Finite Group Databasebeta

← C2×#11476 #480102

Subgroups — C2×#11476 #480102

Order 512.

1258 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#124C211yesmaximal, characteristic
2C2×#1461C212yesmaximal, complemented
3#11476C218yesmaximal, direct product factor
4C2×#1324C212yesmaximal, complemented
5C2×#1318C212yesmaximal
6C22×#124C411yescharacteristic
7C22×C4×Q8C2211yescharacteristic
8C22×C4×D4C411yescharacteristic
9C2×#431—22no—
10C4×#124—24no—
11C4×#124C414yes—
12C4×#124C2214yes—
13C2×#391C411yescharacteristic
14C2×#390C2211yescharacteristic
15C2×#388—22no—
16C2×#382C2211yescharacteristic
17C2×C4×C22⋊C4—22no—
18C2×C43C411yescharacteristic
19#1461—24no—
20#1461C2218yescomplemented
21C2×#324—22no—
22C2×#324C2214yes—
23#1324C2218yescomplemented
24#1318C2218yes—
25C23×Q8C2×C411yescharacteristic
26C23×D4C2×C411yescharacteristic
27C24×C4—21no—
28C2×#124—22no—
29C2×#124—24no—
30C2×#124C818yescomplemented
31C2×#124C2×C414yes—
32C2×C4×Q8—41no—
33C2×C4×Q8—42no—
34C2×C4×Q8—41no—
35C2×C4×Q8C2×C412yes—
36C2×C4×Q8D414yes—
37C2×C4×Q8C2312yes—
38C2×C4×D4—22no—
39C2×C4×D4—41no—
40C2×C4×D4—42no—
41C2×C4×D4—41no—
42C2×C4×D4C2×C414yes—
43C22×C4⋊C4C2×C411yescharacteristic
44C22×C4⋊C4D412yes—
45C22×C4⋊C4C2311yescharacteristic
46C22×C22⋊C4—22no—
47C22×C22⋊C4—21no—
48C22×C22⋊C4—22no—
49C22×C42—21no—
50C22×C42—21no—
51C22×C42C2×C411yescharacteristic
52C22×C42C2×C411yescharacteristic
53C22×C42C2×C411yescharacteristic
54C22×C42D412yes—
55#431—28no—
56#431—44no—
57C2×C4⋊C8—42no—
58C2×C22⋊C8—24no—
59C2×C4×C8—42no—
60#391—22no—
61#391C2×C414yes—
62#390—22no—
63#390C2×C412yes—
64#390C2312yes—
65#388—28no—
66#388—28no—
67#382—22no—
68#382C2×C412yes—
69#382C2312yes—
70C4×C22⋊C4—28no—
71C4×C22⋊C4—28no—
72C2×#95—22no—
73C2×#95—22no—
74C43—22no—
75C43C2×C414yes—
76#324—28no—
77#324—24no—
78#324C2318yes—
79C25—21no—
80C22×Q8—41no—
81C22×Q8—41no—
82C22×Q8—42no—
83C22×Q8C22⋊C412yes—
84C22×Q8C2×C814yes—
85C22×Q8M1614yes—
86C22×Q8C22×C412yes—
87C22×D4—21no—
88C22×D4—22no—
89C22×D4—41no—
90C22×D4—41no—
91C22×D4—42no—
92C22×D4C2×C814yes—
93C22×D4C22×C412yes—
94C23×C4—21no—
95C23×C4—21no—
96C23×C4—21no—
97C23×C4—24no—
98C23×C4—48no—
99C23×C4—42no—
100C23×C4—41no—
101C23×C4—41no—
102C23×C4C22⋊C412yes—
103C23×C4C22⋊C411yescharacteristic
104C23×C4C22⋊C411yescharacteristic
105C23×C4C22×C411yescharacteristic
106C23×C4C2×D412yes—
107C22×C8—44no—
108#124—216no—
109#124—28no—
110#124C2×C8116yescomplemented
111C4×Q8—42no—
112C4×Q8—42no—
113C4×Q8—44no—
114C4×Q8—44no—
115C4×Q8—42no—
116C4×Q8—42no—
117C4×D4—44no—
118C4×D4—44no—
119C4×D4—44no—
120C4×D4—44no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—42no—
123C2×C4⋊C4—42no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4—41no—
128C2×C4⋊C4C22⋊C414yes—
129C2×C4⋊C4C22×C412yes—
130C2×C4⋊C4C22×C411yescharacteristic
131C2×C4⋊C4C2×D414yes—
132C2×C4⋊C4C2×D412yes—
133C2×C4⋊C4C2411yescharacteristic
134C2×C22⋊C4—216no—
135C2×C22⋊C4—28no—
136C2×C22⋊C4—24no—
137C2×C22⋊C4—24no—
138C2×C22⋊C4—24no—
139C2×C22⋊C4—48no—
140C2×C22⋊C4—42no—
141C2×C22⋊C4—42no—
142C2×C42—21no—
143C2×C42—22no—
144C2×C42—22no—
145C2×C42—24no—
146C2×C42—21no—
147C2×C42—22no—
148C2×C42—21no—
149C2×C42—22no—
150C2×C42—21no—
151C2×C42—24no—
152C2×C42—24no—
153C2×C42—42no—
154C2×C42—44no—
155C2×C42—44no—
156C2×C42C22⋊C412yes—
157C2×C42C22⋊C414yes—
158C2×C42C2×C814yes—
159C2×C42C22×C412yes—
160C2×C42C22×C412yes—
161C2×C42C22×C412yes—
162C2×C42C2×D414yes—
163C4⋊C8—48no—
164C22⋊C8—28no—
165C22⋊C8—44no—
166C4×C8—48no—
167#95—24no—
168#95—28no—
169#95—24no—
170C24—22no—
171C24—24no—
172C24—44no—
173C24—44no—
174C24—41no—
175C24—41no—
176C24—42no—
177C24C2×C22⋊C411yescharacteristic
178C2×Q8—42no—
179C2×Q8—42no—
