Finite Group Databasebeta

← C2×#11884 #482058

Subgroups — C2×#11884 #482058

Order 512.

1432 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2543C211yesmaximal, characteristic
2C2×#1800C211yesmaximal, characteristic, complemented
3C2×#1459C211yesmaximal, characteristic, complemented
4#11884C218yesmaximal, direct product factor
5C2×#1346C212yesmaximal, complemented
6C2×#1345C212yesmaximal, complemented
7C22×#121—21no—
8C22×#121C411yescharacteristic
9C22×C4×D4C2211yescharacteristic
10C2×#423—21no—
11C22×#100—21no—
12C22×C22⋊C8—21no—
13#2543—22no—
14#2543—22no—
15#2543C414yes—
16#2543C2214yes—
17C2×#398C2211yescharacteristic
18C2×#397C411yescharacteristic
19C2×#394C2211yescharacteristic
20C2×#392C411yescharacteristic
21C2×#388—21no—
22C2×#386—21no—
23C2×#386—21no—
24C22×#95C411yescharacteristic
25#1800—22no—
26#1800C2214yescomplemented
27C2×#343C2212yes—
28#1459—22no—
29#1459C2214yescomplemented
30C2×#324C2212yes—
31C2×#323—21no—
32#1346C2218yescomplemented
33#1345C2218yescomplemented
34C23×D4—21no—
35C23×D4—21no—
36C23×D4C2×C411yescharacteristic
37C23×D4D411yescharacteristic
38C24×C4—21no—
39C24×C4C2×C411yescharacteristic
40C24×C4D411yescharacteristic
41C22×M16—22no—
42C23×C8—41no—
43C2×#121—24no—
44C2×#121—24no—
45C2×#121—22no—
46C2×#121—44no—
47C2×#121—44no—
48C2×#121—42no—
49C2×#121—41no—
50C2×#121—41no—
51C2×#121C2×C414yes—
52C2×C4×D4—41no—
53C2×C4×D4—41no—
54C2×C4×D4—42no—
55C2×C4×D4C2×C412yes—
56C2×C4×D4D412yes—
57C2×C4×D4D412yes—
58C2×C4×D4C2312yes—
59C22×C4⋊C4—21no—
60C22×C4⋊C4C2×C411yescharacteristic
61C22×C4⋊C4C2311yescharacteristic
62C22×C22⋊C4—21no—
63C22×C22⋊C4—21no—
64C22×C22⋊C4—21no—
65C22×C22⋊C4—21no—
66C22×C22⋊C4—21no—
67C22×C22⋊C4C2×C411yescharacteristic
68C22×C22⋊C4D411yescharacteristic
69C22×C42D411yescharacteristic
70#423—24no—
71#423—42no—
72C2×C4⋊C8—41no—
73C2×C4⋊C8—41no—
74C2×#100—24no—
75C2×#100—44no—
76C2×C22⋊C8—22no—
77C2×C22⋊C8—24no—
78C2×C22⋊C8—42no—
79C2×C22⋊C8—41no—
80#398—21no—
81#398—21no—
82#398C2×C412yes—
83#398C2312yes—
84#397—22no—
85#397C2×C414yes—
86#394—21no—
87#394—21no—
88#394C2×C412yes—
89#394C2312yes—
90#392—22no—
91#392C2×C414yes—
92#388—24no—
93#388—24no—
94#386—24no—
95#386—24no—
96#386—24no—
97#386—24no—
98C2×#95—21no—
99C2×#95—22no—
100C2×#95—21no—
101C2×#95—21no—
102C2×#95C2×C411yescharacteristic
103C2×#95C2×C411yescharacteristic
104C2×#95C2×C414yes—
105#343—22no—
106#343C2314yes—
107#324—22no—
108#324C2314yes—
109#323—24no—
110C25—21no—
111C25C22⋊C411yescharacteristic
112C25C22⋊C411yescharacteristic
113C22×D4—24no—
114C22×D4—24no—
115C22×D4—21no—
116C22×D4—41no—
117C22×D4—41no—
118C22×D4—42no—
119C22×D4—41no—
120C22×D4—41no—
121C22×D4—44no—
122C22×D4—42no—
123C22×D4—42no—
124C22×D4—44no—
125C22×D4—44no—
126C22×D4—44no—
127C22×D4—82no—
128C22×D4—82no—
129C22×D4C22⋊C412yes—
130C22×D4D814yes—
131C22×D4SD1614yes—
132C22×D4C22×C412yes—
133C22×D4C2×D412yes—
134C23×C4—21no—
135C23×C4—21no—
136C23×C4—22no—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4—21no—
140C23×C4—22no—
141C23×C4—21no—
142C23×C4—21no—
143C23×C4—24no—
144C23×C4—44no—
145C23×C4—44no—
146C23×C4—82no—
147C23×C4—82no—
