Finite Group Databasebeta

← C2×#11571 #480540

Subgroups — C2×#11571 #480540

Order 512.

904 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2565C211yesmaximal, characteristic
2C2×#1467C211yesmaximal, characteristic
3C2×#1461C211yesmaximal, characteristic
4#11571C218yesmaximal, direct product factor
5C2×#1325C212yesmaximal
6C2×#1324C212yesmaximal
7C22×#125C411yescharacteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#432—21no—
10C2×#431—21no—
11#2565—22no—
12#2565—22no—
13#2565C414yes—
14#2565C2214yes—
15C2×#398—21no—
16C2×#398—21no—
17C2×#391C411yescharacteristic
18C2×#391C411yescharacteristic
19C2×#387—21no—
20C2×#387—21no—
21C2×#384C2211yescharacteristic
22C2×#382C2211yescharacteristic
23C2×C4×C4⋊C4C411yescharacteristic
24#1467—22no—
25#1467C2214yes—
26#1461—22no—
27#1461C2214yes—
28C2×#324—21no—
29C2×#324—21no—
30C2×#324C2212yes—
31C2×#324C2212yes—
32#1325C2218yes—
33#1324C2218yes—
34C23×Q8C2×C411yescharacteristic
35C2×#125—22no—
36C2×#125—42no—
37C2×#125—41no—
38C2×#125—41no—
39C2×#125C2×C414yes—
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—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4C2×C411yescharacteristic
53C22×C4⋊C4C2×C411yescharacteristic
54C22×C4⋊C4D411yescharacteristic
55C22×C4⋊C4D411yescharacteristic
56C22×C4⋊C4C2311yescharacteristic
57C22×C42C2×C411yescharacteristic
58C22×C42C2×C411yescharacteristic
59C22×C42C2×C411yescharacteristic
60C22×C42D411yescharacteristic
61C22×C42D411yescharacteristic
62#432—24no—
63#432—42no—
64#431—24no—
65#431—42no—
66C2×C4⋊C8—41no—
67C2×C4⋊C8—41no—
68C2×C22⋊C8—22no—
69C2×C22⋊C8—22no—
70C2×#97—41no—
71C2×C4×C8—41no—
72#398—24no—
73#398—24no—
74#398—24no—
75#398—24no—
76#391—22no—
77#391—22no—
78#391C2×C414yes—
79#391C2×C414yes—
80#387—24no—
81#387—24no—
82#387—24no—
83#387—24no—
84#384—21no—
85#384—21no—
86#384C2×C412yes—
87#384C2312yes—
88#382—21no—
89#382—21no—
90#382C2×C412yes—
91#382C2312yes—
92C4×C4⋊C4—22no—
93C4×C4⋊C4C2×C414yes—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101#324—24no—
102#324—24no—
103#324—22no—
104#324—22no—
105#324C2314yes—
106#324C2314yes—
107C22×Q8—24no—
108C22×Q8—24no—
109C22×Q8—41no—
110C22×Q8—41no—
111C22×Q8C22⋊C412yes—
112C22×Q8C22×C412yes—
113C23×C4—21no—
114C23×C4—21no—
115C23×C4—21no—
116C23×C4—21no—
117C23×C4C22⋊C411yescharacteristic
118C23×C4C22⋊C411yescharacteristic
119C23×C4C22⋊C411yescharacteristic
120C23×C4C22⋊C411yescharacteristic
121C23×C4C22×C411yescharacteristic
122C23×C4C2×D411yescharacteristic
123C23×C4C2×D411yescharacteristic
124C22×C8—42no—
125C22×C8—42no—
126#125—44no—
127#125—44no—
128#125—44no—
129#125—44no—
130C4×Q8—42no—
131C4×Q8—42no—
132C4×Q8—42no—
133C4×Q8—42no—
134C4×Q8—42no—
135C4×Q8—42no—
136C4×Q8—42no—
137C4×Q8—42no—
138C2×C4⋊C4—24no—
139C2×C4⋊C4—24no—
140C2×C4⋊C4—24no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—44no—
158C2×C4⋊C4—44no—
159C2×C4⋊C4—44no—
160C2×C4⋊C4—42no—
161C2×C4⋊C4—42no—
162C2×C4⋊C4—42no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4—41no—
165C2×C4⋊C4C22⋊C412yes—
166C2×C4⋊C4C22⋊C412yes—
167C2×C4⋊C4C22×C412yes—
168C2×C4⋊C4C22×C412yes—
169C2×C4⋊C4C22×C411yescharacteristic
170C2×C4⋊C4C2×D412yes—
171C2×C4⋊C4C2×D412yes—
172C2×C4⋊C4C2×D411yescharacteristic
173C2×C4⋊C4C2×D411yescharacteristic
174C2×C4⋊C4C2411yescharacteristic
175C2×C42—22no—