180C2×Q8—42no—
181C2×Q8—44no—
182C2×Q8—44no—
183C2×Q8—44no—
184C2×Q8—44no—
185C2×Q8—42no—
186C2×Q8C22⋊C818yes—
187C2×Q8C22×C814yes—
188C2×Q8C2×M1614yes—
189C2×D4—22no—
190C2×D4—24no—
191C2×D4—42no—
192C2×D4—44no—
193C2×D4—44no—
194C2×D4—42no—
195C2×D4—42no—
196C2×D4—42no—
197C2×D4—44no—
198C2×D4—44no—
199C2×D4C22×C814yes—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—24no—
206C22×C4—24no—
207C22×C4—24no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—24no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—416no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—44no—
223C22×C4—44no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—44no—
227C22×C4—44no—
228C22×C4—84no—
229C22×C4—88no—
230C22×C4—84no—
231C22×C4C22⋊C818yes—
232C22×C4#9911yescharacteristic
233C22×C4#9912yes—
234C22×C4#9911yescharacteristic
235C22×C4C2×C22⋊C414yes—
236C22×C4C2×C22⋊C411yescharacteristic
237C22×C4C2×C22⋊C412yes—
238C22×C4C2×C22⋊C412yes—
239C22×C4C2×C22⋊C412yes—
240C22×C4C22×C812yes—
241C22×C4C2×M1612yes—
242C22×C4C23×C411yescharacteristic
243C22×C4C22×D412yes—
244C2×C8—48no—
245C2×C8—88no—
246C4⋊C4—44no—
247C4⋊C4—41no—
248C4⋊C4—42no—
249C4⋊C4—44no—
250C4⋊C4—41no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C22⋊C4—232no—
254C22⋊C4—48no—
255C22⋊C4—48no—
256C22⋊C4—48no—
257C42—22no—
258C42—24no—
259C42—24no—
260C42—24no—
261C42—22no—
262C42—22no—
263C42—24no—
264C42—24no—
265C42—22no—
266C42—22no—
267C42—42no—
268C42—42no—
269C42—48no—
270C42—48no—
271C42C22×C814yes—
272C23—22no—
273C23—22no—
274C23—24no—
275C23—44no—
276C23—44no—
277C23—416no—
278C23—42no—
279C23—42no—
280C23—44no—
281C23—44no—
282C23—82no—
283C23—82no—
284C23—88no—
285C23—82no—
286C23—82no—
287C23C2×C22⋊C812yes—
288C23C2×#9911yescharacteristic
289C23C2×#9911yescharacteristic
290C23#41312yes—
291C23C22×C22⋊C411yescharacteristic
292Q8—48no—
293Q8—44no—
294Q8—44no—
295D4—44no—
296D4—44no—
297D4—48no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—24no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—24no—
304C2×C4—22no—
305C2×C4—28no—
306C2×C4—28no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—48no—
322C2×C4—48no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—44no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—44no—
331C2×C4—42no—
332C2×C4—88no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—88no—
337C2×C4#35514yes—
338C2×C4C2×C22⋊C812yes—
339C2×C4C2×C22⋊C818yes—
340C2×C4C2×#9912yes—
341C2×C4C2×#9912yes—
342C2×C4C23×C811yescharacteristic
343C2×C4C22×M1611yescharacteristic
344C8—88no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—24no—
350C22—24no—
351C22—48no—
352C22—44no—
353C22—84no—
354C22—88no—
355C22—82no—
356C22—82no—
357C22—88no—
358C22#145912yes—
359C22#145912yes—
360C22#212612yes—
361C22C2×#35512yes—
362C22C22×C22⋊C811yescharacteristic
363C22C22×#9911yescharacteristic
364C22C2×#41311yescharacteristic
365C4—22no—
366C4—21no—
367C4—21no—
368C4—22no—
369C4—28no—
370C4—44no—
371C4—44no—
372C4—42no—
373C4—42no—
374C4—42no—
375C4—82no—
376C4C2×#35514yes—
377C2—21no—
378C2—21no—
379C2—22no—
380C2—84no—
381C2#1147614yesdirect product factor
382C2C2×#145911yescharacteristic
383C2C2×#212611yescharacteristic
384C2C22×#35511yescharacteristic
subgroupG/H
centerC22×C4#99
commutatorC2×C4C23×C8
Frattini, cosocleC2×C4⋊C4C24
socleC23C2×#99
prime radicalC23×D4C2×C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1461C2semidirect
3. #11476C2direct (N × H)
4. C2×#1324C2semidirect
20. #1461C22semidirect
23. #1324C22semidirect
30. C2×#124C8semidirect
110. #124C2×C8semidirect
381. C2#11476direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#1242
C2×#14612
#114762
C2×#13242
C2×#13182