Finite Group Databasebeta

← C2×#11532 #480337

Subgroups — C2×#11532 #480337

Order 512.

1106 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊Q8C211yesmaximal, characteristic
2C2×#1467C212yesmaximal
3#11532C218yesmaximal, direct product factor
4C2×#1325C212yesmaximal
5C2×#1319C212yesmaximal
6C22×C4⋊Q8C411yescharacteristic
7C22×C4×Q8C411yescharacteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#432—22no—
10C4×C4⋊Q8—24no—
11C4×C4⋊Q8C414yes—
12C4×C4⋊Q8C2214yes—
13C2×#391C411yescharacteristic
14C2×#391C2211yescharacteristic
15C2×#389—22no—
16C2×#384C2211yescharacteristic
17C2×C4×C4⋊C4—22no—
18C2×C43C411yescharacteristic
19#1467—24no—
20#1467C2218yes—
21C2×#324—22no—
22C2×#324C2214yes—
23#1325C2218yes—
24#1319C2218yes—
25C23×Q8C2×C411yescharacteristic
26C23×Q8C2×C411yescharacteristic
27C2×C4⋊Q8—22no—
28C2×C4⋊Q8—24no—
29C2×C4⋊Q8—24no—
30C2×C4⋊Q8C2×C414yes—
31C2×C4×Q8—22no—
32C2×C4×Q8—41no—
33C2×C4×Q8—41no—
34C2×C4×Q8—42no—
35C2×C4×Q8—42no—
36C2×C4×Q8—41no—
37C2×C4×Q8—41no—
38C2×C4×Q8C2×C414yes—
39C2×C4×Q8C2×C412yes—
40C2×C4×Q8D414yes—
41C2×C4×Q8C2312yes—
42C22×C4⋊C4—22no—
43C22×C4⋊C4—21no—
44C22×C4⋊C4—22no—
45C22×C4⋊C4C2×C411yescharacteristic
46C22×C4⋊C4D412yes—
47C22×C4⋊C4C2311yescharacteristic
48C22×C42—21no—
49C22×C42—21no—
50C22×C42—21no—
51C22×C42C2×C411yescharacteristic
52C22×C42C2×C411yescharacteristic
53C22×C42C2×C411yescharacteristic
54C22×C42D412yes—
55#432—28no—
56#432—44no—
57C2×C4⋊C8—42no—
58C2×C22⋊C8—24no—
59C2×#97—42no—
60#391—22no—
61#391—22no—
62#391C2×C412yes—
63#391C2×C414yes—
64#391C2312yes—
65#389—28no—
66#389—28no—
67#384—22no—
68#384C2×C412yes—
69#384C2312yes—
70C4×C4⋊C4—28no—
71C4×C4⋊C4—28no—
72C2×#95—22no—
73C2×#95—22no—
74C43—22no—
75C43C2×C414yes—
76#324—28no—
77#324—24no—
78#324C2318yes—
79C22×Q8—21no—
80C22×Q8—22no—
81C22×Q8—22no—
82C22×Q8—22no—
83C22×Q8—41no—
84C22×Q8—41no—
85C22×Q8—42no—
86C22×Q8—41no—
87C22×Q8—41no—
88C22×Q8—42no—
89C22×Q8C22⋊C412yes—
90C22×Q8M1614yes—
91C22×Q8C22×C412yes—
92C22×Q8C22×C412yes—
93C23×C4—21no—
94C23×C4—21no—
95C23×C4—21no—
96C23×C4—21no—
97C23×C4C22⋊C412yes—
98C23×C4C22⋊C411yescharacteristic
99C23×C4C22⋊C411yescharacteristic
100C23×C4C22×C411yescharacteristic
101C23×C4C2×D412yes—
102C22×C8—44no—
103C4⋊Q8—216no—
104C4⋊Q8—28no—
105C4⋊Q8—28no—
106C4×Q8—42no—
107C4×Q8—42no—
108C4×Q8—44no—
109C4×Q8—44no—
110C4×Q8—42no—
111C4×Q8—42no—
112C4×Q8—44no—
113C4×Q8—44no—
114C4×Q8—44no—
115C4×Q8—44no—
116C2×C4⋊C4—216no—
117C2×C4⋊C4—28no—
118C2×C4⋊C4—24no—
119C2×C4⋊C4—24no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—24no—
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⋊C4—48no—
129C2×C4⋊C4—42no—
130C2×C4⋊C4—42no—
131C2×C4⋊C4C22⋊C414yes—
132C2×C4⋊C4C22×C412yes—
133C2×C4⋊C4C22×C411yescharacteristic
134C2×C4⋊C4C2×D414yes—
135C2×C4⋊C4C2×D412yes—
136C2×C4⋊C4C2411yescharacteristic
137C2×C42—28no—
138C2×C42—22no—
139C2×C42—21no—
140C2×C42—21no—
141C2×C42—22no—
142C2×C42—22no—
143C2×C42—24no—
144C2×C42—21no—
145C2×C42—24no—
146C2×C42—22no—
147C2×C42—24no—
148C2×C42—21no—
149C2×C42—24no—
150C2×C42—42no—
151C2×C42—44no—
152C2×C42—42no—
153C2×C42—41no—
154C2×C42—41no—
155C2×C42C22⋊C412yes—
156C2×C42C22⋊C414yes—
157C2×C42M1614yes—
158C2×C42C22×C412yes—
159C2×C42C22×C412yes—
160C2×C42C22×C412yes—
161C2×C42C2×D414yes—
162C4⋊C8—48no—
