Finite Group Databasebeta

← C2×#11793 #481644

Subgroups — C2×#11793 #481644

Order 512.

1204 conjugacy classes of subgroups.

The subgroup lattice has 493 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2564C211yesmaximal, characteristic
2C2×C4×#100C211yesmaximal, characteristic
3C2×#1465C211yesmaximal, characteristic
4#11793C218yesmaximal, direct product factor
5C2×#1354C212yesmaximal, complemented
6C2×#1353C212yesmaximal, complemented
7C22×C22⋊Q8C411yescharacteristic
8C22×C4×D4C2211yescharacteristic
9C22×#100—21no—
10C2×#407—21no—
11C2×C4×M16—21no—
12#2564—22no—
13#2564—22no—
14#2564C414yes—
15#2564C2214yes—
16C2×#400C2211yescharacteristic
17C2×#399C411yescharacteristic
18C2×#395C2211yescharacteristic
19C2×#393C411yescharacteristic
20C2×#387—21no—
21C2×#386—21no—
22C2×#385—21no—
23C2×#380—21no—
24C22×#95C411yescharacteristic
25C4×#100—22no—
26C4×#100C2214yes—
27C2×#343C2212yes—
28#1465—22no—
29#1465C2214yes—
30C2×#324C2212yes—
31C2×#323—21no—
32#1354C2218yescomplemented
33#1353C2218yescomplemented
34C23×Q8C2×C411yescharacteristic
35C23×D4D411yescharacteristic
36C24×C4—21no—
37C24×C4C2×C411yescharacteristic
38C24×C4D411yescharacteristic
39C22×M16—22no—
40C22×M16—41no—
41C2×C22⋊Q8—22no—
42C2×C22⋊Q8—42no—
43C2×C22⋊Q8—41no—
44C2×C22⋊Q8—41no—
45C2×C22⋊Q8C2×C414yes—
46C2×C4×D4—41no—
47C2×C4×D4—41no—
48C2×C4×D4—42no—
49C2×C4×D4C2×C412yes—
50C2×C4×D4D412yes—
51C2×C4×D4D412yes—
52C2×C4×D4C2312yes—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4C2×C411yescharacteristic
57C22×C4⋊C4C2311yescharacteristic
58C22×C22⋊C4—21no—
59C22×C22⋊C4—21no—
60C22×C22⋊C4—21no—
61C22×C22⋊C4C2×C411yescharacteristic
62C22×C22⋊C4D411yescharacteristic
63C22×C42D411yescharacteristic
64C2×#100—28no—
65C2×#100—24no—
66#407—24no—
67#407—42no—
68C2×C22⋊C8—22no—
69C2×C22⋊C8—41no—
70C4×M16—24no—
71C4×M16—42no—
72C2×#97—41no—
73C2×C4×C8—41no—
74#400—21no—
75#400—21no—
76#400C2×C412yes—
77#400C2312yes—
78#399—22no—
79#399C2×C414yes—
80#395—21no—
81#395—21no—
82#395C2×C412yes—
83#395C2312yes—
84#393—22no—
85#393C2×C414yes—
86#387—24no—
87#387—24no—
88#386—24no—
89#386—24no—
90#385—24no—
91#385—24no—
92#380—24no—
93#380—24no—
94C2×#95—22no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95C2×C414yes—
101C2×#95C2×C411yescharacteristic
102C2×#95C2×C411yescharacteristic
103#343—22no—
104#343C2314yes—
105#324—22no—
106#324C2314yes—
107#323—24no—
108C25C22⋊C411yescharacteristic
109C25C22⋊C411yescharacteristic
110C22×Q8—21no—
111C22×Q8—41no—
112C22×Q8—41no—
113C22×Q8—82no—
114C22×Q8C22×C412yes—
115C22×D4—24no—
116C22×D4—24no—
117C22×D4—41no—
118C22×D4—41no—
119C22×D4C22⋊C412yes—
120C22×D4C2×D412yes—
121C23×C4—21no—
122C23×C4—21no—
123C23×C4—22no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—22no—
128C23×C4—21no—
