Finite Group Databasebeta

← #16902

Subgroups — #16902

Order 256.

653 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 653 conjugacy classes of subgroups — too many to draw. Only its 159 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#1445C212yesmaximal, complemented
2#1445C212yesmaximal, complemented
3#1443C212yesmaximal, complemented
4#1441C212yesmaximal, complemented
5#1439C212yesmaximal
6#1439C212yesmaximal
7C22⋊#95C211yesmaximal, characteristic
8C22⋊#95C211yesmaximal, characteristic
9C22⋊#95C211yesmaximal, characteristic
10C24×C4C2211yescharacteristic
11C22×C4⋊C4C2212yes—
12C22×C4⋊C4C2212yes—
13C22×C22⋊C4C2212yes—
14C22×C22⋊C4C2212yes—
15C22×C22⋊C4C2211yescharacteristic
16C22×C22⋊C4C2211yescharacteristic
17C2×#95C2212yes—
18C2×#95C2211yescharacteristic
19C2×#95C2212yes—
20C2×#95C2212yes—
21C2×#95C2211yescharacteristic
22C2×#95C2212yes—
23C2×#95C2211yescharacteristic
24C2×#95C2212yes—
25C2×#95C2211yescharacteristic
26C2×#95C2212yes—
27C2×#95C2212yes—
28C2×#95C2212yes—
29C2×#95C2212yes—
30C2×#95C2212yes—
31C25C2311yescharacteristic
32C23×C4—41no—
33C23×C4—41no—
34C23×C4—42no—
35C23×C4—42no—
36C23×C4Q814yes—
37C23×C4C2312yes—
38C23×C4C2312yes—
39C23×C4C2312yes—
40C23×C4C2312yes—
41C23×C4C2311yescharacteristic
42C23×C4C2311yescharacteristic
43C23×C4C2312yes—
44C23×C4C2312yes—
45C2×C4⋊C4—24no—
46C2×C4⋊C4—24no—
47C2×C4⋊C4—24no—
48C2×C4⋊C4—42no—
49C2×C4⋊C4—42no—
50C2×C4⋊C4—42no—
51C2×C22⋊C4—24no—
52C2×C22⋊C4—24no—
53C2×C22⋊C4—22no—
54C2×C22⋊C4—22no—
55C2×C22⋊C4—24no—
56C2×C22⋊C4—24no—
57C2×C22⋊C4—42no—
58C2×C22⋊C4—42no—
59C2×C22⋊C4—41no—
60C2×C22⋊C4—41no—
61C2×C22⋊C4—41no—
62C2×C22⋊C4—41no—
63#95—24no—
64#95—42no—
65#95—42no—
66#95—42no—
67#95—41no—
68#95—41no—
69#95—42no—
70#95—42no—
71#95—41no—
72#95—41no—
73#95—42no—
74#95—42no—
75#95—42no—
76#95—42no—
77C24—22no—
78C24—22no—
79C24—21no—
80C24—21no—
81C24—21no—
82C24—22no—
83C24—22no—
84C24—21no—
85C24C2×Q812yes—
86C24#4112yes—
87C24#4112yes—
88C24C2411yescharacteristic
89C22×C4—22no—
90C22×C4—22no—
91C22×C4—22no—
92C22×C4—22no—
93C22×C4—22no—
94C22×C4—22no—
95C22×C4—22no—
96C22×C4—22no—
97C22×C4—22no—
98C22×C4—22no—
99C22×C4—22no—
100C22×C4—21no—
101C22×C4—21no—
102C22×C4—21no—
103C22×C4—21no—
104C22×C4—22no—
105C22×C4—22no—
106C22×C4—22no—
107C22×C4—22no—
108C22×C4—22no—
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—22no—
121C22×C4—22no—
122C22×C4—22no—
123C22×C4—22no—
124C22×C4—22no—
125C22×C4—22no—
126C22×C4—22no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—22no—
136C22×C4—22no—
137C22×C4—44no—
138C22×C4—44no—
139C22×C4—44no—
140C22×C4—48no—
141C22×C4—48no—
142C22×C4C2×Q812yes—
143C22×C4C2×Q812yes—
144C22×C4#4114yes—
145C22×C4#4114yes—
146C4⋊C4—48no—
147C4⋊C4—48no—
148C22⋊C4—48no—
149C22⋊C4—48no—
150C22⋊C4—44no—
151C22⋊C4—44no—
152C23—22no—
153C23—22no—
154C23—22no—
155C23—22no—
156C23—22no—
157C23—22no—
158C23—22no—
159C23—22no—
160C23—22no—
161C23—22no—
162C23—24no—
163C23—24no—
164C23—24no—
165C23—24no—
166C23—42no—
167C23—42no—
168C23—42no—
169C23—42no—
170C23—42no—
171C23—42no—
172C23—42no—
173C23—42no—
174C23#12514yes—
175C23C22×Q811yescharacteristic
176C23C2×#4111yescharacteristic
177C23C2×#4111yescharacteristic
178C23C2×#4112yes—
179C23C2×#4112yes—
180C23H(5,𝔽2)11yescharacteristic
181C23H(5,𝔽2)11yescharacteristic
182C23H(5,𝔽2)11yescharacteristic
183C23H(5,𝔽2)12yes—
184C23H(5,𝔽2)12yes—
185C232−1+411yescharacteristic
186C2×C4—24no—
187C2×C4—24no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—24no—
198C2×C4—416no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
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—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—
239C22—24no—
240C22—24no—
241C22—24no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22—44no—
247C22—44no—
248C22—44no—
249C22—44no—
250C22C2×#12511yescharacteristic
251C22#53311yescharacteristic
252C22#53311yescharacteristic
253C22#53811yescharacteristic
254C22#53811yescharacteristic
255C22#53812yes—
256C22#53911yescharacteristic
257C22#53911yescharacteristic
258C22#53912yes—
259C22#54012yes—
260C22#54212yes—
261C22#54311yescharacteristic
262C22#54311yescharacteristic
263C22#54311yescharacteristic
264C22#54411yescharacteristic
265C22#55112yes—
266C22#55112yes—
267C22#55112yes—
268C22#55312yes—
269C22#55312yes—
270C22#55912yes—
271C22#56012yes—
272C22#56012yes—
273C4—42no—
274C4—42no—
275C4—44no—
276C4—44no—
277C4—82no—
278C4—82no—
279C4—82no—
280C4—82no—
281C2—44no—
282C2#256911yescharacteristic
283C2#256911yescharacteristic
284C2#260711yescharacteristic
285C2#264611yescharacteristic
286C2#266511yescharacteristic
287C2#266711yescharacteristic
288C2#274612yes—
289C2#274912yes—
290C2#279612yes—
291C2#279712yes—
292C2#284211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C24
prime radicalC25C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #1445C2semidirect
2. #1445C2semidirect
3. #1443C2semidirect
4. #1441C2semidirect

Maximal subgroups

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

subgroupindex
#14452
#14432
#14412
#14392
C22⋊#952