Finite Group Databasebeta

← #2435×C163 #35211193

Subgroups — #2435×C163 #35211193

Order 20864.

1088 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 248 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
1C23×D4×C163C211yesmaximal, characteristic
2C2×#124×C163C212yesmaximal, complemented
3C2×C22⋊Q8×C163C211yesmaximal, characteristic, complemented
4#394×C163C214yesmaximal, complemented
5#390×C163C212yesmaximal, complemented
6#379×C163C214yesmaximal, complemented
7C4×C22⋊C4×C163C211yesmaximal, characteristic, complemented
8C25×C163C2212yes—
9C22×Q8×C163C2211yescharacteristic, complemented
10C22×D4×C163—28no—
11C22×D4×C163—24no—
12C22×D4×C163C2212yes—
13C22×D4×C163C2212yes—
14C23×C4×C163C2211yescharacteristic
15#124×C163—28no—
16C22⋊Q8×C163—24no—
17C2×C4⋊C4×C163C2211yescharacteristic, complemented
18C2×C4⋊C4×C163C2212yescomplemented
19C2×C22⋊C4×C163C2212yes—
20C2×C22⋊C4×C163C2212yes—
21C2×C22⋊C4×C163C2218yescomplemented
22C2×C22⋊C4×C163C2218yescomplemented
23C2×C42×C163C2212yescomplemented
24#95×C163C2212yescomplemented
25C24×C163—28no—
26C24×C163—24no—
27C24×C163—28no—
28C24×C163—44no—
29C24×C163C2314yes—
30C24×C163C2311yescharacteristic
31C2×Q8×C163—22no—
32C2×Q8×C163—24no—
33C2×D4×C163—232no—
34C2×D4×C163—28no—
35C2×D4×C163—24no—
36C2×D4×C163—24no—
37C2×D4×C163—24no—
38C2×D4×C163D418yes—
39C22×C4×C163—24no—
40C22×C4×C163D414yes—
41C22×C4×C163C2314yes—
42C22×C4×C163C2312yes—
43C22×C4×C163C2312yes—
44C22×C4×C163C2311yescharacteristic
45C22×C4×C163C2311yescharacteristic
46C4⋊C4×C163—22no—
47C4⋊C4×C163—24no—
48C22⋊C4×C163—24no—
49C22⋊C4×C163—216no—
50C22⋊C4×C163—24no—
51C22⋊C4×C163—48no—
52C42×C163—24no—
53C23×C163—22no—
54C23×C163—22no—
55C23×C163—216no—
56C23×C163—24no—
57C23×C163—24no—
58C23×C163—28no—
59C23×C163—28no—
60C23×C163—432no—
61C23×C163—48no—
62C23×C163—48no—
63C23×C163C2×D418yes—
64C23×C163C2×D412yes—
65C23×C163#4114yes—
66C23×C163C2411yescharacteristic
67Q8×C163—44no—
68D4×C163—216no—
69D4×C163—216no—
70C2×C4×C163—22no—
71C2×C4×C163—28no—
72C2×C4×C163—24no—
73C2×C4×C163—24no—
74C2×C4×C163—22no—
75C2×C4×C163—22no—
76C2×C4×C163—24no—
77C2×C4×C163—24no—
78C2×C4×C163—24no—
79C2×C4×C163C2×D412yes—
80C2×C4×C163C2×D414yes—
81C2×C4×C163C2×D412yes—
82C22×C163—22no—
83C22×C163—22no—
84C22×C163—28no—
85C22×C163—28no—
86C22×C163—216no—
87C22×C163—432no—
88C22×C163—44no—
89C22×C163—44no—
90C22×C163—48no—
91C22×C163#12414yescomplemented
92C22×C163C22×D411yescharacteristic
93C22×C163C22×D412yes—
94C22×C163C2×#4112yes—
95C22×C163H(5,𝔽2)12yes—
96C4×C163—22no—
97C4×C163—42no—
98C4×C163—42no—
99C4×C163—44no—
100C4×C163#12014yes—
101C2×C163—24no—
102C2×C163—48no—
103C2×C163C2×#12011yescharacteristic
104C2×C163C2×#12411yescharacteristic
105C2×C163#53511yescharacteristic
106C2×C163#54614yes—
107C163#243511yescharacteristic, direct product factor, Sylow
108#2435C16311yesmaximal, characteristic, direct product factor, Sylow
109C23×D4C2×C16311yescharacteristic
110C2×#124C2×C16312yescomplemented
111C2×C22⋊Q8C2×C16311yescharacteristic, complemented
112#394C2×C16314yescomplemented
113#390C2×C16312yescomplemented
114#379C2×C16314yescomplemented
115C4×C22⋊C4C2×C16311yescharacteristic, complemented
116C25C22×C16312yes—
117C22×Q8C22×C16311yescharacteristic, complemented
