Finite Group Databasebeta

← #35213549

Subgroups — #35213549

Order 20864.

232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 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#23782255C211yesmaximal, characteristic
2#23781978C211yesmaximal, characteristic, complemented
3#23781591C211yesmaximal, characteristic, complemented
4#23781402C211yesmaximal, characteristic, complemented
5#23781400C211yesmaximal, characteristic, complemented
6#23781388C211yesmaximal, characteristic, complemented
7#483×C163C211yesmaximal, characteristic, complemented
8#19104730—21no—
9#19104724—21no—
10#19104720—21no—
11#19104710—21no—
12#19104709C2211yescharacteristic
13#19104705—21no—
14(C22⋊D163)⋊C4—21no—
15C2×(C2×D163)⋊C4—21no—
16C2×(C2×D163)⋊C4C2211yescharacteristic
17#19104668—21no—
18#19104655—21no—
19C22⋊(C163⋊C8)C2211yescharacteristic
20C163⋊#95—21no—
21C163⋊#95C2211yescharacteristic
22C22⋊Q8×C163C2211yescharacteristic
23C2×C4⋊C4×C163C2211yescharacteristic
24#106×C163—21no—
25#103×C163—21no—
26C22⋊C8×C163C2211yescharacteristic
27C23×D163D411yescharacteristic
28C2×D652—21no—
29C2×D652—21no—
30C2×D652D411yescharacteristic
31C2×C22⋊D163—21no—
32C22×Dic163—21no—
33C22×Dic163D411yescharacteristic
34C2×C4×D163—21no—
35C2×C163⋊C8—21no—
36C4⋊Dic163D411yescharacteristic
37Dic163⋊C4—21no—
38(C2×D163)⋊C4—21no—
39(C2×D163)⋊C4—21no—
40(C2×D163)⋊C4—21no—
41(C2×D163)⋊C4—21no—
42(C2×D163)⋊C4—21no—
43(C2×D163)⋊C4—21no—
44(C2×D163)⋊C4—42no—
45C4×Dic163—21no—
46C2×Q8×C163D411yescharacteristic
47C22×C4×C163—21no—
48C22×C4×C163C2311yescharacteristic
49C2×C8×C163—21no—
50C4⋊C4×C163—21no—
51C4⋊C4×C163—21no—
52C4⋊C4×C163—21no—
53C4⋊C4×C163D411yescharacteristic
54C22⋊C4×C163—21no—
55C22×D163—21no—
56C22×D163—21no—
57C22×D163—21no—
58C22×D163—21no—
59C22×D163—41no—
60C22×D163—41no—
61D652—41no—
62D652—81no—
63D652—81no—
64C22⋊D163—41no—
65C22⋊D163—41no—
66C2×Dic163—21no—
67C2×Dic163—21no—
68C2×Dic163—41no—
69C2×Dic163—41no—
70C2×Dic163—41no—
71C2×Dic163—41no—
72C4×D163—81no—
73C163⋊C8—41no—
74C23×C163C2×D411yescharacteristic
75Q8×C163—41no—
76C2×C4×C163—21no—
77C2×C4×C163—21no—
78C2×C4×C163—41no—
79C2×C4×C163—41no—
80C2×C4×C163—41no—
81C2×C4×C163—41no—
82C2×C4×C163C2×D411yescharacteristic
83C2×C4×C163C2×D411yescharacteristic
84C8×C163—41no—
85C22×C163—21no—
86C22×C163—21no—
87C22×C163#12011yescharacteristic
88C22×C163#13511yescharacteristic
89C22×C163AGL(1,ℤ/8)11yescharacteristic
90C2×D163—42no—
91C2×D163—41no—
92C2×D163—41no—
93C2×D163—41no—
94C2×D163—41no—
95C2×D163—41no—
96C2×D163—41no—
97C2×D163—81no—
98C4×C163—21no—
99C4×C163—21no—
100C4×C163—41no—
101C4×C163—41no—
102C4×C163—81no—
103Dic163—41no—
104Dic163—41no—
105Dic163—81no—
106C2×C163—21no—
107C2×C163—21no—
108C2×C163#44911yescharacteristic
109C2×C163#45511yescharacteristic
110C2×C163#45811yescharacteristic