176C2×C42—21no—
177C2×C42—21no—
178C2×C42—21no—
179C2×C42—21no—
180C2×C42—21no—
181C2×C42—21no—
182C2×C42—22no—
183C2×C42—22no—
184C2×C42—24no—
185C2×C42—24no—
186C2×C42—21no—
187C2×C42—21no—
188C2×C42C22⋊C412yes—
189C2×C42C22⋊C412yes—
190C2×C42C22⋊C412yes—
191C2×C42C22×C412yes—
192C2×C42C22×C412yes—
193C2×C42C22×C412yes—
194C2×C42C2×D412yes—
195C2×C42C2×D412yes—
196C4⋊C8—44no—
197C4⋊C8—44no—
198C22⋊C8—24no—
199C22⋊C8—24no—
200C22⋊C8—42no—
201C22⋊C8—42no—
202#97—44no—
203C4×C8—44no—
204#95—24no—
205#95—22no—
206#95—22no—
207#95—24no—
208#95—24no—
209#95—24no—
210#95—24no—
211#95—22no—
212#95—22no—
213C24C2×C22⋊C411yescharacteristic
214C2×Q8—24no—
215C2×Q8—24no—
216C2×Q8—24no—
217C2×Q8—24no—
218C2×Q8—42no—
219C2×Q8—42no—
220C2×Q8—48no—
221C2×Q8—48no—
222C22×C4—22no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—24no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—44no—
254C22×C4—42no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4#9911yescharacteristic
260C22×C4#9911yescharacteristic
261C22×C4#9912yes—
262C22×C4#10114yes—
263C22×C4C2×C22⋊C412yes—
264C22×C4C2×C22⋊C411yescharacteristic
265C22×C4C2×C22⋊C412yes—
266C22×C4C2×C22⋊C411yescharacteristic
267C22×C4C2×C22⋊C411yescharacteristic
268C22×C4C2×C22⋊C412yes—
269C22×C4C2×C22⋊C412yes—
270C22×C4#13114yes—
271C22×C4C23×C411yescharacteristic
272C22×C4C22×D411yescharacteristic
273C22×C4C22×D411yescharacteristic
274C2×C8—44no—
275C2×C8—44no—
276C2×C8—84no—
277C2×C8—84no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C4⋊C4—41no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—48no—
289C4⋊C4—44no—
290C4⋊C4—44no—
291C4⋊C4—44no—
292C4⋊C4—44no—
293C4⋊C4—42no—
294C4⋊C4—42no—
295C4⋊C4—48no—
296C4⋊C4—44no—
297C4⋊C4—44no—
298C42—22no—
299C42—22no—
300C42—22no—
301C42—22no—
302C42—22no—
303C42—22no—
304C42—22no—
305C42—22no—
306C42—22no—
307C42—22no—
308C42—22no—
309C42—22no—
310C42—24no—
311C42—24no—
312C42—42no—
313C42—42no—
314C23—22no—
315C23—22no—
316C23#40812yes—
317C23C2×#9911yescharacteristic
318C23C2×#9911yescharacteristic
319C23C2×#10112yes—
320C23C22×C22⋊C411yescharacteristic
321Q8—48no—
322Q8—48no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—48no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—44no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—84no—
371C2×C4—82no—
372C2×C4—82no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4#40812yes—
376C2×C4C2×#9912yes—
377C2×C4C2×#9912yes—
378C2×C4C2×#10114yes—
379C2×C4C2×#13112yes—
380C8—84no—
381C8—84no—
382C22—24no—
383C22—24no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22#147212yes—
389C22#147212yes—
390C22#212612yes—
391C22#213312yes—
392C22C2×#40811yescharacteristic
393C22C22×#9911yescharacteristic
394C22C22×#10111yescharacteristic
395C4—22no—
396C4—22no—
397C4—22no—
398C4—22no—
399C4—24no—
400C4—44no—
401C4—41no—
402C4—41no—
403C4—42no—
404C4—41no—
405C4—41no—
406C4—42no—
407C4—82no—
408C4—82no—
409C4—82no—
410C2—21no—
411C2—21no—
412C2—22no—
413C2#1157114yesdirect product factor
414C2C2×#147211yescharacteristic
415C2C2×#212611yescharacteristic
416C2C2×#213311yescharacteristic
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. #11571C2direct (N × H)
413. C2#11571direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25652
C2×#14672
C2×#14612
#115712
C2×#13252
C2×#13242