Finite Group Databasebeta

← #16696

Subgroups — #16696

Order 256.

561 conjugacy classes of subgroups.

The subgroup lattice has 277 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#391C211yesmaximal, characteristic
2C2×#383C211yesmaximal, characteristic
3#1446C211yesmaximal, characteristic
4#1446C211yesmaximal, characteristic
5#1445C212yesmaximal
6#1444C211yesmaximal, characteristic
7#1443C212yesmaximal
8#1443C212yesmaximal
9#1442C212yesmaximal
10#1442C211yesmaximal, characteristic
11#1434C211yesmaximal, characteristic
12C23×Q8C2211yescharacteristic
13C22×C4⋊C4C2212yes—
14C22×C4⋊C4C2211yescharacteristic
15C22×C42C2211yescharacteristic
16#391—24no—
17#383—24no—
18C2×#95C2212yes—
19C2×#95C2211yescharacteristic
20C2×#95C2211yescharacteristic
21C2×#95C2211yescharacteristic
22C2×#95C2212yes—
23C2×#95C2212yes—
24C2×#95C2211yescharacteristic
25C2×#95C2212yes—
26C2×#95C2212yes—
27C2×#95C2211yescharacteristic
28C2×#95C2211yescharacteristic
29C2×#95C2212yes—
30C2×#95C2211yescharacteristic
31C2×#95C2211yescharacteristic
32C2×#95C2212yes—
33C2×#95C2212yes—
34C2×#95C2212yes—
35C2×#95C2212yes—
36C2×#95C2212yes—
37C22×Q8—22no—
38C22×Q8—24no—
39C22×Q8—22no—
40C22×Q8—22no—
41C22×Q8—42no—
42C23×C4C2311yescharacteristic
43C23×C4C2312yes—
44C23×C4C2311yescharacteristic
45C23×C4C2311yescharacteristic
46C23×C4C2311yescharacteristic
47C23×C4C2312yes—
48C23×C4C2311yescharacteristic
49C23×C4C2311yescharacteristic
50C23×C4C2312yes—
51C23×C4C2312yes—
52C23×C4C2311yescharacteristic
53C2×C4⋊C4—22no—
54C2×C4⋊C4—24no—
55C2×C4⋊C4—42no—
56C2×C4⋊C4—42no—
57C2×C4⋊C4—42no—
58C2×C42—22no—
59C2×C42—22no—
60C2×C42D414yes—
61#95—22no—
62#95—22no—
63#95—22no—
64#95—22no—
65#95—22no—
66#95—22no—
67#95—24no—
68#95—24no—
69#95—22no—
70#95—24no—
71#95—24no—
72#95—24no—
73#95—24no—
74#95—22no—
75#95—42no—
76#95—42no—
77#95—42no—
78#95—42no—
79#95—42no—
80C24C2411yescharacteristic
81C2×Q8—28no—
82C2×Q8—48no—
83C2×Q8—48no—
84C2×Q8—44no—
85C2×Q8—44no—
86C22×C4—22no—
87C22×C4—22no—
88C22×C4—22no—
89C22×C4—22no—
90C22×C4—22no—
91C22×C4—22no—
92C22×C4—21no—
93C22×C4—21no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4—22no—
97C22×C4—22no—
98C22×C4—22no—
99C22×C4—21no—
100C22×C4—22no—
101C22×C4—22no—
102C22×C4—22no—
103C22×C4—22no—
104C22×C4—21no—
105C22×C4—21no—
106C22×C4—22no—
107C22×C4—21no—
108C22×C4—22no—
109C22×C4—22no—
110C22×C4—21no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—22no—
115C22×C4—22no—
116C22×C4—22no—
117C22×C4—22no—
118C22×C4—22no—
119C22×C4—22no—
120C22×C4—22no—
121C22×C4—22no—
122C22×C4—22no—
123C22×C4—22no—
124C22×C4—22no—
125C22×C4—21no—
126C22×C4—22no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—22no—
132C22×C4—21no—
133C22×C4—22no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—22no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4C2×D412yes—
145C22×C4C2×D412yes—
146C22×C4C2×D412yes—
147C22×C4#4114yes—
148C22×C4#4114yes—
149C22×C4#4112yes—
150C22×C4#4112yes—
151C4⋊C4—44no—
152C4⋊C4—48no—
153C42—28no—
154C23C22×D411yescharacteristic
155C23C2×#4111yescharacteristic
156C23C2×#4111yescharacteristic
157C23C2×#4112yes—
158C23C2×#4112yes—
159C23H(5,𝔽2)12yes—
160C23H(5,𝔽2)11yescharacteristic
161C232−1+411yescharacteristic
162C232−1+412yes—
163C232−1+411yescharacteristic
164C232−1+411yescharacteristic
165Q8—416no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—24no—
169C2×C4—24no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—24no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—24no—
179C2×C4—24no—
180C2×C4—24no—
181C2×C4—24no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4#12314yes—
231C22C2×#12311yescharacteristic
232C22#52511yescharacteristic
233C22#53211yescharacteristic
234C22#53511yescharacteristic
235C22#53611yescharacteristic
236C22#53611yescharacteristic
237C22#53711yescharacteristic
238C22#53812yes—
239C22#54111yescharacteristic
240C22#54111yescharacteristic
241C22#54112yes—
242C22#54211yescharacteristic
243C22#54211yescharacteristic
244C22#54212yes—
245C22#54212yes—
246C22#55112yes—
247C22#55112yes—
248C22#55212yes—
249C22#55212yes—
250C22#55612yes—
251C22#55612yes—
252C22#56312yes—
253C22#56312yes—
254C4—24no—
255C4—42no—
256C4—44no—
257C4—42no—
258C4—44no—
259C4—81no—
260C4—81no—
261C4—81no—
262C4—82no—
263C4—81no—
264C4—82no—
265C2#248211yescharacteristic
266C2#249911yescharacteristic
267C2#260411yescharacteristic
268C2#262511yescharacteristic
269C2#263711yescharacteristic
270C2#266211yescharacteristic
271C2#275812yes—
272C2#275912yes—
273C2#276212yes—
274C2#276412yes—
275C2#282111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC24C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#3912
C2×#3832
#14462
#14452
#14442
#14432
#14422
#14342