Finite Group Databasebeta

← C2×#11876 #482045

Subgroups — C2×#11876 #482045

Order 512.

1460 conjugacy classes of subgroups.

The subgroup lattice has 579 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2543C211yesmaximal, characteristic
2C2×#1799C211yesmaximal, characteristic, complemented
3C2×#1460C211yesmaximal, characteristic, complemented
4#11876C218yesmaximal, direct product factor
5C2×#1344C212yesmaximal, complemented
6C2×#1343C212yesmaximal, complemented
7C22×#121—21no—
8C22×#121C411yescharacteristic, complemented
9C22×C4×D4C2211yescharacteristic
10C2×#431—21no—
11C22×#99—21no—
12#2543—22no—
13#2543—22no—
14#2543C414yescomplemented
15#2543C2214yes—
16C2×#398C411yescharacteristic, complemented
17C2×#397C2211yescharacteristic
18C2×#394C411yescharacteristic, complemented
19C2×#392C2211yescharacteristic
20C2×#388—21no—
21C2×#386—21no—
22C2×#386—21no—
23C2×#380—21no—
24C22×#95C411yescharacteristic, complemented
25#1799—22no—
26#1799C2214yescomplemented
27C2×#342C2212yes—
28#1460—22no—
29#1460C2214yescomplemented
30C2×#323—21no—
31C2×#323C2212yes—
32#1344C2218yescomplemented
33#1343C2218yescomplemented
34C23×D4—21no—
35C23×D4—21no—
36C23×D4C2×C411yescharacteristic
37C23×D4D411yescharacteristic
38C24×C4—21no—
39C24×C4C2×C411yescharacteristic
40C24×C4D411yescharacteristic
41C2×#121—24no—
42C2×#121—24no—
43C2×#121—22no—
44C2×#121—44no—
45C2×#121—44no—
46C2×#121—42no—
47C2×#121—41no—
48C2×#121—41no—
49C2×#121C2×C414yescomplemented
50C2×C4×D4—41no—
51C2×C4×D4—41no—
52C2×C4×D4—42no—
53C2×C4×D4C2×C412yes—
54C2×C4×D4D412yes—
55C2×C4×D4D412yes—
56C2×C4×D4C2312yes—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—41no—
59C22×C4⋊C4C2×C411yescharacteristic
60C22×C4⋊C4C2×C411yescharacteristic
61C22×C22⋊C4—21no—
62C22×C22⋊C4—21no—
63C22×C22⋊C4—21no—
64C22×C22⋊C4—21no—
65C22×C22⋊C4—21no—
66C22×C22⋊C4—22no—
67C22×C22⋊C4D411yescharacteristic
68C22×C22⋊C4C2311yescharacteristic
69C22×C42D411yescharacteristic
70#431—24no—
71#431—42no—
72C2×C4⋊C8—41no—
73C2×#99—24no—
74C2×#99—44no—
75C2×C22⋊C8—22no—
76C2×C4×C8—41no—
77#398—22no—
78#398C2×C414yescomplemented
79#397—21no—
80#397—21no—
81#397C2×C412yes—
82#397C2312yes—
83#394—22no—
84#394C2×C414yescomplemented
85#392—21no—
86#392—21no—
87#392C2×C412yes—
88#392C2312yes—
89#388—24no—
90#388—24no—
91#386—24no—
92#386—24no—
93#386—24no—
94#386—24no—
95#380—24no—
96#380—42no—
97C2×#95—21no—
98C2×#95—22no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95—41no—
102C2×#95C2×C411yescharacteristic
103C2×#95C2×C411yescharacteristic
104C2×#95C2×C414yescomplemented
105#342—22no—
106#342C2314yes—
107#323—24no—
108#323—22no—
109#323C2314yes—
110C25—21no—
111C25C22⋊C411yescharacteristic
112C25C2×D411yescharacteristic
113C22×D4—24no—
114C22×D4—22no—
115C22×D4—22no—
116C22×D4—21no—
117C22×D4—41no—
118C22×D4—41no—
119C22×D4—42no—
120C22×D4—41no—
121C22×D4—41no—
122C22×D4—44no—
123C22×D4—42no—
124C22×D4—42no—
125C22×D4—44no—
126C22×D4—44no—
127C22×D4—42no—
128C22×D4—42no—
129C22×D4—82no—
130C22×D4—82no—
131C22×D4C22⋊C412yes—
132C22×D4D814yes—
133C22×D4SD1614yes—
134C22×D4C22×C412yes—
135C22×D4C2×D412yes—
136C23×C4—21no—
137C23×C4—21no—
138C23×C4—22no—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—22no—
143C23×C4—21no—
144C23×C4—21no—
145C23×C4—24no—
146C23×C4—44no—
147C23×C4—44no—
148C23×C4—42no—
149C23×C4—82no—
150C23×C4—82no—
151C23×C4—82no—
152C23×C4C22⋊C411yescharacteristic
153C23×C4C22⋊C411yescharacteristic
154C23×C4C22⋊C412yes—
155C23×C4C22⋊C412yes—
156C23×C4C22⋊C411yescharacteristic
