Finite Group Databasebeta

← #35213579

Subgroups — #35213579

Order 20864.

202 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 51 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#23782294C211yesmaximal, characteristic
2#23782001C211yesmaximal, characteristic
3#23781998C211yesmaximal, characteristic
4#23781605C211yesmaximal, characteristic
5#23781401C211yesmaximal, characteristic
6#23781390C211yesmaximal, characteristic
7#328×C163C211yesmaximal, characteristic
8#19104734—21no—
9#19104733—21no—
10#19104725—21no—
11#19104725—21no—
12#19104714C2211yescharacteristic
13#19104712—21no—
14#19104691—21no—
15C2×C4⋊Dic163C2211yescharacteristic
16C2×Dic163⋊C4C2211yescharacteristic
17#19104669—21no—
18#19104668—21no—
19#19104660—21no—
20#19104659—21no—
21C22⋊(C163⋊C8)C2211yescharacteristic
22C163⋊#95—21no—
23C163⋊#95—21no—
24C22⋊Q8×C163C2211yescharacteristic
25C22⋊C8×C163C2211yescharacteristic
26#95×C163C2211yescharacteristic
27C2×Dic326—21no—
28C2×Dic326D411yescharacteristic
29C22×Dic163—21no—
30C22×Dic163D411yescharacteristic
31C22×Dic163D411yescharacteristic
32C2×C163⋊C8—21no—
33C4⋊Dic163—21no—
34C4⋊Dic163—21no—
35C4⋊Dic163—21no—
36C4⋊Dic163D411yescharacteristic
37Dic163⋊C4—21no—
38Dic163⋊C4—21no—
39Dic163⋊C4—21no—
40Dic163⋊C4—21no—
41Dic163⋊C4—21no—
42Dic163⋊C4—21no—
43Dic163⋊C4—21no—
44C22⋊Dic163—21no—
45C4×Dic163—21no—
46C4×Dic163—21no—
47C2×Q8×C163D411yescharacteristic
48C22×C4×C163—21no—
49C22×C4×C163C2311yescharacteristic
50C2×C8×C163—21no—
51C4⋊C4×C163—21no—
52C4⋊C4×C163D411yescharacteristic
53C22⋊C4×C163—21no—
54Dic326—41no—
55Dic326—81no—
56C2×Dic163—21no—
57C2×Dic163—21no—
58C2×Dic163—21no—
59C2×Dic163—21no—
60C2×Dic163—21no—
61C2×Dic163—41no—
62C2×Dic163—42no—
63C2×Dic163—41no—
64C2×Dic163Q1612yes—
65C163⋊C8—41no—
66C23×C163C2×D411yescharacteristic
67Q8×C163—41no—
68C2×C4×C163—21no—
69C2×C4×C163—21no—
70C2×C4×C163—41no—
71C2×C4×C163—41no—
72C2×C4×C163—41no—
73C2×C4×C163—41no—
74C2×C4×C163C2×D411yescharacteristic
75C2×C4×C163C2×D411yescharacteristic
76C8×C163—41no—
77C22×C163—21no—
78C22×C163—21no—
79C22×C163#12011yescharacteristic
80C22×C163C2×Q1611yescharacteristic
81C22×C163#13711yescharacteristic
82C4×C163—21no—
83C4×C163—21no—
84C4×C163—41no—
85C4×C163—41no—
86C4×C163—81no—
87Dic163—22no—
88Dic163—41no—
89Dic163—41no—
90Dic163—41no—
91Dic163—81no—
92C2×C163—21no—
93C2×C163—21no—
94C2×C163#45111yescharacteristic
95C2×C163#45411yescharacteristic
96C2×C163#45811yescharacteristic
97C163#161711yescharacteristic, complemented, Sylow
98#1617—1631nomaximal, Sylow
99#544—1631no—
100#484—1631no—
101#484—1631no—
102#400—1631no—
103#328—1631no—
104#328D16311yescharacteristic
105#324—1631no—
106C4⋊Q8—3261no—
107C4⋊Q8—3261no—
108#125—3261no—
109#125—3261no—
110C22⋊Q8—3261no—
111C22⋊Q8—1631no—
112C22⋊Q8C2×D16311yescharacteristic
113#117—3261no—
114C2×C4⋊C4—1631no—
115C2×C4⋊C4—1631no—
116#107—3261no—
117#107—3261no—
118#103—3261no—
119#103—3261no—
120C22⋊C8—1631no—
121C22⋊C8C2×D16311yescharacteristic
122#95—3261no—
123#95—3261no—
124#95C2×D16311yescharacteristic
125C2×Q8—3261no—
126C2×Q8—1631no—
127C2×Q8D65211yescharacteristic
128C22×C4—21no—
129C22×C4—3261no—
130C22×C4—1631no—
131C22×C4—1631no—
132C22×C4C22×D16311yescharacteristic
133C2×C8—21no—
134C2×C8—3261no—
135C4⋊C4—21no—
136C4⋊C4—3261no—
137C4⋊C4—3261no—
138C4⋊C4—3261no—
139C4⋊C4—3261no—
140C4⋊C4—3261no—
141C4⋊C4—3261no—
142C4⋊C4—3261no—
143C4⋊C4—3261no—
144C4⋊C4—3261no—
145C4⋊C4—3261no—
146C4⋊C4—1631no—
147C4⋊C4D65211yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—3261no—
150C42—3261no—
151C42—3261no—
152C23D4×D16311yescharacteristic
153Q8—41no—
154Q8—13041no—
155Q8—6521no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—3261no—
163C2×C4—3261no—
164C2×C4—3261no—
165C2×C4—3261no—
166C2×C4—3261no—
167C2×C4—6522no—
168C2×C4—6521no—
169C2×C4—6521no—
170C2×C4—1632no—
171C2×C4D4×D16311yescharacteristic
172C2×C4C2×D65211yescharacteristic
173C8—41no—
174C8—6521no—
175C22—21no—
176C22—21no—
177C22#1910470511yescharacteristic
178C22Q16×D16311yescharacteristic
179C22#1910476411yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—13041no—
186C4—3262no—
187C4—6521no—
188C4—6521no—
189C4—6521no—
190C2—21no—
191C2—21no—
192C2#2378182211yescharacteristic
193C2#2378183911yescharacteristic
194C2#2378185611yescharacteristic
subgroupG/H
centerC22#19104705
commutator, cosocleC22×C4×C163C23
FrattiniC22×C4C22×D163
Fitting#328×C163C2
socleC22×C163#120
prime radicalC23×C163C2×D4
hypercenter#328D163
hypocenterC163#1617
LCSG ▷ C22×C4×C163 ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
97. C163#1617semidirect

Maximal subgroups

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

subgroupindex
#237822942
#237820012
#237819982
#237816052
#237814012
#237813902
#328×C1632
#1617163