Finite Group Databasebeta

← C2×#13277 #495355

Subgroups — C2×#13277 #495355

Order 512.

938 conjugacy classes of subgroups.

The subgroup lattice has 242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#499C211yesmaximal, characteristic
2C22×C4⋊C16C211yesmaximal, characteristic
3C2×C4×#107C211yesmaximal, characteristic
4#13277C218yesmaximal, direct product factor
5C2×#1380C212yesmaximal
6C2×#1380C212yesmaximal
7C22×#125—21no—
8C23×C16C2212yes—
9C2×#499—24no—
10C2×#499—22no—
11C2×#499C418yescomplemented
12C2×#499C2214yes—
13C22×#107C2211yescharacteristic
14C22×#107C2211yescharacteristic
15C22×#107C2212yes—
16C22×#106—21no—
17C22×C4×C8C2211yescharacteristic
18C2×C4×C4⋊C4—21no—
19C2×C4⋊C16—24no—
20C2×C4⋊C16C2214yes—
21C4×#107—22no—
22C4×#107C2214yes—
23C2×#340—21no—
24#1380C2218yes—
25#1380C2218yes—
26C23×C8D411yescharacteristic
27C23×C8C2311yescharacteristic
28C2×#125—28no—
29C2×#125—24no—
30C2×#125—42no—
31C2×#125—44no—
32C22×C4⋊C4—21no—
33C22×C4⋊C4—21no—
34C22×C4⋊C4—22no—
35C22×C4⋊C4—41no—
36C22×C4⋊C4—41no—
37C22×C42—41no—
38C22×C42D411yescharacteristic
39C22×C16—24no—
40C22×C16—28no—
41C22×C16C2314yes—
42#499—216no—
43#499—28no—
44#499C2×C4116yescomplemented
45C2×#107—21no—
46C2×#107—21no—
47C2×#107—22no—
48C2×#107—22no—
49C2×#107—22no—
50C2×#107—24no—
51C2×#107C2×C414yes—
52C2×#107C2×C414yes—
53C2×#107Q818yes—
54C2×#107C2312yes—
55C2×#107C2312yes—
56C2×#107C2314yes—
57C2×#106—28no—
58C2×#106—24no—
59C2×C4×C8C2×C414yes—
60C2×C4×C8D412yes—
61C2×C4×C8D414yes—
62C2×C4×C8C2312yes—
63C4×C4⋊C4—24no—
64C4×C4⋊C4—42no—
65C2×#95—41no—
66C4⋊C16—28no—
67#340—24no—
68C23×C4—41no—
69C23×C4—41no—
70C23×C4—42no—
71C23×C4D811yescharacteristic
72C23×C4D811yescharacteristic
73C23×C4C2×D411yescharacteristic
74C22×C8—24no—
75C22×C8C22⋊C414yes—
76C22×C8C22×C412yes—
77C22×C8C2×D412yes—
78C22×C8C2×D411yescharacteristic
79C22×C8C2×D412yes—
80C22×C8C2×Q814yes—
81C22×C8#4114yes—
82C22×C8C2411yescharacteristic
83#125—216no—
84#125—416no—
85#125—48no—
86C2×C4⋊C4—24no—
87C2×C4⋊C4—24no—
88C2×C4⋊C4—28no—
89C2×C4⋊C4—22no—
90C2×C4⋊C4—22no—
91C2×C4⋊C4—24no—
92C2×C4⋊C4—48no—
93C2×C4⋊C4—48no—
94C2×C4⋊C4—41no—
95C2×C4⋊C4—41no—
96C2×C4⋊C4—42no—
97C2×C4⋊C4—44no—
98C2×C4⋊C4—44no—
99C2×C4⋊C4—42no—
100C2×C4⋊C4—42no—
101C2×C4⋊C4—44no—
102C2×C42—44no—
103C2×C42—84no—
104C2×C42C22⋊C414yes—
105C2×C42D812yes—
106C2×C42SD1614yes—
107C2×C42C2×D412yes—
108C2×C16—24no—
109C2×C16—28no—
110C2×C16—48no—
111#107—24no—
112#107—24no—
113#107—28no—
114#107—22no—
115#107—22no—
116#107—24no—
117#107C22×C414yes—
118#107C22×C414yes—
119#107C2×Q818yes—
120#106—216no—
121C4×C8C22⋊C418yes—
122C4×C8C22×C414yes—
123C4×C8C2×D414yes—
124#95—44no—
125C24C2×D811yescharacteristic
