Finite Group Databasebeta

← #35213758

Subgroups — #35213758

Order 20864.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#23782395C211yesmaximal, characteristic
2#23782015C211yesmaximal, characteristic
3#23781951C211yesmaximal, characteristic
4#23781876C211yesmaximal, characteristic
5#23781395C211yesmaximal, characteristic
6#23781395C211yesmaximal, characteristic
7#333×C163C211yesmaximal, characteristic
8C2×Dic652—21no—
9#19104735C2211yescharacteristic
10#19104734—21no—
11#19104734—21no—
12#19104733—22no—
13C4×Dic326C2211yescharacteristic
14C4×Dic326C2211yescharacteristic
15#19104700—21no—
16#19104700—21no—
17#19104667—21no—
18#19104660—21no—
19#19104660—21no—
20#19104659—22no—
21C4×C163⋊C8C2211yescharacteristic
22C4⋊Q8×C163C2211yescharacteristic
23C4⋊C8×C163C2211yescharacteristic
24C4⋊C8×C163C2211yescharacteristic
25C2×Dic326—22no—
26C2×Dic326—21no—
27C2×Dic326D411yescharacteristic
28C2×Dic326D411yescharacteristic
29Dic652—42no—
30C2×C163⋊C8—21no—
31C4⋊Dic163—21no—
32C4⋊Dic163—21no—
33C4⋊Dic163D411yescharacteristic
34C4⋊Dic163D411yescharacteristic
35Dic163⋊C4—22no—
36Dic163⋊C4—22no—
37Dic163⋊C4—21no—
38Dic163⋊C4—21no—
39C4×Dic163—22no—
40C4×Dic163—21no—
41C4×Dic163—21no—
42C2×Q8×C163D412yes—
43C2×C8×C163—21no—
44C2×C8×C163—21no—
45C4⋊C4×C163—21no—
46C4⋊C4×C163—21no—
47C42×C163C2311yescharacteristic
48Dic326—21no—
49Dic326—21no—
50Dic326—41no—
51Dic326—41no—
52Dic326—82no—
53Dic326SD1612yes—
54Dic326Q1612yescomplemented
55C2×Dic163—21no—
56C2×Dic163—21no—
57C2×Dic163—21no—
58C2×Dic163—21no—
59C2×Dic163—41no—
60C163⋊C8—41no—
61Q8×C163—42no—
62C2×C4×C163—22no—
63C2×C4×C163C2×D411yescharacteristic
64C2×C4×C163C2×D411yescharacteristic
65C2×C4×C163C2×D411yescharacteristic
66C8×C163—41no—
67C8×C163—41no—
68C22×C163#12011yescharacteristic
69C4×C163—21no—
70C4×C163—42no—
71C4×C163C2×SD1611yescharacteristic
72C4×C163C2×Q1611yescharacteristic
73C4×C163#13711yescharacteristic
74C4×C163#13711yescharacteristic
75Dic163—22no—
76Dic163—22no—
77Dic163—41no—
78Dic163—41no—
79Dic163—81no—
80C2×C163#44811yescharacteristic
81C2×C163#45111yescharacteristic
82C2×C163#45511yescharacteristic
83C163#164511yescharacteristic, complemented, Sylow
84#1645—1631nomaximal, Sylow
85Q82—1631no—
86#487—1631no—
87#475—1631no—
88#462—1631no—
89#333D16311yescharacteristic
90Q8⋊C8—1631no—
91Q8⋊C8—1631no—
92C2×Q16—3261no—
93C4⋊Q8—3261no—
94C4⋊Q8—3261no—
95C4⋊Q8—3262no—
96C4⋊Q8—1631no—
97C4⋊Q8C2×D16311yescharacteristic
98C4×Q8—3261no—
99C4×Q8—3261no—
100C4×Q8—1631no—
101C4×Q8—1631no—
102#106—3261no—
103C4⋊C8C2×D16311yescharacteristic
104C4⋊C8C2×D16311yescharacteristic
105#103—3261no—
106#103—3262no—
107#103—3261no—
108C4×C8—1631no—
109C2×Q8—3262no—
110C2×Q8—3261no—
111C2×Q8—1631no—
112C2×Q8—1631no—
113C2×Q8D65212yes—
114Q16—6522no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—3261no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—3262no—
121C4⋊C4—3262no—
122C4⋊C4—3261no—
123C4⋊C4—3261no—
124C4⋊C4—3261no—
125C4⋊C4—3261no—
126C4⋊C4—1631no—
127C4⋊C4—1631no—
128C42—3262no—
129C42—3261no—
130C42—3261no—
131C42C22×D16311yescharacteristic
132Q8—42no—
133Q8—13042no—
134Q8—3261no—
135Q8—3261no—
136Q8—6521no—
137Q8—6521no—
138Q8—1632no—
139Q8—1632no—
140C2×C4—22no—
141C2×C4—3261no—
142C2×C4—3261no—
143C2×C4—3261no—
144C2×C4—3261no—
145C2×C4—6521no—
146C2×C4D4×D16311yescharacteristic
147C2×C4D4×D16311yescharacteristic
148C2×C4C2×D65211yescharacteristic
149C8—41no—
150C8—41no—
151C8—6521no—
152C22#1910470511yescharacteristic
153C4—21no—
154C4—42no—
155C4—13041no—
156C4—3262no—
157C4—3262no—
158C4—6521no—
159C4—6521no—
160C4SD16×D16311yescharacteristic
161C4Q16×D16311yescharacteristic
162C4#1910476411yescharacteristic
163C4#1910476711yescharacteristic
164C2#2378180511yescharacteristic
165C2#2378182211yescharacteristic
166C2#2378184511yescharacteristic
subgroupG/H
centerC22#19104705
commutator, cosocleC42×C163C23
FrattiniC42C22×D163
Fitting#333×C163C2
socle, prime radicalC22×C163#120
hypercenter#333D163
hypocenterC163#1645
LCSG ▷ C42×C163 ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
54. Dic326Q16semidirect
83. C163#1645semidirect

Maximal subgroups

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

subgroupindex
#237823952
#237820152
#237819512
#237818762
#237813952
#333×C1632
#1645163