Finite Group Databasebeta

← C2×#11848 #482169

Subgroups — C2×#11848 #482169

Order 512.

1758 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2406C211yesmaximal, characteristic
2C2×#1821C211yesmaximal, characteristic, complemented
3C22×#324C211yesmaximal, characteristic, complemented
4#11848C218yesmaximal, direct product factor
5C2×#1354C212yesmaximal, complemented
6C2×#1345C212yesmaximal, complemented
7C23×#41C411yescharacteristic
8C22×#123—21no—
9C23×C4⋊C4C2211yescharacteristic
10C2×#407—21no—
11C22×C22⋊C8—21no—
12#2406—22no—
13#2406—22no—
14#2406C414yes—
15#2406C2214yes—
16C2×#395C411yescharacteristic
17C2×#395C2211yescharacteristic
18C2×#394C411yescharacteristic
19C2×#394C2211yescharacteristic
20C2×#386—21no—
21C2×#385—21no—
22C2×#385—21no—
23C2×#381C411yescharacteristic
24#1821—22no—
25#1821C2214yescomplemented
26C2×#343—21no—
27C2×#343C2212yes—
28C2×#324—22no—
29C2×#324—21no—
30C2×#324C2212yes—
31C2×#324C2214yescomplemented
32#1354C2218yescomplemented
33#1345C2218yescomplemented
34C22×#41—22no—
35C22×#41—42no—
36C22×#41—41no—
37C22×#41—41no—
38C22×#41—48no—
39C22×#41C2×C414yes—
40C23×Q8C2×C411yescharacteristic
41C23×D4—21no—
42C23×D4C2×C411yescharacteristic
43C24×C4—21no—
44C24×C4C2×C411yescharacteristic
45C24×C4D411yescharacteristic
46C24×C4D411yescharacteristic
47C22×M16—22no—
48C23×C8—41no—
49C2×#123—24no—
50C2×#123—24no—
51C2×#123—48no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—41no—
55C22×C4⋊C4—41no—
56C22×C4⋊C4—42no—
57C22×C4⋊C4C2×C411yescharacteristic
58C22×C4⋊C4C2×C412yes—
59C22×C4⋊C4D412yes—
60C22×C4⋊C4D412yes—
61C22×C4⋊C4D411yescharacteristic
62C22×C4⋊C4D411yescharacteristic
63C22×C4⋊C4C2312yes—
64C22×C4⋊C4C2311yescharacteristic
65C22×C22⋊C4—21no—
66C22×C22⋊C4—21no—
67C22×C22⋊C4—21no—
68C22×C22⋊C4—21no—
69C22×C22⋊C4—21no—
70#407—24no—
71#407—42no—
72C2×C22⋊C8—22no—
73C2×C22⋊C8—24no—
74C2×C22⋊C8—42no—
75C2×C22⋊C8—41no—
76C2×C22⋊C8—41no—
77C2×C22⋊C8—41no—
78#395—22no—
79#395—21no—
80#395—21no—
81#395C2×C414yes—
82#395C2×C412yes—
83#395C2312yes—
84#394—22no—
85#394—21no—
86#394—21no—
87#394C2×C414yes—
88#394C2×C412yes—
89#394C2312yes—
90#386—24no—
91#386—24no—
92#385—24no—
93#385—24no—
94#385—24no—
95#385—24no—
96#381—22no—
97#381C2×C414yes—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95C2×C411yescharacteristic
102C2×#95C2×C411yescharacteristic
103#343—22no—
104#343—24no—
105#343C2314yes—
106#324—22no—
107#324—24no—
108#324C2314yes—
109C25—21no—
110C25C22⋊C411yescharacteristic
111C2×#41—44no—
112C2×#41—44no—
113C2×#41—44no—
114C2×#41—44no—
115C2×#41—416no—
116C2×#41—416no—
117C2×#41—48no—
118C2×#41—432no—
119C2×#41—48no—
120C2×#41—48no—
121C2×#41—48no—
122C22×Q8—21no—
123C22×Q8—44no—
124C22×Q8—41no—
125C22×Q8—41no—
126C22×Q8C22×C412yes—
127C22×D4—28no—
128C22×D4—24no—
129C22×D4—21no—
130C22×D4—41no—
131C22×D4—41no—
132C22×D4—44no—
133C22×D4—42no—
134C22×D4—41no—
135C22×D4—41no—
136C22×D4—44no—
137C22×D4C22×C412yes—
138C23×C4—21no—
139C23×C4—22no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—21no—
143C23×C4—21no—
144C23×C4—22no—
145C23×C4—21no—
146C23×C4—22no—
147C23×C4—21no—
148C23×C4—24no—
149C23×C4—21no—
150C23×C4—21no—
151C23×C4—24no—
152C23×C4—42no—
153C23×C4—44no—
154C23×C4—42no—