148C23×C4—82no—
149C23×C4C22⋊C411yescharacteristic
150C23×C4C22⋊C412yes—
151C23×C4C22⋊C412yes—
152C23×C4C22⋊C411yescharacteristic
153C23×C4C22×C411yescharacteristic
154C23×C4C22×C412yes—
155C23×C4C2×D411yescharacteristic
156C23×C4C2×D411yescharacteristic
157C23×C4C2×D412yes—
158C2×M16—24no—
159C2×M16—42no—
160C2×M16—44no—
161C2×M16—44no—
162C22×C8—42no—
163C22×C8—44no—
164C22×C8—42no—
165C22×C8—84no—
166#121—44no—
167#121—44no—
168#121—416no—
169#121—48no—
170#121—48no—
171#121—44no—
172#121—44no—
173C4×D4—42no—
174C4×D4—42no—
175C4×D4—42no—
176C4×D4—42no—
177C4×D4—42no—
178C4×D4—42no—
179C4×D4—42no—
180C4×D4—42no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—41no—
185C2×C4⋊C4—41no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4—42no—
189C2×C4⋊C4—42no—
190C2×C4⋊C4C22×C412yes—
191C2×C4⋊C4C22×C411yescharacteristic
192C2×C4⋊C4C2×D411yescharacteristic
193C2×C4⋊C4C2×D411yescharacteristic
194C2×C4⋊C4C2411yescharacteristic
195C2×C22⋊C4—24no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—24no—
198C2×C22⋊C4—24no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—41no—
203C2×C22⋊C4—41no—
204C2×C22⋊C4—41no—
205C2×C22⋊C4—41no—
206C2×C22⋊C4—44no—
207C2×C22⋊C4—44no—
208C2×C22⋊C4—42no—
209C2×C22⋊C4—41no—
210C2×C22⋊C4—41no—
211C2×C22⋊C4—42no—
212C2×C22⋊C4—42no—
213C2×C22⋊C4—82no—
214C2×C22⋊C4C22⋊C412yes—
215C2×C22⋊C4C22⋊C412yes—
216C2×C22⋊C4C22×C412yes—
217C2×C22⋊C4C2×D412yes—
218C2×C42—21no—
219C2×C42—21no—
220C2×C42—22no—
221C2×C42C22⋊C412yes—
222C2×C42C2×D412yes—
223C4⋊C8—44no—
224C4⋊C8—44no—
225#100—48no—
226C22⋊C8—24no—
227C22⋊C8—42no—
228C22⋊C8—44no—
229#95—24no—
230#95—21no—
231#95—21no—
232#95—22no—
233#95—24no—
234#95—22no—
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—
257C24#10214yes—
258C24C2×C22⋊C411yescharacteristic
259C24C2×C22⋊C412yes—
260C24C2×C22⋊C412yes—
261C2×D4—42no—
262C2×D4—42no—
263C2×D4—42no—
264C2×D4—44no—
265C2×D4—44no—
266C2×D4—44no—
267C2×D4—44no—
268C2×D4—42no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4—48no—
272C2×D4—48no—
273C2×D4—48no—
274C2×D4—48no—
275C2×D4—48no—
276C2×D4—84no—
277C2×D4—82no—
278C2×D4—816no—
279C2×D4—84no—
280C2×D4—84no—
281C2×D4—82no—
282C2×D4—88no—
283C2×D4—88no—
284C2×D4#10218yes—
285C2×D4C2×D814yes—
286C2×D4C2×SD1614yes—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—22no—
290C22×C4—24no—
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—42no—
309C22×C4—44no—
310C22×C4—48no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—48no—
323C22×C4—42no—
324C22×C4—82no—
325C22×C4—82no—
326C22×C4—82no—
327C22×C4—82no—
328C22×C4—82no—
329C22×C4—84no—
330C22×C4—84no—
331C22×C4—84no—
332C22×C4—82no—
333C22×C4—82no—
334C22×C4—816no—
335C22×C4#9911yescharacteristic
336C22×C4#9911yescharacteristic
337C22×C4#9912yes—
338C22×C4C2×C22⋊C411yescharacteristic
339C22×C4C2×C22⋊C412yes—
340C22×C4C2×C22⋊C411yescharacteristic
341C22×C4C2×C22⋊C411yescharacteristic
342C22×C4C2×C22⋊C412yes—
343C22×C4C2×D812yes—
344C22×C4C2×SD1612yes—
345C22×C4C23×C411yescharacteristic
346C22×C4C22×D411yescharacteristic
347C22×C4C22×D411yescharacteristic
348M16—44no—
349M16—44no—
350M16—84no—