163C22⋊C8—28no—
164C22⋊C8—44no—
165#97—48no—
166#95—24no—
167#95—28no—
168#95—24no—
169C24C2×C22⋊C411yescharacteristic
170C2×Q8—22no—
171C2×Q8—22no—
172C2×Q8—22no—
173C2×Q8—24no—
174C2×Q8—24no—
175C2×Q8—42no—
176C2×Q8—42no—
177C2×Q8—42no—
178C2×Q8—42no—
179C2×Q8—42no—
180C2×Q8—42no—
181C2×Q8—44no—
182C2×Q8—44no—
183C2×Q8—44no—
184C2×Q8—44no—
185C2×Q8—44no—
186C2×Q8—44no—
187C2×Q8—42no—
188C2×Q8—44no—
189C2×Q8—44no—
190C2×Q8—42no—
191C2×Q8C2×M1614yes—
192C22×C4—24no—
193C22×C4—24no—
194C22×C4—22no—
195C22×C4—24no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—22no—
199C22×C4—24no—
200C22×C4—24no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—24no—
204C22×C4—24no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—24no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—42no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—44no—
220C22×C4—44no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4#9912yes—
224C22×C4#9911yescharacteristic
225C22×C4#9911yescharacteristic
226C22×C4C2×C22⋊C414yes—
227C22×C4C2×C22⋊C411yescharacteristic
228C22×C4C2×C22⋊C412yes—
229C22×C4C2×C22⋊C412yes—
230C22×C4C2×C22⋊C412yes—
231C22×C4C2×M1612yes—
232C22×C4C2×M1612yes—
233C22×C4C23×C411yescharacteristic
234C22×C4C22×D412yes—
235C2×C8—48no—
236C2×C8—88no—
237C4⋊C4—232no—
238C4⋊C4—44no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—44no—
242C4⋊C4—41no—
243C4⋊C4—42no—
244C4⋊C4—48no—
245C4⋊C4—48no—
246C4⋊C4—42no—
247C4⋊C4—48no—
248C42—216no—
249C42—22no—
250C42—24no—
251C42—24no—
252C42—24no—
253C42—24no—
254C42—24no—
255C42—22no—
256C42—22no—
257C42—22no—
258C42—22no—
259C42—42no—
260C42—48no—
261C42—42no—
262C42—44no—
263C42—44no—
264C42C2×M1614yes—
265C23—22no—
266C23—22no—
267C23#40712yes—
268C23C2×#9911yescharacteristic
269C23C2×#9911yescharacteristic
270C23#41312yes—
271C23C22×C22⋊C411yescharacteristic
272Q8—44no—
273Q8—44no—
274Q8—44no—
275Q8—44no—
276Q8—48no—
277Q8—48no—
278C2×C4—24no—
279C2×C4—24no—
280C2×C4—216no—
281C2×C4—24no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—24no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—42no—
302C2×C4—48no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4—42no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—82no—
321C2×C4#35614yes—
322C2×C4#40712yes—
323C2×C4C2×#9912yes—
324C2×C4C2×#9912yes—
325C2×C4C22×M1611yescharacteristic
326C2×C4C22×M1611yescharacteristic
327C8—88no—
328C22—24no—
329C22—24no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22#146512yes—
335C22#146512yes—
336C22#212612yes—
337C22C2×#35612yes—
338C22C2×#40711yescharacteristic
339C22C22×#9911yescharacteristic
340C22C2×#41311yescharacteristic
341C4—28no—
342C4—22no—
343C4—21no—
344C4—21no—
345C4—22no—
346C4—44no—
347C4—42no—
348C4—42no—
349C4—42no—
350C4—44no—
351C4—44no—
352C4—82no—
353C4C2×#35614yes—
354C2—21no—
355C2—21no—
356C2—22no—
357C2#1153214yesdirect product factor
358C2C2×#146511yescharacteristic
359C2C2×#212611yescharacteristic
360C2C22×#35611yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC24C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ 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
3. #11532C2direct (N × H)
357. C2#11532direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊Q82
C2×#14672
#115322
C2×#13252
C2×#13192