157C23×C4C22×C411yescharacteristic
158C23×C4C22×C412yes—
159C23×C4C2×D411yescharacteristic
160C23×C4C2×D412yes—
161C22×C8—42no—
162#121—44no—
163#121—44no—
164#121—416no—
165#121—48no—
166#121—48no—
167#121—44no—
168#121—44no—
169C4×D4—42no—
170C4×D4—42no—
171C4×D4—42no—
172C4×D4—42no—
173C4×D4—42no—
174C4×D4—42no—
175C4×D4—42no—
176C4×D4—42no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4—44no—
184C2×C4⋊C4—44no—
185C2×C4⋊C4—84no—
186C2×C4⋊C4C22⋊C412yes—
187C2×C4⋊C4C22×C412yes—
188C2×C4⋊C4C22×C412yes—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—24no—
192C2×C22⋊C4—24no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—24no—
196C2×C22⋊C4—24no—
197C2×C22⋊C4—41no—
198C2×C22⋊C4—41no—
199C2×C22⋊C4—41no—
200C2×C22⋊C4—41no—
201C2×C22⋊C4—44no—
202C2×C22⋊C4—42no—
203C2×C22⋊C4—42no—
204C2×C22⋊C4—42no—
205C2×C22⋊C4—41no—
206C2×C22⋊C4—41no—
207C2×C22⋊C4—44no—
208C2×C22⋊C4—44no—
209C2×C22⋊C4—44no—
210C2×C22⋊C4—42no—
211C2×C22⋊C4—82no—
212C2×C22⋊C4C22⋊C412yes—
213C2×C22⋊C4C22×C411yescharacteristic
214C2×C22⋊C4C2×D411yescharacteristic
215C2×C22⋊C4C2×D412yes—
216C2×C22⋊C4C2×D411yescharacteristic
217C2×C22⋊C4C2411yescharacteristic
218C2×C42—21no—
219C2×C42—21no—
220C2×C42—22no—
221C2×C42C22⋊C412yes—
222C2×C42C2×D412yes—
223C4⋊C8—44no—
224#99—48no—
225C22⋊C8—24no—
226C22⋊C8—42no—
227C4×C8—44no—
228#95—21no—
229#95—21no—
230#95—24no—
231#95—24no—
232#95—22no—
233#95—22no—
234#95—44no—
235#95C22×C412yes—
236#95C22×C412yes—
237C24—21no—
238C24—21no—
239C24—21no—
240C24—22no—
241C24—21no—
242C24—22no—
243C24—22no—
244C24—42no—
245C24—42no—
246C24—42no—
247C24—42no—
248C24—42no—
249C24—42no—
250C24—42no—
251C24—42no—
252C24—41no—
253C24—41no—
254C24—42no—
255C24—42no—
256C24#10214yes—
257C24C2×C22⋊C411yescharacteristic
258C24C2×C22⋊C411yescharacteristic
259C24C2×C22⋊C412yes—
260C24C2×D812yes—
261C24C2×SD1612yes—
262C24C22×D411yescharacteristic
263C2×D4—42no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4—44no—
267C2×D4—44no—
268C2×D4—44no—
269C2×D4—44no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—44no—
274C2×D4—44no—
275C2×D4—48no—
276C2×D4—48no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—44no—
280C2×D4—48no—
281C2×D4—82no—
282C2×D4—82no—
283C2×D4—82no—
284C2×D4—88no—
285C2×D4—88no—
286C2×D4—84no—
287C2×D4—84no—
288C2×D4—82no—
289C2×D4—88no—
290C2×D4—88no—
291C2×D4#10218yes—
292C2×D4C2×D814yes—
293C2×D4C2×SD1614yes—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—24no—
298C22×C4—22no—
299C22×C4—21no—
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—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—42no—
316C22×C4—44no—
317C22×C4—48no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—48no—
330C22×C4—42no—
331C22×C4—44no—
332C22×C4—82no—
333C22×C4—82no—
334C22×C4—82no—
335C22×C4—82no—
336C22×C4—82no—
337C22×C4—84no—
338C22×C4—84no—
339C22×C4—84no—
340C22×C4—82no—
341C22×C4—82no—
342C22×C4—816no—
343C22×C4—84no—
344C22×C4—84no—
345C22×C4—84no—
346C22×C4#9911yescharacteristic
347C22×C4#9911yescharacteristic
348C22×C4#9912yes—
349C22×C4#10214yes—
350C22×C4C2×C22⋊C412yes—
351C22×C4C2×C22⋊C411yescharacteristic
352C22×C4C2×C22⋊C412yes—
353C22×C4C2×C22⋊C411yescharacteristic
354C22×C4C2×C22⋊C412yes—
355C22×C4C23×C411yescharacteristic
356C22×C4C22×D411yescharacteristic
357C2×C8—44no—
358C2×C8—84no—
359C4⋊C4—42no—
360C4⋊C4—42no—
361C4⋊C4—42no—
362C4⋊C4—42no—
363C4⋊C4—48no—
364C4⋊C4—88no—
365C22⋊C4—42no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—42no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C22⋊C4—44no—
