Finite Group Databasebeta

← #35213466

Subgroups — #35213466

Order 20864.

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

normal subgroups only

This group has 272 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#23782260C211yesmaximal, characteristic, complemented
2#23781818C211yesmaximal, characteristic, complemented
3#23781798C211yesmaximal, characteristic
4#23781583C211yesmaximal, characteristic, complemented
5#23781401C211yesmaximal, characteristic, complemented
6#23781390C211yesmaximal, characteristic, complemented
7#327×C163C211yesmaximal, characteristic, complemented
8C22×D652C2211yescharacteristic
9C2×#14579688—21no—
10C2×#14579684—21no—
11#19104728—21no—
12#19104725—21no—
13#19104716—21no—
14#19104716—21no—
15#19104714C2211yescharacteristic
16#19104712—21no—
17D4×Dic163—21no—
18C2×Dic163⋊C4C2211yescharacteristic
19C2×(C2×D163)⋊C4—21no—
20C2×(C2×D163)⋊C4—21no—
21#19104657—21no—
22#19104655—21no—
23C22⋊(C163⋊C8)C2211yescharacteristic
24#121×C163C2211yescharacteristic
25C22⋊C8×C163C2211yescharacteristic
26#95×C163C2211yescharacteristic
27C23×D163—21no—
28C2×Dic326D411yescharacteristic
29C2×D652—21no—
30C2×D652—21no—
31C2×D652—42no—
32C22×Dic163—21no—
33C22×Dic163D411yescharacteristic
34C22×Dic163D411yescharacteristic
35#14579688—42no—
36#14579684—42no—
37C2×C163⋊C8—21no—
38C4⋊Dic163—21no—
39C4⋊Dic163D411yescharacteristic
40Dic163⋊C4—21no—
41Dic163⋊C4—21no—
42Dic163⋊C4—21no—
43Dic163⋊C4—21no—
44Dic163⋊C4—21no—
45C22⋊Dic163—21no—
46C22⋊Dic163—21no—
47C22⋊Dic163—21no—
48C22⋊Dic163—21no—
49(C2×D163)⋊C4—42no—
50(C2×D163)⋊C4—42no—
51C4×Dic163—21no—
52C2×D4×C163—21no—
53C2×D4×C163D411yescharacteristic
54C22×C4×C163—21no—
55C22×C4×C163C2311yescharacteristic
56C2×C8×C163—21no—
57C4⋊C4×C163D411yescharacteristic
58C22⋊C4×C163—21no—
59C22×D163—22no—
60C22×D163—41no—
61C22×D163—41no—
62C22×D163—41no—
63C22×D163—41no—
64C22×D163—41no—
65C22×D163—41no—
66Dic326—41no—
67D652—22no—
68D652—22no—
69D652—41no—
70D652—41no—
71C2×Dic163—21no—
72C2×Dic163—21no—
73C2×Dic163—21no—
74C2×Dic163—21no—
75C2×Dic163—21no—
76C2×Dic163—21no—
77C2×Dic163—41no—
78C2×Dic163—81no—
79C163⋊C8—41no—
80C23×C163—21no—
81C23×C163C2×D411yescharacteristic
82D4×C163—41no—
83D4×C163—41no—
84D4×C163—41no—
85C2×C4×C163—21no—
86C2×C4×C163—41no—
87C2×C4×C163—41no—
88C2×C4×C163—41no—
89C2×C4×C163—41no—
90C2×C4×C163C2×D411yescharacteristic
91C2×C4×C163C2×D411yescharacteristic
92C8×C163—41no—
93C22×C163—21no—
94C22×C163—21no—
95C22×C163—41no—
96C22×C163—41no—
97C22×C163—41no—
98C22×C163#12011yescharacteristic
99C22×C163#13511yescharacteristic
100C22×C163AGL(1,ℤ/8)11yescharacteristic
101C2×D163—42no—
102C2×D163—42no—
103C2×D163—42no—
104C2×D163—81no—
105C2×D163—81no—
106C2×D163—81no—
107C2×D163—81no—
108C4×C163—21no—
109C4×C163—21no—
110C4×C163—41no—
111C4×C163—81no—
112Dic163—41no—
113Dic163—41no—
114Dic163—41no—
115Dic163—41no—
116C2×C163—21no—
117C2×C163—21no—
118C2×C163—81no—
119C2×C163#44911yescharacteristic
120C2×C163#45411yescharacteristic