155C23×C4—42no—
156C23×C4—44no—
157C23×C4—44no—
158C23×C4—44no—
159C23×C4C22⋊C411yescharacteristic
160C23×C4C22⋊C412yes—
161C23×C4C22⋊C411yescharacteristic
162C23×C4C22⋊C412yes—
163C23×C4C22⋊C411yescharacteristic
164C23×C4C22⋊C412yes—
165C23×C4C22×C411yescharacteristic
166C23×C4C22×C412yes—
167C23×C4C2×D412yes—
168C23×C4C2×D411yescharacteristic
169C23×C4C2×D411yescharacteristic
170C23×C4C2×D412yes—
171C2×M16—24no—
172C2×M16—42no—
173C2×M16—44no—
174C2×M16—44no—
175C22×C8—44no—
176C22×C8—42no—
177C22×C8—42no—
178C22×C8—84no—
179#123—416no—
180#123—416no—
181C2×C4⋊C4—24no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—41no—
186C2×C4⋊C4—42no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4—42no—
191C2×C4⋊C4—42no—
192C2×C4⋊C4—42no—
193C2×C4⋊C4—41no—
194C2×C4⋊C4—42no—
195C2×C4⋊C4—41no—
196C2×C4⋊C4—41no—
197C2×C4⋊C4—41no—
198C2×C4⋊C4—42no—
199C2×C4⋊C4—42no—
200C2×C4⋊C4—44no—
201C2×C4⋊C4—44no—
202C2×C4⋊C4C22⋊C412yes—
203C2×C4⋊C4C22⋊C412yes—
204C2×C4⋊C4C22⋊C412yes—
205C2×C4⋊C4C22×C412yes—
206C2×C4⋊C4C22×C411yescharacteristic
207C2×C4⋊C4C2×D412yes—
208C2×C4⋊C4C2×D411yescharacteristic
209C2×C4⋊C4C2×D412yes—
210C2×C4⋊C4C2×D411yescharacteristic
211C2×C4⋊C4C2411yescharacteristic
212C2×C22⋊C4—24no—
213C2×C22⋊C4—24no—
214C2×C22⋊C4—22no—
215C2×C22⋊C4—24no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—44no—
220C2×C22⋊C4—44no—
221C2×C22⋊C4—44no—
222C2×C22⋊C4—44no—
223C2×C22⋊C4—44no—
224C22⋊C8—24no—
225C22⋊C8—42no—
226C22⋊C8—44no—
227C22⋊C8—44no—
228C22⋊C8—44no—
229#95—24no—
230#95—24no—
231#95—22no—
232#95—21no—
233#95—21no—
234#95—22no—
235#95C22×C412yes—
236#95C22×C412yes—
237C24—24no—
238C24—22no—
239C24—22no—
240C24—24no—
241C24—22no—
242C24—42no—
243C24—42no—
244C24—42no—
245C24—42no—
246C24—41no—
247C24—41no—
248C24—42no—
249C24—42no—
250C24#9911yescharacteristic
251C24#9912yes—
252C24#9911yescharacteristic
253C24C2×C22⋊C412yes—
254C24C2×C22⋊C411yescharacteristic
255#41—416no—
256#41—416no—
257#41—432no—
258#41—432no—
259#41—416no—
260#41—416no—
261C2×Q8—44no—
262C2×Q8—44no—
263C2×Q8—42no—
264C2×Q8—42no—
265C2×Q8—48no—
266C2×Q8—44no—
267C2×Q8—44no—
268C2×D4—216no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4—48no—
272C2×D4—416no—
273C2×D4—48no—
274C2×D4—44no—
275C2×D4—44no—
276C2×D4—48no—
277C2×D4—44no—
278C2×D4—48no—
279C2×D4—44no—
280C2×D4—44no—
281C2×D4—44no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—24no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—21no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—44no—
318C22×C4—44no—
319C22×C4—48no—
320C22×C4—48no—
321C22×C4—48no—
322C22×C4—42no—
323C22×C4—48no—
324C22×C4—48no—
325C22×C4—44no—
326C22×C4—416no—
327C22×C4—416no—
328C22×C4—44no—
329C22×C4—44no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—42no—
333C22×C4—44no—
334C22×C4—42no—
335C22×C4—44no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—44no—
339C22×C4—44no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—84no—
347C22×C4—82no—
348C22×C4C2×C22⋊C412yes—
349C22×C4C2×C22⋊C411yescharacteristic
350C22×C4C2×C22⋊C412yes—
351C22×C4C2×C22⋊C411yescharacteristic
352C22×C4C2×C22⋊C411yescharacteristic
353C22×C4C2×C22⋊C412yes—
354C22×C4#13514yes—
355C22×C4C23×C411yescharacteristic
