Finite Group Databasebeta

← C2×#11518 #480294

Subgroups — C2×#11518 #480294

Order 512.

1230 conjugacy classes of subgroups; only the 234 normal subgroups are shown.

normal subgroups only

This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 234 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
1C2×#2296C211yesmaximal, characteristic
2C2×#1464C212yesmaximal
3#11518C218yesmaximal, direct product factor
4C2×#1326C214yesmaximal
5C22×#117C411yescharacteristic
6C22×#117C2211yescharacteristic
7C23×C42C411yescharacteristic
8C2×#432—22no—
9#2296—24no—
10#2296C414yes—
11#2296C2214yes—
12C2×#389—22no—
13C2×#385C412yes—
14C2×#385C2212yes—
15C2×C4×C4⋊C4—22no—
16#1464—24no—
17#1464C2218yes—
18C2×#324—22no—
19C2×#323C2214yes—
20#1326C22116yes—
21C24×C4C2×C411yescharacteristic
22C24×C4C2×C412yes—
23C2×#117—22no—
24C2×#117—28no—
25C2×#117—42no—
26C2×#117—42no—
27C2×#117C2×C414yes—
28C2×#117C2×C412yes—
29C2×#117D414yes—
30C2×#117C2312yes—
31C22×C4⋊C4—21no—
32C22×C4⋊C4—22no—
33C22×C4⋊C4—22no—
34C22×C4⋊C4D412yes—
35C22×C22⋊C4C2×C412yes—
36C22×C22⋊C4C2×C411yescharacteristic
37C22×C22⋊C4C2311yescharacteristic
38C22×C42—21no—
39C22×C42—21no—
40C22×C42—22no—
41C22×C42—21no—
42C22×C42—42no—
43C22×C42—42no—
44C22×C42C2×C414yes—
45C22×C42D412yes—
46#432—28no—
47#432—44no—
48C2×C4⋊C8—42no—
49C2×C22⋊C8—24no—
50C2×#97—42no—
51#389—28no—
52#389—28no—
53#385—24no—
54#385—22no—
55#385—22no—
56#385C2×C418yes—
57#385C2×C414yes—
58#385C2314yes—
59C4×C4⋊C4—28no—
60C4×C4⋊C4—28no—
61C2×#95—22no—
62C2×#95—22no—
63#324—28no—
64#323—24no—
65#323C2318yes—
66C25C22×C411yescharacteristic
67C23×C4—24no—
68C23×C4—22no—
69C23×C4—22no—
70C23×C4—24no—
71C23×C4—22no—
72C23×C4—22no—
73C23×C4—22no—
74C23×C4—48no—
75C23×C4—42no—
76C23×C4—42no—
77C23×C4C22⋊C412yes—
78C23×C4C22⋊C411yescharacteristic
79C23×C4C22⋊C412yes—
80C23×C4C22⋊C411yescharacteristic
81C23×C4C22×C412yes—
82C23×C4C22×C414yes—
83C23×C4C2×D412yes—
84C22×C8—44no—
85#117—216no—
86#117—216no—
87#117—44no—
88#117—44no—
89#117—44no—
90#117—44no—
91C2×C4⋊C4—28no—
92C2×C4⋊C4—24no—
93C2×C4⋊C4—24no—
94C2×C4⋊C4—28no—
95C2×C4⋊C4—24no—
96C2×C4⋊C4—42no—
97C2×C4⋊C4—42no—
98C2×C4⋊C4—48no—
99C2×C4⋊C4—48no—
100C2×C4⋊C4C22⋊C414yes—
101C2×C4⋊C4C2×D414yes—
102C2×C22⋊C4—22no—
103C2×C22⋊C4—24no—
104C2×C22⋊C4—41no—
105C2×C22⋊C4—41no—
106C2×C22⋊C4—41no—
107C2×C22⋊C4—41no—
108C2×C22⋊C4C22⋊C412yes—
109C2×C22⋊C4M1618yes—
110C2×C22⋊C4C22×C414yes—
111C2×C22⋊C4C22×C412yes—
112C2×C22⋊C4C22×C411yescharacteristic
113C2×C22⋊C4C2×D412yes—
114C2×C22⋊C4C2411yescharacteristic
115C2×C42—28no—
116C2×C42—22no—
117C2×C42—22no—
118C2×C42—24no—
119C2×C42—24no—
120C2×C42—24no—
121C2×C42—24no—
122C2×C42—42no—
123C2×C42—42no—
124C2×C42—48no—
125C2×C42—42no—
126C2×C42—42no—
127C2×C42—48no—
128C2×C42C22⋊C414yes—
129C2×C42C2×D414yes—
130C4⋊C8—48no—
131C22⋊C8—28no—
132C22⋊C8—44no—
133#97—48no—
134#95—24no—
135#95—28no—
136#95—24no—
137C24—21no—
138C24—21no—
139C24—22no—
140C24—44no—
141C24C2×C22⋊C411yescharacteristic
