Finite Group Databasebeta

← C2×#11767 #481699

Subgroups — C2×#11767 #481699

Order 512.

1134 conjugacy classes of subgroups.

The subgroup lattice has 465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2611C211yesmaximal, characteristic
2C2×#1742C211yesmaximal, characteristic
3C2×#1464C211yesmaximal, characteristic
4#11767C218yesmaximal, direct product factor
5C2×#1353C212yesmaximal, complemented
6C2×#1346C212yesmaximal, complemented
7C23×M16—21no—
8C22×#125C411yescharacteristic
9C22×#117C2211yescharacteristic
10C2×#432—21no—
11#2611—22no—
12#2611—22no—
13#2611C414yes—
14#2611C2214yes—
15C2×#400C2211yescharacteristic
16C2×#399C411yescharacteristic
17C2×#398C2211yescharacteristic
18C2×#397C411yescharacteristic
19C2×#389—21no—
20C2×#388—21no—
21C2×#387—21no—
22C2×#385—21no—
23C2×#376C411yescharacteristic
24#1742—22no—
25#1742C2214yes—
26C2×#343—21no—
27C2×#343C2212yes—
28#1464—22no—
29#1464C2214yes—
30C2×#324C2212yes—
31C2×#323—21no—
32#1353C2218yescomplemented
33#1346C2218yescomplemented
34C24×C4D411yescharacteristic
35C22×M16—28no—
36C22×M16—22no—
37C22×M16—24no—
38C22×M16—41no—
39C22×M16—42no—
40C22×M16—44no—
41C23×C8—41no—
42C2×#125—22no—
43C2×#125—42no—
44C2×#125—41no—
45C2×#125—41no—
46C2×#125C2×C414yes—
47C2×#117—41no—
48C2×#117—41no—
49C2×#117—42no—
50C2×#117C2×C412yes—
51C2×#117D412yes—
52C2×#117D412yes—
53C2×#117C2312yes—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4C2×C411yescharacteristic
59C22×C4⋊C4C2×C411yescharacteristic
60C22×C4⋊C4D411yescharacteristic
61C22×C4⋊C4C2311yescharacteristic
62C22×C22⋊C4—21no—
63C22×C22⋊C4—21no—
64C22×C22⋊C4C2×C411yescharacteristic
65C22×C22⋊C4D411yescharacteristic
66C22×C42—21no—
67C22×C42C2×C411yescharacteristic
68C22×C42D411yescharacteristic
69#432—24no—
70#432—42no—
71C2×C4⋊C8—41no—
72C2×C22⋊C8—22no—
73C2×#97—41no—
74#400—21no—
75#400—21no—
76#400C2×C412yes—
77#400C2312yes—
78#399—22no—
79#399C2×C414yes—
80#398—21no—
81#398—21no—
82#398C2×C412yes—
83#398C2312yes—
84#397—22no—
85#397C2×C414yes—
86#389—24no—
87#389—24no—
88#388—24no—
89#388—24no—
90#387—24no—
91#387—24no—
92#385—24no—
93#385—24no—
94#376—22no—
95#376C2×C414yes—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95C2×C411yescharacteristic
102C2×#95C2×C411yescharacteristic
103#343—24no—
104#343—22no—
105#343C2314yes—
106#324—22no—
107#324C2314yes—
108#323—24no—
109C25C22⋊C411yescharacteristic
110C23×C4—24no—
111C23×C4—21no—
112C23×C4—22no—
113C23×C4—21no—
114C23×C4—22no—
115C23×C4—22no—
116C23×C4—21no—
117C23×C4—21no—
118C23×C4—21no—
119C23×C4—21no—
120C23×C4C22⋊C412yes—
121C23×C4C22⋊C411yescharacteristic
122C23×C4C22⋊C411yescharacteristic
123C23×C4C22⋊C411yescharacteristic
124C23×C4C22×C411yescharacteristic
125C23×C4C2×D412yes—
126C23×C4C2×D411yescharacteristic
127C23×C4C2×D411yescharacteristic
128C2×M16—28no—
129C2×M16—216no—
130C2×M16—24no—
131C2×M16—416no—
132C2×M16—48no—
133C2×M16—42no—
134C2×M16—44no—
135C2×M16—48no—
136C2×M16—44no—
137C22×C8—48no—
138C22×C8—42no—
139C22×C8—44no—
140C22×C8—42no—
141#125—44no—
142#125—44no—
143#125—44no—
144#125—44no—
145#117—42no—
146#117—42no—
147#117—42no—
148#117—42no—
149#117—42no—
150#117—42no—
151#117—42no—
152#117—42no—
153C2×C4⋊C4—24no—
154C2×C4⋊C4—24no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—24no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—41no—
161C2×C4⋊C4—41no—
162C2×C4⋊C4—41no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4—41no—
165C2×C4⋊C4—41no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—44no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4—42no—
171C2×C4⋊C4—42no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—42no—
175C2×C4⋊C4—42no—
176C2×C4⋊C4C22⋊C412yes—
177C2×C4⋊C4C22×C412yes—
178C2×C4⋊C4C22×C412yes—
179C2×C4⋊C4C22×C411yescharacteristic
180C2×C4⋊C4C2×D412yes—
181C2×C4⋊C4C2×D411yescharacteristic
182C2×C4⋊C4C2×D411yescharacteristic
183C2×C4⋊C4C2411yescharacteristic
184C2×C22⋊C4—24no—
185C2×C22⋊C4—24no—
186C2×C22⋊C4—41no—
187C2×C22⋊C4—41no—
188C2×C22⋊C4—41no—
189C2×C22⋊C4—41no—
190C2×C22⋊C4—44no—
191C2×C22⋊C4—44no—
192C2×C22⋊C4C22⋊C412yes—
