Finite Group Databasebeta

← C2×#11524 #480317

Subgroups — C2×#11524 #480317

Order 512.

750 conjugacy classes of subgroups.

The subgroup lattice has 323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2922C211yesmaximal, characteristic
2C2×#2165C212yesmaximal, complemented
3#11524C218yesmaximal, direct product factor
4C2×#1328C212yesmaximal, complemented
5C2×#1321C212yesmaximal
6C2×C4×#41C411yescharacteristic
7#2922—24no—
8#2922C414yes—
9#2922C2214yes—
10C2×#433—22no—
11C2×#431—22no—
12C2×#424C411yescharacteristic
13C2×#424C2211yescharacteristic
14C2×#408C411yescharacteristic
15C2×#408C2211yescharacteristic
16C2×C4×M16C2211yescharacteristic
17C22×C4×C8C411yescharacteristic
18#2165—24no—
19#2165C2218yescomplemented
20C2×#364—22no—
21C2×#349C2214yes—
22C2×#347—22no—
23#1328C2218yescomplemented
24#1321C2218yes—
25C22×#41C2×C411yescharacteristic
26C22×M16C2×C411yescharacteristic
27C22×M16C2311yescharacteristic
28C23×C8C2×C411yescharacteristic
29C23×C8C2×C411yescharacteristic
30C4×#41—22no—
31C4×#41—22no—
32C4×#41—22no—
33C4×#41C2×C414yes—
34C2×C4×Q8—21no—
35C2×C4×D4—21no—
36C2×C4×D4—22no—
37C2×#117—21no—
38C2×#117C2×C411yescharacteristic
39C22×C42—21no—
40C22×C42C2×C411yescharacteristic
41C2×M32—24no—
42#433—28no—
43#433—28no—
44#431—28no—
45#431—28no—
46#424—22no—
47#424—22no—
48#424C2×C414yes—
49#424C2×C412yes—
50#424C2312yes—
51C2×C4⋊C8—22no—
52C2×C4⋊C8—22no—
53#408—22no—
54#408—22no—
55#408C2×C414yes—
56#408C2×C412yes—
57#408C2312yes—
58C2×C22⋊C8—22no—
59C2×C22⋊C8—22no—
60C4×M16C2×C412yes—
61C4×M16D414yes—
62C4×M16C2312yes—
63C2×#97D412yes—
64C2×C4×C8—21no—
65C2×C4×C8—22no—
66C2×C4×C8—21no—
67C2×C4×C8C2×C414yes—
68C2×C4×C8D412yes—
69#364—28no—
70#349—24no—
71#349C2318yes—
72#347—28no—
73C2×#41—21no—
74C2×#41—21no—
75C2×#41—41no—
76C2×#41—41no—
77C2×#41—41no—
78C2×#41—41no—
79C2×#41M1612yes—
80C2×#41C22×C412yes—
81C22×Q8M1611yescharacteristic
82C22×D4—21no—
83C22×D4M1611yescharacteristic
84C23×C4—22no—
85C23×C4—21no—
86C23×C4—21no—
87C23×C4C22×C411yescharacteristic
88C2×M16—41no—
89C2×M16—41no—
90C2×M16—41no—
91C2×M16—41no—
92C2×M16C22⋊C412yes—
93C2×M16C22×C412yes—
94C2×M16C22×C411yescharacteristic
95C2×M16C2×D412yes—
96C2×M16C2411yescharacteristic
97C22×C8—21no—
98C22×C8—21no—
99C22×C8—21no—
100C22×C8—21no—
101C22×C8—41no—
102C22×C8—41no—
103C22×C8—41no—
104C22×C8—41no—
105C22×C8C22⋊C412yes—
106C22×C8C22×C412yes—
107C22×C8C22×C412yes—
108C22×C8C2×D412yes—
109C4×Q8—24no—
110C4×Q8—24no—
111C4×D4—28no—
112C4×D4—24no—
113C4×D4—24no—
114C4×D4—28no—
115#117—24no—
116#117—21no—
117#117—21no—
118#117—24no—
119#117M1612yes—
120#117C22×C412yes—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—21no—
123C2×C22⋊C4—22no—
124C2×C22⋊C4M1612yes—
125C2×C42—22no—
126C2×C42—24no—
127C2×C42—21no—
128C2×C42—21no—
129C2×C42—21no—
130C2×C42—21no—
131C2×C42—24no—
132C2×C42C22⋊C412yes—
133C2×C42C22⋊C411yescharacteristic
134C2×C42C22⋊C411yescharacteristic
135C2×C42C22×C412yes—
136M32—28no—
137M32—44no—
138C2×C16—44no—
139C4⋊C8—24no—
140C4⋊C8—28no—
141C4⋊C8—24no—
142C22⋊C8—24no—
143C22⋊C8—28no—
144C22⋊C8—24no—
145#97C22⋊C414yes—
146#97C2×D414yes—
147C4×C8—24no—
148C4×C8—24no—
149C4×C8C22⋊C414yes—
150C4×C8C2×D414yes—
151C24—21no—
152C24C2×M1611yescharacteristic