111D163—81no—
112D163—81no—
113C163#161211yescharacteristic, complemented, Sylow
114#1612—1631nomaximal, Sylow
115#538—1631no—
116#483D16311yescharacteristic, complemented
117#480—1631no—
118#397—1631no—
119#328—1631no—
120#327—1631no—
121#323—1631no—
122#126—3261no—
123#124—3261no—
124#123—3261no—
125C22⋊Q8C2×D16311yescharacteristic
126#121—3261no—
127#121—1631no—
128#120—3261no—
129C4×D4—3261no—
130C2×C4⋊C4C2×D16311yescharacteristic
131C2×C22⋊C4—3261no—
132C2×C22⋊C4—1631no—
133#107—3261no—
134#106—21no—
135#103—21no—
136#102—3261no—
137C22⋊C8—1631no—
138C22⋊C8C2×D16311yescharacteristic
139#95—3261no—
140#95—1631no—
141C24—1631no—
142C2×Q8C22⋊D16311yescharacteristic
143C2×D4—3261no—
144C2×D4—3261no—
145C2×D4—3261no—
146C2×D4—1631no—
147C22×C4—21no—
148C22×C4—3261no—
149C22×C4—3261no—
150C22×C4—1631no—
151C22×C4C22×D16311yescharacteristic
152C2×C8—21no—
153C2×C8—3261no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—3261no—
158C4⋊C4—1631no—
159C4⋊C4C22⋊D16311yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—3261no—
162C22⋊C4—3261no—
163C22⋊C4—3261no—
164C22⋊C4—3261no—
165C22⋊C4—3261no—
166C22⋊C4—3261no—
167C22⋊C4—6522no—
168C42—3261no—
169C23—3261no—
170C23—3261no—
171C23—3261no—
172C23—3261no—
173C23—6521no—
174C23—6521no—
175C23D4×D16311yescharacteristic
176Q8—41no—
177D4—13041no—
178D4—13041no—
179D4—6521no—
180D4—6521no—
181D4—6521no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—13041no—
189C2×C4—3261no—
190C2×C4—3261no—
191C2×C4—6521no—
192C2×C4—6521no—
193C2×C4—6521no—
194C2×C4—6521no—
195C2×C4D4×D16311yescharacteristic
196C2×C4C2×C22⋊D16311yescharacteristic
197C8—41no—
198C8—6521no—
199C22—21no—
200C22—21no—
201C22—13041no—
202C22—6522no—
203C22—6521no—
204C22—6521no—
205C22—6521no—
206C22—6521no—
207C22—6521no—
208C22—6521no—
209C22#1910470311yescharacteristic
210C22#1910475611yescharacteristic
211C22#1910476211yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—81no—
217C4—13041no—
218C4—6521no—
219C4—6521no—
220C2—21no—
221C2—21no—
222C2—13041no—
223C2—13041no—
224C2#2378180911yescharacteristic
225C2#2378184111yescharacteristic
226C2#2378185411yescharacteristic
subgroupG/H
centerC22#19104703
commutator, cosocleC22×C4×C163C23
FrattiniC22×C4C22×D163
Fitting#483×C163C2
socleC22×C163#120
prime radical#23782255C2
hypercenter#483D163
hypocenterC163#1612
LCSG ▷ C22×C4×C163 ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. #23781978C2semidirect
3. #23781591C2semidirect
4. #23781402C2semidirect
5. #23781400C2semidirect
6. #23781388C2semidirect
7. #483×C163C2semidirect
113. C163#1612semidirect
116. #483D163semidirect

Maximal subgroups

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

subgroupindex
#237822552
#237819782
#237815912
#237814022
#237814002
#237813882
#483×C1632
#1612163