Finite Group Databasebeta

← #35215604

Subgroups — #35215604

Order 20864.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#23782465C211yesmaximal, characteristic, complemented
2#23782177C212yesmaximal, complemented
3#23781683C212yesmaximal, complemented
4#23781628C211yesmaximal, characteristic, complemented
5H(3,ℤ/4)×C163C211yesmaximal, characteristic, complemented
6C2×#14579699C2212yes—
7C22×C4×D163C2211yescharacteristic
8#19104768—22no—
9#19104763—22no—
10#19104757—22no—
11C2×#14579683C2211yescharacteristic
12#19104719—22no—
13#19104715—22no—
14#19104710—22no—
15#19104705—22no—
16C4×D652—24no—
17#19104663—24no—
18(C2×D163)⋊C8—22no—
19C2×M16×C163C2211yescharacteristic
20#117×C163C2212yes—
21C23×D163D411yescharacteristic
22#14579699—22no—
23#14579699—22no—
24#14579699—22no—
25#14579699—22no—
26C2×Dic326D412yescomplemented
27C2×D652—24no—
28C2×D652D412yescomplemented
29C2×C22⋊D163—22no—
30C22×Dic163D411yescharacteristic
31C2×C4×D163—21no—
32C2×C4×D163—22no—
33C2×C4×D163—22no—
34C2×C4×D163—22no—
35C2×C4×D163—21no—
36Dic652—22no—
37#14579688—24no—
38D1304—22no—
39#14579683—22no—
40C2×C163⋊C8—21no—
41C4⋊Dic163—24no—
42(C2×D163)⋊C4—24no—
43(C2×D163)⋊C4—24no—
44C22×C4×C163C2311yescharacteristic
45M16×C163—22no—
46C2×C8×C163D412yescomplemented
47C4⋊C4×C163—22no—
48C22⋊C4×C163—22no—
49C42×C163D414yescomplemented
50C22×D163—22no—
51C22×D163—21no—
52C22×D163—22no—
53C22×D163—42no—
54Dic326—22no—
55Dic326—22no—
56D652—22no—
57D652—22no—
58D652—48no—
59C22⋊D163—42no—
60C22⋊D163—42no—
61C2×Dic163—22no—
62C2×Dic163—22no—
63C2×Dic163—21no—
64C4×D163—41no—
65C4×D163—42no—
66C4×D163—42no—
67C4×D163—41no—
68C4×D163—42no—
69C163⋊C8—41no—
70C23×C163C2×D411yescharacteristic
71C2×C4×C163—24no—
72C2×C4×C163C2×D412yes—
73C2×C4×C163C2×D411yescharacteristic
74C2×C4×C163C2×D412yes—
75C2×C4×C163#4111yescharacteristic
76C8×C163—22no—
77C22×C163—41no—
78C22×C163#12012yes—
79C22×C163#12111yescharacteristic
80C2×D163—24no—
81C2×D163—22no—
82C2×D163—42no—
83C2×D163—41no—
84C2×D163—41no—
85C2×D163—44no—
86C2×D163—42no—
87C4×C163—44no—
88C4×C163#12011yescharacteristic
89C4×C163#12112yes—
90C4×C163#12711yescharacteristic
91Dic163—41no—
92Dic163—42no—
93C2×C163—22no—
94C2×C163—21no—
95C2×C163#39211yescharacteristic
96D163—42no—
97D163—82no—
98C163#201011yescharacteristic, complemented, Sylow
99#2010—1631nomaximal, Sylow
100#575—1631no—
101#525—1632no—
102#421—1632no—
103#407—1631no—
104H(3,ℤ/4)D16311yescharacteristic, complemented
105C2×#41—1632no—
106C23×C4—1631no—
107#137—3262no—
108AGL(1,ℤ/8)—3262no—
109#135—3262no—
110C2×M16—1631no—
111C2×M16C2×D16311yescharacteristic
112#123—3262no—
113C22⋊Q8—3262no—
114#121—3262no—
115#120—3262no—
116C4×D4—3264no—
117#117C2×D16312yes—
118#104—3264no—
119C22⋊C8—3262no—
120C24—1631no—
121#41—3262no—
122#41—3262no—
123#41—3262no—
124#41—3262no—
125C2×Q8—1632no—
126C2×D4—3264no—
127C2×D4—3262no—
128C2×D4—1632no—
129C22×C4—3262no—
130C22×C4—3261no—
131C22×C4—3262no—
132C22×C4—3262no—
133C22×C4—3261no—
134C22×C4—1631no—
135C22×C4C22×D16311yescharacteristic
136Q16—3262no—
137SD16—3264no—
138D8—3262no—
139M16—22no—
140M16—3262no—
141C2×C8—3261no—
142C2×C8D65212yescomplemented
143C4⋊C4—22no—
144C4⋊C4—3264no—
145C22⋊C4—22no—
146C22⋊C4—3264no—
147C22⋊C4—3264no—
148C42D65214yescomplemented
149C23—3262no—
150C23—3261no—
151C23—3262no—
152C23—6522no—
153C23D4×D16311yescharacteristic
154Q8—3262no—
155Q8—3262no—
156D4—3262no—
157D4—3262no—
158D4—6528no—
159D4—6522no—
160D4—6522no—
161C2×C4—24no—
162C2×C4—3262no—
163C2×C4—3262no—
164C2×C4—3261no—
165C2×C4—6521no—
166C2×C4—6522no—
167C2×C4—6522no—
168C2×C4—6521no—
169C2×C4—6522no—
170C2×C4D4×D16312yes—
171C2×C4C2×D65211yescharacteristic
172C2×C4C2×D65212yes—
173C2×C4#1457970011yescharacteristic
174C8—22no—
175C8—6521no—
176C22—41no—
177C22—3264no—
178C22—3262no—
179C22—6524no—
180C22—6522no—
181C22—6521no—
182C22—6522no—
183C22—6521no—
184C22#1910470512yes—
185C22#1910471011yescharacteristic
186C4—44no—
187C4—6521no—
188C4—6522no—
189C4#1910470511yescharacteristic
190C4#1910471012yes—
191C4#1910473211yescharacteristic
192C2—22no—
193C2—21no—
194C2—13042no—
195C2—6522no—
196C2#2378157511yescharacteristic
subgroupG/H
centerC4#19104732
commutator, cosocleC22×C4×C163C23
FrattiniC22×C4C22×D163
FittingH(3,ℤ/4)×C163C2
socleC2×C163#392
hypercenterH(3,ℤ/4)D163
hypocenterC163#2010
LCSG ▷ C22×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #23782465C2semidirect
2. #23782177C2semidirect
3. #23781683C2semidirect
4. #23781628C2semidirect
5. H(3,ℤ/4)×C163C2semidirect
26. C2×Dic326D4semidirect
28. C2×D652D4semidirect
46. C2×C8×C163D4semidirect
49. C42×C163D4semidirect
98. C163#2010semidirect
104. H(3,ℤ/4)D163semidirect
142. C2×C8D652semidirect
148. C42D652semidirect

Maximal subgroups

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

subgroupindex
#237824652
#237821772
#237816832
#237816282
H(3,ℤ/4)×C1632
#2010163