153#41—42no—
154#41—42no—
155#41—42no—
156#41—42no—
157#41—42no—
158#41—42no—
159#41—42no—
160#41—42no—
161C2×Q8—21no—
162C2×Q8—41no—
163C2×Q8—41no—
164C2×Q8C2×M1612yes—
165C2×D4—22no—
166C2×D4—22no—
167C2×D4—21no—
168C2×D4—41no—
169C2×D4—41no—
170C2×D4—42no—
171C2×D4—42no—
172C2×D4C2×M1612yes—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—28no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—21no—
182C22×C4—22no—
183C22×C4—21no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—44no—
187C22×C4—48no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4C2×C22⋊C411yescharacteristic
193C22×C4C2×C22⋊C411yescharacteristic
194C22×C4C2×M1611yescharacteristic
195C22×C4C2×M1611yescharacteristic
196C22×C4C2×M1611yescharacteristic
197C22×C4C23×C411yescharacteristic
198M16—42no—
199M16—41no—
200M16—42no—
201M16—42no—
202M16—41no—
203C2×C8—22no—
204C2×C8—22no—
205C2×C8—22no—
206C2×C8—22no—
207C2×C8—22no—
208C2×C8—22no—
209C2×C8—42no—
210C2×C8—42no—
211C2×C8—41no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—42no—
216C2×C8—42no—
217C2×C8C2×C22⋊C412yes—
218C2×C8C2×C22⋊C414yes—
219C2×C8C22×D412yes—
220C4⋊C4—28no—
221C4⋊C4—22no—
222C4⋊C4—22no—
223C22⋊C4—28no—
224C22⋊C4—22no—
225C22⋊C4C2×M1614yes—
226C42—28no—
227C42—22no—
228C42—22no—
229C42—21no—
230C42—22no—
231C42—22no—
232C42—21no—
233C42C2×C22⋊C412yes—
234C42C2×C22⋊C412yes—
235C16—48no—
236C23—21no—
237C23—21no—
238C23—22no—
239C23—42no—
240C23—44no—
241C23—41no—
242C23—41no—
243C23#40711yescharacteristic
244C23#40711yescharacteristic
245C23C22×M1611yescharacteristic
246Q8—42no—
247Q8—42no—
248D4—42no—
249D4—42no—
250D4—44no—
251D4—44no—
252C2×C4—24no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—24no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—44no—
268C2×C4—44no—
269C2×C4—416no—
270C2×C4—44no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4#40711yescharacteristic
279C2×C4#40711yescharacteristic
280C2×C4#41011yescharacteristic
281C2×C4#41011yescharacteristic
282C2×C4#41311yescharacteristic
283C2×C4#41311yescharacteristic
284C2×C4C22×C22⋊C411yescharacteristic
285C2×C4C22×M1611yescharacteristic
286C8—22no—
287C8—22no—
288C8—24no—
289C8—42no—
290C8—42no—
291C22—22no—
292C22—21no—
293C22—21no—
294C22—41no—
295C22—41no—
296C22—42no—
297C22—44no—
298C22—42no—
299C22—42no—
300C22—82no—
301C22—82no—
302C22#146411yescharacteristic
303C22#146411yescharacteristic
304C22C2×#40711yescharacteristic
305C4—24no—
306C4—21no—
307C4—21no—
308C4—44no—
309C4—42no—
310C4—42no—
311C4#146411yescharacteristic
312C4#146411yescharacteristic
313C4C2×#41011yescharacteristic
314C4C2×#41311yescharacteristic
315C2—21no—
316C2—21no—
317C2—41no—
318C2—41no—
319C2—82no—
320C2#1152412yesdirect product factor
321C2C2×#146411yescharacteristic
subgroupG/H
centerC2×C4#410
commutatorC22×C4C23×C4
Frattini, cosocleC2×M16C24
socleC22#1464
prime radicalC22×#41C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×M16 ◁ G
LECSG ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2165C2semidirect
3. #11524C2direct (N × H)
4. C2×#1328C2semidirect
19. #2165C22semidirect
23. #1328C22semidirect
320. C2#11524direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29222
C2×#21652
#115242
C2×#13282
C2×#13212