126C22×C4—24no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—44no—
130C22×C4—42no—
131C22×C4—42no—
132C22×C4—44no—
133C22×C4—44no—
134C22×C4—48no—
135C22×C4—84no—
136C22×C4—84no—
137C22×C4—84no—
138C22×C4—82no—
139C22×C4—82no—
140C22×C4#10214yes—
141C22×C4#10214yes—
142C22×C4C2×C22⋊C412yes—
143C22×C4C22⋊Q814yes—
144C22×C4C2×D812yes—
145C22×C4C2×D812yes—
146C22×C4C2×D811yescharacteristic
147C22×C4C2×SD1612yes—
148C22×C4#13714yes—
149C22×C4C22×D411yescharacteristic
150C2×C8—24no—
151C2×C8—28no—
152C2×C8C2×C22⋊C414yes—
153C2×C8C2×C22⋊C412yes—
154C2×C8C4×Q818yes—
155C2×C8C22⋊Q814yes—
156C2×C8#12414yes—
157C2×C8C4⋊Q814yes—
158C2×C8C23×C411yescharacteristic
159C2×C8C22×D411yescharacteristic
160C2×C8C22×Q812yes—
161C2×C8C2×#4112yes—
162C4⋊C4—24no—
163C4⋊C4—24no—
164C4⋊C4—28no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—44no—
168C4⋊C4—44no—
169C4⋊C4—44no—
170C4⋊C4—416no—
171C4⋊C4—416no—
172C4⋊C4—48no—
173C42—88no—
174C42#10218yes—
175C42C2×C22⋊C414yes—
176C42C2×SD1614yes—
177C16—44no—
178C23C2×#10212yes—
179C23#47414yes—
180C23#50814yes—
181C23#50912yes—
182C23#51012yes—
183C23C22×D811yescharacteristic
184C2×C4—24no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—28no—
188C2×C4—28no—
189C2×C4—44no—
190C2×C4—44no—
191C2×C4—48no—
192C2×C4—84no—
193C2×C4—84no—
194C2×C4—84no—
195C2×C4—82no—
196C2×C4—82no—
197C2×C4—88no—
198C2×C4—88no—
199C2×C4—816no—
200C2×C4#39114yes—
201C2×C4C2×#10214yes—
202C2×C4C2×#10214yes—
203C2×C4C2×#10212yes—
204C2×C4#41914yes—
205C2×C4#47414yes—
206C2×C4#47518yes—
207C2×C4C22×C22⋊C411yescharacteristic
208C2×C4C2×C22⋊Q812yes—
209C2×C4C22×SD1611yescharacteristic
210C2×C4C2×#13712yes—
211C8—24no—
212C8#39114yes—
213C8C2×C4×Q812yes—
214C8C2×#12411yescharacteristic
215C8C2×C4⋊Q811yescharacteristic
216C22#198814yes—
217C22#213814yes—
218C22#213914yes—
219C22#222818yes—
220C22#222918yes—
221C22C22×#10211yescharacteristic
222C22C2×#47412yes—
223C22C2×#50812yes—
224C22C2×#50911yescharacteristic
225C22C2×#51011yescharacteristic
226C4—24no—
227C4—24no—
228C4—88no—
229C4—84no—
230C4—84no—
231C4#198814yes—
232C4C2×#39111yescharacteristic
233C4C2×#41911yescharacteristic
234C4C2×#47512yes—
235C2#1327718yesdirect product factor
236C2C2×#198811yescharacteristic
237C2C2×#213811yescharacteristic
238C2C2×#213911yescharacteristic
239C2C2×#222812yes—
240C2C2×#222912yes—
subgroupG/H
center, socle, prime radicalC24C2×D8
commutatorC2×C8C23×C4
Frattini, cosocleC22×C8C24
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4×C8 ◁ G
LECSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #13277C2direct (N × H)
11. C2×#499C4semidirect
44. #499C2×C4semidirect
235. C2#13277direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4992
C22×C4⋊C162
C2×C4×#1072
#132772
C2×#13802