
133C4⋊C4—3261no—
134C4⋊C4—6522no—
135C4⋊C4—1631no—
136C4⋊C4—1631no—
137C22⋊C4—3261no—
138C22⋊C4—3261no—
139C22⋊C4—3261no—
140C22⋊C4—3261no—
141C22⋊C4—3261no—
142C42—3261no—
143C42C4×D16311yescharacteristic
144C42C4×D16311yescharacteristic
145C42C22⋊D16311yescharacteristic
146C42C22⋊D16311yescharacteristic
147C23—3261no—
148C23C2×D65211yescharacteristic
149Q8—6521no—
150D4—6521no—
151D4—6521no—
152D4—6521no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—3261no—
158C2×C4—3261no—
159C2×C4—3261no—
160C2×C4—6522no—
161C2×C4—6522no—
162C2×C4—6522no—
163C2×C4—6522no—
164C2×C4(C2×D163)⋊C411yescharacteristic
165C2×C4(C2×D163)⋊C411yescharacteristic
166C2×C4(C2×D163)⋊C411yescharacteristic
167C2×C4(C2×D163)⋊C411yescharacteristic
168C2×C4C2×C4×D16311yescharacteristic
169C2×C4C2×C22⋊D16311yescharacteristic
170C8—42no—
171C22—21no—
172C22—21no—
173C22—6521no—
174C22—6521no—
175C22—6521no—
176C22C2×(C2×D163)⋊C411yescharacteristic
177C22#1910476311yescharacteristic
178C22#1910476811yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—13042no—
186C4—6521no—
187C4—6521no—
188C4—6521no—
189C2—21no—
190C2—21no—
191C2—13041no—
192C2#2378163811yescharacteristic
193C2#2378166711yescharacteristic
194C2#2378168111yescharacteristic
subgroupG/H
centerC22C2×(C2×D163)⋊C4
commutatorC2×C4×C163C22×C4
FrattiniC22×C4C22×D163
Fitting#432×C163C2
socleC22×C163C2×C22⋊C4
prime radical#19104709C22
cosocleC22×C4×C163C23
hypercenter#432D163
hypocenterC163#1512
LCSG ▷ C2×C4×C163 ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #23781531C2semidirect
3. #23781403C2semidirect
5. #432×C163C2semidirect
7. #19104727C4semidirect
8. #19104723C4semidirect
12. C4×Dic326C4semidirect
13. C4×D652C4semidirect
97. C163#1512semidirect
100. #432D163semidirect

Maximal subgroups

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

subgroupindex
#237821992
#237815312
#237814032
#237814002
#432×C1632
#1512163