351C2×C8—44no—
352C2×C8—44no—
353C2×C8—84no—
354C2×C8—88no—
355C2×C8—84no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—42no—
361C4⋊C4—42no—
362C4⋊C4—42no—
363C4⋊C4—42no—
364C4⋊C4—44no—
365C22⋊C4—42no—
366C22⋊C4—42no—
367C22⋊C4—42no—
368C22⋊C4—42no—
369C22⋊C4—48no—
370C22⋊C4—48no—
371C22⋊C4—42no—
372C22⋊C4—42no—
373C22⋊C4—44no—
374C22⋊C4—44no—
375C22⋊C4—44no—
376C22⋊C4—82no—
377C22⋊C4—82no—
378C42—22no—
379C42—22no—
380C42—22no—
381C42—22no—
382C23—22no—
383C23—22no—
384C23—22no—
385C23—22no—
386C23—22no—
387C23—24no—
388C23—24no—
389C23—24no—
390C23—22no—
391C23—24no—
392C23—42no—
393C23—42no—
394C23—48no—
395C23—42no—
396C23—42no—
397C23—48no—
398C23—42no—
399C23—42no—
400C23—48no—
401C23—42no—
402C23—42no—
403C23—42no—
404C23—42no—
405C23—42no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—81no—
413C23—81no—
414C23—84no—
415C23—82no—
416C23—84no—
417C23—82no—
418C23—84no—
419C23—84no—
420C23—84no—
421C23—82no—
422C23—82no—
423C23—82no—
424C23—82no—
425C23C2×#9911yescharacteristic
426C23C2×#9911yescharacteristic
427C23C2×#10212yes—
428C23C2×#10214yes—
429C23C2×#10214yes—
430C23#42112yes—
431C23C22×C22⋊C411yescharacteristic
432D4—48no—
433D4—44no—
434D4—44no—
435D4—816no—
436D4—84no—
437D4—84no—
438D4—816no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—22no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—44no—
458C2×C4—44no—
459C2×C4—42no—
460C2×C4—48no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—82no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4—82no—
483C2×C4—81no—
484C2×C4—81no—
485C2×C4—816no—
486C2×C4—84no—
487C2×C4—82no—
488C2×C4—82no—
489C2×C4C2×#9912yes—
490C2×C4C2×#9912yes—
491C2×C4C2×#10212yes—
492C2×C4C22×D811yescharacteristic
493C2×C4C22×SD1611yescharacteristic
494C8—84no—
495C8—84no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—24no—
501C22—24no—
502C22—24no—
503C22—24no—
504C22—44no—
505C22—44no—
506C22—44no—
507C22—48no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—48no—
513C22—48no—
514C22—82no—
515C22—84no—
516C22—82no—
517C22—82no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—82no—
523C22—164no—
524C22—164no—
525C22#151912yes—
526C22#151912yes—
527C22#212112yes—
528C22#213212yes—
529C22C22×#9911yescharacteristic
530C22C22×#10211yescharacteristic
531C22C2×#42111yescharacteristic
532C4—22no—
533C4—22no—
534C4—21no—
535C4—21no—
536C4—22no—
537C4—44no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—42no—
543C4—82no—
544C4—82no—
545C2—21no—
546C2—21no—
547C2—22no—
548C2—44no—
549C2—44no—
550C2—162no—
551C2#1188414yesdirect product factor
552C2C2×#151911yescharacteristic
553C2C2×#212111yescharacteristic
554C2C2×#213211yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC2×#2543C2
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
2. C2×#1800C2semidirect
3. C2×#1459C2semidirect
4. #11884C2direct (N × H)
5. C2×#1346C2semidirect
6. C2×#1345C2semidirect
26. #1800C22semidirect
29. #1459C22semidirect
32. #1346C22semidirect
33. #1345C22semidirect
551. C2#11884direct (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×#18002
C2×#14592
#118842
C2×#13462
C2×#13452