Finite Group Databasebeta

← #16567

Subgroups — #16567

Order 256.

597 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#400C211yesmaximal, characteristic
2C2×#389C211yesmaximal, characteristic
3C2×#387C211yesmaximal, characteristic
4C2×#382C211yesmaximal, characteristic
5#1445C211yesmaximal, characteristic
6#1444C211yesmaximal, characteristic
7#1442C212yesmaximal
8#1441C211yesmaximal, characteristic
9#1441C212yesmaximal
10#1441C212yesmaximal
11#1441C212yesmaximal
12C22×C4⋊C4C2211yescharacteristic
13C22×C4⋊C4C2211yescharacteristic
14C22×C4⋊C4C2211yescharacteristic
15C22×C4⋊C4C2212yes—
16C22×C4⋊C4C2211yescharacteristic
17C22×C4⋊C4C2212yes—
18C22×C4⋊C4C2212yes—
19C22×C42C2211yescharacteristic
20#400—24no—
21#389—24no—
22#387—24no—
23#382—24no—
24C2×#95C2212yes—
25C2×#95C2212yes—
26C2×#95C2212yes—
27C2×#95C2211yescharacteristic
28C2×#95C2211yescharacteristic
29C2×#95C2212yes—
30C2×#95C2212yes—
31C2×#95C2211yescharacteristic
32C2×#95C2211yescharacteristic
33C2×#95C2211yescharacteristic
34C2×#95C2212yes—
35C2×#95C2212yes—
36C2×#95C2212yes—
37C2×#95C2212yes—
38C2×#95C2211yescharacteristic
39C23×C4C2311yescharacteristic
40C23×C4C2312yes—
41C23×C4C2311yescharacteristic
42C23×C4C2312yes—
43C23×C4C2312yes—
44C23×C4C2311yescharacteristic
45C23×C4C2311yescharacteristic
46C23×C4C2311yescharacteristic
47C23×C4C2312yes—
48C23×C4C2311yescharacteristic
49C23×C4C2311yescharacteristic
50C2×C4⋊C4—22no—
51C2×C4⋊C4—22no—
52C2×C4⋊C4—24no—
53C2×C4⋊C4—22no—
54C2×C4⋊C4—24no—
55C2×C4⋊C4—22no—
56C2×C4⋊C4—24no—
57C2×C4⋊C4—22no—
58C2×C4⋊C4—22no—
59C2×C4⋊C4—22no—
60C2×C4⋊C4—24no—
61C2×C4⋊C4—24no—
62C2×C4⋊C4—22no—
63C2×C4⋊C4—22no—
64C2×C4⋊C4—42no—
65C2×C4⋊C4—42no—
66C2×C4⋊C4—42no—
67C2×C4⋊C4—42no—
68C2×C4⋊C4—42no—
69C2×C4⋊C4Q814yes—
70C2×C42—22no—
71C2×C42—22no—
72C2×C42D414yes—
73#95—24no—
74#95—22no—
75#95—22no—
76#95—22no—
77#95—22no—
78#95—22no—
79#95—24no—
80#95—24no—
81#95—24no—
82#95—24no—
83#95—42no—
84#95—42no—
85#95—42no—
86#95—42no—
87#95D414yes—
88C24C2411yescharacteristic
89C22×C4—21no—
90C22×C4—21no—
91C22×C4—22no—
92C22×C4—21no—
93C22×C4—22no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4—21no—
99C22×C4—22no—
100C22×C4—21no—
101C22×C4—21no—
102C22×C4—21no—
103C22×C4—22no—
104C22×C4—22no—
105C22×C4—22no—
106C22×C4—21no—
107C22×C4—22no—
108C22×C4—21no—
109C22×C4—22no—
110C22×C4—22no—
111C22×C4—22no—
112C22×C4—22no—
113C22×C4—22no—
114C22×C4—22no—
115C22×C4—22no—
116C22×C4—22no—
117C22×C4—22no—
118C22×C4—22no—
119C22×C4—22no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—22no—
124C22×C4—21no—
125C22×C4—22no—
126C22×C4—22no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—21no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—22no—
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—21no—
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—21no—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4C2×D414yes—
146C22×C4C2×D412yes—
147C22×C4C2×D412yes—
148C22×C4C2×D412yes—
149C22×C4C2×D412yes—
150C22×C4C2×Q812yes—
151C22×C4C2×Q812yes—
152C22×C4C2×Q812yes—
153C22×C4#4114yes—
154C22×C4#4112yes—
155C22×C4#4112yes—
156C4⋊C4—28no—
157C4⋊C4—28no—
158C4⋊C4—48no—
159C4⋊C4—48no—
160C4⋊C4—48no—
161C4⋊C4—44no—
162C4⋊C4—44no—
163C42—28no—
164C23C22×D411yescharacteristic
165C23C22×D411yescharacteristic
166C23C22×Q811yescharacteristic
167C23C2×#4111yescharacteristic
168C23C2×#4111yescharacteristic
169C23C2×#4112yes—
170C23H(5,𝔽2)12yes—
171C23H(5,𝔽2)11yescharacteristic
172C232−1+412yes—
173C232−1+412yes—
174C232−1+411yescharacteristic
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—24no—
192C2×C4—24no—
193C2×C4—24no—
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—41no—
200C2×C4—42no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—41no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4#12114yes—
241C2×C4C22⋊Q814yes—
242C22C2×#12111yescharacteristic
243C22C2×C22⋊Q811yescharacteristic
244C22#52511yescharacteristic
245C22#53511yescharacteristic
246C22#53611yescharacteristic
247C22#53611yescharacteristic
248C22#53711yescharacteristic
249C22#53712yes—
250C22#53812yes—
251C22#53912yes—
252C22#54212yes—
253C22#54212yes—
254C22#54412yes—
255C22#54611yescharacteristic
256C22#54712yes—
257C22D4×Q811yescharacteristic
258C22#55212yes—
259C22#55211yescharacteristic
260C22#55411yescharacteristic
261C22#55612yes—
262C22#55712yes—
263C22#56312yes—
264C22#56412yes—
265C4—24no—
266C4—24no—
267C4—42no—
268C4—42no—
269C4—44no—
270C4—42no—
271C4—44no—
272C4—82no—
273C4—81no—
274C4—81no—
275C4—82no—
276C2#241311yescharacteristic
277C2#241711yescharacteristic
278C2#258111yescharacteristic
279C2#262011yescharacteristic
280C2#262811yescharacteristic
281C2#263611yescharacteristic
282C2#271512yes—
283C2#272612yes—
284C2#276712yes—
285C2#277412yes—
286C2#282211yescharacteristic
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×#4002
C2×#3892
C2×#3872
C2×#3822
#14452
#14442
#14422
#14412