372C22⋊C4—44no—
373C22⋊C4—42no—
374C22⋊C4—42no—
375C22⋊C4—44no—
376C22⋊C4—44no—
377C22⋊C4—44no—
378C22⋊C4—48no—
379C22⋊C4—44no—
380C22⋊C4—44no—
381C22⋊C4—84no—
382C22⋊C4—84no—
383C42—22no—
384C42—22no—
385C42—22no—
386C42—22no—
387C23—22no—
388C23—22no—
389C23—21no—
390C23—22no—
391C23—21no—
392C23—22no—
393C23—22no—
394C23—24no—
395C23—24no—
396C23—22no—
397C23—21no—
398C23—21no—
399C23—22no—
400C23—22no—
401C23—42no—
402C23—42no—
403C23—48no—
404C23—42no—
405C23—42no—
406C23—48no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23—44no—
412C23—44no—
413C23—42no—
414C23—42no—
415C23—42no—
416C23—42no—
417C23—42no—
418C23—42no—
419C23—42no—
420C23—42no—
421C23—42no—
422C23—42no—
423C23—42no—
424C23—81no—
425C23—81no—
426C23—84no—
427C23—82no—
428C23—84no—
429C23—82no—
430C23—84no—
431C23—84no—
432C23—84no—
433C23—82no—
434C23—82no—
435C23—82no—
436C23—82no—
437C23C2×#9911yescharacteristic
438C23C2×#9911yescharacteristic
439C23C2×#10212yes—
440C23C2×#10212yes—
441C23C2×#10214yes—
442C23#42112yes—
443C23C22×C22⋊C411yescharacteristic
444C23C22×D811yescharacteristic
445C23C22×SD1611yescharacteristic
446D4—48no—
447D4—44no—
448D4—44no—
449D4—84no—
450D4—84no—
451D4—88no—
452D4—84no—
453D4—84no—
454D4—816no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—44no—
470C2×C4—44no—
471C2×C4—42no—
472C2×C4—48no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—82no—
490C2×C4—82no—
491C2×C4—82no—
492C2×C4—82no—
493C2×C4—82no—
494C2×C4—82no—
495C2×C4—81no—
496C2×C4—81no—
497C2×C4—816no—
498C2×C4—84no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—84no—
502C2×C4—84no—
503C2×C4—84no—
504C2×C4—168no—
505C2×C4C2×#9912yes—
506C2×C4C2×#9912yes—
507C2×C4C2×#10214yes—
508C8—84no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—24no—
514C22—24no—
515C22—21no—
516C22—24no—
517C22—21no—
518C22—22no—
519C22—44no—
520C22—41no—
521C22—41no—
522C22—42no—
523C22—44no—
524C22—48no—
525C22—41no—
526C22—41no—
527C22—42no—
528C22—41no—
529C22—42no—
530C22—41no—
531C22—44no—
532C22—48no—
533C22—44no—
534C22—81no—
535C22—81no—
536C22—82no—
537C22—82no—
538C22—82no—
539C22—82no—
540C22—82no—
541C22—82no—
542C22—82no—
543C22—82no—
544C22—82no—
545C22—164no—
546C22—164no—
547C22#151912yes—
548C22#151912yes—
549C22#212112yes—
550C22#212612yes—
551C22C22×#9911yescharacteristic
552C22C22×#10211yescharacteristic
553C22C2×#42111yescharacteristic
554C4—22no—
555C4—22no—
556C4—24no—
557C4—44no—
558C4—42no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—82no—
564C4—82no—
565C4—164no—
566C2—21no—
567C2—21no—
568C2—22no—
569C2—41no—
570C2—44no—
571C2—41no—
572C2—42no—
573C2—162no—
574C2#1187614yesdirect product factor
575C2C2×#151911yescharacteristic
576C2C2×#212111yescharacteristic
577C2C2×#212611yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC2×#2543C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×D4 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1799C2semidirect
3. C2×#1460C2semidirect
4. #11876C2direct (N × H)
5. C2×#1344C2semidirect
6. C2×#1343C2semidirect
8. C22×#121C4semidirect
14. #2543C4semidirect
16. C2×#398C4semidirect
18. C2×#394C4semidirect
24. C22×#95C4semidirect
26. #1799C22semidirect
29. #1460C22semidirect
32. #1344C22semidirect
33. #1343C22semidirect
49. C2×#121C2×C4semidirect
78. #398C2×C4semidirect
84. #394C2×C4semidirect
104. C2×#95C2×C4semidirect
574. C2#11876direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25432
C2×#17992
C2×#14602
#118762
C2×#13442
C2×#13432