Finite Group Databasebeta

← C2×#11568 #480519

Subgroups — C2×#11568 #480519

Order 512.

1056 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2546C211yesmaximal, characteristic
2C2×#1467C211yesmaximal, characteristic
3C2×#1461C211yesmaximal, characteristic
4#11568C218yesmaximal, direct product factor
5C2×#1319C214yesmaximal
6C22×C4⋊Q8C411yescharacteristic
7C22×C4⋊Q8C412yes—
8C22×C4×Q8C2211yescharacteristic
9C2×#432—21no—
10C2×#431—21no—
11#2546—22no—
12#2546—22no—
13#2546C414yes—
14#2546C2214yes—
15C2×#398—21no—
16C2×#398—21no—
17C2×#391C2212yes—
18C2×#389—21no—
19C2×#389—21no—
20C2×C4×C4⋊C4C411yescharacteristic
21#1467—22no—
22#1467C2214yes—
23#1461—22no—
24#1461C2214yes—
25C2×#324—21no—
26C2×#324—21no—
27C2×#324C2212yes—
28C2×#324C2212yes—
29#1319C22116yes—
30C23×Q8C2×C412yes—
31C23×Q8C2×C411yescharacteristic
32C2×C4⋊Q8—24no—
33C2×C4⋊Q8—22no—
34C2×C4⋊Q8—42no—
35C2×C4⋊Q8—41no—
36C2×C4⋊Q8—41no—
37C2×C4⋊Q8—48no—
38C2×C4⋊Q8C2×C414yes—
39C2×C4⋊Q8C2×C418yes—
40C2×C4×Q8—41no—
41C2×C4×Q8—41no—
42C2×C4×Q8—42no—
43C2×C4×Q8C2×C412yes—
44C2×C4×Q8D412yes—
45C2×C4×Q8D412yes—
46C2×C4×Q8C2312yes—
47C22×C4⋊C4—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—22no—
50C22×C4⋊C4—22no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4D411yescharacteristic
53C22×C4⋊C4D411yescharacteristic
54C22×C4⋊C4C2311yescharacteristic
55C22×C42C2×C411yescharacteristic
56C22×C42C2×C412yes—
57C22×C42D411yescharacteristic
58C22×C42D411yescharacteristic
59#432—24no—
60#432—42no—
61#431—24no—
62#431—42no—
63C2×C4⋊C8—41no—
64C2×C4⋊C8—41no—
65C2×C22⋊C8—22no—
66C2×C22⋊C8—22no—
67C2×#97—41no—
68C2×C4×C8—41no—
69#398—24no—
70#398—24no—
71#398—24no—
72#398—24no—
73#391—22no—
74#391—22no—
75#391C2×C414yes—
76#391C2314yes—
77#389—24no—
78#389—24no—
79#389—24no—
80#389—24no—
81C4×C4⋊C4—22no—
82C4×C4⋊C4C2×C414yes—
83C2×#95—21no—
84C2×#95—22no—
85C2×#95—22no—
86#324—24no—
87#324—24no—
88#324—22no—
89#324—22no—
90#324C2314yes—
91#324C2314yes—
92C22×Q8—24no—
93C22×Q8—22no—
94C22×Q8—24no—
95C22×Q8—28no—
96C22×Q8—41no—
97C22×Q8—41no—
98C22×Q8—42no—
99C22×Q8—42no—
100C22×Q8—44no—
101C22×Q8C22⋊C412yes—
102C22×Q8C22×C414yes—
103C22×Q8C22×C412yes—
104C23×C4—22no—
105C23×C4—22no—
106C23×C4C22⋊C411yescharacteristic
107C23×C4C22⋊C411yescharacteristic
108C23×C4C22⋊C411yescharacteristic
109C23×C4C22⋊C411yescharacteristic
110C23×C4C22×C411yescharacteristic
111C23×C4C2×D411yescharacteristic
112C23×C4C2×D411yescharacteristic
113C22×C8—42no—
114C22×C8—42no—
115C4⋊Q8—44no—
116C4⋊Q8—44no—
117C4⋊Q8—44no—
118C4⋊Q8—44no—
119C4⋊Q8—416no—
120C4⋊Q8—416no—
121C4×Q8—42no—
122C4×Q8—42no—
123C4×Q8—42no—
124C4×Q8—42no—
125C4×Q8—42no—
126C4×Q8—42no—
127C4×Q8—42no—
128C4×Q8—42no—
129C2×C4⋊C4—28no—
130C2×C4⋊C4—24no—
131C2×C4⋊C4—24no—
132C2×C4⋊C4—28no—
133C2×C4⋊C4—28no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4—41no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4—42no—
142C2×C4⋊C4—42no—
143C2×C4⋊C4—48no—
144C2×C4⋊C4—42no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4—41no—
147C2×C4⋊C4—48no—
148C2×C4⋊C4C22⋊C412yes—
149C2×C4⋊C4C22⋊C412yes—
150C2×C4⋊C4C22×C411yescharacteristic
151C2×C4⋊C4C2×D412yes—
152C2×C4⋊C4C2×D412yes—
153C2×C4⋊C4C2×D411yescharacteristic
154C2×C4⋊C4C2×D411yescharacteristic
155C2×C4⋊C4C2411yescharacteristic
156C2×C42—22no—
157C2×C42—21no—
158C2×C42—21no—
159C2×C42—21no—
160C2×C42—21no—
161C2×C42—21no—
