Finite Group Databasebeta

← C2×#11522 #480313

Subgroups — C2×#11522 #480313

Order 512.

744 conjugacy classes of subgroups.

The subgroup lattice has 331 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2921C211yesmaximal, characteristic
2C2×#2165C212yesmaximal, complemented
3#11522C218yesmaximal, direct product factor
4C2×#1327C212yesmaximal, complemented
5C2×#1320C212yesmaximal
6C22×#117C411yescharacteristic
7#2921—24no—
8#2921C414yes—
9#2921C2214yes—
10C2×#433—22no—
11C2×#433—22no—
12C2×#423C411yescharacteristic
13C2×#423C2211yescharacteristic
14C2×#407C411yescharacteristic
15C2×#407C2211yescharacteristic
16C2×C4×M16C411yescharacteristic
17C2×C4×M16C2211yescharacteristic
18#2165—24no—
19#2165C2218yescomplemented
20C2×#364—22no—
21C2×#349C2214yes—
22C2×#347—22no—
23#1327C2218yescomplemented
24#1320C2218yes—
25C24×C4C2×C411yescharacteristic
26C22×M16C2×C411yescharacteristic
27C22×M16C2×C411yescharacteristic
28C22×M16C2×C411yescharacteristic
29C22×M16C2311yescharacteristic
30C2×#117—22no—
31C2×#117—21no—
32C2×#117—22no—
33C2×#117—21no—
34C2×#117—22no—
35C2×#117—22no—
36C2×#117C2×C414yes—
37C22×C4⋊C4—21no—
38C22×C22⋊C4—21no—
39C22×C42C2×C411yescharacteristic
40C22×C42C2×C411yescharacteristic
41C2×M32—24no—
42#433—28no—
43#433—28no—
44#433—28no—
45#433—28no—
46#423—22no—
47#423—22no—
48#423C2×C414yes—
49#423C2×C412yes—
50#423C2312yes—
51C2×C4⋊C8—22no—
52C2×C4⋊C8—22no—
53#407—22no—
54#407—22no—
55#407C2×C414yes—
56#407C2×C412yes—
57#407C2312yes—
58C2×C22⋊C8—22no—
59C2×C22⋊C8—22no—
60C4×M16—22no—
61C4×M16C2×C414yes—
62C4×M16C2×C412yes—
63C4×M16D414yes—
64C4×M16C2312yes—
65C2×#97—21no—
66C2×#97D412yes—
67C2×C4×C8—21no—
68C2×C4×C8D412yes—
69#364—28no—
70#349—24no—
71#349C2318yes—
72#347—28no—
73C25M1611yescharacteristic
74C23×C4—21no—
75C23×C4—21no—
76C23×C4—21no—
77C23×C4—21no—
78C23×C4—21no—
79C23×C4—21no—
80C23×C4—41no—
81C23×C4—41no—
82C23×C4—41no—
83C23×C4—41no—
84C23×C4M1611yescharacteristic
85C23×C4M1612yes—
86C23×C4C22×C411yescharacteristic
87C23×C4C22×C412yes—
88C2×M16—21no—
89C2×M16—21no—
90C2×M16—41no—
91C2×M16—41no—
92C2×M16—41no—
93C2×M16—41no—
94C2×M16—41no—
95C2×M16—41no—
96C2×M16—41no—
97C2×M16—41no—
98C2×M16C22⋊C412yes—
99C2×M16C22×C412yes—
100C2×M16C22×C412yes—
101C2×M16C22×C412yes—
102C2×M16C22×C411yescharacteristic
103C2×M16C2×D412yes—
104C2×M16C2411yescharacteristic
105C22×C8—21no—
106C22×C8—21no—
107C22×C8C22⋊C412yes—
108C22×C8C2×D412yes—
109#117—24no—
110#117—28no—
111#117—24no—
112#117—24no—
113#117—24no—
114#117—28no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—24no—
118C2×C4⋊C4—24no—
119C2×C22⋊C4—22no—
120C2×C22⋊C4—22no—
121C2×C22⋊C4—24no—
122C2×C22⋊C4—24no—
123C2×C42—21no—
124C2×C42—21no—
125C2×C42—21no—
126C2×C42—21no—
127C2×C42—21no—
128C2×C42—21no—
129C2×C42C22⋊C411yescharacteristic
130C2×C42C22⋊C412yes—
131C2×C42C22⋊C411yescharacteristic
132C2×C42M1612yes—
133C2×C42M1612yes—
134C2×C42C22×C412yes—
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#97—24no—
146#97C22⋊C414yes—
147#97C2×D414yes—
148C4×C8—24no—
149C4×C8C22⋊C414yes—
150C4×C8C2×D414yes—
151C24—21no—
152C24—21no—