118C22×D4—28no—
119C22×D4—24no—
120C22×D4C22×C16312yes—
121C22×D4C22×C16312yes—
122C23×C4C22×C16311yescharacteristic
123#124—28no—
124C22⋊Q8—24no—
125C2×C4⋊C4C22×C16311yescharacteristic, complemented
126C2×C4⋊C4C22×C16312yescomplemented
127C2×C22⋊C4C22×C16312yes—
128C2×C22⋊C4C22×C16312yes—
129C2×C22⋊C4C22×C16318yescomplemented
130C2×C22⋊C4C22×C16318yescomplemented
131C2×C42C22×C16312yescomplemented
132#95C22×C16312yescomplemented
133C24—28no—
134C24—24no—
135C24—28no—
136C24—44no—
137C24C23×C16314yes—
138C24C23×C16311yescharacteristic
139C2×Q8—22no—
140C2×Q8—24no—
141C2×D4—232no—
142C2×D4—28no—
143C2×D4—24no—
144C2×D4—24no—
145C2×D4—24no—
146C2×D4D4×C16318yes—
147C22×C4—24no—
148C22×C4D4×C16314yes—
149C22×C4C23×C16314yes—
150C22×C4C23×C16312yes—
151C22×C4C23×C16312yes—
152C22×C4C23×C16311yescharacteristic
153C22×C4C23×C16311yescharacteristic
154C4⋊C4—22no—
155C4⋊C4—24no—
156C22⋊C4—24no—
157C22⋊C4—216no—
158C22⋊C4—24no—
159C22⋊C4—48no—
160C42—24no—
161C23—22no—
162C23—22no—
163C23—216no—
164C23—24no—
165C23—24no—
166C23—28no—
167C23—28no—
168C23—432no—
169C23—48no—
170C23—48no—
171C23C2×D4×C16318yes—
172C23C2×D4×C16312yes—
173C23#41×C16314yes—
174C23C24×C16311yescharacteristic
175Q8—44no—
176D4—216no—
177D4—216no—
178C2×C4—22no—
179C2×C4—28no—
180C2×C4—24no—
181C2×C4—24no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—24no—
187C2×C4C2×D4×C16312yes—
188C2×C4C2×D4×C16314yes—
189C2×C4C2×D4×C16312yes—
190C22—22no—
191C22—22no—
192C22—28no—
193C22—28no—
194C22—216no—
195C22—432no—
196C22—44no—
197C22—44no—
198C22—48no—
199C22#124×C16314yescomplemented
200C22C22×D4×C16311yescharacteristic
201C22C22×D4×C16312yes—
202C22C2×#41×C16312yes—
203C22H(5,𝔽2)×C16312yes—
204C4—22no—
205C4—42no—
206C4—42no—
207C4—44no—
208C4#120×C16314yes—
209C2—24no—
210C2—48no—
211C2C2×#120×C16311yescharacteristic
212C2C2×#124×C16311yescharacteristic
213C2#535×C16311yescharacteristic
214C2#546×C16314yes—
subgroupG/H
center, socleC23×C163C24
commutator, Frattini, cosocleC23C24×C163
prime radicalC23×D4×C163C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C163 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#124×C163C2semidirect
3. C2×C22⋊Q8×C163C2semidirect
4. #394×C163C2semidirect
5. #390×C163C2semidirect
6. #379×C163C2semidirect
7. C4×C22⋊C4×C163C2semidirect
9. C22×Q8×C163C22semidirect
17. C2×C4⋊C4×C163C22semidirect
18. C2×C4⋊C4×C163C22semidirect
21. C2×C22⋊C4×C163C22semidirect
22. C2×C22⋊C4×C163C22semidirect
23. C2×C42×C163C22semidirect
24. #95×C163C22semidirect
91. C22×C163#124semidirect
107. C163#2435direct (N × H)
108. #2435C163direct (N × H)
110. C2×#124C2×C163semidirect
111. C2×C22⋊Q8C2×C163semidirect
112. #394C2×C163semidirect
113. #390C2×C163semidirect
114. #379C2×C163semidirect
115. C4×C22⋊C4C2×C163semidirect
117. C22×Q8C22×C163semidirect
125. C2×C4⋊C4C22×C163semidirect
126. C2×C4⋊C4C22×C163semidirect
129. C2×C22⋊C4C22×C163semidirect
130. C2×C22⋊C4C22×C163semidirect
131. C2×C42C22×C163semidirect
132. #95C22×C163semidirect
199. C22#124×C163semidirect

Maximal subgroups

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

subgroupindex
C23×D4×C1632
C2×#124×C1632
C2×C22⋊Q8×C1632
#394×C1632
#390×C1632
#379×C1632
C4×C22⋊C4×C1632
#2435163