129C23×C4—21no—
130C23×C4—21no—
131C23×C4—24no—
132C23×C4—44no—
133C23×C4—44no—
134C23×C4—82no—
135C23×C4—82no—
136C23×C4—82no—
137C23×C4C22⋊C411yescharacteristic
138C23×C4C22⋊C412yes—
139C23×C4C22⋊C412yes—
140C23×C4C22⋊C411yescharacteristic
141C23×C4C22×C411yescharacteristic
142C23×C4C22×C412yes—
143C23×C4C2×D411yescharacteristic
144C23×C4C2×D411yescharacteristic
145C23×C4C2×D412yes—
146C2×M16—28no—
147C2×M16—24no—
148C2×M16—42no—
149C2×M16—44no—
150C2×M16—44no—
151C2×M16—84no—
152C22×C8—42no—
153C22×C8—42no—
154C22⋊Q8—44no—
155C22⋊Q8—44no—
156C22⋊Q8—44no—
157C22⋊Q8—44no—
158C4×D4—42no—
159C4×D4—42no—
160C4×D4—42no—
161C4×D4—42no—
162C4×D4—42no—
163C4×D4—42no—
164C4×D4—42no—
165C4×D4—42no—
166C2×C4⋊C4—24no—
167C2×C4⋊C4—24no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—44no—
176C2×C4⋊C4—42no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—82no—
180C2×C4⋊C4C22×C412yes—
181C2×C4⋊C4C22×C411yescharacteristic
182C2×C4⋊C4C2×D411yescharacteristic
183C2×C4⋊C4C2×D411yescharacteristic
184C2×C4⋊C4C2411yescharacteristic
185C2×C22⋊C4—24no—
186C2×C22⋊C4—24no—
187C2×C22⋊C4—24no—
188C2×C22⋊C4—41no—
189C2×C22⋊C4—41no—
190C2×C22⋊C4—41no—
191C2×C22⋊C4—41no—
192C2×C22⋊C4—44no—
193C2×C22⋊C4—42no—
194C2×C22⋊C4—42no—
195C2×C22⋊C4—82no—
196C2×C22⋊C4C22⋊C412yes—
197C2×C22⋊C4C22⋊C412yes—
198C2×C22⋊C4C22×C412yes—
199C2×C22⋊C4C2×D412yes—
200C2×C42—21no—
201C2×C42—21no—
202C2×C42—22no—
203C2×C42C22⋊C412yes—
204C2×C42C2×D412yes—
205#100—216no—
206C22⋊C8—24no—
207C22⋊C8—42no—
208C22⋊C8—44no—
209#97—44no—
210C4×C8—44no—
211#95—24no—
212#95—21no—
213#95—21no—
214#95—22no—
215#95—24no—
216#95—22no—
217#95—22no—
218#95—22no—
219#95—22no—
220#95—22no—
221#95C22×C412yes—
222#95C22×C412yes—
223C24—21no—
224C24—21no—
225C24—22no—
226C24—21no—
227C24—22no—
228C24—21no—
229C24—22no—
230C24—42no—
231C24—42no—
232C24—42no—
233C24—42no—
234C24#10414yes—
235C24C2×C22⋊C411yescharacteristic
236C24C2×C22⋊C412yes—
237C24C2×C22⋊C412yes—
238C2×Q8—42no—
239C2×Q8—42no—
240C2×Q8—82no—
241C2×Q8—82no—
242C2×Q8—84no—
243C2×Q8—84no—
244C2×D4—24no—
245C2×D4—24no—
246C2×D4—24no—
247C2×D4—24no—
248C2×D4—42no—
249C2×D4—42no—
250C2×D4—48no—
251C2×D4—48no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—24no—
256C22×C4—22no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—42no—
275C22×C4—44no—
276C22×C4—48no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—48no—
293C22×C4—42no—
294C22×C4—82no—
295C22×C4—82no—
296C22×C4—82no—
297C22×C4—82no—
298C22×C4—82no—
299C22×C4—84no—
300C22×C4—84no—
301C22×C4—84no—
302C22×C4—82no—
303C22×C4—82no—
304C22×C4—816no—
305C22×C4#9911yescharacteristic
306C22×C4#9911yescharacteristic
307C22×C4#9912yes—
308C22×C4C2×C22⋊C411yescharacteristic
309C22×C4C2×C22⋊C412yes—
