Finite Group Databasebeta

← #35213111

Subgroups — #35213111

Order 20864.

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

normal subgroups only

This group has 218 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#23781718C211yesmaximal, characteristic, complemented
3#23781401C212yesmaximal, complemented
4#23781398C212yesmaximal
5#383×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—
16C4⋊(C163⋊C8)—21no—
17C22⋊(C163⋊C8)C2212yes—
18C4×C163⋊C8—21no—
19C2×C42×C163C2211yescharacteristic
20#95×C163—21no—
21#95×C163—21no—
22#95×C163C2212yes—
23C2×Dic326C2×C411yescharacteristic
24C2×D652C2×C411yescharacteristic
25C2×C22⋊D163—21no—
26C2×C4×D163—21no—
27C2×C163⋊C8—22no—
28C4⋊Dic163C2×C411yescharacteristic
29C4⋊Dic163C2×C411yescharacteristic
30Dic163⋊C4—21no—
31Dic163⋊C4—21no—
32Dic163⋊C4—21no—
33Dic163⋊C4—21no—
34C22⋊Dic163—21no—
35(C2×D163)⋊C4—21no—
36(C2×D163)⋊C4—21no—
37(C2×D163)⋊C4—21no—
38(C2×D163)⋊C4—21no—
39C4×Dic163—21no—
40C22×C4×C163—22no—
41C22×C4×C163D411yescharacteristic
42C22×C4×C163D411yescharacteristic
43C22×C4×C163C2311yescharacteristic
44C42×C163C2×C411yescharacteristic
45C42×C163C2×C411yescharacteristic
46C42×C163D411yescharacteristic
47C42×C163D411yescharacteristic
48C22×D163—21no—
49Dic326—41no—
50D652—41no—
51C22⋊D163—42no—
52C2×Dic163—21no—
53C2×Dic163—21no—
54C2×Dic163—21no—
55C4×D163—42no—
56C163⋊C8—42no—
57C23×C163C2×D411yescharacteristic
58C2×C4×C163—22no—
59C2×C4×C163—41no—
60C2×C4×C163—41no—
61C2×C4×C163—42no—
62C2×C4×C163—42no—
63C2×C4×C163—42no—
64C2×C4×C163C22⋊C411yescharacteristic
65C2×C4×C163C22⋊C411yescharacteristic
66C2×C4×C163C22⋊C411yescharacteristic
67C2×C4×C163C22⋊C411yescharacteristic
68C2×C4×C163C22×C411yescharacteristic
69C2×C4×C163C2×D411yescharacteristic
70C22×C163—21no—
71C22×C163—21no—
72C22×C163C2×C22⋊C411yescharacteristic
73C22×C163#13512yes—
74C2×D163—41no—
75C2×D163—41no—
76C2×D163—41no—
77C4×C163—21no—
78C4×C163—21no—
79C4×C163—21no—
80C4×C163—21no—
81C4×C163—21no—
82C4×C163—21no—
83C4×C163—82no—
84Dic163—41no—
85Dic163—41no—
86Dic163—41no—
87C2×C163—22no—
88C2×C163#41011yescharacteristic
89C2×C163#41611yescharacteristic
90C2×C163#42111yescharacteristic
91D163—81no—
92C163#152111yescharacteristic, complemented, Sylow
93#1521—1631nomaximal, Sylow
94#529—1631no—
95#431—1631no—
96#383D16311yescharacteristic, complemented
97#328—1632no—
98#327—1632no—
99#126—3261no—
100#125—1631no—
101#124—1631no—
102#123—3261no—
103C22⋊Q8—1631no—
104#121—1631no—
105C4×Q8—1631no—
106C4×D4—3261no—
107C4×D4—1631no—
108#117—3261no—
109C2×C42C2×D16311yescharacteristic
110C4⋊C8—3261no—
111C22⋊C8—1632no—
112C4×C8—3261no—
113#95—21no—
114#95—21no—
115#95C2×D16312yes—
116C2×Q8—1631no—
117C2×D4—3261no—
118C2×D4—1631no—
119C22×C4—22no—
120C22×C4—3261no—
121C22×C4C22⋊D16311yescharacteristic
122C22×C4C22⋊D16311yescharacteristic
123C22×C4C22×D16311yescharacteristic
124C2×C8—3262no—
125C4⋊C4—3261no—
126C4⋊C4—3261no—
127C4⋊C4—3261no—
128C4⋊C4—3261no—
129C4⋊C4—1631no—
130C4⋊C4—1631no—
131C22⋊C4—3261no—
132C22⋊C4—3261no—
133C22⋊C4—3261no—
134C22⋊C4—3261no—
135C22⋊C4—3261no—
136C42—3261no—
137C42C4×D16311yescharacteristic
138C42C4×D16311yescharacteristic
139C42D65211yescharacteristic
140C42D65211yescharacteristic
141C23—3261no—
142C23C2×C22⋊D16311yescharacteristic
143Q8—6521no—
144D4—6521no—
145D4—6522no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—3261no—
153C2×C4—3261no—
154C2×C4—3261no—
155C2×C4—6522no—
156C2×C4(C2×D163)⋊C411yescharacteristic
157C2×C4(C2×D163)⋊C411yescharacteristic
158C2×C4(C2×D163)⋊C411yescharacteristic
159C2×C4(C2×D163)⋊C411yescharacteristic
160C2×C4C2×C4×D16311yescharacteristic
161C2×C4C2×D65211yescharacteristic
162C8—6522no—
163C22—21no—
164C22—21no—
165C22—6521no—
166C22—6521no—
167C22—6521no—
168C22C2×(C2×D163)⋊C411yescharacteristic
169C22#1910475512yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—82no—
177C4—6521no—
178C4—6521no—
179C4—6521no—
180C2—22no—
181C2—13041no—
182C2#2378163811yescharacteristic
183C2#2378165911yescharacteristic
184C2#2378168311yescharacteristic
subgroupG/H
centerC22C2×(C2×D163)⋊C4
commutatorC2×C4×C163C22×C4
FrattiniC22×C4C22×D163
Fitting#383×C163C2
socleC22×C163C2×C22⋊C4
prime radical#19104709C22
cosocleC22×C4×C163C23
hypercenter#383D163
hypocenterC163#1521
LCSG ▷ C2×C4×C163 ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
2. #23781718C2semidirect
3. #23781401C2semidirect
5. #383×C163C2semidirect
7. #19104727C4semidirect
8. #19104723C4semidirect
12. C4×Dic326C4semidirect
13. C4×D652C4semidirect
92. C163#1521semidirect
96. #383D163semidirect

Maximal subgroups

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

subgroupindex
#237821992
#237817182
#237814012
#237813982
#383×C1632
#1521163