142C24C2×C22⋊C411yescharacteristic
143C24C2×M1614yes—
144C24C23×C411yescharacteristic
145C22×C4—216no—
146C22×C4—216no—
147C22×C4—24no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—24no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—22no—
154C22×C4—24no—
155C22×C4—24no—
156C22×C4—24no—
157C22×C4—24no—
158C22×C4—28no—
159C22×C4—24no—
160C22×C4—24no—
161C22×C4—28no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—48no—
167C22×C4—48no—
168C22×C4—44no—
169C22×C4—44no—
170C22×C4—44no—
171C22×C4—44no—
172C22×C4—416no—
173C22×C4—48no—
174C22×C4—42no—
175C22×C4—42no—
176C22×C4—44no—
177C22×C4—48no—
178C22×C4—44no—
179C22×C4—44no—
180C22×C4#9912yes—
181C22×C4#9912yes—
182C22×C4#10114yes—
183C22×C4C2×C22⋊C412yes—
184C22×C4C2×C22⋊C412yes—
185C22×C4C2×C22⋊C412yes—
186C22×C4C2×C22⋊C414yes—
187C22×C4C22×D412yes—
188C2×C8—48no—
189C2×C8—88no—
190C4⋊C4—216no—
191C4⋊C4—44no—
192C4⋊C4—44no—
193C4⋊C4—416no—
194C4⋊C4—48no—
195C4⋊C4—48no—
196C22⋊C4—24no—
197C22⋊C4—28no—
198C22⋊C4—42no—
199C22⋊C4—42no—
200C22⋊C4—41no—
201C22⋊C4—42no—
202C22⋊C4—41no—
203C22⋊C4C2×M1618yes—
204C42—216no—
205C42—24no—
206C42—24no—
207C42—24no—
208C42—24no—
209C42—48no—
210C42—48no—
211C23—24no—
212C23—21no—
213C23—21no—
214C23—21no—
215C23—21no—
216C23—24no—
217C23—24no—
218C23—42no—
219C23—42no—
220C23—48no—
221C23—44no—
222C23—48no—
223C23—44no—
224C23#40712yes—
225C23#40712yes—
226C23C2×#9911yescharacteristic
227C23C2×#9911yescharacteristic
228C23C2×#10112yes—
229C23C22×C22⋊C411yescharacteristic
230C23C22×M1612yes—
231C2×C4—216no—
232C2×C4—216no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—24no—
238C2×C4—24no—
239C2×C4—24no—
240C2×C4—24no—
241C2×C4—28no—
242C2×C4—28no—
243C2×C4—22no—
244C2×C4—24no—
245C2×C4—22no—
246C2×C4—44no—
247C2×C4—44no—
248C2×C4—416no—
249C2×C4—44no—
250C2×C4—48no—
251C2×C4—416no—
252C2×C4—48no—
253C2×C4—44no—
254C2×C4—44no—
255C2×C4—44no—
256C2×C4—48no—
257C2×C4—44no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—48no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4C2×#9914yes—
264C2×C4C2×#10114yes—
265C8—88no—
266C22—22no—
267C22—22no—
268C22—24no—
269C22—24no—
270C22—22no—
271C22—22no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—48no—
277C22—42no—
278C22—42no—
279C22—48no—
280C22#146312yes—
281C22#146312yes—
282C22#212014yes—
283C22C2×#40711yescharacteristic
284C22C22×#9911yescharacteristic
285C22C22×#10111yescharacteristic
286C4—24no—
287C4—24no—
288C4—48no—
289C4—42no—
290C4—48no—
291C4—42no—
292C4—44no—
293C2—21no—
294C2—21no—
295C2—22no—
296C2—42no—
297C2—42no—
298C2#1151814yesdirect product factor
299C2C2×#146311yescharacteristic
300C2C2×#212012yes—
subgroupG/H
center, socleC23C2×#99
commutatorC24C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC25C22×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#117 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #11518C2direct (N × H)
298. C2#11518direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#22962
C2×#14642
#115182
C2×#13262