193C2×C22⋊C4C22⋊C412yes—
194C2×C22⋊C4C22×C412yes—
195C2×C22⋊C4C2×D412yes—
196C2×C42—22no—
197C2×C42—21no—
198C2×C42—21no—
199C2×C42—21no—
200C2×C42—21no—
201C2×C42—22no—
202C2×C42—24no—
203C2×C42—44no—
204C2×C42C22⋊C412yes—
205C2×C42C22⋊C412yes—
206C2×C42C22×C412yes—
207C2×C42C2×D412yes—
208C4⋊C8—44no—
209C22⋊C8—24no—
210C22⋊C8—42no—
211#97—44no—
212#95—24no—
213#95—22no—
214#95—22no—
215#95—22no—
216#95—24no—
217#95—21no—
218#95—21no—
219#95—22no—
220#95—22no—
221#95—22no—
222#95C22×C412yes—
223#95C22×C412yes—
224C24—21no—
225C24—21no—
226C24—22no—
227C24—42no—
228C24—42no—
229C24#10414yes—
230C24C2×C22⋊C411yescharacteristic
231C24C2×C22⋊C412yes—
232C22×C4—24no—
233C22×C4—28no—
234C22×C4—24no—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—28no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—24no—
242C22×C4—22no—
243C22×C4—24no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—24no—
252C22×C4—24no—
253C22×C4—22no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4#9912yes—
283C22×C4#9911yescharacteristic
284C22×C4#9911yescharacteristic
285C22×C4C2×C22⋊C412yes—
286C22×C4C2×C22⋊C411yescharacteristic
287C22×C4C2×C22⋊C411yescharacteristic
288C22×C4C2×C22⋊C411yescharacteristic
289C22×C4C2×C22⋊C412yes—
290C22×C4C2×C22⋊C412yes—
291C22×C4AGL(1,ℤ/8)12yes—
292C22×C4#13712yes—
293C22×C4C23×C411yescharacteristic
294C22×C4C22×D411yescharacteristic
295C22×C4C22×D411yescharacteristic
296M16—28no—
297M16—416no—
298M16—48no—
299M16—44no—
300C2×C8—416no—
301C2×C8—44no—
302C2×C8—48no—
303C2×C8—44no—
304C2×C8—84no—
305C4⋊C4—42no—
306C4⋊C4—41no—
307C4⋊C4—42no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4—48no—
314C4⋊C4—48no—
315C4⋊C4—42no—
316C4⋊C4—42no—
317C4⋊C4—42no—
318C4⋊C4—42no—
319C4⋊C4—44no—
320C4⋊C4—44no—
321C4⋊C4—44no—
322C22⋊C4—42no—
323C22⋊C4—42no—
324C22⋊C4—42no—
325C22⋊C4—42no—
326C22⋊C4—48no—
327C22⋊C4—48no—
328C42—22no—
329C42—22no—
330C42—22no—
331C42—22no—
332C42—22no—
333C42—22no—
334C42—22no—
335C42—22no—
336C42—48no—
337C23—22no—
338C23—22no—
339C23—22no—
340C23—24no—
341C23—22no—
342C23—24no—
343C23—42no—
344C23—48no—
345C23—42no—
346C23—42no—
347C23—42no—
348C23—81no—
349C23—81no—
350C23—84no—
351C23C2×#9911yescharacteristic
352C23C2×#9911yescharacteristic
353C23#41712yes—
354C23C2×#10412yes—
355C23C2×#10414yes—
356C23C22×C22⋊C411yescharacteristic
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—28no—
362C2×C4—28no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—22no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—24no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—24no—
377C2×C4—21no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—42no—
384C2×C4—48no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—84no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—82no—
414C2×C4C2×#9912yes—
415C2×C4C2×#9912yes—
416C2×C4#41712yes—
417C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
418C2×C4C2×#13711yescharacteristic
419C8—48no—
420C8—84no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—24no—
426C22—24no—
427C22—24no—
428C22—44no—
429C22—42no—
430C22—42no—
431C22—48no—
432C22—82no—
433C22—84no—
434C22#150412yes—
435C22#150412yes—
436C22#212312yes—
437C22#213212yes—
438C22C22×#9911yescharacteristic
439C22C2×#41711yescharacteristic
440C22C22×#10411yescharacteristic
441C4—21no—
442C4—21no—
443C4—22no—
444C4—22no—
445C4—22no—
446C4—44no—
447C4—41no—
448C4—41no—
449C4—41no—
450C4—41no—
451C4—42no—
452C4—42no—
453C4—82no—
454C4—82no—
455C4—82no—
456C2—21no—
457C2—21no—
458C2—22no—
459C2—44no—
460C2#1176714yesdirect product factor
461C2C2×#150411yescharacteristic
462C2C2×#212311yescharacteristic
463C2C2×#213211yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC25C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#117 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11767C2direct (N × H)
5. C2×#1353C2semidirect
6. C2×#1346C2semidirect
32. #1353C22semidirect
33. #1346C22semidirect
460. C2#11767direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#26112
C2×#17422
C2×#14642
#117672
C2×#13532
C2×#13462