356C22×C4C22×D411yescharacteristic
357C22×C4C22×D411yescharacteristic
358M16—44no—
359M16—44no—
360M16—84no—
361C2×C8—44no—
362C2×C8—44no—
363C2×C8—84no—
364C2×C8—88no—
365C2×C8—84no—
366C4⋊C4—42no—
367C4⋊C4—42no—
368C4⋊C4—42no—
369C4⋊C4—41no—
370C4⋊C4—42no—
371C4⋊C4—42no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—42no—
375C4⋊C4—41no—
376C4⋊C4—48no—
377C4⋊C4—44no—
378C4⋊C4—44no—
379C22⋊C4—48no—
380C22⋊C4—48no—
381C22⋊C4—44no—
382C22⋊C4—44no—
383C22⋊C4—48no—
384C22⋊C4—44no—
385C22⋊C4—44no—
386C23—22no—
387C23—22no—
388C23—22no—
389C23—22no—
390C23—24no—
391C23—24no—
392C23—22no—
393C23—22no—
394C23—22no—
395C23—22no—
396C23—24no—
397C23—22no—
398C23—24no—
399C23—42no—
400C23—42no—
401C23—48no—
402C23—48no—
403C23—42no—
404C23—44no—
405C23—48no—
406C23—48no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—44no—
411C23—42no—
412C23—42no—
413C23—84no—
414C23—84no—
415C23—82no—
416C23—82no—
417C23—82no—
418C23—82no—
419C23AΣL(1,𝔽16)14yes—
420C23C2×#9912yes—
421C23C2×#9912yes—
422C23C2×#9911yescharacteristic
423C23C2×#9911yescharacteristic
424C23#41612yes—
425C23#42112yes—
426C23C22×C22⋊C411yescharacteristic
427Q8—44no—
428Q8—44no—
429Q8—48no—
430D4—416no—
431D4—44no—
432D4—44no—
433D4—48no—
434D4—416no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—22no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—44no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—44no—
458C2×C4—42no—
459C2×C4—44no—
460C2×C4—44no—
461C2×C4—432no—
462C2×C4—42no—
463C2×C4—44no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—44no—
467C2×C4—42no—
468C2×C4—44no—
469C2×C4—44no—
470C2×C4—44no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—81no—
487C2×C4—82no—
488C2×C4—81no—
489C2×C4—82no—
490C2×C4—84no—
491C2×C4—84no—
492C2×C4#41612yes—
493C2×C4C2×#13512yes—
494C8—84no—
495C8—84no—
496C22—21no—
497C22—21no—
498C22—24no—
499C22—24no—
500C22—28no—
501C22—21no—
502C22—21no—
503C22—22no—
504C22—22no—
505C22—22no—
506C22—22no—
507C22—22no—
508C22—44no—
509C22—44no—
510C22—48no—
511C22—44no—
512C22—44no—
513C22—44no—
514C22—44no—
515C22—82no—
516C22—82no—
517C22—88no—
518C22—88no—
519C22—82no—
520C22—82no—
521C22#151612yes—
522C22#151612yes—
523C22C2×AΣL(1,𝔽16)14yes—
524C22C2×AΣL(1,𝔽16)12yes—
525C22#213312yes—
526C22C22×#9911yescharacteristic
527C22C2×#41611yescharacteristic
528C22C2×#42111yescharacteristic
529C4—22no—
530C4—22no—
531C4—41no—
532C4—42no—
533C4—44no—
534C4—41no—
535C4—41no—
536C4—42no—
537C4—41no—
538C4—42no—
539C4—82no—
540C4—82no—
541C2—21no—
542C2—21no—
543C2—22no—
544C2—24no—
545C2—42no—
546C2—84no—
547C2#1184814yesdirect product factor
548C2C2×#151611yescharacteristic
549C2C22×AΣL(1,𝔽16)11yescharacteristic
550C2C2×#213311yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC23×#41C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C25 ◁ C23×C4⋊C4 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1821C2semidirect
3. C22×#324C2semidirect
4. #11848C2direct (N × H)
5. C2×#1354C2semidirect
6. C2×#1345C2semidirect
25. #1821C22semidirect
31. C2×#324C22semidirect
32. #1354C22semidirect
33. #1345C22semidirect
547. C2#11848direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24062
C2×#18212
C22×#3242
#118482
C2×#13542
C2×#13452