153C24—41no—
154C24—41no—
155C24—82no—
156C24C2×M1611yescharacteristic
157C24C2×M1612yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—22no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—42no—
176C22×C4—42no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4—42no—
180C22×C4—42no—
181C22×C4—42no—
182C22×C4—42no—
183C22×C4—42no—
184C22×C4—42no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—82no—
192C22×C4—82no—
193C22×C4C2×C22⋊C411yescharacteristic
194C22×C4C2×C22⋊C411yescharacteristic
195C22×C4C2×M1611yescharacteristic
196C22×C4C2×M1611yescharacteristic
197C22×C4C2×M1611yescharacteristic
198C22×C4C2×M1612yes—
199C22×C4C23×C411yescharacteristic
200M16—42no—
201M16—41no—
202M16—42no—
203M16—42no—
204M16—41no—
205M16—42no—
206M16—42no—
207M16—42no—
208M16—42no—
209C2×C8—22no—
210C2×C8—22no—
211C2×C8—22no—
212C2×C8—22no—
213C2×C8—22no—
214C2×C8—22no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8C2×C22⋊C412yes—
220C2×C8C2×C22⋊C414yes—
221C2×C8C22×D412yes—
222C4⋊C4—28no—
223C4⋊C4—28no—
224C22⋊C4—28no—
225C22⋊C4—28no—
226C42—22no—
227C42—22no—
228C42—22no—
229C42—21no—
230C42—21no—
231C42—22no—
232C42—22no—
233C42C2×C22⋊C412yes—
234C42C2×C22⋊C412yes—
235C42C2×M1614yes—
236C16—48no—
237C23—21no—
238C23—21no—
239C23—22no—
240C23—42no—
241C23—42no—
242C23—44no—
243C23—42no—
244C23—41no—
245C23—41no—
246C23—82no—
247C23—82no—
248C23—84no—
249C23—84no—
250C23#40711yescharacteristic
251C23#40711yescharacteristic
252C23C22×M1611yescharacteristic
253C2×C4—21no—
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—22no—
264C2×C4—22no—
265C2×C4—24no—
266C2×C4—22no—
267C2×C4—44no—
268C2×C4—44no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—44no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—82no—
281C2×C4—82no—
282C2×C4—82no—
283C2×C4—82no—
284C2×C4#40711yescharacteristic
285C2×C4#40711yescharacteristic
286C2×C4#41011yescharacteristic
287C2×C4#41011yescharacteristic
288C2×C4#41311yescharacteristic
289C2×C4#41311yescharacteristic
290C2×C4C22×C22⋊C411yescharacteristic
291C2×C4C22×M1611yescharacteristic
292C8—22no—
293C8—22no—
294C8—24no—
295C8—42no—
296C8—42no—
297C22—22no—
298C22—21no—
299C22—21no—
300C22—41no—
301C22—41no—
302C22—42no—
303C22—44no—
304C22—42no—
305C22—42no—
306C22—82no—
307C22—84no—
308C22—84no—
309C22—82no—
310C22#146411yescharacteristic
311C22#146411yescharacteristic
312C22C2×#40711yescharacteristic
313C4—21no—
314C4—21no—
315C4—42no—
316C4—42no—
317C4—44no—
318C4—42no—
319C4#146411yescharacteristic
320C4#146411yescharacteristic
321C4C2×#41011yescharacteristic
322C4C2×#41311yescharacteristic
323C2—21no—
324C2—21no—
325C2—41no—
326C2—41no—
327C2—82no—
328C2#1152212yesdirect product factor
329C2C2×#146411yescharacteristic
subgroupG/H
centerC2×C4#410
commutatorC22×C4C23×C4
Frattini, cosocleC2×M16C24
socleC22#1464
prime radicalC25M16
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. #11522C2direct (N × H)
4. C2×#1327C2semidirect
19. #2165C22semidirect
23. #1327C22semidirect
328. C2#11522direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29212
C2×#21652
#115222
C2×#13272
C2×#13202