162C2×C42—21no—
163C2×C42—22no—
164C2×C42—22no—
165C2×C42—22no—
166C2×C42—44no—
167C2×C42C22⋊C412yes—
168C2×C42C22⋊C412yes—
169C2×C42C22⋊C412yes—
170C2×C42C22×C412yes—
171C2×C42C22×C414yes—
172C2×C42C2×D412yes—
173C2×C42C2×D412yes—
174C4⋊C8—44no—
175C4⋊C8—44no—
176C22⋊C8—24no—
177C22⋊C8—24no—
178C22⋊C8—42no—
179C22⋊C8—42no—
180#97—44no—
181C4×C8—44no—
182#95—24no—
183#95—24no—
184#95—24no—
185#95—24no—
186#95—24no—
187C24C2×C22⋊C411yescharacteristic
188C2×Q8—24no—
189C2×Q8—24no—
190C2×Q8—24no—
191C2×Q8—24no—
192C2×Q8—28no—
193C2×Q8—42no—
194C2×Q8—42no—
195C2×Q8—48no—
196C2×Q8—48no—
197C2×Q8—44no—
198C2×Q8—44no—
199C2×Q8—44no—
200C2×Q8—44no—
201C2×Q8—44no—
202C2×Q8—88no—
203C2×Q8—88no—
204C22×C4—22no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—24no—
211C22×C4—28no—
212C22×C4—24no—
213C22×C4—22no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—24no—
224C22×C4—44no—
225C22×C4—44no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—44no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—44no—
233C22×C4#9912yes—
234C22×C4#9911yescharacteristic
235C22×C4#9911yescharacteristic
236C22×C4#10014yes—
237C22×C4C2×C22⋊C412yes—
238C22×C4C2×C22⋊C411yescharacteristic
239C22×C4C2×C22⋊C412yes—
240C22×C4C2×C22⋊C412yes—
241C22×C4C2×C22⋊C411yescharacteristic
242C22×C4C2×C22⋊C411yescharacteristic
243C22×C4C2×C22⋊C412yes—
244C22×C4#13114yes—
245C22×C4C23×C411yescharacteristic
246C22×C4C22×D411yescharacteristic
247C22×C4C22×D411yescharacteristic
248C2×C8—44no—
249C2×C8—44no—
250C2×C8—84no—
251C2×C8—84no—
252C4⋊C4—216no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—42no—
260C4⋊C4—41no—
261C4⋊C4—48no—
262C4⋊C4—416no—
263C4⋊C4—44no—
264C4⋊C4—44no—
265C4⋊C4—416no—
266C42—22no—
267C42—22no—
268C42—22no—
269C42—22no—
270C42—22no—
271C42—22no—
272C42—22no—
273C42—22no—
274C42—22no—
275C42—22no—
276C42—22no—
277C42—22no—
278C42—44no—
279C42—44no—
280C23—22no—
281C23—22no—
282C23#40812yes—
283C23C2×#9911yescharacteristic
284C23C2×#9911yescharacteristic
285C23C2×#10012yes—
286C23C22×C22⋊C411yescharacteristic
287Q8—48no—
288Q8—48no—
289Q8—88no—
290Q8—88no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—24no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—28no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—416no—
314C2×C4—44no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—44no—
328C2×C4—44no—
329C2×C4—44no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—84no—
333C2×C4—84no—
334C2×C4#35614yes—
335C2×C4#40812yes—
336C2×C4C2×#9912yes—
337C2×C4C2×#9912yes—
338C2×C4C2×#10014yes—
339C2×C4C2×#13112yes—
340C8—84no—
341C8—84no—
342C22—24no—
343C22—24no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22#147112yes—
349C22#147112yes—
350C22#212912yes—
351C22C2×#35612yes—
352C22C2×#40811yescharacteristic
353C22C22×#9911yescharacteristic
354C22C22×#10011yescharacteristic
355C4—22no—
356C4—22no—
357C4—22no—
358C4—24no—
359C4—48no—
360C4—41no—
361C4—41no—
362C4—42no—
363C4—41no—
364C4—41no—
365C4—42no—
366C4—84no—
367C4C2×#35614yes—
368C2—21no—
369C2—21no—
370C2—22no—
371C2#1156814yesdirect product factor
372C2C2×#147111yescharacteristic
373C2C2×#212911yescharacteristic
374C2C22×#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
4. #11568C2direct (N × H)
371. C2#11568direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25462
C2×#14672
C2×#14612
#115682
C2×#13192