310C22×C4C2×C22⋊C411yescharacteristic
311C22×C4C2×C22⋊C411yescharacteristic
312C22×C4C2×C22⋊C412yes—
313C22×C4#13714yes—
314C22×C4C23×C411yescharacteristic
315C22×C4C22×D411yescharacteristic
316C22×C4C22×D411yescharacteristic
317M16—28no—
318M16—48no—
319M16—44no—
320M16—88no—
321C2×C8—44no—
322C2×C8—48no—
323C2×C8—44no—
324C2×C8—84no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—42no—
330C4⋊C4—48no—
331C4⋊C4—42no—
332C4⋊C4—44no—
333C4⋊C4—44no—
334C4⋊C4—82no—
335C4⋊C4—82no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—48no—
341C22⋊C4—48no—
342C22⋊C4—84no—
343C42—22no—
344C42—22no—
345C42—22no—
346C42—22no—
347C23—22no—
348C23—22no—
349C23—22no—
350C23—22no—
351C23—24no—
352C23—24no—
353C23—22no—
354C23—22no—
355C23—22no—
356C23—42no—
357C23—42no—
358C23—48no—
359C23—42no—
360C23—48no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—48no—
365C23—42no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—42no—
370C23—42no—
371C23—81no—
372C23—81no—
373C23—84no—
374C23C2×#9911yescharacteristic
375C23C2×#9911yescharacteristic
376C23#41912yes—
377C23C2×#10412yes—
378C23C2×#10414yes—
379C23C22×C22⋊C411yescharacteristic
380Q8—84no—
381Q8—84no—
382D4—48no—
383D4—48no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—24no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—22no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—44no—
401C2×C4—44no—
402C2×C4—42no—
403C2×C4—48no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4—816no—
432C2×C4—82no—
433C2×C4—84no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4C2×#9912yes—
438C2×C4C2×#9912yes—
439C2×C4#41912yes—
440C2×C4C2×#13712yes—
441C8—48no—
442C8—84no—
443C22—24no—
444C22—24no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—24no—
450C22—44no—
451C22—44no—
452C22—48no—
453C22—44no—
454C22—48no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—82no—
461C22—84no—
462C22—84no—
463C22#150812yes—
464C22#150812yes—
465C22#212112yes—
466C22#213212yes—
467C22C22×#9911yescharacteristic
468C22C2×#41911yescharacteristic
469C22C22×#10411yescharacteristic
470C4—22no—
471C4—22no—
472C4—22no—
473C4—22no—
474C4—44no—
475C4—41no—
476C4—41no—
477C4—41no—
478C4—41no—
479C4—42no—
480C4—82no—
481C4—82no—
482C4—82no—
483C2—21no—
484C2—21no—
485C2—22no—
486C2—44no—
487C2—82no—
488C2#1179314yesdirect product factor
489C2C2×#150811yescharacteristic
490C2C2×#212111yescharacteristic
491C2C2×#213211yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×D4 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11793C2direct (N × H)
5. C2×#1354C2semidirect
6. C2×#1353C2semidirect
32. #1354C22semidirect
33. #1353C22semidirect
488. C2#11793direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25642
C2×C4×#1002
C2×#14652
#117932
C2×#13542
C2×#13532