121C2×C163B(4,𝔽2)11yescharacteristic
122D163—82no—
123C163#159711yescharacteristic, complemented, Sylow
124#1597—1631nomaximal, Sylow
125#539—1631no—
126#450—1631no—
127#447—1631no—
128#394—1631no—
129#328—1631no—
130#327D16311yescharacteristic, complemented
131#324—1631no—
132C22×D4—1631no—
133C2×SD16—3261no—
134C2×D8—3261no—
135#126—3261no—
136#125—3261no—
137#123—3261no—
138#123—3261no—
139C22⋊Q8—3261no—
140C22⋊Q8—1631no—
141#121C2×D16311yescharacteristic
142C4×D4—3261no—
143C2×C4⋊C4—1631no—
144C2×C22⋊C4—3261no—
145C2×C22⋊C4—3261no—
146#102—3261no—
147#102—3261no—
148C22⋊C8—1631no—
149C22⋊C8C2×D16311yescharacteristic
150#95C2×D16311yescharacteristic
151C24—3261no—
152C2×Q8—1631no—
153C2×D4—21no—
154C2×D4—3261no—
155C2×D4—3261no—
156C2×D4—6522no—
157C2×D4D65211yescharacteristic
158C22×C4—21no—
159C22×C4—3261no—
160C22×C4—1631no—
161C22×C4—1631no—
162C22×C4C22×D16311yescharacteristic
163SD16—6522no—
164D8—6522no—
165C2×C8—21no—
166C2×C8—3261no—
167C4⋊C4—3261no—
168C4⋊C4—3261no—
169C4⋊C4—3261no—
170C4⋊C4—3261no—
171C4⋊C4—3261no—
172C4⋊C4—3261no—
173C4⋊C4—1631no—
174C4⋊C4D65211yescharacteristic
175C22⋊C4—21no—
176C22⋊C4—3261no—
177C22⋊C4—3261no—
178C22⋊C4—3261no—
179C22⋊C4—3261no—
180C22⋊C4—6522no—
181C22⋊C4—6522no—
182C42—3261no—
183C23—21no—
184C23—3262no—
185C23—6521no—
186C23—6521no—
187C23—6521no—
188C23—6521no—
189C23—6521no—
190C23—6521no—
191C23D4×D16311yescharacteristic
192Q8—6521no—
193D4—41no—
194D4—41no—
195D4—41no—
196D4—3262no—
197D4—3262no—
198D4—6521no—
199D4—6521no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—13041no—
206C2×C4—3261no—
207C2×C4—3261no—
208C2×C4—3261no—
209C2×C4—3261no—
210C2×C4—3261no—
211C2×C4—3261no—
212C2×C4—6521no—
213C2×C4D4×D16311yescharacteristic
214C2×C4C2×D65211yescharacteristic
215C8—41no—
216C8—6521no—
217C22—21no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—13041no—
223C22—13041no—
224C22—13041no—
225C22—13041no—
226C22—6522no—
227C22—6522no—
228C22—6522no—
229C22#1910470511yescharacteristic
230C22#1910475611yescharacteristic
231C22#1910475911yescharacteristic
232C4—21no—
233C4—21no—
234C4—41no—
235C4—81no—
236C4—6521no—
237C4—6521no—
238C4—6521no—
239C4—6521no—
240C2—21no—
241C2—21no—
242C2—81no—
243C2—13042no—
244C2#2378181111yescharacteristic
245C2#2378183911yescharacteristic
246C2#2378185311yescharacteristic
subgroupG/H
centerC22#19104705
commutator, cosocleC22×C4×C163C23
FrattiniC22×C4C22×D163
Fitting#327×C163C2
socleC22×C163#120
prime radical#23781798C2
hypercenter#327D163
hypocenterC163#1597
LCSG ▷ C22×C4×C163 ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
1. #23782260C2semidirect
2. #23781818C2semidirect
4. #23781583C2semidirect
5. #23781401C2semidirect
6. #23781390C2semidirect
7. #327×C163C2semidirect
123. C163#1597semidirect
130. #327D163semidirect

Maximal subgroups

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

subgroupindex
#237822602
#237818182
#237817982
#237815832
#237814012
#237813902
#327×C1632
#1597163